From cc00f6cdf91f9fc2e5aa02a01a541126956cbfc5 Mon Sep 17 00:00:00 2001 From: Michael Dickens Date: Thu, 23 Nov 2023 10:55:10 -0800 Subject: [PATCH 1/7] docs: init Sphinx docs --- docs/Makefile | 19 + docs/build/doctrees/README.doctree | Bin 0 -> 50071 bytes docs/build/doctrees/environment.pickle | Bin 0 -> 81020 bytes docs/build/doctrees/index.doctree | Bin 0 -> 4974 bytes docs/build/html/.buildinfo | 4 + docs/build/html/README.html | 893 ++ docs/build/html/_sources/README.rst.txt | 531 + docs/build/html/_sources/index.rst.txt | 18 + docs/build/html/_static/alabaster.css | 703 ++ docs/build/html/_static/basic.css | 925 ++ docs/build/html/_static/custom.css | 1 + docs/build/html/_static/doctools.js | 156 + .../html/_static/documentation_options.js | 13 + docs/build/html/_static/file.png | Bin 0 -> 286 bytes docs/build/html/_static/jquery.js | 10365 ++++++++++++++++ docs/build/html/_static/language_data.js | 199 + docs/build/html/_static/minus.png | Bin 0 -> 90 bytes 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create mode 100644 docs/build/html/_static/scripts/bootstrap.js.map create mode 100644 docs/build/html/_static/scripts/pydata-sphinx-theme.js create mode 100644 docs/build/html/_static/scripts/pydata-sphinx-theme.js.map create mode 100644 docs/build/html/_static/searchtools.js create mode 100644 docs/build/html/_static/sphinx_highlight.js create mode 100644 docs/build/html/_static/styles/bootstrap.css create mode 100644 docs/build/html/_static/styles/bootstrap.css.map create mode 100644 docs/build/html/_static/styles/pydata-sphinx-theme.css create mode 100644 docs/build/html/_static/styles/pydata-sphinx-theme.css.map create mode 100644 docs/build/html/_static/styles/theme.css create mode 100644 docs/build/html/_static/underscore.js create mode 100644 docs/build/html/_static/vendor/fontawesome/6.1.2/LICENSE.txt create mode 100644 docs/build/html/_static/vendor/fontawesome/6.1.2/css/all.min.css create mode 100644 docs/build/html/_static/vendor/fontawesome/6.1.2/js/all.min.js create mode 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + +
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+ + + Ctrl+K +
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+

Squigglepy: Implementation of Squiggle in Python#

+

Squiggle is a “simple +programming language for intuitive probabilistic estimation”. It serves +as its own standalone programming language with its own syntax, but it +is implemented in JavaScript. I like the features of Squiggle and intend +to use it frequently, but I also sometimes want to use similar +functionalities in Python, especially alongside other Python statistical +programming packages like Numpy, Pandas, and Matplotlib. The +squigglepy package here implements many Squiggle-like +functionalities in Python.

+
+

Installation#

+
pip install squigglepy
+
+
+

For plotting support, you can also use the plots extra:

+
pip install squigglepy[plots]
+
+
+
+
+

Usage#

+
+

Piano Tuners Example#

+

Here’s the Squigglepy implementation of the example from Squiggle +Docs:

+
import squigglepy as sq
+import numpy as np
+import matplotlib.pyplot as plt
+from squigglepy.numbers import K, M
+from pprint import pprint
+
+pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)  # This means that you're 90% confident the value is between 8.1 and 8.4 Million.
+pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01  # We assume there are almost no people with multiple pianos
+pianos_per_piano_tuner = sq.to(2*K, 50*K)
+piano_tuners_per_piano = 1 / pianos_per_piano_tuner
+total_tuners_in_2022 = pop_of_ny_2022 * pct_of_pop_w_pianos * piano_tuners_per_piano
+samples = total_tuners_in_2022 @ 1000  # Note: `@ 1000` is shorthand to get 1000 samples
+
+# Get mean and SD
+print('Mean: {}, SD: {}'.format(round(np.mean(samples), 2),
+                                round(np.std(samples), 2)))
+
+# Get percentiles
+pprint(sq.get_percentiles(samples, digits=0))
+
+# Histogram
+plt.hist(samples, bins=200)
+plt.show()
+
+# Shorter histogram
+total_tuners_in_2022.plot()
+
+
+

And the version from the Squiggle doc that incorporates time:

+
import squigglepy as sq
+from squigglepy.numbers import K, M
+
+pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)
+pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01
+pianos_per_piano_tuner = sq.to(2*K, 50*K)
+piano_tuners_per_piano = 1 / pianos_per_piano_tuner
+
+def pop_at_time(t):  # t = Time in years after 2022
+    avg_yearly_pct_change = sq.to(-0.01, 0.05)  # We're expecting NYC to continuously grow with an mean of roughly between -1% and +4% per year
+    return pop_of_ny_2022 * ((avg_yearly_pct_change + 1) ** t)
+
+def total_tuners_at_time(t):
+    return pop_at_time(t) * pct_of_pop_w_pianos * piano_tuners_per_piano
+
+# Get total piano tuners at 2030
+sq.get_percentiles(total_tuners_at_time(2030-2022) @ 1000)
+
+
+

WARNING: Be careful about dividing by K, M, etc. 1/2*K = +500 in Python. Use 1/(2*K) instead to get the expected outcome.

+

WARNING: Be careful about using K to get sample counts. Use +sq.norm(2, 3) @ (2*K)… sq.norm(2, 3) @ 2*K will return only +two samples, multiplied by 1000.

+
+
+

Distributions#

+
import squigglepy as sq
+
+# Normal distribution
+sq.norm(1, 3)  # 90% interval from 1 to 3
+
+# Distribution can be sampled with mean and sd too
+sq.norm(mean=0, sd=1)
+
+# Shorthand to get one sample
+~sq.norm(1, 3)
+
+# Shorthand to get more than one sample
+sq.norm(1, 3) @ 100
+
+# Longhand version to get more than one sample
+sq.sample(sq.norm(1, 3), n=100)
+
+# Nice progress reporter
+sq.sample(sq.norm(1, 3), n=1000, verbose=True)
+
+# Other distributions exist
+sq.lognorm(1, 10)
+sq.tdist(1, 10, t=5)
+sq.triangular(1, 2, 3)
+sq.pert(1, 2, 3, lam=2)
+sq.binomial(p=0.5, n=5)
+sq.beta(a=1, b=2)
+sq.bernoulli(p=0.5)
+sq.poisson(10)
+sq.chisquare(2)
+sq.gamma(3, 2)
+sq.pareto(1)
+sq.exponential(scale=1)
+sq.geometric(p=0.5)
+
+# Discrete sampling
+sq.discrete({'A': 0.1, 'B': 0.9})
+
+# Can return integers
+sq.discrete({0: 0.1, 1: 0.3, 2: 0.3, 3: 0.15, 4: 0.15})
+
+# Alternate format (also can be used to return more complex objects)
+sq.discrete([[0.1,  0],
+             [0.3,  1],
+             [0.3,  2],
+             [0.15, 3],
+             [0.15, 4]])
+
+sq.discrete([0, 1, 2]) # No weights assumes equal weights
+
+# You can mix distributions together
+sq.mixture([sq.norm(1, 3),
+            sq.norm(4, 10),
+            sq.lognorm(1, 10)],  # Distributions to mix
+           [0.3, 0.3, 0.4])     # These are the weights on each distribution
+
+# This is equivalent to the above, just a different way of doing the notation
+sq.mixture([[0.3, sq.norm(1,3)],
+            [0.3, sq.norm(4,10)],
+            [0.4, sq.lognorm(1,10)]])
+
+# Make a zero-inflated distribution
+# 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`.
+sq.zero_inflated(0.6, sq.norm(1, 2))
+
+
+
+
+

Additional Features#

+
import squigglepy as sq
+
+# You can add and subtract distributions
+(sq.norm(1,3) + sq.norm(4,5)) @ 100
+(sq.norm(1,3) - sq.norm(4,5)) @ 100
+(sq.norm(1,3) * sq.norm(4,5)) @ 100
+(sq.norm(1,3) / sq.norm(4,5)) @ 100
+
+# You can also do math with numbers
+~((sq.norm(sd=5) + 2) * 2)
+~(-sq.lognorm(0.1, 1) * sq.pareto(1) / 10)
+
+# You can change the CI from 90% (default) to 80%
+sq.norm(1, 3, credibility=80)
+
+# You can clip
+sq.norm(0, 3, lclip=0, rclip=5) # Sample norm with a 90% CI from 0-3, but anything lower than 0 gets clipped to 0 and anything higher than 5 gets clipped to 5.
+
+# You can also clip with a function, and use pipes
+sq.norm(0, 3) >> sq.clip(0, 5)
+
+# You can correlate continuous distributions
+a, b = sq.uniform(-1, 1), sq.to(0, 3)
+a, b = sq.correlate((a, b), 0.5)  # Correlate a and b with a correlation of 0.5
+# You can even pass your own correlation matrix!
+a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]])
+
+
+
+

Example: Rolling a Die#

+

An example of how to use distributions to build tools:

+
import squigglepy as sq
+
+def roll_die(sides, n=1):
+    return sq.discrete(list(range(1, sides + 1))) @ n if sides > 0 else None
+
+roll_die(sides=6, n=10)
+# [2, 6, 5, 2, 6, 2, 3, 1, 5, 2]
+
+
+

This is already included standard in the utils of this package. Use +sq.roll_die.

+
+
+
+

Bayesian inference#

+

1% of women at age forty who participate in routine screening have +breast cancer. 80% of women with breast cancer will get positive +mammographies. 9.6% of women without breast cancer will also get +positive mammographies.

+

A woman in this age group had a positive mammography in a routine +screening. What is the probability that she actually has breast cancer?

+

We can approximate the answer with a Bayesian network (uses rejection +sampling):

+
import squigglepy as sq
+from squigglepy import bayes
+from squigglepy.numbers import M
+
+def mammography(has_cancer):
+    return sq.event(0.8 if has_cancer else 0.096)
+
+def define_event():
+    cancer = ~sq.bernoulli(0.01)
+    return({'mammography': mammography(cancer),
+            'cancer': cancer})
+
+bayes.bayesnet(define_event,
+               find=lambda e: e['cancer'],
+               conditional_on=lambda e: e['mammography'],
+               n=1*M)
+# 0.07723995880535531
+
+
+

Or if we have the information immediately on hand, we can directly +calculate it. Though this doesn’t work for very complex stuff.

+
from squigglepy import bayes
+bayes.simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096)
+# 0.07763975155279504
+
+
+

You can also make distributions and update them:

+
import matplotlib.pyplot as plt
+import squigglepy as sq
+from squigglepy import bayes
+from squigglepy.numbers import K
+import numpy as np
+
+print('Prior')
+prior = sq.norm(1,5)
+prior_samples = prior @ (10*K)
+plt.hist(prior_samples, bins = 200)
+plt.show()
+print(sq.get_percentiles(prior_samples))
+print('Prior Mean: {} SD: {}'.format(np.mean(prior_samples), np.std(prior_samples)))
+print('-')
+
+print('Evidence')
+evidence = sq.norm(2,3)
+evidence_samples = evidence @ (10*K)
+plt.hist(evidence_samples, bins = 200)
+plt.show()
+print(sq.get_percentiles(evidence_samples))
+print('Evidence Mean: {} SD: {}'.format(np.mean(evidence_samples), np.std(evidence_samples)))
+print('-')
+
+print('Posterior')
+posterior = bayes.update(prior, evidence)
+posterior_samples = posterior @ (10*K)
+plt.hist(posterior_samples, bins = 200)
+plt.show()
+print(sq.get_percentiles(posterior_samples))
+print('Posterior Mean: {} SD: {}'.format(np.mean(posterior_samples), np.std(posterior_samples)))
+
+print('Average')
+average = bayes.average(prior, evidence)
+average_samples = average @ (10*K)
+plt.hist(average_samples, bins = 200)
+plt.show()
+print(sq.get_percentiles(average_samples))
+print('Average Mean: {} SD: {}'.format(np.mean(average_samples), np.std(average_samples)))
+
+
+
+

Example: Alarm net#

+

This is the alarm network from Bayesian Artificial Intelligence - +Section +2.5.1:

+
+

Assume your house has an alarm system against burglary.

+

You live in the seismically active area and the alarm system can get +occasionally set off by an earthquake.

+

You have two neighbors, Mary and John, who do not know each other. If +they hear the alarm they call you, but this is not guaranteed.

+

The chance of a burglary on a particular day is 0.1%. The chance of +an earthquake on a particular day is 0.2%.

+

The alarm will go off 95% of the time with both a burglary and an +earthquake, 94% of the time with just a burglary, 29% of the time +with just an earthquake, and 0.1% of the time with nothing (total +false alarm).

+

John will call you 90% of the time when the alarm goes off. But on 5% +of the days, John will just call to say “hi”. Mary will call you 70% +of the time when the alarm goes off. But on 1% of the days, Mary will +just call to say “hi”.

+
+
import squigglepy as sq
+from squigglepy import bayes
+from squigglepy.numbers import M
+
+def p_alarm_goes_off(burglary, earthquake):
+    if burglary and earthquake:
+        return 0.95
+    elif burglary and not earthquake:
+        return 0.94
+    elif not burglary and earthquake:
+        return 0.29
+    elif not burglary and not earthquake:
+        return 0.001
+
+def p_john_calls(alarm_goes_off):
+    return 0.9 if alarm_goes_off else 0.05
+
+def p_mary_calls(alarm_goes_off):
+    return 0.7 if alarm_goes_off else 0.01
+
+def define_event():
+    burglary_happens = sq.event(p=0.001)
+    earthquake_happens = sq.event(p=0.002)
+    alarm_goes_off = sq.event(p_alarm_goes_off(burglary_happens, earthquake_happens))
+    john_calls = sq.event(p_john_calls(alarm_goes_off))
+    mary_calls = sq.event(p_mary_calls(alarm_goes_off))
+    return {'burglary': burglary_happens,
+            'earthquake': earthquake_happens,
+            'alarm_goes_off': alarm_goes_off,
+            'john_calls': john_calls,
+            'mary_calls': mary_calls}
+
+# What are the chances that both John and Mary call if an earthquake happens?
+bayes.bayesnet(define_event,
+               n=1*M,
+               find=lambda e: (e['mary_calls'] and e['john_calls']),
+               conditional_on=lambda e: e['earthquake'])
+# Result will be ~0.19, though it varies because it is based on a random sample.
+# This also may take a minute to run.
+
+# If both John and Mary call, what is the chance there's been a burglary?
+bayes.bayesnet(define_event,
+               n=1*M,
+               find=lambda e: e['burglary'],
+               conditional_on=lambda e: (e['mary_calls'] and e['john_calls']))
+# Result will be ~0.27, though it varies because it is based on a random sample.
+# This will run quickly because there is a built-in cache.
+# Use `cache=False` to not build a cache and `reload_cache=True` to recalculate the cache.
+
+
+

Note that the amount of Bayesian analysis that squigglepy can do is +pretty limited. For more complex bayesian analysis, consider +sorobn, +pomegranate, +bnlearn, or +pyMC.

+
+
+

Example: A Demonstration of the Monty Hall Problem#

+
import squigglepy as sq
+from squigglepy import bayes
+from squigglepy.numbers import K, M, B, T
+
+
+def monte_hall(door_picked, switch=False):
+    doors = ['A', 'B', 'C']
+    car_is_behind_door = ~sq.discrete(doors)
+    reveal_door = ~sq.discrete([d for d in doors if d != door_picked and d != car_is_behind_door])
+
+    if switch:
+        old_door_picked = door_picked
+        door_picked = [d for d in doors if d != old_door_picked and d != reveal_door][0]
+
+    won_car = (car_is_behind_door == door_picked)
+    return won_car
+
+
+def define_event():
+    door = ~sq.discrete(['A', 'B', 'C'])
+    switch = sq.event(0.5)
+    return {'won': monte_hall(door_picked=door, switch=switch),
+            'switched': switch}
+
+RUNS = 10*K
+r = bayes.bayesnet(define_event,
+                   find=lambda e: e['won'],
+                   conditional_on=lambda e: e['switched'],
+                   verbose=True,
+                   n=RUNS)
+print('Win {}% of the time when switching'.format(int(r * 100)))
+
+r = bayes.bayesnet(define_event,
+                   find=lambda e: e['won'],
+                   conditional_on=lambda e: not e['switched'],
+                   verbose=True,
+                   n=RUNS)
+print('Win {}% of the time when not switching'.format(int(r * 100)))
+
+# Win 66% of the time when switching
+# Win 34% of the time when not switching
+
+
+
+
+

Example: More complex coin/dice interactions#

+
+

Imagine that I flip a coin. If heads, I take a random die out of my +blue bag. If tails, I take a random die out of my red bag. The blue +bag contains only 6-sided dice. The red bag contains a 4-sided die, a +6-sided die, a 10-sided die, and a 20-sided die. I then roll the +random die I took. What is the chance that I roll a 6?

+
+
import squigglepy as sq
+from squigglepy.numbers import K, M, B, T
+from squigglepy import bayes
+
+def define_event():
+    if sq.flip_coin() == 'heads': # Blue bag
+        return sq.roll_die(6)
+    else: # Red bag
+        return sq.discrete([4, 6, 10, 20]) >> sq.roll_die
+
+
+bayes.bayesnet(define_event,
+               find=lambda e: e == 6,
+               verbose=True,
+               n=100*K)
+# This run for me returned 0.12306 which is pretty close to the correct answer of 0.12292
+
+
+
+
+
+

Kelly betting#

+

You can use probability generated, combine with a bankroll to determine +bet sizing using Kelly +criterion.

+

For example, if you want to Kelly bet and you’ve…

+
    +

  • determined that your price (your probability of the event in question +happening / the market in question resolving in your favor) is $0.70 +(70%)

    • +

  • see that the market is pricing at $0.65

    • +

  • you have a bankroll of $1000 that you are willing to bet

    • +
+

You should bet as follows:

+
import squigglepy as sq
+kelly_data = sq.kelly(my_price=0.70, market_price=0.65, bankroll=1000)
+kelly_data['kelly']  # What fraction of my bankroll should I bet on this?
+# 0.143
+kelly_data['target']  # How much money should be invested in this?
+# 142.86
+kelly_data['expected_roi']  # What is the expected ROI of this bet?
+# 0.077
+
+
+
+
+

More examples#

+

You can see more examples of squigglepy in action +here.

+
+
+
+

Run tests#

+

Use black . for formatting.

+

Run +ruff check . && pytest && pip3 install . && python3 tests/integration.py

+
+
+

Disclaimers#

+

This package is unofficial and supported by myself and Rethink +Priorities. It is not affiliated with or associated with the Quantified +Uncertainty Research Institute, which maintains the Squiggle language +(in JavaScript).

+

This package is also new and not yet in a stable production version, so +you may encounter bugs and other errors. Please report those so they can +be fixed. It’s also possible that future versions of the package may +introduce breaking changes.

+

This package is available under an MIT License.

+
+
+

Acknowledgements#

+
    +

  • The primary author of this package is Peter Wildeford. Agustín +Covarrubias and Bernardo Baron contributed several key features and +developments.

    • +

  • Thanks to Ozzie Gooen and the Quantified Uncertainty Research +Institute for creating and maintaining the original Squiggle +language.

    • +

  • Thanks to Dawn Drescher for helping me implement math between +distributions.

    • +

  • Thanks to Dawn Drescher for coming up with the idea to use ~ as a +shorthand for sample, as well as helping me implement it.

    • +
+
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+ + \ No newline at end of file diff --git a/docs/build/html/_sources/README.rst.txt b/docs/build/html/_sources/README.rst.txt new file mode 100644 index 0000000..f5ec681 --- /dev/null +++ b/docs/build/html/_sources/README.rst.txt @@ -0,0 +1,531 @@ +Squigglepy: Implementation of Squiggle in Python +================================================ + +`Squiggle `__ is a “simple +programming language for intuitive probabilistic estimation”. It serves +as its own standalone programming language with its own syntax, but it +is implemented in JavaScript. I like the features of Squiggle and intend +to use it frequently, but I also sometimes want to use similar +functionalities in Python, especially alongside other Python statistical +programming packages like Numpy, Pandas, and Matplotlib. The +**squigglepy** package here implements many Squiggle-like +functionalities in Python. + +Installation +------------ + +.. code:: shell + + pip install squigglepy + +For plotting support, you can also use the ``plots`` extra: + +.. code:: shell + + pip install squigglepy[plots] + +Usage +----- + +Piano Tuners Example +~~~~~~~~~~~~~~~~~~~~ + +Here’s the Squigglepy implementation of `the example from Squiggle +Docs `__: + +.. code:: python + + import squigglepy as sq + import numpy as np + import matplotlib.pyplot as plt + from squigglepy.numbers import K, M + from pprint import pprint + + pop_of_ny_2022 = sq.to(8.1*M, 8.4*M) # This means that you're 90% confident the value is between 8.1 and 8.4 Million. + pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01 # We assume there are almost no people with multiple pianos + pianos_per_piano_tuner = sq.to(2*K, 50*K) + piano_tuners_per_piano = 1 / pianos_per_piano_tuner + total_tuners_in_2022 = pop_of_ny_2022 * pct_of_pop_w_pianos * piano_tuners_per_piano + samples = total_tuners_in_2022 @ 1000 # Note: `@ 1000` is shorthand to get 1000 samples + + # Get mean and SD + print('Mean: {}, SD: {}'.format(round(np.mean(samples), 2), + round(np.std(samples), 2))) + + # Get percentiles + pprint(sq.get_percentiles(samples, digits=0)) + + # Histogram + plt.hist(samples, bins=200) + plt.show() + + # Shorter histogram + total_tuners_in_2022.plot() + +And the version from the Squiggle doc that incorporates time: + +.. code:: python + + import squigglepy as sq + from squigglepy.numbers import K, M + + pop_of_ny_2022 = sq.to(8.1*M, 8.4*M) + pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01 + pianos_per_piano_tuner = sq.to(2*K, 50*K) + piano_tuners_per_piano = 1 / pianos_per_piano_tuner + + def pop_at_time(t): # t = Time in years after 2022 + avg_yearly_pct_change = sq.to(-0.01, 0.05) # We're expecting NYC to continuously grow with an mean of roughly between -1% and +4% per year + return pop_of_ny_2022 * ((avg_yearly_pct_change + 1) ** t) + + def total_tuners_at_time(t): + return pop_at_time(t) * pct_of_pop_w_pianos * piano_tuners_per_piano + + # Get total piano tuners at 2030 + sq.get_percentiles(total_tuners_at_time(2030-2022) @ 1000) + +**WARNING:** Be careful about dividing by ``K``, ``M``, etc. ``1/2*K`` = +500 in Python. Use ``1/(2*K)`` instead to get the expected outcome. + +**WARNING:** Be careful about using ``K`` to get sample counts. Use +``sq.norm(2, 3) @ (2*K)``\ … ``sq.norm(2, 3) @ 2*K`` will return only +two samples, multiplied by 1000. + +Distributions +~~~~~~~~~~~~~ + +.. code:: python + + import squigglepy as sq + + # Normal distribution + sq.norm(1, 3) # 90% interval from 1 to 3 + + # Distribution can be sampled with mean and sd too + sq.norm(mean=0, sd=1) + + # Shorthand to get one sample + ~sq.norm(1, 3) + + # Shorthand to get more than one sample + sq.norm(1, 3) @ 100 + + # Longhand version to get more than one sample + sq.sample(sq.norm(1, 3), n=100) + + # Nice progress reporter + sq.sample(sq.norm(1, 3), n=1000, verbose=True) + + # Other distributions exist + sq.lognorm(1, 10) + sq.tdist(1, 10, t=5) + sq.triangular(1, 2, 3) + sq.pert(1, 2, 3, lam=2) + sq.binomial(p=0.5, n=5) + sq.beta(a=1, b=2) + sq.bernoulli(p=0.5) + sq.poisson(10) + sq.chisquare(2) + sq.gamma(3, 2) + sq.pareto(1) + sq.exponential(scale=1) + sq.geometric(p=0.5) + + # Discrete sampling + sq.discrete({'A': 0.1, 'B': 0.9}) + + # Can return integers + sq.discrete({0: 0.1, 1: 0.3, 2: 0.3, 3: 0.15, 4: 0.15}) + + # Alternate format (also can be used to return more complex objects) + sq.discrete([[0.1, 0], + [0.3, 1], + [0.3, 2], + [0.15, 3], + [0.15, 4]]) + + sq.discrete([0, 1, 2]) # No weights assumes equal weights + + # You can mix distributions together + sq.mixture([sq.norm(1, 3), + sq.norm(4, 10), + sq.lognorm(1, 10)], # Distributions to mix + [0.3, 0.3, 0.4]) # These are the weights on each distribution + + # This is equivalent to the above, just a different way of doing the notation + sq.mixture([[0.3, sq.norm(1,3)], + [0.3, sq.norm(4,10)], + [0.4, sq.lognorm(1,10)]]) + + # Make a zero-inflated distribution + # 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`. + sq.zero_inflated(0.6, sq.norm(1, 2)) + +Additional Features +~~~~~~~~~~~~~~~~~~~ + +.. code:: python + + import squigglepy as sq + + # You can add and subtract distributions + (sq.norm(1,3) + sq.norm(4,5)) @ 100 + (sq.norm(1,3) - sq.norm(4,5)) @ 100 + (sq.norm(1,3) * sq.norm(4,5)) @ 100 + (sq.norm(1,3) / sq.norm(4,5)) @ 100 + + # You can also do math with numbers + ~((sq.norm(sd=5) + 2) * 2) + ~(-sq.lognorm(0.1, 1) * sq.pareto(1) / 10) + + # You can change the CI from 90% (default) to 80% + sq.norm(1, 3, credibility=80) + + # You can clip + sq.norm(0, 3, lclip=0, rclip=5) # Sample norm with a 90% CI from 0-3, but anything lower than 0 gets clipped to 0 and anything higher than 5 gets clipped to 5. + + # You can also clip with a function, and use pipes + sq.norm(0, 3) >> sq.clip(0, 5) + + # You can correlate continuous distributions + a, b = sq.uniform(-1, 1), sq.to(0, 3) + a, b = sq.correlate((a, b), 0.5) # Correlate a and b with a correlation of 0.5 + # You can even pass your own correlation matrix! + a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]]) + +Example: Rolling a Die +^^^^^^^^^^^^^^^^^^^^^^ + +An example of how to use distributions to build tools: + +.. code:: python + + import squigglepy as sq + + def roll_die(sides, n=1): + return sq.discrete(list(range(1, sides + 1))) @ n if sides > 0 else None + + roll_die(sides=6, n=10) + # [2, 6, 5, 2, 6, 2, 3, 1, 5, 2] + +This is already included standard in the utils of this package. Use +``sq.roll_die``. + +Bayesian inference +~~~~~~~~~~~~~~~~~~ + +1% of women at age forty who participate in routine screening have +breast cancer. 80% of women with breast cancer will get positive +mammographies. 9.6% of women without breast cancer will also get +positive mammographies. + +A woman in this age group had a positive mammography in a routine +screening. What is the probability that she actually has breast cancer? + +We can approximate the answer with a Bayesian network (uses rejection +sampling): + +.. code:: python + + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import M + + def mammography(has_cancer): + return sq.event(0.8 if has_cancer else 0.096) + + def define_event(): + cancer = ~sq.bernoulli(0.01) + return({'mammography': mammography(cancer), + 'cancer': cancer}) + + bayes.bayesnet(define_event, + find=lambda e: e['cancer'], + conditional_on=lambda e: e['mammography'], + n=1*M) + # 0.07723995880535531 + +Or if we have the information immediately on hand, we can directly +calculate it. Though this doesn’t work for very complex stuff. + +.. code:: python + + from squigglepy import bayes + bayes.simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096) + # 0.07763975155279504 + +You can also make distributions and update them: + +.. code:: python + + import matplotlib.pyplot as plt + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import K + import numpy as np + + print('Prior') + prior = sq.norm(1,5) + prior_samples = prior @ (10*K) + plt.hist(prior_samples, bins = 200) + plt.show() + print(sq.get_percentiles(prior_samples)) + print('Prior Mean: {} SD: {}'.format(np.mean(prior_samples), np.std(prior_samples))) + print('-') + + print('Evidence') + evidence = sq.norm(2,3) + evidence_samples = evidence @ (10*K) + plt.hist(evidence_samples, bins = 200) + plt.show() + print(sq.get_percentiles(evidence_samples)) + print('Evidence Mean: {} SD: {}'.format(np.mean(evidence_samples), np.std(evidence_samples))) + print('-') + + print('Posterior') + posterior = bayes.update(prior, evidence) + posterior_samples = posterior @ (10*K) + plt.hist(posterior_samples, bins = 200) + plt.show() + print(sq.get_percentiles(posterior_samples)) + print('Posterior Mean: {} SD: {}'.format(np.mean(posterior_samples), np.std(posterior_samples))) + + print('Average') + average = bayes.average(prior, evidence) + average_samples = average @ (10*K) + plt.hist(average_samples, bins = 200) + plt.show() + print(sq.get_percentiles(average_samples)) + print('Average Mean: {} SD: {}'.format(np.mean(average_samples), np.std(average_samples))) + +Example: Alarm net +^^^^^^^^^^^^^^^^^^ + +This is the alarm network from `Bayesian Artificial Intelligence - +Section +2.5.1 `__: + + Assume your house has an alarm system against burglary. + + You live in the seismically active area and the alarm system can get + occasionally set off by an earthquake. + + You have two neighbors, Mary and John, who do not know each other. If + they hear the alarm they call you, but this is not guaranteed. + + The chance of a burglary on a particular day is 0.1%. The chance of + an earthquake on a particular day is 0.2%. + + The alarm will go off 95% of the time with both a burglary and an + earthquake, 94% of the time with just a burglary, 29% of the time + with just an earthquake, and 0.1% of the time with nothing (total + false alarm). + + John will call you 90% of the time when the alarm goes off. But on 5% + of the days, John will just call to say “hi”. Mary will call you 70% + of the time when the alarm goes off. But on 1% of the days, Mary will + just call to say “hi”. + +.. code:: python + + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import M + + def p_alarm_goes_off(burglary, earthquake): + if burglary and earthquake: + return 0.95 + elif burglary and not earthquake: + return 0.94 + elif not burglary and earthquake: + return 0.29 + elif not burglary and not earthquake: + return 0.001 + + def p_john_calls(alarm_goes_off): + return 0.9 if alarm_goes_off else 0.05 + + def p_mary_calls(alarm_goes_off): + return 0.7 if alarm_goes_off else 0.01 + + def define_event(): + burglary_happens = sq.event(p=0.001) + earthquake_happens = sq.event(p=0.002) + alarm_goes_off = sq.event(p_alarm_goes_off(burglary_happens, earthquake_happens)) + john_calls = sq.event(p_john_calls(alarm_goes_off)) + mary_calls = sq.event(p_mary_calls(alarm_goes_off)) + return {'burglary': burglary_happens, + 'earthquake': earthquake_happens, + 'alarm_goes_off': alarm_goes_off, + 'john_calls': john_calls, + 'mary_calls': mary_calls} + + # What are the chances that both John and Mary call if an earthquake happens? + bayes.bayesnet(define_event, + n=1*M, + find=lambda e: (e['mary_calls'] and e['john_calls']), + conditional_on=lambda e: e['earthquake']) + # Result will be ~0.19, though it varies because it is based on a random sample. + # This also may take a minute to run. + + # If both John and Mary call, what is the chance there's been a burglary? + bayes.bayesnet(define_event, + n=1*M, + find=lambda e: e['burglary'], + conditional_on=lambda e: (e['mary_calls'] and e['john_calls'])) + # Result will be ~0.27, though it varies because it is based on a random sample. + # This will run quickly because there is a built-in cache. + # Use `cache=False` to not build a cache and `reload_cache=True` to recalculate the cache. + +Note that the amount of Bayesian analysis that squigglepy can do is +pretty limited. For more complex bayesian analysis, consider +`sorobn `__, +`pomegranate `__, +`bnlearn `__, or +`pyMC `__. + +Example: A Demonstration of the Monty Hall Problem +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code:: python + + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import K, M, B, T + + + def monte_hall(door_picked, switch=False): + doors = ['A', 'B', 'C'] + car_is_behind_door = ~sq.discrete(doors) + reveal_door = ~sq.discrete([d for d in doors if d != door_picked and d != car_is_behind_door]) + + if switch: + old_door_picked = door_picked + door_picked = [d for d in doors if d != old_door_picked and d != reveal_door][0] + + won_car = (car_is_behind_door == door_picked) + return won_car + + + def define_event(): + door = ~sq.discrete(['A', 'B', 'C']) + switch = sq.event(0.5) + return {'won': monte_hall(door_picked=door, switch=switch), + 'switched': switch} + + RUNS = 10*K + r = bayes.bayesnet(define_event, + find=lambda e: e['won'], + conditional_on=lambda e: e['switched'], + verbose=True, + n=RUNS) + print('Win {}% of the time when switching'.format(int(r * 100))) + + r = bayes.bayesnet(define_event, + find=lambda e: e['won'], + conditional_on=lambda e: not e['switched'], + verbose=True, + n=RUNS) + print('Win {}% of the time when not switching'.format(int(r * 100))) + + # Win 66% of the time when switching + # Win 34% of the time when not switching + +Example: More complex coin/dice interactions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + + Imagine that I flip a coin. If heads, I take a random die out of my + blue bag. If tails, I take a random die out of my red bag. The blue + bag contains only 6-sided dice. The red bag contains a 4-sided die, a + 6-sided die, a 10-sided die, and a 20-sided die. I then roll the + random die I took. What is the chance that I roll a 6? + +.. code:: python + + import squigglepy as sq + from squigglepy.numbers import K, M, B, T + from squigglepy import bayes + + def define_event(): + if sq.flip_coin() == 'heads': # Blue bag + return sq.roll_die(6) + else: # Red bag + return sq.discrete([4, 6, 10, 20]) >> sq.roll_die + + + bayes.bayesnet(define_event, + find=lambda e: e == 6, + verbose=True, + n=100*K) + # This run for me returned 0.12306 which is pretty close to the correct answer of 0.12292 + +Kelly betting +~~~~~~~~~~~~~ + +You can use probability generated, combine with a bankroll to determine +bet sizing using `Kelly +criterion `__. + +For example, if you want to Kelly bet and you’ve… + +- determined that your price (your probability of the event in question + happening / the market in question resolving in your favor) is $0.70 + (70%) +- see that the market is pricing at $0.65 +- you have a bankroll of $1000 that you are willing to bet + +You should bet as follows: + +.. code:: python + + import squigglepy as sq + kelly_data = sq.kelly(my_price=0.70, market_price=0.65, bankroll=1000) + kelly_data['kelly'] # What fraction of my bankroll should I bet on this? + # 0.143 + kelly_data['target'] # How much money should be invested in this? + # 142.86 + kelly_data['expected_roi'] # What is the expected ROI of this bet? + # 0.077 + +More examples +~~~~~~~~~~~~~ + +You can see more examples of squigglepy in action +`here `__. + +Run tests +--------- + +Use ``black .`` for formatting. + +Run +``ruff check . && pytest && pip3 install . && python3 tests/integration.py`` + +Disclaimers +----------- + +This package is unofficial and supported by myself and Rethink +Priorities. It is not affiliated with or associated with the Quantified +Uncertainty Research Institute, which maintains the Squiggle language +(in JavaScript). + +This package is also new and not yet in a stable production version, so +you may encounter bugs and other errors. Please report those so they can +be fixed. It’s also possible that future versions of the package may +introduce breaking changes. + +This package is available under an MIT License. + +Acknowledgements +---------------- + +- The primary author of this package is Peter Wildeford. Agustín + Covarrubias and Bernardo Baron contributed several key features and + developments. +- Thanks to Ozzie Gooen and the Quantified Uncertainty Research + Institute for creating and maintaining the original Squiggle + language. +- Thanks to Dawn Drescher for helping me implement math between + distributions. +- Thanks to Dawn Drescher for coming up with the idea to use ``~`` as a + shorthand for ``sample``, as well as helping me implement it. diff --git a/docs/build/html/_sources/index.rst.txt b/docs/build/html/_sources/index.rst.txt new file mode 100644 index 0000000..9a79421 --- /dev/null +++ b/docs/build/html/_sources/index.rst.txt @@ -0,0 +1,18 @@ +Squigglepy: Implementation of Squiggle in Python +================================================ + +`Squiggle `__ is a “simple +programming language for intuitive probabilistic estimation”. It serves +as its own standalone programming language with its own syntax, but it +is implemented in JavaScript. I like the features of Squiggle and intend +to use it frequently, but I also sometimes want to use similar +functionalities in Python, especially alongside other Python statistical +programming packages like Numpy, Pandas, and Matplotlib. The +**squigglepy** package here implements many Squiggle-like +functionalities in Python. + +.. toctree:: + :maxdepth: 2 + :caption: Contents: + +Check out the :doc:`README ` to get started. diff --git a/docs/build/html/_static/alabaster.css b/docs/build/html/_static/alabaster.css new file mode 100644 index 0000000..517d0b2 --- /dev/null +++ b/docs/build/html/_static/alabaster.css @@ -0,0 +1,703 @@ +@import url("basic.css"); + +/* -- page layout ----------------------------------------------------------- */ + +body { + font-family: Georgia, serif; + font-size: 17px; + background-color: #fff; + color: #000; + margin: 0; + padding: 0; +} + + +div.document { + width: 940px; + margin: 30px auto 0 auto; +} + +div.documentwrapper { + float: left; + width: 100%; +} + +div.bodywrapper { + margin: 0 0 0 220px; +} + +div.sphinxsidebar { + width: 220px; + font-size: 14px; + line-height: 1.5; +} + +hr { + border: 1px solid #B1B4B6; +} + +div.body { + background-color: #fff; + color: #3E4349; + padding: 0 30px 0 30px; 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+} + +div.related li.right { + float: right; + margin-right: 5px; +} + +/* -- sidebar --------------------------------------------------------------- */ + +div.sphinxsidebarwrapper { + padding: 10px 5px 0 10px; +} + +div.sphinxsidebar { + float: left; + width: 270px; + margin-left: -100%; + font-size: 90%; + word-wrap: break-word; + overflow-wrap : break-word; +} + +div.sphinxsidebar ul { + list-style: none; +} + +div.sphinxsidebar ul ul, +div.sphinxsidebar ul.want-points { + margin-left: 20px; + list-style: square; +} + +div.sphinxsidebar ul ul { + margin-top: 0; + margin-bottom: 0; +} + +div.sphinxsidebar form { + margin-top: 10px; +} + +div.sphinxsidebar input { + border: 1px solid #98dbcc; + font-family: sans-serif; + font-size: 1em; +} + +div.sphinxsidebar #searchbox form.search { + overflow: hidden; +} + +div.sphinxsidebar #searchbox input[type="text"] { + float: left; + width: 80%; + padding: 0.25em; + box-sizing: border-box; +} + +div.sphinxsidebar #searchbox input[type="submit"] { + float: left; + width: 20%; + border-left: none; + padding: 0.25em; + box-sizing: border-box; +} + + +img { + border: 0; + max-width: 100%; +} + +/* -- search page ----------------------------------------------------------- */ + +ul.search { + margin: 10px 0 0 20px; + padding: 0; +} + +ul.search li { + padding: 5px 0 5px 20px; + background-image: url(file.png); + background-repeat: no-repeat; + background-position: 0 7px; +} + +ul.search li a { + font-weight: bold; +} + +ul.search li p.context { + color: #888; + margin: 2px 0 0 30px; + text-align: left; +} + +ul.keywordmatches li.goodmatch a { + font-weight: bold; +} + +/* -- index page ------------------------------------------------------------ */ + +table.contentstable { + width: 90%; + margin-left: auto; + margin-right: auto; +} + +table.contentstable p.biglink { + line-height: 150%; +} + +a.biglink { + font-size: 1.3em; +} + +span.linkdescr { + font-style: italic; + padding-top: 5px; + font-size: 90%; +} + +/* -- general index --------------------------------------------------------- */ + +table.indextable { + width: 100%; +} + +table.indextable td { + text-align: left; + vertical-align: top; +} + +table.indextable ul { + margin-top: 0; + margin-bottom: 0; + list-style-type: none; +} + +table.indextable > tbody > tr > td > ul { + padding-left: 0em; +} + +table.indextable tr.pcap { + height: 10px; +} + +table.indextable tr.cap { + margin-top: 10px; + background-color: #f2f2f2; +} + +img.toggler { + margin-right: 3px; + margin-top: 3px; + cursor: pointer; +} + +div.modindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +div.genindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +/* -- domain module index --------------------------------------------------- */ + +table.modindextable td { + padding: 2px; + border-collapse: collapse; +} + +/* -- general body styles --------------------------------------------------- */ + +div.body { + min-width: 360px; + max-width: 800px; +} + +div.body p, div.body dd, div.body li, div.body blockquote { + -moz-hyphens: auto; + -ms-hyphens: auto; + -webkit-hyphens: auto; + hyphens: auto; +} + +a.headerlink { + visibility: hidden; +} + +a:visited { + color: #551A8B; +} + +h1:hover > a.headerlink, +h2:hover > a.headerlink, +h3:hover > a.headerlink, +h4:hover > a.headerlink, +h5:hover > a.headerlink, +h6:hover > a.headerlink, +dt:hover > a.headerlink, +caption:hover > a.headerlink, +p.caption:hover > a.headerlink, +div.code-block-caption:hover > a.headerlink { + visibility: visible; +} + +div.body p.caption { + text-align: inherit; +} + +div.body td { + text-align: left; +} + +.first { + margin-top: 0 !important; +} + +p.rubric { + margin-top: 30px; + font-weight: bold; +} + +img.align-left, figure.align-left, .figure.align-left, object.align-left { + clear: left; + float: left; + margin-right: 1em; +} + +img.align-right, figure.align-right, .figure.align-right, object.align-right { + clear: right; + float: right; + margin-left: 1em; +} + +img.align-center, figure.align-center, .figure.align-center, object.align-center { + display: block; + margin-left: auto; + margin-right: auto; +} + +img.align-default, figure.align-default, .figure.align-default { + display: block; + margin-left: auto; + margin-right: auto; +} + +.align-left { + text-align: left; +} + +.align-center { + text-align: center; +} + +.align-default { + text-align: center; +} + +.align-right { + text-align: right; +} + +/* -- sidebars -------------------------------------------------------------- */ + +div.sidebar, +aside.sidebar { + margin: 0 0 0.5em 1em; + border: 1px solid #ddb; + padding: 7px; + background-color: #ffe; + width: 40%; + float: right; + clear: right; + overflow-x: auto; +} + +p.sidebar-title { + font-weight: bold; +} + +nav.contents, +aside.topic, +div.admonition, div.topic, blockquote { + clear: left; +} + +/* -- topics ---------------------------------------------------------------- */ + +nav.contents, +aside.topic, +div.topic { + border: 1px solid #ccc; + padding: 7px; + margin: 10px 0 10px 0; +} + +p.topic-title { + font-size: 1.1em; + font-weight: bold; + margin-top: 10px; +} + +/* -- admonitions ----------------------------------------------------------- */ + +div.admonition { + margin-top: 10px; + margin-bottom: 10px; + padding: 7px; +} + +div.admonition dt { + font-weight: bold; +} + +p.admonition-title { + margin: 0px 10px 5px 0px; + font-weight: bold; +} + +div.body p.centered { + text-align: center; + margin-top: 25px; +} + +/* -- content of sidebars/topics/admonitions -------------------------------- */ + +div.sidebar > :last-child, +aside.sidebar > :last-child, +nav.contents > :last-child, +aside.topic > :last-child, +div.topic > :last-child, +div.admonition > :last-child { + margin-bottom: 0; +} + +div.sidebar::after, +aside.sidebar::after, +nav.contents::after, +aside.topic::after, +div.topic::after, +div.admonition::after, +blockquote::after { + display: block; + content: ''; + clear: both; +} + +/* -- tables ---------------------------------------------------------------- */ + +table.docutils { + margin-top: 10px; + margin-bottom: 10px; + border: 0; + border-collapse: collapse; +} + +table.align-center { + margin-left: auto; + margin-right: auto; +} + +table.align-default { + margin-left: auto; + margin-right: auto; +} + +table caption span.caption-number { + font-style: italic; +} + +table caption span.caption-text { +} + +table.docutils td, table.docutils th { + padding: 1px 8px 1px 5px; + border-top: 0; + border-left: 0; + border-right: 0; + border-bottom: 1px solid #aaa; +} + +th { + text-align: left; + padding-right: 5px; +} + +table.citation { + border-left: solid 1px gray; + margin-left: 1px; +} + +table.citation td { + border-bottom: none; +} + +th > :first-child, +td > :first-child { + margin-top: 0px; +} + +th > :last-child, +td > :last-child { + margin-bottom: 0px; +} + +/* -- figures --------------------------------------------------------------- */ + +div.figure, figure { + margin: 0.5em; + padding: 0.5em; +} + +div.figure p.caption, figcaption { + padding: 0.3em; +} + +div.figure p.caption span.caption-number, +figcaption span.caption-number { + font-style: italic; +} + +div.figure p.caption span.caption-text, +figcaption span.caption-text { +} + +/* -- field list styles ----------------------------------------------------- */ + +table.field-list td, table.field-list th { + border: 0 !important; +} + +.field-list ul { + margin: 0; + padding-left: 1em; +} + +.field-list p { + margin: 0; +} + +.field-name { + -moz-hyphens: manual; + -ms-hyphens: manual; + -webkit-hyphens: manual; + hyphens: manual; +} + +/* -- hlist styles ---------------------------------------------------------- */ + +table.hlist { + margin: 1em 0; +} + +table.hlist td { + vertical-align: top; +} + +/* -- object description styles --------------------------------------------- */ + +.sig { + font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace; +} + +.sig-name, code.descname { + background-color: transparent; + font-weight: bold; +} + +.sig-name { + font-size: 1.1em; +} + +code.descname { + font-size: 1.2em; +} + +.sig-prename, code.descclassname { + background-color: transparent; +} + +.optional { + font-size: 1.3em; +} + +.sig-paren { + font-size: larger; +} + +.sig-param.n { + font-style: italic; +} + +/* C++ specific styling */ + +.sig-inline.c-texpr, +.sig-inline.cpp-texpr { + font-family: unset; +} + +.sig.c .k, .sig.c .kt, +.sig.cpp .k, .sig.cpp .kt { + color: #0033B3; +} + +.sig.c .m, +.sig.cpp .m { + color: #1750EB; +} + +.sig.c .s, .sig.c .sc, +.sig.cpp .s, .sig.cpp .sc { + color: #067D17; +} + + +/* -- other body styles ----------------------------------------------------- */ + +ol.arabic { + list-style: decimal; +} + +ol.loweralpha { + list-style: lower-alpha; +} + +ol.upperalpha { + list-style: upper-alpha; +} + +ol.lowerroman { + list-style: lower-roman; +} + +ol.upperroman { + list-style: upper-roman; +} + +:not(li) > ol > li:first-child > :first-child, +:not(li) > ul > li:first-child > :first-child { + margin-top: 0px; +} + +:not(li) > ol > li:last-child > :last-child, +:not(li) > ul > li:last-child > :last-child { + margin-bottom: 0px; +} + +ol.simple ol p, +ol.simple ul p, +ul.simple ol p, +ul.simple ul p { + margin-top: 0; +} + +ol.simple > li:not(:first-child) > p, +ul.simple > li:not(:first-child) > p { + margin-top: 0; +} + +ol.simple p, +ul.simple p { + margin-bottom: 0; +} + +aside.footnote > span, +div.citation > span { + float: left; +} +aside.footnote > span:last-of-type, +div.citation > span:last-of-type { + padding-right: 0.5em; +} +aside.footnote > p { + margin-left: 2em; +} +div.citation > p { + margin-left: 4em; +} +aside.footnote > p:last-of-type, +div.citation > p:last-of-type { + margin-bottom: 0em; +} +aside.footnote > p:last-of-type:after, +div.citation > p:last-of-type:after { + content: ""; + clear: both; +} + +dl.field-list { + display: grid; + grid-template-columns: fit-content(30%) auto; +} + +dl.field-list > dt { + font-weight: bold; + word-break: break-word; + padding-left: 0.5em; + padding-right: 5px; +} + +dl.field-list > dd { + padding-left: 0.5em; + margin-top: 0em; + margin-left: 0em; + margin-bottom: 0em; +} + +dl { + margin-bottom: 15px; +} + +dd > :first-child { + margin-top: 0px; +} + +dd ul, dd table { + margin-bottom: 10px; +} + +dd { + margin-top: 3px; + margin-bottom: 10px; + margin-left: 30px; +} + +.sig dd { + margin-top: 0px; + margin-bottom: 0px; +} + +.sig dl { + margin-top: 0px; + margin-bottom: 0px; +} + +dl > dd:last-child, +dl > dd:last-child > :last-child { + margin-bottom: 0; +} + +dt:target, span.highlighted { + background-color: #fbe54e; +} + +rect.highlighted { + fill: #fbe54e; +} + +dl.glossary dt { + font-weight: bold; + font-size: 1.1em; +} + +.versionmodified { + font-style: italic; +} + +.system-message { + background-color: #fda; + padding: 5px; + border: 3px solid red; +} + +.footnote:target { + background-color: #ffa; +} + +.line-block { + display: block; + margin-top: 1em; + margin-bottom: 1em; +} + +.line-block .line-block { + margin-top: 0; + margin-bottom: 0; + margin-left: 1.5em; +} + +.guilabel, .menuselection { + font-family: sans-serif; +} + +.accelerator { + text-decoration: underline; +} + +.classifier { + font-style: oblique; +} + +.classifier:before { + font-style: normal; + margin: 0 0.5em; + content: ":"; + display: inline-block; +} + +abbr, acronym { + border-bottom: dotted 1px; + cursor: help; +} + +.translated { + background-color: rgba(207, 255, 207, 0.2) +} + +.untranslated { + background-color: rgba(255, 207, 207, 0.2) +} + +/* -- code displays --------------------------------------------------------- */ + +pre { + overflow: auto; + overflow-y: hidden; /* fixes display issues on Chrome browsers */ +} + +pre, div[class*="highlight-"] { + clear: both; +} + +span.pre { + -moz-hyphens: none; + -ms-hyphens: none; + -webkit-hyphens: none; + hyphens: none; + white-space: nowrap; +} + +div[class*="highlight-"] { + margin: 1em 0; +} + +td.linenos pre { + border: 0; + background-color: transparent; + color: #aaa; +} + +table.highlighttable { + display: block; +} + +table.highlighttable tbody { + display: block; +} + +table.highlighttable tr { + display: flex; +} + +table.highlighttable td { + margin: 0; + padding: 0; +} + +table.highlighttable td.linenos { + padding-right: 0.5em; +} + +table.highlighttable td.code { + flex: 1; + overflow: hidden; +} + +.highlight .hll { + display: block; +} + +div.highlight pre, +table.highlighttable pre { + margin: 0; +} + +div.code-block-caption + div { + margin-top: 0; +} + +div.code-block-caption { + margin-top: 1em; + padding: 2px 5px; + font-size: small; +} + +div.code-block-caption code { + background-color: transparent; +} + +table.highlighttable td.linenos, +span.linenos, +div.highlight span.gp { /* gp: Generic.Prompt */ + user-select: none; + -webkit-user-select: text; /* Safari fallback only */ + -webkit-user-select: none; /* Chrome/Safari */ + -moz-user-select: none; /* Firefox */ + -ms-user-select: none; /* IE10+ */ +} + +div.code-block-caption span.caption-number { + padding: 0.1em 0.3em; + font-style: italic; +} + +div.code-block-caption span.caption-text { +} + +div.literal-block-wrapper { + margin: 1em 0; +} + +code.xref, a code { + background-color: transparent; + font-weight: bold; +} + +h1 code, h2 code, h3 code, h4 code, h5 code, h6 code { + background-color: transparent; +} + +.viewcode-link { + float: right; +} + +.viewcode-back { + float: right; + font-family: sans-serif; +} + +div.viewcode-block:target { + margin: -1px -10px; + padding: 0 10px; +} + +/* -- math display ---------------------------------------------------------- */ + +img.math { + vertical-align: middle; +} + +div.body div.math p { + text-align: center; +} + +span.eqno { + float: right; +} + +span.eqno a.headerlink { + position: absolute; + z-index: 1; +} + +div.math:hover a.headerlink { + visibility: visible; +} + +/* -- printout stylesheet --------------------------------------------------- */ + +@media print { + div.document, + div.documentwrapper, + div.bodywrapper { + margin: 0 !important; + width: 100%; + } + + div.sphinxsidebar, + div.related, + div.footer, + #top-link { + display: none; + } +} \ No newline at end of file diff --git a/docs/build/html/_static/custom.css b/docs/build/html/_static/custom.css new file mode 100644 index 0000000..2a924f1 --- /dev/null +++ b/docs/build/html/_static/custom.css @@ -0,0 +1 @@ +/* This file intentionally left blank. */ diff --git a/docs/build/html/_static/doctools.js b/docs/build/html/_static/doctools.js new file mode 100644 index 0000000..d06a71d --- /dev/null +++ b/docs/build/html/_static/doctools.js @@ -0,0 +1,156 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Base JavaScript utilities for all Sphinx HTML documentation. + * + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ +"use strict"; + +const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([ + "TEXTAREA", + "INPUT", + "SELECT", + "BUTTON", +]); + +const _ready = (callback) => { + if (document.readyState !== "loading") { + callback(); + } else { + document.addEventListener("DOMContentLoaded", callback); + } +}; + +/** + * Small JavaScript module for the documentation. + */ +const Documentation = { + init: () => { + Documentation.initDomainIndexTable(); + Documentation.initOnKeyListeners(); + }, + + /** + * i18n support + */ + TRANSLATIONS: {}, + PLURAL_EXPR: (n) => (n === 1 ? 0 : 1), + LOCALE: "unknown", + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext: (string) => { + const translated = Documentation.TRANSLATIONS[string]; + switch (typeof translated) { + case "undefined": + return string; // no translation + case "string": + return translated; // translation exists + default: + return translated[0]; // (singular, plural) translation tuple exists + } + }, + + ngettext: (singular, plural, n) => { + const translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated !== "undefined") + return translated[Documentation.PLURAL_EXPR(n)]; + return n === 1 ? singular : plural; + }, + + addTranslations: (catalog) => { + Object.assign(Documentation.TRANSLATIONS, catalog.messages); + Documentation.PLURAL_EXPR = new Function( + "n", + `return (${catalog.plural_expr})` + ); + Documentation.LOCALE = catalog.locale; + }, + + /** + * helper function to focus on search bar + */ + focusSearchBar: () => { + document.querySelectorAll("input[name=q]")[0]?.focus(); + }, + + /** + * Initialise the domain index toggle buttons + */ + initDomainIndexTable: () => { + const toggler = (el) => { + const idNumber = el.id.substr(7); + const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`); + if (el.src.substr(-9) === "minus.png") { + el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`; + toggledRows.forEach((el) => (el.style.display = "none")); + } else { + el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`; + toggledRows.forEach((el) => (el.style.display = "")); + } + }; + + const togglerElements = document.querySelectorAll("img.toggler"); + togglerElements.forEach((el) => + el.addEventListener("click", (event) => toggler(event.currentTarget)) + ); + togglerElements.forEach((el) => (el.style.display = "")); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler); + }, + + initOnKeyListeners: () => { + // only install a listener if it is really needed + if ( + !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS && + !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS + ) + return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.altKey || event.ctrlKey || event.metaKey) return; + + if (!event.shiftKey) { + switch (event.key) { + case "ArrowLeft": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const prevLink = document.querySelector('link[rel="prev"]'); + if (prevLink && prevLink.href) { + window.location.href = prevLink.href; + event.preventDefault(); + } + break; + case "ArrowRight": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const nextLink = document.querySelector('link[rel="next"]'); + if (nextLink && nextLink.href) { + window.location.href = nextLink.href; + event.preventDefault(); + } + break; + } + } + + // some keyboard layouts may need Shift to get / + switch (event.key) { + case "/": + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break; + Documentation.focusSearchBar(); + event.preventDefault(); + } + }); + }, +}; + +// quick alias for translations +const _ = Documentation.gettext; + +_ready(Documentation.init); diff --git a/docs/build/html/_static/documentation_options.js b/docs/build/html/_static/documentation_options.js new file mode 100644 index 0000000..7e4c114 --- /dev/null +++ b/docs/build/html/_static/documentation_options.js @@ -0,0 +1,13 @@ +const DOCUMENTATION_OPTIONS = { + VERSION: '', + LANGUAGE: 'en', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '.txt', + NAVIGATION_WITH_KEYS: false, + SHOW_SEARCH_SUMMARY: true, + ENABLE_SEARCH_SHORTCUTS: true, +}; \ No newline at end of file diff --git a/docs/build/html/_static/file.png b/docs/build/html/_static/file.png new file mode 100644 index 0000000000000000000000000000000000000000..a858a410e4faa62ce324d814e4b816fff83a6fb3 GIT binary patch literal 286 zcmV+(0pb3MP)s`hMrGg#P~ix$^RISR_I47Y|r1 z_CyJOe}D1){SET-^Amu_i71Lt6eYfZjRyw@I6OQAIXXHDfiX^GbOlHe=Ae4>0m)d(f|Me07*qoM6N<$f}vM^LjV8( literal 0 HcmV?d00001 diff --git a/docs/build/html/_static/jquery.js b/docs/build/html/_static/jquery.js new file mode 100644 index 0000000..7e32910 --- /dev/null +++ b/docs/build/html/_static/jquery.js @@ -0,0 +1,10365 @@ +/*! + * jQuery JavaScript Library v3.3.1-dfsg + * https://jquery.com/ + * + * Includes Sizzle.js + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://jquery.org/license + * + * Date: 2019-04-19T06:52Z + */ +( function( global, factory ) { + + "use strict"; + + if ( typeof module === "object" && typeof module.exports === "object" ) { + + // For CommonJS and CommonJS-like environments where a proper `window` + // is present, execute the factory and get jQuery. + // For environments that do not have a `window` with a `document` + // (such as Node.js), expose a factory as module.exports. + // This accentuates the need for the creation of a real `window`. + // e.g. var jQuery = require("jquery")(window); + // See ticket #14549 for more info. + module.exports = global.document ? + factory( global, true ) : + function( w ) { + if ( !w.document ) { + throw new Error( "jQuery requires a window with a document" ); + } + return factory( w ); + }; + } else { + factory( global ); + } + +// Pass this if window is not defined yet +} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { + +// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 +// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode +// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common +// enough that all such attempts are guarded in a try block. + + +var arr = []; + +var document = window.document; + +var getProto = Object.getPrototypeOf; + +var slice = arr.slice; + +var concat = arr.concat; + +var push = arr.push; + +var indexOf = arr.indexOf; + +var class2type = {}; + +var toString = class2type.toString; + +var hasOwn = class2type.hasOwnProperty; + +var fnToString = hasOwn.toString; + +var ObjectFunctionString = fnToString.call( Object ); + +var support = {}; + +var isFunction = function isFunction( obj ) { + + // Support: Chrome <=57, Firefox <=52 + // In some browsers, typeof returns "function" for HTML elements + // (i.e., `typeof document.createElement( "object" ) === "function"`). + // We don't want to classify *any* DOM node as a function. + return typeof obj === "function" && typeof obj.nodeType !== "number"; + }; + + +var isWindow = function isWindow( obj ) { + return obj != null && obj === obj.window; + }; + + + + + var preservedScriptAttributes = { + type: true, + src: true, + noModule: true + }; + + function DOMEval( code, doc, node ) { + doc = doc || document; + + var i, + script = doc.createElement( "script" ); + + script.text = code; + if ( node ) { + for ( i in preservedScriptAttributes ) { + if ( node[ i ] ) { + script[ i ] = node[ i ]; + } + } + } + doc.head.appendChild( script ).parentNode.removeChild( script ); + } + + +function toType( obj ) { + if ( obj == null ) { + return obj + ""; + } + + // Support: Android <=2.3 only (functionish RegExp) + return typeof obj === "object" || typeof obj === "function" ? + class2type[ toString.call( obj ) ] || "object" : + typeof obj; +} +/* global Symbol */ +// Defining this global in .eslintrc.json would create a danger of using the global +// unguarded in another place, it seems safer to define global only for this module + + + +var + version = "3.3.1", + + // Define a local copy of jQuery + jQuery = function( selector, context ) { + + // The jQuery object is actually just the init constructor 'enhanced' + // Need init if jQuery is called (just allow error to be thrown if not included) + return new jQuery.fn.init( selector, context ); + }, + + // Support: Android <=4.0 only + // Make sure we trim BOM and NBSP + rtrim = /^[\s\uFEFF\xA0]+|[\s\uFEFF\xA0]+$/g; + +jQuery.fn = jQuery.prototype = { + + // The current version of jQuery being used + jquery: version, + + constructor: jQuery, + + // The default length of a jQuery object is 0 + length: 0, + + toArray: function() { + return slice.call( this ); + }, + + // Get the Nth element in the matched element set OR + // Get the whole matched element set as a clean array + get: function( num ) { + + // Return all the elements in a clean array + if ( num == null ) { + return slice.call( this ); + } + + // Return just the one element from the set + return num < 0 ? this[ num + this.length ] : this[ num ]; + }, + + // Take an array of elements and push it onto the stack + // (returning the new matched element set) + pushStack: function( elems ) { + + // Build a new jQuery matched element set + var ret = jQuery.merge( this.constructor(), elems ); + + // Add the old object onto the stack (as a reference) + ret.prevObject = this; + + // Return the newly-formed element set + return ret; + }, + + // Execute a callback for every element in the matched set. + each: function( callback ) { + return jQuery.each( this, callback ); + }, + + map: function( callback ) { + return this.pushStack( jQuery.map( this, function( elem, i ) { + return callback.call( elem, i, elem ); + } ) ); + }, + + slice: function() { + return this.pushStack( slice.apply( this, arguments ) ); + }, + + first: function() { + return this.eq( 0 ); + }, + + last: function() { + return this.eq( -1 ); + }, + + eq: function( i ) { + var len = this.length, + j = +i + ( i < 0 ? len : 0 ); + return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); + }, + + end: function() { + return this.prevObject || this.constructor(); + }, + + // For internal use only. + // Behaves like an Array's method, not like a jQuery method. + push: push, + sort: arr.sort, + splice: arr.splice +}; + +jQuery.extend = jQuery.fn.extend = function() { + var options, name, src, copy, copyIsArray, clone, + target = arguments[ 0 ] || {}, + i = 1, + length = arguments.length, + deep = false; + + // Handle a deep copy situation + if ( typeof target === "boolean" ) { + deep = target; + + // Skip the boolean and the target + target = arguments[ i ] || {}; + i++; + } + + // Handle case when target is a string or something (possible in deep copy) + if ( typeof target !== "object" && !isFunction( target ) ) { + target = {}; + } + + // Extend jQuery itself if only one argument is passed + if ( i === length ) { + target = this; + i--; + } + + for ( ; i < length; i++ ) { + + // Only deal with non-null/undefined values + if ( ( options = arguments[ i ] ) != null ) { + + // Extend the base object + for ( name in options ) { + src = target[ name ]; + copy = options[ name ]; + + // Prevent Object.prototype pollution + // Prevent never-ending loop + if ( name === "__proto__" || target === copy ) { + continue; + } + + // Recurse if we're merging plain objects or arrays + if ( deep && copy && ( jQuery.isPlainObject( copy ) || + ( copyIsArray = Array.isArray( copy ) ) ) ) { + + if ( copyIsArray ) { + copyIsArray = false; + clone = src && Array.isArray( src ) ? src : []; + + } else { + clone = src && jQuery.isPlainObject( src ) ? src : {}; + } + + // Never move original objects, clone them + target[ name ] = jQuery.extend( deep, clone, copy ); + + // Don't bring in undefined values + } else if ( copy !== undefined ) { + target[ name ] = copy; + } + } + } + } + + // Return the modified object + return target; +}; + +jQuery.extend( { + + // Unique for each copy of jQuery on the page + expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), + + // Assume jQuery is ready without the ready module + isReady: true, + + error: function( msg ) { + throw new Error( msg ); + }, + + noop: function() {}, + + isPlainObject: function( obj ) { + var proto, Ctor; + + // Detect obvious negatives + // Use toString instead of jQuery.type to catch host objects + if ( !obj || toString.call( obj ) !== "[object Object]" ) { + return false; + } + + proto = getProto( obj ); + + // Objects with no prototype (e.g., `Object.create( null )`) are plain + if ( !proto ) { + return true; + } + + // Objects with prototype are plain iff they were constructed by a global Object function + Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; + return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; + }, + + isEmptyObject: function( obj ) { + + /* eslint-disable no-unused-vars */ + // See https://github.com/eslint/eslint/issues/6125 + var name; + + for ( name in obj ) { + return false; + } + return true; + }, + + // Evaluates a script in a global context + globalEval: function( code ) { + DOMEval( code ); + }, + + each: function( obj, callback ) { + var length, i = 0; + + if ( isArrayLike( obj ) ) { + length = obj.length; + for ( ; i < length; i++ ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } else { + for ( i in obj ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } + + return obj; + }, + + // Support: Android <=4.0 only + trim: function( text ) { + return text == null ? + "" : + ( text + "" ).replace( rtrim, "" ); + }, + + // results is for internal usage only + makeArray: function( arr, results ) { + var ret = results || []; + + if ( arr != null ) { + if ( isArrayLike( Object( arr ) ) ) { + jQuery.merge( ret, + typeof arr === "string" ? + [ arr ] : arr + ); + } else { + push.call( ret, arr ); + } + } + + return ret; + }, + + inArray: function( elem, arr, i ) { + return arr == null ? -1 : indexOf.call( arr, elem, i ); + }, + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + merge: function( first, second ) { + var len = +second.length, + j = 0, + i = first.length; + + for ( ; j < len; j++ ) { + first[ i++ ] = second[ j ]; + } + + first.length = i; + + return first; + }, + + grep: function( elems, callback, invert ) { + var callbackInverse, + matches = [], + i = 0, + length = elems.length, + callbackExpect = !invert; + + // Go through the array, only saving the items + // that pass the validator function + for ( ; i < length; i++ ) { + callbackInverse = !callback( elems[ i ], i ); + if ( callbackInverse !== callbackExpect ) { + matches.push( elems[ i ] ); + } + } + + return matches; + }, + + // arg is for internal usage only + map: function( elems, callback, arg ) { + var length, value, + i = 0, + ret = []; + + // Go through the array, translating each of the items to their new values + if ( isArrayLike( elems ) ) { + length = elems.length; + for ( ; i < length; i++ ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + + // Go through every key on the object, + } else { + for ( i in elems ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + } + + // Flatten any nested arrays + return concat.apply( [], ret ); + }, + + // A global GUID counter for objects + guid: 1, + + // jQuery.support is not used in Core but other projects attach their + // properties to it so it needs to exist. + support: support +} ); + +if ( typeof Symbol === "function" ) { + jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; +} + +// Populate the class2type map +jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), +function( i, name ) { + class2type[ "[object " + name + "]" ] = name.toLowerCase(); +} ); + +function isArrayLike( obj ) { + + // Support: real iOS 8.2 only (not reproducible in simulator) + // `in` check used to prevent JIT error (gh-2145) + // hasOwn isn't used here due to false negatives + // regarding Nodelist length in IE + var length = !!obj && "length" in obj && obj.length, + type = toType( obj ); + + if ( isFunction( obj ) || isWindow( obj ) ) { + return false; + } + + return type === "array" || length === 0 || + typeof length === "number" && length > 0 && ( length - 1 ) in obj; +} +var Sizzle = +/*! + * Sizzle CSS Selector Engine v2.3.3 + * https://sizzlejs.com/ + * + * Copyright jQuery Foundation and other contributors + * Released under the MIT license + * http://jquery.org/license + * + * Date: 2016-08-08 + */ +(function( window ) { + +var i, + support, + Expr, + getText, + isXML, + tokenize, + compile, + select, + outermostContext, + sortInput, + hasDuplicate, + + // Local document vars + setDocument, + document, + docElem, + documentIsHTML, + rbuggyQSA, + rbuggyMatches, + matches, + contains, + + // Instance-specific data + expando = "sizzle" + 1 * new Date(), + preferredDoc = window.document, + dirruns = 0, + done = 0, + classCache = createCache(), + tokenCache = createCache(), + compilerCache = createCache(), + sortOrder = function( a, b ) { + if ( a === b ) { + hasDuplicate = true; + } + return 0; + }, + + // Instance methods + hasOwn = ({}).hasOwnProperty, + arr = [], + pop = arr.pop, + push_native = arr.push, + push = arr.push, + slice = arr.slice, + // Use a stripped-down indexOf as it's faster than native + // https://jsperf.com/thor-indexof-vs-for/5 + indexOf = function( list, elem ) { + var i = 0, + len = list.length; + for ( ; i < len; i++ ) { + if ( list[i] === elem ) { + return i; + } + } + return -1; + }, + + booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped", + + // Regular expressions + + // http://www.w3.org/TR/css3-selectors/#whitespace + whitespace = "[\\x20\\t\\r\\n\\f]", + + // http://www.w3.org/TR/CSS21/syndata.html#value-def-identifier + identifier = "(?:\\\\.|[\\w-]|[^\0-\\xa0])+", + + // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors + attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + + // Operator (capture 2) + "*([*^$|!~]?=)" + whitespace + + // "Attribute values must be CSS identifiers [capture 5] or strings [capture 3 or capture 4]" + "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + whitespace + + "*\\]", + + pseudos = ":(" + identifier + ")(?:\\((" + + // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: + // 1. quoted (capture 3; capture 4 or capture 5) + "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + + // 2. simple (capture 6) + "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + + // 3. anything else (capture 2) + ".*" + + ")\\)|)", + + // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter + rwhitespace = new RegExp( whitespace + "+", "g" ), + rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + whitespace + "+$", "g" ), + + rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), + rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + "*" ), + + rattributeQuotes = new RegExp( "=" + whitespace + "*([^\\]'\"]*?)" + whitespace + "*\\]", "g" ), + + rpseudo = new RegExp( pseudos ), + ridentifier = new RegExp( "^" + identifier + "$" ), + + matchExpr = { + "ID": new RegExp( "^#(" + identifier + ")" ), + "CLASS": new RegExp( "^\\.(" + identifier + ")" ), + "TAG": new RegExp( "^(" + identifier + "|[*])" ), + "ATTR": new RegExp( "^" + attributes ), + "PSEUDO": new RegExp( "^" + pseudos ), + "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + whitespace + + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + whitespace + + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), + "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), + // For use in libraries implementing .is() + // We use this for POS matching in `select` + "needsContext": new RegExp( "^" + whitespace + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + + whitespace + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) + }, + + rinputs = /^(?:input|select|textarea|button)$/i, + rheader = /^h\d$/i, + + rnative = /^[^{]+\{\s*\[native \w/, + + // Easily-parseable/retrievable ID or TAG or CLASS selectors + rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, + + rsibling = /[+~]/, + + // CSS escapes + // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters + runescape = new RegExp( "\\\\([\\da-f]{1,6}" + whitespace + "?|(" + whitespace + ")|.)", "ig" ), + funescape = function( _, escaped, escapedWhitespace ) { + var high = "0x" + escaped - 0x10000; + // NaN means non-codepoint + // Support: Firefox<24 + // Workaround erroneous numeric interpretation of +"0x" + return high !== high || escapedWhitespace ? + escaped : + high < 0 ? + // BMP codepoint + String.fromCharCode( high + 0x10000 ) : + // Supplemental Plane codepoint (surrogate pair) + String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); + }, + + // CSS string/identifier serialization + // https://drafts.csswg.org/cssom/#common-serializing-idioms + rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, + fcssescape = function( ch, asCodePoint ) { + if ( asCodePoint ) { + + // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER + if ( ch === "\0" ) { + return "\uFFFD"; + } + + // Control characters and (dependent upon position) numbers get escaped as code points + return ch.slice( 0, -1 ) + "\\" + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; + } + + // Other potentially-special ASCII characters get backslash-escaped + return "\\" + ch; + }, + + // Used for iframes + // See setDocument() + // Removing the function wrapper causes a "Permission Denied" + // error in IE + unloadHandler = function() { + setDocument(); + }, + + disabledAncestor = addCombinator( + function( elem ) { + return elem.disabled === true && ("form" in elem || "label" in elem); + }, + { dir: "parentNode", next: "legend" } + ); + +// Optimize for push.apply( _, NodeList ) +try { + push.apply( + (arr = slice.call( preferredDoc.childNodes )), + preferredDoc.childNodes + ); + // Support: Android<4.0 + // Detect silently failing push.apply + arr[ preferredDoc.childNodes.length ].nodeType; +} catch ( e ) { + push = { apply: arr.length ? + + // Leverage slice if possible + function( target, els ) { + push_native.apply( target, slice.call(els) ); + } : + + // Support: IE<9 + // Otherwise append directly + function( target, els ) { + var j = target.length, + i = 0; + // Can't trust NodeList.length + while ( (target[j++] = els[i++]) ) {} + target.length = j - 1; + } + }; +} + +function Sizzle( selector, context, results, seed ) { + var m, i, elem, nid, match, groups, newSelector, + newContext = context && context.ownerDocument, + + // nodeType defaults to 9, since context defaults to document + nodeType = context ? context.nodeType : 9; + + results = results || []; + + // Return early from calls with invalid selector or context + if ( typeof selector !== "string" || !selector || + nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { + + return results; + } + + // Try to shortcut find operations (as opposed to filters) in HTML documents + if ( !seed ) { + + if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) { + setDocument( context ); + } + context = context || document; + + if ( documentIsHTML ) { + + // If the selector is sufficiently simple, try using a "get*By*" DOM method + // (excepting DocumentFragment context, where the methods don't exist) + if ( nodeType !== 11 && (match = rquickExpr.exec( selector )) ) { + + // ID selector + if ( (m = match[1]) ) { + + // Document context + if ( nodeType === 9 ) { + if ( (elem = context.getElementById( m )) ) { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( elem.id === m ) { + results.push( elem ); + return results; + } + } else { + return results; + } + + // Element context + } else { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( newContext && (elem = newContext.getElementById( m )) && + contains( context, elem ) && + elem.id === m ) { + + results.push( elem ); + return results; + } + } + + // Type selector + } else if ( match[2] ) { + push.apply( results, context.getElementsByTagName( selector ) ); + return results; + + // Class selector + } else if ( (m = match[3]) && support.getElementsByClassName && + context.getElementsByClassName ) { + + push.apply( results, context.getElementsByClassName( m ) ); + return results; + } + } + + // Take advantage of querySelectorAll + if ( support.qsa && + !compilerCache[ selector + " " ] && + (!rbuggyQSA || !rbuggyQSA.test( selector )) ) { + + if ( nodeType !== 1 ) { + newContext = context; + newSelector = selector; + + // qSA looks outside Element context, which is not what we want + // Thanks to Andrew Dupont for this workaround technique + // Support: IE <=8 + // Exclude object elements + } else if ( context.nodeName.toLowerCase() !== "object" ) { + + // Capture the context ID, setting it first if necessary + if ( (nid = context.getAttribute( "id" )) ) { + nid = nid.replace( rcssescape, fcssescape ); + } else { + context.setAttribute( "id", (nid = expando) ); + } + + // Prefix every selector in the list + groups = tokenize( selector ); + i = groups.length; + while ( i-- ) { + groups[i] = "#" + nid + " " + toSelector( groups[i] ); + } + newSelector = groups.join( "," ); + + // Expand context for sibling selectors + newContext = rsibling.test( selector ) && testContext( context.parentNode ) || + context; + } + + if ( newSelector ) { + try { + push.apply( results, + newContext.querySelectorAll( newSelector ) + ); + return results; + } catch ( qsaError ) { + } finally { + if ( nid === expando ) { + context.removeAttribute( "id" ); + } + } + } + } + } + } + + // All others + return select( selector.replace( rtrim, "$1" ), context, results, seed ); +} + +/** + * Create key-value caches of limited size + * @returns {function(string, object)} Returns the Object data after storing it on itself with + * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) + * deleting the oldest entry + */ +function createCache() { + var keys = []; + + function cache( key, value ) { + // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) + if ( keys.push( key + " " ) > Expr.cacheLength ) { + // Only keep the most recent entries + delete cache[ keys.shift() ]; + } + return (cache[ key + " " ] = value); + } + return cache; +} + +/** + * Mark a function for special use by Sizzle + * @param {Function} fn The function to mark + */ +function markFunction( fn ) { + fn[ expando ] = true; + return fn; +} + +/** + * Support testing using an element + * @param {Function} fn Passed the created element and returns a boolean result + */ +function assert( fn ) { + var el = document.createElement("fieldset"); + + try { + return !!fn( el ); + } catch (e) { + return false; + } finally { + // Remove from its parent by default + if ( el.parentNode ) { + el.parentNode.removeChild( el ); + } + // release memory in IE + el = null; + } +} + +/** + * Adds the same handler for all of the specified attrs + * @param {String} attrs Pipe-separated list of attributes + * @param {Function} handler The method that will be applied + */ +function addHandle( attrs, handler ) { + var arr = attrs.split("|"), + i = arr.length; + + while ( i-- ) { + Expr.attrHandle[ arr[i] ] = handler; + } +} + +/** + * Checks document order of two siblings + * @param {Element} a + * @param {Element} b + * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b + */ +function siblingCheck( a, b ) { + var cur = b && a, + diff = cur && a.nodeType === 1 && b.nodeType === 1 && + a.sourceIndex - b.sourceIndex; + + // Use IE sourceIndex if available on both nodes + if ( diff ) { + return diff; + } + + // Check if b follows a + if ( cur ) { + while ( (cur = cur.nextSibling) ) { + if ( cur === b ) { + return -1; + } + } + } + + return a ? 1 : -1; +} + +/** + * Returns a function to use in pseudos for input types + * @param {String} type + */ +function createInputPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for buttons + * @param {String} type + */ +function createButtonPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return (name === "input" || name === "button") && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for :enabled/:disabled + * @param {Boolean} disabled true for :disabled; false for :enabled + */ +function createDisabledPseudo( disabled ) { + + // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable + return function( elem ) { + + // Only certain elements can match :enabled or :disabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled + if ( "form" in elem ) { + + // Check for inherited disabledness on relevant non-disabled elements: + // * listed form-associated elements in a disabled fieldset + // https://html.spec.whatwg.org/multipage/forms.html#category-listed + // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled + // * option elements in a disabled optgroup + // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled + // All such elements have a "form" property. + if ( elem.parentNode && elem.disabled === false ) { + + // Option elements defer to a parent optgroup if present + if ( "label" in elem ) { + if ( "label" in elem.parentNode ) { + return elem.parentNode.disabled === disabled; + } else { + return elem.disabled === disabled; + } + } + + // Support: IE 6 - 11 + // Use the isDisabled shortcut property to check for disabled fieldset ancestors + return elem.isDisabled === disabled || + + // Where there is no isDisabled, check manually + /* jshint -W018 */ + elem.isDisabled !== !disabled && + disabledAncestor( elem ) === disabled; + } + + return elem.disabled === disabled; + + // Try to winnow out elements that can't be disabled before trusting the disabled property. + // Some victims get caught in our net (label, legend, menu, track), but it shouldn't + // even exist on them, let alone have a boolean value. + } else if ( "label" in elem ) { + return elem.disabled === disabled; + } + + // Remaining elements are neither :enabled nor :disabled + return false; + }; +} + +/** + * Returns a function to use in pseudos for positionals + * @param {Function} fn + */ +function createPositionalPseudo( fn ) { + return markFunction(function( argument ) { + argument = +argument; + return markFunction(function( seed, matches ) { + var j, + matchIndexes = fn( [], seed.length, argument ), + i = matchIndexes.length; + + // Match elements found at the specified indexes + while ( i-- ) { + if ( seed[ (j = matchIndexes[i]) ] ) { + seed[j] = !(matches[j] = seed[j]); + } + } + }); + }); +} + +/** + * Checks a node for validity as a Sizzle context + * @param {Element|Object=} context + * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value + */ +function testContext( context ) { + return context && typeof context.getElementsByTagName !== "undefined" && context; +} + +// Expose support vars for convenience +support = Sizzle.support = {}; + +/** + * Detects XML nodes + * @param {Element|Object} elem An element or a document + * @returns {Boolean} True iff elem is a non-HTML XML node + */ +isXML = Sizzle.isXML = function( elem ) { + // documentElement is verified for cases where it doesn't yet exist + // (such as loading iframes in IE - #4833) + var documentElement = elem && (elem.ownerDocument || elem).documentElement; + return documentElement ? documentElement.nodeName !== "HTML" : false; +}; + +/** + * Sets document-related variables once based on the current document + * @param {Element|Object} [doc] An element or document object to use to set the document + * @returns {Object} Returns the current document + */ +setDocument = Sizzle.setDocument = function( node ) { + var hasCompare, subWindow, + doc = node ? node.ownerDocument || node : preferredDoc; + + // Return early if doc is invalid or already selected + if ( doc === document || doc.nodeType !== 9 || !doc.documentElement ) { + return document; + } + + // Update global variables + document = doc; + docElem = document.documentElement; + documentIsHTML = !isXML( document ); + + // Support: IE 9-11, Edge + // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) + if ( preferredDoc !== document && + (subWindow = document.defaultView) && subWindow.top !== subWindow ) { + + // Support: IE 11, Edge + if ( subWindow.addEventListener ) { + subWindow.addEventListener( "unload", unloadHandler, false ); + + // Support: IE 9 - 10 only + } else if ( subWindow.attachEvent ) { + subWindow.attachEvent( "onunload", unloadHandler ); + } + } + + /* Attributes + ---------------------------------------------------------------------- */ + + // Support: IE<8 + // Verify that getAttribute really returns attributes and not properties + // (excepting IE8 booleans) + support.attributes = assert(function( el ) { + el.className = "i"; + return !el.getAttribute("className"); + }); + + /* getElement(s)By* + ---------------------------------------------------------------------- */ + + // Check if getElementsByTagName("*") returns only elements + support.getElementsByTagName = assert(function( el ) { + el.appendChild( document.createComment("") ); + return !el.getElementsByTagName("*").length; + }); + + // Support: IE<9 + support.getElementsByClassName = rnative.test( document.getElementsByClassName ); + + // Support: IE<10 + // Check if getElementById returns elements by name + // The broken getElementById methods don't pick up programmatically-set names, + // so use a roundabout getElementsByName test + support.getById = assert(function( el ) { + docElem.appendChild( el ).id = expando; + return !document.getElementsByName || !document.getElementsByName( expando ).length; + }); + + // ID filter and find + if ( support.getById ) { + Expr.filter["ID"] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + return elem.getAttribute("id") === attrId; + }; + }; + Expr.find["ID"] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var elem = context.getElementById( id ); + return elem ? [ elem ] : []; + } + }; + } else { + Expr.filter["ID"] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + var node = typeof elem.getAttributeNode !== "undefined" && + elem.getAttributeNode("id"); + return node && node.value === attrId; + }; + }; + + // Support: IE 6 - 7 only + // getElementById is not reliable as a find shortcut + Expr.find["ID"] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var node, i, elems, + elem = context.getElementById( id ); + + if ( elem ) { + + // Verify the id attribute + node = elem.getAttributeNode("id"); + if ( node && node.value === id ) { + return [ elem ]; + } + + // Fall back on getElementsByName + elems = context.getElementsByName( id ); + i = 0; + while ( (elem = elems[i++]) ) { + node = elem.getAttributeNode("id"); + if ( node && node.value === id ) { + return [ elem ]; + } + } + } + + return []; + } + }; + } + + // Tag + Expr.find["TAG"] = support.getElementsByTagName ? + function( tag, context ) { + if ( typeof context.getElementsByTagName !== "undefined" ) { + return context.getElementsByTagName( tag ); + + // DocumentFragment nodes don't have gEBTN + } else if ( support.qsa ) { + return context.querySelectorAll( tag ); + } + } : + + function( tag, context ) { + var elem, + tmp = [], + i = 0, + // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too + results = context.getElementsByTagName( tag ); + + // Filter out possible comments + if ( tag === "*" ) { + while ( (elem = results[i++]) ) { + if ( elem.nodeType === 1 ) { + tmp.push( elem ); + } + } + + return tmp; + } + return results; + }; + + // Class + Expr.find["CLASS"] = support.getElementsByClassName && function( className, context ) { + if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { + return context.getElementsByClassName( className ); + } + }; + + /* QSA/matchesSelector + ---------------------------------------------------------------------- */ + + // QSA and matchesSelector support + + // matchesSelector(:active) reports false when true (IE9/Opera 11.5) + rbuggyMatches = []; + + // qSa(:focus) reports false when true (Chrome 21) + // We allow this because of a bug in IE8/9 that throws an error + // whenever `document.activeElement` is accessed on an iframe + // So, we allow :focus to pass through QSA all the time to avoid the IE error + // See https://bugs.jquery.com/ticket/13378 + rbuggyQSA = []; + + if ( (support.qsa = rnative.test( document.querySelectorAll )) ) { + // Build QSA regex + // Regex strategy adopted from Diego Perini + assert(function( el ) { + // Select is set to empty string on purpose + // This is to test IE's treatment of not explicitly + // setting a boolean content attribute, + // since its presence should be enough + // https://bugs.jquery.com/ticket/12359 + docElem.appendChild( el ).innerHTML = "" + + ""; + + // Support: IE8, Opera 11-12.16 + // Nothing should be selected when empty strings follow ^= or $= or *= + // The test attribute must be unknown in Opera but "safe" for WinRT + // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section + if ( el.querySelectorAll("[msallowcapture^='']").length ) { + rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); + } + + // Support: IE8 + // Boolean attributes and "value" are not treated correctly + if ( !el.querySelectorAll("[selected]").length ) { + rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); + } + + // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ + if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { + rbuggyQSA.push("~="); + } + + // Webkit/Opera - :checked should return selected option elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + // IE8 throws error here and will not see later tests + if ( !el.querySelectorAll(":checked").length ) { + rbuggyQSA.push(":checked"); + } + + // Support: Safari 8+, iOS 8+ + // https://bugs.webkit.org/show_bug.cgi?id=136851 + // In-page `selector#id sibling-combinator selector` fails + if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { + rbuggyQSA.push(".#.+[+~]"); + } + }); + + assert(function( el ) { + el.innerHTML = "" + + ""; + + // Support: Windows 8 Native Apps + // The type and name attributes are restricted during .innerHTML assignment + var input = document.createElement("input"); + input.setAttribute( "type", "hidden" ); + el.appendChild( input ).setAttribute( "name", "D" ); + + // Support: IE8 + // Enforce case-sensitivity of name attribute + if ( el.querySelectorAll("[name=d]").length ) { + rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); + } + + // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) + // IE8 throws error here and will not see later tests + if ( el.querySelectorAll(":enabled").length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: IE9-11+ + // IE's :disabled selector does not pick up the children of disabled fieldsets + docElem.appendChild( el ).disabled = true; + if ( el.querySelectorAll(":disabled").length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Opera 10-11 does not throw on post-comma invalid pseudos + el.querySelectorAll("*,:x"); + rbuggyQSA.push(",.*:"); + }); + } + + if ( (support.matchesSelector = rnative.test( (matches = docElem.matches || + docElem.webkitMatchesSelector || + docElem.mozMatchesSelector || + docElem.oMatchesSelector || + docElem.msMatchesSelector) )) ) { + + assert(function( el ) { + // Check to see if it's possible to do matchesSelector + // on a disconnected node (IE 9) + support.disconnectedMatch = matches.call( el, "*" ); + + // This should fail with an exception + // Gecko does not error, returns false instead + matches.call( el, "[s!='']:x" ); + rbuggyMatches.push( "!=", pseudos ); + }); + } + + rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join("|") ); + rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join("|") ); + + /* Contains + ---------------------------------------------------------------------- */ + hasCompare = rnative.test( docElem.compareDocumentPosition ); + + // Element contains another + // Purposefully self-exclusive + // As in, an element does not contain itself + contains = hasCompare || rnative.test( docElem.contains ) ? + function( a, b ) { + var adown = a.nodeType === 9 ? a.documentElement : a, + bup = b && b.parentNode; + return a === bup || !!( bup && bup.nodeType === 1 && ( + adown.contains ? + adown.contains( bup ) : + a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 + )); + } : + function( a, b ) { + if ( b ) { + while ( (b = b.parentNode) ) { + if ( b === a ) { + return true; + } + } + } + return false; + }; + + /* Sorting + ---------------------------------------------------------------------- */ + + // Document order sorting + sortOrder = hasCompare ? + function( a, b ) { + + // Flag for duplicate removal + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + // Sort on method existence if only one input has compareDocumentPosition + var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; + if ( compare ) { + return compare; + } + + // Calculate position if both inputs belong to the same document + compare = ( a.ownerDocument || a ) === ( b.ownerDocument || b ) ? + a.compareDocumentPosition( b ) : + + // Otherwise we know they are disconnected + 1; + + // Disconnected nodes + if ( compare & 1 || + (!support.sortDetached && b.compareDocumentPosition( a ) === compare) ) { + + // Choose the first element that is related to our preferred document + if ( a === document || a.ownerDocument === preferredDoc && contains(preferredDoc, a) ) { + return -1; + } + if ( b === document || b.ownerDocument === preferredDoc && contains(preferredDoc, b) ) { + return 1; + } + + // Maintain original order + return sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + } + + return compare & 4 ? -1 : 1; + } : + function( a, b ) { + // Exit early if the nodes are identical + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + var cur, + i = 0, + aup = a.parentNode, + bup = b.parentNode, + ap = [ a ], + bp = [ b ]; + + // Parentless nodes are either documents or disconnected + if ( !aup || !bup ) { + return a === document ? -1 : + b === document ? 1 : + aup ? -1 : + bup ? 1 : + sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + + // If the nodes are siblings, we can do a quick check + } else if ( aup === bup ) { + return siblingCheck( a, b ); + } + + // Otherwise we need full lists of their ancestors for comparison + cur = a; + while ( (cur = cur.parentNode) ) { + ap.unshift( cur ); + } + cur = b; + while ( (cur = cur.parentNode) ) { + bp.unshift( cur ); + } + + // Walk down the tree looking for a discrepancy + while ( ap[i] === bp[i] ) { + i++; + } + + return i ? + // Do a sibling check if the nodes have a common ancestor + siblingCheck( ap[i], bp[i] ) : + + // Otherwise nodes in our document sort first + ap[i] === preferredDoc ? -1 : + bp[i] === preferredDoc ? 1 : + 0; + }; + + return document; +}; + +Sizzle.matches = function( expr, elements ) { + return Sizzle( expr, null, null, elements ); +}; + +Sizzle.matchesSelector = function( elem, expr ) { + // Set document vars if needed + if ( ( elem.ownerDocument || elem ) !== document ) { + setDocument( elem ); + } + + // Make sure that attribute selectors are quoted + expr = expr.replace( rattributeQuotes, "='$1']" ); + + if ( support.matchesSelector && documentIsHTML && + !compilerCache[ expr + " " ] && + ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && + ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { + + try { + var ret = matches.call( elem, expr ); + + // IE 9's matchesSelector returns false on disconnected nodes + if ( ret || support.disconnectedMatch || + // As well, disconnected nodes are said to be in a document + // fragment in IE 9 + elem.document && elem.document.nodeType !== 11 ) { + return ret; + } + } catch (e) {} + } + + return Sizzle( expr, document, null, [ elem ] ).length > 0; +}; + +Sizzle.contains = function( context, elem ) { + // Set document vars if needed + if ( ( context.ownerDocument || context ) !== document ) { + setDocument( context ); + } + return contains( context, elem ); +}; + +Sizzle.attr = function( elem, name ) { + // Set document vars if needed + if ( ( elem.ownerDocument || elem ) !== document ) { + setDocument( elem ); + } + + var fn = Expr.attrHandle[ name.toLowerCase() ], + // Don't get fooled by Object.prototype properties (jQuery #13807) + val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? + fn( elem, name, !documentIsHTML ) : + undefined; + + return val !== undefined ? + val : + support.attributes || !documentIsHTML ? + elem.getAttribute( name ) : + (val = elem.getAttributeNode(name)) && val.specified ? + val.value : + null; +}; + +Sizzle.escape = function( sel ) { + return (sel + "").replace( rcssescape, fcssescape ); +}; + +Sizzle.error = function( msg ) { + throw new Error( "Syntax error, unrecognized expression: " + msg ); +}; + +/** + * Document sorting and removing duplicates + * @param {ArrayLike} results + */ +Sizzle.uniqueSort = function( results ) { + var elem, + duplicates = [], + j = 0, + i = 0; + + // Unless we *know* we can detect duplicates, assume their presence + hasDuplicate = !support.detectDuplicates; + sortInput = !support.sortStable && results.slice( 0 ); + results.sort( sortOrder ); + + if ( hasDuplicate ) { + while ( (elem = results[i++]) ) { + if ( elem === results[ i ] ) { + j = duplicates.push( i ); + } + } + while ( j-- ) { + results.splice( duplicates[ j ], 1 ); + } + } + + // Clear input after sorting to release objects + // See https://github.com/jquery/sizzle/pull/225 + sortInput = null; + + return results; +}; + +/** + * Utility function for retrieving the text value of an array of DOM nodes + * @param {Array|Element} elem + */ +getText = Sizzle.getText = function( elem ) { + var node, + ret = "", + i = 0, + nodeType = elem.nodeType; + + if ( !nodeType ) { + // If no nodeType, this is expected to be an array + while ( (node = elem[i++]) ) { + // Do not traverse comment nodes + ret += getText( node ); + } + } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { + // Use textContent for elements + // innerText usage removed for consistency of new lines (jQuery #11153) + if ( typeof elem.textContent === "string" ) { + return elem.textContent; + } else { + // Traverse its children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + ret += getText( elem ); + } + } + } else if ( nodeType === 3 || nodeType === 4 ) { + return elem.nodeValue; + } + // Do not include comment or processing instruction nodes + + return ret; +}; + +Expr = Sizzle.selectors = { + + // Can be adjusted by the user + cacheLength: 50, + + createPseudo: markFunction, + + match: matchExpr, + + attrHandle: {}, + + find: {}, + + relative: { + ">": { dir: "parentNode", first: true }, + " ": { dir: "parentNode" }, + "+": { dir: "previousSibling", first: true }, + "~": { dir: "previousSibling" } + }, + + preFilter: { + "ATTR": function( match ) { + match[1] = match[1].replace( runescape, funescape ); + + // Move the given value to match[3] whether quoted or unquoted + match[3] = ( match[3] || match[4] || match[5] || "" ).replace( runescape, funescape ); + + if ( match[2] === "~=" ) { + match[3] = " " + match[3] + " "; + } + + return match.slice( 0, 4 ); + }, + + "CHILD": function( match ) { + /* matches from matchExpr["CHILD"] + 1 type (only|nth|...) + 2 what (child|of-type) + 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) + 4 xn-component of xn+y argument ([+-]?\d*n|) + 5 sign of xn-component + 6 x of xn-component + 7 sign of y-component + 8 y of y-component + */ + match[1] = match[1].toLowerCase(); + + if ( match[1].slice( 0, 3 ) === "nth" ) { + // nth-* requires argument + if ( !match[3] ) { + Sizzle.error( match[0] ); + } + + // numeric x and y parameters for Expr.filter.CHILD + // remember that false/true cast respectively to 0/1 + match[4] = +( match[4] ? match[5] + (match[6] || 1) : 2 * ( match[3] === "even" || match[3] === "odd" ) ); + match[5] = +( ( match[7] + match[8] ) || match[3] === "odd" ); + + // other types prohibit arguments + } else if ( match[3] ) { + Sizzle.error( match[0] ); + } + + return match; + }, + + "PSEUDO": function( match ) { + var excess, + unquoted = !match[6] && match[2]; + + if ( matchExpr["CHILD"].test( match[0] ) ) { + return null; + } + + // Accept quoted arguments as-is + if ( match[3] ) { + match[2] = match[4] || match[5] || ""; + + // Strip excess characters from unquoted arguments + } else if ( unquoted && rpseudo.test( unquoted ) && + // Get excess from tokenize (recursively) + (excess = tokenize( unquoted, true )) && + // advance to the next closing parenthesis + (excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length) ) { + + // excess is a negative index + match[0] = match[0].slice( 0, excess ); + match[2] = unquoted.slice( 0, excess ); + } + + // Return only captures needed by the pseudo filter method (type and argument) + return match.slice( 0, 3 ); + } + }, + + filter: { + + "TAG": function( nodeNameSelector ) { + var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); + return nodeNameSelector === "*" ? + function() { return true; } : + function( elem ) { + return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; + }; + }, + + "CLASS": function( className ) { + var pattern = classCache[ className + " " ]; + + return pattern || + (pattern = new RegExp( "(^|" + whitespace + ")" + className + "(" + whitespace + "|$)" )) && + classCache( className, function( elem ) { + return pattern.test( typeof elem.className === "string" && elem.className || typeof elem.getAttribute !== "undefined" && elem.getAttribute("class") || "" ); + }); + }, + + "ATTR": function( name, operator, check ) { + return function( elem ) { + var result = Sizzle.attr( elem, name ); + + if ( result == null ) { + return operator === "!="; + } + if ( !operator ) { + return true; + } + + result += ""; + + return operator === "=" ? result === check : + operator === "!=" ? result !== check : + operator === "^=" ? check && result.indexOf( check ) === 0 : + operator === "*=" ? check && result.indexOf( check ) > -1 : + operator === "$=" ? check && result.slice( -check.length ) === check : + operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : + operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : + false; + }; + }, + + "CHILD": function( type, what, argument, first, last ) { + var simple = type.slice( 0, 3 ) !== "nth", + forward = type.slice( -4 ) !== "last", + ofType = what === "of-type"; + + return first === 1 && last === 0 ? + + // Shortcut for :nth-*(n) + function( elem ) { + return !!elem.parentNode; + } : + + function( elem, context, xml ) { + var cache, uniqueCache, outerCache, node, nodeIndex, start, + dir = simple !== forward ? "nextSibling" : "previousSibling", + parent = elem.parentNode, + name = ofType && elem.nodeName.toLowerCase(), + useCache = !xml && !ofType, + diff = false; + + if ( parent ) { + + // :(first|last|only)-(child|of-type) + if ( simple ) { + while ( dir ) { + node = elem; + while ( (node = node[ dir ]) ) { + if ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) { + + return false; + } + } + // Reverse direction for :only-* (if we haven't yet done so) + start = dir = type === "only" && !start && "nextSibling"; + } + return true; + } + + start = [ forward ? parent.firstChild : parent.lastChild ]; + + // non-xml :nth-child(...) stores cache data on `parent` + if ( forward && useCache ) { + + // Seek `elem` from a previously-cached index + + // ...in a gzip-friendly way + node = parent; + outerCache = node[ expando ] || (node[ expando ] = {}); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + (outerCache[ node.uniqueID ] = {}); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex && cache[ 2 ]; + node = nodeIndex && parent.childNodes[ nodeIndex ]; + + while ( (node = ++nodeIndex && node && node[ dir ] || + + // Fallback to seeking `elem` from the start + (diff = nodeIndex = 0) || start.pop()) ) { + + // When found, cache indexes on `parent` and break + if ( node.nodeType === 1 && ++diff && node === elem ) { + uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; + break; + } + } + + } else { + // Use previously-cached element index if available + if ( useCache ) { + // ...in a gzip-friendly way + node = elem; + outerCache = node[ expando ] || (node[ expando ] = {}); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + (outerCache[ node.uniqueID ] = {}); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex; + } + + // xml :nth-child(...) + // or :nth-last-child(...) or :nth(-last)?-of-type(...) + if ( diff === false ) { + // Use the same loop as above to seek `elem` from the start + while ( (node = ++nodeIndex && node && node[ dir ] || + (diff = nodeIndex = 0) || start.pop()) ) { + + if ( ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) && + ++diff ) { + + // Cache the index of each encountered element + if ( useCache ) { + outerCache = node[ expando ] || (node[ expando ] = {}); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + (outerCache[ node.uniqueID ] = {}); + + uniqueCache[ type ] = [ dirruns, diff ]; + } + + if ( node === elem ) { + break; + } + } + } + } + } + + // Incorporate the offset, then check against cycle size + diff -= last; + return diff === first || ( diff % first === 0 && diff / first >= 0 ); + } + }; + }, + + "PSEUDO": function( pseudo, argument ) { + // pseudo-class names are case-insensitive + // http://www.w3.org/TR/selectors/#pseudo-classes + // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters + // Remember that setFilters inherits from pseudos + var args, + fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || + Sizzle.error( "unsupported pseudo: " + pseudo ); + + // The user may use createPseudo to indicate that + // arguments are needed to create the filter function + // just as Sizzle does + if ( fn[ expando ] ) { + return fn( argument ); + } + + // But maintain support for old signatures + if ( fn.length > 1 ) { + args = [ pseudo, pseudo, "", argument ]; + return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? + markFunction(function( seed, matches ) { + var idx, + matched = fn( seed, argument ), + i = matched.length; + while ( i-- ) { + idx = indexOf( seed, matched[i] ); + seed[ idx ] = !( matches[ idx ] = matched[i] ); + } + }) : + function( elem ) { + return fn( elem, 0, args ); + }; + } + + return fn; + } + }, + + pseudos: { + // Potentially complex pseudos + "not": markFunction(function( selector ) { + // Trim the selector passed to compile + // to avoid treating leading and trailing + // spaces as combinators + var input = [], + results = [], + matcher = compile( selector.replace( rtrim, "$1" ) ); + + return matcher[ expando ] ? + markFunction(function( seed, matches, context, xml ) { + var elem, + unmatched = matcher( seed, null, xml, [] ), + i = seed.length; + + // Match elements unmatched by `matcher` + while ( i-- ) { + if ( (elem = unmatched[i]) ) { + seed[i] = !(matches[i] = elem); + } + } + }) : + function( elem, context, xml ) { + input[0] = elem; + matcher( input, null, xml, results ); + // Don't keep the element (issue #299) + input[0] = null; + return !results.pop(); + }; + }), + + "has": markFunction(function( selector ) { + return function( elem ) { + return Sizzle( selector, elem ).length > 0; + }; + }), + + "contains": markFunction(function( text ) { + text = text.replace( runescape, funescape ); + return function( elem ) { + return ( elem.textContent || elem.innerText || getText( elem ) ).indexOf( text ) > -1; + }; + }), + + // "Whether an element is represented by a :lang() selector + // is based solely on the element's language value + // being equal to the identifier C, + // or beginning with the identifier C immediately followed by "-". + // The matching of C against the element's language value is performed case-insensitively. + // The identifier C does not have to be a valid language name." + // http://www.w3.org/TR/selectors/#lang-pseudo + "lang": markFunction( function( lang ) { + // lang value must be a valid identifier + if ( !ridentifier.test(lang || "") ) { + Sizzle.error( "unsupported lang: " + lang ); + } + lang = lang.replace( runescape, funescape ).toLowerCase(); + return function( elem ) { + var elemLang; + do { + if ( (elemLang = documentIsHTML ? + elem.lang : + elem.getAttribute("xml:lang") || elem.getAttribute("lang")) ) { + + elemLang = elemLang.toLowerCase(); + return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; + } + } while ( (elem = elem.parentNode) && elem.nodeType === 1 ); + return false; + }; + }), + + // Miscellaneous + "target": function( elem ) { + var hash = window.location && window.location.hash; + return hash && hash.slice( 1 ) === elem.id; + }, + + "root": function( elem ) { + return elem === docElem; + }, + + "focus": function( elem ) { + return elem === document.activeElement && (!document.hasFocus || document.hasFocus()) && !!(elem.type || elem.href || ~elem.tabIndex); + }, + + // Boolean properties + "enabled": createDisabledPseudo( false ), + "disabled": createDisabledPseudo( true ), + + "checked": function( elem ) { + // In CSS3, :checked should return both checked and selected elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + var nodeName = elem.nodeName.toLowerCase(); + return (nodeName === "input" && !!elem.checked) || (nodeName === "option" && !!elem.selected); + }, + + "selected": function( elem ) { + // Accessing this property makes selected-by-default + // options in Safari work properly + if ( elem.parentNode ) { + elem.parentNode.selectedIndex; + } + + return elem.selected === true; + }, + + // Contents + "empty": function( elem ) { + // http://www.w3.org/TR/selectors/#empty-pseudo + // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), + // but not by others (comment: 8; processing instruction: 7; etc.) + // nodeType < 6 works because attributes (2) do not appear as children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + if ( elem.nodeType < 6 ) { + return false; + } + } + return true; + }, + + "parent": function( elem ) { + return !Expr.pseudos["empty"]( elem ); + }, + + // Element/input types + "header": function( elem ) { + return rheader.test( elem.nodeName ); + }, + + "input": function( elem ) { + return rinputs.test( elem.nodeName ); + }, + + "button": function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === "button" || name === "button"; + }, + + "text": function( elem ) { + var attr; + return elem.nodeName.toLowerCase() === "input" && + elem.type === "text" && + + // Support: IE<8 + // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" + ( (attr = elem.getAttribute("type")) == null || attr.toLowerCase() === "text" ); + }, + + // Position-in-collection + "first": createPositionalPseudo(function() { + return [ 0 ]; + }), + + "last": createPositionalPseudo(function( matchIndexes, length ) { + return [ length - 1 ]; + }), + + "eq": createPositionalPseudo(function( matchIndexes, length, argument ) { + return [ argument < 0 ? argument + length : argument ]; + }), + + "even": createPositionalPseudo(function( matchIndexes, length ) { + var i = 0; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + }), + + "odd": createPositionalPseudo(function( matchIndexes, length ) { + var i = 1; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + }), + + "lt": createPositionalPseudo(function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; --i >= 0; ) { + matchIndexes.push( i ); + } + return matchIndexes; + }), + + "gt": createPositionalPseudo(function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; ++i < length; ) { + matchIndexes.push( i ); + } + return matchIndexes; + }) + } +}; + +Expr.pseudos["nth"] = Expr.pseudos["eq"]; + +// Add button/input type pseudos +for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { + Expr.pseudos[ i ] = createInputPseudo( i ); +} +for ( i in { submit: true, reset: true } ) { + Expr.pseudos[ i ] = createButtonPseudo( i ); +} + +// Easy API for creating new setFilters +function setFilters() {} +setFilters.prototype = Expr.filters = Expr.pseudos; +Expr.setFilters = new setFilters(); + +tokenize = Sizzle.tokenize = function( selector, parseOnly ) { + var matched, match, tokens, type, + soFar, groups, preFilters, + cached = tokenCache[ selector + " " ]; + + if ( cached ) { + return parseOnly ? 0 : cached.slice( 0 ); + } + + soFar = selector; + groups = []; + preFilters = Expr.preFilter; + + while ( soFar ) { + + // Comma and first run + if ( !matched || (match = rcomma.exec( soFar )) ) { + if ( match ) { + // Don't consume trailing commas as valid + soFar = soFar.slice( match[0].length ) || soFar; + } + groups.push( (tokens = []) ); + } + + matched = false; + + // Combinators + if ( (match = rcombinators.exec( soFar )) ) { + matched = match.shift(); + tokens.push({ + value: matched, + // Cast descendant combinators to space + type: match[0].replace( rtrim, " " ) + }); + soFar = soFar.slice( matched.length ); + } + + // Filters + for ( type in Expr.filter ) { + if ( (match = matchExpr[ type ].exec( soFar )) && (!preFilters[ type ] || + (match = preFilters[ type ]( match ))) ) { + matched = match.shift(); + tokens.push({ + value: matched, + type: type, + matches: match + }); + soFar = soFar.slice( matched.length ); + } + } + + if ( !matched ) { + break; + } + } + + // Return the length of the invalid excess + // if we're just parsing + // Otherwise, throw an error or return tokens + return parseOnly ? + soFar.length : + soFar ? + Sizzle.error( selector ) : + // Cache the tokens + tokenCache( selector, groups ).slice( 0 ); +}; + +function toSelector( tokens ) { + var i = 0, + len = tokens.length, + selector = ""; + for ( ; i < len; i++ ) { + selector += tokens[i].value; + } + return selector; +} + +function addCombinator( matcher, combinator, base ) { + var dir = combinator.dir, + skip = combinator.next, + key = skip || dir, + checkNonElements = base && key === "parentNode", + doneName = done++; + + return combinator.first ? + // Check against closest ancestor/preceding element + function( elem, context, xml ) { + while ( (elem = elem[ dir ]) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + return matcher( elem, context, xml ); + } + } + return false; + } : + + // Check against all ancestor/preceding elements + function( elem, context, xml ) { + var oldCache, uniqueCache, outerCache, + newCache = [ dirruns, doneName ]; + + // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching + if ( xml ) { + while ( (elem = elem[ dir ]) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + if ( matcher( elem, context, xml ) ) { + return true; + } + } + } + } else { + while ( (elem = elem[ dir ]) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + outerCache = elem[ expando ] || (elem[ expando ] = {}); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ elem.uniqueID ] || (outerCache[ elem.uniqueID ] = {}); + + if ( skip && skip === elem.nodeName.toLowerCase() ) { + elem = elem[ dir ] || elem; + } else if ( (oldCache = uniqueCache[ key ]) && + oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { + + // Assign to newCache so results back-propagate to previous elements + return (newCache[ 2 ] = oldCache[ 2 ]); + } else { + // Reuse newcache so results back-propagate to previous elements + uniqueCache[ key ] = newCache; + + // A match means we're done; a fail means we have to keep checking + if ( (newCache[ 2 ] = matcher( elem, context, xml )) ) { + return true; + } + } + } + } + } + return false; + }; +} + +function elementMatcher( matchers ) { + return matchers.length > 1 ? + function( elem, context, xml ) { + var i = matchers.length; + while ( i-- ) { + if ( !matchers[i]( elem, context, xml ) ) { + return false; + } + } + return true; + } : + matchers[0]; +} + +function multipleContexts( selector, contexts, results ) { + var i = 0, + len = contexts.length; + for ( ; i < len; i++ ) { + Sizzle( selector, contexts[i], results ); + } + return results; +} + +function condense( unmatched, map, filter, context, xml ) { + var elem, + newUnmatched = [], + i = 0, + len = unmatched.length, + mapped = map != null; + + for ( ; i < len; i++ ) { + if ( (elem = unmatched[i]) ) { + if ( !filter || filter( elem, context, xml ) ) { + newUnmatched.push( elem ); + if ( mapped ) { + map.push( i ); + } + } + } + } + + return newUnmatched; +} + +function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { + if ( postFilter && !postFilter[ expando ] ) { + postFilter = setMatcher( postFilter ); + } + if ( postFinder && !postFinder[ expando ] ) { + postFinder = setMatcher( postFinder, postSelector ); + } + return markFunction(function( seed, results, context, xml ) { + var temp, i, elem, + preMap = [], + postMap = [], + preexisting = results.length, + + // Get initial elements from seed or context + elems = seed || multipleContexts( selector || "*", context.nodeType ? [ context ] : context, [] ), + + // Prefilter to get matcher input, preserving a map for seed-results synchronization + matcherIn = preFilter && ( seed || !selector ) ? + condense( elems, preMap, preFilter, context, xml ) : + elems, + + matcherOut = matcher ? + // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, + postFinder || ( seed ? preFilter : preexisting || postFilter ) ? + + // ...intermediate processing is necessary + [] : + + // ...otherwise use results directly + results : + matcherIn; + + // Find primary matches + if ( matcher ) { + matcher( matcherIn, matcherOut, context, xml ); + } + + // Apply postFilter + if ( postFilter ) { + temp = condense( matcherOut, postMap ); + postFilter( temp, [], context, xml ); + + // Un-match failing elements by moving them back to matcherIn + i = temp.length; + while ( i-- ) { + if ( (elem = temp[i]) ) { + matcherOut[ postMap[i] ] = !(matcherIn[ postMap[i] ] = elem); + } + } + } + + if ( seed ) { + if ( postFinder || preFilter ) { + if ( postFinder ) { + // Get the final matcherOut by condensing this intermediate into postFinder contexts + temp = []; + i = matcherOut.length; + while ( i-- ) { + if ( (elem = matcherOut[i]) ) { + // Restore matcherIn since elem is not yet a final match + temp.push( (matcherIn[i] = elem) ); + } + } + postFinder( null, (matcherOut = []), temp, xml ); + } + + // Move matched elements from seed to results to keep them synchronized + i = matcherOut.length; + while ( i-- ) { + if ( (elem = matcherOut[i]) && + (temp = postFinder ? indexOf( seed, elem ) : preMap[i]) > -1 ) { + + seed[temp] = !(results[temp] = elem); + } + } + } + + // Add elements to results, through postFinder if defined + } else { + matcherOut = condense( + matcherOut === results ? + matcherOut.splice( preexisting, matcherOut.length ) : + matcherOut + ); + if ( postFinder ) { + postFinder( null, results, matcherOut, xml ); + } else { + push.apply( results, matcherOut ); + } + } + }); +} + +function matcherFromTokens( tokens ) { + var checkContext, matcher, j, + len = tokens.length, + leadingRelative = Expr.relative[ tokens[0].type ], + implicitRelative = leadingRelative || Expr.relative[" "], + i = leadingRelative ? 1 : 0, + + // The foundational matcher ensures that elements are reachable from top-level context(s) + matchContext = addCombinator( function( elem ) { + return elem === checkContext; + }, implicitRelative, true ), + matchAnyContext = addCombinator( function( elem ) { + return indexOf( checkContext, elem ) > -1; + }, implicitRelative, true ), + matchers = [ function( elem, context, xml ) { + var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( + (checkContext = context).nodeType ? + matchContext( elem, context, xml ) : + matchAnyContext( elem, context, xml ) ); + // Avoid hanging onto element (issue #299) + checkContext = null; + return ret; + } ]; + + for ( ; i < len; i++ ) { + if ( (matcher = Expr.relative[ tokens[i].type ]) ) { + matchers = [ addCombinator(elementMatcher( matchers ), matcher) ]; + } else { + matcher = Expr.filter[ tokens[i].type ].apply( null, tokens[i].matches ); + + // Return special upon seeing a positional matcher + if ( matcher[ expando ] ) { + // Find the next relative operator (if any) for proper handling + j = ++i; + for ( ; j < len; j++ ) { + if ( Expr.relative[ tokens[j].type ] ) { + break; + } + } + return setMatcher( + i > 1 && elementMatcher( matchers ), + i > 1 && toSelector( + // If the preceding token was a descendant combinator, insert an implicit any-element `*` + tokens.slice( 0, i - 1 ).concat({ value: tokens[ i - 2 ].type === " " ? "*" : "" }) + ).replace( rtrim, "$1" ), + matcher, + i < j && matcherFromTokens( tokens.slice( i, j ) ), + j < len && matcherFromTokens( (tokens = tokens.slice( j )) ), + j < len && toSelector( tokens ) + ); + } + matchers.push( matcher ); + } + } + + return elementMatcher( matchers ); +} + +function matcherFromGroupMatchers( elementMatchers, setMatchers ) { + var bySet = setMatchers.length > 0, + byElement = elementMatchers.length > 0, + superMatcher = function( seed, context, xml, results, outermost ) { + var elem, j, matcher, + matchedCount = 0, + i = "0", + unmatched = seed && [], + setMatched = [], + contextBackup = outermostContext, + // We must always have either seed elements or outermost context + elems = seed || byElement && Expr.find["TAG"]( "*", outermost ), + // Use integer dirruns iff this is the outermost matcher + dirrunsUnique = (dirruns += contextBackup == null ? 1 : Math.random() || 0.1), + len = elems.length; + + if ( outermost ) { + outermostContext = context === document || context || outermost; + } + + // Add elements passing elementMatchers directly to results + // Support: IE<9, Safari + // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id + for ( ; i !== len && (elem = elems[i]) != null; i++ ) { + if ( byElement && elem ) { + j = 0; + if ( !context && elem.ownerDocument !== document ) { + setDocument( elem ); + xml = !documentIsHTML; + } + while ( (matcher = elementMatchers[j++]) ) { + if ( matcher( elem, context || document, xml) ) { + results.push( elem ); + break; + } + } + if ( outermost ) { + dirruns = dirrunsUnique; + } + } + + // Track unmatched elements for set filters + if ( bySet ) { + // They will have gone through all possible matchers + if ( (elem = !matcher && elem) ) { + matchedCount--; + } + + // Lengthen the array for every element, matched or not + if ( seed ) { + unmatched.push( elem ); + } + } + } + + // `i` is now the count of elements visited above, and adding it to `matchedCount` + // makes the latter nonnegative. + matchedCount += i; + + // Apply set filters to unmatched elements + // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` + // equals `i`), unless we didn't visit _any_ elements in the above loop because we have + // no element matchers and no seed. + // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that + // case, which will result in a "00" `matchedCount` that differs from `i` but is also + // numerically zero. + if ( bySet && i !== matchedCount ) { + j = 0; + while ( (matcher = setMatchers[j++]) ) { + matcher( unmatched, setMatched, context, xml ); + } + + if ( seed ) { + // Reintegrate element matches to eliminate the need for sorting + if ( matchedCount > 0 ) { + while ( i-- ) { + if ( !(unmatched[i] || setMatched[i]) ) { + setMatched[i] = pop.call( results ); + } + } + } + + // Discard index placeholder values to get only actual matches + setMatched = condense( setMatched ); + } + + // Add matches to results + push.apply( results, setMatched ); + + // Seedless set matches succeeding multiple successful matchers stipulate sorting + if ( outermost && !seed && setMatched.length > 0 && + ( matchedCount + setMatchers.length ) > 1 ) { + + Sizzle.uniqueSort( results ); + } + } + + // Override manipulation of globals by nested matchers + if ( outermost ) { + dirruns = dirrunsUnique; + outermostContext = contextBackup; + } + + return unmatched; + }; + + return bySet ? + markFunction( superMatcher ) : + superMatcher; +} + +compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { + var i, + setMatchers = [], + elementMatchers = [], + cached = compilerCache[ selector + " " ]; + + if ( !cached ) { + // Generate a function of recursive functions that can be used to check each element + if ( !match ) { + match = tokenize( selector ); + } + i = match.length; + while ( i-- ) { + cached = matcherFromTokens( match[i] ); + if ( cached[ expando ] ) { + setMatchers.push( cached ); + } else { + elementMatchers.push( cached ); + } + } + + // Cache the compiled function + cached = compilerCache( selector, matcherFromGroupMatchers( elementMatchers, setMatchers ) ); + + // Save selector and tokenization + cached.selector = selector; + } + return cached; +}; + +/** + * A low-level selection function that works with Sizzle's compiled + * selector functions + * @param {String|Function} selector A selector or a pre-compiled + * selector function built with Sizzle.compile + * @param {Element} context + * @param {Array} [results] + * @param {Array} [seed] A set of elements to match against + */ +select = Sizzle.select = function( selector, context, results, seed ) { + var i, tokens, token, type, find, + compiled = typeof selector === "function" && selector, + match = !seed && tokenize( (selector = compiled.selector || selector) ); + + results = results || []; + + // Try to minimize operations if there is only one selector in the list and no seed + // (the latter of which guarantees us context) + if ( match.length === 1 ) { + + // Reduce context if the leading compound selector is an ID + tokens = match[0] = match[0].slice( 0 ); + if ( tokens.length > 2 && (token = tokens[0]).type === "ID" && + context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[1].type ] ) { + + context = ( Expr.find["ID"]( token.matches[0].replace(runescape, funescape), context ) || [] )[0]; + if ( !context ) { + return results; + + // Precompiled matchers will still verify ancestry, so step up a level + } else if ( compiled ) { + context = context.parentNode; + } + + selector = selector.slice( tokens.shift().value.length ); + } + + // Fetch a seed set for right-to-left matching + i = matchExpr["needsContext"].test( selector ) ? 0 : tokens.length; + while ( i-- ) { + token = tokens[i]; + + // Abort if we hit a combinator + if ( Expr.relative[ (type = token.type) ] ) { + break; + } + if ( (find = Expr.find[ type ]) ) { + // Search, expanding context for leading sibling combinators + if ( (seed = find( + token.matches[0].replace( runescape, funescape ), + rsibling.test( tokens[0].type ) && testContext( context.parentNode ) || context + )) ) { + + // If seed is empty or no tokens remain, we can return early + tokens.splice( i, 1 ); + selector = seed.length && toSelector( tokens ); + if ( !selector ) { + push.apply( results, seed ); + return results; + } + + break; + } + } + } + } + + // Compile and execute a filtering function if one is not provided + // Provide `match` to avoid retokenization if we modified the selector above + ( compiled || compile( selector, match ) )( + seed, + context, + !documentIsHTML, + results, + !context || rsibling.test( selector ) && testContext( context.parentNode ) || context + ); + return results; +}; + +// One-time assignments + +// Sort stability +support.sortStable = expando.split("").sort( sortOrder ).join("") === expando; + +// Support: Chrome 14-35+ +// Always assume duplicates if they aren't passed to the comparison function +support.detectDuplicates = !!hasDuplicate; + +// Initialize against the default document +setDocument(); + +// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) +// Detached nodes confoundingly follow *each other* +support.sortDetached = assert(function( el ) { + // Should return 1, but returns 4 (following) + return el.compareDocumentPosition( document.createElement("fieldset") ) & 1; +}); + +// Support: IE<8 +// Prevent attribute/property "interpolation" +// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx +if ( !assert(function( el ) { + el.innerHTML = ""; + return el.firstChild.getAttribute("href") === "#" ; +}) ) { + addHandle( "type|href|height|width", function( elem, name, isXML ) { + if ( !isXML ) { + return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); + } + }); +} + +// Support: IE<9 +// Use defaultValue in place of getAttribute("value") +if ( !support.attributes || !assert(function( el ) { + el.innerHTML = ""; + el.firstChild.setAttribute( "value", "" ); + return el.firstChild.getAttribute( "value" ) === ""; +}) ) { + addHandle( "value", function( elem, name, isXML ) { + if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { + return elem.defaultValue; + } + }); +} + +// Support: IE<9 +// Use getAttributeNode to fetch booleans when getAttribute lies +if ( !assert(function( el ) { + return el.getAttribute("disabled") == null; +}) ) { + addHandle( booleans, function( elem, name, isXML ) { + var val; + if ( !isXML ) { + return elem[ name ] === true ? name.toLowerCase() : + (val = elem.getAttributeNode( name )) && val.specified ? + val.value : + null; + } + }); +} + +return Sizzle; + +})( window ); + + + +jQuery.find = Sizzle; +jQuery.expr = Sizzle.selectors; + +// Deprecated +jQuery.expr[ ":" ] = jQuery.expr.pseudos; +jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; +jQuery.text = Sizzle.getText; +jQuery.isXMLDoc = Sizzle.isXML; +jQuery.contains = Sizzle.contains; +jQuery.escapeSelector = Sizzle.escape; + + + + +var dir = function( elem, dir, until ) { + var matched = [], + truncate = until !== undefined; + + while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { + if ( elem.nodeType === 1 ) { + if ( truncate && jQuery( elem ).is( until ) ) { + break; + } + matched.push( elem ); + } + } + return matched; +}; + + +var siblings = function( n, elem ) { + var matched = []; + + for ( ; n; n = n.nextSibling ) { + if ( n.nodeType === 1 && n !== elem ) { + matched.push( n ); + } + } + + return matched; +}; + + +var rneedsContext = jQuery.expr.match.needsContext; + + + +function nodeName( elem, name ) { + + return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); + +}; +var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); + + + +// Implement the identical functionality for filter and not +function winnow( elements, qualifier, not ) { + if ( isFunction( qualifier ) ) { + return jQuery.grep( elements, function( elem, i ) { + return !!qualifier.call( elem, i, elem ) !== not; + } ); + } + + // Single element + if ( qualifier.nodeType ) { + return jQuery.grep( elements, function( elem ) { + return ( elem === qualifier ) !== not; + } ); + } + + // Arraylike of elements (jQuery, arguments, Array) + if ( typeof qualifier !== "string" ) { + return jQuery.grep( elements, function( elem ) { + return ( indexOf.call( qualifier, elem ) > -1 ) !== not; + } ); + } + + // Filtered directly for both simple and complex selectors + return jQuery.filter( qualifier, elements, not ); +} + +jQuery.filter = function( expr, elems, not ) { + var elem = elems[ 0 ]; + + if ( not ) { + expr = ":not(" + expr + ")"; + } + + if ( elems.length === 1 && elem.nodeType === 1 ) { + return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; + } + + return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { + return elem.nodeType === 1; + } ) ); +}; + +jQuery.fn.extend( { + find: function( selector ) { + var i, ret, + len = this.length, + self = this; + + if ( typeof selector !== "string" ) { + return this.pushStack( jQuery( selector ).filter( function() { + for ( i = 0; i < len; i++ ) { + if ( jQuery.contains( self[ i ], this ) ) { + return true; + } + } + } ) ); + } + + ret = this.pushStack( [] ); + + for ( i = 0; i < len; i++ ) { + jQuery.find( selector, self[ i ], ret ); + } + + return len > 1 ? jQuery.uniqueSort( ret ) : ret; + }, + filter: function( selector ) { + return this.pushStack( winnow( this, selector || [], false ) ); + }, + not: function( selector ) { + return this.pushStack( winnow( this, selector || [], true ) ); + }, + is: function( selector ) { + return !!winnow( + this, + + // If this is a positional/relative selector, check membership in the returned set + // so $("p:first").is("p:last") won't return true for a doc with two "p". + typeof selector === "string" && rneedsContext.test( selector ) ? + jQuery( selector ) : + selector || [], + false + ).length; + } +} ); + + +// Initialize a jQuery object + + +// A central reference to the root jQuery(document) +var rootjQuery, + + // A simple way to check for HTML strings + // Prioritize #id over to avoid XSS via location.hash (#9521) + // Strict HTML recognition (#11290: must start with <) + // Shortcut simple #id case for speed + rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, + + init = jQuery.fn.init = function( selector, context, root ) { + var match, elem; + + // HANDLE: $(""), $(null), $(undefined), $(false) + if ( !selector ) { + return this; + } + + // Method init() accepts an alternate rootjQuery + // so migrate can support jQuery.sub (gh-2101) + root = root || rootjQuery; + + // Handle HTML strings + if ( typeof selector === "string" ) { + if ( selector[ 0 ] === "<" && + selector[ selector.length - 1 ] === ">" && + selector.length >= 3 ) { + + // Assume that strings that start and end with <> are HTML and skip the regex check + match = [ null, selector, null ]; + + } else { + match = rquickExpr.exec( selector ); + } + + // Match html or make sure no context is specified for #id + if ( match && ( match[ 1 ] || !context ) ) { + + // HANDLE: $(html) -> $(array) + if ( match[ 1 ] ) { + context = context instanceof jQuery ? context[ 0 ] : context; + + // Option to run scripts is true for back-compat + // Intentionally let the error be thrown if parseHTML is not present + jQuery.merge( this, jQuery.parseHTML( + match[ 1 ], + context && context.nodeType ? context.ownerDocument || context : document, + true + ) ); + + // HANDLE: $(html, props) + if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { + for ( match in context ) { + + // Properties of context are called as methods if possible + if ( isFunction( this[ match ] ) ) { + this[ match ]( context[ match ] ); + + // ...and otherwise set as attributes + } else { + this.attr( match, context[ match ] ); + } + } + } + + return this; + + // HANDLE: $(#id) + } else { + elem = document.getElementById( match[ 2 ] ); + + if ( elem ) { + + // Inject the element directly into the jQuery object + this[ 0 ] = elem; + this.length = 1; + } + return this; + } + + // HANDLE: $(expr, $(...)) + } else if ( !context || context.jquery ) { + return ( context || root ).find( selector ); + + // HANDLE: $(expr, context) + // (which is just equivalent to: $(context).find(expr) + } else { + return this.constructor( context ).find( selector ); + } + + // HANDLE: $(DOMElement) + } else if ( selector.nodeType ) { + this[ 0 ] = selector; + this.length = 1; + return this; + + // HANDLE: $(function) + // Shortcut for document ready + } else if ( isFunction( selector ) ) { + return root.ready !== undefined ? + root.ready( selector ) : + + // Execute immediately if ready is not present + selector( jQuery ); + } + + return jQuery.makeArray( selector, this ); + }; + +// Give the init function the jQuery prototype for later instantiation +init.prototype = jQuery.fn; + +// Initialize central reference +rootjQuery = jQuery( document ); + + +var rparentsprev = /^(?:parents|prev(?:Until|All))/, + + // Methods guaranteed to produce a unique set when starting from a unique set + guaranteedUnique = { + children: true, + contents: true, + next: true, + prev: true + }; + +jQuery.fn.extend( { + has: function( target ) { + var targets = jQuery( target, this ), + l = targets.length; + + return this.filter( function() { + var i = 0; + for ( ; i < l; i++ ) { + if ( jQuery.contains( this, targets[ i ] ) ) { + return true; + } + } + } ); + }, + + closest: function( selectors, context ) { + var cur, + i = 0, + l = this.length, + matched = [], + targets = typeof selectors !== "string" && jQuery( selectors ); + + // Positional selectors never match, since there's no _selection_ context + if ( !rneedsContext.test( selectors ) ) { + for ( ; i < l; i++ ) { + for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { + + // Always skip document fragments + if ( cur.nodeType < 11 && ( targets ? + targets.index( cur ) > -1 : + + // Don't pass non-elements to Sizzle + cur.nodeType === 1 && + jQuery.find.matchesSelector( cur, selectors ) ) ) { + + matched.push( cur ); + break; + } + } + } + } + + return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); + }, + + // Determine the position of an element within the set + index: function( elem ) { + + // No argument, return index in parent + if ( !elem ) { + return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; + } + + // Index in selector + if ( typeof elem === "string" ) { + return indexOf.call( jQuery( elem ), this[ 0 ] ); + } + + // Locate the position of the desired element + return indexOf.call( this, + + // If it receives a jQuery object, the first element is used + elem.jquery ? elem[ 0 ] : elem + ); + }, + + add: function( selector, context ) { + return this.pushStack( + jQuery.uniqueSort( + jQuery.merge( this.get(), jQuery( selector, context ) ) + ) + ); + }, + + addBack: function( selector ) { + return this.add( selector == null ? + this.prevObject : this.prevObject.filter( selector ) + ); + } +} ); + +function sibling( cur, dir ) { + while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} + return cur; +} + +jQuery.each( { + parent: function( elem ) { + var parent = elem.parentNode; + return parent && parent.nodeType !== 11 ? parent : null; + }, + parents: function( elem ) { + return dir( elem, "parentNode" ); + }, + parentsUntil: function( elem, i, until ) { + return dir( elem, "parentNode", until ); + }, + next: function( elem ) { + return sibling( elem, "nextSibling" ); + }, + prev: function( elem ) { + return sibling( elem, "previousSibling" ); + }, + nextAll: function( elem ) { + return dir( elem, "nextSibling" ); + }, + prevAll: function( elem ) { + return dir( elem, "previousSibling" ); + }, + nextUntil: function( elem, i, until ) { + return dir( elem, "nextSibling", until ); + }, + prevUntil: function( elem, i, until ) { + return dir( elem, "previousSibling", until ); + }, + siblings: function( elem ) { + return siblings( ( elem.parentNode || {} ).firstChild, elem ); + }, + children: function( elem ) { + return siblings( elem.firstChild ); + }, + contents: function( elem ) { + if ( nodeName( elem, "iframe" ) ) { + return elem.contentDocument; + } + + // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only + // Treat the template element as a regular one in browsers that + // don't support it. + if ( nodeName( elem, "template" ) ) { + elem = elem.content || elem; + } + + return jQuery.merge( [], elem.childNodes ); + } +}, function( name, fn ) { + jQuery.fn[ name ] = function( until, selector ) { + var matched = jQuery.map( this, fn, until ); + + if ( name.slice( -5 ) !== "Until" ) { + selector = until; + } + + if ( selector && typeof selector === "string" ) { + matched = jQuery.filter( selector, matched ); + } + + if ( this.length > 1 ) { + + // Remove duplicates + if ( !guaranteedUnique[ name ] ) { + jQuery.uniqueSort( matched ); + } + + // Reverse order for parents* and prev-derivatives + if ( rparentsprev.test( name ) ) { + matched.reverse(); + } + } + + return this.pushStack( matched ); + }; +} ); +var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); + + + +// Convert String-formatted options into Object-formatted ones +function createOptions( options ) { + var object = {}; + jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { + object[ flag ] = true; + } ); + return object; +} + +/* + * Create a callback list using the following parameters: + * + * options: an optional list of space-separated options that will change how + * the callback list behaves or a more traditional option object + * + * By default a callback list will act like an event callback list and can be + * "fired" multiple times. + * + * Possible options: + * + * once: will ensure the callback list can only be fired once (like a Deferred) + * + * memory: will keep track of previous values and will call any callback added + * after the list has been fired right away with the latest "memorized" + * values (like a Deferred) + * + * unique: will ensure a callback can only be added once (no duplicate in the list) + * + * stopOnFalse: interrupt callings when a callback returns false + * + */ +jQuery.Callbacks = function( options ) { + + // Convert options from String-formatted to Object-formatted if needed + // (we check in cache first) + options = typeof options === "string" ? + createOptions( options ) : + jQuery.extend( {}, options ); + + var // Flag to know if list is currently firing + firing, + + // Last fire value for non-forgettable lists + memory, + + // Flag to know if list was already fired + fired, + + // Flag to prevent firing + locked, + + // Actual callback list + list = [], + + // Queue of execution data for repeatable lists + queue = [], + + // Index of currently firing callback (modified by add/remove as needed) + firingIndex = -1, + + // Fire callbacks + fire = function() { + + // Enforce single-firing + locked = locked || options.once; + + // Execute callbacks for all pending executions, + // respecting firingIndex overrides and runtime changes + fired = firing = true; + for ( ; queue.length; firingIndex = -1 ) { + memory = queue.shift(); + while ( ++firingIndex < list.length ) { + + // Run callback and check for early termination + if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && + options.stopOnFalse ) { + + // Jump to end and forget the data so .add doesn't re-fire + firingIndex = list.length; + memory = false; + } + } + } + + // Forget the data if we're done with it + if ( !options.memory ) { + memory = false; + } + + firing = false; + + // Clean up if we're done firing for good + if ( locked ) { + + // Keep an empty list if we have data for future add calls + if ( memory ) { + list = []; + + // Otherwise, this object is spent + } else { + list = ""; + } + } + }, + + // Actual Callbacks object + self = { + + // Add a callback or a collection of callbacks to the list + add: function() { + if ( list ) { + + // If we have memory from a past run, we should fire after adding + if ( memory && !firing ) { + firingIndex = list.length - 1; + queue.push( memory ); + } + + ( function add( args ) { + jQuery.each( args, function( _, arg ) { + if ( isFunction( arg ) ) { + if ( !options.unique || !self.has( arg ) ) { + list.push( arg ); + } + } else if ( arg && arg.length && toType( arg ) !== "string" ) { + + // Inspect recursively + add( arg ); + } + } ); + } )( arguments ); + + if ( memory && !firing ) { + fire(); + } + } + return this; + }, + + // Remove a callback from the list + remove: function() { + jQuery.each( arguments, function( _, arg ) { + var index; + while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { + list.splice( index, 1 ); + + // Handle firing indexes + if ( index <= firingIndex ) { + firingIndex--; + } + } + } ); + return this; + }, + + // Check if a given callback is in the list. + // If no argument is given, return whether or not list has callbacks attached. + has: function( fn ) { + return fn ? + jQuery.inArray( fn, list ) > -1 : + list.length > 0; + }, + + // Remove all callbacks from the list + empty: function() { + if ( list ) { + list = []; + } + return this; + }, + + // Disable .fire and .add + // Abort any current/pending executions + // Clear all callbacks and values + disable: function() { + locked = queue = []; + list = memory = ""; + return this; + }, + disabled: function() { + return !list; + }, + + // Disable .fire + // Also disable .add unless we have memory (since it would have no effect) + // Abort any pending executions + lock: function() { + locked = queue = []; + if ( !memory && !firing ) { + list = memory = ""; + } + return this; + }, + locked: function() { + return !!locked; + }, + + // Call all callbacks with the given context and arguments + fireWith: function( context, args ) { + if ( !locked ) { + args = args || []; + args = [ context, args.slice ? args.slice() : args ]; + queue.push( args ); + if ( !firing ) { + fire(); + } + } + return this; + }, + + // Call all the callbacks with the given arguments + fire: function() { + self.fireWith( this, arguments ); + return this; + }, + + // To know if the callbacks have already been called at least once + fired: function() { + return !!fired; + } + }; + + return self; +}; + + +function Identity( v ) { + return v; +} +function Thrower( ex ) { + throw ex; +} + +function adoptValue( value, resolve, reject, noValue ) { + var method; + + try { + + // Check for promise aspect first to privilege synchronous behavior + if ( value && isFunction( ( method = value.promise ) ) ) { + method.call( value ).done( resolve ).fail( reject ); + + // Other thenables + } else if ( value && isFunction( ( method = value.then ) ) ) { + method.call( value, resolve, reject ); + + // Other non-thenables + } else { + + // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: + // * false: [ value ].slice( 0 ) => resolve( value ) + // * true: [ value ].slice( 1 ) => resolve() + resolve.apply( undefined, [ value ].slice( noValue ) ); + } + + // For Promises/A+, convert exceptions into rejections + // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in + // Deferred#then to conditionally suppress rejection. + } catch ( value ) { + + // Support: Android 4.0 only + // Strict mode functions invoked without .call/.apply get global-object context + reject.apply( undefined, [ value ] ); + } +} + +jQuery.extend( { + + Deferred: function( func ) { + var tuples = [ + + // action, add listener, callbacks, + // ... .then handlers, argument index, [final state] + [ "notify", "progress", jQuery.Callbacks( "memory" ), + jQuery.Callbacks( "memory" ), 2 ], + [ "resolve", "done", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 0, "resolved" ], + [ "reject", "fail", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 1, "rejected" ] + ], + state = "pending", + promise = { + state: function() { + return state; + }, + always: function() { + deferred.done( arguments ).fail( arguments ); + return this; + }, + "catch": function( fn ) { + return promise.then( null, fn ); + }, + + // Keep pipe for back-compat + pipe: function( /* fnDone, fnFail, fnProgress */ ) { + var fns = arguments; + + return jQuery.Deferred( function( newDefer ) { + jQuery.each( tuples, function( i, tuple ) { + + // Map tuples (progress, done, fail) to arguments (done, fail, progress) + var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; + + // deferred.progress(function() { bind to newDefer or newDefer.notify }) + // deferred.done(function() { bind to newDefer or newDefer.resolve }) + // deferred.fail(function() { bind to newDefer or newDefer.reject }) + deferred[ tuple[ 1 ] ]( function() { + var returned = fn && fn.apply( this, arguments ); + if ( returned && isFunction( returned.promise ) ) { + returned.promise() + .progress( newDefer.notify ) + .done( newDefer.resolve ) + .fail( newDefer.reject ); + } else { + newDefer[ tuple[ 0 ] + "With" ]( + this, + fn ? [ returned ] : arguments + ); + } + } ); + } ); + fns = null; + } ).promise(); + }, + then: function( onFulfilled, onRejected, onProgress ) { + var maxDepth = 0; + function resolve( depth, deferred, handler, special ) { + return function() { + var that = this, + args = arguments, + mightThrow = function() { + var returned, then; + + // Support: Promises/A+ section 2.3.3.3.3 + // https://promisesaplus.com/#point-59 + // Ignore double-resolution attempts + if ( depth < maxDepth ) { + return; + } + + returned = handler.apply( that, args ); + + // Support: Promises/A+ section 2.3.1 + // https://promisesaplus.com/#point-48 + if ( returned === deferred.promise() ) { + throw new TypeError( "Thenable self-resolution" ); + } + + // Support: Promises/A+ sections 2.3.3.1, 3.5 + // https://promisesaplus.com/#point-54 + // https://promisesaplus.com/#point-75 + // Retrieve `then` only once + then = returned && + + // Support: Promises/A+ section 2.3.4 + // https://promisesaplus.com/#point-64 + // Only check objects and functions for thenability + ( typeof returned === "object" || + typeof returned === "function" ) && + returned.then; + + // Handle a returned thenable + if ( isFunction( then ) ) { + + // Special processors (notify) just wait for resolution + if ( special ) { + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ) + ); + + // Normal processors (resolve) also hook into progress + } else { + + // ...and disregard older resolution values + maxDepth++; + + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ), + resolve( maxDepth, deferred, Identity, + deferred.notifyWith ) + ); + } + + // Handle all other returned values + } else { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Identity ) { + that = undefined; + args = [ returned ]; + } + + // Process the value(s) + // Default process is resolve + ( special || deferred.resolveWith )( that, args ); + } + }, + + // Only normal processors (resolve) catch and reject exceptions + process = special ? + mightThrow : + function() { + try { + mightThrow(); + } catch ( e ) { + + if ( jQuery.Deferred.exceptionHook ) { + jQuery.Deferred.exceptionHook( e, + process.stackTrace ); + } + + // Support: Promises/A+ section 2.3.3.3.4.1 + // https://promisesaplus.com/#point-61 + // Ignore post-resolution exceptions + if ( depth + 1 >= maxDepth ) { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Thrower ) { + that = undefined; + args = [ e ]; + } + + deferred.rejectWith( that, args ); + } + } + }; + + // Support: Promises/A+ section 2.3.3.3.1 + // https://promisesaplus.com/#point-57 + // Re-resolve promises immediately to dodge false rejection from + // subsequent errors + if ( depth ) { + process(); + } else { + + // Call an optional hook to record the stack, in case of exception + // since it's otherwise lost when execution goes async + if ( jQuery.Deferred.getStackHook ) { + process.stackTrace = jQuery.Deferred.getStackHook(); + } + window.setTimeout( process ); + } + }; + } + + return jQuery.Deferred( function( newDefer ) { + + // progress_handlers.add( ... ) + tuples[ 0 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onProgress ) ? + onProgress : + Identity, + newDefer.notifyWith + ) + ); + + // fulfilled_handlers.add( ... ) + tuples[ 1 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onFulfilled ) ? + onFulfilled : + Identity + ) + ); + + // rejected_handlers.add( ... ) + tuples[ 2 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onRejected ) ? + onRejected : + Thrower + ) + ); + } ).promise(); + }, + + // Get a promise for this deferred + // If obj is provided, the promise aspect is added to the object + promise: function( obj ) { + return obj != null ? jQuery.extend( obj, promise ) : promise; + } + }, + deferred = {}; + + // Add list-specific methods + jQuery.each( tuples, function( i, tuple ) { + var list = tuple[ 2 ], + stateString = tuple[ 5 ]; + + // promise.progress = list.add + // promise.done = list.add + // promise.fail = list.add + promise[ tuple[ 1 ] ] = list.add; + + // Handle state + if ( stateString ) { + list.add( + function() { + + // state = "resolved" (i.e., fulfilled) + // state = "rejected" + state = stateString; + }, + + // rejected_callbacks.disable + // fulfilled_callbacks.disable + tuples[ 3 - i ][ 2 ].disable, + + // rejected_handlers.disable + // fulfilled_handlers.disable + tuples[ 3 - i ][ 3 ].disable, + + // progress_callbacks.lock + tuples[ 0 ][ 2 ].lock, + + // progress_handlers.lock + tuples[ 0 ][ 3 ].lock + ); + } + + // progress_handlers.fire + // fulfilled_handlers.fire + // rejected_handlers.fire + list.add( tuple[ 3 ].fire ); + + // deferred.notify = function() { deferred.notifyWith(...) } + // deferred.resolve = function() { deferred.resolveWith(...) } + // deferred.reject = function() { deferred.rejectWith(...) } + deferred[ tuple[ 0 ] ] = function() { + deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); + return this; + }; + + // deferred.notifyWith = list.fireWith + // deferred.resolveWith = list.fireWith + // deferred.rejectWith = list.fireWith + deferred[ tuple[ 0 ] + "With" ] = list.fireWith; + } ); + + // Make the deferred a promise + promise.promise( deferred ); + + // Call given func if any + if ( func ) { + func.call( deferred, deferred ); + } + + // All done! + return deferred; + }, + + // Deferred helper + when: function( singleValue ) { + var + + // count of uncompleted subordinates + remaining = arguments.length, + + // count of unprocessed arguments + i = remaining, + + // subordinate fulfillment data + resolveContexts = Array( i ), + resolveValues = slice.call( arguments ), + + // the master Deferred + master = jQuery.Deferred(), + + // subordinate callback factory + updateFunc = function( i ) { + return function( value ) { + resolveContexts[ i ] = this; + resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; + if ( !( --remaining ) ) { + master.resolveWith( resolveContexts, resolveValues ); + } + }; + }; + + // Single- and empty arguments are adopted like Promise.resolve + if ( remaining <= 1 ) { + adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject, + !remaining ); + + // Use .then() to unwrap secondary thenables (cf. gh-3000) + if ( master.state() === "pending" || + isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { + + return master.then(); + } + } + + // Multiple arguments are aggregated like Promise.all array elements + while ( i-- ) { + adoptValue( resolveValues[ i ], updateFunc( i ), master.reject ); + } + + return master.promise(); + } +} ); + + +// These usually indicate a programmer mistake during development, +// warn about them ASAP rather than swallowing them by default. +var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; + +jQuery.Deferred.exceptionHook = function( error, stack ) { + + // Support: IE 8 - 9 only + // Console exists when dev tools are open, which can happen at any time + if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { + window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); + } +}; + + + + +jQuery.readyException = function( error ) { + window.setTimeout( function() { + throw error; + } ); +}; + + + + +// The deferred used on DOM ready +var readyList = jQuery.Deferred(); + +jQuery.fn.ready = function( fn ) { + + readyList + .then( fn ) + + // Wrap jQuery.readyException in a function so that the lookup + // happens at the time of error handling instead of callback + // registration. + .catch( function( error ) { + jQuery.readyException( error ); + } ); + + return this; +}; + +jQuery.extend( { + + // Is the DOM ready to be used? Set to true once it occurs. + isReady: false, + + // A counter to track how many items to wait for before + // the ready event fires. See #6781 + readyWait: 1, + + // Handle when the DOM is ready + ready: function( wait ) { + + // Abort if there are pending holds or we're already ready + if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { + return; + } + + // Remember that the DOM is ready + jQuery.isReady = true; + + // If a normal DOM Ready event fired, decrement, and wait if need be + if ( wait !== true && --jQuery.readyWait > 0 ) { + return; + } + + // If there are functions bound, to execute + readyList.resolveWith( document, [ jQuery ] ); + } +} ); + +jQuery.ready.then = readyList.then; + +// The ready event handler and self cleanup method +function completed() { + document.removeEventListener( "DOMContentLoaded", completed ); + window.removeEventListener( "load", completed ); + jQuery.ready(); +} + +// Catch cases where $(document).ready() is called +// after the browser event has already occurred. +// Support: IE <=9 - 10 only +// Older IE sometimes signals "interactive" too soon +if ( document.readyState === "complete" || + ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { + + // Handle it asynchronously to allow scripts the opportunity to delay ready + window.setTimeout( jQuery.ready ); + +} else { + + // Use the handy event callback + document.addEventListener( "DOMContentLoaded", completed ); + + // A fallback to window.onload, that will always work + window.addEventListener( "load", completed ); +} + + + + +// Multifunctional method to get and set values of a collection +// The value/s can optionally be executed if it's a function +var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { + var i = 0, + len = elems.length, + bulk = key == null; + + // Sets many values + if ( toType( key ) === "object" ) { + chainable = true; + for ( i in key ) { + access( elems, fn, i, key[ i ], true, emptyGet, raw ); + } + + // Sets one value + } else if ( value !== undefined ) { + chainable = true; + + if ( !isFunction( value ) ) { + raw = true; + } + + if ( bulk ) { + + // Bulk operations run against the entire set + if ( raw ) { + fn.call( elems, value ); + fn = null; + + // ...except when executing function values + } else { + bulk = fn; + fn = function( elem, key, value ) { + return bulk.call( jQuery( elem ), value ); + }; + } + } + + if ( fn ) { + for ( ; i < len; i++ ) { + fn( + elems[ i ], key, raw ? + value : + value.call( elems[ i ], i, fn( elems[ i ], key ) ) + ); + } + } + } + + if ( chainable ) { + return elems; + } + + // Gets + if ( bulk ) { + return fn.call( elems ); + } + + return len ? fn( elems[ 0 ], key ) : emptyGet; +}; + + +// Matches dashed string for camelizing +var rmsPrefix = /^-ms-/, + rdashAlpha = /-([a-z])/g; + +// Used by camelCase as callback to replace() +function fcamelCase( all, letter ) { + return letter.toUpperCase(); +} + +// Convert dashed to camelCase; used by the css and data modules +// Support: IE <=9 - 11, Edge 12 - 15 +// Microsoft forgot to hump their vendor prefix (#9572) +function camelCase( string ) { + return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); +} +var acceptData = function( owner ) { + + // Accepts only: + // - Node + // - Node.ELEMENT_NODE + // - Node.DOCUMENT_NODE + // - Object + // - Any + return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); +}; + + + + +function Data() { + this.expando = jQuery.expando + Data.uid++; +} + +Data.uid = 1; + +Data.prototype = { + + cache: function( owner ) { + + // Check if the owner object already has a cache + var value = owner[ this.expando ]; + + // If not, create one + if ( !value ) { + value = {}; + + // We can accept data for non-element nodes in modern browsers, + // but we should not, see #8335. + // Always return an empty object. + if ( acceptData( owner ) ) { + + // If it is a node unlikely to be stringify-ed or looped over + // use plain assignment + if ( owner.nodeType ) { + owner[ this.expando ] = value; + + // Otherwise secure it in a non-enumerable property + // configurable must be true to allow the property to be + // deleted when data is removed + } else { + Object.defineProperty( owner, this.expando, { + value: value, + configurable: true + } ); + } + } + } + + return value; + }, + set: function( owner, data, value ) { + var prop, + cache = this.cache( owner ); + + // Handle: [ owner, key, value ] args + // Always use camelCase key (gh-2257) + if ( typeof data === "string" ) { + cache[ camelCase( data ) ] = value; + + // Handle: [ owner, { properties } ] args + } else { + + // Copy the properties one-by-one to the cache object + for ( prop in data ) { + cache[ camelCase( prop ) ] = data[ prop ]; + } + } + return cache; + }, + get: function( owner, key ) { + return key === undefined ? + this.cache( owner ) : + + // Always use camelCase key (gh-2257) + owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; + }, + access: function( owner, key, value ) { + + // In cases where either: + // + // 1. No key was specified + // 2. A string key was specified, but no value provided + // + // Take the "read" path and allow the get method to determine + // which value to return, respectively either: + // + // 1. The entire cache object + // 2. The data stored at the key + // + if ( key === undefined || + ( ( key && typeof key === "string" ) && value === undefined ) ) { + + return this.get( owner, key ); + } + + // When the key is not a string, or both a key and value + // are specified, set or extend (existing objects) with either: + // + // 1. An object of properties + // 2. A key and value + // + this.set( owner, key, value ); + + // Since the "set" path can have two possible entry points + // return the expected data based on which path was taken[*] + return value !== undefined ? value : key; + }, + remove: function( owner, key ) { + var i, + cache = owner[ this.expando ]; + + if ( cache === undefined ) { + return; + } + + if ( key !== undefined ) { + + // Support array or space separated string of keys + if ( Array.isArray( key ) ) { + + // If key is an array of keys... + // We always set camelCase keys, so remove that. + key = key.map( camelCase ); + } else { + key = camelCase( key ); + + // If a key with the spaces exists, use it. + // Otherwise, create an array by matching non-whitespace + key = key in cache ? + [ key ] : + ( key.match( rnothtmlwhite ) || [] ); + } + + i = key.length; + + while ( i-- ) { + delete cache[ key[ i ] ]; + } + } + + // Remove the expando if there's no more data + if ( key === undefined || jQuery.isEmptyObject( cache ) ) { + + // Support: Chrome <=35 - 45 + // Webkit & Blink performance suffers when deleting properties + // from DOM nodes, so set to undefined instead + // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) + if ( owner.nodeType ) { + owner[ this.expando ] = undefined; + } else { + delete owner[ this.expando ]; + } + } + }, + hasData: function( owner ) { + var cache = owner[ this.expando ]; + return cache !== undefined && !jQuery.isEmptyObject( cache ); + } +}; +var dataPriv = new Data(); + +var dataUser = new Data(); + + + +// Implementation Summary +// +// 1. Enforce API surface and semantic compatibility with 1.9.x branch +// 2. Improve the module's maintainability by reducing the storage +// paths to a single mechanism. +// 3. Use the same single mechanism to support "private" and "user" data. +// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) +// 5. Avoid exposing implementation details on user objects (eg. expando properties) +// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 + +var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, + rmultiDash = /[A-Z]/g; + +function getData( data ) { + if ( data === "true" ) { + return true; + } + + if ( data === "false" ) { + return false; + } + + if ( data === "null" ) { + return null; + } + + // Only convert to a number if it doesn't change the string + if ( data === +data + "" ) { + return +data; + } + + if ( rbrace.test( data ) ) { + return JSON.parse( data ); + } + + return data; +} + +function dataAttr( elem, key, data ) { + var name; + + // If nothing was found internally, try to fetch any + // data from the HTML5 data-* attribute + if ( data === undefined && elem.nodeType === 1 ) { + name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); + data = elem.getAttribute( name ); + + if ( typeof data === "string" ) { + try { + data = getData( data ); + } catch ( e ) {} + + // Make sure we set the data so it isn't changed later + dataUser.set( elem, key, data ); + } else { + data = undefined; + } + } + return data; +} + +jQuery.extend( { + hasData: function( elem ) { + return dataUser.hasData( elem ) || dataPriv.hasData( elem ); + }, + + data: function( elem, name, data ) { + return dataUser.access( elem, name, data ); + }, + + removeData: function( elem, name ) { + dataUser.remove( elem, name ); + }, + + // TODO: Now that all calls to _data and _removeData have been replaced + // with direct calls to dataPriv methods, these can be deprecated. + _data: function( elem, name, data ) { + return dataPriv.access( elem, name, data ); + }, + + _removeData: function( elem, name ) { + dataPriv.remove( elem, name ); + } +} ); + +jQuery.fn.extend( { + data: function( key, value ) { + var i, name, data, + elem = this[ 0 ], + attrs = elem && elem.attributes; + + // Gets all values + if ( key === undefined ) { + if ( this.length ) { + data = dataUser.get( elem ); + + if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { + i = attrs.length; + while ( i-- ) { + + // Support: IE 11 only + // The attrs elements can be null (#14894) + if ( attrs[ i ] ) { + name = attrs[ i ].name; + if ( name.indexOf( "data-" ) === 0 ) { + name = camelCase( name.slice( 5 ) ); + dataAttr( elem, name, data[ name ] ); + } + } + } + dataPriv.set( elem, "hasDataAttrs", true ); + } + } + + return data; + } + + // Sets multiple values + if ( typeof key === "object" ) { + return this.each( function() { + dataUser.set( this, key ); + } ); + } + + return access( this, function( value ) { + var data; + + // The calling jQuery object (element matches) is not empty + // (and therefore has an element appears at this[ 0 ]) and the + // `value` parameter was not undefined. An empty jQuery object + // will result in `undefined` for elem = this[ 0 ] which will + // throw an exception if an attempt to read a data cache is made. + if ( elem && value === undefined ) { + + // Attempt to get data from the cache + // The key will always be camelCased in Data + data = dataUser.get( elem, key ); + if ( data !== undefined ) { + return data; + } + + // Attempt to "discover" the data in + // HTML5 custom data-* attrs + data = dataAttr( elem, key ); + if ( data !== undefined ) { + return data; + } + + // We tried really hard, but the data doesn't exist. + return; + } + + // Set the data... + this.each( function() { + + // We always store the camelCased key + dataUser.set( this, key, value ); + } ); + }, null, value, arguments.length > 1, null, true ); + }, + + removeData: function( key ) { + return this.each( function() { + dataUser.remove( this, key ); + } ); + } +} ); + + +jQuery.extend( { + queue: function( elem, type, data ) { + var queue; + + if ( elem ) { + type = ( type || "fx" ) + "queue"; + queue = dataPriv.get( elem, type ); + + // Speed up dequeue by getting out quickly if this is just a lookup + if ( data ) { + if ( !queue || Array.isArray( data ) ) { + queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); + } else { + queue.push( data ); + } + } + return queue || []; + } + }, + + dequeue: function( elem, type ) { + type = type || "fx"; + + var queue = jQuery.queue( elem, type ), + startLength = queue.length, + fn = queue.shift(), + hooks = jQuery._queueHooks( elem, type ), + next = function() { + jQuery.dequeue( elem, type ); + }; + + // If the fx queue is dequeued, always remove the progress sentinel + if ( fn === "inprogress" ) { + fn = queue.shift(); + startLength--; + } + + if ( fn ) { + + // Add a progress sentinel to prevent the fx queue from being + // automatically dequeued + if ( type === "fx" ) { + queue.unshift( "inprogress" ); + } + + // Clear up the last queue stop function + delete hooks.stop; + fn.call( elem, next, hooks ); + } + + if ( !startLength && hooks ) { + hooks.empty.fire(); + } + }, + + // Not public - generate a queueHooks object, or return the current one + _queueHooks: function( elem, type ) { + var key = type + "queueHooks"; + return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { + empty: jQuery.Callbacks( "once memory" ).add( function() { + dataPriv.remove( elem, [ type + "queue", key ] ); + } ) + } ); + } +} ); + +jQuery.fn.extend( { + queue: function( type, data ) { + var setter = 2; + + if ( typeof type !== "string" ) { + data = type; + type = "fx"; + setter--; + } + + if ( arguments.length < setter ) { + return jQuery.queue( this[ 0 ], type ); + } + + return data === undefined ? + this : + this.each( function() { + var queue = jQuery.queue( this, type, data ); + + // Ensure a hooks for this queue + jQuery._queueHooks( this, type ); + + if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { + jQuery.dequeue( this, type ); + } + } ); + }, + dequeue: function( type ) { + return this.each( function() { + jQuery.dequeue( this, type ); + } ); + }, + clearQueue: function( type ) { + return this.queue( type || "fx", [] ); + }, + + // Get a promise resolved when queues of a certain type + // are emptied (fx is the type by default) + promise: function( type, obj ) { + var tmp, + count = 1, + defer = jQuery.Deferred(), + elements = this, + i = this.length, + resolve = function() { + if ( !( --count ) ) { + defer.resolveWith( elements, [ elements ] ); + } + }; + + if ( typeof type !== "string" ) { + obj = type; + type = undefined; + } + type = type || "fx"; + + while ( i-- ) { + tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); + if ( tmp && tmp.empty ) { + count++; + tmp.empty.add( resolve ); + } + } + resolve(); + return defer.promise( obj ); + } +} ); +var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; + +var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); + + +var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; + +var isHiddenWithinTree = function( elem, el ) { + + // isHiddenWithinTree might be called from jQuery#filter function; + // in that case, element will be second argument + elem = el || elem; + + // Inline style trumps all + return elem.style.display === "none" || + elem.style.display === "" && + + // Otherwise, check computed style + // Support: Firefox <=43 - 45 + // Disconnected elements can have computed display: none, so first confirm that elem is + // in the document. + jQuery.contains( elem.ownerDocument, elem ) && + + jQuery.css( elem, "display" ) === "none"; + }; + +var swap = function( elem, options, callback, args ) { + var ret, name, + old = {}; + + // Remember the old values, and insert the new ones + for ( name in options ) { + old[ name ] = elem.style[ name ]; + elem.style[ name ] = options[ name ]; + } + + ret = callback.apply( elem, args || [] ); + + // Revert the old values + for ( name in options ) { + elem.style[ name ] = old[ name ]; + } + + return ret; +}; + + + + +function adjustCSS( elem, prop, valueParts, tween ) { + var adjusted, scale, + maxIterations = 20, + currentValue = tween ? + function() { + return tween.cur(); + } : + function() { + return jQuery.css( elem, prop, "" ); + }, + initial = currentValue(), + unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), + + // Starting value computation is required for potential unit mismatches + initialInUnit = ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && + rcssNum.exec( jQuery.css( elem, prop ) ); + + if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { + + // Support: Firefox <=54 + // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) + initial = initial / 2; + + // Trust units reported by jQuery.css + unit = unit || initialInUnit[ 3 ]; + + // Iteratively approximate from a nonzero starting point + initialInUnit = +initial || 1; + + while ( maxIterations-- ) { + + // Evaluate and update our best guess (doubling guesses that zero out). + // Finish if the scale equals or crosses 1 (making the old*new product non-positive). + jQuery.style( elem, prop, initialInUnit + unit ); + if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { + maxIterations = 0; + } + initialInUnit = initialInUnit / scale; + + } + + initialInUnit = initialInUnit * 2; + jQuery.style( elem, prop, initialInUnit + unit ); + + // Make sure we update the tween properties later on + valueParts = valueParts || []; + } + + if ( valueParts ) { + initialInUnit = +initialInUnit || +initial || 0; + + // Apply relative offset (+=/-=) if specified + adjusted = valueParts[ 1 ] ? + initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : + +valueParts[ 2 ]; + if ( tween ) { + tween.unit = unit; + tween.start = initialInUnit; + tween.end = adjusted; + } + } + return adjusted; +} + + +var defaultDisplayMap = {}; + +function getDefaultDisplay( elem ) { + var temp, + doc = elem.ownerDocument, + nodeName = elem.nodeName, + display = defaultDisplayMap[ nodeName ]; + + if ( display ) { + return display; + } + + temp = doc.body.appendChild( doc.createElement( nodeName ) ); + display = jQuery.css( temp, "display" ); + + temp.parentNode.removeChild( temp ); + + if ( display === "none" ) { + display = "block"; + } + defaultDisplayMap[ nodeName ] = display; + + return display; +} + +function showHide( elements, show ) { + var display, elem, + values = [], + index = 0, + length = elements.length; + + // Determine new display value for elements that need to change + for ( ; index < length; index++ ) { + elem = elements[ index ]; + if ( !elem.style ) { + continue; + } + + display = elem.style.display; + if ( show ) { + + // Since we force visibility upon cascade-hidden elements, an immediate (and slow) + // check is required in this first loop unless we have a nonempty display value (either + // inline or about-to-be-restored) + if ( display === "none" ) { + values[ index ] = dataPriv.get( elem, "display" ) || null; + if ( !values[ index ] ) { + elem.style.display = ""; + } + } + if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { + values[ index ] = getDefaultDisplay( elem ); + } + } else { + if ( display !== "none" ) { + values[ index ] = "none"; + + // Remember what we're overwriting + dataPriv.set( elem, "display", display ); + } + } + } + + // Set the display of the elements in a second loop to avoid constant reflow + for ( index = 0; index < length; index++ ) { + if ( values[ index ] != null ) { + elements[ index ].style.display = values[ index ]; + } + } + + return elements; +} + +jQuery.fn.extend( { + show: function() { + return showHide( this, true ); + }, + hide: function() { + return showHide( this ); + }, + toggle: function( state ) { + if ( typeof state === "boolean" ) { + return state ? this.show() : this.hide(); + } + + return this.each( function() { + if ( isHiddenWithinTree( this ) ) { + jQuery( this ).show(); + } else { + jQuery( this ).hide(); + } + } ); + } +} ); +var rcheckableType = ( /^(?:checkbox|radio)$/i ); + +var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]+)/i ); + +var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); + + + +// We have to close these tags to support XHTML (#13200) +var wrapMap = { + + // Support: IE <=9 only + option: [ 1, "" ], + + // XHTML parsers do not magically insert elements in the + // same way that tag soup parsers do. So we cannot shorten + // this by omitting or other required elements. + thead: [ 1, "", "
" ], + col: [ 2, "", "
" ], + tr: [ 2, "", "
" ], + td: [ 3, "", "
" ], + + _default: [ 0, "", "" ] +}; + +// Support: IE <=9 only +wrapMap.optgroup = wrapMap.option; + +wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; +wrapMap.th = wrapMap.td; + + +function getAll( context, tag ) { + + // Support: IE <=9 - 11 only + // Use typeof to avoid zero-argument method invocation on host objects (#15151) + var ret; + + if ( typeof context.getElementsByTagName !== "undefined" ) { + ret = context.getElementsByTagName( tag || "*" ); + + } else if ( typeof context.querySelectorAll !== "undefined" ) { + ret = context.querySelectorAll( tag || "*" ); + + } else { + ret = []; + } + + if ( tag === undefined || tag && nodeName( context, tag ) ) { + return jQuery.merge( [ context ], ret ); + } + + return ret; +} + + +// Mark scripts as having already been evaluated +function setGlobalEval( elems, refElements ) { + var i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + dataPriv.set( + elems[ i ], + "globalEval", + !refElements || dataPriv.get( refElements[ i ], "globalEval" ) + ); + } +} + + +var rhtml = /<|&#?\w+;/; + +function buildFragment( elems, context, scripts, selection, ignored ) { + var elem, tmp, tag, wrap, contains, j, + fragment = context.createDocumentFragment(), + nodes = [], + i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + elem = elems[ i ]; + + if ( elem || elem === 0 ) { + + // Add nodes directly + if ( toType( elem ) === "object" ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); + + // Convert non-html into a text node + } else if ( !rhtml.test( elem ) ) { + nodes.push( context.createTextNode( elem ) ); + + // Convert html into DOM nodes + } else { + tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); + + // Deserialize a standard representation + tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); + wrap = wrapMap[ tag ] || wrapMap._default; + tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; + + // Descend through wrappers to the right content + j = wrap[ 0 ]; + while ( j-- ) { + tmp = tmp.lastChild; + } + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, tmp.childNodes ); + + // Remember the top-level container + tmp = fragment.firstChild; + + // Ensure the created nodes are orphaned (#12392) + tmp.textContent = ""; + } + } + } + + // Remove wrapper from fragment + fragment.textContent = ""; + + i = 0; + while ( ( elem = nodes[ i++ ] ) ) { + + // Skip elements already in the context collection (trac-4087) + if ( selection && jQuery.inArray( elem, selection ) > -1 ) { + if ( ignored ) { + ignored.push( elem ); + } + continue; + } + + contains = jQuery.contains( elem.ownerDocument, elem ); + + // Append to fragment + tmp = getAll( fragment.appendChild( elem ), "script" ); + + // Preserve script evaluation history + if ( contains ) { + setGlobalEval( tmp ); + } + + // Capture executables + if ( scripts ) { + j = 0; + while ( ( elem = tmp[ j++ ] ) ) { + if ( rscriptType.test( elem.type || "" ) ) { + scripts.push( elem ); + } + } + } + } + + return fragment; +} + + +( function() { + var fragment = document.createDocumentFragment(), + div = fragment.appendChild( document.createElement( "div" ) ), + input = document.createElement( "input" ); + + // Support: Android 4.0 - 4.3 only + // Check state lost if the name is set (#11217) + // Support: Windows Web Apps (WWA) + // `name` and `type` must use .setAttribute for WWA (#14901) + input.setAttribute( "type", "radio" ); + input.setAttribute( "checked", "checked" ); + input.setAttribute( "name", "t" ); + + div.appendChild( input ); + + // Support: Android <=4.1 only + // Older WebKit doesn't clone checked state correctly in fragments + support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; + + // Support: IE <=11 only + // Make sure textarea (and checkbox) defaultValue is properly cloned + div.innerHTML = ""; + support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; +} )(); +var documentElement = document.documentElement; + + + +var + rkeyEvent = /^key/, + rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/, + rtypenamespace = /^([^.]*)(?:\.(.+)|)/; + +function returnTrue() { + return true; +} + +function returnFalse() { + return false; +} + +// Support: IE <=9 only +// See #13393 for more info +function safeActiveElement() { + try { + return document.activeElement; + } catch ( err ) { } +} + +function on( elem, types, selector, data, fn, one ) { + var origFn, type; + + // Types can be a map of types/handlers + if ( typeof types === "object" ) { + + // ( types-Object, selector, data ) + if ( typeof selector !== "string" ) { + + // ( types-Object, data ) + data = data || selector; + selector = undefined; + } + for ( type in types ) { + on( elem, type, selector, data, types[ type ], one ); + } + return elem; + } + + if ( data == null && fn == null ) { + + // ( types, fn ) + fn = selector; + data = selector = undefined; + } else if ( fn == null ) { + if ( typeof selector === "string" ) { + + // ( types, selector, fn ) + fn = data; + data = undefined; + } else { + + // ( types, data, fn ) + fn = data; + data = selector; + selector = undefined; + } + } + if ( fn === false ) { + fn = returnFalse; + } else if ( !fn ) { + return elem; + } + + if ( one === 1 ) { + origFn = fn; + fn = function( event ) { + + // Can use an empty set, since event contains the info + jQuery().off( event ); + return origFn.apply( this, arguments ); + }; + + // Use same guid so caller can remove using origFn + fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); + } + return elem.each( function() { + jQuery.event.add( this, types, fn, data, selector ); + } ); +} + +/* + * Helper functions for managing events -- not part of the public interface. + * Props to Dean Edwards' addEvent library for many of the ideas. + */ +jQuery.event = { + + global: {}, + + add: function( elem, types, handler, data, selector ) { + + var handleObjIn, eventHandle, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.get( elem ); + + // Don't attach events to noData or text/comment nodes (but allow plain objects) + if ( !elemData ) { + return; + } + + // Caller can pass in an object of custom data in lieu of the handler + if ( handler.handler ) { + handleObjIn = handler; + handler = handleObjIn.handler; + selector = handleObjIn.selector; + } + + // Ensure that invalid selectors throw exceptions at attach time + // Evaluate against documentElement in case elem is a non-element node (e.g., document) + if ( selector ) { + jQuery.find.matchesSelector( documentElement, selector ); + } + + // Make sure that the handler has a unique ID, used to find/remove it later + if ( !handler.guid ) { + handler.guid = jQuery.guid++; + } + + // Init the element's event structure and main handler, if this is the first + if ( !( events = elemData.events ) ) { + events = elemData.events = {}; + } + if ( !( eventHandle = elemData.handle ) ) { + eventHandle = elemData.handle = function( e ) { + + // Discard the second event of a jQuery.event.trigger() and + // when an event is called after a page has unloaded + return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? + jQuery.event.dispatch.apply( elem, arguments ) : undefined; + }; + } + + // Handle multiple events separated by a space + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // There *must* be a type, no attaching namespace-only handlers + if ( !type ) { + continue; + } + + // If event changes its type, use the special event handlers for the changed type + special = jQuery.event.special[ type ] || {}; + + // If selector defined, determine special event api type, otherwise given type + type = ( selector ? special.delegateType : special.bindType ) || type; + + // Update special based on newly reset type + special = jQuery.event.special[ type ] || {}; + + // handleObj is passed to all event handlers + handleObj = jQuery.extend( { + type: type, + origType: origType, + data: data, + handler: handler, + guid: handler.guid, + selector: selector, + needsContext: selector && jQuery.expr.match.needsContext.test( selector ), + namespace: namespaces.join( "." ) + }, handleObjIn ); + + // Init the event handler queue if we're the first + if ( !( handlers = events[ type ] ) ) { + handlers = events[ type ] = []; + handlers.delegateCount = 0; + + // Only use addEventListener if the special events handler returns false + if ( !special.setup || + special.setup.call( elem, data, namespaces, eventHandle ) === false ) { + + if ( elem.addEventListener ) { + elem.addEventListener( type, eventHandle ); + } + } + } + + if ( special.add ) { + special.add.call( elem, handleObj ); + + if ( !handleObj.handler.guid ) { + handleObj.handler.guid = handler.guid; + } + } + + // Add to the element's handler list, delegates in front + if ( selector ) { + handlers.splice( handlers.delegateCount++, 0, handleObj ); + } else { + handlers.push( handleObj ); + } + + // Keep track of which events have ever been used, for event optimization + jQuery.event.global[ type ] = true; + } + + }, + + // Detach an event or set of events from an element + remove: function( elem, types, handler, selector, mappedTypes ) { + + var j, origCount, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); + + if ( !elemData || !( events = elemData.events ) ) { + return; + } + + // Once for each type.namespace in types; type may be omitted + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // Unbind all events (on this namespace, if provided) for the element + if ( !type ) { + for ( type in events ) { + jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); + } + continue; + } + + special = jQuery.event.special[ type ] || {}; + type = ( selector ? special.delegateType : special.bindType ) || type; + handlers = events[ type ] || []; + tmp = tmp[ 2 ] && + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); + + // Remove matching events + origCount = j = handlers.length; + while ( j-- ) { + handleObj = handlers[ j ]; + + if ( ( mappedTypes || origType === handleObj.origType ) && + ( !handler || handler.guid === handleObj.guid ) && + ( !tmp || tmp.test( handleObj.namespace ) ) && + ( !selector || selector === handleObj.selector || + selector === "**" && handleObj.selector ) ) { + handlers.splice( j, 1 ); + + if ( handleObj.selector ) { + handlers.delegateCount--; + } + if ( special.remove ) { + special.remove.call( elem, handleObj ); + } + } + } + + // Remove generic event handler if we removed something and no more handlers exist + // (avoids potential for endless recursion during removal of special event handlers) + if ( origCount && !handlers.length ) { + if ( !special.teardown || + special.teardown.call( elem, namespaces, elemData.handle ) === false ) { + + jQuery.removeEvent( elem, type, elemData.handle ); + } + + delete events[ type ]; + } + } + + // Remove data and the expando if it's no longer used + if ( jQuery.isEmptyObject( events ) ) { + dataPriv.remove( elem, "handle events" ); + } + }, + + dispatch: function( nativeEvent ) { + + // Make a writable jQuery.Event from the native event object + var event = jQuery.event.fix( nativeEvent ); + + var i, j, ret, matched, handleObj, handlerQueue, + args = new Array( arguments.length ), + handlers = ( dataPriv.get( this, "events" ) || {} )[ event.type ] || [], + special = jQuery.event.special[ event.type ] || {}; + + // Use the fix-ed jQuery.Event rather than the (read-only) native event + args[ 0 ] = event; + + for ( i = 1; i < arguments.length; i++ ) { + args[ i ] = arguments[ i ]; + } + + event.delegateTarget = this; + + // Call the preDispatch hook for the mapped type, and let it bail if desired + if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { + return; + } + + // Determine handlers + handlerQueue = jQuery.event.handlers.call( this, event, handlers ); + + // Run delegates first; they may want to stop propagation beneath us + i = 0; + while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { + event.currentTarget = matched.elem; + + j = 0; + while ( ( handleObj = matched.handlers[ j++ ] ) && + !event.isImmediatePropagationStopped() ) { + + // Triggered event must either 1) have no namespace, or 2) have namespace(s) + // a subset or equal to those in the bound event (both can have no namespace). + if ( !event.rnamespace || event.rnamespace.test( handleObj.namespace ) ) { + + event.handleObj = handleObj; + event.data = handleObj.data; + + ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || + handleObj.handler ).apply( matched.elem, args ); + + if ( ret !== undefined ) { + if ( ( event.result = ret ) === false ) { + event.preventDefault(); + event.stopPropagation(); + } + } + } + } + } + + // Call the postDispatch hook for the mapped type + if ( special.postDispatch ) { + special.postDispatch.call( this, event ); + } + + return event.result; + }, + + handlers: function( event, handlers ) { + var i, handleObj, sel, matchedHandlers, matchedSelectors, + handlerQueue = [], + delegateCount = handlers.delegateCount, + cur = event.target; + + // Find delegate handlers + if ( delegateCount && + + // Support: IE <=9 + // Black-hole SVG instance trees (trac-13180) + cur.nodeType && + + // Support: Firefox <=42 + // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) + // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click + // Support: IE 11 only + // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) + !( event.type === "click" && event.button >= 1 ) ) { + + for ( ; cur !== this; cur = cur.parentNode || this ) { + + // Don't check non-elements (#13208) + // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) + if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { + matchedHandlers = []; + matchedSelectors = {}; + for ( i = 0; i < delegateCount; i++ ) { + handleObj = handlers[ i ]; + + // Don't conflict with Object.prototype properties (#13203) + sel = handleObj.selector + " "; + + if ( matchedSelectors[ sel ] === undefined ) { + matchedSelectors[ sel ] = handleObj.needsContext ? + jQuery( sel, this ).index( cur ) > -1 : + jQuery.find( sel, this, null, [ cur ] ).length; + } + if ( matchedSelectors[ sel ] ) { + matchedHandlers.push( handleObj ); + } + } + if ( matchedHandlers.length ) { + handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); + } + } + } + } + + // Add the remaining (directly-bound) handlers + cur = this; + if ( delegateCount < handlers.length ) { + handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); + } + + return handlerQueue; + }, + + addProp: function( name, hook ) { + Object.defineProperty( jQuery.Event.prototype, name, { + enumerable: true, + configurable: true, + + get: isFunction( hook ) ? + function() { + if ( this.originalEvent ) { + return hook( this.originalEvent ); + } + } : + function() { + if ( this.originalEvent ) { + return this.originalEvent[ name ]; + } + }, + + set: function( value ) { + Object.defineProperty( this, name, { + enumerable: true, + configurable: true, + writable: true, + value: value + } ); + } + } ); + }, + + fix: function( originalEvent ) { + return originalEvent[ jQuery.expando ] ? + originalEvent : + new jQuery.Event( originalEvent ); + }, + + special: { + load: { + + // Prevent triggered image.load events from bubbling to window.load + noBubble: true + }, + focus: { + + // Fire native event if possible so blur/focus sequence is correct + trigger: function() { + if ( this !== safeActiveElement() && this.focus ) { + this.focus(); + return false; + } + }, + delegateType: "focusin" + }, + blur: { + trigger: function() { + if ( this === safeActiveElement() && this.blur ) { + this.blur(); + return false; + } + }, + delegateType: "focusout" + }, + click: { + + // For checkbox, fire native event so checked state will be right + trigger: function() { + if ( this.type === "checkbox" && this.click && nodeName( this, "input" ) ) { + this.click(); + return false; + } + }, + + // For cross-browser consistency, don't fire native .click() on links + _default: function( event ) { + return nodeName( event.target, "a" ); + } + }, + + beforeunload: { + postDispatch: function( event ) { + + // Support: Firefox 20+ + // Firefox doesn't alert if the returnValue field is not set. + if ( event.result !== undefined && event.originalEvent ) { + event.originalEvent.returnValue = event.result; + } + } + } + } +}; + +jQuery.removeEvent = function( elem, type, handle ) { + + // This "if" is needed for plain objects + if ( elem.removeEventListener ) { + elem.removeEventListener( type, handle ); + } +}; + +jQuery.Event = function( src, props ) { + + // Allow instantiation without the 'new' keyword + if ( !( this instanceof jQuery.Event ) ) { + return new jQuery.Event( src, props ); + } + + // Event object + if ( src && src.type ) { + this.originalEvent = src; + this.type = src.type; + + // Events bubbling up the document may have been marked as prevented + // by a handler lower down the tree; reflect the correct value. + this.isDefaultPrevented = src.defaultPrevented || + src.defaultPrevented === undefined && + + // Support: Android <=2.3 only + src.returnValue === false ? + returnTrue : + returnFalse; + + // Create target properties + // Support: Safari <=6 - 7 only + // Target should not be a text node (#504, #13143) + this.target = ( src.target && src.target.nodeType === 3 ) ? + src.target.parentNode : + src.target; + + this.currentTarget = src.currentTarget; + this.relatedTarget = src.relatedTarget; + + // Event type + } else { + this.type = src; + } + + // Put explicitly provided properties onto the event object + if ( props ) { + jQuery.extend( this, props ); + } + + // Create a timestamp if incoming event doesn't have one + this.timeStamp = src && src.timeStamp || Date.now(); + + // Mark it as fixed + this[ jQuery.expando ] = true; +}; + +// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding +// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html +jQuery.Event.prototype = { + constructor: jQuery.Event, + isDefaultPrevented: returnFalse, + isPropagationStopped: returnFalse, + isImmediatePropagationStopped: returnFalse, + isSimulated: false, + + preventDefault: function() { + var e = this.originalEvent; + + this.isDefaultPrevented = returnTrue; + + if ( e && !this.isSimulated ) { + e.preventDefault(); + } + }, + stopPropagation: function() { + var e = this.originalEvent; + + this.isPropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopPropagation(); + } + }, + stopImmediatePropagation: function() { + var e = this.originalEvent; + + this.isImmediatePropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopImmediatePropagation(); + } + + this.stopPropagation(); + } +}; + +// Includes all common event props including KeyEvent and MouseEvent specific props +jQuery.each( { + altKey: true, + bubbles: true, + cancelable: true, + changedTouches: true, + ctrlKey: true, + detail: true, + eventPhase: true, + metaKey: true, + pageX: true, + pageY: true, + shiftKey: true, + view: true, + "char": true, + charCode: true, + key: true, + keyCode: true, + button: true, + buttons: true, + clientX: true, + clientY: true, + offsetX: true, + offsetY: true, + pointerId: true, + pointerType: true, + screenX: true, + screenY: true, + targetTouches: true, + toElement: true, + touches: true, + + which: function( event ) { + var button = event.button; + + // Add which for key events + if ( event.which == null && rkeyEvent.test( event.type ) ) { + return event.charCode != null ? event.charCode : event.keyCode; + } + + // Add which for click: 1 === left; 2 === middle; 3 === right + if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) { + if ( button & 1 ) { + return 1; + } + + if ( button & 2 ) { + return 3; + } + + if ( button & 4 ) { + return 2; + } + + return 0; + } + + return event.which; + } +}, jQuery.event.addProp ); + +// Create mouseenter/leave events using mouseover/out and event-time checks +// so that event delegation works in jQuery. +// Do the same for pointerenter/pointerleave and pointerover/pointerout +// +// Support: Safari 7 only +// Safari sends mouseenter too often; see: +// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 +// for the description of the bug (it existed in older Chrome versions as well). +jQuery.each( { + mouseenter: "mouseover", + mouseleave: "mouseout", + pointerenter: "pointerover", + pointerleave: "pointerout" +}, function( orig, fix ) { + jQuery.event.special[ orig ] = { + delegateType: fix, + bindType: fix, + + handle: function( event ) { + var ret, + target = this, + related = event.relatedTarget, + handleObj = event.handleObj; + + // For mouseenter/leave call the handler if related is outside the target. + // NB: No relatedTarget if the mouse left/entered the browser window + if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { + event.type = handleObj.origType; + ret = handleObj.handler.apply( this, arguments ); + event.type = fix; + } + return ret; + } + }; +} ); + +jQuery.fn.extend( { + + on: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn ); + }, + one: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn, 1 ); + }, + off: function( types, selector, fn ) { + var handleObj, type; + if ( types && types.preventDefault && types.handleObj ) { + + // ( event ) dispatched jQuery.Event + handleObj = types.handleObj; + jQuery( types.delegateTarget ).off( + handleObj.namespace ? + handleObj.origType + "." + handleObj.namespace : + handleObj.origType, + handleObj.selector, + handleObj.handler + ); + return this; + } + if ( typeof types === "object" ) { + + // ( types-object [, selector] ) + for ( type in types ) { + this.off( type, selector, types[ type ] ); + } + return this; + } + if ( selector === false || typeof selector === "function" ) { + + // ( types [, fn] ) + fn = selector; + selector = undefined; + } + if ( fn === false ) { + fn = returnFalse; + } + return this.each( function() { + jQuery.event.remove( this, types, fn, selector ); + } ); + } +} ); + + +var + + /* eslint-disable max-len */ + + // See https://github.com/eslint/eslint/issues/3229 + rxhtmlTag = /<(?!area|br|col|embed|hr|img|input|link|meta|param)(([a-z][^\/\0>\x20\t\r\n\f]*)[^>]*)\/>/gi, + + /* eslint-enable */ + + // Support: IE <=10 - 11, Edge 12 - 13 only + // In IE/Edge using regex groups here causes severe slowdowns. + // See https://connect.microsoft.com/IE/feedback/details/1736512/ + rnoInnerhtml = /\s*$/g; + +// Prefer a tbody over its parent table for containing new rows +function manipulationTarget( elem, content ) { + if ( nodeName( elem, "table" ) && + nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { + + return jQuery( elem ).children( "tbody" )[ 0 ] || elem; + } + + return elem; +} + +// Replace/restore the type attribute of script elements for safe DOM manipulation +function disableScript( elem ) { + elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; + return elem; +} +function restoreScript( elem ) { + if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { + elem.type = elem.type.slice( 5 ); + } else { + elem.removeAttribute( "type" ); + } + + return elem; +} + +function cloneCopyEvent( src, dest ) { + var i, l, type, pdataOld, pdataCur, udataOld, udataCur, events; + + if ( dest.nodeType !== 1 ) { + return; + } + + // 1. Copy private data: events, handlers, etc. + if ( dataPriv.hasData( src ) ) { + pdataOld = dataPriv.access( src ); + pdataCur = dataPriv.set( dest, pdataOld ); + events = pdataOld.events; + + if ( events ) { + delete pdataCur.handle; + pdataCur.events = {}; + + for ( type in events ) { + for ( i = 0, l = events[ type ].length; i < l; i++ ) { + jQuery.event.add( dest, type, events[ type ][ i ] ); + } + } + } + } + + // 2. Copy user data + if ( dataUser.hasData( src ) ) { + udataOld = dataUser.access( src ); + udataCur = jQuery.extend( {}, udataOld ); + + dataUser.set( dest, udataCur ); + } +} + +// Fix IE bugs, see support tests +function fixInput( src, dest ) { + var nodeName = dest.nodeName.toLowerCase(); + + // Fails to persist the checked state of a cloned checkbox or radio button. + if ( nodeName === "input" && rcheckableType.test( src.type ) ) { + dest.checked = src.checked; + + // Fails to return the selected option to the default selected state when cloning options + } else if ( nodeName === "input" || nodeName === "textarea" ) { + dest.defaultValue = src.defaultValue; + } +} + +function domManip( collection, args, callback, ignored ) { + + // Flatten any nested arrays + args = concat.apply( [], args ); + + var fragment, first, scripts, hasScripts, node, doc, + i = 0, + l = collection.length, + iNoClone = l - 1, + value = args[ 0 ], + valueIsFunction = isFunction( value ); + + // We can't cloneNode fragments that contain checked, in WebKit + if ( valueIsFunction || + ( l > 1 && typeof value === "string" && + !support.checkClone && rchecked.test( value ) ) ) { + return collection.each( function( index ) { + var self = collection.eq( index ); + if ( valueIsFunction ) { + args[ 0 ] = value.call( this, index, self.html() ); + } + domManip( self, args, callback, ignored ); + } ); + } + + if ( l ) { + fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); + first = fragment.firstChild; + + if ( fragment.childNodes.length === 1 ) { + fragment = first; + } + + // Require either new content or an interest in ignored elements to invoke the callback + if ( first || ignored ) { + scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); + hasScripts = scripts.length; + + // Use the original fragment for the last item + // instead of the first because it can end up + // being emptied incorrectly in certain situations (#8070). + for ( ; i < l; i++ ) { + node = fragment; + + if ( i !== iNoClone ) { + node = jQuery.clone( node, true, true ); + + // Keep references to cloned scripts for later restoration + if ( hasScripts ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( scripts, getAll( node, "script" ) ); + } + } + + callback.call( collection[ i ], node, i ); + } + + if ( hasScripts ) { + doc = scripts[ scripts.length - 1 ].ownerDocument; + + // Reenable scripts + jQuery.map( scripts, restoreScript ); + + // Evaluate executable scripts on first document insertion + for ( i = 0; i < hasScripts; i++ ) { + node = scripts[ i ]; + if ( rscriptType.test( node.type || "" ) && + !dataPriv.access( node, "globalEval" ) && + jQuery.contains( doc, node ) ) { + + if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { + + // Optional AJAX dependency, but won't run scripts if not present + if ( jQuery._evalUrl ) { + jQuery._evalUrl( node.src ); + } + } else { + DOMEval( node.textContent.replace( rcleanScript, "" ), doc, node ); + } + } + } + } + } + } + + return collection; +} + +function remove( elem, selector, keepData ) { + var node, + nodes = selector ? jQuery.filter( selector, elem ) : elem, + i = 0; + + for ( ; ( node = nodes[ i ] ) != null; i++ ) { + if ( !keepData && node.nodeType === 1 ) { + jQuery.cleanData( getAll( node ) ); + } + + if ( node.parentNode ) { + if ( keepData && jQuery.contains( node.ownerDocument, node ) ) { + setGlobalEval( getAll( node, "script" ) ); + } + node.parentNode.removeChild( node ); + } + } + + return elem; +} + +jQuery.extend( { + htmlPrefilter: function( html ) { + return html.replace( rxhtmlTag, "<$1>" ); + }, + + clone: function( elem, dataAndEvents, deepDataAndEvents ) { + var i, l, srcElements, destElements, + clone = elem.cloneNode( true ), + inPage = jQuery.contains( elem.ownerDocument, elem ); + + // Fix IE cloning issues + if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && + !jQuery.isXMLDoc( elem ) ) { + + // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 + destElements = getAll( clone ); + srcElements = getAll( elem ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + fixInput( srcElements[ i ], destElements[ i ] ); + } + } + + // Copy the events from the original to the clone + if ( dataAndEvents ) { + if ( deepDataAndEvents ) { + srcElements = srcElements || getAll( elem ); + destElements = destElements || getAll( clone ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + cloneCopyEvent( srcElements[ i ], destElements[ i ] ); + } + } else { + cloneCopyEvent( elem, clone ); + } + } + + // Preserve script evaluation history + destElements = getAll( clone, "script" ); + if ( destElements.length > 0 ) { + setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); + } + + // Return the cloned set + return clone; + }, + + cleanData: function( elems ) { + var data, elem, type, + special = jQuery.event.special, + i = 0; + + for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { + if ( acceptData( elem ) ) { + if ( ( data = elem[ dataPriv.expando ] ) ) { + if ( data.events ) { + for ( type in data.events ) { + if ( special[ type ] ) { + jQuery.event.remove( elem, type ); + + // This is a shortcut to avoid jQuery.event.remove's overhead + } else { + jQuery.removeEvent( elem, type, data.handle ); + } + } + } + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataPriv.expando ] = undefined; + } + if ( elem[ dataUser.expando ] ) { + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataUser.expando ] = undefined; + } + } + } + } +} ); + +jQuery.fn.extend( { + detach: function( selector ) { + return remove( this, selector, true ); + }, + + remove: function( selector ) { + return remove( this, selector ); + }, + + text: function( value ) { + return access( this, function( value ) { + return value === undefined ? + jQuery.text( this ) : + this.empty().each( function() { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + this.textContent = value; + } + } ); + }, null, value, arguments.length ); + }, + + append: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.appendChild( elem ); + } + } ); + }, + + prepend: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.insertBefore( elem, target.firstChild ); + } + } ); + }, + + before: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this ); + } + } ); + }, + + after: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this.nextSibling ); + } + } ); + }, + + empty: function() { + var elem, + i = 0; + + for ( ; ( elem = this[ i ] ) != null; i++ ) { + if ( elem.nodeType === 1 ) { + + // Prevent memory leaks + jQuery.cleanData( getAll( elem, false ) ); + + // Remove any remaining nodes + elem.textContent = ""; + } + } + + return this; + }, + + clone: function( dataAndEvents, deepDataAndEvents ) { + dataAndEvents = dataAndEvents == null ? false : dataAndEvents; + deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; + + return this.map( function() { + return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); + } ); + }, + + html: function( value ) { + return access( this, function( value ) { + var elem = this[ 0 ] || {}, + i = 0, + l = this.length; + + if ( value === undefined && elem.nodeType === 1 ) { + return elem.innerHTML; + } + + // See if we can take a shortcut and just use innerHTML + if ( typeof value === "string" && !rnoInnerhtml.test( value ) && + !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { + + value = jQuery.htmlPrefilter( value ); + + try { + for ( ; i < l; i++ ) { + elem = this[ i ] || {}; + + // Remove element nodes and prevent memory leaks + if ( elem.nodeType === 1 ) { + jQuery.cleanData( getAll( elem, false ) ); + elem.innerHTML = value; + } + } + + elem = 0; + + // If using innerHTML throws an exception, use the fallback method + } catch ( e ) {} + } + + if ( elem ) { + this.empty().append( value ); + } + }, null, value, arguments.length ); + }, + + replaceWith: function() { + var ignored = []; + + // Make the changes, replacing each non-ignored context element with the new content + return domManip( this, arguments, function( elem ) { + var parent = this.parentNode; + + if ( jQuery.inArray( this, ignored ) < 0 ) { + jQuery.cleanData( getAll( this ) ); + if ( parent ) { + parent.replaceChild( elem, this ); + } + } + + // Force callback invocation + }, ignored ); + } +} ); + +jQuery.each( { + appendTo: "append", + prependTo: "prepend", + insertBefore: "before", + insertAfter: "after", + replaceAll: "replaceWith" +}, function( name, original ) { + jQuery.fn[ name ] = function( selector ) { + var elems, + ret = [], + insert = jQuery( selector ), + last = insert.length - 1, + i = 0; + + for ( ; i <= last; i++ ) { + elems = i === last ? this : this.clone( true ); + jQuery( insert[ i ] )[ original ]( elems ); + + // Support: Android <=4.0 only, PhantomJS 1 only + // .get() because push.apply(_, arraylike) throws on ancient WebKit + push.apply( ret, elems.get() ); + } + + return this.pushStack( ret ); + }; +} ); +var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); + +var getStyles = function( elem ) { + + // Support: IE <=11 only, Firefox <=30 (#15098, #14150) + // IE throws on elements created in popups + // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" + var view = elem.ownerDocument.defaultView; + + if ( !view || !view.opener ) { + view = window; + } + + return view.getComputedStyle( elem ); + }; + +var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); + + + +( function() { + + // Executing both pixelPosition & boxSizingReliable tests require only one layout + // so they're executed at the same time to save the second computation. + function computeStyleTests() { + + // This is a singleton, we need to execute it only once + if ( !div ) { + return; + } + + container.style.cssText = "position:absolute;left:-11111px;width:60px;" + + "margin-top:1px;padding:0;border:0"; + div.style.cssText = + "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + + "margin:auto;border:1px;padding:1px;" + + "width:60%;top:1%"; + documentElement.appendChild( container ).appendChild( div ); + + var divStyle = window.getComputedStyle( div ); + pixelPositionVal = divStyle.top !== "1%"; + + // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 + reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; + + // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 + // Some styles come back with percentage values, even though they shouldn't + div.style.right = "60%"; + pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; + + // Support: IE 9 - 11 only + // Detect misreporting of content dimensions for box-sizing:border-box elements + boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; + + // Support: IE 9 only + // Detect overflow:scroll screwiness (gh-3699) + div.style.position = "absolute"; + scrollboxSizeVal = div.offsetWidth === 36 || "absolute"; + + documentElement.removeChild( container ); + + // Nullify the div so it wouldn't be stored in the memory and + // it will also be a sign that checks already performed + div = null; + } + + function roundPixelMeasures( measure ) { + return Math.round( parseFloat( measure ) ); + } + + var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, + reliableMarginLeftVal, + container = document.createElement( "div" ), + div = document.createElement( "div" ); + + // Finish early in limited (non-browser) environments + if ( !div.style ) { + return; + } + + // Support: IE <=9 - 11 only + // Style of cloned element affects source element cloned (#8908) + div.style.backgroundClip = "content-box"; + div.cloneNode( true ).style.backgroundClip = ""; + support.clearCloneStyle = div.style.backgroundClip === "content-box"; + + jQuery.extend( support, { + boxSizingReliable: function() { + computeStyleTests(); + return boxSizingReliableVal; + }, + pixelBoxStyles: function() { + computeStyleTests(); + return pixelBoxStylesVal; + }, + pixelPosition: function() { + computeStyleTests(); + return pixelPositionVal; + }, + reliableMarginLeft: function() { + computeStyleTests(); + return reliableMarginLeftVal; + }, + scrollboxSize: function() { + computeStyleTests(); + return scrollboxSizeVal; + } + } ); +} )(); + + +function curCSS( elem, name, computed ) { + var width, minWidth, maxWidth, ret, + + // Support: Firefox 51+ + // Retrieving style before computed somehow + // fixes an issue with getting wrong values + // on detached elements + style = elem.style; + + computed = computed || getStyles( elem ); + + // getPropertyValue is needed for: + // .css('filter') (IE 9 only, #12537) + // .css('--customProperty) (#3144) + if ( computed ) { + ret = computed.getPropertyValue( name ) || computed[ name ]; + + if ( ret === "" && !jQuery.contains( elem.ownerDocument, elem ) ) { + ret = jQuery.style( elem, name ); + } + + // A tribute to the "awesome hack by Dean Edwards" + // Android Browser returns percentage for some values, + // but width seems to be reliably pixels. + // This is against the CSSOM draft spec: + // https://drafts.csswg.org/cssom/#resolved-values + if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { + + // Remember the original values + width = style.width; + minWidth = style.minWidth; + maxWidth = style.maxWidth; + + // Put in the new values to get a computed value out + style.minWidth = style.maxWidth = style.width = ret; + ret = computed.width; + + // Revert the changed values + style.width = width; + style.minWidth = minWidth; + style.maxWidth = maxWidth; + } + } + + return ret !== undefined ? + + // Support: IE <=9 - 11 only + // IE returns zIndex value as an integer. + ret + "" : + ret; +} + + +function addGetHookIf( conditionFn, hookFn ) { + + // Define the hook, we'll check on the first run if it's really needed. + return { + get: function() { + if ( conditionFn() ) { + + // Hook not needed (or it's not possible to use it due + // to missing dependency), remove it. + delete this.get; + return; + } + + // Hook needed; redefine it so that the support test is not executed again. + return ( this.get = hookFn ).apply( this, arguments ); + } + }; +} + + +var + + // Swappable if display is none or starts with table + // except "table", "table-cell", or "table-caption" + // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display + rdisplayswap = /^(none|table(?!-c[ea]).+)/, + rcustomProp = /^--/, + cssShow = { position: "absolute", visibility: "hidden", display: "block" }, + cssNormalTransform = { + letterSpacing: "0", + fontWeight: "400" + }, + + cssPrefixes = [ "Webkit", "Moz", "ms" ], + emptyStyle = document.createElement( "div" ).style; + +// Return a css property mapped to a potentially vendor prefixed property +function vendorPropName( name ) { + + // Shortcut for names that are not vendor prefixed + if ( name in emptyStyle ) { + return name; + } + + // Check for vendor prefixed names + var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), + i = cssPrefixes.length; + + while ( i-- ) { + name = cssPrefixes[ i ] + capName; + if ( name in emptyStyle ) { + return name; + } + } +} + +// Return a property mapped along what jQuery.cssProps suggests or to +// a vendor prefixed property. +function finalPropName( name ) { + var ret = jQuery.cssProps[ name ]; + if ( !ret ) { + ret = jQuery.cssProps[ name ] = vendorPropName( name ) || name; + } + return ret; +} + +function setPositiveNumber( elem, value, subtract ) { + + // Any relative (+/-) values have already been + // normalized at this point + var matches = rcssNum.exec( value ); + return matches ? + + // Guard against undefined "subtract", e.g., when used as in cssHooks + Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : + value; +} + +function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { + var i = dimension === "width" ? 1 : 0, + extra = 0, + delta = 0; + + // Adjustment may not be necessary + if ( box === ( isBorderBox ? "border" : "content" ) ) { + return 0; + } + + for ( ; i < 4; i += 2 ) { + + // Both box models exclude margin + if ( box === "margin" ) { + delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); + } + + // If we get here with a content-box, we're seeking "padding" or "border" or "margin" + if ( !isBorderBox ) { + + // Add padding + delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + + // For "border" or "margin", add border + if ( box !== "padding" ) { + delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + + // But still keep track of it otherwise + } else { + extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + + // If we get here with a border-box (content + padding + border), we're seeking "content" or + // "padding" or "margin" + } else { + + // For "content", subtract padding + if ( box === "content" ) { + delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + } + + // For "content" or "padding", subtract border + if ( box !== "margin" ) { + delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + } + } + + // Account for positive content-box scroll gutter when requested by providing computedVal + if ( !isBorderBox && computedVal >= 0 ) { + + // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border + // Assuming integer scroll gutter, subtract the rest and round down + delta += Math.max( 0, Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + computedVal - + delta - + extra - + 0.5 + ) ); + } + + return delta; +} + +function getWidthOrHeight( elem, dimension, extra ) { + + // Start with computed style + var styles = getStyles( elem ), + val = curCSS( elem, dimension, styles ), + isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + valueIsBorderBox = isBorderBox; + + // Support: Firefox <=54 + // Return a confounding non-pixel value or feign ignorance, as appropriate. + if ( rnumnonpx.test( val ) ) { + if ( !extra ) { + return val; + } + val = "auto"; + } + + // Check for style in case a browser which returns unreliable values + // for getComputedStyle silently falls back to the reliable elem.style + valueIsBorderBox = valueIsBorderBox && + ( support.boxSizingReliable() || val === elem.style[ dimension ] ); + + // Fall back to offsetWidth/offsetHeight when value is "auto" + // This happens for inline elements with no explicit setting (gh-3571) + // Support: Android <=4.1 - 4.3 only + // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) + if ( val === "auto" || + !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) { + + val = elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ]; + + // offsetWidth/offsetHeight provide border-box values + valueIsBorderBox = true; + } + + // Normalize "" and auto + val = parseFloat( val ) || 0; + + // Adjust for the element's box model + return ( val + + boxModelAdjustment( + elem, + dimension, + extra || ( isBorderBox ? "border" : "content" ), + valueIsBorderBox, + styles, + + // Provide the current computed size to request scroll gutter calculation (gh-3589) + val + ) + ) + "px"; +} + +jQuery.extend( { + + // Add in style property hooks for overriding the default + // behavior of getting and setting a style property + cssHooks: { + opacity: { + get: function( elem, computed ) { + if ( computed ) { + + // We should always get a number back from opacity + var ret = curCSS( elem, "opacity" ); + return ret === "" ? "1" : ret; + } + } + } + }, + + // Don't automatically add "px" to these possibly-unitless properties + cssNumber: { + "animationIterationCount": true, + "columnCount": true, + "fillOpacity": true, + "flexGrow": true, + "flexShrink": true, + "fontWeight": true, + "lineHeight": true, + "opacity": true, + "order": true, + "orphans": true, + "widows": true, + "zIndex": true, + "zoom": true + }, + + // Add in properties whose names you wish to fix before + // setting or getting the value + cssProps: {}, + + // Get and set the style property on a DOM Node + style: function( elem, name, value, extra ) { + + // Don't set styles on text and comment nodes + if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { + return; + } + + // Make sure that we're working with the right name + var ret, type, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ), + style = elem.style; + + // Make sure that we're working with the right name. We don't + // want to query the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Gets hook for the prefixed version, then unprefixed version + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // Check if we're setting a value + if ( value !== undefined ) { + type = typeof value; + + // Convert "+=" or "-=" to relative numbers (#7345) + if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { + value = adjustCSS( elem, name, ret ); + + // Fixes bug #9237 + type = "number"; + } + + // Make sure that null and NaN values aren't set (#7116) + if ( value == null || value !== value ) { + return; + } + + // If a number was passed in, add the unit (except for certain CSS properties) + if ( type === "number" ) { + value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); + } + + // background-* props affect original clone's values + if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { + style[ name ] = "inherit"; + } + + // If a hook was provided, use that value, otherwise just set the specified value + if ( !hooks || !( "set" in hooks ) || + ( value = hooks.set( elem, value, extra ) ) !== undefined ) { + + if ( isCustomProp ) { + style.setProperty( name, value ); + } else { + style[ name ] = value; + } + } + + } else { + + // If a hook was provided get the non-computed value from there + if ( hooks && "get" in hooks && + ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { + + return ret; + } + + // Otherwise just get the value from the style object + return style[ name ]; + } + }, + + css: function( elem, name, extra, styles ) { + var val, num, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ); + + // Make sure that we're working with the right name. We don't + // want to modify the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Try prefixed name followed by the unprefixed name + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // If a hook was provided get the computed value from there + if ( hooks && "get" in hooks ) { + val = hooks.get( elem, true, extra ); + } + + // Otherwise, if a way to get the computed value exists, use that + if ( val === undefined ) { + val = curCSS( elem, name, styles ); + } + + // Convert "normal" to computed value + if ( val === "normal" && name in cssNormalTransform ) { + val = cssNormalTransform[ name ]; + } + + // Make numeric if forced or a qualifier was provided and val looks numeric + if ( extra === "" || extra ) { + num = parseFloat( val ); + return extra === true || isFinite( num ) ? num || 0 : val; + } + + return val; + } +} ); + +jQuery.each( [ "height", "width" ], function( i, dimension ) { + jQuery.cssHooks[ dimension ] = { + get: function( elem, computed, extra ) { + if ( computed ) { + + // Certain elements can have dimension info if we invisibly show them + // but it must have a current display style that would benefit + return rdisplayswap.test( jQuery.css( elem, "display" ) ) && + + // Support: Safari 8+ + // Table columns in Safari have non-zero offsetWidth & zero + // getBoundingClientRect().width unless display is changed. + // Support: IE <=11 only + // Running getBoundingClientRect on a disconnected node + // in IE throws an error. + ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? + swap( elem, cssShow, function() { + return getWidthOrHeight( elem, dimension, extra ); + } ) : + getWidthOrHeight( elem, dimension, extra ); + } + }, + + set: function( elem, value, extra ) { + var matches, + styles = getStyles( elem ), + isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + subtract = extra && boxModelAdjustment( + elem, + dimension, + extra, + isBorderBox, + styles + ); + + // Account for unreliable border-box dimensions by comparing offset* to computed and + // faking a content-box to get border and padding (gh-3699) + if ( isBorderBox && support.scrollboxSize() === styles.position ) { + subtract -= Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + parseFloat( styles[ dimension ] ) - + boxModelAdjustment( elem, dimension, "border", false, styles ) - + 0.5 + ); + } + + // Convert to pixels if value adjustment is needed + if ( subtract && ( matches = rcssNum.exec( value ) ) && + ( matches[ 3 ] || "px" ) !== "px" ) { + + elem.style[ dimension ] = value; + value = jQuery.css( elem, dimension ); + } + + return setPositiveNumber( elem, value, subtract ); + } + }; +} ); + +jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, + function( elem, computed ) { + if ( computed ) { + return ( parseFloat( curCSS( elem, "marginLeft" ) ) || + elem.getBoundingClientRect().left - + swap( elem, { marginLeft: 0 }, function() { + return elem.getBoundingClientRect().left; + } ) + ) + "px"; + } + } +); + +// These hooks are used by animate to expand properties +jQuery.each( { + margin: "", + padding: "", + border: "Width" +}, function( prefix, suffix ) { + jQuery.cssHooks[ prefix + suffix ] = { + expand: function( value ) { + var i = 0, + expanded = {}, + + // Assumes a single number if not a string + parts = typeof value === "string" ? value.split( " " ) : [ value ]; + + for ( ; i < 4; i++ ) { + expanded[ prefix + cssExpand[ i ] + suffix ] = + parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; + } + + return expanded; + } + }; + + if ( prefix !== "margin" ) { + jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; + } +} ); + +jQuery.fn.extend( { + css: function( name, value ) { + return access( this, function( elem, name, value ) { + var styles, len, + map = {}, + i = 0; + + if ( Array.isArray( name ) ) { + styles = getStyles( elem ); + len = name.length; + + for ( ; i < len; i++ ) { + map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); + } + + return map; + } + + return value !== undefined ? + jQuery.style( elem, name, value ) : + jQuery.css( elem, name ); + }, name, value, arguments.length > 1 ); + } +} ); + + +function Tween( elem, options, prop, end, easing ) { + return new Tween.prototype.init( elem, options, prop, end, easing ); +} +jQuery.Tween = Tween; + +Tween.prototype = { + constructor: Tween, + init: function( elem, options, prop, end, easing, unit ) { + this.elem = elem; + this.prop = prop; + this.easing = easing || jQuery.easing._default; + this.options = options; + this.start = this.now = this.cur(); + this.end = end; + this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); + }, + cur: function() { + var hooks = Tween.propHooks[ this.prop ]; + + return hooks && hooks.get ? + hooks.get( this ) : + Tween.propHooks._default.get( this ); + }, + run: function( percent ) { + var eased, + hooks = Tween.propHooks[ this.prop ]; + + if ( this.options.duration ) { + this.pos = eased = jQuery.easing[ this.easing ]( + percent, this.options.duration * percent, 0, 1, this.options.duration + ); + } else { + this.pos = eased = percent; + } + this.now = ( this.end - this.start ) * eased + this.start; + + if ( this.options.step ) { + this.options.step.call( this.elem, this.now, this ); + } + + if ( hooks && hooks.set ) { + hooks.set( this ); + } else { + Tween.propHooks._default.set( this ); + } + return this; + } +}; + +Tween.prototype.init.prototype = Tween.prototype; + +Tween.propHooks = { + _default: { + get: function( tween ) { + var result; + + // Use a property on the element directly when it is not a DOM element, + // or when there is no matching style property that exists. + if ( tween.elem.nodeType !== 1 || + tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { + return tween.elem[ tween.prop ]; + } + + // Passing an empty string as a 3rd parameter to .css will automatically + // attempt a parseFloat and fallback to a string if the parse fails. + // Simple values such as "10px" are parsed to Float; + // complex values such as "rotate(1rad)" are returned as-is. + result = jQuery.css( tween.elem, tween.prop, "" ); + + // Empty strings, null, undefined and "auto" are converted to 0. + return !result || result === "auto" ? 0 : result; + }, + set: function( tween ) { + + // Use step hook for back compat. + // Use cssHook if its there. + // Use .style if available and use plain properties where available. + if ( jQuery.fx.step[ tween.prop ] ) { + jQuery.fx.step[ tween.prop ]( tween ); + } else if ( tween.elem.nodeType === 1 && + ( tween.elem.style[ jQuery.cssProps[ tween.prop ] ] != null || + jQuery.cssHooks[ tween.prop ] ) ) { + jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); + } else { + tween.elem[ tween.prop ] = tween.now; + } + } + } +}; + +// Support: IE <=9 only +// Panic based approach to setting things on disconnected nodes +Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { + set: function( tween ) { + if ( tween.elem.nodeType && tween.elem.parentNode ) { + tween.elem[ tween.prop ] = tween.now; + } + } +}; + +jQuery.easing = { + linear: function( p ) { + return p; + }, + swing: function( p ) { + return 0.5 - Math.cos( p * Math.PI ) / 2; + }, + _default: "swing" +}; + +jQuery.fx = Tween.prototype.init; + +// Back compat <1.8 extension point +jQuery.fx.step = {}; + + + + +var + fxNow, inProgress, + rfxtypes = /^(?:toggle|show|hide)$/, + rrun = /queueHooks$/; + +function schedule() { + if ( inProgress ) { + if ( document.hidden === false && window.requestAnimationFrame ) { + window.requestAnimationFrame( schedule ); + } else { + window.setTimeout( schedule, jQuery.fx.interval ); + } + + jQuery.fx.tick(); + } +} + +// Animations created synchronously will run synchronously +function createFxNow() { + window.setTimeout( function() { + fxNow = undefined; + } ); + return ( fxNow = Date.now() ); +} + +// Generate parameters to create a standard animation +function genFx( type, includeWidth ) { + var which, + i = 0, + attrs = { height: type }; + + // If we include width, step value is 1 to do all cssExpand values, + // otherwise step value is 2 to skip over Left and Right + includeWidth = includeWidth ? 1 : 0; + for ( ; i < 4; i += 2 - includeWidth ) { + which = cssExpand[ i ]; + attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; + } + + if ( includeWidth ) { + attrs.opacity = attrs.width = type; + } + + return attrs; +} + +function createTween( value, prop, animation ) { + var tween, + collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), + index = 0, + length = collection.length; + for ( ; index < length; index++ ) { + if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { + + // We're done with this property + return tween; + } + } +} + +function defaultPrefilter( elem, props, opts ) { + var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, + isBox = "width" in props || "height" in props, + anim = this, + orig = {}, + style = elem.style, + hidden = elem.nodeType && isHiddenWithinTree( elem ), + dataShow = dataPriv.get( elem, "fxshow" ); + + // Queue-skipping animations hijack the fx hooks + if ( !opts.queue ) { + hooks = jQuery._queueHooks( elem, "fx" ); + if ( hooks.unqueued == null ) { + hooks.unqueued = 0; + oldfire = hooks.empty.fire; + hooks.empty.fire = function() { + if ( !hooks.unqueued ) { + oldfire(); + } + }; + } + hooks.unqueued++; + + anim.always( function() { + + // Ensure the complete handler is called before this completes + anim.always( function() { + hooks.unqueued--; + if ( !jQuery.queue( elem, "fx" ).length ) { + hooks.empty.fire(); + } + } ); + } ); + } + + // Detect show/hide animations + for ( prop in props ) { + value = props[ prop ]; + if ( rfxtypes.test( value ) ) { + delete props[ prop ]; + toggle = toggle || value === "toggle"; + if ( value === ( hidden ? "hide" : "show" ) ) { + + // Pretend to be hidden if this is a "show" and + // there is still data from a stopped show/hide + if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { + hidden = true; + + // Ignore all other no-op show/hide data + } else { + continue; + } + } + orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); + } + } + + // Bail out if this is a no-op like .hide().hide() + propTween = !jQuery.isEmptyObject( props ); + if ( !propTween && jQuery.isEmptyObject( orig ) ) { + return; + } + + // Restrict "overflow" and "display" styles during box animations + if ( isBox && elem.nodeType === 1 ) { + + // Support: IE <=9 - 11, Edge 12 - 15 + // Record all 3 overflow attributes because IE does not infer the shorthand + // from identically-valued overflowX and overflowY and Edge just mirrors + // the overflowX value there. + opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; + + // Identify a display type, preferring old show/hide data over the CSS cascade + restoreDisplay = dataShow && dataShow.display; + if ( restoreDisplay == null ) { + restoreDisplay = dataPriv.get( elem, "display" ); + } + display = jQuery.css( elem, "display" ); + if ( display === "none" ) { + if ( restoreDisplay ) { + display = restoreDisplay; + } else { + + // Get nonempty value(s) by temporarily forcing visibility + showHide( [ elem ], true ); + restoreDisplay = elem.style.display || restoreDisplay; + display = jQuery.css( elem, "display" ); + showHide( [ elem ] ); + } + } + + // Animate inline elements as inline-block + if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { + if ( jQuery.css( elem, "float" ) === "none" ) { + + // Restore the original display value at the end of pure show/hide animations + if ( !propTween ) { + anim.done( function() { + style.display = restoreDisplay; + } ); + if ( restoreDisplay == null ) { + display = style.display; + restoreDisplay = display === "none" ? "" : display; + } + } + style.display = "inline-block"; + } + } + } + + if ( opts.overflow ) { + style.overflow = "hidden"; + anim.always( function() { + style.overflow = opts.overflow[ 0 ]; + style.overflowX = opts.overflow[ 1 ]; + style.overflowY = opts.overflow[ 2 ]; + } ); + } + + // Implement show/hide animations + propTween = false; + for ( prop in orig ) { + + // General show/hide setup for this element animation + if ( !propTween ) { + if ( dataShow ) { + if ( "hidden" in dataShow ) { + hidden = dataShow.hidden; + } + } else { + dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); + } + + // Store hidden/visible for toggle so `.stop().toggle()` "reverses" + if ( toggle ) { + dataShow.hidden = !hidden; + } + + // Show elements before animating them + if ( hidden ) { + showHide( [ elem ], true ); + } + + /* eslint-disable no-loop-func */ + + anim.done( function() { + + /* eslint-enable no-loop-func */ + + // The final step of a "hide" animation is actually hiding the element + if ( !hidden ) { + showHide( [ elem ] ); + } + dataPriv.remove( elem, "fxshow" ); + for ( prop in orig ) { + jQuery.style( elem, prop, orig[ prop ] ); + } + } ); + } + + // Per-property setup + propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); + if ( !( prop in dataShow ) ) { + dataShow[ prop ] = propTween.start; + if ( hidden ) { + propTween.end = propTween.start; + propTween.start = 0; + } + } + } +} + +function propFilter( props, specialEasing ) { + var index, name, easing, value, hooks; + + // camelCase, specialEasing and expand cssHook pass + for ( index in props ) { + name = camelCase( index ); + easing = specialEasing[ name ]; + value = props[ index ]; + if ( Array.isArray( value ) ) { + easing = value[ 1 ]; + value = props[ index ] = value[ 0 ]; + } + + if ( index !== name ) { + props[ name ] = value; + delete props[ index ]; + } + + hooks = jQuery.cssHooks[ name ]; + if ( hooks && "expand" in hooks ) { + value = hooks.expand( value ); + delete props[ name ]; + + // Not quite $.extend, this won't overwrite existing keys. + // Reusing 'index' because we have the correct "name" + for ( index in value ) { + if ( !( index in props ) ) { + props[ index ] = value[ index ]; + specialEasing[ index ] = easing; + } + } + } else { + specialEasing[ name ] = easing; + } + } +} + +function Animation( elem, properties, options ) { + var result, + stopped, + index = 0, + length = Animation.prefilters.length, + deferred = jQuery.Deferred().always( function() { + + // Don't match elem in the :animated selector + delete tick.elem; + } ), + tick = function() { + if ( stopped ) { + return false; + } + var currentTime = fxNow || createFxNow(), + remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), + + // Support: Android 2.3 only + // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) + temp = remaining / animation.duration || 0, + percent = 1 - temp, + index = 0, + length = animation.tweens.length; + + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( percent ); + } + + deferred.notifyWith( elem, [ animation, percent, remaining ] ); + + // If there's more to do, yield + if ( percent < 1 && length ) { + return remaining; + } + + // If this was an empty animation, synthesize a final progress notification + if ( !length ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + } + + // Resolve the animation and report its conclusion + deferred.resolveWith( elem, [ animation ] ); + return false; + }, + animation = deferred.promise( { + elem: elem, + props: jQuery.extend( {}, properties ), + opts: jQuery.extend( true, { + specialEasing: {}, + easing: jQuery.easing._default + }, options ), + originalProperties: properties, + originalOptions: options, + startTime: fxNow || createFxNow(), + duration: options.duration, + tweens: [], + createTween: function( prop, end ) { + var tween = jQuery.Tween( elem, animation.opts, prop, end, + animation.opts.specialEasing[ prop ] || animation.opts.easing ); + animation.tweens.push( tween ); + return tween; + }, + stop: function( gotoEnd ) { + var index = 0, + + // If we are going to the end, we want to run all the tweens + // otherwise we skip this part + length = gotoEnd ? animation.tweens.length : 0; + if ( stopped ) { + return this; + } + stopped = true; + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( 1 ); + } + + // Resolve when we played the last frame; otherwise, reject + if ( gotoEnd ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + deferred.resolveWith( elem, [ animation, gotoEnd ] ); + } else { + deferred.rejectWith( elem, [ animation, gotoEnd ] ); + } + return this; + } + } ), + props = animation.props; + + propFilter( props, animation.opts.specialEasing ); + + for ( ; index < length; index++ ) { + result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); + if ( result ) { + if ( isFunction( result.stop ) ) { + jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = + result.stop.bind( result ); + } + return result; + } + } + + jQuery.map( props, createTween, animation ); + + if ( isFunction( animation.opts.start ) ) { + animation.opts.start.call( elem, animation ); + } + + // Attach callbacks from options + animation + .progress( animation.opts.progress ) + .done( animation.opts.done, animation.opts.complete ) + .fail( animation.opts.fail ) + .always( animation.opts.always ); + + jQuery.fx.timer( + jQuery.extend( tick, { + elem: elem, + anim: animation, + queue: animation.opts.queue + } ) + ); + + return animation; +} + +jQuery.Animation = jQuery.extend( Animation, { + + tweeners: { + "*": [ function( prop, value ) { + var tween = this.createTween( prop, value ); + adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); + return tween; + } ] + }, + + tweener: function( props, callback ) { + if ( isFunction( props ) ) { + callback = props; + props = [ "*" ]; + } else { + props = props.match( rnothtmlwhite ); + } + + var prop, + index = 0, + length = props.length; + + for ( ; index < length; index++ ) { + prop = props[ index ]; + Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; + Animation.tweeners[ prop ].unshift( callback ); + } + }, + + prefilters: [ defaultPrefilter ], + + prefilter: function( callback, prepend ) { + if ( prepend ) { + Animation.prefilters.unshift( callback ); + } else { + Animation.prefilters.push( callback ); + } + } +} ); + +jQuery.speed = function( speed, easing, fn ) { + var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { + complete: fn || !fn && easing || + isFunction( speed ) && speed, + duration: speed, + easing: fn && easing || easing && !isFunction( easing ) && easing + }; + + // Go to the end state if fx are off + if ( jQuery.fx.off ) { + opt.duration = 0; + + } else { + if ( typeof opt.duration !== "number" ) { + if ( opt.duration in jQuery.fx.speeds ) { + opt.duration = jQuery.fx.speeds[ opt.duration ]; + + } else { + opt.duration = jQuery.fx.speeds._default; + } + } + } + + // Normalize opt.queue - true/undefined/null -> "fx" + if ( opt.queue == null || opt.queue === true ) { + opt.queue = "fx"; + } + + // Queueing + opt.old = opt.complete; + + opt.complete = function() { + if ( isFunction( opt.old ) ) { + opt.old.call( this ); + } + + if ( opt.queue ) { + jQuery.dequeue( this, opt.queue ); + } + }; + + return opt; +}; + +jQuery.fn.extend( { + fadeTo: function( speed, to, easing, callback ) { + + // Show any hidden elements after setting opacity to 0 + return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() + + // Animate to the value specified + .end().animate( { opacity: to }, speed, easing, callback ); + }, + animate: function( prop, speed, easing, callback ) { + var empty = jQuery.isEmptyObject( prop ), + optall = jQuery.speed( speed, easing, callback ), + doAnimation = function() { + + // Operate on a copy of prop so per-property easing won't be lost + var anim = Animation( this, jQuery.extend( {}, prop ), optall ); + + // Empty animations, or finishing resolves immediately + if ( empty || dataPriv.get( this, "finish" ) ) { + anim.stop( true ); + } + }; + doAnimation.finish = doAnimation; + + return empty || optall.queue === false ? + this.each( doAnimation ) : + this.queue( optall.queue, doAnimation ); + }, + stop: function( type, clearQueue, gotoEnd ) { + var stopQueue = function( hooks ) { + var stop = hooks.stop; + delete hooks.stop; + stop( gotoEnd ); + }; + + if ( typeof type !== "string" ) { + gotoEnd = clearQueue; + clearQueue = type; + type = undefined; + } + if ( clearQueue && type !== false ) { + this.queue( type || "fx", [] ); + } + + return this.each( function() { + var dequeue = true, + index = type != null && type + "queueHooks", + timers = jQuery.timers, + data = dataPriv.get( this ); + + if ( index ) { + if ( data[ index ] && data[ index ].stop ) { + stopQueue( data[ index ] ); + } + } else { + for ( index in data ) { + if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { + stopQueue( data[ index ] ); + } + } + } + + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && + ( type == null || timers[ index ].queue === type ) ) { + + timers[ index ].anim.stop( gotoEnd ); + dequeue = false; + timers.splice( index, 1 ); + } + } + + // Start the next in the queue if the last step wasn't forced. + // Timers currently will call their complete callbacks, which + // will dequeue but only if they were gotoEnd. + if ( dequeue || !gotoEnd ) { + jQuery.dequeue( this, type ); + } + } ); + }, + finish: function( type ) { + if ( type !== false ) { + type = type || "fx"; + } + return this.each( function() { + var index, + data = dataPriv.get( this ), + queue = data[ type + "queue" ], + hooks = data[ type + "queueHooks" ], + timers = jQuery.timers, + length = queue ? queue.length : 0; + + // Enable finishing flag on private data + data.finish = true; + + // Empty the queue first + jQuery.queue( this, type, [] ); + + if ( hooks && hooks.stop ) { + hooks.stop.call( this, true ); + } + + // Look for any active animations, and finish them + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && timers[ index ].queue === type ) { + timers[ index ].anim.stop( true ); + timers.splice( index, 1 ); + } + } + + // Look for any animations in the old queue and finish them + for ( index = 0; index < length; index++ ) { + if ( queue[ index ] && queue[ index ].finish ) { + queue[ index ].finish.call( this ); + } + } + + // Turn off finishing flag + delete data.finish; + } ); + } +} ); + +jQuery.each( [ "toggle", "show", "hide" ], function( i, name ) { + var cssFn = jQuery.fn[ name ]; + jQuery.fn[ name ] = function( speed, easing, callback ) { + return speed == null || typeof speed === "boolean" ? + cssFn.apply( this, arguments ) : + this.animate( genFx( name, true ), speed, easing, callback ); + }; +} ); + +// Generate shortcuts for custom animations +jQuery.each( { + slideDown: genFx( "show" ), + slideUp: genFx( "hide" ), + slideToggle: genFx( "toggle" ), + fadeIn: { opacity: "show" }, + fadeOut: { opacity: "hide" }, + fadeToggle: { opacity: "toggle" } +}, function( name, props ) { + jQuery.fn[ name ] = function( speed, easing, callback ) { + return this.animate( props, speed, easing, callback ); + }; +} ); + +jQuery.timers = []; +jQuery.fx.tick = function() { + var timer, + i = 0, + timers = jQuery.timers; + + fxNow = Date.now(); + + for ( ; i < timers.length; i++ ) { + timer = timers[ i ]; + + // Run the timer and safely remove it when done (allowing for external removal) + if ( !timer() && timers[ i ] === timer ) { + timers.splice( i--, 1 ); + } + } + + if ( !timers.length ) { + jQuery.fx.stop(); + } + fxNow = undefined; +}; + +jQuery.fx.timer = function( timer ) { + jQuery.timers.push( timer ); + jQuery.fx.start(); +}; + +jQuery.fx.interval = 13; +jQuery.fx.start = function() { + if ( inProgress ) { + return; + } + + inProgress = true; + schedule(); +}; + +jQuery.fx.stop = function() { + inProgress = null; +}; + +jQuery.fx.speeds = { + slow: 600, + fast: 200, + + // Default speed + _default: 400 +}; + + +// Based off of the plugin by Clint Helfers, with permission. +// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ +jQuery.fn.delay = function( time, type ) { + time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; + type = type || "fx"; + + return this.queue( type, function( next, hooks ) { + var timeout = window.setTimeout( next, time ); + hooks.stop = function() { + window.clearTimeout( timeout ); + }; + } ); +}; + + +( function() { + var input = document.createElement( "input" ), + select = document.createElement( "select" ), + opt = select.appendChild( document.createElement( "option" ) ); + + input.type = "checkbox"; + + // Support: Android <=4.3 only + // Default value for a checkbox should be "on" + support.checkOn = input.value !== ""; + + // Support: IE <=11 only + // Must access selectedIndex to make default options select + support.optSelected = opt.selected; + + // Support: IE <=11 only + // An input loses its value after becoming a radio + input = document.createElement( "input" ); + input.value = "t"; + input.type = "radio"; + support.radioValue = input.value === "t"; +} )(); + + +var boolHook, + attrHandle = jQuery.expr.attrHandle; + +jQuery.fn.extend( { + attr: function( name, value ) { + return access( this, jQuery.attr, name, value, arguments.length > 1 ); + }, + + removeAttr: function( name ) { + return this.each( function() { + jQuery.removeAttr( this, name ); + } ); + } +} ); + +jQuery.extend( { + attr: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set attributes on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + // Fallback to prop when attributes are not supported + if ( typeof elem.getAttribute === "undefined" ) { + return jQuery.prop( elem, name, value ); + } + + // Attribute hooks are determined by the lowercase version + // Grab necessary hook if one is defined + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + hooks = jQuery.attrHooks[ name.toLowerCase() ] || + ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); + } + + if ( value !== undefined ) { + if ( value === null ) { + jQuery.removeAttr( elem, name ); + return; + } + + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + elem.setAttribute( name, value + "" ); + return value; + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + ret = jQuery.find.attr( elem, name ); + + // Non-existent attributes return null, we normalize to undefined + return ret == null ? undefined : ret; + }, + + attrHooks: { + type: { + set: function( elem, value ) { + if ( !support.radioValue && value === "radio" && + nodeName( elem, "input" ) ) { + var val = elem.value; + elem.setAttribute( "type", value ); + if ( val ) { + elem.value = val; + } + return value; + } + } + } + }, + + removeAttr: function( elem, value ) { + var name, + i = 0, + + // Attribute names can contain non-HTML whitespace characters + // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 + attrNames = value && value.match( rnothtmlwhite ); + + if ( attrNames && elem.nodeType === 1 ) { + while ( ( name = attrNames[ i++ ] ) ) { + elem.removeAttribute( name ); + } + } + } +} ); + +// Hooks for boolean attributes +boolHook = { + set: function( elem, value, name ) { + if ( value === false ) { + + // Remove boolean attributes when set to false + jQuery.removeAttr( elem, name ); + } else { + elem.setAttribute( name, name ); + } + return name; + } +}; + +jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( i, name ) { + var getter = attrHandle[ name ] || jQuery.find.attr; + + attrHandle[ name ] = function( elem, name, isXML ) { + var ret, handle, + lowercaseName = name.toLowerCase(); + + if ( !isXML ) { + + // Avoid an infinite loop by temporarily removing this function from the getter + handle = attrHandle[ lowercaseName ]; + attrHandle[ lowercaseName ] = ret; + ret = getter( elem, name, isXML ) != null ? + lowercaseName : + null; + attrHandle[ lowercaseName ] = handle; + } + return ret; + }; +} ); + + + + +var rfocusable = /^(?:input|select|textarea|button)$/i, + rclickable = /^(?:a|area)$/i; + +jQuery.fn.extend( { + prop: function( name, value ) { + return access( this, jQuery.prop, name, value, arguments.length > 1 ); + }, + + removeProp: function( name ) { + return this.each( function() { + delete this[ jQuery.propFix[ name ] || name ]; + } ); + } +} ); + +jQuery.extend( { + prop: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set properties on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + + // Fix name and attach hooks + name = jQuery.propFix[ name ] || name; + hooks = jQuery.propHooks[ name ]; + } + + if ( value !== undefined ) { + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + return ( elem[ name ] = value ); + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + return elem[ name ]; + }, + + propHooks: { + tabIndex: { + get: function( elem ) { + + // Support: IE <=9 - 11 only + // elem.tabIndex doesn't always return the + // correct value when it hasn't been explicitly set + // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ + // Use proper attribute retrieval(#12072) + var tabindex = jQuery.find.attr( elem, "tabindex" ); + + if ( tabindex ) { + return parseInt( tabindex, 10 ); + } + + if ( + rfocusable.test( elem.nodeName ) || + rclickable.test( elem.nodeName ) && + elem.href + ) { + return 0; + } + + return -1; + } + } + }, + + propFix: { + "for": "htmlFor", + "class": "className" + } +} ); + +// Support: IE <=11 only +// Accessing the selectedIndex property +// forces the browser to respect setting selected +// on the option +// The getter ensures a default option is selected +// when in an optgroup +// eslint rule "no-unused-expressions" is disabled for this code +// since it considers such accessions noop +if ( !support.optSelected ) { + jQuery.propHooks.selected = { + get: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent && parent.parentNode ) { + parent.parentNode.selectedIndex; + } + return null; + }, + set: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent ) { + parent.selectedIndex; + + if ( parent.parentNode ) { + parent.parentNode.selectedIndex; + } + } + } + }; +} + +jQuery.each( [ + "tabIndex", + "readOnly", + "maxLength", + "cellSpacing", + "cellPadding", + "rowSpan", + "colSpan", + "useMap", + "frameBorder", + "contentEditable" +], function() { + jQuery.propFix[ this.toLowerCase() ] = this; +} ); + + + + + // Strip and collapse whitespace according to HTML spec + // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace + function stripAndCollapse( value ) { + var tokens = value.match( rnothtmlwhite ) || []; + return tokens.join( " " ); + } + + +function getClass( elem ) { + return elem.getAttribute && elem.getAttribute( "class" ) || ""; +} + +function classesToArray( value ) { + if ( Array.isArray( value ) ) { + return value; + } + if ( typeof value === "string" ) { + return value.match( rnothtmlwhite ) || []; + } + return []; +} + +jQuery.fn.extend( { + addClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + if ( cur.indexOf( " " + clazz + " " ) < 0 ) { + cur += clazz + " "; + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + removeClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + if ( !arguments.length ) { + return this.attr( "class", "" ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + + // This expression is here for better compressibility (see addClass) + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + + // Remove *all* instances + while ( cur.indexOf( " " + clazz + " " ) > -1 ) { + cur = cur.replace( " " + clazz + " ", " " ); + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + toggleClass: function( value, stateVal ) { + var type = typeof value, + isValidValue = type === "string" || Array.isArray( value ); + + if ( typeof stateVal === "boolean" && isValidValue ) { + return stateVal ? this.addClass( value ) : this.removeClass( value ); + } + + if ( isFunction( value ) ) { + return this.each( function( i ) { + jQuery( this ).toggleClass( + value.call( this, i, getClass( this ), stateVal ), + stateVal + ); + } ); + } + + return this.each( function() { + var className, i, self, classNames; + + if ( isValidValue ) { + + // Toggle individual class names + i = 0; + self = jQuery( this ); + classNames = classesToArray( value ); + + while ( ( className = classNames[ i++ ] ) ) { + + // Check each className given, space separated list + if ( self.hasClass( className ) ) { + self.removeClass( className ); + } else { + self.addClass( className ); + } + } + + // Toggle whole class name + } else if ( value === undefined || type === "boolean" ) { + className = getClass( this ); + if ( className ) { + + // Store className if set + dataPriv.set( this, "__className__", className ); + } + + // If the element has a class name or if we're passed `false`, + // then remove the whole classname (if there was one, the above saved it). + // Otherwise bring back whatever was previously saved (if anything), + // falling back to the empty string if nothing was stored. + if ( this.setAttribute ) { + this.setAttribute( "class", + className || value === false ? + "" : + dataPriv.get( this, "__className__" ) || "" + ); + } + } + } ); + }, + + hasClass: function( selector ) { + var className, elem, + i = 0; + + className = " " + selector + " "; + while ( ( elem = this[ i++ ] ) ) { + if ( elem.nodeType === 1 && + ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { + return true; + } + } + + return false; + } +} ); + + + + +var rreturn = /\r/g; + +jQuery.fn.extend( { + val: function( value ) { + var hooks, ret, valueIsFunction, + elem = this[ 0 ]; + + if ( !arguments.length ) { + if ( elem ) { + hooks = jQuery.valHooks[ elem.type ] || + jQuery.valHooks[ elem.nodeName.toLowerCase() ]; + + if ( hooks && + "get" in hooks && + ( ret = hooks.get( elem, "value" ) ) !== undefined + ) { + return ret; + } + + ret = elem.value; + + // Handle most common string cases + if ( typeof ret === "string" ) { + return ret.replace( rreturn, "" ); + } + + // Handle cases where value is null/undef or number + return ret == null ? "" : ret; + } + + return; + } + + valueIsFunction = isFunction( value ); + + return this.each( function( i ) { + var val; + + if ( this.nodeType !== 1 ) { + return; + } + + if ( valueIsFunction ) { + val = value.call( this, i, jQuery( this ).val() ); + } else { + val = value; + } + + // Treat null/undefined as ""; convert numbers to string + if ( val == null ) { + val = ""; + + } else if ( typeof val === "number" ) { + val += ""; + + } else if ( Array.isArray( val ) ) { + val = jQuery.map( val, function( value ) { + return value == null ? "" : value + ""; + } ); + } + + hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; + + // If set returns undefined, fall back to normal setting + if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { + this.value = val; + } + } ); + } +} ); + +jQuery.extend( { + valHooks: { + option: { + get: function( elem ) { + + var val = jQuery.find.attr( elem, "value" ); + return val != null ? + val : + + // Support: IE <=10 - 11 only + // option.text throws exceptions (#14686, #14858) + // Strip and collapse whitespace + // https://html.spec.whatwg.org/#strip-and-collapse-whitespace + stripAndCollapse( jQuery.text( elem ) ); + } + }, + select: { + get: function( elem ) { + var value, option, i, + options = elem.options, + index = elem.selectedIndex, + one = elem.type === "select-one", + values = one ? null : [], + max = one ? index + 1 : options.length; + + if ( index < 0 ) { + i = max; + + } else { + i = one ? index : 0; + } + + // Loop through all the selected options + for ( ; i < max; i++ ) { + option = options[ i ]; + + // Support: IE <=9 only + // IE8-9 doesn't update selected after form reset (#2551) + if ( ( option.selected || i === index ) && + + // Don't return options that are disabled or in a disabled optgroup + !option.disabled && + ( !option.parentNode.disabled || + !nodeName( option.parentNode, "optgroup" ) ) ) { + + // Get the specific value for the option + value = jQuery( option ).val(); + + // We don't need an array for one selects + if ( one ) { + return value; + } + + // Multi-Selects return an array + values.push( value ); + } + } + + return values; + }, + + set: function( elem, value ) { + var optionSet, option, + options = elem.options, + values = jQuery.makeArray( value ), + i = options.length; + + while ( i-- ) { + option = options[ i ]; + + /* eslint-disable no-cond-assign */ + + if ( option.selected = + jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 + ) { + optionSet = true; + } + + /* eslint-enable no-cond-assign */ + } + + // Force browsers to behave consistently when non-matching value is set + if ( !optionSet ) { + elem.selectedIndex = -1; + } + return values; + } + } + } +} ); + +// Radios and checkboxes getter/setter +jQuery.each( [ "radio", "checkbox" ], function() { + jQuery.valHooks[ this ] = { + set: function( elem, value ) { + if ( Array.isArray( value ) ) { + return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); + } + } + }; + if ( !support.checkOn ) { + jQuery.valHooks[ this ].get = function( elem ) { + return elem.getAttribute( "value" ) === null ? "on" : elem.value; + }; + } +} ); + + + + +// Return jQuery for attributes-only inclusion + + +support.focusin = "onfocusin" in window; + + +var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, + stopPropagationCallback = function( e ) { + e.stopPropagation(); + }; + +jQuery.extend( jQuery.event, { + + trigger: function( event, data, elem, onlyHandlers ) { + + var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, + eventPath = [ elem || document ], + type = hasOwn.call( event, "type" ) ? event.type : event, + namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; + + cur = lastElement = tmp = elem = elem || document; + + // Don't do events on text and comment nodes + if ( elem.nodeType === 3 || elem.nodeType === 8 ) { + return; + } + + // focus/blur morphs to focusin/out; ensure we're not firing them right now + if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { + return; + } + + if ( type.indexOf( "." ) > -1 ) { + + // Namespaced trigger; create a regexp to match event type in handle() + namespaces = type.split( "." ); + type = namespaces.shift(); + namespaces.sort(); + } + ontype = type.indexOf( ":" ) < 0 && "on" + type; + + // Caller can pass in a jQuery.Event object, Object, or just an event type string + event = event[ jQuery.expando ] ? + event : + new jQuery.Event( type, typeof event === "object" && event ); + + // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) + event.isTrigger = onlyHandlers ? 2 : 3; + event.namespace = namespaces.join( "." ); + event.rnamespace = event.namespace ? + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : + null; + + // Clean up the event in case it is being reused + event.result = undefined; + if ( !event.target ) { + event.target = elem; + } + + // Clone any incoming data and prepend the event, creating the handler arg list + data = data == null ? + [ event ] : + jQuery.makeArray( data, [ event ] ); + + // Allow special events to draw outside the lines + special = jQuery.event.special[ type ] || {}; + if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { + return; + } + + // Determine event propagation path in advance, per W3C events spec (#9951) + // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) + if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { + + bubbleType = special.delegateType || type; + if ( !rfocusMorph.test( bubbleType + type ) ) { + cur = cur.parentNode; + } + for ( ; cur; cur = cur.parentNode ) { + eventPath.push( cur ); + tmp = cur; + } + + // Only add window if we got to document (e.g., not plain obj or detached DOM) + if ( tmp === ( elem.ownerDocument || document ) ) { + eventPath.push( tmp.defaultView || tmp.parentWindow || window ); + } + } + + // Fire handlers on the event path + i = 0; + while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { + lastElement = cur; + event.type = i > 1 ? + bubbleType : + special.bindType || type; + + // jQuery handler + handle = ( dataPriv.get( cur, "events" ) || {} )[ event.type ] && + dataPriv.get( cur, "handle" ); + if ( handle ) { + handle.apply( cur, data ); + } + + // Native handler + handle = ontype && cur[ ontype ]; + if ( handle && handle.apply && acceptData( cur ) ) { + event.result = handle.apply( cur, data ); + if ( event.result === false ) { + event.preventDefault(); + } + } + } + event.type = type; + + // If nobody prevented the default action, do it now + if ( !onlyHandlers && !event.isDefaultPrevented() ) { + + if ( ( !special._default || + special._default.apply( eventPath.pop(), data ) === false ) && + acceptData( elem ) ) { + + // Call a native DOM method on the target with the same name as the event. + // Don't do default actions on window, that's where global variables be (#6170) + if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { + + // Don't re-trigger an onFOO event when we call its FOO() method + tmp = elem[ ontype ]; + + if ( tmp ) { + elem[ ontype ] = null; + } + + // Prevent re-triggering of the same event, since we already bubbled it above + jQuery.event.triggered = type; + + if ( event.isPropagationStopped() ) { + lastElement.addEventListener( type, stopPropagationCallback ); + } + + elem[ type ](); + + if ( event.isPropagationStopped() ) { + lastElement.removeEventListener( type, stopPropagationCallback ); + } + + jQuery.event.triggered = undefined; + + if ( tmp ) { + elem[ ontype ] = tmp; + } + } + } + } + + return event.result; + }, + + // Piggyback on a donor event to simulate a different one + // Used only for `focus(in | out)` events + simulate: function( type, elem, event ) { + var e = jQuery.extend( + new jQuery.Event(), + event, + { + type: type, + isSimulated: true + } + ); + + jQuery.event.trigger( e, null, elem ); + } + +} ); + +jQuery.fn.extend( { + + trigger: function( type, data ) { + return this.each( function() { + jQuery.event.trigger( type, data, this ); + } ); + }, + triggerHandler: function( type, data ) { + var elem = this[ 0 ]; + if ( elem ) { + return jQuery.event.trigger( type, data, elem, true ); + } + } +} ); + + +// Support: Firefox <=44 +// Firefox doesn't have focus(in | out) events +// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 +// +// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 +// focus(in | out) events fire after focus & blur events, +// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order +// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 +if ( !support.focusin ) { + jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { + + // Attach a single capturing handler on the document while someone wants focusin/focusout + var handler = function( event ) { + jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); + }; + + jQuery.event.special[ fix ] = { + setup: function() { + var doc = this.ownerDocument || this, + attaches = dataPriv.access( doc, fix ); + + if ( !attaches ) { + doc.addEventListener( orig, handler, true ); + } + dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); + }, + teardown: function() { + var doc = this.ownerDocument || this, + attaches = dataPriv.access( doc, fix ) - 1; + + if ( !attaches ) { + doc.removeEventListener( orig, handler, true ); + dataPriv.remove( doc, fix ); + + } else { + dataPriv.access( doc, fix, attaches ); + } + } + }; + } ); +} +var location = window.location; + +var nonce = Date.now(); + +var rquery = ( /\?/ ); + + + +// Cross-browser xml parsing +jQuery.parseXML = function( data ) { + var xml; + if ( !data || typeof data !== "string" ) { + return null; + } + + // Support: IE 9 - 11 only + // IE throws on parseFromString with invalid input. + try { + xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); + } catch ( e ) { + xml = undefined; + } + + if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) { + jQuery.error( "Invalid XML: " + data ); + } + return xml; +}; + + +var + rbracket = /\[\]$/, + rCRLF = /\r?\n/g, + rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, + rsubmittable = /^(?:input|select|textarea|keygen)/i; + +function buildParams( prefix, obj, traditional, add ) { + var name; + + if ( Array.isArray( obj ) ) { + + // Serialize array item. + jQuery.each( obj, function( i, v ) { + if ( traditional || rbracket.test( prefix ) ) { + + // Treat each array item as a scalar. + add( prefix, v ); + + } else { + + // Item is non-scalar (array or object), encode its numeric index. + buildParams( + prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", + v, + traditional, + add + ); + } + } ); + + } else if ( !traditional && toType( obj ) === "object" ) { + + // Serialize object item. + for ( name in obj ) { + buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); + } + + } else { + + // Serialize scalar item. + add( prefix, obj ); + } +} + +// Serialize an array of form elements or a set of +// key/values into a query string +jQuery.param = function( a, traditional ) { + var prefix, + s = [], + add = function( key, valueOrFunction ) { + + // If value is a function, invoke it and use its return value + var value = isFunction( valueOrFunction ) ? + valueOrFunction() : + valueOrFunction; + + s[ s.length ] = encodeURIComponent( key ) + "=" + + encodeURIComponent( value == null ? "" : value ); + }; + + // If an array was passed in, assume that it is an array of form elements. + if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { + + // Serialize the form elements + jQuery.each( a, function() { + add( this.name, this.value ); + } ); + + } else { + + // If traditional, encode the "old" way (the way 1.3.2 or older + // did it), otherwise encode params recursively. + for ( prefix in a ) { + buildParams( prefix, a[ prefix ], traditional, add ); + } + } + + // Return the resulting serialization + return s.join( "&" ); +}; + +jQuery.fn.extend( { + serialize: function() { + return jQuery.param( this.serializeArray() ); + }, + serializeArray: function() { + return this.map( function() { + + // Can add propHook for "elements" to filter or add form elements + var elements = jQuery.prop( this, "elements" ); + return elements ? jQuery.makeArray( elements ) : this; + } ) + .filter( function() { + var type = this.type; + + // Use .is( ":disabled" ) so that fieldset[disabled] works + return this.name && !jQuery( this ).is( ":disabled" ) && + rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && + ( this.checked || !rcheckableType.test( type ) ); + } ) + .map( function( i, elem ) { + var val = jQuery( this ).val(); + + if ( val == null ) { + return null; + } + + if ( Array.isArray( val ) ) { + return jQuery.map( val, function( val ) { + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ); + } + + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ).get(); + } +} ); + + +var + r20 = /%20/g, + rhash = /#.*$/, + rantiCache = /([?&])_=[^&]*/, + rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, + + // #7653, #8125, #8152: local protocol detection + rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, + rnoContent = /^(?:GET|HEAD)$/, + rprotocol = /^\/\//, + + /* Prefilters + * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) + * 2) These are called: + * - BEFORE asking for a transport + * - AFTER param serialization (s.data is a string if s.processData is true) + * 3) key is the dataType + * 4) the catchall symbol "*" can be used + * 5) execution will start with transport dataType and THEN continue down to "*" if needed + */ + prefilters = {}, + + /* Transports bindings + * 1) key is the dataType + * 2) the catchall symbol "*" can be used + * 3) selection will start with transport dataType and THEN go to "*" if needed + */ + transports = {}, + + // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression + allTypes = "*/".concat( "*" ), + + // Anchor tag for parsing the document origin + originAnchor = document.createElement( "a" ); + originAnchor.href = location.href; + +// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport +function addToPrefiltersOrTransports( structure ) { + + // dataTypeExpression is optional and defaults to "*" + return function( dataTypeExpression, func ) { + + if ( typeof dataTypeExpression !== "string" ) { + func = dataTypeExpression; + dataTypeExpression = "*"; + } + + var dataType, + i = 0, + dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; + + if ( isFunction( func ) ) { + + // For each dataType in the dataTypeExpression + while ( ( dataType = dataTypes[ i++ ] ) ) { + + // Prepend if requested + if ( dataType[ 0 ] === "+" ) { + dataType = dataType.slice( 1 ) || "*"; + ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); + + // Otherwise append + } else { + ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); + } + } + } + }; +} + +// Base inspection function for prefilters and transports +function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { + + var inspected = {}, + seekingTransport = ( structure === transports ); + + function inspect( dataType ) { + var selected; + inspected[ dataType ] = true; + jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { + var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); + if ( typeof dataTypeOrTransport === "string" && + !seekingTransport && !inspected[ dataTypeOrTransport ] ) { + + options.dataTypes.unshift( dataTypeOrTransport ); + inspect( dataTypeOrTransport ); + return false; + } else if ( seekingTransport ) { + return !( selected = dataTypeOrTransport ); + } + } ); + return selected; + } + + return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); +} + +// A special extend for ajax options +// that takes "flat" options (not to be deep extended) +// Fixes #9887 +function ajaxExtend( target, src ) { + var key, deep, + flatOptions = jQuery.ajaxSettings.flatOptions || {}; + + for ( key in src ) { + if ( src[ key ] !== undefined ) { + ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; + } + } + if ( deep ) { + jQuery.extend( true, target, deep ); + } + + return target; +} + +/* Handles responses to an ajax request: + * - finds the right dataType (mediates between content-type and expected dataType) + * - returns the corresponding response + */ +function ajaxHandleResponses( s, jqXHR, responses ) { + + var ct, type, finalDataType, firstDataType, + contents = s.contents, + dataTypes = s.dataTypes; + + // Remove auto dataType and get content-type in the process + while ( dataTypes[ 0 ] === "*" ) { + dataTypes.shift(); + if ( ct === undefined ) { + ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); + } + } + + // Check if we're dealing with a known content-type + if ( ct ) { + for ( type in contents ) { + if ( contents[ type ] && contents[ type ].test( ct ) ) { + dataTypes.unshift( type ); + break; + } + } + } + + // Check to see if we have a response for the expected dataType + if ( dataTypes[ 0 ] in responses ) { + finalDataType = dataTypes[ 0 ]; + } else { + + // Try convertible dataTypes + for ( type in responses ) { + if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { + finalDataType = type; + break; + } + if ( !firstDataType ) { + firstDataType = type; + } + } + + // Or just use first one + finalDataType = finalDataType || firstDataType; + } + + // If we found a dataType + // We add the dataType to the list if needed + // and return the corresponding response + if ( finalDataType ) { + if ( finalDataType !== dataTypes[ 0 ] ) { + dataTypes.unshift( finalDataType ); + } + return responses[ finalDataType ]; + } +} + +/* Chain conversions given the request and the original response + * Also sets the responseXXX fields on the jqXHR instance + */ +function ajaxConvert( s, response, jqXHR, isSuccess ) { + var conv2, current, conv, tmp, prev, + converters = {}, + + // Work with a copy of dataTypes in case we need to modify it for conversion + dataTypes = s.dataTypes.slice(); + + // Create converters map with lowercased keys + if ( dataTypes[ 1 ] ) { + for ( conv in s.converters ) { + converters[ conv.toLowerCase() ] = s.converters[ conv ]; + } + } + + current = dataTypes.shift(); + + // Convert to each sequential dataType + while ( current ) { + + if ( s.responseFields[ current ] ) { + jqXHR[ s.responseFields[ current ] ] = response; + } + + // Apply the dataFilter if provided + if ( !prev && isSuccess && s.dataFilter ) { + response = s.dataFilter( response, s.dataType ); + } + + prev = current; + current = dataTypes.shift(); + + if ( current ) { + + // There's only work to do if current dataType is non-auto + if ( current === "*" ) { + + current = prev; + + // Convert response if prev dataType is non-auto and differs from current + } else if ( prev !== "*" && prev !== current ) { + + // Seek a direct converter + conv = converters[ prev + " " + current ] || converters[ "* " + current ]; + + // If none found, seek a pair + if ( !conv ) { + for ( conv2 in converters ) { + + // If conv2 outputs current + tmp = conv2.split( " " ); + if ( tmp[ 1 ] === current ) { + + // If prev can be converted to accepted input + conv = converters[ prev + " " + tmp[ 0 ] ] || + converters[ "* " + tmp[ 0 ] ]; + if ( conv ) { + + // Condense equivalence converters + if ( conv === true ) { + conv = converters[ conv2 ]; + + // Otherwise, insert the intermediate dataType + } else if ( converters[ conv2 ] !== true ) { + current = tmp[ 0 ]; + dataTypes.unshift( tmp[ 1 ] ); + } + break; + } + } + } + } + + // Apply converter (if not an equivalence) + if ( conv !== true ) { + + // Unless errors are allowed to bubble, catch and return them + if ( conv && s.throws ) { + response = conv( response ); + } else { + try { + response = conv( response ); + } catch ( e ) { + return { + state: "parsererror", + error: conv ? e : "No conversion from " + prev + " to " + current + }; + } + } + } + } + } + } + + return { state: "success", data: response }; +} + +jQuery.extend( { + + // Counter for holding the number of active queries + active: 0, + + // Last-Modified header cache for next request + lastModified: {}, + etag: {}, + + ajaxSettings: { + url: location.href, + type: "GET", + isLocal: rlocalProtocol.test( location.protocol ), + global: true, + processData: true, + async: true, + contentType: "application/x-www-form-urlencoded; charset=UTF-8", + + /* + timeout: 0, + data: null, + dataType: null, + username: null, + password: null, + cache: null, + throws: false, + traditional: false, + headers: {}, + */ + + accepts: { + "*": allTypes, + text: "text/plain", + html: "text/html", + xml: "application/xml, text/xml", + json: "application/json, text/javascript" + }, + + contents: { + xml: /\bxml\b/, + html: /\bhtml/, + json: /\bjson\b/ + }, + + responseFields: { + xml: "responseXML", + text: "responseText", + json: "responseJSON" + }, + + // Data converters + // Keys separate source (or catchall "*") and destination types with a single space + converters: { + + // Convert anything to text + "* text": String, + + // Text to html (true = no transformation) + "text html": true, + + // Evaluate text as a json expression + "text json": JSON.parse, + + // Parse text as xml + "text xml": jQuery.parseXML + }, + + // For options that shouldn't be deep extended: + // you can add your own custom options here if + // and when you create one that shouldn't be + // deep extended (see ajaxExtend) + flatOptions: { + url: true, + context: true + } + }, + + // Creates a full fledged settings object into target + // with both ajaxSettings and settings fields. + // If target is omitted, writes into ajaxSettings. + ajaxSetup: function( target, settings ) { + return settings ? + + // Building a settings object + ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : + + // Extending ajaxSettings + ajaxExtend( jQuery.ajaxSettings, target ); + }, + + ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), + ajaxTransport: addToPrefiltersOrTransports( transports ), + + // Main method + ajax: function( url, options ) { + + // If url is an object, simulate pre-1.5 signature + if ( typeof url === "object" ) { + options = url; + url = undefined; + } + + // Force options to be an object + options = options || {}; + + var transport, + + // URL without anti-cache param + cacheURL, + + // Response headers + responseHeadersString, + responseHeaders, + + // timeout handle + timeoutTimer, + + // Url cleanup var + urlAnchor, + + // Request state (becomes false upon send and true upon completion) + completed, + + // To know if global events are to be dispatched + fireGlobals, + + // Loop variable + i, + + // uncached part of the url + uncached, + + // Create the final options object + s = jQuery.ajaxSetup( {}, options ), + + // Callbacks context + callbackContext = s.context || s, + + // Context for global events is callbackContext if it is a DOM node or jQuery collection + globalEventContext = s.context && + ( callbackContext.nodeType || callbackContext.jquery ) ? + jQuery( callbackContext ) : + jQuery.event, + + // Deferreds + deferred = jQuery.Deferred(), + completeDeferred = jQuery.Callbacks( "once memory" ), + + // Status-dependent callbacks + statusCode = s.statusCode || {}, + + // Headers (they are sent all at once) + requestHeaders = {}, + requestHeadersNames = {}, + + // Default abort message + strAbort = "canceled", + + // Fake xhr + jqXHR = { + readyState: 0, + + // Builds headers hashtable if needed + getResponseHeader: function( key ) { + var match; + if ( completed ) { + if ( !responseHeaders ) { + responseHeaders = {}; + while ( ( match = rheaders.exec( responseHeadersString ) ) ) { + responseHeaders[ match[ 1 ].toLowerCase() ] = match[ 2 ]; + } + } + match = responseHeaders[ key.toLowerCase() ]; + } + return match == null ? null : match; + }, + + // Raw string + getAllResponseHeaders: function() { + return completed ? responseHeadersString : null; + }, + + // Caches the header + setRequestHeader: function( name, value ) { + if ( completed == null ) { + name = requestHeadersNames[ name.toLowerCase() ] = + requestHeadersNames[ name.toLowerCase() ] || name; + requestHeaders[ name ] = value; + } + return this; + }, + + // Overrides response content-type header + overrideMimeType: function( type ) { + if ( completed == null ) { + s.mimeType = type; + } + return this; + }, + + // Status-dependent callbacks + statusCode: function( map ) { + var code; + if ( map ) { + if ( completed ) { + + // Execute the appropriate callbacks + jqXHR.always( map[ jqXHR.status ] ); + } else { + + // Lazy-add the new callbacks in a way that preserves old ones + for ( code in map ) { + statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; + } + } + } + return this; + }, + + // Cancel the request + abort: function( statusText ) { + var finalText = statusText || strAbort; + if ( transport ) { + transport.abort( finalText ); + } + done( 0, finalText ); + return this; + } + }; + + // Attach deferreds + deferred.promise( jqXHR ); + + // Add protocol if not provided (prefilters might expect it) + // Handle falsy url in the settings object (#10093: consistency with old signature) + // We also use the url parameter if available + s.url = ( ( url || s.url || location.href ) + "" ) + .replace( rprotocol, location.protocol + "//" ); + + // Alias method option to type as per ticket #12004 + s.type = options.method || options.type || s.method || s.type; + + // Extract dataTypes list + s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; + + // A cross-domain request is in order when the origin doesn't match the current origin. + if ( s.crossDomain == null ) { + urlAnchor = document.createElement( "a" ); + + // Support: IE <=8 - 11, Edge 12 - 15 + // IE throws exception on accessing the href property if url is malformed, + // e.g. http://example.com:80x/ + try { + urlAnchor.href = s.url; + + // Support: IE <=8 - 11 only + // Anchor's host property isn't correctly set when s.url is relative + urlAnchor.href = urlAnchor.href; + s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== + urlAnchor.protocol + "//" + urlAnchor.host; + } catch ( e ) { + + // If there is an error parsing the URL, assume it is crossDomain, + // it can be rejected by the transport if it is invalid + s.crossDomain = true; + } + } + + // Convert data if not already a string + if ( s.data && s.processData && typeof s.data !== "string" ) { + s.data = jQuery.param( s.data, s.traditional ); + } + + // Apply prefilters + inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); + + // If request was aborted inside a prefilter, stop there + if ( completed ) { + return jqXHR; + } + + // We can fire global events as of now if asked to + // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) + fireGlobals = jQuery.event && s.global; + + // Watch for a new set of requests + if ( fireGlobals && jQuery.active++ === 0 ) { + jQuery.event.trigger( "ajaxStart" ); + } + + // Uppercase the type + s.type = s.type.toUpperCase(); + + // Determine if request has content + s.hasContent = !rnoContent.test( s.type ); + + // Save the URL in case we're toying with the If-Modified-Since + // and/or If-None-Match header later on + // Remove hash to simplify url manipulation + cacheURL = s.url.replace( rhash, "" ); + + // More options handling for requests with no content + if ( !s.hasContent ) { + + // Remember the hash so we can put it back + uncached = s.url.slice( cacheURL.length ); + + // If data is available and should be processed, append data to url + if ( s.data && ( s.processData || typeof s.data === "string" ) ) { + cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; + + // #9682: remove data so that it's not used in an eventual retry + delete s.data; + } + + // Add or update anti-cache param if needed + if ( s.cache === false ) { + cacheURL = cacheURL.replace( rantiCache, "$1" ); + uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce++ ) + uncached; + } + + // Put hash and anti-cache on the URL that will be requested (gh-1732) + s.url = cacheURL + uncached; + + // Change '%20' to '+' if this is encoded form body content (gh-2658) + } else if ( s.data && s.processData && + ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { + s.data = s.data.replace( r20, "+" ); + } + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + if ( jQuery.lastModified[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); + } + if ( jQuery.etag[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); + } + } + + // Set the correct header, if data is being sent + if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { + jqXHR.setRequestHeader( "Content-Type", s.contentType ); + } + + // Set the Accepts header for the server, depending on the dataType + jqXHR.setRequestHeader( + "Accept", + s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? + s.accepts[ s.dataTypes[ 0 ] ] + + ( s.dataTypes[ 0 ] !== "*" ? 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Squigglepy: Implementation of Squiggle in Python#

+

Squiggle is a “simple +programming language for intuitive probabilistic estimation”. It serves +as its own standalone programming language with its own syntax, but it +is implemented in JavaScript. I like the features of Squiggle and intend +to use it frequently, but I also sometimes want to use similar +functionalities in Python, especially alongside other Python statistical +programming packages like Numpy, Pandas, and Matplotlib. The +squigglepy package here implements many Squiggle-like +functionalities in Python.

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Check out the README to get started.

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b/docs/make.bat @@ -0,0 +1,35 @@ +@ECHO OFF + +pushd %~dp0 + +REM Command file for Sphinx documentation + +if "%SPHINXBUILD%" == "" ( + set SPHINXBUILD=sphinx-build +) +set SOURCEDIR=source +set BUILDDIR=build + +if "%1" == "" goto help + +%SPHINXBUILD% >NUL 2>NUL +if errorlevel 9009 ( + echo. + echo.The 'sphinx-build' command was not found. Make sure you have Sphinx + echo.installed, then set the SPHINXBUILD environment variable to point + echo.to the full path of the 'sphinx-build' executable. Alternatively you + echo.may add the Sphinx directory to PATH. + echo. + echo.If you don't have Sphinx installed, grab it from + echo.http://sphinx-doc.org/ + exit /b 1 +) + +%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% +goto end + +:help +%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% + +:end +popd diff --git a/docs/source/README.rst b/docs/source/README.rst new file mode 100644 index 0000000..f5ec681 --- /dev/null +++ b/docs/source/README.rst @@ -0,0 +1,531 @@ +Squigglepy: Implementation of Squiggle in Python +================================================ + +`Squiggle `__ is a “simple +programming language for intuitive probabilistic estimation”. It serves +as its own standalone programming language with its own syntax, but it +is implemented in JavaScript. I like the features of Squiggle and intend +to use it frequently, but I also sometimes want to use similar +functionalities in Python, especially alongside other Python statistical +programming packages like Numpy, Pandas, and Matplotlib. The +**squigglepy** package here implements many Squiggle-like +functionalities in Python. + +Installation +------------ + +.. code:: shell + + pip install squigglepy + +For plotting support, you can also use the ``plots`` extra: + +.. code:: shell + + pip install squigglepy[plots] + +Usage +----- + +Piano Tuners Example +~~~~~~~~~~~~~~~~~~~~ + +Here’s the Squigglepy implementation of `the example from Squiggle +Docs `__: + +.. code:: python + + import squigglepy as sq + import numpy as np + import matplotlib.pyplot as plt + from squigglepy.numbers import K, M + from pprint import pprint + + pop_of_ny_2022 = sq.to(8.1*M, 8.4*M) # This means that you're 90% confident the value is between 8.1 and 8.4 Million. + pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01 # We assume there are almost no people with multiple pianos + pianos_per_piano_tuner = sq.to(2*K, 50*K) + piano_tuners_per_piano = 1 / pianos_per_piano_tuner + total_tuners_in_2022 = pop_of_ny_2022 * pct_of_pop_w_pianos * piano_tuners_per_piano + samples = total_tuners_in_2022 @ 1000 # Note: `@ 1000` is shorthand to get 1000 samples + + # Get mean and SD + print('Mean: {}, SD: {}'.format(round(np.mean(samples), 2), + round(np.std(samples), 2))) + + # Get percentiles + pprint(sq.get_percentiles(samples, digits=0)) + + # Histogram + plt.hist(samples, bins=200) + plt.show() + + # Shorter histogram + total_tuners_in_2022.plot() + +And the version from the Squiggle doc that incorporates time: + +.. code:: python + + import squigglepy as sq + from squigglepy.numbers import K, M + + pop_of_ny_2022 = sq.to(8.1*M, 8.4*M) + pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01 + pianos_per_piano_tuner = sq.to(2*K, 50*K) + piano_tuners_per_piano = 1 / pianos_per_piano_tuner + + def pop_at_time(t): # t = Time in years after 2022 + avg_yearly_pct_change = sq.to(-0.01, 0.05) # We're expecting NYC to continuously grow with an mean of roughly between -1% and +4% per year + return pop_of_ny_2022 * ((avg_yearly_pct_change + 1) ** t) + + def total_tuners_at_time(t): + return pop_at_time(t) * pct_of_pop_w_pianos * piano_tuners_per_piano + + # Get total piano tuners at 2030 + sq.get_percentiles(total_tuners_at_time(2030-2022) @ 1000) + +**WARNING:** Be careful about dividing by ``K``, ``M``, etc. ``1/2*K`` = +500 in Python. Use ``1/(2*K)`` instead to get the expected outcome. + +**WARNING:** Be careful about using ``K`` to get sample counts. Use +``sq.norm(2, 3) @ (2*K)``\ … ``sq.norm(2, 3) @ 2*K`` will return only +two samples, multiplied by 1000. + +Distributions +~~~~~~~~~~~~~ + +.. code:: python + + import squigglepy as sq + + # Normal distribution + sq.norm(1, 3) # 90% interval from 1 to 3 + + # Distribution can be sampled with mean and sd too + sq.norm(mean=0, sd=1) + + # Shorthand to get one sample + ~sq.norm(1, 3) + + # Shorthand to get more than one sample + sq.norm(1, 3) @ 100 + + # Longhand version to get more than one sample + sq.sample(sq.norm(1, 3), n=100) + + # Nice progress reporter + sq.sample(sq.norm(1, 3), n=1000, verbose=True) + + # Other distributions exist + sq.lognorm(1, 10) + sq.tdist(1, 10, t=5) + sq.triangular(1, 2, 3) + sq.pert(1, 2, 3, lam=2) + sq.binomial(p=0.5, n=5) + sq.beta(a=1, b=2) + sq.bernoulli(p=0.5) + sq.poisson(10) + sq.chisquare(2) + sq.gamma(3, 2) + sq.pareto(1) + sq.exponential(scale=1) + sq.geometric(p=0.5) + + # Discrete sampling + sq.discrete({'A': 0.1, 'B': 0.9}) + + # Can return integers + sq.discrete({0: 0.1, 1: 0.3, 2: 0.3, 3: 0.15, 4: 0.15}) + + # Alternate format (also can be used to return more complex objects) + sq.discrete([[0.1, 0], + [0.3, 1], + [0.3, 2], + [0.15, 3], + [0.15, 4]]) + + sq.discrete([0, 1, 2]) # No weights assumes equal weights + + # You can mix distributions together + sq.mixture([sq.norm(1, 3), + sq.norm(4, 10), + sq.lognorm(1, 10)], # Distributions to mix + [0.3, 0.3, 0.4]) # These are the weights on each distribution + + # This is equivalent to the above, just a different way of doing the notation + sq.mixture([[0.3, sq.norm(1,3)], + [0.3, sq.norm(4,10)], + [0.4, sq.lognorm(1,10)]]) + + # Make a zero-inflated distribution + # 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`. + sq.zero_inflated(0.6, sq.norm(1, 2)) + +Additional Features +~~~~~~~~~~~~~~~~~~~ + +.. code:: python + + import squigglepy as sq + + # You can add and subtract distributions + (sq.norm(1,3) + sq.norm(4,5)) @ 100 + (sq.norm(1,3) - sq.norm(4,5)) @ 100 + (sq.norm(1,3) * sq.norm(4,5)) @ 100 + (sq.norm(1,3) / sq.norm(4,5)) @ 100 + + # You can also do math with numbers + ~((sq.norm(sd=5) + 2) * 2) + ~(-sq.lognorm(0.1, 1) * sq.pareto(1) / 10) + + # You can change the CI from 90% (default) to 80% + sq.norm(1, 3, credibility=80) + + # You can clip + sq.norm(0, 3, lclip=0, rclip=5) # Sample norm with a 90% CI from 0-3, but anything lower than 0 gets clipped to 0 and anything higher than 5 gets clipped to 5. + + # You can also clip with a function, and use pipes + sq.norm(0, 3) >> sq.clip(0, 5) + + # You can correlate continuous distributions + a, b = sq.uniform(-1, 1), sq.to(0, 3) + a, b = sq.correlate((a, b), 0.5) # Correlate a and b with a correlation of 0.5 + # You can even pass your own correlation matrix! + a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]]) + +Example: Rolling a Die +^^^^^^^^^^^^^^^^^^^^^^ + +An example of how to use distributions to build tools: + +.. code:: python + + import squigglepy as sq + + def roll_die(sides, n=1): + return sq.discrete(list(range(1, sides + 1))) @ n if sides > 0 else None + + roll_die(sides=6, n=10) + # [2, 6, 5, 2, 6, 2, 3, 1, 5, 2] + +This is already included standard in the utils of this package. Use +``sq.roll_die``. + +Bayesian inference +~~~~~~~~~~~~~~~~~~ + +1% of women at age forty who participate in routine screening have +breast cancer. 80% of women with breast cancer will get positive +mammographies. 9.6% of women without breast cancer will also get +positive mammographies. + +A woman in this age group had a positive mammography in a routine +screening. What is the probability that she actually has breast cancer? + +We can approximate the answer with a Bayesian network (uses rejection +sampling): + +.. code:: python + + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import M + + def mammography(has_cancer): + return sq.event(0.8 if has_cancer else 0.096) + + def define_event(): + cancer = ~sq.bernoulli(0.01) + return({'mammography': mammography(cancer), + 'cancer': cancer}) + + bayes.bayesnet(define_event, + find=lambda e: e['cancer'], + conditional_on=lambda e: e['mammography'], + n=1*M) + # 0.07723995880535531 + +Or if we have the information immediately on hand, we can directly +calculate it. Though this doesn’t work for very complex stuff. + +.. code:: python + + from squigglepy import bayes + bayes.simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096) + # 0.07763975155279504 + +You can also make distributions and update them: + +.. code:: python + + import matplotlib.pyplot as plt + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import K + import numpy as np + + print('Prior') + prior = sq.norm(1,5) + prior_samples = prior @ (10*K) + plt.hist(prior_samples, bins = 200) + plt.show() + print(sq.get_percentiles(prior_samples)) + print('Prior Mean: {} SD: {}'.format(np.mean(prior_samples), np.std(prior_samples))) + print('-') + + print('Evidence') + evidence = sq.norm(2,3) + evidence_samples = evidence @ (10*K) + plt.hist(evidence_samples, bins = 200) + plt.show() + print(sq.get_percentiles(evidence_samples)) + print('Evidence Mean: {} SD: {}'.format(np.mean(evidence_samples), np.std(evidence_samples))) + print('-') + + print('Posterior') + posterior = bayes.update(prior, evidence) + posterior_samples = posterior @ (10*K) + plt.hist(posterior_samples, bins = 200) + plt.show() + print(sq.get_percentiles(posterior_samples)) + print('Posterior Mean: {} SD: {}'.format(np.mean(posterior_samples), np.std(posterior_samples))) + + print('Average') + average = bayes.average(prior, evidence) + average_samples = average @ (10*K) + plt.hist(average_samples, bins = 200) + plt.show() + print(sq.get_percentiles(average_samples)) + print('Average Mean: {} SD: {}'.format(np.mean(average_samples), np.std(average_samples))) + +Example: Alarm net +^^^^^^^^^^^^^^^^^^ + +This is the alarm network from `Bayesian Artificial Intelligence - +Section +2.5.1 `__: + + Assume your house has an alarm system against burglary. + + You live in the seismically active area and the alarm system can get + occasionally set off by an earthquake. + + You have two neighbors, Mary and John, who do not know each other. If + they hear the alarm they call you, but this is not guaranteed. + + The chance of a burglary on a particular day is 0.1%. The chance of + an earthquake on a particular day is 0.2%. + + The alarm will go off 95% of the time with both a burglary and an + earthquake, 94% of the time with just a burglary, 29% of the time + with just an earthquake, and 0.1% of the time with nothing (total + false alarm). + + John will call you 90% of the time when the alarm goes off. But on 5% + of the days, John will just call to say “hi”. Mary will call you 70% + of the time when the alarm goes off. But on 1% of the days, Mary will + just call to say “hi”. + +.. code:: python + + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import M + + def p_alarm_goes_off(burglary, earthquake): + if burglary and earthquake: + return 0.95 + elif burglary and not earthquake: + return 0.94 + elif not burglary and earthquake: + return 0.29 + elif not burglary and not earthquake: + return 0.001 + + def p_john_calls(alarm_goes_off): + return 0.9 if alarm_goes_off else 0.05 + + def p_mary_calls(alarm_goes_off): + return 0.7 if alarm_goes_off else 0.01 + + def define_event(): + burglary_happens = sq.event(p=0.001) + earthquake_happens = sq.event(p=0.002) + alarm_goes_off = sq.event(p_alarm_goes_off(burglary_happens, earthquake_happens)) + john_calls = sq.event(p_john_calls(alarm_goes_off)) + mary_calls = sq.event(p_mary_calls(alarm_goes_off)) + return {'burglary': burglary_happens, + 'earthquake': earthquake_happens, + 'alarm_goes_off': alarm_goes_off, + 'john_calls': john_calls, + 'mary_calls': mary_calls} + + # What are the chances that both John and Mary call if an earthquake happens? + bayes.bayesnet(define_event, + n=1*M, + find=lambda e: (e['mary_calls'] and e['john_calls']), + conditional_on=lambda e: e['earthquake']) + # Result will be ~0.19, though it varies because it is based on a random sample. + # This also may take a minute to run. + + # If both John and Mary call, what is the chance there's been a burglary? + bayes.bayesnet(define_event, + n=1*M, + find=lambda e: e['burglary'], + conditional_on=lambda e: (e['mary_calls'] and e['john_calls'])) + # Result will be ~0.27, though it varies because it is based on a random sample. + # This will run quickly because there is a built-in cache. + # Use `cache=False` to not build a cache and `reload_cache=True` to recalculate the cache. + +Note that the amount of Bayesian analysis that squigglepy can do is +pretty limited. For more complex bayesian analysis, consider +`sorobn `__, +`pomegranate `__, +`bnlearn `__, or +`pyMC `__. + +Example: A Demonstration of the Monty Hall Problem +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code:: python + + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import K, M, B, T + + + def monte_hall(door_picked, switch=False): + doors = ['A', 'B', 'C'] + car_is_behind_door = ~sq.discrete(doors) + reveal_door = ~sq.discrete([d for d in doors if d != door_picked and d != car_is_behind_door]) + + if switch: + old_door_picked = door_picked + door_picked = [d for d in doors if d != old_door_picked and d != reveal_door][0] + + won_car = (car_is_behind_door == door_picked) + return won_car + + + def define_event(): + door = ~sq.discrete(['A', 'B', 'C']) + switch = sq.event(0.5) + return {'won': monte_hall(door_picked=door, switch=switch), + 'switched': switch} + + RUNS = 10*K + r = bayes.bayesnet(define_event, + find=lambda e: e['won'], + conditional_on=lambda e: e['switched'], + verbose=True, + n=RUNS) + print('Win {}% of the time when switching'.format(int(r * 100))) + + r = bayes.bayesnet(define_event, + find=lambda e: e['won'], + conditional_on=lambda e: not e['switched'], + verbose=True, + n=RUNS) + print('Win {}% of the time when not switching'.format(int(r * 100))) + + # Win 66% of the time when switching + # Win 34% of the time when not switching + +Example: More complex coin/dice interactions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + + Imagine that I flip a coin. If heads, I take a random die out of my + blue bag. If tails, I take a random die out of my red bag. The blue + bag contains only 6-sided dice. The red bag contains a 4-sided die, a + 6-sided die, a 10-sided die, and a 20-sided die. I then roll the + random die I took. What is the chance that I roll a 6? + +.. code:: python + + import squigglepy as sq + from squigglepy.numbers import K, M, B, T + from squigglepy import bayes + + def define_event(): + if sq.flip_coin() == 'heads': # Blue bag + return sq.roll_die(6) + else: # Red bag + return sq.discrete([4, 6, 10, 20]) >> sq.roll_die + + + bayes.bayesnet(define_event, + find=lambda e: e == 6, + verbose=True, + n=100*K) + # This run for me returned 0.12306 which is pretty close to the correct answer of 0.12292 + +Kelly betting +~~~~~~~~~~~~~ + +You can use probability generated, combine with a bankroll to determine +bet sizing using `Kelly +criterion `__. + +For example, if you want to Kelly bet and you’ve… + +- determined that your price (your probability of the event in question + happening / the market in question resolving in your favor) is $0.70 + (70%) +- see that the market is pricing at $0.65 +- you have a bankroll of $1000 that you are willing to bet + +You should bet as follows: + +.. code:: python + + import squigglepy as sq + kelly_data = sq.kelly(my_price=0.70, market_price=0.65, bankroll=1000) + kelly_data['kelly'] # What fraction of my bankroll should I bet on this? + # 0.143 + kelly_data['target'] # How much money should be invested in this? + # 142.86 + kelly_data['expected_roi'] # What is the expected ROI of this bet? + # 0.077 + +More examples +~~~~~~~~~~~~~ + +You can see more examples of squigglepy in action +`here `__. + +Run tests +--------- + +Use ``black .`` for formatting. + +Run +``ruff check . && pytest && pip3 install . && python3 tests/integration.py`` + +Disclaimers +----------- + +This package is unofficial and supported by myself and Rethink +Priorities. It is not affiliated with or associated with the Quantified +Uncertainty Research Institute, which maintains the Squiggle language +(in JavaScript). + +This package is also new and not yet in a stable production version, so +you may encounter bugs and other errors. Please report those so they can +be fixed. It’s also possible that future versions of the package may +introduce breaking changes. + +This package is available under an MIT License. + +Acknowledgements +---------------- + +- The primary author of this package is Peter Wildeford. Agustín + Covarrubias and Bernardo Baron contributed several key features and + developments. +- Thanks to Ozzie Gooen and the Quantified Uncertainty Research + Institute for creating and maintaining the original Squiggle + language. +- Thanks to Dawn Drescher for helping me implement math between + distributions. +- Thanks to Dawn Drescher for coming up with the idea to use ``~`` as a + shorthand for ``sample``, as well as helping me implement it. diff --git a/docs/source/conf.py b/docs/source/conf.py new file mode 100644 index 0000000..1a3efc3 --- /dev/null +++ b/docs/source/conf.py @@ -0,0 +1,179 @@ +# -*- coding: utf-8 -*- +# +# Configuration file for the Sphinx documentation builder. +# +# This file does only contain a selection of the most common options. For a +# full list see the documentation: +# http://www.sphinx-doc.org/en/master/config + +# -- Path setup -------------------------------------------------------------- + +# If extensions (or modules to document with autodoc) are in another directory, +# add these directories to sys.path here. If the directory is relative to the +# documentation root, use os.path.abspath to make it absolute, like shown here. +# +# import os +# import sys +# sys.path.insert(0, os.path.abspath('.')) + + +# -- Project information ----------------------------------------------------- + +project = 'Squigglepy' +copyright = '2023, Peter Wildeford' +author = 'Peter Wildeford' + +# The short X.Y version +version = '' +# The full version, including alpha/beta/rc tags +release = '' + + +# -- General configuration --------------------------------------------------- + +# If your documentation needs a minimal Sphinx version, state it here. +# +# needs_sphinx = '1.0' + +# Add any Sphinx extension module names here, as strings. They can be +# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom +# ones. +extensions = [ + 'sphinx.ext.autodoc', + 'sphinx.ext.imgmath', + 'sphinx.ext.viewcode', +] + +# Add any paths that contain templates here, relative to this directory. +templates_path = ['_templates'] + +# The suffix(es) of source filenames. +# You can specify multiple suffix as a list of string: +# +# source_suffix = ['.rst', '.md'] +source_suffix = '.rst' + +# The master toctree document. +master_doc = 'index' + +# The language for content autogenerated by Sphinx. Refer to documentation +# for a list of supported languages. +# +# This is also used if you do content translation via gettext catalogs. +# Usually you set "language" from the command line for these cases. +language = 'en' + +# List of patterns, relative to source directory, that match files and +# directories to ignore when looking for source files. +# This pattern also affects html_static_path and html_extra_path. +exclude_patterns = [] + +# The name of the Pygments (syntax highlighting) style to use. +pygments_style = None + + +# -- Options for HTML output ------------------------------------------------- + +# The theme to use for HTML and HTML Help pages. See the documentation for +# a list of builtin themes. +# +html_theme = "pydata_sphinx_theme" + +# Theme options are theme-specific and customize the look and feel of a theme +# further. For a list of options available for each theme, see the +# documentation. +# +# html_theme_options = {} + +# Add any paths that contain custom static files (such as style sheets) here, +# relative to this directory. They are copied after the builtin static files, +# so a file named "default.css" will overwrite the builtin "default.css". +html_static_path = ['_static'] + +# Custom sidebar templates, must be a dictionary that maps document names +# to template names. +# +# The default sidebars (for documents that don't match any pattern) are +# defined by theme itself. Builtin themes are using these templates by +# default: ``['localtoc.html', 'relations.html', 'sourcelink.html', +# 'searchbox.html']``. +# +# html_sidebars = {} + + +# -- Options for HTMLHelp output --------------------------------------------- + +# Output file base name for HTML help builder. +htmlhelp_basename = 'Squigglepydoc' + + +# -- Options for LaTeX output ------------------------------------------------ + +latex_elements = { + # The paper size ('letterpaper' or 'a4paper'). + # + # 'papersize': 'letterpaper', + + # The font size ('10pt', '11pt' or '12pt'). + # + # 'pointsize': '10pt', + + # Additional stuff for the LaTeX preamble. + # + # 'preamble': '', + + # Latex figure (float) alignment + # + # 'figure_align': 'htbp', +} + +# Grouping the document tree into LaTeX files. List of tuples +# (source start file, target name, title, +# author, documentclass [howto, manual, or own class]). +latex_documents = [ + (master_doc, 'Squigglepy.tex', 'Squigglepy Documentation', + 'Peter Wildeford', 'manual'), +] + + +# -- Options for manual page output ------------------------------------------ + +# One entry per manual page. List of tuples +# (source start file, name, description, authors, manual section). +man_pages = [ + (master_doc, 'squigglepy', 'Squigglepy Documentation', + [author], 1) +] + + +# -- Options for Texinfo output ---------------------------------------------- + +# Grouping the document tree into Texinfo files. List of tuples +# (source start file, target name, title, author, +# dir menu entry, description, category) +texinfo_documents = [ + (master_doc, 'Squigglepy', 'Squigglepy Documentation', + author, 'Squigglepy', 'One line description of project.', + 'Miscellaneous'), +] + + +# -- Options for Epub output ------------------------------------------------- + +# Bibliographic Dublin Core info. +epub_title = project + +# The unique identifier of the text. This can be a ISBN number +# or the project homepage. +# +# epub_identifier = '' + +# A unique identification for the text. +# +# epub_uid = '' + +# A list of files that should not be packed into the epub file. +epub_exclude_files = ['search.html'] + + +# -- Extension configuration ------------------------------------------------- diff --git a/docs/source/index.rst b/docs/source/index.rst new file mode 100644 index 0000000..9a79421 --- /dev/null +++ b/docs/source/index.rst @@ -0,0 +1,18 @@ +Squigglepy: Implementation of Squiggle in Python +================================================ + +`Squiggle `__ is a “simple +programming language for intuitive probabilistic estimation”. It serves +as its own standalone programming language with its own syntax, but it +is implemented in JavaScript. I like the features of Squiggle and intend +to use it frequently, but I also sometimes want to use similar +functionalities in Python, especially alongside other Python statistical +programming packages like Numpy, Pandas, and Matplotlib. The +**squigglepy** package here implements many Squiggle-like +functionalities in Python. + +.. toctree:: + :maxdepth: 2 + :caption: Contents: + +Check out the :doc:`README ` to get started. 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docs/source/reference/squigglepy.utils.rst create mode 100644 docs/source/reference/squigglepy.version.rst diff --git a/docs/Makefile b/docs/Makefile index 69fe55e..be9d2e1 100644 --- a/docs/Makefile +++ b/docs/Makefile @@ -16,4 +16,9 @@ help: # Catch-all target: route all unknown targets to Sphinx using the new # "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS). %: Makefile - @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) \ No newline at end of file + @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) + +buildapi: + sphinx-apidoc -efM ../squigglepy -o source/reference + @echo "Auto-generation of API documentation finished. 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+ + \ No newline at end of file diff --git a/docs/build/html/_modules/squigglepy/bayes.html b/docs/build/html/_modules/squigglepy/bayes.html new file mode 100644 index 0000000..c759bab --- /dev/null +++ b/docs/build/html/_modules/squigglepy/bayes.html @@ -0,0 +1,804 @@ + + + + + + + + + + squigglepy.bayes — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Source code for squigglepy.bayes

+"""
+This modules includes functions for Bayesian inference.
+"""
+
+import os
+import time
+import math
+import msgspec
+
+import numpy as np
+import pathos.multiprocessing as mp
+
+from datetime import datetime
+
+from .distributions import BetaDistribution, NormalDistribution, norm, beta, mixture
+from .utils import _core_cuts, _init_tqdm, _tick_tqdm, _flush_tqdm
+
+
+_squigglepy_internal_bayesnet_caches = {}
+
+
+

+[docs]
+def simple_bayes(likelihood_h, likelihood_not_h, prior):
+    """
+    Calculate Bayes rule.
+
+    p(h|e) = (p(e|h)*p(h)) / (p(e|h)*p(h) + p(e|~h)*(1-p(h)))
+    p(h|e) is called posterior
+    p(e|h) is called likelihood
+    p(h) is called prior
+
+    Parameters
+    ----------
+    likelihood_h : float
+        The likelihood (given that the hypothesis is true), aka p(e|h)
+    likelihood_not_h : float
+        The likelihood given the hypothesis is not true, aka p(e|~h)
+    prior : float
+        The prior probability, aka p(h)
+
+    Returns
+    -------
+    float
+        The result of Bayes rule, aka p(h|e)
+
+    Examples
+    --------
+    # Cancer example: prior of having cancer is 1%, the likelihood of a positive
+    # mammography given cancer is 80% (true positive rate), and the likelihood of
+    # a positive mammography given no cancer is 9.6% (false positive rate).
+    # Given this, what is the probability of cancer given a positive mammography?
+    >>> simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096)
+    0.07763975155279504
+    """
+    return (likelihood_h * prior) / (likelihood_h * prior + likelihood_not_h * (1 - prior))

+
+
+
+

+[docs]
+def bayesnet(
+    event_fn=None,
+    n=1,
+    find=None,
+    conditional_on=None,
+    reduce_fn=None,
+    raw=False,
+    memcache=True,
+    memcache_load=True,
+    memcache_save=True,
+    reload_cache=False,
+    dump_cache_file=None,
+    load_cache_file=None,
+    cache_file_primary=False,
+    verbose=False,
+    cores=1,
+):
+    """
+    Calculate a Bayesian network.
+
+    Allows you to find conditional probabilities of custom events based on
+    rejection sampling.
+
+    Parameters
+    ----------
+    event_fn : function
+        A function that defines the bayesian network
+    n : int
+        The number of samples to generate
+    find : a function or None
+        What do we want to know the probability of?
+    conditional_on : a function or None
+        When finding the probability, what do we want to condition on?
+    reduce_fn : a function or None
+        When taking all the results of the simulations, how do we aggregate them
+        into a final answer? Defaults to ``np.mean``.
+    raw : bool
+        If True, just return the results of each simulation without aggregating.
+    memcache : bool
+        If True, cache the results in-memory for future calculations. Each cache
+        will be matched based on the ``event_fn``. Default ``True``.
+    memcache_load : bool
+        If True, load cache from the in-memory. This will be true if ``memcache``
+        is True. Cache will be matched based on the ``event_fn``. Default ``True``.
+    memcache_save : bool
+        If True, save results to an in-memory cache. This will be true if ``memcache``
+        is True. Cache will be matched based on the ``event_fn``. Default ``True``.
+    reload_cache : bool
+        If True, any existing cache will be ignored and recalculated. Default ``False``.
+    dump_cache_file : str or None
+        If present, will write out the cache to a binary file with this path with
+        ``.sqlcache`` appended to the file name.
+    load_cache_file : str or None
+        If present, will first attempt to load and use a cache from a file with this
+        path with ``.sqlcache`` appended to the file name.
+    cache_file_primary : bool
+        If both an in-memory cache and file cache are present, the file
+        cache will be used for the cache if this is True, and the in-memory cache
+        will be used otherwise. Defaults to False.
+    verbose : bool
+        If True, will print out statements on computational progress.
+    cores : int
+        If 1, runs on a single core / process. If greater than 1, will run on a multiprocessing
+        pool with that many cores / processes.
+
+    Returns
+    -------
+    various
+        The result of ``reduce_fn`` on ``n`` simulations of ``event_fn``.
+
+    Examples
+    --------
+    # Cancer example: prior of having cancer is 1%, the likelihood of a positive
+    # mammography given cancer is 80% (true positive rate), and the likelihood of
+    # a positive mammography given no cancer is 9.6% (false positive rate).
+    # Given this, what is the probability of cancer given a positive mammography?
+    >> def mammography(has_cancer):
+    >>    p = 0.8 if has_cancer else 0.096
+    >>    return bool(sq.sample(sq.bernoulli(p)))
+    >>
+    >> def define_event():
+    >>    cancer = sq.sample(sq.bernoulli(0.01))
+    >>    return({'mammography': mammography(cancer),
+    >>            'cancer': cancer})
+    >>
+    >> bayes.bayesnet(define_event,
+    >>                find=lambda e: e['cancer'],
+    >>                conditional_on=lambda e: e['mammography'],
+    >>                n=1*M)
+    0.07723995880535531
+    """
+    events = None
+    if memcache is True:
+        memcache_load = True
+        memcache_save = True
+    elif memcache is False:
+        memcache_load = False
+        memcache_save = False
+    has_in_mem_cache = event_fn in _squigglepy_internal_bayesnet_caches
+    cache_path = load_cache_file + ".sqcache" if load_cache_file else None
+    has_file_cache = os.path.exists(cache_path) if load_cache_file else False
+
+    if load_cache_file or dump_cache_file or cores > 1:
+        encoder = msgspec.msgpack.Encoder()
+        decoder = msgspec.msgpack.Decoder()
+
+    if load_cache_file and not has_file_cache and verbose:
+        print("Warning: cache file `{}.sqcache` not found.".format(load_cache_file))
+
+    if not reload_cache:
+        if load_cache_file and has_file_cache and (not has_in_mem_cache or cache_file_primary):
+            if verbose:
+                print("Loading from cache file (`{}`)...".format(cache_path))
+            with open(cache_path, "rb") as f:
+                events = decoder.decode(f.read())
+
+        elif memcache_load and has_in_mem_cache:
+            if verbose:
+                print("Loading from in-memory cache...")
+            events = _squigglepy_internal_bayesnet_caches.get(event_fn)
+
+        if events:
+            if events["metadata"]["n"] < n:
+                raise ValueError(
+                    ("insufficient samples - {} results cached but " + "requested {}").format(
+                        events["metadata"]["n"], n
+                    )
+                )
+
+            events = events["events"]
+            if verbose:
+                print("...Loaded")
+
+    elif verbose:
+        print("Reloading cache...")
+
+    if events is None:
+        if event_fn is None:
+            return None
+
+        def run_event_fn(pbar=None, total_cores=1):
+            _tick_tqdm(pbar, total_cores)
+            return event_fn()
+
+        if cores == 1:
+            if verbose:
+                print("Generating Bayes net...")
+            r_ = range(n)
+            pbar = _init_tqdm(verbose=verbose, total=n)
+            events = [run_event_fn(pbar=pbar, total_cores=1) for _ in r_]
+            _flush_tqdm(pbar)
+        else:
+            if verbose:
+                print("Generating Bayes net with {} cores...".format(cores))
+            with mp.ProcessingPool(cores) as pool:
+                cuts = _core_cuts(n, cores)
+
+                def multicore_event_fn(core, total_cores=1, verbose=False):
+                    r_ = range(cuts[core])
+                    pbar = _init_tqdm(verbose=verbose, total=n)
+                    batch = [run_event_fn(pbar=pbar, total_cores=total_cores) for _ in r_]
+                    _flush_tqdm(pbar)
+
+                    if verbose:
+                        print("Shuffling data...")
+
+                    while not os.path.exists("test-core-{}.sqcache".format(core)):
+                        with open("test-core-{}.sqcache".format(core), "wb") as outfile:
+                            encoder = msgspec.msgpack.Encoder()
+                            outfile.write(encoder.encode(batch))
+                        if verbose:
+                            print("Writing data...")
+                            time.sleep(1)
+
+                pool_results = pool.amap(multicore_event_fn, list(range(cores - 1)))
+                multicore_event_fn(cores - 1, total_cores=cores, verbose=verbose)
+                if verbose:
+                    print("Waiting for other cores...")
+                while not pool_results.ready():
+                    if verbose:
+                        print(".", end="", flush=True)
+                    time.sleep(1)
+
+        if cores > 1:
+            if verbose:
+                print("Collecting data...")
+            events = []
+            pbar = _init_tqdm(verbose=verbose, total=cores)
+            for c in range(cores):
+                _tick_tqdm(pbar, 1)
+                with open("test-core-{}.sqcache".format(c), "rb") as infile:
+                    events += decoder.decode(infile.read())
+                os.remove("test-core-{}.sqcache".format(c))
+            _flush_tqdm(pbar)
+            if verbose:
+                print("...Collected!")
+
+    metadata = {"n": n, "last_generated": datetime.now()}
+    cache_data = {"events": events, "metadata": metadata}
+    if memcache_save and (not has_in_mem_cache or reload_cache):
+        if verbose:
+            print("Caching in-memory...")
+        _squigglepy_internal_bayesnet_caches[event_fn] = cache_data
+        if verbose:
+            print("...Cached!")
+
+    if dump_cache_file:
+        cache_path = dump_cache_file + ".sqcache"
+        if verbose:
+            print("Writing cache to file `{}`...".format(cache_path))
+        with open(cache_path, "wb") as f:
+            f.write(encoder.encode(cache_data))
+        if verbose:
+            print("...Cached!")
+
+    if conditional_on is not None:
+        if verbose:
+            print("Filtering conditional...")
+        events = [e for e in events if conditional_on(e)]
+
+    if len(events) < 1:
+        raise ValueError("insufficient samples for condition")
+
+    if conditional_on and verbose:
+        print("...Filtered!")
+
+    if find is None:
+        if verbose:
+            print("...Reducing")
+        events = events if reduce_fn is None else reduce_fn(events)
+        if verbose:
+            print("...Reduced!")
+    else:
+        if verbose:
+            print("...Finding")
+        events = [find(e) for e in events]
+        if verbose:
+            print("...Found!")
+        if not raw:
+            if verbose:
+                print("...Reducing")
+            reduce_fn = np.mean if reduce_fn is None else reduce_fn
+            events = reduce_fn(events)
+            if verbose:
+                print("...Reduced!")
+    if verbose:
+        print("...All done!")
+    return events

+
+
+
+

+[docs]
+def update(prior, evidence, evidence_weight=1):
+    """
+    Update a distribution.
+
+    Starting with a prior distribution, use Bayesian inference to perform an update,
+    producing a posterior distribution from the evidence distribution.
+
+    Parameters
+    ----------
+    prior : Distribution
+        The prior distribution. Currently must either be normal or beta type. Other
+        types are not yet supported.
+    evidence : Distribution
+        The distribution used to update the prior. Currently must either be normal
+        or beta type. Other types are not yet supported.
+    evidence_weight : float
+        How much weight to put on the evidence distribution? Currently this only matters
+        for normal distributions, where this should be equivalent to the sample weight.
+
+    Returns
+    -------
+    Distribution
+        The posterior distribution
+
+    Examples
+    --------
+    >> prior = sq.norm(1,5)
+    >> evidence = sq.norm(2,3)
+    >> bayes.update(prior, evidence)
+    <Distribution> norm(mean=2.53, sd=0.29)
+    """
+    if isinstance(prior, NormalDistribution) and isinstance(evidence, NormalDistribution):
+        prior_mean = prior.mean
+        prior_var = prior.sd**2
+        evidence_mean = evidence.mean
+        evidence_var = evidence.sd**2
+        return norm(
+            mean=(
+                (evidence_var * prior_mean + evidence_weight * (prior_var * evidence_mean))
+                / (evidence_weight * prior_var + evidence_var)
+            ),
+            sd=math.sqrt(
+                (evidence_var * prior_var) / (evidence_weight * prior_var + evidence_var)
+            ),
+        )
+    elif isinstance(prior, BetaDistribution) and isinstance(evidence, BetaDistribution):
+        prior_a = prior.a
+        prior_b = prior.b
+        evidence_a = evidence.a
+        evidence_b = evidence.b
+        return beta(prior_a + evidence_a, prior_b + evidence_b)
+    elif type(prior) != type(evidence):
+        print(type(prior), type(evidence))
+        raise ValueError("can only update distributions of the same type.")
+    else:
+        raise ValueError("type `{}` not supported.".format(prior.__class__.__name__))

+
+
+
+

+[docs]
+def average(prior, evidence, weights=[0.5, 0.5], relative_weights=None):
+    """
+    Average two distributions.
+
+    Parameters
+    ----------
+    prior : Distribution
+        The prior distribution.
+    evidence : Distribution
+        The distribution used to average with the prior.
+    weights : list or np.array or float
+        How much weight to put on ``prior`` versus ``evidence`` when averaging? If
+        only one weight is passed, the other weight will be inferred to make the
+        total weights sum to 1. Defaults to 50-50 weights.
+    relative_weights : list or None
+        Relative weights, which if given will be weights that are normalized
+        to sum to 1.
+
+    Returns
+    -------
+    Distribution
+        A mixture distribution that accords weights to ``prior`` and ``evidence``.
+
+    Examples
+    --------
+    >> prior = sq.norm(1,5)
+    >> evidence = sq.norm(2,3)
+    >> bayes.average(prior, evidence)
+    <Distribution> mixture
+    """
+    return mixture(dists=[prior, evidence], weights=weights, relative_weights=relative_weights)

+
+
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+ + © Copyright 2023, Peter Wildeford. +
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+ +

Source code for squigglepy.correlation

+"""
+This module implements the Iman-Conover method for inducing correlations between distributions.
+
+Some of the code has been adapted from Abraham Lee's mcerp package (https://github.com/tisimst/mcerp/).
+"""
+
+# Parts of `induce_correlation` are licensed as follows:
+
+# BSD 3-Clause License
+
+# Copyright (c) 2018, Abraham Lee
+# All rights reserved.
+
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions are met:
+
+# * Redistributions of source code must retain the above copyright notice, this
+#   list of conditions and the following disclaimer.
+
+# * Redistributions in binary form must reproduce the above copyright notice,
+#   this list of conditions and the following disclaimer in the documentation
+#   and/or other materials provided with the distribution.
+
+# * Neither the name of the copyright holder nor the names of its
+#   contributors may be used to endorse or promote products derived from
+#   this software without specific prior written permission.
+
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+import numpy as np
+from scipy.linalg import cholesky
+from scipy.stats import rankdata, spearmanr
+from scipy.stats.distributions import norm as _scipy_norm
+from numpy.typing import NDArray
+from copy import deepcopy
+
+from typing import TYPE_CHECKING, Union
+
+if TYPE_CHECKING:
+    from .distributions import OperableDistribution
+
+
+

+[docs]
+def correlate(
+    variables: tuple[OperableDistribution, ...],
+    correlation: Union[NDArray[np.float64], list[list[float]], np.float64, float],
+    tolerance: Union[float, np.float64, None] = 0.05,
+    _min_unique_samples: int = 100,
+):
+    """
+    Correlate a set of variables according to a rank correlation matrix.
+
+    This employs the Iman-Conover method to induce the correlation while
+    preserving the original marginal distributions.
+
+    This method works on a best-effort basis, and may fail to induce the desired
+    correlation depending on the distributions provided. An exception will be raised
+    if that's the case.
+
+    Parameters
+    ----------
+    variables : tuple of distributions
+        The variables to correlate as a tuple of distributions.
+
+        The distributions must be able to produce enough unique samples for the method
+        to be able to induce the desired correlation by shuffling the samples.
+
+        Discrete distributions are notably hard to correlate this way,
+        as it's common for them to result in very few unique samples.
+
+    correlation : 2d-array or float
+        An n-by-n array that defines the desired Spearman rank correlation coefficients.
+        This matrix must be symmetric and positive semi-definite; and must not be confused with
+        a covariance matrix.
+
+        Correlation parameters can only be between -1 and 1, exclusive
+        (including extremely close approximations).
+
+        If a float is provided, all variables will be correlated with the same coefficient.
+
+    tolerance : float, optional
+        If provided, overrides the absolute tolerance used to check if the resulting
+        correlation matrix matches the desired correlation matrix. Defaults to 0.05.
+
+        Checking can also be disabled by passing None.
+
+    Returns
+    -------
+    correlated_variables : tuple of distributions
+        The correlated variables as a tuple of distributions in the same order as
+        the input variables.
+
+    Examples
+    --------
+    Suppose we want to correlate two variables with a correlation coefficient of 0.65:
+    >>> solar_radiation, temperature = sq.gamma(300, 100), sq.to(22, 28)
+    >>> solar_radiation, temperature = sq.correlate((solar_radiation, temperature), 0.7)
+    >>> print(np.corrcoef(solar_radiation @ 1000, temperature @ 1000)[0, 1])
+        0.6975960649767123
+
+    Or you could pass a correlation matrix:
+    >>> funding_gap, cost_per_delivery, effect_size = (
+            sq.to(20_000, 80_000), sq.to(30, 80), sq.beta(2, 5)
+        )
+    >>> funding_gap, cost_per_delivery, effect_size = sq.correlate(
+            (funding_gap, cost_per_delivery, effect_size),
+            [[1, 0.6, -0.5], [0.6, 1, -0.2], [-0.5, -0.2, 1]]
+        )
+    >>> print(np.corrcoef(funding_gap @ 1000, cost_per_delivery @ 1000, effect_size @ 1000))
+        array([[ 1.      ,  0.580520  , -0.480149],
+               [ 0.580962,  1.        , -0.187831],
+               [-0.480149, -0.187831  ,  1.        ]])
+
+    """
+    if not isinstance(variables, tuple):
+        variables = tuple(variables)
+
+    if len(variables) < 2:
+        raise ValueError("You must provide at least two variables to correlate.")
+
+    assert all(v.correlation_group is None for v in variables)
+
+    # Convert a float to a correlation matrix
+    if (
+        isinstance(correlation, float)
+        or isinstance(correlation, np.floating)
+        or isinstance(correlation, int)
+    ):
+        correlation_parameter = np.float64(correlation)
+
+        assert (
+            -1 < correlation_parameter < 1
+        ), "Correlation parameter must be between -1 and 1, exclusive."
+        # Generate a correlation matrix with
+        # pairwise correlations equal to the correlation parameter
+        correlation_matrix: NDArray[np.float64] = np.full(
+            (len(variables), len(variables)), correlation_parameter
+        )
+        # Set the diagonal to 1
+        np.fill_diagonal(correlation_matrix, 1)
+    else:
+        # Coerce the correlation matrix into a numpy array
+        correlation_matrix: NDArray[np.float64] = np.array(correlation, dtype=np.float64)
+
+    tolerance = float(tolerance) if tolerance is not None else None
+
+    # Deepcopy the variables to avoid modifying the originals
+    variables = deepcopy(variables)
+
+    # Create the correlation group
+    CorrelationGroup(variables, correlation_matrix, tolerance, _min_unique_samples)
+
+    return variables

+
+
+
+

+[docs]
+@dataclass
+class CorrelationGroup:
+    """
+    An object that holds metadata for a group of correlated distributions.
+    This object is not intended to be used directly by the user, but
+    rather during sampling to induce correlations between distributions.
+    """
+
+    correlated_dists: tuple[OperableDistribution]
+    correlation_matrix: NDArray[np.float64]
+    correlation_tolerance: Union[float, None] = 0.05
+    min_unique_samples: int = 100
+
+    def __post_init__(self):
+        # Check that the correlation matrix is square of the expected size
+        assert (
+            self.correlation_matrix.shape[0]
+            == self.correlation_matrix.shape[1]
+            == len(self.correlated_dists)
+        ), "Correlation matrix must be square, and of the length of the number of dists. provided."
+
+        # Check that the diagonal of the correlation matrix is all ones
+        assert np.all(np.diag(self.correlation_matrix) == 1), "Diagonal must be all ones."
+
+        # Check that values are between -1 and 1
+        assert (
+            -1 <= np.min(self.correlation_matrix) and np.max(self.correlation_matrix) <= 1
+        ), "Correlation matrix values must be between -1 and 1."
+
+        # Check that the correlation matrix is positive semi-definite
+        assert np.all(
+            np.linalg.eigvals(self.correlation_matrix) >= 0
+        ), "Matrix must be positive semi-definite."
+
+        # Check that the correlation matrix is symmetric
+        assert np.all(
+            self.correlation_matrix == self.correlation_matrix.T
+        ), "Matrix must be symmetric."
+
+        # Link the correlation group to each distribution
+        for dist in self.correlated_dists:
+            dist.correlation_group = self
+
+

+[docs]
+    def induce_correlation(self, data: NDArray[np.float64]) -> NDArray[np.float64]:
+        """
+        Induce a set of correlations on a column-wise dataset
+
+        Parameters
+        ----------
+        data : 2d-array
+            An m-by-n array where m is the number of samples and n is the
+            number of independent variables, each column of the array corresponding
+            to each variable
+        corrmat : 2d-array
+            An n-by-n array that defines the desired correlation coefficients
+            (between -1 and 1). Note: the matrix must be symmetric and
+            positive-definite in order to induce.
+
+        Returns
+        -------
+        new_data : 2d-array
+            An m-by-n array that has the desired correlations.
+
+        """
+        # Check that each column doesn't have too little unique values
+        for column in data.T:
+            if not self.has_sufficient_sample_diversity(column):
+                raise ValueError(
+                    "The data has too many repeated values to induce a correlation. "
+                    "This might be because of too few samples, or too many repeated samples."
+                )
+
+        # If the correlation matrix is the identity matrix, just return the data
+        if np.all(self.correlation_matrix == np.eye(self.correlation_matrix.shape[0])):
+            return data
+
+        # Create a rank-matrix
+        data_rank = np.vstack([rankdata(datai, method="min") for datai in data.T]).T
+
+        # Generate van der Waerden scores
+        data_rank_score = data_rank / (data_rank.shape[0] + 1.0)
+        data_rank_score = _scipy_norm(0, 1).ppf(data_rank_score)
+
+        # Calculate the lower triangular matrix of the Cholesky decomposition
+        # of the desired correlation matrix
+        p = cholesky(self.correlation_matrix, lower=True)
+
+        # Calculate the current correlations
+        t = np.corrcoef(data_rank_score, rowvar=False)
+
+        # Calculate the lower triangular matrix of the Cholesky decomposition
+        # of the current correlation matrix
+        q = cholesky(t, lower=True)
+
+        # Calculate the re-correlation matrix
+        s = np.dot(p, np.linalg.inv(q))
+
+        # Calculate the re-sampled matrix
+        new_data = np.dot(data_rank_score, s.T)
+
+        # Create the new rank matrix
+        new_data_rank = np.vstack([rankdata(datai, method="min") for datai in new_data.T]).T
+
+        # Sort the original data according to the new rank matrix
+        self._sort_data_according_to_rank(data, data_rank, new_data_rank)
+
+        # # Check correlation
+        if self.correlation_tolerance:
+            self._check_empirical_correlation(data)
+
+        return data

+
+
+    def _sort_data_according_to_rank(
+        self,
+        data: NDArray[np.float64],
+        data_rank: NDArray[np.float64],
+        new_data_rank: NDArray[np.float64],
+    ):
+        """Sorts the original data according to new_data_rank, in place."""
+        assert (
+            data.shape == data_rank.shape == new_data_rank.shape
+        ), "All input arrays must have the same shape"
+        for i in range(data.shape[1]):
+            _, order = np.unique(
+                np.hstack((data_rank[:, i], new_data_rank[:, i])), return_inverse=True
+            )
+            old_order = order[: new_data_rank.shape[0]]
+            new_order = order[-new_data_rank.shape[0] :]
+            tmp = data[np.argsort(old_order), i][new_order]
+            data[:, i] = tmp[:]
+
+    def _check_empirical_correlation(self, samples: NDArray[np.float64]):
+        """
+        Ensures that the empirical correlation matrix is
+        the same as the desired correlation matrix.
+        """
+        assert self.correlation_tolerance is not None
+
+        # Compute the empirical correlation matrix
+        empirical_correlation = spearmanr(samples).statistic
+        if len(self.correlated_dists) == 2:
+            # empirical_correlation is a scalar
+            properly_correlated = np.isclose(
+                empirical_correlation,
+                self.correlation_matrix[0, 1],
+                atol=self.correlation_tolerance,
+                rtol=0,
+            )
+        else:
+            # empirical_correlation is a matrix
+            properly_correlated = np.allclose(
+                empirical_correlation,
+                self.correlation_matrix,
+                atol=self.correlation_tolerance,
+                rtol=0,
+            )
+        if not properly_correlated:
+            raise RuntimeError(
+                "Failed to induce the desired correlation between samples. "
+                "This might be because of too little diversity in the samples. "
+                "You can relax the tolerance by passing `tolerance` to correlate()."
+            )
+
+

+[docs]
+    def has_sufficient_sample_diversity(
+        self,
+        samples: NDArray[np.float64],
+        relative_threshold: float = 0.7,
+        absolute_threshold=None,
+    ) -> bool:
+        """
+        Check if there is there are sufficient unique samples to work with in the data.
+        """
+
+        if absolute_threshold is None:
+            absolute_threshold = self.min_unique_samples
+
+        unique_samples = len(np.unique(samples, axis=0))
+        n_samples = len(samples)
+
+        diversity = unique_samples / n_samples
+
+        return (diversity >= relative_threshold) and (unique_samples >= absolute_threshold)

+

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+ +
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+ +
+ + + + +
+
+ +
+ +
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+

+ + © Copyright 2023, Peter Wildeford. +
+ +

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+ +

Source code for squigglepy.distributions

+"""
+A collection of probability distributions and functions to operate on them.
+"""
+
+import operator
+import math
+import numpy as np
+import scipy.stats
+
+from typing import Optional, Union
+
+from .utils import _process_weights_values, _is_numpy, is_dist, _round
+from .version import __version__
+from .correlation import CorrelationGroup
+
+from collections.abc import Iterable
+
+from abc import ABC, abstractmethod
+
+
+

+[docs]
+class BaseDistribution(ABC):
+    def __init__(self):
+        self.x = None
+        self.y = None
+        self.n = None
+        self.p = None
+        self.t = None
+        self.a = None
+        self.b = None
+        self.shape = None
+        self.scale = None
+        self.credibility = None
+        self.mean = None
+        self.sd = None
+        self.left = None
+        self.mode = None
+        self.right = None
+        self.fn = None
+        self.fn_str = None
+        self.lclip = None
+        self.rclip = None
+        self.lam = None
+        self.df = None
+        self.items = None
+        self.dists = None
+        self.weights = None
+        self._version = __version__
+
+        # Correlation metadata
+        self.correlation_group: Optional[CorrelationGroup] = None
+        self._correlated_samples: Optional[np.ndarray] = None
+
+    @abstractmethod
+    def __str__(self) -> str:
+        ...
+
+    def __repr__(self):
+        if self.correlation_group:
+            return (
+                self.__str__() + f" (version {self._version}, corr_group {self.correlation_group})"
+            )
+        return self.__str__() + f" (version {self._version})"

+
+
+
+

+[docs]
+class OperableDistribution(BaseDistribution):
+    def __init__(self):
+        super().__init__()
+
+

+[docs]
+    def plot(self, num_samples=None, bins=None):
+        """
+        Plot a histogram of the samples.
+
+        Parameters
+        ----------
+        num_samples : int
+            The number of samples to draw for plotting. Defaults to 1000 if not set.
+        bins : int
+            The number of bins to plot. Defaults to 200 if not set.
+
+        Examples
+        --------
+        >>> sq.norm(5, 10).plot()
+        """
+        from matplotlib import pyplot as plt
+
+        num_samples = 1000 if num_samples is None else num_samples
+        bins = 200 if bins is None else bins
+
+        samples = self @ num_samples
+
+        plt.hist(samples, bins=bins)
+        plt.show()

+
+
+    def __invert__(self):
+        from .samplers import sample
+
+        return sample(self)
+
+    def __matmul__(self, n):
+        try:
+            n = int(n)
+        except ValueError:
+            raise ValueError("number of samples must be an integer")
+        from .samplers import sample
+
+        return sample(self, n=n)
+
+    def __rshift__(self, fn):
+        if callable(fn):
+            return fn(self)
+        elif isinstance(fn, ComplexDistribution):
+            return ComplexDistribution(self, fn.left, fn.fn, fn.fn_str, infix=False)
+        else:
+            raise ValueError
+
+    def __rmatmul__(self, n):
+        return self.__matmul__(n)
+
+    def __gt__(self, dist):
+        return ComplexDistribution(self, dist, operator.gt, ">")
+
+    def __ge__(self, dist):
+        return ComplexDistribution(self, dist, operator.ge, ">=")
+
+    def __lt__(self, dist):
+        return ComplexDistribution(self, dist, operator.lt, "<")
+
+    def __le__(self, dist):
+        return ComplexDistribution(self, dist, operator.le, "<=")
+
+    def __eq__(self, dist):
+        return ComplexDistribution(self, dist, operator.le, "==")
+
+    def __ne__(self, dist):
+        return ComplexDistribution(self, dist, operator.le, "!=")
+
+    def __neg__(self):
+        return ComplexDistribution(self, None, operator.neg, "-")
+
+    def __add__(self, dist):
+        return ComplexDistribution(self, dist, operator.add, "+")
+
+    def __radd__(self, dist):
+        return ComplexDistribution(dist, self, operator.add, "+")
+
+    def __sub__(self, dist):
+        return ComplexDistribution(self, dist, operator.sub, "-")
+
+    def __rsub__(self, dist):
+        return ComplexDistribution(dist, self, operator.sub, "-")
+
+    def __mul__(self, dist):
+        return ComplexDistribution(self, dist, operator.mul, "*")
+
+    def __rmul__(self, dist):
+        return ComplexDistribution(dist, self, operator.mul, "*")
+
+    def __truediv__(self, dist):
+        return ComplexDistribution(self, dist, operator.truediv, "/")
+
+    def __rtruediv__(self, dist):
+        return ComplexDistribution(dist, self, operator.truediv, "/")
+
+    def __floordiv__(self, dist):
+        return ComplexDistribution(self, dist, operator.floordiv, "//")
+
+    def __rfloordiv__(self, dist):
+        return ComplexDistribution(dist, self, operator.floordiv, "//")
+
+    def __pow__(self, dist):
+        return ComplexDistribution(self, dist, operator.pow, "**")
+
+    def __rpow__(self, dist):
+        return ComplexDistribution(dist, self, operator.pow, "**")
+
+    def __hash__(self):
+        return hash(repr(self))

+
+
+
+# Distribution are either discrete, continuous, or composite
+
+
+

+[docs]
+class DiscreteDistribution(OperableDistribution, ABC):
+    ...

+
+
+
+

+[docs]
+class ContinuousDistribution(OperableDistribution, ABC):
+    ...

+
+
+
+

+[docs]
+class CompositeDistribution(OperableDistribution):
+    def __init__(self):
+        super().__init__()
+        # Whether this distribution contains any correlated variables
+        self.contains_correlated: Optional[bool] = None
+
+    def __post_init__(self):
+        assert self.contains_correlated is not None, "contains_correlated must be set"
+
+    def _check_correlated(self, dists: Iterable) -> None:
+        for dist in dists:
+            if isinstance(dist, BaseDistribution) and dist.correlation_group is not None:
+                self.contains_correlated = True
+                break
+            if isinstance(dist, CompositeDistribution):
+                if dist.contains_correlated:
+                    self.contains_correlated = True
+                    break

+
+
+
+

+[docs]
+class ComplexDistribution(CompositeDistribution):
+    def __init__(self, left, right=None, fn=operator.add, fn_str="+", infix=True):
+        super().__init__()
+        self.left = left
+        self.right = right
+        self.fn = fn
+        self.fn_str = fn_str
+        self.infix = infix
+        self._check_correlated((left, right))
+
+    def __str__(self):
+        if self.right is None and self.infix:
+            if self.fn_str == "-":
+                out = "<Distribution> {}{}"
+            else:
+                out = "<Distribution> {} {}"
+            out = out.format(self.fn_str, str(self.left).replace("<Distribution> ", ""))
+        elif self.right is None and not self.infix:
+            out = "<Distribution> {}({})".format(
+                self.fn_str, str(self.left).replace("<Distribution> ", "")
+            )
+        elif self.right is not None and self.infix:
+            out = "<Distribution> {} {} {}".format(
+                str(self.left).replace("<Distribution> ", ""),
+                self.fn_str,
+                str(self.right).replace("<Distribution> ", ""),
+            )
+        elif self.right is not None and not self.infix:
+            out = "<Distribution> {}({}, {})"
+            out = out.format(
+                self.fn_str,
+                str(self.left).replace("<Distribution> ", ""),
+                str(self.right).replace("<Distribution> ", ""),
+            )
+        else:
+            raise ValueError
+        return out

+
+
+
+def _get_fname(f, name):
+    if name is None:
+        if isinstance(f, np.vectorize):
+            name = f.pyfunc.__name__
+        else:
+            name = f.__name__
+    return name
+
+
+

+[docs]
+def dist_fn(dist1, dist2=None, fn=None, name=None):
+    """
+    Initialize a distribution that has a custom function applied to the result.
+
+    The function won't be applied until the distribution is sampled.
+
+    Parameters
+    ----------
+    dist1 : Distribution or function or list
+        Typically, the distribution to apply the function to. Could also be a function
+        or list of functions if ``dist_fn`` is being used in a pipe.
+    dist2 : Distribution or function or list or None
+        Typically, the second distribution to apply the function to if the function takes
+        two arguments. Could also be a function or list of functions if ``dist_fn`` is
+        being used in a pipe.
+    fn : function or None
+        The function to apply to the distribution(s).
+    name : str or None
+        By default, ``fn.__name__`` will be used to name the function. But you can pass
+        a custom name.
+
+    Returns
+    -------
+    ComplexDistribution or function
+        This will be a lazy evaluation of the desired function that will then be calculated
+        when it is sampled.
+
+    Examples
+    --------
+    >>> def double(x):
+    >>>     return x * 2
+    >>> dist_fn(norm(0, 1), double)
+    <Distribution> double(norm(mean=0.5, sd=0.3))
+    >>> norm(0, 1) >> dist_fn(double)
+    <Distribution> double(norm(mean=0.5, sd=0.3))
+    """
+    if isinstance(dist1, list) and callable(dist1[0]) and dist2 is None and fn is None:
+        fn = dist1
+
+        def out_fn(d):
+            out = d
+            for f in fn:
+                out = ComplexDistribution(out, None, fn=f, fn_str=_get_fname(f, name), infix=False)
+            return out
+
+        return out_fn
+
+    if callable(dist1) and dist2 is None and fn is None:
+        return lambda d: dist_fn(d, fn=dist1)
+
+    if isinstance(dist2, list) and callable(dist2[0]) and fn is None:
+        fn = dist2
+        dist2 = None
+
+    if callable(dist2) and fn is None:
+        fn = dist2
+        dist2 = None
+
+    if not isinstance(fn, list):
+        fn = [fn]
+
+    out = dist1
+    for f in fn:
+        out = ComplexDistribution(out, dist2, fn=f, fn_str=_get_fname(f, name), infix=False)
+
+    return out

+
+
+
+

+[docs]
+def dist_max(dist1, dist2=None):
+    """
+    Initialize the calculation of the maximum value of two distributions.
+
+    The function won't be applied until the distribution is sampled.
+
+    Parameters
+    ----------
+    dist1 : Distribution
+        The distribution to sample and determine the max of.
+    dist2 : Distribution
+        The second distribution to sample and determine the max of.
+
+    Returns
+    -------
+    ComplexDistribution or function
+        This will be a lazy evaluation of the desired function that will then be calculated
+        when it is sampled.
+
+    Examples
+    --------
+    >>> dist_max(norm(0, 1), norm(1, 2))
+    <Distribution> max(norm(mean=0.5, sd=0.3), norm(mean=1.5, sd=0.3))
+    """
+    if is_dist(dist1) and dist2 is None:
+        return lambda d: dist_fn(d, dist1, np.maximum, name="max")
+    else:
+        return dist_fn(dist1, dist2, np.maximum, name="max")

+
+
+
+

+[docs]
+def dist_min(dist1, dist2=None):
+    """
+    Initialize the calculation of the minimum value of two distributions.
+
+    The function won't be applied until the distribution is sampled.
+
+    Parameters
+    ----------
+    dist1 : Distribution
+        The distribution to sample and determine the min of.
+    dist2 : Distribution
+        The second distribution to sample and determine the min of.
+
+    Returns
+    -------
+    ComplexDistribution or function
+        This will be a lazy evaluation of the desired function that will then be calculated
+
+    Examples
+    --------
+    >>> dist_min(norm(0, 1), norm(1, 2))
+    <Distribution> min(norm(mean=0.5, sd=0.3), norm(mean=1.5, sd=0.3))
+    """
+    if is_dist(dist1) and dist2 is None:
+        return lambda d: dist_fn(d, dist1, np.minimum, name="min")
+    else:
+        return dist_fn(dist1, dist2, np.minimum, name="min")

+
+
+
+

+[docs]
+def dist_round(dist1, digits=0):
+    """
+    Initialize the rounding of the output of the distribution.
+
+    The function won't be applied until the distribution is sampled.
+
+    Parameters
+    ----------
+    dist1 : Distribution
+        The distribution to sample and then round.
+    digits : int
+        The number of digits to round to.
+
+    Returns
+    -------
+    ComplexDistribution or function
+        This will be a lazy evaluation of the desired function that will then be calculated
+
+    Examples
+    --------
+    >>> dist_round(norm(0, 1))
+    <Distribution> round(norm(mean=0.5, sd=0.3), 0)
+    """
+    if isinstance(dist1, int) and digits == 0:
+        return lambda d: dist_round(d, digits=dist1)
+    else:
+        return dist_fn(dist1, digits, _round, name="round")

+
+
+
+

+[docs]
+def dist_ceil(dist1):
+    """
+    Initialize the ceiling rounding of the output of the distribution.
+
+    The function won't be applied until the distribution is sampled.
+
+    Parameters
+    ----------
+    dist1 : Distribution
+        The distribution to sample and then ceiling round.
+
+    Returns
+    -------
+    ComplexDistribution or function
+        This will be a lazy evaluation of the desired function that will then be calculated
+
+    Examples
+    --------
+    >>> dist_ceil(norm(0, 1))
+    <Distribution> ceil(norm(mean=0.5, sd=0.3))
+    """
+    return dist_fn(dist1, None, np.ceil)

+
+
+
+

+[docs]
+def dist_floor(dist1):
+    """
+    Initialize the floor rounding of the output of the distribution.
+
+    The function won't be applied until the distribution is sampled.
+
+    Parameters
+    ----------
+    dist1 : Distribution
+        The distribution to sample and then floor round.
+
+    Returns
+    -------
+    ComplexDistribution or function
+        This will be a lazy evaluation of the desired function that will then be calculated
+
+    Examples
+    --------
+    >>> dist_floor(norm(0, 1))
+    <Distribution> floor(norm(mean=0.5, sd=0.3))
+    """
+    return dist_fn(dist1, None, np.floor)

+
+
+
+

+[docs]
+def dist_log(dist1, base=math.e):
+    """
+    Initialize the log of the output of the distribution.
+
+    The function won't be applied until the distribution is sampled.
+
+    Parameters
+    ----------
+    dist1 : Distribution
+        The distribution to sample and then take the log of.
+
+    Returns
+    -------
+    ComplexDistribution or function
+        This will be a lazy evaluation of the desired function that will then be calculated
+
+    Examples
+    --------
+    >>> dist_log(norm(0, 1), 10)
+    <Distribution> log(norm(mean=0.5, sd=0.3), const(10))
+    """
+    return dist_fn(dist1, const(base), math.log)

+
+
+
+

+[docs]
+def dist_exp(dist1):
+    """
+    Initialize the exp of the output of the distribution.
+
+    The function won't be applied until the distribution is sampled.
+
+    Parameters
+    ----------
+    dist1 : Distribution
+        The distribution to sample and then take the exp of.
+
+    Returns
+    -------
+    ComplexDistribution or function
+        This will be a lazy evaluation of the desired function that will then be calculated
+
+    Examples
+    --------
+    >>> dist_exp(norm(0, 1))
+    <Distribution> exp(norm(mean=0.5, sd=0.3))
+    """
+    return dist_fn(dist1, None, math.exp)

+
+
+
+@np.vectorize
+def _lclip(n, val=None):
+    if val is None:
+        return n
+    else:
+        return val if n < val else n
+
+
+

+[docs]
+def lclip(dist1, val=None):
+    """
+    Initialize the clipping/bounding of the output of the distribution by the lower value.
+
+    The function won't be applied until the distribution is sampled.
+
+    Parameters
+    ----------
+    dist1 : Distribution or function
+        The distribution to clip. If this is a funciton, it will return a partial that will
+        be suitable for use in piping.
+    val : int or float or None
+        The value to use as the lower bound for clipping.
+
+    Returns
+    -------
+    ComplexDistribution or function
+        This will be a lazy evaluation of the desired function that will then be calculated
+
+    Examples
+    --------
+    >>> lclip(norm(0, 1), 0.5)
+    <Distribution> lclip(norm(mean=0.5, sd=0.3), 0.5)
+    """
+    if (isinstance(dist1, int) or isinstance(dist1, float)) and val is None:
+        return lambda d: lclip(d, dist1)
+    elif is_dist(dist1):
+        return dist_fn(dist1, val, _lclip, name="lclip")
+    else:
+        return _lclip(dist1, val)

+
+
+
+@np.vectorize
+def _rclip(n, val=None):
+    if val is None:
+        return n
+    else:
+        return val if n > val else n
+
+
+

+[docs]
+def rclip(dist1, val=None):
+    """
+    Initialize the clipping/bounding of the output of the distribution by the upper value.
+
+    The function won't be applied until the distribution is sampled.
+
+    Parameters
+    ----------
+    dist1 : Distribution or function
+        The distribution to clip. If this is a funciton, it will return a partial that will
+        be suitable for use in piping.
+    val : int or float or None
+        The value to use as the upper bound for clipping.
+
+    Returns
+    -------
+    ComplexDistribution or function
+        This will be a lazy evaluation of the desired function that will then be calculated
+
+    Examples
+    --------
+    >>> rclip(norm(0, 1), 0.5)
+    <Distribution> rclip(norm(mean=0.5, sd=0.3), 0.5)
+    """
+    if (isinstance(dist1, int) or isinstance(dist1, float)) and val is None:
+        return lambda d: rclip(d, dist1)
+    elif is_dist(dist1):
+        return dist_fn(dist1, val, _rclip, name="rclip")
+    else:
+        return _rclip(dist1, val)

+
+
+
+

+[docs]
+def clip(dist1, left, right=None):
+    """
+    Initialize the clipping/bounding of the output of the distribution.
+
+    The function won't be applied until the distribution is sampled.
+
+    Parameters
+    ----------
+    dist1 : Distribution or function
+        The distribution to clip. If this is a funciton, it will return a partial that will
+        be suitable for use in piping.
+    left : int or float or None
+        The value to use as the lower bound for clipping.
+    right : int or float or None
+        The value to use as the upper bound for clipping.
+
+    Returns
+    -------
+    ComplexDistribution or function
+        This will be a lazy evaluation of the desired function that will then be calculated
+
+    Examples
+    --------
+    >>> clip(norm(0, 1), 0.5, 0.9)
+    <Distribution> rclip(lclip(norm(mean=0.5, sd=0.3), 0.5), 0.9)
+    """
+    if (
+        (isinstance(dist1, int) or isinstance(dist1, float))
+        and (isinstance(left, int) or isinstance(left, float))
+        and right is None
+    ):
+        return lambda d: rclip(lclip(d, dist1), left)
+    else:
+        return rclip(lclip(dist1, left), right)

+
+
+
+

+[docs]
+class ConstantDistribution(DiscreteDistribution):
+    def __init__(self, x):
+        super().__init__()
+        self.x = x
+
+    def __str__(self):
+        return "<Distribution> const({})".format(self.x)

+
+
+
+

+[docs]
+def const(x):
+    """
+    Initialize a constant distribution.
+
+    Constant distributions always return the same value no matter what.
+
+    Parameters
+    ----------
+    x : anything
+        The value the constant distribution should always return.
+
+    Returns
+    -------
+    ConstantDistribution
+
+    Examples
+    --------
+    >>> const(1)
+    <Distribution> const(1)
+    """
+    return ConstantDistribution(x)

+
+
+
+

+[docs]
+class UniformDistribution(ContinuousDistribution):
+    def __init__(self, x, y):
+        super().__init__()
+        self.x = x
+        self.y = y
+        assert x < y, "x must be less than y"
+
+    def __str__(self):
+        return "<Distribution> uniform({}, {})".format(self.x, self.y)

+
+
+
+

+[docs]
+def uniform(x, y):
+    """
+    Initialize a uniform random distribution.
+
+    Parameters
+    ----------
+    x : float
+        The smallest value the uniform distribution will return.
+    y : float
+        The largest value the uniform distribution will return.
+
+    Returns
+    -------
+    UniformDistribution
+
+    Examples
+    --------
+    >>> uniform(0, 1)
+    <Distribution> uniform(0, 1)
+    """
+    return UniformDistribution(x=x, y=y)

+
+
+
+

+[docs]
+class NormalDistribution(ContinuousDistribution):
+    def __init__(self, x=None, y=None, mean=None, sd=None, credibility=90, lclip=None, rclip=None):
+        super().__init__()
+        self.x = x
+        self.y = y
+        self.credibility = credibility
+        self.mean = mean
+        self.sd = sd
+        self.lclip = lclip
+        self.rclip = rclip
+
+        if self.x is not None and self.y is not None and self.x > self.y:
+            raise ValueError("`high value` cannot be lower than `low value`")
+
+        if (self.x is None or self.y is None) and self.sd is None:
+            raise ValueError("must define either x/y or mean/sd")
+        elif (self.x is not None or self.y is not None) and self.sd is not None:
+            raise ValueError("must define either x/y or mean/sd -- cannot define both")
+        elif self.sd is not None and self.mean is None:
+            self.mean = 0
+
+        if self.mean is None and self.sd is None:
+            self.mean = (self.x + self.y) / 2
+            cdf_value = 0.5 + 0.5 * (self.credibility / 100)
+            normed_sigma = scipy.stats.norm.ppf(cdf_value)
+            self.sd = (self.y - self.mean) / normed_sigma
+
+    def __str__(self):
+        out = "<Distribution> norm(mean={}, sd={}".format(round(self.mean, 2), round(self.sd, 2))
+        if self.lclip is not None:
+            out += ", lclip={}".format(self.lclip)
+        if self.rclip is not None:
+            out += ", rclip={}".format(self.rclip)
+        out += ")"
+        return out

+
+
+
+

+[docs]
+def norm(
+    x=None, y=None, credibility=90, mean=None, sd=None, lclip=None, rclip=None
+) -> NormalDistribution:
+    """
+    Initialize a normal distribution.
+
+    Can be defined either via a credible interval from ``x`` to ``y`` (use ``credibility`` or
+    it will default to being a 90% CI) or defined via ``mean`` and ``sd``.
+
+    Parameters
+    ----------
+    x : float
+        The low value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
+    y : float
+        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
+    credibility : float
+        The range of the credibility interval. Defaults to 90. Ignored if the distribution is
+        defined instead by ``mean`` and ``sd``.
+    mean : float or None
+        The mean of the normal distribution. If not defined, defaults to 0.
+    sd : float
+        The standard deviation of the normal distribution.
+    lclip : float or None
+        If not None, any value below ``lclip`` will be coerced to ``lclip``.
+    rclip : float or None
+        If not None, any value below ``rclip`` will be coerced to ``rclip``.
+
+    Returns
+    -------
+    NormalDistribution
+
+    Examples
+    --------
+    >>> norm(0, 1)
+    <Distribution> norm(mean=0.5, sd=0.3)
+    >>> norm(mean=1, sd=2)
+    <Distribution> norm(mean=1, sd=2)
+    """
+    return NormalDistribution(
+        x=x, y=y, credibility=credibility, mean=mean, sd=sd, lclip=lclip, rclip=rclip
+    )

+
+
+
+

+[docs]
+class LognormalDistribution(ContinuousDistribution):
+    def __init__(
+        self,
+        x=None,
+        y=None,
+        norm_mean=None,
+        norm_sd=None,
+        lognorm_mean=None,
+        lognorm_sd=None,
+        credibility=90,
+        lclip=None,
+        rclip=None,
+    ):
+        super().__init__()
+        self.x = x
+        self.y = y
+        self.credibility = credibility
+        self.norm_mean = norm_mean
+        self.norm_sd = norm_sd
+        self.lognorm_mean = lognorm_mean
+        self.lognorm_sd = lognorm_sd
+        self.lclip = lclip
+        self.rclip = rclip
+
+        if self.x is not None and self.y is not None and self.x > self.y:
+            raise ValueError("`high value` cannot be lower than `low value`")
+        if self.x is not None and self.x <= 0:
+            raise ValueError("lognormal distribution must have values > 0")
+
+        if (self.x is None or self.y is None) and self.norm_sd is None and self.lognorm_sd is None:
+            raise ValueError(
+                ("must define only one of x/y, norm_mean/norm_sd, " "or lognorm_mean/lognorm_sd")
+            )
+        elif (self.x is not None or self.y is not None) and (
+            self.norm_sd is not None or self.lognorm_sd is not None
+        ):
+            raise ValueError(
+                ("must define only one of x/y, norm_mean/norm_sd, " "or lognorm_mean/lognorm_sd")
+            )
+        elif (self.norm_sd is not None or self.norm_mean is not None) and (
+            self.lognorm_sd is not None or self.lognorm_mean is not None
+        ):
+            raise ValueError(
+                ("must define only one of x/y, norm_mean/norm_sd, " "or lognorm_mean/lognorm_sd")
+            )
+        elif self.norm_sd is not None and self.norm_mean is None:
+            self.norm_mean = 0
+        elif self.lognorm_sd is not None and self.lognorm_mean is None:
+            self.lognorm_mean = 1
+
+        if self.x is not None:
+            self.norm_mean = (np.log(self.x) + np.log(self.y)) / 2
+            cdf_value = 0.5 + 0.5 * (self.credibility / 100)
+            normed_sigma = scipy.stats.norm.ppf(cdf_value)
+            self.norm_sd = (np.log(self.y) - self.norm_mean) / normed_sigma
+
+        if self.lognorm_sd is None:
+            self.lognorm_mean = np.exp(self.norm_mean + self.norm_sd**2 / 2)
+            self.lognorm_sd = (
+                (np.exp(self.norm_sd**2) - 1) * np.exp(2 * self.norm_mean + self.norm_sd**2)
+            ) ** 0.5
+        elif self.norm_sd is None:
+            self.norm_mean = np.log(
+                (self.lognorm_mean**2 / np.sqrt(self.lognorm_sd**2 + self.lognorm_mean**2))
+            )
+            self.norm_sd = np.sqrt(np.log(1 + self.lognorm_sd**2 / self.lognorm_mean**2))
+
+    def __str__(self):
+        out = "<Distribution> lognorm(lognorm_mean={}, lognorm_sd={}, norm_mean={}, norm_sd={}"
+        out = out.format(
+            round(self.lognorm_mean, 2),
+            round(self.lognorm_sd, 2),
+            round(self.norm_mean, 2),
+            round(self.norm_sd, 2),
+        )
+        if self.lclip is not None:
+            out += ", lclip={}".format(self.lclip)
+        if self.rclip is not None:
+            out += ", rclip={}".format(self.rclip)
+        out += ")"
+        return out

+
+
+
+

+[docs]
+def lognorm(
+    x=None,
+    y=None,
+    credibility=90,
+    norm_mean=None,
+    norm_sd=None,
+    lognorm_mean=None,
+    lognorm_sd=None,
+    lclip=None,
+    rclip=None,
+):
+    """
+    Initialize a lognormal distribution.
+
+    Can be defined either via a credible interval from ``x`` to ``y`` (use ``credibility`` or
+    it will default to being a 90% CI) or defined via ``mean`` and ``sd``.
+
+    Parameters
+    ----------
+    x : float
+        The low value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
+        Must be a value greater than 0.
+    y : float
+        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
+        Must be a value greater than 0.
+    credibility : float
+        The range of the credibility interval. Defaults to 90. Ignored if the distribution is
+        defined instead by ``mean`` and ``sd``.
+    norm_mean : float or None
+        The mean of the underlying normal distribution. If not defined, defaults to 0.
+    norm_sd : float
+        The standard deviation of the underlying normal distribution.
+    lognorm_mean : float or None
+        The mean of the lognormal distribution. If not defined, defaults to 1.
+    lognorm_sd : float
+        The standard deviation of the lognormal distribution.
+    lclip : float or None
+        If not None, any value below ``lclip`` will be coerced to ``lclip``.
+    rclip : float or None
+        If not None, any value below ``rclip`` will be coerced to ``rclip``.
+
+    Returns
+    -------
+    LognormalDistribution
+
+    Examples
+    --------
+    >>> lognorm(1, 10)
+    <Distribution> lognorm(lognorm_mean=4.04, lognorm_sd=3.21, norm_mean=1.15, norm_sd=0.7)
+    >>> lognorm(norm_mean=1, norm_sd=2)
+    <Distribution> lognorm(lognorm_mean=20.09, lognorm_sd=147.05, norm_mean=1, norm_sd=2)
+    >>> lognorm(lognorm_mean=1, lognorm_sd=2)
+    <Distribution> lognorm(lognorm_mean=1, lognorm_sd=2, norm_mean=-0.8, norm_sd=1.27)
+    """
+    return LognormalDistribution(
+        x=x,
+        y=y,
+        credibility=credibility,
+        norm_mean=norm_mean,
+        norm_sd=norm_sd,
+        lognorm_mean=lognorm_mean,
+        lognorm_sd=lognorm_sd,
+        lclip=lclip,
+        rclip=rclip,
+    )

+
+
+
+

+[docs]
+def to(
+    x, y, credibility=90, lclip=None, rclip=None
+) -> Union[LognormalDistribution, NormalDistribution]:
+    """
+    Initialize a distribution from ``x`` to ``y``.
+
+    The distribution will be lognormal by default, unless ``x`` is less than or equal to 0,
+    in which case it will become a normal distribution.
+
+    The distribution will default to be a 90% credible interval between ``x`` and ``y`` unless
+    ``credibility`` is passed.
+
+    Parameters
+    ----------
+    x : float
+        The low value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
+    y : float
+        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
+    credibility : float
+        The range of the credibility interval. Defaults to 90.
+    lclip : float or None
+        If not None, any value below ``lclip`` will be coerced to ``lclip``.
+    rclip : float or None
+        If not None, any value below ``rclip`` will be coerced to ``rclip``.
+
+    Returns
+    -------
+    ``LognormalDistribution`` if ``x`` > 0, otherwise a ``NormalDistribution``
+
+    Examples
+    --------
+    >>> to(1, 10)
+    <Distribution> lognorm(mean=1.15, sd=0.7)
+    >>> to(-10, 10)
+    <Distribution> norm(mean=0.0, sd=6.08)
+    """
+    if x > 0:
+        return lognorm(x=x, y=y, credibility=credibility, lclip=lclip, rclip=rclip)
+    else:
+        return norm(x=x, y=y, credibility=credibility, lclip=lclip, rclip=rclip)

+
+
+
+

+[docs]
+class BinomialDistribution(DiscreteDistribution):
+    def __init__(self, n, p):
+        super().__init__()
+        self.n = n
+        self.p = p
+        if self.p <= 0 or self.p >= 1:
+            raise ValueError("p must be between 0 and 1 (exclusive)")
+
+    def __str__(self):
+        return "<Distribution> binomial(n={}, p={})".format(self.n, self.p)

+
+
+
+

+[docs]
+def binomial(n, p):
+    """
+    Initialize a binomial distribution.
+
+    Parameters
+    ----------
+    n : int
+        The number of trials.
+    p : float
+        The probability of success for each trial. Must be between 0 and 1.
+
+    Returns
+    -------
+    BinomialDistribution
+
+    Examples
+    --------
+    >>> binomial(1, 0.1)
+    <Distribution> binomial(1, 0.1)
+    """
+    return BinomialDistribution(n=n, p=p)

+
+
+
+

+[docs]
+class BetaDistribution(ContinuousDistribution):
+    def __init__(self, a, b):
+        super().__init__()
+        self.a = a
+        self.b = b
+
+    def __str__(self):
+        return "<Distribution> beta(a={}, b={})".format(self.a, self.b)

+
+
+
+

+[docs]
+def beta(a, b):
+    """
+    Initialize a beta distribution.
+
+    Parameters
+    ----------
+    a : float
+        The alpha shape value of the distribution. Typically takes the value of the
+        number of trials that resulted in a success.
+    b : float
+        The beta shape value of the distribution. Typically takes the value of the
+        number of trials that resulted in a failure.
+
+    Returns
+    -------
+    BetaDistribution
+
+    Examples
+    --------
+    >>> beta(1, 2)
+    <Distribution> beta(1, 2)
+    """
+    return BetaDistribution(a, b)

+
+
+
+

+[docs]
+class BernoulliDistribution(DiscreteDistribution):
+    def __init__(self, p):
+        super().__init__()
+        if not isinstance(p, float) or isinstance(p, int):
+            raise ValueError("bernoulli p must be a float or int")
+        if p <= 0 or p >= 1:
+            raise ValueError("bernoulli p must be 0-1 (exclusive)")
+        self.p = p
+
+    def __str__(self):
+        return "<Distribution> bernoulli(p={})".format(self.p)

+
+
+
+

+[docs]
+def bernoulli(p):
+    """
+    Initialize a Bernoulli distribution.
+
+    Parameters
+    ----------
+    p : float
+        The probability of the binary event. Must be between 0 and 1.
+
+    Returns
+    -------
+    BernoulliDistribution
+
+    Examples
+    --------
+    >>> bernoulli(0.1)
+    <Distribution> bernoulli(p=0.1)
+    """
+    return BernoulliDistribution(p)

+
+
+
+

+[docs]
+class CategoricalDistribution(DiscreteDistribution):
+    def __init__(self, items):
+        super().__init__()
+        if not isinstance(items, dict) and not isinstance(items, list) and not _is_numpy(items):
+            raise ValueError("inputs to categorical must be a dict or list")
+        assert len(items) > 0, "inputs to categorical must be non-empty"
+        self.items = list(items) if _is_numpy(items) else items
+
+    def __str__(self):
+        return "<Distribution> categorical({})".format(self.items)

+
+
+
+

+[docs]
+def discrete(items):
+    """
+    Initialize a discrete distribution (aka categorical distribution).
+
+    Parameters
+    ----------
+    items : list or dict
+        The values that the discrete distribution will return and their associated
+        weights (or likelihoods of being returned when sampled).
+
+    Returns
+    -------
+    CategoricalDistribution
+
+    Examples
+    --------
+    >>> discrete({0: 0.1, 1: 0.9})  # 10% chance of returning 0, 90% chance of returning 1
+    <Distribution> categorical({0: 0.1, 1: 0.9})
+    >>> discrete([[0.1, 0], [0.9, 1]])  # Different notation for the same thing.
+    <Distribution> categorical([[0.1, 0], [0.9, 1]])
+    >>> discrete([0, 1, 2])  # When no weights are given, all have equal chance of happening.
+    <Distribution> categorical([0, 1, 2])
+    >>> discrete({'a': 0.1, 'b': 0.9})  # Values do not have to be numbers.
+    <Distribution> categorical({'a': 0.1, 'b': 0.9})
+    """
+    return CategoricalDistribution(items)

+
+
+
+

+[docs]
+class TDistribution(ContinuousDistribution):
+    def __init__(self, x=None, y=None, t=20, credibility=90, lclip=None, rclip=None):
+        super().__init__()
+        self.x = x
+        self.y = y
+        self.t = t
+        self.df = t
+        self.credibility = credibility
+        self.lclip = lclip
+        self.rclip = rclip
+
+        if (self.x is None or self.y is None) and not (self.x is None and self.y is None):
+            raise ValueError("must define either both `x` and `y` or neither.")
+        elif self.x is not None and self.y is not None and self.x > self.y:
+            raise ValueError("`high value` cannot be lower than `low value`")
+
+        if self.x is None:
+            self.credibility = None
+
+    def __str__(self):
+        if self.x is not None:
+            out = "<Distribution> tdist(x={}, y={}, t={}".format(self.x, self.y, self.t)
+        else:
+            out = "<Distribution> tdist(t={}".format(self.t)
+        if self.credibility != 90 and self.credibility is not None:
+            out += ", credibility={}".format(self.credibility)
+        if self.lclip is not None:
+            out += ", lclip={}".format(self.lclip)
+        if self.rclip is not None:
+            out += ", rclip={}".format(self.rclip)
+        out += ")"
+        return out

+
+
+
+

+[docs]
+def tdist(x=None, y=None, t=20, credibility=90, lclip=None, rclip=None):
+    """
+    Initialize a t-distribution.
+
+    Is defined either via a loose credible interval from ``x`` to ``y`` (use ``credibility`` or
+    it will default to being a 90% CI). Unlike the normal and lognormal distributions, this
+    credible interval is an approximation and is not precisely defined.
+
+    If ``x`` and ``y`` are not defined, can just return a classic t-distribution defined via
+    ``t`` as the number of degrees of freedom.
+
+    Parameters
+    ----------
+    x : float or None
+        The low value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
+    y : float or None
+        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
+    t : float
+        The number of degrees of freedom of the t-distribution. Defaults to 20.
+    credibility : float
+        The range of the credibility interval. Defaults to 90.
+    lclip : float or None
+        If not None, any value below ``lclip`` will be coerced to ``lclip``.
+    rclip : float or None
+        If not None, any value below ``rclip`` will be coerced to ``rclip``.
+
+    Returns
+    -------
+    TDistribution
+
+    Examples
+    --------
+    >>> tdist(0, 1, 2)
+    <Distribution> tdist(x=0, y=1, t=2)
+    >>> tdist()
+    <Distribution> tdist(t=1)
+    """
+    return TDistribution(x=x, y=y, t=t, credibility=credibility, lclip=lclip, rclip=rclip)

+
+
+
+

+[docs]
+class LogTDistribution(ContinuousDistribution):
+    def __init__(self, x=None, y=None, t=1, credibility=90, lclip=None, rclip=None):
+        super().__init__()
+        self.x = x
+        self.y = y
+        self.t = t
+        self.df = t
+        self.credibility = credibility
+        self.lclip = lclip
+        self.rclip = rclip
+
+        if (self.x is None or self.y is None) and not (self.x is None and self.y is None):
+            raise ValueError("must define either both `x` and `y` or neither.")
+        if self.x is not None and self.y is not None and self.x > self.y:
+            raise ValueError("`high value` cannot be lower than `low value`")
+        if self.x is not None and self.x <= 0:
+            raise ValueError("`low value` must be greater than 0.")
+
+        if self.x is None:
+            self.credibility = None
+
+    def __str__(self):
+        if self.x is not None:
+            out = "<Distribution> log_tdist(x={}, y={}, t={}".format(self.x, self.y, self.t)
+        else:
+            out = "<Distribution> log_tdist(t={}".format(self.t)
+        if self.credibility != 90 and self.credibility is not None:
+            out += ", credibility={}".format(self.credibility)
+        if self.lclip is not None:
+            out += ", lclip={}".format(self.lclip)
+        if self.rclip is not None:
+            out += ", rclip={}".format(self.rclip)
+        out += ")"
+        return out

+
+
+
+

+[docs]
+def log_tdist(x=None, y=None, t=1, credibility=90, lclip=None, rclip=None):
+    """
+    Initialize a log t-distribution, which is a t-distribution in log-space.
+
+    Is defined either via a loose credible interval from ``x`` to ``y`` (use ``credibility`` or
+    it will default to being a 90% CI). Unlike the normal and lognormal distributions, this
+    credible interval is an approximation and is not precisely defined.
+
+    If ``x`` and ``y`` are not defined, can just return a classic t-distribution defined via
+    ``t`` as the number of degrees of freedom, but in log-space.
+
+    Parameters
+    ----------
+    x : float or None
+        The low value of a credible interval defined by ``credibility``. Must be greater than 0.
+        Defaults to a 90% CI.
+    y : float or None
+        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
+    t : float
+        The number of degrees of freedom of the t-distribution. Defaults to 1.
+    credibility : float
+        The range of the credibility interval. Defaults to 90.
+    lclip : float or None
+        If not None, any value below ``lclip`` will be coerced to ``lclip``.
+    rclip : float or None
+        If not None, any value below ``rclip`` will be coerced to ``rclip``.
+
+    Returns
+    -------
+    LogTDistribution
+
+    Examples
+    --------
+    >>> log_tdist(0, 1, 2)
+    <Distribution> log_tdist(x=0, y=1, t=2)
+    >>> log_tdist()
+    <Distribution> log_tdist(t=1)
+    """
+    return LogTDistribution(x=x, y=y, t=t, credibility=credibility, lclip=lclip, rclip=rclip)

+
+
+
+

+[docs]
+class TriangularDistribution(ContinuousDistribution):
+    def __init__(self, left, mode, right):
+        super().__init__()
+        if left > mode:
+            raise ValueError("left must be less than or equal to mode")
+        if right < mode:
+            raise ValueError("right must be greater than or equal to mode")
+        if left == right:
+            raise ValueError("left and right must be different")
+        self.left = left
+        self.mode = mode
+        self.right = right
+
+    def __str__(self):
+        return "<Distribution> triangular({}, {}, {})".format(self.left, self.mode, self.right)

+
+
+
+

+[docs]
+def triangular(left, mode, right, lclip=None, rclip=None):
+    """
+    Initialize a triangular distribution.
+
+    Parameters
+    ----------
+    left : float
+        The smallest value of the triangular distribution.
+    mode : float
+        The most common value of the triangular distribution.
+    right : float
+        The largest value of the triangular distribution.
+
+    Returns
+    -------
+    TriangularDistribution
+
+    Examples
+    --------
+    >>> triangular(1, 2, 3)
+    <Distribution> triangular(1, 2, 3)
+    """
+    return TriangularDistribution(left=left, mode=mode, right=right)

+
+
+
+

+[docs]
+class PERTDistribution(ContinuousDistribution):
+    def __init__(self, left, mode, right, lam=4, lclip=None, rclip=None):
+        super().__init__()
+        if left > mode:
+            raise ValueError("left must be less than or equal to mode")
+        if right < mode:
+            raise ValueError("right must be greater than or equal to mode")
+        if lam < 0:
+            raise ValueError("the shape parameter must be positive")
+        if left == right:
+            raise ValueError("left and right must be different")
+
+        self.left = left
+        self.mode = mode
+        self.right = right
+        self.lam = lam
+        self.lclip = lclip
+        self.rclip = rclip
+
+    def __str__(self):
+        out = "<Distribution> PERT({}, {}, {}, lam={}".format(
+            self.left, self.mode, self.right, self.lam
+        )
+        if self.lclip is not None:
+            out += ", lclip={}".format(self.lclip)
+        if self.rclip is not None:
+            out += ", rclip={}".format(self.rclip)
+        out += ")"
+        return out

+
+
+
+

+[docs]
+def pert(left, mode, right, lam=4, lclip=None, rclip=None):
+    """
+    Initialize a PERT distribution.
+
+    Parameters
+    ----------
+    left : float
+        The smallest value of the PERT distribution.
+    mode : float
+        The most common value of the PERT distribution.
+    right : float
+        The largest value of the PERT distribution.
+    lam : float
+        The lambda value of the PERT distribution. Defaults to 4.
+    lclip : float or None
+        If not None, any value below ``lclip`` will be coerced to ``lclip``.
+    rclip : float or None
+        If not None, any value below ``rclip`` will be coerced to ``rclip``.
+
+    Returns
+    -------
+    PERTDistribution
+
+    Examples
+    --------
+    >>> pert(1, 2, 3)
+    <Distribution> PERT(1, 2, 3)
+    """
+    return PERTDistribution(left=left, mode=mode, right=right, lam=lam, lclip=lclip, rclip=rclip)

+
+
+
+

+[docs]
+class PoissonDistribution(DiscreteDistribution):
+    def __init__(self, lam, lclip=None, rclip=None):
+        super().__init__()
+        self.lam = lam
+        self.lclip = lclip
+        self.rclip = rclip
+
+    def __str__(self):
+        out = "<Distribution> poisson({}".format(self.lam)
+        if self.lclip is not None:
+            out += ", lclip={}".format(self.lclip)
+        if self.rclip is not None:
+            out += ", rclip={}".format(self.rclip)
+        out += ")"
+        return out

+
+
+
+

+[docs]
+def poisson(lam, lclip=None, rclip=None):
+    """
+    Initialize a poisson distribution.
+
+    Parameters
+    ----------
+    lam : float
+        The lambda value of the poisson distribution.
+    lclip : float or None
+        If not None, any value below ``lclip`` will be coerced to ``lclip``.
+    rclip : float or None
+        If not None, any value below ``rclip`` will be coerced to ``rclip``.
+
+    Returns
+    -------
+    PoissonDistribution
+
+    Examples
+    --------
+    >>> poisson(1)
+    <Distribution> poisson(1)
+    """
+    return PoissonDistribution(lam=lam, lclip=lclip, rclip=rclip)

+
+
+
+

+[docs]
+class ChiSquareDistribution(ContinuousDistribution):
+    def __init__(self, df):
+        super().__init__()
+        self.df = df
+        if self.df <= 0:
+            raise ValueError("df must be positive")
+
+    def __str__(self):
+        return "<Distribution> chisquare({})".format(self.df)

+
+
+
+

+[docs]
+def chisquare(df):
+    """
+    Initialize a chi-square distribution.
+
+    Parameters
+    ----------
+    df : float
+        The degrees of freedom. Must be positive.
+
+    Returns
+    -------
+    ChiSquareDistribution
+
+    Examples
+    --------
+    >>> chisquare(2)
+    <Distribution> chiaquare(2)
+    """
+    return ChiSquareDistribution(df=df)

+
+
+
+

+[docs]
+class ExponentialDistribution(ContinuousDistribution):
+    def __init__(self, scale, lclip=None, rclip=None):
+        super().__init__()
+        assert scale > 0, "scale must be positive"
+        # Prevent numeric overflows
+        assert scale < 1e20, "scale must be less than 1e20"
+        self.scale = scale
+        self.lclip = lclip
+        self.rclip = rclip
+
+    def __str__(self):
+        out = "<Distribution> exponential({}".format(self.scale)
+        if self.lclip is not None:
+            out += ", lclip={}".format(self.lclip)
+        if self.rclip is not None:
+            out += ", rclip={}".format(self.rclip)
+        out += ")"
+        return out

+
+
+
+

+[docs]
+def exponential(scale, lclip=None, rclip=None):
+    """
+    Initialize an exponential distribution.
+
+    Parameters
+    ----------
+    scale : float
+        The scale value of the exponential distribution (> 0)
+    lclip : float or None
+        If not None, any value below ``lclip`` will be coerced to ``lclip``.
+    rclip : float or None
+        If not None, any value below ``rclip`` will be coerced to ``rclip``.
+
+    Returns
+    -------
+    ExponentialDistribution
+
+    Examples
+    --------
+    >>> exponential(1)
+    <Distribution> exponential(1)
+    """
+    return ExponentialDistribution(scale=scale, lclip=lclip, rclip=rclip)

+
+
+
+

+[docs]
+class GammaDistribution(ContinuousDistribution):
+    def __init__(self, shape, scale=1, lclip=None, rclip=None):
+        super().__init__()
+        self.shape = shape
+        self.scale = scale
+        self.lclip = lclip
+        self.rclip = rclip
+
+    def __str__(self):
+        out = "<Distribution> gamma(shape={}, scale={}".format(self.shape, self.scale)
+        if self.lclip is not None:
+            out += ", lclip={}".format(self.lclip)
+        if self.rclip is not None:
+            out += ", rclip={}".format(self.rclip)
+        out += ")"
+        return out

+
+
+
+

+[docs]
+def gamma(shape, scale=1, lclip=None, rclip=None):
+    """
+    Initialize a gamma distribution.
+
+    Parameters
+    ----------
+    shape : float
+        The shape value of the gamma distribution.
+    scale : float
+        The scale value of the gamma distribution. Defaults to 1.
+    lclip : float or None
+        If not None, any value below ``lclip`` will be coerced to ``lclip``.
+    rclip : float or None
+        If not None, any value below ``rclip`` will be coerced to ``rclip``.
+
+    Returns
+    -------
+    GammaDistribution
+
+    Examples
+    --------
+    >>> gamma(10, 1)
+    <Distribution> gamma(shape=10, scale=1)
+    """
+    return GammaDistribution(shape=shape, scale=scale, lclip=lclip, rclip=rclip)

+
+
+
+

+[docs]
+class ParetoDistribution(ContinuousDistribution):
+    def __init__(self, shape):
+        super().__init__()
+        self.shape = shape
+
+    def __str__(self):
+        return "<Distribution> pareto({})".format(self.shape)

+
+
+
+

+[docs]
+def pareto(shape):
+    """
+    Initialize a pareto distribution.
+
+    Parameters
+    ----------
+    shape : float
+        The shape value of the pareto distribution.
+
+    Returns
+    -------
+    ParetoDistribution
+
+    Examples
+    --------
+    >>> pareto(1)
+    <Distribution> pareto(1)
+    """
+    return ParetoDistribution(shape=shape)

+
+
+
+

+[docs]
+class MixtureDistribution(CompositeDistribution):
+    def __init__(self, dists, weights=None, relative_weights=None, lclip=None, rclip=None):
+        super().__init__()
+        weights, dists = _process_weights_values(weights, relative_weights, dists)
+        self.dists = dists
+        self.weights = weights
+        self.lclip = lclip
+        self.rclip = rclip
+        self._check_correlated(dists)
+
+    def __str__(self):
+        out = "<Distribution> mixture"
+        for i in range(len(self.dists)):
+            out += "\n - {} weight on {}".format(self.weights[i], self.dists[i])
+        return out

+
+
+
+

+[docs]
+def mixture(dists, weights=None, relative_weights=None, lclip=None, rclip=None):
+    """
+    Initialize a mixture distribution, which is a combination of different distributions.
+
+    Parameters
+    ----------
+    dists : list or dict
+        The distributions to mix. Can also be defined as a list of weights and distributions.
+    weights : list or None
+        The weights for each distribution.
+    relative_weights : list or None
+        Relative weights, which if given will be weights that are normalized
+        to sum to 1.
+    lclip : float or None
+        If not None, any value below ``lclip`` will be coerced to ``lclip``.
+    rclip : float or None
+        If not None, any value below ``rclip`` will be coerced to ``rclip``.
+
+    Returns
+    -------
+    MixtureDistribution
+
+    Examples
+    --------
+    >>> mixture([norm(1, 2), norm(3, 4)], weights=[0.1, 0.9])
+    <Distribution> mixture
+     - <Distribution> norm(mean=1.5, sd=0.3)
+     - <Distribution> norm(mean=3.5, sd=0.3)
+    >>> mixture([[0.1, norm(1, 2)], [0.9, norm(3, 4)]])  # Different notation for the same thing.
+    <Distribution> mixture
+     - <Distribution> norm(mean=1.5, sd=0.3)
+     - <Distribution> norm(mean=3.5, sd=0.3)
+    >>> mixture([norm(1, 2), norm(3, 4)])  # When no weights are given, all have equal chance
+    >>>                                    # of happening.
+    <Distribution> mixture
+     - <Distribution> norm(mean=1.5, sd=0.3)
+     - <Distribution> norm(mean=3.5, sd=0.3)
+    """
+    return MixtureDistribution(
+        dists=dists,
+        weights=weights,
+        relative_weights=relative_weights,
+        lclip=lclip,
+        rclip=rclip,
+    )

+
+
+
+

+[docs]
+def zero_inflated(p_zero, dist):
+    """
+    Initialize an arbitrary zero-inflated distribution.
+
+    Parameters
+    ----------
+    p_zero : float
+        The chance of the distribution returning zero
+    dist : Distribution
+        The distribution to sample from when not zero
+
+    Returns
+    -------
+    MixtureDistribution
+
+    Examples
+    --------
+    >>> zero_inflated(0.6, norm(1, 2))
+    <Distribution> mixture
+     - 0
+     - <Distribution> norm(mean=1.5, sd=0.3)
+    """
+    if p_zero > 1 or p_zero < 0 or not isinstance(p_zero, float):
+        raise ValueError("`p_zero` must be between 0 and 1")
+    return MixtureDistribution(dists=[0, dist], weights=p_zero)

+
+
+
+

+[docs]
+def inf0(p_zero, dist):
+    """
+    Initialize an arbitrary zero-inflated distribution.
+
+    Alias for ``zero_inflated``.
+
+    Parameters
+    ----------
+    p_zero : float
+        The chance of the distribution returning zero
+    dist : Distribution
+        The distribution to sample from when not zero
+
+    Returns
+    -------
+    MixtureDistribution
+
+    Examples
+    --------
+    >>> inf0(0.6, norm(1, 2))
+    <Distribution> mixture
+     - 0
+     - <Distribution> norm(mean=1.5, sd=0.3)
+    """
+    return zero_inflated(p_zero=p_zero, dist=dist)

+
+
+
+

+[docs]
+class GeometricDistribution(OperableDistribution):
+    def __init__(self, p):
+        super().__init__()
+        self.p = p
+        if self.p < 0 or self.p > 1:
+            raise ValueError("p must be between 0 and 1")
+
+    def __str__(self):
+        return "<Distribution> geometric(p={})".format(self.p)

+
+
+
+

+[docs]
+def geometric(p):
+    """
+    Initialize a geometric distribution.
+
+    Parameters
+    ----------
+    p : float
+        The probability of success of an individual trial. Must be between 0 and 1.
+
+    Returns
+    -------
+    GeometricDistribution
+
+    Examples
+    --------
+    >>> geometric(0.1)
+    <Distribution> geometric(0.1)
+    """
+    return GeometricDistribution(p=p)

+
+
+ +
+ + + + + +
+ +
+
+
+ +
+ + + + +
+
+ +
+ +
+
+
+ + + + + +
+
+ +
+ +
+

+ + © Copyright 2023, Peter Wildeford. +
+ +

+
+ +
+

+ Created using Sphinx 7.2.6. +
+

+
+ +
+ + + +
+ +

+ Built with the PyData Sphinx Theme 0.14.3. +

+ +
+ +
+ +
+ + \ No newline at end of file diff --git a/docs/build/html/_modules/squigglepy/rng.html b/docs/build/html/_modules/squigglepy/rng.html new file mode 100644 index 0000000..af027d7 --- /dev/null +++ b/docs/build/html/_modules/squigglepy/rng.html @@ -0,0 +1,389 @@ + + + + + + + + + + squigglepy.rng — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + +
+
+
+
+ + + Ctrl+K +
+
+ + + +
+
+ +
+ + + +
+ + +
+ +
+ +
+ + + +
+ +
+
+ +
+ +
+ + +
+
+ + + + +
+ +
+ + +
+
+ +
+
+ +
+ +
+ + + + +
+ +
+ + +
+
+ + + + + +
+ +

Source code for squigglepy.rng

+import numpy as np
+
+_squigglepy_internal_rng = np.random.default_rng()
+
+
+

+[docs]
+def set_seed(seed):
+    """
+    Set the seed of the random number generator used by Squigglepy.
+
+    The RNG is a ``np.random.default_rng`` under the hood.
+
+    Parameters
+    ----------
+    seed : float
+        The seed to use for the RNG.
+
+    Returns
+    -------
+    np.random.default_rng
+        The RNG used internally.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    Generator(PCG64) at 0x127EDE9E0
+    """
+    global _squigglepy_internal_rng
+    _squigglepy_internal_rng = np.random.default_rng(seed)
+    return _squigglepy_internal_rng

+
+
+ +
+ + + + + +
+ +
+
+
+ +
+ + + + +
+
+ +
+ +
+
+
+ + + + + +
+
+ +
+ +
+

+ + © Copyright 2023, Peter Wildeford. +
+ +

+
+ +
+

+ Created using Sphinx 7.2.6. +
+

+
+ +
+ + + +
+ +

+ Built with the PyData Sphinx Theme 0.14.3. +

+ +
+ +
+ +
+ + \ No newline at end of file diff --git a/docs/build/html/_modules/squigglepy/samplers.html b/docs/build/html/_modules/squigglepy/samplers.html new file mode 100644 index 0000000..9118039 --- /dev/null +++ b/docs/build/html/_modules/squigglepy/samplers.html @@ -0,0 +1,1560 @@ + + + + + + + + + + squigglepy.samplers — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + +
+
+
+
+ + + Ctrl+K +
+
+ + + +
+
+ +
+ + + +
+ + +
+ +
+ +
+ + + +
+ +
+
+ +
+ +
+ + +
+
+ + + + +
+ +
+ + +
+
+ +
+
+ +
+ +
+ + + + +
+ +
+ + +
+
+ + + + + +
+ +

Source code for squigglepy.samplers

+import bisect
+import os
+import time
+
+import numpy as np
+import pathos.multiprocessing as mp
+
+from numpy.typing import NDArray
+
+from scipy import stats
+
+from .utils import (
+    _process_weights_values,
+    _process_discrete_weights_values,
+    is_dist,
+    is_sampleable,
+    _simplify,
+    _enlist,
+    _safe_len,
+    _core_cuts,
+    _init_tqdm,
+    _tick_tqdm,
+    _flush_tqdm,
+)
+
+from .distributions import (
+    BaseDistribution,
+    BernoulliDistribution,
+    BetaDistribution,
+    BinomialDistribution,
+    ChiSquareDistribution,
+    ComplexDistribution,
+    ConstantDistribution,
+    CategoricalDistribution,
+    ExponentialDistribution,
+    GammaDistribution,
+    GeometricDistribution,
+    LogTDistribution,
+    LognormalDistribution,
+    MixtureDistribution,
+    NormalDistribution,
+    ParetoDistribution,
+    PoissonDistribution,
+    TDistribution,
+    TriangularDistribution,
+    PERTDistribution,
+    UniformDistribution,
+    const,
+)
+
+_squigglepy_internal_sample_caches = {}
+
+
+def _get_rng():
+    from .rng import _squigglepy_internal_rng
+
+    return _squigglepy_internal_rng
+
+
+

+[docs]
+def normal_sample(mean, sd, samples=1):
+    """
+    Sample a random number according to a normal distribution.
+
+    Parameters
+    ----------
+    mean : float
+        The mean of the normal distribution that is being sampled.
+    sd : float
+        The standard deviation of the normal distribution that is being sampled.
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    float
+        A random number sampled from a normal distribution defined by
+        ``mean`` and ``sd``.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> normal_sample(0, 1)
+    0.30471707975443135
+    """
+    return _simplify(_get_rng().normal(mean, sd, samples))

+
+
+
+

+[docs]
+def lognormal_sample(mean, sd, samples=1):
+    """
+    Sample a random number according to a lognormal distribution.
+
+    Parameters
+    ----------
+    mean : float
+        The mean of the lognormal distribution that is being sampled.
+    sd : float
+        The standard deviation of the lognormal distribution that is being sampled.
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    float
+        A random number sampled from a lognormal distribution defined by
+        ``mean`` and ``sd``.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> lognormal_sample(0, 1)
+    1.3562412406168636
+    """
+    return _simplify(_get_rng().lognormal(mean, sd, samples))

+
+
+
+

+[docs]
+def t_sample(low=None, high=None, t=20, samples=1, credibility=90):
+    """
+    Sample a random number according to a t-distribution.
+
+    The t-distribution is defined with degrees of freedom via the ``t``
+    parameter. Additionally, a loose credibility interval can be defined
+    via the t-distribution using the ``low`` and ``high`` values. This will be a
+    90% CI by default unless you change ``credibility.`` Unlike the normal and
+    lognormal samplers, this credible interval is an approximation and is
+    not precisely defined.
+
+    Parameters
+    ----------
+    low : float or None
+        The low value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
+    high : float or None
+        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
+    t : float
+        The number of degrees of freedom of the t-distribution. Defaults to 20.
+    samples : int
+        The number of samples to return.
+    credibility : float
+        The range of the credibility interval. Defaults to 90.
+
+    Returns
+    -------
+    float
+        A random number sampled from a lognormal distribution defined by
+        ``mean`` and ``sd``.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> t_sample(1, 2, t=4)
+    2.7887113716855985
+    """
+    if low is None and high is None:
+        return _get_rng().standard_t(t, samples)
+    elif low is None or high is None:
+        raise ValueError("must define either both `x` and `y` or neither.")
+    elif low > high:
+        raise ValueError("`high value` cannot be lower than `low value`")
+    elif low == high:
+        return low
+    else:
+        mu = (high + low) / 2
+        cdf_value = 0.5 + 0.5 * (credibility / 100)
+        normed_sigma = stats.norm.ppf(cdf_value)
+        sigma = (high - mu) / normed_sigma
+        return _simplify(
+            normal_sample(mu, sigma, samples) / ((chi_square_sample(t, samples) / t) ** 0.5)
+        )

+
+
+
+

+[docs]
+def log_t_sample(low=None, high=None, t=20, samples=1, credibility=90):
+    """
+    Sample a random number according to a log-t-distribution.
+
+    The log-t-distribution is a t-distribution in log-space. It is defined with
+    degrees of freedom via the ``t`` parameter. Additionally, a loose credibility
+    interval can be defined via the t-distribution using the ``low`` and ``high``
+    values. This will be a 90% CI by default unless you change ``credibility.``
+    Unlike the normal and lognormal samplers, this credible interval is an
+    approximation and is not precisely defined.
+
+    Parameters
+    ----------
+    low : float or None
+        The low value of a credible interval defined by ``credibility``.
+        Must be greater than 0. Defaults to a 90% CI.
+    high : float or None
+        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
+    t : float
+        The number of degrees of freedom of the t-distribution. Defaults to 20.
+    samples : int
+        The number of samples to return.
+    credibility : float
+        The range of the credibility interval. Defaults to 90.
+
+    Returns
+    -------
+    float
+        A random number sampled from a lognormal distribution defined by
+        ``mean`` and ``sd``.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> log_t_sample(1, 2, t=4)
+    2.052949773846356
+    """
+    if low is None and high is None:
+        return np.exp(_get_rng().standard_t(t))
+    elif low > high:
+        raise ValueError("`high value` cannot be lower than `low value`")
+    elif low < 0:
+        raise ValueError("log_t_sample cannot handle negative values")
+    elif low == high:
+        return low
+    else:
+        log_low = np.log(low)
+        log_high = np.log(high)
+        mu = (log_high + log_low) / 2
+        cdf_value = 0.5 + 0.5 * (credibility / 100)
+        normed_sigma = stats.norm.ppf(cdf_value)
+        sigma = (log_high - mu) / normed_sigma
+        return _simplify(
+            np.exp(
+                normal_sample(mu, sigma, samples) / ((chi_square_sample(t, samples) / t) ** 0.5)
+            )
+        )

+
+
+
+

+[docs]
+def binomial_sample(n, p, samples=1):
+    """
+    Sample a random number according to a binomial distribution.
+
+    Parameters
+    ----------
+    n : int
+        The number of trials.
+    p : float
+        The probability of success for each trial. Must be between 0 and 1.
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    int
+        A random number sampled from a binomial distribution defined by
+        ``n`` and ``p``. The random number should be between 0 and ``n``.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> binomial_sample(10, 0.1)
+    2
+    """
+    return _simplify(_get_rng().binomial(n, p, samples))

+
+
+
+

+[docs]
+def beta_sample(a, b, samples=1):
+    """
+    Sample a random number according to a beta distribution.
+
+    Parameters
+    ----------
+    a : float
+        The alpha shape value of the distribution. Typically takes the value of the
+        number of trials that resulted in a success.
+    b : float
+        The beta shape value of the distribution. Typically takes the value of the
+        number of trials that resulted in a failure.
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    float
+        A random number sampled from a beta distribution defined by
+        ``a`` and ``b``.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> beta_sample(1, 1)
+    0.22145847498048798
+    """
+    return _simplify(_get_rng().beta(a, b, samples))

+
+
+
+

+[docs]
+def bernoulli_sample(p, samples=1):
+    """
+    Sample 1 with probability ``p`` and 0 otherwise.
+
+    Parameters
+    ----------
+    p : float
+        The probability of success. Must be between 0 and 1.
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    int
+        Either 0 or 1
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> bernoulli_sample(0.5)
+    0
+    """
+    a = uniform_sample(0, 1, samples)
+    if _safe_len(a) == 1:
+        return int(a < p)
+    else:
+        return (a < p).astype(int)

+
+
+
+

+[docs]
+def triangular_sample(left, mode, right, samples=1):
+    """
+    Sample a random number according to a triangular distribution.
+
+    Parameters
+    ----------
+    left : float
+        The smallest value of the triangular distribution.
+    mode : float
+        The most common value of the triangular distribution.
+    right : float
+        The largest value of the triangular distribution.
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    float
+        A random number sampled from a triangular distribution.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> triangular_sample(1, 2, 3)
+    2.327625176788963
+    """
+    return _simplify(_get_rng().triangular(left, mode, right, samples))

+
+
+
+

+[docs]
+def pert_sample(left, mode, right, lam, samples=1):
+    """
+    Sample a random number according to a PERT distribution.
+
+    Parameters
+    ----------
+    left : float
+        The smallest value of the PERT distribution.
+    mode : float
+        The most common value of the PERT distribution.
+    right : float
+        The largest value of the PERT distribution.
+    lam : float
+        The lambda of the PERT distribution.
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    float
+        A random number sampled from a PERT distribution.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> pert_sample(1, 2, 3, 4)
+    2.327625176788963
+    """
+    r = right - left
+    alpha = 1 + lam * (mode - left) / r
+    beta = 1 + lam * (right - mode) / r
+    return left + beta_sample(a=alpha, b=beta, samples=samples) * r

+
+
+
+

+[docs]
+def poisson_sample(lam, samples=1):
+    """
+    Sample a random number according to a poisson distribution.
+
+    Parameters
+    ----------
+    lam : float
+        The lambda value of the poisson distribution.
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    int
+        A random number sampled from a poisson distribution.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> poisson_sample(10)
+    13
+    """
+    return _simplify(_get_rng().poisson(lam, samples))

+
+
+
+

+[docs]
+def exponential_sample(scale, samples=1):
+    """
+    Sample a random number according to an exponential distribution.
+
+    Parameters
+    ----------
+    scale : float
+        The scale value of the exponential distribution.
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    int
+        A random number sampled from an exponential distribution.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> exponential_sample(10)
+    24.042086039659946
+    """
+    return _simplify(_get_rng().exponential(scale, samples))

+
+
+
+

+[docs]
+def gamma_sample(shape, scale, samples=1):
+    """
+    Sample a random number according to a gamma distribution.
+
+    Parameters
+    ----------
+    shape : float
+        The shape value of the gamma distribution.
+    scale : float
+        The scale value of the gamma distribution. Defaults to 1.
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    int
+        A random number sampled from an gamma distribution.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> gamma_sample(10, 2)
+    21.290716894247602
+    """
+    return _simplify(_get_rng().gamma(shape, scale, samples))

+
+
+
+

+[docs]
+def pareto_sample(shape, samples=1):
+    """
+    Sample a random number according to a pareto distribution.
+
+    Parameters
+    ----------
+    shape : float
+        The shape value of the pareto distribution.
+
+    Returns
+    -------
+    int
+        A random number sampled from an pareto distribution.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> pareto_sample(1)
+    10.069666324736094
+    """
+    return _simplify(_get_rng().pareto(shape, samples))

+
+
+
+

+[docs]
+def uniform_sample(low, high, samples=1):
+    """
+    Sample a random number according to a uniform distribution.
+
+    Parameters
+    ----------
+    low : float
+        The smallest value the uniform distribution will return.
+    high : float
+        The largest value the uniform distribution will return.
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    float
+        A random number sampled from a uniform distribution between
+        ```low``` and ```high```.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> uniform_sample(0, 1)
+    0.7739560485559633
+    """
+    return _simplify(_get_rng().uniform(low, high, samples))

+
+
+
+

+[docs]
+def chi_square_sample(df, samples=1):
+    """
+    Sample a random number according to a chi-square distribution.
+
+    Parameters
+    ----------
+    df : float
+        The number of degrees of freedom
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    float
+        A random number sampled from a chi-square distribution.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> chi_square_sample(2)
+    4.808417207931989
+    """
+    return _simplify(_get_rng().chisquare(df, samples))

+
+
+
+

+[docs]
+def discrete_sample(items, samples=1, verbose=False, _multicore_tqdm_n=1, _multicore_tqdm_cores=1):
+    """
+    Sample a random value from a discrete distribution (aka categorical distribution).
+
+    Parameters
+    ----------
+    items : list or dict
+        The values that the discrete distribution will return and their associated
+        weights (or likelihoods of being returned when sampled).
+    samples : int
+        The number of samples to return.
+    verbose : bool
+        If True, will print out statements on computational progress.
+    _multicore_tqdm_n : int
+        The total number of samples to use for printing tqdm's interface. This is meant to only
+        be used internally by squigglepy to make the progress bar printing work well for
+        multicore. This parameter can be safely ignored by the user.
+    _multicore_tqdm_cores : int
+        The total number of cores to use for printing tqdm's interface. This is meant to only
+        be used internally by squigglepy to make the progress bar printing work well for
+        multicore. This parameter can be safely ignored by the user.
+
+    Returns
+    -------
+    Various, based on items in ``items``
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> # 10% chance of returning 0, 90% chance of returning 1
+    >>> discrete_sample({0: 0.1, 1: 0.9})
+    1
+    >>> discrete_sample([[0.1, 0], [0.9, 1]])  # Different notation for the same thing.
+    1
+    >>> # When no weights are given, all have equal chance of happening.
+    >>> discrete_sample([0, 1, 2])
+    2
+    >>> discrete_sample({'a': 0.1, 'b': 0.9})  # Values do not have to be numbers.
+    'b'
+    """
+    weights, values = _process_discrete_weights_values(items)
+
+    values = [const(v) for v in values]
+
+    return mixture_sample(
+        values=values,
+        weights=weights,
+        samples=samples,
+        verbose=verbose,
+        _multicore_tqdm_n=_multicore_tqdm_n,
+        _multicore_tqdm_cores=_multicore_tqdm_cores,
+    )

+
+
+
+

+[docs]
+def geometric_sample(p, samples=1):
+    """
+    Sample a random number according to a geometric distribution.
+
+    Parameters
+    ----------
+    p : float
+        The probability of success of an individual trial. Must be between 0 and 1.
+    samples : int
+        The number of samples to return.
+
+    Returns
+    -------
+    int
+        A random number sampled from a geometric distribution.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> geometric_sample(0.1)
+    2
+    """
+    return _simplify(_get_rng().geometric(p, samples))

+
+
+
+def _mixture_sample_for_large_n(
+    values,
+    weights=None,
+    relative_weights=None,
+    samples=1,
+    verbose=False,
+    _multicore_tqdm_n=1,
+    _multicore_tqdm_cores=1,
+):
+    def _run_presample(dist, pbar):
+        _tick_tqdm(pbar)
+        return _enlist(sample(dist, n=samples))
+
+    pbar = _init_tqdm(verbose=verbose, total=len(values))
+    values = [_run_presample(v, pbar) for v in values]
+    _flush_tqdm(pbar)
+
+    def _run_mixture(picker, i, pbar):
+        _tick_tqdm(pbar, _multicore_tqdm_cores)
+        index = bisect.bisect_left(weights, picker)
+        return values[index][i]
+
+    weights = np.cumsum(weights)
+    picker = uniform_sample(0, 1, samples=samples)
+
+    tqdm_samples = samples if _multicore_tqdm_cores == 1 else _multicore_tqdm_n
+    pbar = _init_tqdm(verbose=verbose, total=tqdm_samples)
+    out = _simplify([_run_mixture(p, i, pbar) for i, p in enumerate(_enlist(picker))])
+    _flush_tqdm(pbar)
+
+    return out
+
+
+def _mixture_sample_for_small_n(
+    values,
+    weights=None,
+    relative_weights=None,
+    samples=1,
+    verbose=False,
+    _multicore_tqdm_n=1,
+    _multicore_tqdm_cores=1,
+):
+    def _run_mixture(values, weights, pbar=None, tick=1):
+        r_ = uniform_sample(0, 1)
+        _tick_tqdm(pbar, tick)
+        for i, dist in enumerate(values):
+            weight = weights[i]
+            if r_ <= weight:
+                return sample(dist)
+        return sample(dist)
+
+    weights = np.cumsum(weights)
+    tqdm_samples = samples if _multicore_tqdm_cores == 1 else _multicore_tqdm_n
+    pbar = _init_tqdm(verbose=verbose, total=tqdm_samples)
+    out = _simplify(
+        [
+            _run_mixture(values=values, weights=weights, pbar=pbar, tick=_multicore_tqdm_cores)
+            for _ in range(samples)
+        ]
+    )
+    _flush_tqdm(pbar)
+    return out
+
+
+

+[docs]
+def mixture_sample(
+    values,
+    weights=None,
+    relative_weights=None,
+    samples=1,
+    verbose=False,
+    _multicore_tqdm_n=1,
+    _multicore_tqdm_cores=1,
+):
+    """
+    Sample a ranom number from a mixture distribution.
+
+    Parameters
+    ----------
+    values : list or dict
+        The distributions to mix. Can also be defined as a list of weights and distributions.
+    weights : list or None
+        The weights for each distribution.
+    relative_weights : list or None
+        Relative weights, which if given will be weights that are normalized
+        to sum to 1.
+    samples : int
+        The number of samples to return.
+    verbose : bool
+        If True, will print out statements on computational progress.
+    _multicore_tqdm_n : int
+        The total number of samples to use for printing tqdm's interface. This is meant to only
+        be used internally by squigglepy to make the progress bar printing work well for
+        multicore. This parameter can be safely ignored by the user.
+    _multicore_tqdm_cores : int
+        The total number of cores to use for printing tqdm's interface. This is meant to only
+        be used internally by squigglepy to make the progress bar printing work well for
+        multicore. This parameter can be safely ignored by the user.
+
+    Returns
+    -------
+    Various, based on items in ``values``
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> mixture_sample([norm(1, 2), norm(3, 4)], weights=[0.1, 0.9])
+    3.183867278765718
+    >>> # Different notation for the same thing.
+    >>> mixture_sample([[0.1, norm(1, 2)], [0.9, norm(3, 4)]])
+    3.7859113725925972
+    >>> # When no weights are given, all have equal chance of happening.
+    >>> mixture_sample([norm(1, 2), norm(3, 4)])
+    1.1041655362137777
+    """
+    weights, values = _process_weights_values(weights, relative_weights, values)
+
+    if len(values) == 1:
+        return sample(values[0], n=samples)
+
+    if samples > 100:
+        return _mixture_sample_for_large_n(
+            values=values,
+            weights=weights,
+            samples=samples,
+            verbose=verbose,
+            _multicore_tqdm_n=_multicore_tqdm_n,
+            _multicore_tqdm_cores=_multicore_tqdm_cores,
+        )
+    else:
+        return _mixture_sample_for_small_n(
+            values=values,
+            weights=weights,
+            samples=samples,
+            verbose=verbose,
+            _multicore_tqdm_n=_multicore_tqdm_n,
+            _multicore_tqdm_cores=_multicore_tqdm_cores,
+        )

+
+
+
+

+[docs]
+def sample_correlated_group(
+    requested_dist: BaseDistribution, n: int, verbose=False
+) -> NDArray[np.float64]:
+    """
+    Samples a correlated distribution, alongside
+    all other correlated distributions in the same group.
+
+    The samples for other variables are stored in the distributions themselves
+    (in `_correlated_samples`).
+
+    This is necessary, because the sampling needs to happen all at once, regardless
+    of where the distributions are used in the binary tree of operations.
+    """
+    group = requested_dist.correlation_group
+    assert group is not None
+
+    samples = np.column_stack(
+        [
+            # Skip correlation to prevent infinite recursion
+            # TODO: Check that this does not interfere
+            # with other correlated distributions downstream
+            sample(dist, n, verbose=verbose, _correlate_if_needed=False)
+            for dist in group.correlated_dists
+        ]
+    )
+    # Induce correlation
+    samples = group.induce_correlation(samples)
+
+    # Store the samples in each distribution
+    # except the one we are sampling from
+    # so it requires resampling next time
+    requested_samples = None
+    for i, target_distribution in enumerate(group.correlated_dists):
+        if requested_dist is not target_distribution:
+            # Store the samples in the distribution
+            target_distribution._correlated_samples = samples[:, i]
+        else:
+            # Store the samples we requested
+            requested_samples = samples[:, i]
+
+    assert requested_samples is not None
+
+    return requested_samples

+
+
+
+

+[docs]
+def sample(
+    dist=None,
+    n=1,
+    lclip=None,
+    rclip=None,
+    memcache=False,
+    reload_cache=False,
+    dump_cache_file=None,
+    load_cache_file=None,
+    cache_file_primary=False,
+    verbose=None,
+    cores=1,
+    _multicore_tqdm_n=1,
+    _multicore_tqdm_cores=1,
+    _correlate_if_needed=True,
+):
+    """
+    Sample random numbers from a given distribution.
+
+    Parameters
+    ----------
+    dist : Distribution
+        The distribution to sample random number from.
+    n : int
+        The number of random numbers to sample from the distribution. Default to 1.
+    lclip : float or None
+        If not None, any value below ``lclip`` will be coerced to ``lclip``.
+    rclip : float or None
+        If not None, any value below ``rclip`` will be coerced to ``rclip``.
+    memcache : bool
+        If True, will attempt to load the results in-memory for future calculations if
+        a cache is present. Otherwise will save the results to an in-memory cache. Each cache
+        will be matched based on ``dist``. Default ``False``.
+    reload_cache : bool
+        If True, any existing cache will be ignored and recalculated. Default ``False``.
+    dump_cache_file : str or None
+        If present, will write out the cache to a numpy file with this path with
+        ``.sqlcache.npy`` appended to the file name.
+    load_cache_file : str or None
+        If present, will first attempt to load and use a cache from a file with this
+        path with ``.sqlcache.npy`` appended to the file name.
+    cache_file_primary : bool
+        If both an in-memory cache and file cache are present, the file
+        cache will be used for the cache if this is True, and the in-memory cache
+        will be used otherwise. Defaults to False.
+    verbose : bool
+        If True, will print out statements on computational progress. If False, will not.
+        If None (default), will be True when ``n`` is greater than or equal to 1M.
+    cores : int
+        If 1, runs on a single core / process. If greater than 1, will run on a multiprocessing
+        pool with that many cores / processes.
+    _multicore_tqdm_n : int
+        The total number of samples to use for printing tqdm's interface. This is meant to only
+        be used internally by squigglepy to make the progress bar printing work well for
+        multicore. This parameter can be safely ignored by the user.
+    _multicore_tqdm_cores : int
+        The total number of cores to use for printing tqdm's interface. This is meant to only
+        be used internally by squigglepy to make the progress bar printing work well for
+        multicore. This parameter can be safely ignored by the user.
+
+    Returns
+    -------
+    Various, based on ``dist``.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> sample(norm(1, 2))
+    1.592627415218455
+    >>> sample(mixture([norm(1, 2), norm(3, 4)]))
+    1.7281209657534462
+    >>> sample(lognorm(1, 10), n=5, lclip=3)
+    array([6.10817361, 3.        , 3.        , 3.45828454, 3.        ])
+    """
+    n = int(n)
+    if n <= 0:
+        raise ValueError("n must be >= 1")
+
+    if not is_sampleable(dist):
+        error = "input to sample is malformed - {} is not a sampleable type.".format(type(dist))
+        raise ValueError(error)
+
+    if verbose is None:
+        verbose = n >= 1000000
+
+    # Handle loading from cache
+    samples = None
+    has_in_mem_cache = str(dist) in _squigglepy_internal_sample_caches
+    if load_cache_file:
+        cache_path = load_cache_file + ".sqcache.npy"
+        has_file_cache = os.path.exists(cache_path) if load_cache_file else False
+
+    if load_cache_file and not has_file_cache and verbose:
+        print("Warning: cache file `{}.sqcache.npy` not found.".format(load_cache_file))
+
+    if (load_cache_file or memcache) and not reload_cache:
+        if load_cache_file and has_file_cache and (not has_in_mem_cache or cache_file_primary):
+            if verbose:
+                print("Loading from cache file (`{}`)...".format(cache_path))
+            with open(cache_path, "rb") as f:
+                samples = np.load(f)
+
+        elif memcache and has_in_mem_cache:
+            if verbose:
+                print("Loading from in-memory cache...")
+            samples = _squigglepy_internal_sample_caches.get(str(dist))
+
+    # Handle multicore
+    if samples is None and cores > 1:
+        if verbose:
+            print("Generating samples with {} cores...".format(cores))
+        with mp.ProcessingPool(cores) as pool:
+            cuts = _core_cuts(n, cores)
+
+            def multicore_sample(core, total_n=n, total_cores=cores, verbose=False):
+                batch = sample(
+                    dist=dist,
+                    n=cuts[core],
+                    _multicore_tqdm_n=total_n,
+                    _multicore_tqdm_cores=total_cores,
+                    lclip=lclip,
+                    rclip=rclip,
+                    memcache=False,
+                    verbose=verbose,
+                    cores=1,
+                )
+                if verbose:
+                    print("Shuffling data...")
+                with open("test-core-{}.npy".format(core), "wb") as f:
+                    np.save(f, batch)
+                return None
+
+            pool_results = pool.amap(multicore_sample, range(cores - 1))
+            multicore_sample(cores - 1, verbose=verbose)
+            if verbose:
+                print("Waiting for other cores...")
+            while not pool_results.ready():
+                if verbose:
+                    print(".", end="", flush=True)
+                time.sleep(1)
+
+        if verbose:
+            print("Collecting data...")
+        samples = np.array([])
+        pbar = _init_tqdm(verbose=verbose, total=cores)
+        for core in range(cores):
+            with open("test-core-{}.npy".format(core), "rb") as f:
+                samples = np.concatenate((samples, np.load(f, allow_pickle=True)), axis=None)
+            os.remove("test-core-{}.npy".format(core))
+            _tick_tqdm(pbar, 1)
+        _flush_tqdm(pbar)
+        if verbose:
+            print("...Collected!")
+
+    # Handle lclip/rclip
+    if samples is None:
+        lclip_ = None
+        rclip_ = None
+        if is_dist(dist):
+            lclip_ = dist.lclip
+            rclip_ = dist.rclip
+
+        if lclip is None and lclip_ is not None:
+            lclip = lclip_
+        elif lclip is not None and lclip_ is not None:
+            lclip = max(lclip, lclip_)
+
+        if rclip is None and rclip_ is not None:
+            rclip = rclip_
+        elif rclip is not None and rclip_ is not None:
+            rclip = min(rclip, rclip_)
+
+    # Start sampling
+    if samples is None:
+        if callable(dist):
+            if n > 1:
+
+                def run_dist(dist, pbar=None, tick=1):
+                    dist = dist()
+                    _tick_tqdm(pbar, tick)
+                    return dist
+
+                tqdm_samples = n if _multicore_tqdm_cores == 1 else _multicore_tqdm_n
+                pbar = _init_tqdm(verbose=verbose, total=tqdm_samples)
+                out = np.array(
+                    [run_dist(dist=dist, pbar=pbar, tick=_multicore_tqdm_cores) for _ in range(n)]
+                )
+                _flush_tqdm(pbar)
+            else:
+                out = [dist()]
+
+            def run_dist(dist, pbar=None, tick=1):
+                samp = sample(dist) if is_dist(dist) or callable(dist) else dist
+                _tick_tqdm(pbar, tick)
+                return samp
+
+            pbar = _init_tqdm(verbose=verbose, total=len(out) * _multicore_tqdm_cores)
+            samples = _simplify(
+                np.array([run_dist(dist=o, pbar=pbar, tick=_multicore_tqdm_cores) for o in out])
+            )
+            _flush_tqdm(pbar)
+
+        elif (
+            isinstance(dist, float)
+            or isinstance(dist, int)
+            or isinstance(dist, str)
+            or dist is None
+        ):
+            samples = _simplify(np.array([dist for _ in range(n)]))
+
+        # Distribution is part of a correlation group
+        # and has not been sampled yet
+        elif (
+            isinstance(dist, BaseDistribution)
+            and _correlate_if_needed
+            and dist.correlation_group is not None
+            and dist._correlated_samples is None
+        ):
+            # Samples the entire correlated group at once
+            samples = sample_correlated_group(dist, n=n, verbose=verbose)
+
+        # Distribution has already been sampled
+        # as part of a correlation group
+        elif (
+            isinstance(dist, BaseDistribution)
+            and _correlate_if_needed
+            and dist.correlation_group is not None
+            and dist._correlated_samples is not None
+        ):
+            samples = dist._correlated_samples
+            # This forces the distribution to be resampled
+            # if the user attempts to sample from it again
+            dist._correlated_samples = None
+
+        elif isinstance(dist, ConstantDistribution):
+            samples = _simplify(np.array([dist.x for _ in range(n)]))
+
+        elif isinstance(dist, UniformDistribution):
+            samples = uniform_sample(dist.x, dist.y, samples=n)
+
+        elif isinstance(dist, CategoricalDistribution):
+            samples = discrete_sample(
+                dist.items,
+                samples=n,
+                _multicore_tqdm_n=_multicore_tqdm_n,
+                _multicore_tqdm_cores=_multicore_tqdm_cores,
+            )
+
+        elif isinstance(dist, NormalDistribution):
+            samples = normal_sample(mean=dist.mean, sd=dist.sd, samples=n)
+
+        elif isinstance(dist, LognormalDistribution):
+            samples = lognormal_sample(mean=dist.norm_mean, sd=dist.norm_sd, samples=n)
+
+        elif isinstance(dist, BinomialDistribution):
+            samples = binomial_sample(n=dist.n, p=dist.p, samples=n)
+
+        elif isinstance(dist, BetaDistribution):
+            samples = beta_sample(a=dist.a, b=dist.b, samples=n)
+
+        elif isinstance(dist, BernoulliDistribution):
+            samples = bernoulli_sample(p=dist.p, samples=n)
+
+        elif isinstance(dist, PoissonDistribution):
+            samples = poisson_sample(lam=dist.lam, samples=n)
+
+        elif isinstance(dist, ChiSquareDistribution):
+            samples = chi_square_sample(df=dist.df, samples=n)
+
+        elif isinstance(dist, ExponentialDistribution):
+            samples = exponential_sample(scale=dist.scale, samples=n)
+
+        elif isinstance(dist, GammaDistribution):
+            samples = gamma_sample(shape=dist.shape, scale=dist.scale, samples=n)
+
+        elif isinstance(dist, ParetoDistribution):
+            samples = pareto_sample(shape=dist.shape, samples=n)
+
+        elif isinstance(dist, TriangularDistribution):
+            samples = triangular_sample(dist.left, dist.mode, dist.right, samples=n)
+
+        elif isinstance(dist, PERTDistribution):
+            samples = pert_sample(dist.left, dist.mode, dist.right, dist.lam, samples=n)
+
+        elif isinstance(dist, TDistribution):
+            samples = t_sample(dist.x, dist.y, dist.t, credibility=dist.credibility, samples=n)
+
+        elif isinstance(dist, LogTDistribution):
+            samples = log_t_sample(dist.x, dist.y, dist.t, credibility=dist.credibility, samples=n)
+
+        elif isinstance(dist, MixtureDistribution):
+            samples = mixture_sample(
+                dist.dists,
+                dist.weights,
+                samples=n,
+                verbose=verbose,
+                _multicore_tqdm_n=_multicore_tqdm_n,
+                _multicore_tqdm_cores=_multicore_tqdm_cores,
+            )
+
+        elif isinstance(dist, GeometricDistribution):
+            samples = geometric_sample(p=dist.p, samples=n)
+
+        elif isinstance(dist, ComplexDistribution):
+            if dist.right is None:
+                samples = dist.fn(sample(dist.left, n=n, verbose=verbose))
+            else:
+                samples = dist.fn(
+                    sample(dist.left, n=n, verbose=verbose),
+                    sample(dist.right, n=n, verbose=verbose),
+                )
+
+            if is_dist(samples) or callable(samples):
+                samples = sample(samples, n=n)
+
+        else:
+            raise ValueError("{} sampler not found".format(type(dist)))
+
+    # Use lclip / rclip
+    if _safe_len(samples) > 1:
+        if lclip is not None:
+            samples = np.maximum(samples, lclip)
+        if rclip is not None:
+            samples = np.minimum(samples, rclip)
+    else:
+        if lclip is not None:
+            samples = lclip if samples < lclip else samples
+        if rclip is not None:
+            samples = rclip if samples > rclip else samples
+
+    # Save to cache
+    if memcache and (not has_in_mem_cache or reload_cache):
+        if verbose:
+            print("Caching in-memory...")
+        _squigglepy_internal_sample_caches[str(dist)] = samples
+        if verbose:
+            print("...Cached")
+
+    if dump_cache_file:
+        cache_path = dump_cache_file + ".sqcache.npy"
+        if verbose:
+            print("Writing cache to file `{}`...".format(cache_path))
+        with open(cache_path, "wb") as f:
+            np.save(f, samples)
+        if verbose:
+            print("...Cached")
+
+    # Return
+    return np.array(samples) if isinstance(samples, list) else samples

+
+
+ +
+ + + + + +
+ +
+
+
+ +
+ + + + +
+
+ +
+ +
+
+
+ + + + + +
+
+ +
+ +
+

+ + © Copyright 2023, Peter Wildeford. +
+ +

+
+ +
+

+ Created using Sphinx 7.2.6. +
+

+
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+ +

+ Built with the PyData Sphinx Theme 0.14.3. +

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+ + + + + +
+ +

Source code for squigglepy.utils

+import math
+import numpy as np
+
+from tqdm import tqdm
+from datetime import datetime
+from collections import Counter
+from collections.abc import Iterable
+
+import importlib
+import importlib.util
+import sys
+
+
+def _check_pandas_series(values):
+    """Check if values is a pandas series. Only imports pandas if necessary."""
+    if "pandas" not in sys.modules:
+        return False
+
+    pd = importlib.import_module("pandas")
+    return isinstance(values, pd.core.series.Series)
+
+
+def _process_weights_values(weights=None, relative_weights=None, values=None, drop_na=False):
+    if weights is not None and relative_weights is not None:
+        raise ValueError("can only pass either `weights` or `relative_weights`, not both.")
+    if values is None or _safe_len(values) == 0:
+        raise ValueError("must pass `values`")
+
+    relative = False
+    if relative_weights is not None:
+        weights = relative_weights
+        relative = True
+
+    if isinstance(weights, float):
+        weights = [weights]
+    elif isinstance(weights, np.ndarray):
+        weights = list(weights)
+    elif weights is not None and not _is_iterable(weights):
+        raise ValueError("passed weights must be an iterable")
+
+    if isinstance(values, np.ndarray):
+        values = list(values)
+    elif _check_pandas_series(values):
+        values = values.values.tolist()
+    elif isinstance(values, dict):
+        if weights is None:
+            weights = list(values.values())
+            values = list(values.keys())
+        else:
+            raise ValueError("cannot pass dict and weights separately")
+    elif values is not None and not _is_iterable(values):
+        raise ValueError("passed values must be an iterable")
+
+    if weights is None:
+        if isinstance(values[0], list) and len(values[0]) == 2:
+            weights = [v[0] for v in values]
+            values = [v[1] for v in values]
+            if drop_na and any([_is_na_like(v) for v in values]):
+                raise ValueError("cannot drop NA and process weights")
+        else:
+            if drop_na:
+                values = [v for v in values if not _is_na_like(v)]
+            len_ = len(values)
+            weights = [1 / len_ for _ in range(len_)]
+    elif drop_na and any([_is_na_like(v) for v in values]):
+        raise ValueError("cannot drop NA and process weights")
+
+    if any([_is_na_like(w) for w in weights]):
+        raise ValueError("cannot handle NA-like values in weights")
+    sum_weights = sum(weights)
+
+    if relative:
+        weights = normalize(weights)
+    else:
+        if len(weights) == len(values) - 1 and sum_weights < 1:
+            weights.append(1 - sum_weights)
+        elif sum_weights <= 0.99 or sum_weights >= 1.01:
+            raise ValueError("weights don't sum to 1 -" + " they sum to {}".format(sum_weights))
+
+    if len(weights) != len(values):
+        raise ValueError("weights and values not same length")
+
+    new_weights = []
+    new_values = []
+    for i, w in enumerate(weights):
+        if w < 0:
+            raise ValueError("weight cannot be negative")
+        if w > 0:  # Note that w = 0 is dropped here
+            new_weights.append(w)
+            new_values.append(values[i])
+
+    return new_weights, new_values
+
+
+def _process_discrete_weights_values(items):
+    if (
+        len(items) >= 100
+        and not isinstance(items, dict)
+        and not isinstance(items[0], list)
+        and _safe_len(_safe_set(items)) < _safe_len(items)
+    ):
+        vcounter = Counter(items)
+        sumv = sum([v for k, v in vcounter.items()])
+        items = {k: v / sumv for k, v in vcounter.items()}
+
+    return _process_weights_values(values=items)
+
+
+def _is_numpy(a):
+    return type(a).__module__ == np.__name__
+
+
+def _is_iterable(a):
+    iterx = isinstance(a, dict) or isinstance(a, Iterable)
+    return iterx and not isinstance(a, str)
+
+
+def _is_na_like(a):
+    return a is None or np.isnan(a)
+
+
+def _round(x, digits=0):
+    if digits is None:
+        return x
+
+    x = np.round(x, digits)
+
+    if _safe_len(x) > 1:
+        return np.array([int(y) if digits == 0 else y for y in x])
+    else:
+        return int(x) if digits <= 0 else x
+
+
+def _simplify(a):
+    if _is_numpy(a):
+        a = a.tolist() if a.size == 1 else a
+    if isinstance(a, list):
+        a = a[0] if len(a) == 1 else a
+    return a
+
+
+def _enlist(a):
+    if _is_numpy(a) and isinstance(a, np.ndarray):
+        return a.tolist()
+    elif _is_iterable(a):
+        return a
+    else:
+        return [a]
+
+
+def _safe_len(a):
+    if _is_numpy(a):
+        return a.size
+    elif is_dist(a):
+        return 1
+    elif isinstance(a, list):
+        return len(a)
+    elif a is None:
+        return 0
+    else:
+        return 1
+
+
+def _safe_set(a):
+    if _is_numpy(a):
+        return set(_enlist(a))
+    elif is_dist(a):
+        return a
+    elif isinstance(a, list):
+        try:
+            return set(a)
+        except TypeError:
+            return a
+    elif a is None:
+        return None
+    else:
+        return a
+
+
+def _core_cuts(n, cores):
+    cuts = [math.floor(n / cores) for _ in range(cores)]
+    delta = n - sum(cuts)
+    cuts[-1] += delta
+    return cuts
+
+
+def _init_tqdm(verbose=True, total=None):
+    if verbose:
+        return tqdm(total=total)
+    else:
+        return None
+
+
+def _tick_tqdm(pbar, tick_size=1):
+    if pbar:
+        pbar.update(tick_size)
+    return pbar
+
+
+def _flush_tqdm(pbar):
+    if pbar is not None:
+        pbar.close()
+    return pbar
+
+
+

+[docs]
+def is_dist(obj):
+    """
+    Test if a given object is a Squigglepy distribution.
+
+    Parameters
+    ----------
+    obj : object
+        The object to test.
+
+    Returns
+    -------
+    bool
+        True, if the object is a distribution. False if not.
+
+    Examples
+    --------
+    >>> is_dist(norm(0, 1))
+    True
+    >>> is_dist(0)
+    False
+    """
+    from .distributions import BaseDistribution
+
+    return isinstance(obj, BaseDistribution)

+
+
+
+

+[docs]
+def is_continuous_dist(obj):
+    from .distributions import (
+        ContinuousDistribution,
+        CompositeDistribution,
+        ComplexDistribution,
+        MixtureDistribution,
+    )
+
+    if isinstance(obj, ContinuousDistribution):
+        return True
+    elif isinstance(obj, CompositeDistribution):
+        if isinstance(obj, ComplexDistribution):
+            return is_continuous_dist(obj.left) and is_continuous_dist(obj.right)
+        elif isinstance(obj, MixtureDistribution):
+            return all([is_continuous_dist(d) for d in obj.dists])
+        else:
+            raise ValueError("Unknown composite distribution")
+    return False

+
+
+
+

+[docs]
+def is_sampleable(obj):
+    """
+    Test if a given object can be sampled from.
+
+    This includes distributions, integers, floats, `None`,
+    strings, and callables.
+
+    Parameters
+    ----------
+    obj : object
+        The object to test.
+
+    Returns
+    -------
+    bool
+        True, if the object can be sampled from. False if not.
+
+    Examples
+    --------
+    >>> is_sampleable(norm(0, 1))
+    True
+    >>> is_sampleable(0)
+    True
+    >>> is_sampleable([0, 1])
+    False
+    """
+    return (
+        is_dist(obj)
+        or isinstance(obj, int)
+        or isinstance(obj, float)
+        or isinstance(obj, str)
+        or obj is None
+        or callable(obj)
+    )

+
+
+
+

+[docs]
+def normalize(lst):
+    """
+    Normalize a list to sum to 1.
+
+    Parameters
+    ----------
+    lst : list
+        The list to normalize.
+
+    Returns
+    -------
+    list
+        A list where each value is normalized such that the list sums to 1.
+
+    Examples
+    --------
+    >>> normalize([0.1, 0.2, 0.2])
+    [0.2, 0.4, 0.4]
+    """
+    sum_lst = sum(lst)
+    return [lx / sum_lst for lx in lst]

+
+
+
+

+[docs]
+def event_occurs(p):
+    """
+    Return True with probability ``p`` and False with probability ``1 - p``.
+
+    Parameters
+    ----------
+    p : float
+        The probability of returning True. Must be between 0 and 1.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> event_occurs(p=0.5)
+    False
+    """
+    if is_dist(p) or callable(p):
+        from .samplers import sample
+
+        p = sample(p)
+    from .rng import _squigglepy_internal_rng
+
+    return _squigglepy_internal_rng.uniform(0, 1) < p

+
+
+
+

+[docs]
+def event_happens(p):
+    """
+    Return True with probability ``p`` and False with probability ``1 - p``.
+
+    Alias for ``event_occurs``.
+
+    Parameters
+    ----------
+    p : float
+        The probability of returning True. Must be between 0 and 1.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> event_happens(p=0.5)
+    False
+    """
+    return event_occurs(p)

+
+
+
+

+[docs]
+def event(p):
+    """
+    Return True with probability ``p`` and False with probability ``1 - p``.
+
+    Alias for ``event_occurs``.
+
+    Parameters
+    ----------
+    p : float
+        The probability of returning True. Must be between 0 and 1.
+
+    Returns
+    -------
+    bool
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> event(p=0.5)
+    False
+    """
+    return event_occurs(p)

+
+
+
+

+[docs]
+def one_in(p, digits=0, verbose=True):
+    """
+    Convert a probability into "1 in X" notation.
+
+    Parameters
+    ----------
+    p : float
+        The probability to convert.
+    digits : int
+        The number of digits to round the result to. Defaults to 0. If ``digits``
+        is 0, the result will be converted to int instead of float.
+    verbose : logical
+        If True, will return a string with "1 in X". If False, will just return X.
+
+    Returns
+    -------
+    str if ``verbose`` is True. Otherwise, int if ``digits`` is 0 or float if ``digits`` > 0.
+
+    Examples
+    --------
+    >>> one_in(0.1)
+    "1 in 10"
+    """
+    p = _round(1 / p, digits)
+    return "1 in {:,}".format(p) if verbose else p

+
+
+
+

+[docs]
+def get_percentiles(
+    data,
+    percentiles=[1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99],
+    reverse=False,
+    digits=None,
+):
+    """
+    Print the percentiles of the data.
+
+    Parameters
+    ----------
+    data : list or np.array
+        The data to calculate percentiles for.
+    percentiles : list
+        A list of percentiles to calculate. Must be values between 0 and 100.
+    reverse : bool
+        If `True`, the percentile values are reversed (e.g., 95th and 5th percentile
+        swap values.)
+    digits : int or None
+        The number of digits to display (using rounding).
+
+    Returns
+    -------
+    dict
+        A dictionary of the given percentiles.
+
+    Examples
+    --------
+    >>> get_percentiles(range(100), percentiles=[25, 50, 75])
+    {25: 24.75, 50: 49.5, 75: 74.25}
+    """
+    percentiles = percentiles if isinstance(percentiles, list) else [percentiles]
+    percentile_labels = list(reversed(percentiles)) if reverse else percentiles
+    percentiles = np.percentile(data, percentiles)
+    percentiles = [_round(p, digits) for p in percentiles]
+    if len(percentile_labels) == 1:
+        return percentiles[0]
+    else:
+        return dict(list(zip(percentile_labels, percentiles)))

+
+
+
+

+[docs]
+def get_log_percentiles(
+    data,
+    percentiles=[1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99],
+    reverse=False,
+    display=True,
+    digits=1,
+):
+    """
+    Print the log (base 10) of the percentiles of the data.
+
+    Parameters
+    ----------
+    data : list or np.array
+        The data to calculate percentiles for.
+    percentiles : list
+        A list of percentiles to calculate. Must be values between 0 and 100.
+    reverse : bool
+        If True, the percentile values are reversed (e.g., 95th and 5th percentile
+        swap values.)
+    display : bool
+        If True, the function returns an easy to read display.
+    digits : int or None
+        The number of digits to display (using rounding).
+
+    Returns
+    -------
+    dict
+        A dictionary of the given percentiles. If ``display`` is true, will be str values.
+        Otherwise will be float values. 10 to the power of the value gives the true percentile.
+
+    Examples
+    --------
+    >>> get_percentiles(range(100), percentiles=[25, 50, 75])
+    {25: 24.75, 50: 49.5, 75: 74.25}
+    """
+    percentiles = get_percentiles(data, percentiles=percentiles, reverse=reverse, digits=digits)
+    if isinstance(percentiles, dict):
+        if display:
+            return dict(
+                [(k, ("{:." + str(digits) + "e}").format(v)) for k, v in percentiles.items()]
+            )
+        else:
+            return dict([(k, _round(np.log10(v), digits)) for k, v in percentiles.items()])
+    else:
+        if display:
+            digit_str = "{:." + str(digits) + "e}"
+            digit_str.format(percentiles)
+        else:
+            return _round(np.log10(percentiles), digits)

+
+
+
+

+[docs]
+def get_mean_and_ci(data, credibility=90, digits=None):
+    """
+    Return the mean and percentiles of the data.
+
+    Parameters
+    ----------
+    data : list or np.array
+        The data to calculate the mean and CI for.
+    credibility : float
+        The credibility of the interval. Must be values between 0 and 100. Default 90 for 90% CI.
+    digits : int or None
+        The number of digits to display (using rounding).
+
+    Returns
+    -------
+    dict
+        A dictionary with the mean and CI.
+
+    Examples
+    --------
+    >>> get_mean_and_ci(range(100))
+    {'mean': 49.5, 'ci_low': 4.95, 'ci_high': 94.05}
+    """
+    ci_low = (100 - credibility) / 2
+    ci_high = 100 - ci_low
+    percentiles = get_percentiles(data, percentiles=[ci_low, ci_high], digits=digits)
+    return {
+        "mean": _round(np.mean(data), digits),
+        "ci_low": percentiles[ci_low],
+        "ci_high": percentiles[ci_high],
+    }

+
+
+
+

+[docs]
+def get_median_and_ci(data, credibility=90, digits=None):
+    """
+    Return the median and percentiles of the data.
+
+    Parameters
+    ----------
+    data : list or np.array
+        The data to calculate the mean and CI for.
+    credibility : float
+        The credibility of the interval. Must be values between 0 and 100. Default 90 for 90% CI.
+    digits : int or None
+        The number of digits to display (using rounding).
+
+    Returns
+    -------
+    dict
+        A dictionary with the median and CI.
+
+    Examples
+    --------
+    >>> get_median_and_ci(range(100))
+    {'mean': 49.5, 'ci_low': 4.95, 'ci_high': 94.05}
+    """
+    ci_low = (100 - credibility) / 2
+    ci_high = 100 - ci_low
+    percentiles = get_percentiles(data, percentiles=[ci_low, 50, ci_high], digits=digits)
+    return {
+        "median": percentiles[50],
+        "ci_low": percentiles[ci_low],
+        "ci_high": percentiles[ci_high],
+    }

+
+
+
+

+[docs]
+def geomean(a, weights=None, relative_weights=None, drop_na=True):
+    """
+    Calculate the geometric mean.
+
+    Parameters
+    ----------
+    a : list or np.array
+        The values to calculate the geometric mean of.
+    weights : list or None
+        The weights, if a weighted geometric mean is desired.
+    relative_weights : list or None
+        Relative weights, which if given will be weights that are normalized
+        to sum to 1.
+    drop_na : boolean
+        Should NA-like values be dropped when calculating the geomean?
+
+    Returns
+    -------
+    float
+
+    Examples
+    --------
+    >>> geomean([1, 3, 10])
+    3.1072325059538595
+    """
+    weights, a = _process_weights_values(weights, relative_weights, a, drop_na=drop_na)
+    log_a = np.log(a)
+    return np.exp(np.average(log_a, weights=weights))

+
+
+
+

+[docs]
+def p_to_odds(p):
+    """
+    Calculate the decimal odds from a given probability.
+
+    Parameters
+    ----------
+    p : float
+        The probability to calculate decimal odds for. Must be between 0 and 1.
+
+    Returns
+    -------
+    float
+        Decimal odds
+
+    Examples
+    --------
+    >>> p_to_odds(0.1)
+    0.1111111111111111
+    """
+
+    def _convert(p):
+        if _is_na_like(p):
+            return p
+        if p <= 0 or p >= 1:
+            raise ValueError("p must be between 0 and 1")
+        return p / (1 - p)
+
+    return _simplify(np.array([_convert(p) for p in _enlist(p)]))

+
+
+
+

+[docs]
+def odds_to_p(odds):
+    """
+    Calculate the probability from given decimal odds.
+
+    Parameters
+    ----------
+    odds : float
+        The decimal odds to calculate the probability for.
+
+    Returns
+    -------
+    float
+        Probability
+
+    Examples
+    --------
+    >>> odds_to_p(0.1)
+    0.09090909090909091
+    """
+
+    def _convert(o):
+        if _is_na_like(o):
+            return o
+        if o <= 0:
+            raise ValueError("odds must be greater than 0")
+        return o / (1 + o)
+
+    return _simplify(np.array([_convert(o) for o in _enlist(odds)]))

+
+
+
+

+[docs]
+def geomean_odds(a, weights=None, relative_weights=None, drop_na=True):
+    """
+    Calculate the geometric mean of odds.
+
+    Parameters
+    ----------
+    a : list or np.array
+        The probabilities to calculate the geometric mean of. These are converted to odds
+        before the geometric mean is taken..
+    weights : list or None
+        The weights, if a weighted geometric mean is desired.
+    relative_weights : list or None
+        Relative weights, which if given will be weights that are normalized
+        to sum to 1.
+    drop_na : boolean
+        Should NA-like values be dropped when calculating the geomean?
+
+    Returns
+    -------
+    float
+
+    Examples
+    --------
+    >>> geomean_odds([0.1, 0.3, 0.9])
+    0.42985748800076845
+    """
+    weights, a = _process_weights_values(weights, relative_weights, a, drop_na=drop_na)
+    return odds_to_p(geomean(p_to_odds(a), weights=weights))

+
+
+
+

+[docs]
+def laplace(s, n=None, time_passed=None, time_remaining=None, time_fixed=False):
+    """
+    Return probability of success on next trial given Laplace's law of succession.
+
+    Also can be used to calculate a time-invariant version defined in
+    https://www.lesswrong.com/posts/wE7SK8w8AixqknArs/a-time-invariant-version-of-laplace-s-rule
+
+    Parameters
+    ----------
+    s : int
+        The number of successes among ``n`` past trials or among ``time_passed`` amount of time.
+    n : int or None
+        The number of trials that contain the successes (and/or failures). Leave as None if
+        time-invariant mode is desired.
+    time_passed : float or None
+        The amount of time that has passed when the successes (and/or failures) occured for
+        calculating a time-invariant Laplace.
+    time_remaining : float or None
+        We are calculating the likelihood of observing at least one success over this time
+        period.
+    time_fixed : bool
+        This should be False if the time period is variable - that is, if the time period
+        was chosen specifically to include the most recent success. Otherwise the time period
+        is fixed and this should be True. Defaults to False.
+
+    Returns
+    -------
+    float
+        The probability of at least one success in the next trial or ``time_remaining`` amount
+        of time.
+
+    Examples
+    --------
+    >>> # The sun has risen the past 100,000 days. What are the odds it rises again tomorrow?
+    >>> laplace(s=100*K, n=100*K)
+    0.999990000199996
+    >>> # The last time a nuke was used in war was 77 years ago. What are the odds a nuke
+    >>> # is used in the next year, not considering any information other than this naive prior?
+    >>> laplace(s=1, time_passed=77, time_remaining=1, time_fixed=False)
+    0.012820512820512664
+    """
+    if n is not None and s > n:
+        raise ValueError("`s` cannot be greater than `n`")
+    elif time_passed is None and time_remaining is None and n is not None:
+        return (s + 1) / (n + 2)
+    elif time_passed is not None and time_remaining is not None and s == 0:
+        return 1 - ((1 + time_remaining / time_passed) ** -1)
+    elif time_passed is not None and time_remaining is not None and s > 0 and not time_fixed:
+        return 1 - ((1 + time_remaining / time_passed) ** -s)
+    elif time_passed is not None and time_remaining is not None and s > 0 and time_fixed:
+        return 1 - ((1 + time_remaining / time_passed) ** -(s + 1))
+    elif time_passed is not None and time_remaining is None and s == 0:
+        return 1 - ((1 + 1 / time_passed) ** -1)
+    elif time_passed is not None and time_remaining is None and s > 0 and not time_fixed:
+        return 1 - ((1 + 1 / time_passed) ** -s)
+    elif time_passed is not None and time_remaining is None and s > 0 and time_fixed:
+        return 1 - ((1 + 1 / time_passed) ** -(s + 1))
+    elif time_passed is None and n is None:
+        raise ValueError("Must define `time_passed` or `n`")
+    elif time_passed is None and time_remaining is not None:
+        raise ValueError("Must define `time_passed`")
+    else:
+        raise ValueError("Fatal logic error - programmer made mistake!")

+
+
+
+

+[docs]
+def growth_rate_to_doubling_time(growth_rate):
+    """
+    Convert a positive growth rate to a doubling rate.
+
+    Growth rate must be expressed as a number, numpy array or distribution
+    where 0.05 means +5% to a doubling time. The time unit remains the same, so if we've
+    got +5% annual growth, the returned value is the doubling time in years.
+
+    NOTE: This only works works for numbers, arrays and distributions where all numbers
+    are above 0. (Otherwise it makes no sense to talk about doubling times.)
+
+    Parameters
+    ----------
+    growth_rate : float or np.array or BaseDistribution
+        The growth rate expressed as a fraction (the percentage divided by 100).
+
+    Returns
+    -------
+    float or np.array or ComplexDistribution
+        Returns the doubling time.
+
+    Examples
+    --------
+    >>> growth_rate_to_doubling_time(0.01)
+    69.66071689357483
+    """
+    if is_dist(growth_rate):
+        from .distributions import dist_log
+
+        return math.log(2) / dist_log(1.0 + growth_rate)
+    elif _is_numpy(growth_rate):
+        return np.log(2) / np.log(1.0 + growth_rate)
+    else:
+        return math.log(2) / math.log(1.0 + growth_rate)

+
+
+
+

+[docs]
+def doubling_time_to_growth_rate(doubling_time):
+    """
+    Convert a doubling time to a growth rate.
+
+    Doubling time is expressed as a number, numpy array or distribution in any
+    time unit. Growth rate is set where e.g. 0.05 means +5%. The time unit remains the
+    same, so if we've got a doubling time of 2 years, the returned value is the annual
+    growth rate.
+
+    NOTE: This only works works for numbers, arrays and distributions where all numbers
+    are above 0. (Otherwise it makes no sense to talk about doubling times.)
+
+    Parameters
+    ----------
+    doubling_time : float or np.array or BaseDistribution
+        The doubling time expressed in any time unit.
+
+    Returns
+    -------
+    float or np.array or ComplexDistribution
+        Returns the growth rate expressed as a fraction (the percentage divided by 100).
+
+    Examples
+    --------
+    >>> doubling_time_to_growth_rate(12)
+    0.05946309435929531
+    """
+    if is_dist(doubling_time):
+        from .distributions import dist_exp
+
+        return dist_exp(math.log(2) / doubling_time) - 1
+    elif _is_numpy(doubling_time):
+        return np.exp(np.log(2) / doubling_time) - 1
+    else:
+        return math.exp(math.log(2) / doubling_time) - 1

+
+
+
+

+[docs]
+def roll_die(sides, n=1):
+    """
+    Roll a die.
+
+    Parameters
+    ----------
+    sides : int
+        The number of sides of the die that is rolled.
+    n : int
+        The number of dice to be rolled.
+
+    Returns
+    -------
+    int or list
+        Returns the value of each die roll.
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> roll_die(6)
+    5
+    """
+    if is_dist(sides) or callable(sides):
+        from .samplers import sample
+
+        sides = sample(sides)
+    if not isinstance(n, int):
+        raise ValueError("can only roll an integer number of times")
+    elif sides < 2:
+        raise ValueError("cannot roll less than a 2-sided die.")
+    elif not isinstance(sides, int):
+        raise ValueError("can only roll an integer number of sides")
+    else:
+        from .samplers import sample
+        from .distributions import discrete
+
+        return sample(discrete(list(range(1, sides + 1))), n=n) if sides > 0 else None

+
+
+
+

+[docs]
+def flip_coin(n=1):
+    """
+    Flip a coin.
+
+    Parameters
+    ----------
+    n : int
+        The number of coins to be flipped.
+
+    Returns
+    -------
+    str or list
+        Returns the value of each coin flip, as either "heads" or "tails"
+
+    Examples
+    --------
+    >>> set_seed(42)
+    >>> flip_coin()
+    'heads'
+    """
+    rolls = roll_die(2, n=n)
+    if isinstance(rolls, int):
+        rolls = [rolls]
+    flips = ["heads" if d == 2 else "tails" for d in rolls]
+    return flips[0] if len(flips) == 1 else flips

+
+
+
+

+[docs]
+def kelly(my_price, market_price, deference=0, bankroll=1, resolve_date=None, current=0):
+    """
+    Calculate the Kelly criterion.
+
+    Parameters
+    ----------
+    my_price : float
+        The price (or probability) you give for the given event.
+    market_price : float
+        The price the market is giving for that event.
+    deference : float
+        How much deference (or weight) do you give the market price? Use 0.5 for half Kelly
+        and 0.75 for quarter Kelly. Defaults to 0, which is full Kelly.
+    bankroll : float
+        How much money do you have to bet? Defaults to 1.
+    resolve_date : str or None
+        When will the event happen, the market resolve, and you get your money back? Used for
+        calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
+        ARR is not calculated.
+    current : float
+        How much do you already have invested in this event? Used for calculating the
+        additional amount you should invest. Defaults to 0.
+
+    Returns
+    -------
+    dict
+        A dict of values specifying:
+        * ``my_price``
+        * ``market_price``
+        * ``deference``
+        * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
+          into account.
+        * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
+        * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
+          ``market_price``.
+        * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
+          you should bet.
+        * ``target`` : the target amount of money you should have invested
+        * ``current``
+        * ``delta`` : the amount of money you should invest given what you already
+          have invested
+        * ``max_gain`` : the amount of money you would gain if you win
+        * ``modeled_gain`` : the expected value you would win given ``adj_price``
+        * ``expected_roi`` : the expected return on investment
+        * ``expected_arr`` : the expected ARR given ``resolve_date``
+        * ``resolve_date``
+
+    Examples
+    --------
+    >>> kelly(my_price=0.7, market_price=0.4, deference=0.5, bankroll=100)
+    {'my_price': 0.7, 'market_price': 0.4, 'deference': 0.5, 'adj_price': 0.55,
+     'delta_price': 0.3, 'adj_delta_price': 0.15, 'kelly': 0.25, 'target': 25.0,
+     'current': 0, 'delta': 25.0, 'max_gain': 62.5, 'modeled_gain': 23.13,
+     'expected_roi': 0.375, 'expected_arr': None, 'resolve_date': None}
+    """
+    if market_price >= 1 or market_price <= 0:
+        raise ValueError("market_price must be >0 and <1")
+    if my_price >= 1 or my_price <= 0:
+        raise ValueError("my_price must be >0 and <1")
+    if deference > 1 or deference < 0:
+        raise ValueError("deference must be >=0 and <=1")
+    adj_price = my_price * (1 - deference) + market_price * deference
+    kelly = np.abs(adj_price - ((1 - adj_price) * (market_price / (1 - market_price))))
+    target = bankroll * kelly
+    expected_roi = np.abs((adj_price / market_price) - 1)
+    if resolve_date is None:
+        expected_arr = None
+    else:
+        resolve_date = datetime.strptime(resolve_date, "%Y-%m-%d")
+        expected_arr = ((expected_roi + 1) ** (365 / (resolve_date - datetime.now()).days)) - 1
+    return {
+        "my_price": round(my_price, 2),
+        "market_price": round(market_price, 2),
+        "deference": round(deference, 3),
+        "adj_price": round(adj_price, 2),
+        "delta_price": round(np.abs(market_price - my_price), 2),
+        "adj_delta_price": round(np.abs(market_price - adj_price), 2),
+        "kelly": round(kelly, 3),
+        "target": round(target, 2),
+        "current": round(current, 2),
+        "delta": round(target - current, 2),
+        "max_gain": round(target / market_price, 2),
+        "modeled_gain": round(
+            (adj_price * (target / market_price) + (1 - adj_price) * -target), 2
+        ),
+        "expected_roi": round(expected_roi, 3),
+        "expected_arr": round(expected_arr, 3) if expected_arr is not None else None,
+        "resolve_date": resolve_date,
+    }

+
+
+
+

+[docs]
+def full_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0):
+    """
+    Alias for ``kelly`` where ``deference`` is 0.
+
+    Parameters
+    ----------
+    my_price : float
+        The price (or probability) you give for the given event.
+    market_price : float
+        The price the market is giving for that event.
+    bankroll : float
+        How much money do you have to bet? Defaults to 1.
+    resolve_date : str or None
+        When will the event happen, the market resolve, and you get your money back? Used for
+        calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
+        ARR is not calculated.
+    current : float
+        How much do you already have invested in this event? Used for calculating the
+        additional amount you should invest. Defaults to 0.
+
+    Returns
+    -------
+    dict
+        A dict of values specifying:
+        * ``my_price``
+        * ``market_price``
+        * ``deference``
+        * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
+          into account.
+        * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
+        * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
+          ``market_price``.
+        * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
+          you should bet.
+        * ``target`` : the target amount of money you should have invested
+        * ``current``
+        * ``delta`` : the amount of money you should invest given what you already
+          have invested
+        * ``max_gain`` : the amount of money you would gain if you win
+        * ``modeled_gain`` : the expected value you would win given ``adj_price``
+        * ``expected_roi`` : the expected return on investment
+        * ``expected_arr`` : the expected ARR given ``resolve_date``
+        * ``resolve_date``
+
+    Examples
+    --------
+    >>> full_kelly(my_price=0.7, market_price=0.4, bankroll=100)
+    {'my_price': 0.7, 'market_price': 0.4, 'deference': 0, 'adj_price': 0.7,
+     'delta_price': 0.3, 'adj_delta_price': 0.3, 'kelly': 0.5, 'target': 50.0,
+     'current': 0, 'delta': 50.0, 'max_gain': 125.0, 'modeled_gain': 72.5,
+     'expected_roi': 0.75, 'expected_arr': None, 'resolve_date': None}
+    """
+    return kelly(
+        my_price=my_price,
+        market_price=market_price,
+        bankroll=bankroll,
+        resolve_date=resolve_date,
+        current=current,
+        deference=0,
+    )

+
+
+
+

+[docs]
+def half_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0):
+    """
+    Alias for ``kelly`` where ``deference`` is 0.5.
+
+    Parameters
+    ----------
+    my_price : float
+        The price (or probability) you give for the given event.
+    market_price : float
+        The price the market is giving for that event.
+    bankroll : float
+        How much money do you have to bet? Defaults to 1.
+    resolve_date : str or None
+        When will the event happen, the market resolve, and you get your money back? Used for
+        calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
+        ARR is not calculated.
+    current : float
+        How much do you already have invested in this event? Used for calculating the
+        additional amount you should invest. Defaults to 0.
+
+    Returns
+    -------
+    dict
+        A dict of values specifying:
+        * ``my_price``
+        * ``market_price``
+        * ``deference``
+        * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
+          into account.
+        * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
+        * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
+          ``market_price``.
+        * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
+          you should bet.
+        * ``target`` : the target amount of money you should have invested
+        * ``current``
+        * ``delta`` : the amount of money you should invest given what you already
+          have invested
+        * ``max_gain`` : the amount of money you would gain if you win
+        * ``modeled_gain`` : the expected value you would win given ``adj_price``
+        * ``expected_roi`` : the expected return on investment
+        * ``expected_arr`` : the expected ARR given ``resolve_date``
+        * ``resolve_date``
+
+    Examples
+    --------
+    >>> half_kelly(my_price=0.7, market_price=0.4, bankroll=100)
+    {'my_price': 0.7, 'market_price': 0.4, 'deference': 0.5, 'adj_price': 0.55,
+     'delta_price': 0.3, 'adj_delta_price': 0.15, 'kelly': 0.25, 'target': 25.0,
+     'current': 0, 'delta': 25.0, 'max_gain': 62.5, 'modeled_gain': 23.13,
+     'expected_roi': 0.375, 'expected_arr': None, 'resolve_date': None}
+    """
+    return kelly(
+        my_price=my_price,
+        market_price=market_price,
+        bankroll=bankroll,
+        resolve_date=resolve_date,
+        current=current,
+        deference=0.5,
+    )

+
+
+
+

+[docs]
+def quarter_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0):
+    """
+    Alias for ``kelly`` where ``deference`` is 0.75.
+
+    Parameters
+    ----------
+    my_price : float
+        The price (or probability) you give for the given event.
+    market_price : float
+        The price the market is giving for that event.
+    bankroll : float
+        How much money do you have to bet? Defaults to 1.
+    resolve_date : str or None
+        When will the event happen, the market resolve, and you get your money back? Used for
+        calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
+        ARR is not calculated.
+    current : float
+        How much do you already have invested in this event? Used for calculating the
+        additional amount you should invest. Defaults to 0.
+
+    Returns
+    -------
+    dict
+        A dict of values specifying:
+        * ``my_price``
+        * ``market_price``
+        * ``deference``
+        * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
+          into account.
+        * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
+        * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
+          ``market_price``.
+        * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
+          you should bet.
+        * ``target`` : the target amount of money you should have invested
+        * ``current``
+        * ``delta`` : the amount of money you should invest given what you already
+          have invested
+        * ``max_gain`` : the amount of money you would gain if you win
+        * ``modeled_gain`` : the expected value you would win given ``adj_price``
+        * ``expected_roi`` : the expected return on investment
+        * ``expected_arr`` : the expected ARR given ``resolve_date``
+        * ``resolve_date``
+
+    Examples
+    --------
+    >>> quarter_kelly(my_price=0.7, market_price=0.4, bankroll=100)
+    {'my_price': 0.7, 'market_price': 0.4, 'deference': 0.75, 'adj_price': 0.48,
+     'delta_price': 0.3, 'adj_delta_price': 0.08, 'kelly': 0.125, 'target': 12.5,
+     'current': 0, 'delta': 12.5, 'max_gain': 31.25, 'modeled_gain': 8.28,
+     'expected_roi': 0.188, 'expected_arr': None, 'resolve_date': None}
+    """
+    return kelly(
+        my_price=my_price,
+        market_price=market_price,
+        bankroll=bankroll,
+        resolve_date=resolve_date,
+        current=current,
+        deference=0.75,
+    )

+
+
+
+

+[docs]
+def extremize(p, e):
+    """
+    Extremize a prediction.
+
+    Parameters
+    ----------
+    p : float
+        The prediction to extremize. Must be within 0-1.
+    e : float
+        The extremization factor.
+
+    Returns
+    -------
+    float
+        The extremized prediction
+
+    Examples
+    --------
+    >>> # Extremizing of 1.73 per https://arxiv.org/abs/2111.03153
+    >>> extremize(p=0.7, e=1.73)
+    0.875428191155692
+    """
+    if p <= 0 or p >= 1:
+        raise ValueError("`p` must be greater than 0 and less than 1")
+
+    if p > 0.5:
+        return 1 - ((1 - p) ** e)
+    else:
+        return p**e

+
+
+ +
+ + + + + +
+ +
+
+
+ +
+ + + + +
+
+ +
+ +
+
+
+ + + + + +
+
+ +
+ +
+

+ + © Copyright 2023, Peter Wildeford. +
+ +

+
+ +
+

+ Created using Sphinx 7.2.6. +
+

+
+ +
+ + + +
+ +

+ Built with the PyData Sphinx Theme 0.14.3. +

+ +
+ +
+ +
+ + \ No newline at end of file diff --git a/docs/build/html/_sources/examples.rst.txt b/docs/build/html/_sources/examples.rst.txt new file mode 100644 index 0000000..c00053f --- /dev/null +++ b/docs/build/html/_sources/examples.rst.txt @@ -0,0 +1,468 @@ +Examples +======== + +Piano Tuners Example +~~~~~~~~~~~~~~~~~~~~ + +Here’s the Squigglepy implementation of `the example from Squiggle +Docs `__: + +.. code:: python + + import squigglepy as sq + import numpy as np + import matplotlib.pyplot as plt + from squigglepy.numbers import K, M + from pprint import pprint + + pop_of_ny_2022 = sq.to(8.1*M, 8.4*M) # This means that you're 90% confident the value is between 8.1 and 8.4 Million. + pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01 # We assume there are almost no people with multiple pianos + pianos_per_piano_tuner = sq.to(2*K, 50*K) + piano_tuners_per_piano = 1 / pianos_per_piano_tuner + total_tuners_in_2022 = pop_of_ny_2022 * pct_of_pop_w_pianos * piano_tuners_per_piano + samples = total_tuners_in_2022 @ 1000 # Note: `@ 1000` is shorthand to get 1000 samples + + # Get mean and SD + print('Mean: {}, SD: {}'.format(round(np.mean(samples), 2), + round(np.std(samples), 2))) + + # Get percentiles + pprint(sq.get_percentiles(samples, digits=0)) + + # Histogram + plt.hist(samples, bins=200) + plt.show() + + # Shorter histogram + total_tuners_in_2022.plot() + +And the version from the Squiggle doc that incorporates time: + +.. code:: python + + import squigglepy as sq + from squigglepy.numbers import K, M + + pop_of_ny_2022 = sq.to(8.1*M, 8.4*M) + pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01 + pianos_per_piano_tuner = sq.to(2*K, 50*K) + piano_tuners_per_piano = 1 / pianos_per_piano_tuner + + def pop_at_time(t): # t = Time in years after 2022 + avg_yearly_pct_change = sq.to(-0.01, 0.05) # We're expecting NYC to continuously grow with an mean of roughly between -1% and +4% per year + return pop_of_ny_2022 * ((avg_yearly_pct_change + 1) ** t) + + def total_tuners_at_time(t): + return pop_at_time(t) * pct_of_pop_w_pianos * piano_tuners_per_piano + + # Get total piano tuners at 2030 + sq.get_percentiles(total_tuners_at_time(2030-2022) @ 1000) + +**WARNING:** Be careful about dividing by ``K``, ``M``, etc. ``1/2*K`` = +500 in Python. Use ``1/(2*K)`` instead to get the expected outcome. + +**WARNING:** Be careful about using ``K`` to get sample counts. Use +``sq.norm(2, 3) @ (2*K)``\ … ``sq.norm(2, 3) @ 2*K`` will return only +two samples, multiplied by 1000. + +Distributions +~~~~~~~~~~~~~ + +.. code:: python + + import squigglepy as sq + + # Normal distribution + sq.norm(1, 3) # 90% interval from 1 to 3 + + # Distribution can be sampled with mean and sd too + sq.norm(mean=0, sd=1) + + # Shorthand to get one sample + ~sq.norm(1, 3) + + # Shorthand to get more than one sample + sq.norm(1, 3) @ 100 + + # Longhand version to get more than one sample + sq.sample(sq.norm(1, 3), n=100) + + # Nice progress reporter + sq.sample(sq.norm(1, 3), n=1000, verbose=True) + + # Other distributions exist + sq.lognorm(1, 10) + sq.tdist(1, 10, t=5) + sq.triangular(1, 2, 3) + sq.pert(1, 2, 3, lam=2) + sq.binomial(p=0.5, n=5) + sq.beta(a=1, b=2) + sq.bernoulli(p=0.5) + sq.poisson(10) + sq.chisquare(2) + sq.gamma(3, 2) + sq.pareto(1) + sq.exponential(scale=1) + sq.geometric(p=0.5) + + # Discrete sampling + sq.discrete({'A': 0.1, 'B': 0.9}) + + # Can return integers + sq.discrete({0: 0.1, 1: 0.3, 2: 0.3, 3: 0.15, 4: 0.15}) + + # Alternate format (also can be used to return more complex objects) + sq.discrete([[0.1, 0], + [0.3, 1], + [0.3, 2], + [0.15, 3], + [0.15, 4]]) + + sq.discrete([0, 1, 2]) # No weights assumes equal weights + + # You can mix distributions together + sq.mixture([sq.norm(1, 3), + sq.norm(4, 10), + sq.lognorm(1, 10)], # Distributions to mix + [0.3, 0.3, 0.4]) # These are the weights on each distribution + + # This is equivalent to the above, just a different way of doing the notation + sq.mixture([[0.3, sq.norm(1,3)], + [0.3, sq.norm(4,10)], + [0.4, sq.lognorm(1,10)]]) + + # Make a zero-inflated distribution + # 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`. + sq.zero_inflated(0.6, sq.norm(1, 2)) + +Additional Features +~~~~~~~~~~~~~~~~~~~ + +.. code:: python + + import squigglepy as sq + + # You can add and subtract distributions + (sq.norm(1,3) + sq.norm(4,5)) @ 100 + (sq.norm(1,3) - sq.norm(4,5)) @ 100 + (sq.norm(1,3) * sq.norm(4,5)) @ 100 + (sq.norm(1,3) / sq.norm(4,5)) @ 100 + + # You can also do math with numbers + ~((sq.norm(sd=5) + 2) * 2) + ~(-sq.lognorm(0.1, 1) * sq.pareto(1) / 10) + + # You can change the CI from 90% (default) to 80% + sq.norm(1, 3, credibility=80) + + # You can clip + sq.norm(0, 3, lclip=0, rclip=5) # Sample norm with a 90% CI from 0-3, but anything lower than 0 gets clipped to 0 and anything higher than 5 gets clipped to 5. + + # You can also clip with a function, and use pipes + sq.norm(0, 3) >> sq.clip(0, 5) + + # You can correlate continuous distributions + a, b = sq.uniform(-1, 1), sq.to(0, 3) + a, b = sq.correlate((a, b), 0.5) # Correlate a and b with a correlation of 0.5 + # You can even pass your own correlation matrix! + a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]]) + +Example: Rolling a Die +^^^^^^^^^^^^^^^^^^^^^^ + +An example of how to use distributions to build tools: + +.. code:: python + + import squigglepy as sq + + def roll_die(sides, n=1): + return sq.discrete(list(range(1, sides + 1))) @ n if sides > 0 else None + + roll_die(sides=6, n=10) + # [2, 6, 5, 2, 6, 2, 3, 1, 5, 2] + +This is already included standard in the utils of this package. Use +``sq.roll_die``. + +Bayesian inference +~~~~~~~~~~~~~~~~~~ + +1% of women at age forty who participate in routine screening have +breast cancer. 80% of women with breast cancer will get positive +mammographies. 9.6% of women without breast cancer will also get +positive mammographies. + +A woman in this age group had a positive mammography in a routine +screening. What is the probability that she actually has breast cancer? + +We can approximate the answer with a Bayesian network (uses rejection +sampling): + +.. code:: python + + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import M + + def mammography(has_cancer): + return sq.event(0.8 if has_cancer else 0.096) + + def define_event(): + cancer = ~sq.bernoulli(0.01) + return({'mammography': mammography(cancer), + 'cancer': cancer}) + + bayes.bayesnet(define_event, + find=lambda e: e['cancer'], + conditional_on=lambda e: e['mammography'], + n=1*M) + # 0.07723995880535531 + +Or if we have the information immediately on hand, we can directly +calculate it. Though this doesn’t work for very complex stuff. + +.. code:: python + + from squigglepy import bayes + bayes.simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096) + # 0.07763975155279504 + +You can also make distributions and update them: + +.. code:: python + + import matplotlib.pyplot as plt + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import K + import numpy as np + + print('Prior') + prior = sq.norm(1,5) + prior_samples = prior @ (10*K) + plt.hist(prior_samples, bins = 200) + plt.show() + print(sq.get_percentiles(prior_samples)) + print('Prior Mean: {} SD: {}'.format(np.mean(prior_samples), np.std(prior_samples))) + print('-') + + print('Evidence') + evidence = sq.norm(2,3) + evidence_samples = evidence @ (10*K) + plt.hist(evidence_samples, bins = 200) + plt.show() + print(sq.get_percentiles(evidence_samples)) + print('Evidence Mean: {} SD: {}'.format(np.mean(evidence_samples), np.std(evidence_samples))) + print('-') + + print('Posterior') + posterior = bayes.update(prior, evidence) + posterior_samples = posterior @ (10*K) + plt.hist(posterior_samples, bins = 200) + plt.show() + print(sq.get_percentiles(posterior_samples)) + print('Posterior Mean: {} SD: {}'.format(np.mean(posterior_samples), np.std(posterior_samples))) + + print('Average') + average = bayes.average(prior, evidence) + average_samples = average @ (10*K) + plt.hist(average_samples, bins = 200) + plt.show() + print(sq.get_percentiles(average_samples)) + print('Average Mean: {} SD: {}'.format(np.mean(average_samples), np.std(average_samples))) + +Example: Alarm net +^^^^^^^^^^^^^^^^^^ + +This is the alarm network from `Bayesian Artificial Intelligence - +Section +2.5.1 `__: + + Assume your house has an alarm system against burglary. + + You live in the seismically active area and the alarm system can get + occasionally set off by an earthquake. + + You have two neighbors, Mary and John, who do not know each other. If + they hear the alarm they call you, but this is not guaranteed. + + The chance of a burglary on a particular day is 0.1%. The chance of + an earthquake on a particular day is 0.2%. + + The alarm will go off 95% of the time with both a burglary and an + earthquake, 94% of the time with just a burglary, 29% of the time + with just an earthquake, and 0.1% of the time with nothing (total + false alarm). + + John will call you 90% of the time when the alarm goes off. But on 5% + of the days, John will just call to say “hi”. Mary will call you 70% + of the time when the alarm goes off. But on 1% of the days, Mary will + just call to say “hi”. + +.. code:: python + + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import M + + def p_alarm_goes_off(burglary, earthquake): + if burglary and earthquake: + return 0.95 + elif burglary and not earthquake: + return 0.94 + elif not burglary and earthquake: + return 0.29 + elif not burglary and not earthquake: + return 0.001 + + def p_john_calls(alarm_goes_off): + return 0.9 if alarm_goes_off else 0.05 + + def p_mary_calls(alarm_goes_off): + return 0.7 if alarm_goes_off else 0.01 + + def define_event(): + burglary_happens = sq.event(p=0.001) + earthquake_happens = sq.event(p=0.002) + alarm_goes_off = sq.event(p_alarm_goes_off(burglary_happens, earthquake_happens)) + john_calls = sq.event(p_john_calls(alarm_goes_off)) + mary_calls = sq.event(p_mary_calls(alarm_goes_off)) + return {'burglary': burglary_happens, + 'earthquake': earthquake_happens, + 'alarm_goes_off': alarm_goes_off, + 'john_calls': john_calls, + 'mary_calls': mary_calls} + + # What are the chances that both John and Mary call if an earthquake happens? + bayes.bayesnet(define_event, + n=1*M, + find=lambda e: (e['mary_calls'] and e['john_calls']), + conditional_on=lambda e: e['earthquake']) + # Result will be ~0.19, though it varies because it is based on a random sample. + # This also may take a minute to run. + + # If both John and Mary call, what is the chance there's been a burglary? + bayes.bayesnet(define_event, + n=1*M, + find=lambda e: e['burglary'], + conditional_on=lambda e: (e['mary_calls'] and e['john_calls'])) + # Result will be ~0.27, though it varies because it is based on a random sample. + # This will run quickly because there is a built-in cache. + # Use `cache=False` to not build a cache and `reload_cache=True` to recalculate the cache. + +Note that the amount of Bayesian analysis that squigglepy can do is +pretty limited. For more complex bayesian analysis, consider +`sorobn `__, +`pomegranate `__, +`bnlearn `__, or +`pyMC `__. + +Example: A Demonstration of the Monty Hall Problem +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code:: python + + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import K, M, B, T + + + def monte_hall(door_picked, switch=False): + doors = ['A', 'B', 'C'] + car_is_behind_door = ~sq.discrete(doors) + reveal_door = ~sq.discrete([d for d in doors if d != door_picked and d != car_is_behind_door]) + + if switch: + old_door_picked = door_picked + door_picked = [d for d in doors if d != old_door_picked and d != reveal_door][0] + + won_car = (car_is_behind_door == door_picked) + return won_car + + + def define_event(): + door = ~sq.discrete(['A', 'B', 'C']) + switch = sq.event(0.5) + return {'won': monte_hall(door_picked=door, switch=switch), + 'switched': switch} + + RUNS = 10*K + r = bayes.bayesnet(define_event, + find=lambda e: e['won'], + conditional_on=lambda e: e['switched'], + verbose=True, + n=RUNS) + print('Win {}% of the time when switching'.format(int(r * 100))) + + r = bayes.bayesnet(define_event, + find=lambda e: e['won'], + conditional_on=lambda e: not e['switched'], + verbose=True, + n=RUNS) + print('Win {}% of the time when not switching'.format(int(r * 100))) + + # Win 66% of the time when switching + # Win 34% of the time when not switching + +Example: More complex coin/dice interactions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + + Imagine that I flip a coin. If heads, I take a random die out of my + blue bag. If tails, I take a random die out of my red bag. The blue + bag contains only 6-sided dice. The red bag contains a 4-sided die, a + 6-sided die, a 10-sided die, and a 20-sided die. I then roll the + random die I took. What is the chance that I roll a 6? + +.. code:: python + + import squigglepy as sq + from squigglepy.numbers import K, M, B, T + from squigglepy import bayes + + def define_event(): + if sq.flip_coin() == 'heads': # Blue bag + return sq.roll_die(6) + else: # Red bag + return sq.discrete([4, 6, 10, 20]) >> sq.roll_die + + + bayes.bayesnet(define_event, + find=lambda e: e == 6, + verbose=True, + n=100*K) + # This run for me returned 0.12306 which is pretty close to the correct answer of 0.12292 + +Kelly betting +~~~~~~~~~~~~~ + +You can use probability generated, combine with a bankroll to determine +bet sizing using `Kelly +criterion `__. + +For example, if you want to Kelly bet and you’ve… + +- determined that your price (your probability of the event in question + happening / the market in question resolving in your favor) is $0.70 + (70%) +- see that the market is pricing at $0.65 +- you have a bankroll of $1000 that you are willing to bet + +You should bet as follows: + +.. code:: python + + import squigglepy as sq + kelly_data = sq.kelly(my_price=0.70, market_price=0.65, bankroll=1000) + kelly_data['kelly'] # What fraction of my bankroll should I bet on this? + # 0.143 + kelly_data['target'] # How much money should be invested in this? + # 142.86 + kelly_data['expected_roi'] # What is the expected ROI of this bet? + # 0.077 + +More examples +~~~~~~~~~~~~~ + +You can see more examples of squigglepy in action +`here `__. diff --git a/docs/build/html/_sources/index.rst.txt b/docs/build/html/_sources/index.rst.txt index 9a79421..1fdb7aa 100644 --- a/docs/build/html/_sources/index.rst.txt +++ b/docs/build/html/_sources/index.rst.txt @@ -1,8 +1,8 @@ Squigglepy: Implementation of Squiggle in Python ================================================ -`Squiggle `__ is a “simple -programming language for intuitive probabilistic estimation”. It serves +`Squiggle `__ is a "simple +programming language for intuitive probabilistic estimation". It serves as its own standalone programming language with its own syntax, but it is implemented in JavaScript. I like the features of Squiggle and intend to use it frequently, but I also sometimes want to use similar @@ -12,7 +12,58 @@ programming packages like Numpy, Pandas, and Matplotlib. The functionalities in Python. .. toctree:: - :maxdepth: 2 - :caption: Contents: + :maxdepth: 3 + :caption: Contents -Check out the :doc:`README ` to get started. + API Reference + Examples + +Installation +------------ + +.. code:: shell + + pip install squigglepy + +For plotting support, you can also use the ``plots`` extra: + +.. code:: shell + + pip install squigglepy[plots] + +Run tests +--------- + +Use ``black .`` for formatting. + +Run +``ruff check . && pytest && pip3 install . && python3 tests/integration.py`` + +Disclaimers +----------- + +This package is unofficial and supported by Peter Wildeford and Rethink +Priorities. It is not affiliated with or associated with the Quantified +Uncertainty Research Institute, which maintains the Squiggle language +(in JavaScript). + +This package is also new and not yet in a stable production version, so +you may encounter bugs and other errors. Please report those so they can +be fixed. It’s also possible that future versions of the package may +introduce breaking changes. + +This package is available under an MIT License. + +Acknowledgements +---------------- + +- The primary author of this package is Peter Wildeford. Agustín + Covarrubias and Bernardo Baron contributed several key features and + developments. +- Thanks to Ozzie Gooen and the Quantified Uncertainty Research + Institute for creating and maintaining the original Squiggle + language. +- Thanks to Dawn Drescher for helping me implement math between + distributions. +- Thanks to Dawn Drescher for coming up with the idea to use ``~`` as a + shorthand for ``sample``, as well as helping me implement it. diff --git a/docs/build/html/_sources/reference/modules.rst.txt b/docs/build/html/_sources/reference/modules.rst.txt new file mode 100644 index 0000000..57192bd --- /dev/null +++ b/docs/build/html/_sources/reference/modules.rst.txt @@ -0,0 +1,7 @@ +squigglepy +========== + +.. toctree:: + :maxdepth: 4 + + squigglepy diff --git a/docs/build/html/_sources/reference/squigglepy.bayes.rst.txt b/docs/build/html/_sources/reference/squigglepy.bayes.rst.txt new file mode 100644 index 0000000..8a445be --- /dev/null +++ b/docs/build/html/_sources/reference/squigglepy.bayes.rst.txt @@ -0,0 +1,7 @@ +squigglepy.bayes module +======================= + +.. automodule:: squigglepy.bayes + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/build/html/_sources/reference/squigglepy.correlation.rst.txt b/docs/build/html/_sources/reference/squigglepy.correlation.rst.txt new file mode 100644 index 0000000..c99cf14 --- /dev/null +++ b/docs/build/html/_sources/reference/squigglepy.correlation.rst.txt @@ -0,0 +1,7 @@ +squigglepy.correlation module +============================= + +.. automodule:: squigglepy.correlation + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/build/html/_sources/reference/squigglepy.distributions.rst.txt b/docs/build/html/_sources/reference/squigglepy.distributions.rst.txt new file mode 100644 index 0000000..bfbdb38 --- /dev/null +++ b/docs/build/html/_sources/reference/squigglepy.distributions.rst.txt @@ -0,0 +1,7 @@ +squigglepy.distributions module +=============================== + +.. automodule:: squigglepy.distributions + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/build/html/_sources/reference/squigglepy.numbers.rst.txt b/docs/build/html/_sources/reference/squigglepy.numbers.rst.txt new file mode 100644 index 0000000..524cbcd --- /dev/null +++ b/docs/build/html/_sources/reference/squigglepy.numbers.rst.txt @@ -0,0 +1,7 @@ +squigglepy.numbers module +========================= + +.. automodule:: squigglepy.numbers + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/build/html/_sources/reference/squigglepy.rng.rst.txt b/docs/build/html/_sources/reference/squigglepy.rng.rst.txt new file mode 100644 index 0000000..84ec740 --- /dev/null +++ b/docs/build/html/_sources/reference/squigglepy.rng.rst.txt @@ -0,0 +1,7 @@ +squigglepy.rng module +===================== + +.. automodule:: squigglepy.rng + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/build/html/_sources/reference/squigglepy.rst.txt b/docs/build/html/_sources/reference/squigglepy.rst.txt new file mode 100644 index 0000000..b629fda --- /dev/null +++ b/docs/build/html/_sources/reference/squigglepy.rst.txt @@ -0,0 +1,22 @@ +squigglepy package +================== + +.. automodule:: squigglepy + :members: + :undoc-members: + :show-inheritance: + +Submodules +---------- + +.. toctree:: + :maxdepth: 4 + + squigglepy.bayes + squigglepy.correlation + squigglepy.distributions + squigglepy.numbers + squigglepy.rng + squigglepy.samplers + squigglepy.utils + squigglepy.version diff --git a/docs/build/html/_sources/reference/squigglepy.samplers.rst.txt b/docs/build/html/_sources/reference/squigglepy.samplers.rst.txt new file mode 100644 index 0000000..ae3e754 --- /dev/null +++ b/docs/build/html/_sources/reference/squigglepy.samplers.rst.txt @@ -0,0 +1,7 @@ +squigglepy.samplers module +========================== + +.. automodule:: squigglepy.samplers + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/build/html/_sources/reference/squigglepy.squigglepy.rst.txt b/docs/build/html/_sources/reference/squigglepy.squigglepy.rst.txt new file mode 100644 index 0000000..9271ec8 --- /dev/null +++ b/docs/build/html/_sources/reference/squigglepy.squigglepy.rst.txt @@ -0,0 +1,78 @@ +squigglepy.squigglepy package +============================= + +Submodules +---------- + +squigglepy.squigglepy.bayes module +---------------------------------- + +.. automodule:: squigglepy.squigglepy.bayes + :members: + :undoc-members: + :show-inheritance: + +squigglepy.squigglepy.correlation module +---------------------------------------- + +.. automodule:: squigglepy.squigglepy.correlation + :members: + :undoc-members: + :show-inheritance: + +squigglepy.squigglepy.distributions module +------------------------------------------ + +.. automodule:: squigglepy.squigglepy.distributions + :members: + :undoc-members: + :show-inheritance: + +squigglepy.squigglepy.numbers module +------------------------------------ + +.. automodule:: squigglepy.squigglepy.numbers + :members: + :undoc-members: + :show-inheritance: + +squigglepy.squigglepy.rng module +-------------------------------- + +.. automodule:: squigglepy.squigglepy.rng + :members: + :undoc-members: + :show-inheritance: + +squigglepy.squigglepy.samplers module +------------------------------------- + +.. automodule:: squigglepy.squigglepy.samplers + :members: + :undoc-members: + :show-inheritance: + +squigglepy.squigglepy.utils module +---------------------------------- + +.. automodule:: squigglepy.squigglepy.utils + :members: + :undoc-members: + :show-inheritance: + +squigglepy.squigglepy.version module +------------------------------------ + +.. automodule:: squigglepy.squigglepy.version + :members: + :undoc-members: + :show-inheritance: + + +Module contents +--------------- + +.. automodule:: squigglepy.squigglepy + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/build/html/_sources/reference/squigglepy.tests.rst.txt b/docs/build/html/_sources/reference/squigglepy.tests.rst.txt new file mode 100644 index 0000000..cf175cf --- /dev/null +++ b/docs/build/html/_sources/reference/squigglepy.tests.rst.txt @@ -0,0 +1,86 @@ +squigglepy.tests package +======================== + +Submodules +---------- + +squigglepy.tests.integration module +----------------------------------- + +.. automodule:: squigglepy.tests.integration + :members: + :undoc-members: + :show-inheritance: + +squigglepy.tests.strategies module +---------------------------------- + +.. automodule:: squigglepy.tests.strategies + :members: + :undoc-members: + :show-inheritance: + +squigglepy.tests.test\_bayes module +----------------------------------- + +.. automodule:: squigglepy.tests.test_bayes + :members: + :undoc-members: + :show-inheritance: + +squigglepy.tests.test\_correlation module +----------------------------------------- + +.. automodule:: squigglepy.tests.test_correlation + :members: + :undoc-members: + :show-inheritance: + +squigglepy.tests.test\_distributions module +------------------------------------------- + +.. automodule:: squigglepy.tests.test_distributions + :members: + :undoc-members: + :show-inheritance: + +squigglepy.tests.test\_numbers module +------------------------------------- + +.. automodule:: squigglepy.tests.test_numbers + :members: + :undoc-members: + :show-inheritance: + +squigglepy.tests.test\_rng module +--------------------------------- + +.. automodule:: squigglepy.tests.test_rng + :members: + :undoc-members: + :show-inheritance: + +squigglepy.tests.test\_samplers module +-------------------------------------- + +.. automodule:: squigglepy.tests.test_samplers + :members: + :undoc-members: + :show-inheritance: + +squigglepy.tests.test\_utils module +----------------------------------- + +.. automodule:: squigglepy.tests.test_utils + :members: + :undoc-members: + :show-inheritance: + + +Module contents +--------------- + +.. automodule:: squigglepy.tests + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/build/html/_sources/reference/squigglepy.utils.rst.txt b/docs/build/html/_sources/reference/squigglepy.utils.rst.txt new file mode 100644 index 0000000..8af5f44 --- /dev/null +++ b/docs/build/html/_sources/reference/squigglepy.utils.rst.txt @@ -0,0 +1,7 @@ +squigglepy.utils module +======================= + +.. automodule:: squigglepy.utils + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/build/html/_sources/reference/squigglepy.version.rst.txt b/docs/build/html/_sources/reference/squigglepy.version.rst.txt new file mode 100644 index 0000000..efe11f5 --- /dev/null +++ b/docs/build/html/_sources/reference/squigglepy.version.rst.txt @@ -0,0 +1,7 @@ +squigglepy.version module +========================= + +.. automodule:: squigglepy.version + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/build/html/examples.html b/docs/build/html/examples.html new file mode 100644 index 0000000..0011e57 --- /dev/null +++ b/docs/build/html/examples.html @@ -0,0 +1,891 @@ + + + + + + + + + + + Examples — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + +
+
+
+
+ + + Ctrl+K +
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+ + + + + +
+ +
+

Examples#

+
+

Piano Tuners Example#

+

Here’s the Squigglepy implementation of the example from Squiggle +Docs:

+
import squigglepy as sq
+import numpy as np
+import matplotlib.pyplot as plt
+from squigglepy.numbers import K, M
+from pprint import pprint
+
+pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)  # This means that you're 90% confident the value is between 8.1 and 8.4 Million.
+pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01  # We assume there are almost no people with multiple pianos
+pianos_per_piano_tuner = sq.to(2*K, 50*K)
+piano_tuners_per_piano = 1 / pianos_per_piano_tuner
+total_tuners_in_2022 = pop_of_ny_2022 * pct_of_pop_w_pianos * piano_tuners_per_piano
+samples = total_tuners_in_2022 @ 1000  # Note: `@ 1000` is shorthand to get 1000 samples
+
+# Get mean and SD
+print('Mean: {}, SD: {}'.format(round(np.mean(samples), 2),
+                                round(np.std(samples), 2)))
+
+# Get percentiles
+pprint(sq.get_percentiles(samples, digits=0))
+
+# Histogram
+plt.hist(samples, bins=200)
+plt.show()
+
+# Shorter histogram
+total_tuners_in_2022.plot()
+
+
+

And the version from the Squiggle doc that incorporates time:

+
import squigglepy as sq
+from squigglepy.numbers import K, M
+
+pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)
+pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01
+pianos_per_piano_tuner = sq.to(2*K, 50*K)
+piano_tuners_per_piano = 1 / pianos_per_piano_tuner
+
+def pop_at_time(t):  # t = Time in years after 2022
+    avg_yearly_pct_change = sq.to(-0.01, 0.05)  # We're expecting NYC to continuously grow with an mean of roughly between -1% and +4% per year
+    return pop_of_ny_2022 * ((avg_yearly_pct_change + 1) ** t)
+
+def total_tuners_at_time(t):
+    return pop_at_time(t) * pct_of_pop_w_pianos * piano_tuners_per_piano
+
+# Get total piano tuners at 2030
+sq.get_percentiles(total_tuners_at_time(2030-2022) @ 1000)
+
+
+

WARNING: Be careful about dividing by K, M, etc. 1/2*K = +500 in Python. Use 1/(2*K) instead to get the expected outcome.

+

WARNING: Be careful about using K to get sample counts. Use +sq.norm(2, 3) @ (2*K)… sq.norm(2, 3) @ 2*K will return only +two samples, multiplied by 1000.

+
+
+

Distributions#

+
import squigglepy as sq
+
+# Normal distribution
+sq.norm(1, 3)  # 90% interval from 1 to 3
+
+# Distribution can be sampled with mean and sd too
+sq.norm(mean=0, sd=1)
+
+# Shorthand to get one sample
+~sq.norm(1, 3)
+
+# Shorthand to get more than one sample
+sq.norm(1, 3) @ 100
+
+# Longhand version to get more than one sample
+sq.sample(sq.norm(1, 3), n=100)
+
+# Nice progress reporter
+sq.sample(sq.norm(1, 3), n=1000, verbose=True)
+
+# Other distributions exist
+sq.lognorm(1, 10)
+sq.tdist(1, 10, t=5)
+sq.triangular(1, 2, 3)
+sq.pert(1, 2, 3, lam=2)
+sq.binomial(p=0.5, n=5)
+sq.beta(a=1, b=2)
+sq.bernoulli(p=0.5)
+sq.poisson(10)
+sq.chisquare(2)
+sq.gamma(3, 2)
+sq.pareto(1)
+sq.exponential(scale=1)
+sq.geometric(p=0.5)
+
+# Discrete sampling
+sq.discrete({'A': 0.1, 'B': 0.9})
+
+# Can return integers
+sq.discrete({0: 0.1, 1: 0.3, 2: 0.3, 3: 0.15, 4: 0.15})
+
+# Alternate format (also can be used to return more complex objects)
+sq.discrete([[0.1,  0],
+             [0.3,  1],
+             [0.3,  2],
+             [0.15, 3],
+             [0.15, 4]])
+
+sq.discrete([0, 1, 2]) # No weights assumes equal weights
+
+# You can mix distributions together
+sq.mixture([sq.norm(1, 3),
+            sq.norm(4, 10),
+            sq.lognorm(1, 10)],  # Distributions to mix
+           [0.3, 0.3, 0.4])     # These are the weights on each distribution
+
+# This is equivalent to the above, just a different way of doing the notation
+sq.mixture([[0.3, sq.norm(1,3)],
+            [0.3, sq.norm(4,10)],
+            [0.4, sq.lognorm(1,10)]])
+
+# Make a zero-inflated distribution
+# 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`.
+sq.zero_inflated(0.6, sq.norm(1, 2))
+
+
+
+
+

Additional Features#

+
import squigglepy as sq
+
+# You can add and subtract distributions
+(sq.norm(1,3) + sq.norm(4,5)) @ 100
+(sq.norm(1,3) - sq.norm(4,5)) @ 100
+(sq.norm(1,3) * sq.norm(4,5)) @ 100
+(sq.norm(1,3) / sq.norm(4,5)) @ 100
+
+# You can also do math with numbers
+~((sq.norm(sd=5) + 2) * 2)
+~(-sq.lognorm(0.1, 1) * sq.pareto(1) / 10)
+
+# You can change the CI from 90% (default) to 80%
+sq.norm(1, 3, credibility=80)
+
+# You can clip
+sq.norm(0, 3, lclip=0, rclip=5) # Sample norm with a 90% CI from 0-3, but anything lower than 0 gets clipped to 0 and anything higher than 5 gets clipped to 5.
+
+# You can also clip with a function, and use pipes
+sq.norm(0, 3) >> sq.clip(0, 5)
+
+# You can correlate continuous distributions
+a, b = sq.uniform(-1, 1), sq.to(0, 3)
+a, b = sq.correlate((a, b), 0.5)  # Correlate a and b with a correlation of 0.5
+# You can even pass your own correlation matrix!
+a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]])
+
+
+
+

Example: Rolling a Die#

+

An example of how to use distributions to build tools:

+
import squigglepy as sq
+
+def roll_die(sides, n=1):
+    return sq.discrete(list(range(1, sides + 1))) @ n if sides > 0 else None
+
+roll_die(sides=6, n=10)
+# [2, 6, 5, 2, 6, 2, 3, 1, 5, 2]
+
+
+

This is already included standard in the utils of this package. Use +sq.roll_die.

+
+
+
+

Bayesian inference#

+

1% of women at age forty who participate in routine screening have +breast cancer. 80% of women with breast cancer will get positive +mammographies. 9.6% of women without breast cancer will also get +positive mammographies.

+

A woman in this age group had a positive mammography in a routine +screening. What is the probability that she actually has breast cancer?

+

We can approximate the answer with a Bayesian network (uses rejection +sampling):

+
import squigglepy as sq
+from squigglepy import bayes
+from squigglepy.numbers import M
+
+def mammography(has_cancer):
+    return sq.event(0.8 if has_cancer else 0.096)
+
+def define_event():
+    cancer = ~sq.bernoulli(0.01)
+    return({'mammography': mammography(cancer),
+            'cancer': cancer})
+
+bayes.bayesnet(define_event,
+               find=lambda e: e['cancer'],
+               conditional_on=lambda e: e['mammography'],
+               n=1*M)
+# 0.07723995880535531
+
+
+

Or if we have the information immediately on hand, we can directly +calculate it. Though this doesn’t work for very complex stuff.

+
from squigglepy import bayes
+bayes.simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096)
+# 0.07763975155279504
+
+
+

You can also make distributions and update them:

+
import matplotlib.pyplot as plt
+import squigglepy as sq
+from squigglepy import bayes
+from squigglepy.numbers import K
+import numpy as np
+
+print('Prior')
+prior = sq.norm(1,5)
+prior_samples = prior @ (10*K)
+plt.hist(prior_samples, bins = 200)
+plt.show()
+print(sq.get_percentiles(prior_samples))
+print('Prior Mean: {} SD: {}'.format(np.mean(prior_samples), np.std(prior_samples)))
+print('-')
+
+print('Evidence')
+evidence = sq.norm(2,3)
+evidence_samples = evidence @ (10*K)
+plt.hist(evidence_samples, bins = 200)
+plt.show()
+print(sq.get_percentiles(evidence_samples))
+print('Evidence Mean: {} SD: {}'.format(np.mean(evidence_samples), np.std(evidence_samples)))
+print('-')
+
+print('Posterior')
+posterior = bayes.update(prior, evidence)
+posterior_samples = posterior @ (10*K)
+plt.hist(posterior_samples, bins = 200)
+plt.show()
+print(sq.get_percentiles(posterior_samples))
+print('Posterior Mean: {} SD: {}'.format(np.mean(posterior_samples), np.std(posterior_samples)))
+
+print('Average')
+average = bayes.average(prior, evidence)
+average_samples = average @ (10*K)
+plt.hist(average_samples, bins = 200)
+plt.show()
+print(sq.get_percentiles(average_samples))
+print('Average Mean: {} SD: {}'.format(np.mean(average_samples), np.std(average_samples)))
+
+
+
+

Example: Alarm net#

+

This is the alarm network from Bayesian Artificial Intelligence - +Section +2.5.1:

+
+

Assume your house has an alarm system against burglary.

+

You live in the seismically active area and the alarm system can get +occasionally set off by an earthquake.

+

You have two neighbors, Mary and John, who do not know each other. If +they hear the alarm they call you, but this is not guaranteed.

+

The chance of a burglary on a particular day is 0.1%. The chance of +an earthquake on a particular day is 0.2%.

+

The alarm will go off 95% of the time with both a burglary and an +earthquake, 94% of the time with just a burglary, 29% of the time +with just an earthquake, and 0.1% of the time with nothing (total +false alarm).

+

John will call you 90% of the time when the alarm goes off. But on 5% +of the days, John will just call to say “hi”. Mary will call you 70% +of the time when the alarm goes off. But on 1% of the days, Mary will +just call to say “hi”.

+
+
import squigglepy as sq
+from squigglepy import bayes
+from squigglepy.numbers import M
+
+def p_alarm_goes_off(burglary, earthquake):
+    if burglary and earthquake:
+        return 0.95
+    elif burglary and not earthquake:
+        return 0.94
+    elif not burglary and earthquake:
+        return 0.29
+    elif not burglary and not earthquake:
+        return 0.001
+
+def p_john_calls(alarm_goes_off):
+    return 0.9 if alarm_goes_off else 0.05
+
+def p_mary_calls(alarm_goes_off):
+    return 0.7 if alarm_goes_off else 0.01
+
+def define_event():
+    burglary_happens = sq.event(p=0.001)
+    earthquake_happens = sq.event(p=0.002)
+    alarm_goes_off = sq.event(p_alarm_goes_off(burglary_happens, earthquake_happens))
+    john_calls = sq.event(p_john_calls(alarm_goes_off))
+    mary_calls = sq.event(p_mary_calls(alarm_goes_off))
+    return {'burglary': burglary_happens,
+            'earthquake': earthquake_happens,
+            'alarm_goes_off': alarm_goes_off,
+            'john_calls': john_calls,
+            'mary_calls': mary_calls}
+
+# What are the chances that both John and Mary call if an earthquake happens?
+bayes.bayesnet(define_event,
+               n=1*M,
+               find=lambda e: (e['mary_calls'] and e['john_calls']),
+               conditional_on=lambda e: e['earthquake'])
+# Result will be ~0.19, though it varies because it is based on a random sample.
+# This also may take a minute to run.
+
+# If both John and Mary call, what is the chance there's been a burglary?
+bayes.bayesnet(define_event,
+               n=1*M,
+               find=lambda e: e['burglary'],
+               conditional_on=lambda e: (e['mary_calls'] and e['john_calls']))
+# Result will be ~0.27, though it varies because it is based on a random sample.
+# This will run quickly because there is a built-in cache.
+# Use `cache=False` to not build a cache and `reload_cache=True` to recalculate the cache.
+
+
+

Note that the amount of Bayesian analysis that squigglepy can do is +pretty limited. For more complex bayesian analysis, consider +sorobn, +pomegranate, +bnlearn, or +pyMC.

+
+
+

Example: A Demonstration of the Monty Hall Problem#

+
import squigglepy as sq
+from squigglepy import bayes
+from squigglepy.numbers import K, M, B, T
+
+
+def monte_hall(door_picked, switch=False):
+    doors = ['A', 'B', 'C']
+    car_is_behind_door = ~sq.discrete(doors)
+    reveal_door = ~sq.discrete([d for d in doors if d != door_picked and d != car_is_behind_door])
+
+    if switch:
+        old_door_picked = door_picked
+        door_picked = [d for d in doors if d != old_door_picked and d != reveal_door][0]
+
+    won_car = (car_is_behind_door == door_picked)
+    return won_car
+
+
+def define_event():
+    door = ~sq.discrete(['A', 'B', 'C'])
+    switch = sq.event(0.5)
+    return {'won': monte_hall(door_picked=door, switch=switch),
+            'switched': switch}
+
+RUNS = 10*K
+r = bayes.bayesnet(define_event,
+                   find=lambda e: e['won'],
+                   conditional_on=lambda e: e['switched'],
+                   verbose=True,
+                   n=RUNS)
+print('Win {}% of the time when switching'.format(int(r * 100)))
+
+r = bayes.bayesnet(define_event,
+                   find=lambda e: e['won'],
+                   conditional_on=lambda e: not e['switched'],
+                   verbose=True,
+                   n=RUNS)
+print('Win {}% of the time when not switching'.format(int(r * 100)))
+
+# Win 66% of the time when switching
+# Win 34% of the time when not switching
+
+
+
+
+

Example: More complex coin/dice interactions#

+
+

Imagine that I flip a coin. If heads, I take a random die out of my +blue bag. If tails, I take a random die out of my red bag. The blue +bag contains only 6-sided dice. The red bag contains a 4-sided die, a +6-sided die, a 10-sided die, and a 20-sided die. I then roll the +random die I took. What is the chance that I roll a 6?

+
+
import squigglepy as sq
+from squigglepy.numbers import K, M, B, T
+from squigglepy import bayes
+
+def define_event():
+    if sq.flip_coin() == 'heads': # Blue bag
+        return sq.roll_die(6)
+    else: # Red bag
+        return sq.discrete([4, 6, 10, 20]) >> sq.roll_die
+
+
+bayes.bayesnet(define_event,
+               find=lambda e: e == 6,
+               verbose=True,
+               n=100*K)
+# This run for me returned 0.12306 which is pretty close to the correct answer of 0.12292
+
+
+
+
+
+

Kelly betting#

+

You can use probability generated, combine with a bankroll to determine +bet sizing using Kelly +criterion.

+

For example, if you want to Kelly bet and you’ve…

+
    +

  • determined that your price (your probability of the event in question +happening / the market in question resolving in your favor) is $0.70 +(70%)

    • +

  • see that the market is pricing at $0.65

    • +

  • you have a bankroll of $1000 that you are willing to bet

    • +
+

You should bet as follows:

+
import squigglepy as sq
+kelly_data = sq.kelly(my_price=0.70, market_price=0.65, bankroll=1000)
+kelly_data['kelly']  # What fraction of my bankroll should I bet on this?
+# 0.143
+kelly_data['target']  # How much money should be invested in this?
+# 142.86
+kelly_data['expected_roi']  # What is the expected ROI of this bet?
+# 0.077
+
+
+
+
+

More examples#

+

You can see more examples of squigglepy in action +here.

+
+
+ + +
+ + + + + + + +
+ + + +
+ +
+
+ On this page +
+
+ +
+
+ + Show Source + +
+
+ +
+ + +
+
+ +
+ +
+
+
+ + + + + +
+
+ +
+ +
+

+ + © Copyright 2023, Peter Wildeford. +
+ +

+
+ +
+

+ Created using Sphinx 7.2.6. +
+

+
+ +
+ + + +
+ +

+ Built with the PyData Sphinx Theme 0.14.3. +

+ +
+ +
+ +
+ + \ No newline at end of file diff --git a/docs/build/html/genindex.html b/docs/build/html/genindex.html index 23b4876..2671007 100644 --- a/docs/build/html/genindex.html +++ b/docs/build/html/genindex.html @@ -131,6 +131,19 @@

@@ -208,6 +221,19 @@

@@ -259,8 +285,509 @@

Index

+ A + | B + | C + | D + | E + | F + | G + | H + | I + | K + | L + | M + | N + | O + | P + | Q + | R + | S + | T + | U + | Z
+

A

+ + +
+ +

B

+ + + +
+ +

C

+ + + +
+ +

D

+ + + +
+ +

E

+ + + +
+ +

F

+ + + +
+ +

G

+ + + +
+ +

H

+ + + +
+ +

I

+ + + +
+ +

K

+ + +
+ +

L

+ + + +
+ +

M

+ + +
+ +

N

+ + + +
+ +

O

+ + + +
+ +

P

+ + + +
+ +

Q

+ + +
+ +

R

+ + + +
+ +

S

+ + + +
    +
  • + squigglepy.numbers + +
    • +
  • + squigglepy.rng + +
    • +
  • + squigglepy.samplers + +
    • +
  • + squigglepy.utils + +
    • +
  • + squigglepy.version + +
    • +
+ +

T

+ + + +
+ +

U

+ + + +
+ +

Z

+ + +
+ diff --git a/docs/build/html/index.html b/docs/build/html/index.html index acead48..f6b31ee 100644 --- a/docs/build/html/index.html +++ b/docs/build/html/index.html @@ -41,6 +41,7 @@ + @@ -132,6 +133,19 @@

@@ -213,6 +227,19 @@

@@ -272,8 +299,77 @@

Squigglepy: Implementation of Squiggle in Python +

Contents

+ + +
+

Installation#

+
pip install squigglepy
+
-

Check out the README to get started.

+

For plotting support, you can also use the plots extra:

+
pip install squigglepy[plots]
+
+
+
+
+

Run tests#

+

Use black . for formatting.

+

Run +ruff check . && pytest && pip3 install . && python3 tests/integration.py

+
+
+

Disclaimers#

+

This package is unofficial and supported by Peter Wildeford and Rethink +Priorities. It is not affiliated with or associated with the Quantified +Uncertainty Research Institute, which maintains the Squiggle language +(in JavaScript).

+

This package is also new and not yet in a stable production version, so +you may encounter bugs and other errors. Please report those so they can +be fixed. It’s also possible that future versions of the package may +introduce breaking changes.

+

This package is available under an MIT License.

+
+
+

Acknowledgements#

+
    +

  • The primary author of this package is Peter Wildeford. Agustín +Covarrubias and Bernardo Baron contributed several key features and +developments.

    • +

  • Thanks to Ozzie Gooen and the Quantified Uncertainty Research +Institute for creating and maintaining the original Squiggle +language.

    • +

  • Thanks to Dawn Drescher for helping me implement math between +distributions.

    • +

  • Thanks to Dawn Drescher for coming up with the idea to use ~ as a +shorthand for sample, as well as helping me implement it.

    • +
+
@@ -286,6 +382,15 @@

Squigglepy: Implementation of Squiggle in Python
+ +
+

next

+

squigglepy

+
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Squigglepy: Implementation of Squiggle in Python
+
+
+ On this page +
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diff --git a/docs/build/html/objects.inv b/docs/build/html/objects.inv index 3a5c908166e70f24a93dc0a41ec8dca8a4e4c2e7..e0602553fc716976229bdff18ba9472893628d7d 100644 GIT binary patch delta 1230 zcmV;<1Tp)R0=5c}cz?Z`%W|AJ6o&Wx6snrp+LLU(%Q!Aqs^W<&$*fgsIDjfb!n$O- z^YkMS(DV&(`J8NAZ8&_tu7_Vj?j^{wRM6~Mv%jlN9u%;5%t8ScbOwL9G2piHwfZB4 z-2BOIHj`Uhu?M$I=)x8`x8f&QQ9{crg3i1&n!R5nUPN_&HGg;vmXmd(fRA;3D=##; z@NcYTW~>Dzx`!8=e-b>`3DdCq!|z9HLeq+5N;r3|sAn3lfR8sJ=ecygYh~fRmD>;- zic&FN;I)WKyWgwnjf!JE(&=R@;kXM$Au|cub0@mdoXa@bob+k_gRe|ZqAqnFGT^7< zl}@mhng=ak0)O;X#UD-Ma9uNpm%#0S?}`=!R;1FS@VVK19Qe0z@NsfwaXw$rnHK=7 zO;Ab_t9U^xAhoHbP^2RFap;uB%8Xj4lHXo}u(UmYZ`xV5BiAr7TT$0UJ1?}S7V%OC z6C9~bgl86r8|-1%7#&|K)Dz}W)HUtAe*_cXNpVV&s(*Yo<#%cUZEQ{49Zz!S194XQ zhrSwLnrOkc3VyrDZKI4|wn49zdVcsyJG!3ZtHc{x2_u~|npA_fk-l3gbQzSeq%!|% zS;Q$qs<9nB-5Q_!dbk%P+}^=au(L|K&QOuSm2613t*fB`=e@-sVtbx}RAg}2HDv5U z8Dr__ntu$fOi9MB#g2|G>Dt7apmPd39NaSnzHCi133%|z6mY4FcNAPjm0shN;l8~@ z1aJL31-ecqo&rr({Je@(@P$hlIDG2{BC|5C7~ zh{pog$zI??`;`qkI4)~=TGybXhcyB^cw(N=*`0I3rw+CWo!nUv3ToO*L?`#w1D#7$ z++;iOvC(tjLzCe^=hE=_yH({%! zj(;ge*1+RLh&}b6uee?L0em8JkqO6*i}Dd zgEl!FWeW^`B~*boG^LAkX7~Wl*RFI|P=66oDYv&D4KaXdO{YYoM21qPWYmxnVVfG- zk=LNWG;o}h+O%cDN?YyX%!9?72iC-dpUXFPKzD?2%?Z>#@XTy{efaS4>47<)-{mG_ zH}6@x(gm__BjApGYUe~9^Hw@TXo~SJi~aSy_m$Bb*!3s=CcxoZLO%5WZA#Em=YO#4 zLY3HpYJ-QXDfm>O)4@aTd*|Vwao2BEIiyEg#HQ5!;oZj(q z&Lze3Ej@OXHK#gk{4MEC_x;#~=SSx>+6}=a{;+|^PM(|Nj+=W+@S`;kyF{3iNsFQ- sjYFjhfKJ{pC&?f;rU*}fv{P1JloT?KJTRa&+Vl89~bJ@Yr>vw_W%F@ delta 164 zcmV;V09*gI3X}qncz+9Wb#(D{RVXe=u}aBLR?sz62m*`fWt8ORCzR+T8pUEY=oO>cS)-=KAKRlmhiZ9DpQCKph*z5>(yAsfk6&8K@c| SVo)zY + + + + + + + + Python Module Index — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ + © Copyright 2023, Peter Wildeford. +
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+ Created using Sphinx 7.2.6. +
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+ Built with the PyData Sphinx Theme 0.14.3. +

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+ + \ No newline at end of file diff --git a/docs/build/html/reference/modules.html b/docs/build/html/reference/modules.html new file mode 100644 index 0000000..b879c7e --- /dev/null +++ b/docs/build/html/reference/modules.html @@ -0,0 +1,675 @@ + + + + + + + + + + + squigglepy — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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squigglepy#

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+ + © Copyright 2023, Peter Wildeford. +
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+ Created using Sphinx 7.2.6. +
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+ Built with the PyData Sphinx Theme 0.14.3. +

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+ + \ No newline at end of file diff --git a/docs/build/html/reference/squigglepy.bayes.html b/docs/build/html/reference/squigglepy.bayes.html new file mode 100644 index 0000000..504e459 --- /dev/null +++ b/docs/build/html/reference/squigglepy.bayes.html @@ -0,0 +1,649 @@ + + + + + + + + + + + squigglepy.bayes module — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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squigglepy.bayes module#

+

This modules includes functions for Bayesian inference.

+
+
+squigglepy.bayes.average(prior, evidence, weights=[0.5, 0.5], relative_weights=None)[source]#
+

Average two distributions.

+
+

Parameters#

+
+
priorDistribution

The prior distribution.

+
+
evidenceDistribution

The distribution used to average with the prior.

+
+
weightslist or np.array or float

How much weight to put on prior versus evidence when averaging? If +only one weight is passed, the other weight will be inferred to make the +total weights sum to 1. Defaults to 50-50 weights.

+
+
relative_weightslist or None

Relative weights, which if given will be weights that are normalized +to sum to 1.

+
+
+
+
+

Returns#

+
+
Distribution

A mixture distribution that accords weights to prior and evidence.

+
+
+
+
+

Examples#

+

>> prior = sq.norm(1,5) +>> evidence = sq.norm(2,3) +>> bayes.average(prior, evidence) +<Distribution> mixture

+
+
+ +
+
+squigglepy.bayes.bayesnet(event_fn=None, n=1, find=None, conditional_on=None, reduce_fn=None, raw=False, memcache=True, memcache_load=True, memcache_save=True, reload_cache=False, dump_cache_file=None, load_cache_file=None, cache_file_primary=False, verbose=False, cores=1)[source]#
+

Calculate a Bayesian network.

+

Allows you to find conditional probabilities of custom events based on +rejection sampling.

+
+

Parameters#

+
+
event_fnfunction

A function that defines the bayesian network

+
+
nint

The number of samples to generate

+
+
finda function or None

What do we want to know the probability of?

+
+
conditional_ona function or None

When finding the probability, what do we want to condition on?

+
+
reduce_fna function or None

When taking all the results of the simulations, how do we aggregate them +into a final answer? Defaults to np.mean.

+
+
rawbool

If True, just return the results of each simulation without aggregating.

+
+
memcachebool

If True, cache the results in-memory for future calculations. Each cache +will be matched based on the event_fn. Default True.

+
+
memcache_loadbool

If True, load cache from the in-memory. This will be true if memcache +is True. Cache will be matched based on the event_fn. Default True.

+
+
memcache_savebool

If True, save results to an in-memory cache. This will be true if memcache +is True. Cache will be matched based on the event_fn. Default True.

+
+
reload_cachebool

If True, any existing cache will be ignored and recalculated. Default False.

+
+
dump_cache_filestr or None

If present, will write out the cache to a binary file with this path with +.sqlcache appended to the file name.

+
+
load_cache_filestr or None

If present, will first attempt to load and use a cache from a file with this +path with .sqlcache appended to the file name.

+
+
cache_file_primarybool

If both an in-memory cache and file cache are present, the file +cache will be used for the cache if this is True, and the in-memory cache +will be used otherwise. Defaults to False.

+
+
verbosebool

If True, will print out statements on computational progress.

+
+
coresint

If 1, runs on a single core / process. If greater than 1, will run on a multiprocessing +pool with that many cores / processes.

+
+
+
+
+

Returns#

+
+
various

The result of reduce_fn on n simulations of event_fn.

+
+
+
+
+

Examples#

+

# Cancer example: prior of having cancer is 1%, the likelihood of a positive +# mammography given cancer is 80% (true positive rate), and the likelihood of +# a positive mammography given no cancer is 9.6% (false positive rate). +# Given this, what is the probability of cancer given a positive mammography? +>> def mammography(has_cancer): +>> p = 0.8 if has_cancer else 0.096 +>> return bool(sq.sample(sq.bernoulli(p))) +>> +>> def define_event(): +>> cancer = sq.sample(sq.bernoulli(0.01)) +>> return({‘mammography’: mammography(cancer), +>> ‘cancer’: cancer}) +>> +>> bayes.bayesnet(define_event, +>> find=lambda e: e[‘cancer’], +>> conditional_on=lambda e: e[‘mammography’], +>> n=1*M) +0.07723995880535531

+
+
+ +
+
+squigglepy.bayes.simple_bayes(likelihood_h, likelihood_not_h, prior)[source]#
+

Calculate Bayes rule.

+

p(h|e) = (p(e|h)*p(h)) / (p(e|h)*p(h) + p(e|~h)*(1-p(h))) +p(h|e) is called posterior +p(e|h) is called likelihood +p(h) is called prior

+
+

Parameters#

+
+
likelihood_hfloat

The likelihood (given that the hypothesis is true), aka p(e|h)

+
+
likelihood_not_hfloat

The likelihood given the hypothesis is not true, aka p(e|~h)

+
+
priorfloat

The prior probability, aka p(h)

+
+
+
+
+

Returns#

+
+
float

The result of Bayes rule, aka p(h|e)

+
+
+
+
+

Examples#

+

# Cancer example: prior of having cancer is 1%, the likelihood of a positive +# mammography given cancer is 80% (true positive rate), and the likelihood of +# a positive mammography given no cancer is 9.6% (false positive rate). +# Given this, what is the probability of cancer given a positive mammography? +>>> simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096) +0.07763975155279504

+
+
+ +
+
+squigglepy.bayes.update(prior, evidence, evidence_weight=1)[source]#
+

Update a distribution.

+

Starting with a prior distribution, use Bayesian inference to perform an update, +producing a posterior distribution from the evidence distribution.

+
+

Parameters#

+
+
priorDistribution

The prior distribution. Currently must either be normal or beta type. Other +types are not yet supported.

+
+
evidenceDistribution

The distribution used to update the prior. Currently must either be normal +or beta type. Other types are not yet supported.

+
+
evidence_weightfloat

How much weight to put on the evidence distribution? Currently this only matters +for normal distributions, where this should be equivalent to the sample weight.

+
+
+
+
+

Returns#

+
+
Distribution

The posterior distribution

+
+
+
+
+

Examples#

+

>> prior = sq.norm(1,5) +>> evidence = sq.norm(2,3) +>> bayes.update(prior, evidence) +<Distribution> norm(mean=2.53, sd=0.29)

+
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+ + © Copyright 2023, Peter Wildeford. +
+ +

+
+ +
+

+ Created using Sphinx 7.2.6. +
+

+
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+ Built with the PyData Sphinx Theme 0.14.3. +

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+ + \ No newline at end of file diff --git a/docs/build/html/reference/squigglepy.correlation.html b/docs/build/html/reference/squigglepy.correlation.html new file mode 100644 index 0000000..421fb0d --- /dev/null +++ b/docs/build/html/reference/squigglepy.correlation.html @@ -0,0 +1,597 @@ + + + + + + + + + + + squigglepy.correlation module — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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squigglepy.correlation module#

+

This module implements the Iman-Conover method for inducing correlations between distributions.

+

Some of the code has been adapted from Abraham Lee’s mcerp package (tisimst/mcerp).

+
+
+class squigglepy.correlation.CorrelationGroup(correlated_dists: tuple[OperableDistribution], correlation_matrix: NDArray[np.float64], correlation_tolerance: float | None = 0.05, min_unique_samples: int = 100)[source]#
+

Bases: object

+

An object that holds metadata for a group of correlated distributions. +This object is not intended to be used directly by the user, but +rather during sampling to induce correlations between distributions.

+
+
+correlated_dists: tuple[OperableDistribution]#
+
+ +
+
+correlation_matrix: NDArray[np.float64]#
+
+ +
+
+correlation_tolerance: float | None = 0.05#
+
+ +
+
+has_sufficient_sample_diversity(samples: ndarray[Any, dtype[float64]], relative_threshold: float = 0.7, absolute_threshold=None) → bool[source]#
+

Check if there is there are sufficient unique samples to work with in the data.

+
+ +
+
+induce_correlation(data: ndarray[Any, dtype[float64]]) → ndarray[Any, dtype[float64]][source]#
+

Induce a set of correlations on a column-wise dataset

+
+

Parameters#

+
+
data2d-array

An m-by-n array where m is the number of samples and n is the +number of independent variables, each column of the array corresponding +to each variable

+
+
corrmat2d-array

An n-by-n array that defines the desired correlation coefficients +(between -1 and 1). Note: the matrix must be symmetric and +positive-definite in order to induce.

+
+
+
+
+

Returns#

+
+
new_data2d-array

An m-by-n array that has the desired correlations.

+
+
+
+
+ +
+
+min_unique_samples: int = 100#
+
+ +
+ +
+
+squigglepy.correlation.correlate(variables: tuple[OperableDistribution, ...], correlation: NDArray[np.float64] | list[list[float]] | np.float64 | float, tolerance: float | np.float64 | None = 0.05, _min_unique_samples: int = 100)[source]#
+

Correlate a set of variables according to a rank correlation matrix.

+

This employs the Iman-Conover method to induce the correlation while +preserving the original marginal distributions.

+

This method works on a best-effort basis, and may fail to induce the desired +correlation depending on the distributions provided. An exception will be raised +if that’s the case.

+
+

Parameters#

+
+
variablestuple of distributions

The variables to correlate as a tuple of distributions.

+

The distributions must be able to produce enough unique samples for the method +to be able to induce the desired correlation by shuffling the samples.

+

Discrete distributions are notably hard to correlate this way, +as it’s common for them to result in very few unique samples.

+
+
correlation2d-array or float

An n-by-n array that defines the desired Spearman rank correlation coefficients. +This matrix must be symmetric and positive semi-definite; and must not be confused with +a covariance matrix.

+

Correlation parameters can only be between -1 and 1, exclusive +(including extremely close approximations).

+

If a float is provided, all variables will be correlated with the same coefficient.

+
+
tolerancefloat, optional

If provided, overrides the absolute tolerance used to check if the resulting +correlation matrix matches the desired correlation matrix. Defaults to 0.05.

+

Checking can also be disabled by passing None.

+
+
+
+
+

Returns#

+
+
correlated_variablestuple of distributions

The correlated variables as a tuple of distributions in the same order as +the input variables.

+
+
+
+
+

Examples#

+

Suppose we want to correlate two variables with a correlation coefficient of 0.65: +>>> solar_radiation, temperature = sq.gamma(300, 100), sq.to(22, 28) +>>> solar_radiation, temperature = sq.correlate((solar_radiation, temperature), 0.7) +>>> print(np.corrcoef(solar_radiation @ 1000, temperature @ 1000)[0, 1])

+
+

0.6975960649767123

+
+

Or you could pass a correlation matrix: +>>> funding_gap, cost_per_delivery, effect_size = (

+
+
+

sq.to(20_000, 80_000), sq.to(30, 80), sq.beta(2, 5)

+
+

)

+
+
>>> funding_gap, cost_per_delivery, effect_size = sq.correlate(
+        (funding_gap, cost_per_delivery, effect_size),
+        [[1, 0.6, -0.5], [0.6, 1, -0.2], [-0.5, -0.2, 1]]
+    )
+>>> print(np.corrcoef(funding_gap @ 1000, cost_per_delivery @ 1000, effect_size @ 1000))
+    array([[ 1.      ,  0.580520  , -0.480149],
+           [ 0.580962,  1.        , -0.187831],
+           [-0.480149, -0.187831  ,  1.        ]])
+
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+ + © Copyright 2023, Peter Wildeford. +
+ +

+
+ +
+

+ Created using Sphinx 7.2.6. +
+

+
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+ Built with the PyData Sphinx Theme 0.14.3. +

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+ + \ No newline at end of file diff --git a/docs/build/html/reference/squigglepy.distributions.html b/docs/build/html/reference/squigglepy.distributions.html new file mode 100644 index 0000000..bb56a44 --- /dev/null +++ b/docs/build/html/reference/squigglepy.distributions.html @@ -0,0 +1,1721 @@ + + + + + + + + + + + squigglepy.distributions module — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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squigglepy.distributions module#

+

A collection of probability distributions and functions to operate on them.

+
+
+class squigglepy.distributions.BaseDistribution[source]#
+

Bases: ABC

+
+ +
+
+class squigglepy.distributions.BernoulliDistribution(p)[source]#
+

Bases: DiscreteDistribution

+
+ +
+
+class squigglepy.distributions.BetaDistribution(a, b)[source]#
+

Bases: ContinuousDistribution

+
+ +
+
+class squigglepy.distributions.BinomialDistribution(n, p)[source]#
+

Bases: DiscreteDistribution

+
+ +
+
+class squigglepy.distributions.CategoricalDistribution(items)[source]#
+

Bases: DiscreteDistribution

+
+ +
+
+class squigglepy.distributions.ChiSquareDistribution(df)[source]#
+

Bases: ContinuousDistribution

+
+ +
+
+class squigglepy.distributions.ComplexDistribution(left, right=None, fn=<built-in function add>, fn_str='+', infix=True)[source]#
+

Bases: CompositeDistribution

+
+ +
+
+class squigglepy.distributions.CompositeDistribution[source]#
+

Bases: OperableDistribution

+
+ +
+
+class squigglepy.distributions.ConstantDistribution(x)[source]#
+

Bases: DiscreteDistribution

+
+ +
+
+class squigglepy.distributions.ContinuousDistribution[source]#
+

Bases: OperableDistribution, ABC

+
+ +
+
+class squigglepy.distributions.DiscreteDistribution[source]#
+

Bases: OperableDistribution, ABC

+
+ +
+
+class squigglepy.distributions.ExponentialDistribution(scale, lclip=None, rclip=None)[source]#
+

Bases: ContinuousDistribution

+
+ +
+
+class squigglepy.distributions.GammaDistribution(shape, scale=1, lclip=None, rclip=None)[source]#
+

Bases: ContinuousDistribution

+
+ +
+
+class squigglepy.distributions.GeometricDistribution(p)[source]#
+

Bases: OperableDistribution

+
+ +
+
+class squigglepy.distributions.LogTDistribution(x=None, y=None, t=1, credibility=90, lclip=None, rclip=None)[source]#
+

Bases: ContinuousDistribution

+
+ +
+
+class squigglepy.distributions.LognormalDistribution(x=None, y=None, norm_mean=None, norm_sd=None, lognorm_mean=None, lognorm_sd=None, credibility=90, lclip=None, rclip=None)[source]#
+

Bases: ContinuousDistribution

+
+ +
+
+class squigglepy.distributions.MixtureDistribution(dists, weights=None, relative_weights=None, lclip=None, rclip=None)[source]#
+

Bases: CompositeDistribution

+
+ +
+
+class squigglepy.distributions.NormalDistribution(x=None, y=None, mean=None, sd=None, credibility=90, lclip=None, rclip=None)[source]#
+

Bases: ContinuousDistribution

+
+ +
+
+class squigglepy.distributions.OperableDistribution[source]#
+

Bases: BaseDistribution

+
+
+plot(num_samples=None, bins=None)[source]#
+

Plot a histogram of the samples.

+
+

Parameters#

+
+
num_samplesint

The number of samples to draw for plotting. Defaults to 1000 if not set.

+
+
binsint

The number of bins to plot. Defaults to 200 if not set.

+
+
+
+
+

Examples#

+
>>> sq.norm(5, 10).plot()
+
+
+
+
+ +
+ +
+
+class squigglepy.distributions.PERTDistribution(left, mode, right, lam=4, lclip=None, rclip=None)[source]#
+

Bases: ContinuousDistribution

+
+ +
+
+class squigglepy.distributions.ParetoDistribution(shape)[source]#
+

Bases: ContinuousDistribution

+
+ +
+
+class squigglepy.distributions.PoissonDistribution(lam, lclip=None, rclip=None)[source]#
+

Bases: DiscreteDistribution

+
+ +
+
+class squigglepy.distributions.TDistribution(x=None, y=None, t=20, credibility=90, lclip=None, rclip=None)[source]#
+

Bases: ContinuousDistribution

+
+ +
+
+class squigglepy.distributions.TriangularDistribution(left, mode, right)[source]#
+

Bases: ContinuousDistribution

+
+ +
+
+class squigglepy.distributions.UniformDistribution(x, y)[source]#
+

Bases: ContinuousDistribution

+
+ +
+
+squigglepy.distributions.bernoulli(p)[source]#
+

Initialize a Bernoulli distribution.

+
+

Parameters#

+
+
pfloat

The probability of the binary event. Must be between 0 and 1.

+
+
+
+
+

Returns#

+

BernoulliDistribution

+
+
+

Examples#

+
>>> bernoulli(0.1)
+<Distribution> bernoulli(p=0.1)
+
+
+
+
+ +
+
+squigglepy.distributions.beta(a, b)[source]#
+

Initialize a beta distribution.

+
+

Parameters#

+
+
afloat

The alpha shape value of the distribution. Typically takes the value of the +number of trials that resulted in a success.

+
+
bfloat

The beta shape value of the distribution. Typically takes the value of the +number of trials that resulted in a failure.

+
+
+
+
+

Returns#

+

BetaDistribution

+
+
+

Examples#

+
>>> beta(1, 2)
+<Distribution> beta(1, 2)
+
+
+
+
+ +
+
+squigglepy.distributions.binomial(n, p)[source]#
+

Initialize a binomial distribution.

+
+

Parameters#

+
+
nint

The number of trials.

+
+
pfloat

The probability of success for each trial. Must be between 0 and 1.

+
+
+
+
+

Returns#

+

BinomialDistribution

+
+
+

Examples#

+
>>> binomial(1, 0.1)
+<Distribution> binomial(1, 0.1)
+
+
+
+
+ +
+
+squigglepy.distributions.chisquare(df)[source]#
+

Initialize a chi-square distribution.

+
+

Parameters#

+
+
dffloat

The degrees of freedom. Must be positive.

+
+
+
+
+

Returns#

+

ChiSquareDistribution

+
+
+

Examples#

+
>>> chisquare(2)
+<Distribution> chiaquare(2)
+
+
+
+
+ +
+
+squigglepy.distributions.clip(dist1, left, right=None)[source]#
+

Initialize the clipping/bounding of the output of the distribution.

+

The function won’t be applied until the distribution is sampled.

+
+

Parameters#

+
+
dist1Distribution or function

The distribution to clip. If this is a funciton, it will return a partial that will +be suitable for use in piping.

+
+
leftint or float or None

The value to use as the lower bound for clipping.

+
+
rightint or float or None

The value to use as the upper bound for clipping.

+
+
+
+
+

Returns#

+
+
ComplexDistribution or function

This will be a lazy evaluation of the desired function that will then be calculated

+
+
+
+
+

Examples#

+
>>> clip(norm(0, 1), 0.5, 0.9)
+<Distribution> rclip(lclip(norm(mean=0.5, sd=0.3), 0.5), 0.9)
+
+
+
+
+ +
+
+squigglepy.distributions.const(x)[source]#
+

Initialize a constant distribution.

+

Constant distributions always return the same value no matter what.

+
+

Parameters#

+
+
xanything

The value the constant distribution should always return.

+
+
+
+
+

Returns#

+

ConstantDistribution

+
+
+

Examples#

+
>>> const(1)
+<Distribution> const(1)
+
+
+
+
+ +
+
+squigglepy.distributions.discrete(items)[source]#
+

Initialize a discrete distribution (aka categorical distribution).

+
+

Parameters#

+
+
itemslist or dict

The values that the discrete distribution will return and their associated +weights (or likelihoods of being returned when sampled).

+
+
+
+
+

Returns#

+

CategoricalDistribution

+
+
+

Examples#

+
>>> discrete({0: 0.1, 1: 0.9})  # 10% chance of returning 0, 90% chance of returning 1
+<Distribution> categorical({0: 0.1, 1: 0.9})
+>>> discrete([[0.1, 0], [0.9, 1]])  # Different notation for the same thing.
+<Distribution> categorical([[0.1, 0], [0.9, 1]])
+>>> discrete([0, 1, 2])  # When no weights are given, all have equal chance of happening.
+<Distribution> categorical([0, 1, 2])
+>>> discrete({'a': 0.1, 'b': 0.9})  # Values do not have to be numbers.
+<Distribution> categorical({'a': 0.1, 'b': 0.9})
+
+
+
+
+ +
+
+squigglepy.distributions.dist_ceil(dist1)[source]#
+

Initialize the ceiling rounding of the output of the distribution.

+

The function won’t be applied until the distribution is sampled.

+
+

Parameters#

+
+
dist1Distribution

The distribution to sample and then ceiling round.

+
+
+
+
+

Returns#

+
+
ComplexDistribution or function

This will be a lazy evaluation of the desired function that will then be calculated

+
+
+
+
+

Examples#

+
>>> dist_ceil(norm(0, 1))
+<Distribution> ceil(norm(mean=0.5, sd=0.3))
+
+
+
+
+ +
+
+squigglepy.distributions.dist_exp(dist1)[source]#
+

Initialize the exp of the output of the distribution.

+

The function won’t be applied until the distribution is sampled.

+
+

Parameters#

+
+
dist1Distribution

The distribution to sample and then take the exp of.

+
+
+
+
+

Returns#

+
+
ComplexDistribution or function

This will be a lazy evaluation of the desired function that will then be calculated

+
+
+
+
+

Examples#

+
>>> dist_exp(norm(0, 1))
+<Distribution> exp(norm(mean=0.5, sd=0.3))
+
+
+
+
+ +
+
+squigglepy.distributions.dist_floor(dist1)[source]#
+

Initialize the floor rounding of the output of the distribution.

+

The function won’t be applied until the distribution is sampled.

+
+

Parameters#

+
+
dist1Distribution

The distribution to sample and then floor round.

+
+
+
+
+

Returns#

+
+
ComplexDistribution or function

This will be a lazy evaluation of the desired function that will then be calculated

+
+
+
+
+

Examples#

+
>>> dist_floor(norm(0, 1))
+<Distribution> floor(norm(mean=0.5, sd=0.3))
+
+
+
+
+ +
+
+squigglepy.distributions.dist_fn(dist1, dist2=None, fn=None, name=None)[source]#
+

Initialize a distribution that has a custom function applied to the result.

+

The function won’t be applied until the distribution is sampled.

+
+

Parameters#

+
+
dist1Distribution or function or list

Typically, the distribution to apply the function to. Could also be a function +or list of functions if dist_fn is being used in a pipe.

+
+
dist2Distribution or function or list or None

Typically, the second distribution to apply the function to if the function takes +two arguments. Could also be a function or list of functions if dist_fn is +being used in a pipe.

+
+
fnfunction or None

The function to apply to the distribution(s).

+
+
namestr or None

By default, fn.__name__ will be used to name the function. But you can pass +a custom name.

+
+
+
+
+

Returns#

+
+
ComplexDistribution or function

This will be a lazy evaluation of the desired function that will then be calculated +when it is sampled.

+
+
+
+
+

Examples#

+
>>> def double(x):
+>>>     return x * 2
+>>> dist_fn(norm(0, 1), double)
+<Distribution> double(norm(mean=0.5, sd=0.3))
+>>> norm(0, 1) >> dist_fn(double)
+<Distribution> double(norm(mean=0.5, sd=0.3))
+
+
+
+
+ +
+
+squigglepy.distributions.dist_log(dist1, base=2.718281828459045)[source]#
+

Initialize the log of the output of the distribution.

+

The function won’t be applied until the distribution is sampled.

+
+

Parameters#

+
+
dist1Distribution

The distribution to sample and then take the log of.

+
+
+
+
+

Returns#

+
+
ComplexDistribution or function

This will be a lazy evaluation of the desired function that will then be calculated

+
+
+
+
+

Examples#

+
>>> dist_log(norm(0, 1), 10)
+<Distribution> log(norm(mean=0.5, sd=0.3), const(10))
+
+
+
+
+ +
+
+squigglepy.distributions.dist_max(dist1, dist2=None)[source]#
+

Initialize the calculation of the maximum value of two distributions.

+

The function won’t be applied until the distribution is sampled.

+
+

Parameters#

+
+
dist1Distribution

The distribution to sample and determine the max of.

+
+
dist2Distribution

The second distribution to sample and determine the max of.

+
+
+
+
+

Returns#

+
+
ComplexDistribution or function

This will be a lazy evaluation of the desired function that will then be calculated +when it is sampled.

+
+
+
+
+

Examples#

+
>>> dist_max(norm(0, 1), norm(1, 2))
+<Distribution> max(norm(mean=0.5, sd=0.3), norm(mean=1.5, sd=0.3))
+
+
+
+
+ +
+
+squigglepy.distributions.dist_min(dist1, dist2=None)[source]#
+

Initialize the calculation of the minimum value of two distributions.

+

The function won’t be applied until the distribution is sampled.

+
+

Parameters#

+
+
dist1Distribution

The distribution to sample and determine the min of.

+
+
dist2Distribution

The second distribution to sample and determine the min of.

+
+
+
+
+

Returns#

+
+
ComplexDistribution or function

This will be a lazy evaluation of the desired function that will then be calculated

+
+
+
+
+

Examples#

+
>>> dist_min(norm(0, 1), norm(1, 2))
+<Distribution> min(norm(mean=0.5, sd=0.3), norm(mean=1.5, sd=0.3))
+
+
+
+
+ +
+
+squigglepy.distributions.dist_round(dist1, digits=0)[source]#
+

Initialize the rounding of the output of the distribution.

+

The function won’t be applied until the distribution is sampled.

+
+

Parameters#

+
+
dist1Distribution

The distribution to sample and then round.

+
+
digitsint

The number of digits to round to.

+
+
+
+
+

Returns#

+
+
ComplexDistribution or function

This will be a lazy evaluation of the desired function that will then be calculated

+
+
+
+
+

Examples#

+
>>> dist_round(norm(0, 1))
+<Distribution> round(norm(mean=0.5, sd=0.3), 0)
+
+
+
+
+ +
+
+squigglepy.distributions.exponential(scale, lclip=None, rclip=None)[source]#
+

Initialize an exponential distribution.

+
+

Parameters#

+
+
scalefloat

The scale value of the exponential distribution (> 0)

+
+
lclipfloat or None

If not None, any value below lclip will be coerced to lclip.

+
+
rclipfloat or None

If not None, any value below rclip will be coerced to rclip.

+
+
+
+
+

Returns#

+

ExponentialDistribution

+
+
+

Examples#

+
>>> exponential(1)
+<Distribution> exponential(1)
+
+
+
+
+ +
+
+squigglepy.distributions.gamma(shape, scale=1, lclip=None, rclip=None)[source]#
+

Initialize a gamma distribution.

+
+

Parameters#

+
+
shapefloat

The shape value of the gamma distribution.

+
+
scalefloat

The scale value of the gamma distribution. Defaults to 1.

+
+
lclipfloat or None

If not None, any value below lclip will be coerced to lclip.

+
+
rclipfloat or None

If not None, any value below rclip will be coerced to rclip.

+
+
+
+
+

Returns#

+

GammaDistribution

+
+
+

Examples#

+
>>> gamma(10, 1)
+<Distribution> gamma(shape=10, scale=1)
+
+
+
+
+ +
+
+squigglepy.distributions.geometric(p)[source]#
+

Initialize a geometric distribution.

+
+

Parameters#

+
+
pfloat

The probability of success of an individual trial. Must be between 0 and 1.

+
+
+
+
+

Returns#

+

GeometricDistribution

+
+
+

Examples#

+
>>> geometric(0.1)
+<Distribution> geometric(0.1)
+
+
+
+
+ +
+
+squigglepy.distributions.inf0(p_zero, dist)[source]#
+

Initialize an arbitrary zero-inflated distribution.

+

Alias for zero_inflated.

+
+

Parameters#

+
+
p_zerofloat

The chance of the distribution returning zero

+
+
distDistribution

The distribution to sample from when not zero

+
+
+
+
+

Returns#

+

MixtureDistribution

+
+
+

Examples#

+
>>> inf0(0.6, norm(1, 2))
+<Distribution> mixture
+ - 0
+ - <Distribution> norm(mean=1.5, sd=0.3)
+
+
+
+
+ +
+
+squigglepy.distributions.lclip(dist1, val=None)[source]#
+

Initialize the clipping/bounding of the output of the distribution by the lower value.

+

The function won’t be applied until the distribution is sampled.

+
+

Parameters#

+
+
dist1Distribution or function

The distribution to clip. If this is a funciton, it will return a partial that will +be suitable for use in piping.

+
+
valint or float or None

The value to use as the lower bound for clipping.

+
+
+
+
+

Returns#

+
+
ComplexDistribution or function

This will be a lazy evaluation of the desired function that will then be calculated

+
+
+
+
+

Examples#

+
>>> lclip(norm(0, 1), 0.5)
+<Distribution> lclip(norm(mean=0.5, sd=0.3), 0.5)
+
+
+
+
+ +
+
+squigglepy.distributions.log_tdist(x=None, y=None, t=1, credibility=90, lclip=None, rclip=None)[source]#
+

Initialize a log t-distribution, which is a t-distribution in log-space.

+

Is defined either via a loose credible interval from x to y (use credibility or +it will default to being a 90% CI). Unlike the normal and lognormal distributions, this +credible interval is an approximation and is not precisely defined.

+

If x and y are not defined, can just return a classic t-distribution defined via +t as the number of degrees of freedom, but in log-space.

+
+

Parameters#

+
+
xfloat or None

The low value of a credible interval defined by credibility. Must be greater than 0. +Defaults to a 90% CI.

+
+
yfloat or None

The high value of a credible interval defined by credibility. Defaults to a 90% CI.

+
+
tfloat

The number of degrees of freedom of the t-distribution. Defaults to 1.

+
+
credibilityfloat

The range of the credibility interval. Defaults to 90.

+
+
lclipfloat or None

If not None, any value below lclip will be coerced to lclip.

+
+
rclipfloat or None

If not None, any value below rclip will be coerced to rclip.

+
+
+
+
+

Returns#

+

LogTDistribution

+
+
+

Examples#

+
>>> log_tdist(0, 1, 2)
+<Distribution> log_tdist(x=0, y=1, t=2)
+>>> log_tdist()
+<Distribution> log_tdist(t=1)
+
+
+
+
+ +
+
+squigglepy.distributions.lognorm(x=None, y=None, credibility=90, norm_mean=None, norm_sd=None, lognorm_mean=None, lognorm_sd=None, lclip=None, rclip=None)[source]#
+

Initialize a lognormal distribution.

+

Can be defined either via a credible interval from x to y (use credibility or +it will default to being a 90% CI) or defined via mean and sd.

+
+

Parameters#

+
+
xfloat

The low value of a credible interval defined by credibility. Defaults to a 90% CI. +Must be a value greater than 0.

+
+
yfloat

The high value of a credible interval defined by credibility. Defaults to a 90% CI. +Must be a value greater than 0.

+
+
credibilityfloat

The range of the credibility interval. Defaults to 90. Ignored if the distribution is +defined instead by mean and sd.

+
+
norm_meanfloat or None

The mean of the underlying normal distribution. If not defined, defaults to 0.

+
+
norm_sdfloat

The standard deviation of the underlying normal distribution.

+
+
lognorm_meanfloat or None

The mean of the lognormal distribution. If not defined, defaults to 1.

+
+
lognorm_sdfloat

The standard deviation of the lognormal distribution.

+
+
lclipfloat or None

If not None, any value below lclip will be coerced to lclip.

+
+
rclipfloat or None

If not None, any value below rclip will be coerced to rclip.

+
+
+
+
+

Returns#

+

LognormalDistribution

+
+
+

Examples#

+
>>> lognorm(1, 10)
+<Distribution> lognorm(lognorm_mean=4.04, lognorm_sd=3.21, norm_mean=1.15, norm_sd=0.7)
+>>> lognorm(norm_mean=1, norm_sd=2)
+<Distribution> lognorm(lognorm_mean=20.09, lognorm_sd=147.05, norm_mean=1, norm_sd=2)
+>>> lognorm(lognorm_mean=1, lognorm_sd=2)
+<Distribution> lognorm(lognorm_mean=1, lognorm_sd=2, norm_mean=-0.8, norm_sd=1.27)
+
+
+
+
+ +
+
+squigglepy.distributions.mixture(dists, weights=None, relative_weights=None, lclip=None, rclip=None)[source]#
+

Initialize a mixture distribution, which is a combination of different distributions.

+
+

Parameters#

+
+
distslist or dict

The distributions to mix. Can also be defined as a list of weights and distributions.

+
+
weightslist or None

The weights for each distribution.

+
+
relative_weightslist or None

Relative weights, which if given will be weights that are normalized +to sum to 1.

+
+
lclipfloat or None

If not None, any value below lclip will be coerced to lclip.

+
+
rclipfloat or None

If not None, any value below rclip will be coerced to rclip.

+
+
+
+
+

Returns#

+

MixtureDistribution

+
+
+

Examples#

+
>>> mixture([norm(1, 2), norm(3, 4)], weights=[0.1, 0.9])
+<Distribution> mixture
+ - <Distribution> norm(mean=1.5, sd=0.3)
+ - <Distribution> norm(mean=3.5, sd=0.3)
+>>> mixture([[0.1, norm(1, 2)], [0.9, norm(3, 4)]])  # Different notation for the same thing.
+<Distribution> mixture
+ - <Distribution> norm(mean=1.5, sd=0.3)
+ - <Distribution> norm(mean=3.5, sd=0.3)
+>>> mixture([norm(1, 2), norm(3, 4)])  # When no weights are given, all have equal chance
+>>>                                    # of happening.
+<Distribution> mixture
+ - <Distribution> norm(mean=1.5, sd=0.3)
+ - <Distribution> norm(mean=3.5, sd=0.3)
+
+
+
+
+ +
+
+squigglepy.distributions.norm(x=None, y=None, credibility=90, mean=None, sd=None, lclip=None, rclip=None) → NormalDistribution[source]#
+

Initialize a normal distribution.

+

Can be defined either via a credible interval from x to y (use credibility or +it will default to being a 90% CI) or defined via mean and sd.

+
+

Parameters#

+
+
xfloat

The low value of a credible interval defined by credibility. Defaults to a 90% CI.

+
+
yfloat

The high value of a credible interval defined by credibility. Defaults to a 90% CI.

+
+
credibilityfloat

The range of the credibility interval. Defaults to 90. Ignored if the distribution is +defined instead by mean and sd.

+
+
meanfloat or None

The mean of the normal distribution. If not defined, defaults to 0.

+
+
sdfloat

The standard deviation of the normal distribution.

+
+
lclipfloat or None

If not None, any value below lclip will be coerced to lclip.

+
+
rclipfloat or None

If not None, any value below rclip will be coerced to rclip.

+
+
+
+
+

Returns#

+

NormalDistribution

+
+
+

Examples#

+
>>> norm(0, 1)
+<Distribution> norm(mean=0.5, sd=0.3)
+>>> norm(mean=1, sd=2)
+<Distribution> norm(mean=1, sd=2)
+
+
+
+
+ +
+
+squigglepy.distributions.pareto(shape)[source]#
+

Initialize a pareto distribution.

+
+

Parameters#

+
+
shapefloat

The shape value of the pareto distribution.

+
+
+
+
+

Returns#

+

ParetoDistribution

+
+
+

Examples#

+
>>> pareto(1)
+<Distribution> pareto(1)
+
+
+
+
+ +
+
+squigglepy.distributions.pert(left, mode, right, lam=4, lclip=None, rclip=None)[source]#
+

Initialize a PERT distribution.

+
+

Parameters#

+
+
leftfloat

The smallest value of the PERT distribution.

+
+
modefloat

The most common value of the PERT distribution.

+
+
rightfloat

The largest value of the PERT distribution.

+
+
lamfloat

The lambda value of the PERT distribution. Defaults to 4.

+
+
lclipfloat or None

If not None, any value below lclip will be coerced to lclip.

+
+
rclipfloat or None

If not None, any value below rclip will be coerced to rclip.

+
+
+
+
+

Returns#

+

PERTDistribution

+
+
+

Examples#

+
>>> pert(1, 2, 3)
+<Distribution> PERT(1, 2, 3)
+
+
+
+
+ +
+
+squigglepy.distributions.poisson(lam, lclip=None, rclip=None)[source]#
+

Initialize a poisson distribution.

+
+

Parameters#

+
+
lamfloat

The lambda value of the poisson distribution.

+
+
lclipfloat or None

If not None, any value below lclip will be coerced to lclip.

+
+
rclipfloat or None

If not None, any value below rclip will be coerced to rclip.

+
+
+
+
+

Returns#

+

PoissonDistribution

+
+
+

Examples#

+
>>> poisson(1)
+<Distribution> poisson(1)
+
+
+
+
+ +
+
+squigglepy.distributions.rclip(dist1, val=None)[source]#
+

Initialize the clipping/bounding of the output of the distribution by the upper value.

+

The function won’t be applied until the distribution is sampled.

+
+

Parameters#

+
+
dist1Distribution or function

The distribution to clip. If this is a funciton, it will return a partial that will +be suitable for use in piping.

+
+
valint or float or None

The value to use as the upper bound for clipping.

+
+
+
+
+

Returns#

+
+
ComplexDistribution or function

This will be a lazy evaluation of the desired function that will then be calculated

+
+
+
+
+

Examples#

+
>>> rclip(norm(0, 1), 0.5)
+<Distribution> rclip(norm(mean=0.5, sd=0.3), 0.5)
+
+
+
+
+ +
+
+squigglepy.distributions.tdist(x=None, y=None, t=20, credibility=90, lclip=None, rclip=None)[source]#
+

Initialize a t-distribution.

+

Is defined either via a loose credible interval from x to y (use credibility or +it will default to being a 90% CI). Unlike the normal and lognormal distributions, this +credible interval is an approximation and is not precisely defined.

+

If x and y are not defined, can just return a classic t-distribution defined via +t as the number of degrees of freedom.

+
+

Parameters#

+
+
xfloat or None

The low value of a credible interval defined by credibility. Defaults to a 90% CI.

+
+
yfloat or None

The high value of a credible interval defined by credibility. Defaults to a 90% CI.

+
+
tfloat

The number of degrees of freedom of the t-distribution. Defaults to 20.

+
+
credibilityfloat

The range of the credibility interval. Defaults to 90.

+
+
lclipfloat or None

If not None, any value below lclip will be coerced to lclip.

+
+
rclipfloat or None

If not None, any value below rclip will be coerced to rclip.

+
+
+
+
+

Returns#

+

TDistribution

+
+
+

Examples#

+
>>> tdist(0, 1, 2)
+<Distribution> tdist(x=0, y=1, t=2)
+>>> tdist()
+<Distribution> tdist(t=1)
+
+
+
+
+ +
+
+squigglepy.distributions.to(x, y, credibility=90, lclip=None, rclip=None) → LognormalDistribution | NormalDistribution[source]#
+

Initialize a distribution from x to y.

+

The distribution will be lognormal by default, unless x is less than or equal to 0, +in which case it will become a normal distribution.

+

The distribution will default to be a 90% credible interval between x and y unless +credibility is passed.

+
+

Parameters#

+
+
xfloat

The low value of a credible interval defined by credibility. Defaults to a 90% CI.

+
+
yfloat

The high value of a credible interval defined by credibility. Defaults to a 90% CI.

+
+
credibilityfloat

The range of the credibility interval. Defaults to 90.

+
+
lclipfloat or None

If not None, any value below lclip will be coerced to lclip.

+
+
rclipfloat or None

If not None, any value below rclip will be coerced to rclip.

+
+
+
+
+

Returns#

+

LognormalDistribution if x > 0, otherwise a NormalDistribution

+
+
+

Examples#

+
>>> to(1, 10)
+<Distribution> lognorm(mean=1.15, sd=0.7)
+>>> to(-10, 10)
+<Distribution> norm(mean=0.0, sd=6.08)
+
+
+
+
+ +
+
+squigglepy.distributions.triangular(left, mode, right, lclip=None, rclip=None)[source]#
+

Initialize a triangular distribution.

+
+

Parameters#

+
+
leftfloat

The smallest value of the triangular distribution.

+
+
modefloat

The most common value of the triangular distribution.

+
+
rightfloat

The largest value of the triangular distribution.

+
+
+
+
+

Returns#

+

TriangularDistribution

+
+
+

Examples#

+
>>> triangular(1, 2, 3)
+<Distribution> triangular(1, 2, 3)
+
+
+
+
+ +
+
+squigglepy.distributions.uniform(x, y)[source]#
+

Initialize a uniform random distribution.

+
+

Parameters#

+
+
xfloat

The smallest value the uniform distribution will return.

+
+
yfloat

The largest value the uniform distribution will return.

+
+
+
+
+

Returns#

+

UniformDistribution

+
+
+

Examples#

+
>>> uniform(0, 1)
+<Distribution> uniform(0, 1)
+
+
+
+
+ +
+
+squigglepy.distributions.zero_inflated(p_zero, dist)[source]#
+

Initialize an arbitrary zero-inflated distribution.

+
+

Parameters#

+
+
p_zerofloat

The chance of the distribution returning zero

+
+
distDistribution

The distribution to sample from when not zero

+
+
+
+
+

Returns#

+

MixtureDistribution

+
+
+

Examples#

+
>>> zero_inflated(0.6, norm(1, 2))
+<Distribution> mixture
+ - 0
+ - <Distribution> norm(mean=1.5, sd=0.3)
+
+
+
+
+ +
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+ + © Copyright 2023, Peter Wildeford. +
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+
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+ Created using Sphinx 7.2.6. +
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+ + \ No newline at end of file diff --git a/docs/build/html/reference/squigglepy.html b/docs/build/html/reference/squigglepy.html new file mode 100644 index 0000000..a762c2b --- /dev/null +++ b/docs/build/html/reference/squigglepy.html @@ -0,0 +1,602 @@ + + + + + + + + + + + squigglepy package — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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squigglepy package#

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Submodules#

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+ Built with the PyData Sphinx Theme 0.14.3. +

+ +
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+ + \ No newline at end of file diff --git a/docs/build/html/reference/squigglepy.numbers.html b/docs/build/html/reference/squigglepy.numbers.html new file mode 100644 index 0000000..aeb3d8b --- /dev/null +++ b/docs/build/html/reference/squigglepy.numbers.html @@ -0,0 +1,446 @@ + + + + + + + + + + + squigglepy.numbers module — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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squigglepy.numbers module#

+
+ + +
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+ + \ No newline at end of file diff --git a/docs/build/html/reference/squigglepy.rng.html b/docs/build/html/reference/squigglepy.rng.html new file mode 100644 index 0000000..c722461 --- /dev/null +++ b/docs/build/html/reference/squigglepy.rng.html @@ -0,0 +1,484 @@ + + + + + + + + + + + squigglepy.rng module — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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squigglepy.rng module#

+
+
+squigglepy.rng.set_seed(seed)[source]#
+

Set the seed of the random number generator used by Squigglepy.

+

The RNG is a np.random.default_rng under the hood.

+
+

Parameters#

+
+
seedfloat

The seed to use for the RNG.

+
+
+
+
+

Returns#

+
+
np.random.default_rng

The RNG used internally.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+Generator(PCG64) at 0x127EDE9E0
+
+
+
+
+ +
+ + +
+ + + + + + + +
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+ Built with the PyData Sphinx Theme 0.14.3. +

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+ + \ No newline at end of file diff --git a/docs/build/html/reference/squigglepy.samplers.html b/docs/build/html/reference/squigglepy.samplers.html new file mode 100644 index 0000000..81cb1e3 --- /dev/null +++ b/docs/build/html/reference/squigglepy.samplers.html @@ -0,0 +1,1179 @@ + + + + + + + + + + + squigglepy.samplers module — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + +
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+ + +
+
+ + + + + +
+ +
+

squigglepy.samplers module#

+
+
+squigglepy.samplers.bernoulli_sample(p, samples=1)[source]#
+

Sample 1 with probability p and 0 otherwise.

+
+

Parameters#

+
+
pfloat

The probability of success. Must be between 0 and 1.

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
int

Either 0 or 1

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> bernoulli_sample(0.5)
+0
+
+
+
+
+ +
+
+squigglepy.samplers.beta_sample(a, b, samples=1)[source]#
+

Sample a random number according to a beta distribution.

+
+

Parameters#

+
+
afloat

The alpha shape value of the distribution. Typically takes the value of the +number of trials that resulted in a success.

+
+
bfloat

The beta shape value of the distribution. Typically takes the value of the +number of trials that resulted in a failure.

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
float

A random number sampled from a beta distribution defined by +a and b.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> beta_sample(1, 1)
+0.22145847498048798
+
+
+
+
+ +
+
+squigglepy.samplers.binomial_sample(n, p, samples=1)[source]#
+

Sample a random number according to a binomial distribution.

+
+

Parameters#

+
+
nint

The number of trials.

+
+
pfloat

The probability of success for each trial. Must be between 0 and 1.

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
int

A random number sampled from a binomial distribution defined by +n and p. The random number should be between 0 and n.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> binomial_sample(10, 0.1)
+2
+
+
+
+
+ +
+
+squigglepy.samplers.chi_square_sample(df, samples=1)[source]#
+

Sample a random number according to a chi-square distribution.

+
+

Parameters#

+
+
dffloat

The number of degrees of freedom

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
float

A random number sampled from a chi-square distribution.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> chi_square_sample(2)
+4.808417207931989
+
+
+
+
+ +
+
+squigglepy.samplers.discrete_sample(items, samples=1, verbose=False, _multicore_tqdm_n=1, _multicore_tqdm_cores=1)[source]#
+

Sample a random value from a discrete distribution (aka categorical distribution).

+
+

Parameters#

+
+
itemslist or dict

The values that the discrete distribution will return and their associated +weights (or likelihoods of being returned when sampled).

+
+
samplesint

The number of samples to return.

+
+
verbosebool

If True, will print out statements on computational progress.

+
+
_multicore_tqdm_nint

The total number of samples to use for printing tqdm’s interface. This is meant to only +be used internally by squigglepy to make the progress bar printing work well for +multicore. This parameter can be safely ignored by the user.

+
+
_multicore_tqdm_coresint

The total number of cores to use for printing tqdm’s interface. This is meant to only +be used internally by squigglepy to make the progress bar printing work well for +multicore. This parameter can be safely ignored by the user.

+
+
+
+
+

Returns#

+

Various, based on items in items

+
+
+

Examples#

+
>>> set_seed(42)
+>>> # 10% chance of returning 0, 90% chance of returning 1
+>>> discrete_sample({0: 0.1, 1: 0.9})
+1
+>>> discrete_sample([[0.1, 0], [0.9, 1]])  # Different notation for the same thing.
+1
+>>> # When no weights are given, all have equal chance of happening.
+>>> discrete_sample([0, 1, 2])
+2
+>>> discrete_sample({'a': 0.1, 'b': 0.9})  # Values do not have to be numbers.
+'b'
+
+
+
+
+ +
+
+squigglepy.samplers.exponential_sample(scale, samples=1)[source]#
+

Sample a random number according to an exponential distribution.

+
+

Parameters#

+
+
scalefloat

The scale value of the exponential distribution.

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
int

A random number sampled from an exponential distribution.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> exponential_sample(10)
+24.042086039659946
+
+
+
+
+ +
+
+squigglepy.samplers.gamma_sample(shape, scale, samples=1)[source]#
+

Sample a random number according to a gamma distribution.

+
+

Parameters#

+
+
shapefloat

The shape value of the gamma distribution.

+
+
scalefloat

The scale value of the gamma distribution. Defaults to 1.

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
int

A random number sampled from an gamma distribution.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> gamma_sample(10, 2)
+21.290716894247602
+
+
+
+
+ +
+
+squigglepy.samplers.geometric_sample(p, samples=1)[source]#
+

Sample a random number according to a geometric distribution.

+
+

Parameters#

+
+
pfloat

The probability of success of an individual trial. Must be between 0 and 1.

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
int

A random number sampled from a geometric distribution.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> geometric_sample(0.1)
+2
+
+
+
+
+ +
+
+squigglepy.samplers.log_t_sample(low=None, high=None, t=20, samples=1, credibility=90)[source]#
+

Sample a random number according to a log-t-distribution.

+

The log-t-distribution is a t-distribution in log-space. It is defined with +degrees of freedom via the t parameter. Additionally, a loose credibility +interval can be defined via the t-distribution using the low and high +values. This will be a 90% CI by default unless you change credibility. +Unlike the normal and lognormal samplers, this credible interval is an +approximation and is not precisely defined.

+
+

Parameters#

+
+
lowfloat or None

The low value of a credible interval defined by credibility. +Must be greater than 0. Defaults to a 90% CI.

+
+
highfloat or None

The high value of a credible interval defined by credibility. Defaults to a 90% CI.

+
+
tfloat

The number of degrees of freedom of the t-distribution. Defaults to 20.

+
+
samplesint

The number of samples to return.

+
+
credibilityfloat

The range of the credibility interval. Defaults to 90.

+
+
+
+
+

Returns#

+
+
float

A random number sampled from a lognormal distribution defined by +mean and sd.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> log_t_sample(1, 2, t=4)
+2.052949773846356
+
+
+
+
+ +
+
+squigglepy.samplers.lognormal_sample(mean, sd, samples=1)[source]#
+

Sample a random number according to a lognormal distribution.

+
+

Parameters#

+
+
meanfloat

The mean of the lognormal distribution that is being sampled.

+
+
sdfloat

The standard deviation of the lognormal distribution that is being sampled.

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
float

A random number sampled from a lognormal distribution defined by +mean and sd.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> lognormal_sample(0, 1)
+1.3562412406168636
+
+
+
+
+ +
+
+squigglepy.samplers.mixture_sample(values, weights=None, relative_weights=None, samples=1, verbose=False, _multicore_tqdm_n=1, _multicore_tqdm_cores=1)[source]#
+

Sample a ranom number from a mixture distribution.

+
+

Parameters#

+
+
valueslist or dict

The distributions to mix. Can also be defined as a list of weights and distributions.

+
+
weightslist or None

The weights for each distribution.

+
+
relative_weightslist or None

Relative weights, which if given will be weights that are normalized +to sum to 1.

+
+
samplesint

The number of samples to return.

+
+
verbosebool

If True, will print out statements on computational progress.

+
+
_multicore_tqdm_nint

The total number of samples to use for printing tqdm’s interface. This is meant to only +be used internally by squigglepy to make the progress bar printing work well for +multicore. This parameter can be safely ignored by the user.

+
+
_multicore_tqdm_coresint

The total number of cores to use for printing tqdm’s interface. This is meant to only +be used internally by squigglepy to make the progress bar printing work well for +multicore. This parameter can be safely ignored by the user.

+
+
+
+
+

Returns#

+

Various, based on items in values

+
+
+

Examples#

+
>>> set_seed(42)
+>>> mixture_sample([norm(1, 2), norm(3, 4)], weights=[0.1, 0.9])
+3.183867278765718
+>>> # Different notation for the same thing.
+>>> mixture_sample([[0.1, norm(1, 2)], [0.9, norm(3, 4)]])
+3.7859113725925972
+>>> # When no weights are given, all have equal chance of happening.
+>>> mixture_sample([norm(1, 2), norm(3, 4)])
+1.1041655362137777
+
+
+
+
+ +
+
+squigglepy.samplers.normal_sample(mean, sd, samples=1)[source]#
+

Sample a random number according to a normal distribution.

+
+

Parameters#

+
+
meanfloat

The mean of the normal distribution that is being sampled.

+
+
sdfloat

The standard deviation of the normal distribution that is being sampled.

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
float

A random number sampled from a normal distribution defined by +mean and sd.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> normal_sample(0, 1)
+0.30471707975443135
+
+
+
+
+ +
+
+squigglepy.samplers.pareto_sample(shape, samples=1)[source]#
+

Sample a random number according to a pareto distribution.

+
+

Parameters#

+
+
shapefloat

The shape value of the pareto distribution.

+
+
+
+
+

Returns#

+
+
int

A random number sampled from an pareto distribution.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> pareto_sample(1)
+10.069666324736094
+
+
+
+
+ +
+
+squigglepy.samplers.pert_sample(left, mode, right, lam, samples=1)[source]#
+

Sample a random number according to a PERT distribution.

+
+

Parameters#

+
+
leftfloat

The smallest value of the PERT distribution.

+
+
modefloat

The most common value of the PERT distribution.

+
+
rightfloat

The largest value of the PERT distribution.

+
+
lamfloat

The lambda of the PERT distribution.

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
float

A random number sampled from a PERT distribution.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> pert_sample(1, 2, 3, 4)
+2.327625176788963
+
+
+
+
+ +
+
+squigglepy.samplers.poisson_sample(lam, samples=1)[source]#
+

Sample a random number according to a poisson distribution.

+
+

Parameters#

+
+
lamfloat

The lambda value of the poisson distribution.

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
int

A random number sampled from a poisson distribution.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> poisson_sample(10)
+13
+
+
+
+
+ +
+
+squigglepy.samplers.sample(dist=None, n=1, lclip=None, rclip=None, memcache=False, reload_cache=False, dump_cache_file=None, load_cache_file=None, cache_file_primary=False, verbose=None, cores=1, _multicore_tqdm_n=1, _multicore_tqdm_cores=1, _correlate_if_needed=True)[source]#
+

Sample random numbers from a given distribution.

+
+

Parameters#

+
+
distDistribution

The distribution to sample random number from.

+
+
nint

The number of random numbers to sample from the distribution. Default to 1.

+
+
lclipfloat or None

If not None, any value below lclip will be coerced to lclip.

+
+
rclipfloat or None

If not None, any value below rclip will be coerced to rclip.

+
+
memcachebool

If True, will attempt to load the results in-memory for future calculations if +a cache is present. Otherwise will save the results to an in-memory cache. Each cache +will be matched based on dist. Default False.

+
+
reload_cachebool

If True, any existing cache will be ignored and recalculated. Default False.

+
+
dump_cache_filestr or None

If present, will write out the cache to a numpy file with this path with +.sqlcache.npy appended to the file name.

+
+
load_cache_filestr or None

If present, will first attempt to load and use a cache from a file with this +path with .sqlcache.npy appended to the file name.

+
+
cache_file_primarybool

If both an in-memory cache and file cache are present, the file +cache will be used for the cache if this is True, and the in-memory cache +will be used otherwise. Defaults to False.

+
+
verbosebool

If True, will print out statements on computational progress. If False, will not. +If None (default), will be True when n is greater than or equal to 1M.

+
+
coresint

If 1, runs on a single core / process. If greater than 1, will run on a multiprocessing +pool with that many cores / processes.

+
+
_multicore_tqdm_nint

The total number of samples to use for printing tqdm’s interface. This is meant to only +be used internally by squigglepy to make the progress bar printing work well for +multicore. This parameter can be safely ignored by the user.

+
+
_multicore_tqdm_coresint

The total number of cores to use for printing tqdm’s interface. This is meant to only +be used internally by squigglepy to make the progress bar printing work well for +multicore. This parameter can be safely ignored by the user.

+
+
+
+
+

Returns#

+

Various, based on dist.

+
+
+

Examples#

+
>>> set_seed(42)
+>>> sample(norm(1, 2))
+1.592627415218455
+>>> sample(mixture([norm(1, 2), norm(3, 4)]))
+1.7281209657534462
+>>> sample(lognorm(1, 10), n=5, lclip=3)
+array([6.10817361, 3.        , 3.        , 3.45828454, 3.        ])
+
+
+
+
+ +
+
+squigglepy.samplers.sample_correlated_group(requested_dist: BaseDistribution, n: int, verbose=False) → ndarray[Any, dtype[float64]][source]#
+

Samples a correlated distribution, alongside +all other correlated distributions in the same group.

+

The samples for other variables are stored in the distributions themselves +(in _correlated_samples).

+

This is necessary, because the sampling needs to happen all at once, regardless +of where the distributions are used in the binary tree of operations.

+
+ +
+
+squigglepy.samplers.t_sample(low=None, high=None, t=20, samples=1, credibility=90)[source]#
+

Sample a random number according to a t-distribution.

+

The t-distribution is defined with degrees of freedom via the t +parameter. Additionally, a loose credibility interval can be defined +via the t-distribution using the low and high values. This will be a +90% CI by default unless you change credibility. Unlike the normal and +lognormal samplers, this credible interval is an approximation and is +not precisely defined.

+
+

Parameters#

+
+
lowfloat or None

The low value of a credible interval defined by credibility. Defaults to a 90% CI.

+
+
highfloat or None

The high value of a credible interval defined by credibility. Defaults to a 90% CI.

+
+
tfloat

The number of degrees of freedom of the t-distribution. Defaults to 20.

+
+
samplesint

The number of samples to return.

+
+
credibilityfloat

The range of the credibility interval. Defaults to 90.

+
+
+
+
+

Returns#

+
+
float

A random number sampled from a lognormal distribution defined by +mean and sd.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> t_sample(1, 2, t=4)
+2.7887113716855985
+
+
+
+
+ +
+
+squigglepy.samplers.triangular_sample(left, mode, right, samples=1)[source]#
+

Sample a random number according to a triangular distribution.

+
+

Parameters#

+
+
leftfloat

The smallest value of the triangular distribution.

+
+
modefloat

The most common value of the triangular distribution.

+
+
rightfloat

The largest value of the triangular distribution.

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
float

A random number sampled from a triangular distribution.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> triangular_sample(1, 2, 3)
+2.327625176788963
+
+
+
+
+ +
+
+squigglepy.samplers.uniform_sample(low, high, samples=1)[source]#
+

Sample a random number according to a uniform distribution.

+
+

Parameters#

+
+
lowfloat

The smallest value the uniform distribution will return.

+
+
highfloat

The largest value the uniform distribution will return.

+
+
samplesint

The number of samples to return.

+
+
+
+
+

Returns#

+
+
float

A random number sampled from a uniform distribution between +`low` and `high`.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> uniform_sample(0, 1)
+0.7739560485559633
+
+
+
+
+ +
+ + +
+ + + + + + + +
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+ On this page +
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+ +
+

+ + © Copyright 2023, Peter Wildeford. +
+ +

+
+ +
+

+ Created using Sphinx 7.2.6. +
+

+
+ +
+ + + +
+ +

+ Built with the PyData Sphinx Theme 0.14.3. +

+ +
+ +
+ +
+ + \ No newline at end of file diff --git a/docs/build/html/reference/squigglepy.squigglepy.html b/docs/build/html/reference/squigglepy.squigglepy.html new file mode 100644 index 0000000..0bf0f9c --- /dev/null +++ b/docs/build/html/reference/squigglepy.squigglepy.html @@ -0,0 +1,434 @@ + + + + + + + + + + + squigglepy.squigglepy package — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + +
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+ +
+

squigglepy.squigglepy package#

+
+

Submodules#

+
+
+

squigglepy.squigglepy.bayes module#

+
+
+

squigglepy.squigglepy.correlation module#

+
+
+

squigglepy.squigglepy.distributions module#

+
+
+

squigglepy.squigglepy.numbers module#

+
+
+

squigglepy.squigglepy.rng module#

+
+
+

squigglepy.squigglepy.samplers module#

+
+
+

squigglepy.squigglepy.utils module#

+
+
+

squigglepy.squigglepy.version module#

+
+
+

Module contents#

+
+
+ + +
+ + + + + +
+ +
+
+
+ +
+ + + +
+ +
+
+ On this page +
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+
+ + Show Source + +
+
+ +
+ + +
+
+ +
+ +
+
+
+ + + + + +
+
+ +
+ +
+

+ + © Copyright 2023, Peter Wildeford. +
+ +

+
+ +
+

+ Created using Sphinx 7.2.6. +
+

+
+ +
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+ +

+ Built with the PyData Sphinx Theme 0.14.3. +

+ +
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+ + \ No newline at end of file diff --git a/docs/build/html/reference/squigglepy.tests.html b/docs/build/html/reference/squigglepy.tests.html new file mode 100644 index 0000000..32fb9e5 --- /dev/null +++ b/docs/build/html/reference/squigglepy.tests.html @@ -0,0 +1,438 @@ + + + + + + + + + + + squigglepy.tests package — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + +
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squigglepy.tests package#

+
+

Submodules#

+
+
+

squigglepy.tests.integration module#

+
+
+

squigglepy.tests.strategies module#

+
+
+

squigglepy.tests.test_bayes module#

+
+
+

squigglepy.tests.test_correlation module#

+
+
+

squigglepy.tests.test_distributions module#

+
+
+

squigglepy.tests.test_numbers module#

+
+
+

squigglepy.tests.test_rng module#

+
+
+

squigglepy.tests.test_samplers module#

+
+
+

squigglepy.tests.test_utils module#

+
+
+

Module contents#

+
+
+ + +
+ + + + + +
+ +
+
+
+ +
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+ +
+
+ On this page +
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+ + © Copyright 2023, Peter Wildeford. +
+ +

+
+ +
+

+ Created using Sphinx 7.2.6. +
+

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+ Built with the PyData Sphinx Theme 0.14.3. +

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+ + \ No newline at end of file diff --git a/docs/build/html/reference/squigglepy.utils.html b/docs/build/html/reference/squigglepy.utils.html new file mode 100644 index 0000000..5bce7e5 --- /dev/null +++ b/docs/build/html/reference/squigglepy.utils.html @@ -0,0 +1,1383 @@ + + + + + + + + + + + squigglepy.utils module — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + +
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+ +
+

squigglepy.utils module#

+
+
+squigglepy.utils.doubling_time_to_growth_rate(doubling_time)[source]#
+

Convert a doubling time to a growth rate.

+

Doubling time is expressed as a number, numpy array or distribution in any +time unit. Growth rate is set where e.g. 0.05 means +5%. The time unit remains the +same, so if we’ve got a doubling time of 2 years, the returned value is the annual +growth rate.

+

NOTE: This only works works for numbers, arrays and distributions where all numbers +are above 0. (Otherwise it makes no sense to talk about doubling times.)

+
+

Parameters#

+
+
doubling_timefloat or np.array or BaseDistribution

The doubling time expressed in any time unit.

+
+
+
+
+

Returns#

+
+
float or np.array or ComplexDistribution

Returns the growth rate expressed as a fraction (the percentage divided by 100).

+
+
+
+
+

Examples#

+
>>> doubling_time_to_growth_rate(12)
+0.05946309435929531
+
+
+
+
+ +
+
+squigglepy.utils.event(p)[source]#
+

Return True with probability p and False with probability 1 - p.

+

Alias for event_occurs.

+
+

Parameters#

+
+
pfloat

The probability of returning True. Must be between 0 and 1.

+
+
+
+
+

Returns#

+

bool

+
+
+

Examples#

+
>>> set_seed(42)
+>>> event(p=0.5)
+False
+
+
+
+
+ +
+
+squigglepy.utils.event_happens(p)[source]#
+

Return True with probability p and False with probability 1 - p.

+

Alias for event_occurs.

+
+

Parameters#

+
+
pfloat

The probability of returning True. Must be between 0 and 1.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> event_happens(p=0.5)
+False
+
+
+
+
+ +
+
+squigglepy.utils.event_occurs(p)[source]#
+

Return True with probability p and False with probability 1 - p.

+
+

Parameters#

+
+
pfloat

The probability of returning True. Must be between 0 and 1.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> event_occurs(p=0.5)
+False
+
+
+
+
+ +
+
+squigglepy.utils.extremize(p, e)[source]#
+

Extremize a prediction.

+
+

Parameters#

+
+
pfloat

The prediction to extremize. Must be within 0-1.

+
+
efloat

The extremization factor.

+
+
+
+
+

Returns#

+
+
float

The extremized prediction

+
+
+
+
+

Examples#

+
>>> # Extremizing of 1.73 per https://arxiv.org/abs/2111.03153
+>>> extremize(p=0.7, e=1.73)
+0.875428191155692
+
+
+
+
+ +
+
+squigglepy.utils.flip_coin(n=1)[source]#
+

Flip a coin.

+
+

Parameters#

+
+
nint

The number of coins to be flipped.

+
+
+
+
+

Returns#

+
+
str or list

Returns the value of each coin flip, as either “heads” or “tails”

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> flip_coin()
+'heads'
+
+
+
+
+ +
+
+squigglepy.utils.full_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0)[source]#
+

Alias for kelly where deference is 0.

+
+

Parameters#

+
+
my_pricefloat

The price (or probability) you give for the given event.

+
+
market_pricefloat

The price the market is giving for that event.

+
+
bankrollfloat

How much money do you have to bet? Defaults to 1.

+
+
resolve_datestr or None

When will the event happen, the market resolve, and you get your money back? Used for +calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means +ARR is not calculated.

+
+
currentfloat

How much do you already have invested in this event? Used for calculating the +additional amount you should invest. Defaults to 0.

+
+
+
+
+

Returns#

+
+
dict

A dict of values specifying: +* my_price +* market_price +* deference +* adj_price : an adjustment to my_price once deference is taken

+
+

into account.

+
+
    +

  • delta_price : the absolute difference between my_price and market_price.

    • +

  • adj_delta_price : the absolute difference between adj_price and +market_price.

    • +

  • kelly : the kelly criterion indicating the percentage of bankroll +you should bet.

    • +

  • target : the target amount of money you should have invested

    • +

  • current

    • +

  • delta : the amount of money you should invest given what you already +have invested

    • +

  • max_gain : the amount of money you would gain if you win

    • +

  • modeled_gain : the expected value you would win given adj_price

    • +

  • expected_roi : the expected return on investment

    • +

  • expected_arr : the expected ARR given resolve_date

    • +

  • resolve_date

    • +
+
+
+
+
+

Examples#

+
>>> full_kelly(my_price=0.7, market_price=0.4, bankroll=100)
+{'my_price': 0.7, 'market_price': 0.4, 'deference': 0, 'adj_price': 0.7,
+ 'delta_price': 0.3, 'adj_delta_price': 0.3, 'kelly': 0.5, 'target': 50.0,
+ 'current': 0, 'delta': 50.0, 'max_gain': 125.0, 'modeled_gain': 72.5,
+ 'expected_roi': 0.75, 'expected_arr': None, 'resolve_date': None}
+
+
+
+
+ +
+
+squigglepy.utils.geomean(a, weights=None, relative_weights=None, drop_na=True)[source]#
+

Calculate the geometric mean.

+
+

Parameters#

+
+
alist or np.array

The values to calculate the geometric mean of.

+
+
weightslist or None

The weights, if a weighted geometric mean is desired.

+
+
relative_weightslist or None

Relative weights, which if given will be weights that are normalized +to sum to 1.

+
+
drop_naboolean

Should NA-like values be dropped when calculating the geomean?

+
+
+
+
+

Returns#

+

float

+
+
+

Examples#

+
>>> geomean([1, 3, 10])
+3.1072325059538595
+
+
+
+
+ +
+
+squigglepy.utils.geomean_odds(a, weights=None, relative_weights=None, drop_na=True)[source]#
+

Calculate the geometric mean of odds.

+
+

Parameters#

+
+
alist or np.array

The probabilities to calculate the geometric mean of. These are converted to odds +before the geometric mean is taken..

+
+
weightslist or None

The weights, if a weighted geometric mean is desired.

+
+
relative_weightslist or None

Relative weights, which if given will be weights that are normalized +to sum to 1.

+
+
drop_naboolean

Should NA-like values be dropped when calculating the geomean?

+
+
+
+
+

Returns#

+

float

+
+
+

Examples#

+
>>> geomean_odds([0.1, 0.3, 0.9])
+0.42985748800076845
+
+
+
+
+ +
+
+squigglepy.utils.get_log_percentiles(data, percentiles=[1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99], reverse=False, display=True, digits=1)[source]#
+

Print the log (base 10) of the percentiles of the data.

+
+

Parameters#

+
+
datalist or np.array

The data to calculate percentiles for.

+
+
percentileslist

A list of percentiles to calculate. Must be values between 0 and 100.

+
+
reversebool

If True, the percentile values are reversed (e.g., 95th and 5th percentile +swap values.)

+
+
displaybool

If True, the function returns an easy to read display.

+
+
digitsint or None

The number of digits to display (using rounding).

+
+
+
+
+

Returns#

+
+
dict

A dictionary of the given percentiles. If display is true, will be str values. +Otherwise will be float values. 10 to the power of the value gives the true percentile.

+
+
+
+
+

Examples#

+
>>> get_percentiles(range(100), percentiles=[25, 50, 75])
+{25: 24.75, 50: 49.5, 75: 74.25}
+
+
+
+
+ +
+
+squigglepy.utils.get_mean_and_ci(data, credibility=90, digits=None)[source]#
+

Return the mean and percentiles of the data.

+
+

Parameters#

+
+
datalist or np.array

The data to calculate the mean and CI for.

+
+
credibilityfloat

The credibility of the interval. Must be values between 0 and 100. Default 90 for 90% CI.

+
+
digitsint or None

The number of digits to display (using rounding).

+
+
+
+
+

Returns#

+
+
dict

A dictionary with the mean and CI.

+
+
+
+
+

Examples#

+
>>> get_mean_and_ci(range(100))
+{'mean': 49.5, 'ci_low': 4.95, 'ci_high': 94.05}
+
+
+
+
+ +
+
+squigglepy.utils.get_median_and_ci(data, credibility=90, digits=None)[source]#
+

Return the median and percentiles of the data.

+
+

Parameters#

+
+
datalist or np.array

The data to calculate the mean and CI for.

+
+
credibilityfloat

The credibility of the interval. Must be values between 0 and 100. Default 90 for 90% CI.

+
+
digitsint or None

The number of digits to display (using rounding).

+
+
+
+
+

Returns#

+
+
dict

A dictionary with the median and CI.

+
+
+
+
+

Examples#

+
>>> get_median_and_ci(range(100))
+{'mean': 49.5, 'ci_low': 4.95, 'ci_high': 94.05}
+
+
+
+
+ +
+
+squigglepy.utils.get_percentiles(data, percentiles=[1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99], reverse=False, digits=None)[source]#
+

Print the percentiles of the data.

+
+

Parameters#

+
+
datalist or np.array

The data to calculate percentiles for.

+
+
percentileslist

A list of percentiles to calculate. Must be values between 0 and 100.

+
+
reversebool

If True, the percentile values are reversed (e.g., 95th and 5th percentile +swap values.)

+
+
digitsint or None

The number of digits to display (using rounding).

+
+
+
+
+

Returns#

+
+
dict

A dictionary of the given percentiles.

+
+
+
+
+

Examples#

+
>>> get_percentiles(range(100), percentiles=[25, 50, 75])
+{25: 24.75, 50: 49.5, 75: 74.25}
+
+
+
+
+ +
+
+squigglepy.utils.growth_rate_to_doubling_time(growth_rate)[source]#
+

Convert a positive growth rate to a doubling rate.

+

Growth rate must be expressed as a number, numpy array or distribution +where 0.05 means +5% to a doubling time. The time unit remains the same, so if we’ve +got +5% annual growth, the returned value is the doubling time in years.

+

NOTE: This only works works for numbers, arrays and distributions where all numbers +are above 0. (Otherwise it makes no sense to talk about doubling times.)

+
+

Parameters#

+
+
growth_ratefloat or np.array or BaseDistribution

The growth rate expressed as a fraction (the percentage divided by 100).

+
+
+
+
+

Returns#

+
+
float or np.array or ComplexDistribution

Returns the doubling time.

+
+
+
+
+

Examples#

+
>>> growth_rate_to_doubling_time(0.01)
+69.66071689357483
+
+
+
+
+ +
+
+squigglepy.utils.half_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0)[source]#
+

Alias for kelly where deference is 0.5.

+
+

Parameters#

+
+
my_pricefloat

The price (or probability) you give for the given event.

+
+
market_pricefloat

The price the market is giving for that event.

+
+
bankrollfloat

How much money do you have to bet? Defaults to 1.

+
+
resolve_datestr or None

When will the event happen, the market resolve, and you get your money back? Used for +calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means +ARR is not calculated.

+
+
currentfloat

How much do you already have invested in this event? Used for calculating the +additional amount you should invest. Defaults to 0.

+
+
+
+
+

Returns#

+
+
dict

A dict of values specifying: +* my_price +* market_price +* deference +* adj_price : an adjustment to my_price once deference is taken

+
+

into account.

+
+
    +

  • delta_price : the absolute difference between my_price and market_price.

    • +

  • adj_delta_price : the absolute difference between adj_price and +market_price.

    • +

  • kelly : the kelly criterion indicating the percentage of bankroll +you should bet.

    • +

  • target : the target amount of money you should have invested

    • +

  • current

    • +

  • delta : the amount of money you should invest given what you already +have invested

    • +

  • max_gain : the amount of money you would gain if you win

    • +

  • modeled_gain : the expected value you would win given adj_price

    • +

  • expected_roi : the expected return on investment

    • +

  • expected_arr : the expected ARR given resolve_date

    • +

  • resolve_date

    • +
+
+
+
+
+

Examples#

+
>>> half_kelly(my_price=0.7, market_price=0.4, bankroll=100)
+{'my_price': 0.7, 'market_price': 0.4, 'deference': 0.5, 'adj_price': 0.55,
+ 'delta_price': 0.3, 'adj_delta_price': 0.15, 'kelly': 0.25, 'target': 25.0,
+ 'current': 0, 'delta': 25.0, 'max_gain': 62.5, 'modeled_gain': 23.13,
+ 'expected_roi': 0.375, 'expected_arr': None, 'resolve_date': None}
+
+
+
+
+ +
+
+squigglepy.utils.is_continuous_dist(obj)[source]#
+
+ +
+
+squigglepy.utils.is_dist(obj)[source]#
+

Test if a given object is a Squigglepy distribution.

+
+

Parameters#

+
+
objobject

The object to test.

+
+
+
+
+

Returns#

+
+
bool

True, if the object is a distribution. False if not.

+
+
+
+
+

Examples#

+
>>> is_dist(norm(0, 1))
+True
+>>> is_dist(0)
+False
+
+
+
+
+ +
+
+squigglepy.utils.is_sampleable(obj)[source]#
+

Test if a given object can be sampled from.

+

This includes distributions, integers, floats, None, +strings, and callables.

+
+

Parameters#

+
+
objobject

The object to test.

+
+
+
+
+

Returns#

+
+
bool

True, if the object can be sampled from. False if not.

+
+
+
+
+

Examples#

+
>>> is_sampleable(norm(0, 1))
+True
+>>> is_sampleable(0)
+True
+>>> is_sampleable([0, 1])
+False
+
+
+
+
+ +
+
+squigglepy.utils.kelly(my_price, market_price, deference=0, bankroll=1, resolve_date=None, current=0)[source]#
+

Calculate the Kelly criterion.

+
+

Parameters#

+
+
my_pricefloat

The price (or probability) you give for the given event.

+
+
market_pricefloat

The price the market is giving for that event.

+
+
deferencefloat

How much deference (or weight) do you give the market price? Use 0.5 for half Kelly +and 0.75 for quarter Kelly. Defaults to 0, which is full Kelly.

+
+
bankrollfloat

How much money do you have to bet? Defaults to 1.

+
+
resolve_datestr or None

When will the event happen, the market resolve, and you get your money back? Used for +calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means +ARR is not calculated.

+
+
currentfloat

How much do you already have invested in this event? Used for calculating the +additional amount you should invest. Defaults to 0.

+
+
+
+
+

Returns#

+
+
dict

A dict of values specifying: +* my_price +* market_price +* deference +* adj_price : an adjustment to my_price once deference is taken

+
+

into account.

+
+
    +

  • delta_price : the absolute difference between my_price and market_price.

    • +

  • adj_delta_price : the absolute difference between adj_price and +market_price.

    • +

  • kelly : the kelly criterion indicating the percentage of bankroll +you should bet.

    • +

  • target : the target amount of money you should have invested

    • +

  • current

    • +

  • delta : the amount of money you should invest given what you already +have invested

    • +

  • max_gain : the amount of money you would gain if you win

    • +

  • modeled_gain : the expected value you would win given adj_price

    • +

  • expected_roi : the expected return on investment

    • +

  • expected_arr : the expected ARR given resolve_date

    • +

  • resolve_date

    • +
+
+
+
+
+

Examples#

+
>>> kelly(my_price=0.7, market_price=0.4, deference=0.5, bankroll=100)
+{'my_price': 0.7, 'market_price': 0.4, 'deference': 0.5, 'adj_price': 0.55,
+ 'delta_price': 0.3, 'adj_delta_price': 0.15, 'kelly': 0.25, 'target': 25.0,
+ 'current': 0, 'delta': 25.0, 'max_gain': 62.5, 'modeled_gain': 23.13,
+ 'expected_roi': 0.375, 'expected_arr': None, 'resolve_date': None}
+
+
+
+
+ +
+
+squigglepy.utils.laplace(s, n=None, time_passed=None, time_remaining=None, time_fixed=False)[source]#
+

Return probability of success on next trial given Laplace’s law of succession.

+

Also can be used to calculate a time-invariant version defined in +https://www.lesswrong.com/posts/wE7SK8w8AixqknArs/a-time-invariant-version-of-laplace-s-rule

+
+

Parameters#

+
+
sint

The number of successes among n past trials or among time_passed amount of time.

+
+
nint or None

The number of trials that contain the successes (and/or failures). Leave as None if +time-invariant mode is desired.

+
+
time_passedfloat or None

The amount of time that has passed when the successes (and/or failures) occured for +calculating a time-invariant Laplace.

+
+
time_remainingfloat or None

We are calculating the likelihood of observing at least one success over this time +period.

+
+
time_fixedbool

This should be False if the time period is variable - that is, if the time period +was chosen specifically to include the most recent success. Otherwise the time period +is fixed and this should be True. Defaults to False.

+
+
+
+
+

Returns#

+
+
float

The probability of at least one success in the next trial or time_remaining amount +of time.

+
+
+
+
+

Examples#

+
>>> # The sun has risen the past 100,000 days. What are the odds it rises again tomorrow?
+>>> laplace(s=100*K, n=100*K)
+0.999990000199996
+>>> # The last time a nuke was used in war was 77 years ago. What are the odds a nuke
+>>> # is used in the next year, not considering any information other than this naive prior?
+>>> laplace(s=1, time_passed=77, time_remaining=1, time_fixed=False)
+0.012820512820512664
+
+
+
+
+ +
+
+squigglepy.utils.normalize(lst)[source]#
+

Normalize a list to sum to 1.

+
+

Parameters#

+
+
lstlist

The list to normalize.

+
+
+
+
+

Returns#

+
+
list

A list where each value is normalized such that the list sums to 1.

+
+
+
+
+

Examples#

+
>>> normalize([0.1, 0.2, 0.2])
+[0.2, 0.4, 0.4]
+
+
+
+
+ +
+
+squigglepy.utils.odds_to_p(odds)[source]#
+

Calculate the probability from given decimal odds.

+
+

Parameters#

+
+
oddsfloat

The decimal odds to calculate the probability for.

+
+
+
+
+

Returns#

+
+
float

Probability

+
+
+
+
+

Examples#

+
>>> odds_to_p(0.1)
+0.09090909090909091
+
+
+
+
+ +
+
+squigglepy.utils.one_in(p, digits=0, verbose=True)[source]#
+

Convert a probability into “1 in X” notation.

+
+

Parameters#

+
+
pfloat

The probability to convert.

+
+
digitsint

The number of digits to round the result to. Defaults to 0. If digits +is 0, the result will be converted to int instead of float.

+
+
verboselogical

If True, will return a string with “1 in X”. If False, will just return X.

+
+
+
+
+

Returns#

+

str if verbose is True. Otherwise, int if digits is 0 or float if digits > 0.

+
+
+

Examples#

+
>>> one_in(0.1)
+"1 in 10"
+
+
+
+
+ +
+
+squigglepy.utils.p_to_odds(p)[source]#
+

Calculate the decimal odds from a given probability.

+
+

Parameters#

+
+
pfloat

The probability to calculate decimal odds for. Must be between 0 and 1.

+
+
+
+
+

Returns#

+
+
float

Decimal odds

+
+
+
+
+

Examples#

+
>>> p_to_odds(0.1)
+0.1111111111111111
+
+
+
+
+ +
+
+squigglepy.utils.quarter_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0)[source]#
+

Alias for kelly where deference is 0.75.

+
+

Parameters#

+
+
my_pricefloat

The price (or probability) you give for the given event.

+
+
market_pricefloat

The price the market is giving for that event.

+
+
bankrollfloat

How much money do you have to bet? Defaults to 1.

+
+
resolve_datestr or None

When will the event happen, the market resolve, and you get your money back? Used for +calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means +ARR is not calculated.

+
+
currentfloat

How much do you already have invested in this event? Used for calculating the +additional amount you should invest. Defaults to 0.

+
+
+
+
+

Returns#

+
+
dict

A dict of values specifying: +* my_price +* market_price +* deference +* adj_price : an adjustment to my_price once deference is taken

+
+

into account.

+
+
    +

  • delta_price : the absolute difference between my_price and market_price.

    • +

  • adj_delta_price : the absolute difference between adj_price and +market_price.

    • +

  • kelly : the kelly criterion indicating the percentage of bankroll +you should bet.

    • +

  • target : the target amount of money you should have invested

    • +

  • current

    • +

  • delta : the amount of money you should invest given what you already +have invested

    • +

  • max_gain : the amount of money you would gain if you win

    • +

  • modeled_gain : the expected value you would win given adj_price

    • +

  • expected_roi : the expected return on investment

    • +

  • expected_arr : the expected ARR given resolve_date

    • +

  • resolve_date

    • +
+
+
+
+
+

Examples#

+
>>> quarter_kelly(my_price=0.7, market_price=0.4, bankroll=100)
+{'my_price': 0.7, 'market_price': 0.4, 'deference': 0.75, 'adj_price': 0.48,
+ 'delta_price': 0.3, 'adj_delta_price': 0.08, 'kelly': 0.125, 'target': 12.5,
+ 'current': 0, 'delta': 12.5, 'max_gain': 31.25, 'modeled_gain': 8.28,
+ 'expected_roi': 0.188, 'expected_arr': None, 'resolve_date': None}
+
+
+
+
+ +
+
+squigglepy.utils.roll_die(sides, n=1)[source]#
+

Roll a die.

+
+

Parameters#

+
+
sidesint

The number of sides of the die that is rolled.

+
+
nint

The number of dice to be rolled.

+
+
+
+
+

Returns#

+
+
int or list

Returns the value of each die roll.

+
+
+
+
+

Examples#

+
>>> set_seed(42)
+>>> roll_die(6)
+5
+
+
+
+
+ +
+ + +
+ + + + + + + +
+ + + +
+ +
+
+ On this page +
+
+ +
+
+ + Show Source + +
+
+ +
+ + +
+
+ +
+ +
+
+
+ + + + + +
+
+ +
+ +
+

+ + © Copyright 2023, Peter Wildeford. +
+ +

+
+ +
+

+ Created using Sphinx 7.2.6. +
+

+
+ +
+ + + +
+ +

+ Built with the PyData Sphinx Theme 0.14.3. +

+ +
+ +
+ +
+ + \ No newline at end of file diff --git a/docs/build/html/reference/squigglepy.version.html b/docs/build/html/reference/squigglepy.version.html new file mode 100644 index 0000000..e202776 --- /dev/null +++ b/docs/build/html/reference/squigglepy.version.html @@ -0,0 +1,446 @@ + + + + + + + + + + + squigglepy.version module — Squigglepy documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + +
+
+
+
+ + + Ctrl+K +
+
+ + + +
+
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+ + + +
+ + +
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+ +
+ + + +
+ +
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+ +
+ +
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+ + +
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+ + + + +
+ +
+ + +
+
+ +
+
+ +
+ +
+ + + + +
+ +
+ + +
+
+ + + + + +
+ +
+

squigglepy.version module#

+
+ + +
+ + + + + + + +
+ + + +
+ +
+
+ + Show Source + +
+
+ +
+ + +
+
+ +
+ +
+
+
+ + + + + +
+
+ +
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+

+ + © Copyright 2023, Peter Wildeford. +
+ +

+
+ +
+

+ Created using Sphinx 7.2.6. +
+

+
+ +
+ + + +
+ +

+ Built with the PyData Sphinx Theme 0.14.3. +

+ +
+ +
+ +
+ + \ No newline at end of file diff --git a/docs/build/html/search.html b/docs/build/html/search.html index 41857b5..814b3e6 100644 --- a/docs/build/html/search.html +++ b/docs/build/html/search.html @@ -133,6 +133,19 @@

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b/docs/source/examples.rst new file mode 100644 index 0000000..c00053f --- /dev/null +++ b/docs/source/examples.rst @@ -0,0 +1,468 @@ +Examples +======== + +Piano Tuners Example +~~~~~~~~~~~~~~~~~~~~ + +Here’s the Squigglepy implementation of `the example from Squiggle +Docs `__: + +.. code:: python + + import squigglepy as sq + import numpy as np + import matplotlib.pyplot as plt + from squigglepy.numbers import K, M + from pprint import pprint + + pop_of_ny_2022 = sq.to(8.1*M, 8.4*M) # This means that you're 90% confident the value is between 8.1 and 8.4 Million. + pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01 # We assume there are almost no people with multiple pianos + pianos_per_piano_tuner = sq.to(2*K, 50*K) + piano_tuners_per_piano = 1 / pianos_per_piano_tuner + total_tuners_in_2022 = pop_of_ny_2022 * pct_of_pop_w_pianos * piano_tuners_per_piano + samples = total_tuners_in_2022 @ 1000 # Note: `@ 1000` is shorthand to get 1000 samples + + # Get mean and SD + print('Mean: {}, SD: {}'.format(round(np.mean(samples), 2), + round(np.std(samples), 2))) + + # Get percentiles + pprint(sq.get_percentiles(samples, digits=0)) + + # Histogram + plt.hist(samples, bins=200) + plt.show() + + # Shorter histogram + total_tuners_in_2022.plot() + +And the version from the Squiggle doc that incorporates time: + +.. code:: python + + import squigglepy as sq + from squigglepy.numbers import K, M + + pop_of_ny_2022 = sq.to(8.1*M, 8.4*M) + pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01 + pianos_per_piano_tuner = sq.to(2*K, 50*K) + piano_tuners_per_piano = 1 / pianos_per_piano_tuner + + def pop_at_time(t): # t = Time in years after 2022 + avg_yearly_pct_change = sq.to(-0.01, 0.05) # We're expecting NYC to continuously grow with an mean of roughly between -1% and +4% per year + return pop_of_ny_2022 * ((avg_yearly_pct_change + 1) ** t) + + def total_tuners_at_time(t): + return pop_at_time(t) * pct_of_pop_w_pianos * piano_tuners_per_piano + + # Get total piano tuners at 2030 + sq.get_percentiles(total_tuners_at_time(2030-2022) @ 1000) + +**WARNING:** Be careful about dividing by ``K``, ``M``, etc. ``1/2*K`` = +500 in Python. Use ``1/(2*K)`` instead to get the expected outcome. + +**WARNING:** Be careful about using ``K`` to get sample counts. Use +``sq.norm(2, 3) @ (2*K)``\ … ``sq.norm(2, 3) @ 2*K`` will return only +two samples, multiplied by 1000. + +Distributions +~~~~~~~~~~~~~ + +.. code:: python + + import squigglepy as sq + + # Normal distribution + sq.norm(1, 3) # 90% interval from 1 to 3 + + # Distribution can be sampled with mean and sd too + sq.norm(mean=0, sd=1) + + # Shorthand to get one sample + ~sq.norm(1, 3) + + # Shorthand to get more than one sample + sq.norm(1, 3) @ 100 + + # Longhand version to get more than one sample + sq.sample(sq.norm(1, 3), n=100) + + # Nice progress reporter + sq.sample(sq.norm(1, 3), n=1000, verbose=True) + + # Other distributions exist + sq.lognorm(1, 10) + sq.tdist(1, 10, t=5) + sq.triangular(1, 2, 3) + sq.pert(1, 2, 3, lam=2) + sq.binomial(p=0.5, n=5) + sq.beta(a=1, b=2) + sq.bernoulli(p=0.5) + sq.poisson(10) + sq.chisquare(2) + sq.gamma(3, 2) + sq.pareto(1) + sq.exponential(scale=1) + sq.geometric(p=0.5) + + # Discrete sampling + sq.discrete({'A': 0.1, 'B': 0.9}) + + # Can return integers + sq.discrete({0: 0.1, 1: 0.3, 2: 0.3, 3: 0.15, 4: 0.15}) + + # Alternate format (also can be used to return more complex objects) + sq.discrete([[0.1, 0], + [0.3, 1], + [0.3, 2], + [0.15, 3], + [0.15, 4]]) + + sq.discrete([0, 1, 2]) # No weights assumes equal weights + + # You can mix distributions together + sq.mixture([sq.norm(1, 3), + sq.norm(4, 10), + sq.lognorm(1, 10)], # Distributions to mix + [0.3, 0.3, 0.4]) # These are the weights on each distribution + + # This is equivalent to the above, just a different way of doing the notation + sq.mixture([[0.3, sq.norm(1,3)], + [0.3, sq.norm(4,10)], + [0.4, sq.lognorm(1,10)]]) + + # Make a zero-inflated distribution + # 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`. + sq.zero_inflated(0.6, sq.norm(1, 2)) + +Additional Features +~~~~~~~~~~~~~~~~~~~ + +.. code:: python + + import squigglepy as sq + + # You can add and subtract distributions + (sq.norm(1,3) + sq.norm(4,5)) @ 100 + (sq.norm(1,3) - sq.norm(4,5)) @ 100 + (sq.norm(1,3) * sq.norm(4,5)) @ 100 + (sq.norm(1,3) / sq.norm(4,5)) @ 100 + + # You can also do math with numbers + ~((sq.norm(sd=5) + 2) * 2) + ~(-sq.lognorm(0.1, 1) * sq.pareto(1) / 10) + + # You can change the CI from 90% (default) to 80% + sq.norm(1, 3, credibility=80) + + # You can clip + sq.norm(0, 3, lclip=0, rclip=5) # Sample norm with a 90% CI from 0-3, but anything lower than 0 gets clipped to 0 and anything higher than 5 gets clipped to 5. + + # You can also clip with a function, and use pipes + sq.norm(0, 3) >> sq.clip(0, 5) + + # You can correlate continuous distributions + a, b = sq.uniform(-1, 1), sq.to(0, 3) + a, b = sq.correlate((a, b), 0.5) # Correlate a and b with a correlation of 0.5 + # You can even pass your own correlation matrix! + a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]]) + +Example: Rolling a Die +^^^^^^^^^^^^^^^^^^^^^^ + +An example of how to use distributions to build tools: + +.. code:: python + + import squigglepy as sq + + def roll_die(sides, n=1): + return sq.discrete(list(range(1, sides + 1))) @ n if sides > 0 else None + + roll_die(sides=6, n=10) + # [2, 6, 5, 2, 6, 2, 3, 1, 5, 2] + +This is already included standard in the utils of this package. Use +``sq.roll_die``. + +Bayesian inference +~~~~~~~~~~~~~~~~~~ + +1% of women at age forty who participate in routine screening have +breast cancer. 80% of women with breast cancer will get positive +mammographies. 9.6% of women without breast cancer will also get +positive mammographies. + +A woman in this age group had a positive mammography in a routine +screening. What is the probability that she actually has breast cancer? + +We can approximate the answer with a Bayesian network (uses rejection +sampling): + +.. code:: python + + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import M + + def mammography(has_cancer): + return sq.event(0.8 if has_cancer else 0.096) + + def define_event(): + cancer = ~sq.bernoulli(0.01) + return({'mammography': mammography(cancer), + 'cancer': cancer}) + + bayes.bayesnet(define_event, + find=lambda e: e['cancer'], + conditional_on=lambda e: e['mammography'], + n=1*M) + # 0.07723995880535531 + +Or if we have the information immediately on hand, we can directly +calculate it. Though this doesn’t work for very complex stuff. + +.. code:: python + + from squigglepy import bayes + bayes.simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096) + # 0.07763975155279504 + +You can also make distributions and update them: + +.. code:: python + + import matplotlib.pyplot as plt + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import K + import numpy as np + + print('Prior') + prior = sq.norm(1,5) + prior_samples = prior @ (10*K) + plt.hist(prior_samples, bins = 200) + plt.show() + print(sq.get_percentiles(prior_samples)) + print('Prior Mean: {} SD: {}'.format(np.mean(prior_samples), np.std(prior_samples))) + print('-') + + print('Evidence') + evidence = sq.norm(2,3) + evidence_samples = evidence @ (10*K) + plt.hist(evidence_samples, bins = 200) + plt.show() + print(sq.get_percentiles(evidence_samples)) + print('Evidence Mean: {} SD: {}'.format(np.mean(evidence_samples), np.std(evidence_samples))) + print('-') + + print('Posterior') + posterior = bayes.update(prior, evidence) + posterior_samples = posterior @ (10*K) + plt.hist(posterior_samples, bins = 200) + plt.show() + print(sq.get_percentiles(posterior_samples)) + print('Posterior Mean: {} SD: {}'.format(np.mean(posterior_samples), np.std(posterior_samples))) + + print('Average') + average = bayes.average(prior, evidence) + average_samples = average @ (10*K) + plt.hist(average_samples, bins = 200) + plt.show() + print(sq.get_percentiles(average_samples)) + print('Average Mean: {} SD: {}'.format(np.mean(average_samples), np.std(average_samples))) + +Example: Alarm net +^^^^^^^^^^^^^^^^^^ + +This is the alarm network from `Bayesian Artificial Intelligence - +Section +2.5.1 `__: + + Assume your house has an alarm system against burglary. + + You live in the seismically active area and the alarm system can get + occasionally set off by an earthquake. + + You have two neighbors, Mary and John, who do not know each other. If + they hear the alarm they call you, but this is not guaranteed. + + The chance of a burglary on a particular day is 0.1%. The chance of + an earthquake on a particular day is 0.2%. + + The alarm will go off 95% of the time with both a burglary and an + earthquake, 94% of the time with just a burglary, 29% of the time + with just an earthquake, and 0.1% of the time with nothing (total + false alarm). + + John will call you 90% of the time when the alarm goes off. But on 5% + of the days, John will just call to say “hi”. Mary will call you 70% + of the time when the alarm goes off. But on 1% of the days, Mary will + just call to say “hi”. + +.. code:: python + + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import M + + def p_alarm_goes_off(burglary, earthquake): + if burglary and earthquake: + return 0.95 + elif burglary and not earthquake: + return 0.94 + elif not burglary and earthquake: + return 0.29 + elif not burglary and not earthquake: + return 0.001 + + def p_john_calls(alarm_goes_off): + return 0.9 if alarm_goes_off else 0.05 + + def p_mary_calls(alarm_goes_off): + return 0.7 if alarm_goes_off else 0.01 + + def define_event(): + burglary_happens = sq.event(p=0.001) + earthquake_happens = sq.event(p=0.002) + alarm_goes_off = sq.event(p_alarm_goes_off(burglary_happens, earthquake_happens)) + john_calls = sq.event(p_john_calls(alarm_goes_off)) + mary_calls = sq.event(p_mary_calls(alarm_goes_off)) + return {'burglary': burglary_happens, + 'earthquake': earthquake_happens, + 'alarm_goes_off': alarm_goes_off, + 'john_calls': john_calls, + 'mary_calls': mary_calls} + + # What are the chances that both John and Mary call if an earthquake happens? + bayes.bayesnet(define_event, + n=1*M, + find=lambda e: (e['mary_calls'] and e['john_calls']), + conditional_on=lambda e: e['earthquake']) + # Result will be ~0.19, though it varies because it is based on a random sample. + # This also may take a minute to run. + + # If both John and Mary call, what is the chance there's been a burglary? + bayes.bayesnet(define_event, + n=1*M, + find=lambda e: e['burglary'], + conditional_on=lambda e: (e['mary_calls'] and e['john_calls'])) + # Result will be ~0.27, though it varies because it is based on a random sample. + # This will run quickly because there is a built-in cache. + # Use `cache=False` to not build a cache and `reload_cache=True` to recalculate the cache. + +Note that the amount of Bayesian analysis that squigglepy can do is +pretty limited. For more complex bayesian analysis, consider +`sorobn `__, +`pomegranate `__, +`bnlearn `__, or +`pyMC `__. + +Example: A Demonstration of the Monty Hall Problem +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code:: python + + import squigglepy as sq + from squigglepy import bayes + from squigglepy.numbers import K, M, B, T + + + def monte_hall(door_picked, switch=False): + doors = ['A', 'B', 'C'] + car_is_behind_door = ~sq.discrete(doors) + reveal_door = ~sq.discrete([d for d in doors if d != door_picked and d != car_is_behind_door]) + + if switch: + old_door_picked = door_picked + door_picked = [d for d in doors if d != old_door_picked and d != reveal_door][0] + + won_car = (car_is_behind_door == door_picked) + return won_car + + + def define_event(): + door = ~sq.discrete(['A', 'B', 'C']) + switch = sq.event(0.5) + return {'won': monte_hall(door_picked=door, switch=switch), + 'switched': switch} + + RUNS = 10*K + r = bayes.bayesnet(define_event, + find=lambda e: e['won'], + conditional_on=lambda e: e['switched'], + verbose=True, + n=RUNS) + print('Win {}% of the time when switching'.format(int(r * 100))) + + r = bayes.bayesnet(define_event, + find=lambda e: e['won'], + conditional_on=lambda e: not e['switched'], + verbose=True, + n=RUNS) + print('Win {}% of the time when not switching'.format(int(r * 100))) + + # Win 66% of the time when switching + # Win 34% of the time when not switching + +Example: More complex coin/dice interactions +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + + Imagine that I flip a coin. If heads, I take a random die out of my + blue bag. If tails, I take a random die out of my red bag. The blue + bag contains only 6-sided dice. The red bag contains a 4-sided die, a + 6-sided die, a 10-sided die, and a 20-sided die. I then roll the + random die I took. What is the chance that I roll a 6? + +.. code:: python + + import squigglepy as sq + from squigglepy.numbers import K, M, B, T + from squigglepy import bayes + + def define_event(): + if sq.flip_coin() == 'heads': # Blue bag + return sq.roll_die(6) + else: # Red bag + return sq.discrete([4, 6, 10, 20]) >> sq.roll_die + + + bayes.bayesnet(define_event, + find=lambda e: e == 6, + verbose=True, + n=100*K) + # This run for me returned 0.12306 which is pretty close to the correct answer of 0.12292 + +Kelly betting +~~~~~~~~~~~~~ + +You can use probability generated, combine with a bankroll to determine +bet sizing using `Kelly +criterion `__. + +For example, if you want to Kelly bet and you’ve… + +- determined that your price (your probability of the event in question + happening / the market in question resolving in your favor) is $0.70 + (70%) +- see that the market is pricing at $0.65 +- you have a bankroll of $1000 that you are willing to bet + +You should bet as follows: + +.. code:: python + + import squigglepy as sq + kelly_data = sq.kelly(my_price=0.70, market_price=0.65, bankroll=1000) + kelly_data['kelly'] # What fraction of my bankroll should I bet on this? + # 0.143 + kelly_data['target'] # How much money should be invested in this? + # 142.86 + kelly_data['expected_roi'] # What is the expected ROI of this bet? + # 0.077 + +More examples +~~~~~~~~~~~~~ + +You can see more examples of squigglepy in action +`here `__. diff --git a/docs/source/index.rst b/docs/source/index.rst index 9a79421..1fdb7aa 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -1,8 +1,8 @@ Squigglepy: Implementation of Squiggle in Python ================================================ -`Squiggle `__ is a “simple -programming language for intuitive probabilistic estimation”. It serves +`Squiggle `__ is a "simple +programming language for intuitive probabilistic estimation". It serves as its own standalone programming language with its own syntax, but it is implemented in JavaScript. I like the features of Squiggle and intend to use it frequently, but I also sometimes want to use similar @@ -12,7 +12,58 @@ programming packages like Numpy, Pandas, and Matplotlib. The functionalities in Python. .. toctree:: - :maxdepth: 2 - :caption: Contents: + :maxdepth: 3 + :caption: Contents -Check out the :doc:`README ` to get started. + API Reference + Examples + +Installation +------------ + +.. code:: shell + + pip install squigglepy + +For plotting support, you can also use the ``plots`` extra: + +.. code:: shell + + pip install squigglepy[plots] + +Run tests +--------- + +Use ``black .`` for formatting. + +Run +``ruff check . && pytest && pip3 install . && python3 tests/integration.py`` + +Disclaimers +----------- + +This package is unofficial and supported by Peter Wildeford and Rethink +Priorities. It is not affiliated with or associated with the Quantified +Uncertainty Research Institute, which maintains the Squiggle language +(in JavaScript). + +This package is also new and not yet in a stable production version, so +you may encounter bugs and other errors. Please report those so they can +be fixed. It’s also possible that future versions of the package may +introduce breaking changes. + +This package is available under an MIT License. + +Acknowledgements +---------------- + +- The primary author of this package is Peter Wildeford. Agustín + Covarrubias and Bernardo Baron contributed several key features and + developments. +- Thanks to Ozzie Gooen and the Quantified Uncertainty Research + Institute for creating and maintaining the original Squiggle + language. +- Thanks to Dawn Drescher for helping me implement math between + distributions. +- Thanks to Dawn Drescher for coming up with the idea to use ``~`` as a + shorthand for ``sample``, as well as helping me implement it. diff --git a/docs/source/reference/modules.rst b/docs/source/reference/modules.rst new file mode 100644 index 0000000..57192bd --- /dev/null +++ b/docs/source/reference/modules.rst @@ -0,0 +1,7 @@ +squigglepy +========== + +.. toctree:: + :maxdepth: 4 + + squigglepy diff --git a/docs/source/reference/squigglepy.bayes.rst b/docs/source/reference/squigglepy.bayes.rst new file mode 100644 index 0000000..8a445be --- /dev/null +++ b/docs/source/reference/squigglepy.bayes.rst @@ -0,0 +1,7 @@ +squigglepy.bayes module +======================= + +.. automodule:: squigglepy.bayes + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/source/reference/squigglepy.correlation.rst b/docs/source/reference/squigglepy.correlation.rst new file mode 100644 index 0000000..c99cf14 --- /dev/null +++ b/docs/source/reference/squigglepy.correlation.rst @@ -0,0 +1,7 @@ +squigglepy.correlation module +============================= + +.. automodule:: squigglepy.correlation + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/source/reference/squigglepy.distributions.rst b/docs/source/reference/squigglepy.distributions.rst new file mode 100644 index 0000000..bfbdb38 --- /dev/null +++ b/docs/source/reference/squigglepy.distributions.rst @@ -0,0 +1,7 @@ +squigglepy.distributions module +=============================== + +.. automodule:: squigglepy.distributions + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/source/reference/squigglepy.numbers.rst b/docs/source/reference/squigglepy.numbers.rst new file mode 100644 index 0000000..524cbcd --- /dev/null +++ b/docs/source/reference/squigglepy.numbers.rst @@ -0,0 +1,7 @@ +squigglepy.numbers module +========================= + +.. automodule:: squigglepy.numbers + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/source/reference/squigglepy.rng.rst b/docs/source/reference/squigglepy.rng.rst new file mode 100644 index 0000000..84ec740 --- /dev/null +++ b/docs/source/reference/squigglepy.rng.rst @@ -0,0 +1,7 @@ +squigglepy.rng module +===================== + +.. automodule:: squigglepy.rng + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/source/reference/squigglepy.rst b/docs/source/reference/squigglepy.rst new file mode 100644 index 0000000..b629fda --- /dev/null +++ b/docs/source/reference/squigglepy.rst @@ -0,0 +1,22 @@ +squigglepy package +================== + +.. automodule:: squigglepy + :members: + :undoc-members: + :show-inheritance: + +Submodules +---------- + +.. toctree:: + :maxdepth: 4 + + squigglepy.bayes + squigglepy.correlation + squigglepy.distributions + squigglepy.numbers + squigglepy.rng + squigglepy.samplers + squigglepy.utils + squigglepy.version diff --git a/docs/source/reference/squigglepy.samplers.rst b/docs/source/reference/squigglepy.samplers.rst new file mode 100644 index 0000000..ae3e754 --- /dev/null +++ b/docs/source/reference/squigglepy.samplers.rst @@ -0,0 +1,7 @@ +squigglepy.samplers module +========================== + +.. automodule:: squigglepy.samplers + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/source/reference/squigglepy.utils.rst b/docs/source/reference/squigglepy.utils.rst new file mode 100644 index 0000000..8af5f44 --- /dev/null +++ b/docs/source/reference/squigglepy.utils.rst @@ -0,0 +1,7 @@ +squigglepy.utils module +======================= + +.. automodule:: squigglepy.utils + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/source/reference/squigglepy.version.rst b/docs/source/reference/squigglepy.version.rst new file mode 100644 index 0000000..efe11f5 --- /dev/null +++ b/docs/source/reference/squigglepy.version.rst @@ -0,0 +1,7 @@ +squigglepy.version module +========================= + +.. automodule:: squigglepy.version + :members: + :undoc-members: + :show-inheritance: diff --git a/squigglepy/bayes.py b/squigglepy/bayes.py index 415f29a..e3fec17 100644 --- a/squigglepy/bayes.py +++ b/squigglepy/bayes.py @@ -1,3 +1,7 @@ +""" +This modules includes functions for Bayesian inference. +""" + import os import time import math diff --git a/squigglepy/distributions.py b/squigglepy/distributions.py index 413e749..7b01f7a 100644 --- a/squigglepy/distributions.py +++ b/squigglepy/distributions.py @@ -1,3 +1,7 @@ +""" +A collection of probability distributions and functions to operate on them. +""" + import operator import math import numpy as np From 14461120b93a8523d3c27a9087b17b248bb25974 Mon Sep 17 00:00:00 2001 From: Michael Dickens Date: Thu, 23 Nov 2023 12:48:08 -0800 Subject: [PATCH 3/7] docs: write better index page and link to all docs from index --- docs/build/doctrees/environment.pickle | Bin 1496050 -> 1536662 bytes docs/build/doctrees/index.doctree | Bin 10780 -> 8842 bytes docs/build/doctrees/installation.doctree | Bin 0 -> 3197 bytes .../reference/squigglepy.correlation.doctree | Bin 56364 -> 54192 bytes docs/build/doctrees/usage.doctree | Bin 0 -> 43099 bytes docs/build/html/_modules/index.html | 30 +- .../html/_modules/squigglepy/correlation.html | 43 +- docs/build/html/_sources/index.rst.txt | 26 +- docs/build/html/_sources/installation.rst.txt | 12 + .../html/_sources/usage.rst.txt} | 16 +- docs/build/html/genindex.html | 30 +- docs/build/html/index.html | 84 +- docs/build/html/installation.html | 454 +++++++++ docs/build/html/objects.inv | Bin 1334 -> 1336 bytes docs/build/html/py-modindex.html | 30 +- docs/build/html/reference/modules.html | 364 +++---- .../reference/squigglepy.correlation.html | 26 +- docs/build/html/search.html | 30 +- docs/build/html/searchindex.js | 2 +- docs/build/html/usage.html | 894 ++++++++++++++++++ docs/source/deleteme | 0 docs/source/index.rst | 26 +- docs/source/installation.rst | 12 + docs/source/{README.rst => usage.rst} | 67 +- squigglepy/correlation.py | 9 +- 25 files changed, 1705 insertions(+), 450 deletions(-) create mode 100644 docs/build/doctrees/installation.doctree create mode 100644 docs/build/doctrees/usage.doctree create mode 100644 docs/build/html/_sources/installation.rst.txt rename docs/{source/examples.rst => build/html/_sources/usage.rst.txt} (98%) create mode 100644 docs/build/html/installation.html create mode 100644 docs/build/html/usage.html delete mode 100644 docs/source/deleteme create mode 100644 docs/source/installation.rst rename docs/source/{README.rst => usage.rst} (88%) diff --git a/docs/build/doctrees/environment.pickle b/docs/build/doctrees/environment.pickle index 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@@ -208,6 +221,19 @@

@@ -340,7 +366,7 @@

Source code for squigglepy.correlation

 
 
 

-[docs]
+[docs]
 def correlate(
     variables: tuple[OperableDistribution, ...],
     correlation: Union[NDArray[np.float64], list[list[float]], np.float64, float],
@@ -396,9 +422,10 @@ 
Source code for squigglepy.correlation
     >>> solar_radiation, temperature = sq.gamma(300, 100), sq.to(22, 28)
     >>> solar_radiation, temperature = sq.correlate((solar_radiation, temperature), 0.7)
     >>> print(np.corrcoef(solar_radiation @ 1000, temperature @ 1000)[0, 1])
-        0.6975960649767123
+    0.6975960649767123
 
     Or you could pass a correlation matrix:
+
     >>> funding_gap, cost_per_delivery, effect_size = (
             sq.to(20_000, 80_000), sq.to(30, 80), sq.beta(2, 5)
         )
@@ -407,9 +434,9 @@ 
Source code for squigglepy.correlation
             [[1, 0.6, -0.5], [0.6, 1, -0.2], [-0.5, -0.2, 1]]
         )
     >>> print(np.corrcoef(funding_gap @ 1000, cost_per_delivery @ 1000, effect_size @ 1000))
-        array([[ 1.      ,  0.580520  , -0.480149],
-               [ 0.580962,  1.        , -0.187831],
-               [-0.480149, -0.187831  ,  1.        ]])
+    array([[ 1.      ,  0.580520  , -0.480149],
+           [ 0.580962,  1.        , -0.187831],
+           [-0.480149, -0.187831  ,  1.        ]])
 
     """
     if not isinstance(variables, tuple):
@@ -455,7 +482,7 @@ 
Source code for squigglepy.correlation
 
 
 

-[docs]
+[docs]
 @dataclass
 class CorrelationGroup:
     """
@@ -500,7 +527,7 @@ 
Source code for squigglepy.correlation
             dist.correlation_group = self
 
 

-[docs]
+[docs]
     def induce_correlation(self, data: NDArray[np.float64]) -> NDArray[np.float64]:
         """
         Induce a set of correlations on a column-wise dataset
@@ -623,7 +650,7 @@ 
Source code for squigglepy.correlation
             )
 
 

-[docs]
+[docs]
     def has_sufficient_sample_diversity(
         self,
         samples: NDArray[np.float64],
diff --git a/docs/build/html/_sources/index.rst.txt b/docs/build/html/_sources/index.rst.txt
index 1fdb7aa..89b8383 100644
--- a/docs/build/html/_sources/index.rst.txt
+++ b/docs/build/html/_sources/index.rst.txt
@@ -12,32 +12,12 @@ programming packages like Numpy, Pandas, and Matplotlib. The
 functionalities in Python.
 
 .. toctree::
-   :maxdepth: 3
+   :maxdepth: 2
    :caption: Contents
 
+   Installation 
+   Usage 
    API Reference 
-   Examples 
-
-Installation
-------------
-
-.. code:: shell
-
-   pip install squigglepy
-
-For plotting support, you can also use the ``plots`` extra:
-
-.. code:: shell
-
-   pip install squigglepy[plots]
-
-Run tests
----------
-
-Use ``black .`` for formatting.
-
-Run
-``ruff check . && pytest && pip3 install . && python3 tests/integration.py``
 
 Disclaimers
 -----------
diff --git a/docs/build/html/_sources/installation.rst.txt b/docs/build/html/_sources/installation.rst.txt
new file mode 100644
index 0000000..fb5e8d9
--- /dev/null
+++ b/docs/build/html/_sources/installation.rst.txt
@@ -0,0 +1,12 @@
+Installation
+============
+
+.. code:: shell
+
+   pip install squigglepy
+
+For plotting support, you can also use the ``plots`` extra:
+
+.. code:: shell
+
+   pip install squigglepy[plots]
diff --git a/docs/source/examples.rst b/docs/build/html/_sources/usage.rst.txt
similarity index 98%
rename from docs/source/examples.rst
rename to docs/build/html/_sources/usage.rst.txt
index c00053f..3e03a70 100644
--- a/docs/source/examples.rst
+++ b/docs/build/html/_sources/usage.rst.txt
@@ -1,7 +1,7 @@
 Examples
 ========
 
-Piano Tuners Example
+Piano tuners example
 ~~~~~~~~~~~~~~~~~~~~
 
 Here’s the Squigglepy implementation of `the example from Squiggle
@@ -135,7 +135,7 @@ Distributions
    # 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`.
    sq.zero_inflated(0.6, sq.norm(1, 2))
 
-Additional Features
+Additional features
 ~~~~~~~~~~~~~~~~~~~
 
 .. code:: python
@@ -167,7 +167,7 @@ Additional Features
    # You can even pass your own correlation matrix!
    a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]])
 
-Example: Rolling a Die
+Example: Rolling a die
 ^^^^^^^^^^^^^^^^^^^^^^
 
 An example of how to use distributions to build tools:
@@ -358,7 +358,7 @@ pretty limited. For more complex bayesian analysis, consider
 `bnlearn `__, or
 `pyMC `__.
 
-Example: A Demonstration of the Monty Hall Problem
+Example: A demonstration of the Monty Hall Problem
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
 .. code:: python
@@ -466,3 +466,11 @@ More examples
 
 You can see more examples of squigglepy in action
 `here `__.
+
+Run tests
+---------
+
+Use ``black .`` for formatting.
+
+Run
+``ruff check . && pytest && pip3 install . && python3 tests/integration.py``
diff --git a/docs/build/html/genindex.html b/docs/build/html/genindex.html
index 2671007..0709a93 100644
--- a/docs/build/html/genindex.html
+++ b/docs/build/html/genindex.html
@@ -132,15 +132,22 @@
   

-

-
Installation#

-
pip install squigglepy
-

-

-
For plotting support, you can also use the plots extra:

-
pip install squigglepy[plots]
-

-

-

-

-
Run tests#

-
Use black . for formatting.

-
Run
-ruff check . && pytest && pip3 install . && python3 tests/integration.py

-

 

 
Disclaimers#

 
This package is unofficial and supported by Peter Wildeford and Rethink
@@ -383,11 +371,11 @@ 
Acknowledgements
     
       

         
next

-        
squigglepy

+        
Installation

       

       
     
@@ -406,8 +394,6 @@ 
Acknowledgements
     
diff --git a/docs/build/html/installation.html b/docs/build/html/installation.html
new file mode 100644
index 0000000..58f24e1
--- /dev/null
+++ b/docs/build/html/installation.html
@@ -0,0 +1,454 @@
+
+
+
+
+
+
+  
+    
+    
+
+    Installation — Squigglepy  documentation
+  
+  
+  
+  
+  
+  
+  
+
+
+
+  
+  
+  
+
+
+
+    
+  
+  
+  
+
+  
+
+    
+    
+    
+    
+    
+    
+    
+    
+  
+  
+  
+  
+  
+  
+
+  
+  
+  
+  
+  

+
+  
+  
+
+  
+  
+  
+  
+  
+  
+  
+  

+    

+    

+

+  
+  
+  Ctrl+K
+

+  

+  
+    
+  
+  

+    

+      
+      

+        
+
+  
+  

+    
+    
+      

+        
+          

+        
+      

+    
+    
+    
+      

+        
+          

+

+        
+      

+    
+  

+  
+  
+  

+  

+  
+  
+
+
+      

+      
+      

+        
+        
+          

+            

+              
+              

+

+  
+    

+      
+        

+
+
+
+
+

+      
+    

+  
+  
+

+

+              
+              
+              
+                
+
+                

+                  
+  

+
Installation#

+
pip install squigglepy
+

+

+
For plotting support, you can also use the plots extra:

+
pip install squigglepy[plots]
+

+

+

+
+
+                

+              
+              
+              
+              
+              
+                
+              
+            

+            
+            
+              
+                

+
+  

+  

+    
+       Show Source
+    
+  

+

+
+

+              
+            
+          

+          

+            
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+        
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+    

+  

+  
+  
+  
+
+
+  

+

+  
+    

+      
+        

+  

+    
+      © Copyright 2023, Peter Wildeford.
+      

+    
+  

+

+      
+        

+  

+    Created using Sphinx 7.2.6.
+    

+  

+

+      
+    

+  
+  
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+    

+      
+        

+  Built with the PyData Sphinx Theme 0.14.3.
+

+      
+    

+  
+

+
+  

+  
+
\ No newline at end of file
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  • 
-                      
-                        API Reference
+                      
+                        Installation
                       
                     
    • 
                 
 
                     
  • 
-                      
-                        Examples
+                      
+                        Usage
+                      
+                    
    • 
+                
+
+                    
  • 
+                      
+                        API Reference
                       
                     
    • 
                 
@@ -225,15 +232,22 @@
   
    
diff --git a/docs/build/html/search.html b/docs/build/html/search.html
index 814b3e6..ccbf991 100644
--- a/docs/build/html/search.html
+++ b/docs/build/html/search.html
@@ -134,15 +134,22 @@
   
    
       
@@ -208,6 +228,26 @@
   
    
   
 
    
         
@@ -491,7 +531,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def is_dist(obj):
     """
     Test if a given object is a Squigglepy distribution.
@@ -520,7 +560,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def is_continuous_dist(obj):
     from .distributions import (
         ContinuousDistribution,
@@ -543,7 +583,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def is_sampleable(obj):
     """
     Test if a given object can be sampled from.
@@ -582,7 +622,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def normalize(lst):
     """
     Normalize a list to sum to 1.
@@ -608,7 +648,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def event_occurs(p):
     """
     Return True with probability ``p`` and False with probability ``1 - p``.
@@ -635,7 +675,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def event_happens(p):
     """
     Return True with probability ``p`` and False with probability ``1 - p``.
@@ -658,7 +698,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def event(p):
     """
     Return True with probability ``p`` and False with probability ``1 - p``.
@@ -685,7 +725,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def one_in(p, digits=0, verbose=True):
     """
     Convert a probability into "1 in X" notation.
@@ -715,7 +755,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def get_percentiles(
     data,
     percentiles=[1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99],
@@ -759,7 +799,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def get_log_percentiles(
     data,
     percentiles=[1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99],
@@ -813,7 +853,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def get_mean_and_ci(data, credibility=90, digits=None):
     """
     Return the mean and percentiles of the data.
@@ -849,7 +889,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def get_median_and_ci(data, credibility=90, digits=None):
     """
     Return the median and percentiles of the data.
@@ -885,7 +925,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def geomean(a, weights=None, relative_weights=None, drop_na=True):
     """
     Calculate the geometric mean.
@@ -918,7 +958,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def p_to_odds(p):
     """
     Calculate the decimal odds from a given probability.
@@ -951,7 +991,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def odds_to_p(odds):
     """
     Calculate the probability from given decimal odds.
@@ -984,7 +1024,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def geomean_odds(a, weights=None, relative_weights=None, drop_na=True):
     """
     Calculate the geometric mean of odds.
@@ -1017,7 +1057,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def laplace(s, n=None, time_passed=None, time_remaining=None, time_fixed=False):
     """
     Return probability of success on next trial given Laplace's law of succession.
@@ -1085,7 +1125,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def growth_rate_to_doubling_time(growth_rate):
     """
     Convert a positive growth rate to a doubling rate.
@@ -1124,7 +1164,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def doubling_time_to_growth_rate(doubling_time):
     """
     Convert a doubling time to a growth rate.
@@ -1164,7 +1204,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def roll_die(sides, n=1):
     """
     Roll a die.
@@ -1206,7 +1246,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def flip_coin(n=1):
     """
     Flip a coin.
@@ -1236,7 +1276,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def kelly(my_price, market_price, deference=0, bankroll=1, resolve_date=None, current=0):
     """
     Calculate the Kelly criterion.
@@ -1264,25 +1304,25 @@ 
    Source code for squigglepy.utils
         -------
     dict
         A dict of values specifying:
-        * ``my_price``
-        * ``market_price``
-        * ``deference``
-        * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
-          into account.
-        * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
-        * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
-          ``market_price``.
-        * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
-          you should bet.
-        * ``target`` : the target amount of money you should have invested
-        * ``current``
-        * ``delta`` : the amount of money you should invest given what you already
-          have invested
-        * ``max_gain`` : the amount of money you would gain if you win
-        * ``modeled_gain`` : the expected value you would win given ``adj_price``
-        * ``expected_roi`` : the expected return on investment
-        * ``expected_arr`` : the expected ARR given ``resolve_date``
-        * ``resolve_date``
+            * ``my_price``
+            * ``market_price``
+            * ``deference``
+            * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
+              into account.
+            * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
+            * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
+              ``market_price``.
+            * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
+              you should bet.
+            * ``target`` : the target amount of money you should have invested
+            * ``current``
+            * ``delta`` : the amount of money you should invest given what you already
+              have invested
+            * ``max_gain`` : the amount of money you would gain if you win
+            * ``modeled_gain`` : the expected value you would win given ``adj_price``
+            * ``expected_roi`` : the expected return on investment
+            * ``expected_arr`` : the expected ARR given ``resolve_date``
+            * ``resolve_date``
 
     Examples
     --------
@@ -1330,7 +1370,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def full_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0):
     """
     Alias for ``kelly`` where ``deference`` is 0.
@@ -1355,25 +1395,25 @@ 
    Source code for squigglepy.utils
         -------
     dict
         A dict of values specifying:
-        * ``my_price``
-        * ``market_price``
-        * ``deference``
-        * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
-          into account.
-        * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
-        * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
-          ``market_price``.
-        * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
-          you should bet.
-        * ``target`` : the target amount of money you should have invested
-        * ``current``
-        * ``delta`` : the amount of money you should invest given what you already
-          have invested
-        * ``max_gain`` : the amount of money you would gain if you win
-        * ``modeled_gain`` : the expected value you would win given ``adj_price``
-        * ``expected_roi`` : the expected return on investment
-        * ``expected_arr`` : the expected ARR given ``resolve_date``
-        * ``resolve_date``
+            * ``my_price``
+            * ``market_price``
+            * ``deference``
+            * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
+              into account.
+            * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
+            * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
+              ``market_price``.
+            * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
+              you should bet.
+            * ``target`` : the target amount of money you should have invested
+            * ``current``
+            * ``delta`` : the amount of money you should invest given what you already
+              have invested
+            * ``max_gain`` : the amount of money you would gain if you win
+            * ``modeled_gain`` : the expected value you would win given ``adj_price``
+            * ``expected_roi`` : the expected return on investment
+            * ``expected_arr`` : the expected ARR given ``resolve_date``
+            * ``resolve_date``
 
     Examples
     --------
@@ -1395,7 +1435,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def half_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0):
     """
     Alias for ``kelly`` where ``deference`` is 0.5.
@@ -1420,25 +1460,25 @@ 
    Source code for squigglepy.utils
         -------
     dict
         A dict of values specifying:
-        * ``my_price``
-        * ``market_price``
-        * ``deference``
-        * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
-          into account.
-        * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
-        * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
-          ``market_price``.
-        * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
-          you should bet.
-        * ``target`` : the target amount of money you should have invested
-        * ``current``
-        * ``delta`` : the amount of money you should invest given what you already
-          have invested
-        * ``max_gain`` : the amount of money you would gain if you win
-        * ``modeled_gain`` : the expected value you would win given ``adj_price``
-        * ``expected_roi`` : the expected return on investment
-        * ``expected_arr`` : the expected ARR given ``resolve_date``
-        * ``resolve_date``
+            * ``my_price``
+            * ``market_price``
+            * ``deference``
+            * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
+              into account.
+            * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
+            * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
+              ``market_price``.
+            * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
+              you should bet.
+            * ``target`` : the target amount of money you should have invested
+            * ``current``
+            * ``delta`` : the amount of money you should invest given what you already
+              have invested
+            * ``max_gain`` : the amount of money you would gain if you win
+            * ``modeled_gain`` : the expected value you would win given ``adj_price``
+            * ``expected_roi`` : the expected return on investment
+            * ``expected_arr`` : the expected ARR given ``resolve_date``
+            * ``resolve_date``
 
     Examples
     --------
@@ -1460,7 +1500,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def quarter_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0):
     """
     Alias for ``kelly`` where ``deference`` is 0.75.
@@ -1485,25 +1525,25 @@ 
    Source code for squigglepy.utils
         -------
     dict
         A dict of values specifying:
-        * ``my_price``
-        * ``market_price``
-        * ``deference``
-        * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
-          into account.
-        * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
-        * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
-          ``market_price``.
-        * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
-          you should bet.
-        * ``target`` : the target amount of money you should have invested
-        * ``current``
-        * ``delta`` : the amount of money you should invest given what you already
-          have invested
-        * ``max_gain`` : the amount of money you would gain if you win
-        * ``modeled_gain`` : the expected value you would win given ``adj_price``
-        * ``expected_roi`` : the expected return on investment
-        * ``expected_arr`` : the expected ARR given ``resolve_date``
-        * ``resolve_date``
+            * ``my_price``
+            * ``market_price``
+            * ``deference``
+            * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
+              into account.
+            * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
+            * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
+              ``market_price``.
+            * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
+              you should bet.
+            * ``target`` : the target amount of money you should have invested
+            * ``current``
+            * ``delta`` : the amount of money you should invest given what you already
+              have invested
+            * ``max_gain`` : the amount of money you would gain if you win
+            * ``modeled_gain`` : the expected value you would win given ``adj_price``
+            * ``expected_roi`` : the expected return on investment
+            * ``expected_arr`` : the expected ARR given ``resolve_date``
+            * ``resolve_date``
 
     Examples
     --------
@@ -1525,7 +1565,7 @@ 
    Source code for squigglepy.utils
     
 
 
    
-[docs]
+[docs]
 def extremize(p, e):
     """
     Extremize a prediction.
diff --git a/docs/build/html/_sources/README.rst.txt b/doc/build/html/_sources/README.rst.txt
similarity index 100%
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squigglepy.distributions)": [[6, "squigglepy.distributions.zero_inflated"]], "bernoulli_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.bernoulli_sample"]], "beta_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.beta_sample"]], "binomial_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.binomial_sample"]], "chi_square_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.chi_square_sample"]], "discrete_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.discrete_sample"]], "exponential_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.exponential_sample"]], "gamma_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.gamma_sample"]], "geometric_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.geometric_sample"]], "log_t_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.log_t_sample"]], "lognormal_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.lognormal_sample"]], "mixture_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.mixture_sample"]], "normal_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.normal_sample"]], "pareto_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.pareto_sample"]], "pert_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.pert_sample"]], "poisson_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.poisson_sample"]], "sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.sample"]], "sample_correlated_group() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.sample_correlated_group"]], "squigglepy.samplers": [[9, "module-squigglepy.samplers"]], "t_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.t_sample"]], "triangular_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.triangular_sample"]], "uniform_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.uniform_sample"]], "doubling_time_to_growth_rate() (in module squigglepy.utils)": [[10, "squigglepy.utils.doubling_time_to_growth_rate"]], "event() (in module squigglepy.utils)": [[10, "squigglepy.utils.event"]], "event_happens() (in module squigglepy.utils)": [[10, "squigglepy.utils.event_happens"]], "event_occurs() (in module squigglepy.utils)": [[10, "squigglepy.utils.event_occurs"]], "extremize() (in module squigglepy.utils)": [[10, "squigglepy.utils.extremize"]], "flip_coin() (in module squigglepy.utils)": [[10, "squigglepy.utils.flip_coin"]], "full_kelly() (in module squigglepy.utils)": [[10, "squigglepy.utils.full_kelly"]], "geomean() (in module squigglepy.utils)": [[10, "squigglepy.utils.geomean"]], "geomean_odds() (in module squigglepy.utils)": [[10, "squigglepy.utils.geomean_odds"]], "get_log_percentiles() (in module squigglepy.utils)": [[10, "squigglepy.utils.get_log_percentiles"]], "get_mean_and_ci() (in module squigglepy.utils)": [[10, "squigglepy.utils.get_mean_and_ci"]], "get_median_and_ci() (in module squigglepy.utils)": [[10, "squigglepy.utils.get_median_and_ci"]], "get_percentiles() (in module squigglepy.utils)": [[10, "squigglepy.utils.get_percentiles"]], "growth_rate_to_doubling_time() (in module squigglepy.utils)": [[10, "squigglepy.utils.growth_rate_to_doubling_time"]], "half_kelly() (in module squigglepy.utils)": [[10, "squigglepy.utils.half_kelly"]], "is_continuous_dist() (in module squigglepy.utils)": [[10, "squigglepy.utils.is_continuous_dist"]], "is_dist() (in module squigglepy.utils)": [[10, "squigglepy.utils.is_dist"]], "is_sampleable() (in module squigglepy.utils)": [[10, "squigglepy.utils.is_sampleable"]], "kelly() (in module squigglepy.utils)": [[10, "squigglepy.utils.kelly"]], "laplace() (in module squigglepy.utils)": [[10, "squigglepy.utils.laplace"]], "normalize() (in module squigglepy.utils)": [[10, "squigglepy.utils.normalize"]], "odds_to_p() (in module squigglepy.utils)": [[10, "squigglepy.utils.odds_to_p"]], "one_in() (in module squigglepy.utils)": [[10, "squigglepy.utils.one_in"]], "p_to_odds() (in module squigglepy.utils)": [[10, "squigglepy.utils.p_to_odds"]], "quarter_kelly() (in module squigglepy.utils)": [[10, "squigglepy.utils.quarter_kelly"]], "roll_die() (in module squigglepy.utils)": [[10, "squigglepy.utils.roll_die"]], "squigglepy.utils": [[10, "module-squigglepy.utils"]]}})
\ No newline at end of file
diff --git a/docs/build/html/usage.html b/doc/build/html/usage.html
similarity index 100%
rename from docs/build/html/usage.html
rename to doc/build/html/usage.html
diff --git a/docs/make.bat b/doc/make.bat
similarity index 100%
rename from docs/make.bat
rename to doc/make.bat
diff --git a/docs/source/conf.py b/doc/source/conf.py
similarity index 85%
rename from docs/source/conf.py
rename to doc/source/conf.py
index 1a3efc3..372fb64 100644
--- a/docs/source/conf.py
+++ b/doc/source/conf.py
@@ -19,14 +19,14 @@
 
 # -- Project information -----------------------------------------------------
 
-project = 'Squigglepy'
-copyright = '2023, Peter Wildeford'
-author = 'Peter Wildeford'
+project = "Squigglepy"
+copyright = "2023, Peter Wildeford"
+author = "Peter Wildeford"
 
 # The short X.Y version
-version = ''
+version = ""
 # The full version, including alpha/beta/rc tags
-release = ''
+release = ""
 
 
 # -- General configuration ---------------------------------------------------
@@ -39,29 +39,29 @@
 # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
 # ones.
 extensions = [
-    'sphinx.ext.autodoc',
-    'sphinx.ext.imgmath',
-    'sphinx.ext.viewcode',
+    "sphinx.ext.autodoc",
+    "sphinx.ext.imgmath",
+    "sphinx.ext.viewcode",
 ]
 
 # Add any paths that contain templates here, relative to this directory.
-templates_path = ['_templates']
+templates_path = ["_templates"]
 
 # The suffix(es) of source filenames.
 # You can specify multiple suffix as a list of string:
 #
 # source_suffix = ['.rst', '.md']
-source_suffix = '.rst'
+source_suffix = ".rst"
 
 # The master toctree document.
-master_doc = 'index'
+master_doc = "index"
 
 # The language for content autogenerated by Sphinx. Refer to documentation
 # for a list of supported languages.
 #
 # This is also used if you do content translation via gettext catalogs.
 # Usually you set "language" from the command line for these cases.
-language = 'en'
+language = "en"
 
 # List of patterns, relative to source directory, that match files and
 # directories to ignore when looking for source files.
@@ -88,7 +88,7 @@
 # Add any paths that contain custom static files (such as style sheets) here,
 # relative to this directory. They are copied after the builtin static files,
 # so a file named "default.css" will overwrite the builtin "default.css".
-html_static_path = ['_static']
+html_static_path = ["_static"]
 
 # Custom sidebar templates, must be a dictionary that maps document names
 # to template names.
@@ -104,7 +104,7 @@
 # -- Options for HTMLHelp output ---------------------------------------------
 
 # Output file base name for HTML help builder.
-htmlhelp_basename = 'Squigglepydoc'
+htmlhelp_basename = "Squigglepydoc"
 
 
 # -- Options for LaTeX output ------------------------------------------------
@@ -113,15 +113,12 @@
     # The paper size ('letterpaper' or 'a4paper').
     #
     # 'papersize': 'letterpaper',
-
     # The font size ('10pt', '11pt' or '12pt').
     #
     # 'pointsize': '10pt',
-
     # Additional stuff for the LaTeX preamble.
     #
     # 'preamble': '',
-
     # Latex figure (float) alignment
     #
     # 'figure_align': 'htbp',
@@ -131,8 +128,7 @@
 # (source start file, target name, title,
 #  author, documentclass [howto, manual, or own class]).
 latex_documents = [
-    (master_doc, 'Squigglepy.tex', 'Squigglepy Documentation',
-     'Peter Wildeford', 'manual'),
+    (master_doc, "Squigglepy.tex", "Squigglepy Documentation", "Peter Wildeford", "manual"),
 ]
 
 
@@ -140,10 +136,7 @@
 
 # One entry per manual page. List of tuples
 # (source start file, name, description, authors, manual section).
-man_pages = [
-    (master_doc, 'squigglepy', 'Squigglepy Documentation',
-     [author], 1)
-]
+man_pages = [(master_doc, "squigglepy", "Squigglepy Documentation", [author], 1)]
 
 
 # -- Options for Texinfo output ----------------------------------------------
@@ -152,9 +145,15 @@
 # (source start file, target name, title, author,
 #  dir menu entry, description, category)
 texinfo_documents = [
-    (master_doc, 'Squigglepy', 'Squigglepy Documentation',
-     author, 'Squigglepy', 'One line description of project.',
-     'Miscellaneous'),
+    (
+        master_doc,
+        "Squigglepy",
+        "Squigglepy Documentation",
+        author,
+        "Squigglepy",
+        "One line description of project.",
+        "Miscellaneous",
+    ),
 ]
 
 
@@ -173,7 +172,7 @@
 # epub_uid = ''
 
 # A list of files that should not be packed into the epub file.
-epub_exclude_files = ['search.html']
+epub_exclude_files = ["search.html"]
 
 
 # -- Extension configuration -------------------------------------------------
diff --git a/docs/source/index.rst b/doc/source/index.rst
similarity index 100%
rename from docs/source/index.rst
rename to doc/source/index.rst
diff --git a/docs/source/installation.rst b/doc/source/installation.rst
similarity index 100%
rename from docs/source/installation.rst
rename to doc/source/installation.rst
diff --git a/docs/source/reference/modules.rst b/doc/source/reference/modules.rst
similarity index 100%
rename from docs/source/reference/modules.rst
rename to doc/source/reference/modules.rst
diff --git a/docs/source/reference/squigglepy.bayes.rst b/doc/source/reference/squigglepy.bayes.rst
similarity index 100%
rename from docs/source/reference/squigglepy.bayes.rst
rename to doc/source/reference/squigglepy.bayes.rst
diff --git a/docs/source/reference/squigglepy.correlation.rst b/doc/source/reference/squigglepy.correlation.rst
similarity index 100%
rename from docs/source/reference/squigglepy.correlation.rst
rename to doc/source/reference/squigglepy.correlation.rst
diff --git a/docs/source/reference/squigglepy.distributions.rst b/doc/source/reference/squigglepy.distributions.rst
similarity index 100%
rename from docs/source/reference/squigglepy.distributions.rst
rename to doc/source/reference/squigglepy.distributions.rst
diff --git a/docs/source/reference/squigglepy.numbers.rst b/doc/source/reference/squigglepy.numbers.rst
similarity index 100%
rename from docs/source/reference/squigglepy.numbers.rst
rename to doc/source/reference/squigglepy.numbers.rst
diff --git a/docs/source/reference/squigglepy.rng.rst b/doc/source/reference/squigglepy.rng.rst
similarity index 100%
rename from docs/source/reference/squigglepy.rng.rst
rename to doc/source/reference/squigglepy.rng.rst
diff --git a/docs/source/reference/squigglepy.rst b/doc/source/reference/squigglepy.rst
similarity index 100%
rename from docs/source/reference/squigglepy.rst
rename to doc/source/reference/squigglepy.rst
diff --git a/docs/source/reference/squigglepy.samplers.rst b/doc/source/reference/squigglepy.samplers.rst
similarity index 100%
rename from docs/source/reference/squigglepy.samplers.rst
rename to doc/source/reference/squigglepy.samplers.rst
diff --git a/docs/source/reference/squigglepy.utils.rst b/doc/source/reference/squigglepy.utils.rst
similarity index 100%
rename from docs/source/reference/squigglepy.utils.rst
rename to doc/source/reference/squigglepy.utils.rst
diff --git a/docs/source/reference/squigglepy.version.rst b/doc/source/reference/squigglepy.version.rst
similarity index 100%
rename from docs/source/reference/squigglepy.version.rst
rename to doc/source/reference/squigglepy.version.rst
diff --git a/docs/source/usage.rst b/doc/source/usage.rst
similarity index 100%
rename from docs/source/usage.rst
rename to doc/source/usage.rst
diff --git a/docs/build/doctrees/environment.pickle b/docs/build/doctrees/environment.pickle
deleted file mode 100644
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h+TJq*+qXp$xhVJO809`IjZtnc
Date: Thu, 23 Nov 2023 13:36:18 -0800
Subject: [PATCH 5/7] docs: update Poetry dependencies for Sphinx requirements

---
 poetry.lock | 269 +++++++++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 268 insertions(+), 1 deletion(-)

diff --git a/poetry.lock b/poetry.lock
index 86c4e93..42f9236 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1,5 +1,30 @@
 # This file is automatically @generated by Poetry 1.5.1 and should not be changed by hand.
 
+[[package]]
+name = "accessible-pygments"
+version = "0.0.4"
+description = "A collection of accessible pygments styles"
+optional = false
+python-versions = "*"
+files = [
+    {file = "accessible-pygments-0.0.4.tar.gz", hash = "sha256:e7b57a9b15958e9601c7e9eb07a440c813283545a20973f2574a5f453d0e953e"},
+    {file = "accessible_pygments-0.0.4-py2.py3-none-any.whl", hash = "sha256:416c6d8c1ea1c5ad8701903a20fcedf953c6e720d64f33dc47bfb2d3f2fa4e8d"},
+]
+
+[package.dependencies]
+pygments = ">=1.5"
+
+[[package]]
+name = "alabaster"
+version = "0.7.13"
+description = "A configurable sidebar-enabled Sphinx theme"
+optional = false
+python-versions = ">=3.6"
+files = [
+    {file = "alabaster-0.7.13-py3-none-any.whl", hash = "sha256:1ee19aca801bbabb5ba3f5f258e4422dfa86f82f3e9cefb0859b283cdd7f62a3"},
+    {file = "alabaster-0.7.13.tar.gz", hash = "sha256:a27a4a084d5e690e16e01e03ad2b2e552c61a65469419b907243193de1a84ae2"},
+]
+
 [[package]]
 name = "ansi2html"
 version = "1.8.0"
@@ -33,6 +58,38 @@ docs = ["furo", "myst-parser", "sphinx", "sphinx-notfound-page", "sphinxcontrib-
 tests = ["attrs[tests-no-zope]", "zope-interface"]
 tests-no-zope = ["cloudpickle", "hypothesis", "mypy (>=1.1.1)", "pympler", "pytest (>=4.3.0)", "pytest-mypy-plugins", "pytest-xdist[psutil]"]
 
+[[package]]
+name = "babel"
+version = "2.13.1"
+description = "Internationalization utilities"
+optional = false
+python-versions = ">=3.7"
+files = [
+    {file = "Babel-2.13.1-py3-none-any.whl", hash = "sha256:7077a4984b02b6727ac10f1f7294484f737443d7e2e66c5e4380e41a3ae0b4ed"},
+    {file = "Babel-2.13.1.tar.gz", hash = "sha256:33e0952d7dd6374af8dbf6768cc4ddf3ccfefc244f9986d4074704f2fbd18900"},
+]
+
+[package.extras]
+dev = ["freezegun (>=1.0,<2.0)", "pytest (>=6.0)", "pytest-cov"]
+
+[[package]]
+name = "beautifulsoup4"
+version = "4.12.2"
+description = "Screen-scraping library"
+optional = false
+python-versions = ">=3.6.0"
+files = [
+    {file = "beautifulsoup4-4.12.2-py3-none-any.whl", hash = "sha256:bd2520ca0d9d7d12694a53d44ac482d181b4ec1888909b035a3dbf40d0f57d4a"},
+    {file = "beautifulsoup4-4.12.2.tar.gz", hash = "sha256:492bbc69dca35d12daac71c4db1bfff0c876c00ef4a2ffacce226d4638eb72da"},
+]
+
+[package.dependencies]
+soupsieve = ">1.2"
+
+[package.extras]
+html5lib = ["html5lib"]
+lxml = ["lxml"]
+
 [[package]]
 name = "black"
 version = "23.3.0"
@@ -438,6 +495,17 @@ files = [
 [package.extras]
 graph = ["objgraph (>=1.7.2)"]
 
+[[package]]
+name = "docutils"
+version = "0.20.1"
+description = "Docutils -- Python Documentation Utilities"
+optional = false
+python-versions = ">=3.7"
+files = [
+    {file = "docutils-0.20.1-py3-none-any.whl", hash = "sha256:96f387a2c5562db4476f09f13bbab2192e764cac08ebbf3a34a95d9b1e4a59d6"},
+    {file = "docutils-0.20.1.tar.gz", hash = "sha256:f08a4e276c3a1583a86dce3e34aba3fe04d02bba2dd51ed16106244e8a923e3b"},
+]
+
 [[package]]
 name = "exceptiongroup"
 version = "1.1.1"
@@ -602,6 +670,17 @@ files = [
     {file = "idna-3.4.tar.gz", hash = "sha256:814f528e8dead7d329833b91c5faa87d60bf71824cd12a7530b5526063d02cb4"},
 ]
 
+[[package]]
+name = "imagesize"
+version = "1.4.1"
+description = "Getting image size from png/jpeg/jpeg2000/gif file"
+optional = false
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
+files = [
+    {file = "imagesize-1.4.1-py2.py3-none-any.whl", hash = "sha256:0d8d18d08f840c19d0ee7ca1fd82490fdc3729b7ac93f49870406ddde8ef8d8b"},
+    {file = "imagesize-1.4.1.tar.gz", hash = "sha256:69150444affb9cb0d5cc5a92b3676f0b2fb7cd9ae39e947a5e11a36b4497cd4a"},
+]
+
 [[package]]
 name = "importlib-metadata"
 version = "6.7.0"
@@ -1369,6 +1448,33 @@ files = [
 [package.extras]
 test = ["enum34", "ipaddress", "mock", "pywin32", "wmi"]
 
+[[package]]
+name = "pydata-sphinx-theme"
+version = "0.14.3"
+description = "Bootstrap-based Sphinx theme from the PyData community"
+optional = false
+python-versions = ">=3.8"
+files = [
+    {file = "pydata_sphinx_theme-0.14.3-py3-none-any.whl", hash = "sha256:b7e40cd75a20449adfe2d7525be379b9fe92f6d31e5233e449fa34ddcd4398d9"},
+    {file = "pydata_sphinx_theme-0.14.3.tar.gz", hash = "sha256:bd474f347895f3fc5b6ce87390af64330ee54f11ebf9660d5bc3f87d532d4e5c"},
+]
+
+[package.dependencies]
+accessible-pygments = "*"
+Babel = "*"
+beautifulsoup4 = "*"
+docutils = "!=0.17.0"
+packaging = "*"
+pygments = ">=2.7"
+sphinx = ">=5.0"
+typing-extensions = "*"
+
+[package.extras]
+a11y = ["pytest-playwright"]
+dev = ["nox", "pre-commit", "pydata-sphinx-theme[doc,test]", "pyyaml"]
+doc = ["ablog (>=0.11.0rc2)", "colorama", "ipykernel", "ipyleaflet", "jupyter_sphinx", "jupyterlite-sphinx", "linkify-it-py", "matplotlib", "myst-parser", "nbsphinx", "numpy", "numpydoc", "pandas", "plotly", "rich", "sphinx-autoapi (>=3.0.0)", "sphinx-copybutton", "sphinx-design", "sphinx-favicon (>=1.0.1)", "sphinx-sitemap", "sphinx-togglebutton", "sphinxcontrib-youtube (<1.4)", "sphinxext-rediraffe", "xarray"]
+test = ["pytest", "pytest-cov", "pytest-regressions"]
+
 [[package]]
 name = "pygments"
 version = "2.15.1"
@@ -1659,6 +1765,17 @@ files = [
     {file = "six-1.16.0.tar.gz", hash = "sha256:1e61c37477a1626458e36f7b1d82aa5c9b094fa4802892072e49de9c60c4c926"},
 ]
 
+[[package]]
+name = "snowballstemmer"
+version = "2.2.0"
+description = "This package provides 29 stemmers for 28 languages generated from Snowball algorithms."
+optional = false
+python-versions = "*"
+files = [
+    {file = "snowballstemmer-2.2.0-py2.py3-none-any.whl", hash = "sha256:c8e1716e83cc398ae16824e5572ae04e0d9fc2c6b985fb0f900f5f0c96ecba1a"},
+    {file = "snowballstemmer-2.2.0.tar.gz", hash = "sha256:09b16deb8547d3412ad7b590689584cd0fe25ec8db3be37788be3810cbf19cb1"},
+]
+
 [[package]]
 name = "sortedcontainers"
 version = "2.4.0"
@@ -1670,6 +1787,156 @@ files = [
     {file = "sortedcontainers-2.4.0.tar.gz", hash = "sha256:25caa5a06cc30b6b83d11423433f65d1f9d76c4c6a0c90e3379eaa43b9bfdb88"},
 ]
 
+[[package]]
+name = "soupsieve"
+version = "2.5"
+description = "A modern CSS selector implementation for Beautiful Soup."
+optional = false
+python-versions = ">=3.8"
+files = [
+    {file = "soupsieve-2.5-py3-none-any.whl", hash = "sha256:eaa337ff55a1579b6549dc679565eac1e3d000563bcb1c8ab0d0fefbc0c2cdc7"},
+    {file = "soupsieve-2.5.tar.gz", hash = "sha256:5663d5a7b3bfaeee0bc4372e7fc48f9cff4940b3eec54a6451cc5299f1097690"},
+]
+
+[[package]]
+name = "sphinx"
+version = "7.2.6"
+description = "Python documentation generator"
+optional = false
+python-versions = ">=3.9"
+files = [
+    {file = "sphinx-7.2.6-py3-none-any.whl", hash = "sha256:1e09160a40b956dc623c910118fa636da93bd3ca0b9876a7b3df90f07d691560"},
+    {file = "sphinx-7.2.6.tar.gz", hash = "sha256:9a5160e1ea90688d5963ba09a2dcd8bdd526620edbb65c328728f1b2228d5ab5"},
+]
+
+[package.dependencies]
+alabaster = ">=0.7,<0.8"
+babel = ">=2.9"
+colorama = {version = ">=0.4.5", markers = "sys_platform == \"win32\""}
+docutils = ">=0.18.1,<0.21"
+imagesize = ">=1.3"
+importlib-metadata = {version = ">=4.8", markers = "python_version < \"3.10\""}
+Jinja2 = ">=3.0"
+packaging = ">=21.0"
+Pygments = ">=2.14"
+requests = ">=2.25.0"
+snowballstemmer = ">=2.0"
+sphinxcontrib-applehelp = "*"
+sphinxcontrib-devhelp = "*"
+sphinxcontrib-htmlhelp = ">=2.0.0"
+sphinxcontrib-jsmath = "*"
+sphinxcontrib-qthelp = "*"
+sphinxcontrib-serializinghtml = ">=1.1.9"
+
+[package.extras]
+docs = ["sphinxcontrib-websupport"]
+lint = ["docutils-stubs", "flake8 (>=3.5.0)", "flake8-simplify", "isort", "mypy (>=0.990)", "ruff", "sphinx-lint", "types-requests"]
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+
+[[package]]
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+version = "1.0.7"
+description = "sphinxcontrib-applehelp is a Sphinx extension which outputs Apple help books"
+optional = false
+python-versions = ">=3.9"
+files = [
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+
+[[package]]
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+[package.extras]
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+test = ["html5lib", "pytest"]
+
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+description = "A sphinx extension which renders display math in HTML via JavaScript"
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+[package.extras]
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+
+[[package]]
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+version = "1.0.6"
+description = "sphinxcontrib-qthelp is a sphinx extension which outputs QtHelp documents"
+optional = false
+python-versions = ">=3.9"
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+    {file = "sphinxcontrib_qthelp-1.0.6.tar.gz", hash = "sha256:62b9d1a186ab7f5ee3356d906f648cacb7a6bdb94d201ee7adf26db55092982d"},
+]
+
+[package.dependencies]
+Sphinx = ">=5"
+
+[package.extras]
+lint = ["docutils-stubs", "flake8", "mypy"]
+test = ["pytest"]
+
+[[package]]
+name = "sphinxcontrib-serializinghtml"
+version = "1.1.9"
+description = "sphinxcontrib-serializinghtml is a sphinx extension which outputs \"serialized\" HTML files (json and pickle)"
+optional = false
+python-versions = ">=3.9"
+files = [
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+    {file = "sphinxcontrib_serializinghtml-1.1.9.tar.gz", hash = "sha256:0c64ff898339e1fac29abd2bf5f11078f3ec413cfe9c046d3120d7ca65530b54"},
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+Sphinx = ">=5"
+
+[package.extras]
+lint = ["docutils-stubs", "flake8", "mypy"]
+test = ["pytest"]
+
 [[package]]
 name = "tenacity"
 version = "8.2.2"
@@ -1809,4 +2076,4 @@ plots = ["matplotlib"]
 [metadata]
 lock-version = "2.0"
 python-versions = ">=3.9,<3.12"
-content-hash = "5625f6f3eec6de2121f93d9cb0591c23402a9c232f824ce8353c50b7441e3a9d"
+content-hash = "f9f1beabf7d339e2173f854e8559f6bd9f1fbb28d711802c3d0d831a7b1fa2b5"

From ffd5250ae5968900eb86226e76d0d752ed0522b4 Mon Sep 17 00:00:00 2001
From: Michael Dickens 
Date: Thu, 23 Nov 2023 13:36:41 -0800
Subject: [PATCH 6/7] docs: support numpydoc docstring style

---
 doc/build/doctrees/environment.pickle         |  Bin 1424287 -> 1521208 bytes
 doc/build/doctrees/index.doctree              |  Bin 8841 -> 9496 bytes
 .../reference/squigglepy.bayes.doctree        |  Bin 53324 -> 57815 bytes
 .../reference/squigglepy.correlation.doctree  |  Bin 54191 -> 61358 bytes
 .../squigglepy.distributions.doctree          |  Bin 332702 -> 390640 bytes
 .../doctrees/reference/squigglepy.doctree     |  Bin 3632 -> 3886 bytes
 .../reference/squigglepy.numbers.doctree      |  Bin 2849 -> 3110 bytes
 .../doctrees/reference/squigglepy.rng.doctree |  Bin 7309 -> 7951 bytes
 .../reference/squigglepy.samplers.doctree     |  Bin 171574 -> 176788 bytes
 .../reference/squigglepy.utils.doctree        |  Bin 214438 -> 219063 bytes
 .../reference/squigglepy.version.doctree      |  Bin 2849 -> 3110 bytes
 doc/build/html/.buildinfo                     |    2 +-
 .../_modules/squigglepy/distributions.html    |  158 ++-
 doc/build/html/_sources/index.rst.txt         |    2 +
 doc/build/html/index.html                     |    4 +
 .../html/reference/squigglepy.bayes.html      |  130 +-
 .../reference/squigglepy.correlation.html     |   61 +-
 .../reference/squigglepy.distributions.html   | 1101 ++++++++++-------
 doc/build/html/reference/squigglepy.rng.html  |   22 +-
 .../html/reference/squigglepy.samplers.html   |  532 ++++----
 .../html/reference/squigglepy.utils.html      |  628 +++++-----
 doc/build/html/searchindex.js                 |    2 +-
 doc/source/conf.py                            |    3 +
 doc/source/index.rst                          |    2 +
 pyproject.toml                                |    1 +
 25 files changed, 1398 insertions(+), 1250 deletions(-)

diff --git a/doc/build/doctrees/environment.pickle b/doc/build/doctrees/environment.pickle
index 456a719c76a64ecbca44be6ea25533047f2d6c83..8945c72dd012e574ee5b7bf717599676ac920a65 100644
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diff --git a/doc/build/doctrees/index.doctree b/doc/build/doctrees/index.doctree
index 7f9e77d024ebca52e3e146fb65ed8763eb7ab265..e87e59add7cad7b0b116433923d8f637f7d364d8 100644
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diff --git a/doc/build/doctrees/reference/squigglepy.bayes.doctree b/doc/build/doctrees/reference/squigglepy.bayes.doctree
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diff --git a/doc/build/doctrees/reference/squigglepy.doctree b/doc/build/doctrees/reference/squigglepy.doctree
index 52234e6a5bd1dab29bce26161608c9bfe285924f..5864f8f532f0557054590f8cc31166c3343886a5 100644
GIT binary patch
delta 311
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delta 144
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diff --git a/doc/build/doctrees/reference/squigglepy.numbers.doctree b/doc/build/doctrees/reference/squigglepy.numbers.doctree
index c681073644806d45613a546a1fb397e825029d25..1748e4356048c693dc07c32f32266c1858ffa6f2 100644
GIT binary patch
delta 253
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delta 71
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diff --git a/doc/build/doctrees/reference/squigglepy.rng.doctree b/doc/build/doctrees/reference/squigglepy.rng.doctree
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delta 71
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diff --git a/doc/build/html/.buildinfo b/doc/build/html/.buildinfo
index 89a4dd5..67b86aa 100644
--- a/doc/build/html/.buildinfo
+++ b/doc/build/html/.buildinfo
@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: 9f8d51c5fcb3931d93e7669f4628efd8
+config: de91ded5cec9d4685caf230095b3197b
 tags: 645f666f9bcd5a90fca523b33c5a78b7
diff --git a/doc/build/html/_modules/squigglepy/distributions.html b/doc/build/html/_modules/squigglepy/distributions.html
index 2ac9dc3..8353a85 100644
--- a/doc/build/html/_modules/squigglepy/distributions.html
+++ b/doc/build/html/_modules/squigglepy/distributions.html
@@ -131,6 +131,26 @@
   
    
       
 
    • 
       
@@ -208,6 +228,26 @@
   
    
   
 
    
         
@@ -306,7 +346,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class BaseDistribution(ABC):
     def __init__(self):
         self.x = None
@@ -353,13 +393,13 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class OperableDistribution(BaseDistribution):
     def __init__(self):
         super().__init__()
 
 
    
-[docs]
+[docs]
     def plot(self, num_samples=None, bins=None):
         """
         Plot a histogram of the samples.
@@ -477,21 +517,21 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class DiscreteDistribution(OperableDistribution, ABC):
     ...
    
 
 
 
 
    
-[docs]
+[docs]
 class ContinuousDistribution(OperableDistribution, ABC):
     ...
    
 
 
 
 
    
-[docs]
+[docs]
 class CompositeDistribution(OperableDistribution):
     def __init__(self):
         super().__init__()
@@ -514,7 +554,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class ComplexDistribution(CompositeDistribution):
     def __init__(self, left, right=None, fn=operator.add, fn_str="+", infix=True):
         super().__init__()
@@ -565,7 +605,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def dist_fn(dist1, dist2=None, fn=None, name=None):
     """
     Initialize a distribution that has a custom function applied to the result.
@@ -636,7 +676,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def dist_max(dist1, dist2=None):
     """
     Initialize the calculation of the maximum value of two distributions.
@@ -669,7 +709,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def dist_min(dist1, dist2=None):
     """
     Initialize the calculation of the minimum value of two distributions.
@@ -701,7 +741,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def dist_round(dist1, digits=0):
     """
     Initialize the rounding of the output of the distribution.
@@ -733,7 +773,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def dist_ceil(dist1):
     """
     Initialize the ceiling rounding of the output of the distribution.
@@ -760,7 +800,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def dist_floor(dist1):
     """
     Initialize the floor rounding of the output of the distribution.
@@ -787,7 +827,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def dist_log(dist1, base=math.e):
     """
     Initialize the log of the output of the distribution.
@@ -814,7 +854,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def dist_exp(dist1):
     """
     Initialize the exp of the output of the distribution.
@@ -849,7 +889,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def lclip(dist1, val=None):
     """
     Initialize the clipping/bounding of the output of the distribution by the lower value.
@@ -892,7 +932,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def rclip(dist1, val=None):
     """
     Initialize the clipping/bounding of the output of the distribution by the upper value.
@@ -927,7 +967,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def clip(dist1, left, right=None):
     """
     Initialize the clipping/bounding of the output of the distribution.
@@ -966,7 +1006,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class ConstantDistribution(DiscreteDistribution):
     def __init__(self, x):
         super().__init__()
@@ -978,7 +1018,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def const(x):
     """
     Initialize a constant distribution.
@@ -1004,7 +1044,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class UniformDistribution(ContinuousDistribution):
     def __init__(self, x, y):
         super().__init__()
@@ -1018,7 +1058,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def uniform(x, y):
     """
     Initialize a uniform random distribution.
@@ -1044,7 +1084,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class NormalDistribution(ContinuousDistribution):
     def __init__(self, x=None, y=None, mean=None, sd=None, credibility=90, lclip=None, rclip=None):
         super().__init__()
@@ -1084,7 +1124,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def norm(
     x=None, y=None, credibility=90, mean=None, sd=None, lclip=None, rclip=None
 ) -> NormalDistribution:
@@ -1130,7 +1170,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class LognormalDistribution(ContinuousDistribution):
     def __init__(
         self,
@@ -1216,7 +1256,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def lognorm(
     x=None,
     y=None,
@@ -1286,7 +1326,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def to(
     x, y, credibility=90, lclip=None, rclip=None
 ) -> Union[LognormalDistribution, NormalDistribution]:
@@ -1331,7 +1371,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class BinomialDistribution(DiscreteDistribution):
     def __init__(self, n, p):
         super().__init__()
@@ -1346,7 +1386,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def binomial(n, p):
     """
     Initialize a binomial distribution.
@@ -1372,7 +1412,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class BetaDistribution(ContinuousDistribution):
     def __init__(self, a, b):
         super().__init__()
@@ -1385,7 +1425,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def beta(a, b):
     """
     Initialize a beta distribution.
@@ -1413,7 +1453,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class BernoulliDistribution(DiscreteDistribution):
     def __init__(self, p):
         super().__init__()
@@ -1429,7 +1469,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def bernoulli(p):
     """
     Initialize a Bernoulli distribution.
@@ -1453,7 +1493,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class CategoricalDistribution(DiscreteDistribution):
     def __init__(self, items):
         super().__init__()
@@ -1468,7 +1508,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def discrete(items):
     """
     Initialize a discrete distribution (aka categorical distribution).
@@ -1499,7 +1539,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class TDistribution(ContinuousDistribution):
     def __init__(self, x=None, y=None, t=20, credibility=90, lclip=None, rclip=None):
         super().__init__()
@@ -1536,7 +1576,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def tdist(x=None, y=None, t=20, credibility=90, lclip=None, rclip=None):
     """
     Initialize a t-distribution.
@@ -1579,7 +1619,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class LogTDistribution(ContinuousDistribution):
     def __init__(self, x=None, y=None, t=1, credibility=90, lclip=None, rclip=None):
         super().__init__()
@@ -1618,7 +1658,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def log_tdist(x=None, y=None, t=1, credibility=90, lclip=None, rclip=None):
     """
     Initialize a log t-distribution, which is a t-distribution in log-space.
@@ -1662,7 +1702,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class TriangularDistribution(ContinuousDistribution):
     def __init__(self, left, mode, right):
         super().__init__()
@@ -1682,7 +1722,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def triangular(left, mode, right, lclip=None, rclip=None):
     """
     Initialize a triangular distribution.
@@ -1710,7 +1750,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class PERTDistribution(ContinuousDistribution):
     def __init__(self, left, mode, right, lam=4, lclip=None, rclip=None):
         super().__init__()
@@ -1744,7 +1784,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def pert(left, mode, right, lam=4, lclip=None, rclip=None):
     """
     Initialize a PERT distribution.
@@ -1778,7 +1818,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class PoissonDistribution(DiscreteDistribution):
     def __init__(self, lam, lclip=None, rclip=None):
         super().__init__()
@@ -1798,7 +1838,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def poisson(lam, lclip=None, rclip=None):
     """
     Initialize a poisson distribution.
@@ -1826,7 +1866,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class ChiSquareDistribution(ContinuousDistribution):
     def __init__(self, df):
         super().__init__()
@@ -1840,7 +1880,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def chisquare(df):
     """
     Initialize a chi-square distribution.
@@ -1864,7 +1904,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class ExponentialDistribution(ContinuousDistribution):
     def __init__(self, scale, lclip=None, rclip=None):
         super().__init__()
@@ -1887,7 +1927,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def exponential(scale, lclip=None, rclip=None):
     """
     Initialize an exponential distribution.
@@ -1915,7 +1955,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class GammaDistribution(ContinuousDistribution):
     def __init__(self, shape, scale=1, lclip=None, rclip=None):
         super().__init__()
@@ -1936,7 +1976,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def gamma(shape, scale=1, lclip=None, rclip=None):
     """
     Initialize a gamma distribution.
@@ -1966,7 +2006,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class ParetoDistribution(ContinuousDistribution):
     def __init__(self, shape):
         super().__init__()
@@ -1978,7 +2018,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def pareto(shape):
     """
     Initialize a pareto distribution.
@@ -2002,7 +2042,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class MixtureDistribution(CompositeDistribution):
     def __init__(self, dists, weights=None, relative_weights=None, lclip=None, rclip=None):
         super().__init__()
@@ -2022,7 +2062,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def mixture(dists, weights=None, relative_weights=None, lclip=None, rclip=None):
     """
     Initialize a mixture distribution, which is a combination of different distributions.
@@ -2072,7 +2112,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def zero_inflated(p_zero, dist):
     """
     Initialize an arbitrary zero-inflated distribution.
@@ -2102,7 +2142,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def inf0(p_zero, dist):
     """
     Initialize an arbitrary zero-inflated distribution.
@@ -2132,7 +2172,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 class GeometricDistribution(OperableDistribution):
     def __init__(self, p):
         super().__init__()
@@ -2146,7 +2186,7 @@ 
    Source code for squigglepy.distributions
     
 
 
    
-[docs]
+[docs]
 def geometric(p):
     """
     Initialize a geometric distribution.
diff --git a/doc/build/html/_sources/index.rst.txt b/doc/build/html/_sources/index.rst.txt
index 89b8383..3461183 100644
--- a/doc/build/html/_sources/index.rst.txt
+++ b/doc/build/html/_sources/index.rst.txt
@@ -47,3 +47,5 @@ Acknowledgements
    distributions.
 -  Thanks to Dawn Drescher for coming up with the idea to use ``~`` as a
    shorthand for ``sample``, as well as helping me implement it.
+
+.. autosummary::
diff --git a/doc/build/html/index.html b/doc/build/html/index.html
index 196b18e..50ecd3c 100644
--- a/doc/build/html/index.html
+++ b/doc/build/html/index.html
@@ -357,6 +357,10 @@ 
    Acknowledgements~ as a
 shorthand for sample, as well as helping me implement it.
    
 
+
+
+
+
    
 
 
 
diff --git a/doc/build/html/reference/squigglepy.bayes.html b/doc/build/html/reference/squigglepy.bayes.html
index 5a322dc..ada266d 100644
--- a/doc/build/html/reference/squigglepy.bayes.html
+++ b/doc/build/html/reference/squigglepy.bayes.html
@@ -362,36 +362,34 @@
 
    
 squigglepy.bayes.average(prior, evidence, weights=[0.5, 0.5], relative_weights=None)[source]#
    
 
    Average two distributions.
    
-
    
-
    Parameters#
    
-
    
-
    priorDistribution
    The prior distribution.
    
+
    
+
    Parameters:
    
+
    
+
    priorDistribution
    The prior distribution.
    
 
    
-
    evidenceDistribution
    The distribution used to average with the prior.
    
+
    evidenceDistribution
    The distribution used to average with the prior.
    
 
    
-
    weightslist or np.array or float
    How much weight to put on prior versus evidence when averaging? If
+
    weightslist or np.array or float
    How much weight to put on prior versus evidence when averaging? If
 only one weight is passed, the other weight will be inferred to make the
 total weights sum to 1. Defaults to 50-50 weights.
    
 
    
-
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
+
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
 to sum to 1.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    Distribution
    A mixture distribution that accords weights to prior and evidence.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
+
    Examples
    
 
    >> prior = sq.norm(1,5)
 >> evidence = sq.norm(2,3)
 >> bayes.average(prior, evidence)
 <Distribution> mixture
    
-
 
 
 
    
@@ -400,59 +398,58 @@ 
    Examples
 
    Calculate a Bayesian network.
    
 
    Allows you to find conditional probabilities of custom events based on
 rejection sampling.
    
-
    
-
    Parameters#
    
-
    
-
    event_fnfunction
    A function that defines the bayesian network
    
+
    
+
    Parameters:
    
+
    
+
    event_fnfunction
    A function that defines the bayesian network
    
 
    
-
    nint
    The number of samples to generate
    
+
    nint
    The number of samples to generate
    
 
    
-
    finda function or None
    What do we want to know the probability of?
    
+
    finda function or None
    What do we want to know the probability of?
    
 
    
-
    conditional_ona function or None
    When finding the probability, what do we want to condition on?
    
+
    conditional_ona function or None
    When finding the probability, what do we want to condition on?
    
 
    
-
    reduce_fna function or None
    When taking all the results of the simulations, how do we aggregate them
+
    reduce_fna function or None
    When taking all the results of the simulations, how do we aggregate them
 into a final answer? Defaults to np.mean.
    
 
    
-
    rawbool
    If True, just return the results of each simulation without aggregating.
    
+
    rawbool
    If True, just return the results of each simulation without aggregating.
    
 
    
-
    memcachebool
    If True, cache the results in-memory for future calculations. Each cache
+
    memcachebool
    If True, cache the results in-memory for future calculations. Each cache
 will be matched based on the event_fn. Default True.
    
 
    
-
    memcache_loadbool
    If True, load cache from the in-memory. This will be true if memcache
+
    memcache_loadbool
    If True, load cache from the in-memory. This will be true if memcache
 is True. Cache will be matched based on the event_fn. Default True.
    
 
    
-
    memcache_savebool
    If True, save results to an in-memory cache. This will be true if memcache
+
    memcache_savebool
    If True, save results to an in-memory cache. This will be true if memcache
 is True. Cache will be matched based on the event_fn. Default True.
    
 
    
-
    reload_cachebool
    If True, any existing cache will be ignored and recalculated. Default False.
    
+
    reload_cachebool
    If True, any existing cache will be ignored and recalculated. Default False.
    
 
    
-
    dump_cache_filestr or None
    If present, will write out the cache to a binary file with this path with
+
    dump_cache_filestr or None
    If present, will write out the cache to a binary file with this path with
 .sqlcache appended to the file name.
    
 
    
-
    load_cache_filestr or None
    If present, will first attempt to load and use a cache from a file with this
+
    load_cache_filestr or None
    If present, will first attempt to load and use a cache from a file with this
 path with .sqlcache appended to the file name.
    
 
    
-
    cache_file_primarybool
    If both an in-memory cache and file cache are present, the file
+
    cache_file_primarybool
    If both an in-memory cache and file cache are present, the file
 cache will be used for the cache if this is True, and the in-memory cache
 will be used otherwise. Defaults to False.
    
 
    
-
    verbosebool
    If True, will print out statements on computational progress.
    
+
    verbosebool
    If True, will print out statements on computational progress.
    
 
    
-
    coresint
    If 1, runs on a single core / process. If greater than 1, will run on a multiprocessing
+
    coresint
    If 1, runs on a single core / process. If greater than 1, will run on a multiprocessing
 pool with that many cores / processes.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    various
    The result of reduce_fn on n simulations of event_fn.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    # Cancer example: prior of having cancer is 1%, the likelihood of a positive
 # mammography given cancer is 80% (true positive rate), and the likelihood of
 # a positive mammography given no cancer is 9.6% (false positive rate).
@@ -471,7 +468,6 @@ 
    Examples#
 >>                conditional_on=lambda e: e[‘mammography’],
 >>                n=1*M)
 0.07723995880535531
    
-
 
 
 
    
@@ -482,33 +478,31 @@ 
    Examples#
 p(h|e) is called posterior
 p(e|h) is called likelihood
 p(h) is called prior
    
-
    
-
    Parameters#
    
-
    
-
    likelihood_hfloat
    The likelihood (given that the hypothesis is true), aka p(e|h)
    
+
    
+
    Parameters:
    
+
    
+
    likelihood_hfloat
    The likelihood (given that the hypothesis is true), aka p(e|h)
    
 
    
-
    likelihood_not_hfloat
    The likelihood given the hypothesis is not true, aka p(e|~h)
    
+
    likelihood_not_hfloat
    The likelihood given the hypothesis is not true, aka p(e|~h)
    
 
    
-
    priorfloat
    The prior probability, aka p(h)
    
+
    priorfloat
    The prior probability, aka p(h)
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
+
    Returns:
    
+
    
 
    float
    The result of Bayes rule, aka p(h|e)
    
 
    
 
    
-
    
-
    
-
    Examples#
    
+
+
    
+
    Examples
    
 
    # Cancer example: prior of having cancer is 1%, the likelihood of a positive
 # mammography given cancer is 80% (true positive rate), and the likelihood of
 # a positive mammography given no cancer is 9.6% (false positive rate).
 # Given this, what is the probability of cancer given a positive mammography?
 >>> simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096)
 0.07763975155279504
    
-
 
 
 
    
@@ -517,34 +511,32 @@ 
    Examples#
 
    Update a distribution.
    
 
    Starting with a prior distribution, use Bayesian inference to perform an update,
 producing a posterior distribution from the evidence distribution.
    
-
    
-
    Parameters#
    
-
    
-
    priorDistribution
    The prior distribution. Currently must either be normal or beta type. Other
+
    
+
    Parameters:
    
+
    
+
    priorDistribution
    The prior distribution. Currently must either be normal or beta type. Other
 types are not yet supported.
    
 
    
-
    evidenceDistribution
    The distribution used to update the prior. Currently must either be normal
+
    evidenceDistribution
    The distribution used to update the prior. Currently must either be normal
 or beta type. Other types are not yet supported.
    
 
    
-
    evidence_weightfloat
    How much weight to put on the evidence distribution? Currently this only matters
+
    evidence_weightfloat
    How much weight to put on the evidence distribution? Currently this only matters
 for normal distributions, where this should be equivalent to the sample weight.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    Distribution
    The posterior distribution
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >> prior = sq.norm(1,5)
 >> evidence = sq.norm(2,3)
 >> bayes.update(prior, evidence)
 <Distribution> norm(mean=2.53, sd=0.29)
    
-
 
 
 
diff --git a/doc/build/html/reference/squigglepy.correlation.html b/doc/build/html/reference/squigglepy.correlation.html
index d19ed30..df78a95 100644
--- a/doc/build/html/reference/squigglepy.correlation.html
+++ b/doc/build/html/reference/squigglepy.correlation.html
@@ -366,6 +366,17 @@
 
    An object that holds metadata for a group of correlated distributions.
 This object is not intended to be used directly by the user, but
 rather during sampling to induce correlations between distributions.
    
+
    Methods
    
+
+
+
+
+
+
+
+
+
+
    has_sufficient_sample_diversity(samples[, ...])
    Check if there is there are sufficient unique samples to work with in the data.
    induce_correlation(data)
    Induce a set of correlations on a column-wise dataset
    
 
    
 
    
 correlated_dists: tuple[OperableDistribution]#
    
@@ -391,26 +402,26 @@
 
    
 induce_correlation(data: ndarray[Any, dtype[float64]]) → ndarray[Any, dtype[float64]][source]#
    
 
    Induce a set of correlations on a column-wise dataset
    
-
    
-
    Parameters#
    
-
    
-
    data2d-array
    An m-by-n array where m is the number of samples and n is the
+
    
+
    Parameters:
    
+
    
+
    data2d-array
    An m-by-n array where m is the number of samples and n is the
 number of independent variables, each column of the array corresponding
 to each variable
    
 
    
-
    corrmat2d-array
    An n-by-n array that defines the desired correlation coefficients
+
    corrmat2d-array
    An n-by-n array that defines the desired correlation coefficients
 (between -1 and 1). Note: the matrix must be symmetric and
 positive-definite in order to induce.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
-
    new_data2d-array
    An m-by-n array that has the desired correlations.
    
+
    
+
    Returns:
    
+
    
+
    new_data2d-array
    An m-by-n array that has the desired correlations.
    
+
    
+
    
 
    
 
    
-
    
 
    
 
 
    
@@ -429,38 +440,37 @@ 
    Returns#<
 
    This method works on a best-effort basis, and may fail to induce the desired
 correlation depending on the distributions provided. An exception will be raised
 if that’s the case.
    
-
    
-
    Parameters#
    
-
    
-
    variablestuple of distributions
    The variables to correlate as a tuple of distributions.
    
+
    
+
    Parameters:
    
+
    
+
    variablestuple of distributions
    The variables to correlate as a tuple of distributions.
    
 
    The distributions must be able to produce enough unique samples for the method
 to be able to induce the desired correlation by shuffling the samples.
    
 
    Discrete distributions are notably hard to correlate this way,
 as it’s common for them to result in very few unique samples.
    
 
    
-
    correlation2d-array or float
    An n-by-n array that defines the desired Spearman rank correlation coefficients.
+
    correlation2d-array or float
    An n-by-n array that defines the desired Spearman rank correlation coefficients.
 This matrix must be symmetric and positive semi-definite; and must not be confused with
 a covariance matrix.
    
 
    Correlation parameters can only be between -1 and 1, exclusive
 (including extremely close approximations).
    
 
    If a float is provided, all variables will be correlated with the same coefficient.
    
 
    
-
    tolerancefloat, optional
    If provided, overrides the absolute tolerance used to check if the resulting
+
    tolerancefloat, optional
    If provided, overrides the absolute tolerance used to check if the resulting
 correlation matrix matches the desired correlation matrix. Defaults to 0.05.
    
 
    Checking can also be disabled by passing None.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
-
    correlated_variablestuple of distributions
    The correlated variables as a tuple of distributions in the same order as
+
    
+
    Returns:
    
+
    
+
    correlated_variablestuple of distributions
    The correlated variables as a tuple of distributions in the same order as
 the input variables.
    
 
    
 
    
-
    
-
    
-
    Examples#
    
+
+
    
+
    Examples
    
 
    Suppose we want to correlate two variables with a correlation coefficient of 0.65:
 >>> solar_radiation, temperature = sq.gamma(300, 100), sq.to(22, 28)
 >>> solar_radiation, temperature = sq.correlate((solar_radiation, temperature), 0.7)
@@ -480,7 +490,6 @@ 
    Examples
        [-0.480149, -0.187831  ,  1.        ]])
 
    
 
    
-
 
 
 
diff --git a/doc/build/html/reference/squigglepy.distributions.html b/doc/build/html/reference/squigglepy.distributions.html
index 5ac9aa9..233fb54 100644
--- a/doc/build/html/reference/squigglepy.distributions.html
+++ b/doc/build/html/reference/squigglepy.distributions.html
@@ -368,127 +368,270 @@
 
    
 class squigglepy.distributions.BernoulliDistribution(p)[source]#
    
 
    Bases: DiscreteDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.BetaDistribution(a, b)[source]#
    
 
    Bases: ContinuousDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.BinomialDistribution(n, p)[source]#
    
 
    Bases: DiscreteDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.CategoricalDistribution(items)[source]#
    
 
    Bases: DiscreteDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.ChiSquareDistribution(df)[source]#
    
 
    Bases: ContinuousDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.ComplexDistribution(left, right=None, fn=<built-in function add>, fn_str='+', infix=True)[source]#
    
 
    Bases: CompositeDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.CompositeDistribution[source]#
    
 
    Bases: OperableDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.ConstantDistribution(x)[source]#
    
 
    Bases: DiscreteDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.ContinuousDistribution[source]#
    
 
    Bases: OperableDistribution, ABC
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.DiscreteDistribution[source]#
    
 
    Bases: OperableDistribution, ABC
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.ExponentialDistribution(scale, lclip=None, rclip=None)[source]#
    
 
    Bases: ContinuousDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.GammaDistribution(shape, scale=1, lclip=None, rclip=None)[source]#
    
 
    Bases: ContinuousDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.GeometricDistribution(p)[source]#
    
 
    Bases: OperableDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.LogTDistribution(x=None, y=None, t=1, credibility=90, lclip=None, rclip=None)[source]#
    
 
    Bases: ContinuousDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.LognormalDistribution(x=None, y=None, norm_mean=None, norm_sd=None, lognorm_mean=None, lognorm_sd=None, credibility=90, lclip=None, rclip=None)[source]#
    
 
    Bases: ContinuousDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.MixtureDistribution(dists, weights=None, relative_weights=None, lclip=None, rclip=None)[source]#
    
 
    Bases: CompositeDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.NormalDistribution(x=None, y=None, mean=None, sd=None, credibility=90, lclip=None, rclip=None)[source]#
    
 
    Bases: ContinuousDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.OperableDistribution[source]#
    
 
    Bases: BaseDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
    
 plot(num_samples=None, bins=None)[source]#
    
 
    Plot a histogram of the samples.
    
-
    
-
    Parameters#
    
-
    
-
    num_samplesint
    The number of samples to draw for plotting. Defaults to 1000 if not set.
    
+
    
+
    Parameters:
    
+
    
+
    num_samplesint
    The number of samples to draw for plotting. Defaults to 1000 if not set.
    
 
    
-
    binsint
    The number of bins to plot. Defaults to 200 if not set.
    
+
    binsint
    The number of bins to plot. Defaults to 200 if not set.
    
 
    
 
    
-
    
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> sq.norm(5, 10).plot()
 
    
 
    
-
 
    
 
 
@@ -497,138 +640,186 @@ 
    Examples
 
    
 class squigglepy.distributions.PERTDistribution(left, mode, right, lam=4, lclip=None, rclip=None)[source]#
    
 
    Bases: ContinuousDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.ParetoDistribution(shape)[source]#
    
 
    Bases: ContinuousDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.PoissonDistribution(lam, lclip=None, rclip=None)[source]#
    
 
    Bases: DiscreteDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.TDistribution(x=None, y=None, t=20, credibility=90, lclip=None, rclip=None)[source]#
    
 
    Bases: ContinuousDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.TriangularDistribution(left, mode, right)[source]#
    
 
    Bases: ContinuousDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 class squigglepy.distributions.UniformDistribution(x, y)[source]#
    
 
    Bases: ContinuousDistribution
    
+
    Methods
    
+
+
+
+
+
+
+
    plot([num_samples, bins])
    Plot a histogram of the samples.
    
 
    
 
 
    
 
    
 squigglepy.distributions.bernoulli(p)[source]#
    
 
    Initialize a Bernoulli distribution.
    
-
    
-
    Parameters#
    
-
    
-
    pfloat
    The probability of the binary event. Must be between 0 and 1.
    
+
    
+
    Parameters:
    
+
    
+
    pfloat
    The probability of the binary event. Must be between 0 and 1.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    BernoulliDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    BernoulliDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> bernoulli(0.1)
 <Distribution> bernoulli(p=0.1)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.beta(a, b)[source]#
    
 
    Initialize a beta distribution.
    
-
    
-
    Parameters#
    
-
    
-
    afloat
    The alpha shape value of the distribution. Typically takes the value of the
+
    
+
    Parameters:
    
+
    
+
    afloat
    The alpha shape value of the distribution. Typically takes the value of the
 number of trials that resulted in a success.
    
 
    
-
    bfloat
    The beta shape value of the distribution. Typically takes the value of the
+
    bfloat
    The beta shape value of the distribution. Typically takes the value of the
 number of trials that resulted in a failure.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    BetaDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    BetaDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> beta(1, 2)
 <Distribution> beta(1, 2)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.binomial(n, p)[source]#
    
 
    Initialize a binomial distribution.
    
-
    
-
    Parameters#
    
-
    
-
    nint
    The number of trials.
    
+
    
+
    Parameters:
    
+
    
+
    nint
    The number of trials.
    
 
    
-
    pfloat
    The probability of success for each trial. Must be between 0 and 1.
    
+
    pfloat
    The probability of success for each trial. Must be between 0 and 1.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    BinomialDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    BinomialDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> binomial(1, 0.1)
 <Distribution> binomial(1, 0.1)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.chisquare(df)[source]#
    
 
    Initialize a chi-square distribution.
    
-
    
-
    Parameters#
    
-
    
-
    dffloat
    The degrees of freedom. Must be positive.
    
+
    
+
    Parameters:
    
+
    
+
    dffloat
    The degrees of freedom. Must be positive.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    ChiSquareDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    ChiSquareDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> chisquare(2)
 <Distribution> chiaquare(2)
 
    
 
    
-
 
 
 
    
@@ -636,32 +827,30 @@ 
    Examples#squigglepy.distributions.clip(dist1, left, right=None)[source]#
 
    Initialize the clipping/bounding of the output of the distribution.
    
 
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters#
    
-
    
-
    dist1Distribution or function
    The distribution to clip. If this is a funciton, it will return a partial that will
+
    
+
    Parameters:
    
+
    
+
    dist1Distribution or function
    The distribution to clip. If this is a funciton, it will return a partial that will
 be suitable for use in piping.
    
 
    
-
    leftint or float or None
    The value to use as the lower bound for clipping.
    
+
    leftint or float or None
    The value to use as the lower bound for clipping.
    
 
    
-
    rightint or float or None
    The value to use as the upper bound for clipping.
    
+
    rightint or float or None
    The value to use as the upper bound for clipping.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> clip(norm(0, 1), 0.5, 0.9)
 <Distribution> rclip(lclip(norm(mean=0.5, sd=0.3), 0.5), 0.9)
 
    
 
    
-
 
 
 
    
@@ -669,44 +858,45 @@ 
    Examples#squigglepy.distributions.const(x)[source]#
 
    Initialize a constant distribution.
    
 
    Constant distributions always return the same value no matter what.
    
-
    
-
    Parameters#
    
-
    
-
    xanything
    The value the constant distribution should always return.
    
+
    
+
    Parameters:
    
+
    
+
    xanything
    The value the constant distribution should always return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    ConstantDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    ConstantDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> const(1)
 <Distribution> const(1)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.discrete(items)[source]#
    
 
    Initialize a discrete distribution (aka categorical distribution).
    
-
    
-
    Parameters#
    
-
    
-
    itemslist or dict
    The values that the discrete distribution will return and their associated
+
    
+
    Parameters:
    
+
    
+
    itemslist or dict
    The values that the discrete distribution will return and their associated
 weights (or likelihoods of being returned when sampled).
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    CategoricalDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    CategoricalDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> discrete({0: 0.1, 1: 0.9})  # 10% chance of returning 0, 90% chance of returning 1
 <Distribution> categorical({0: 0.1, 1: 0.9})
 >>> discrete([[0.1, 0], [0.9, 1]])  # Different notation for the same thing.
@@ -717,7 +907,6 @@ 
    Examples#<Distribution> categorical({'a': 0.1, 'b': 0.9})
 
    
 
    
-
 
 
 
    
@@ -725,27 +914,25 @@ 
    Examples#squigglepy.distributions.dist_ceil(dist1)[source]#
 
    Initialize the ceiling rounding of the output of the distribution.
    
 
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters#
    
-
    
-
    dist1Distribution
    The distribution to sample and then ceiling round.
    
+
    
+
    Parameters:
    
+
    
+
    dist1Distribution
    The distribution to sample and then ceiling round.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> dist_ceil(norm(0, 1))
 <Distribution> ceil(norm(mean=0.5, sd=0.3))
 
    
 
    
-
 
 
 
    
@@ -753,27 +940,25 @@ 
    Examples#squigglepy.distributions.dist_exp(dist1)[source]#
 
    Initialize the exp of the output of the distribution.
    
 
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters#
    
-
    
-
    dist1Distribution
    The distribution to sample and then take the exp of.
    
+
    
+
    Parameters:
    
+
    
+
    dist1Distribution
    The distribution to sample and then take the exp of.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> dist_exp(norm(0, 1))
 <Distribution> exp(norm(mean=0.5, sd=0.3))
 
    
 
    
-
 
 
 
    
@@ -781,27 +966,25 @@ 
    Examples#squigglepy.distributions.dist_floor(dist1)[source]#
 
    Initialize the floor rounding of the output of the distribution.
    
 
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters#
    
-
    
-
    dist1Distribution
    The distribution to sample and then floor round.
    
+
    
+
    Parameters:
    
+
    
+
    dist1Distribution
    The distribution to sample and then floor round.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> dist_floor(norm(0, 1))
 <Distribution> floor(norm(mean=0.5, sd=0.3))
 
    
 
    
-
 
 
 
    
@@ -809,33 +992,32 @@ 
    Examples#squigglepy.distributions.dist_fn(dist1, dist2=None, fn=None, name=None)[source]#
 
    Initialize a distribution that has a custom function applied to the result.
    
 
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters#
    
-
    
-
    dist1Distribution or function or list
    Typically, the distribution to apply the function to. Could also be a function
+
    
+
    Parameters:
    
+
    
+
    dist1Distribution or function or list
    Typically, the distribution to apply the function to. Could also be a function
 or list of functions if dist_fn is being used in a pipe.
    
 
    
-
    dist2Distribution or function or list or None
    Typically, the second distribution to apply the function to if the function takes
+
    dist2Distribution or function or list or None
    Typically, the second distribution to apply the function to if the function takes
 two arguments. Could also be a function or list of functions if dist_fn is
 being used in a pipe.
    
 
    
-
    fnfunction or None
    The function to apply to the distribution(s).
    
+
    fnfunction or None
    The function to apply to the distribution(s).
    
 
    
-
    namestr or None
    By default, fn.__name__ will be used to name the function. But you can pass
+
    namestr or None
    By default, fn.__name__ will be used to name the function. But you can pass
 a custom name.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
 when it is sampled.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> def double(x):
 >>>     return x * 2
 >>> dist_fn(norm(0, 1), double)
@@ -844,7 +1026,6 @@ 
    Examples#<Distribution> double(norm(mean=0.5, sd=0.3))
 
    
 
    
-
 
 
 
    
@@ -852,27 +1033,25 @@ 
    Examples#squigglepy.distributions.dist_log(dist1, base=2.718281828459045)[source]#
 
    Initialize the log of the output of the distribution.
    
 
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters#
    
-
    
-
    dist1Distribution
    The distribution to sample and then take the log of.
    
+
    
+
    Parameters:
    
+
    
+
    dist1Distribution
    The distribution to sample and then take the log of.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> dist_log(norm(0, 1), 10)
 <Distribution> log(norm(mean=0.5, sd=0.3), const(10))
 
    
 
    
-
 
 
 
    
@@ -880,30 +1059,28 @@ 
    Examples#squigglepy.distributions.dist_max(dist1, dist2=None)[source]#
 
    Initialize the calculation of the maximum value of two distributions.
    
 
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters#
    
-
    
-
    dist1Distribution
    The distribution to sample and determine the max of.
    
+
    
+
    Parameters:
    
+
    
+
    dist1Distribution
    The distribution to sample and determine the max of.
    
 
    
-
    dist2Distribution
    The second distribution to sample and determine the max of.
    
+
    dist2Distribution
    The second distribution to sample and determine the max of.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
 when it is sampled.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> dist_max(norm(0, 1), norm(1, 2))
 <Distribution> max(norm(mean=0.5, sd=0.3), norm(mean=1.5, sd=0.3))
 
    
 
    
-
 
 
 
    
@@ -911,29 +1088,27 @@ 
    Examples#squigglepy.distributions.dist_min(dist1, dist2=None)[source]#
 
    Initialize the calculation of the minimum value of two distributions.
    
 
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters#
    
-
    
-
    dist1Distribution
    The distribution to sample and determine the min of.
    
+
    
+
    Parameters:
    
+
    
+
    dist1Distribution
    The distribution to sample and determine the min of.
    
 
    
-
    dist2Distribution
    The second distribution to sample and determine the min of.
    
+
    dist2Distribution
    The second distribution to sample and determine the min of.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> dist_min(norm(0, 1), norm(1, 2))
 <Distribution> min(norm(mean=0.5, sd=0.3), norm(mean=1.5, sd=0.3))
 
    
 
    
-
 
 
 
    
@@ -941,111 +1116,109 @@ 
    Examples#squigglepy.distributions.dist_round(dist1, digits=0)[source]#
 
    Initialize the rounding of the output of the distribution.
    
 
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters#
    
-
    
-
    dist1Distribution
    The distribution to sample and then round.
    
+
    
+
    Parameters:
    
+
    
+
    dist1Distribution
    The distribution to sample and then round.
    
 
    
-
    digitsint
    The number of digits to round to.
    
+
    digitsint
    The number of digits to round to.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> dist_round(norm(0, 1))
 <Distribution> round(norm(mean=0.5, sd=0.3), 0)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.exponential(scale, lclip=None, rclip=None)[source]#
    
 
    Initialize an exponential distribution.
    
-
    
-
    Parameters#
    
-
    
-
    scalefloat
    The scale value of the exponential distribution (> 0)
    
+
    
+
    Parameters:
    
+
    
+
    scalefloat
    The scale value of the exponential distribution (> 0)
    
 
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
+
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
 
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
+
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    ExponentialDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    ExponentialDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> exponential(1)
 <Distribution> exponential(1)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.gamma(shape, scale=1, lclip=None, rclip=None)[source]#
    
 
    Initialize a gamma distribution.
    
-
    
-
    Parameters#
    
-
    
-
    shapefloat
    The shape value of the gamma distribution.
    
+
    
+
    Parameters:
    
+
    
+
    shapefloat
    The shape value of the gamma distribution.
    
 
    
-
    scalefloat
    The scale value of the gamma distribution. Defaults to 1.
    
+
    scalefloat
    The scale value of the gamma distribution. Defaults to 1.
    
 
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
+
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
 
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
+
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    GammaDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    GammaDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> gamma(10, 1)
 <Distribution> gamma(shape=10, scale=1)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.geometric(p)[source]#
    
 
    Initialize a geometric distribution.
    
-
    
-
    Parameters#
    
-
    
-
    pfloat
    The probability of success of an individual trial. Must be between 0 and 1.
    
+
    
+
    Parameters:
    
+
    
+
    pfloat
    The probability of success of an individual trial. Must be between 0 and 1.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    GeometricDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    GeometricDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> geometric(0.1)
 <Distribution> geometric(0.1)
 
    
 
    
-
 
 
 
    
@@ -1053,28 +1226,28 @@ 
    Examples#squigglepy.distributions.inf0(p_zero, dist)[source]#
 
    Initialize an arbitrary zero-inflated distribution.
    
 
    Alias for zero_inflated.
    
-
    
-
    Parameters#
    
-
    
-
    p_zerofloat
    The chance of the distribution returning zero
    
+
    
+
    Parameters:
    
+
    
+
    p_zerofloat
    The chance of the distribution returning zero
    
 
    
-
    distDistribution
    The distribution to sample from when not zero
    
+
    distDistribution
    The distribution to sample from when not zero
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    MixtureDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    MixtureDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> inf0(0.6, norm(1, 2))
 <Distribution> mixture
  - 0
  - <Distribution> norm(mean=1.5, sd=0.3)
 
    
 
    
-
 
 
 
    
@@ -1082,30 +1255,28 @@ 
    Examples#squigglepy.distributions.lclip(dist1, val=None)[source]#
 
    Initialize the clipping/bounding of the output of the distribution by the lower value.
    
 
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters#
    
-
    
-
    dist1Distribution or function
    The distribution to clip. If this is a funciton, it will return a partial that will
+
    
+
    Parameters:
    
+
    
+
    dist1Distribution or function
    The distribution to clip. If this is a funciton, it will return a partial that will
 be suitable for use in piping.
    
 
    
-
    valint or float or None
    The value to use as the lower bound for clipping.
    
+
    valint or float or None
    The value to use as the lower bound for clipping.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> lclip(norm(0, 1), 0.5)
 <Distribution> lclip(norm(mean=0.5, sd=0.3), 0.5)
 
    
 
    
-
 
 
 
    
@@ -1117,37 +1288,37 @@ 
    Examples#
 
    If x and y are not defined, can just return a classic t-distribution defined via
 t as the number of degrees of freedom, but in log-space.
    
-
    
-
    Parameters#
    
-
    
-
    xfloat or None
    The low value of a credible interval defined by credibility. Must be greater than 0.
+
    
+
    Parameters:
    
+
    
+
    xfloat or None
    The low value of a credible interval defined by credibility. Must be greater than 0.
 Defaults to a 90% CI.
    
 
    
-
    yfloat or None
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
+
    yfloat or None
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
 
    
-
    tfloat
    The number of degrees of freedom of the t-distribution. Defaults to 1.
    
+
    tfloat
    The number of degrees of freedom of the t-distribution. Defaults to 1.
    
 
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
+
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
 
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
+
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
 
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
+
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    LogTDistribution
    
-
    
-
    
-
    Examples#
    
+
+
    Returns:
    
+
    
+
    LogTDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> log_tdist(0, 1, 2)
 <Distribution> log_tdist(x=0, y=1, t=2)
 >>> log_tdist()
 <Distribution> log_tdist(t=1)
 
    
 
    
-
 
 
 
    
@@ -1156,38 +1327,39 @@ 
    Examples#
    Initialize a lognormal distribution.
    
 
    Can be defined either via a credible interval from x to y (use credibility or
 it will default to being a 90% CI) or defined via mean and sd.
    
-
    
-
    Parameters#
    
-
    
-
    xfloat
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
+
    
+
    Parameters:
    
+
    
+
    xfloat
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
 Must be a value greater than 0.
    
 
    
-
    yfloat
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
+
    yfloat
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
 Must be a value greater than 0.
    
 
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90. Ignored if the distribution is
+
    credibilityfloat
    The range of the credibility interval. Defaults to 90. Ignored if the distribution is
 defined instead by mean and sd.
    
 
    
-
    norm_meanfloat or None
    The mean of the underlying normal distribution. If not defined, defaults to 0.
    
+
    norm_meanfloat or None
    The mean of the underlying normal distribution. If not defined, defaults to 0.
    
 
    
-
    norm_sdfloat
    The standard deviation of the underlying normal distribution.
    
+
    norm_sdfloat
    The standard deviation of the underlying normal distribution.
    
 
    
-
    lognorm_meanfloat or None
    The mean of the lognormal distribution. If not defined, defaults to 1.
    
+
    lognorm_meanfloat or None
    The mean of the lognormal distribution. If not defined, defaults to 1.
    
 
    
-
    lognorm_sdfloat
    The standard deviation of the lognormal distribution.
    
+
    lognorm_sdfloat
    The standard deviation of the lognormal distribution.
    
 
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
+
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
 
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
+
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    LognormalDistribution
    
-
    
-
    
-
    Examples#
    
+
+
    Returns:
    
+
    
+
    LognormalDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> lognorm(1, 10)
 <Distribution> lognorm(lognorm_mean=4.04, lognorm_sd=3.21, norm_mean=1.15, norm_sd=0.7)
 >>> lognorm(norm_mean=1, norm_sd=2)
@@ -1196,35 +1368,35 @@ 
    Examples#<Distribution> lognorm(lognorm_mean=1, lognorm_sd=2, norm_mean=-0.8, norm_sd=1.27)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.mixture(dists, weights=None, relative_weights=None, lclip=None, rclip=None)[source]#
    
 
    Initialize a mixture distribution, which is a combination of different distributions.
    
-
    
-
    Parameters#
    
-
    
-
    distslist or dict
    The distributions to mix. Can also be defined as a list of weights and distributions.
    
+
    
+
    Parameters:
    
+
    
+
    distslist or dict
    The distributions to mix. Can also be defined as a list of weights and distributions.
    
 
    
-
    weightslist or None
    The weights for each distribution.
    
+
    weightslist or None
    The weights for each distribution.
    
 
    
-
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
+
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
 to sum to 1.
    
 
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
+
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
 
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
+
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    MixtureDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    MixtureDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> mixture([norm(1, 2), norm(3, 4)], weights=[0.1, 0.9])
 <Distribution> mixture
  - <Distribution> norm(mean=1.5, sd=0.3)
@@ -1240,7 +1412,6 @@ 
    Examples# - <Distribution> norm(mean=3.5, sd=0.3)
 
    
 
    
-
 
 
 
    
@@ -1249,125 +1420,125 @@ 
    Examples#
    Initialize a normal distribution.
    
 
    Can be defined either via a credible interval from x to y (use credibility or
 it will default to being a 90% CI) or defined via mean and sd.
    
-
    
-
    Parameters#
    
-
    
-
    xfloat
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
    
+
    
+
    Parameters:
    
+
    
+
    xfloat
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
    
 
    
-
    yfloat
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
+
    yfloat
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
 
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90. Ignored if the distribution is
+
    credibilityfloat
    The range of the credibility interval. Defaults to 90. Ignored if the distribution is
 defined instead by mean and sd.
    
 
    
-
    meanfloat or None
    The mean of the normal distribution. If not defined, defaults to 0.
    
+
    meanfloat or None
    The mean of the normal distribution. If not defined, defaults to 0.
    
 
    
-
    sdfloat
    The standard deviation of the normal distribution.
    
+
    sdfloat
    The standard deviation of the normal distribution.
    
 
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
+
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
 
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
+
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    NormalDistribution
    
-
    
-
    
-
    Examples#
    
+
+
    Returns:
    
+
    
+
    NormalDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> norm(0, 1)
 <Distribution> norm(mean=0.5, sd=0.3)
 >>> norm(mean=1, sd=2)
 <Distribution> norm(mean=1, sd=2)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.pareto(shape)[source]#
    
 
    Initialize a pareto distribution.
    
-
    
-
    Parameters#
    
-
    
-
    shapefloat
    The shape value of the pareto distribution.
    
+
    
+
    Parameters:
    
+
    
+
    shapefloat
    The shape value of the pareto distribution.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    ParetoDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    ParetoDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> pareto(1)
 <Distribution> pareto(1)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.pert(left, mode, right, lam=4, lclip=None, rclip=None)[source]#
    
 
    Initialize a PERT distribution.
    
-
    
-
    Parameters#
    
-
    
-
    leftfloat
    The smallest value of the PERT distribution.
    
+
    
+
    Parameters:
    
+
    
+
    leftfloat
    The smallest value of the PERT distribution.
    
 
    
-
    modefloat
    The most common value of the PERT distribution.
    
+
    modefloat
    The most common value of the PERT distribution.
    
 
    
-
    rightfloat
    The largest value of the PERT distribution.
    
+
    rightfloat
    The largest value of the PERT distribution.
    
 
    
-
    lamfloat
    The lambda value of the PERT distribution. Defaults to 4.
    
+
    lamfloat
    The lambda value of the PERT distribution. Defaults to 4.
    
 
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
+
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
 
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
+
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    PERTDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    PERTDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> pert(1, 2, 3)
 <Distribution> PERT(1, 2, 3)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.poisson(lam, lclip=None, rclip=None)[source]#
    
 
    Initialize a poisson distribution.
    
-
    
-
    Parameters#
    
-
    
-
    lamfloat
    The lambda value of the poisson distribution.
    
+
    
+
    Parameters:
    
+
    
+
    lamfloat
    The lambda value of the poisson distribution.
    
 
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
+
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
 
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
+
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    PoissonDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    PoissonDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> poisson(1)
 <Distribution> poisson(1)
 
    
 
    
-
 
 
 
    
@@ -1375,30 +1546,28 @@ 
    Examples#squigglepy.distributions.rclip(dist1, val=None)[source]#
 
    Initialize the clipping/bounding of the output of the distribution by the upper value.
    
 
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters#
    
-
    
-
    dist1Distribution or function
    The distribution to clip. If this is a funciton, it will return a partial that will
+
    
+
    Parameters:
    
+
    
+
    dist1Distribution or function
    The distribution to clip. If this is a funciton, it will return a partial that will
 be suitable for use in piping.
    
 
    
-
    valint or float or None
    The value to use as the upper bound for clipping.
    
+
    valint or float or None
    The value to use as the upper bound for clipping.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> rclip(norm(0, 1), 0.5)
 <Distribution> rclip(norm(mean=0.5, sd=0.3), 0.5)
 
    
 
    
-
 
 
 
    
@@ -1410,36 +1579,36 @@ 
    Examples#
 
    If x and y are not defined, can just return a classic t-distribution defined via
 t as the number of degrees of freedom.
    
-
    
-
    Parameters#
    
-
    
-
    xfloat or None
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
    
+
    
+
    Parameters:
    
+
    
+
    xfloat or None
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
    
 
    
-
    yfloat or None
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
+
    yfloat or None
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
 
    
-
    tfloat
    The number of degrees of freedom of the t-distribution. Defaults to 20.
    
+
    tfloat
    The number of degrees of freedom of the t-distribution. Defaults to 20.
    
 
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
+
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
 
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
+
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
 
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
+
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    TDistribution
    
-
    
-
    
-
    Examples#
    
+
+
    Returns:
    
+
    
+
    TDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> tdist(0, 1, 2)
 <Distribution> tdist(x=0, y=1, t=2)
 >>> tdist()
 <Distribution> tdist(t=1)
 
    
 
    
-
 
 
 
    
@@ -1450,116 +1619,116 @@ 
    Examples#
 
    The distribution will default to be a 90% credible interval between x and y unless
 credibility is passed.
    
-
    
-
    Parameters#
    
-
    
-
    xfloat
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
    
+
    
+
    Parameters:
    
+
    
+
    xfloat
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
    
 
    
-
    yfloat
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
+
    yfloat
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
 
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
+
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
 
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
+
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
 
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
+
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    LognormalDistribution if x > 0, otherwise a NormalDistribution
    
-
    
-
    
-
    Examples#
    
+
+
    Returns:
    
+
    
+
    LognormalDistribution if x > 0, otherwise a NormalDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> to(1, 10)
 <Distribution> lognorm(mean=1.15, sd=0.7)
 >>> to(-10, 10)
 <Distribution> norm(mean=0.0, sd=6.08)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.triangular(left, mode, right, lclip=None, rclip=None)[source]#
    
 
    Initialize a triangular distribution.
    
-
    
-
    Parameters#
    
-
    
-
    leftfloat
    The smallest value of the triangular distribution.
    
+
    
+
    Parameters:
    
+
    
+
    leftfloat
    The smallest value of the triangular distribution.
    
 
    
-
    modefloat
    The most common value of the triangular distribution.
    
+
    modefloat
    The most common value of the triangular distribution.
    
 
    
-
    rightfloat
    The largest value of the triangular distribution.
    
+
    rightfloat
    The largest value of the triangular distribution.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    TriangularDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    TriangularDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> triangular(1, 2, 3)
 <Distribution> triangular(1, 2, 3)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.uniform(x, y)[source]#
    
 
    Initialize a uniform random distribution.
    
-
    
-
    Parameters#
    
-
    
-
    xfloat
    The smallest value the uniform distribution will return.
    
+
    
+
    Parameters:
    
+
    
+
    xfloat
    The smallest value the uniform distribution will return.
    
 
    
-
    yfloat
    The largest value the uniform distribution will return.
    
+
    yfloat
    The largest value the uniform distribution will return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    UniformDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    UniformDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> uniform(0, 1)
 <Distribution> uniform(0, 1)
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.distributions.zero_inflated(p_zero, dist)[source]#
    
 
    Initialize an arbitrary zero-inflated distribution.
    
-
    
-
    Parameters#
    
-
    
-
    p_zerofloat
    The chance of the distribution returning zero
    
+
    
+
    Parameters:
    
+
    
+
    p_zerofloat
    The chance of the distribution returning zero
    
 
    
-
    distDistribution
    The distribution to sample from when not zero
    
+
    distDistribution
    The distribution to sample from when not zero
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    MixtureDistribution
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    MixtureDistribution
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> zero_inflated(0.6, norm(1, 2))
 <Distribution> mixture
  - 0
  - <Distribution> norm(mean=1.5, sd=0.3)
 
    
 
    
-
 
 
 
diff --git a/doc/build/html/reference/squigglepy.rng.html b/doc/build/html/reference/squigglepy.rng.html
index 2827765..5399ed3 100644
--- a/doc/build/html/reference/squigglepy.rng.html
+++ b/doc/build/html/reference/squigglepy.rng.html
@@ -362,27 +362,25 @@
 squigglepy.rng.set_seed(seed)[source]#
 
    Set the seed of the random number generator used by Squigglepy.
    
 
    The RNG is a np.random.default_rng under the hood.
    
-
    
-
    Parameters#
    
-
    
-
    seedfloat
    The seed to use for the RNG.
    
+
    
+
    Parameters:
    
+
    
+
    seedfloat
    The seed to use for the RNG.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    np.random.default_rng
    The RNG used internally.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
+
    Examples
    
 
    >>> set_seed(42)
 Generator(PCG64) at 0x127EDE9E0
 
    
 
    
-
 
 
 
diff --git a/doc/build/html/reference/squigglepy.samplers.html b/doc/build/html/reference/squigglepy.samplers.html
index ed8dd05..24cd126 100644
--- a/doc/build/html/reference/squigglepy.samplers.html
+++ b/doc/build/html/reference/squigglepy.samplers.html
@@ -361,160 +361,153 @@
 
    
 squigglepy.samplers.bernoulli_sample(p, samples=1)[source]#
    
 
    Sample 1 with probability p and 0 otherwise.
    
-
    
-
    Parameters#
    
-
    
-
    pfloat
    The probability of success. Must be between 0 and 1.
    
+
    
+
    Parameters:
    
+
    
+
    pfloat
    The probability of success. Must be between 0 and 1.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    int
    Either 0 or 1
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
+
    Examples
    
 
    >>> set_seed(42)
 >>> bernoulli_sample(0.5)
 0
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.beta_sample(a, b, samples=1)[source]#
    
 
    Sample a random number according to a beta distribution.
    
-
    
-
    Parameters#
    
-
    
-
    afloat
    The alpha shape value of the distribution. Typically takes the value of the
+
    
+
    Parameters:
    
+
    
+
    afloat
    The alpha shape value of the distribution. Typically takes the value of the
 number of trials that resulted in a success.
    
 
    
-
    bfloat
    The beta shape value of the distribution. Typically takes the value of the
+
    bfloat
    The beta shape value of the distribution. Typically takes the value of the
 number of trials that resulted in a failure.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    float
    A random number sampled from a beta distribution defined by
 a and b.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> beta_sample(1, 1)
 0.22145847498048798
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.binomial_sample(n, p, samples=1)[source]#
    
 
    Sample a random number according to a binomial distribution.
    
-
    
-
    Parameters#
    
-
    
-
    nint
    The number of trials.
    
+
    
+
    Parameters:
    
+
    
+
    nint
    The number of trials.
    
 
    
-
    pfloat
    The probability of success for each trial. Must be between 0 and 1.
    
+
    pfloat
    The probability of success for each trial. Must be between 0 and 1.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    int
    A random number sampled from a binomial distribution defined by
 n and p. The random number should be between 0 and n.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> binomial_sample(10, 0.1)
 2
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.chi_square_sample(df, samples=1)[source]#
    
 
    Sample a random number according to a chi-square distribution.
    
-
    
-
    Parameters#
    
-
    
-
    dffloat
    The number of degrees of freedom
    
+
    
+
    Parameters:
    
+
    
+
    dffloat
    The number of degrees of freedom
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    float
    A random number sampled from a chi-square distribution.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> chi_square_sample(2)
 4.808417207931989
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.discrete_sample(items, samples=1, verbose=False, _multicore_tqdm_n=1, _multicore_tqdm_cores=1)[source]#
    
 
    Sample a random value from a discrete distribution (aka categorical distribution).
    
-
    
-
    Parameters#
    
-
    
-
    itemslist or dict
    The values that the discrete distribution will return and their associated
+
    
+
    Parameters:
    
+
    
+
    itemslist or dict
    The values that the discrete distribution will return and their associated
 weights (or likelihoods of being returned when sampled).
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
-
    verbosebool
    If True, will print out statements on computational progress.
    
+
    verbosebool
    If True, will print out statements on computational progress.
    
 
    
-
    _multicore_tqdm_nint
    The total number of samples to use for printing tqdm’s interface. This is meant to only
+
    _multicore_tqdm_nint
    The total number of samples to use for printing tqdm’s interface. This is meant to only
 be used internally by squigglepy to make the progress bar printing work well for
 multicore. This parameter can be safely ignored by the user.
    
 
    
-
    _multicore_tqdm_coresint
    The total number of cores to use for printing tqdm’s interface. This is meant to only
+
    _multicore_tqdm_coresint
    The total number of cores to use for printing tqdm’s interface. This is meant to only
 be used internally by squigglepy to make the progress bar printing work well for
 multicore. This parameter can be safely ignored by the user.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    Various, based on items in items
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    Various, based on items in items
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> # 10% chance of returning 0, 90% chance of returning 1
 >>> discrete_sample({0: 0.1, 1: 0.9})
@@ -528,99 +521,92 @@ 
    Examples#'b'
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.exponential_sample(scale, samples=1)[source]#
    
 
    Sample a random number according to an exponential distribution.
    
-
    
-
    Parameters#
    
-
    
-
    scalefloat
    The scale value of the exponential distribution.
    
+
    
+
    Parameters:
    
+
    
+
    scalefloat
    The scale value of the exponential distribution.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    int
    A random number sampled from an exponential distribution.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> exponential_sample(10)
 24.042086039659946
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.gamma_sample(shape, scale, samples=1)[source]#
    
 
    Sample a random number according to a gamma distribution.
    
-
    
-
    Parameters#
    
-
    
-
    shapefloat
    The shape value of the gamma distribution.
    
+
    
+
    Parameters:
    
+
    
+
    shapefloat
    The shape value of the gamma distribution.
    
 
    
-
    scalefloat
    The scale value of the gamma distribution. Defaults to 1.
    
+
    scalefloat
    The scale value of the gamma distribution. Defaults to 1.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    int
    A random number sampled from an gamma distribution.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> gamma_sample(10, 2)
 21.290716894247602
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.geometric_sample(p, samples=1)[source]#
    
 
    Sample a random number according to a geometric distribution.
    
-
    
-
    Parameters#
    
-
    
-
    pfloat
    The probability of success of an individual trial. Must be between 0 and 1.
    
+
    
+
    Parameters:
    
+
    
+
    pfloat
    The probability of success of an individual trial. Must be between 0 and 1.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    int
    A random number sampled from a geometric distribution.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> geometric_sample(0.1)
 2
 
    
 
    
-
 
 
 
    
@@ -633,107 +619,104 @@ 
    Examples#credibility.
 Unlike the normal and lognormal samplers, this credible interval is an
 approximation and is not precisely defined.
    
-
    
-
    Parameters#
    
-
    
-
    lowfloat or None
    The low value of a credible interval defined by credibility.
+
    
+
    Parameters:
    
+
    
+
    lowfloat or None
    The low value of a credible interval defined by credibility.
 Must be greater than 0. Defaults to a 90% CI.
    
 
    
-
    highfloat or None
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
+
    highfloat or None
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
 
    
-
    tfloat
    The number of degrees of freedom of the t-distribution. Defaults to 20.
    
+
    tfloat
    The number of degrees of freedom of the t-distribution. Defaults to 20.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
+
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
+
    Returns:
    
+
    
 
    float
    A random number sampled from a lognormal distribution defined by
 mean and sd.
    
 
    
 
    
-
    
-
    
-
    Examples#
    
+
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> log_t_sample(1, 2, t=4)
 2.052949773846356
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.lognormal_sample(mean, sd, samples=1)[source]#
    
 
    Sample a random number according to a lognormal distribution.
    
-
    
-
    Parameters#
    
-
    
-
    meanfloat
    The mean of the lognormal distribution that is being sampled.
    
+
    
+
    Parameters:
    
+
    
+
    meanfloat
    The mean of the lognormal distribution that is being sampled.
    
 
    
-
    sdfloat
    The standard deviation of the lognormal distribution that is being sampled.
    
+
    sdfloat
    The standard deviation of the lognormal distribution that is being sampled.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    float
    A random number sampled from a lognormal distribution defined by
 mean and sd.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> lognormal_sample(0, 1)
 1.3562412406168636
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.mixture_sample(values, weights=None, relative_weights=None, samples=1, verbose=False, _multicore_tqdm_n=1, _multicore_tqdm_cores=1)[source]#
    
 
    Sample a ranom number from a mixture distribution.
    
-
    
-
    Parameters#
    
-
    
-
    valueslist or dict
    The distributions to mix. Can also be defined as a list of weights and distributions.
    
+
    
+
    Parameters:
    
+
    
+
    valueslist or dict
    The distributions to mix. Can also be defined as a list of weights and distributions.
    
 
    
-
    weightslist or None
    The weights for each distribution.
    
+
    weightslist or None
    The weights for each distribution.
    
 
    
-
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
+
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
 to sum to 1.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
-
    verbosebool
    If True, will print out statements on computational progress.
    
+
    verbosebool
    If True, will print out statements on computational progress.
    
 
    
-
    _multicore_tqdm_nint
    The total number of samples to use for printing tqdm’s interface. This is meant to only
+
    _multicore_tqdm_nint
    The total number of samples to use for printing tqdm’s interface. This is meant to only
 be used internally by squigglepy to make the progress bar printing work well for
 multicore. This parameter can be safely ignored by the user.
    
 
    
-
    _multicore_tqdm_coresint
    The total number of cores to use for printing tqdm’s interface. This is meant to only
+
    _multicore_tqdm_coresint
    The total number of cores to use for printing tqdm’s interface. This is meant to only
 be used internally by squigglepy to make the progress bar printing work well for
 multicore. This parameter can be safely ignored by the user.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    Various, based on items in values
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    Various, based on items in values
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> mixture_sample([norm(1, 2), norm(3, 4)], weights=[0.1, 0.9])
 3.183867278765718
@@ -745,189 +728,181 @@ 
    Examples#1.1041655362137777
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.normal_sample(mean, sd, samples=1)[source]#
    
 
    Sample a random number according to a normal distribution.
    
-
    
-
    Parameters#
    
-
    
-
    meanfloat
    The mean of the normal distribution that is being sampled.
    
+
    
+
    Parameters:
    
+
    
+
    meanfloat
    The mean of the normal distribution that is being sampled.
    
 
    
-
    sdfloat
    The standard deviation of the normal distribution that is being sampled.
    
+
    sdfloat
    The standard deviation of the normal distribution that is being sampled.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    float
    A random number sampled from a normal distribution defined by
 mean and sd.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> normal_sample(0, 1)
 0.30471707975443135
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.pareto_sample(shape, samples=1)[source]#
    
 
    Sample a random number according to a pareto distribution.
    
-
    
-
    Parameters#
    
-
    
-
    shapefloat
    The shape value of the pareto distribution.
    
+
    
+
    Parameters:
    
+
    
+
    shapefloat
    The shape value of the pareto distribution.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    int
    A random number sampled from an pareto distribution.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> pareto_sample(1)
 10.069666324736094
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.pert_sample(left, mode, right, lam, samples=1)[source]#
    
 
    Sample a random number according to a PERT distribution.
    
-
    
-
    Parameters#
    
-
    
-
    leftfloat
    The smallest value of the PERT distribution.
    
+
    
+
    Parameters:
    
+
    
+
    leftfloat
    The smallest value of the PERT distribution.
    
 
    
-
    modefloat
    The most common value of the PERT distribution.
    
+
    modefloat
    The most common value of the PERT distribution.
    
 
    
-
    rightfloat
    The largest value of the PERT distribution.
    
+
    rightfloat
    The largest value of the PERT distribution.
    
 
    
-
    lamfloat
    The lambda of the PERT distribution.
    
+
    lamfloat
    The lambda of the PERT distribution.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    float
    A random number sampled from a PERT distribution.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> pert_sample(1, 2, 3, 4)
 2.327625176788963
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.poisson_sample(lam, samples=1)[source]#
    
 
    Sample a random number according to a poisson distribution.
    
-
    
-
    Parameters#
    
-
    
-
    lamfloat
    The lambda value of the poisson distribution.
    
+
    
+
    Parameters:
    
+
    
+
    lamfloat
    The lambda value of the poisson distribution.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    int
    A random number sampled from a poisson distribution.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> poisson_sample(10)
 13
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.sample(dist=None, n=1, lclip=None, rclip=None, memcache=False, reload_cache=False, dump_cache_file=None, load_cache_file=None, cache_file_primary=False, verbose=None, cores=1, _multicore_tqdm_n=1, _multicore_tqdm_cores=1, _correlate_if_needed=True)[source]#
    
 
    Sample random numbers from a given distribution.
    
-
    
-
    Parameters#
    
-
    
-
    distDistribution
    The distribution to sample random number from.
    
+
    
+
    Parameters:
    
+
    
+
    distDistribution
    The distribution to sample random number from.
    
 
    
-
    nint
    The number of random numbers to sample from the distribution. Default to 1.
    
+
    nint
    The number of random numbers to sample from the distribution. Default to 1.
    
 
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
+
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
 
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
+
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
 
    
-
    memcachebool
    If True, will attempt to load the results in-memory for future calculations if
+
    memcachebool
    If True, will attempt to load the results in-memory for future calculations if
 a cache is present. Otherwise will save the results to an in-memory cache. Each cache
 will be matched based on dist. Default False.
    
 
    
-
    reload_cachebool
    If True, any existing cache will be ignored and recalculated. Default False.
    
+
    reload_cachebool
    If True, any existing cache will be ignored and recalculated. Default False.
    
 
    
-
    dump_cache_filestr or None
    If present, will write out the cache to a numpy file with this path with
+
    dump_cache_filestr or None
    If present, will write out the cache to a numpy file with this path with
 .sqlcache.npy appended to the file name.
    
 
    
-
    load_cache_filestr or None
    If present, will first attempt to load and use a cache from a file with this
+
    load_cache_filestr or None
    If present, will first attempt to load and use a cache from a file with this
 path with .sqlcache.npy appended to the file name.
    
 
    
-
    cache_file_primarybool
    If both an in-memory cache and file cache are present, the file
+
    cache_file_primarybool
    If both an in-memory cache and file cache are present, the file
 cache will be used for the cache if this is True, and the in-memory cache
 will be used otherwise. Defaults to False.
    
 
    
-
    verbosebool
    If True, will print out statements on computational progress. If False, will not.
+
    verbosebool
    If True, will print out statements on computational progress. If False, will not.
 If None (default), will be True when n is greater than or equal to 1M.
    
 
    
-
    coresint
    If 1, runs on a single core / process. If greater than 1, will run on a multiprocessing
+
    coresint
    If 1, runs on a single core / process. If greater than 1, will run on a multiprocessing
 pool with that many cores / processes.
    
 
    
-
    _multicore_tqdm_nint
    The total number of samples to use for printing tqdm’s interface. This is meant to only
+
    _multicore_tqdm_nint
    The total number of samples to use for printing tqdm’s interface. This is meant to only
 be used internally by squigglepy to make the progress bar printing work well for
 multicore. This parameter can be safely ignored by the user.
    
 
    
-
    _multicore_tqdm_coresint
    The total number of cores to use for printing tqdm’s interface. This is meant to only
+
    _multicore_tqdm_coresint
    The total number of cores to use for printing tqdm’s interface. This is meant to only
 be used internally by squigglepy to make the progress bar printing work well for
 multicore. This parameter can be safely ignored by the user.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    Various, based on dist.
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    Various, based on dist.
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> sample(norm(1, 2))
 1.592627415218455
@@ -937,7 +912,6 @@ 
    Examples#array([6.10817361, 3.        , 3.        , 3.45828454, 3.        ])
 
    
 
    
-
 
 
 
    
@@ -961,104 +935,98 @@ 
    Examples#credibility. Unlike the normal and
 lognormal samplers, this credible interval is an approximation and is
 not precisely defined.
    
-
    
-
    Parameters#
    
-
    
-
    lowfloat or None
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
    
+
    
+
    Parameters:
    
+
    
+
    lowfloat or None
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
    
 
    
-
    highfloat or None
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
+
    highfloat or None
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
 
    
-
    tfloat
    The number of degrees of freedom of the t-distribution. Defaults to 20.
    
+
    tfloat
    The number of degrees of freedom of the t-distribution. Defaults to 20.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
+
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
+
    Returns:
    
+
    
 
    float
    A random number sampled from a lognormal distribution defined by
 mean and sd.
    
 
    
 
    
-
    
-
    
-
    Examples#
    
+
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> t_sample(1, 2, t=4)
 2.7887113716855985
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.triangular_sample(left, mode, right, samples=1)[source]#
    
 
    Sample a random number according to a triangular distribution.
    
-
    
-
    Parameters#
    
-
    
-
    leftfloat
    The smallest value of the triangular distribution.
    
+
    
+
    Parameters:
    
+
    
+
    leftfloat
    The smallest value of the triangular distribution.
    
 
    
-
    modefloat
    The most common value of the triangular distribution.
    
+
    modefloat
    The most common value of the triangular distribution.
    
 
    
-
    rightfloat
    The largest value of the triangular distribution.
    
+
    rightfloat
    The largest value of the triangular distribution.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    float
    A random number sampled from a triangular distribution.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> triangular_sample(1, 2, 3)
 2.327625176788963
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.samplers.uniform_sample(low, high, samples=1)[source]#
    
 
    Sample a random number according to a uniform distribution.
    
-
    
-
    Parameters#
    
-
    
-
    lowfloat
    The smallest value the uniform distribution will return.
    
+
    
+
    Parameters:
    
+
    
+
    lowfloat
    The smallest value the uniform distribution will return.
    
 
    
-
    highfloat
    The largest value the uniform distribution will return.
    
+
    highfloat
    The largest value the uniform distribution will return.
    
 
    
-
    samplesint
    The number of samples to return.
    
+
    samplesint
    The number of samples to return.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    float
    A random number sampled from a uniform distribution between
 `low` and `high`.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> uniform_sample(0, 1)
 0.7739560485559633
 
    
 
    
-
 
 
 
diff --git a/doc/build/html/reference/squigglepy.utils.html b/doc/build/html/reference/squigglepy.utils.html
index 37d8b94..b1bb86d 100644
--- a/doc/build/html/reference/squigglepy.utils.html
+++ b/doc/build/html/reference/squigglepy.utils.html
@@ -367,27 +367,25 @@
 growth rate.
    
 
    NOTE: This only works works for numbers, arrays and distributions where all numbers
 are above 0. (Otherwise it makes no sense to talk about doubling times.)
    
-
    
-
    Parameters#
    
-
    
-
    doubling_timefloat or np.array or BaseDistribution
    The doubling time expressed in any time unit.
    
+
    
+
    Parameters:
    
+
    
+
    doubling_timefloat or np.array or BaseDistribution
    The doubling time expressed in any time unit.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
+
    Returns:
    
+
    
 
    float or np.array or ComplexDistribution
    Returns the growth rate expressed as a fraction (the percentage divided by 100).
    
 
    
 
    
-
    
-
    
-
    Examples#
    
+
+
+
    Examples
    
 
    >>> doubling_time_to_growth_rate(12)
 0.05946309435929531
 
    
 
    
-
    
 
 
 
    
@@ -395,25 +393,25 @@ 
    Examples
 squigglepy.utils.event(p)[source]#
 
    Return True with probability p and False with probability 1 - p.
    
 
    Alias for event_occurs.
    
-
    
-
    Parameters#
    
-
    
-
    pfloat
    The probability of returning True. Must be between 0 and 1.
    
+
    
+
    Parameters:
    
+
    
+
    pfloat
    The probability of returning True. Must be between 0 and 1.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    bool
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    bool
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> event(p=0.5)
 False
 
    
 
    
-
 
 
 
    
@@ -421,127 +419,120 @@ 
    Examples#
 squigglepy.utils.event_happens(p)[source]#
 
    Return True with probability p and False with probability 1 - p.
    
 
    Alias for event_occurs.
    
-
    
-
    Parameters#
    
-
    
-
    pfloat
    The probability of returning True. Must be between 0 and 1.
    
+
    
+
    Parameters:
    
+
    
+
    pfloat
    The probability of returning True. Must be between 0 and 1.
    
 
    
 
    
-
    
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> event_happens(p=0.5)
 False
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.event_occurs(p)[source]#
    
 
    Return True with probability p and False with probability 1 - p.
    
-
    
-
    Parameters#
    
-
    
-
    pfloat
    The probability of returning True. Must be between 0 and 1.
    
+
    
+
    Parameters:
    
+
    
+
    pfloat
    The probability of returning True. Must be between 0 and 1.
    
 
    
 
    
-
    
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> event_occurs(p=0.5)
 False
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.extremize(p, e)[source]#
    
 
    Extremize a prediction.
    
-
    
-
    Parameters#
    
-
    
-
    pfloat
    The prediction to extremize. Must be within 0-1.
    
+
    
+
    Parameters:
    
+
    
+
    pfloat
    The prediction to extremize. Must be within 0-1.
    
 
    
-
    efloat
    The extremization factor.
    
+
    efloat
    The extremization factor.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    float
    The extremized prediction
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> # Extremizing of 1.73 per https://arxiv.org/abs/2111.03153
 >>> extremize(p=0.7, e=1.73)
 0.875428191155692
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.flip_coin(n=1)[source]#
    
 
    Flip a coin.
    
-
    
-
    Parameters#
    
-
    
-
    nint
    The number of coins to be flipped.
    
+
    
+
    Parameters:
    
+
    
+
    nint
    The number of coins to be flipped.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    str or list
    Returns the value of each coin flip, as either “heads” or “tails”
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> flip_coin()
 'heads'
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.full_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0)[source]#
    
 
    Alias for kelly where deference is 0.
    
-
    
-
    Parameters#
    
-
    
-
    my_pricefloat
    The price (or probability) you give for the given event.
    
+
    
+
    Parameters:
    
+
    
+
    my_pricefloat
    The price (or probability) you give for the given event.
    
 
    
-
    market_pricefloat
    The price the market is giving for that event.
    
+
    market_pricefloat
    The price the market is giving for that event.
    
 
    
-
    bankrollfloat
    How much money do you have to bet? Defaults to 1.
    
+
    bankrollfloat
    How much money do you have to bet? Defaults to 1.
    
 
    
-
    resolve_datestr or None
    When will the event happen, the market resolve, and you get your money back? Used for
+
    resolve_datestr or None
    When will the event happen, the market resolve, and you get your money back? Used for
 calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
 ARR is not calculated.
    
 
    
-
    currentfloat
    How much do you already have invested in this event? Used for calculating the
+
    currentfloat
    How much do you already have invested in this event? Used for calculating the
 additional amount you should invest. Defaults to 0.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    dict
    
 
    A dict of values specifying:
      
 
    • my_price
      • 
@@ -568,9 +559,9 @@ 
      Returns#
 
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> full_kelly(my_price=0.7, market_price=0.4, bankroll=100)
 {'my_price': 0.7, 'market_price': 0.4, 'deference': 0, 'adj_price': 0.7,
  'delta_price': 0.3, 'adj_delta_price': 0.3, 'kelly': 0.5, 'target': 50.0,
@@ -578,203 +569,194 @@ 
    Examples# 'expected_roi': 0.75, 'expected_arr': None, 'resolve_date': None}
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.geomean(a, weights=None, relative_weights=None, drop_na=True)[source]#
    
 
    Calculate the geometric mean.
    
-
    
-
    Parameters#
    
-
    
-
    alist or np.array
    The values to calculate the geometric mean of.
    
+
    
+
    Parameters:
    
+
    
+
    alist or np.array
    The values to calculate the geometric mean of.
    
 
    
-
    weightslist or None
    The weights, if a weighted geometric mean is desired.
    
+
    weightslist or None
    The weights, if a weighted geometric mean is desired.
    
 
    
-
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
+
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
 to sum to 1.
    
 
    
-
    drop_naboolean
    Should NA-like values be dropped when calculating the geomean?
    
+
    drop_naboolean
    Should NA-like values be dropped when calculating the geomean?
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    float
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    float
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> geomean([1, 3, 10])
 3.1072325059538595
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.geomean_odds(a, weights=None, relative_weights=None, drop_na=True)[source]#
    
 
    Calculate the geometric mean of odds.
    
-
    
-
    Parameters#
    
-
    
-
    alist or np.array
    The probabilities to calculate the geometric mean of. These are converted to odds
+
    
+
    Parameters:
    
+
    
+
    alist or np.array
    The probabilities to calculate the geometric mean of. These are converted to odds
 before the geometric mean is taken..
    
 
    
-
    weightslist or None
    The weights, if a weighted geometric mean is desired.
    
+
    weightslist or None
    The weights, if a weighted geometric mean is desired.
    
 
    
-
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
+
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
 to sum to 1.
    
 
    
-
    drop_naboolean
    Should NA-like values be dropped when calculating the geomean?
    
+
    drop_naboolean
    Should NA-like values be dropped when calculating the geomean?
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    float
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    float
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> geomean_odds([0.1, 0.3, 0.9])
 0.42985748800076845
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.get_log_percentiles(data, percentiles=[1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99], reverse=False, display=True, digits=1)[source]#
    
 
    Print the log (base 10) of the percentiles of the data.
    
-
    
-
    Parameters#
    
-
    
-
    datalist or np.array
    The data to calculate percentiles for.
    
+
    
+
    Parameters:
    
+
    
+
    datalist or np.array
    The data to calculate percentiles for.
    
 
    
-
    percentileslist
    A list of percentiles to calculate. Must be values between 0 and 100.
    
+
    percentileslist
    A list of percentiles to calculate. Must be values between 0 and 100.
    
 
    
-
    reversebool
    If True, the percentile values are reversed (e.g., 95th and 5th percentile
+
    reversebool
    If True, the percentile values are reversed (e.g., 95th and 5th percentile
 swap values.)
    
 
    
-
    displaybool
    If True, the function returns an easy to read display.
    
+
    displaybool
    If True, the function returns an easy to read display.
    
 
    
-
    digitsint or None
    The number of digits to display (using rounding).
    
+
    digitsint or None
    The number of digits to display (using rounding).
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    dict
    A dictionary of the given percentiles. If display is true, will be str values.
 Otherwise will be float values. 10 to the power of the value gives the true percentile.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> get_percentiles(range(100), percentiles=[25, 50, 75])
 {25: 24.75, 50: 49.5, 75: 74.25}
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.get_mean_and_ci(data, credibility=90, digits=None)[source]#
    
 
    Return the mean and percentiles of the data.
    
-
    
-
    Parameters#
    
-
    
-
    datalist or np.array
    The data to calculate the mean and CI for.
    
+
    
+
    Parameters:
    
+
    
+
    datalist or np.array
    The data to calculate the mean and CI for.
    
 
    
-
    credibilityfloat
    The credibility of the interval. Must be values between 0 and 100. Default 90 for 90% CI.
    
+
    credibilityfloat
    The credibility of the interval. Must be values between 0 and 100. Default 90 for 90% CI.
    
 
    
-
    digitsint or None
    The number of digits to display (using rounding).
    
+
    digitsint or None
    The number of digits to display (using rounding).
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    dict
    A dictionary with the mean and CI.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> get_mean_and_ci(range(100))
 {'mean': 49.5, 'ci_low': 4.95, 'ci_high': 94.05}
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.get_median_and_ci(data, credibility=90, digits=None)[source]#
    
 
    Return the median and percentiles of the data.
    
-
    
-
    Parameters#
    
-
    
-
    datalist or np.array
    The data to calculate the mean and CI for.
    
+
    
+
    Parameters:
    
+
    
+
    datalist or np.array
    The data to calculate the mean and CI for.
    
 
    
-
    credibilityfloat
    The credibility of the interval. Must be values between 0 and 100. Default 90 for 90% CI.
    
+
    credibilityfloat
    The credibility of the interval. Must be values between 0 and 100. Default 90 for 90% CI.
    
 
    
-
    digitsint or None
    The number of digits to display (using rounding).
    
+
    digitsint or None
    The number of digits to display (using rounding).
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    dict
    A dictionary with the median and CI.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> get_median_and_ci(range(100))
 {'mean': 49.5, 'ci_low': 4.95, 'ci_high': 94.05}
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.get_percentiles(data, percentiles=[1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99], reverse=False, digits=None)[source]#
    
 
    Print the percentiles of the data.
    
-
    
-
    Parameters#
    
-
    
-
    datalist or np.array
    The data to calculate percentiles for.
    
+
    
+
    Parameters:
    
+
    
+
    datalist or np.array
    The data to calculate percentiles for.
    
 
    
-
    percentileslist
    A list of percentiles to calculate. Must be values between 0 and 100.
    
+
    percentileslist
    A list of percentiles to calculate. Must be values between 0 and 100.
    
 
    
-
    reversebool
    If True, the percentile values are reversed (e.g., 95th and 5th percentile
+
    reversebool
    If True, the percentile values are reversed (e.g., 95th and 5th percentile
 swap values.)
    
 
    
-
    digitsint or None
    The number of digits to display (using rounding).
    
+
    digitsint or None
    The number of digits to display (using rounding).
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    dict
    A dictionary of the given percentiles.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> get_percentiles(range(100), percentiles=[25, 50, 75])
 {25: 24.75, 50: 49.5, 75: 74.25}
 
    
 
    
-
 
 
 
    
@@ -786,54 +768,51 @@ 
    Examples#
 
    NOTE: This only works works for numbers, arrays and distributions where all numbers
 are above 0. (Otherwise it makes no sense to talk about doubling times.)
    
-
    
-
    Parameters#
    
-
    
-
    growth_ratefloat or np.array or BaseDistribution
    The growth rate expressed as a fraction (the percentage divided by 100).
    
+
    
+
    Parameters:
    
+
    
+
    growth_ratefloat or np.array or BaseDistribution
    The growth rate expressed as a fraction (the percentage divided by 100).
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
+
    Returns:
    
+
    
 
    float or np.array or ComplexDistribution
    Returns the doubling time.
    
 
    
 
    
-
    
-
    
-
    Examples#
    
+
+
    
+
    Examples
    
 
    >>> growth_rate_to_doubling_time(0.01)
 69.66071689357483
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.half_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0)[source]#
    
 
    Alias for kelly where deference is 0.5.
    
-
    
-
    Parameters#
    
-
    
-
    my_pricefloat
    The price (or probability) you give for the given event.
    
+
    
+
    Parameters:
    
+
    
+
    my_pricefloat
    The price (or probability) you give for the given event.
    
 
    
-
    market_pricefloat
    The price the market is giving for that event.
    
+
    market_pricefloat
    The price the market is giving for that event.
    
 
    
-
    bankrollfloat
    How much money do you have to bet? Defaults to 1.
    
+
    bankrollfloat
    How much money do you have to bet? Defaults to 1.
    
 
    
-
    resolve_datestr or None
    When will the event happen, the market resolve, and you get your money back? Used for
+
    resolve_datestr or None
    When will the event happen, the market resolve, and you get your money back? Used for
 calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
 ARR is not calculated.
    
 
    
-
    currentfloat
    How much do you already have invested in this event? Used for calculating the
+
    currentfloat
    How much do you already have invested in this event? Used for calculating the
 additional amount you should invest. Defaults to 0.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    dict
    
 
    A dict of values specifying:
      
 
    • my_price
      • 
@@ -860,9 +839,9 @@ 
      Returns#
 
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> half_kelly(my_price=0.7, market_price=0.4, bankroll=100)
 {'my_price': 0.7, 'market_price': 0.4, 'deference': 0.5, 'adj_price': 0.55,
  'delta_price': 0.3, 'adj_delta_price': 0.15, 'kelly': 0.25, 'target': 25.0,
@@ -870,7 +849,6 @@ 
    Examples# 'expected_roi': 0.375, 'expected_arr': None, 'resolve_date': None}
 
    
 
    
-
 
 
 
    
@@ -882,29 +860,27 @@ 
    Examples#
 squigglepy.utils.is_dist(obj)[source]#
 
    Test if a given object is a Squigglepy distribution.
    
-
    
-
    Parameters#
    
-
    
-
    objobject
    The object to test.
    
+
    
+
    Parameters:
    
+
    
+
    objobject
    The object to test.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    bool
    True, if the object is a distribution. False if not.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> is_dist(norm(0, 1))
 True
 >>> is_dist(0)
 False
 
    
 
    
-
 
 
 
    
@@ -913,22 +889,21 @@ 
    Examples#
    Test if a given object can be sampled from.
    
 
    This includes distributions, integers, floats, None,
 strings, and callables.
    
-
    
-
    Parameters#
    
-
    
-
    objobject
    The object to test.
    
+
    
+
    Parameters:
    
+
    
+
    objobject
    The object to test.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
+
    Returns:
    
+
    
 
    bool
    True, if the object can be sampled from. False if not.
    
 
    
 
    
-
    
-
    
-
    Examples#
    
+
+
    
+
    Examples
    
 
    >>> is_sampleable(norm(0, 1))
 True
 >>> is_sampleable(0)
@@ -937,37 +912,35 @@ 
    Examples#False
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.kelly(my_price, market_price, deference=0, bankroll=1, resolve_date=None, current=0)[source]#
    
 
    Calculate the Kelly criterion.
    
-
    
-
    Parameters#
    
-
    
-
    my_pricefloat
    The price (or probability) you give for the given event.
    
+
    
+
    Parameters:
    
+
    
+
    my_pricefloat
    The price (or probability) you give for the given event.
    
 
    
-
    market_pricefloat
    The price the market is giving for that event.
    
+
    market_pricefloat
    The price the market is giving for that event.
    
 
    
-
    deferencefloat
    How much deference (or weight) do you give the market price? Use 0.5 for half Kelly
+
    deferencefloat
    How much deference (or weight) do you give the market price? Use 0.5 for half Kelly
 and 0.75 for quarter Kelly. Defaults to 0, which is full Kelly.
    
 
    
-
    bankrollfloat
    How much money do you have to bet? Defaults to 1.
    
+
    bankrollfloat
    How much money do you have to bet? Defaults to 1.
    
 
    
-
    resolve_datestr or None
    When will the event happen, the market resolve, and you get your money back? Used for
+
    resolve_datestr or None
    When will the event happen, the market resolve, and you get your money back? Used for
 calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
 ARR is not calculated.
    
 
    
-
    currentfloat
    How much do you already have invested in this event? Used for calculating the
+
    currentfloat
    How much do you already have invested in this event? Used for calculating the
 additional amount you should invest. Defaults to 0.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    dict
    
 
    A dict of values specifying:
      
 
    • my_price
      • 
@@ -994,9 +967,9 @@ 
      Returns#
 
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> kelly(my_price=0.7, market_price=0.4, deference=0.5, bankroll=100)
 {'my_price': 0.7, 'market_price': 0.4, 'deference': 0.5, 'adj_price': 0.55,
  'delta_price': 0.3, 'adj_delta_price': 0.15, 'kelly': 0.25, 'target': 25.0,
@@ -1004,7 +977,6 @@ 
    Examples# 'expected_roi': 0.375, 'expected_arr': None, 'resolve_date': None}
 
    
 
    
-
 
 
 
    
@@ -1013,36 +985,35 @@ 
    Examples#
    Return probability of success on next trial given Laplace’s law of succession.
    
 
    Also can be used to calculate a time-invariant version defined in
 https://www.lesswrong.com/posts/wE7SK8w8AixqknArs/a-time-invariant-version-of-laplace-s-rule
    
-
    
-
    Parameters#
    
-
    
-
    sint
    The number of successes among n past trials or among time_passed amount of time.
    
+
    
+
    Parameters:
    
+
    
+
    sint
    The number of successes among n past trials or among time_passed amount of time.
    
 
    
-
    nint or None
    The number of trials that contain the successes (and/or failures). Leave as None if
+
    nint or None
    The number of trials that contain the successes (and/or failures). Leave as None if
 time-invariant mode is desired.
    
 
    
-
    time_passedfloat or None
    The amount of time that has passed when the successes (and/or failures) occured for
+
    time_passedfloat or None
    The amount of time that has passed when the successes (and/or failures) occured for
 calculating a time-invariant Laplace.
    
 
    
-
    time_remainingfloat or None
    We are calculating the likelihood of observing at least one success over this time
+
    time_remainingfloat or None
    We are calculating the likelihood of observing at least one success over this time
 period.
    
 
    
-
    time_fixedbool
    This should be False if the time period is variable - that is, if the time period
+
    time_fixedbool
    This should be False if the time period is variable - that is, if the time period
 was chosen specifically to include the most recent success. Otherwise the time period
 is fixed and this should be True. Defaults to False.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
+
    Returns:
    
+
    
 
    float
    The probability of at least one success in the next trial or time_remaining amount
 of time.
    
 
    
 
    
-
    
-
    
-
    Examples#
    
+
+
    
+
    Examples
    
 
    >>> # The sun has risen the past 100,000 days. What are the odds it rises again tomorrow?
 >>> laplace(s=100*K, n=100*K)
 0.999990000199996
@@ -1052,144 +1023,136 @@ 
    Examples#0.012820512820512664
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.normalize(lst)[source]#
    
 
    Normalize a list to sum to 1.
    
-
    
-
    Parameters#
    
-
    
-
    lstlist
    The list to normalize.
    
+
    
+
    Parameters:
    
+
    
+
    lstlist
    The list to normalize.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    list
    A list where each value is normalized such that the list sums to 1.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> normalize([0.1, 0.2, 0.2])
 [0.2, 0.4, 0.4]
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.odds_to_p(odds)[source]#
    
 
    Calculate the probability from given decimal odds.
    
-
    
-
    Parameters#
    
-
    
-
    oddsfloat
    The decimal odds to calculate the probability for.
    
+
    
+
    Parameters:
    
+
    
+
    oddsfloat
    The decimal odds to calculate the probability for.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    float
    Probability
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> odds_to_p(0.1)
 0.09090909090909091
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.one_in(p, digits=0, verbose=True)[source]#
    
 
    Convert a probability into “1 in X” notation.
    
-
    
-
    Parameters#
    
-
    
-
    pfloat
    The probability to convert.
    
+
    
+
    Parameters:
    
+
    
+
    pfloat
    The probability to convert.
    
 
    
-
    digitsint
    The number of digits to round the result to. Defaults to 0. If digits
+
    digitsint
    The number of digits to round the result to. Defaults to 0. If digits
 is 0, the result will be converted to int instead of float.
    
 
    
-
    verboselogical
    If True, will return a string with “1 in X”. If False, will just return X.
    
+
    verboselogical
    If True, will return a string with “1 in X”. If False, will just return X.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    str if verbose is True. Otherwise, int if digits is 0 or float if digits > 0.
    
-
    
-
    
-
    Examples#
    
+
    
+
    Returns:
    
+
    
+
    str if verbose is True. Otherwise, int if digits is 0 or float if digits > 0.
    
+
    
+
    
+
    
+
    Examples
    
 
    >>> one_in(0.1)
 "1 in 10"
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.p_to_odds(p)[source]#
    
 
    Calculate the decimal odds from a given probability.
    
-
    
-
    Parameters#
    
-
    
-
    pfloat
    The probability to calculate decimal odds for. Must be between 0 and 1.
    
+
    
+
    Parameters:
    
+
    
+
    pfloat
    The probability to calculate decimal odds for. Must be between 0 and 1.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    float
    Decimal odds
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> p_to_odds(0.1)
 0.1111111111111111
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.quarter_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0)[source]#
    
 
    Alias for kelly where deference is 0.75.
    
-
    
-
    Parameters#
    
-
    
-
    my_pricefloat
    The price (or probability) you give for the given event.
    
+
    
+
    Parameters:
    
+
    
+
    my_pricefloat
    The price (or probability) you give for the given event.
    
 
    
-
    market_pricefloat
    The price the market is giving for that event.
    
+
    market_pricefloat
    The price the market is giving for that event.
    
 
    
-
    bankrollfloat
    How much money do you have to bet? Defaults to 1.
    
+
    bankrollfloat
    How much money do you have to bet? Defaults to 1.
    
 
    
-
    resolve_datestr or None
    When will the event happen, the market resolve, and you get your money back? Used for
+
    resolve_datestr or None
    When will the event happen, the market resolve, and you get your money back? Used for
 calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
 ARR is not calculated.
    
 
    
-
    currentfloat
    How much do you already have invested in this event? Used for calculating the
+
    currentfloat
    How much do you already have invested in this event? Used for calculating the
 additional amount you should invest. Defaults to 0.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    dict
    
 
    A dict of values specifying:
      
 
    • my_price
      • 
@@ -1216,9 +1179,9 @@ 
      Returns#
 
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> quarter_kelly(my_price=0.7, market_price=0.4, bankroll=100)
 {'my_price': 0.7, 'market_price': 0.4, 'deference': 0.75, 'adj_price': 0.48,
  'delta_price': 0.3, 'adj_delta_price': 0.08, 'kelly': 0.125, 'target': 12.5,
@@ -1226,37 +1189,34 @@ 
    Examples# 'expected_roi': 0.188, 'expected_arr': None, 'resolve_date': None}
 
    
 
    
-
 
 
 
    
 
    
 squigglepy.utils.roll_die(sides, n=1)[source]#
    
 
    Roll a die.
    
-
    
-
    Parameters#
    
-
    
-
    sidesint
    The number of sides of the die that is rolled.
    
+
    
+
    Parameters:
    
+
    
+
    sidesint
    The number of sides of the die that is rolled.
    
 
    
-
    nint
    The number of dice to be rolled.
    
+
    nint
    The number of dice to be rolled.
    
 
    
 
    
-
    
-
    
-
    Returns#
    
-
    
+
    
+
    Returns:
    
+
    
 
    int or list
    Returns the value of each die roll.
    
 
    
 
    
-
-
    
-
    Examples#
    
+
    
+
    
+
    Examples
    
 
    >>> set_seed(42)
 >>> roll_die(6)
 5
 
    
 
    
-
 
 
 
diff --git a/doc/build/html/searchindex.js b/doc/build/html/searchindex.js
index 8cb21c2..49ba701 100644
--- a/doc/build/html/searchindex.js
+++ b/doc/build/html/searchindex.js
@@ -1 +1 @@
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[[3, "module-squigglepy"]], "Submodules": [[3, "submodules"]], "squigglepy.bayes module": [[4, "module-squigglepy.bayes"]], "squigglepy.correlation module": [[5, "module-squigglepy.correlation"]], "squigglepy.distributions module": [[6, "module-squigglepy.distributions"]], "squigglepy.numbers module": [[7, "module-squigglepy.numbers"]], "squigglepy.rng module": [[8, "module-squigglepy.rng"]], "squigglepy.samplers module": [[9, "module-squigglepy.samplers"]], "squigglepy.utils module": [[10, "module-squigglepy.utils"]], "squigglepy.version module": [[11, "module-squigglepy.version"]], "Examples": [[12, "examples"]], "Piano tuners example": [[12, "piano-tuners-example"]], "Distributions": [[12, "distributions"]], "Additional features": [[12, "additional-features"]], "Example: Rolling a die": [[12, "example-rolling-a-die"]], "Bayesian inference": [[12, "bayesian-inference"]], "Example: Alarm net": [[12, "example-alarm-net"]], "Example: A demonstration of the Monty Hall Problem": [[12, "example-a-demonstration-of-the-monty-hall-problem"]], "Example: More complex coin/dice interactions": [[12, "example-more-complex-coin-dice-interactions"]], "Kelly betting": [[12, "kelly-betting"]], "More examples": [[12, "more-examples"]]}, "indexentries": {"module": [[3, "module-squigglepy"], [4, "module-squigglepy.bayes"], [5, "module-squigglepy.correlation"], [6, "module-squigglepy.distributions"], [7, "module-squigglepy.numbers"], [8, "module-squigglepy.rng"], [9, "module-squigglepy.samplers"], [10, "module-squigglepy.utils"], [11, "module-squigglepy.version"]], "squigglepy": [[3, "module-squigglepy"]], "average() (in module squigglepy.bayes)": [[4, "squigglepy.bayes.average"]], "bayesnet() (in module squigglepy.bayes)": [[4, "squigglepy.bayes.bayesnet"]], "simple_bayes() (in module squigglepy.bayes)": [[4, "squigglepy.bayes.simple_bayes"]], "squigglepy.bayes": [[4, "module-squigglepy.bayes"]], "update() (in module squigglepy.bayes)": [[4, "squigglepy.bayes.update"]], "correlationgroup (class in squigglepy.correlation)": [[5, "squigglepy.correlation.CorrelationGroup"]], "correlate() (in module squigglepy.correlation)": [[5, "squigglepy.correlation.correlate"]], "correlated_dists (squigglepy.correlation.correlationgroup attribute)": [[5, "squigglepy.correlation.CorrelationGroup.correlated_dists"]], "correlation_matrix (squigglepy.correlation.correlationgroup attribute)": [[5, "squigglepy.correlation.CorrelationGroup.correlation_matrix"]], "correlation_tolerance (squigglepy.correlation.correlationgroup attribute)": [[5, "squigglepy.correlation.CorrelationGroup.correlation_tolerance"]], "has_sufficient_sample_diversity() (squigglepy.correlation.correlationgroup method)": [[5, "squigglepy.correlation.CorrelationGroup.has_sufficient_sample_diversity"]], "induce_correlation() (squigglepy.correlation.correlationgroup method)": [[5, "squigglepy.correlation.CorrelationGroup.induce_correlation"]], "min_unique_samples (squigglepy.correlation.correlationgroup attribute)": [[5, "squigglepy.correlation.CorrelationGroup.min_unique_samples"]], "squigglepy.correlation": [[5, "module-squigglepy.correlation"]], "basedistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.BaseDistribution"]], "bernoullidistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.BernoulliDistribution"]], "betadistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.BetaDistribution"]], "binomialdistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.BinomialDistribution"]], "categoricaldistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.CategoricalDistribution"]], "chisquaredistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.ChiSquareDistribution"]], "complexdistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.ComplexDistribution"]], "compositedistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.CompositeDistribution"]], "constantdistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.ConstantDistribution"]], "continuousdistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.ContinuousDistribution"]], "discretedistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.DiscreteDistribution"]], "exponentialdistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.ExponentialDistribution"]], "gammadistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.GammaDistribution"]], "geometricdistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.GeometricDistribution"]], "logtdistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.LogTDistribution"]], "lognormaldistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.LognormalDistribution"]], "mixturedistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.MixtureDistribution"]], "normaldistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.NormalDistribution"]], "operabledistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.OperableDistribution"]], "pertdistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.PERTDistribution"]], "paretodistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.ParetoDistribution"]], "poissondistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.PoissonDistribution"]], "tdistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.TDistribution"]], "triangulardistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.TriangularDistribution"]], "uniformdistribution (class in squigglepy.distributions)": [[6, "squigglepy.distributions.UniformDistribution"]], "bernoulli() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.bernoulli"]], "beta() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.beta"]], "binomial() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.binomial"]], "chisquare() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.chisquare"]], "clip() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.clip"]], "const() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.const"]], "discrete() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.discrete"]], "dist_ceil() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.dist_ceil"]], "dist_exp() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.dist_exp"]], "dist_floor() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.dist_floor"]], "dist_fn() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.dist_fn"]], "dist_log() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.dist_log"]], "dist_max() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.dist_max"]], "dist_min() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.dist_min"]], "dist_round() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.dist_round"]], "exponential() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.exponential"]], "gamma() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.gamma"]], "geometric() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.geometric"]], "inf0() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.inf0"]], "lclip() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.lclip"]], "log_tdist() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.log_tdist"]], "lognorm() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.lognorm"]], "mixture() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.mixture"]], "norm() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.norm"]], "pareto() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.pareto"]], "pert() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.pert"]], "plot() (squigglepy.distributions.operabledistribution method)": [[6, "squigglepy.distributions.OperableDistribution.plot"]], "poisson() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.poisson"]], "rclip() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.rclip"]], "squigglepy.distributions": [[6, "module-squigglepy.distributions"]], "tdist() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.tdist"]], "to() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.to"]], "triangular() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.triangular"]], "uniform() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.uniform"]], "zero_inflated() (in module squigglepy.distributions)": [[6, "squigglepy.distributions.zero_inflated"]], "squigglepy.numbers": [[7, "module-squigglepy.numbers"]], "set_seed() (in module squigglepy.rng)": [[8, "squigglepy.rng.set_seed"]], "squigglepy.rng": [[8, "module-squigglepy.rng"]], "bernoulli_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.bernoulli_sample"]], "beta_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.beta_sample"]], "binomial_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.binomial_sample"]], "chi_square_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.chi_square_sample"]], "discrete_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.discrete_sample"]], "exponential_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.exponential_sample"]], "gamma_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.gamma_sample"]], "geometric_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.geometric_sample"]], "log_t_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.log_t_sample"]], "lognormal_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.lognormal_sample"]], "mixture_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.mixture_sample"]], "normal_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.normal_sample"]], "pareto_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.pareto_sample"]], "pert_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.pert_sample"]], "poisson_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.poisson_sample"]], "sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.sample"]], "sample_correlated_group() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.sample_correlated_group"]], "squigglepy.samplers": [[9, "module-squigglepy.samplers"]], "t_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.t_sample"]], "triangular_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.triangular_sample"]], "uniform_sample() (in module squigglepy.samplers)": [[9, "squigglepy.samplers.uniform_sample"]], "doubling_time_to_growth_rate() (in module squigglepy.utils)": [[10, "squigglepy.utils.doubling_time_to_growth_rate"]], "event() (in module squigglepy.utils)": [[10, "squigglepy.utils.event"]], "event_happens() (in module squigglepy.utils)": [[10, "squigglepy.utils.event_happens"]], "event_occurs() (in module squigglepy.utils)": [[10, "squigglepy.utils.event_occurs"]], "extremize() (in module squigglepy.utils)": [[10, "squigglepy.utils.extremize"]], "flip_coin() (in module squigglepy.utils)": [[10, "squigglepy.utils.flip_coin"]], "full_kelly() (in module squigglepy.utils)": [[10, "squigglepy.utils.full_kelly"]], "geomean() (in module squigglepy.utils)": [[10, "squigglepy.utils.geomean"]], "geomean_odds() (in module squigglepy.utils)": [[10, "squigglepy.utils.geomean_odds"]], "get_log_percentiles() (in module squigglepy.utils)": [[10, "squigglepy.utils.get_log_percentiles"]], "get_mean_and_ci() (in module squigglepy.utils)": [[10, "squigglepy.utils.get_mean_and_ci"]], "get_median_and_ci() (in module squigglepy.utils)": [[10, "squigglepy.utils.get_median_and_ci"]], "get_percentiles() (in module squigglepy.utils)": [[10, "squigglepy.utils.get_percentiles"]], "growth_rate_to_doubling_time() (in module squigglepy.utils)": [[10, "squigglepy.utils.growth_rate_to_doubling_time"]], "half_kelly() (in module squigglepy.utils)": [[10, "squigglepy.utils.half_kelly"]], "is_continuous_dist() (in module squigglepy.utils)": [[10, "squigglepy.utils.is_continuous_dist"]], "is_dist() (in module squigglepy.utils)": [[10, "squigglepy.utils.is_dist"]], "is_sampleable() (in module squigglepy.utils)": [[10, "squigglepy.utils.is_sampleable"]], "kelly() (in module squigglepy.utils)": [[10, "squigglepy.utils.kelly"]], "laplace() (in module squigglepy.utils)": [[10, "squigglepy.utils.laplace"]], "normalize() (in module squigglepy.utils)": [[10, "squigglepy.utils.normalize"]], "odds_to_p() (in module squigglepy.utils)": [[10, "squigglepy.utils.odds_to_p"]], "one_in() (in module squigglepy.utils)": [[10, "squigglepy.utils.one_in"]], "p_to_odds() (in module squigglepy.utils)": [[10, "squigglepy.utils.p_to_odds"]], "quarter_kelly() (in module squigglepy.utils)": [[10, "squigglepy.utils.quarter_kelly"]], "roll_die() (in module squigglepy.utils)": [[10, "squigglepy.utils.roll_die"]], "squigglepy.utils": [[10, "module-squigglepy.utils"]], "squigglepy.version": [[11, "module-squigglepy.version"]]}})
\ No newline at end of file
diff --git a/doc/source/conf.py b/doc/source/conf.py
index 372fb64..ebbe282 100644
--- a/doc/source/conf.py
+++ b/doc/source/conf.py
@@ -42,6 +42,7 @@
     "sphinx.ext.autodoc",
     "sphinx.ext.imgmath",
     "sphinx.ext.viewcode",
+    "numpydoc",
 ]
 
 # Add any paths that contain templates here, relative to this directory.
@@ -176,3 +177,5 @@
 
 
 # -- Extension configuration -------------------------------------------------
+
+numpydoc_class_members_toctree = False
diff --git a/doc/source/index.rst b/doc/source/index.rst
index 89b8383..3461183 100644
--- a/doc/source/index.rst
+++ b/doc/source/index.rst
@@ -47,3 +47,5 @@ Acknowledgements
    distributions.
 -  Thanks to Dawn Drescher for coming up with the idea to use ``~`` as a
    shorthand for ``sample``, as well as helping me implement it.
+
+.. autosummary::
diff --git a/pyproject.toml b/pyproject.toml
index d4e93d2..b35de76 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -23,6 +23,7 @@ pathos = "^0.3.0"
 msgspec = "^0.15.1"
 matplotlib = { version = "^3.7.1", optional = true }
 pandas = { version = "^2.0.2", optional = true }
+pydata-sphinx-theme = "^0.14.3"
 
 
 [tool.poetry.group.dev.dependencies]

From ffd514253624bc8abdef800ef1dac01aebfe345e Mon Sep 17 00:00:00 2001
From: Michael Dickens 
Date: Thu, 23 Nov 2023 13:39:57 -0800
Subject: [PATCH 7/7] docs: don't track build/

---
 .gitignore                                    |     1 +
 doc/build/doctrees/README.doctree             |   Bin 50071 -> 0 bytes
 doc/build/doctrees/environment.pickle         |   Bin 1521208 -> 0 bytes
 doc/build/doctrees/examples.doctree           |   Bin 41989 -> 0 bytes
 doc/build/doctrees/index.doctree              |   Bin 9496 -> 0 bytes
 doc/build/doctrees/installation.doctree       |   Bin 3196 -> 0 bytes
 doc/build/doctrees/reference/modules.doctree  |   Bin 2791 -> 0 bytes
 .../reference/squigglepy.bayes.doctree        |   Bin 57815 -> 0 bytes
 .../reference/squigglepy.correlation.doctree  |   Bin 61358 -> 0 bytes
 .../squigglepy.distributions.doctree          |   Bin 390640 -> 0 bytes
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 doc/build/html/.buildinfo                     |     4 -
 doc/build/html/README.html                    |   893 --
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 doc/build/html/_modules/squigglepy/bayes.html |   804 --
 .../html/_modules/squigglepy/correlation.html |   744 --
 .../_modules/squigglepy/distributions.html    |  2279 ----
 doc/build/html/_modules/squigglepy/rng.html   |   389 -
 .../html/_modules/squigglepy/samplers.html    |  1560 ---
 doc/build/html/_modules/squigglepy/utils.html |  1668 ---
 doc/build/html/_sources/README.rst.txt        |   531 -
 doc/build/html/_sources/examples.rst.txt      |   468 -
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 doc/build/html/_sources/installation.rst.txt  |    12 -
 .../html/_sources/reference/modules.rst.txt   |     7 -
 .../reference/squigglepy.bayes.rst.txt        |     7 -
 .../reference/squigglepy.correlation.rst.txt  |     7 -
 .../squigglepy.distributions.rst.txt          |     7 -
 .../reference/squigglepy.numbers.rst.txt      |     7 -
 .../_sources/reference/squigglepy.rng.rst.txt |     7 -
 .../_sources/reference/squigglepy.rst.txt     |    22 -
 .../reference/squigglepy.samplers.rst.txt     |     7 -
 .../reference/squigglepy.squigglepy.rst.txt   |    78 -
 .../reference/squigglepy.tests.rst.txt        |    86 -
 .../reference/squigglepy.utils.rst.txt        |     7 -
 .../reference/squigglepy.version.rst.txt      |     7 -
 doc/build/html/_sources/usage.rst.txt         |   476 -
 doc/build/html/_static/alabaster.css          |   703 --
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-
    Squigglepy: Implementation of Squiggle in Python#
    
-
    Squiggle is a “simple
-programming language for intuitive probabilistic estimation”. It serves
-as its own standalone programming language with its own syntax, but it
-is implemented in JavaScript. I like the features of Squiggle and intend
-to use it frequently, but I also sometimes want to use similar
-functionalities in Python, especially alongside other Python statistical
-programming packages like Numpy, Pandas, and Matplotlib. The
-squigglepy package here implements many Squiggle-like
-functionalities in Python.
    
-
    
-
    Installation#
    
-
    pip install squigglepy
-
    
-
    
-
    For plotting support, you can also use the plots extra:
    
-
    pip install squigglepy[plots]
-
    
-
    
-
    
-
    
-
    Usage#
    
-
    
-
    Piano Tuners Example#
    
-
    Here’s the Squigglepy implementation of the example from Squiggle
-Docs:
    
-
    import squigglepy as sq
-import numpy as np
-import matplotlib.pyplot as plt
-from squigglepy.numbers import K, M
-from pprint import pprint
-
-pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)  # This means that you're 90% confident the value is between 8.1 and 8.4 Million.
-pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01  # We assume there are almost no people with multiple pianos
-pianos_per_piano_tuner = sq.to(2*K, 50*K)
-piano_tuners_per_piano = 1 / pianos_per_piano_tuner
-total_tuners_in_2022 = pop_of_ny_2022 * pct_of_pop_w_pianos * piano_tuners_per_piano
-samples = total_tuners_in_2022 @ 1000  # Note: `@ 1000` is shorthand to get 1000 samples
-
-# Get mean and SD
-print('Mean: {}, SD: {}'.format(round(np.mean(samples), 2),
-                                round(np.std(samples), 2)))
-
-# Get percentiles
-pprint(sq.get_percentiles(samples, digits=0))
-
-# Histogram
-plt.hist(samples, bins=200)
-plt.show()
-
-# Shorter histogram
-total_tuners_in_2022.plot()
-
    
-
    
-
    And the version from the Squiggle doc that incorporates time:
    
-
    import squigglepy as sq
-from squigglepy.numbers import K, M
-
-pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)
-pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01
-pianos_per_piano_tuner = sq.to(2*K, 50*K)
-piano_tuners_per_piano = 1 / pianos_per_piano_tuner
-
-def pop_at_time(t):  # t = Time in years after 2022
-    avg_yearly_pct_change = sq.to(-0.01, 0.05)  # We're expecting NYC to continuously grow with an mean of roughly between -1% and +4% per year
-    return pop_of_ny_2022 * ((avg_yearly_pct_change + 1) ** t)
-
-def total_tuners_at_time(t):
-    return pop_at_time(t) * pct_of_pop_w_pianos * piano_tuners_per_piano
-
-# Get total piano tuners at 2030
-sq.get_percentiles(total_tuners_at_time(2030-2022) @ 1000)
-
    
-
    
-
    WARNING: Be careful about dividing by K, M, etc. 1/2*K =
-500 in Python. Use 1/(2*K) instead to get the expected outcome.
    
-
    WARNING: Be careful about using K to get sample counts. Use
-sq.norm(2, 3) @ (2*K)… sq.norm(2, 3) @ 2*K will return only
-two samples, multiplied by 1000.
    
-
    
-
    
-
    Distributions#
    
-
    import squigglepy as sq
-
-# Normal distribution
-sq.norm(1, 3)  # 90% interval from 1 to 3
-
-# Distribution can be sampled with mean and sd too
-sq.norm(mean=0, sd=1)
-
-# Shorthand to get one sample
-~sq.norm(1, 3)
-
-# Shorthand to get more than one sample
-sq.norm(1, 3) @ 100
-
-# Longhand version to get more than one sample
-sq.sample(sq.norm(1, 3), n=100)
-
-# Nice progress reporter
-sq.sample(sq.norm(1, 3), n=1000, verbose=True)
-
-# Other distributions exist
-sq.lognorm(1, 10)
-sq.tdist(1, 10, t=5)
-sq.triangular(1, 2, 3)
-sq.pert(1, 2, 3, lam=2)
-sq.binomial(p=0.5, n=5)
-sq.beta(a=1, b=2)
-sq.bernoulli(p=0.5)
-sq.poisson(10)
-sq.chisquare(2)
-sq.gamma(3, 2)
-sq.pareto(1)
-sq.exponential(scale=1)
-sq.geometric(p=0.5)
-
-# Discrete sampling
-sq.discrete({'A': 0.1, 'B': 0.9})
-
-# Can return integers
-sq.discrete({0: 0.1, 1: 0.3, 2: 0.3, 3: 0.15, 4: 0.15})
-
-# Alternate format (also can be used to return more complex objects)
-sq.discrete([[0.1,  0],
-             [0.3,  1],
-             [0.3,  2],
-             [0.15, 3],
-             [0.15, 4]])
-
-sq.discrete([0, 1, 2]) # No weights assumes equal weights
-
-# You can mix distributions together
-sq.mixture([sq.norm(1, 3),
-            sq.norm(4, 10),
-            sq.lognorm(1, 10)],  # Distributions to mix
-           [0.3, 0.3, 0.4])     # These are the weights on each distribution
-
-# This is equivalent to the above, just a different way of doing the notation
-sq.mixture([[0.3, sq.norm(1,3)],
-            [0.3, sq.norm(4,10)],
-            [0.4, sq.lognorm(1,10)]])
-
-# Make a zero-inflated distribution
-# 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`.
-sq.zero_inflated(0.6, sq.norm(1, 2))
-
    
-
    
-
    
-
    
-
    Additional Features#
    
-
    import squigglepy as sq
-
-# You can add and subtract distributions
-(sq.norm(1,3) + sq.norm(4,5)) @ 100
-(sq.norm(1,3) - sq.norm(4,5)) @ 100
-(sq.norm(1,3) * sq.norm(4,5)) @ 100
-(sq.norm(1,3) / sq.norm(4,5)) @ 100
-
-# You can also do math with numbers
-~((sq.norm(sd=5) + 2) * 2)
-~(-sq.lognorm(0.1, 1) * sq.pareto(1) / 10)
-
-# You can change the CI from 90% (default) to 80%
-sq.norm(1, 3, credibility=80)
-
-# You can clip
-sq.norm(0, 3, lclip=0, rclip=5) # Sample norm with a 90% CI from 0-3, but anything lower than 0 gets clipped to 0 and anything higher than 5 gets clipped to 5.
-
-# You can also clip with a function, and use pipes
-sq.norm(0, 3) >> sq.clip(0, 5)
-
-# You can correlate continuous distributions
-a, b = sq.uniform(-1, 1), sq.to(0, 3)
-a, b = sq.correlate((a, b), 0.5)  # Correlate a and b with a correlation of 0.5
-# You can even pass your own correlation matrix!
-a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]])
-
    
-
    
-
    
-
    Example: Rolling a Die#
    
-
    An example of how to use distributions to build tools:
    
-
    import squigglepy as sq
-
-def roll_die(sides, n=1):
-    return sq.discrete(list(range(1, sides + 1))) @ n if sides > 0 else None
-
-roll_die(sides=6, n=10)
-# [2, 6, 5, 2, 6, 2, 3, 1, 5, 2]
-
    
-
    
-
    This is already included standard in the utils of this package. Use
-sq.roll_die.
    
-
    
-
    
-
    
-
    Bayesian inference#
    
-
    1% of women at age forty who participate in routine screening have
-breast cancer. 80% of women with breast cancer will get positive
-mammographies. 9.6% of women without breast cancer will also get
-positive mammographies.
    
-
    A woman in this age group had a positive mammography in a routine
-screening. What is the probability that she actually has breast cancer?
    
-
    We can approximate the answer with a Bayesian network (uses rejection
-sampling):
    
-
    import squigglepy as sq
-from squigglepy import bayes
-from squigglepy.numbers import M
-
-def mammography(has_cancer):
-    return sq.event(0.8 if has_cancer else 0.096)
-
-def define_event():
-    cancer = ~sq.bernoulli(0.01)
-    return({'mammography': mammography(cancer),
-            'cancer': cancer})
-
-bayes.bayesnet(define_event,
-               find=lambda e: e['cancer'],
-               conditional_on=lambda e: e['mammography'],
-               n=1*M)
-# 0.07723995880535531
-
    
-
    
-
    Or if we have the information immediately on hand, we can directly
-calculate it. Though this doesn’t work for very complex stuff.
    
-
    from squigglepy import bayes
-bayes.simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096)
-# 0.07763975155279504
-
    
-
    
-
    You can also make distributions and update them:
    
-
    import matplotlib.pyplot as plt
-import squigglepy as sq
-from squigglepy import bayes
-from squigglepy.numbers import K
-import numpy as np
-
-print('Prior')
-prior = sq.norm(1,5)
-prior_samples = prior @ (10*K)
-plt.hist(prior_samples, bins = 200)
-plt.show()
-print(sq.get_percentiles(prior_samples))
-print('Prior Mean: {} SD: {}'.format(np.mean(prior_samples), np.std(prior_samples)))
-print('-')
-
-print('Evidence')
-evidence = sq.norm(2,3)
-evidence_samples = evidence @ (10*K)
-plt.hist(evidence_samples, bins = 200)
-plt.show()
-print(sq.get_percentiles(evidence_samples))
-print('Evidence Mean: {} SD: {}'.format(np.mean(evidence_samples), np.std(evidence_samples)))
-print('-')
-
-print('Posterior')
-posterior = bayes.update(prior, evidence)
-posterior_samples = posterior @ (10*K)
-plt.hist(posterior_samples, bins = 200)
-plt.show()
-print(sq.get_percentiles(posterior_samples))
-print('Posterior Mean: {} SD: {}'.format(np.mean(posterior_samples), np.std(posterior_samples)))
-
-print('Average')
-average = bayes.average(prior, evidence)
-average_samples = average @ (10*K)
-plt.hist(average_samples, bins = 200)
-plt.show()
-print(sq.get_percentiles(average_samples))
-print('Average Mean: {} SD: {}'.format(np.mean(average_samples), np.std(average_samples)))
-
    
-
    
-
    
-
    Example: Alarm net#
    
-
    This is the alarm network from Bayesian Artificial Intelligence -
-Section
-2.5.1:
    
-
    
-
    Assume your house has an alarm system against burglary.
    
-
    You live in the seismically active area and the alarm system can get
-occasionally set off by an earthquake.
    
-
    You have two neighbors, Mary and John, who do not know each other. If
-they hear the alarm they call you, but this is not guaranteed.
    
-
    The chance of a burglary on a particular day is 0.1%. The chance of
-an earthquake on a particular day is 0.2%.
    
-
    The alarm will go off 95% of the time with both a burglary and an
-earthquake, 94% of the time with just a burglary, 29% of the time
-with just an earthquake, and 0.1% of the time with nothing (total
-false alarm).
    
-
    John will call you 90% of the time when the alarm goes off. But on 5%
-of the days, John will just call to say “hi”. Mary will call you 70%
-of the time when the alarm goes off. But on 1% of the days, Mary will
-just call to say “hi”.
    
-
    
-
    import squigglepy as sq
-from squigglepy import bayes
-from squigglepy.numbers import M
-
-def p_alarm_goes_off(burglary, earthquake):
-    if burglary and earthquake:
-        return 0.95
-    elif burglary and not earthquake:
-        return 0.94
-    elif not burglary and earthquake:
-        return 0.29
-    elif not burglary and not earthquake:
-        return 0.001
-
-def p_john_calls(alarm_goes_off):
-    return 0.9 if alarm_goes_off else 0.05
-
-def p_mary_calls(alarm_goes_off):
-    return 0.7 if alarm_goes_off else 0.01
-
-def define_event():
-    burglary_happens = sq.event(p=0.001)
-    earthquake_happens = sq.event(p=0.002)
-    alarm_goes_off = sq.event(p_alarm_goes_off(burglary_happens, earthquake_happens))
-    john_calls = sq.event(p_john_calls(alarm_goes_off))
-    mary_calls = sq.event(p_mary_calls(alarm_goes_off))
-    return {'burglary': burglary_happens,
-            'earthquake': earthquake_happens,
-            'alarm_goes_off': alarm_goes_off,
-            'john_calls': john_calls,
-            'mary_calls': mary_calls}
-
-# What are the chances that both John and Mary call if an earthquake happens?
-bayes.bayesnet(define_event,
-               n=1*M,
-               find=lambda e: (e['mary_calls'] and e['john_calls']),
-               conditional_on=lambda e: e['earthquake'])
-# Result will be ~0.19, though it varies because it is based on a random sample.
-# This also may take a minute to run.
-
-# If both John and Mary call, what is the chance there's been a burglary?
-bayes.bayesnet(define_event,
-               n=1*M,
-               find=lambda e: e['burglary'],
-               conditional_on=lambda e: (e['mary_calls'] and e['john_calls']))
-# Result will be ~0.27, though it varies because it is based on a random sample.
-# This will run quickly because there is a built-in cache.
-# Use `cache=False` to not build a cache and `reload_cache=True` to recalculate the cache.
-
    
-
    
-
    Note that the amount of Bayesian analysis that squigglepy can do is
-pretty limited. For more complex bayesian analysis, consider
-sorobn,
-pomegranate,
-bnlearn, or
-pyMC.
    
-
    
-
    
-
    Example: A Demonstration of the Monty Hall Problem#
    
-
    import squigglepy as sq
-from squigglepy import bayes
-from squigglepy.numbers import K, M, B, T
-
-
-def monte_hall(door_picked, switch=False):
-    doors = ['A', 'B', 'C']
-    car_is_behind_door = ~sq.discrete(doors)
-    reveal_door = ~sq.discrete([d for d in doors if d != door_picked and d != car_is_behind_door])
-
-    if switch:
-        old_door_picked = door_picked
-        door_picked = [d for d in doors if d != old_door_picked and d != reveal_door][0]
-
-    won_car = (car_is_behind_door == door_picked)
-    return won_car
-
-
-def define_event():
-    door = ~sq.discrete(['A', 'B', 'C'])
-    switch = sq.event(0.5)
-    return {'won': monte_hall(door_picked=door, switch=switch),
-            'switched': switch}
-
-RUNS = 10*K
-r = bayes.bayesnet(define_event,
-                   find=lambda e: e['won'],
-                   conditional_on=lambda e: e['switched'],
-                   verbose=True,
-                   n=RUNS)
-print('Win {}% of the time when switching'.format(int(r * 100)))
-
-r = bayes.bayesnet(define_event,
-                   find=lambda e: e['won'],
-                   conditional_on=lambda e: not e['switched'],
-                   verbose=True,
-                   n=RUNS)
-print('Win {}% of the time when not switching'.format(int(r * 100)))
-
-# Win 66% of the time when switching
-# Win 34% of the time when not switching
-
    
-
    
-
    
-
    
-
    Example: More complex coin/dice interactions#
    
-
    
-
    Imagine that I flip a coin. If heads, I take a random die out of my
-blue bag. If tails, I take a random die out of my red bag. The blue
-bag contains only 6-sided dice. The red bag contains a 4-sided die, a
-6-sided die, a 10-sided die, and a 20-sided die. I then roll the
-random die I took. What is the chance that I roll a 6?
    
-
    
-
    import squigglepy as sq
-from squigglepy.numbers import K, M, B, T
-from squigglepy import bayes
-
-def define_event():
-    if sq.flip_coin() == 'heads': # Blue bag
-        return sq.roll_die(6)
-    else: # Red bag
-        return sq.discrete([4, 6, 10, 20]) >> sq.roll_die
-
-
-bayes.bayesnet(define_event,
-               find=lambda e: e == 6,
-               verbose=True,
-               n=100*K)
-# This run for me returned 0.12306 which is pretty close to the correct answer of 0.12292
-
    
-
    
-
    
-
    
-
    
-
    Kelly betting#
    
-
    You can use probability generated, combine with a bankroll to determine
-bet sizing using Kelly
-criterion.
    
-
    For example, if you want to Kelly bet and you’ve…
    
-
      
-
    • determined that your price (your probability of the event in question
-happening / the market in question resolving in your favor) is $0.70
-(70%)
      • 
-
    • see that the market is pricing at $0.65
      • 
-
    • you have a bankroll of $1000 that you are willing to bet
      • 
-
    
-
    You should bet as follows:
    
-
    import squigglepy as sq
-kelly_data = sq.kelly(my_price=0.70, market_price=0.65, bankroll=1000)
-kelly_data['kelly']  # What fraction of my bankroll should I bet on this?
-# 0.143
-kelly_data['target']  # How much money should be invested in this?
-# 142.86
-kelly_data['expected_roi']  # What is the expected ROI of this bet?
-# 0.077
-
    
-
    
-
    
-
    
-
    More examples#
    
-
    You can see more examples of squigglepy in action
-here.
    
-
    
-
    
-
    
-
    Run tests#
    
-
    Use black . for formatting.
    
-
    Run
-ruff check . && pytest && pip3 install . && python3 tests/integration.py
    
-
    
-
    
-
    Disclaimers#
    
-
    This package is unofficial and supported by myself and Rethink
-Priorities. It is not affiliated with or associated with the Quantified
-Uncertainty Research Institute, which maintains the Squiggle language
-(in JavaScript).
    
-
    This package is also new and not yet in a stable production version, so
-you may encounter bugs and other errors. Please report those so they can
-be fixed. It’s also possible that future versions of the package may
-introduce breaking changes.
    
-
    This package is available under an MIT License.
    
-
    
-
    
-
    Acknowledgements#
    
-
      
-
    • The primary author of this package is Peter Wildeford. Agustín
-Covarrubias and Bernardo Baron contributed several key features and
-developments.
      • 
-
    • Thanks to Ozzie Gooen and the Quantified Uncertainty Research
-Institute for creating and maintaining the original Squiggle
-language.
      • 
-
    • Thanks to Dawn Drescher for helping me implement math between
-distributions.
      • 
-
    • Thanks to Dawn Drescher for coming up with the idea to use ~ as a
-shorthand for sample, as well as helping me implement it.
      • 
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-    
    
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diff --git a/doc/build/html/_modules/squigglepy/bayes.html b/doc/build/html/_modules/squigglepy/bayes.html
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-  
    Source code for squigglepy.bayes
    -"""
-This modules includes functions for Bayesian inference.
-"""
-
-import os
-import time
-import math
-import msgspec
-
-import numpy as np
-import pathos.multiprocessing as mp
-
-from datetime import datetime
-
-from .distributions import BetaDistribution, NormalDistribution, norm, beta, mixture
-from .utils import _core_cuts, _init_tqdm, _tick_tqdm, _flush_tqdm
-
-
-_squigglepy_internal_bayesnet_caches = {}
-
-
-
    
-[docs]
-def simple_bayes(likelihood_h, likelihood_not_h, prior):
-    """
-    Calculate Bayes rule.
-
-    p(h|e) = (p(e|h)*p(h)) / (p(e|h)*p(h) + p(e|~h)*(1-p(h)))
-    p(h|e) is called posterior
-    p(e|h) is called likelihood
-    p(h) is called prior
-
-    Parameters
-    ----------
-    likelihood_h : float
-        The likelihood (given that the hypothesis is true), aka p(e|h)
-    likelihood_not_h : float
-        The likelihood given the hypothesis is not true, aka p(e|~h)
-    prior : float
-        The prior probability, aka p(h)
-
-    Returns
-    -------
-    float
-        The result of Bayes rule, aka p(h|e)
-
-    Examples
-    --------
-    # Cancer example: prior of having cancer is 1%, the likelihood of a positive
-    # mammography given cancer is 80% (true positive rate), and the likelihood of
-    # a positive mammography given no cancer is 9.6% (false positive rate).
-    # Given this, what is the probability of cancer given a positive mammography?
-    >>> simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096)
-    0.07763975155279504
-    """
-    return (likelihood_h * prior) / (likelihood_h * prior + likelihood_not_h * (1 - prior))
    
-
-
-
-
    
-[docs]
-def bayesnet(
-    event_fn=None,
-    n=1,
-    find=None,
-    conditional_on=None,
-    reduce_fn=None,
-    raw=False,
-    memcache=True,
-    memcache_load=True,
-    memcache_save=True,
-    reload_cache=False,
-    dump_cache_file=None,
-    load_cache_file=None,
-    cache_file_primary=False,
-    verbose=False,
-    cores=1,
-):
-    """
-    Calculate a Bayesian network.
-
-    Allows you to find conditional probabilities of custom events based on
-    rejection sampling.
-
-    Parameters
-    ----------
-    event_fn : function
-        A function that defines the bayesian network
-    n : int
-        The number of samples to generate
-    find : a function or None
-        What do we want to know the probability of?
-    conditional_on : a function or None
-        When finding the probability, what do we want to condition on?
-    reduce_fn : a function or None
-        When taking all the results of the simulations, how do we aggregate them
-        into a final answer? Defaults to ``np.mean``.
-    raw : bool
-        If True, just return the results of each simulation without aggregating.
-    memcache : bool
-        If True, cache the results in-memory for future calculations. Each cache
-        will be matched based on the ``event_fn``. Default ``True``.
-    memcache_load : bool
-        If True, load cache from the in-memory. This will be true if ``memcache``
-        is True. Cache will be matched based on the ``event_fn``. Default ``True``.
-    memcache_save : bool
-        If True, save results to an in-memory cache. This will be true if ``memcache``
-        is True. Cache will be matched based on the ``event_fn``. Default ``True``.
-    reload_cache : bool
-        If True, any existing cache will be ignored and recalculated. Default ``False``.
-    dump_cache_file : str or None
-        If present, will write out the cache to a binary file with this path with
-        ``.sqlcache`` appended to the file name.
-    load_cache_file : str or None
-        If present, will first attempt to load and use a cache from a file with this
-        path with ``.sqlcache`` appended to the file name.
-    cache_file_primary : bool
-        If both an in-memory cache and file cache are present, the file
-        cache will be used for the cache if this is True, and the in-memory cache
-        will be used otherwise. Defaults to False.
-    verbose : bool
-        If True, will print out statements on computational progress.
-    cores : int
-        If 1, runs on a single core / process. If greater than 1, will run on a multiprocessing
-        pool with that many cores / processes.
-
-    Returns
-    -------
-    various
-        The result of ``reduce_fn`` on ``n`` simulations of ``event_fn``.
-
-    Examples
-    --------
-    # Cancer example: prior of having cancer is 1%, the likelihood of a positive
-    # mammography given cancer is 80% (true positive rate), and the likelihood of
-    # a positive mammography given no cancer is 9.6% (false positive rate).
-    # Given this, what is the probability of cancer given a positive mammography?
-    >> def mammography(has_cancer):
-    >>    p = 0.8 if has_cancer else 0.096
-    >>    return bool(sq.sample(sq.bernoulli(p)))
-    >>
-    >> def define_event():
-    >>    cancer = sq.sample(sq.bernoulli(0.01))
-    >>    return({'mammography': mammography(cancer),
-    >>            'cancer': cancer})
-    >>
-    >> bayes.bayesnet(define_event,
-    >>                find=lambda e: e['cancer'],
-    >>                conditional_on=lambda e: e['mammography'],
-    >>                n=1*M)
-    0.07723995880535531
-    """
-    events = None
-    if memcache is True:
-        memcache_load = True
-        memcache_save = True
-    elif memcache is False:
-        memcache_load = False
-        memcache_save = False
-    has_in_mem_cache = event_fn in _squigglepy_internal_bayesnet_caches
-    cache_path = load_cache_file + ".sqcache" if load_cache_file else None
-    has_file_cache = os.path.exists(cache_path) if load_cache_file else False
-
-    if load_cache_file or dump_cache_file or cores > 1:
-        encoder = msgspec.msgpack.Encoder()
-        decoder = msgspec.msgpack.Decoder()
-
-    if load_cache_file and not has_file_cache and verbose:
-        print("Warning: cache file `{}.sqcache` not found.".format(load_cache_file))
-
-    if not reload_cache:
-        if load_cache_file and has_file_cache and (not has_in_mem_cache or cache_file_primary):
-            if verbose:
-                print("Loading from cache file (`{}`)...".format(cache_path))
-            with open(cache_path, "rb") as f:
-                events = decoder.decode(f.read())
-
-        elif memcache_load and has_in_mem_cache:
-            if verbose:
-                print("Loading from in-memory cache...")
-            events = _squigglepy_internal_bayesnet_caches.get(event_fn)
-
-        if events:
-            if events["metadata"]["n"] < n:
-                raise ValueError(
-                    ("insufficient samples - {} results cached but " + "requested {}").format(
-                        events["metadata"]["n"], n
-                    )
-                )
-
-            events = events["events"]
-            if verbose:
-                print("...Loaded")
-
-    elif verbose:
-        print("Reloading cache...")
-
-    if events is None:
-        if event_fn is None:
-            return None
-
-        def run_event_fn(pbar=None, total_cores=1):
-            _tick_tqdm(pbar, total_cores)
-            return event_fn()
-
-        if cores == 1:
-            if verbose:
-                print("Generating Bayes net...")
-            r_ = range(n)
-            pbar = _init_tqdm(verbose=verbose, total=n)
-            events = [run_event_fn(pbar=pbar, total_cores=1) for _ in r_]
-            _flush_tqdm(pbar)
-        else:
-            if verbose:
-                print("Generating Bayes net with {} cores...".format(cores))
-            with mp.ProcessingPool(cores) as pool:
-                cuts = _core_cuts(n, cores)
-
-                def multicore_event_fn(core, total_cores=1, verbose=False):
-                    r_ = range(cuts[core])
-                    pbar = _init_tqdm(verbose=verbose, total=n)
-                    batch = [run_event_fn(pbar=pbar, total_cores=total_cores) for _ in r_]
-                    _flush_tqdm(pbar)
-
-                    if verbose:
-                        print("Shuffling data...")
-
-                    while not os.path.exists("test-core-{}.sqcache".format(core)):
-                        with open("test-core-{}.sqcache".format(core), "wb") as outfile:
-                            encoder = msgspec.msgpack.Encoder()
-                            outfile.write(encoder.encode(batch))
-                        if verbose:
-                            print("Writing data...")
-                            time.sleep(1)
-
-                pool_results = pool.amap(multicore_event_fn, list(range(cores - 1)))
-                multicore_event_fn(cores - 1, total_cores=cores, verbose=verbose)
-                if verbose:
-                    print("Waiting for other cores...")
-                while not pool_results.ready():
-                    if verbose:
-                        print(".", end="", flush=True)
-                    time.sleep(1)
-
-        if cores > 1:
-            if verbose:
-                print("Collecting data...")
-            events = []
-            pbar = _init_tqdm(verbose=verbose, total=cores)
-            for c in range(cores):
-                _tick_tqdm(pbar, 1)
-                with open("test-core-{}.sqcache".format(c), "rb") as infile:
-                    events += decoder.decode(infile.read())
-                os.remove("test-core-{}.sqcache".format(c))
-            _flush_tqdm(pbar)
-            if verbose:
-                print("...Collected!")
-
-    metadata = {"n": n, "last_generated": datetime.now()}
-    cache_data = {"events": events, "metadata": metadata}
-    if memcache_save and (not has_in_mem_cache or reload_cache):
-        if verbose:
-            print("Caching in-memory...")
-        _squigglepy_internal_bayesnet_caches[event_fn] = cache_data
-        if verbose:
-            print("...Cached!")
-
-    if dump_cache_file:
-        cache_path = dump_cache_file + ".sqcache"
-        if verbose:
-            print("Writing cache to file `{}`...".format(cache_path))
-        with open(cache_path, "wb") as f:
-            f.write(encoder.encode(cache_data))
-        if verbose:
-            print("...Cached!")
-
-    if conditional_on is not None:
-        if verbose:
-            print("Filtering conditional...")
-        events = [e for e in events if conditional_on(e)]
-
-    if len(events) < 1:
-        raise ValueError("insufficient samples for condition")
-
-    if conditional_on and verbose:
-        print("...Filtered!")
-
-    if find is None:
-        if verbose:
-            print("...Reducing")
-        events = events if reduce_fn is None else reduce_fn(events)
-        if verbose:
-            print("...Reduced!")
-    else:
-        if verbose:
-            print("...Finding")
-        events = [find(e) for e in events]
-        if verbose:
-            print("...Found!")
-        if not raw:
-            if verbose:
-                print("...Reducing")
-            reduce_fn = np.mean if reduce_fn is None else reduce_fn
-            events = reduce_fn(events)
-            if verbose:
-                print("...Reduced!")
-    if verbose:
-        print("...All done!")
-    return events
    
-
-
-
-
    
-[docs]
-def update(prior, evidence, evidence_weight=1):
-    """
-    Update a distribution.
-
-    Starting with a prior distribution, use Bayesian inference to perform an update,
-    producing a posterior distribution from the evidence distribution.
-
-    Parameters
-    ----------
-    prior : Distribution
-        The prior distribution. Currently must either be normal or beta type. Other
-        types are not yet supported.
-    evidence : Distribution
-        The distribution used to update the prior. Currently must either be normal
-        or beta type. Other types are not yet supported.
-    evidence_weight : float
-        How much weight to put on the evidence distribution? Currently this only matters
-        for normal distributions, where this should be equivalent to the sample weight.
-
-    Returns
-    -------
-    Distribution
-        The posterior distribution
-
-    Examples
-    --------
-    >> prior = sq.norm(1,5)
-    >> evidence = sq.norm(2,3)
-    >> bayes.update(prior, evidence)
-    <Distribution> norm(mean=2.53, sd=0.29)
-    """
-    if isinstance(prior, NormalDistribution) and isinstance(evidence, NormalDistribution):
-        prior_mean = prior.mean
-        prior_var = prior.sd**2
-        evidence_mean = evidence.mean
-        evidence_var = evidence.sd**2
-        return norm(
-            mean=(
-                (evidence_var * prior_mean + evidence_weight * (prior_var * evidence_mean))
-                / (evidence_weight * prior_var + evidence_var)
-            ),
-            sd=math.sqrt(
-                (evidence_var * prior_var) / (evidence_weight * prior_var + evidence_var)
-            ),
-        )
-    elif isinstance(prior, BetaDistribution) and isinstance(evidence, BetaDistribution):
-        prior_a = prior.a
-        prior_b = prior.b
-        evidence_a = evidence.a
-        evidence_b = evidence.b
-        return beta(prior_a + evidence_a, prior_b + evidence_b)
-    elif type(prior) != type(evidence):
-        print(type(prior), type(evidence))
-        raise ValueError("can only update distributions of the same type.")
-    else:
-        raise ValueError("type `{}` not supported.".format(prior.__class__.__name__))
    
-
-
-
-
    
-[docs]
-def average(prior, evidence, weights=[0.5, 0.5], relative_weights=None):
-    """
-    Average two distributions.
-
-    Parameters
-    ----------
-    prior : Distribution
-        The prior distribution.
-    evidence : Distribution
-        The distribution used to average with the prior.
-    weights : list or np.array or float
-        How much weight to put on ``prior`` versus ``evidence`` when averaging? If
-        only one weight is passed, the other weight will be inferred to make the
-        total weights sum to 1. Defaults to 50-50 weights.
-    relative_weights : list or None
-        Relative weights, which if given will be weights that are normalized
-        to sum to 1.
-
-    Returns
-    -------
-    Distribution
-        A mixture distribution that accords weights to ``prior`` and ``evidence``.
-
-    Examples
-    --------
-    >> prior = sq.norm(1,5)
-    >> evidence = sq.norm(2,3)
-    >> bayes.average(prior, evidence)
-    <Distribution> mixture
-    """
-    return mixture(dists=[prior, evidence], weights=weights, relative_weights=relative_weights)
    
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-    
    
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    -"""
-This module implements the Iman-Conover method for inducing correlations between distributions.
-
-Some of the code has been adapted from Abraham Lee's mcerp package (https://github.com/tisimst/mcerp/).
-"""
-
-# Parts of `induce_correlation` are licensed as follows:
-
-# BSD 3-Clause License
-
-# Copyright (c) 2018, Abraham Lee
-# All rights reserved.
-
-# Redistribution and use in source and binary forms, with or without
-# modification, are permitted provided that the following conditions are met:
-
-# * Redistributions of source code must retain the above copyright notice, this
-#   list of conditions and the following disclaimer.
-
-# * Redistributions in binary form must reproduce the above copyright notice,
-#   this list of conditions and the following disclaimer in the documentation
-#   and/or other materials provided with the distribution.
-
-# * Neither the name of the copyright holder nor the names of its
-#   contributors may be used to endorse or promote products derived from
-#   this software without specific prior written permission.
-
-# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
-# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
-# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
-# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
-# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
-# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
-# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
-# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-
-from __future__ import annotations
-
-from dataclasses import dataclass
-import numpy as np
-from scipy.linalg import cholesky
-from scipy.stats import rankdata, spearmanr
-from scipy.stats.distributions import norm as _scipy_norm
-from numpy.typing import NDArray
-from copy import deepcopy
-
-from typing import TYPE_CHECKING, Union
-
-if TYPE_CHECKING:
-    from .distributions import OperableDistribution
-
-
-
    
-[docs]
-def correlate(
-    variables: tuple[OperableDistribution, ...],
-    correlation: Union[NDArray[np.float64], list[list[float]], np.float64, float],
-    tolerance: Union[float, np.float64, None] = 0.05,
-    _min_unique_samples: int = 100,
-):
-    """
-    Correlate a set of variables according to a rank correlation matrix.
-
-    This employs the Iman-Conover method to induce the correlation while
-    preserving the original marginal distributions.
-
-    This method works on a best-effort basis, and may fail to induce the desired
-    correlation depending on the distributions provided. An exception will be raised
-    if that's the case.
-
-    Parameters
-    ----------
-    variables : tuple of distributions
-        The variables to correlate as a tuple of distributions.
-
-        The distributions must be able to produce enough unique samples for the method
-        to be able to induce the desired correlation by shuffling the samples.
-
-        Discrete distributions are notably hard to correlate this way,
-        as it's common for them to result in very few unique samples.
-
-    correlation : 2d-array or float
-        An n-by-n array that defines the desired Spearman rank correlation coefficients.
-        This matrix must be symmetric and positive semi-definite; and must not be confused with
-        a covariance matrix.
-
-        Correlation parameters can only be between -1 and 1, exclusive
-        (including extremely close approximations).
-
-        If a float is provided, all variables will be correlated with the same coefficient.
-
-    tolerance : float, optional
-        If provided, overrides the absolute tolerance used to check if the resulting
-        correlation matrix matches the desired correlation matrix. Defaults to 0.05.
-
-        Checking can also be disabled by passing None.
-
-    Returns
-    -------
-    correlated_variables : tuple of distributions
-        The correlated variables as a tuple of distributions in the same order as
-        the input variables.
-
-    Examples
-    --------
-    Suppose we want to correlate two variables with a correlation coefficient of 0.65:
-    >>> solar_radiation, temperature = sq.gamma(300, 100), sq.to(22, 28)
-    >>> solar_radiation, temperature = sq.correlate((solar_radiation, temperature), 0.7)
-    >>> print(np.corrcoef(solar_radiation @ 1000, temperature @ 1000)[0, 1])
-    0.6975960649767123
-
-    Or you could pass a correlation matrix:
-
-    >>> funding_gap, cost_per_delivery, effect_size = (
-            sq.to(20_000, 80_000), sq.to(30, 80), sq.beta(2, 5)
-        )
-    >>> funding_gap, cost_per_delivery, effect_size = sq.correlate(
-            (funding_gap, cost_per_delivery, effect_size),
-            [[1, 0.6, -0.5], [0.6, 1, -0.2], [-0.5, -0.2, 1]]
-        )
-    >>> print(np.corrcoef(funding_gap @ 1000, cost_per_delivery @ 1000, effect_size @ 1000))
-    array([[ 1.      ,  0.580520  , -0.480149],
-           [ 0.580962,  1.        , -0.187831],
-           [-0.480149, -0.187831  ,  1.        ]])
-
-    """
-    if not isinstance(variables, tuple):
-        variables = tuple(variables)
-
-    if len(variables) < 2:
-        raise ValueError("You must provide at least two variables to correlate.")
-
-    assert all(v.correlation_group is None for v in variables)
-
-    # Convert a float to a correlation matrix
-    if (
-        isinstance(correlation, float)
-        or isinstance(correlation, np.floating)
-        or isinstance(correlation, int)
-    ):
-        correlation_parameter = np.float64(correlation)
-
-        assert (
-            -1 < correlation_parameter < 1
-        ), "Correlation parameter must be between -1 and 1, exclusive."
-        # Generate a correlation matrix with
-        # pairwise correlations equal to the correlation parameter
-        correlation_matrix: NDArray[np.float64] = np.full(
-            (len(variables), len(variables)), correlation_parameter
-        )
-        # Set the diagonal to 1
-        np.fill_diagonal(correlation_matrix, 1)
-    else:
-        # Coerce the correlation matrix into a numpy array
-        correlation_matrix: NDArray[np.float64] = np.array(correlation, dtype=np.float64)
-
-    tolerance = float(tolerance) if tolerance is not None else None
-
-    # Deepcopy the variables to avoid modifying the originals
-    variables = deepcopy(variables)
-
-    # Create the correlation group
-    CorrelationGroup(variables, correlation_matrix, tolerance, _min_unique_samples)
-
-    return variables
    
-
-
-
-
    
-[docs]
-@dataclass
-class CorrelationGroup:
-    """
-    An object that holds metadata for a group of correlated distributions.
-    This object is not intended to be used directly by the user, but
-    rather during sampling to induce correlations between distributions.
-    """
-
-    correlated_dists: tuple[OperableDistribution]
-    correlation_matrix: NDArray[np.float64]
-    correlation_tolerance: Union[float, None] = 0.05
-    min_unique_samples: int = 100
-
-    def __post_init__(self):
-        # Check that the correlation matrix is square of the expected size
-        assert (
-            self.correlation_matrix.shape[0]
-            == self.correlation_matrix.shape[1]
-            == len(self.correlated_dists)
-        ), "Correlation matrix must be square, and of the length of the number of dists. provided."
-
-        # Check that the diagonal of the correlation matrix is all ones
-        assert np.all(np.diag(self.correlation_matrix) == 1), "Diagonal must be all ones."
-
-        # Check that values are between -1 and 1
-        assert (
-            -1 <= np.min(self.correlation_matrix) and np.max(self.correlation_matrix) <= 1
-        ), "Correlation matrix values must be between -1 and 1."
-
-        # Check that the correlation matrix is positive semi-definite
-        assert np.all(
-            np.linalg.eigvals(self.correlation_matrix) >= 0
-        ), "Matrix must be positive semi-definite."
-
-        # Check that the correlation matrix is symmetric
-        assert np.all(
-            self.correlation_matrix == self.correlation_matrix.T
-        ), "Matrix must be symmetric."
-
-        # Link the correlation group to each distribution
-        for dist in self.correlated_dists:
-            dist.correlation_group = self
-
-
    
-[docs]
-    def induce_correlation(self, data: NDArray[np.float64]) -> NDArray[np.float64]:
-        """
-        Induce a set of correlations on a column-wise dataset
-
-        Parameters
-        ----------
-        data : 2d-array
-            An m-by-n array where m is the number of samples and n is the
-            number of independent variables, each column of the array corresponding
-            to each variable
-        corrmat : 2d-array
-            An n-by-n array that defines the desired correlation coefficients
-            (between -1 and 1). Note: the matrix must be symmetric and
-            positive-definite in order to induce.
-
-        Returns
-        -------
-        new_data : 2d-array
-            An m-by-n array that has the desired correlations.
-
-        """
-        # Check that each column doesn't have too little unique values
-        for column in data.T:
-            if not self.has_sufficient_sample_diversity(column):
-                raise ValueError(
-                    "The data has too many repeated values to induce a correlation. "
-                    "This might be because of too few samples, or too many repeated samples."
-                )
-
-        # If the correlation matrix is the identity matrix, just return the data
-        if np.all(self.correlation_matrix == np.eye(self.correlation_matrix.shape[0])):
-            return data
-
-        # Create a rank-matrix
-        data_rank = np.vstack([rankdata(datai, method="min") for datai in data.T]).T
-
-        # Generate van der Waerden scores
-        data_rank_score = data_rank / (data_rank.shape[0] + 1.0)
-        data_rank_score = _scipy_norm(0, 1).ppf(data_rank_score)
-
-        # Calculate the lower triangular matrix of the Cholesky decomposition
-        # of the desired correlation matrix
-        p = cholesky(self.correlation_matrix, lower=True)
-
-        # Calculate the current correlations
-        t = np.corrcoef(data_rank_score, rowvar=False)
-
-        # Calculate the lower triangular matrix of the Cholesky decomposition
-        # of the current correlation matrix
-        q = cholesky(t, lower=True)
-
-        # Calculate the re-correlation matrix
-        s = np.dot(p, np.linalg.inv(q))
-
-        # Calculate the re-sampled matrix
-        new_data = np.dot(data_rank_score, s.T)
-
-        # Create the new rank matrix
-        new_data_rank = np.vstack([rankdata(datai, method="min") for datai in new_data.T]).T
-
-        # Sort the original data according to the new rank matrix
-        self._sort_data_according_to_rank(data, data_rank, new_data_rank)
-
-        # # Check correlation
-        if self.correlation_tolerance:
-            self._check_empirical_correlation(data)
-
-        return data
    
-
-
-    def _sort_data_according_to_rank(
-        self,
-        data: NDArray[np.float64],
-        data_rank: NDArray[np.float64],
-        new_data_rank: NDArray[np.float64],
-    ):
-        """Sorts the original data according to new_data_rank, in place."""
-        assert (
-            data.shape == data_rank.shape == new_data_rank.shape
-        ), "All input arrays must have the same shape"
-        for i in range(data.shape[1]):
-            _, order = np.unique(
-                np.hstack((data_rank[:, i], new_data_rank[:, i])), return_inverse=True
-            )
-            old_order = order[: new_data_rank.shape[0]]
-            new_order = order[-new_data_rank.shape[0] :]
-            tmp = data[np.argsort(old_order), i][new_order]
-            data[:, i] = tmp[:]
-
-    def _check_empirical_correlation(self, samples: NDArray[np.float64]):
-        """
-        Ensures that the empirical correlation matrix is
-        the same as the desired correlation matrix.
-        """
-        assert self.correlation_tolerance is not None
-
-        # Compute the empirical correlation matrix
-        empirical_correlation = spearmanr(samples).statistic
-        if len(self.correlated_dists) == 2:
-            # empirical_correlation is a scalar
-            properly_correlated = np.isclose(
-                empirical_correlation,
-                self.correlation_matrix[0, 1],
-                atol=self.correlation_tolerance,
-                rtol=0,
-            )
-        else:
-            # empirical_correlation is a matrix
-            properly_correlated = np.allclose(
-                empirical_correlation,
-                self.correlation_matrix,
-                atol=self.correlation_tolerance,
-                rtol=0,
-            )
-        if not properly_correlated:
-            raise RuntimeError(
-                "Failed to induce the desired correlation between samples. "
-                "This might be because of too little diversity in the samples. "
-                "You can relax the tolerance by passing `tolerance` to correlate()."
-            )
-
-
    
-[docs]
-    def has_sufficient_sample_diversity(
-        self,
-        samples: NDArray[np.float64],
-        relative_threshold: float = 0.7,
-        absolute_threshold=None,
-    ) -> bool:
-        """
-        Check if there is there are sufficient unique samples to work with in the data.
-        """
-
-        if absolute_threshold is None:
-            absolute_threshold = self.min_unique_samples
-
-        unique_samples = len(np.unique(samples, axis=0))
-        n_samples = len(samples)
-
-        diversity = unique_samples / n_samples
-
-        return (diversity >= relative_threshold) and (unique_samples >= absolute_threshold)
    
-
    
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-      
    
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-    
    
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-    squigglepy.distributions — Squigglepy  documentation
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-                  
-  
    Source code for squigglepy.distributions
    -"""
-A collection of probability distributions and functions to operate on them.
-"""
-
-import operator
-import math
-import numpy as np
-import scipy.stats
-
-from typing import Optional, Union
-
-from .utils import _process_weights_values, _is_numpy, is_dist, _round
-from .version import __version__
-from .correlation import CorrelationGroup
-
-from collections.abc import Iterable
-
-from abc import ABC, abstractmethod
-
-
-
    
-[docs]
-class BaseDistribution(ABC):
-    def __init__(self):
-        self.x = None
-        self.y = None
-        self.n = None
-        self.p = None
-        self.t = None
-        self.a = None
-        self.b = None
-        self.shape = None
-        self.scale = None
-        self.credibility = None
-        self.mean = None
-        self.sd = None
-        self.left = None
-        self.mode = None
-        self.right = None
-        self.fn = None
-        self.fn_str = None
-        self.lclip = None
-        self.rclip = None
-        self.lam = None
-        self.df = None
-        self.items = None
-        self.dists = None
-        self.weights = None
-        self._version = __version__
-
-        # Correlation metadata
-        self.correlation_group: Optional[CorrelationGroup] = None
-        self._correlated_samples: Optional[np.ndarray] = None
-
-    @abstractmethod
-    def __str__(self) -> str:
-        ...
-
-    def __repr__(self):
-        if self.correlation_group:
-            return (
-                self.__str__() + f" (version {self._version}, corr_group {self.correlation_group})"
-            )
-        return self.__str__() + f" (version {self._version})"
    
-
-
-
-
    
-[docs]
-class OperableDistribution(BaseDistribution):
-    def __init__(self):
-        super().__init__()
-
-
    
-[docs]
-    def plot(self, num_samples=None, bins=None):
-        """
-        Plot a histogram of the samples.
-
-        Parameters
-        ----------
-        num_samples : int
-            The number of samples to draw for plotting. Defaults to 1000 if not set.
-        bins : int
-            The number of bins to plot. Defaults to 200 if not set.
-
-        Examples
-        --------
-        >>> sq.norm(5, 10).plot()
-        """
-        from matplotlib import pyplot as plt
-
-        num_samples = 1000 if num_samples is None else num_samples
-        bins = 200 if bins is None else bins
-
-        samples = self @ num_samples
-
-        plt.hist(samples, bins=bins)
-        plt.show()
    
-
-
-    def __invert__(self):
-        from .samplers import sample
-
-        return sample(self)
-
-    def __matmul__(self, n):
-        try:
-            n = int(n)
-        except ValueError:
-            raise ValueError("number of samples must be an integer")
-        from .samplers import sample
-
-        return sample(self, n=n)
-
-    def __rshift__(self, fn):
-        if callable(fn):
-            return fn(self)
-        elif isinstance(fn, ComplexDistribution):
-            return ComplexDistribution(self, fn.left, fn.fn, fn.fn_str, infix=False)
-        else:
-            raise ValueError
-
-    def __rmatmul__(self, n):
-        return self.__matmul__(n)
-
-    def __gt__(self, dist):
-        return ComplexDistribution(self, dist, operator.gt, ">")
-
-    def __ge__(self, dist):
-        return ComplexDistribution(self, dist, operator.ge, ">=")
-
-    def __lt__(self, dist):
-        return ComplexDistribution(self, dist, operator.lt, "<")
-
-    def __le__(self, dist):
-        return ComplexDistribution(self, dist, operator.le, "<=")
-
-    def __eq__(self, dist):
-        return ComplexDistribution(self, dist, operator.le, "==")
-
-    def __ne__(self, dist):
-        return ComplexDistribution(self, dist, operator.le, "!=")
-
-    def __neg__(self):
-        return ComplexDistribution(self, None, operator.neg, "-")
-
-    def __add__(self, dist):
-        return ComplexDistribution(self, dist, operator.add, "+")
-
-    def __radd__(self, dist):
-        return ComplexDistribution(dist, self, operator.add, "+")
-
-    def __sub__(self, dist):
-        return ComplexDistribution(self, dist, operator.sub, "-")
-
-    def __rsub__(self, dist):
-        return ComplexDistribution(dist, self, operator.sub, "-")
-
-    def __mul__(self, dist):
-        return ComplexDistribution(self, dist, operator.mul, "*")
-
-    def __rmul__(self, dist):
-        return ComplexDistribution(dist, self, operator.mul, "*")
-
-    def __truediv__(self, dist):
-        return ComplexDistribution(self, dist, operator.truediv, "/")
-
-    def __rtruediv__(self, dist):
-        return ComplexDistribution(dist, self, operator.truediv, "/")
-
-    def __floordiv__(self, dist):
-        return ComplexDistribution(self, dist, operator.floordiv, "//")
-
-    def __rfloordiv__(self, dist):
-        return ComplexDistribution(dist, self, operator.floordiv, "//")
-
-    def __pow__(self, dist):
-        return ComplexDistribution(self, dist, operator.pow, "**")
-
-    def __rpow__(self, dist):
-        return ComplexDistribution(dist, self, operator.pow, "**")
-
-    def __hash__(self):
-        return hash(repr(self))
    
-
-
-
-# Distribution are either discrete, continuous, or composite
-
-
-
    
-[docs]
-class DiscreteDistribution(OperableDistribution, ABC):
-    ...
    
-
-
-
-
    
-[docs]
-class ContinuousDistribution(OperableDistribution, ABC):
-    ...
    
-
-
-
-
    
-[docs]
-class CompositeDistribution(OperableDistribution):
-    def __init__(self):
-        super().__init__()
-        # Whether this distribution contains any correlated variables
-        self.contains_correlated: Optional[bool] = None
-
-    def __post_init__(self):
-        assert self.contains_correlated is not None, "contains_correlated must be set"
-
-    def _check_correlated(self, dists: Iterable) -> None:
-        for dist in dists:
-            if isinstance(dist, BaseDistribution) and dist.correlation_group is not None:
-                self.contains_correlated = True
-                break
-            if isinstance(dist, CompositeDistribution):
-                if dist.contains_correlated:
-                    self.contains_correlated = True
-                    break
    
-
-
-
-
    
-[docs]
-class ComplexDistribution(CompositeDistribution):
-    def __init__(self, left, right=None, fn=operator.add, fn_str="+", infix=True):
-        super().__init__()
-        self.left = left
-        self.right = right
-        self.fn = fn
-        self.fn_str = fn_str
-        self.infix = infix
-        self._check_correlated((left, right))
-
-    def __str__(self):
-        if self.right is None and self.infix:
-            if self.fn_str == "-":
-                out = "<Distribution> {}{}"
-            else:
-                out = "<Distribution> {} {}"
-            out = out.format(self.fn_str, str(self.left).replace("<Distribution> ", ""))
-        elif self.right is None and not self.infix:
-            out = "<Distribution> {}({})".format(
-                self.fn_str, str(self.left).replace("<Distribution> ", "")
-            )
-        elif self.right is not None and self.infix:
-            out = "<Distribution> {} {} {}".format(
-                str(self.left).replace("<Distribution> ", ""),
-                self.fn_str,
-                str(self.right).replace("<Distribution> ", ""),
-            )
-        elif self.right is not None and not self.infix:
-            out = "<Distribution> {}({}, {})"
-            out = out.format(
-                self.fn_str,
-                str(self.left).replace("<Distribution> ", ""),
-                str(self.right).replace("<Distribution> ", ""),
-            )
-        else:
-            raise ValueError
-        return out
    
-
-
-
-def _get_fname(f, name):
-    if name is None:
-        if isinstance(f, np.vectorize):
-            name = f.pyfunc.__name__
-        else:
-            name = f.__name__
-    return name
-
-
-
    
-[docs]
-def dist_fn(dist1, dist2=None, fn=None, name=None):
-    """
-    Initialize a distribution that has a custom function applied to the result.
-
-    The function won't be applied until the distribution is sampled.
-
-    Parameters
-    ----------
-    dist1 : Distribution or function or list
-        Typically, the distribution to apply the function to. Could also be a function
-        or list of functions if ``dist_fn`` is being used in a pipe.
-    dist2 : Distribution or function or list or None
-        Typically, the second distribution to apply the function to if the function takes
-        two arguments. Could also be a function or list of functions if ``dist_fn`` is
-        being used in a pipe.
-    fn : function or None
-        The function to apply to the distribution(s).
-    name : str or None
-        By default, ``fn.__name__`` will be used to name the function. But you can pass
-        a custom name.
-
-    Returns
-    -------
-    ComplexDistribution or function
-        This will be a lazy evaluation of the desired function that will then be calculated
-        when it is sampled.
-
-    Examples
-    --------
-    >>> def double(x):
-    >>>     return x * 2
-    >>> dist_fn(norm(0, 1), double)
-    <Distribution> double(norm(mean=0.5, sd=0.3))
-    >>> norm(0, 1) >> dist_fn(double)
-    <Distribution> double(norm(mean=0.5, sd=0.3))
-    """
-    if isinstance(dist1, list) and callable(dist1[0]) and dist2 is None and fn is None:
-        fn = dist1
-
-        def out_fn(d):
-            out = d
-            for f in fn:
-                out = ComplexDistribution(out, None, fn=f, fn_str=_get_fname(f, name), infix=False)
-            return out
-
-        return out_fn
-
-    if callable(dist1) and dist2 is None and fn is None:
-        return lambda d: dist_fn(d, fn=dist1)
-
-    if isinstance(dist2, list) and callable(dist2[0]) and fn is None:
-        fn = dist2
-        dist2 = None
-
-    if callable(dist2) and fn is None:
-        fn = dist2
-        dist2 = None
-
-    if not isinstance(fn, list):
-        fn = [fn]
-
-    out = dist1
-    for f in fn:
-        out = ComplexDistribution(out, dist2, fn=f, fn_str=_get_fname(f, name), infix=False)
-
-    return out
    
-
-
-
-
    
-[docs]
-def dist_max(dist1, dist2=None):
-    """
-    Initialize the calculation of the maximum value of two distributions.
-
-    The function won't be applied until the distribution is sampled.
-
-    Parameters
-    ----------
-    dist1 : Distribution
-        The distribution to sample and determine the max of.
-    dist2 : Distribution
-        The second distribution to sample and determine the max of.
-
-    Returns
-    -------
-    ComplexDistribution or function
-        This will be a lazy evaluation of the desired function that will then be calculated
-        when it is sampled.
-
-    Examples
-    --------
-    >>> dist_max(norm(0, 1), norm(1, 2))
-    <Distribution> max(norm(mean=0.5, sd=0.3), norm(mean=1.5, sd=0.3))
-    """
-    if is_dist(dist1) and dist2 is None:
-        return lambda d: dist_fn(d, dist1, np.maximum, name="max")
-    else:
-        return dist_fn(dist1, dist2, np.maximum, name="max")
    
-
-
-
-
    
-[docs]
-def dist_min(dist1, dist2=None):
-    """
-    Initialize the calculation of the minimum value of two distributions.
-
-    The function won't be applied until the distribution is sampled.
-
-    Parameters
-    ----------
-    dist1 : Distribution
-        The distribution to sample and determine the min of.
-    dist2 : Distribution
-        The second distribution to sample and determine the min of.
-
-    Returns
-    -------
-    ComplexDistribution or function
-        This will be a lazy evaluation of the desired function that will then be calculated
-
-    Examples
-    --------
-    >>> dist_min(norm(0, 1), norm(1, 2))
-    <Distribution> min(norm(mean=0.5, sd=0.3), norm(mean=1.5, sd=0.3))
-    """
-    if is_dist(dist1) and dist2 is None:
-        return lambda d: dist_fn(d, dist1, np.minimum, name="min")
-    else:
-        return dist_fn(dist1, dist2, np.minimum, name="min")
    
-
-
-
-
    
-[docs]
-def dist_round(dist1, digits=0):
-    """
-    Initialize the rounding of the output of the distribution.
-
-    The function won't be applied until the distribution is sampled.
-
-    Parameters
-    ----------
-    dist1 : Distribution
-        The distribution to sample and then round.
-    digits : int
-        The number of digits to round to.
-
-    Returns
-    -------
-    ComplexDistribution or function
-        This will be a lazy evaluation of the desired function that will then be calculated
-
-    Examples
-    --------
-    >>> dist_round(norm(0, 1))
-    <Distribution> round(norm(mean=0.5, sd=0.3), 0)
-    """
-    if isinstance(dist1, int) and digits == 0:
-        return lambda d: dist_round(d, digits=dist1)
-    else:
-        return dist_fn(dist1, digits, _round, name="round")
    
-
-
-
-
    
-[docs]
-def dist_ceil(dist1):
-    """
-    Initialize the ceiling rounding of the output of the distribution.
-
-    The function won't be applied until the distribution is sampled.
-
-    Parameters
-    ----------
-    dist1 : Distribution
-        The distribution to sample and then ceiling round.
-
-    Returns
-    -------
-    ComplexDistribution or function
-        This will be a lazy evaluation of the desired function that will then be calculated
-
-    Examples
-    --------
-    >>> dist_ceil(norm(0, 1))
-    <Distribution> ceil(norm(mean=0.5, sd=0.3))
-    """
-    return dist_fn(dist1, None, np.ceil)
    
-
-
-
-
    
-[docs]
-def dist_floor(dist1):
-    """
-    Initialize the floor rounding of the output of the distribution.
-
-    The function won't be applied until the distribution is sampled.
-
-    Parameters
-    ----------
-    dist1 : Distribution
-        The distribution to sample and then floor round.
-
-    Returns
-    -------
-    ComplexDistribution or function
-        This will be a lazy evaluation of the desired function that will then be calculated
-
-    Examples
-    --------
-    >>> dist_floor(norm(0, 1))
-    <Distribution> floor(norm(mean=0.5, sd=0.3))
-    """
-    return dist_fn(dist1, None, np.floor)
    
-
-
-
-
    
-[docs]
-def dist_log(dist1, base=math.e):
-    """
-    Initialize the log of the output of the distribution.
-
-    The function won't be applied until the distribution is sampled.
-
-    Parameters
-    ----------
-    dist1 : Distribution
-        The distribution to sample and then take the log of.
-
-    Returns
-    -------
-    ComplexDistribution or function
-        This will be a lazy evaluation of the desired function that will then be calculated
-
-    Examples
-    --------
-    >>> dist_log(norm(0, 1), 10)
-    <Distribution> log(norm(mean=0.5, sd=0.3), const(10))
-    """
-    return dist_fn(dist1, const(base), math.log)
    
-
-
-
-
    
-[docs]
-def dist_exp(dist1):
-    """
-    Initialize the exp of the output of the distribution.
-
-    The function won't be applied until the distribution is sampled.
-
-    Parameters
-    ----------
-    dist1 : Distribution
-        The distribution to sample and then take the exp of.
-
-    Returns
-    -------
-    ComplexDistribution or function
-        This will be a lazy evaluation of the desired function that will then be calculated
-
-    Examples
-    --------
-    >>> dist_exp(norm(0, 1))
-    <Distribution> exp(norm(mean=0.5, sd=0.3))
-    """
-    return dist_fn(dist1, None, math.exp)
    
-
-
-
-@np.vectorize
-def _lclip(n, val=None):
-    if val is None:
-        return n
-    else:
-        return val if n < val else n
-
-
-
    
-[docs]
-def lclip(dist1, val=None):
-    """
-    Initialize the clipping/bounding of the output of the distribution by the lower value.
-
-    The function won't be applied until the distribution is sampled.
-
-    Parameters
-    ----------
-    dist1 : Distribution or function
-        The distribution to clip. If this is a funciton, it will return a partial that will
-        be suitable for use in piping.
-    val : int or float or None
-        The value to use as the lower bound for clipping.
-
-    Returns
-    -------
-    ComplexDistribution or function
-        This will be a lazy evaluation of the desired function that will then be calculated
-
-    Examples
-    --------
-    >>> lclip(norm(0, 1), 0.5)
-    <Distribution> lclip(norm(mean=0.5, sd=0.3), 0.5)
-    """
-    if (isinstance(dist1, int) or isinstance(dist1, float)) and val is None:
-        return lambda d: lclip(d, dist1)
-    elif is_dist(dist1):
-        return dist_fn(dist1, val, _lclip, name="lclip")
-    else:
-        return _lclip(dist1, val)
    
-
-
-
-@np.vectorize
-def _rclip(n, val=None):
-    if val is None:
-        return n
-    else:
-        return val if n > val else n
-
-
-
    
-[docs]
-def rclip(dist1, val=None):
-    """
-    Initialize the clipping/bounding of the output of the distribution by the upper value.
-
-    The function won't be applied until the distribution is sampled.
-
-    Parameters
-    ----------
-    dist1 : Distribution or function
-        The distribution to clip. If this is a funciton, it will return a partial that will
-        be suitable for use in piping.
-    val : int or float or None
-        The value to use as the upper bound for clipping.
-
-    Returns
-    -------
-    ComplexDistribution or function
-        This will be a lazy evaluation of the desired function that will then be calculated
-
-    Examples
-    --------
-    >>> rclip(norm(0, 1), 0.5)
-    <Distribution> rclip(norm(mean=0.5, sd=0.3), 0.5)
-    """
-    if (isinstance(dist1, int) or isinstance(dist1, float)) and val is None:
-        return lambda d: rclip(d, dist1)
-    elif is_dist(dist1):
-        return dist_fn(dist1, val, _rclip, name="rclip")
-    else:
-        return _rclip(dist1, val)
    
-
-
-
-
    
-[docs]
-def clip(dist1, left, right=None):
-    """
-    Initialize the clipping/bounding of the output of the distribution.
-
-    The function won't be applied until the distribution is sampled.
-
-    Parameters
-    ----------
-    dist1 : Distribution or function
-        The distribution to clip. If this is a funciton, it will return a partial that will
-        be suitable for use in piping.
-    left : int or float or None
-        The value to use as the lower bound for clipping.
-    right : int or float or None
-        The value to use as the upper bound for clipping.
-
-    Returns
-    -------
-    ComplexDistribution or function
-        This will be a lazy evaluation of the desired function that will then be calculated
-
-    Examples
-    --------
-    >>> clip(norm(0, 1), 0.5, 0.9)
-    <Distribution> rclip(lclip(norm(mean=0.5, sd=0.3), 0.5), 0.9)
-    """
-    if (
-        (isinstance(dist1, int) or isinstance(dist1, float))
-        and (isinstance(left, int) or isinstance(left, float))
-        and right is None
-    ):
-        return lambda d: rclip(lclip(d, dist1), left)
-    else:
-        return rclip(lclip(dist1, left), right)
    
-
-
-
-
    
-[docs]
-class ConstantDistribution(DiscreteDistribution):
-    def __init__(self, x):
-        super().__init__()
-        self.x = x
-
-    def __str__(self):
-        return "<Distribution> const({})".format(self.x)
    
-
-
-
-
    
-[docs]
-def const(x):
-    """
-    Initialize a constant distribution.
-
-    Constant distributions always return the same value no matter what.
-
-    Parameters
-    ----------
-    x : anything
-        The value the constant distribution should always return.
-
-    Returns
-    -------
-    ConstantDistribution
-
-    Examples
-    --------
-    >>> const(1)
-    <Distribution> const(1)
-    """
-    return ConstantDistribution(x)
    
-
-
-
-
    
-[docs]
-class UniformDistribution(ContinuousDistribution):
-    def __init__(self, x, y):
-        super().__init__()
-        self.x = x
-        self.y = y
-        assert x < y, "x must be less than y"
-
-    def __str__(self):
-        return "<Distribution> uniform({}, {})".format(self.x, self.y)
    
-
-
-
-
    
-[docs]
-def uniform(x, y):
-    """
-    Initialize a uniform random distribution.
-
-    Parameters
-    ----------
-    x : float
-        The smallest value the uniform distribution will return.
-    y : float
-        The largest value the uniform distribution will return.
-
-    Returns
-    -------
-    UniformDistribution
-
-    Examples
-    --------
-    >>> uniform(0, 1)
-    <Distribution> uniform(0, 1)
-    """
-    return UniformDistribution(x=x, y=y)
    
-
-
-
-
    
-[docs]
-class NormalDistribution(ContinuousDistribution):
-    def __init__(self, x=None, y=None, mean=None, sd=None, credibility=90, lclip=None, rclip=None):
-        super().__init__()
-        self.x = x
-        self.y = y
-        self.credibility = credibility
-        self.mean = mean
-        self.sd = sd
-        self.lclip = lclip
-        self.rclip = rclip
-
-        if self.x is not None and self.y is not None and self.x > self.y:
-            raise ValueError("`high value` cannot be lower than `low value`")
-
-        if (self.x is None or self.y is None) and self.sd is None:
-            raise ValueError("must define either x/y or mean/sd")
-        elif (self.x is not None or self.y is not None) and self.sd is not None:
-            raise ValueError("must define either x/y or mean/sd -- cannot define both")
-        elif self.sd is not None and self.mean is None:
-            self.mean = 0
-
-        if self.mean is None and self.sd is None:
-            self.mean = (self.x + self.y) / 2
-            cdf_value = 0.5 + 0.5 * (self.credibility / 100)
-            normed_sigma = scipy.stats.norm.ppf(cdf_value)
-            self.sd = (self.y - self.mean) / normed_sigma
-
-    def __str__(self):
-        out = "<Distribution> norm(mean={}, sd={}".format(round(self.mean, 2), round(self.sd, 2))
-        if self.lclip is not None:
-            out += ", lclip={}".format(self.lclip)
-        if self.rclip is not None:
-            out += ", rclip={}".format(self.rclip)
-        out += ")"
-        return out
    
-
-
-
-
    
-[docs]
-def norm(
-    x=None, y=None, credibility=90, mean=None, sd=None, lclip=None, rclip=None
-) -> NormalDistribution:
-    """
-    Initialize a normal distribution.
-
-    Can be defined either via a credible interval from ``x`` to ``y`` (use ``credibility`` or
-    it will default to being a 90% CI) or defined via ``mean`` and ``sd``.
-
-    Parameters
-    ----------
-    x : float
-        The low value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
-    y : float
-        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
-    credibility : float
-        The range of the credibility interval. Defaults to 90. Ignored if the distribution is
-        defined instead by ``mean`` and ``sd``.
-    mean : float or None
-        The mean of the normal distribution. If not defined, defaults to 0.
-    sd : float
-        The standard deviation of the normal distribution.
-    lclip : float or None
-        If not None, any value below ``lclip`` will be coerced to ``lclip``.
-    rclip : float or None
-        If not None, any value below ``rclip`` will be coerced to ``rclip``.
-
-    Returns
-    -------
-    NormalDistribution
-
-    Examples
-    --------
-    >>> norm(0, 1)
-    <Distribution> norm(mean=0.5, sd=0.3)
-    >>> norm(mean=1, sd=2)
-    <Distribution> norm(mean=1, sd=2)
-    """
-    return NormalDistribution(
-        x=x, y=y, credibility=credibility, mean=mean, sd=sd, lclip=lclip, rclip=rclip
-    )
    
-
-
-
-
    
-[docs]
-class LognormalDistribution(ContinuousDistribution):
-    def __init__(
-        self,
-        x=None,
-        y=None,
-        norm_mean=None,
-        norm_sd=None,
-        lognorm_mean=None,
-        lognorm_sd=None,
-        credibility=90,
-        lclip=None,
-        rclip=None,
-    ):
-        super().__init__()
-        self.x = x
-        self.y = y
-        self.credibility = credibility
-        self.norm_mean = norm_mean
-        self.norm_sd = norm_sd
-        self.lognorm_mean = lognorm_mean
-        self.lognorm_sd = lognorm_sd
-        self.lclip = lclip
-        self.rclip = rclip
-
-        if self.x is not None and self.y is not None and self.x > self.y:
-            raise ValueError("`high value` cannot be lower than `low value`")
-        if self.x is not None and self.x <= 0:
-            raise ValueError("lognormal distribution must have values > 0")
-
-        if (self.x is None or self.y is None) and self.norm_sd is None and self.lognorm_sd is None:
-            raise ValueError(
-                ("must define only one of x/y, norm_mean/norm_sd, " "or lognorm_mean/lognorm_sd")
-            )
-        elif (self.x is not None or self.y is not None) and (
-            self.norm_sd is not None or self.lognorm_sd is not None
-        ):
-            raise ValueError(
-                ("must define only one of x/y, norm_mean/norm_sd, " "or lognorm_mean/lognorm_sd")
-            )
-        elif (self.norm_sd is not None or self.norm_mean is not None) and (
-            self.lognorm_sd is not None or self.lognorm_mean is not None
-        ):
-            raise ValueError(
-                ("must define only one of x/y, norm_mean/norm_sd, " "or lognorm_mean/lognorm_sd")
-            )
-        elif self.norm_sd is not None and self.norm_mean is None:
-            self.norm_mean = 0
-        elif self.lognorm_sd is not None and self.lognorm_mean is None:
-            self.lognorm_mean = 1
-
-        if self.x is not None:
-            self.norm_mean = (np.log(self.x) + np.log(self.y)) / 2
-            cdf_value = 0.5 + 0.5 * (self.credibility / 100)
-            normed_sigma = scipy.stats.norm.ppf(cdf_value)
-            self.norm_sd = (np.log(self.y) - self.norm_mean) / normed_sigma
-
-        if self.lognorm_sd is None:
-            self.lognorm_mean = np.exp(self.norm_mean + self.norm_sd**2 / 2)
-            self.lognorm_sd = (
-                (np.exp(self.norm_sd**2) - 1) * np.exp(2 * self.norm_mean + self.norm_sd**2)
-            ) ** 0.5
-        elif self.norm_sd is None:
-            self.norm_mean = np.log(
-                (self.lognorm_mean**2 / np.sqrt(self.lognorm_sd**2 + self.lognorm_mean**2))
-            )
-            self.norm_sd = np.sqrt(np.log(1 + self.lognorm_sd**2 / self.lognorm_mean**2))
-
-    def __str__(self):
-        out = "<Distribution> lognorm(lognorm_mean={}, lognorm_sd={}, norm_mean={}, norm_sd={}"
-        out = out.format(
-            round(self.lognorm_mean, 2),
-            round(self.lognorm_sd, 2),
-            round(self.norm_mean, 2),
-            round(self.norm_sd, 2),
-        )
-        if self.lclip is not None:
-            out += ", lclip={}".format(self.lclip)
-        if self.rclip is not None:
-            out += ", rclip={}".format(self.rclip)
-        out += ")"
-        return out
    
-
-
-
-
    
-[docs]
-def lognorm(
-    x=None,
-    y=None,
-    credibility=90,
-    norm_mean=None,
-    norm_sd=None,
-    lognorm_mean=None,
-    lognorm_sd=None,
-    lclip=None,
-    rclip=None,
-):
-    """
-    Initialize a lognormal distribution.
-
-    Can be defined either via a credible interval from ``x`` to ``y`` (use ``credibility`` or
-    it will default to being a 90% CI) or defined via ``mean`` and ``sd``.
-
-    Parameters
-    ----------
-    x : float
-        The low value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
-        Must be a value greater than 0.
-    y : float
-        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
-        Must be a value greater than 0.
-    credibility : float
-        The range of the credibility interval. Defaults to 90. Ignored if the distribution is
-        defined instead by ``mean`` and ``sd``.
-    norm_mean : float or None
-        The mean of the underlying normal distribution. If not defined, defaults to 0.
-    norm_sd : float
-        The standard deviation of the underlying normal distribution.
-    lognorm_mean : float or None
-        The mean of the lognormal distribution. If not defined, defaults to 1.
-    lognorm_sd : float
-        The standard deviation of the lognormal distribution.
-    lclip : float or None
-        If not None, any value below ``lclip`` will be coerced to ``lclip``.
-    rclip : float or None
-        If not None, any value below ``rclip`` will be coerced to ``rclip``.
-
-    Returns
-    -------
-    LognormalDistribution
-
-    Examples
-    --------
-    >>> lognorm(1, 10)
-    <Distribution> lognorm(lognorm_mean=4.04, lognorm_sd=3.21, norm_mean=1.15, norm_sd=0.7)
-    >>> lognorm(norm_mean=1, norm_sd=2)
-    <Distribution> lognorm(lognorm_mean=20.09, lognorm_sd=147.05, norm_mean=1, norm_sd=2)
-    >>> lognorm(lognorm_mean=1, lognorm_sd=2)
-    <Distribution> lognorm(lognorm_mean=1, lognorm_sd=2, norm_mean=-0.8, norm_sd=1.27)
-    """
-    return LognormalDistribution(
-        x=x,
-        y=y,
-        credibility=credibility,
-        norm_mean=norm_mean,
-        norm_sd=norm_sd,
-        lognorm_mean=lognorm_mean,
-        lognorm_sd=lognorm_sd,
-        lclip=lclip,
-        rclip=rclip,
-    )
    
-
-
-
-
    
-[docs]
-def to(
-    x, y, credibility=90, lclip=None, rclip=None
-) -> Union[LognormalDistribution, NormalDistribution]:
-    """
-    Initialize a distribution from ``x`` to ``y``.
-
-    The distribution will be lognormal by default, unless ``x`` is less than or equal to 0,
-    in which case it will become a normal distribution.
-
-    The distribution will default to be a 90% credible interval between ``x`` and ``y`` unless
-    ``credibility`` is passed.
-
-    Parameters
-    ----------
-    x : float
-        The low value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
-    y : float
-        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
-    credibility : float
-        The range of the credibility interval. Defaults to 90.
-    lclip : float or None
-        If not None, any value below ``lclip`` will be coerced to ``lclip``.
-    rclip : float or None
-        If not None, any value below ``rclip`` will be coerced to ``rclip``.
-
-    Returns
-    -------
-    ``LognormalDistribution`` if ``x`` > 0, otherwise a ``NormalDistribution``
-
-    Examples
-    --------
-    >>> to(1, 10)
-    <Distribution> lognorm(mean=1.15, sd=0.7)
-    >>> to(-10, 10)
-    <Distribution> norm(mean=0.0, sd=6.08)
-    """
-    if x > 0:
-        return lognorm(x=x, y=y, credibility=credibility, lclip=lclip, rclip=rclip)
-    else:
-        return norm(x=x, y=y, credibility=credibility, lclip=lclip, rclip=rclip)
    
-
-
-
-
    
-[docs]
-class BinomialDistribution(DiscreteDistribution):
-    def __init__(self, n, p):
-        super().__init__()
-        self.n = n
-        self.p = p
-        if self.p <= 0 or self.p >= 1:
-            raise ValueError("p must be between 0 and 1 (exclusive)")
-
-    def __str__(self):
-        return "<Distribution> binomial(n={}, p={})".format(self.n, self.p)
    
-
-
-
-
    
-[docs]
-def binomial(n, p):
-    """
-    Initialize a binomial distribution.
-
-    Parameters
-    ----------
-    n : int
-        The number of trials.
-    p : float
-        The probability of success for each trial. Must be between 0 and 1.
-
-    Returns
-    -------
-    BinomialDistribution
-
-    Examples
-    --------
-    >>> binomial(1, 0.1)
-    <Distribution> binomial(1, 0.1)
-    """
-    return BinomialDistribution(n=n, p=p)
    
-
-
-
-
    
-[docs]
-class BetaDistribution(ContinuousDistribution):
-    def __init__(self, a, b):
-        super().__init__()
-        self.a = a
-        self.b = b
-
-    def __str__(self):
-        return "<Distribution> beta(a={}, b={})".format(self.a, self.b)
    
-
-
-
-
    
-[docs]
-def beta(a, b):
-    """
-    Initialize a beta distribution.
-
-    Parameters
-    ----------
-    a : float
-        The alpha shape value of the distribution. Typically takes the value of the
-        number of trials that resulted in a success.
-    b : float
-        The beta shape value of the distribution. Typically takes the value of the
-        number of trials that resulted in a failure.
-
-    Returns
-    -------
-    BetaDistribution
-
-    Examples
-    --------
-    >>> beta(1, 2)
-    <Distribution> beta(1, 2)
-    """
-    return BetaDistribution(a, b)
    
-
-
-
-
    
-[docs]
-class BernoulliDistribution(DiscreteDistribution):
-    def __init__(self, p):
-        super().__init__()
-        if not isinstance(p, float) or isinstance(p, int):
-            raise ValueError("bernoulli p must be a float or int")
-        if p <= 0 or p >= 1:
-            raise ValueError("bernoulli p must be 0-1 (exclusive)")
-        self.p = p
-
-    def __str__(self):
-        return "<Distribution> bernoulli(p={})".format(self.p)
    
-
-
-
-
    
-[docs]
-def bernoulli(p):
-    """
-    Initialize a Bernoulli distribution.
-
-    Parameters
-    ----------
-    p : float
-        The probability of the binary event. Must be between 0 and 1.
-
-    Returns
-    -------
-    BernoulliDistribution
-
-    Examples
-    --------
-    >>> bernoulli(0.1)
-    <Distribution> bernoulli(p=0.1)
-    """
-    return BernoulliDistribution(p)
    
-
-
-
-
    
-[docs]
-class CategoricalDistribution(DiscreteDistribution):
-    def __init__(self, items):
-        super().__init__()
-        if not isinstance(items, dict) and not isinstance(items, list) and not _is_numpy(items):
-            raise ValueError("inputs to categorical must be a dict or list")
-        assert len(items) > 0, "inputs to categorical must be non-empty"
-        self.items = list(items) if _is_numpy(items) else items
-
-    def __str__(self):
-        return "<Distribution> categorical({})".format(self.items)
    
-
-
-
-
    
-[docs]
-def discrete(items):
-    """
-    Initialize a discrete distribution (aka categorical distribution).
-
-    Parameters
-    ----------
-    items : list or dict
-        The values that the discrete distribution will return and their associated
-        weights (or likelihoods of being returned when sampled).
-
-    Returns
-    -------
-    CategoricalDistribution
-
-    Examples
-    --------
-    >>> discrete({0: 0.1, 1: 0.9})  # 10% chance of returning 0, 90% chance of returning 1
-    <Distribution> categorical({0: 0.1, 1: 0.9})
-    >>> discrete([[0.1, 0], [0.9, 1]])  # Different notation for the same thing.
-    <Distribution> categorical([[0.1, 0], [0.9, 1]])
-    >>> discrete([0, 1, 2])  # When no weights are given, all have equal chance of happening.
-    <Distribution> categorical([0, 1, 2])
-    >>> discrete({'a': 0.1, 'b': 0.9})  # Values do not have to be numbers.
-    <Distribution> categorical({'a': 0.1, 'b': 0.9})
-    """
-    return CategoricalDistribution(items)
    
-
-
-
-
    
-[docs]
-class TDistribution(ContinuousDistribution):
-    def __init__(self, x=None, y=None, t=20, credibility=90, lclip=None, rclip=None):
-        super().__init__()
-        self.x = x
-        self.y = y
-        self.t = t
-        self.df = t
-        self.credibility = credibility
-        self.lclip = lclip
-        self.rclip = rclip
-
-        if (self.x is None or self.y is None) and not (self.x is None and self.y is None):
-            raise ValueError("must define either both `x` and `y` or neither.")
-        elif self.x is not None and self.y is not None and self.x > self.y:
-            raise ValueError("`high value` cannot be lower than `low value`")
-
-        if self.x is None:
-            self.credibility = None
-
-    def __str__(self):
-        if self.x is not None:
-            out = "<Distribution> tdist(x={}, y={}, t={}".format(self.x, self.y, self.t)
-        else:
-            out = "<Distribution> tdist(t={}".format(self.t)
-        if self.credibility != 90 and self.credibility is not None:
-            out += ", credibility={}".format(self.credibility)
-        if self.lclip is not None:
-            out += ", lclip={}".format(self.lclip)
-        if self.rclip is not None:
-            out += ", rclip={}".format(self.rclip)
-        out += ")"
-        return out
    
-
-
-
-
    
-[docs]
-def tdist(x=None, y=None, t=20, credibility=90, lclip=None, rclip=None):
-    """
-    Initialize a t-distribution.
-
-    Is defined either via a loose credible interval from ``x`` to ``y`` (use ``credibility`` or
-    it will default to being a 90% CI). Unlike the normal and lognormal distributions, this
-    credible interval is an approximation and is not precisely defined.
-
-    If ``x`` and ``y`` are not defined, can just return a classic t-distribution defined via
-    ``t`` as the number of degrees of freedom.
-
-    Parameters
-    ----------
-    x : float or None
-        The low value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
-    y : float or None
-        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
-    t : float
-        The number of degrees of freedom of the t-distribution. Defaults to 20.
-    credibility : float
-        The range of the credibility interval. Defaults to 90.
-    lclip : float or None
-        If not None, any value below ``lclip`` will be coerced to ``lclip``.
-    rclip : float or None
-        If not None, any value below ``rclip`` will be coerced to ``rclip``.
-
-    Returns
-    -------
-    TDistribution
-
-    Examples
-    --------
-    >>> tdist(0, 1, 2)
-    <Distribution> tdist(x=0, y=1, t=2)
-    >>> tdist()
-    <Distribution> tdist(t=1)
-    """
-    return TDistribution(x=x, y=y, t=t, credibility=credibility, lclip=lclip, rclip=rclip)
    
-
-
-
-
    
-[docs]
-class LogTDistribution(ContinuousDistribution):
-    def __init__(self, x=None, y=None, t=1, credibility=90, lclip=None, rclip=None):
-        super().__init__()
-        self.x = x
-        self.y = y
-        self.t = t
-        self.df = t
-        self.credibility = credibility
-        self.lclip = lclip
-        self.rclip = rclip
-
-        if (self.x is None or self.y is None) and not (self.x is None and self.y is None):
-            raise ValueError("must define either both `x` and `y` or neither.")
-        if self.x is not None and self.y is not None and self.x > self.y:
-            raise ValueError("`high value` cannot be lower than `low value`")
-        if self.x is not None and self.x <= 0:
-            raise ValueError("`low value` must be greater than 0.")
-
-        if self.x is None:
-            self.credibility = None
-
-    def __str__(self):
-        if self.x is not None:
-            out = "<Distribution> log_tdist(x={}, y={}, t={}".format(self.x, self.y, self.t)
-        else:
-            out = "<Distribution> log_tdist(t={}".format(self.t)
-        if self.credibility != 90 and self.credibility is not None:
-            out += ", credibility={}".format(self.credibility)
-        if self.lclip is not None:
-            out += ", lclip={}".format(self.lclip)
-        if self.rclip is not None:
-            out += ", rclip={}".format(self.rclip)
-        out += ")"
-        return out
    
-
-
-
-
    
-[docs]
-def log_tdist(x=None, y=None, t=1, credibility=90, lclip=None, rclip=None):
-    """
-    Initialize a log t-distribution, which is a t-distribution in log-space.
-
-    Is defined either via a loose credible interval from ``x`` to ``y`` (use ``credibility`` or
-    it will default to being a 90% CI). Unlike the normal and lognormal distributions, this
-    credible interval is an approximation and is not precisely defined.
-
-    If ``x`` and ``y`` are not defined, can just return a classic t-distribution defined via
-    ``t`` as the number of degrees of freedom, but in log-space.
-
-    Parameters
-    ----------
-    x : float or None
-        The low value of a credible interval defined by ``credibility``. Must be greater than 0.
-        Defaults to a 90% CI.
-    y : float or None
-        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
-    t : float
-        The number of degrees of freedom of the t-distribution. Defaults to 1.
-    credibility : float
-        The range of the credibility interval. Defaults to 90.
-    lclip : float or None
-        If not None, any value below ``lclip`` will be coerced to ``lclip``.
-    rclip : float or None
-        If not None, any value below ``rclip`` will be coerced to ``rclip``.
-
-    Returns
-    -------
-    LogTDistribution
-
-    Examples
-    --------
-    >>> log_tdist(0, 1, 2)
-    <Distribution> log_tdist(x=0, y=1, t=2)
-    >>> log_tdist()
-    <Distribution> log_tdist(t=1)
-    """
-    return LogTDistribution(x=x, y=y, t=t, credibility=credibility, lclip=lclip, rclip=rclip)
    
-
-
-
-
    
-[docs]
-class TriangularDistribution(ContinuousDistribution):
-    def __init__(self, left, mode, right):
-        super().__init__()
-        if left > mode:
-            raise ValueError("left must be less than or equal to mode")
-        if right < mode:
-            raise ValueError("right must be greater than or equal to mode")
-        if left == right:
-            raise ValueError("left and right must be different")
-        self.left = left
-        self.mode = mode
-        self.right = right
-
-    def __str__(self):
-        return "<Distribution> triangular({}, {}, {})".format(self.left, self.mode, self.right)
    
-
-
-
-
    
-[docs]
-def triangular(left, mode, right, lclip=None, rclip=None):
-    """
-    Initialize a triangular distribution.
-
-    Parameters
-    ----------
-    left : float
-        The smallest value of the triangular distribution.
-    mode : float
-        The most common value of the triangular distribution.
-    right : float
-        The largest value of the triangular distribution.
-
-    Returns
-    -------
-    TriangularDistribution
-
-    Examples
-    --------
-    >>> triangular(1, 2, 3)
-    <Distribution> triangular(1, 2, 3)
-    """
-    return TriangularDistribution(left=left, mode=mode, right=right)
    
-
-
-
-
    
-[docs]
-class PERTDistribution(ContinuousDistribution):
-    def __init__(self, left, mode, right, lam=4, lclip=None, rclip=None):
-        super().__init__()
-        if left > mode:
-            raise ValueError("left must be less than or equal to mode")
-        if right < mode:
-            raise ValueError("right must be greater than or equal to mode")
-        if lam < 0:
-            raise ValueError("the shape parameter must be positive")
-        if left == right:
-            raise ValueError("left and right must be different")
-
-        self.left = left
-        self.mode = mode
-        self.right = right
-        self.lam = lam
-        self.lclip = lclip
-        self.rclip = rclip
-
-    def __str__(self):
-        out = "<Distribution> PERT({}, {}, {}, lam={}".format(
-            self.left, self.mode, self.right, self.lam
-        )
-        if self.lclip is not None:
-            out += ", lclip={}".format(self.lclip)
-        if self.rclip is not None:
-            out += ", rclip={}".format(self.rclip)
-        out += ")"
-        return out
    
-
-
-
-
    
-[docs]
-def pert(left, mode, right, lam=4, lclip=None, rclip=None):
-    """
-    Initialize a PERT distribution.
-
-    Parameters
-    ----------
-    left : float
-        The smallest value of the PERT distribution.
-    mode : float
-        The most common value of the PERT distribution.
-    right : float
-        The largest value of the PERT distribution.
-    lam : float
-        The lambda value of the PERT distribution. Defaults to 4.
-    lclip : float or None
-        If not None, any value below ``lclip`` will be coerced to ``lclip``.
-    rclip : float or None
-        If not None, any value below ``rclip`` will be coerced to ``rclip``.
-
-    Returns
-    -------
-    PERTDistribution
-
-    Examples
-    --------
-    >>> pert(1, 2, 3)
-    <Distribution> PERT(1, 2, 3)
-    """
-    return PERTDistribution(left=left, mode=mode, right=right, lam=lam, lclip=lclip, rclip=rclip)
    
-
-
-
-
    
-[docs]
-class PoissonDistribution(DiscreteDistribution):
-    def __init__(self, lam, lclip=None, rclip=None):
-        super().__init__()
-        self.lam = lam
-        self.lclip = lclip
-        self.rclip = rclip
-
-    def __str__(self):
-        out = "<Distribution> poisson({}".format(self.lam)
-        if self.lclip is not None:
-            out += ", lclip={}".format(self.lclip)
-        if self.rclip is not None:
-            out += ", rclip={}".format(self.rclip)
-        out += ")"
-        return out
    
-
-
-
-
    
-[docs]
-def poisson(lam, lclip=None, rclip=None):
-    """
-    Initialize a poisson distribution.
-
-    Parameters
-    ----------
-    lam : float
-        The lambda value of the poisson distribution.
-    lclip : float or None
-        If not None, any value below ``lclip`` will be coerced to ``lclip``.
-    rclip : float or None
-        If not None, any value below ``rclip`` will be coerced to ``rclip``.
-
-    Returns
-    -------
-    PoissonDistribution
-
-    Examples
-    --------
-    >>> poisson(1)
-    <Distribution> poisson(1)
-    """
-    return PoissonDistribution(lam=lam, lclip=lclip, rclip=rclip)
    
-
-
-
-
    
-[docs]
-class ChiSquareDistribution(ContinuousDistribution):
-    def __init__(self, df):
-        super().__init__()
-        self.df = df
-        if self.df <= 0:
-            raise ValueError("df must be positive")
-
-    def __str__(self):
-        return "<Distribution> chisquare({})".format(self.df)
    
-
-
-
-
    
-[docs]
-def chisquare(df):
-    """
-    Initialize a chi-square distribution.
-
-    Parameters
-    ----------
-    df : float
-        The degrees of freedom. Must be positive.
-
-    Returns
-    -------
-    ChiSquareDistribution
-
-    Examples
-    --------
-    >>> chisquare(2)
-    <Distribution> chiaquare(2)
-    """
-    return ChiSquareDistribution(df=df)
    
-
-
-
-
    
-[docs]
-class ExponentialDistribution(ContinuousDistribution):
-    def __init__(self, scale, lclip=None, rclip=None):
-        super().__init__()
-        assert scale > 0, "scale must be positive"
-        # Prevent numeric overflows
-        assert scale < 1e20, "scale must be less than 1e20"
-        self.scale = scale
-        self.lclip = lclip
-        self.rclip = rclip
-
-    def __str__(self):
-        out = "<Distribution> exponential({}".format(self.scale)
-        if self.lclip is not None:
-            out += ", lclip={}".format(self.lclip)
-        if self.rclip is not None:
-            out += ", rclip={}".format(self.rclip)
-        out += ")"
-        return out
    
-
-
-
-
    
-[docs]
-def exponential(scale, lclip=None, rclip=None):
-    """
-    Initialize an exponential distribution.
-
-    Parameters
-    ----------
-    scale : float
-        The scale value of the exponential distribution (> 0)
-    lclip : float or None
-        If not None, any value below ``lclip`` will be coerced to ``lclip``.
-    rclip : float or None
-        If not None, any value below ``rclip`` will be coerced to ``rclip``.
-
-    Returns
-    -------
-    ExponentialDistribution
-
-    Examples
-    --------
-    >>> exponential(1)
-    <Distribution> exponential(1)
-    """
-    return ExponentialDistribution(scale=scale, lclip=lclip, rclip=rclip)
    
-
-
-
-
    
-[docs]
-class GammaDistribution(ContinuousDistribution):
-    def __init__(self, shape, scale=1, lclip=None, rclip=None):
-        super().__init__()
-        self.shape = shape
-        self.scale = scale
-        self.lclip = lclip
-        self.rclip = rclip
-
-    def __str__(self):
-        out = "<Distribution> gamma(shape={}, scale={}".format(self.shape, self.scale)
-        if self.lclip is not None:
-            out += ", lclip={}".format(self.lclip)
-        if self.rclip is not None:
-            out += ", rclip={}".format(self.rclip)
-        out += ")"
-        return out
    
-
-
-
-
    
-[docs]
-def gamma(shape, scale=1, lclip=None, rclip=None):
-    """
-    Initialize a gamma distribution.
-
-    Parameters
-    ----------
-    shape : float
-        The shape value of the gamma distribution.
-    scale : float
-        The scale value of the gamma distribution. Defaults to 1.
-    lclip : float or None
-        If not None, any value below ``lclip`` will be coerced to ``lclip``.
-    rclip : float or None
-        If not None, any value below ``rclip`` will be coerced to ``rclip``.
-
-    Returns
-    -------
-    GammaDistribution
-
-    Examples
-    --------
-    >>> gamma(10, 1)
-    <Distribution> gamma(shape=10, scale=1)
-    """
-    return GammaDistribution(shape=shape, scale=scale, lclip=lclip, rclip=rclip)
    
-
-
-
-
    
-[docs]
-class ParetoDistribution(ContinuousDistribution):
-    def __init__(self, shape):
-        super().__init__()
-        self.shape = shape
-
-    def __str__(self):
-        return "<Distribution> pareto({})".format(self.shape)
    
-
-
-
-
    
-[docs]
-def pareto(shape):
-    """
-    Initialize a pareto distribution.
-
-    Parameters
-    ----------
-    shape : float
-        The shape value of the pareto distribution.
-
-    Returns
-    -------
-    ParetoDistribution
-
-    Examples
-    --------
-    >>> pareto(1)
-    <Distribution> pareto(1)
-    """
-    return ParetoDistribution(shape=shape)
    
-
-
-
-
    
-[docs]
-class MixtureDistribution(CompositeDistribution):
-    def __init__(self, dists, weights=None, relative_weights=None, lclip=None, rclip=None):
-        super().__init__()
-        weights, dists = _process_weights_values(weights, relative_weights, dists)
-        self.dists = dists
-        self.weights = weights
-        self.lclip = lclip
-        self.rclip = rclip
-        self._check_correlated(dists)
-
-    def __str__(self):
-        out = "<Distribution> mixture"
-        for i in range(len(self.dists)):
-            out += "\n - {} weight on {}".format(self.weights[i], self.dists[i])
-        return out
    
-
-
-
-
    
-[docs]
-def mixture(dists, weights=None, relative_weights=None, lclip=None, rclip=None):
-    """
-    Initialize a mixture distribution, which is a combination of different distributions.
-
-    Parameters
-    ----------
-    dists : list or dict
-        The distributions to mix. Can also be defined as a list of weights and distributions.
-    weights : list or None
-        The weights for each distribution.
-    relative_weights : list or None
-        Relative weights, which if given will be weights that are normalized
-        to sum to 1.
-    lclip : float or None
-        If not None, any value below ``lclip`` will be coerced to ``lclip``.
-    rclip : float or None
-        If not None, any value below ``rclip`` will be coerced to ``rclip``.
-
-    Returns
-    -------
-    MixtureDistribution
-
-    Examples
-    --------
-    >>> mixture([norm(1, 2), norm(3, 4)], weights=[0.1, 0.9])
-    <Distribution> mixture
-     - <Distribution> norm(mean=1.5, sd=0.3)
-     - <Distribution> norm(mean=3.5, sd=0.3)
-    >>> mixture([[0.1, norm(1, 2)], [0.9, norm(3, 4)]])  # Different notation for the same thing.
-    <Distribution> mixture
-     - <Distribution> norm(mean=1.5, sd=0.3)
-     - <Distribution> norm(mean=3.5, sd=0.3)
-    >>> mixture([norm(1, 2), norm(3, 4)])  # When no weights are given, all have equal chance
-    >>>                                    # of happening.
-    <Distribution> mixture
-     - <Distribution> norm(mean=1.5, sd=0.3)
-     - <Distribution> norm(mean=3.5, sd=0.3)
-    """
-    return MixtureDistribution(
-        dists=dists,
-        weights=weights,
-        relative_weights=relative_weights,
-        lclip=lclip,
-        rclip=rclip,
-    )
    
-
-
-
-
    
-[docs]
-def zero_inflated(p_zero, dist):
-    """
-    Initialize an arbitrary zero-inflated distribution.
-
-    Parameters
-    ----------
-    p_zero : float
-        The chance of the distribution returning zero
-    dist : Distribution
-        The distribution to sample from when not zero
-
-    Returns
-    -------
-    MixtureDistribution
-
-    Examples
-    --------
-    >>> zero_inflated(0.6, norm(1, 2))
-    <Distribution> mixture
-     - 0
-     - <Distribution> norm(mean=1.5, sd=0.3)
-    """
-    if p_zero > 1 or p_zero < 0 or not isinstance(p_zero, float):
-        raise ValueError("`p_zero` must be between 0 and 1")
-    return MixtureDistribution(dists=[0, dist], weights=p_zero)
    
-
-
-
-
    
-[docs]
-def inf0(p_zero, dist):
-    """
-    Initialize an arbitrary zero-inflated distribution.
-
-    Alias for ``zero_inflated``.
-
-    Parameters
-    ----------
-    p_zero : float
-        The chance of the distribution returning zero
-    dist : Distribution
-        The distribution to sample from when not zero
-
-    Returns
-    -------
-    MixtureDistribution
-
-    Examples
-    --------
-    >>> inf0(0.6, norm(1, 2))
-    <Distribution> mixture
-     - 0
-     - <Distribution> norm(mean=1.5, sd=0.3)
-    """
-    return zero_inflated(p_zero=p_zero, dist=dist)
    
-
-
-
-
    
-[docs]
-class GeometricDistribution(OperableDistribution):
-    def __init__(self, p):
-        super().__init__()
-        self.p = p
-        if self.p < 0 or self.p > 1:
-            raise ValueError("p must be between 0 and 1")
-
-    def __str__(self):
-        return "<Distribution> geometric(p={})".format(self.p)
    
-
-
-
-
    
-[docs]
-def geometric(p):
-    """
-    Initialize a geometric distribution.
-
-    Parameters
-    ----------
-    p : float
-        The probability of success of an individual trial. Must be between 0 and 1.
-
-    Returns
-    -------
-    GeometricDistribution
-
-    Examples
-    --------
-    >>> geometric(0.1)
-    <Distribution> geometric(0.1)
-    """
-    return GeometricDistribution(p=p)
    
-
-
    
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    Source code for squigglepy.rng
    -import numpy as np
-
-_squigglepy_internal_rng = np.random.default_rng()
-
-
-
    
-[docs]
-def set_seed(seed):
-    """
-    Set the seed of the random number generator used by Squigglepy.
-
-    The RNG is a ``np.random.default_rng`` under the hood.
-
-    Parameters
-    ----------
-    seed : float
-        The seed to use for the RNG.
-
-    Returns
-    -------
-    np.random.default_rng
-        The RNG used internally.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    Generator(PCG64) at 0x127EDE9E0
-    """
-    global _squigglepy_internal_rng
-    _squigglepy_internal_rng = np.random.default_rng(seed)
-    return _squigglepy_internal_rng
    
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-  
    Source code for squigglepy.samplers
    -import bisect
-import os
-import time
-
-import numpy as np
-import pathos.multiprocessing as mp
-
-from numpy.typing import NDArray
-
-from scipy import stats
-
-from .utils import (
-    _process_weights_values,
-    _process_discrete_weights_values,
-    is_dist,
-    is_sampleable,
-    _simplify,
-    _enlist,
-    _safe_len,
-    _core_cuts,
-    _init_tqdm,
-    _tick_tqdm,
-    _flush_tqdm,
-)
-
-from .distributions import (
-    BaseDistribution,
-    BernoulliDistribution,
-    BetaDistribution,
-    BinomialDistribution,
-    ChiSquareDistribution,
-    ComplexDistribution,
-    ConstantDistribution,
-    CategoricalDistribution,
-    ExponentialDistribution,
-    GammaDistribution,
-    GeometricDistribution,
-    LogTDistribution,
-    LognormalDistribution,
-    MixtureDistribution,
-    NormalDistribution,
-    ParetoDistribution,
-    PoissonDistribution,
-    TDistribution,
-    TriangularDistribution,
-    PERTDistribution,
-    UniformDistribution,
-    const,
-)
-
-_squigglepy_internal_sample_caches = {}
-
-
-def _get_rng():
-    from .rng import _squigglepy_internal_rng
-
-    return _squigglepy_internal_rng
-
-
-
    
-[docs]
-def normal_sample(mean, sd, samples=1):
-    """
-    Sample a random number according to a normal distribution.
-
-    Parameters
-    ----------
-    mean : float
-        The mean of the normal distribution that is being sampled.
-    sd : float
-        The standard deviation of the normal distribution that is being sampled.
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    float
-        A random number sampled from a normal distribution defined by
-        ``mean`` and ``sd``.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> normal_sample(0, 1)
-    0.30471707975443135
-    """
-    return _simplify(_get_rng().normal(mean, sd, samples))
    
-
-
-
-
    
-[docs]
-def lognormal_sample(mean, sd, samples=1):
-    """
-    Sample a random number according to a lognormal distribution.
-
-    Parameters
-    ----------
-    mean : float
-        The mean of the lognormal distribution that is being sampled.
-    sd : float
-        The standard deviation of the lognormal distribution that is being sampled.
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    float
-        A random number sampled from a lognormal distribution defined by
-        ``mean`` and ``sd``.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> lognormal_sample(0, 1)
-    1.3562412406168636
-    """
-    return _simplify(_get_rng().lognormal(mean, sd, samples))
    
-
-
-
-
    
-[docs]
-def t_sample(low=None, high=None, t=20, samples=1, credibility=90):
-    """
-    Sample a random number according to a t-distribution.
-
-    The t-distribution is defined with degrees of freedom via the ``t``
-    parameter. Additionally, a loose credibility interval can be defined
-    via the t-distribution using the ``low`` and ``high`` values. This will be a
-    90% CI by default unless you change ``credibility.`` Unlike the normal and
-    lognormal samplers, this credible interval is an approximation and is
-    not precisely defined.
-
-    Parameters
-    ----------
-    low : float or None
-        The low value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
-    high : float or None
-        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
-    t : float
-        The number of degrees of freedom of the t-distribution. Defaults to 20.
-    samples : int
-        The number of samples to return.
-    credibility : float
-        The range of the credibility interval. Defaults to 90.
-
-    Returns
-    -------
-    float
-        A random number sampled from a lognormal distribution defined by
-        ``mean`` and ``sd``.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> t_sample(1, 2, t=4)
-    2.7887113716855985
-    """
-    if low is None and high is None:
-        return _get_rng().standard_t(t, samples)
-    elif low is None or high is None:
-        raise ValueError("must define either both `x` and `y` or neither.")
-    elif low > high:
-        raise ValueError("`high value` cannot be lower than `low value`")
-    elif low == high:
-        return low
-    else:
-        mu = (high + low) / 2
-        cdf_value = 0.5 + 0.5 * (credibility / 100)
-        normed_sigma = stats.norm.ppf(cdf_value)
-        sigma = (high - mu) / normed_sigma
-        return _simplify(
-            normal_sample(mu, sigma, samples) / ((chi_square_sample(t, samples) / t) ** 0.5)
-        )
    
-
-
-
-
    
-[docs]
-def log_t_sample(low=None, high=None, t=20, samples=1, credibility=90):
-    """
-    Sample a random number according to a log-t-distribution.
-
-    The log-t-distribution is a t-distribution in log-space. It is defined with
-    degrees of freedom via the ``t`` parameter. Additionally, a loose credibility
-    interval can be defined via the t-distribution using the ``low`` and ``high``
-    values. This will be a 90% CI by default unless you change ``credibility.``
-    Unlike the normal and lognormal samplers, this credible interval is an
-    approximation and is not precisely defined.
-
-    Parameters
-    ----------
-    low : float or None
-        The low value of a credible interval defined by ``credibility``.
-        Must be greater than 0. Defaults to a 90% CI.
-    high : float or None
-        The high value of a credible interval defined by ``credibility``. Defaults to a 90% CI.
-    t : float
-        The number of degrees of freedom of the t-distribution. Defaults to 20.
-    samples : int
-        The number of samples to return.
-    credibility : float
-        The range of the credibility interval. Defaults to 90.
-
-    Returns
-    -------
-    float
-        A random number sampled from a lognormal distribution defined by
-        ``mean`` and ``sd``.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> log_t_sample(1, 2, t=4)
-    2.052949773846356
-    """
-    if low is None and high is None:
-        return np.exp(_get_rng().standard_t(t))
-    elif low > high:
-        raise ValueError("`high value` cannot be lower than `low value`")
-    elif low < 0:
-        raise ValueError("log_t_sample cannot handle negative values")
-    elif low == high:
-        return low
-    else:
-        log_low = np.log(low)
-        log_high = np.log(high)
-        mu = (log_high + log_low) / 2
-        cdf_value = 0.5 + 0.5 * (credibility / 100)
-        normed_sigma = stats.norm.ppf(cdf_value)
-        sigma = (log_high - mu) / normed_sigma
-        return _simplify(
-            np.exp(
-                normal_sample(mu, sigma, samples) / ((chi_square_sample(t, samples) / t) ** 0.5)
-            )
-        )
    
-
-
-
-
    
-[docs]
-def binomial_sample(n, p, samples=1):
-    """
-    Sample a random number according to a binomial distribution.
-
-    Parameters
-    ----------
-    n : int
-        The number of trials.
-    p : float
-        The probability of success for each trial. Must be between 0 and 1.
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    int
-        A random number sampled from a binomial distribution defined by
-        ``n`` and ``p``. The random number should be between 0 and ``n``.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> binomial_sample(10, 0.1)
-    2
-    """
-    return _simplify(_get_rng().binomial(n, p, samples))
    
-
-
-
-
    
-[docs]
-def beta_sample(a, b, samples=1):
-    """
-    Sample a random number according to a beta distribution.
-
-    Parameters
-    ----------
-    a : float
-        The alpha shape value of the distribution. Typically takes the value of the
-        number of trials that resulted in a success.
-    b : float
-        The beta shape value of the distribution. Typically takes the value of the
-        number of trials that resulted in a failure.
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    float
-        A random number sampled from a beta distribution defined by
-        ``a`` and ``b``.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> beta_sample(1, 1)
-    0.22145847498048798
-    """
-    return _simplify(_get_rng().beta(a, b, samples))
    
-
-
-
-
    
-[docs]
-def bernoulli_sample(p, samples=1):
-    """
-    Sample 1 with probability ``p`` and 0 otherwise.
-
-    Parameters
-    ----------
-    p : float
-        The probability of success. Must be between 0 and 1.
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    int
-        Either 0 or 1
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> bernoulli_sample(0.5)
-    0
-    """
-    a = uniform_sample(0, 1, samples)
-    if _safe_len(a) == 1:
-        return int(a < p)
-    else:
-        return (a < p).astype(int)
    
-
-
-
-
    
-[docs]
-def triangular_sample(left, mode, right, samples=1):
-    """
-    Sample a random number according to a triangular distribution.
-
-    Parameters
-    ----------
-    left : float
-        The smallest value of the triangular distribution.
-    mode : float
-        The most common value of the triangular distribution.
-    right : float
-        The largest value of the triangular distribution.
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    float
-        A random number sampled from a triangular distribution.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> triangular_sample(1, 2, 3)
-    2.327625176788963
-    """
-    return _simplify(_get_rng().triangular(left, mode, right, samples))
    
-
-
-
-
    
-[docs]
-def pert_sample(left, mode, right, lam, samples=1):
-    """
-    Sample a random number according to a PERT distribution.
-
-    Parameters
-    ----------
-    left : float
-        The smallest value of the PERT distribution.
-    mode : float
-        The most common value of the PERT distribution.
-    right : float
-        The largest value of the PERT distribution.
-    lam : float
-        The lambda of the PERT distribution.
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    float
-        A random number sampled from a PERT distribution.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> pert_sample(1, 2, 3, 4)
-    2.327625176788963
-    """
-    r = right - left
-    alpha = 1 + lam * (mode - left) / r
-    beta = 1 + lam * (right - mode) / r
-    return left + beta_sample(a=alpha, b=beta, samples=samples) * r
    
-
-
-
-
    
-[docs]
-def poisson_sample(lam, samples=1):
-    """
-    Sample a random number according to a poisson distribution.
-
-    Parameters
-    ----------
-    lam : float
-        The lambda value of the poisson distribution.
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    int
-        A random number sampled from a poisson distribution.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> poisson_sample(10)
-    13
-    """
-    return _simplify(_get_rng().poisson(lam, samples))
    
-
-
-
-
    
-[docs]
-def exponential_sample(scale, samples=1):
-    """
-    Sample a random number according to an exponential distribution.
-
-    Parameters
-    ----------
-    scale : float
-        The scale value of the exponential distribution.
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    int
-        A random number sampled from an exponential distribution.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> exponential_sample(10)
-    24.042086039659946
-    """
-    return _simplify(_get_rng().exponential(scale, samples))
    
-
-
-
-
    
-[docs]
-def gamma_sample(shape, scale, samples=1):
-    """
-    Sample a random number according to a gamma distribution.
-
-    Parameters
-    ----------
-    shape : float
-        The shape value of the gamma distribution.
-    scale : float
-        The scale value of the gamma distribution. Defaults to 1.
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    int
-        A random number sampled from an gamma distribution.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> gamma_sample(10, 2)
-    21.290716894247602
-    """
-    return _simplify(_get_rng().gamma(shape, scale, samples))
    
-
-
-
-
    
-[docs]
-def pareto_sample(shape, samples=1):
-    """
-    Sample a random number according to a pareto distribution.
-
-    Parameters
-    ----------
-    shape : float
-        The shape value of the pareto distribution.
-
-    Returns
-    -------
-    int
-        A random number sampled from an pareto distribution.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> pareto_sample(1)
-    10.069666324736094
-    """
-    return _simplify(_get_rng().pareto(shape, samples))
    
-
-
-
-
    
-[docs]
-def uniform_sample(low, high, samples=1):
-    """
-    Sample a random number according to a uniform distribution.
-
-    Parameters
-    ----------
-    low : float
-        The smallest value the uniform distribution will return.
-    high : float
-        The largest value the uniform distribution will return.
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    float
-        A random number sampled from a uniform distribution between
-        ```low``` and ```high```.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> uniform_sample(0, 1)
-    0.7739560485559633
-    """
-    return _simplify(_get_rng().uniform(low, high, samples))
    
-
-
-
-
    
-[docs]
-def chi_square_sample(df, samples=1):
-    """
-    Sample a random number according to a chi-square distribution.
-
-    Parameters
-    ----------
-    df : float
-        The number of degrees of freedom
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    float
-        A random number sampled from a chi-square distribution.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> chi_square_sample(2)
-    4.808417207931989
-    """
-    return _simplify(_get_rng().chisquare(df, samples))
    
-
-
-
-
    
-[docs]
-def discrete_sample(items, samples=1, verbose=False, _multicore_tqdm_n=1, _multicore_tqdm_cores=1):
-    """
-    Sample a random value from a discrete distribution (aka categorical distribution).
-
-    Parameters
-    ----------
-    items : list or dict
-        The values that the discrete distribution will return and their associated
-        weights (or likelihoods of being returned when sampled).
-    samples : int
-        The number of samples to return.
-    verbose : bool
-        If True, will print out statements on computational progress.
-    _multicore_tqdm_n : int
-        The total number of samples to use for printing tqdm's interface. This is meant to only
-        be used internally by squigglepy to make the progress bar printing work well for
-        multicore. This parameter can be safely ignored by the user.
-    _multicore_tqdm_cores : int
-        The total number of cores to use for printing tqdm's interface. This is meant to only
-        be used internally by squigglepy to make the progress bar printing work well for
-        multicore. This parameter can be safely ignored by the user.
-
-    Returns
-    -------
-    Various, based on items in ``items``
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> # 10% chance of returning 0, 90% chance of returning 1
-    >>> discrete_sample({0: 0.1, 1: 0.9})
-    1
-    >>> discrete_sample([[0.1, 0], [0.9, 1]])  # Different notation for the same thing.
-    1
-    >>> # When no weights are given, all have equal chance of happening.
-    >>> discrete_sample([0, 1, 2])
-    2
-    >>> discrete_sample({'a': 0.1, 'b': 0.9})  # Values do not have to be numbers.
-    'b'
-    """
-    weights, values = _process_discrete_weights_values(items)
-
-    values = [const(v) for v in values]
-
-    return mixture_sample(
-        values=values,
-        weights=weights,
-        samples=samples,
-        verbose=verbose,
-        _multicore_tqdm_n=_multicore_tqdm_n,
-        _multicore_tqdm_cores=_multicore_tqdm_cores,
-    )
    
-
-
-
-
    
-[docs]
-def geometric_sample(p, samples=1):
-    """
-    Sample a random number according to a geometric distribution.
-
-    Parameters
-    ----------
-    p : float
-        The probability of success of an individual trial. Must be between 0 and 1.
-    samples : int
-        The number of samples to return.
-
-    Returns
-    -------
-    int
-        A random number sampled from a geometric distribution.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> geometric_sample(0.1)
-    2
-    """
-    return _simplify(_get_rng().geometric(p, samples))
    
-
-
-
-def _mixture_sample_for_large_n(
-    values,
-    weights=None,
-    relative_weights=None,
-    samples=1,
-    verbose=False,
-    _multicore_tqdm_n=1,
-    _multicore_tqdm_cores=1,
-):
-    def _run_presample(dist, pbar):
-        _tick_tqdm(pbar)
-        return _enlist(sample(dist, n=samples))
-
-    pbar = _init_tqdm(verbose=verbose, total=len(values))
-    values = [_run_presample(v, pbar) for v in values]
-    _flush_tqdm(pbar)
-
-    def _run_mixture(picker, i, pbar):
-        _tick_tqdm(pbar, _multicore_tqdm_cores)
-        index = bisect.bisect_left(weights, picker)
-        return values[index][i]
-
-    weights = np.cumsum(weights)
-    picker = uniform_sample(0, 1, samples=samples)
-
-    tqdm_samples = samples if _multicore_tqdm_cores == 1 else _multicore_tqdm_n
-    pbar = _init_tqdm(verbose=verbose, total=tqdm_samples)
-    out = _simplify([_run_mixture(p, i, pbar) for i, p in enumerate(_enlist(picker))])
-    _flush_tqdm(pbar)
-
-    return out
-
-
-def _mixture_sample_for_small_n(
-    values,
-    weights=None,
-    relative_weights=None,
-    samples=1,
-    verbose=False,
-    _multicore_tqdm_n=1,
-    _multicore_tqdm_cores=1,
-):
-    def _run_mixture(values, weights, pbar=None, tick=1):
-        r_ = uniform_sample(0, 1)
-        _tick_tqdm(pbar, tick)
-        for i, dist in enumerate(values):
-            weight = weights[i]
-            if r_ <= weight:
-                return sample(dist)
-        return sample(dist)
-
-    weights = np.cumsum(weights)
-    tqdm_samples = samples if _multicore_tqdm_cores == 1 else _multicore_tqdm_n
-    pbar = _init_tqdm(verbose=verbose, total=tqdm_samples)
-    out = _simplify(
-        [
-            _run_mixture(values=values, weights=weights, pbar=pbar, tick=_multicore_tqdm_cores)
-            for _ in range(samples)
-        ]
-    )
-    _flush_tqdm(pbar)
-    return out
-
-
-
    
-[docs]
-def mixture_sample(
-    values,
-    weights=None,
-    relative_weights=None,
-    samples=1,
-    verbose=False,
-    _multicore_tqdm_n=1,
-    _multicore_tqdm_cores=1,
-):
-    """
-    Sample a ranom number from a mixture distribution.
-
-    Parameters
-    ----------
-    values : list or dict
-        The distributions to mix. Can also be defined as a list of weights and distributions.
-    weights : list or None
-        The weights for each distribution.
-    relative_weights : list or None
-        Relative weights, which if given will be weights that are normalized
-        to sum to 1.
-    samples : int
-        The number of samples to return.
-    verbose : bool
-        If True, will print out statements on computational progress.
-    _multicore_tqdm_n : int
-        The total number of samples to use for printing tqdm's interface. This is meant to only
-        be used internally by squigglepy to make the progress bar printing work well for
-        multicore. This parameter can be safely ignored by the user.
-    _multicore_tqdm_cores : int
-        The total number of cores to use for printing tqdm's interface. This is meant to only
-        be used internally by squigglepy to make the progress bar printing work well for
-        multicore. This parameter can be safely ignored by the user.
-
-    Returns
-    -------
-    Various, based on items in ``values``
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> mixture_sample([norm(1, 2), norm(3, 4)], weights=[0.1, 0.9])
-    3.183867278765718
-    >>> # Different notation for the same thing.
-    >>> mixture_sample([[0.1, norm(1, 2)], [0.9, norm(3, 4)]])
-    3.7859113725925972
-    >>> # When no weights are given, all have equal chance of happening.
-    >>> mixture_sample([norm(1, 2), norm(3, 4)])
-    1.1041655362137777
-    """
-    weights, values = _process_weights_values(weights, relative_weights, values)
-
-    if len(values) == 1:
-        return sample(values[0], n=samples)
-
-    if samples > 100:
-        return _mixture_sample_for_large_n(
-            values=values,
-            weights=weights,
-            samples=samples,
-            verbose=verbose,
-            _multicore_tqdm_n=_multicore_tqdm_n,
-            _multicore_tqdm_cores=_multicore_tqdm_cores,
-        )
-    else:
-        return _mixture_sample_for_small_n(
-            values=values,
-            weights=weights,
-            samples=samples,
-            verbose=verbose,
-            _multicore_tqdm_n=_multicore_tqdm_n,
-            _multicore_tqdm_cores=_multicore_tqdm_cores,
-        )
    
-
-
-
-
    
-[docs]
-def sample_correlated_group(
-    requested_dist: BaseDistribution, n: int, verbose=False
-) -> NDArray[np.float64]:
-    """
-    Samples a correlated distribution, alongside
-    all other correlated distributions in the same group.
-
-    The samples for other variables are stored in the distributions themselves
-    (in `_correlated_samples`).
-
-    This is necessary, because the sampling needs to happen all at once, regardless
-    of where the distributions are used in the binary tree of operations.
-    """
-    group = requested_dist.correlation_group
-    assert group is not None
-
-    samples = np.column_stack(
-        [
-            # Skip correlation to prevent infinite recursion
-            # TODO: Check that this does not interfere
-            # with other correlated distributions downstream
-            sample(dist, n, verbose=verbose, _correlate_if_needed=False)
-            for dist in group.correlated_dists
-        ]
-    )
-    # Induce correlation
-    samples = group.induce_correlation(samples)
-
-    # Store the samples in each distribution
-    # except the one we are sampling from
-    # so it requires resampling next time
-    requested_samples = None
-    for i, target_distribution in enumerate(group.correlated_dists):
-        if requested_dist is not target_distribution:
-            # Store the samples in the distribution
-            target_distribution._correlated_samples = samples[:, i]
-        else:
-            # Store the samples we requested
-            requested_samples = samples[:, i]
-
-    assert requested_samples is not None
-
-    return requested_samples
    
-
-
-
-
    
-[docs]
-def sample(
-    dist=None,
-    n=1,
-    lclip=None,
-    rclip=None,
-    memcache=False,
-    reload_cache=False,
-    dump_cache_file=None,
-    load_cache_file=None,
-    cache_file_primary=False,
-    verbose=None,
-    cores=1,
-    _multicore_tqdm_n=1,
-    _multicore_tqdm_cores=1,
-    _correlate_if_needed=True,
-):
-    """
-    Sample random numbers from a given distribution.
-
-    Parameters
-    ----------
-    dist : Distribution
-        The distribution to sample random number from.
-    n : int
-        The number of random numbers to sample from the distribution. Default to 1.
-    lclip : float or None
-        If not None, any value below ``lclip`` will be coerced to ``lclip``.
-    rclip : float or None
-        If not None, any value below ``rclip`` will be coerced to ``rclip``.
-    memcache : bool
-        If True, will attempt to load the results in-memory for future calculations if
-        a cache is present. Otherwise will save the results to an in-memory cache. Each cache
-        will be matched based on ``dist``. Default ``False``.
-    reload_cache : bool
-        If True, any existing cache will be ignored and recalculated. Default ``False``.
-    dump_cache_file : str or None
-        If present, will write out the cache to a numpy file with this path with
-        ``.sqlcache.npy`` appended to the file name.
-    load_cache_file : str or None
-        If present, will first attempt to load and use a cache from a file with this
-        path with ``.sqlcache.npy`` appended to the file name.
-    cache_file_primary : bool
-        If both an in-memory cache and file cache are present, the file
-        cache will be used for the cache if this is True, and the in-memory cache
-        will be used otherwise. Defaults to False.
-    verbose : bool
-        If True, will print out statements on computational progress. If False, will not.
-        If None (default), will be True when ``n`` is greater than or equal to 1M.
-    cores : int
-        If 1, runs on a single core / process. If greater than 1, will run on a multiprocessing
-        pool with that many cores / processes.
-    _multicore_tqdm_n : int
-        The total number of samples to use for printing tqdm's interface. This is meant to only
-        be used internally by squigglepy to make the progress bar printing work well for
-        multicore. This parameter can be safely ignored by the user.
-    _multicore_tqdm_cores : int
-        The total number of cores to use for printing tqdm's interface. This is meant to only
-        be used internally by squigglepy to make the progress bar printing work well for
-        multicore. This parameter can be safely ignored by the user.
-
-    Returns
-    -------
-    Various, based on ``dist``.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> sample(norm(1, 2))
-    1.592627415218455
-    >>> sample(mixture([norm(1, 2), norm(3, 4)]))
-    1.7281209657534462
-    >>> sample(lognorm(1, 10), n=5, lclip=3)
-    array([6.10817361, 3.        , 3.        , 3.45828454, 3.        ])
-    """
-    n = int(n)
-    if n <= 0:
-        raise ValueError("n must be >= 1")
-
-    if not is_sampleable(dist):
-        error = "input to sample is malformed - {} is not a sampleable type.".format(type(dist))
-        raise ValueError(error)
-
-    if verbose is None:
-        verbose = n >= 1000000
-
-    # Handle loading from cache
-    samples = None
-    has_in_mem_cache = str(dist) in _squigglepy_internal_sample_caches
-    if load_cache_file:
-        cache_path = load_cache_file + ".sqcache.npy"
-        has_file_cache = os.path.exists(cache_path) if load_cache_file else False
-
-    if load_cache_file and not has_file_cache and verbose:
-        print("Warning: cache file `{}.sqcache.npy` not found.".format(load_cache_file))
-
-    if (load_cache_file or memcache) and not reload_cache:
-        if load_cache_file and has_file_cache and (not has_in_mem_cache or cache_file_primary):
-            if verbose:
-                print("Loading from cache file (`{}`)...".format(cache_path))
-            with open(cache_path, "rb") as f:
-                samples = np.load(f)
-
-        elif memcache and has_in_mem_cache:
-            if verbose:
-                print("Loading from in-memory cache...")
-            samples = _squigglepy_internal_sample_caches.get(str(dist))
-
-    # Handle multicore
-    if samples is None and cores > 1:
-        if verbose:
-            print("Generating samples with {} cores...".format(cores))
-        with mp.ProcessingPool(cores) as pool:
-            cuts = _core_cuts(n, cores)
-
-            def multicore_sample(core, total_n=n, total_cores=cores, verbose=False):
-                batch = sample(
-                    dist=dist,
-                    n=cuts[core],
-                    _multicore_tqdm_n=total_n,
-                    _multicore_tqdm_cores=total_cores,
-                    lclip=lclip,
-                    rclip=rclip,
-                    memcache=False,
-                    verbose=verbose,
-                    cores=1,
-                )
-                if verbose:
-                    print("Shuffling data...")
-                with open("test-core-{}.npy".format(core), "wb") as f:
-                    np.save(f, batch)
-                return None
-
-            pool_results = pool.amap(multicore_sample, range(cores - 1))
-            multicore_sample(cores - 1, verbose=verbose)
-            if verbose:
-                print("Waiting for other cores...")
-            while not pool_results.ready():
-                if verbose:
-                    print(".", end="", flush=True)
-                time.sleep(1)
-
-        if verbose:
-            print("Collecting data...")
-        samples = np.array([])
-        pbar = _init_tqdm(verbose=verbose, total=cores)
-        for core in range(cores):
-            with open("test-core-{}.npy".format(core), "rb") as f:
-                samples = np.concatenate((samples, np.load(f, allow_pickle=True)), axis=None)
-            os.remove("test-core-{}.npy".format(core))
-            _tick_tqdm(pbar, 1)
-        _flush_tqdm(pbar)
-        if verbose:
-            print("...Collected!")
-
-    # Handle lclip/rclip
-    if samples is None:
-        lclip_ = None
-        rclip_ = None
-        if is_dist(dist):
-            lclip_ = dist.lclip
-            rclip_ = dist.rclip
-
-        if lclip is None and lclip_ is not None:
-            lclip = lclip_
-        elif lclip is not None and lclip_ is not None:
-            lclip = max(lclip, lclip_)
-
-        if rclip is None and rclip_ is not None:
-            rclip = rclip_
-        elif rclip is not None and rclip_ is not None:
-            rclip = min(rclip, rclip_)
-
-    # Start sampling
-    if samples is None:
-        if callable(dist):
-            if n > 1:
-
-                def run_dist(dist, pbar=None, tick=1):
-                    dist = dist()
-                    _tick_tqdm(pbar, tick)
-                    return dist
-
-                tqdm_samples = n if _multicore_tqdm_cores == 1 else _multicore_tqdm_n
-                pbar = _init_tqdm(verbose=verbose, total=tqdm_samples)
-                out = np.array(
-                    [run_dist(dist=dist, pbar=pbar, tick=_multicore_tqdm_cores) for _ in range(n)]
-                )
-                _flush_tqdm(pbar)
-            else:
-                out = [dist()]
-
-            def run_dist(dist, pbar=None, tick=1):
-                samp = sample(dist) if is_dist(dist) or callable(dist) else dist
-                _tick_tqdm(pbar, tick)
-                return samp
-
-            pbar = _init_tqdm(verbose=verbose, total=len(out) * _multicore_tqdm_cores)
-            samples = _simplify(
-                np.array([run_dist(dist=o, pbar=pbar, tick=_multicore_tqdm_cores) for o in out])
-            )
-            _flush_tqdm(pbar)
-
-        elif (
-            isinstance(dist, float)
-            or isinstance(dist, int)
-            or isinstance(dist, str)
-            or dist is None
-        ):
-            samples = _simplify(np.array([dist for _ in range(n)]))
-
-        # Distribution is part of a correlation group
-        # and has not been sampled yet
-        elif (
-            isinstance(dist, BaseDistribution)
-            and _correlate_if_needed
-            and dist.correlation_group is not None
-            and dist._correlated_samples is None
-        ):
-            # Samples the entire correlated group at once
-            samples = sample_correlated_group(dist, n=n, verbose=verbose)
-
-        # Distribution has already been sampled
-        # as part of a correlation group
-        elif (
-            isinstance(dist, BaseDistribution)
-            and _correlate_if_needed
-            and dist.correlation_group is not None
-            and dist._correlated_samples is not None
-        ):
-            samples = dist._correlated_samples
-            # This forces the distribution to be resampled
-            # if the user attempts to sample from it again
-            dist._correlated_samples = None
-
-        elif isinstance(dist, ConstantDistribution):
-            samples = _simplify(np.array([dist.x for _ in range(n)]))
-
-        elif isinstance(dist, UniformDistribution):
-            samples = uniform_sample(dist.x, dist.y, samples=n)
-
-        elif isinstance(dist, CategoricalDistribution):
-            samples = discrete_sample(
-                dist.items,
-                samples=n,
-                _multicore_tqdm_n=_multicore_tqdm_n,
-                _multicore_tqdm_cores=_multicore_tqdm_cores,
-            )
-
-        elif isinstance(dist, NormalDistribution):
-            samples = normal_sample(mean=dist.mean, sd=dist.sd, samples=n)
-
-        elif isinstance(dist, LognormalDistribution):
-            samples = lognormal_sample(mean=dist.norm_mean, sd=dist.norm_sd, samples=n)
-
-        elif isinstance(dist, BinomialDistribution):
-            samples = binomial_sample(n=dist.n, p=dist.p, samples=n)
-
-        elif isinstance(dist, BetaDistribution):
-            samples = beta_sample(a=dist.a, b=dist.b, samples=n)
-
-        elif isinstance(dist, BernoulliDistribution):
-            samples = bernoulli_sample(p=dist.p, samples=n)
-
-        elif isinstance(dist, PoissonDistribution):
-            samples = poisson_sample(lam=dist.lam, samples=n)
-
-        elif isinstance(dist, ChiSquareDistribution):
-            samples = chi_square_sample(df=dist.df, samples=n)
-
-        elif isinstance(dist, ExponentialDistribution):
-            samples = exponential_sample(scale=dist.scale, samples=n)
-
-        elif isinstance(dist, GammaDistribution):
-            samples = gamma_sample(shape=dist.shape, scale=dist.scale, samples=n)
-
-        elif isinstance(dist, ParetoDistribution):
-            samples = pareto_sample(shape=dist.shape, samples=n)
-
-        elif isinstance(dist, TriangularDistribution):
-            samples = triangular_sample(dist.left, dist.mode, dist.right, samples=n)
-
-        elif isinstance(dist, PERTDistribution):
-            samples = pert_sample(dist.left, dist.mode, dist.right, dist.lam, samples=n)
-
-        elif isinstance(dist, TDistribution):
-            samples = t_sample(dist.x, dist.y, dist.t, credibility=dist.credibility, samples=n)
-
-        elif isinstance(dist, LogTDistribution):
-            samples = log_t_sample(dist.x, dist.y, dist.t, credibility=dist.credibility, samples=n)
-
-        elif isinstance(dist, MixtureDistribution):
-            samples = mixture_sample(
-                dist.dists,
-                dist.weights,
-                samples=n,
-                verbose=verbose,
-                _multicore_tqdm_n=_multicore_tqdm_n,
-                _multicore_tqdm_cores=_multicore_tqdm_cores,
-            )
-
-        elif isinstance(dist, GeometricDistribution):
-            samples = geometric_sample(p=dist.p, samples=n)
-
-        elif isinstance(dist, ComplexDistribution):
-            if dist.right is None:
-                samples = dist.fn(sample(dist.left, n=n, verbose=verbose))
-            else:
-                samples = dist.fn(
-                    sample(dist.left, n=n, verbose=verbose),
-                    sample(dist.right, n=n, verbose=verbose),
-                )
-
-            if is_dist(samples) or callable(samples):
-                samples = sample(samples, n=n)
-
-        else:
-            raise ValueError("{} sampler not found".format(type(dist)))
-
-    # Use lclip / rclip
-    if _safe_len(samples) > 1:
-        if lclip is not None:
-            samples = np.maximum(samples, lclip)
-        if rclip is not None:
-            samples = np.minimum(samples, rclip)
-    else:
-        if lclip is not None:
-            samples = lclip if samples < lclip else samples
-        if rclip is not None:
-            samples = rclip if samples > rclip else samples
-
-    # Save to cache
-    if memcache and (not has_in_mem_cache or reload_cache):
-        if verbose:
-            print("Caching in-memory...")
-        _squigglepy_internal_sample_caches[str(dist)] = samples
-        if verbose:
-            print("...Cached")
-
-    if dump_cache_file:
-        cache_path = dump_cache_file + ".sqcache.npy"
-        if verbose:
-            print("Writing cache to file `{}`...".format(cache_path))
-        with open(cache_path, "wb") as f:
-            np.save(f, samples)
-        if verbose:
-            print("...Cached")
-
-    # Return
-    return np.array(samples) if isinstance(samples, list) else samples
    
-
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-      
    
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-    
    
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-    squigglepy.utils — Squigglepy  documentation
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    Source code for squigglepy.utils
    -import math
-import numpy as np
-
-from tqdm import tqdm
-from datetime import datetime
-from collections import Counter
-from collections.abc import Iterable
-
-import importlib
-import importlib.util
-import sys
-
-
-def _check_pandas_series(values):
-    """Check if values is a pandas series. Only imports pandas if necessary."""
-    if "pandas" not in sys.modules:
-        return False
-
-    pd = importlib.import_module("pandas")
-    return isinstance(values, pd.core.series.Series)
-
-
-def _process_weights_values(weights=None, relative_weights=None, values=None, drop_na=False):
-    if weights is not None and relative_weights is not None:
-        raise ValueError("can only pass either `weights` or `relative_weights`, not both.")
-    if values is None or _safe_len(values) == 0:
-        raise ValueError("must pass `values`")
-
-    relative = False
-    if relative_weights is not None:
-        weights = relative_weights
-        relative = True
-
-    if isinstance(weights, float):
-        weights = [weights]
-    elif isinstance(weights, np.ndarray):
-        weights = list(weights)
-    elif weights is not None and not _is_iterable(weights):
-        raise ValueError("passed weights must be an iterable")
-
-    if isinstance(values, np.ndarray):
-        values = list(values)
-    elif _check_pandas_series(values):
-        values = values.values.tolist()
-    elif isinstance(values, dict):
-        if weights is None:
-            weights = list(values.values())
-            values = list(values.keys())
-        else:
-            raise ValueError("cannot pass dict and weights separately")
-    elif values is not None and not _is_iterable(values):
-        raise ValueError("passed values must be an iterable")
-
-    if weights is None:
-        if isinstance(values[0], list) and len(values[0]) == 2:
-            weights = [v[0] for v in values]
-            values = [v[1] for v in values]
-            if drop_na and any([_is_na_like(v) for v in values]):
-                raise ValueError("cannot drop NA and process weights")
-        else:
-            if drop_na:
-                values = [v for v in values if not _is_na_like(v)]
-            len_ = len(values)
-            weights = [1 / len_ for _ in range(len_)]
-    elif drop_na and any([_is_na_like(v) for v in values]):
-        raise ValueError("cannot drop NA and process weights")
-
-    if any([_is_na_like(w) for w in weights]):
-        raise ValueError("cannot handle NA-like values in weights")
-    sum_weights = sum(weights)
-
-    if relative:
-        weights = normalize(weights)
-    else:
-        if len(weights) == len(values) - 1 and sum_weights < 1:
-            weights.append(1 - sum_weights)
-        elif sum_weights <= 0.99 or sum_weights >= 1.01:
-            raise ValueError("weights don't sum to 1 -" + " they sum to {}".format(sum_weights))
-
-    if len(weights) != len(values):
-        raise ValueError("weights and values not same length")
-
-    new_weights = []
-    new_values = []
-    for i, w in enumerate(weights):
-        if w < 0:
-            raise ValueError("weight cannot be negative")
-        if w > 0:  # Note that w = 0 is dropped here
-            new_weights.append(w)
-            new_values.append(values[i])
-
-    return new_weights, new_values
-
-
-def _process_discrete_weights_values(items):
-    if (
-        len(items) >= 100
-        and not isinstance(items, dict)
-        and not isinstance(items[0], list)
-        and _safe_len(_safe_set(items)) < _safe_len(items)
-    ):
-        vcounter = Counter(items)
-        sumv = sum([v for k, v in vcounter.items()])
-        items = {k: v / sumv for k, v in vcounter.items()}
-
-    return _process_weights_values(values=items)
-
-
-def _is_numpy(a):
-    return type(a).__module__ == np.__name__
-
-
-def _is_iterable(a):
-    iterx = isinstance(a, dict) or isinstance(a, Iterable)
-    return iterx and not isinstance(a, str)
-
-
-def _is_na_like(a):
-    return a is None or np.isnan(a)
-
-
-def _round(x, digits=0):
-    if digits is None:
-        return x
-
-    x = np.round(x, digits)
-
-    if _safe_len(x) > 1:
-        return np.array([int(y) if digits == 0 else y for y in x])
-    else:
-        return int(x) if digits <= 0 else x
-
-
-def _simplify(a):
-    if _is_numpy(a):
-        a = a.tolist() if a.size == 1 else a
-    if isinstance(a, list):
-        a = a[0] if len(a) == 1 else a
-    return a
-
-
-def _enlist(a):
-    if _is_numpy(a) and isinstance(a, np.ndarray):
-        return a.tolist()
-    elif _is_iterable(a):
-        return a
-    else:
-        return [a]
-
-
-def _safe_len(a):
-    if _is_numpy(a):
-        return a.size
-    elif is_dist(a):
-        return 1
-    elif isinstance(a, list):
-        return len(a)
-    elif a is None:
-        return 0
-    else:
-        return 1
-
-
-def _safe_set(a):
-    if _is_numpy(a):
-        return set(_enlist(a))
-    elif is_dist(a):
-        return a
-    elif isinstance(a, list):
-        try:
-            return set(a)
-        except TypeError:
-            return a
-    elif a is None:
-        return None
-    else:
-        return a
-
-
-def _core_cuts(n, cores):
-    cuts = [math.floor(n / cores) for _ in range(cores)]
-    delta = n - sum(cuts)
-    cuts[-1] += delta
-    return cuts
-
-
-def _init_tqdm(verbose=True, total=None):
-    if verbose:
-        return tqdm(total=total)
-    else:
-        return None
-
-
-def _tick_tqdm(pbar, tick_size=1):
-    if pbar:
-        pbar.update(tick_size)
-    return pbar
-
-
-def _flush_tqdm(pbar):
-    if pbar is not None:
-        pbar.close()
-    return pbar
-
-
-
    
-[docs]
-def is_dist(obj):
-    """
-    Test if a given object is a Squigglepy distribution.
-
-    Parameters
-    ----------
-    obj : object
-        The object to test.
-
-    Returns
-    -------
-    bool
-        True, if the object is a distribution. False if not.
-
-    Examples
-    --------
-    >>> is_dist(norm(0, 1))
-    True
-    >>> is_dist(0)
-    False
-    """
-    from .distributions import BaseDistribution
-
-    return isinstance(obj, BaseDistribution)
    
-
-
-
-
    
-[docs]
-def is_continuous_dist(obj):
-    from .distributions import (
-        ContinuousDistribution,
-        CompositeDistribution,
-        ComplexDistribution,
-        MixtureDistribution,
-    )
-
-    if isinstance(obj, ContinuousDistribution):
-        return True
-    elif isinstance(obj, CompositeDistribution):
-        if isinstance(obj, ComplexDistribution):
-            return is_continuous_dist(obj.left) and is_continuous_dist(obj.right)
-        elif isinstance(obj, MixtureDistribution):
-            return all([is_continuous_dist(d) for d in obj.dists])
-        else:
-            raise ValueError("Unknown composite distribution")
-    return False
    
-
-
-
-
    
-[docs]
-def is_sampleable(obj):
-    """
-    Test if a given object can be sampled from.
-
-    This includes distributions, integers, floats, `None`,
-    strings, and callables.
-
-    Parameters
-    ----------
-    obj : object
-        The object to test.
-
-    Returns
-    -------
-    bool
-        True, if the object can be sampled from. False if not.
-
-    Examples
-    --------
-    >>> is_sampleable(norm(0, 1))
-    True
-    >>> is_sampleable(0)
-    True
-    >>> is_sampleable([0, 1])
-    False
-    """
-    return (
-        is_dist(obj)
-        or isinstance(obj, int)
-        or isinstance(obj, float)
-        or isinstance(obj, str)
-        or obj is None
-        or callable(obj)
-    )
    
-
-
-
-
    
-[docs]
-def normalize(lst):
-    """
-    Normalize a list to sum to 1.
-
-    Parameters
-    ----------
-    lst : list
-        The list to normalize.
-
-    Returns
-    -------
-    list
-        A list where each value is normalized such that the list sums to 1.
-
-    Examples
-    --------
-    >>> normalize([0.1, 0.2, 0.2])
-    [0.2, 0.4, 0.4]
-    """
-    sum_lst = sum(lst)
-    return [lx / sum_lst for lx in lst]
    
-
-
-
-
    
-[docs]
-def event_occurs(p):
-    """
-    Return True with probability ``p`` and False with probability ``1 - p``.
-
-    Parameters
-    ----------
-    p : float
-        The probability of returning True. Must be between 0 and 1.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> event_occurs(p=0.5)
-    False
-    """
-    if is_dist(p) or callable(p):
-        from .samplers import sample
-
-        p = sample(p)
-    from .rng import _squigglepy_internal_rng
-
-    return _squigglepy_internal_rng.uniform(0, 1) < p
    
-
-
-
-
    
-[docs]
-def event_happens(p):
-    """
-    Return True with probability ``p`` and False with probability ``1 - p``.
-
-    Alias for ``event_occurs``.
-
-    Parameters
-    ----------
-    p : float
-        The probability of returning True. Must be between 0 and 1.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> event_happens(p=0.5)
-    False
-    """
-    return event_occurs(p)
    
-
-
-
-
    
-[docs]
-def event(p):
-    """
-    Return True with probability ``p`` and False with probability ``1 - p``.
-
-    Alias for ``event_occurs``.
-
-    Parameters
-    ----------
-    p : float
-        The probability of returning True. Must be between 0 and 1.
-
-    Returns
-    -------
-    bool
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> event(p=0.5)
-    False
-    """
-    return event_occurs(p)
    
-
-
-
-
    
-[docs]
-def one_in(p, digits=0, verbose=True):
-    """
-    Convert a probability into "1 in X" notation.
-
-    Parameters
-    ----------
-    p : float
-        The probability to convert.
-    digits : int
-        The number of digits to round the result to. Defaults to 0. If ``digits``
-        is 0, the result will be converted to int instead of float.
-    verbose : logical
-        If True, will return a string with "1 in X". If False, will just return X.
-
-    Returns
-    -------
-    str if ``verbose`` is True. Otherwise, int if ``digits`` is 0 or float if ``digits`` > 0.
-
-    Examples
-    --------
-    >>> one_in(0.1)
-    "1 in 10"
-    """
-    p = _round(1 / p, digits)
-    return "1 in {:,}".format(p) if verbose else p
    
-
-
-
-
    
-[docs]
-def get_percentiles(
-    data,
-    percentiles=[1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99],
-    reverse=False,
-    digits=None,
-):
-    """
-    Print the percentiles of the data.
-
-    Parameters
-    ----------
-    data : list or np.array
-        The data to calculate percentiles for.
-    percentiles : list
-        A list of percentiles to calculate. Must be values between 0 and 100.
-    reverse : bool
-        If `True`, the percentile values are reversed (e.g., 95th and 5th percentile
-        swap values.)
-    digits : int or None
-        The number of digits to display (using rounding).
-
-    Returns
-    -------
-    dict
-        A dictionary of the given percentiles.
-
-    Examples
-    --------
-    >>> get_percentiles(range(100), percentiles=[25, 50, 75])
-    {25: 24.75, 50: 49.5, 75: 74.25}
-    """
-    percentiles = percentiles if isinstance(percentiles, list) else [percentiles]
-    percentile_labels = list(reversed(percentiles)) if reverse else percentiles
-    percentiles = np.percentile(data, percentiles)
-    percentiles = [_round(p, digits) for p in percentiles]
-    if len(percentile_labels) == 1:
-        return percentiles[0]
-    else:
-        return dict(list(zip(percentile_labels, percentiles)))
    
-
-
-
-
    
-[docs]
-def get_log_percentiles(
-    data,
-    percentiles=[1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99],
-    reverse=False,
-    display=True,
-    digits=1,
-):
-    """
-    Print the log (base 10) of the percentiles of the data.
-
-    Parameters
-    ----------
-    data : list or np.array
-        The data to calculate percentiles for.
-    percentiles : list
-        A list of percentiles to calculate. Must be values between 0 and 100.
-    reverse : bool
-        If True, the percentile values are reversed (e.g., 95th and 5th percentile
-        swap values.)
-    display : bool
-        If True, the function returns an easy to read display.
-    digits : int or None
-        The number of digits to display (using rounding).
-
-    Returns
-    -------
-    dict
-        A dictionary of the given percentiles. If ``display`` is true, will be str values.
-        Otherwise will be float values. 10 to the power of the value gives the true percentile.
-
-    Examples
-    --------
-    >>> get_percentiles(range(100), percentiles=[25, 50, 75])
-    {25: 24.75, 50: 49.5, 75: 74.25}
-    """
-    percentiles = get_percentiles(data, percentiles=percentiles, reverse=reverse, digits=digits)
-    if isinstance(percentiles, dict):
-        if display:
-            return dict(
-                [(k, ("{:." + str(digits) + "e}").format(v)) for k, v in percentiles.items()]
-            )
-        else:
-            return dict([(k, _round(np.log10(v), digits)) for k, v in percentiles.items()])
-    else:
-        if display:
-            digit_str = "{:." + str(digits) + "e}"
-            digit_str.format(percentiles)
-        else:
-            return _round(np.log10(percentiles), digits)
    
-
-
-
-
    
-[docs]
-def get_mean_and_ci(data, credibility=90, digits=None):
-    """
-    Return the mean and percentiles of the data.
-
-    Parameters
-    ----------
-    data : list or np.array
-        The data to calculate the mean and CI for.
-    credibility : float
-        The credibility of the interval. Must be values between 0 and 100. Default 90 for 90% CI.
-    digits : int or None
-        The number of digits to display (using rounding).
-
-    Returns
-    -------
-    dict
-        A dictionary with the mean and CI.
-
-    Examples
-    --------
-    >>> get_mean_and_ci(range(100))
-    {'mean': 49.5, 'ci_low': 4.95, 'ci_high': 94.05}
-    """
-    ci_low = (100 - credibility) / 2
-    ci_high = 100 - ci_low
-    percentiles = get_percentiles(data, percentiles=[ci_low, ci_high], digits=digits)
-    return {
-        "mean": _round(np.mean(data), digits),
-        "ci_low": percentiles[ci_low],
-        "ci_high": percentiles[ci_high],
-    }
    
-
-
-
-
    
-[docs]
-def get_median_and_ci(data, credibility=90, digits=None):
-    """
-    Return the median and percentiles of the data.
-
-    Parameters
-    ----------
-    data : list or np.array
-        The data to calculate the mean and CI for.
-    credibility : float
-        The credibility of the interval. Must be values between 0 and 100. Default 90 for 90% CI.
-    digits : int or None
-        The number of digits to display (using rounding).
-
-    Returns
-    -------
-    dict
-        A dictionary with the median and CI.
-
-    Examples
-    --------
-    >>> get_median_and_ci(range(100))
-    {'mean': 49.5, 'ci_low': 4.95, 'ci_high': 94.05}
-    """
-    ci_low = (100 - credibility) / 2
-    ci_high = 100 - ci_low
-    percentiles = get_percentiles(data, percentiles=[ci_low, 50, ci_high], digits=digits)
-    return {
-        "median": percentiles[50],
-        "ci_low": percentiles[ci_low],
-        "ci_high": percentiles[ci_high],
-    }
    
-
-
-
-
    
-[docs]
-def geomean(a, weights=None, relative_weights=None, drop_na=True):
-    """
-    Calculate the geometric mean.
-
-    Parameters
-    ----------
-    a : list or np.array
-        The values to calculate the geometric mean of.
-    weights : list or None
-        The weights, if a weighted geometric mean is desired.
-    relative_weights : list or None
-        Relative weights, which if given will be weights that are normalized
-        to sum to 1.
-    drop_na : boolean
-        Should NA-like values be dropped when calculating the geomean?
-
-    Returns
-    -------
-    float
-
-    Examples
-    --------
-    >>> geomean([1, 3, 10])
-    3.1072325059538595
-    """
-    weights, a = _process_weights_values(weights, relative_weights, a, drop_na=drop_na)
-    log_a = np.log(a)
-    return np.exp(np.average(log_a, weights=weights))
    
-
-
-
-
    
-[docs]
-def p_to_odds(p):
-    """
-    Calculate the decimal odds from a given probability.
-
-    Parameters
-    ----------
-    p : float
-        The probability to calculate decimal odds for. Must be between 0 and 1.
-
-    Returns
-    -------
-    float
-        Decimal odds
-
-    Examples
-    --------
-    >>> p_to_odds(0.1)
-    0.1111111111111111
-    """
-
-    def _convert(p):
-        if _is_na_like(p):
-            return p
-        if p <= 0 or p >= 1:
-            raise ValueError("p must be between 0 and 1")
-        return p / (1 - p)
-
-    return _simplify(np.array([_convert(p) for p in _enlist(p)]))
    
-
-
-
-
    
-[docs]
-def odds_to_p(odds):
-    """
-    Calculate the probability from given decimal odds.
-
-    Parameters
-    ----------
-    odds : float
-        The decimal odds to calculate the probability for.
-
-    Returns
-    -------
-    float
-        Probability
-
-    Examples
-    --------
-    >>> odds_to_p(0.1)
-    0.09090909090909091
-    """
-
-    def _convert(o):
-        if _is_na_like(o):
-            return o
-        if o <= 0:
-            raise ValueError("odds must be greater than 0")
-        return o / (1 + o)
-
-    return _simplify(np.array([_convert(o) for o in _enlist(odds)]))
    
-
-
-
-
    
-[docs]
-def geomean_odds(a, weights=None, relative_weights=None, drop_na=True):
-    """
-    Calculate the geometric mean of odds.
-
-    Parameters
-    ----------
-    a : list or np.array
-        The probabilities to calculate the geometric mean of. These are converted to odds
-        before the geometric mean is taken..
-    weights : list or None
-        The weights, if a weighted geometric mean is desired.
-    relative_weights : list or None
-        Relative weights, which if given will be weights that are normalized
-        to sum to 1.
-    drop_na : boolean
-        Should NA-like values be dropped when calculating the geomean?
-
-    Returns
-    -------
-    float
-
-    Examples
-    --------
-    >>> geomean_odds([0.1, 0.3, 0.9])
-    0.42985748800076845
-    """
-    weights, a = _process_weights_values(weights, relative_weights, a, drop_na=drop_na)
-    return odds_to_p(geomean(p_to_odds(a), weights=weights))
    
-
-
-
-
    
-[docs]
-def laplace(s, n=None, time_passed=None, time_remaining=None, time_fixed=False):
-    """
-    Return probability of success on next trial given Laplace's law of succession.
-
-    Also can be used to calculate a time-invariant version defined in
-    https://www.lesswrong.com/posts/wE7SK8w8AixqknArs/a-time-invariant-version-of-laplace-s-rule
-
-    Parameters
-    ----------
-    s : int
-        The number of successes among ``n`` past trials or among ``time_passed`` amount of time.
-    n : int or None
-        The number of trials that contain the successes (and/or failures). Leave as None if
-        time-invariant mode is desired.
-    time_passed : float or None
-        The amount of time that has passed when the successes (and/or failures) occured for
-        calculating a time-invariant Laplace.
-    time_remaining : float or None
-        We are calculating the likelihood of observing at least one success over this time
-        period.
-    time_fixed : bool
-        This should be False if the time period is variable - that is, if the time period
-        was chosen specifically to include the most recent success. Otherwise the time period
-        is fixed and this should be True. Defaults to False.
-
-    Returns
-    -------
-    float
-        The probability of at least one success in the next trial or ``time_remaining`` amount
-        of time.
-
-    Examples
-    --------
-    >>> # The sun has risen the past 100,000 days. What are the odds it rises again tomorrow?
-    >>> laplace(s=100*K, n=100*K)
-    0.999990000199996
-    >>> # The last time a nuke was used in war was 77 years ago. What are the odds a nuke
-    >>> # is used in the next year, not considering any information other than this naive prior?
-    >>> laplace(s=1, time_passed=77, time_remaining=1, time_fixed=False)
-    0.012820512820512664
-    """
-    if n is not None and s > n:
-        raise ValueError("`s` cannot be greater than `n`")
-    elif time_passed is None and time_remaining is None and n is not None:
-        return (s + 1) / (n + 2)
-    elif time_passed is not None and time_remaining is not None and s == 0:
-        return 1 - ((1 + time_remaining / time_passed) ** -1)
-    elif time_passed is not None and time_remaining is not None and s > 0 and not time_fixed:
-        return 1 - ((1 + time_remaining / time_passed) ** -s)
-    elif time_passed is not None and time_remaining is not None and s > 0 and time_fixed:
-        return 1 - ((1 + time_remaining / time_passed) ** -(s + 1))
-    elif time_passed is not None and time_remaining is None and s == 0:
-        return 1 - ((1 + 1 / time_passed) ** -1)
-    elif time_passed is not None and time_remaining is None and s > 0 and not time_fixed:
-        return 1 - ((1 + 1 / time_passed) ** -s)
-    elif time_passed is not None and time_remaining is None and s > 0 and time_fixed:
-        return 1 - ((1 + 1 / time_passed) ** -(s + 1))
-    elif time_passed is None and n is None:
-        raise ValueError("Must define `time_passed` or `n`")
-    elif time_passed is None and time_remaining is not None:
-        raise ValueError("Must define `time_passed`")
-    else:
-        raise ValueError("Fatal logic error - programmer made mistake!")
    
-
-
-
-
    
-[docs]
-def growth_rate_to_doubling_time(growth_rate):
-    """
-    Convert a positive growth rate to a doubling rate.
-
-    Growth rate must be expressed as a number, numpy array or distribution
-    where 0.05 means +5% to a doubling time. The time unit remains the same, so if we've
-    got +5% annual growth, the returned value is the doubling time in years.
-
-    NOTE: This only works works for numbers, arrays and distributions where all numbers
-    are above 0. (Otherwise it makes no sense to talk about doubling times.)
-
-    Parameters
-    ----------
-    growth_rate : float or np.array or BaseDistribution
-        The growth rate expressed as a fraction (the percentage divided by 100).
-
-    Returns
-    -------
-    float or np.array or ComplexDistribution
-        Returns the doubling time.
-
-    Examples
-    --------
-    >>> growth_rate_to_doubling_time(0.01)
-    69.66071689357483
-    """
-    if is_dist(growth_rate):
-        from .distributions import dist_log
-
-        return math.log(2) / dist_log(1.0 + growth_rate)
-    elif _is_numpy(growth_rate):
-        return np.log(2) / np.log(1.0 + growth_rate)
-    else:
-        return math.log(2) / math.log(1.0 + growth_rate)
    
-
-
-
-
    
-[docs]
-def doubling_time_to_growth_rate(doubling_time):
-    """
-    Convert a doubling time to a growth rate.
-
-    Doubling time is expressed as a number, numpy array or distribution in any
-    time unit. Growth rate is set where e.g. 0.05 means +5%. The time unit remains the
-    same, so if we've got a doubling time of 2 years, the returned value is the annual
-    growth rate.
-
-    NOTE: This only works works for numbers, arrays and distributions where all numbers
-    are above 0. (Otherwise it makes no sense to talk about doubling times.)
-
-    Parameters
-    ----------
-    doubling_time : float or np.array or BaseDistribution
-        The doubling time expressed in any time unit.
-
-    Returns
-    -------
-    float or np.array or ComplexDistribution
-        Returns the growth rate expressed as a fraction (the percentage divided by 100).
-
-    Examples
-    --------
-    >>> doubling_time_to_growth_rate(12)
-    0.05946309435929531
-    """
-    if is_dist(doubling_time):
-        from .distributions import dist_exp
-
-        return dist_exp(math.log(2) / doubling_time) - 1
-    elif _is_numpy(doubling_time):
-        return np.exp(np.log(2) / doubling_time) - 1
-    else:
-        return math.exp(math.log(2) / doubling_time) - 1
    
-
-
-
-
    
-[docs]
-def roll_die(sides, n=1):
-    """
-    Roll a die.
-
-    Parameters
-    ----------
-    sides : int
-        The number of sides of the die that is rolled.
-    n : int
-        The number of dice to be rolled.
-
-    Returns
-    -------
-    int or list
-        Returns the value of each die roll.
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> roll_die(6)
-    5
-    """
-    if is_dist(sides) or callable(sides):
-        from .samplers import sample
-
-        sides = sample(sides)
-    if not isinstance(n, int):
-        raise ValueError("can only roll an integer number of times")
-    elif sides < 2:
-        raise ValueError("cannot roll less than a 2-sided die.")
-    elif not isinstance(sides, int):
-        raise ValueError("can only roll an integer number of sides")
-    else:
-        from .samplers import sample
-        from .distributions import discrete
-
-        return sample(discrete(list(range(1, sides + 1))), n=n) if sides > 0 else None
    
-
-
-
-
    
-[docs]
-def flip_coin(n=1):
-    """
-    Flip a coin.
-
-    Parameters
-    ----------
-    n : int
-        The number of coins to be flipped.
-
-    Returns
-    -------
-    str or list
-        Returns the value of each coin flip, as either "heads" or "tails"
-
-    Examples
-    --------
-    >>> set_seed(42)
-    >>> flip_coin()
-    'heads'
-    """
-    rolls = roll_die(2, n=n)
-    if isinstance(rolls, int):
-        rolls = [rolls]
-    flips = ["heads" if d == 2 else "tails" for d in rolls]
-    return flips[0] if len(flips) == 1 else flips
    
-
-
-
-
    
-[docs]
-def kelly(my_price, market_price, deference=0, bankroll=1, resolve_date=None, current=0):
-    """
-    Calculate the Kelly criterion.
-
-    Parameters
-    ----------
-    my_price : float
-        The price (or probability) you give for the given event.
-    market_price : float
-        The price the market is giving for that event.
-    deference : float
-        How much deference (or weight) do you give the market price? Use 0.5 for half Kelly
-        and 0.75 for quarter Kelly. Defaults to 0, which is full Kelly.
-    bankroll : float
-        How much money do you have to bet? Defaults to 1.
-    resolve_date : str or None
-        When will the event happen, the market resolve, and you get your money back? Used for
-        calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
-        ARR is not calculated.
-    current : float
-        How much do you already have invested in this event? Used for calculating the
-        additional amount you should invest. Defaults to 0.
-
-    Returns
-    -------
-    dict
-        A dict of values specifying:
-            * ``my_price``
-            * ``market_price``
-            * ``deference``
-            * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
-              into account.
-            * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
-            * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
-              ``market_price``.
-            * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
-              you should bet.
-            * ``target`` : the target amount of money you should have invested
-            * ``current``
-            * ``delta`` : the amount of money you should invest given what you already
-              have invested
-            * ``max_gain`` : the amount of money you would gain if you win
-            * ``modeled_gain`` : the expected value you would win given ``adj_price``
-            * ``expected_roi`` : the expected return on investment
-            * ``expected_arr`` : the expected ARR given ``resolve_date``
-            * ``resolve_date``
-
-    Examples
-    --------
-    >>> kelly(my_price=0.7, market_price=0.4, deference=0.5, bankroll=100)
-    {'my_price': 0.7, 'market_price': 0.4, 'deference': 0.5, 'adj_price': 0.55,
-     'delta_price': 0.3, 'adj_delta_price': 0.15, 'kelly': 0.25, 'target': 25.0,
-     'current': 0, 'delta': 25.0, 'max_gain': 62.5, 'modeled_gain': 23.13,
-     'expected_roi': 0.375, 'expected_arr': None, 'resolve_date': None}
-    """
-    if market_price >= 1 or market_price <= 0:
-        raise ValueError("market_price must be >0 and <1")
-    if my_price >= 1 or my_price <= 0:
-        raise ValueError("my_price must be >0 and <1")
-    if deference > 1 or deference < 0:
-        raise ValueError("deference must be >=0 and <=1")
-    adj_price = my_price * (1 - deference) + market_price * deference
-    kelly = np.abs(adj_price - ((1 - adj_price) * (market_price / (1 - market_price))))
-    target = bankroll * kelly
-    expected_roi = np.abs((adj_price / market_price) - 1)
-    if resolve_date is None:
-        expected_arr = None
-    else:
-        resolve_date = datetime.strptime(resolve_date, "%Y-%m-%d")
-        expected_arr = ((expected_roi + 1) ** (365 / (resolve_date - datetime.now()).days)) - 1
-    return {
-        "my_price": round(my_price, 2),
-        "market_price": round(market_price, 2),
-        "deference": round(deference, 3),
-        "adj_price": round(adj_price, 2),
-        "delta_price": round(np.abs(market_price - my_price), 2),
-        "adj_delta_price": round(np.abs(market_price - adj_price), 2),
-        "kelly": round(kelly, 3),
-        "target": round(target, 2),
-        "current": round(current, 2),
-        "delta": round(target - current, 2),
-        "max_gain": round(target / market_price, 2),
-        "modeled_gain": round(
-            (adj_price * (target / market_price) + (1 - adj_price) * -target), 2
-        ),
-        "expected_roi": round(expected_roi, 3),
-        "expected_arr": round(expected_arr, 3) if expected_arr is not None else None,
-        "resolve_date": resolve_date,
-    }
    
-
-
-
-
    
-[docs]
-def full_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0):
-    """
-    Alias for ``kelly`` where ``deference`` is 0.
-
-    Parameters
-    ----------
-    my_price : float
-        The price (or probability) you give for the given event.
-    market_price : float
-        The price the market is giving for that event.
-    bankroll : float
-        How much money do you have to bet? Defaults to 1.
-    resolve_date : str or None
-        When will the event happen, the market resolve, and you get your money back? Used for
-        calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
-        ARR is not calculated.
-    current : float
-        How much do you already have invested in this event? Used for calculating the
-        additional amount you should invest. Defaults to 0.
-
-    Returns
-    -------
-    dict
-        A dict of values specifying:
-            * ``my_price``
-            * ``market_price``
-            * ``deference``
-            * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
-              into account.
-            * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
-            * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
-              ``market_price``.
-            * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
-              you should bet.
-            * ``target`` : the target amount of money you should have invested
-            * ``current``
-            * ``delta`` : the amount of money you should invest given what you already
-              have invested
-            * ``max_gain`` : the amount of money you would gain if you win
-            * ``modeled_gain`` : the expected value you would win given ``adj_price``
-            * ``expected_roi`` : the expected return on investment
-            * ``expected_arr`` : the expected ARR given ``resolve_date``
-            * ``resolve_date``
-
-    Examples
-    --------
-    >>> full_kelly(my_price=0.7, market_price=0.4, bankroll=100)
-    {'my_price': 0.7, 'market_price': 0.4, 'deference': 0, 'adj_price': 0.7,
-     'delta_price': 0.3, 'adj_delta_price': 0.3, 'kelly': 0.5, 'target': 50.0,
-     'current': 0, 'delta': 50.0, 'max_gain': 125.0, 'modeled_gain': 72.5,
-     'expected_roi': 0.75, 'expected_arr': None, 'resolve_date': None}
-    """
-    return kelly(
-        my_price=my_price,
-        market_price=market_price,
-        bankroll=bankroll,
-        resolve_date=resolve_date,
-        current=current,
-        deference=0,
-    )
    
-
-
-
-
    
-[docs]
-def half_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0):
-    """
-    Alias for ``kelly`` where ``deference`` is 0.5.
-
-    Parameters
-    ----------
-    my_price : float
-        The price (or probability) you give for the given event.
-    market_price : float
-        The price the market is giving for that event.
-    bankroll : float
-        How much money do you have to bet? Defaults to 1.
-    resolve_date : str or None
-        When will the event happen, the market resolve, and you get your money back? Used for
-        calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
-        ARR is not calculated.
-    current : float
-        How much do you already have invested in this event? Used for calculating the
-        additional amount you should invest. Defaults to 0.
-
-    Returns
-    -------
-    dict
-        A dict of values specifying:
-            * ``my_price``
-            * ``market_price``
-            * ``deference``
-            * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
-              into account.
-            * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
-            * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
-              ``market_price``.
-            * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
-              you should bet.
-            * ``target`` : the target amount of money you should have invested
-            * ``current``
-            * ``delta`` : the amount of money you should invest given what you already
-              have invested
-            * ``max_gain`` : the amount of money you would gain if you win
-            * ``modeled_gain`` : the expected value you would win given ``adj_price``
-            * ``expected_roi`` : the expected return on investment
-            * ``expected_arr`` : the expected ARR given ``resolve_date``
-            * ``resolve_date``
-
-    Examples
-    --------
-    >>> half_kelly(my_price=0.7, market_price=0.4, bankroll=100)
-    {'my_price': 0.7, 'market_price': 0.4, 'deference': 0.5, 'adj_price': 0.55,
-     'delta_price': 0.3, 'adj_delta_price': 0.15, 'kelly': 0.25, 'target': 25.0,
-     'current': 0, 'delta': 25.0, 'max_gain': 62.5, 'modeled_gain': 23.13,
-     'expected_roi': 0.375, 'expected_arr': None, 'resolve_date': None}
-    """
-    return kelly(
-        my_price=my_price,
-        market_price=market_price,
-        bankroll=bankroll,
-        resolve_date=resolve_date,
-        current=current,
-        deference=0.5,
-    )
    
-
-
-
-
    
-[docs]
-def quarter_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0):
-    """
-    Alias for ``kelly`` where ``deference`` is 0.75.
-
-    Parameters
-    ----------
-    my_price : float
-        The price (or probability) you give for the given event.
-    market_price : float
-        The price the market is giving for that event.
-    bankroll : float
-        How much money do you have to bet? Defaults to 1.
-    resolve_date : str or None
-        When will the event happen, the market resolve, and you get your money back? Used for
-        calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
-        ARR is not calculated.
-    current : float
-        How much do you already have invested in this event? Used for calculating the
-        additional amount you should invest. Defaults to 0.
-
-    Returns
-    -------
-    dict
-        A dict of values specifying:
-            * ``my_price``
-            * ``market_price``
-            * ``deference``
-            * ``adj_price`` : an adjustment to ``my_price`` once ``deference`` is taken
-              into account.
-            * ``delta_price`` : the absolute difference between ``my_price`` and ``market_price``.
-            * ``adj_delta_price`` : the absolute difference between ``adj_price`` and
-              ``market_price``.
-            * ``kelly`` : the kelly criterion indicating the percentage of ``bankroll``
-              you should bet.
-            * ``target`` : the target amount of money you should have invested
-            * ``current``
-            * ``delta`` : the amount of money you should invest given what you already
-              have invested
-            * ``max_gain`` : the amount of money you would gain if you win
-            * ``modeled_gain`` : the expected value you would win given ``adj_price``
-            * ``expected_roi`` : the expected return on investment
-            * ``expected_arr`` : the expected ARR given ``resolve_date``
-            * ``resolve_date``
-
-    Examples
-    --------
-    >>> quarter_kelly(my_price=0.7, market_price=0.4, bankroll=100)
-    {'my_price': 0.7, 'market_price': 0.4, 'deference': 0.75, 'adj_price': 0.48,
-     'delta_price': 0.3, 'adj_delta_price': 0.08, 'kelly': 0.125, 'target': 12.5,
-     'current': 0, 'delta': 12.5, 'max_gain': 31.25, 'modeled_gain': 8.28,
-     'expected_roi': 0.188, 'expected_arr': None, 'resolve_date': None}
-    """
-    return kelly(
-        my_price=my_price,
-        market_price=market_price,
-        bankroll=bankroll,
-        resolve_date=resolve_date,
-        current=current,
-        deference=0.75,
-    )
    
-
-
-
-
    
-[docs]
-def extremize(p, e):
-    """
-    Extremize a prediction.
-
-    Parameters
-    ----------
-    p : float
-        The prediction to extremize. Must be within 0-1.
-    e : float
-        The extremization factor.
-
-    Returns
-    -------
-    float
-        The extremized prediction
-
-    Examples
-    --------
-    >>> # Extremizing of 1.73 per https://arxiv.org/abs/2111.03153
-    >>> extremize(p=0.7, e=1.73)
-    0.875428191155692
-    """
-    if p <= 0 or p >= 1:
-        raise ValueError("`p` must be greater than 0 and less than 1")
-
-    if p > 0.5:
-        return 1 - ((1 - p) ** e)
-    else:
-        return p**e
    
-
-
    
-
-                
    
-              
-              
-              
-              
-              
-                
    
-                  
-
    
-
    
-                
    
-              
-            
    
-            
-            
-              
-            
-          
    
-          
    
-            
-          
    
-        
-      
    
-    
    
-  
    
-  
-  
-  
-
-
-  
    
-
    
-  
-    
    
-      
-        
    
-  
    
-    
-      © Copyright 2023, Peter Wildeford.
-      
    
-    
-  
    
-
    
-      
-        
    
-  
    
-    Created using Sphinx 7.2.6.
-    
    
-  
    
-
    
-      
-    
    
-  
-  
-  
-    
    
-      
-        
    
-  Built with the PyData Sphinx Theme 0.14.3.
-
    
-      
-    
    
-  
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-  
-
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diff --git a/doc/build/html/_sources/README.rst.txt b/doc/build/html/_sources/README.rst.txt
deleted file mode 100644
index f5ec681..0000000
--- a/doc/build/html/_sources/README.rst.txt
+++ /dev/null
@@ -1,531 +0,0 @@
-Squigglepy: Implementation of Squiggle in Python
-================================================
-
-`Squiggle `__ is a “simple
-programming language for intuitive probabilistic estimation”. It serves
-as its own standalone programming language with its own syntax, but it
-is implemented in JavaScript. I like the features of Squiggle and intend
-to use it frequently, but I also sometimes want to use similar
-functionalities in Python, especially alongside other Python statistical
-programming packages like Numpy, Pandas, and Matplotlib. The
-**squigglepy** package here implements many Squiggle-like
-functionalities in Python.
-
-Installation
-------------
-
-.. code:: shell
-
-   pip install squigglepy
-
-For plotting support, you can also use the ``plots`` extra:
-
-.. code:: shell
-
-   pip install squigglepy[plots]
-
-Usage
------
-
-Piano Tuners Example
-~~~~~~~~~~~~~~~~~~~~
-
-Here’s the Squigglepy implementation of `the example from Squiggle
-Docs `__:
-
-.. code:: python
-
-   import squigglepy as sq
-   import numpy as np
-   import matplotlib.pyplot as plt
-   from squigglepy.numbers import K, M
-   from pprint import pprint
-
-   pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)  # This means that you're 90% confident the value is between 8.1 and 8.4 Million.
-   pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01  # We assume there are almost no people with multiple pianos
-   pianos_per_piano_tuner = sq.to(2*K, 50*K)
-   piano_tuners_per_piano = 1 / pianos_per_piano_tuner
-   total_tuners_in_2022 = pop_of_ny_2022 * pct_of_pop_w_pianos * piano_tuners_per_piano
-   samples = total_tuners_in_2022 @ 1000  # Note: `@ 1000` is shorthand to get 1000 samples
-
-   # Get mean and SD
-   print('Mean: {}, SD: {}'.format(round(np.mean(samples), 2),
-                                   round(np.std(samples), 2)))
-
-   # Get percentiles
-   pprint(sq.get_percentiles(samples, digits=0))
-
-   # Histogram
-   plt.hist(samples, bins=200)
-   plt.show()
-
-   # Shorter histogram
-   total_tuners_in_2022.plot()
-
-And the version from the Squiggle doc that incorporates time:
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy.numbers import K, M
-
-   pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)
-   pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01
-   pianos_per_piano_tuner = sq.to(2*K, 50*K)
-   piano_tuners_per_piano = 1 / pianos_per_piano_tuner
-
-   def pop_at_time(t):  # t = Time in years after 2022
-       avg_yearly_pct_change = sq.to(-0.01, 0.05)  # We're expecting NYC to continuously grow with an mean of roughly between -1% and +4% per year
-       return pop_of_ny_2022 * ((avg_yearly_pct_change + 1) ** t)
-
-   def total_tuners_at_time(t):
-       return pop_at_time(t) * pct_of_pop_w_pianos * piano_tuners_per_piano
-
-   # Get total piano tuners at 2030
-   sq.get_percentiles(total_tuners_at_time(2030-2022) @ 1000)
-
-**WARNING:** Be careful about dividing by ``K``, ``M``, etc. ``1/2*K`` =
-500 in Python. Use ``1/(2*K)`` instead to get the expected outcome.
-
-**WARNING:** Be careful about using ``K`` to get sample counts. Use
-``sq.norm(2, 3) @ (2*K)``\ … ``sq.norm(2, 3) @ 2*K`` will return only
-two samples, multiplied by 1000.
-
-Distributions
-~~~~~~~~~~~~~
-
-.. code:: python
-
-   import squigglepy as sq
-
-   # Normal distribution
-   sq.norm(1, 3)  # 90% interval from 1 to 3
-
-   # Distribution can be sampled with mean and sd too
-   sq.norm(mean=0, sd=1)
-
-   # Shorthand to get one sample
-   ~sq.norm(1, 3)
-
-   # Shorthand to get more than one sample
-   sq.norm(1, 3) @ 100
-
-   # Longhand version to get more than one sample
-   sq.sample(sq.norm(1, 3), n=100)
-
-   # Nice progress reporter
-   sq.sample(sq.norm(1, 3), n=1000, verbose=True)
-
-   # Other distributions exist
-   sq.lognorm(1, 10)
-   sq.tdist(1, 10, t=5)
-   sq.triangular(1, 2, 3)
-   sq.pert(1, 2, 3, lam=2)
-   sq.binomial(p=0.5, n=5)
-   sq.beta(a=1, b=2)
-   sq.bernoulli(p=0.5)
-   sq.poisson(10)
-   sq.chisquare(2)
-   sq.gamma(3, 2)
-   sq.pareto(1)
-   sq.exponential(scale=1)
-   sq.geometric(p=0.5)
-
-   # Discrete sampling
-   sq.discrete({'A': 0.1, 'B': 0.9})
-
-   # Can return integers
-   sq.discrete({0: 0.1, 1: 0.3, 2: 0.3, 3: 0.15, 4: 0.15})
-
-   # Alternate format (also can be used to return more complex objects)
-   sq.discrete([[0.1,  0],
-                [0.3,  1],
-                [0.3,  2],
-                [0.15, 3],
-                [0.15, 4]])
-
-   sq.discrete([0, 1, 2]) # No weights assumes equal weights
-
-   # You can mix distributions together
-   sq.mixture([sq.norm(1, 3),
-               sq.norm(4, 10),
-               sq.lognorm(1, 10)],  # Distributions to mix
-              [0.3, 0.3, 0.4])     # These are the weights on each distribution
-
-   # This is equivalent to the above, just a different way of doing the notation
-   sq.mixture([[0.3, sq.norm(1,3)],
-               [0.3, sq.norm(4,10)],
-               [0.4, sq.lognorm(1,10)]])
-
-   # Make a zero-inflated distribution
-   # 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`.
-   sq.zero_inflated(0.6, sq.norm(1, 2))
-
-Additional Features
-~~~~~~~~~~~~~~~~~~~
-
-.. code:: python
-
-   import squigglepy as sq
-
-   # You can add and subtract distributions
-   (sq.norm(1,3) + sq.norm(4,5)) @ 100
-   (sq.norm(1,3) - sq.norm(4,5)) @ 100
-   (sq.norm(1,3) * sq.norm(4,5)) @ 100
-   (sq.norm(1,3) / sq.norm(4,5)) @ 100
-
-   # You can also do math with numbers
-   ~((sq.norm(sd=5) + 2) * 2)
-   ~(-sq.lognorm(0.1, 1) * sq.pareto(1) / 10)
-
-   # You can change the CI from 90% (default) to 80%
-   sq.norm(1, 3, credibility=80)
-
-   # You can clip
-   sq.norm(0, 3, lclip=0, rclip=5) # Sample norm with a 90% CI from 0-3, but anything lower than 0 gets clipped to 0 and anything higher than 5 gets clipped to 5.
-
-   # You can also clip with a function, and use pipes
-   sq.norm(0, 3) >> sq.clip(0, 5)
-
-   # You can correlate continuous distributions
-   a, b = sq.uniform(-1, 1), sq.to(0, 3)
-   a, b = sq.correlate((a, b), 0.5)  # Correlate a and b with a correlation of 0.5
-   # You can even pass your own correlation matrix!
-   a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]])
-
-Example: Rolling a Die
-^^^^^^^^^^^^^^^^^^^^^^
-
-An example of how to use distributions to build tools:
-
-.. code:: python
-
-   import squigglepy as sq
-
-   def roll_die(sides, n=1):
-       return sq.discrete(list(range(1, sides + 1))) @ n if sides > 0 else None
-
-   roll_die(sides=6, n=10)
-   # [2, 6, 5, 2, 6, 2, 3, 1, 5, 2]
-
-This is already included standard in the utils of this package. Use
-``sq.roll_die``.
-
-Bayesian inference
-~~~~~~~~~~~~~~~~~~
-
-1% of women at age forty who participate in routine screening have
-breast cancer. 80% of women with breast cancer will get positive
-mammographies. 9.6% of women without breast cancer will also get
-positive mammographies.
-
-A woman in this age group had a positive mammography in a routine
-screening. What is the probability that she actually has breast cancer?
-
-We can approximate the answer with a Bayesian network (uses rejection
-sampling):
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy import bayes
-   from squigglepy.numbers import M
-
-   def mammography(has_cancer):
-       return sq.event(0.8 if has_cancer else 0.096)
-
-   def define_event():
-       cancer = ~sq.bernoulli(0.01)
-       return({'mammography': mammography(cancer),
-               'cancer': cancer})
-
-   bayes.bayesnet(define_event,
-                  find=lambda e: e['cancer'],
-                  conditional_on=lambda e: e['mammography'],
-                  n=1*M)
-   # 0.07723995880535531
-
-Or if we have the information immediately on hand, we can directly
-calculate it. Though this doesn’t work for very complex stuff.
-
-.. code:: python
-
-   from squigglepy import bayes
-   bayes.simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096)
-   # 0.07763975155279504
-
-You can also make distributions and update them:
-
-.. code:: python
-
-   import matplotlib.pyplot as plt
-   import squigglepy as sq
-   from squigglepy import bayes
-   from squigglepy.numbers import K
-   import numpy as np
-
-   print('Prior')
-   prior = sq.norm(1,5)
-   prior_samples = prior @ (10*K)
-   plt.hist(prior_samples, bins = 200)
-   plt.show()
-   print(sq.get_percentiles(prior_samples))
-   print('Prior Mean: {} SD: {}'.format(np.mean(prior_samples), np.std(prior_samples)))
-   print('-')
-
-   print('Evidence')
-   evidence = sq.norm(2,3)
-   evidence_samples = evidence @ (10*K)
-   plt.hist(evidence_samples, bins = 200)
-   plt.show()
-   print(sq.get_percentiles(evidence_samples))
-   print('Evidence Mean: {} SD: {}'.format(np.mean(evidence_samples), np.std(evidence_samples)))
-   print('-')
-
-   print('Posterior')
-   posterior = bayes.update(prior, evidence)
-   posterior_samples = posterior @ (10*K)
-   plt.hist(posterior_samples, bins = 200)
-   plt.show()
-   print(sq.get_percentiles(posterior_samples))
-   print('Posterior Mean: {} SD: {}'.format(np.mean(posterior_samples), np.std(posterior_samples)))
-
-   print('Average')
-   average = bayes.average(prior, evidence)
-   average_samples = average @ (10*K)
-   plt.hist(average_samples, bins = 200)
-   plt.show()
-   print(sq.get_percentiles(average_samples))
-   print('Average Mean: {} SD: {}'.format(np.mean(average_samples), np.std(average_samples)))
-
-Example: Alarm net
-^^^^^^^^^^^^^^^^^^
-
-This is the alarm network from `Bayesian Artificial Intelligence -
-Section
-2.5.1 `__:
-
-   Assume your house has an alarm system against burglary.
-
-   You live in the seismically active area and the alarm system can get
-   occasionally set off by an earthquake.
-
-   You have two neighbors, Mary and John, who do not know each other. If
-   they hear the alarm they call you, but this is not guaranteed.
-
-   The chance of a burglary on a particular day is 0.1%. The chance of
-   an earthquake on a particular day is 0.2%.
-
-   The alarm will go off 95% of the time with both a burglary and an
-   earthquake, 94% of the time with just a burglary, 29% of the time
-   with just an earthquake, and 0.1% of the time with nothing (total
-   false alarm).
-
-   John will call you 90% of the time when the alarm goes off. But on 5%
-   of the days, John will just call to say “hi”. Mary will call you 70%
-   of the time when the alarm goes off. But on 1% of the days, Mary will
-   just call to say “hi”.
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy import bayes
-   from squigglepy.numbers import M
-
-   def p_alarm_goes_off(burglary, earthquake):
-       if burglary and earthquake:
-           return 0.95
-       elif burglary and not earthquake:
-           return 0.94
-       elif not burglary and earthquake:
-           return 0.29
-       elif not burglary and not earthquake:
-           return 0.001
-
-   def p_john_calls(alarm_goes_off):
-       return 0.9 if alarm_goes_off else 0.05
-
-   def p_mary_calls(alarm_goes_off):
-       return 0.7 if alarm_goes_off else 0.01
-
-   def define_event():
-       burglary_happens = sq.event(p=0.001)
-       earthquake_happens = sq.event(p=0.002)
-       alarm_goes_off = sq.event(p_alarm_goes_off(burglary_happens, earthquake_happens))
-       john_calls = sq.event(p_john_calls(alarm_goes_off))
-       mary_calls = sq.event(p_mary_calls(alarm_goes_off))
-       return {'burglary': burglary_happens,
-               'earthquake': earthquake_happens,
-               'alarm_goes_off': alarm_goes_off,
-               'john_calls': john_calls,
-               'mary_calls': mary_calls}
-
-   # What are the chances that both John and Mary call if an earthquake happens?
-   bayes.bayesnet(define_event,
-                  n=1*M,
-                  find=lambda e: (e['mary_calls'] and e['john_calls']),
-                  conditional_on=lambda e: e['earthquake'])
-   # Result will be ~0.19, though it varies because it is based on a random sample.
-   # This also may take a minute to run.
-
-   # If both John and Mary call, what is the chance there's been a burglary?
-   bayes.bayesnet(define_event,
-                  n=1*M,
-                  find=lambda e: e['burglary'],
-                  conditional_on=lambda e: (e['mary_calls'] and e['john_calls']))
-   # Result will be ~0.27, though it varies because it is based on a random sample.
-   # This will run quickly because there is a built-in cache.
-   # Use `cache=False` to not build a cache and `reload_cache=True` to recalculate the cache.
-
-Note that the amount of Bayesian analysis that squigglepy can do is
-pretty limited. For more complex bayesian analysis, consider
-`sorobn `__,
-`pomegranate `__,
-`bnlearn `__, or
-`pyMC `__.
-
-Example: A Demonstration of the Monty Hall Problem
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy import bayes
-   from squigglepy.numbers import K, M, B, T
-
-
-   def monte_hall(door_picked, switch=False):
-       doors = ['A', 'B', 'C']
-       car_is_behind_door = ~sq.discrete(doors)
-       reveal_door = ~sq.discrete([d for d in doors if d != door_picked and d != car_is_behind_door])
-
-       if switch:
-           old_door_picked = door_picked
-           door_picked = [d for d in doors if d != old_door_picked and d != reveal_door][0]
-
-       won_car = (car_is_behind_door == door_picked)
-       return won_car
-
-
-   def define_event():
-       door = ~sq.discrete(['A', 'B', 'C'])
-       switch = sq.event(0.5)
-       return {'won': monte_hall(door_picked=door, switch=switch),
-               'switched': switch}
-
-   RUNS = 10*K
-   r = bayes.bayesnet(define_event,
-                      find=lambda e: e['won'],
-                      conditional_on=lambda e: e['switched'],
-                      verbose=True,
-                      n=RUNS)
-   print('Win {}% of the time when switching'.format(int(r * 100)))
-
-   r = bayes.bayesnet(define_event,
-                      find=lambda e: e['won'],
-                      conditional_on=lambda e: not e['switched'],
-                      verbose=True,
-                      n=RUNS)
-   print('Win {}% of the time when not switching'.format(int(r * 100)))
-
-   # Win 66% of the time when switching
-   # Win 34% of the time when not switching
-
-Example: More complex coin/dice interactions
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-   Imagine that I flip a coin. If heads, I take a random die out of my
-   blue bag. If tails, I take a random die out of my red bag. The blue
-   bag contains only 6-sided dice. The red bag contains a 4-sided die, a
-   6-sided die, a 10-sided die, and a 20-sided die. I then roll the
-   random die I took. What is the chance that I roll a 6?
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy.numbers import K, M, B, T
-   from squigglepy import bayes
-
-   def define_event():
-       if sq.flip_coin() == 'heads': # Blue bag
-           return sq.roll_die(6)
-       else: # Red bag
-           return sq.discrete([4, 6, 10, 20]) >> sq.roll_die
-
-
-   bayes.bayesnet(define_event,
-                  find=lambda e: e == 6,
-                  verbose=True,
-                  n=100*K)
-   # This run for me returned 0.12306 which is pretty close to the correct answer of 0.12292
-
-Kelly betting
-~~~~~~~~~~~~~
-
-You can use probability generated, combine with a bankroll to determine
-bet sizing using `Kelly
-criterion `__.
-
-For example, if you want to Kelly bet and you’ve…
-
--  determined that your price (your probability of the event in question
-   happening / the market in question resolving in your favor) is $0.70
-   (70%)
--  see that the market is pricing at $0.65
--  you have a bankroll of $1000 that you are willing to bet
-
-You should bet as follows:
-
-.. code:: python
-
-   import squigglepy as sq
-   kelly_data = sq.kelly(my_price=0.70, market_price=0.65, bankroll=1000)
-   kelly_data['kelly']  # What fraction of my bankroll should I bet on this?
-   # 0.143
-   kelly_data['target']  # How much money should be invested in this?
-   # 142.86
-   kelly_data['expected_roi']  # What is the expected ROI of this bet?
-   # 0.077
-
-More examples
-~~~~~~~~~~~~~
-
-You can see more examples of squigglepy in action
-`here `__.
-
-Run tests
----------
-
-Use ``black .`` for formatting.
-
-Run
-``ruff check . && pytest && pip3 install . && python3 tests/integration.py``
-
-Disclaimers
------------
-
-This package is unofficial and supported by myself and Rethink
-Priorities. It is not affiliated with or associated with the Quantified
-Uncertainty Research Institute, which maintains the Squiggle language
-(in JavaScript).
-
-This package is also new and not yet in a stable production version, so
-you may encounter bugs and other errors. Please report those so they can
-be fixed. It’s also possible that future versions of the package may
-introduce breaking changes.
-
-This package is available under an MIT License.
-
-Acknowledgements
-----------------
-
--  The primary author of this package is Peter Wildeford. Agustín
-   Covarrubias and Bernardo Baron contributed several key features and
-   developments.
--  Thanks to Ozzie Gooen and the Quantified Uncertainty Research
-   Institute for creating and maintaining the original Squiggle
-   language.
--  Thanks to Dawn Drescher for helping me implement math between
-   distributions.
--  Thanks to Dawn Drescher for coming up with the idea to use ``~`` as a
-   shorthand for ``sample``, as well as helping me implement it.
diff --git a/doc/build/html/_sources/examples.rst.txt b/doc/build/html/_sources/examples.rst.txt
deleted file mode 100644
index c00053f..0000000
--- a/doc/build/html/_sources/examples.rst.txt
+++ /dev/null
@@ -1,468 +0,0 @@
-Examples
-========
-
-Piano Tuners Example
-~~~~~~~~~~~~~~~~~~~~
-
-Here’s the Squigglepy implementation of `the example from Squiggle
-Docs `__:
-
-.. code:: python
-
-   import squigglepy as sq
-   import numpy as np
-   import matplotlib.pyplot as plt
-   from squigglepy.numbers import K, M
-   from pprint import pprint
-
-   pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)  # This means that you're 90% confident the value is between 8.1 and 8.4 Million.
-   pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01  # We assume there are almost no people with multiple pianos
-   pianos_per_piano_tuner = sq.to(2*K, 50*K)
-   piano_tuners_per_piano = 1 / pianos_per_piano_tuner
-   total_tuners_in_2022 = pop_of_ny_2022 * pct_of_pop_w_pianos * piano_tuners_per_piano
-   samples = total_tuners_in_2022 @ 1000  # Note: `@ 1000` is shorthand to get 1000 samples
-
-   # Get mean and SD
-   print('Mean: {}, SD: {}'.format(round(np.mean(samples), 2),
-                                   round(np.std(samples), 2)))
-
-   # Get percentiles
-   pprint(sq.get_percentiles(samples, digits=0))
-
-   # Histogram
-   plt.hist(samples, bins=200)
-   plt.show()
-
-   # Shorter histogram
-   total_tuners_in_2022.plot()
-
-And the version from the Squiggle doc that incorporates time:
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy.numbers import K, M
-
-   pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)
-   pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01
-   pianos_per_piano_tuner = sq.to(2*K, 50*K)
-   piano_tuners_per_piano = 1 / pianos_per_piano_tuner
-
-   def pop_at_time(t):  # t = Time in years after 2022
-       avg_yearly_pct_change = sq.to(-0.01, 0.05)  # We're expecting NYC to continuously grow with an mean of roughly between -1% and +4% per year
-       return pop_of_ny_2022 * ((avg_yearly_pct_change + 1) ** t)
-
-   def total_tuners_at_time(t):
-       return pop_at_time(t) * pct_of_pop_w_pianos * piano_tuners_per_piano
-
-   # Get total piano tuners at 2030
-   sq.get_percentiles(total_tuners_at_time(2030-2022) @ 1000)
-
-**WARNING:** Be careful about dividing by ``K``, ``M``, etc. ``1/2*K`` =
-500 in Python. Use ``1/(2*K)`` instead to get the expected outcome.
-
-**WARNING:** Be careful about using ``K`` to get sample counts. Use
-``sq.norm(2, 3) @ (2*K)``\ … ``sq.norm(2, 3) @ 2*K`` will return only
-two samples, multiplied by 1000.
-
-Distributions
-~~~~~~~~~~~~~
-
-.. code:: python
-
-   import squigglepy as sq
-
-   # Normal distribution
-   sq.norm(1, 3)  # 90% interval from 1 to 3
-
-   # Distribution can be sampled with mean and sd too
-   sq.norm(mean=0, sd=1)
-
-   # Shorthand to get one sample
-   ~sq.norm(1, 3)
-
-   # Shorthand to get more than one sample
-   sq.norm(1, 3) @ 100
-
-   # Longhand version to get more than one sample
-   sq.sample(sq.norm(1, 3), n=100)
-
-   # Nice progress reporter
-   sq.sample(sq.norm(1, 3), n=1000, verbose=True)
-
-   # Other distributions exist
-   sq.lognorm(1, 10)
-   sq.tdist(1, 10, t=5)
-   sq.triangular(1, 2, 3)
-   sq.pert(1, 2, 3, lam=2)
-   sq.binomial(p=0.5, n=5)
-   sq.beta(a=1, b=2)
-   sq.bernoulli(p=0.5)
-   sq.poisson(10)
-   sq.chisquare(2)
-   sq.gamma(3, 2)
-   sq.pareto(1)
-   sq.exponential(scale=1)
-   sq.geometric(p=0.5)
-
-   # Discrete sampling
-   sq.discrete({'A': 0.1, 'B': 0.9})
-
-   # Can return integers
-   sq.discrete({0: 0.1, 1: 0.3, 2: 0.3, 3: 0.15, 4: 0.15})
-
-   # Alternate format (also can be used to return more complex objects)
-   sq.discrete([[0.1,  0],
-                [0.3,  1],
-                [0.3,  2],
-                [0.15, 3],
-                [0.15, 4]])
-
-   sq.discrete([0, 1, 2]) # No weights assumes equal weights
-
-   # You can mix distributions together
-   sq.mixture([sq.norm(1, 3),
-               sq.norm(4, 10),
-               sq.lognorm(1, 10)],  # Distributions to mix
-              [0.3, 0.3, 0.4])     # These are the weights on each distribution
-
-   # This is equivalent to the above, just a different way of doing the notation
-   sq.mixture([[0.3, sq.norm(1,3)],
-               [0.3, sq.norm(4,10)],
-               [0.4, sq.lognorm(1,10)]])
-
-   # Make a zero-inflated distribution
-   # 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`.
-   sq.zero_inflated(0.6, sq.norm(1, 2))
-
-Additional Features
-~~~~~~~~~~~~~~~~~~~
-
-.. code:: python
-
-   import squigglepy as sq
-
-   # You can add and subtract distributions
-   (sq.norm(1,3) + sq.norm(4,5)) @ 100
-   (sq.norm(1,3) - sq.norm(4,5)) @ 100
-   (sq.norm(1,3) * sq.norm(4,5)) @ 100
-   (sq.norm(1,3) / sq.norm(4,5)) @ 100
-
-   # You can also do math with numbers
-   ~((sq.norm(sd=5) + 2) * 2)
-   ~(-sq.lognorm(0.1, 1) * sq.pareto(1) / 10)
-
-   # You can change the CI from 90% (default) to 80%
-   sq.norm(1, 3, credibility=80)
-
-   # You can clip
-   sq.norm(0, 3, lclip=0, rclip=5) # Sample norm with a 90% CI from 0-3, but anything lower than 0 gets clipped to 0 and anything higher than 5 gets clipped to 5.
-
-   # You can also clip with a function, and use pipes
-   sq.norm(0, 3) >> sq.clip(0, 5)
-
-   # You can correlate continuous distributions
-   a, b = sq.uniform(-1, 1), sq.to(0, 3)
-   a, b = sq.correlate((a, b), 0.5)  # Correlate a and b with a correlation of 0.5
-   # You can even pass your own correlation matrix!
-   a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]])
-
-Example: Rolling a Die
-^^^^^^^^^^^^^^^^^^^^^^
-
-An example of how to use distributions to build tools:
-
-.. code:: python
-
-   import squigglepy as sq
-
-   def roll_die(sides, n=1):
-       return sq.discrete(list(range(1, sides + 1))) @ n if sides > 0 else None
-
-   roll_die(sides=6, n=10)
-   # [2, 6, 5, 2, 6, 2, 3, 1, 5, 2]
-
-This is already included standard in the utils of this package. Use
-``sq.roll_die``.
-
-Bayesian inference
-~~~~~~~~~~~~~~~~~~
-
-1% of women at age forty who participate in routine screening have
-breast cancer. 80% of women with breast cancer will get positive
-mammographies. 9.6% of women without breast cancer will also get
-positive mammographies.
-
-A woman in this age group had a positive mammography in a routine
-screening. What is the probability that she actually has breast cancer?
-
-We can approximate the answer with a Bayesian network (uses rejection
-sampling):
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy import bayes
-   from squigglepy.numbers import M
-
-   def mammography(has_cancer):
-       return sq.event(0.8 if has_cancer else 0.096)
-
-   def define_event():
-       cancer = ~sq.bernoulli(0.01)
-       return({'mammography': mammography(cancer),
-               'cancer': cancer})
-
-   bayes.bayesnet(define_event,
-                  find=lambda e: e['cancer'],
-                  conditional_on=lambda e: e['mammography'],
-                  n=1*M)
-   # 0.07723995880535531
-
-Or if we have the information immediately on hand, we can directly
-calculate it. Though this doesn’t work for very complex stuff.
-
-.. code:: python
-
-   from squigglepy import bayes
-   bayes.simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096)
-   # 0.07763975155279504
-
-You can also make distributions and update them:
-
-.. code:: python
-
-   import matplotlib.pyplot as plt
-   import squigglepy as sq
-   from squigglepy import bayes
-   from squigglepy.numbers import K
-   import numpy as np
-
-   print('Prior')
-   prior = sq.norm(1,5)
-   prior_samples = prior @ (10*K)
-   plt.hist(prior_samples, bins = 200)
-   plt.show()
-   print(sq.get_percentiles(prior_samples))
-   print('Prior Mean: {} SD: {}'.format(np.mean(prior_samples), np.std(prior_samples)))
-   print('-')
-
-   print('Evidence')
-   evidence = sq.norm(2,3)
-   evidence_samples = evidence @ (10*K)
-   plt.hist(evidence_samples, bins = 200)
-   plt.show()
-   print(sq.get_percentiles(evidence_samples))
-   print('Evidence Mean: {} SD: {}'.format(np.mean(evidence_samples), np.std(evidence_samples)))
-   print('-')
-
-   print('Posterior')
-   posterior = bayes.update(prior, evidence)
-   posterior_samples = posterior @ (10*K)
-   plt.hist(posterior_samples, bins = 200)
-   plt.show()
-   print(sq.get_percentiles(posterior_samples))
-   print('Posterior Mean: {} SD: {}'.format(np.mean(posterior_samples), np.std(posterior_samples)))
-
-   print('Average')
-   average = bayes.average(prior, evidence)
-   average_samples = average @ (10*K)
-   plt.hist(average_samples, bins = 200)
-   plt.show()
-   print(sq.get_percentiles(average_samples))
-   print('Average Mean: {} SD: {}'.format(np.mean(average_samples), np.std(average_samples)))
-
-Example: Alarm net
-^^^^^^^^^^^^^^^^^^
-
-This is the alarm network from `Bayesian Artificial Intelligence -
-Section
-2.5.1 `__:
-
-   Assume your house has an alarm system against burglary.
-
-   You live in the seismically active area and the alarm system can get
-   occasionally set off by an earthquake.
-
-   You have two neighbors, Mary and John, who do not know each other. If
-   they hear the alarm they call you, but this is not guaranteed.
-
-   The chance of a burglary on a particular day is 0.1%. The chance of
-   an earthquake on a particular day is 0.2%.
-
-   The alarm will go off 95% of the time with both a burglary and an
-   earthquake, 94% of the time with just a burglary, 29% of the time
-   with just an earthquake, and 0.1% of the time with nothing (total
-   false alarm).
-
-   John will call you 90% of the time when the alarm goes off. But on 5%
-   of the days, John will just call to say “hi”. Mary will call you 70%
-   of the time when the alarm goes off. But on 1% of the days, Mary will
-   just call to say “hi”.
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy import bayes
-   from squigglepy.numbers import M
-
-   def p_alarm_goes_off(burglary, earthquake):
-       if burglary and earthquake:
-           return 0.95
-       elif burglary and not earthquake:
-           return 0.94
-       elif not burglary and earthquake:
-           return 0.29
-       elif not burglary and not earthquake:
-           return 0.001
-
-   def p_john_calls(alarm_goes_off):
-       return 0.9 if alarm_goes_off else 0.05
-
-   def p_mary_calls(alarm_goes_off):
-       return 0.7 if alarm_goes_off else 0.01
-
-   def define_event():
-       burglary_happens = sq.event(p=0.001)
-       earthquake_happens = sq.event(p=0.002)
-       alarm_goes_off = sq.event(p_alarm_goes_off(burglary_happens, earthquake_happens))
-       john_calls = sq.event(p_john_calls(alarm_goes_off))
-       mary_calls = sq.event(p_mary_calls(alarm_goes_off))
-       return {'burglary': burglary_happens,
-               'earthquake': earthquake_happens,
-               'alarm_goes_off': alarm_goes_off,
-               'john_calls': john_calls,
-               'mary_calls': mary_calls}
-
-   # What are the chances that both John and Mary call if an earthquake happens?
-   bayes.bayesnet(define_event,
-                  n=1*M,
-                  find=lambda e: (e['mary_calls'] and e['john_calls']),
-                  conditional_on=lambda e: e['earthquake'])
-   # Result will be ~0.19, though it varies because it is based on a random sample.
-   # This also may take a minute to run.
-
-   # If both John and Mary call, what is the chance there's been a burglary?
-   bayes.bayesnet(define_event,
-                  n=1*M,
-                  find=lambda e: e['burglary'],
-                  conditional_on=lambda e: (e['mary_calls'] and e['john_calls']))
-   # Result will be ~0.27, though it varies because it is based on a random sample.
-   # This will run quickly because there is a built-in cache.
-   # Use `cache=False` to not build a cache and `reload_cache=True` to recalculate the cache.
-
-Note that the amount of Bayesian analysis that squigglepy can do is
-pretty limited. For more complex bayesian analysis, consider
-`sorobn `__,
-`pomegranate `__,
-`bnlearn `__, or
-`pyMC `__.
-
-Example: A Demonstration of the Monty Hall Problem
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy import bayes
-   from squigglepy.numbers import K, M, B, T
-
-
-   def monte_hall(door_picked, switch=False):
-       doors = ['A', 'B', 'C']
-       car_is_behind_door = ~sq.discrete(doors)
-       reveal_door = ~sq.discrete([d for d in doors if d != door_picked and d != car_is_behind_door])
-
-       if switch:
-           old_door_picked = door_picked
-           door_picked = [d for d in doors if d != old_door_picked and d != reveal_door][0]
-
-       won_car = (car_is_behind_door == door_picked)
-       return won_car
-
-
-   def define_event():
-       door = ~sq.discrete(['A', 'B', 'C'])
-       switch = sq.event(0.5)
-       return {'won': monte_hall(door_picked=door, switch=switch),
-               'switched': switch}
-
-   RUNS = 10*K
-   r = bayes.bayesnet(define_event,
-                      find=lambda e: e['won'],
-                      conditional_on=lambda e: e['switched'],
-                      verbose=True,
-                      n=RUNS)
-   print('Win {}% of the time when switching'.format(int(r * 100)))
-
-   r = bayes.bayesnet(define_event,
-                      find=lambda e: e['won'],
-                      conditional_on=lambda e: not e['switched'],
-                      verbose=True,
-                      n=RUNS)
-   print('Win {}% of the time when not switching'.format(int(r * 100)))
-
-   # Win 66% of the time when switching
-   # Win 34% of the time when not switching
-
-Example: More complex coin/dice interactions
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-   Imagine that I flip a coin. If heads, I take a random die out of my
-   blue bag. If tails, I take a random die out of my red bag. The blue
-   bag contains only 6-sided dice. The red bag contains a 4-sided die, a
-   6-sided die, a 10-sided die, and a 20-sided die. I then roll the
-   random die I took. What is the chance that I roll a 6?
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy.numbers import K, M, B, T
-   from squigglepy import bayes
-
-   def define_event():
-       if sq.flip_coin() == 'heads': # Blue bag
-           return sq.roll_die(6)
-       else: # Red bag
-           return sq.discrete([4, 6, 10, 20]) >> sq.roll_die
-
-
-   bayes.bayesnet(define_event,
-                  find=lambda e: e == 6,
-                  verbose=True,
-                  n=100*K)
-   # This run for me returned 0.12306 which is pretty close to the correct answer of 0.12292
-
-Kelly betting
-~~~~~~~~~~~~~
-
-You can use probability generated, combine with a bankroll to determine
-bet sizing using `Kelly
-criterion `__.
-
-For example, if you want to Kelly bet and you’ve…
-
--  determined that your price (your probability of the event in question
-   happening / the market in question resolving in your favor) is $0.70
-   (70%)
--  see that the market is pricing at $0.65
--  you have a bankroll of $1000 that you are willing to bet
-
-You should bet as follows:
-
-.. code:: python
-
-   import squigglepy as sq
-   kelly_data = sq.kelly(my_price=0.70, market_price=0.65, bankroll=1000)
-   kelly_data['kelly']  # What fraction of my bankroll should I bet on this?
-   # 0.143
-   kelly_data['target']  # How much money should be invested in this?
-   # 142.86
-   kelly_data['expected_roi']  # What is the expected ROI of this bet?
-   # 0.077
-
-More examples
-~~~~~~~~~~~~~
-
-You can see more examples of squigglepy in action
-`here `__.
diff --git a/doc/build/html/_sources/index.rst.txt b/doc/build/html/_sources/index.rst.txt
deleted file mode 100644
index 3461183..0000000
--- a/doc/build/html/_sources/index.rst.txt
+++ /dev/null
@@ -1,51 +0,0 @@
-Squigglepy: Implementation of Squiggle in Python
-================================================
-
-`Squiggle `__ is a "simple
-programming language for intuitive probabilistic estimation". It serves
-as its own standalone programming language with its own syntax, but it
-is implemented in JavaScript. I like the features of Squiggle and intend
-to use it frequently, but I also sometimes want to use similar
-functionalities in Python, especially alongside other Python statistical
-programming packages like Numpy, Pandas, and Matplotlib. The
-**squigglepy** package here implements many Squiggle-like
-functionalities in Python.
-
-.. toctree::
-   :maxdepth: 2
-   :caption: Contents
-
-   Installation 
-   Usage 
-   API Reference 
-
-Disclaimers
------------
-
-This package is unofficial and supported by Peter Wildeford and Rethink
-Priorities. It is not affiliated with or associated with the Quantified
-Uncertainty Research Institute, which maintains the Squiggle language
-(in JavaScript).
-
-This package is also new and not yet in a stable production version, so
-you may encounter bugs and other errors. Please report those so they can
-be fixed. It’s also possible that future versions of the package may
-introduce breaking changes.
-
-This package is available under an MIT License.
-
-Acknowledgements
-----------------
-
--  The primary author of this package is Peter Wildeford. Agustín
-   Covarrubias and Bernardo Baron contributed several key features and
-   developments.
--  Thanks to Ozzie Gooen and the Quantified Uncertainty Research
-   Institute for creating and maintaining the original Squiggle
-   language.
--  Thanks to Dawn Drescher for helping me implement math between
-   distributions.
--  Thanks to Dawn Drescher for coming up with the idea to use ``~`` as a
-   shorthand for ``sample``, as well as helping me implement it.
-
-.. autosummary::
diff --git a/doc/build/html/_sources/installation.rst.txt b/doc/build/html/_sources/installation.rst.txt
deleted file mode 100644
index fb5e8d9..0000000
--- a/doc/build/html/_sources/installation.rst.txt
+++ /dev/null
@@ -1,12 +0,0 @@
-Installation
-============
-
-.. code:: shell
-
-   pip install squigglepy
-
-For plotting support, you can also use the ``plots`` extra:
-
-.. code:: shell
-
-   pip install squigglepy[plots]
diff --git a/doc/build/html/_sources/reference/modules.rst.txt b/doc/build/html/_sources/reference/modules.rst.txt
deleted file mode 100644
index 57192bd..0000000
--- a/doc/build/html/_sources/reference/modules.rst.txt
+++ /dev/null
@@ -1,7 +0,0 @@
-squigglepy
-==========
-
-.. toctree::
-   :maxdepth: 4
-
-   squigglepy
diff --git a/doc/build/html/_sources/reference/squigglepy.bayes.rst.txt b/doc/build/html/_sources/reference/squigglepy.bayes.rst.txt
deleted file mode 100644
index 8a445be..0000000
--- a/doc/build/html/_sources/reference/squigglepy.bayes.rst.txt
+++ /dev/null
@@ -1,7 +0,0 @@
-squigglepy.bayes module
-=======================
-
-.. automodule:: squigglepy.bayes
-   :members:
-   :undoc-members:
-   :show-inheritance:
diff --git a/doc/build/html/_sources/reference/squigglepy.correlation.rst.txt b/doc/build/html/_sources/reference/squigglepy.correlation.rst.txt
deleted file mode 100644
index c99cf14..0000000
--- a/doc/build/html/_sources/reference/squigglepy.correlation.rst.txt
+++ /dev/null
@@ -1,7 +0,0 @@
-squigglepy.correlation module
-=============================
-
-.. automodule:: squigglepy.correlation
-   :members:
-   :undoc-members:
-   :show-inheritance:
diff --git a/doc/build/html/_sources/reference/squigglepy.distributions.rst.txt b/doc/build/html/_sources/reference/squigglepy.distributions.rst.txt
deleted file mode 100644
index bfbdb38..0000000
--- a/doc/build/html/_sources/reference/squigglepy.distributions.rst.txt
+++ /dev/null
@@ -1,7 +0,0 @@
-squigglepy.distributions module
-===============================
-
-.. automodule:: squigglepy.distributions
-   :members:
-   :undoc-members:
-   :show-inheritance:
diff --git a/doc/build/html/_sources/reference/squigglepy.numbers.rst.txt b/doc/build/html/_sources/reference/squigglepy.numbers.rst.txt
deleted file mode 100644
index 524cbcd..0000000
--- a/doc/build/html/_sources/reference/squigglepy.numbers.rst.txt
+++ /dev/null
@@ -1,7 +0,0 @@
-squigglepy.numbers module
-=========================
-
-.. automodule:: squigglepy.numbers
-   :members:
-   :undoc-members:
-   :show-inheritance:
diff --git a/doc/build/html/_sources/reference/squigglepy.rng.rst.txt b/doc/build/html/_sources/reference/squigglepy.rng.rst.txt
deleted file mode 100644
index 84ec740..0000000
--- a/doc/build/html/_sources/reference/squigglepy.rng.rst.txt
+++ /dev/null
@@ -1,7 +0,0 @@
-squigglepy.rng module
-=====================
-
-.. automodule:: squigglepy.rng
-   :members:
-   :undoc-members:
-   :show-inheritance:
diff --git a/doc/build/html/_sources/reference/squigglepy.rst.txt b/doc/build/html/_sources/reference/squigglepy.rst.txt
deleted file mode 100644
index b629fda..0000000
--- a/doc/build/html/_sources/reference/squigglepy.rst.txt
+++ /dev/null
@@ -1,22 +0,0 @@
-squigglepy package
-==================
-
-.. automodule:: squigglepy
-   :members:
-   :undoc-members:
-   :show-inheritance:
-
-Submodules
-----------
-
-.. toctree::
-   :maxdepth: 4
-
-   squigglepy.bayes
-   squigglepy.correlation
-   squigglepy.distributions
-   squigglepy.numbers
-   squigglepy.rng
-   squigglepy.samplers
-   squigglepy.utils
-   squigglepy.version
diff --git a/doc/build/html/_sources/reference/squigglepy.samplers.rst.txt b/doc/build/html/_sources/reference/squigglepy.samplers.rst.txt
deleted file mode 100644
index ae3e754..0000000
--- a/doc/build/html/_sources/reference/squigglepy.samplers.rst.txt
+++ /dev/null
@@ -1,7 +0,0 @@
-squigglepy.samplers module
-==========================
-
-.. automodule:: squigglepy.samplers
-   :members:
-   :undoc-members:
-   :show-inheritance:
diff --git a/doc/build/html/_sources/reference/squigglepy.squigglepy.rst.txt b/doc/build/html/_sources/reference/squigglepy.squigglepy.rst.txt
deleted file mode 100644
index 9271ec8..0000000
--- a/doc/build/html/_sources/reference/squigglepy.squigglepy.rst.txt
+++ /dev/null
@@ -1,78 +0,0 @@
-squigglepy.squigglepy package
-=============================
-
-Submodules
-----------
-
-squigglepy.squigglepy.bayes module
-----------------------------------
-
-.. automodule:: squigglepy.squigglepy.bayes
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.squigglepy.correlation module
-----------------------------------------
-
-.. automodule:: squigglepy.squigglepy.correlation
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.squigglepy.distributions module
-------------------------------------------
-
-.. automodule:: squigglepy.squigglepy.distributions
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.squigglepy.numbers module
-------------------------------------
-
-.. automodule:: squigglepy.squigglepy.numbers
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.squigglepy.rng module
---------------------------------
-
-.. automodule:: squigglepy.squigglepy.rng
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.squigglepy.samplers module
--------------------------------------
-
-.. automodule:: squigglepy.squigglepy.samplers
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.squigglepy.utils module
-----------------------------------
-
-.. automodule:: squigglepy.squigglepy.utils
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.squigglepy.version module
-------------------------------------
-
-.. automodule:: squigglepy.squigglepy.version
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-
-Module contents
----------------
-
-.. automodule:: squigglepy.squigglepy
-    :members:
-    :undoc-members:
-    :show-inheritance:
diff --git a/doc/build/html/_sources/reference/squigglepy.tests.rst.txt b/doc/build/html/_sources/reference/squigglepy.tests.rst.txt
deleted file mode 100644
index cf175cf..0000000
--- a/doc/build/html/_sources/reference/squigglepy.tests.rst.txt
+++ /dev/null
@@ -1,86 +0,0 @@
-squigglepy.tests package
-========================
-
-Submodules
-----------
-
-squigglepy.tests.integration module
------------------------------------
-
-.. automodule:: squigglepy.tests.integration
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.tests.strategies module
-----------------------------------
-
-.. automodule:: squigglepy.tests.strategies
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.tests.test\_bayes module
------------------------------------
-
-.. automodule:: squigglepy.tests.test_bayes
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.tests.test\_correlation module
------------------------------------------
-
-.. automodule:: squigglepy.tests.test_correlation
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.tests.test\_distributions module
--------------------------------------------
-
-.. automodule:: squigglepy.tests.test_distributions
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.tests.test\_numbers module
--------------------------------------
-
-.. automodule:: squigglepy.tests.test_numbers
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.tests.test\_rng module
----------------------------------
-
-.. automodule:: squigglepy.tests.test_rng
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.tests.test\_samplers module
---------------------------------------
-
-.. automodule:: squigglepy.tests.test_samplers
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-squigglepy.tests.test\_utils module
------------------------------------
-
-.. automodule:: squigglepy.tests.test_utils
-    :members:
-    :undoc-members:
-    :show-inheritance:
-
-
-Module contents
----------------
-
-.. automodule:: squigglepy.tests
-    :members:
-    :undoc-members:
-    :show-inheritance:
diff --git a/doc/build/html/_sources/reference/squigglepy.utils.rst.txt b/doc/build/html/_sources/reference/squigglepy.utils.rst.txt
deleted file mode 100644
index 8af5f44..0000000
--- a/doc/build/html/_sources/reference/squigglepy.utils.rst.txt
+++ /dev/null
@@ -1,7 +0,0 @@
-squigglepy.utils module
-=======================
-
-.. automodule:: squigglepy.utils
-   :members:
-   :undoc-members:
-   :show-inheritance:
diff --git a/doc/build/html/_sources/reference/squigglepy.version.rst.txt b/doc/build/html/_sources/reference/squigglepy.version.rst.txt
deleted file mode 100644
index efe11f5..0000000
--- a/doc/build/html/_sources/reference/squigglepy.version.rst.txt
+++ /dev/null
@@ -1,7 +0,0 @@
-squigglepy.version module
-=========================
-
-.. automodule:: squigglepy.version
-   :members:
-   :undoc-members:
-   :show-inheritance:
diff --git a/doc/build/html/_sources/usage.rst.txt b/doc/build/html/_sources/usage.rst.txt
deleted file mode 100644
index 3e03a70..0000000
--- a/doc/build/html/_sources/usage.rst.txt
+++ /dev/null
@@ -1,476 +0,0 @@
-Examples
-========
-
-Piano tuners example
-~~~~~~~~~~~~~~~~~~~~
-
-Here’s the Squigglepy implementation of `the example from Squiggle
-Docs `__:
-
-.. code:: python
-
-   import squigglepy as sq
-   import numpy as np
-   import matplotlib.pyplot as plt
-   from squigglepy.numbers import K, M
-   from pprint import pprint
-
-   pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)  # This means that you're 90% confident the value is between 8.1 and 8.4 Million.
-   pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01  # We assume there are almost no people with multiple pianos
-   pianos_per_piano_tuner = sq.to(2*K, 50*K)
-   piano_tuners_per_piano = 1 / pianos_per_piano_tuner
-   total_tuners_in_2022 = pop_of_ny_2022 * pct_of_pop_w_pianos * piano_tuners_per_piano
-   samples = total_tuners_in_2022 @ 1000  # Note: `@ 1000` is shorthand to get 1000 samples
-
-   # Get mean and SD
-   print('Mean: {}, SD: {}'.format(round(np.mean(samples), 2),
-                                   round(np.std(samples), 2)))
-
-   # Get percentiles
-   pprint(sq.get_percentiles(samples, digits=0))
-
-   # Histogram
-   plt.hist(samples, bins=200)
-   plt.show()
-
-   # Shorter histogram
-   total_tuners_in_2022.plot()
-
-And the version from the Squiggle doc that incorporates time:
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy.numbers import K, M
-
-   pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)
-   pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01
-   pianos_per_piano_tuner = sq.to(2*K, 50*K)
-   piano_tuners_per_piano = 1 / pianos_per_piano_tuner
-
-   def pop_at_time(t):  # t = Time in years after 2022
-       avg_yearly_pct_change = sq.to(-0.01, 0.05)  # We're expecting NYC to continuously grow with an mean of roughly between -1% and +4% per year
-       return pop_of_ny_2022 * ((avg_yearly_pct_change + 1) ** t)
-
-   def total_tuners_at_time(t):
-       return pop_at_time(t) * pct_of_pop_w_pianos * piano_tuners_per_piano
-
-   # Get total piano tuners at 2030
-   sq.get_percentiles(total_tuners_at_time(2030-2022) @ 1000)
-
-**WARNING:** Be careful about dividing by ``K``, ``M``, etc. ``1/2*K`` =
-500 in Python. Use ``1/(2*K)`` instead to get the expected outcome.
-
-**WARNING:** Be careful about using ``K`` to get sample counts. Use
-``sq.norm(2, 3) @ (2*K)``\ … ``sq.norm(2, 3) @ 2*K`` will return only
-two samples, multiplied by 1000.
-
-Distributions
-~~~~~~~~~~~~~
-
-.. code:: python
-
-   import squigglepy as sq
-
-   # Normal distribution
-   sq.norm(1, 3)  # 90% interval from 1 to 3
-
-   # Distribution can be sampled with mean and sd too
-   sq.norm(mean=0, sd=1)
-
-   # Shorthand to get one sample
-   ~sq.norm(1, 3)
-
-   # Shorthand to get more than one sample
-   sq.norm(1, 3) @ 100
-
-   # Longhand version to get more than one sample
-   sq.sample(sq.norm(1, 3), n=100)
-
-   # Nice progress reporter
-   sq.sample(sq.norm(1, 3), n=1000, verbose=True)
-
-   # Other distributions exist
-   sq.lognorm(1, 10)
-   sq.tdist(1, 10, t=5)
-   sq.triangular(1, 2, 3)
-   sq.pert(1, 2, 3, lam=2)
-   sq.binomial(p=0.5, n=5)
-   sq.beta(a=1, b=2)
-   sq.bernoulli(p=0.5)
-   sq.poisson(10)
-   sq.chisquare(2)
-   sq.gamma(3, 2)
-   sq.pareto(1)
-   sq.exponential(scale=1)
-   sq.geometric(p=0.5)
-
-   # Discrete sampling
-   sq.discrete({'A': 0.1, 'B': 0.9})
-
-   # Can return integers
-   sq.discrete({0: 0.1, 1: 0.3, 2: 0.3, 3: 0.15, 4: 0.15})
-
-   # Alternate format (also can be used to return more complex objects)
-   sq.discrete([[0.1,  0],
-                [0.3,  1],
-                [0.3,  2],
-                [0.15, 3],
-                [0.15, 4]])
-
-   sq.discrete([0, 1, 2]) # No weights assumes equal weights
-
-   # You can mix distributions together
-   sq.mixture([sq.norm(1, 3),
-               sq.norm(4, 10),
-               sq.lognorm(1, 10)],  # Distributions to mix
-              [0.3, 0.3, 0.4])     # These are the weights on each distribution
-
-   # This is equivalent to the above, just a different way of doing the notation
-   sq.mixture([[0.3, sq.norm(1,3)],
-               [0.3, sq.norm(4,10)],
-               [0.4, sq.lognorm(1,10)]])
-
-   # Make a zero-inflated distribution
-   # 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`.
-   sq.zero_inflated(0.6, sq.norm(1, 2))
-
-Additional features
-~~~~~~~~~~~~~~~~~~~
-
-.. code:: python
-
-   import squigglepy as sq
-
-   # You can add and subtract distributions
-   (sq.norm(1,3) + sq.norm(4,5)) @ 100
-   (sq.norm(1,3) - sq.norm(4,5)) @ 100
-   (sq.norm(1,3) * sq.norm(4,5)) @ 100
-   (sq.norm(1,3) / sq.norm(4,5)) @ 100
-
-   # You can also do math with numbers
-   ~((sq.norm(sd=5) + 2) * 2)
-   ~(-sq.lognorm(0.1, 1) * sq.pareto(1) / 10)
-
-   # You can change the CI from 90% (default) to 80%
-   sq.norm(1, 3, credibility=80)
-
-   # You can clip
-   sq.norm(0, 3, lclip=0, rclip=5) # Sample norm with a 90% CI from 0-3, but anything lower than 0 gets clipped to 0 and anything higher than 5 gets clipped to 5.
-
-   # You can also clip with a function, and use pipes
-   sq.norm(0, 3) >> sq.clip(0, 5)
-
-   # You can correlate continuous distributions
-   a, b = sq.uniform(-1, 1), sq.to(0, 3)
-   a, b = sq.correlate((a, b), 0.5)  # Correlate a and b with a correlation of 0.5
-   # You can even pass your own correlation matrix!
-   a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]])
-
-Example: Rolling a die
-^^^^^^^^^^^^^^^^^^^^^^
-
-An example of how to use distributions to build tools:
-
-.. code:: python
-
-   import squigglepy as sq
-
-   def roll_die(sides, n=1):
-       return sq.discrete(list(range(1, sides + 1))) @ n if sides > 0 else None
-
-   roll_die(sides=6, n=10)
-   # [2, 6, 5, 2, 6, 2, 3, 1, 5, 2]
-
-This is already included standard in the utils of this package. Use
-``sq.roll_die``.
-
-Bayesian inference
-~~~~~~~~~~~~~~~~~~
-
-1% of women at age forty who participate in routine screening have
-breast cancer. 80% of women with breast cancer will get positive
-mammographies. 9.6% of women without breast cancer will also get
-positive mammographies.
-
-A woman in this age group had a positive mammography in a routine
-screening. What is the probability that she actually has breast cancer?
-
-We can approximate the answer with a Bayesian network (uses rejection
-sampling):
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy import bayes
-   from squigglepy.numbers import M
-
-   def mammography(has_cancer):
-       return sq.event(0.8 if has_cancer else 0.096)
-
-   def define_event():
-       cancer = ~sq.bernoulli(0.01)
-       return({'mammography': mammography(cancer),
-               'cancer': cancer})
-
-   bayes.bayesnet(define_event,
-                  find=lambda e: e['cancer'],
-                  conditional_on=lambda e: e['mammography'],
-                  n=1*M)
-   # 0.07723995880535531
-
-Or if we have the information immediately on hand, we can directly
-calculate it. Though this doesn’t work for very complex stuff.
-
-.. code:: python
-
-   from squigglepy import bayes
-   bayes.simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096)
-   # 0.07763975155279504
-
-You can also make distributions and update them:
-
-.. code:: python
-
-   import matplotlib.pyplot as plt
-   import squigglepy as sq
-   from squigglepy import bayes
-   from squigglepy.numbers import K
-   import numpy as np
-
-   print('Prior')
-   prior = sq.norm(1,5)
-   prior_samples = prior @ (10*K)
-   plt.hist(prior_samples, bins = 200)
-   plt.show()
-   print(sq.get_percentiles(prior_samples))
-   print('Prior Mean: {} SD: {}'.format(np.mean(prior_samples), np.std(prior_samples)))
-   print('-')
-
-   print('Evidence')
-   evidence = sq.norm(2,3)
-   evidence_samples = evidence @ (10*K)
-   plt.hist(evidence_samples, bins = 200)
-   plt.show()
-   print(sq.get_percentiles(evidence_samples))
-   print('Evidence Mean: {} SD: {}'.format(np.mean(evidence_samples), np.std(evidence_samples)))
-   print('-')
-
-   print('Posterior')
-   posterior = bayes.update(prior, evidence)
-   posterior_samples = posterior @ (10*K)
-   plt.hist(posterior_samples, bins = 200)
-   plt.show()
-   print(sq.get_percentiles(posterior_samples))
-   print('Posterior Mean: {} SD: {}'.format(np.mean(posterior_samples), np.std(posterior_samples)))
-
-   print('Average')
-   average = bayes.average(prior, evidence)
-   average_samples = average @ (10*K)
-   plt.hist(average_samples, bins = 200)
-   plt.show()
-   print(sq.get_percentiles(average_samples))
-   print('Average Mean: {} SD: {}'.format(np.mean(average_samples), np.std(average_samples)))
-
-Example: Alarm net
-^^^^^^^^^^^^^^^^^^
-
-This is the alarm network from `Bayesian Artificial Intelligence -
-Section
-2.5.1 `__:
-
-   Assume your house has an alarm system against burglary.
-
-   You live in the seismically active area and the alarm system can get
-   occasionally set off by an earthquake.
-
-   You have two neighbors, Mary and John, who do not know each other. If
-   they hear the alarm they call you, but this is not guaranteed.
-
-   The chance of a burglary on a particular day is 0.1%. The chance of
-   an earthquake on a particular day is 0.2%.
-
-   The alarm will go off 95% of the time with both a burglary and an
-   earthquake, 94% of the time with just a burglary, 29% of the time
-   with just an earthquake, and 0.1% of the time with nothing (total
-   false alarm).
-
-   John will call you 90% of the time when the alarm goes off. But on 5%
-   of the days, John will just call to say “hi”. Mary will call you 70%
-   of the time when the alarm goes off. But on 1% of the days, Mary will
-   just call to say “hi”.
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy import bayes
-   from squigglepy.numbers import M
-
-   def p_alarm_goes_off(burglary, earthquake):
-       if burglary and earthquake:
-           return 0.95
-       elif burglary and not earthquake:
-           return 0.94
-       elif not burglary and earthquake:
-           return 0.29
-       elif not burglary and not earthquake:
-           return 0.001
-
-   def p_john_calls(alarm_goes_off):
-       return 0.9 if alarm_goes_off else 0.05
-
-   def p_mary_calls(alarm_goes_off):
-       return 0.7 if alarm_goes_off else 0.01
-
-   def define_event():
-       burglary_happens = sq.event(p=0.001)
-       earthquake_happens = sq.event(p=0.002)
-       alarm_goes_off = sq.event(p_alarm_goes_off(burglary_happens, earthquake_happens))
-       john_calls = sq.event(p_john_calls(alarm_goes_off))
-       mary_calls = sq.event(p_mary_calls(alarm_goes_off))
-       return {'burglary': burglary_happens,
-               'earthquake': earthquake_happens,
-               'alarm_goes_off': alarm_goes_off,
-               'john_calls': john_calls,
-               'mary_calls': mary_calls}
-
-   # What are the chances that both John and Mary call if an earthquake happens?
-   bayes.bayesnet(define_event,
-                  n=1*M,
-                  find=lambda e: (e['mary_calls'] and e['john_calls']),
-                  conditional_on=lambda e: e['earthquake'])
-   # Result will be ~0.19, though it varies because it is based on a random sample.
-   # This also may take a minute to run.
-
-   # If both John and Mary call, what is the chance there's been a burglary?
-   bayes.bayesnet(define_event,
-                  n=1*M,
-                  find=lambda e: e['burglary'],
-                  conditional_on=lambda e: (e['mary_calls'] and e['john_calls']))
-   # Result will be ~0.27, though it varies because it is based on a random sample.
-   # This will run quickly because there is a built-in cache.
-   # Use `cache=False` to not build a cache and `reload_cache=True` to recalculate the cache.
-
-Note that the amount of Bayesian analysis that squigglepy can do is
-pretty limited. For more complex bayesian analysis, consider
-`sorobn `__,
-`pomegranate `__,
-`bnlearn `__, or
-`pyMC `__.
-
-Example: A demonstration of the Monty Hall Problem
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy import bayes
-   from squigglepy.numbers import K, M, B, T
-
-
-   def monte_hall(door_picked, switch=False):
-       doors = ['A', 'B', 'C']
-       car_is_behind_door = ~sq.discrete(doors)
-       reveal_door = ~sq.discrete([d for d in doors if d != door_picked and d != car_is_behind_door])
-
-       if switch:
-           old_door_picked = door_picked
-           door_picked = [d for d in doors if d != old_door_picked and d != reveal_door][0]
-
-       won_car = (car_is_behind_door == door_picked)
-       return won_car
-
-
-   def define_event():
-       door = ~sq.discrete(['A', 'B', 'C'])
-       switch = sq.event(0.5)
-       return {'won': monte_hall(door_picked=door, switch=switch),
-               'switched': switch}
-
-   RUNS = 10*K
-   r = bayes.bayesnet(define_event,
-                      find=lambda e: e['won'],
-                      conditional_on=lambda e: e['switched'],
-                      verbose=True,
-                      n=RUNS)
-   print('Win {}% of the time when switching'.format(int(r * 100)))
-
-   r = bayes.bayesnet(define_event,
-                      find=lambda e: e['won'],
-                      conditional_on=lambda e: not e['switched'],
-                      verbose=True,
-                      n=RUNS)
-   print('Win {}% of the time when not switching'.format(int(r * 100)))
-
-   # Win 66% of the time when switching
-   # Win 34% of the time when not switching
-
-Example: More complex coin/dice interactions
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-   Imagine that I flip a coin. If heads, I take a random die out of my
-   blue bag. If tails, I take a random die out of my red bag. The blue
-   bag contains only 6-sided dice. The red bag contains a 4-sided die, a
-   6-sided die, a 10-sided die, and a 20-sided die. I then roll the
-   random die I took. What is the chance that I roll a 6?
-
-.. code:: python
-
-   import squigglepy as sq
-   from squigglepy.numbers import K, M, B, T
-   from squigglepy import bayes
-
-   def define_event():
-       if sq.flip_coin() == 'heads': # Blue bag
-           return sq.roll_die(6)
-       else: # Red bag
-           return sq.discrete([4, 6, 10, 20]) >> sq.roll_die
-
-
-   bayes.bayesnet(define_event,
-                  find=lambda e: e == 6,
-                  verbose=True,
-                  n=100*K)
-   # This run for me returned 0.12306 which is pretty close to the correct answer of 0.12292
-
-Kelly betting
-~~~~~~~~~~~~~
-
-You can use probability generated, combine with a bankroll to determine
-bet sizing using `Kelly
-criterion `__.
-
-For example, if you want to Kelly bet and you’ve…
-
--  determined that your price (your probability of the event in question
-   happening / the market in question resolving in your favor) is $0.70
-   (70%)
--  see that the market is pricing at $0.65
--  you have a bankroll of $1000 that you are willing to bet
-
-You should bet as follows:
-
-.. code:: python
-
-   import squigglepy as sq
-   kelly_data = sq.kelly(my_price=0.70, market_price=0.65, bankroll=1000)
-   kelly_data['kelly']  # What fraction of my bankroll should I bet on this?
-   # 0.143
-   kelly_data['target']  # How much money should be invested in this?
-   # 142.86
-   kelly_data['expected_roi']  # What is the expected ROI of this bet?
-   # 0.077
-
-More examples
-~~~~~~~~~~~~~
-
-You can see more examples of squigglepy in action
-`here `__.
-
-Run tests
----------
-
-Use ``black .`` for formatting.
-
-Run
-``ruff check . && pytest && pip3 install . && python3 tests/integration.py``
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deleted file mode 100644
index 517d0b2..0000000
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-  -moz-user-select: none; /* Firefox */
-  -ms-user-select: none; /* IE10+ */
-}
-
-div.code-block-caption span.caption-number {
-    padding: 0.1em 0.3em;
-    font-style: italic;
-}
-
-div.code-block-caption span.caption-text {
-}
-
-div.literal-block-wrapper {
-    margin: 1em 0;
-}
-
-code.xref, a code {
-    background-color: transparent;
-    font-weight: bold;
-}
-
-h1 code, h2 code, h3 code, h4 code, h5 code, h6 code {
-    background-color: transparent;
-}
-
-.viewcode-link {
-    float: right;
-}
-
-.viewcode-back {
-    float: right;
-    font-family: sans-serif;
-}
-
-div.viewcode-block:target {
-    margin: -1px -10px;
-    padding: 0 10px;
-}
-
-/* -- math display ---------------------------------------------------------- */
-
-img.math {
-    vertical-align: middle;
-}
-
-div.body div.math p {
-    text-align: center;
-}
-
-span.eqno {
-    float: right;
-}
-
-span.eqno a.headerlink {
-    position: absolute;
-    z-index: 1;
-}
-
-div.math:hover a.headerlink {
-    visibility: visible;
-}
-
-/* -- printout stylesheet --------------------------------------------------- */
-
-@media print {
-    div.document,
-    div.documentwrapper,
-    div.bodywrapper {
-        margin: 0 !important;
-        width: 100%;
-    }
-
-    div.sphinxsidebar,
-    div.related,
-    div.footer,
-    #top-link {
-        display: none;
-    }
-}
\ No newline at end of file
diff --git a/doc/build/html/_static/custom.css b/doc/build/html/_static/custom.css
deleted file mode 100644
index 2a924f1..0000000
--- a/doc/build/html/_static/custom.css
+++ /dev/null
@@ -1 +0,0 @@
-/* This file intentionally left blank. */
diff --git a/doc/build/html/_static/doctools.js b/doc/build/html/_static/doctools.js
deleted file mode 100644
index d06a71d..0000000
--- a/doc/build/html/_static/doctools.js
+++ /dev/null
@@ -1,156 +0,0 @@
-/*
- * doctools.js
- * ~~~~~~~~~~~
- *
- * Base JavaScript utilities for all Sphinx HTML documentation.
- *
- * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS.
- * :license: BSD, see LICENSE for details.
- *
- */
-"use strict";
-
-const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([
-  "TEXTAREA",
-  "INPUT",
-  "SELECT",
-  "BUTTON",
-]);
-
-const _ready = (callback) => {
-  if (document.readyState !== "loading") {
-    callback();
-  } else {
-    document.addEventListener("DOMContentLoaded", callback);
-  }
-};
-
-/**
- * Small JavaScript module for the documentation.
- */
-const Documentation = {
-  init: () => {
-    Documentation.initDomainIndexTable();
-    Documentation.initOnKeyListeners();
-  },
-
-  /**
-   * i18n support
-   */
-  TRANSLATIONS: {},
-  PLURAL_EXPR: (n) => (n === 1 ? 0 : 1),
-  LOCALE: "unknown",
-
-  // gettext and ngettext don't access this so that the functions
-  // can safely bound to a different name (_ = Documentation.gettext)
-  gettext: (string) => {
-    const translated = Documentation.TRANSLATIONS[string];
-    switch (typeof translated) {
-      case "undefined":
-        return string; // no translation
-      case "string":
-        return translated; // translation exists
-      default:
-        return translated[0]; // (singular, plural) translation tuple exists
-    }
-  },
-
-  ngettext: (singular, plural, n) => {
-    const translated = Documentation.TRANSLATIONS[singular];
-    if (typeof translated !== "undefined")
-      return translated[Documentation.PLURAL_EXPR(n)];
-    return n === 1 ? singular : plural;
-  },
-
-  addTranslations: (catalog) => {
-    Object.assign(Documentation.TRANSLATIONS, catalog.messages);
-    Documentation.PLURAL_EXPR = new Function(
-      "n",
-      `return (${catalog.plural_expr})`
-    );
-    Documentation.LOCALE = catalog.locale;
-  },
-
-  /**
-   * helper function to focus on search bar
-   */
-  focusSearchBar: () => {
-    document.querySelectorAll("input[name=q]")[0]?.focus();
-  },
-
-  /**
-   * Initialise the domain index toggle buttons
-   */
-  initDomainIndexTable: () => {
-    const toggler = (el) => {
-      const idNumber = el.id.substr(7);
-      const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`);
-      if (el.src.substr(-9) === "minus.png") {
-        el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`;
-        toggledRows.forEach((el) => (el.style.display = "none"));
-      } else {
-        el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`;
-        toggledRows.forEach((el) => (el.style.display = ""));
-      }
-    };
-
-    const togglerElements = document.querySelectorAll("img.toggler");
-    togglerElements.forEach((el) =>
-      el.addEventListener("click", (event) => toggler(event.currentTarget))
-    );
-    togglerElements.forEach((el) => (el.style.display = ""));
-    if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler);
-  },
-
-  initOnKeyListeners: () => {
-    // only install a listener if it is really needed
-    if (
-      !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS &&
-      !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS
-    )
-      return;
-
-    document.addEventListener("keydown", (event) => {
-      // bail for input elements
-      if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
-      // bail with special keys
-      if (event.altKey || event.ctrlKey || event.metaKey) return;
-
-      if (!event.shiftKey) {
-        switch (event.key) {
-          case "ArrowLeft":
-            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
-
-            const prevLink = document.querySelector('link[rel="prev"]');
-            if (prevLink && prevLink.href) {
-              window.location.href = prevLink.href;
-              event.preventDefault();
-            }
-            break;
-          case "ArrowRight":
-            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
-
-            const nextLink = document.querySelector('link[rel="next"]');
-            if (nextLink && nextLink.href) {
-              window.location.href = nextLink.href;
-              event.preventDefault();
-            }
-            break;
-        }
-      }
-
-      // some keyboard layouts may need Shift to get /
-      switch (event.key) {
-        case "/":
-          if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break;
-          Documentation.focusSearchBar();
-          event.preventDefault();
-      }
-    });
-  },
-};
-
-// quick alias for translations
-const _ = Documentation.gettext;
-
-_ready(Documentation.init);
diff --git a/doc/build/html/_static/documentation_options.js b/doc/build/html/_static/documentation_options.js
deleted file mode 100644
index 7e4c114..0000000
--- a/doc/build/html/_static/documentation_options.js
+++ /dev/null
@@ -1,13 +0,0 @@
-const DOCUMENTATION_OPTIONS = {
-    VERSION: '',
-    LANGUAGE: 'en',
-    COLLAPSE_INDEX: false,
-    BUILDER: 'html',
-    FILE_SUFFIX: '.html',
-    LINK_SUFFIX: '.html',
-    HAS_SOURCE: true,
-    SOURCELINK_SUFFIX: '.txt',
-    NAVIGATION_WITH_KEYS: false,
-    SHOW_SEARCH_SUMMARY: true,
-    ENABLE_SEARCH_SHORTCUTS: true,
-};
\ No newline at end of file
diff --git a/doc/build/html/_static/file.png b/doc/build/html/_static/file.png
deleted file mode 100644
index a858a410e4faa62ce324d814e4b816fff83a6fb3..0000000000000000000000000000000000000000
GIT binary patch
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diff --git a/doc/build/html/_static/jquery.js b/doc/build/html/_static/jquery.js
deleted file mode 100644
index 7e32910..0000000
--- a/doc/build/html/_static/jquery.js
+++ /dev/null
@@ -1,10365 +0,0 @@
-/*!
- * jQuery JavaScript Library v3.3.1-dfsg
- * https://jquery.com/
- *
- * Includes Sizzle.js
- * https://sizzlejs.com/
- *
- * Copyright JS Foundation and other contributors
- * Released under the MIT license
- * https://jquery.org/license
- *
- * Date: 2019-04-19T06:52Z
- */
-( function( global, factory ) {
-
-	"use strict";
-
-	if ( typeof module === "object" && typeof module.exports === "object" ) {
-
-		// For CommonJS and CommonJS-like environments where a proper `window`
-		// is present, execute the factory and get jQuery.
-		// For environments that do not have a `window` with a `document`
-		// (such as Node.js), expose a factory as module.exports.
-		// This accentuates the need for the creation of a real `window`.
-		// e.g. var jQuery = require("jquery")(window);
-		// See ticket #14549 for more info.
-		module.exports = global.document ?
-			factory( global, true ) :
-			function( w ) {
-				if ( !w.document ) {
-					throw new Error( "jQuery requires a window with a document" );
-				}
-				return factory( w );
-			};
-	} else {
-		factory( global );
-	}
-
-// Pass this if window is not defined yet
-} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) {
-
-// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1
-// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode
-// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common
-// enough that all such attempts are guarded in a try block.
-
-
-var arr = [];
-
-var document = window.document;
-
-var getProto = Object.getPrototypeOf;
-
-var slice = arr.slice;
-
-var concat = arr.concat;
-
-var push = arr.push;
-
-var indexOf = arr.indexOf;
-
-var class2type = {};
-
-var toString = class2type.toString;
-
-var hasOwn = class2type.hasOwnProperty;
-
-var fnToString = hasOwn.toString;
-
-var ObjectFunctionString = fnToString.call( Object );
-
-var support = {};
-
-var isFunction = function isFunction( obj ) {
-
-      // Support: Chrome <=57, Firefox <=52
-      // In some browsers, typeof returns "function" for HTML  elements
-      // (i.e., `typeof document.createElement( "object" ) === "function"`).
-      // We don't want to classify *any* DOM node as a function.
-      return typeof obj === "function" && typeof obj.nodeType !== "number";
-  };
-
-
-var isWindow = function isWindow( obj ) {
-		return obj != null && obj === obj.window;
-	};
-
-
-
-
-	var preservedScriptAttributes = {
-		type: true,
-		src: true,
-		noModule: true
-	};
-
-	function DOMEval( code, doc, node ) {
-		doc = doc || document;
-
-		var i,
-			script = doc.createElement( "script" );
-
-		script.text = code;
-		if ( node ) {
-			for ( i in preservedScriptAttributes ) {
-				if ( node[ i ] ) {
-					script[ i ] = node[ i ];
-				}
-			}
-		}
-		doc.head.appendChild( script ).parentNode.removeChild( script );
-	}
-
-
-function toType( obj ) {
-	if ( obj == null ) {
-		return obj + "";
-	}
-
-	// Support: Android <=2.3 only (functionish RegExp)
-	return typeof obj === "object" || typeof obj === "function" ?
-		class2type[ toString.call( obj ) ] || "object" :
-		typeof obj;
-}
-/* global Symbol */
-// Defining this global in .eslintrc.json would create a danger of using the global
-// unguarded in another place, it seems safer to define global only for this module
-
-
-
-var
-	version = "3.3.1",
-
-	// Define a local copy of jQuery
-	jQuery = function( selector, context ) {
-
-		// The jQuery object is actually just the init constructor 'enhanced'
-		// Need init if jQuery is called (just allow error to be thrown if not included)
-		return new jQuery.fn.init( selector, context );
-	},
-
-	// Support: Android <=4.0 only
-	// Make sure we trim BOM and NBSP
-	rtrim = /^[\s\uFEFF\xA0]+|[\s\uFEFF\xA0]+$/g;
-
-jQuery.fn = jQuery.prototype = {
-
-	// The current version of jQuery being used
-	jquery: version,
-
-	constructor: jQuery,
-
-	// The default length of a jQuery object is 0
-	length: 0,
-
-	toArray: function() {
-		return slice.call( this );
-	},
-
-	// Get the Nth element in the matched element set OR
-	// Get the whole matched element set as a clean array
-	get: function( num ) {
-
-		// Return all the elements in a clean array
-		if ( num == null ) {
-			return slice.call( this );
-		}
-
-		// Return just the one element from the set
-		return num < 0 ? this[ num + this.length ] : this[ num ];
-	},
-
-	// Take an array of elements and push it onto the stack
-	// (returning the new matched element set)
-	pushStack: function( elems ) {
-
-		// Build a new jQuery matched element set
-		var ret = jQuery.merge( this.constructor(), elems );
-
-		// Add the old object onto the stack (as a reference)
-		ret.prevObject = this;
-
-		// Return the newly-formed element set
-		return ret;
-	},
-
-	// Execute a callback for every element in the matched set.
-	each: function( callback ) {
-		return jQuery.each( this, callback );
-	},
-
-	map: function( callback ) {
-		return this.pushStack( jQuery.map( this, function( elem, i ) {
-			return callback.call( elem, i, elem );
-		} ) );
-	},
-
-	slice: function() {
-		return this.pushStack( slice.apply( this, arguments ) );
-	},
-
-	first: function() {
-		return this.eq( 0 );
-	},
-
-	last: function() {
-		return this.eq( -1 );
-	},
-
-	eq: function( i ) {
-		var len = this.length,
-			j = +i + ( i < 0 ? len : 0 );
-		return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] );
-	},
-
-	end: function() {
-		return this.prevObject || this.constructor();
-	},
-
-	// For internal use only.
-	// Behaves like an Array's method, not like a jQuery method.
-	push: push,
-	sort: arr.sort,
-	splice: arr.splice
-};
-
-jQuery.extend = jQuery.fn.extend = function() {
-	var options, name, src, copy, copyIsArray, clone,
-		target = arguments[ 0 ] || {},
-		i = 1,
-		length = arguments.length,
-		deep = false;
-
-	// Handle a deep copy situation
-	if ( typeof target === "boolean" ) {
-		deep = target;
-
-		// Skip the boolean and the target
-		target = arguments[ i ] || {};
-		i++;
-	}
-
-	// Handle case when target is a string or something (possible in deep copy)
-	if ( typeof target !== "object" && !isFunction( target ) ) {
-		target = {};
-	}
-
-	// Extend jQuery itself if only one argument is passed
-	if ( i === length ) {
-		target = this;
-		i--;
-	}
-
-	for ( ; i < length; i++ ) {
-
-		// Only deal with non-null/undefined values
-		if ( ( options = arguments[ i ] ) != null ) {
-
-			// Extend the base object
-			for ( name in options ) {
-				src = target[ name ];
-				copy = options[ name ];
-
-				// Prevent Object.prototype pollution
-				// Prevent never-ending loop
-				if ( name === "__proto__" || target === copy ) {
-					continue;
-				}
-
-				// Recurse if we're merging plain objects or arrays
-				if ( deep && copy && ( jQuery.isPlainObject( copy ) ||
-					( copyIsArray = Array.isArray( copy ) ) ) ) {
-
-					if ( copyIsArray ) {
-						copyIsArray = false;
-						clone = src && Array.isArray( src ) ? src : [];
-
-					} else {
-						clone = src && jQuery.isPlainObject( src ) ? src : {};
-					}
-
-					// Never move original objects, clone them
-					target[ name ] = jQuery.extend( deep, clone, copy );
-
-				// Don't bring in undefined values
-				} else if ( copy !== undefined ) {
-					target[ name ] = copy;
-				}
-			}
-		}
-	}
-
-	// Return the modified object
-	return target;
-};
-
-jQuery.extend( {
-
-	// Unique for each copy of jQuery on the page
-	expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ),
-
-	// Assume jQuery is ready without the ready module
-	isReady: true,
-
-	error: function( msg ) {
-		throw new Error( msg );
-	},
-
-	noop: function() {},
-
-	isPlainObject: function( obj ) {
-		var proto, Ctor;
-
-		// Detect obvious negatives
-		// Use toString instead of jQuery.type to catch host objects
-		if ( !obj || toString.call( obj ) !== "[object Object]" ) {
-			return false;
-		}
-
-		proto = getProto( obj );
-
-		// Objects with no prototype (e.g., `Object.create( null )`) are plain
-		if ( !proto ) {
-			return true;
-		}
-
-		// Objects with prototype are plain iff they were constructed by a global Object function
-		Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor;
-		return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString;
-	},
-
-	isEmptyObject: function( obj ) {
-
-		/* eslint-disable no-unused-vars */
-		// See https://github.com/eslint/eslint/issues/6125
-		var name;
-
-		for ( name in obj ) {
-			return false;
-		}
-		return true;
-	},
-
-	// Evaluates a script in a global context
-	globalEval: function( code ) {
-		DOMEval( code );
-	},
-
-	each: function( obj, callback ) {
-		var length, i = 0;
-
-		if ( isArrayLike( obj ) ) {
-			length = obj.length;
-			for ( ; i < length; i++ ) {
-				if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
-					break;
-				}
-			}
-		} else {
-			for ( i in obj ) {
-				if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
-					break;
-				}
-			}
-		}
-
-		return obj;
-	},
-
-	// Support: Android <=4.0 only
-	trim: function( text ) {
-		return text == null ?
-			"" :
-			( text + "" ).replace( rtrim, "" );
-	},
-
-	// results is for internal usage only
-	makeArray: function( arr, results ) {
-		var ret = results || [];
-
-		if ( arr != null ) {
-			if ( isArrayLike( Object( arr ) ) ) {
-				jQuery.merge( ret,
-					typeof arr === "string" ?
-					[ arr ] : arr
-				);
-			} else {
-				push.call( ret, arr );
-			}
-		}
-
-		return ret;
-	},
-
-	inArray: function( elem, arr, i ) {
-		return arr == null ? -1 : indexOf.call( arr, elem, i );
-	},
-
-	// Support: Android <=4.0 only, PhantomJS 1 only
-	// push.apply(_, arraylike) throws on ancient WebKit
-	merge: function( first, second ) {
-		var len = +second.length,
-			j = 0,
-			i = first.length;
-
-		for ( ; j < len; j++ ) {
-			first[ i++ ] = second[ j ];
-		}
-
-		first.length = i;
-
-		return first;
-	},
-
-	grep: function( elems, callback, invert ) {
-		var callbackInverse,
-			matches = [],
-			i = 0,
-			length = elems.length,
-			callbackExpect = !invert;
-
-		// Go through the array, only saving the items
-		// that pass the validator function
-		for ( ; i < length; i++ ) {
-			callbackInverse = !callback( elems[ i ], i );
-			if ( callbackInverse !== callbackExpect ) {
-				matches.push( elems[ i ] );
-			}
-		}
-
-		return matches;
-	},
-
-	// arg is for internal usage only
-	map: function( elems, callback, arg ) {
-		var length, value,
-			i = 0,
-			ret = [];
-
-		// Go through the array, translating each of the items to their new values
-		if ( isArrayLike( elems ) ) {
-			length = elems.length;
-			for ( ; i < length; i++ ) {
-				value = callback( elems[ i ], i, arg );
-
-				if ( value != null ) {
-					ret.push( value );
-				}
-			}
-
-		// Go through every key on the object,
-		} else {
-			for ( i in elems ) {
-				value = callback( elems[ i ], i, arg );
-
-				if ( value != null ) {
-					ret.push( value );
-				}
-			}
-		}
-
-		// Flatten any nested arrays
-		return concat.apply( [], ret );
-	},
-
-	// A global GUID counter for objects
-	guid: 1,
-
-	// jQuery.support is not used in Core but other projects attach their
-	// properties to it so it needs to exist.
-	support: support
-} );
-
-if ( typeof Symbol === "function" ) {
-	jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ];
-}
-
-// Populate the class2type map
-jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ),
-function( i, name ) {
-	class2type[ "[object " + name + "]" ] = name.toLowerCase();
-} );
-
-function isArrayLike( obj ) {
-
-	// Support: real iOS 8.2 only (not reproducible in simulator)
-	// `in` check used to prevent JIT error (gh-2145)
-	// hasOwn isn't used here due to false negatives
-	// regarding Nodelist length in IE
-	var length = !!obj && "length" in obj && obj.length,
-		type = toType( obj );
-
-	if ( isFunction( obj ) || isWindow( obj ) ) {
-		return false;
-	}
-
-	return type === "array" || length === 0 ||
-		typeof length === "number" && length > 0 && ( length - 1 ) in obj;
-}
-var Sizzle =
-/*!
- * Sizzle CSS Selector Engine v2.3.3
- * https://sizzlejs.com/
- *
- * Copyright jQuery Foundation and other contributors
- * Released under the MIT license
- * http://jquery.org/license
- *
- * Date: 2016-08-08
- */
-(function( window ) {
-
-var i,
-	support,
-	Expr,
-	getText,
-	isXML,
-	tokenize,
-	compile,
-	select,
-	outermostContext,
-	sortInput,
-	hasDuplicate,
-
-	// Local document vars
-	setDocument,
-	document,
-	docElem,
-	documentIsHTML,
-	rbuggyQSA,
-	rbuggyMatches,
-	matches,
-	contains,
-
-	// Instance-specific data
-	expando = "sizzle" + 1 * new Date(),
-	preferredDoc = window.document,
-	dirruns = 0,
-	done = 0,
-	classCache = createCache(),
-	tokenCache = createCache(),
-	compilerCache = createCache(),
-	sortOrder = function( a, b ) {
-		if ( a === b ) {
-			hasDuplicate = true;
-		}
-		return 0;
-	},
-
-	// Instance methods
-	hasOwn = ({}).hasOwnProperty,
-	arr = [],
-	pop = arr.pop,
-	push_native = arr.push,
-	push = arr.push,
-	slice = arr.slice,
-	// Use a stripped-down indexOf as it's faster than native
-	// https://jsperf.com/thor-indexof-vs-for/5
-	indexOf = function( list, elem ) {
-		var i = 0,
-			len = list.length;
-		for ( ; i < len; i++ ) {
-			if ( list[i] === elem ) {
-				return i;
-			}
-		}
-		return -1;
-	},
-
-	booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped",
-
-	// Regular expressions
-
-	// http://www.w3.org/TR/css3-selectors/#whitespace
-	whitespace = "[\\x20\\t\\r\\n\\f]",
-
-	// http://www.w3.org/TR/CSS21/syndata.html#value-def-identifier
-	identifier = "(?:\\\\.|[\\w-]|[^\0-\\xa0])+",
-
-	// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
-	attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
-		// Operator (capture 2)
-		"*([*^$|!~]?=)" + whitespace +
-		// "Attribute values must be CSS identifiers [capture 5] or strings [capture 3 or capture 4]"
-		"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + whitespace +
-		"*\\]",
-
-	pseudos = ":(" + identifier + ")(?:\\((" +
-		// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
-		// 1. quoted (capture 3; capture 4 or capture 5)
-		"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
-		// 2. simple (capture 6)
-		"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
-		// 3. anything else (capture 2)
-		".*" +
-		")\\)|)",
-
-	// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
-	rwhitespace = new RegExp( whitespace + "+", "g" ),
-	rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + whitespace + "+$", "g" ),
-
-	rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
-	rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + "*" ),
-
-	rattributeQuotes = new RegExp( "=" + whitespace + "*([^\\]'\"]*?)" + whitespace + "*\\]", "g" ),
-
-	rpseudo = new RegExp( pseudos ),
-	ridentifier = new RegExp( "^" + identifier + "$" ),
-
-	matchExpr = {
-		"ID": new RegExp( "^#(" + identifier + ")" ),
-		"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
-		"TAG": new RegExp( "^(" + identifier + "|[*])" ),
-		"ATTR": new RegExp( "^" + attributes ),
-		"PSEUDO": new RegExp( "^" + pseudos ),
-		"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + whitespace +
-			"*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + whitespace +
-			"*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
-		"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
-		// For use in libraries implementing .is()
-		// We use this for POS matching in `select`
-		"needsContext": new RegExp( "^" + whitespace + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" +
-			whitespace + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
-	},
-
-	rinputs = /^(?:input|select|textarea|button)$/i,
-	rheader = /^h\d$/i,
-
-	rnative = /^[^{]+\{\s*\[native \w/,
-
-	// Easily-parseable/retrievable ID or TAG or CLASS selectors
-	rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
-
-	rsibling = /[+~]/,
-
-	// CSS escapes
-	// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
-	runescape = new RegExp( "\\\\([\\da-f]{1,6}" + whitespace + "?|(" + whitespace + ")|.)", "ig" ),
-	funescape = function( _, escaped, escapedWhitespace ) {
-		var high = "0x" + escaped - 0x10000;
-		// NaN means non-codepoint
-		// Support: Firefox<24
-		// Workaround erroneous numeric interpretation of +"0x"
-		return high !== high || escapedWhitespace ?
-			escaped :
-			high < 0 ?
-				// BMP codepoint
-				String.fromCharCode( high + 0x10000 ) :
-				// Supplemental Plane codepoint (surrogate pair)
-				String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
-	},
-
-	// CSS string/identifier serialization
-	// https://drafts.csswg.org/cssom/#common-serializing-idioms
-	rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
-	fcssescape = function( ch, asCodePoint ) {
-		if ( asCodePoint ) {
-
-			// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
-			if ( ch === "\0" ) {
-				return "\uFFFD";
-			}
-
-			// Control characters and (dependent upon position) numbers get escaped as code points
-			return ch.slice( 0, -1 ) + "\\" + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
-		}
-
-		// Other potentially-special ASCII characters get backslash-escaped
-		return "\\" + ch;
-	},
-
-	// Used for iframes
-	// See setDocument()
-	// Removing the function wrapper causes a "Permission Denied"
-	// error in IE
-	unloadHandler = function() {
-		setDocument();
-	},
-
-	disabledAncestor = addCombinator(
-		function( elem ) {
-			return elem.disabled === true && ("form" in elem || "label" in elem);
-		},
-		{ dir: "parentNode", next: "legend" }
-	);
-
-// Optimize for push.apply( _, NodeList )
-try {
-	push.apply(
-		(arr = slice.call( preferredDoc.childNodes )),
-		preferredDoc.childNodes
-	);
-	// Support: Android<4.0
-	// Detect silently failing push.apply
-	arr[ preferredDoc.childNodes.length ].nodeType;
-} catch ( e ) {
-	push = { apply: arr.length ?
-
-		// Leverage slice if possible
-		function( target, els ) {
-			push_native.apply( target, slice.call(els) );
-		} :
-
-		// Support: IE<9
-		// Otherwise append directly
-		function( target, els ) {
-			var j = target.length,
-				i = 0;
-			// Can't trust NodeList.length
-			while ( (target[j++] = els[i++]) ) {}
-			target.length = j - 1;
-		}
-	};
-}
-
-function Sizzle( selector, context, results, seed ) {
-	var m, i, elem, nid, match, groups, newSelector,
-		newContext = context && context.ownerDocument,
-
-		// nodeType defaults to 9, since context defaults to document
-		nodeType = context ? context.nodeType : 9;
-
-	results = results || [];
-
-	// Return early from calls with invalid selector or context
-	if ( typeof selector !== "string" || !selector ||
-		nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
-
-		return results;
-	}
-
-	// Try to shortcut find operations (as opposed to filters) in HTML documents
-	if ( !seed ) {
-
-		if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) {
-			setDocument( context );
-		}
-		context = context || document;
-
-		if ( documentIsHTML ) {
-
-			// If the selector is sufficiently simple, try using a "get*By*" DOM method
-			// (excepting DocumentFragment context, where the methods don't exist)
-			if ( nodeType !== 11 && (match = rquickExpr.exec( selector )) ) {
-
-				// ID selector
-				if ( (m = match[1]) ) {
-
-					// Document context
-					if ( nodeType === 9 ) {
-						if ( (elem = context.getElementById( m )) ) {
-
-							// Support: IE, Opera, Webkit
-							// TODO: identify versions
-							// getElementById can match elements by name instead of ID
-							if ( elem.id === m ) {
-								results.push( elem );
-								return results;
-							}
-						} else {
-							return results;
-						}
-
-					// Element context
-					} else {
-
-						// Support: IE, Opera, Webkit
-						// TODO: identify versions
-						// getElementById can match elements by name instead of ID
-						if ( newContext && (elem = newContext.getElementById( m )) &&
-							contains( context, elem ) &&
-							elem.id === m ) {
-
-							results.push( elem );
-							return results;
-						}
-					}
-
-				// Type selector
-				} else if ( match[2] ) {
-					push.apply( results, context.getElementsByTagName( selector ) );
-					return results;
-
-				// Class selector
-				} else if ( (m = match[3]) && support.getElementsByClassName &&
-					context.getElementsByClassName ) {
-
-					push.apply( results, context.getElementsByClassName( m ) );
-					return results;
-				}
-			}
-
-			// Take advantage of querySelectorAll
-			if ( support.qsa &&
-				!compilerCache[ selector + " " ] &&
-				(!rbuggyQSA || !rbuggyQSA.test( selector )) ) {
-
-				if ( nodeType !== 1 ) {
-					newContext = context;
-					newSelector = selector;
-
-				// qSA looks outside Element context, which is not what we want
-				// Thanks to Andrew Dupont for this workaround technique
-				// Support: IE <=8
-				// Exclude object elements
-				} else if ( context.nodeName.toLowerCase() !== "object" ) {
-
-					// Capture the context ID, setting it first if necessary
-					if ( (nid = context.getAttribute( "id" )) ) {
-						nid = nid.replace( rcssescape, fcssescape );
-					} else {
-						context.setAttribute( "id", (nid = expando) );
-					}
-
-					// Prefix every selector in the list
-					groups = tokenize( selector );
-					i = groups.length;
-					while ( i-- ) {
-						groups[i] = "#" + nid + " " + toSelector( groups[i] );
-					}
-					newSelector = groups.join( "," );
-
-					// Expand context for sibling selectors
-					newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
-						context;
-				}
-
-				if ( newSelector ) {
-					try {
-						push.apply( results,
-							newContext.querySelectorAll( newSelector )
-						);
-						return results;
-					} catch ( qsaError ) {
-					} finally {
-						if ( nid === expando ) {
-							context.removeAttribute( "id" );
-						}
-					}
-				}
-			}
-		}
-	}
-
-	// All others
-	return select( selector.replace( rtrim, "$1" ), context, results, seed );
-}
-
-/**
- * Create key-value caches of limited size
- * @returns {function(string, object)} Returns the Object data after storing it on itself with
- *	property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
- *	deleting the oldest entry
- */
-function createCache() {
-	var keys = [];
-
-	function cache( key, value ) {
-		// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
-		if ( keys.push( key + " " ) > Expr.cacheLength ) {
-			// Only keep the most recent entries
-			delete cache[ keys.shift() ];
-		}
-		return (cache[ key + " " ] = value);
-	}
-	return cache;
-}
-
-/**
- * Mark a function for special use by Sizzle
- * @param {Function} fn The function to mark
- */
-function markFunction( fn ) {
-	fn[ expando ] = true;
-	return fn;
-}
-
-/**
- * Support testing using an element
- * @param {Function} fn Passed the created element and returns a boolean result
- */
-function assert( fn ) {
-	var el = document.createElement("fieldset");
-
-	try {
-		return !!fn( el );
-	} catch (e) {
-		return false;
-	} finally {
-		// Remove from its parent by default
-		if ( el.parentNode ) {
-			el.parentNode.removeChild( el );
-		}
-		// release memory in IE
-		el = null;
-	}
-}
-
-/**
- * Adds the same handler for all of the specified attrs
- * @param {String} attrs Pipe-separated list of attributes
- * @param {Function} handler The method that will be applied
- */
-function addHandle( attrs, handler ) {
-	var arr = attrs.split("|"),
-		i = arr.length;
-
-	while ( i-- ) {
-		Expr.attrHandle[ arr[i] ] = handler;
-	}
-}
-
-/**
- * Checks document order of two siblings
- * @param {Element} a
- * @param {Element} b
- * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
- */
-function siblingCheck( a, b ) {
-	var cur = b && a,
-		diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
-			a.sourceIndex - b.sourceIndex;
-
-	// Use IE sourceIndex if available on both nodes
-	if ( diff ) {
-		return diff;
-	}
-
-	// Check if b follows a
-	if ( cur ) {
-		while ( (cur = cur.nextSibling) ) {
-			if ( cur === b ) {
-				return -1;
-			}
-		}
-	}
-
-	return a ? 1 : -1;
-}
-
-/**
- * Returns a function to use in pseudos for input types
- * @param {String} type
- */
-function createInputPseudo( type ) {
-	return function( elem ) {
-		var name = elem.nodeName.toLowerCase();
-		return name === "input" && elem.type === type;
-	};
-}
-
-/**
- * Returns a function to use in pseudos for buttons
- * @param {String} type
- */
-function createButtonPseudo( type ) {
-	return function( elem ) {
-		var name = elem.nodeName.toLowerCase();
-		return (name === "input" || name === "button") && elem.type === type;
-	};
-}
-
-/**
- * Returns a function to use in pseudos for :enabled/:disabled
- * @param {Boolean} disabled true for :disabled; false for :enabled
- */
-function createDisabledPseudo( disabled ) {
-
-	// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
-	return function( elem ) {
-
-		// Only certain elements can match :enabled or :disabled
-		// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
-		// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
-		if ( "form" in elem ) {
-
-			// Check for inherited disabledness on relevant non-disabled elements:
-			// * listed form-associated elements in a disabled fieldset
-			//   https://html.spec.whatwg.org/multipage/forms.html#category-listed
-			//   https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
-			// * option elements in a disabled optgroup
-			//   https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
-			// All such elements have a "form" property.
-			if ( elem.parentNode && elem.disabled === false ) {
-
-				// Option elements defer to a parent optgroup if present
-				if ( "label" in elem ) {
-					if ( "label" in elem.parentNode ) {
-						return elem.parentNode.disabled === disabled;
-					} else {
-						return elem.disabled === disabled;
-					}
-				}
-
-				// Support: IE 6 - 11
-				// Use the isDisabled shortcut property to check for disabled fieldset ancestors
-				return elem.isDisabled === disabled ||
-
-					// Where there is no isDisabled, check manually
-					/* jshint -W018 */
-					elem.isDisabled !== !disabled &&
-						disabledAncestor( elem ) === disabled;
-			}
-
-			return elem.disabled === disabled;
-
-		// Try to winnow out elements that can't be disabled before trusting the disabled property.
-		// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
-		// even exist on them, let alone have a boolean value.
-		} else if ( "label" in elem ) {
-			return elem.disabled === disabled;
-		}
-
-		// Remaining elements are neither :enabled nor :disabled
-		return false;
-	};
-}
-
-/**
- * Returns a function to use in pseudos for positionals
- * @param {Function} fn
- */
-function createPositionalPseudo( fn ) {
-	return markFunction(function( argument ) {
-		argument = +argument;
-		return markFunction(function( seed, matches ) {
-			var j,
-				matchIndexes = fn( [], seed.length, argument ),
-				i = matchIndexes.length;
-
-			// Match elements found at the specified indexes
-			while ( i-- ) {
-				if ( seed[ (j = matchIndexes[i]) ] ) {
-					seed[j] = !(matches[j] = seed[j]);
-				}
-			}
-		});
-	});
-}
-
-/**
- * Checks a node for validity as a Sizzle context
- * @param {Element|Object=} context
- * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
- */
-function testContext( context ) {
-	return context && typeof context.getElementsByTagName !== "undefined" && context;
-}
-
-// Expose support vars for convenience
-support = Sizzle.support = {};
-
-/**
- * Detects XML nodes
- * @param {Element|Object} elem An element or a document
- * @returns {Boolean} True iff elem is a non-HTML XML node
- */
-isXML = Sizzle.isXML = function( elem ) {
-	// documentElement is verified for cases where it doesn't yet exist
-	// (such as loading iframes in IE - #4833)
-	var documentElement = elem && (elem.ownerDocument || elem).documentElement;
-	return documentElement ? documentElement.nodeName !== "HTML" : false;
-};
-
-/**
- * Sets document-related variables once based on the current document
- * @param {Element|Object} [doc] An element or document object to use to set the document
- * @returns {Object} Returns the current document
- */
-setDocument = Sizzle.setDocument = function( node ) {
-	var hasCompare, subWindow,
-		doc = node ? node.ownerDocument || node : preferredDoc;
-
-	// Return early if doc is invalid or already selected
-	if ( doc === document || doc.nodeType !== 9 || !doc.documentElement ) {
-		return document;
-	}
-
-	// Update global variables
-	document = doc;
-	docElem = document.documentElement;
-	documentIsHTML = !isXML( document );
-
-	// Support: IE 9-11, Edge
-	// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
-	if ( preferredDoc !== document &&
-		(subWindow = document.defaultView) && subWindow.top !== subWindow ) {
-
-		// Support: IE 11, Edge
-		if ( subWindow.addEventListener ) {
-			subWindow.addEventListener( "unload", unloadHandler, false );
-
-		// Support: IE 9 - 10 only
-		} else if ( subWindow.attachEvent ) {
-			subWindow.attachEvent( "onunload", unloadHandler );
-		}
-	}
-
-	/* Attributes
-	---------------------------------------------------------------------- */
-
-	// Support: IE<8
-	// Verify that getAttribute really returns attributes and not properties
-	// (excepting IE8 booleans)
-	support.attributes = assert(function( el ) {
-		el.className = "i";
-		return !el.getAttribute("className");
-	});
-
-	/* getElement(s)By*
-	---------------------------------------------------------------------- */
-
-	// Check if getElementsByTagName("*") returns only elements
-	support.getElementsByTagName = assert(function( el ) {
-		el.appendChild( document.createComment("") );
-		return !el.getElementsByTagName("*").length;
-	});
-
-	// Support: IE<9
-	support.getElementsByClassName = rnative.test( document.getElementsByClassName );
-
-	// Support: IE<10
-	// Check if getElementById returns elements by name
-	// The broken getElementById methods don't pick up programmatically-set names,
-	// so use a roundabout getElementsByName test
-	support.getById = assert(function( el ) {
-		docElem.appendChild( el ).id = expando;
-		return !document.getElementsByName || !document.getElementsByName( expando ).length;
-	});
-
-	// ID filter and find
-	if ( support.getById ) {
-		Expr.filter["ID"] = function( id ) {
-			var attrId = id.replace( runescape, funescape );
-			return function( elem ) {
-				return elem.getAttribute("id") === attrId;
-			};
-		};
-		Expr.find["ID"] = function( id, context ) {
-			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
-				var elem = context.getElementById( id );
-				return elem ? [ elem ] : [];
-			}
-		};
-	} else {
-		Expr.filter["ID"] =  function( id ) {
-			var attrId = id.replace( runescape, funescape );
-			return function( elem ) {
-				var node = typeof elem.getAttributeNode !== "undefined" &&
-					elem.getAttributeNode("id");
-				return node && node.value === attrId;
-			};
-		};
-
-		// Support: IE 6 - 7 only
-		// getElementById is not reliable as a find shortcut
-		Expr.find["ID"] = function( id, context ) {
-			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
-				var node, i, elems,
-					elem = context.getElementById( id );
-
-				if ( elem ) {
-
-					// Verify the id attribute
-					node = elem.getAttributeNode("id");
-					if ( node && node.value === id ) {
-						return [ elem ];
-					}
-
-					// Fall back on getElementsByName
-					elems = context.getElementsByName( id );
-					i = 0;
-					while ( (elem = elems[i++]) ) {
-						node = elem.getAttributeNode("id");
-						if ( node && node.value === id ) {
-							return [ elem ];
-						}
-					}
-				}
-
-				return [];
-			}
-		};
-	}
-
-	// Tag
-	Expr.find["TAG"] = support.getElementsByTagName ?
-		function( tag, context ) {
-			if ( typeof context.getElementsByTagName !== "undefined" ) {
-				return context.getElementsByTagName( tag );
-
-			// DocumentFragment nodes don't have gEBTN
-			} else if ( support.qsa ) {
-				return context.querySelectorAll( tag );
-			}
-		} :
-
-		function( tag, context ) {
-			var elem,
-				tmp = [],
-				i = 0,
-				// By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
-				results = context.getElementsByTagName( tag );
-
-			// Filter out possible comments
-			if ( tag === "*" ) {
-				while ( (elem = results[i++]) ) {
-					if ( elem.nodeType === 1 ) {
-						tmp.push( elem );
-					}
-				}
-
-				return tmp;
-			}
-			return results;
-		};
-
-	// Class
-	Expr.find["CLASS"] = support.getElementsByClassName && function( className, context ) {
-		if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
-			return context.getElementsByClassName( className );
-		}
-	};
-
-	/* QSA/matchesSelector
-	---------------------------------------------------------------------- */
-
-	// QSA and matchesSelector support
-
-	// matchesSelector(:active) reports false when true (IE9/Opera 11.5)
-	rbuggyMatches = [];
-
-	// qSa(:focus) reports false when true (Chrome 21)
-	// We allow this because of a bug in IE8/9 that throws an error
-	// whenever `document.activeElement` is accessed on an iframe
-	// So, we allow :focus to pass through QSA all the time to avoid the IE error
-	// See https://bugs.jquery.com/ticket/13378
-	rbuggyQSA = [];
-
-	if ( (support.qsa = rnative.test( document.querySelectorAll )) ) {
-		// Build QSA regex
-		// Regex strategy adopted from Diego Perini
-		assert(function( el ) {
-			// Select is set to empty string on purpose
-			// This is to test IE's treatment of not explicitly
-			// setting a boolean content attribute,
-			// since its presence should be enough
-			// https://bugs.jquery.com/ticket/12359
-			docElem.appendChild( el ).innerHTML = "" +
-				"";
-
-			// Support: IE8, Opera 11-12.16
-			// Nothing should be selected when empty strings follow ^= or $= or *=
-			// The test attribute must be unknown in Opera but "safe" for WinRT
-			// https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
-			if ( el.querySelectorAll("[msallowcapture^='']").length ) {
-				rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
-			}
-
-			// Support: IE8
-			// Boolean attributes and "value" are not treated correctly
-			if ( !el.querySelectorAll("[selected]").length ) {
-				rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
-			}
-
-			// Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
-			if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
-				rbuggyQSA.push("~=");
-			}
-
-			// Webkit/Opera - :checked should return selected option elements
-			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
-			// IE8 throws error here and will not see later tests
-			if ( !el.querySelectorAll(":checked").length ) {
-				rbuggyQSA.push(":checked");
-			}
-
-			// Support: Safari 8+, iOS 8+
-			// https://bugs.webkit.org/show_bug.cgi?id=136851
-			// In-page `selector#id sibling-combinator selector` fails
-			if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
-				rbuggyQSA.push(".#.+[+~]");
-			}
-		});
-
-		assert(function( el ) {
-			el.innerHTML = "" +
-				"";
-
-			// Support: Windows 8 Native Apps
-			// The type and name attributes are restricted during .innerHTML assignment
-			var input = document.createElement("input");
-			input.setAttribute( "type", "hidden" );
-			el.appendChild( input ).setAttribute( "name", "D" );
-
-			// Support: IE8
-			// Enforce case-sensitivity of name attribute
-			if ( el.querySelectorAll("[name=d]").length ) {
-				rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
-			}
-
-			// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
-			// IE8 throws error here and will not see later tests
-			if ( el.querySelectorAll(":enabled").length !== 2 ) {
-				rbuggyQSA.push( ":enabled", ":disabled" );
-			}
-
-			// Support: IE9-11+
-			// IE's :disabled selector does not pick up the children of disabled fieldsets
-			docElem.appendChild( el ).disabled = true;
-			if ( el.querySelectorAll(":disabled").length !== 2 ) {
-				rbuggyQSA.push( ":enabled", ":disabled" );
-			}
-
-			// Opera 10-11 does not throw on post-comma invalid pseudos
-			el.querySelectorAll("*,:x");
-			rbuggyQSA.push(",.*:");
-		});
-	}
-
-	if ( (support.matchesSelector = rnative.test( (matches = docElem.matches ||
-		docElem.webkitMatchesSelector ||
-		docElem.mozMatchesSelector ||
-		docElem.oMatchesSelector ||
-		docElem.msMatchesSelector) )) ) {
-
-		assert(function( el ) {
-			// Check to see if it's possible to do matchesSelector
-			// on a disconnected node (IE 9)
-			support.disconnectedMatch = matches.call( el, "*" );
-
-			// This should fail with an exception
-			// Gecko does not error, returns false instead
-			matches.call( el, "[s!='']:x" );
-			rbuggyMatches.push( "!=", pseudos );
-		});
-	}
-
-	rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join("|") );
-	rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join("|") );
-
-	/* Contains
-	---------------------------------------------------------------------- */
-	hasCompare = rnative.test( docElem.compareDocumentPosition );
-
-	// Element contains another
-	// Purposefully self-exclusive
-	// As in, an element does not contain itself
-	contains = hasCompare || rnative.test( docElem.contains ) ?
-		function( a, b ) {
-			var adown = a.nodeType === 9 ? a.documentElement : a,
-				bup = b && b.parentNode;
-			return a === bup || !!( bup && bup.nodeType === 1 && (
-				adown.contains ?
-					adown.contains( bup ) :
-					a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
-			));
-		} :
-		function( a, b ) {
-			if ( b ) {
-				while ( (b = b.parentNode) ) {
-					if ( b === a ) {
-						return true;
-					}
-				}
-			}
-			return false;
-		};
-
-	/* Sorting
-	---------------------------------------------------------------------- */
-
-	// Document order sorting
-	sortOrder = hasCompare ?
-	function( a, b ) {
-
-		// Flag for duplicate removal
-		if ( a === b ) {
-			hasDuplicate = true;
-			return 0;
-		}
-
-		// Sort on method existence if only one input has compareDocumentPosition
-		var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
-		if ( compare ) {
-			return compare;
-		}
-
-		// Calculate position if both inputs belong to the same document
-		compare = ( a.ownerDocument || a ) === ( b.ownerDocument || b ) ?
-			a.compareDocumentPosition( b ) :
-
-			// Otherwise we know they are disconnected
-			1;
-
-		// Disconnected nodes
-		if ( compare & 1 ||
-			(!support.sortDetached && b.compareDocumentPosition( a ) === compare) ) {
-
-			// Choose the first element that is related to our preferred document
-			if ( a === document || a.ownerDocument === preferredDoc && contains(preferredDoc, a) ) {
-				return -1;
-			}
-			if ( b === document || b.ownerDocument === preferredDoc && contains(preferredDoc, b) ) {
-				return 1;
-			}
-
-			// Maintain original order
-			return sortInput ?
-				( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
-				0;
-		}
-
-		return compare & 4 ? -1 : 1;
-	} :
-	function( a, b ) {
-		// Exit early if the nodes are identical
-		if ( a === b ) {
-			hasDuplicate = true;
-			return 0;
-		}
-
-		var cur,
-			i = 0,
-			aup = a.parentNode,
-			bup = b.parentNode,
-			ap = [ a ],
-			bp = [ b ];
-
-		// Parentless nodes are either documents or disconnected
-		if ( !aup || !bup ) {
-			return a === document ? -1 :
-				b === document ? 1 :
-				aup ? -1 :
-				bup ? 1 :
-				sortInput ?
-				( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
-				0;
-
-		// If the nodes are siblings, we can do a quick check
-		} else if ( aup === bup ) {
-			return siblingCheck( a, b );
-		}
-
-		// Otherwise we need full lists of their ancestors for comparison
-		cur = a;
-		while ( (cur = cur.parentNode) ) {
-			ap.unshift( cur );
-		}
-		cur = b;
-		while ( (cur = cur.parentNode) ) {
-			bp.unshift( cur );
-		}
-
-		// Walk down the tree looking for a discrepancy
-		while ( ap[i] === bp[i] ) {
-			i++;
-		}
-
-		return i ?
-			// Do a sibling check if the nodes have a common ancestor
-			siblingCheck( ap[i], bp[i] ) :
-
-			// Otherwise nodes in our document sort first
-			ap[i] === preferredDoc ? -1 :
-			bp[i] === preferredDoc ? 1 :
-			0;
-	};
-
-	return document;
-};
-
-Sizzle.matches = function( expr, elements ) {
-	return Sizzle( expr, null, null, elements );
-};
-
-Sizzle.matchesSelector = function( elem, expr ) {
-	// Set document vars if needed
-	if ( ( elem.ownerDocument || elem ) !== document ) {
-		setDocument( elem );
-	}
-
-	// Make sure that attribute selectors are quoted
-	expr = expr.replace( rattributeQuotes, "='$1']" );
-
-	if ( support.matchesSelector && documentIsHTML &&
-		!compilerCache[ expr + " " ] &&
-		( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
-		( !rbuggyQSA     || !rbuggyQSA.test( expr ) ) ) {
-
-		try {
-			var ret = matches.call( elem, expr );
-
-			// IE 9's matchesSelector returns false on disconnected nodes
-			if ( ret || support.disconnectedMatch ||
-					// As well, disconnected nodes are said to be in a document
-					// fragment in IE 9
-					elem.document && elem.document.nodeType !== 11 ) {
-				return ret;
-			}
-		} catch (e) {}
-	}
-
-	return Sizzle( expr, document, null, [ elem ] ).length > 0;
-};
-
-Sizzle.contains = function( context, elem ) {
-	// Set document vars if needed
-	if ( ( context.ownerDocument || context ) !== document ) {
-		setDocument( context );
-	}
-	return contains( context, elem );
-};
-
-Sizzle.attr = function( elem, name ) {
-	// Set document vars if needed
-	if ( ( elem.ownerDocument || elem ) !== document ) {
-		setDocument( elem );
-	}
-
-	var fn = Expr.attrHandle[ name.toLowerCase() ],
-		// Don't get fooled by Object.prototype properties (jQuery #13807)
-		val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
-			fn( elem, name, !documentIsHTML ) :
-			undefined;
-
-	return val !== undefined ?
-		val :
-		support.attributes || !documentIsHTML ?
-			elem.getAttribute( name ) :
-			(val = elem.getAttributeNode(name)) && val.specified ?
-				val.value :
-				null;
-};
-
-Sizzle.escape = function( sel ) {
-	return (sel + "").replace( rcssescape, fcssescape );
-};
-
-Sizzle.error = function( msg ) {
-	throw new Error( "Syntax error, unrecognized expression: " + msg );
-};
-
-/**
- * Document sorting and removing duplicates
- * @param {ArrayLike} results
- */
-Sizzle.uniqueSort = function( results ) {
-	var elem,
-		duplicates = [],
-		j = 0,
-		i = 0;
-
-	// Unless we *know* we can detect duplicates, assume their presence
-	hasDuplicate = !support.detectDuplicates;
-	sortInput = !support.sortStable && results.slice( 0 );
-	results.sort( sortOrder );
-
-	if ( hasDuplicate ) {
-		while ( (elem = results[i++]) ) {
-			if ( elem === results[ i ] ) {
-				j = duplicates.push( i );
-			}
-		}
-		while ( j-- ) {
-			results.splice( duplicates[ j ], 1 );
-		}
-	}
-
-	// Clear input after sorting to release objects
-	// See https://github.com/jquery/sizzle/pull/225
-	sortInput = null;
-
-	return results;
-};
-
-/**
- * Utility function for retrieving the text value of an array of DOM nodes
- * @param {Array|Element} elem
- */
-getText = Sizzle.getText = function( elem ) {
-	var node,
-		ret = "",
-		i = 0,
-		nodeType = elem.nodeType;
-
-	if ( !nodeType ) {
-		// If no nodeType, this is expected to be an array
-		while ( (node = elem[i++]) ) {
-			// Do not traverse comment nodes
-			ret += getText( node );
-		}
-	} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
-		// Use textContent for elements
-		// innerText usage removed for consistency of new lines (jQuery #11153)
-		if ( typeof elem.textContent === "string" ) {
-			return elem.textContent;
-		} else {
-			// Traverse its children
-			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
-				ret += getText( elem );
-			}
-		}
-	} else if ( nodeType === 3 || nodeType === 4 ) {
-		return elem.nodeValue;
-	}
-	// Do not include comment or processing instruction nodes
-
-	return ret;
-};
-
-Expr = Sizzle.selectors = {
-
-	// Can be adjusted by the user
-	cacheLength: 50,
-
-	createPseudo: markFunction,
-
-	match: matchExpr,
-
-	attrHandle: {},
-
-	find: {},
-
-	relative: {
-		">": { dir: "parentNode", first: true },
-		" ": { dir: "parentNode" },
-		"+": { dir: "previousSibling", first: true },
-		"~": { dir: "previousSibling" }
-	},
-
-	preFilter: {
-		"ATTR": function( match ) {
-			match[1] = match[1].replace( runescape, funescape );
-
-			// Move the given value to match[3] whether quoted or unquoted
-			match[3] = ( match[3] || match[4] || match[5] || "" ).replace( runescape, funescape );
-
-			if ( match[2] === "~=" ) {
-				match[3] = " " + match[3] + " ";
-			}
-
-			return match.slice( 0, 4 );
-		},
-
-		"CHILD": function( match ) {
-			/* matches from matchExpr["CHILD"]
-				1 type (only|nth|...)
-				2 what (child|of-type)
-				3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
-				4 xn-component of xn+y argument ([+-]?\d*n|)
-				5 sign of xn-component
-				6 x of xn-component
-				7 sign of y-component
-				8 y of y-component
-			*/
-			match[1] = match[1].toLowerCase();
-
-			if ( match[1].slice( 0, 3 ) === "nth" ) {
-				// nth-* requires argument
-				if ( !match[3] ) {
-					Sizzle.error( match[0] );
-				}
-
-				// numeric x and y parameters for Expr.filter.CHILD
-				// remember that false/true cast respectively to 0/1
-				match[4] = +( match[4] ? match[5] + (match[6] || 1) : 2 * ( match[3] === "even" || match[3] === "odd" ) );
-				match[5] = +( ( match[7] + match[8] ) || match[3] === "odd" );
-
-			// other types prohibit arguments
-			} else if ( match[3] ) {
-				Sizzle.error( match[0] );
-			}
-
-			return match;
-		},
-
-		"PSEUDO": function( match ) {
-			var excess,
-				unquoted = !match[6] && match[2];
-
-			if ( matchExpr["CHILD"].test( match[0] ) ) {
-				return null;
-			}
-
-			// Accept quoted arguments as-is
-			if ( match[3] ) {
-				match[2] = match[4] || match[5] || "";
-
-			// Strip excess characters from unquoted arguments
-			} else if ( unquoted && rpseudo.test( unquoted ) &&
-				// Get excess from tokenize (recursively)
-				(excess = tokenize( unquoted, true )) &&
-				// advance to the next closing parenthesis
-				(excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length) ) {
-
-				// excess is a negative index
-				match[0] = match[0].slice( 0, excess );
-				match[2] = unquoted.slice( 0, excess );
-			}
-
-			// Return only captures needed by the pseudo filter method (type and argument)
-			return match.slice( 0, 3 );
-		}
-	},
-
-	filter: {
-
-		"TAG": function( nodeNameSelector ) {
-			var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
-			return nodeNameSelector === "*" ?
-				function() { return true; } :
-				function( elem ) {
-					return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
-				};
-		},
-
-		"CLASS": function( className ) {
-			var pattern = classCache[ className + " " ];
-
-			return pattern ||
-				(pattern = new RegExp( "(^|" + whitespace + ")" + className + "(" + whitespace + "|$)" )) &&
-				classCache( className, function( elem ) {
-					return pattern.test( typeof elem.className === "string" && elem.className || typeof elem.getAttribute !== "undefined" && elem.getAttribute("class") || "" );
-				});
-		},
-
-		"ATTR": function( name, operator, check ) {
-			return function( elem ) {
-				var result = Sizzle.attr( elem, name );
-
-				if ( result == null ) {
-					return operator === "!=";
-				}
-				if ( !operator ) {
-					return true;
-				}
-
-				result += "";
-
-				return operator === "=" ? result === check :
-					operator === "!=" ? result !== check :
-					operator === "^=" ? check && result.indexOf( check ) === 0 :
-					operator === "*=" ? check && result.indexOf( check ) > -1 :
-					operator === "$=" ? check && result.slice( -check.length ) === check :
-					operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
-					operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
-					false;
-			};
-		},
-
-		"CHILD": function( type, what, argument, first, last ) {
-			var simple = type.slice( 0, 3 ) !== "nth",
-				forward = type.slice( -4 ) !== "last",
-				ofType = what === "of-type";
-
-			return first === 1 && last === 0 ?
-
-				// Shortcut for :nth-*(n)
-				function( elem ) {
-					return !!elem.parentNode;
-				} :
-
-				function( elem, context, xml ) {
-					var cache, uniqueCache, outerCache, node, nodeIndex, start,
-						dir = simple !== forward ? "nextSibling" : "previousSibling",
-						parent = elem.parentNode,
-						name = ofType && elem.nodeName.toLowerCase(),
-						useCache = !xml && !ofType,
-						diff = false;
-
-					if ( parent ) {
-
-						// :(first|last|only)-(child|of-type)
-						if ( simple ) {
-							while ( dir ) {
-								node = elem;
-								while ( (node = node[ dir ]) ) {
-									if ( ofType ?
-										node.nodeName.toLowerCase() === name :
-										node.nodeType === 1 ) {
-
-										return false;
-									}
-								}
-								// Reverse direction for :only-* (if we haven't yet done so)
-								start = dir = type === "only" && !start && "nextSibling";
-							}
-							return true;
-						}
-
-						start = [ forward ? parent.firstChild : parent.lastChild ];
-
-						// non-xml :nth-child(...) stores cache data on `parent`
-						if ( forward && useCache ) {
-
-							// Seek `elem` from a previously-cached index
-
-							// ...in a gzip-friendly way
-							node = parent;
-							outerCache = node[ expando ] || (node[ expando ] = {});
-
-							// Support: IE <9 only
-							// Defend against cloned attroperties (jQuery gh-1709)
-							uniqueCache = outerCache[ node.uniqueID ] ||
-								(outerCache[ node.uniqueID ] = {});
-
-							cache = uniqueCache[ type ] || [];
-							nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
-							diff = nodeIndex && cache[ 2 ];
-							node = nodeIndex && parent.childNodes[ nodeIndex ];
-
-							while ( (node = ++nodeIndex && node && node[ dir ] ||
-
-								// Fallback to seeking `elem` from the start
-								(diff = nodeIndex = 0) || start.pop()) ) {
-
-								// When found, cache indexes on `parent` and break
-								if ( node.nodeType === 1 && ++diff && node === elem ) {
-									uniqueCache[ type ] = [ dirruns, nodeIndex, diff ];
-									break;
-								}
-							}
-
-						} else {
-							// Use previously-cached element index if available
-							if ( useCache ) {
-								// ...in a gzip-friendly way
-								node = elem;
-								outerCache = node[ expando ] || (node[ expando ] = {});
-
-								// Support: IE <9 only
-								// Defend against cloned attroperties (jQuery gh-1709)
-								uniqueCache = outerCache[ node.uniqueID ] ||
-									(outerCache[ node.uniqueID ] = {});
-
-								cache = uniqueCache[ type ] || [];
-								nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
-								diff = nodeIndex;
-							}
-
-							// xml :nth-child(...)
-							// or :nth-last-child(...) or :nth(-last)?-of-type(...)
-							if ( diff === false ) {
-								// Use the same loop as above to seek `elem` from the start
-								while ( (node = ++nodeIndex && node && node[ dir ] ||
-									(diff = nodeIndex = 0) || start.pop()) ) {
-
-									if ( ( ofType ?
-										node.nodeName.toLowerCase() === name :
-										node.nodeType === 1 ) &&
-										++diff ) {
-
-										// Cache the index of each encountered element
-										if ( useCache ) {
-											outerCache = node[ expando ] || (node[ expando ] = {});
-
-											// Support: IE <9 only
-											// Defend against cloned attroperties (jQuery gh-1709)
-											uniqueCache = outerCache[ node.uniqueID ] ||
-												(outerCache[ node.uniqueID ] = {});
-
-											uniqueCache[ type ] = [ dirruns, diff ];
-										}
-
-										if ( node === elem ) {
-											break;
-										}
-									}
-								}
-							}
-						}
-
-						// Incorporate the offset, then check against cycle size
-						diff -= last;
-						return diff === first || ( diff % first === 0 && diff / first >= 0 );
-					}
-				};
-		},
-
-		"PSEUDO": function( pseudo, argument ) {
-			// pseudo-class names are case-insensitive
-			// http://www.w3.org/TR/selectors/#pseudo-classes
-			// Prioritize by case sensitivity in case custom pseudos are added with uppercase letters
-			// Remember that setFilters inherits from pseudos
-			var args,
-				fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] ||
-					Sizzle.error( "unsupported pseudo: " + pseudo );
-
-			// The user may use createPseudo to indicate that
-			// arguments are needed to create the filter function
-			// just as Sizzle does
-			if ( fn[ expando ] ) {
-				return fn( argument );
-			}
-
-			// But maintain support for old signatures
-			if ( fn.length > 1 ) {
-				args = [ pseudo, pseudo, "", argument ];
-				return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ?
-					markFunction(function( seed, matches ) {
-						var idx,
-							matched = fn( seed, argument ),
-							i = matched.length;
-						while ( i-- ) {
-							idx = indexOf( seed, matched[i] );
-							seed[ idx ] = !( matches[ idx ] = matched[i] );
-						}
-					}) :
-					function( elem ) {
-						return fn( elem, 0, args );
-					};
-			}
-
-			return fn;
-		}
-	},
-
-	pseudos: {
-		// Potentially complex pseudos
-		"not": markFunction(function( selector ) {
-			// Trim the selector passed to compile
-			// to avoid treating leading and trailing
-			// spaces as combinators
-			var input = [],
-				results = [],
-				matcher = compile( selector.replace( rtrim, "$1" ) );
-
-			return matcher[ expando ] ?
-				markFunction(function( seed, matches, context, xml ) {
-					var elem,
-						unmatched = matcher( seed, null, xml, [] ),
-						i = seed.length;
-
-					// Match elements unmatched by `matcher`
-					while ( i-- ) {
-						if ( (elem = unmatched[i]) ) {
-							seed[i] = !(matches[i] = elem);
-						}
-					}
-				}) :
-				function( elem, context, xml ) {
-					input[0] = elem;
-					matcher( input, null, xml, results );
-					// Don't keep the element (issue #299)
-					input[0] = null;
-					return !results.pop();
-				};
-		}),
-
-		"has": markFunction(function( selector ) {
-			return function( elem ) {
-				return Sizzle( selector, elem ).length > 0;
-			};
-		}),
-
-		"contains": markFunction(function( text ) {
-			text = text.replace( runescape, funescape );
-			return function( elem ) {
-				return ( elem.textContent || elem.innerText || getText( elem ) ).indexOf( text ) > -1;
-			};
-		}),
-
-		// "Whether an element is represented by a :lang() selector
-		// is based solely on the element's language value
-		// being equal to the identifier C,
-		// or beginning with the identifier C immediately followed by "-".
-		// The matching of C against the element's language value is performed case-insensitively.
-		// The identifier C does not have to be a valid language name."
-		// http://www.w3.org/TR/selectors/#lang-pseudo
-		"lang": markFunction( function( lang ) {
-			// lang value must be a valid identifier
-			if ( !ridentifier.test(lang || "") ) {
-				Sizzle.error( "unsupported lang: " + lang );
-			}
-			lang = lang.replace( runescape, funescape ).toLowerCase();
-			return function( elem ) {
-				var elemLang;
-				do {
-					if ( (elemLang = documentIsHTML ?
-						elem.lang :
-						elem.getAttribute("xml:lang") || elem.getAttribute("lang")) ) {
-
-						elemLang = elemLang.toLowerCase();
-						return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0;
-					}
-				} while ( (elem = elem.parentNode) && elem.nodeType === 1 );
-				return false;
-			};
-		}),
-
-		// Miscellaneous
-		"target": function( elem ) {
-			var hash = window.location && window.location.hash;
-			return hash && hash.slice( 1 ) === elem.id;
-		},
-
-		"root": function( elem ) {
-			return elem === docElem;
-		},
-
-		"focus": function( elem ) {
-			return elem === document.activeElement && (!document.hasFocus || document.hasFocus()) && !!(elem.type || elem.href || ~elem.tabIndex);
-		},
-
-		// Boolean properties
-		"enabled": createDisabledPseudo( false ),
-		"disabled": createDisabledPseudo( true ),
-
-		"checked": function( elem ) {
-			// In CSS3, :checked should return both checked and selected elements
-			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
-			var nodeName = elem.nodeName.toLowerCase();
-			return (nodeName === "input" && !!elem.checked) || (nodeName === "option" && !!elem.selected);
-		},
-
-		"selected": function( elem ) {
-			// Accessing this property makes selected-by-default
-			// options in Safari work properly
-			if ( elem.parentNode ) {
-				elem.parentNode.selectedIndex;
-			}
-
-			return elem.selected === true;
-		},
-
-		// Contents
-		"empty": function( elem ) {
-			// http://www.w3.org/TR/selectors/#empty-pseudo
-			// :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5),
-			//   but not by others (comment: 8; processing instruction: 7; etc.)
-			// nodeType < 6 works because attributes (2) do not appear as children
-			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
-				if ( elem.nodeType < 6 ) {
-					return false;
-				}
-			}
-			return true;
-		},
-
-		"parent": function( elem ) {
-			return !Expr.pseudos["empty"]( elem );
-		},
-
-		// Element/input types
-		"header": function( elem ) {
-			return rheader.test( elem.nodeName );
-		},
-
-		"input": function( elem ) {
-			return rinputs.test( elem.nodeName );
-		},
-
-		"button": function( elem ) {
-			var name = elem.nodeName.toLowerCase();
-			return name === "input" && elem.type === "button" || name === "button";
-		},
-
-		"text": function( elem ) {
-			var attr;
-			return elem.nodeName.toLowerCase() === "input" &&
-				elem.type === "text" &&
-
-				// Support: IE<8
-				// New HTML5 attribute values (e.g., "search") appear with elem.type === "text"
-				( (attr = elem.getAttribute("type")) == null || attr.toLowerCase() === "text" );
-		},
-
-		// Position-in-collection
-		"first": createPositionalPseudo(function() {
-			return [ 0 ];
-		}),
-
-		"last": createPositionalPseudo(function( matchIndexes, length ) {
-			return [ length - 1 ];
-		}),
-
-		"eq": createPositionalPseudo(function( matchIndexes, length, argument ) {
-			return [ argument < 0 ? argument + length : argument ];
-		}),
-
-		"even": createPositionalPseudo(function( matchIndexes, length ) {
-			var i = 0;
-			for ( ; i < length; i += 2 ) {
-				matchIndexes.push( i );
-			}
-			return matchIndexes;
-		}),
-
-		"odd": createPositionalPseudo(function( matchIndexes, length ) {
-			var i = 1;
-			for ( ; i < length; i += 2 ) {
-				matchIndexes.push( i );
-			}
-			return matchIndexes;
-		}),
-
-		"lt": createPositionalPseudo(function( matchIndexes, length, argument ) {
-			var i = argument < 0 ? argument + length : argument;
-			for ( ; --i >= 0; ) {
-				matchIndexes.push( i );
-			}
-			return matchIndexes;
-		}),
-
-		"gt": createPositionalPseudo(function( matchIndexes, length, argument ) {
-			var i = argument < 0 ? argument + length : argument;
-			for ( ; ++i < length; ) {
-				matchIndexes.push( i );
-			}
-			return matchIndexes;
-		})
-	}
-};
-
-Expr.pseudos["nth"] = Expr.pseudos["eq"];
-
-// Add button/input type pseudos
-for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) {
-	Expr.pseudos[ i ] = createInputPseudo( i );
-}
-for ( i in { submit: true, reset: true } ) {
-	Expr.pseudos[ i ] = createButtonPseudo( i );
-}
-
-// Easy API for creating new setFilters
-function setFilters() {}
-setFilters.prototype = Expr.filters = Expr.pseudos;
-Expr.setFilters = new setFilters();
-
-tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
-	var matched, match, tokens, type,
-		soFar, groups, preFilters,
-		cached = tokenCache[ selector + " " ];
-
-	if ( cached ) {
-		return parseOnly ? 0 : cached.slice( 0 );
-	}
-
-	soFar = selector;
-	groups = [];
-	preFilters = Expr.preFilter;
-
-	while ( soFar ) {
-
-		// Comma and first run
-		if ( !matched || (match = rcomma.exec( soFar )) ) {
-			if ( match ) {
-				// Don't consume trailing commas as valid
-				soFar = soFar.slice( match[0].length ) || soFar;
-			}
-			groups.push( (tokens = []) );
-		}
-
-		matched = false;
-
-		// Combinators
-		if ( (match = rcombinators.exec( soFar )) ) {
-			matched = match.shift();
-			tokens.push({
-				value: matched,
-				// Cast descendant combinators to space
-				type: match[0].replace( rtrim, " " )
-			});
-			soFar = soFar.slice( matched.length );
-		}
-
-		// Filters
-		for ( type in Expr.filter ) {
-			if ( (match = matchExpr[ type ].exec( soFar )) && (!preFilters[ type ] ||
-				(match = preFilters[ type ]( match ))) ) {
-				matched = match.shift();
-				tokens.push({
-					value: matched,
-					type: type,
-					matches: match
-				});
-				soFar = soFar.slice( matched.length );
-			}
-		}
-
-		if ( !matched ) {
-			break;
-		}
-	}
-
-	// Return the length of the invalid excess
-	// if we're just parsing
-	// Otherwise, throw an error or return tokens
-	return parseOnly ?
-		soFar.length :
-		soFar ?
-			Sizzle.error( selector ) :
-			// Cache the tokens
-			tokenCache( selector, groups ).slice( 0 );
-};
-
-function toSelector( tokens ) {
-	var i = 0,
-		len = tokens.length,
-		selector = "";
-	for ( ; i < len; i++ ) {
-		selector += tokens[i].value;
-	}
-	return selector;
-}
-
-function addCombinator( matcher, combinator, base ) {
-	var dir = combinator.dir,
-		skip = combinator.next,
-		key = skip || dir,
-		checkNonElements = base && key === "parentNode",
-		doneName = done++;
-
-	return combinator.first ?
-		// Check against closest ancestor/preceding element
-		function( elem, context, xml ) {
-			while ( (elem = elem[ dir ]) ) {
-				if ( elem.nodeType === 1 || checkNonElements ) {
-					return matcher( elem, context, xml );
-				}
-			}
-			return false;
-		} :
-
-		// Check against all ancestor/preceding elements
-		function( elem, context, xml ) {
-			var oldCache, uniqueCache, outerCache,
-				newCache = [ dirruns, doneName ];
-
-			// We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching
-			if ( xml ) {
-				while ( (elem = elem[ dir ]) ) {
-					if ( elem.nodeType === 1 || checkNonElements ) {
-						if ( matcher( elem, context, xml ) ) {
-							return true;
-						}
-					}
-				}
-			} else {
-				while ( (elem = elem[ dir ]) ) {
-					if ( elem.nodeType === 1 || checkNonElements ) {
-						outerCache = elem[ expando ] || (elem[ expando ] = {});
-
-						// Support: IE <9 only
-						// Defend against cloned attroperties (jQuery gh-1709)
-						uniqueCache = outerCache[ elem.uniqueID ] || (outerCache[ elem.uniqueID ] = {});
-
-						if ( skip && skip === elem.nodeName.toLowerCase() ) {
-							elem = elem[ dir ] || elem;
-						} else if ( (oldCache = uniqueCache[ key ]) &&
-							oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) {
-
-							// Assign to newCache so results back-propagate to previous elements
-							return (newCache[ 2 ] = oldCache[ 2 ]);
-						} else {
-							// Reuse newcache so results back-propagate to previous elements
-							uniqueCache[ key ] = newCache;
-
-							// A match means we're done; a fail means we have to keep checking
-							if ( (newCache[ 2 ] = matcher( elem, context, xml )) ) {
-								return true;
-							}
-						}
-					}
-				}
-			}
-			return false;
-		};
-}
-
-function elementMatcher( matchers ) {
-	return matchers.length > 1 ?
-		function( elem, context, xml ) {
-			var i = matchers.length;
-			while ( i-- ) {
-				if ( !matchers[i]( elem, context, xml ) ) {
-					return false;
-				}
-			}
-			return true;
-		} :
-		matchers[0];
-}
-
-function multipleContexts( selector, contexts, results ) {
-	var i = 0,
-		len = contexts.length;
-	for ( ; i < len; i++ ) {
-		Sizzle( selector, contexts[i], results );
-	}
-	return results;
-}
-
-function condense( unmatched, map, filter, context, xml ) {
-	var elem,
-		newUnmatched = [],
-		i = 0,
-		len = unmatched.length,
-		mapped = map != null;
-
-	for ( ; i < len; i++ ) {
-		if ( (elem = unmatched[i]) ) {
-			if ( !filter || filter( elem, context, xml ) ) {
-				newUnmatched.push( elem );
-				if ( mapped ) {
-					map.push( i );
-				}
-			}
-		}
-	}
-
-	return newUnmatched;
-}
-
-function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) {
-	if ( postFilter && !postFilter[ expando ] ) {
-		postFilter = setMatcher( postFilter );
-	}
-	if ( postFinder && !postFinder[ expando ] ) {
-		postFinder = setMatcher( postFinder, postSelector );
-	}
-	return markFunction(function( seed, results, context, xml ) {
-		var temp, i, elem,
-			preMap = [],
-			postMap = [],
-			preexisting = results.length,
-
-			// Get initial elements from seed or context
-			elems = seed || multipleContexts( selector || "*", context.nodeType ? [ context ] : context, [] ),
-
-			// Prefilter to get matcher input, preserving a map for seed-results synchronization
-			matcherIn = preFilter && ( seed || !selector ) ?
-				condense( elems, preMap, preFilter, context, xml ) :
-				elems,
-
-			matcherOut = matcher ?
-				// If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results,
-				postFinder || ( seed ? preFilter : preexisting || postFilter ) ?
-
-					// ...intermediate processing is necessary
-					[] :
-
-					// ...otherwise use results directly
-					results :
-				matcherIn;
-
-		// Find primary matches
-		if ( matcher ) {
-			matcher( matcherIn, matcherOut, context, xml );
-		}
-
-		// Apply postFilter
-		if ( postFilter ) {
-			temp = condense( matcherOut, postMap );
-			postFilter( temp, [], context, xml );
-
-			// Un-match failing elements by moving them back to matcherIn
-			i = temp.length;
-			while ( i-- ) {
-				if ( (elem = temp[i]) ) {
-					matcherOut[ postMap[i] ] = !(matcherIn[ postMap[i] ] = elem);
-				}
-			}
-		}
-
-		if ( seed ) {
-			if ( postFinder || preFilter ) {
-				if ( postFinder ) {
-					// Get the final matcherOut by condensing this intermediate into postFinder contexts
-					temp = [];
-					i = matcherOut.length;
-					while ( i-- ) {
-						if ( (elem = matcherOut[i]) ) {
-							// Restore matcherIn since elem is not yet a final match
-							temp.push( (matcherIn[i] = elem) );
-						}
-					}
-					postFinder( null, (matcherOut = []), temp, xml );
-				}
-
-				// Move matched elements from seed to results to keep them synchronized
-				i = matcherOut.length;
-				while ( i-- ) {
-					if ( (elem = matcherOut[i]) &&
-						(temp = postFinder ? indexOf( seed, elem ) : preMap[i]) > -1 ) {
-
-						seed[temp] = !(results[temp] = elem);
-					}
-				}
-			}
-
-		// Add elements to results, through postFinder if defined
-		} else {
-			matcherOut = condense(
-				matcherOut === results ?
-					matcherOut.splice( preexisting, matcherOut.length ) :
-					matcherOut
-			);
-			if ( postFinder ) {
-				postFinder( null, results, matcherOut, xml );
-			} else {
-				push.apply( results, matcherOut );
-			}
-		}
-	});
-}
-
-function matcherFromTokens( tokens ) {
-	var checkContext, matcher, j,
-		len = tokens.length,
-		leadingRelative = Expr.relative[ tokens[0].type ],
-		implicitRelative = leadingRelative || Expr.relative[" "],
-		i = leadingRelative ? 1 : 0,
-
-		// The foundational matcher ensures that elements are reachable from top-level context(s)
-		matchContext = addCombinator( function( elem ) {
-			return elem === checkContext;
-		}, implicitRelative, true ),
-		matchAnyContext = addCombinator( function( elem ) {
-			return indexOf( checkContext, elem ) > -1;
-		}, implicitRelative, true ),
-		matchers = [ function( elem, context, xml ) {
-			var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || (
-				(checkContext = context).nodeType ?
-					matchContext( elem, context, xml ) :
-					matchAnyContext( elem, context, xml ) );
-			// Avoid hanging onto element (issue #299)
-			checkContext = null;
-			return ret;
-		} ];
-
-	for ( ; i < len; i++ ) {
-		if ( (matcher = Expr.relative[ tokens[i].type ]) ) {
-			matchers = [ addCombinator(elementMatcher( matchers ), matcher) ];
-		} else {
-			matcher = Expr.filter[ tokens[i].type ].apply( null, tokens[i].matches );
-
-			// Return special upon seeing a positional matcher
-			if ( matcher[ expando ] ) {
-				// Find the next relative operator (if any) for proper handling
-				j = ++i;
-				for ( ; j < len; j++ ) {
-					if ( Expr.relative[ tokens[j].type ] ) {
-						break;
-					}
-				}
-				return setMatcher(
-					i > 1 && elementMatcher( matchers ),
-					i > 1 && toSelector(
-						// If the preceding token was a descendant combinator, insert an implicit any-element `*`
-						tokens.slice( 0, i - 1 ).concat({ value: tokens[ i - 2 ].type === " " ? "*" : "" })
-					).replace( rtrim, "$1" ),
-					matcher,
-					i < j && matcherFromTokens( tokens.slice( i, j ) ),
-					j < len && matcherFromTokens( (tokens = tokens.slice( j )) ),
-					j < len && toSelector( tokens )
-				);
-			}
-			matchers.push( matcher );
-		}
-	}
-
-	return elementMatcher( matchers );
-}
-
-function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
-	var bySet = setMatchers.length > 0,
-		byElement = elementMatchers.length > 0,
-		superMatcher = function( seed, context, xml, results, outermost ) {
-			var elem, j, matcher,
-				matchedCount = 0,
-				i = "0",
-				unmatched = seed && [],
-				setMatched = [],
-				contextBackup = outermostContext,
-				// We must always have either seed elements or outermost context
-				elems = seed || byElement && Expr.find["TAG"]( "*", outermost ),
-				// Use integer dirruns iff this is the outermost matcher
-				dirrunsUnique = (dirruns += contextBackup == null ? 1 : Math.random() || 0.1),
-				len = elems.length;
-
-			if ( outermost ) {
-				outermostContext = context === document || context || outermost;
-			}
-
-			// Add elements passing elementMatchers directly to results
-			// Support: IE<9, Safari
-			// Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id
-			for ( ; i !== len && (elem = elems[i]) != null; i++ ) {
-				if ( byElement && elem ) {
-					j = 0;
-					if ( !context && elem.ownerDocument !== document ) {
-						setDocument( elem );
-						xml = !documentIsHTML;
-					}
-					while ( (matcher = elementMatchers[j++]) ) {
-						if ( matcher( elem, context || document, xml) ) {
-							results.push( elem );
-							break;
-						}
-					}
-					if ( outermost ) {
-						dirruns = dirrunsUnique;
-					}
-				}
-
-				// Track unmatched elements for set filters
-				if ( bySet ) {
-					// They will have gone through all possible matchers
-					if ( (elem = !matcher && elem) ) {
-						matchedCount--;
-					}
-
-					// Lengthen the array for every element, matched or not
-					if ( seed ) {
-						unmatched.push( elem );
-					}
-				}
-			}
-
-			// `i` is now the count of elements visited above, and adding it to `matchedCount`
-			// makes the latter nonnegative.
-			matchedCount += i;
-
-			// Apply set filters to unmatched elements
-			// NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount`
-			// equals `i`), unless we didn't visit _any_ elements in the above loop because we have
-			// no element matchers and no seed.
-			// Incrementing an initially-string "0" `i` allows `i` to remain a string only in that
-			// case, which will result in a "00" `matchedCount` that differs from `i` but is also
-			// numerically zero.
-			if ( bySet && i !== matchedCount ) {
-				j = 0;
-				while ( (matcher = setMatchers[j++]) ) {
-					matcher( unmatched, setMatched, context, xml );
-				}
-
-				if ( seed ) {
-					// Reintegrate element matches to eliminate the need for sorting
-					if ( matchedCount > 0 ) {
-						while ( i-- ) {
-							if ( !(unmatched[i] || setMatched[i]) ) {
-								setMatched[i] = pop.call( results );
-							}
-						}
-					}
-
-					// Discard index placeholder values to get only actual matches
-					setMatched = condense( setMatched );
-				}
-
-				// Add matches to results
-				push.apply( results, setMatched );
-
-				// Seedless set matches succeeding multiple successful matchers stipulate sorting
-				if ( outermost && !seed && setMatched.length > 0 &&
-					( matchedCount + setMatchers.length ) > 1 ) {
-
-					Sizzle.uniqueSort( results );
-				}
-			}
-
-			// Override manipulation of globals by nested matchers
-			if ( outermost ) {
-				dirruns = dirrunsUnique;
-				outermostContext = contextBackup;
-			}
-
-			return unmatched;
-		};
-
-	return bySet ?
-		markFunction( superMatcher ) :
-		superMatcher;
-}
-
-compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) {
-	var i,
-		setMatchers = [],
-		elementMatchers = [],
-		cached = compilerCache[ selector + " " ];
-
-	if ( !cached ) {
-		// Generate a function of recursive functions that can be used to check each element
-		if ( !match ) {
-			match = tokenize( selector );
-		}
-		i = match.length;
-		while ( i-- ) {
-			cached = matcherFromTokens( match[i] );
-			if ( cached[ expando ] ) {
-				setMatchers.push( cached );
-			} else {
-				elementMatchers.push( cached );
-			}
-		}
-
-		// Cache the compiled function
-		cached = compilerCache( selector, matcherFromGroupMatchers( elementMatchers, setMatchers ) );
-
-		// Save selector and tokenization
-		cached.selector = selector;
-	}
-	return cached;
-};
-
-/**
- * A low-level selection function that works with Sizzle's compiled
- *  selector functions
- * @param {String|Function} selector A selector or a pre-compiled
- *  selector function built with Sizzle.compile
- * @param {Element} context
- * @param {Array} [results]
- * @param {Array} [seed] A set of elements to match against
- */
-select = Sizzle.select = function( selector, context, results, seed ) {
-	var i, tokens, token, type, find,
-		compiled = typeof selector === "function" && selector,
-		match = !seed && tokenize( (selector = compiled.selector || selector) );
-
-	results = results || [];
-
-	// Try to minimize operations if there is only one selector in the list and no seed
-	// (the latter of which guarantees us context)
-	if ( match.length === 1 ) {
-
-		// Reduce context if the leading compound selector is an ID
-		tokens = match[0] = match[0].slice( 0 );
-		if ( tokens.length > 2 && (token = tokens[0]).type === "ID" &&
-				context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[1].type ] ) {
-
-			context = ( Expr.find["ID"]( token.matches[0].replace(runescape, funescape), context ) || [] )[0];
-			if ( !context ) {
-				return results;
-
-			// Precompiled matchers will still verify ancestry, so step up a level
-			} else if ( compiled ) {
-				context = context.parentNode;
-			}
-
-			selector = selector.slice( tokens.shift().value.length );
-		}
-
-		// Fetch a seed set for right-to-left matching
-		i = matchExpr["needsContext"].test( selector ) ? 0 : tokens.length;
-		while ( i-- ) {
-			token = tokens[i];
-
-			// Abort if we hit a combinator
-			if ( Expr.relative[ (type = token.type) ] ) {
-				break;
-			}
-			if ( (find = Expr.find[ type ]) ) {
-				// Search, expanding context for leading sibling combinators
-				if ( (seed = find(
-					token.matches[0].replace( runescape, funescape ),
-					rsibling.test( tokens[0].type ) && testContext( context.parentNode ) || context
-				)) ) {
-
-					// If seed is empty or no tokens remain, we can return early
-					tokens.splice( i, 1 );
-					selector = seed.length && toSelector( tokens );
-					if ( !selector ) {
-						push.apply( results, seed );
-						return results;
-					}
-
-					break;
-				}
-			}
-		}
-	}
-
-	// Compile and execute a filtering function if one is not provided
-	// Provide `match` to avoid retokenization if we modified the selector above
-	( compiled || compile( selector, match ) )(
-		seed,
-		context,
-		!documentIsHTML,
-		results,
-		!context || rsibling.test( selector ) && testContext( context.parentNode ) || context
-	);
-	return results;
-};
-
-// One-time assignments
-
-// Sort stability
-support.sortStable = expando.split("").sort( sortOrder ).join("") === expando;
-
-// Support: Chrome 14-35+
-// Always assume duplicates if they aren't passed to the comparison function
-support.detectDuplicates = !!hasDuplicate;
-
-// Initialize against the default document
-setDocument();
-
-// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27)
-// Detached nodes confoundingly follow *each other*
-support.sortDetached = assert(function( el ) {
-	// Should return 1, but returns 4 (following)
-	return el.compareDocumentPosition( document.createElement("fieldset") ) & 1;
-});
-
-// Support: IE<8
-// Prevent attribute/property "interpolation"
-// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx
-if ( !assert(function( el ) {
-	el.innerHTML = "";
-	return el.firstChild.getAttribute("href") === "#" ;
-}) ) {
-	addHandle( "type|href|height|width", function( elem, name, isXML ) {
-		if ( !isXML ) {
-			return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 );
-		}
-	});
-}
-
-// Support: IE<9
-// Use defaultValue in place of getAttribute("value")
-if ( !support.attributes || !assert(function( el ) {
-	el.innerHTML = "";
-	el.firstChild.setAttribute( "value", "" );
-	return el.firstChild.getAttribute( "value" ) === "";
-}) ) {
-	addHandle( "value", function( elem, name, isXML ) {
-		if ( !isXML && elem.nodeName.toLowerCase() === "input" ) {
-			return elem.defaultValue;
-		}
-	});
-}
-
-// Support: IE<9
-// Use getAttributeNode to fetch booleans when getAttribute lies
-if ( !assert(function( el ) {
-	return el.getAttribute("disabled") == null;
-}) ) {
-	addHandle( booleans, function( elem, name, isXML ) {
-		var val;
-		if ( !isXML ) {
-			return elem[ name ] === true ? name.toLowerCase() :
-					(val = elem.getAttributeNode( name )) && val.specified ?
-					val.value :
-				null;
-		}
-	});
-}
-
-return Sizzle;
-
-})( window );
-
-
-
-jQuery.find = Sizzle;
-jQuery.expr = Sizzle.selectors;
-
-// Deprecated
-jQuery.expr[ ":" ] = jQuery.expr.pseudos;
-jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort;
-jQuery.text = Sizzle.getText;
-jQuery.isXMLDoc = Sizzle.isXML;
-jQuery.contains = Sizzle.contains;
-jQuery.escapeSelector = Sizzle.escape;
-
-
-
-
-var dir = function( elem, dir, until ) {
-	var matched = [],
-		truncate = until !== undefined;
-
-	while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) {
-		if ( elem.nodeType === 1 ) {
-			if ( truncate && jQuery( elem ).is( until ) ) {
-				break;
-			}
-			matched.push( elem );
-		}
-	}
-	return matched;
-};
-
-
-var siblings = function( n, elem ) {
-	var matched = [];
-
-	for ( ; n; n = n.nextSibling ) {
-		if ( n.nodeType === 1 && n !== elem ) {
-			matched.push( n );
-		}
-	}
-
-	return matched;
-};
-
-
-var rneedsContext = jQuery.expr.match.needsContext;
-
-
-
-function nodeName( elem, name ) {
-
-  return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase();
-
-};
-var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i );
-
-
-
-// Implement the identical functionality for filter and not
-function winnow( elements, qualifier, not ) {
-	if ( isFunction( qualifier ) ) {
-		return jQuery.grep( elements, function( elem, i ) {
-			return !!qualifier.call( elem, i, elem ) !== not;
-		} );
-	}
-
-	// Single element
-	if ( qualifier.nodeType ) {
-		return jQuery.grep( elements, function( elem ) {
-			return ( elem === qualifier ) !== not;
-		} );
-	}
-
-	// Arraylike of elements (jQuery, arguments, Array)
-	if ( typeof qualifier !== "string" ) {
-		return jQuery.grep( elements, function( elem ) {
-			return ( indexOf.call( qualifier, elem ) > -1 ) !== not;
-		} );
-	}
-
-	// Filtered directly for both simple and complex selectors
-	return jQuery.filter( qualifier, elements, not );
-}
-
-jQuery.filter = function( expr, elems, not ) {
-	var elem = elems[ 0 ];
-
-	if ( not ) {
-		expr = ":not(" + expr + ")";
-	}
-
-	if ( elems.length === 1 && elem.nodeType === 1 ) {
-		return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : [];
-	}
-
-	return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) {
-		return elem.nodeType === 1;
-	} ) );
-};
-
-jQuery.fn.extend( {
-	find: function( selector ) {
-		var i, ret,
-			len = this.length,
-			self = this;
-
-		if ( typeof selector !== "string" ) {
-			return this.pushStack( jQuery( selector ).filter( function() {
-				for ( i = 0; i < len; i++ ) {
-					if ( jQuery.contains( self[ i ], this ) ) {
-						return true;
-					}
-				}
-			} ) );
-		}
-
-		ret = this.pushStack( [] );
-
-		for ( i = 0; i < len; i++ ) {
-			jQuery.find( selector, self[ i ], ret );
-		}
-
-		return len > 1 ? jQuery.uniqueSort( ret ) : ret;
-	},
-	filter: function( selector ) {
-		return this.pushStack( winnow( this, selector || [], false ) );
-	},
-	not: function( selector ) {
-		return this.pushStack( winnow( this, selector || [], true ) );
-	},
-	is: function( selector ) {
-		return !!winnow(
-			this,
-
-			// If this is a positional/relative selector, check membership in the returned set
-			// so $("p:first").is("p:last") won't return true for a doc with two "p".
-			typeof selector === "string" && rneedsContext.test( selector ) ?
-				jQuery( selector ) :
-				selector || [],
-			false
-		).length;
-	}
-} );
-
-
-// Initialize a jQuery object
-
-
-// A central reference to the root jQuery(document)
-var rootjQuery,
-
-	// A simple way to check for HTML strings
-	// Prioritize #id over  to avoid XSS via location.hash (#9521)
-	// Strict HTML recognition (#11290: must start with <)
-	// Shortcut simple #id case for speed
-	rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/,
-
-	init = jQuery.fn.init = function( selector, context, root ) {
-		var match, elem;
-
-		// HANDLE: $(""), $(null), $(undefined), $(false)
-		if ( !selector ) {
-			return this;
-		}
-
-		// Method init() accepts an alternate rootjQuery
-		// so migrate can support jQuery.sub (gh-2101)
-		root = root || rootjQuery;
-
-		// Handle HTML strings
-		if ( typeof selector === "string" ) {
-			if ( selector[ 0 ] === "<" &&
-				selector[ selector.length - 1 ] === ">" &&
-				selector.length >= 3 ) {
-
-				// Assume that strings that start and end with <> are HTML and skip the regex check
-				match = [ null, selector, null ];
-
-			} else {
-				match = rquickExpr.exec( selector );
-			}
-
-			// Match html or make sure no context is specified for #id
-			if ( match && ( match[ 1 ] || !context ) ) {
-
-				// HANDLE: $(html) -> $(array)
-				if ( match[ 1 ] ) {
-					context = context instanceof jQuery ? context[ 0 ] : context;
-
-					// Option to run scripts is true for back-compat
-					// Intentionally let the error be thrown if parseHTML is not present
-					jQuery.merge( this, jQuery.parseHTML(
-						match[ 1 ],
-						context && context.nodeType ? context.ownerDocument || context : document,
-						true
-					) );
-
-					// HANDLE: $(html, props)
-					if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) {
-						for ( match in context ) {
-
-							// Properties of context are called as methods if possible
-							if ( isFunction( this[ match ] ) ) {
-								this[ match ]( context[ match ] );
-
-							// ...and otherwise set as attributes
-							} else {
-								this.attr( match, context[ match ] );
-							}
-						}
-					}
-
-					return this;
-
-				// HANDLE: $(#id)
-				} else {
-					elem = document.getElementById( match[ 2 ] );
-
-					if ( elem ) {
-
-						// Inject the element directly into the jQuery object
-						this[ 0 ] = elem;
-						this.length = 1;
-					}
-					return this;
-				}
-
-			// HANDLE: $(expr, $(...))
-			} else if ( !context || context.jquery ) {
-				return ( context || root ).find( selector );
-
-			// HANDLE: $(expr, context)
-			// (which is just equivalent to: $(context).find(expr)
-			} else {
-				return this.constructor( context ).find( selector );
-			}
-
-		// HANDLE: $(DOMElement)
-		} else if ( selector.nodeType ) {
-			this[ 0 ] = selector;
-			this.length = 1;
-			return this;
-
-		// HANDLE: $(function)
-		// Shortcut for document ready
-		} else if ( isFunction( selector ) ) {
-			return root.ready !== undefined ?
-				root.ready( selector ) :
-
-				// Execute immediately if ready is not present
-				selector( jQuery );
-		}
-
-		return jQuery.makeArray( selector, this );
-	};
-
-// Give the init function the jQuery prototype for later instantiation
-init.prototype = jQuery.fn;
-
-// Initialize central reference
-rootjQuery = jQuery( document );
-
-
-var rparentsprev = /^(?:parents|prev(?:Until|All))/,
-
-	// Methods guaranteed to produce a unique set when starting from a unique set
-	guaranteedUnique = {
-		children: true,
-		contents: true,
-		next: true,
-		prev: true
-	};
-
-jQuery.fn.extend( {
-	has: function( target ) {
-		var targets = jQuery( target, this ),
-			l = targets.length;
-
-		return this.filter( function() {
-			var i = 0;
-			for ( ; i < l; i++ ) {
-				if ( jQuery.contains( this, targets[ i ] ) ) {
-					return true;
-				}
-			}
-		} );
-	},
-
-	closest: function( selectors, context ) {
-		var cur,
-			i = 0,
-			l = this.length,
-			matched = [],
-			targets = typeof selectors !== "string" && jQuery( selectors );
-
-		// Positional selectors never match, since there's no _selection_ context
-		if ( !rneedsContext.test( selectors ) ) {
-			for ( ; i < l; i++ ) {
-				for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) {
-
-					// Always skip document fragments
-					if ( cur.nodeType < 11 && ( targets ?
-						targets.index( cur ) > -1 :
-
-						// Don't pass non-elements to Sizzle
-						cur.nodeType === 1 &&
-							jQuery.find.matchesSelector( cur, selectors ) ) ) {
-
-						matched.push( cur );
-						break;
-					}
-				}
-			}
-		}
-
-		return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched );
-	},
-
-	// Determine the position of an element within the set
-	index: function( elem ) {
-
-		// No argument, return index in parent
-		if ( !elem ) {
-			return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1;
-		}
-
-		// Index in selector
-		if ( typeof elem === "string" ) {
-			return indexOf.call( jQuery( elem ), this[ 0 ] );
-		}
-
-		// Locate the position of the desired element
-		return indexOf.call( this,
-
-			// If it receives a jQuery object, the first element is used
-			elem.jquery ? elem[ 0 ] : elem
-		);
-	},
-
-	add: function( selector, context ) {
-		return this.pushStack(
-			jQuery.uniqueSort(
-				jQuery.merge( this.get(), jQuery( selector, context ) )
-			)
-		);
-	},
-
-	addBack: function( selector ) {
-		return this.add( selector == null ?
-			this.prevObject : this.prevObject.filter( selector )
-		);
-	}
-} );
-
-function sibling( cur, dir ) {
-	while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {}
-	return cur;
-}
-
-jQuery.each( {
-	parent: function( elem ) {
-		var parent = elem.parentNode;
-		return parent && parent.nodeType !== 11 ? parent : null;
-	},
-	parents: function( elem ) {
-		return dir( elem, "parentNode" );
-	},
-	parentsUntil: function( elem, i, until ) {
-		return dir( elem, "parentNode", until );
-	},
-	next: function( elem ) {
-		return sibling( elem, "nextSibling" );
-	},
-	prev: function( elem ) {
-		return sibling( elem, "previousSibling" );
-	},
-	nextAll: function( elem ) {
-		return dir( elem, "nextSibling" );
-	},
-	prevAll: function( elem ) {
-		return dir( elem, "previousSibling" );
-	},
-	nextUntil: function( elem, i, until ) {
-		return dir( elem, "nextSibling", until );
-	},
-	prevUntil: function( elem, i, until ) {
-		return dir( elem, "previousSibling", until );
-	},
-	siblings: function( elem ) {
-		return siblings( ( elem.parentNode || {} ).firstChild, elem );
-	},
-	children: function( elem ) {
-		return siblings( elem.firstChild );
-	},
-	contents: function( elem ) {
-        if ( nodeName( elem, "iframe" ) ) {
-            return elem.contentDocument;
-        }
-
-        // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only
-        // Treat the template element as a regular one in browsers that
-        // don't support it.
-        if ( nodeName( elem, "template" ) ) {
-            elem = elem.content || elem;
-        }
-
-        return jQuery.merge( [], elem.childNodes );
-	}
-}, function( name, fn ) {
-	jQuery.fn[ name ] = function( until, selector ) {
-		var matched = jQuery.map( this, fn, until );
-
-		if ( name.slice( -5 ) !== "Until" ) {
-			selector = until;
-		}
-
-		if ( selector && typeof selector === "string" ) {
-			matched = jQuery.filter( selector, matched );
-		}
-
-		if ( this.length > 1 ) {
-
-			// Remove duplicates
-			if ( !guaranteedUnique[ name ] ) {
-				jQuery.uniqueSort( matched );
-			}
-
-			// Reverse order for parents* and prev-derivatives
-			if ( rparentsprev.test( name ) ) {
-				matched.reverse();
-			}
-		}
-
-		return this.pushStack( matched );
-	};
-} );
-var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g );
-
-
-
-// Convert String-formatted options into Object-formatted ones
-function createOptions( options ) {
-	var object = {};
-	jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) {
-		object[ flag ] = true;
-	} );
-	return object;
-}
-
-/*
- * Create a callback list using the following parameters:
- *
- *	options: an optional list of space-separated options that will change how
- *			the callback list behaves or a more traditional option object
- *
- * By default a callback list will act like an event callback list and can be
- * "fired" multiple times.
- *
- * Possible options:
- *
- *	once:			will ensure the callback list can only be fired once (like a Deferred)
- *
- *	memory:			will keep track of previous values and will call any callback added
- *					after the list has been fired right away with the latest "memorized"
- *					values (like a Deferred)
- *
- *	unique:			will ensure a callback can only be added once (no duplicate in the list)
- *
- *	stopOnFalse:	interrupt callings when a callback returns false
- *
- */
-jQuery.Callbacks = function( options ) {
-
-	// Convert options from String-formatted to Object-formatted if needed
-	// (we check in cache first)
-	options = typeof options === "string" ?
-		createOptions( options ) :
-		jQuery.extend( {}, options );
-
-	var // Flag to know if list is currently firing
-		firing,
-
-		// Last fire value for non-forgettable lists
-		memory,
-
-		// Flag to know if list was already fired
-		fired,
-
-		// Flag to prevent firing
-		locked,
-
-		// Actual callback list
-		list = [],
-
-		// Queue of execution data for repeatable lists
-		queue = [],
-
-		// Index of currently firing callback (modified by add/remove as needed)
-		firingIndex = -1,
-
-		// Fire callbacks
-		fire = function() {
-
-			// Enforce single-firing
-			locked = locked || options.once;
-
-			// Execute callbacks for all pending executions,
-			// respecting firingIndex overrides and runtime changes
-			fired = firing = true;
-			for ( ; queue.length; firingIndex = -1 ) {
-				memory = queue.shift();
-				while ( ++firingIndex < list.length ) {
-
-					// Run callback and check for early termination
-					if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false &&
-						options.stopOnFalse ) {
-
-						// Jump to end and forget the data so .add doesn't re-fire
-						firingIndex = list.length;
-						memory = false;
-					}
-				}
-			}
-
-			// Forget the data if we're done with it
-			if ( !options.memory ) {
-				memory = false;
-			}
-
-			firing = false;
-
-			// Clean up if we're done firing for good
-			if ( locked ) {
-
-				// Keep an empty list if we have data for future add calls
-				if ( memory ) {
-					list = [];
-
-				// Otherwise, this object is spent
-				} else {
-					list = "";
-				}
-			}
-		},
-
-		// Actual Callbacks object
-		self = {
-
-			// Add a callback or a collection of callbacks to the list
-			add: function() {
-				if ( list ) {
-
-					// If we have memory from a past run, we should fire after adding
-					if ( memory && !firing ) {
-						firingIndex = list.length - 1;
-						queue.push( memory );
-					}
-
-					( function add( args ) {
-						jQuery.each( args, function( _, arg ) {
-							if ( isFunction( arg ) ) {
-								if ( !options.unique || !self.has( arg ) ) {
-									list.push( arg );
-								}
-							} else if ( arg && arg.length && toType( arg ) !== "string" ) {
-
-								// Inspect recursively
-								add( arg );
-							}
-						} );
-					} )( arguments );
-
-					if ( memory && !firing ) {
-						fire();
-					}
-				}
-				return this;
-			},
-
-			// Remove a callback from the list
-			remove: function() {
-				jQuery.each( arguments, function( _, arg ) {
-					var index;
-					while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) {
-						list.splice( index, 1 );
-
-						// Handle firing indexes
-						if ( index <= firingIndex ) {
-							firingIndex--;
-						}
-					}
-				} );
-				return this;
-			},
-
-			// Check if a given callback is in the list.
-			// If no argument is given, return whether or not list has callbacks attached.
-			has: function( fn ) {
-				return fn ?
-					jQuery.inArray( fn, list ) > -1 :
-					list.length > 0;
-			},
-
-			// Remove all callbacks from the list
-			empty: function() {
-				if ( list ) {
-					list = [];
-				}
-				return this;
-			},
-
-			// Disable .fire and .add
-			// Abort any current/pending executions
-			// Clear all callbacks and values
-			disable: function() {
-				locked = queue = [];
-				list = memory = "";
-				return this;
-			},
-			disabled: function() {
-				return !list;
-			},
-
-			// Disable .fire
-			// Also disable .add unless we have memory (since it would have no effect)
-			// Abort any pending executions
-			lock: function() {
-				locked = queue = [];
-				if ( !memory && !firing ) {
-					list = memory = "";
-				}
-				return this;
-			},
-			locked: function() {
-				return !!locked;
-			},
-
-			// Call all callbacks with the given context and arguments
-			fireWith: function( context, args ) {
-				if ( !locked ) {
-					args = args || [];
-					args = [ context, args.slice ? args.slice() : args ];
-					queue.push( args );
-					if ( !firing ) {
-						fire();
-					}
-				}
-				return this;
-			},
-
-			// Call all the callbacks with the given arguments
-			fire: function() {
-				self.fireWith( this, arguments );
-				return this;
-			},
-
-			// To know if the callbacks have already been called at least once
-			fired: function() {
-				return !!fired;
-			}
-		};
-
-	return self;
-};
-
-
-function Identity( v ) {
-	return v;
-}
-function Thrower( ex ) {
-	throw ex;
-}
-
-function adoptValue( value, resolve, reject, noValue ) {
-	var method;
-
-	try {
-
-		// Check for promise aspect first to privilege synchronous behavior
-		if ( value && isFunction( ( method = value.promise ) ) ) {
-			method.call( value ).done( resolve ).fail( reject );
-
-		// Other thenables
-		} else if ( value && isFunction( ( method = value.then ) ) ) {
-			method.call( value, resolve, reject );
-
-		// Other non-thenables
-		} else {
-
-			// Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer:
-			// * false: [ value ].slice( 0 ) => resolve( value )
-			// * true: [ value ].slice( 1 ) => resolve()
-			resolve.apply( undefined, [ value ].slice( noValue ) );
-		}
-
-	// For Promises/A+, convert exceptions into rejections
-	// Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in
-	// Deferred#then to conditionally suppress rejection.
-	} catch ( value ) {
-
-		// Support: Android 4.0 only
-		// Strict mode functions invoked without .call/.apply get global-object context
-		reject.apply( undefined, [ value ] );
-	}
-}
-
-jQuery.extend( {
-
-	Deferred: function( func ) {
-		var tuples = [
-
-				// action, add listener, callbacks,
-				// ... .then handlers, argument index, [final state]
-				[ "notify", "progress", jQuery.Callbacks( "memory" ),
-					jQuery.Callbacks( "memory" ), 2 ],
-				[ "resolve", "done", jQuery.Callbacks( "once memory" ),
-					jQuery.Callbacks( "once memory" ), 0, "resolved" ],
-				[ "reject", "fail", jQuery.Callbacks( "once memory" ),
-					jQuery.Callbacks( "once memory" ), 1, "rejected" ]
-			],
-			state = "pending",
-			promise = {
-				state: function() {
-					return state;
-				},
-				always: function() {
-					deferred.done( arguments ).fail( arguments );
-					return this;
-				},
-				"catch": function( fn ) {
-					return promise.then( null, fn );
-				},
-
-				// Keep pipe for back-compat
-				pipe: function( /* fnDone, fnFail, fnProgress */ ) {
-					var fns = arguments;
-
-					return jQuery.Deferred( function( newDefer ) {
-						jQuery.each( tuples, function( i, tuple ) {
-
-							// Map tuples (progress, done, fail) to arguments (done, fail, progress)
-							var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ];
-
-							// deferred.progress(function() { bind to newDefer or newDefer.notify })
-							// deferred.done(function() { bind to newDefer or newDefer.resolve })
-							// deferred.fail(function() { bind to newDefer or newDefer.reject })
-							deferred[ tuple[ 1 ] ]( function() {
-								var returned = fn && fn.apply( this, arguments );
-								if ( returned && isFunction( returned.promise ) ) {
-									returned.promise()
-										.progress( newDefer.notify )
-										.done( newDefer.resolve )
-										.fail( newDefer.reject );
-								} else {
-									newDefer[ tuple[ 0 ] + "With" ](
-										this,
-										fn ? [ returned ] : arguments
-									);
-								}
-							} );
-						} );
-						fns = null;
-					} ).promise();
-				},
-				then: function( onFulfilled, onRejected, onProgress ) {
-					var maxDepth = 0;
-					function resolve( depth, deferred, handler, special ) {
-						return function() {
-							var that = this,
-								args = arguments,
-								mightThrow = function() {
-									var returned, then;
-
-									// Support: Promises/A+ section 2.3.3.3.3
-									// https://promisesaplus.com/#point-59
-									// Ignore double-resolution attempts
-									if ( depth < maxDepth ) {
-										return;
-									}
-
-									returned = handler.apply( that, args );
-
-									// Support: Promises/A+ section 2.3.1
-									// https://promisesaplus.com/#point-48
-									if ( returned === deferred.promise() ) {
-										throw new TypeError( "Thenable self-resolution" );
-									}
-
-									// Support: Promises/A+ sections 2.3.3.1, 3.5
-									// https://promisesaplus.com/#point-54
-									// https://promisesaplus.com/#point-75
-									// Retrieve `then` only once
-									then = returned &&
-
-										// Support: Promises/A+ section 2.3.4
-										// https://promisesaplus.com/#point-64
-										// Only check objects and functions for thenability
-										( typeof returned === "object" ||
-											typeof returned === "function" ) &&
-										returned.then;
-
-									// Handle a returned thenable
-									if ( isFunction( then ) ) {
-
-										// Special processors (notify) just wait for resolution
-										if ( special ) {
-											then.call(
-												returned,
-												resolve( maxDepth, deferred, Identity, special ),
-												resolve( maxDepth, deferred, Thrower, special )
-											);
-
-										// Normal processors (resolve) also hook into progress
-										} else {
-
-											// ...and disregard older resolution values
-											maxDepth++;
-
-											then.call(
-												returned,
-												resolve( maxDepth, deferred, Identity, special ),
-												resolve( maxDepth, deferred, Thrower, special ),
-												resolve( maxDepth, deferred, Identity,
-													deferred.notifyWith )
-											);
-										}
-
-									// Handle all other returned values
-									} else {
-
-										// Only substitute handlers pass on context
-										// and multiple values (non-spec behavior)
-										if ( handler !== Identity ) {
-											that = undefined;
-											args = [ returned ];
-										}
-
-										// Process the value(s)
-										// Default process is resolve
-										( special || deferred.resolveWith )( that, args );
-									}
-								},
-
-								// Only normal processors (resolve) catch and reject exceptions
-								process = special ?
-									mightThrow :
-									function() {
-										try {
-											mightThrow();
-										} catch ( e ) {
-
-											if ( jQuery.Deferred.exceptionHook ) {
-												jQuery.Deferred.exceptionHook( e,
-													process.stackTrace );
-											}
-
-											// Support: Promises/A+ section 2.3.3.3.4.1
-											// https://promisesaplus.com/#point-61
-											// Ignore post-resolution exceptions
-											if ( depth + 1 >= maxDepth ) {
-
-												// Only substitute handlers pass on context
-												// and multiple values (non-spec behavior)
-												if ( handler !== Thrower ) {
-													that = undefined;
-													args = [ e ];
-												}
-
-												deferred.rejectWith( that, args );
-											}
-										}
-									};
-
-							// Support: Promises/A+ section 2.3.3.3.1
-							// https://promisesaplus.com/#point-57
-							// Re-resolve promises immediately to dodge false rejection from
-							// subsequent errors
-							if ( depth ) {
-								process();
-							} else {
-
-								// Call an optional hook to record the stack, in case of exception
-								// since it's otherwise lost when execution goes async
-								if ( jQuery.Deferred.getStackHook ) {
-									process.stackTrace = jQuery.Deferred.getStackHook();
-								}
-								window.setTimeout( process );
-							}
-						};
-					}
-
-					return jQuery.Deferred( function( newDefer ) {
-
-						// progress_handlers.add( ... )
-						tuples[ 0 ][ 3 ].add(
-							resolve(
-								0,
-								newDefer,
-								isFunction( onProgress ) ?
-									onProgress :
-									Identity,
-								newDefer.notifyWith
-							)
-						);
-
-						// fulfilled_handlers.add( ... )
-						tuples[ 1 ][ 3 ].add(
-							resolve(
-								0,
-								newDefer,
-								isFunction( onFulfilled ) ?
-									onFulfilled :
-									Identity
-							)
-						);
-
-						// rejected_handlers.add( ... )
-						tuples[ 2 ][ 3 ].add(
-							resolve(
-								0,
-								newDefer,
-								isFunction( onRejected ) ?
-									onRejected :
-									Thrower
-							)
-						);
-					} ).promise();
-				},
-
-				// Get a promise for this deferred
-				// If obj is provided, the promise aspect is added to the object
-				promise: function( obj ) {
-					return obj != null ? jQuery.extend( obj, promise ) : promise;
-				}
-			},
-			deferred = {};
-
-		// Add list-specific methods
-		jQuery.each( tuples, function( i, tuple ) {
-			var list = tuple[ 2 ],
-				stateString = tuple[ 5 ];
-
-			// promise.progress = list.add
-			// promise.done = list.add
-			// promise.fail = list.add
-			promise[ tuple[ 1 ] ] = list.add;
-
-			// Handle state
-			if ( stateString ) {
-				list.add(
-					function() {
-
-						// state = "resolved" (i.e., fulfilled)
-						// state = "rejected"
-						state = stateString;
-					},
-
-					// rejected_callbacks.disable
-					// fulfilled_callbacks.disable
-					tuples[ 3 - i ][ 2 ].disable,
-
-					// rejected_handlers.disable
-					// fulfilled_handlers.disable
-					tuples[ 3 - i ][ 3 ].disable,
-
-					// progress_callbacks.lock
-					tuples[ 0 ][ 2 ].lock,
-
-					// progress_handlers.lock
-					tuples[ 0 ][ 3 ].lock
-				);
-			}
-
-			// progress_handlers.fire
-			// fulfilled_handlers.fire
-			// rejected_handlers.fire
-			list.add( tuple[ 3 ].fire );
-
-			// deferred.notify = function() { deferred.notifyWith(...) }
-			// deferred.resolve = function() { deferred.resolveWith(...) }
-			// deferred.reject = function() { deferred.rejectWith(...) }
-			deferred[ tuple[ 0 ] ] = function() {
-				deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments );
-				return this;
-			};
-
-			// deferred.notifyWith = list.fireWith
-			// deferred.resolveWith = list.fireWith
-			// deferred.rejectWith = list.fireWith
-			deferred[ tuple[ 0 ] + "With" ] = list.fireWith;
-		} );
-
-		// Make the deferred a promise
-		promise.promise( deferred );
-
-		// Call given func if any
-		if ( func ) {
-			func.call( deferred, deferred );
-		}
-
-		// All done!
-		return deferred;
-	},
-
-	// Deferred helper
-	when: function( singleValue ) {
-		var
-
-			// count of uncompleted subordinates
-			remaining = arguments.length,
-
-			// count of unprocessed arguments
-			i = remaining,
-
-			// subordinate fulfillment data
-			resolveContexts = Array( i ),
-			resolveValues = slice.call( arguments ),
-
-			// the master Deferred
-			master = jQuery.Deferred(),
-
-			// subordinate callback factory
-			updateFunc = function( i ) {
-				return function( value ) {
-					resolveContexts[ i ] = this;
-					resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value;
-					if ( !( --remaining ) ) {
-						master.resolveWith( resolveContexts, resolveValues );
-					}
-				};
-			};
-
-		// Single- and empty arguments are adopted like Promise.resolve
-		if ( remaining <= 1 ) {
-			adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject,
-				!remaining );
-
-			// Use .then() to unwrap secondary thenables (cf. gh-3000)
-			if ( master.state() === "pending" ||
-				isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) {
-
-				return master.then();
-			}
-		}
-
-		// Multiple arguments are aggregated like Promise.all array elements
-		while ( i-- ) {
-			adoptValue( resolveValues[ i ], updateFunc( i ), master.reject );
-		}
-
-		return master.promise();
-	}
-} );
-
-
-// These usually indicate a programmer mistake during development,
-// warn about them ASAP rather than swallowing them by default.
-var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/;
-
-jQuery.Deferred.exceptionHook = function( error, stack ) {
-
-	// Support: IE 8 - 9 only
-	// Console exists when dev tools are open, which can happen at any time
-	if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) {
-		window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack );
-	}
-};
-
-
-
-
-jQuery.readyException = function( error ) {
-	window.setTimeout( function() {
-		throw error;
-	} );
-};
-
-
-
-
-// The deferred used on DOM ready
-var readyList = jQuery.Deferred();
-
-jQuery.fn.ready = function( fn ) {
-
-	readyList
-		.then( fn )
-
-		// Wrap jQuery.readyException in a function so that the lookup
-		// happens at the time of error handling instead of callback
-		// registration.
-		.catch( function( error ) {
-			jQuery.readyException( error );
-		} );
-
-	return this;
-};
-
-jQuery.extend( {
-
-	// Is the DOM ready to be used? Set to true once it occurs.
-	isReady: false,
-
-	// A counter to track how many items to wait for before
-	// the ready event fires. See #6781
-	readyWait: 1,
-
-	// Handle when the DOM is ready
-	ready: function( wait ) {
-
-		// Abort if there are pending holds or we're already ready
-		if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) {
-			return;
-		}
-
-		// Remember that the DOM is ready
-		jQuery.isReady = true;
-
-		// If a normal DOM Ready event fired, decrement, and wait if need be
-		if ( wait !== true && --jQuery.readyWait > 0 ) {
-			return;
-		}
-
-		// If there are functions bound, to execute
-		readyList.resolveWith( document, [ jQuery ] );
-	}
-} );
-
-jQuery.ready.then = readyList.then;
-
-// The ready event handler and self cleanup method
-function completed() {
-	document.removeEventListener( "DOMContentLoaded", completed );
-	window.removeEventListener( "load", completed );
-	jQuery.ready();
-}
-
-// Catch cases where $(document).ready() is called
-// after the browser event has already occurred.
-// Support: IE <=9 - 10 only
-// Older IE sometimes signals "interactive" too soon
-if ( document.readyState === "complete" ||
-	( document.readyState !== "loading" && !document.documentElement.doScroll ) ) {
-
-	// Handle it asynchronously to allow scripts the opportunity to delay ready
-	window.setTimeout( jQuery.ready );
-
-} else {
-
-	// Use the handy event callback
-	document.addEventListener( "DOMContentLoaded", completed );
-
-	// A fallback to window.onload, that will always work
-	window.addEventListener( "load", completed );
-}
-
-
-
-
-// Multifunctional method to get and set values of a collection
-// The value/s can optionally be executed if it's a function
-var access = function( elems, fn, key, value, chainable, emptyGet, raw ) {
-	var i = 0,
-		len = elems.length,
-		bulk = key == null;
-
-	// Sets many values
-	if ( toType( key ) === "object" ) {
-		chainable = true;
-		for ( i in key ) {
-			access( elems, fn, i, key[ i ], true, emptyGet, raw );
-		}
-
-	// Sets one value
-	} else if ( value !== undefined ) {
-		chainable = true;
-
-		if ( !isFunction( value ) ) {
-			raw = true;
-		}
-
-		if ( bulk ) {
-
-			// Bulk operations run against the entire set
-			if ( raw ) {
-				fn.call( elems, value );
-				fn = null;
-
-			// ...except when executing function values
-			} else {
-				bulk = fn;
-				fn = function( elem, key, value ) {
-					return bulk.call( jQuery( elem ), value );
-				};
-			}
-		}
-
-		if ( fn ) {
-			for ( ; i < len; i++ ) {
-				fn(
-					elems[ i ], key, raw ?
-					value :
-					value.call( elems[ i ], i, fn( elems[ i ], key ) )
-				);
-			}
-		}
-	}
-
-	if ( chainable ) {
-		return elems;
-	}
-
-	// Gets
-	if ( bulk ) {
-		return fn.call( elems );
-	}
-
-	return len ? fn( elems[ 0 ], key ) : emptyGet;
-};
-
-
-// Matches dashed string for camelizing
-var rmsPrefix = /^-ms-/,
-	rdashAlpha = /-([a-z])/g;
-
-// Used by camelCase as callback to replace()
-function fcamelCase( all, letter ) {
-	return letter.toUpperCase();
-}
-
-// Convert dashed to camelCase; used by the css and data modules
-// Support: IE <=9 - 11, Edge 12 - 15
-// Microsoft forgot to hump their vendor prefix (#9572)
-function camelCase( string ) {
-	return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase );
-}
-var acceptData = function( owner ) {
-
-	// Accepts only:
-	//  - Node
-	//    - Node.ELEMENT_NODE
-	//    - Node.DOCUMENT_NODE
-	//  - Object
-	//    - Any
-	return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType );
-};
-
-
-
-
-function Data() {
-	this.expando = jQuery.expando + Data.uid++;
-}
-
-Data.uid = 1;
-
-Data.prototype = {
-
-	cache: function( owner ) {
-
-		// Check if the owner object already has a cache
-		var value = owner[ this.expando ];
-
-		// If not, create one
-		if ( !value ) {
-			value = {};
-
-			// We can accept data for non-element nodes in modern browsers,
-			// but we should not, see #8335.
-			// Always return an empty object.
-			if ( acceptData( owner ) ) {
-
-				// If it is a node unlikely to be stringify-ed or looped over
-				// use plain assignment
-				if ( owner.nodeType ) {
-					owner[ this.expando ] = value;
-
-				// Otherwise secure it in a non-enumerable property
-				// configurable must be true to allow the property to be
-				// deleted when data is removed
-				} else {
-					Object.defineProperty( owner, this.expando, {
-						value: value,
-						configurable: true
-					} );
-				}
-			}
-		}
-
-		return value;
-	},
-	set: function( owner, data, value ) {
-		var prop,
-			cache = this.cache( owner );
-
-		// Handle: [ owner, key, value ] args
-		// Always use camelCase key (gh-2257)
-		if ( typeof data === "string" ) {
-			cache[ camelCase( data ) ] = value;
-
-		// Handle: [ owner, { properties } ] args
-		} else {
-
-			// Copy the properties one-by-one to the cache object
-			for ( prop in data ) {
-				cache[ camelCase( prop ) ] = data[ prop ];
-			}
-		}
-		return cache;
-	},
-	get: function( owner, key ) {
-		return key === undefined ?
-			this.cache( owner ) :
-
-			// Always use camelCase key (gh-2257)
-			owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ];
-	},
-	access: function( owner, key, value ) {
-
-		// In cases where either:
-		//
-		//   1. No key was specified
-		//   2. A string key was specified, but no value provided
-		//
-		// Take the "read" path and allow the get method to determine
-		// which value to return, respectively either:
-		//
-		//   1. The entire cache object
-		//   2. The data stored at the key
-		//
-		if ( key === undefined ||
-				( ( key && typeof key === "string" ) && value === undefined ) ) {
-
-			return this.get( owner, key );
-		}
-
-		// When the key is not a string, or both a key and value
-		// are specified, set or extend (existing objects) with either:
-		//
-		//   1. An object of properties
-		//   2. A key and value
-		//
-		this.set( owner, key, value );
-
-		// Since the "set" path can have two possible entry points
-		// return the expected data based on which path was taken[*]
-		return value !== undefined ? value : key;
-	},
-	remove: function( owner, key ) {
-		var i,
-			cache = owner[ this.expando ];
-
-		if ( cache === undefined ) {
-			return;
-		}
-
-		if ( key !== undefined ) {
-
-			// Support array or space separated string of keys
-			if ( Array.isArray( key ) ) {
-
-				// If key is an array of keys...
-				// We always set camelCase keys, so remove that.
-				key = key.map( camelCase );
-			} else {
-				key = camelCase( key );
-
-				// If a key with the spaces exists, use it.
-				// Otherwise, create an array by matching non-whitespace
-				key = key in cache ?
-					[ key ] :
-					( key.match( rnothtmlwhite ) || [] );
-			}
-
-			i = key.length;
-
-			while ( i-- ) {
-				delete cache[ key[ i ] ];
-			}
-		}
-
-		// Remove the expando if there's no more data
-		if ( key === undefined || jQuery.isEmptyObject( cache ) ) {
-
-			// Support: Chrome <=35 - 45
-			// Webkit & Blink performance suffers when deleting properties
-			// from DOM nodes, so set to undefined instead
-			// https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted)
-			if ( owner.nodeType ) {
-				owner[ this.expando ] = undefined;
-			} else {
-				delete owner[ this.expando ];
-			}
-		}
-	},
-	hasData: function( owner ) {
-		var cache = owner[ this.expando ];
-		return cache !== undefined && !jQuery.isEmptyObject( cache );
-	}
-};
-var dataPriv = new Data();
-
-var dataUser = new Data();
-
-
-
-//	Implementation Summary
-//
-//	1. Enforce API surface and semantic compatibility with 1.9.x branch
-//	2. Improve the module's maintainability by reducing the storage
-//		paths to a single mechanism.
-//	3. Use the same single mechanism to support "private" and "user" data.
-//	4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData)
-//	5. Avoid exposing implementation details on user objects (eg. expando properties)
-//	6. Provide a clear path for implementation upgrade to WeakMap in 2014
-
-var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/,
-	rmultiDash = /[A-Z]/g;
-
-function getData( data ) {
-	if ( data === "true" ) {
-		return true;
-	}
-
-	if ( data === "false" ) {
-		return false;
-	}
-
-	if ( data === "null" ) {
-		return null;
-	}
-
-	// Only convert to a number if it doesn't change the string
-	if ( data === +data + "" ) {
-		return +data;
-	}
-
-	if ( rbrace.test( data ) ) {
-		return JSON.parse( data );
-	}
-
-	return data;
-}
-
-function dataAttr( elem, key, data ) {
-	var name;
-
-	// If nothing was found internally, try to fetch any
-	// data from the HTML5 data-* attribute
-	if ( data === undefined && elem.nodeType === 1 ) {
-		name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase();
-		data = elem.getAttribute( name );
-
-		if ( typeof data === "string" ) {
-			try {
-				data = getData( data );
-			} catch ( e ) {}
-
-			// Make sure we set the data so it isn't changed later
-			dataUser.set( elem, key, data );
-		} else {
-			data = undefined;
-		}
-	}
-	return data;
-}
-
-jQuery.extend( {
-	hasData: function( elem ) {
-		return dataUser.hasData( elem ) || dataPriv.hasData( elem );
-	},
-
-	data: function( elem, name, data ) {
-		return dataUser.access( elem, name, data );
-	},
-
-	removeData: function( elem, name ) {
-		dataUser.remove( elem, name );
-	},
-
-	// TODO: Now that all calls to _data and _removeData have been replaced
-	// with direct calls to dataPriv methods, these can be deprecated.
-	_data: function( elem, name, data ) {
-		return dataPriv.access( elem, name, data );
-	},
-
-	_removeData: function( elem, name ) {
-		dataPriv.remove( elem, name );
-	}
-} );
-
-jQuery.fn.extend( {
-	data: function( key, value ) {
-		var i, name, data,
-			elem = this[ 0 ],
-			attrs = elem && elem.attributes;
-
-		// Gets all values
-		if ( key === undefined ) {
-			if ( this.length ) {
-				data = dataUser.get( elem );
-
-				if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) {
-					i = attrs.length;
-					while ( i-- ) {
-
-						// Support: IE 11 only
-						// The attrs elements can be null (#14894)
-						if ( attrs[ i ] ) {
-							name = attrs[ i ].name;
-							if ( name.indexOf( "data-" ) === 0 ) {
-								name = camelCase( name.slice( 5 ) );
-								dataAttr( elem, name, data[ name ] );
-							}
-						}
-					}
-					dataPriv.set( elem, "hasDataAttrs", true );
-				}
-			}
-
-			return data;
-		}
-
-		// Sets multiple values
-		if ( typeof key === "object" ) {
-			return this.each( function() {
-				dataUser.set( this, key );
-			} );
-		}
-
-		return access( this, function( value ) {
-			var data;
-
-			// The calling jQuery object (element matches) is not empty
-			// (and therefore has an element appears at this[ 0 ]) and the
-			// `value` parameter was not undefined. An empty jQuery object
-			// will result in `undefined` for elem = this[ 0 ] which will
-			// throw an exception if an attempt to read a data cache is made.
-			if ( elem && value === undefined ) {
-
-				// Attempt to get data from the cache
-				// The key will always be camelCased in Data
-				data = dataUser.get( elem, key );
-				if ( data !== undefined ) {
-					return data;
-				}
-
-				// Attempt to "discover" the data in
-				// HTML5 custom data-* attrs
-				data = dataAttr( elem, key );
-				if ( data !== undefined ) {
-					return data;
-				}
-
-				// We tried really hard, but the data doesn't exist.
-				return;
-			}
-
-			// Set the data...
-			this.each( function() {
-
-				// We always store the camelCased key
-				dataUser.set( this, key, value );
-			} );
-		}, null, value, arguments.length > 1, null, true );
-	},
-
-	removeData: function( key ) {
-		return this.each( function() {
-			dataUser.remove( this, key );
-		} );
-	}
-} );
-
-
-jQuery.extend( {
-	queue: function( elem, type, data ) {
-		var queue;
-
-		if ( elem ) {
-			type = ( type || "fx" ) + "queue";
-			queue = dataPriv.get( elem, type );
-
-			// Speed up dequeue by getting out quickly if this is just a lookup
-			if ( data ) {
-				if ( !queue || Array.isArray( data ) ) {
-					queue = dataPriv.access( elem, type, jQuery.makeArray( data ) );
-				} else {
-					queue.push( data );
-				}
-			}
-			return queue || [];
-		}
-	},
-
-	dequeue: function( elem, type ) {
-		type = type || "fx";
-
-		var queue = jQuery.queue( elem, type ),
-			startLength = queue.length,
-			fn = queue.shift(),
-			hooks = jQuery._queueHooks( elem, type ),
-			next = function() {
-				jQuery.dequeue( elem, type );
-			};
-
-		// If the fx queue is dequeued, always remove the progress sentinel
-		if ( fn === "inprogress" ) {
-			fn = queue.shift();
-			startLength--;
-		}
-
-		if ( fn ) {
-
-			// Add a progress sentinel to prevent the fx queue from being
-			// automatically dequeued
-			if ( type === "fx" ) {
-				queue.unshift( "inprogress" );
-			}
-
-			// Clear up the last queue stop function
-			delete hooks.stop;
-			fn.call( elem, next, hooks );
-		}
-
-		if ( !startLength && hooks ) {
-			hooks.empty.fire();
-		}
-	},
-
-	// Not public - generate a queueHooks object, or return the current one
-	_queueHooks: function( elem, type ) {
-		var key = type + "queueHooks";
-		return dataPriv.get( elem, key ) || dataPriv.access( elem, key, {
-			empty: jQuery.Callbacks( "once memory" ).add( function() {
-				dataPriv.remove( elem, [ type + "queue", key ] );
-			} )
-		} );
-	}
-} );
-
-jQuery.fn.extend( {
-	queue: function( type, data ) {
-		var setter = 2;
-
-		if ( typeof type !== "string" ) {
-			data = type;
-			type = "fx";
-			setter--;
-		}
-
-		if ( arguments.length < setter ) {
-			return jQuery.queue( this[ 0 ], type );
-		}
-
-		return data === undefined ?
-			this :
-			this.each( function() {
-				var queue = jQuery.queue( this, type, data );
-
-				// Ensure a hooks for this queue
-				jQuery._queueHooks( this, type );
-
-				if ( type === "fx" && queue[ 0 ] !== "inprogress" ) {
-					jQuery.dequeue( this, type );
-				}
-			} );
-	},
-	dequeue: function( type ) {
-		return this.each( function() {
-			jQuery.dequeue( this, type );
-		} );
-	},
-	clearQueue: function( type ) {
-		return this.queue( type || "fx", [] );
-	},
-
-	// Get a promise resolved when queues of a certain type
-	// are emptied (fx is the type by default)
-	promise: function( type, obj ) {
-		var tmp,
-			count = 1,
-			defer = jQuery.Deferred(),
-			elements = this,
-			i = this.length,
-			resolve = function() {
-				if ( !( --count ) ) {
-					defer.resolveWith( elements, [ elements ] );
-				}
-			};
-
-		if ( typeof type !== "string" ) {
-			obj = type;
-			type = undefined;
-		}
-		type = type || "fx";
-
-		while ( i-- ) {
-			tmp = dataPriv.get( elements[ i ], type + "queueHooks" );
-			if ( tmp && tmp.empty ) {
-				count++;
-				tmp.empty.add( resolve );
-			}
-		}
-		resolve();
-		return defer.promise( obj );
-	}
-} );
-var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source;
-
-var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" );
-
-
-var cssExpand = [ "Top", "Right", "Bottom", "Left" ];
-
-var isHiddenWithinTree = function( elem, el ) {
-
-		// isHiddenWithinTree might be called from jQuery#filter function;
-		// in that case, element will be second argument
-		elem = el || elem;
-
-		// Inline style trumps all
-		return elem.style.display === "none" ||
-			elem.style.display === "" &&
-
-			// Otherwise, check computed style
-			// Support: Firefox <=43 - 45
-			// Disconnected elements can have computed display: none, so first confirm that elem is
-			// in the document.
-			jQuery.contains( elem.ownerDocument, elem ) &&
-
-			jQuery.css( elem, "display" ) === "none";
-	};
-
-var swap = function( elem, options, callback, args ) {
-	var ret, name,
-		old = {};
-
-	// Remember the old values, and insert the new ones
-	for ( name in options ) {
-		old[ name ] = elem.style[ name ];
-		elem.style[ name ] = options[ name ];
-	}
-
-	ret = callback.apply( elem, args || [] );
-
-	// Revert the old values
-	for ( name in options ) {
-		elem.style[ name ] = old[ name ];
-	}
-
-	return ret;
-};
-
-
-
-
-function adjustCSS( elem, prop, valueParts, tween ) {
-	var adjusted, scale,
-		maxIterations = 20,
-		currentValue = tween ?
-			function() {
-				return tween.cur();
-			} :
-			function() {
-				return jQuery.css( elem, prop, "" );
-			},
-		initial = currentValue(),
-		unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ),
-
-		// Starting value computation is required for potential unit mismatches
-		initialInUnit = ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) &&
-			rcssNum.exec( jQuery.css( elem, prop ) );
-
-	if ( initialInUnit && initialInUnit[ 3 ] !== unit ) {
-
-		// Support: Firefox <=54
-		// Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144)
-		initial = initial / 2;
-
-		// Trust units reported by jQuery.css
-		unit = unit || initialInUnit[ 3 ];
-
-		// Iteratively approximate from a nonzero starting point
-		initialInUnit = +initial || 1;
-
-		while ( maxIterations-- ) {
-
-			// Evaluate and update our best guess (doubling guesses that zero out).
-			// Finish if the scale equals or crosses 1 (making the old*new product non-positive).
-			jQuery.style( elem, prop, initialInUnit + unit );
-			if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) {
-				maxIterations = 0;
-			}
-			initialInUnit = initialInUnit / scale;
-
-		}
-
-		initialInUnit = initialInUnit * 2;
-		jQuery.style( elem, prop, initialInUnit + unit );
-
-		// Make sure we update the tween properties later on
-		valueParts = valueParts || [];
-	}
-
-	if ( valueParts ) {
-		initialInUnit = +initialInUnit || +initial || 0;
-
-		// Apply relative offset (+=/-=) if specified
-		adjusted = valueParts[ 1 ] ?
-			initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] :
-			+valueParts[ 2 ];
-		if ( tween ) {
-			tween.unit = unit;
-			tween.start = initialInUnit;
-			tween.end = adjusted;
-		}
-	}
-	return adjusted;
-}
-
-
-var defaultDisplayMap = {};
-
-function getDefaultDisplay( elem ) {
-	var temp,
-		doc = elem.ownerDocument,
-		nodeName = elem.nodeName,
-		display = defaultDisplayMap[ nodeName ];
-
-	if ( display ) {
-		return display;
-	}
-
-	temp = doc.body.appendChild( doc.createElement( nodeName ) );
-	display = jQuery.css( temp, "display" );
-
-	temp.parentNode.removeChild( temp );
-
-	if ( display === "none" ) {
-		display = "block";
-	}
-	defaultDisplayMap[ nodeName ] = display;
-
-	return display;
-}
-
-function showHide( elements, show ) {
-	var display, elem,
-		values = [],
-		index = 0,
-		length = elements.length;
-
-	// Determine new display value for elements that need to change
-	for ( ; index < length; index++ ) {
-		elem = elements[ index ];
-		if ( !elem.style ) {
-			continue;
-		}
-
-		display = elem.style.display;
-		if ( show ) {
-
-			// Since we force visibility upon cascade-hidden elements, an immediate (and slow)
-			// check is required in this first loop unless we have a nonempty display value (either
-			// inline or about-to-be-restored)
-			if ( display === "none" ) {
-				values[ index ] = dataPriv.get( elem, "display" ) || null;
-				if ( !values[ index ] ) {
-					elem.style.display = "";
-				}
-			}
-			if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) {
-				values[ index ] = getDefaultDisplay( elem );
-			}
-		} else {
-			if ( display !== "none" ) {
-				values[ index ] = "none";
-
-				// Remember what we're overwriting
-				dataPriv.set( elem, "display", display );
-			}
-		}
-	}
-
-	// Set the display of the elements in a second loop to avoid constant reflow
-	for ( index = 0; index < length; index++ ) {
-		if ( values[ index ] != null ) {
-			elements[ index ].style.display = values[ index ];
-		}
-	}
-
-	return elements;
-}
-
-jQuery.fn.extend( {
-	show: function() {
-		return showHide( this, true );
-	},
-	hide: function() {
-		return showHide( this );
-	},
-	toggle: function( state ) {
-		if ( typeof state === "boolean" ) {
-			return state ? this.show() : this.hide();
-		}
-
-		return this.each( function() {
-			if ( isHiddenWithinTree( this ) ) {
-				jQuery( this ).show();
-			} else {
-				jQuery( this ).hide();
-			}
-		} );
-	}
-} );
-var rcheckableType = ( /^(?:checkbox|radio)$/i );
-
-var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]+)/i );
-
-var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i );
-
-
-
-// We have to close these tags to support XHTML (#13200)
-var wrapMap = {
-
-	// Support: IE <=9 only
-	option: [ 1, "" ],
-
-	// XHTML parsers do not magically insert elements in the
-	// same way that tag soup parsers do. So we cannot shorten
-	// this by omitting  or other required elements.
-	thead: [ 1, "", "
    " ],
-	col: [ 2, "", "
    " ],
-	tr: [ 2, "", "
    " ],
-	td: [ 3, "", "
    " ],
-
-	_default: [ 0, "", "" ]
-};
-
-// Support: IE <=9 only
-wrapMap.optgroup = wrapMap.option;
-
-wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead;
-wrapMap.th = wrapMap.td;
-
-
-function getAll( context, tag ) {
-
-	// Support: IE <=9 - 11 only
-	// Use typeof to avoid zero-argument method invocation on host objects (#15151)
-	var ret;
-
-	if ( typeof context.getElementsByTagName !== "undefined" ) {
-		ret = context.getElementsByTagName( tag || "*" );
-
-	} else if ( typeof context.querySelectorAll !== "undefined" ) {
-		ret = context.querySelectorAll( tag || "*" );
-
-	} else {
-		ret = [];
-	}
-
-	if ( tag === undefined || tag && nodeName( context, tag ) ) {
-		return jQuery.merge( [ context ], ret );
-	}
-
-	return ret;
-}
-
-
-// Mark scripts as having already been evaluated
-function setGlobalEval( elems, refElements ) {
-	var i = 0,
-		l = elems.length;
-
-	for ( ; i < l; i++ ) {
-		dataPriv.set(
-			elems[ i ],
-			"globalEval",
-			!refElements || dataPriv.get( refElements[ i ], "globalEval" )
-		);
-	}
-}
-
-
-var rhtml = /<|&#?\w+;/;
-
-function buildFragment( elems, context, scripts, selection, ignored ) {
-	var elem, tmp, tag, wrap, contains, j,
-		fragment = context.createDocumentFragment(),
-		nodes = [],
-		i = 0,
-		l = elems.length;
-
-	for ( ; i < l; i++ ) {
-		elem = elems[ i ];
-
-		if ( elem || elem === 0 ) {
-
-			// Add nodes directly
-			if ( toType( elem ) === "object" ) {
-
-				// Support: Android <=4.0 only, PhantomJS 1 only
-				// push.apply(_, arraylike) throws on ancient WebKit
-				jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem );
-
-			// Convert non-html into a text node
-			} else if ( !rhtml.test( elem ) ) {
-				nodes.push( context.createTextNode( elem ) );
-
-			// Convert html into DOM nodes
-			} else {
-				tmp = tmp || fragment.appendChild( context.createElement( "div" ) );
-
-				// Deserialize a standard representation
-				tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase();
-				wrap = wrapMap[ tag ] || wrapMap._default;
-				tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ];
-
-				// Descend through wrappers to the right content
-				j = wrap[ 0 ];
-				while ( j-- ) {
-					tmp = tmp.lastChild;
-				}
-
-				// Support: Android <=4.0 only, PhantomJS 1 only
-				// push.apply(_, arraylike) throws on ancient WebKit
-				jQuery.merge( nodes, tmp.childNodes );
-
-				// Remember the top-level container
-				tmp = fragment.firstChild;
-
-				// Ensure the created nodes are orphaned (#12392)
-				tmp.textContent = "";
-			}
-		}
-	}
-
-	// Remove wrapper from fragment
-	fragment.textContent = "";
-
-	i = 0;
-	while ( ( elem = nodes[ i++ ] ) ) {
-
-		// Skip elements already in the context collection (trac-4087)
-		if ( selection && jQuery.inArray( elem, selection ) > -1 ) {
-			if ( ignored ) {
-				ignored.push( elem );
-			}
-			continue;
-		}
-
-		contains = jQuery.contains( elem.ownerDocument, elem );
-
-		// Append to fragment
-		tmp = getAll( fragment.appendChild( elem ), "script" );
-
-		// Preserve script evaluation history
-		if ( contains ) {
-			setGlobalEval( tmp );
-		}
-
-		// Capture executables
-		if ( scripts ) {
-			j = 0;
-			while ( ( elem = tmp[ j++ ] ) ) {
-				if ( rscriptType.test( elem.type || "" ) ) {
-					scripts.push( elem );
-				}
-			}
-		}
-	}
-
-	return fragment;
-}
-
-
-( function() {
-	var fragment = document.createDocumentFragment(),
-		div = fragment.appendChild( document.createElement( "div" ) ),
-		input = document.createElement( "input" );
-
-	// Support: Android 4.0 - 4.3 only
-	// Check state lost if the name is set (#11217)
-	// Support: Windows Web Apps (WWA)
-	// `name` and `type` must use .setAttribute for WWA (#14901)
-	input.setAttribute( "type", "radio" );
-	input.setAttribute( "checked", "checked" );
-	input.setAttribute( "name", "t" );
-
-	div.appendChild( input );
-
-	// Support: Android <=4.1 only
-	// Older WebKit doesn't clone checked state correctly in fragments
-	support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked;
-
-	// Support: IE <=11 only
-	// Make sure textarea (and checkbox) defaultValue is properly cloned
-	div.innerHTML = "";
-	support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue;
-} )();
-var documentElement = document.documentElement;
-
-
-
-var
-	rkeyEvent = /^key/,
-	rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/,
-	rtypenamespace = /^([^.]*)(?:\.(.+)|)/;
-
-function returnTrue() {
-	return true;
-}
-
-function returnFalse() {
-	return false;
-}
-
-// Support: IE <=9 only
-// See #13393 for more info
-function safeActiveElement() {
-	try {
-		return document.activeElement;
-	} catch ( err ) { }
-}
-
-function on( elem, types, selector, data, fn, one ) {
-	var origFn, type;
-
-	// Types can be a map of types/handlers
-	if ( typeof types === "object" ) {
-
-		// ( types-Object, selector, data )
-		if ( typeof selector !== "string" ) {
-
-			// ( types-Object, data )
-			data = data || selector;
-			selector = undefined;
-		}
-		for ( type in types ) {
-			on( elem, type, selector, data, types[ type ], one );
-		}
-		return elem;
-	}
-
-	if ( data == null && fn == null ) {
-
-		// ( types, fn )
-		fn = selector;
-		data = selector = undefined;
-	} else if ( fn == null ) {
-		if ( typeof selector === "string" ) {
-
-			// ( types, selector, fn )
-			fn = data;
-			data = undefined;
-		} else {
-
-			// ( types, data, fn )
-			fn = data;
-			data = selector;
-			selector = undefined;
-		}
-	}
-	if ( fn === false ) {
-		fn = returnFalse;
-	} else if ( !fn ) {
-		return elem;
-	}
-
-	if ( one === 1 ) {
-		origFn = fn;
-		fn = function( event ) {
-
-			// Can use an empty set, since event contains the info
-			jQuery().off( event );
-			return origFn.apply( this, arguments );
-		};
-
-		// Use same guid so caller can remove using origFn
-		fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ );
-	}
-	return elem.each( function() {
-		jQuery.event.add( this, types, fn, data, selector );
-	} );
-}
-
-/*
- * Helper functions for managing events -- not part of the public interface.
- * Props to Dean Edwards' addEvent library for many of the ideas.
- */
-jQuery.event = {
-
-	global: {},
-
-	add: function( elem, types, handler, data, selector ) {
-
-		var handleObjIn, eventHandle, tmp,
-			events, t, handleObj,
-			special, handlers, type, namespaces, origType,
-			elemData = dataPriv.get( elem );
-
-		// Don't attach events to noData or text/comment nodes (but allow plain objects)
-		if ( !elemData ) {
-			return;
-		}
-
-		// Caller can pass in an object of custom data in lieu of the handler
-		if ( handler.handler ) {
-			handleObjIn = handler;
-			handler = handleObjIn.handler;
-			selector = handleObjIn.selector;
-		}
-
-		// Ensure that invalid selectors throw exceptions at attach time
-		// Evaluate against documentElement in case elem is a non-element node (e.g., document)
-		if ( selector ) {
-			jQuery.find.matchesSelector( documentElement, selector );
-		}
-
-		// Make sure that the handler has a unique ID, used to find/remove it later
-		if ( !handler.guid ) {
-			handler.guid = jQuery.guid++;
-		}
-
-		// Init the element's event structure and main handler, if this is the first
-		if ( !( events = elemData.events ) ) {
-			events = elemData.events = {};
-		}
-		if ( !( eventHandle = elemData.handle ) ) {
-			eventHandle = elemData.handle = function( e ) {
-
-				// Discard the second event of a jQuery.event.trigger() and
-				// when an event is called after a page has unloaded
-				return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ?
-					jQuery.event.dispatch.apply( elem, arguments ) : undefined;
-			};
-		}
-
-		// Handle multiple events separated by a space
-		types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
-		t = types.length;
-		while ( t-- ) {
-			tmp = rtypenamespace.exec( types[ t ] ) || [];
-			type = origType = tmp[ 1 ];
-			namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
-
-			// There *must* be a type, no attaching namespace-only handlers
-			if ( !type ) {
-				continue;
-			}
-
-			// If event changes its type, use the special event handlers for the changed type
-			special = jQuery.event.special[ type ] || {};
-
-			// If selector defined, determine special event api type, otherwise given type
-			type = ( selector ? special.delegateType : special.bindType ) || type;
-
-			// Update special based on newly reset type
-			special = jQuery.event.special[ type ] || {};
-
-			// handleObj is passed to all event handlers
-			handleObj = jQuery.extend( {
-				type: type,
-				origType: origType,
-				data: data,
-				handler: handler,
-				guid: handler.guid,
-				selector: selector,
-				needsContext: selector && jQuery.expr.match.needsContext.test( selector ),
-				namespace: namespaces.join( "." )
-			}, handleObjIn );
-
-			// Init the event handler queue if we're the first
-			if ( !( handlers = events[ type ] ) ) {
-				handlers = events[ type ] = [];
-				handlers.delegateCount = 0;
-
-				// Only use addEventListener if the special events handler returns false
-				if ( !special.setup ||
-					special.setup.call( elem, data, namespaces, eventHandle ) === false ) {
-
-					if ( elem.addEventListener ) {
-						elem.addEventListener( type, eventHandle );
-					}
-				}
-			}
-
-			if ( special.add ) {
-				special.add.call( elem, handleObj );
-
-				if ( !handleObj.handler.guid ) {
-					handleObj.handler.guid = handler.guid;
-				}
-			}
-
-			// Add to the element's handler list, delegates in front
-			if ( selector ) {
-				handlers.splice( handlers.delegateCount++, 0, handleObj );
-			} else {
-				handlers.push( handleObj );
-			}
-
-			// Keep track of which events have ever been used, for event optimization
-			jQuery.event.global[ type ] = true;
-		}
-
-	},
-
-	// Detach an event or set of events from an element
-	remove: function( elem, types, handler, selector, mappedTypes ) {
-
-		var j, origCount, tmp,
-			events, t, handleObj,
-			special, handlers, type, namespaces, origType,
-			elemData = dataPriv.hasData( elem ) && dataPriv.get( elem );
-
-		if ( !elemData || !( events = elemData.events ) ) {
-			return;
-		}
-
-		// Once for each type.namespace in types; type may be omitted
-		types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
-		t = types.length;
-		while ( t-- ) {
-			tmp = rtypenamespace.exec( types[ t ] ) || [];
-			type = origType = tmp[ 1 ];
-			namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
-
-			// Unbind all events (on this namespace, if provided) for the element
-			if ( !type ) {
-				for ( type in events ) {
-					jQuery.event.remove( elem, type + types[ t ], handler, selector, true );
-				}
-				continue;
-			}
-
-			special = jQuery.event.special[ type ] || {};
-			type = ( selector ? special.delegateType : special.bindType ) || type;
-			handlers = events[ type ] || [];
-			tmp = tmp[ 2 ] &&
-				new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" );
-
-			// Remove matching events
-			origCount = j = handlers.length;
-			while ( j-- ) {
-				handleObj = handlers[ j ];
-
-				if ( ( mappedTypes || origType === handleObj.origType ) &&
-					( !handler || handler.guid === handleObj.guid ) &&
-					( !tmp || tmp.test( handleObj.namespace ) ) &&
-					( !selector || selector === handleObj.selector ||
-						selector === "**" && handleObj.selector ) ) {
-					handlers.splice( j, 1 );
-
-					if ( handleObj.selector ) {
-						handlers.delegateCount--;
-					}
-					if ( special.remove ) {
-						special.remove.call( elem, handleObj );
-					}
-				}
-			}
-
-			// Remove generic event handler if we removed something and no more handlers exist
-			// (avoids potential for endless recursion during removal of special event handlers)
-			if ( origCount && !handlers.length ) {
-				if ( !special.teardown ||
-					special.teardown.call( elem, namespaces, elemData.handle ) === false ) {
-
-					jQuery.removeEvent( elem, type, elemData.handle );
-				}
-
-				delete events[ type ];
-			}
-		}
-
-		// Remove data and the expando if it's no longer used
-		if ( jQuery.isEmptyObject( events ) ) {
-			dataPriv.remove( elem, "handle events" );
-		}
-	},
-
-	dispatch: function( nativeEvent ) {
-
-		// Make a writable jQuery.Event from the native event object
-		var event = jQuery.event.fix( nativeEvent );
-
-		var i, j, ret, matched, handleObj, handlerQueue,
-			args = new Array( arguments.length ),
-			handlers = ( dataPriv.get( this, "events" ) || {} )[ event.type ] || [],
-			special = jQuery.event.special[ event.type ] || {};
-
-		// Use the fix-ed jQuery.Event rather than the (read-only) native event
-		args[ 0 ] = event;
-
-		for ( i = 1; i < arguments.length; i++ ) {
-			args[ i ] = arguments[ i ];
-		}
-
-		event.delegateTarget = this;
-
-		// Call the preDispatch hook for the mapped type, and let it bail if desired
-		if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) {
-			return;
-		}
-
-		// Determine handlers
-		handlerQueue = jQuery.event.handlers.call( this, event, handlers );
-
-		// Run delegates first; they may want to stop propagation beneath us
-		i = 0;
-		while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) {
-			event.currentTarget = matched.elem;
-
-			j = 0;
-			while ( ( handleObj = matched.handlers[ j++ ] ) &&
-				!event.isImmediatePropagationStopped() ) {
-
-				// Triggered event must either 1) have no namespace, or 2) have namespace(s)
-				// a subset or equal to those in the bound event (both can have no namespace).
-				if ( !event.rnamespace || event.rnamespace.test( handleObj.namespace ) ) {
-
-					event.handleObj = handleObj;
-					event.data = handleObj.data;
-
-					ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle ||
-						handleObj.handler ).apply( matched.elem, args );
-
-					if ( ret !== undefined ) {
-						if ( ( event.result = ret ) === false ) {
-							event.preventDefault();
-							event.stopPropagation();
-						}
-					}
-				}
-			}
-		}
-
-		// Call the postDispatch hook for the mapped type
-		if ( special.postDispatch ) {
-			special.postDispatch.call( this, event );
-		}
-
-		return event.result;
-	},
-
-	handlers: function( event, handlers ) {
-		var i, handleObj, sel, matchedHandlers, matchedSelectors,
-			handlerQueue = [],
-			delegateCount = handlers.delegateCount,
-			cur = event.target;
-
-		// Find delegate handlers
-		if ( delegateCount &&
-
-			// Support: IE <=9
-			// Black-hole SVG  instance trees (trac-13180)
-			cur.nodeType &&
-
-			// Support: Firefox <=42
-			// Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861)
-			// https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click
-			// Support: IE 11 only
-			// ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343)
-			!( event.type === "click" && event.button >= 1 ) ) {
-
-			for ( ; cur !== this; cur = cur.parentNode || this ) {
-
-				// Don't check non-elements (#13208)
-				// Don't process clicks on disabled elements (#6911, #8165, #11382, #11764)
-				if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) {
-					matchedHandlers = [];
-					matchedSelectors = {};
-					for ( i = 0; i < delegateCount; i++ ) {
-						handleObj = handlers[ i ];
-
-						// Don't conflict with Object.prototype properties (#13203)
-						sel = handleObj.selector + " ";
-
-						if ( matchedSelectors[ sel ] === undefined ) {
-							matchedSelectors[ sel ] = handleObj.needsContext ?
-								jQuery( sel, this ).index( cur ) > -1 :
-								jQuery.find( sel, this, null, [ cur ] ).length;
-						}
-						if ( matchedSelectors[ sel ] ) {
-							matchedHandlers.push( handleObj );
-						}
-					}
-					if ( matchedHandlers.length ) {
-						handlerQueue.push( { elem: cur, handlers: matchedHandlers } );
-					}
-				}
-			}
-		}
-
-		// Add the remaining (directly-bound) handlers
-		cur = this;
-		if ( delegateCount < handlers.length ) {
-			handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } );
-		}
-
-		return handlerQueue;
-	},
-
-	addProp: function( name, hook ) {
-		Object.defineProperty( jQuery.Event.prototype, name, {
-			enumerable: true,
-			configurable: true,
-
-			get: isFunction( hook ) ?
-				function() {
-					if ( this.originalEvent ) {
-							return hook( this.originalEvent );
-					}
-				} :
-				function() {
-					if ( this.originalEvent ) {
-							return this.originalEvent[ name ];
-					}
-				},
-
-			set: function( value ) {
-				Object.defineProperty( this, name, {
-					enumerable: true,
-					configurable: true,
-					writable: true,
-					value: value
-				} );
-			}
-		} );
-	},
-
-	fix: function( originalEvent ) {
-		return originalEvent[ jQuery.expando ] ?
-			originalEvent :
-			new jQuery.Event( originalEvent );
-	},
-
-	special: {
-		load: {
-
-			// Prevent triggered image.load events from bubbling to window.load
-			noBubble: true
-		},
-		focus: {
-
-			// Fire native event if possible so blur/focus sequence is correct
-			trigger: function() {
-				if ( this !== safeActiveElement() && this.focus ) {
-					this.focus();
-					return false;
-				}
-			},
-			delegateType: "focusin"
-		},
-		blur: {
-			trigger: function() {
-				if ( this === safeActiveElement() && this.blur ) {
-					this.blur();
-					return false;
-				}
-			},
-			delegateType: "focusout"
-		},
-		click: {
-
-			// For checkbox, fire native event so checked state will be right
-			trigger: function() {
-				if ( this.type === "checkbox" && this.click && nodeName( this, "input" ) ) {
-					this.click();
-					return false;
-				}
-			},
-
-			// For cross-browser consistency, don't fire native .click() on links
-			_default: function( event ) {
-				return nodeName( event.target, "a" );
-			}
-		},
-
-		beforeunload: {
-			postDispatch: function( event ) {
-
-				// Support: Firefox 20+
-				// Firefox doesn't alert if the returnValue field is not set.
-				if ( event.result !== undefined && event.originalEvent ) {
-					event.originalEvent.returnValue = event.result;
-				}
-			}
-		}
-	}
-};
-
-jQuery.removeEvent = function( elem, type, handle ) {
-
-	// This "if" is needed for plain objects
-	if ( elem.removeEventListener ) {
-		elem.removeEventListener( type, handle );
-	}
-};
-
-jQuery.Event = function( src, props ) {
-
-	// Allow instantiation without the 'new' keyword
-	if ( !( this instanceof jQuery.Event ) ) {
-		return new jQuery.Event( src, props );
-	}
-
-	// Event object
-	if ( src && src.type ) {
-		this.originalEvent = src;
-		this.type = src.type;
-
-		// Events bubbling up the document may have been marked as prevented
-		// by a handler lower down the tree; reflect the correct value.
-		this.isDefaultPrevented = src.defaultPrevented ||
-				src.defaultPrevented === undefined &&
-
-				// Support: Android <=2.3 only
-				src.returnValue === false ?
-			returnTrue :
-			returnFalse;
-
-		// Create target properties
-		// Support: Safari <=6 - 7 only
-		// Target should not be a text node (#504, #13143)
-		this.target = ( src.target && src.target.nodeType === 3 ) ?
-			src.target.parentNode :
-			src.target;
-
-		this.currentTarget = src.currentTarget;
-		this.relatedTarget = src.relatedTarget;
-
-	// Event type
-	} else {
-		this.type = src;
-	}
-
-	// Put explicitly provided properties onto the event object
-	if ( props ) {
-		jQuery.extend( this, props );
-	}
-
-	// Create a timestamp if incoming event doesn't have one
-	this.timeStamp = src && src.timeStamp || Date.now();
-
-	// Mark it as fixed
-	this[ jQuery.expando ] = true;
-};
-
-// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding
-// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html
-jQuery.Event.prototype = {
-	constructor: jQuery.Event,
-	isDefaultPrevented: returnFalse,
-	isPropagationStopped: returnFalse,
-	isImmediatePropagationStopped: returnFalse,
-	isSimulated: false,
-
-	preventDefault: function() {
-		var e = this.originalEvent;
-
-		this.isDefaultPrevented = returnTrue;
-
-		if ( e && !this.isSimulated ) {
-			e.preventDefault();
-		}
-	},
-	stopPropagation: function() {
-		var e = this.originalEvent;
-
-		this.isPropagationStopped = returnTrue;
-
-		if ( e && !this.isSimulated ) {
-			e.stopPropagation();
-		}
-	},
-	stopImmediatePropagation: function() {
-		var e = this.originalEvent;
-
-		this.isImmediatePropagationStopped = returnTrue;
-
-		if ( e && !this.isSimulated ) {
-			e.stopImmediatePropagation();
-		}
-
-		this.stopPropagation();
-	}
-};
-
-// Includes all common event props including KeyEvent and MouseEvent specific props
-jQuery.each( {
-	altKey: true,
-	bubbles: true,
-	cancelable: true,
-	changedTouches: true,
-	ctrlKey: true,
-	detail: true,
-	eventPhase: true,
-	metaKey: true,
-	pageX: true,
-	pageY: true,
-	shiftKey: true,
-	view: true,
-	"char": true,
-	charCode: true,
-	key: true,
-	keyCode: true,
-	button: true,
-	buttons: true,
-	clientX: true,
-	clientY: true,
-	offsetX: true,
-	offsetY: true,
-	pointerId: true,
-	pointerType: true,
-	screenX: true,
-	screenY: true,
-	targetTouches: true,
-	toElement: true,
-	touches: true,
-
-	which: function( event ) {
-		var button = event.button;
-
-		// Add which for key events
-		if ( event.which == null && rkeyEvent.test( event.type ) ) {
-			return event.charCode != null ? event.charCode : event.keyCode;
-		}
-
-		// Add which for click: 1 === left; 2 === middle; 3 === right
-		if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) {
-			if ( button & 1 ) {
-				return 1;
-			}
-
-			if ( button & 2 ) {
-				return 3;
-			}
-
-			if ( button & 4 ) {
-				return 2;
-			}
-
-			return 0;
-		}
-
-		return event.which;
-	}
-}, jQuery.event.addProp );
-
-// Create mouseenter/leave events using mouseover/out and event-time checks
-// so that event delegation works in jQuery.
-// Do the same for pointerenter/pointerleave and pointerover/pointerout
-//
-// Support: Safari 7 only
-// Safari sends mouseenter too often; see:
-// https://bugs.chromium.org/p/chromium/issues/detail?id=470258
-// for the description of the bug (it existed in older Chrome versions as well).
-jQuery.each( {
-	mouseenter: "mouseover",
-	mouseleave: "mouseout",
-	pointerenter: "pointerover",
-	pointerleave: "pointerout"
-}, function( orig, fix ) {
-	jQuery.event.special[ orig ] = {
-		delegateType: fix,
-		bindType: fix,
-
-		handle: function( event ) {
-			var ret,
-				target = this,
-				related = event.relatedTarget,
-				handleObj = event.handleObj;
-
-			// For mouseenter/leave call the handler if related is outside the target.
-			// NB: No relatedTarget if the mouse left/entered the browser window
-			if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) {
-				event.type = handleObj.origType;
-				ret = handleObj.handler.apply( this, arguments );
-				event.type = fix;
-			}
-			return ret;
-		}
-	};
-} );
-
-jQuery.fn.extend( {
-
-	on: function( types, selector, data, fn ) {
-		return on( this, types, selector, data, fn );
-	},
-	one: function( types, selector, data, fn ) {
-		return on( this, types, selector, data, fn, 1 );
-	},
-	off: function( types, selector, fn ) {
-		var handleObj, type;
-		if ( types && types.preventDefault && types.handleObj ) {
-
-			// ( event )  dispatched jQuery.Event
-			handleObj = types.handleObj;
-			jQuery( types.delegateTarget ).off(
-				handleObj.namespace ?
-					handleObj.origType + "." + handleObj.namespace :
-					handleObj.origType,
-				handleObj.selector,
-				handleObj.handler
-			);
-			return this;
-		}
-		if ( typeof types === "object" ) {
-
-			// ( types-object [, selector] )
-			for ( type in types ) {
-				this.off( type, selector, types[ type ] );
-			}
-			return this;
-		}
-		if ( selector === false || typeof selector === "function" ) {
-
-			// ( types [, fn] )
-			fn = selector;
-			selector = undefined;
-		}
-		if ( fn === false ) {
-			fn = returnFalse;
-		}
-		return this.each( function() {
-			jQuery.event.remove( this, types, fn, selector );
-		} );
-	}
-} );
-
-
-var
-
-	/* eslint-disable max-len */
-
-	// See https://github.com/eslint/eslint/issues/3229
-	rxhtmlTag = /<(?!area|br|col|embed|hr|img|input|link|meta|param)(([a-z][^\/\0>\x20\t\r\n\f]*)[^>]*)\/>/gi,
-
-	/* eslint-enable */
-
-	// Support: IE <=10 - 11, Edge 12 - 13 only
-	// In IE/Edge using regex groups here causes severe slowdowns.
-	// See https://connect.microsoft.com/IE/feedback/details/1736512/
-	rnoInnerhtml = /\s*$/g;
-
-// Prefer a tbody over its parent table for containing new rows
-function manipulationTarget( elem, content ) {
-	if ( nodeName( elem, "table" ) &&
-		nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) {
-
-		return jQuery( elem ).children( "tbody" )[ 0 ] || elem;
-	}
-
-	return elem;
-}
-
-// Replace/restore the type attribute of script elements for safe DOM manipulation
-function disableScript( elem ) {
-	elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type;
-	return elem;
-}
-function restoreScript( elem ) {
-	if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) {
-		elem.type = elem.type.slice( 5 );
-	} else {
-		elem.removeAttribute( "type" );
-	}
-
-	return elem;
-}
-
-function cloneCopyEvent( src, dest ) {
-	var i, l, type, pdataOld, pdataCur, udataOld, udataCur, events;
-
-	if ( dest.nodeType !== 1 ) {
-		return;
-	}
-
-	// 1. Copy private data: events, handlers, etc.
-	if ( dataPriv.hasData( src ) ) {
-		pdataOld = dataPriv.access( src );
-		pdataCur = dataPriv.set( dest, pdataOld );
-		events = pdataOld.events;
-
-		if ( events ) {
-			delete pdataCur.handle;
-			pdataCur.events = {};
-
-			for ( type in events ) {
-				for ( i = 0, l = events[ type ].length; i < l; i++ ) {
-					jQuery.event.add( dest, type, events[ type ][ i ] );
-				}
-			}
-		}
-	}
-
-	// 2. Copy user data
-	if ( dataUser.hasData( src ) ) {
-		udataOld = dataUser.access( src );
-		udataCur = jQuery.extend( {}, udataOld );
-
-		dataUser.set( dest, udataCur );
-	}
-}
-
-// Fix IE bugs, see support tests
-function fixInput( src, dest ) {
-	var nodeName = dest.nodeName.toLowerCase();
-
-	// Fails to persist the checked state of a cloned checkbox or radio button.
-	if ( nodeName === "input" && rcheckableType.test( src.type ) ) {
-		dest.checked = src.checked;
-
-	// Fails to return the selected option to the default selected state when cloning options
-	} else if ( nodeName === "input" || nodeName === "textarea" ) {
-		dest.defaultValue = src.defaultValue;
-	}
-}
-
-function domManip( collection, args, callback, ignored ) {
-
-	// Flatten any nested arrays
-	args = concat.apply( [], args );
-
-	var fragment, first, scripts, hasScripts, node, doc,
-		i = 0,
-		l = collection.length,
-		iNoClone = l - 1,
-		value = args[ 0 ],
-		valueIsFunction = isFunction( value );
-
-	// We can't cloneNode fragments that contain checked, in WebKit
-	if ( valueIsFunction ||
-			( l > 1 && typeof value === "string" &&
-				!support.checkClone && rchecked.test( value ) ) ) {
-		return collection.each( function( index ) {
-			var self = collection.eq( index );
-			if ( valueIsFunction ) {
-				args[ 0 ] = value.call( this, index, self.html() );
-			}
-			domManip( self, args, callback, ignored );
-		} );
-	}
-
-	if ( l ) {
-		fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored );
-		first = fragment.firstChild;
-
-		if ( fragment.childNodes.length === 1 ) {
-			fragment = first;
-		}
-
-		// Require either new content or an interest in ignored elements to invoke the callback
-		if ( first || ignored ) {
-			scripts = jQuery.map( getAll( fragment, "script" ), disableScript );
-			hasScripts = scripts.length;
-
-			// Use the original fragment for the last item
-			// instead of the first because it can end up
-			// being emptied incorrectly in certain situations (#8070).
-			for ( ; i < l; i++ ) {
-				node = fragment;
-
-				if ( i !== iNoClone ) {
-					node = jQuery.clone( node, true, true );
-
-					// Keep references to cloned scripts for later restoration
-					if ( hasScripts ) {
-
-						// Support: Android <=4.0 only, PhantomJS 1 only
-						// push.apply(_, arraylike) throws on ancient WebKit
-						jQuery.merge( scripts, getAll( node, "script" ) );
-					}
-				}
-
-				callback.call( collection[ i ], node, i );
-			}
-
-			if ( hasScripts ) {
-				doc = scripts[ scripts.length - 1 ].ownerDocument;
-
-				// Reenable scripts
-				jQuery.map( scripts, restoreScript );
-
-				// Evaluate executable scripts on first document insertion
-				for ( i = 0; i < hasScripts; i++ ) {
-					node = scripts[ i ];
-					if ( rscriptType.test( node.type || "" ) &&
-						!dataPriv.access( node, "globalEval" ) &&
-						jQuery.contains( doc, node ) ) {
-
-						if ( node.src && ( node.type || "" ).toLowerCase()  !== "module" ) {
-
-							// Optional AJAX dependency, but won't run scripts if not present
-							if ( jQuery._evalUrl ) {
-								jQuery._evalUrl( node.src );
-							}
-						} else {
-							DOMEval( node.textContent.replace( rcleanScript, "" ), doc, node );
-						}
-					}
-				}
-			}
-		}
-	}
-
-	return collection;
-}
-
-function remove( elem, selector, keepData ) {
-	var node,
-		nodes = selector ? jQuery.filter( selector, elem ) : elem,
-		i = 0;
-
-	for ( ; ( node = nodes[ i ] ) != null; i++ ) {
-		if ( !keepData && node.nodeType === 1 ) {
-			jQuery.cleanData( getAll( node ) );
-		}
-
-		if ( node.parentNode ) {
-			if ( keepData && jQuery.contains( node.ownerDocument, node ) ) {
-				setGlobalEval( getAll( node, "script" ) );
-			}
-			node.parentNode.removeChild( node );
-		}
-	}
-
-	return elem;
-}
-
-jQuery.extend( {
-	htmlPrefilter: function( html ) {
-		return html.replace( rxhtmlTag, "<$1>" );
-	},
-
-	clone: function( elem, dataAndEvents, deepDataAndEvents ) {
-		var i, l, srcElements, destElements,
-			clone = elem.cloneNode( true ),
-			inPage = jQuery.contains( elem.ownerDocument, elem );
-
-		// Fix IE cloning issues
-		if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) &&
-				!jQuery.isXMLDoc( elem ) ) {
-
-			// We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2
-			destElements = getAll( clone );
-			srcElements = getAll( elem );
-
-			for ( i = 0, l = srcElements.length; i < l; i++ ) {
-				fixInput( srcElements[ i ], destElements[ i ] );
-			}
-		}
-
-		// Copy the events from the original to the clone
-		if ( dataAndEvents ) {
-			if ( deepDataAndEvents ) {
-				srcElements = srcElements || getAll( elem );
-				destElements = destElements || getAll( clone );
-
-				for ( i = 0, l = srcElements.length; i < l; i++ ) {
-					cloneCopyEvent( srcElements[ i ], destElements[ i ] );
-				}
-			} else {
-				cloneCopyEvent( elem, clone );
-			}
-		}
-
-		// Preserve script evaluation history
-		destElements = getAll( clone, "script" );
-		if ( destElements.length > 0 ) {
-			setGlobalEval( destElements, !inPage && getAll( elem, "script" ) );
-		}
-
-		// Return the cloned set
-		return clone;
-	},
-
-	cleanData: function( elems ) {
-		var data, elem, type,
-			special = jQuery.event.special,
-			i = 0;
-
-		for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) {
-			if ( acceptData( elem ) ) {
-				if ( ( data = elem[ dataPriv.expando ] ) ) {
-					if ( data.events ) {
-						for ( type in data.events ) {
-							if ( special[ type ] ) {
-								jQuery.event.remove( elem, type );
-
-							// This is a shortcut to avoid jQuery.event.remove's overhead
-							} else {
-								jQuery.removeEvent( elem, type, data.handle );
-							}
-						}
-					}
-
-					// Support: Chrome <=35 - 45+
-					// Assign undefined instead of using delete, see Data#remove
-					elem[ dataPriv.expando ] = undefined;
-				}
-				if ( elem[ dataUser.expando ] ) {
-
-					// Support: Chrome <=35 - 45+
-					// Assign undefined instead of using delete, see Data#remove
-					elem[ dataUser.expando ] = undefined;
-				}
-			}
-		}
-	}
-} );
-
-jQuery.fn.extend( {
-	detach: function( selector ) {
-		return remove( this, selector, true );
-	},
-
-	remove: function( selector ) {
-		return remove( this, selector );
-	},
-
-	text: function( value ) {
-		return access( this, function( value ) {
-			return value === undefined ?
-				jQuery.text( this ) :
-				this.empty().each( function() {
-					if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
-						this.textContent = value;
-					}
-				} );
-		}, null, value, arguments.length );
-	},
-
-	append: function() {
-		return domManip( this, arguments, function( elem ) {
-			if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
-				var target = manipulationTarget( this, elem );
-				target.appendChild( elem );
-			}
-		} );
-	},
-
-	prepend: function() {
-		return domManip( this, arguments, function( elem ) {
-			if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
-				var target = manipulationTarget( this, elem );
-				target.insertBefore( elem, target.firstChild );
-			}
-		} );
-	},
-
-	before: function() {
-		return domManip( this, arguments, function( elem ) {
-			if ( this.parentNode ) {
-				this.parentNode.insertBefore( elem, this );
-			}
-		} );
-	},
-
-	after: function() {
-		return domManip( this, arguments, function( elem ) {
-			if ( this.parentNode ) {
-				this.parentNode.insertBefore( elem, this.nextSibling );
-			}
-		} );
-	},
-
-	empty: function() {
-		var elem,
-			i = 0;
-
-		for ( ; ( elem = this[ i ] ) != null; i++ ) {
-			if ( elem.nodeType === 1 ) {
-
-				// Prevent memory leaks
-				jQuery.cleanData( getAll( elem, false ) );
-
-				// Remove any remaining nodes
-				elem.textContent = "";
-			}
-		}
-
-		return this;
-	},
-
-	clone: function( dataAndEvents, deepDataAndEvents ) {
-		dataAndEvents = dataAndEvents == null ? false : dataAndEvents;
-		deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents;
-
-		return this.map( function() {
-			return jQuery.clone( this, dataAndEvents, deepDataAndEvents );
-		} );
-	},
-
-	html: function( value ) {
-		return access( this, function( value ) {
-			var elem = this[ 0 ] || {},
-				i = 0,
-				l = this.length;
-
-			if ( value === undefined && elem.nodeType === 1 ) {
-				return elem.innerHTML;
-			}
-
-			// See if we can take a shortcut and just use innerHTML
-			if ( typeof value === "string" && !rnoInnerhtml.test( value ) &&
-				!wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) {
-
-				value = jQuery.htmlPrefilter( value );
-
-				try {
-					for ( ; i < l; i++ ) {
-						elem = this[ i ] || {};
-
-						// Remove element nodes and prevent memory leaks
-						if ( elem.nodeType === 1 ) {
-							jQuery.cleanData( getAll( elem, false ) );
-							elem.innerHTML = value;
-						}
-					}
-
-					elem = 0;
-
-				// If using innerHTML throws an exception, use the fallback method
-				} catch ( e ) {}
-			}
-
-			if ( elem ) {
-				this.empty().append( value );
-			}
-		}, null, value, arguments.length );
-	},
-
-	replaceWith: function() {
-		var ignored = [];
-
-		// Make the changes, replacing each non-ignored context element with the new content
-		return domManip( this, arguments, function( elem ) {
-			var parent = this.parentNode;
-
-			if ( jQuery.inArray( this, ignored ) < 0 ) {
-				jQuery.cleanData( getAll( this ) );
-				if ( parent ) {
-					parent.replaceChild( elem, this );
-				}
-			}
-
-		// Force callback invocation
-		}, ignored );
-	}
-} );
-
-jQuery.each( {
-	appendTo: "append",
-	prependTo: "prepend",
-	insertBefore: "before",
-	insertAfter: "after",
-	replaceAll: "replaceWith"
-}, function( name, original ) {
-	jQuery.fn[ name ] = function( selector ) {
-		var elems,
-			ret = [],
-			insert = jQuery( selector ),
-			last = insert.length - 1,
-			i = 0;
-
-		for ( ; i <= last; i++ ) {
-			elems = i === last ? this : this.clone( true );
-			jQuery( insert[ i ] )[ original ]( elems );
-
-			// Support: Android <=4.0 only, PhantomJS 1 only
-			// .get() because push.apply(_, arraylike) throws on ancient WebKit
-			push.apply( ret, elems.get() );
-		}
-
-		return this.pushStack( ret );
-	};
-} );
-var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" );
-
-var getStyles = function( elem ) {
-
-		// Support: IE <=11 only, Firefox <=30 (#15098, #14150)
-		// IE throws on elements created in popups
-		// FF meanwhile throws on frame elements through "defaultView.getComputedStyle"
-		var view = elem.ownerDocument.defaultView;
-
-		if ( !view || !view.opener ) {
-			view = window;
-		}
-
-		return view.getComputedStyle( elem );
-	};
-
-var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" );
-
-
-
-( function() {
-
-	// Executing both pixelPosition & boxSizingReliable tests require only one layout
-	// so they're executed at the same time to save the second computation.
-	function computeStyleTests() {
-
-		// This is a singleton, we need to execute it only once
-		if ( !div ) {
-			return;
-		}
-
-		container.style.cssText = "position:absolute;left:-11111px;width:60px;" +
-			"margin-top:1px;padding:0;border:0";
-		div.style.cssText =
-			"position:relative;display:block;box-sizing:border-box;overflow:scroll;" +
-			"margin:auto;border:1px;padding:1px;" +
-			"width:60%;top:1%";
-		documentElement.appendChild( container ).appendChild( div );
-
-		var divStyle = window.getComputedStyle( div );
-		pixelPositionVal = divStyle.top !== "1%";
-
-		// Support: Android 4.0 - 4.3 only, Firefox <=3 - 44
-		reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12;
-
-		// Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3
-		// Some styles come back with percentage values, even though they shouldn't
-		div.style.right = "60%";
-		pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36;
-
-		// Support: IE 9 - 11 only
-		// Detect misreporting of content dimensions for box-sizing:border-box elements
-		boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36;
-
-		// Support: IE 9 only
-		// Detect overflow:scroll screwiness (gh-3699)
-		div.style.position = "absolute";
-		scrollboxSizeVal = div.offsetWidth === 36 || "absolute";
-
-		documentElement.removeChild( container );
-
-		// Nullify the div so it wouldn't be stored in the memory and
-		// it will also be a sign that checks already performed
-		div = null;
-	}
-
-	function roundPixelMeasures( measure ) {
-		return Math.round( parseFloat( measure ) );
-	}
-
-	var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal,
-		reliableMarginLeftVal,
-		container = document.createElement( "div" ),
-		div = document.createElement( "div" );
-
-	// Finish early in limited (non-browser) environments
-	if ( !div.style ) {
-		return;
-	}
-
-	// Support: IE <=9 - 11 only
-	// Style of cloned element affects source element cloned (#8908)
-	div.style.backgroundClip = "content-box";
-	div.cloneNode( true ).style.backgroundClip = "";
-	support.clearCloneStyle = div.style.backgroundClip === "content-box";
-
-	jQuery.extend( support, {
-		boxSizingReliable: function() {
-			computeStyleTests();
-			return boxSizingReliableVal;
-		},
-		pixelBoxStyles: function() {
-			computeStyleTests();
-			return pixelBoxStylesVal;
-		},
-		pixelPosition: function() {
-			computeStyleTests();
-			return pixelPositionVal;
-		},
-		reliableMarginLeft: function() {
-			computeStyleTests();
-			return reliableMarginLeftVal;
-		},
-		scrollboxSize: function() {
-			computeStyleTests();
-			return scrollboxSizeVal;
-		}
-	} );
-} )();
-
-
-function curCSS( elem, name, computed ) {
-	var width, minWidth, maxWidth, ret,
-
-		// Support: Firefox 51+
-		// Retrieving style before computed somehow
-		// fixes an issue with getting wrong values
-		// on detached elements
-		style = elem.style;
-
-	computed = computed || getStyles( elem );
-
-	// getPropertyValue is needed for:
-	//   .css('filter') (IE 9 only, #12537)
-	//   .css('--customProperty) (#3144)
-	if ( computed ) {
-		ret = computed.getPropertyValue( name ) || computed[ name ];
-
-		if ( ret === "" && !jQuery.contains( elem.ownerDocument, elem ) ) {
-			ret = jQuery.style( elem, name );
-		}
-
-		// A tribute to the "awesome hack by Dean Edwards"
-		// Android Browser returns percentage for some values,
-		// but width seems to be reliably pixels.
-		// This is against the CSSOM draft spec:
-		// https://drafts.csswg.org/cssom/#resolved-values
-		if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) {
-
-			// Remember the original values
-			width = style.width;
-			minWidth = style.minWidth;
-			maxWidth = style.maxWidth;
-
-			// Put in the new values to get a computed value out
-			style.minWidth = style.maxWidth = style.width = ret;
-			ret = computed.width;
-
-			// Revert the changed values
-			style.width = width;
-			style.minWidth = minWidth;
-			style.maxWidth = maxWidth;
-		}
-	}
-
-	return ret !== undefined ?
-
-		// Support: IE <=9 - 11 only
-		// IE returns zIndex value as an integer.
-		ret + "" :
-		ret;
-}
-
-
-function addGetHookIf( conditionFn, hookFn ) {
-
-	// Define the hook, we'll check on the first run if it's really needed.
-	return {
-		get: function() {
-			if ( conditionFn() ) {
-
-				// Hook not needed (or it's not possible to use it due
-				// to missing dependency), remove it.
-				delete this.get;
-				return;
-			}
-
-			// Hook needed; redefine it so that the support test is not executed again.
-			return ( this.get = hookFn ).apply( this, arguments );
-		}
-	};
-}
-
-
-var
-
-	// Swappable if display is none or starts with table
-	// except "table", "table-cell", or "table-caption"
-	// See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display
-	rdisplayswap = /^(none|table(?!-c[ea]).+)/,
-	rcustomProp = /^--/,
-	cssShow = { position: "absolute", visibility: "hidden", display: "block" },
-	cssNormalTransform = {
-		letterSpacing: "0",
-		fontWeight: "400"
-	},
-
-	cssPrefixes = [ "Webkit", "Moz", "ms" ],
-	emptyStyle = document.createElement( "div" ).style;
-
-// Return a css property mapped to a potentially vendor prefixed property
-function vendorPropName( name ) {
-
-	// Shortcut for names that are not vendor prefixed
-	if ( name in emptyStyle ) {
-		return name;
-	}
-
-	// Check for vendor prefixed names
-	var capName = name[ 0 ].toUpperCase() + name.slice( 1 ),
-		i = cssPrefixes.length;
-
-	while ( i-- ) {
-		name = cssPrefixes[ i ] + capName;
-		if ( name in emptyStyle ) {
-			return name;
-		}
-	}
-}
-
-// Return a property mapped along what jQuery.cssProps suggests or to
-// a vendor prefixed property.
-function finalPropName( name ) {
-	var ret = jQuery.cssProps[ name ];
-	if ( !ret ) {
-		ret = jQuery.cssProps[ name ] = vendorPropName( name ) || name;
-	}
-	return ret;
-}
-
-function setPositiveNumber( elem, value, subtract ) {
-
-	// Any relative (+/-) values have already been
-	// normalized at this point
-	var matches = rcssNum.exec( value );
-	return matches ?
-
-		// Guard against undefined "subtract", e.g., when used as in cssHooks
-		Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) :
-		value;
-}
-
-function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) {
-	var i = dimension === "width" ? 1 : 0,
-		extra = 0,
-		delta = 0;
-
-	// Adjustment may not be necessary
-	if ( box === ( isBorderBox ? "border" : "content" ) ) {
-		return 0;
-	}
-
-	for ( ; i < 4; i += 2 ) {
-
-		// Both box models exclude margin
-		if ( box === "margin" ) {
-			delta += jQuery.css( elem, box + cssExpand[ i ], true, styles );
-		}
-
-		// If we get here with a content-box, we're seeking "padding" or "border" or "margin"
-		if ( !isBorderBox ) {
-
-			// Add padding
-			delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
-
-			// For "border" or "margin", add border
-			if ( box !== "padding" ) {
-				delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
-
-			// But still keep track of it otherwise
-			} else {
-				extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
-			}
-
-		// If we get here with a border-box (content + padding + border), we're seeking "content" or
-		// "padding" or "margin"
-		} else {
-
-			// For "content", subtract padding
-			if ( box === "content" ) {
-				delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
-			}
-
-			// For "content" or "padding", subtract border
-			if ( box !== "margin" ) {
-				delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
-			}
-		}
-	}
-
-	// Account for positive content-box scroll gutter when requested by providing computedVal
-	if ( !isBorderBox && computedVal >= 0 ) {
-
-		// offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border
-		// Assuming integer scroll gutter, subtract the rest and round down
-		delta += Math.max( 0, Math.ceil(
-			elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
-			computedVal -
-			delta -
-			extra -
-			0.5
-		) );
-	}
-
-	return delta;
-}
-
-function getWidthOrHeight( elem, dimension, extra ) {
-
-	// Start with computed style
-	var styles = getStyles( elem ),
-		val = curCSS( elem, dimension, styles ),
-		isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
-		valueIsBorderBox = isBorderBox;
-
-	// Support: Firefox <=54
-	// Return a confounding non-pixel value or feign ignorance, as appropriate.
-	if ( rnumnonpx.test( val ) ) {
-		if ( !extra ) {
-			return val;
-		}
-		val = "auto";
-	}
-
-	// Check for style in case a browser which returns unreliable values
-	// for getComputedStyle silently falls back to the reliable elem.style
-	valueIsBorderBox = valueIsBorderBox &&
-		( support.boxSizingReliable() || val === elem.style[ dimension ] );
-
-	// Fall back to offsetWidth/offsetHeight when value is "auto"
-	// This happens for inline elements with no explicit setting (gh-3571)
-	// Support: Android <=4.1 - 4.3 only
-	// Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602)
-	if ( val === "auto" ||
-		!parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) {
-
-		val = elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ];
-
-		// offsetWidth/offsetHeight provide border-box values
-		valueIsBorderBox = true;
-	}
-
-	// Normalize "" and auto
-	val = parseFloat( val ) || 0;
-
-	// Adjust for the element's box model
-	return ( val +
-		boxModelAdjustment(
-			elem,
-			dimension,
-			extra || ( isBorderBox ? "border" : "content" ),
-			valueIsBorderBox,
-			styles,
-
-			// Provide the current computed size to request scroll gutter calculation (gh-3589)
-			val
-		)
-	) + "px";
-}
-
-jQuery.extend( {
-
-	// Add in style property hooks for overriding the default
-	// behavior of getting and setting a style property
-	cssHooks: {
-		opacity: {
-			get: function( elem, computed ) {
-				if ( computed ) {
-
-					// We should always get a number back from opacity
-					var ret = curCSS( elem, "opacity" );
-					return ret === "" ? "1" : ret;
-				}
-			}
-		}
-	},
-
-	// Don't automatically add "px" to these possibly-unitless properties
-	cssNumber: {
-		"animationIterationCount": true,
-		"columnCount": true,
-		"fillOpacity": true,
-		"flexGrow": true,
-		"flexShrink": true,
-		"fontWeight": true,
-		"lineHeight": true,
-		"opacity": true,
-		"order": true,
-		"orphans": true,
-		"widows": true,
-		"zIndex": true,
-		"zoom": true
-	},
-
-	// Add in properties whose names you wish to fix before
-	// setting or getting the value
-	cssProps: {},
-
-	// Get and set the style property on a DOM Node
-	style: function( elem, name, value, extra ) {
-
-		// Don't set styles on text and comment nodes
-		if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) {
-			return;
-		}
-
-		// Make sure that we're working with the right name
-		var ret, type, hooks,
-			origName = camelCase( name ),
-			isCustomProp = rcustomProp.test( name ),
-			style = elem.style;
-
-		// Make sure that we're working with the right name. We don't
-		// want to query the value if it is a CSS custom property
-		// since they are user-defined.
-		if ( !isCustomProp ) {
-			name = finalPropName( origName );
-		}
-
-		// Gets hook for the prefixed version, then unprefixed version
-		hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
-
-		// Check if we're setting a value
-		if ( value !== undefined ) {
-			type = typeof value;
-
-			// Convert "+=" or "-=" to relative numbers (#7345)
-			if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) {
-				value = adjustCSS( elem, name, ret );
-
-				// Fixes bug #9237
-				type = "number";
-			}
-
-			// Make sure that null and NaN values aren't set (#7116)
-			if ( value == null || value !== value ) {
-				return;
-			}
-
-			// If a number was passed in, add the unit (except for certain CSS properties)
-			if ( type === "number" ) {
-				value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" );
-			}
-
-			// background-* props affect original clone's values
-			if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) {
-				style[ name ] = "inherit";
-			}
-
-			// If a hook was provided, use that value, otherwise just set the specified value
-			if ( !hooks || !( "set" in hooks ) ||
-				( value = hooks.set( elem, value, extra ) ) !== undefined ) {
-
-				if ( isCustomProp ) {
-					style.setProperty( name, value );
-				} else {
-					style[ name ] = value;
-				}
-			}
-
-		} else {
-
-			// If a hook was provided get the non-computed value from there
-			if ( hooks && "get" in hooks &&
-				( ret = hooks.get( elem, false, extra ) ) !== undefined ) {
-
-				return ret;
-			}
-
-			// Otherwise just get the value from the style object
-			return style[ name ];
-		}
-	},
-
-	css: function( elem, name, extra, styles ) {
-		var val, num, hooks,
-			origName = camelCase( name ),
-			isCustomProp = rcustomProp.test( name );
-
-		// Make sure that we're working with the right name. We don't
-		// want to modify the value if it is a CSS custom property
-		// since they are user-defined.
-		if ( !isCustomProp ) {
-			name = finalPropName( origName );
-		}
-
-		// Try prefixed name followed by the unprefixed name
-		hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
-
-		// If a hook was provided get the computed value from there
-		if ( hooks && "get" in hooks ) {
-			val = hooks.get( elem, true, extra );
-		}
-
-		// Otherwise, if a way to get the computed value exists, use that
-		if ( val === undefined ) {
-			val = curCSS( elem, name, styles );
-		}
-
-		// Convert "normal" to computed value
-		if ( val === "normal" && name in cssNormalTransform ) {
-			val = cssNormalTransform[ name ];
-		}
-
-		// Make numeric if forced or a qualifier was provided and val looks numeric
-		if ( extra === "" || extra ) {
-			num = parseFloat( val );
-			return extra === true || isFinite( num ) ? num || 0 : val;
-		}
-
-		return val;
-	}
-} );
-
-jQuery.each( [ "height", "width" ], function( i, dimension ) {
-	jQuery.cssHooks[ dimension ] = {
-		get: function( elem, computed, extra ) {
-			if ( computed ) {
-
-				// Certain elements can have dimension info if we invisibly show them
-				// but it must have a current display style that would benefit
-				return rdisplayswap.test( jQuery.css( elem, "display" ) ) &&
-
-					// Support: Safari 8+
-					// Table columns in Safari have non-zero offsetWidth & zero
-					// getBoundingClientRect().width unless display is changed.
-					// Support: IE <=11 only
-					// Running getBoundingClientRect on a disconnected node
-					// in IE throws an error.
-					( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ?
-						swap( elem, cssShow, function() {
-							return getWidthOrHeight( elem, dimension, extra );
-						} ) :
-						getWidthOrHeight( elem, dimension, extra );
-			}
-		},
-
-		set: function( elem, value, extra ) {
-			var matches,
-				styles = getStyles( elem ),
-				isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
-				subtract = extra && boxModelAdjustment(
-					elem,
-					dimension,
-					extra,
-					isBorderBox,
-					styles
-				);
-
-			// Account for unreliable border-box dimensions by comparing offset* to computed and
-			// faking a content-box to get border and padding (gh-3699)
-			if ( isBorderBox && support.scrollboxSize() === styles.position ) {
-				subtract -= Math.ceil(
-					elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
-					parseFloat( styles[ dimension ] ) -
-					boxModelAdjustment( elem, dimension, "border", false, styles ) -
-					0.5
-				);
-			}
-
-			// Convert to pixels if value adjustment is needed
-			if ( subtract && ( matches = rcssNum.exec( value ) ) &&
-				( matches[ 3 ] || "px" ) !== "px" ) {
-
-				elem.style[ dimension ] = value;
-				value = jQuery.css( elem, dimension );
-			}
-
-			return setPositiveNumber( elem, value, subtract );
-		}
-	};
-} );
-
-jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft,
-	function( elem, computed ) {
-		if ( computed ) {
-			return ( parseFloat( curCSS( elem, "marginLeft" ) ) ||
-				elem.getBoundingClientRect().left -
-					swap( elem, { marginLeft: 0 }, function() {
-						return elem.getBoundingClientRect().left;
-					} )
-				) + "px";
-		}
-	}
-);
-
-// These hooks are used by animate to expand properties
-jQuery.each( {
-	margin: "",
-	padding: "",
-	border: "Width"
-}, function( prefix, suffix ) {
-	jQuery.cssHooks[ prefix + suffix ] = {
-		expand: function( value ) {
-			var i = 0,
-				expanded = {},
-
-				// Assumes a single number if not a string
-				parts = typeof value === "string" ? value.split( " " ) : [ value ];
-
-			for ( ; i < 4; i++ ) {
-				expanded[ prefix + cssExpand[ i ] + suffix ] =
-					parts[ i ] || parts[ i - 2 ] || parts[ 0 ];
-			}
-
-			return expanded;
-		}
-	};
-
-	if ( prefix !== "margin" ) {
-		jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber;
-	}
-} );
-
-jQuery.fn.extend( {
-	css: function( name, value ) {
-		return access( this, function( elem, name, value ) {
-			var styles, len,
-				map = {},
-				i = 0;
-
-			if ( Array.isArray( name ) ) {
-				styles = getStyles( elem );
-				len = name.length;
-
-				for ( ; i < len; i++ ) {
-					map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles );
-				}
-
-				return map;
-			}
-
-			return value !== undefined ?
-				jQuery.style( elem, name, value ) :
-				jQuery.css( elem, name );
-		}, name, value, arguments.length > 1 );
-	}
-} );
-
-
-function Tween( elem, options, prop, end, easing ) {
-	return new Tween.prototype.init( elem, options, prop, end, easing );
-}
-jQuery.Tween = Tween;
-
-Tween.prototype = {
-	constructor: Tween,
-	init: function( elem, options, prop, end, easing, unit ) {
-		this.elem = elem;
-		this.prop = prop;
-		this.easing = easing || jQuery.easing._default;
-		this.options = options;
-		this.start = this.now = this.cur();
-		this.end = end;
-		this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" );
-	},
-	cur: function() {
-		var hooks = Tween.propHooks[ this.prop ];
-
-		return hooks && hooks.get ?
-			hooks.get( this ) :
-			Tween.propHooks._default.get( this );
-	},
-	run: function( percent ) {
-		var eased,
-			hooks = Tween.propHooks[ this.prop ];
-
-		if ( this.options.duration ) {
-			this.pos = eased = jQuery.easing[ this.easing ](
-				percent, this.options.duration * percent, 0, 1, this.options.duration
-			);
-		} else {
-			this.pos = eased = percent;
-		}
-		this.now = ( this.end - this.start ) * eased + this.start;
-
-		if ( this.options.step ) {
-			this.options.step.call( this.elem, this.now, this );
-		}
-
-		if ( hooks && hooks.set ) {
-			hooks.set( this );
-		} else {
-			Tween.propHooks._default.set( this );
-		}
-		return this;
-	}
-};
-
-Tween.prototype.init.prototype = Tween.prototype;
-
-Tween.propHooks = {
-	_default: {
-		get: function( tween ) {
-			var result;
-
-			// Use a property on the element directly when it is not a DOM element,
-			// or when there is no matching style property that exists.
-			if ( tween.elem.nodeType !== 1 ||
-				tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) {
-				return tween.elem[ tween.prop ];
-			}
-
-			// Passing an empty string as a 3rd parameter to .css will automatically
-			// attempt a parseFloat and fallback to a string if the parse fails.
-			// Simple values such as "10px" are parsed to Float;
-			// complex values such as "rotate(1rad)" are returned as-is.
-			result = jQuery.css( tween.elem, tween.prop, "" );
-
-			// Empty strings, null, undefined and "auto" are converted to 0.
-			return !result || result === "auto" ? 0 : result;
-		},
-		set: function( tween ) {
-
-			// Use step hook for back compat.
-			// Use cssHook if its there.
-			// Use .style if available and use plain properties where available.
-			if ( jQuery.fx.step[ tween.prop ] ) {
-				jQuery.fx.step[ tween.prop ]( tween );
-			} else if ( tween.elem.nodeType === 1 &&
-				( tween.elem.style[ jQuery.cssProps[ tween.prop ] ] != null ||
-					jQuery.cssHooks[ tween.prop ] ) ) {
-				jQuery.style( tween.elem, tween.prop, tween.now + tween.unit );
-			} else {
-				tween.elem[ tween.prop ] = tween.now;
-			}
-		}
-	}
-};
-
-// Support: IE <=9 only
-// Panic based approach to setting things on disconnected nodes
-Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = {
-	set: function( tween ) {
-		if ( tween.elem.nodeType && tween.elem.parentNode ) {
-			tween.elem[ tween.prop ] = tween.now;
-		}
-	}
-};
-
-jQuery.easing = {
-	linear: function( p ) {
-		return p;
-	},
-	swing: function( p ) {
-		return 0.5 - Math.cos( p * Math.PI ) / 2;
-	},
-	_default: "swing"
-};
-
-jQuery.fx = Tween.prototype.init;
-
-// Back compat <1.8 extension point
-jQuery.fx.step = {};
-
-
-
-
-var
-	fxNow, inProgress,
-	rfxtypes = /^(?:toggle|show|hide)$/,
-	rrun = /queueHooks$/;
-
-function schedule() {
-	if ( inProgress ) {
-		if ( document.hidden === false && window.requestAnimationFrame ) {
-			window.requestAnimationFrame( schedule );
-		} else {
-			window.setTimeout( schedule, jQuery.fx.interval );
-		}
-
-		jQuery.fx.tick();
-	}
-}
-
-// Animations created synchronously will run synchronously
-function createFxNow() {
-	window.setTimeout( function() {
-		fxNow = undefined;
-	} );
-	return ( fxNow = Date.now() );
-}
-
-// Generate parameters to create a standard animation
-function genFx( type, includeWidth ) {
-	var which,
-		i = 0,
-		attrs = { height: type };
-
-	// If we include width, step value is 1 to do all cssExpand values,
-	// otherwise step value is 2 to skip over Left and Right
-	includeWidth = includeWidth ? 1 : 0;
-	for ( ; i < 4; i += 2 - includeWidth ) {
-		which = cssExpand[ i ];
-		attrs[ "margin" + which ] = attrs[ "padding" + which ] = type;
-	}
-
-	if ( includeWidth ) {
-		attrs.opacity = attrs.width = type;
-	}
-
-	return attrs;
-}
-
-function createTween( value, prop, animation ) {
-	var tween,
-		collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ),
-		index = 0,
-		length = collection.length;
-	for ( ; index < length; index++ ) {
-		if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) {
-
-			// We're done with this property
-			return tween;
-		}
-	}
-}
-
-function defaultPrefilter( elem, props, opts ) {
-	var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display,
-		isBox = "width" in props || "height" in props,
-		anim = this,
-		orig = {},
-		style = elem.style,
-		hidden = elem.nodeType && isHiddenWithinTree( elem ),
-		dataShow = dataPriv.get( elem, "fxshow" );
-
-	// Queue-skipping animations hijack the fx hooks
-	if ( !opts.queue ) {
-		hooks = jQuery._queueHooks( elem, "fx" );
-		if ( hooks.unqueued == null ) {
-			hooks.unqueued = 0;
-			oldfire = hooks.empty.fire;
-			hooks.empty.fire = function() {
-				if ( !hooks.unqueued ) {
-					oldfire();
-				}
-			};
-		}
-		hooks.unqueued++;
-
-		anim.always( function() {
-
-			// Ensure the complete handler is called before this completes
-			anim.always( function() {
-				hooks.unqueued--;
-				if ( !jQuery.queue( elem, "fx" ).length ) {
-					hooks.empty.fire();
-				}
-			} );
-		} );
-	}
-
-	// Detect show/hide animations
-	for ( prop in props ) {
-		value = props[ prop ];
-		if ( rfxtypes.test( value ) ) {
-			delete props[ prop ];
-			toggle = toggle || value === "toggle";
-			if ( value === ( hidden ? "hide" : "show" ) ) {
-
-				// Pretend to be hidden if this is a "show" and
-				// there is still data from a stopped show/hide
-				if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) {
-					hidden = true;
-
-				// Ignore all other no-op show/hide data
-				} else {
-					continue;
-				}
-			}
-			orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop );
-		}
-	}
-
-	// Bail out if this is a no-op like .hide().hide()
-	propTween = !jQuery.isEmptyObject( props );
-	if ( !propTween && jQuery.isEmptyObject( orig ) ) {
-		return;
-	}
-
-	// Restrict "overflow" and "display" styles during box animations
-	if ( isBox && elem.nodeType === 1 ) {
-
-		// Support: IE <=9 - 11, Edge 12 - 15
-		// Record all 3 overflow attributes because IE does not infer the shorthand
-		// from identically-valued overflowX and overflowY and Edge just mirrors
-		// the overflowX value there.
-		opts.overflow = [ style.overflow, style.overflowX, style.overflowY ];
-
-		// Identify a display type, preferring old show/hide data over the CSS cascade
-		restoreDisplay = dataShow && dataShow.display;
-		if ( restoreDisplay == null ) {
-			restoreDisplay = dataPriv.get( elem, "display" );
-		}
-		display = jQuery.css( elem, "display" );
-		if ( display === "none" ) {
-			if ( restoreDisplay ) {
-				display = restoreDisplay;
-			} else {
-
-				// Get nonempty value(s) by temporarily forcing visibility
-				showHide( [ elem ], true );
-				restoreDisplay = elem.style.display || restoreDisplay;
-				display = jQuery.css( elem, "display" );
-				showHide( [ elem ] );
-			}
-		}
-
-		// Animate inline elements as inline-block
-		if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) {
-			if ( jQuery.css( elem, "float" ) === "none" ) {
-
-				// Restore the original display value at the end of pure show/hide animations
-				if ( !propTween ) {
-					anim.done( function() {
-						style.display = restoreDisplay;
-					} );
-					if ( restoreDisplay == null ) {
-						display = style.display;
-						restoreDisplay = display === "none" ? "" : display;
-					}
-				}
-				style.display = "inline-block";
-			}
-		}
-	}
-
-	if ( opts.overflow ) {
-		style.overflow = "hidden";
-		anim.always( function() {
-			style.overflow = opts.overflow[ 0 ];
-			style.overflowX = opts.overflow[ 1 ];
-			style.overflowY = opts.overflow[ 2 ];
-		} );
-	}
-
-	// Implement show/hide animations
-	propTween = false;
-	for ( prop in orig ) {
-
-		// General show/hide setup for this element animation
-		if ( !propTween ) {
-			if ( dataShow ) {
-				if ( "hidden" in dataShow ) {
-					hidden = dataShow.hidden;
-				}
-			} else {
-				dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } );
-			}
-
-			// Store hidden/visible for toggle so `.stop().toggle()` "reverses"
-			if ( toggle ) {
-				dataShow.hidden = !hidden;
-			}
-
-			// Show elements before animating them
-			if ( hidden ) {
-				showHide( [ elem ], true );
-			}
-
-			/* eslint-disable no-loop-func */
-
-			anim.done( function() {
-
-			/* eslint-enable no-loop-func */
-
-				// The final step of a "hide" animation is actually hiding the element
-				if ( !hidden ) {
-					showHide( [ elem ] );
-				}
-				dataPriv.remove( elem, "fxshow" );
-				for ( prop in orig ) {
-					jQuery.style( elem, prop, orig[ prop ] );
-				}
-			} );
-		}
-
-		// Per-property setup
-		propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim );
-		if ( !( prop in dataShow ) ) {
-			dataShow[ prop ] = propTween.start;
-			if ( hidden ) {
-				propTween.end = propTween.start;
-				propTween.start = 0;
-			}
-		}
-	}
-}
-
-function propFilter( props, specialEasing ) {
-	var index, name, easing, value, hooks;
-
-	// camelCase, specialEasing and expand cssHook pass
-	for ( index in props ) {
-		name = camelCase( index );
-		easing = specialEasing[ name ];
-		value = props[ index ];
-		if ( Array.isArray( value ) ) {
-			easing = value[ 1 ];
-			value = props[ index ] = value[ 0 ];
-		}
-
-		if ( index !== name ) {
-			props[ name ] = value;
-			delete props[ index ];
-		}
-
-		hooks = jQuery.cssHooks[ name ];
-		if ( hooks && "expand" in hooks ) {
-			value = hooks.expand( value );
-			delete props[ name ];
-
-			// Not quite $.extend, this won't overwrite existing keys.
-			// Reusing 'index' because we have the correct "name"
-			for ( index in value ) {
-				if ( !( index in props ) ) {
-					props[ index ] = value[ index ];
-					specialEasing[ index ] = easing;
-				}
-			}
-		} else {
-			specialEasing[ name ] = easing;
-		}
-	}
-}
-
-function Animation( elem, properties, options ) {
-	var result,
-		stopped,
-		index = 0,
-		length = Animation.prefilters.length,
-		deferred = jQuery.Deferred().always( function() {
-
-			// Don't match elem in the :animated selector
-			delete tick.elem;
-		} ),
-		tick = function() {
-			if ( stopped ) {
-				return false;
-			}
-			var currentTime = fxNow || createFxNow(),
-				remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ),
-
-				// Support: Android 2.3 only
-				// Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497)
-				temp = remaining / animation.duration || 0,
-				percent = 1 - temp,
-				index = 0,
-				length = animation.tweens.length;
-
-			for ( ; index < length; index++ ) {
-				animation.tweens[ index ].run( percent );
-			}
-
-			deferred.notifyWith( elem, [ animation, percent, remaining ] );
-
-			// If there's more to do, yield
-			if ( percent < 1 && length ) {
-				return remaining;
-			}
-
-			// If this was an empty animation, synthesize a final progress notification
-			if ( !length ) {
-				deferred.notifyWith( elem, [ animation, 1, 0 ] );
-			}
-
-			// Resolve the animation and report its conclusion
-			deferred.resolveWith( elem, [ animation ] );
-			return false;
-		},
-		animation = deferred.promise( {
-			elem: elem,
-			props: jQuery.extend( {}, properties ),
-			opts: jQuery.extend( true, {
-				specialEasing: {},
-				easing: jQuery.easing._default
-			}, options ),
-			originalProperties: properties,
-			originalOptions: options,
-			startTime: fxNow || createFxNow(),
-			duration: options.duration,
-			tweens: [],
-			createTween: function( prop, end ) {
-				var tween = jQuery.Tween( elem, animation.opts, prop, end,
-						animation.opts.specialEasing[ prop ] || animation.opts.easing );
-				animation.tweens.push( tween );
-				return tween;
-			},
-			stop: function( gotoEnd ) {
-				var index = 0,
-
-					// If we are going to the end, we want to run all the tweens
-					// otherwise we skip this part
-					length = gotoEnd ? animation.tweens.length : 0;
-				if ( stopped ) {
-					return this;
-				}
-				stopped = true;
-				for ( ; index < length; index++ ) {
-					animation.tweens[ index ].run( 1 );
-				}
-
-				// Resolve when we played the last frame; otherwise, reject
-				if ( gotoEnd ) {
-					deferred.notifyWith( elem, [ animation, 1, 0 ] );
-					deferred.resolveWith( elem, [ animation, gotoEnd ] );
-				} else {
-					deferred.rejectWith( elem, [ animation, gotoEnd ] );
-				}
-				return this;
-			}
-		} ),
-		props = animation.props;
-
-	propFilter( props, animation.opts.specialEasing );
-
-	for ( ; index < length; index++ ) {
-		result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts );
-		if ( result ) {
-			if ( isFunction( result.stop ) ) {
-				jQuery._queueHooks( animation.elem, animation.opts.queue ).stop =
-					result.stop.bind( result );
-			}
-			return result;
-		}
-	}
-
-	jQuery.map( props, createTween, animation );
-
-	if ( isFunction( animation.opts.start ) ) {
-		animation.opts.start.call( elem, animation );
-	}
-
-	// Attach callbacks from options
-	animation
-		.progress( animation.opts.progress )
-		.done( animation.opts.done, animation.opts.complete )
-		.fail( animation.opts.fail )
-		.always( animation.opts.always );
-
-	jQuery.fx.timer(
-		jQuery.extend( tick, {
-			elem: elem,
-			anim: animation,
-			queue: animation.opts.queue
-		} )
-	);
-
-	return animation;
-}
-
-jQuery.Animation = jQuery.extend( Animation, {
-
-	tweeners: {
-		"*": [ function( prop, value ) {
-			var tween = this.createTween( prop, value );
-			adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween );
-			return tween;
-		} ]
-	},
-
-	tweener: function( props, callback ) {
-		if ( isFunction( props ) ) {
-			callback = props;
-			props = [ "*" ];
-		} else {
-			props = props.match( rnothtmlwhite );
-		}
-
-		var prop,
-			index = 0,
-			length = props.length;
-
-		for ( ; index < length; index++ ) {
-			prop = props[ index ];
-			Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || [];
-			Animation.tweeners[ prop ].unshift( callback );
-		}
-	},
-
-	prefilters: [ defaultPrefilter ],
-
-	prefilter: function( callback, prepend ) {
-		if ( prepend ) {
-			Animation.prefilters.unshift( callback );
-		} else {
-			Animation.prefilters.push( callback );
-		}
-	}
-} );
-
-jQuery.speed = function( speed, easing, fn ) {
-	var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : {
-		complete: fn || !fn && easing ||
-			isFunction( speed ) && speed,
-		duration: speed,
-		easing: fn && easing || easing && !isFunction( easing ) && easing
-	};
-
-	// Go to the end state if fx are off
-	if ( jQuery.fx.off ) {
-		opt.duration = 0;
-
-	} else {
-		if ( typeof opt.duration !== "number" ) {
-			if ( opt.duration in jQuery.fx.speeds ) {
-				opt.duration = jQuery.fx.speeds[ opt.duration ];
-
-			} else {
-				opt.duration = jQuery.fx.speeds._default;
-			}
-		}
-	}
-
-	// Normalize opt.queue - true/undefined/null -> "fx"
-	if ( opt.queue == null || opt.queue === true ) {
-		opt.queue = "fx";
-	}
-
-	// Queueing
-	opt.old = opt.complete;
-
-	opt.complete = function() {
-		if ( isFunction( opt.old ) ) {
-			opt.old.call( this );
-		}
-
-		if ( opt.queue ) {
-			jQuery.dequeue( this, opt.queue );
-		}
-	};
-
-	return opt;
-};
-
-jQuery.fn.extend( {
-	fadeTo: function( speed, to, easing, callback ) {
-
-		// Show any hidden elements after setting opacity to 0
-		return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show()
-
-			// Animate to the value specified
-			.end().animate( { opacity: to }, speed, easing, callback );
-	},
-	animate: function( prop, speed, easing, callback ) {
-		var empty = jQuery.isEmptyObject( prop ),
-			optall = jQuery.speed( speed, easing, callback ),
-			doAnimation = function() {
-
-				// Operate on a copy of prop so per-property easing won't be lost
-				var anim = Animation( this, jQuery.extend( {}, prop ), optall );
-
-				// Empty animations, or finishing resolves immediately
-				if ( empty || dataPriv.get( this, "finish" ) ) {
-					anim.stop( true );
-				}
-			};
-			doAnimation.finish = doAnimation;
-
-		return empty || optall.queue === false ?
-			this.each( doAnimation ) :
-			this.queue( optall.queue, doAnimation );
-	},
-	stop: function( type, clearQueue, gotoEnd ) {
-		var stopQueue = function( hooks ) {
-			var stop = hooks.stop;
-			delete hooks.stop;
-			stop( gotoEnd );
-		};
-
-		if ( typeof type !== "string" ) {
-			gotoEnd = clearQueue;
-			clearQueue = type;
-			type = undefined;
-		}
-		if ( clearQueue && type !== false ) {
-			this.queue( type || "fx", [] );
-		}
-
-		return this.each( function() {
-			var dequeue = true,
-				index = type != null && type + "queueHooks",
-				timers = jQuery.timers,
-				data = dataPriv.get( this );
-
-			if ( index ) {
-				if ( data[ index ] && data[ index ].stop ) {
-					stopQueue( data[ index ] );
-				}
-			} else {
-				for ( index in data ) {
-					if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) {
-						stopQueue( data[ index ] );
-					}
-				}
-			}
-
-			for ( index = timers.length; index--; ) {
-				if ( timers[ index ].elem === this &&
-					( type == null || timers[ index ].queue === type ) ) {
-
-					timers[ index ].anim.stop( gotoEnd );
-					dequeue = false;
-					timers.splice( index, 1 );
-				}
-			}
-
-			// Start the next in the queue if the last step wasn't forced.
-			// Timers currently will call their complete callbacks, which
-			// will dequeue but only if they were gotoEnd.
-			if ( dequeue || !gotoEnd ) {
-				jQuery.dequeue( this, type );
-			}
-		} );
-	},
-	finish: function( type ) {
-		if ( type !== false ) {
-			type = type || "fx";
-		}
-		return this.each( function() {
-			var index,
-				data = dataPriv.get( this ),
-				queue = data[ type + "queue" ],
-				hooks = data[ type + "queueHooks" ],
-				timers = jQuery.timers,
-				length = queue ? queue.length : 0;
-
-			// Enable finishing flag on private data
-			data.finish = true;
-
-			// Empty the queue first
-			jQuery.queue( this, type, [] );
-
-			if ( hooks && hooks.stop ) {
-				hooks.stop.call( this, true );
-			}
-
-			// Look for any active animations, and finish them
-			for ( index = timers.length; index--; ) {
-				if ( timers[ index ].elem === this && timers[ index ].queue === type ) {
-					timers[ index ].anim.stop( true );
-					timers.splice( index, 1 );
-				}
-			}
-
-			// Look for any animations in the old queue and finish them
-			for ( index = 0; index < length; index++ ) {
-				if ( queue[ index ] && queue[ index ].finish ) {
-					queue[ index ].finish.call( this );
-				}
-			}
-
-			// Turn off finishing flag
-			delete data.finish;
-		} );
-	}
-} );
-
-jQuery.each( [ "toggle", "show", "hide" ], function( i, name ) {
-	var cssFn = jQuery.fn[ name ];
-	jQuery.fn[ name ] = function( speed, easing, callback ) {
-		return speed == null || typeof speed === "boolean" ?
-			cssFn.apply( this, arguments ) :
-			this.animate( genFx( name, true ), speed, easing, callback );
-	};
-} );
-
-// Generate shortcuts for custom animations
-jQuery.each( {
-	slideDown: genFx( "show" ),
-	slideUp: genFx( "hide" ),
-	slideToggle: genFx( "toggle" ),
-	fadeIn: { opacity: "show" },
-	fadeOut: { opacity: "hide" },
-	fadeToggle: { opacity: "toggle" }
-}, function( name, props ) {
-	jQuery.fn[ name ] = function( speed, easing, callback ) {
-		return this.animate( props, speed, easing, callback );
-	};
-} );
-
-jQuery.timers = [];
-jQuery.fx.tick = function() {
-	var timer,
-		i = 0,
-		timers = jQuery.timers;
-
-	fxNow = Date.now();
-
-	for ( ; i < timers.length; i++ ) {
-		timer = timers[ i ];
-
-		// Run the timer and safely remove it when done (allowing for external removal)
-		if ( !timer() && timers[ i ] === timer ) {
-			timers.splice( i--, 1 );
-		}
-	}
-
-	if ( !timers.length ) {
-		jQuery.fx.stop();
-	}
-	fxNow = undefined;
-};
-
-jQuery.fx.timer = function( timer ) {
-	jQuery.timers.push( timer );
-	jQuery.fx.start();
-};
-
-jQuery.fx.interval = 13;
-jQuery.fx.start = function() {
-	if ( inProgress ) {
-		return;
-	}
-
-	inProgress = true;
-	schedule();
-};
-
-jQuery.fx.stop = function() {
-	inProgress = null;
-};
-
-jQuery.fx.speeds = {
-	slow: 600,
-	fast: 200,
-
-	// Default speed
-	_default: 400
-};
-
-
-// Based off of the plugin by Clint Helfers, with permission.
-// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/
-jQuery.fn.delay = function( time, type ) {
-	time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time;
-	type = type || "fx";
-
-	return this.queue( type, function( next, hooks ) {
-		var timeout = window.setTimeout( next, time );
-		hooks.stop = function() {
-			window.clearTimeout( timeout );
-		};
-	} );
-};
-
-
-( function() {
-	var input = document.createElement( "input" ),
-		select = document.createElement( "select" ),
-		opt = select.appendChild( document.createElement( "option" ) );
-
-	input.type = "checkbox";
-
-	// Support: Android <=4.3 only
-	// Default value for a checkbox should be "on"
-	support.checkOn = input.value !== "";
-
-	// Support: IE <=11 only
-	// Must access selectedIndex to make default options select
-	support.optSelected = opt.selected;
-
-	// Support: IE <=11 only
-	// An input loses its value after becoming a radio
-	input = document.createElement( "input" );
-	input.value = "t";
-	input.type = "radio";
-	support.radioValue = input.value === "t";
-} )();
-
-
-var boolHook,
-	attrHandle = jQuery.expr.attrHandle;
-
-jQuery.fn.extend( {
-	attr: function( name, value ) {
-		return access( this, jQuery.attr, name, value, arguments.length > 1 );
-	},
-
-	removeAttr: function( name ) {
-		return this.each( function() {
-			jQuery.removeAttr( this, name );
-		} );
-	}
-} );
-
-jQuery.extend( {
-	attr: function( elem, name, value ) {
-		var ret, hooks,
-			nType = elem.nodeType;
-
-		// Don't get/set attributes on text, comment and attribute nodes
-		if ( nType === 3 || nType === 8 || nType === 2 ) {
-			return;
-		}
-
-		// Fallback to prop when attributes are not supported
-		if ( typeof elem.getAttribute === "undefined" ) {
-			return jQuery.prop( elem, name, value );
-		}
-
-		// Attribute hooks are determined by the lowercase version
-		// Grab necessary hook if one is defined
-		if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
-			hooks = jQuery.attrHooks[ name.toLowerCase() ] ||
-				( jQuery.expr.match.bool.test( name ) ? boolHook : undefined );
-		}
-
-		if ( value !== undefined ) {
-			if ( value === null ) {
-				jQuery.removeAttr( elem, name );
-				return;
-			}
-
-			if ( hooks && "set" in hooks &&
-				( ret = hooks.set( elem, value, name ) ) !== undefined ) {
-				return ret;
-			}
-
-			elem.setAttribute( name, value + "" );
-			return value;
-		}
-
-		if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
-			return ret;
-		}
-
-		ret = jQuery.find.attr( elem, name );
-
-		// Non-existent attributes return null, we normalize to undefined
-		return ret == null ? undefined : ret;
-	},
-
-	attrHooks: {
-		type: {
-			set: function( elem, value ) {
-				if ( !support.radioValue && value === "radio" &&
-					nodeName( elem, "input" ) ) {
-					var val = elem.value;
-					elem.setAttribute( "type", value );
-					if ( val ) {
-						elem.value = val;
-					}
-					return value;
-				}
-			}
-		}
-	},
-
-	removeAttr: function( elem, value ) {
-		var name,
-			i = 0,
-
-			// Attribute names can contain non-HTML whitespace characters
-			// https://html.spec.whatwg.org/multipage/syntax.html#attributes-2
-			attrNames = value && value.match( rnothtmlwhite );
-
-		if ( attrNames && elem.nodeType === 1 ) {
-			while ( ( name = attrNames[ i++ ] ) ) {
-				elem.removeAttribute( name );
-			}
-		}
-	}
-} );
-
-// Hooks for boolean attributes
-boolHook = {
-	set: function( elem, value, name ) {
-		if ( value === false ) {
-
-			// Remove boolean attributes when set to false
-			jQuery.removeAttr( elem, name );
-		} else {
-			elem.setAttribute( name, name );
-		}
-		return name;
-	}
-};
-
-jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( i, name ) {
-	var getter = attrHandle[ name ] || jQuery.find.attr;
-
-	attrHandle[ name ] = function( elem, name, isXML ) {
-		var ret, handle,
-			lowercaseName = name.toLowerCase();
-
-		if ( !isXML ) {
-
-			// Avoid an infinite loop by temporarily removing this function from the getter
-			handle = attrHandle[ lowercaseName ];
-			attrHandle[ lowercaseName ] = ret;
-			ret = getter( elem, name, isXML ) != null ?
-				lowercaseName :
-				null;
-			attrHandle[ lowercaseName ] = handle;
-		}
-		return ret;
-	};
-} );
-
-
-
-
-var rfocusable = /^(?:input|select|textarea|button)$/i,
-	rclickable = /^(?:a|area)$/i;
-
-jQuery.fn.extend( {
-	prop: function( name, value ) {
-		return access( this, jQuery.prop, name, value, arguments.length > 1 );
-	},
-
-	removeProp: function( name ) {
-		return this.each( function() {
-			delete this[ jQuery.propFix[ name ] || name ];
-		} );
-	}
-} );
-
-jQuery.extend( {
-	prop: function( elem, name, value ) {
-		var ret, hooks,
-			nType = elem.nodeType;
-
-		// Don't get/set properties on text, comment and attribute nodes
-		if ( nType === 3 || nType === 8 || nType === 2 ) {
-			return;
-		}
-
-		if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
-
-			// Fix name and attach hooks
-			name = jQuery.propFix[ name ] || name;
-			hooks = jQuery.propHooks[ name ];
-		}
-
-		if ( value !== undefined ) {
-			if ( hooks && "set" in hooks &&
-				( ret = hooks.set( elem, value, name ) ) !== undefined ) {
-				return ret;
-			}
-
-			return ( elem[ name ] = value );
-		}
-
-		if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
-			return ret;
-		}
-
-		return elem[ name ];
-	},
-
-	propHooks: {
-		tabIndex: {
-			get: function( elem ) {
-
-				// Support: IE <=9 - 11 only
-				// elem.tabIndex doesn't always return the
-				// correct value when it hasn't been explicitly set
-				// https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/
-				// Use proper attribute retrieval(#12072)
-				var tabindex = jQuery.find.attr( elem, "tabindex" );
-
-				if ( tabindex ) {
-					return parseInt( tabindex, 10 );
-				}
-
-				if (
-					rfocusable.test( elem.nodeName ) ||
-					rclickable.test( elem.nodeName ) &&
-					elem.href
-				) {
-					return 0;
-				}
-
-				return -1;
-			}
-		}
-	},
-
-	propFix: {
-		"for": "htmlFor",
-		"class": "className"
-	}
-} );
-
-// Support: IE <=11 only
-// Accessing the selectedIndex property
-// forces the browser to respect setting selected
-// on the option
-// The getter ensures a default option is selected
-// when in an optgroup
-// eslint rule "no-unused-expressions" is disabled for this code
-// since it considers such accessions noop
-if ( !support.optSelected ) {
-	jQuery.propHooks.selected = {
-		get: function( elem ) {
-
-			/* eslint no-unused-expressions: "off" */
-
-			var parent = elem.parentNode;
-			if ( parent && parent.parentNode ) {
-				parent.parentNode.selectedIndex;
-			}
-			return null;
-		},
-		set: function( elem ) {
-
-			/* eslint no-unused-expressions: "off" */
-
-			var parent = elem.parentNode;
-			if ( parent ) {
-				parent.selectedIndex;
-
-				if ( parent.parentNode ) {
-					parent.parentNode.selectedIndex;
-				}
-			}
-		}
-	};
-}
-
-jQuery.each( [
-	"tabIndex",
-	"readOnly",
-	"maxLength",
-	"cellSpacing",
-	"cellPadding",
-	"rowSpan",
-	"colSpan",
-	"useMap",
-	"frameBorder",
-	"contentEditable"
-], function() {
-	jQuery.propFix[ this.toLowerCase() ] = this;
-} );
-
-
-
-
-	// Strip and collapse whitespace according to HTML spec
-	// https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace
-	function stripAndCollapse( value ) {
-		var tokens = value.match( rnothtmlwhite ) || [];
-		return tokens.join( " " );
-	}
-
-
-function getClass( elem ) {
-	return elem.getAttribute && elem.getAttribute( "class" ) || "";
-}
-
-function classesToArray( value ) {
-	if ( Array.isArray( value ) ) {
-		return value;
-	}
-	if ( typeof value === "string" ) {
-		return value.match( rnothtmlwhite ) || [];
-	}
-	return [];
-}
-
-jQuery.fn.extend( {
-	addClass: function( value ) {
-		var classes, elem, cur, curValue, clazz, j, finalValue,
-			i = 0;
-
-		if ( isFunction( value ) ) {
-			return this.each( function( j ) {
-				jQuery( this ).addClass( value.call( this, j, getClass( this ) ) );
-			} );
-		}
-
-		classes = classesToArray( value );
-
-		if ( classes.length ) {
-			while ( ( elem = this[ i++ ] ) ) {
-				curValue = getClass( elem );
-				cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
-
-				if ( cur ) {
-					j = 0;
-					while ( ( clazz = classes[ j++ ] ) ) {
-						if ( cur.indexOf( " " + clazz + " " ) < 0 ) {
-							cur += clazz + " ";
-						}
-					}
-
-					// Only assign if different to avoid unneeded rendering.
-					finalValue = stripAndCollapse( cur );
-					if ( curValue !== finalValue ) {
-						elem.setAttribute( "class", finalValue );
-					}
-				}
-			}
-		}
-
-		return this;
-	},
-
-	removeClass: function( value ) {
-		var classes, elem, cur, curValue, clazz, j, finalValue,
-			i = 0;
-
-		if ( isFunction( value ) ) {
-			return this.each( function( j ) {
-				jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) );
-			} );
-		}
-
-		if ( !arguments.length ) {
-			return this.attr( "class", "" );
-		}
-
-		classes = classesToArray( value );
-
-		if ( classes.length ) {
-			while ( ( elem = this[ i++ ] ) ) {
-				curValue = getClass( elem );
-
-				// This expression is here for better compressibility (see addClass)
-				cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
-
-				if ( cur ) {
-					j = 0;
-					while ( ( clazz = classes[ j++ ] ) ) {
-
-						// Remove *all* instances
-						while ( cur.indexOf( " " + clazz + " " ) > -1 ) {
-							cur = cur.replace( " " + clazz + " ", " " );
-						}
-					}
-
-					// Only assign if different to avoid unneeded rendering.
-					finalValue = stripAndCollapse( cur );
-					if ( curValue !== finalValue ) {
-						elem.setAttribute( "class", finalValue );
-					}
-				}
-			}
-		}
-
-		return this;
-	},
-
-	toggleClass: function( value, stateVal ) {
-		var type = typeof value,
-			isValidValue = type === "string" || Array.isArray( value );
-
-		if ( typeof stateVal === "boolean" && isValidValue ) {
-			return stateVal ? this.addClass( value ) : this.removeClass( value );
-		}
-
-		if ( isFunction( value ) ) {
-			return this.each( function( i ) {
-				jQuery( this ).toggleClass(
-					value.call( this, i, getClass( this ), stateVal ),
-					stateVal
-				);
-			} );
-		}
-
-		return this.each( function() {
-			var className, i, self, classNames;
-
-			if ( isValidValue ) {
-
-				// Toggle individual class names
-				i = 0;
-				self = jQuery( this );
-				classNames = classesToArray( value );
-
-				while ( ( className = classNames[ i++ ] ) ) {
-
-					// Check each className given, space separated list
-					if ( self.hasClass( className ) ) {
-						self.removeClass( className );
-					} else {
-						self.addClass( className );
-					}
-				}
-
-			// Toggle whole class name
-			} else if ( value === undefined || type === "boolean" ) {
-				className = getClass( this );
-				if ( className ) {
-
-					// Store className if set
-					dataPriv.set( this, "__className__", className );
-				}
-
-				// If the element has a class name or if we're passed `false`,
-				// then remove the whole classname (if there was one, the above saved it).
-				// Otherwise bring back whatever was previously saved (if anything),
-				// falling back to the empty string if nothing was stored.
-				if ( this.setAttribute ) {
-					this.setAttribute( "class",
-						className || value === false ?
-						"" :
-						dataPriv.get( this, "__className__" ) || ""
-					);
-				}
-			}
-		} );
-	},
-
-	hasClass: function( selector ) {
-		var className, elem,
-			i = 0;
-
-		className = " " + selector + " ";
-		while ( ( elem = this[ i++ ] ) ) {
-			if ( elem.nodeType === 1 &&
-				( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) {
-					return true;
-			}
-		}
-
-		return false;
-	}
-} );
-
-
-
-
-var rreturn = /\r/g;
-
-jQuery.fn.extend( {
-	val: function( value ) {
-		var hooks, ret, valueIsFunction,
-			elem = this[ 0 ];
-
-		if ( !arguments.length ) {
-			if ( elem ) {
-				hooks = jQuery.valHooks[ elem.type ] ||
-					jQuery.valHooks[ elem.nodeName.toLowerCase() ];
-
-				if ( hooks &&
-					"get" in hooks &&
-					( ret = hooks.get( elem, "value" ) ) !== undefined
-				) {
-					return ret;
-				}
-
-				ret = elem.value;
-
-				// Handle most common string cases
-				if ( typeof ret === "string" ) {
-					return ret.replace( rreturn, "" );
-				}
-
-				// Handle cases where value is null/undef or number
-				return ret == null ? "" : ret;
-			}
-
-			return;
-		}
-
-		valueIsFunction = isFunction( value );
-
-		return this.each( function( i ) {
-			var val;
-
-			if ( this.nodeType !== 1 ) {
-				return;
-			}
-
-			if ( valueIsFunction ) {
-				val = value.call( this, i, jQuery( this ).val() );
-			} else {
-				val = value;
-			}
-
-			// Treat null/undefined as ""; convert numbers to string
-			if ( val == null ) {
-				val = "";
-
-			} else if ( typeof val === "number" ) {
-				val += "";
-
-			} else if ( Array.isArray( val ) ) {
-				val = jQuery.map( val, function( value ) {
-					return value == null ? "" : value + "";
-				} );
-			}
-
-			hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ];
-
-			// If set returns undefined, fall back to normal setting
-			if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) {
-				this.value = val;
-			}
-		} );
-	}
-} );
-
-jQuery.extend( {
-	valHooks: {
-		option: {
-			get: function( elem ) {
-
-				var val = jQuery.find.attr( elem, "value" );
-				return val != null ?
-					val :
-
-					// Support: IE <=10 - 11 only
-					// option.text throws exceptions (#14686, #14858)
-					// Strip and collapse whitespace
-					// https://html.spec.whatwg.org/#strip-and-collapse-whitespace
-					stripAndCollapse( jQuery.text( elem ) );
-			}
-		},
-		select: {
-			get: function( elem ) {
-				var value, option, i,
-					options = elem.options,
-					index = elem.selectedIndex,
-					one = elem.type === "select-one",
-					values = one ? null : [],
-					max = one ? index + 1 : options.length;
-
-				if ( index < 0 ) {
-					i = max;
-
-				} else {
-					i = one ? index : 0;
-				}
-
-				// Loop through all the selected options
-				for ( ; i < max; i++ ) {
-					option = options[ i ];
-
-					// Support: IE <=9 only
-					// IE8-9 doesn't update selected after form reset (#2551)
-					if ( ( option.selected || i === index ) &&
-
-							// Don't return options that are disabled or in a disabled optgroup
-							!option.disabled &&
-							( !option.parentNode.disabled ||
-								!nodeName( option.parentNode, "optgroup" ) ) ) {
-
-						// Get the specific value for the option
-						value = jQuery( option ).val();
-
-						// We don't need an array for one selects
-						if ( one ) {
-							return value;
-						}
-
-						// Multi-Selects return an array
-						values.push( value );
-					}
-				}
-
-				return values;
-			},
-
-			set: function( elem, value ) {
-				var optionSet, option,
-					options = elem.options,
-					values = jQuery.makeArray( value ),
-					i = options.length;
-
-				while ( i-- ) {
-					option = options[ i ];
-
-					/* eslint-disable no-cond-assign */
-
-					if ( option.selected =
-						jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1
-					) {
-						optionSet = true;
-					}
-
-					/* eslint-enable no-cond-assign */
-				}
-
-				// Force browsers to behave consistently when non-matching value is set
-				if ( !optionSet ) {
-					elem.selectedIndex = -1;
-				}
-				return values;
-			}
-		}
-	}
-} );
-
-// Radios and checkboxes getter/setter
-jQuery.each( [ "radio", "checkbox" ], function() {
-	jQuery.valHooks[ this ] = {
-		set: function( elem, value ) {
-			if ( Array.isArray( value ) ) {
-				return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 );
-			}
-		}
-	};
-	if ( !support.checkOn ) {
-		jQuery.valHooks[ this ].get = function( elem ) {
-			return elem.getAttribute( "value" ) === null ? "on" : elem.value;
-		};
-	}
-} );
-
-
-
-
-// Return jQuery for attributes-only inclusion
-
-
-support.focusin = "onfocusin" in window;
-
-
-var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/,
-	stopPropagationCallback = function( e ) {
-		e.stopPropagation();
-	};
-
-jQuery.extend( jQuery.event, {
-
-	trigger: function( event, data, elem, onlyHandlers ) {
-
-		var i, cur, tmp, bubbleType, ontype, handle, special, lastElement,
-			eventPath = [ elem || document ],
-			type = hasOwn.call( event, "type" ) ? event.type : event,
-			namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : [];
-
-		cur = lastElement = tmp = elem = elem || document;
-
-		// Don't do events on text and comment nodes
-		if ( elem.nodeType === 3 || elem.nodeType === 8 ) {
-			return;
-		}
-
-		// focus/blur morphs to focusin/out; ensure we're not firing them right now
-		if ( rfocusMorph.test( type + jQuery.event.triggered ) ) {
-			return;
-		}
-
-		if ( type.indexOf( "." ) > -1 ) {
-
-			// Namespaced trigger; create a regexp to match event type in handle()
-			namespaces = type.split( "." );
-			type = namespaces.shift();
-			namespaces.sort();
-		}
-		ontype = type.indexOf( ":" ) < 0 && "on" + type;
-
-		// Caller can pass in a jQuery.Event object, Object, or just an event type string
-		event = event[ jQuery.expando ] ?
-			event :
-			new jQuery.Event( type, typeof event === "object" && event );
-
-		// Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true)
-		event.isTrigger = onlyHandlers ? 2 : 3;
-		event.namespace = namespaces.join( "." );
-		event.rnamespace = event.namespace ?
-			new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) :
-			null;
-
-		// Clean up the event in case it is being reused
-		event.result = undefined;
-		if ( !event.target ) {
-			event.target = elem;
-		}
-
-		// Clone any incoming data and prepend the event, creating the handler arg list
-		data = data == null ?
-			[ event ] :
-			jQuery.makeArray( data, [ event ] );
-
-		// Allow special events to draw outside the lines
-		special = jQuery.event.special[ type ] || {};
-		if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) {
-			return;
-		}
-
-		// Determine event propagation path in advance, per W3C events spec (#9951)
-		// Bubble up to document, then to window; watch for a global ownerDocument var (#9724)
-		if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) {
-
-			bubbleType = special.delegateType || type;
-			if ( !rfocusMorph.test( bubbleType + type ) ) {
-				cur = cur.parentNode;
-			}
-			for ( ; cur; cur = cur.parentNode ) {
-				eventPath.push( cur );
-				tmp = cur;
-			}
-
-			// Only add window if we got to document (e.g., not plain obj or detached DOM)
-			if ( tmp === ( elem.ownerDocument || document ) ) {
-				eventPath.push( tmp.defaultView || tmp.parentWindow || window );
-			}
-		}
-
-		// Fire handlers on the event path
-		i = 0;
-		while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) {
-			lastElement = cur;
-			event.type = i > 1 ?
-				bubbleType :
-				special.bindType || type;
-
-			// jQuery handler
-			handle = ( dataPriv.get( cur, "events" ) || {} )[ event.type ] &&
-				dataPriv.get( cur, "handle" );
-			if ( handle ) {
-				handle.apply( cur, data );
-			}
-
-			// Native handler
-			handle = ontype && cur[ ontype ];
-			if ( handle && handle.apply && acceptData( cur ) ) {
-				event.result = handle.apply( cur, data );
-				if ( event.result === false ) {
-					event.preventDefault();
-				}
-			}
-		}
-		event.type = type;
-
-		// If nobody prevented the default action, do it now
-		if ( !onlyHandlers && !event.isDefaultPrevented() ) {
-
-			if ( ( !special._default ||
-				special._default.apply( eventPath.pop(), data ) === false ) &&
-				acceptData( elem ) ) {
-
-				// Call a native DOM method on the target with the same name as the event.
-				// Don't do default actions on window, that's where global variables be (#6170)
-				if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) {
-
-					// Don't re-trigger an onFOO event when we call its FOO() method
-					tmp = elem[ ontype ];
-
-					if ( tmp ) {
-						elem[ ontype ] = null;
-					}
-
-					// Prevent re-triggering of the same event, since we already bubbled it above
-					jQuery.event.triggered = type;
-
-					if ( event.isPropagationStopped() ) {
-						lastElement.addEventListener( type, stopPropagationCallback );
-					}
-
-					elem[ type ]();
-
-					if ( event.isPropagationStopped() ) {
-						lastElement.removeEventListener( type, stopPropagationCallback );
-					}
-
-					jQuery.event.triggered = undefined;
-
-					if ( tmp ) {
-						elem[ ontype ] = tmp;
-					}
-				}
-			}
-		}
-
-		return event.result;
-	},
-
-	// Piggyback on a donor event to simulate a different one
-	// Used only for `focus(in | out)` events
-	simulate: function( type, elem, event ) {
-		var e = jQuery.extend(
-			new jQuery.Event(),
-			event,
-			{
-				type: type,
-				isSimulated: true
-			}
-		);
-
-		jQuery.event.trigger( e, null, elem );
-	}
-
-} );
-
-jQuery.fn.extend( {
-
-	trigger: function( type, data ) {
-		return this.each( function() {
-			jQuery.event.trigger( type, data, this );
-		} );
-	},
-	triggerHandler: function( type, data ) {
-		var elem = this[ 0 ];
-		if ( elem ) {
-			return jQuery.event.trigger( type, data, elem, true );
-		}
-	}
-} );
-
-
-// Support: Firefox <=44
-// Firefox doesn't have focus(in | out) events
-// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787
-//
-// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1
-// focus(in | out) events fire after focus & blur events,
-// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order
-// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857
-if ( !support.focusin ) {
-	jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) {
-
-		// Attach a single capturing handler on the document while someone wants focusin/focusout
-		var handler = function( event ) {
-			jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) );
-		};
-
-		jQuery.event.special[ fix ] = {
-			setup: function() {
-				var doc = this.ownerDocument || this,
-					attaches = dataPriv.access( doc, fix );
-
-				if ( !attaches ) {
-					doc.addEventListener( orig, handler, true );
-				}
-				dataPriv.access( doc, fix, ( attaches || 0 ) + 1 );
-			},
-			teardown: function() {
-				var doc = this.ownerDocument || this,
-					attaches = dataPriv.access( doc, fix ) - 1;
-
-				if ( !attaches ) {
-					doc.removeEventListener( orig, handler, true );
-					dataPriv.remove( doc, fix );
-
-				} else {
-					dataPriv.access( doc, fix, attaches );
-				}
-			}
-		};
-	} );
-}
-var location = window.location;
-
-var nonce = Date.now();
-
-var rquery = ( /\?/ );
-
-
-
-// Cross-browser xml parsing
-jQuery.parseXML = function( data ) {
-	var xml;
-	if ( !data || typeof data !== "string" ) {
-		return null;
-	}
-
-	// Support: IE 9 - 11 only
-	// IE throws on parseFromString with invalid input.
-	try {
-		xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" );
-	} catch ( e ) {
-		xml = undefined;
-	}
-
-	if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) {
-		jQuery.error( "Invalid XML: " + data );
-	}
-	return xml;
-};
-
-
-var
-	rbracket = /\[\]$/,
-	rCRLF = /\r?\n/g,
-	rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i,
-	rsubmittable = /^(?:input|select|textarea|keygen)/i;
-
-function buildParams( prefix, obj, traditional, add ) {
-	var name;
-
-	if ( Array.isArray( obj ) ) {
-
-		// Serialize array item.
-		jQuery.each( obj, function( i, v ) {
-			if ( traditional || rbracket.test( prefix ) ) {
-
-				// Treat each array item as a scalar.
-				add( prefix, v );
-
-			} else {
-
-				// Item is non-scalar (array or object), encode its numeric index.
-				buildParams(
-					prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]",
-					v,
-					traditional,
-					add
-				);
-			}
-		} );
-
-	} else if ( !traditional && toType( obj ) === "object" ) {
-
-		// Serialize object item.
-		for ( name in obj ) {
-			buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add );
-		}
-
-	} else {
-
-		// Serialize scalar item.
-		add( prefix, obj );
-	}
-}
-
-// Serialize an array of form elements or a set of
-// key/values into a query string
-jQuery.param = function( a, traditional ) {
-	var prefix,
-		s = [],
-		add = function( key, valueOrFunction ) {
-
-			// If value is a function, invoke it and use its return value
-			var value = isFunction( valueOrFunction ) ?
-				valueOrFunction() :
-				valueOrFunction;
-
-			s[ s.length ] = encodeURIComponent( key ) + "=" +
-				encodeURIComponent( value == null ? "" : value );
-		};
-
-	// If an array was passed in, assume that it is an array of form elements.
-	if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) {
-
-		// Serialize the form elements
-		jQuery.each( a, function() {
-			add( this.name, this.value );
-		} );
-
-	} else {
-
-		// If traditional, encode the "old" way (the way 1.3.2 or older
-		// did it), otherwise encode params recursively.
-		for ( prefix in a ) {
-			buildParams( prefix, a[ prefix ], traditional, add );
-		}
-	}
-
-	// Return the resulting serialization
-	return s.join( "&" );
-};
-
-jQuery.fn.extend( {
-	serialize: function() {
-		return jQuery.param( this.serializeArray() );
-	},
-	serializeArray: function() {
-		return this.map( function() {
-
-			// Can add propHook for "elements" to filter or add form elements
-			var elements = jQuery.prop( this, "elements" );
-			return elements ? jQuery.makeArray( elements ) : this;
-		} )
-		.filter( function() {
-			var type = this.type;
-
-			// Use .is( ":disabled" ) so that fieldset[disabled] works
-			return this.name && !jQuery( this ).is( ":disabled" ) &&
-				rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) &&
-				( this.checked || !rcheckableType.test( type ) );
-		} )
-		.map( function( i, elem ) {
-			var val = jQuery( this ).val();
-
-			if ( val == null ) {
-				return null;
-			}
-
-			if ( Array.isArray( val ) ) {
-				return jQuery.map( val, function( val ) {
-					return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
-				} );
-			}
-
-			return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
-		} ).get();
-	}
-} );
-
-
-var
-	r20 = /%20/g,
-	rhash = /#.*$/,
-	rantiCache = /([?&])_=[^&]*/,
-	rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg,
-
-	// #7653, #8125, #8152: local protocol detection
-	rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/,
-	rnoContent = /^(?:GET|HEAD)$/,
-	rprotocol = /^\/\//,
-
-	/* Prefilters
-	 * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example)
-	 * 2) These are called:
-	 *    - BEFORE asking for a transport
-	 *    - AFTER param serialization (s.data is a string if s.processData is true)
-	 * 3) key is the dataType
-	 * 4) the catchall symbol "*" can be used
-	 * 5) execution will start with transport dataType and THEN continue down to "*" if needed
-	 */
-	prefilters = {},
-
-	/* Transports bindings
-	 * 1) key is the dataType
-	 * 2) the catchall symbol "*" can be used
-	 * 3) selection will start with transport dataType and THEN go to "*" if needed
-	 */
-	transports = {},
-
-	// Avoid comment-prolog char sequence (#10098); must appease lint and evade compression
-	allTypes = "*/".concat( "*" ),
-
-	// Anchor tag for parsing the document origin
-	originAnchor = document.createElement( "a" );
-	originAnchor.href = location.href;
-
-// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport
-function addToPrefiltersOrTransports( structure ) {
-
-	// dataTypeExpression is optional and defaults to "*"
-	return function( dataTypeExpression, func ) {
-
-		if ( typeof dataTypeExpression !== "string" ) {
-			func = dataTypeExpression;
-			dataTypeExpression = "*";
-		}
-
-		var dataType,
-			i = 0,
-			dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || [];
-
-		if ( isFunction( func ) ) {
-
-			// For each dataType in the dataTypeExpression
-			while ( ( dataType = dataTypes[ i++ ] ) ) {
-
-				// Prepend if requested
-				if ( dataType[ 0 ] === "+" ) {
-					dataType = dataType.slice( 1 ) || "*";
-					( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func );
-
-				// Otherwise append
-				} else {
-					( structure[ dataType ] = structure[ dataType ] || [] ).push( func );
-				}
-			}
-		}
-	};
-}
-
-// Base inspection function for prefilters and transports
-function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) {
-
-	var inspected = {},
-		seekingTransport = ( structure === transports );
-
-	function inspect( dataType ) {
-		var selected;
-		inspected[ dataType ] = true;
-		jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) {
-			var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR );
-			if ( typeof dataTypeOrTransport === "string" &&
-				!seekingTransport && !inspected[ dataTypeOrTransport ] ) {
-
-				options.dataTypes.unshift( dataTypeOrTransport );
-				inspect( dataTypeOrTransport );
-				return false;
-			} else if ( seekingTransport ) {
-				return !( selected = dataTypeOrTransport );
-			}
-		} );
-		return selected;
-	}
-
-	return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" );
-}
-
-// A special extend for ajax options
-// that takes "flat" options (not to be deep extended)
-// Fixes #9887
-function ajaxExtend( target, src ) {
-	var key, deep,
-		flatOptions = jQuery.ajaxSettings.flatOptions || {};
-
-	for ( key in src ) {
-		if ( src[ key ] !== undefined ) {
-			( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ];
-		}
-	}
-	if ( deep ) {
-		jQuery.extend( true, target, deep );
-	}
-
-	return target;
-}
-
-/* Handles responses to an ajax request:
- * - finds the right dataType (mediates between content-type and expected dataType)
- * - returns the corresponding response
- */
-function ajaxHandleResponses( s, jqXHR, responses ) {
-
-	var ct, type, finalDataType, firstDataType,
-		contents = s.contents,
-		dataTypes = s.dataTypes;
-
-	// Remove auto dataType and get content-type in the process
-	while ( dataTypes[ 0 ] === "*" ) {
-		dataTypes.shift();
-		if ( ct === undefined ) {
-			ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" );
-		}
-	}
-
-	// Check if we're dealing with a known content-type
-	if ( ct ) {
-		for ( type in contents ) {
-			if ( contents[ type ] && contents[ type ].test( ct ) ) {
-				dataTypes.unshift( type );
-				break;
-			}
-		}
-	}
-
-	// Check to see if we have a response for the expected dataType
-	if ( dataTypes[ 0 ] in responses ) {
-		finalDataType = dataTypes[ 0 ];
-	} else {
-
-		// Try convertible dataTypes
-		for ( type in responses ) {
-			if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) {
-				finalDataType = type;
-				break;
-			}
-			if ( !firstDataType ) {
-				firstDataType = type;
-			}
-		}
-
-		// Or just use first one
-		finalDataType = finalDataType || firstDataType;
-	}
-
-	// If we found a dataType
-	// We add the dataType to the list if needed
-	// and return the corresponding response
-	if ( finalDataType ) {
-		if ( finalDataType !== dataTypes[ 0 ] ) {
-			dataTypes.unshift( finalDataType );
-		}
-		return responses[ finalDataType ];
-	}
-}
-
-/* Chain conversions given the request and the original response
- * Also sets the responseXXX fields on the jqXHR instance
- */
-function ajaxConvert( s, response, jqXHR, isSuccess ) {
-	var conv2, current, conv, tmp, prev,
-		converters = {},
-
-		// Work with a copy of dataTypes in case we need to modify it for conversion
-		dataTypes = s.dataTypes.slice();
-
-	// Create converters map with lowercased keys
-	if ( dataTypes[ 1 ] ) {
-		for ( conv in s.converters ) {
-			converters[ conv.toLowerCase() ] = s.converters[ conv ];
-		}
-	}
-
-	current = dataTypes.shift();
-
-	// Convert to each sequential dataType
-	while ( current ) {
-
-		if ( s.responseFields[ current ] ) {
-			jqXHR[ s.responseFields[ current ] ] = response;
-		}
-
-		// Apply the dataFilter if provided
-		if ( !prev && isSuccess && s.dataFilter ) {
-			response = s.dataFilter( response, s.dataType );
-		}
-
-		prev = current;
-		current = dataTypes.shift();
-
-		if ( current ) {
-
-			// There's only work to do if current dataType is non-auto
-			if ( current === "*" ) {
-
-				current = prev;
-
-			// Convert response if prev dataType is non-auto and differs from current
-			} else if ( prev !== "*" && prev !== current ) {
-
-				// Seek a direct converter
-				conv = converters[ prev + " " + current ] || converters[ "* " + current ];
-
-				// If none found, seek a pair
-				if ( !conv ) {
-					for ( conv2 in converters ) {
-
-						// If conv2 outputs current
-						tmp = conv2.split( " " );
-						if ( tmp[ 1 ] === current ) {
-
-							// If prev can be converted to accepted input
-							conv = converters[ prev + " " + tmp[ 0 ] ] ||
-								converters[ "* " + tmp[ 0 ] ];
-							if ( conv ) {
-
-								// Condense equivalence converters
-								if ( conv === true ) {
-									conv = converters[ conv2 ];
-
-								// Otherwise, insert the intermediate dataType
-								} else if ( converters[ conv2 ] !== true ) {
-									current = tmp[ 0 ];
-									dataTypes.unshift( tmp[ 1 ] );
-								}
-								break;
-							}
-						}
-					}
-				}
-
-				// Apply converter (if not an equivalence)
-				if ( conv !== true ) {
-
-					// Unless errors are allowed to bubble, catch and return them
-					if ( conv && s.throws ) {
-						response = conv( response );
-					} else {
-						try {
-							response = conv( response );
-						} catch ( e ) {
-							return {
-								state: "parsererror",
-								error: conv ? e : "No conversion from " + prev + " to " + current
-							};
-						}
-					}
-				}
-			}
-		}
-	}
-
-	return { state: "success", data: response };
-}
-
-jQuery.extend( {
-
-	// Counter for holding the number of active queries
-	active: 0,
-
-	// Last-Modified header cache for next request
-	lastModified: {},
-	etag: {},
-
-	ajaxSettings: {
-		url: location.href,
-		type: "GET",
-		isLocal: rlocalProtocol.test( location.protocol ),
-		global: true,
-		processData: true,
-		async: true,
-		contentType: "application/x-www-form-urlencoded; charset=UTF-8",
-
-		/*
-		timeout: 0,
-		data: null,
-		dataType: null,
-		username: null,
-		password: null,
-		cache: null,
-		throws: false,
-		traditional: false,
-		headers: {},
-		*/
-
-		accepts: {
-			"*": allTypes,
-			text: "text/plain",
-			html: "text/html",
-			xml: "application/xml, text/xml",
-			json: "application/json, text/javascript"
-		},
-
-		contents: {
-			xml: /\bxml\b/,
-			html: /\bhtml/,
-			json: /\bjson\b/
-		},
-
-		responseFields: {
-			xml: "responseXML",
-			text: "responseText",
-			json: "responseJSON"
-		},
-
-		// Data converters
-		// Keys separate source (or catchall "*") and destination types with a single space
-		converters: {
-
-			// Convert anything to text
-			"* text": String,
-
-			// Text to html (true = no transformation)
-			"text html": true,
-
-			// Evaluate text as a json expression
-			"text json": JSON.parse,
-
-			// Parse text as xml
-			"text xml": jQuery.parseXML
-		},
-
-		// For options that shouldn't be deep extended:
-		// you can add your own custom options here if
-		// and when you create one that shouldn't be
-		// deep extended (see ajaxExtend)
-		flatOptions: {
-			url: true,
-			context: true
-		}
-	},
-
-	// Creates a full fledged settings object into target
-	// with both ajaxSettings and settings fields.
-	// If target is omitted, writes into ajaxSettings.
-	ajaxSetup: function( target, settings ) {
-		return settings ?
-
-			// Building a settings object
-			ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) :
-
-			// Extending ajaxSettings
-			ajaxExtend( jQuery.ajaxSettings, target );
-	},
-
-	ajaxPrefilter: addToPrefiltersOrTransports( prefilters ),
-	ajaxTransport: addToPrefiltersOrTransports( transports ),
-
-	// Main method
-	ajax: function( url, options ) {
-
-		// If url is an object, simulate pre-1.5 signature
-		if ( typeof url === "object" ) {
-			options = url;
-			url = undefined;
-		}
-
-		// Force options to be an object
-		options = options || {};
-
-		var transport,
-
-			// URL without anti-cache param
-			cacheURL,
-
-			// Response headers
-			responseHeadersString,
-			responseHeaders,
-
-			// timeout handle
-			timeoutTimer,
-
-			// Url cleanup var
-			urlAnchor,
-
-			// Request state (becomes false upon send and true upon completion)
-			completed,
-
-			// To know if global events are to be dispatched
-			fireGlobals,
-
-			// Loop variable
-			i,
-
-			// uncached part of the url
-			uncached,
-
-			// Create the final options object
-			s = jQuery.ajaxSetup( {}, options ),
-
-			// Callbacks context
-			callbackContext = s.context || s,
-
-			// Context for global events is callbackContext if it is a DOM node or jQuery collection
-			globalEventContext = s.context &&
-				( callbackContext.nodeType || callbackContext.jquery ) ?
-					jQuery( callbackContext ) :
-					jQuery.event,
-
-			// Deferreds
-			deferred = jQuery.Deferred(),
-			completeDeferred = jQuery.Callbacks( "once memory" ),
-
-			// Status-dependent callbacks
-			statusCode = s.statusCode || {},
-
-			// Headers (they are sent all at once)
-			requestHeaders = {},
-			requestHeadersNames = {},
-
-			// Default abort message
-			strAbort = "canceled",
-
-			// Fake xhr
-			jqXHR = {
-				readyState: 0,
-
-				// Builds headers hashtable if needed
-				getResponseHeader: function( key ) {
-					var match;
-					if ( completed ) {
-						if ( !responseHeaders ) {
-							responseHeaders = {};
-							while ( ( match = rheaders.exec( responseHeadersString ) ) ) {
-								responseHeaders[ match[ 1 ].toLowerCase() ] = match[ 2 ];
-							}
-						}
-						match = responseHeaders[ key.toLowerCase() ];
-					}
-					return match == null ? null : match;
-				},
-
-				// Raw string
-				getAllResponseHeaders: function() {
-					return completed ? responseHeadersString : null;
-				},
-
-				// Caches the header
-				setRequestHeader: function( name, value ) {
-					if ( completed == null ) {
-						name = requestHeadersNames[ name.toLowerCase() ] =
-							requestHeadersNames[ name.toLowerCase() ] || name;
-						requestHeaders[ name ] = value;
-					}
-					return this;
-				},
-
-				// Overrides response content-type header
-				overrideMimeType: function( type ) {
-					if ( completed == null ) {
-						s.mimeType = type;
-					}
-					return this;
-				},
-
-				// Status-dependent callbacks
-				statusCode: function( map ) {
-					var code;
-					if ( map ) {
-						if ( completed ) {
-
-							// Execute the appropriate callbacks
-							jqXHR.always( map[ jqXHR.status ] );
-						} else {
-
-							// Lazy-add the new callbacks in a way that preserves old ones
-							for ( code in map ) {
-								statusCode[ code ] = [ statusCode[ code ], map[ code ] ];
-							}
-						}
-					}
-					return this;
-				},
-
-				// Cancel the request
-				abort: function( statusText ) {
-					var finalText = statusText || strAbort;
-					if ( transport ) {
-						transport.abort( finalText );
-					}
-					done( 0, finalText );
-					return this;
-				}
-			};
-
-		// Attach deferreds
-		deferred.promise( jqXHR );
-
-		// Add protocol if not provided (prefilters might expect it)
-		// Handle falsy url in the settings object (#10093: consistency with old signature)
-		// We also use the url parameter if available
-		s.url = ( ( url || s.url || location.href ) + "" )
-			.replace( rprotocol, location.protocol + "//" );
-
-		// Alias method option to type as per ticket #12004
-		s.type = options.method || options.type || s.method || s.type;
-
-		// Extract dataTypes list
-		s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ];
-
-		// A cross-domain request is in order when the origin doesn't match the current origin.
-		if ( s.crossDomain == null ) {
-			urlAnchor = document.createElement( "a" );
-
-			// Support: IE <=8 - 11, Edge 12 - 15
-			// IE throws exception on accessing the href property if url is malformed,
-			// e.g. http://example.com:80x/
-			try {
-				urlAnchor.href = s.url;
-
-				// Support: IE <=8 - 11 only
-				// Anchor's host property isn't correctly set when s.url is relative
-				urlAnchor.href = urlAnchor.href;
-				s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !==
-					urlAnchor.protocol + "//" + urlAnchor.host;
-			} catch ( e ) {
-
-				// If there is an error parsing the URL, assume it is crossDomain,
-				// it can be rejected by the transport if it is invalid
-				s.crossDomain = true;
-			}
-		}
-
-		// Convert data if not already a string
-		if ( s.data && s.processData && typeof s.data !== "string" ) {
-			s.data = jQuery.param( s.data, s.traditional );
-		}
-
-		// Apply prefilters
-		inspectPrefiltersOrTransports( prefilters, s, options, jqXHR );
-
-		// If request was aborted inside a prefilter, stop there
-		if ( completed ) {
-			return jqXHR;
-		}
-
-		// We can fire global events as of now if asked to
-		// Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118)
-		fireGlobals = jQuery.event && s.global;
-
-		// Watch for a new set of requests
-		if ( fireGlobals && jQuery.active++ === 0 ) {
-			jQuery.event.trigger( "ajaxStart" );
-		}
-
-		// Uppercase the type
-		s.type = s.type.toUpperCase();
-
-		// Determine if request has content
-		s.hasContent = !rnoContent.test( s.type );
-
-		// Save the URL in case we're toying with the If-Modified-Since
-		// and/or If-None-Match header later on
-		// Remove hash to simplify url manipulation
-		cacheURL = s.url.replace( rhash, "" );
-
-		// More options handling for requests with no content
-		if ( !s.hasContent ) {
-
-			// Remember the hash so we can put it back
-			uncached = s.url.slice( cacheURL.length );
-
-			// If data is available and should be processed, append data to url
-			if ( s.data && ( s.processData || typeof s.data === "string" ) ) {
-				cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data;
-
-				// #9682: remove data so that it's not used in an eventual retry
-				delete s.data;
-			}
-
-			// Add or update anti-cache param if needed
-			if ( s.cache === false ) {
-				cacheURL = cacheURL.replace( rantiCache, "$1" );
-				uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce++ ) + uncached;
-			}
-
-			// Put hash and anti-cache on the URL that will be requested (gh-1732)
-			s.url = cacheURL + uncached;
-
-		// Change '%20' to '+' if this is encoded form body content (gh-2658)
-		} else if ( s.data && s.processData &&
-			( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) {
-			s.data = s.data.replace( r20, "+" );
-		}
-
-		// Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
-		if ( s.ifModified ) {
-			if ( jQuery.lastModified[ cacheURL ] ) {
-				jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] );
-			}
-			if ( jQuery.etag[ cacheURL ] ) {
-				jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] );
-			}
-		}
-
-		// Set the correct header, if data is being sent
-		if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) {
-			jqXHR.setRequestHeader( "Content-Type", s.contentType );
-		}
-
-		// Set the Accepts header for the server, depending on the dataType
-		jqXHR.setRequestHeader(
-			"Accept",
-			s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ?
-				s.accepts[ s.dataTypes[ 0 ] ] +
-					( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) :
-				s.accepts[ "*" ]
-		);
-
-		// Check for headers option
-		for ( i in s.headers ) {
-			jqXHR.setRequestHeader( i, s.headers[ i ] );
-		}
-
-		// Allow custom headers/mimetypes and early abort
-		if ( s.beforeSend &&
-			( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) {
-
-			// Abort if not done already and return
-			return jqXHR.abort();
-		}
-
-		// Aborting is no longer a cancellation
-		strAbort = "abort";
-
-		// Install callbacks on deferreds
-		completeDeferred.add( s.complete );
-		jqXHR.done( s.success );
-		jqXHR.fail( s.error );
-
-		// Get transport
-		transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR );
-
-		// If no transport, we auto-abort
-		if ( !transport ) {
-			done( -1, "No Transport" );
-		} else {
-			jqXHR.readyState = 1;
-
-			// Send global event
-			if ( fireGlobals ) {
-				globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] );
-			}
-
-			// If request was aborted inside ajaxSend, stop there
-			if ( completed ) {
-				return jqXHR;
-			}
-
-			// Timeout
-			if ( s.async && s.timeout > 0 ) {
-				timeoutTimer = window.setTimeout( function() {
-					jqXHR.abort( "timeout" );
-				}, s.timeout );
-			}
-
-			try {
-				completed = false;
-				transport.send( requestHeaders, done );
-			} catch ( e ) {
-
-				// Rethrow post-completion exceptions
-				if ( completed ) {
-					throw e;
-				}
-
-				// Propagate others as results
-				done( -1, e );
-			}
-		}
-
-		// Callback for when everything is done
-		function done( status, nativeStatusText, responses, headers ) {
-			var isSuccess, success, error, response, modified,
-				statusText = nativeStatusText;
-
-			// Ignore repeat invocations
-			if ( completed ) {
-				return;
-			}
-
-			completed = true;
-
-			// Clear timeout if it exists
-			if ( timeoutTimer ) {
-				window.clearTimeout( timeoutTimer );
-			}
-
-			// Dereference transport for early garbage collection
-			// (no matter how long the jqXHR object will be used)
-			transport = undefined;
-
-			// Cache response headers
-			responseHeadersString = headers || "";
-
-			// Set readyState
-			jqXHR.readyState = status > 0 ? 4 : 0;
-
-			// Determine if successful
-			isSuccess = status >= 200 && status < 300 || status === 304;
-
-			// Get response data
-			if ( responses ) {
-				response = ajaxHandleResponses( s, jqXHR, responses );
-			}
-
-			// Convert no matter what (that way responseXXX fields are always set)
-			response = ajaxConvert( s, response, jqXHR, isSuccess );
-
-			// If successful, handle type chaining
-			if ( isSuccess ) {
-
-				// Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
-				if ( s.ifModified ) {
-					modified = jqXHR.getResponseHeader( "Last-Modified" );
-					if ( modified ) {
-						jQuery.lastModified[ cacheURL ] = modified;
-					}
-					modified = jqXHR.getResponseHeader( "etag" );
-					if ( modified ) {
-						jQuery.etag[ cacheURL ] = modified;
-					}
-				}
-
-				// if no content
-				if ( status === 204 || s.type === "HEAD" ) {
-					statusText = "nocontent";
-
-				// if not modified
-				} else if ( status === 304 ) {
-					statusText = "notmodified";
-
-				// If we have data, let's convert it
-				} else {
-					statusText = response.state;
-					success = response.data;
-					error = response.error;
-					isSuccess = !error;
-				}
-			} else {
-
-				// Extract error from statusText and normalize for non-aborts
-				error = statusText;
-				if ( status || !statusText ) {
-					statusText = "error";
-					if ( status < 0 ) {
-						status = 0;
-					}
-				}
-			}
-
-			// Set data for the fake xhr object
-			jqXHR.status = status;
-			jqXHR.statusText = ( nativeStatusText || statusText ) + "";
-
-			// Success/Error
-			if ( isSuccess ) {
-				deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] );
-			} else {
-				deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] );
-			}
-
-			// Status-dependent callbacks
-			jqXHR.statusCode( statusCode );
-			statusCode = undefined;
-
-			if ( fireGlobals ) {
-				globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError",
-					[ jqXHR, s, isSuccess ? success : error ] );
-			}
-
-			// Complete
-			completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] );
-
-			if ( fireGlobals ) {
-				globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] );
-
-				// Handle the global AJAX counter
-				if ( !( --jQuery.active ) ) {
-					jQuery.event.trigger( "ajaxStop" );
-				}
-			}
-		}
-
-		return jqXHR;
-	},
-
-	getJSON: function( url, data, callback ) {
-		return jQuery.get( url, data, callback, "json" );
-	},
-
-	getScript: function( url, callback ) {
-		return jQuery.get( url, undefined, callback, "script" );
-	}
-} );
-
-jQuery.each( [ "get", "post" ], function( i, method ) {
-	jQuery[ method ] = function( url, data, callback, type ) {
-
-		// Shift arguments if data argument was omitted
-		if ( isFunction( data ) ) {
-			type = type || callback;
-			callback = data;
-			data = undefined;
-		}
-
-		// The url can be an options object (which then must have .url)
-		return jQuery.ajax( jQuery.extend( {
-			url: url,
-			type: method,
-			dataType: type,
-			data: data,
-			success: callback
-		}, jQuery.isPlainObject( url ) && url ) );
-	};
-} );
-
-
-jQuery._evalUrl = function( url ) {
-	return jQuery.ajax( {
-		url: url,
-
-		// Make this explicit, since user can override this through ajaxSetup (#11264)
-		type: "GET",
-		dataType: "script",
-		cache: true,
-		async: false,
-		global: false,
-		"throws": true
-	} );
-};
-
-
-jQuery.fn.extend( {
-	wrapAll: function( html ) {
-		var wrap;
-
-		if ( this[ 0 ] ) {
-			if ( isFunction( html ) ) {
-				html = html.call( this[ 0 ] );
-			}
-
-			// The elements to wrap the target around
-			wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true );
-
-			if ( this[ 0 ].parentNode ) {
-				wrap.insertBefore( this[ 0 ] );
-			}
-
-			wrap.map( function() {
-				var elem = this;
-
-				while ( elem.firstElementChild ) {
-					elem = elem.firstElementChild;
-				}
-
-				return elem;
-			} ).append( this );
-		}
-
-		return this;
-	},
-
-	wrapInner: function( html ) {
-		if ( isFunction( html ) ) {
-			return this.each( function( i ) {
-				jQuery( this ).wrapInner( html.call( this, i ) );
-			} );
-		}
-
-		return this.each( function() {
-			var self = jQuery( this ),
-				contents = self.contents();
-
-			if ( contents.length ) {
-				contents.wrapAll( html );
-
-			} else {
-				self.append( html );
-			}
-		} );
-	},
-
-	wrap: function( html ) {
-		var htmlIsFunction = isFunction( html );
-
-		return this.each( function( i ) {
-			jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html );
-		} );
-	},
-
-	unwrap: function( selector ) {
-		this.parent( selector ).not( "body" ).each( function() {
-			jQuery( this ).replaceWith( this.childNodes );
-		} );
-		return this;
-	}
-} );
-
-
-jQuery.expr.pseudos.hidden = function( elem ) {
-	return !jQuery.expr.pseudos.visible( elem );
-};
-jQuery.expr.pseudos.visible = function( elem ) {
-	return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length );
-};
-
-
-
-
-jQuery.ajaxSettings.xhr = function() {
-	try {
-		return new window.XMLHttpRequest();
-	} catch ( e ) {}
-};
-
-var xhrSuccessStatus = {
-
-		// File protocol always yields status code 0, assume 200
-		0: 200,
-
-		// Support: IE <=9 only
-		// #1450: sometimes IE returns 1223 when it should be 204
-		1223: 204
-	},
-	xhrSupported = jQuery.ajaxSettings.xhr();
-
-support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported );
-support.ajax = xhrSupported = !!xhrSupported;
-
-jQuery.ajaxTransport( function( options ) {
-	var callback, errorCallback;
-
-	// Cross domain only allowed if supported through XMLHttpRequest
-	if ( support.cors || xhrSupported && !options.crossDomain ) {
-		return {
-			send: function( headers, complete ) {
-				var i,
-					xhr = options.xhr();
-
-				xhr.open(
-					options.type,
-					options.url,
-					options.async,
-					options.username,
-					options.password
-				);
-
-				// Apply custom fields if provided
-				if ( options.xhrFields ) {
-					for ( i in options.xhrFields ) {
-						xhr[ i ] = options.xhrFields[ i ];
-					}
-				}
-
-				// Override mime type if needed
-				if ( options.mimeType && xhr.overrideMimeType ) {
-					xhr.overrideMimeType( options.mimeType );
-				}
-
-				// X-Requested-With header
-				// For cross-domain requests, seeing as conditions for a preflight are
-				// akin to a jigsaw puzzle, we simply never set it to be sure.
-				// (it can always be set on a per-request basis or even using ajaxSetup)
-				// For same-domain requests, won't change header if already provided.
-				if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) {
-					headers[ "X-Requested-With" ] = "XMLHttpRequest";
-				}
-
-				// Set headers
-				for ( i in headers ) {
-					xhr.setRequestHeader( i, headers[ i ] );
-				}
-
-				// Callback
-				callback = function( type ) {
-					return function() {
-						if ( callback ) {
-							callback = errorCallback = xhr.onload =
-								xhr.onerror = xhr.onabort = xhr.ontimeout =
-									xhr.onreadystatechange = null;
-
-							if ( type === "abort" ) {
-								xhr.abort();
-							} else if ( type === "error" ) {
-
-								// Support: IE <=9 only
-								// On a manual native abort, IE9 throws
-								// errors on any property access that is not readyState
-								if ( typeof xhr.status !== "number" ) {
-									complete( 0, "error" );
-								} else {
-									complete(
-
-										// File: protocol always yields status 0; see #8605, #14207
-										xhr.status,
-										xhr.statusText
-									);
-								}
-							} else {
-								complete(
-									xhrSuccessStatus[ xhr.status ] || xhr.status,
-									xhr.statusText,
-
-									// Support: IE <=9 only
-									// IE9 has no XHR2 but throws on binary (trac-11426)
-									// For XHR2 non-text, let the caller handle it (gh-2498)
-									( xhr.responseType || "text" ) !== "text"  ||
-									typeof xhr.responseText !== "string" ?
-										{ binary: xhr.response } :
-										{ text: xhr.responseText },
-									xhr.getAllResponseHeaders()
-								);
-							}
-						}
-					};
-				};
-
-				// Listen to events
-				xhr.onload = callback();
-				errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" );
-
-				// Support: IE 9 only
-				// Use onreadystatechange to replace onabort
-				// to handle uncaught aborts
-				if ( xhr.onabort !== undefined ) {
-					xhr.onabort = errorCallback;
-				} else {
-					xhr.onreadystatechange = function() {
-
-						// Check readyState before timeout as it changes
-						if ( xhr.readyState === 4 ) {
-
-							// Allow onerror to be called first,
-							// but that will not handle a native abort
-							// Also, save errorCallback to a variable
-							// as xhr.onerror cannot be accessed
-							window.setTimeout( function() {
-								if ( callback ) {
-									errorCallback();
-								}
-							} );
-						}
-					};
-				}
-
-				// Create the abort callback
-				callback = callback( "abort" );
-
-				try {
-
-					// Do send the request (this may raise an exception)
-					xhr.send( options.hasContent && options.data || null );
-				} catch ( e ) {
-
-					// #14683: Only rethrow if this hasn't been notified as an error yet
-					if ( callback ) {
-						throw e;
-					}
-				}
-			},
-
-			abort: function() {
-				if ( callback ) {
-					callback();
-				}
-			}
-		};
-	}
-} );
-
-
-
-
-// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432)
-jQuery.ajaxPrefilter( function( s ) {
-	if ( s.crossDomain ) {
-		s.contents.script = false;
-	}
-} );
-
-// Install script dataType
-jQuery.ajaxSetup( {
-	accepts: {
-		script: "text/javascript, application/javascript, " +
-			"application/ecmascript, application/x-ecmascript"
-	},
-	contents: {
-		script: /\b(?:java|ecma)script\b/
-	},
-	converters: {
-		"text script": function( text ) {
-			jQuery.globalEval( text );
-			return text;
-		}
-	}
-} );
-
-// Handle cache's special case and crossDomain
-jQuery.ajaxPrefilter( "script", function( s ) {
-	if ( s.cache === undefined ) {
-		s.cache = false;
-	}
-	if ( s.crossDomain ) {
-		s.type = "GET";
-	}
-} );
-
-// Bind script tag hack transport
-jQuery.ajaxTransport( "script", function( s ) {
-
-	// This transport only deals with cross domain requests
-	if ( s.crossDomain ) {
-		var script, callback;
-		return {
-			send: function( _, complete ) {
-				script = jQuery( "
-{% endmacro %}
-
-{% macro body_post() %}
-  
-  
-
-{% endmacro %}
\ No newline at end of file
diff --git a/doc/build/html/examples.html b/doc/build/html/examples.html
deleted file mode 100644
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@@ -1,891 +0,0 @@
-
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-  
-    
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-    Examples — Squigglepy  documentation
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-                  
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-
    Examples#
    
-
    
-
    Piano Tuners Example#
    
-
    Here’s the Squigglepy implementation of the example from Squiggle
-Docs:
    
-
    import squigglepy as sq
-import numpy as np
-import matplotlib.pyplot as plt
-from squigglepy.numbers import K, M
-from pprint import pprint
-
-pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)  # This means that you're 90% confident the value is between 8.1 and 8.4 Million.
-pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01  # We assume there are almost no people with multiple pianos
-pianos_per_piano_tuner = sq.to(2*K, 50*K)
-piano_tuners_per_piano = 1 / pianos_per_piano_tuner
-total_tuners_in_2022 = pop_of_ny_2022 * pct_of_pop_w_pianos * piano_tuners_per_piano
-samples = total_tuners_in_2022 @ 1000  # Note: `@ 1000` is shorthand to get 1000 samples
-
-# Get mean and SD
-print('Mean: {}, SD: {}'.format(round(np.mean(samples), 2),
-                                round(np.std(samples), 2)))
-
-# Get percentiles
-pprint(sq.get_percentiles(samples, digits=0))
-
-# Histogram
-plt.hist(samples, bins=200)
-plt.show()
-
-# Shorter histogram
-total_tuners_in_2022.plot()
-
    
-
    
-
    And the version from the Squiggle doc that incorporates time:
    
-
    import squigglepy as sq
-from squigglepy.numbers import K, M
-
-pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)
-pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01
-pianos_per_piano_tuner = sq.to(2*K, 50*K)
-piano_tuners_per_piano = 1 / pianos_per_piano_tuner
-
-def pop_at_time(t):  # t = Time in years after 2022
-    avg_yearly_pct_change = sq.to(-0.01, 0.05)  # We're expecting NYC to continuously grow with an mean of roughly between -1% and +4% per year
-    return pop_of_ny_2022 * ((avg_yearly_pct_change + 1) ** t)
-
-def total_tuners_at_time(t):
-    return pop_at_time(t) * pct_of_pop_w_pianos * piano_tuners_per_piano
-
-# Get total piano tuners at 2030
-sq.get_percentiles(total_tuners_at_time(2030-2022) @ 1000)
-
    
-
    
-
    WARNING: Be careful about dividing by K, M, etc. 1/2*K =
-500 in Python. Use 1/(2*K) instead to get the expected outcome.
    
-
    WARNING: Be careful about using K to get sample counts. Use
-sq.norm(2, 3) @ (2*K)… sq.norm(2, 3) @ 2*K will return only
-two samples, multiplied by 1000.
    
-
    
-
    
-
    Distributions#
    
-
    import squigglepy as sq
-
-# Normal distribution
-sq.norm(1, 3)  # 90% interval from 1 to 3
-
-# Distribution can be sampled with mean and sd too
-sq.norm(mean=0, sd=1)
-
-# Shorthand to get one sample
-~sq.norm(1, 3)
-
-# Shorthand to get more than one sample
-sq.norm(1, 3) @ 100
-
-# Longhand version to get more than one sample
-sq.sample(sq.norm(1, 3), n=100)
-
-# Nice progress reporter
-sq.sample(sq.norm(1, 3), n=1000, verbose=True)
-
-# Other distributions exist
-sq.lognorm(1, 10)
-sq.tdist(1, 10, t=5)
-sq.triangular(1, 2, 3)
-sq.pert(1, 2, 3, lam=2)
-sq.binomial(p=0.5, n=5)
-sq.beta(a=1, b=2)
-sq.bernoulli(p=0.5)
-sq.poisson(10)
-sq.chisquare(2)
-sq.gamma(3, 2)
-sq.pareto(1)
-sq.exponential(scale=1)
-sq.geometric(p=0.5)
-
-# Discrete sampling
-sq.discrete({'A': 0.1, 'B': 0.9})
-
-# Can return integers
-sq.discrete({0: 0.1, 1: 0.3, 2: 0.3, 3: 0.15, 4: 0.15})
-
-# Alternate format (also can be used to return more complex objects)
-sq.discrete([[0.1,  0],
-             [0.3,  1],
-             [0.3,  2],
-             [0.15, 3],
-             [0.15, 4]])
-
-sq.discrete([0, 1, 2]) # No weights assumes equal weights
-
-# You can mix distributions together
-sq.mixture([sq.norm(1, 3),
-            sq.norm(4, 10),
-            sq.lognorm(1, 10)],  # Distributions to mix
-           [0.3, 0.3, 0.4])     # These are the weights on each distribution
-
-# This is equivalent to the above, just a different way of doing the notation
-sq.mixture([[0.3, sq.norm(1,3)],
-            [0.3, sq.norm(4,10)],
-            [0.4, sq.lognorm(1,10)]])
-
-# Make a zero-inflated distribution
-# 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`.
-sq.zero_inflated(0.6, sq.norm(1, 2))
-
    
-
    
-
    
-
    
-
    Additional Features#
    
-
    import squigglepy as sq
-
-# You can add and subtract distributions
-(sq.norm(1,3) + sq.norm(4,5)) @ 100
-(sq.norm(1,3) - sq.norm(4,5)) @ 100
-(sq.norm(1,3) * sq.norm(4,5)) @ 100
-(sq.norm(1,3) / sq.norm(4,5)) @ 100
-
-# You can also do math with numbers
-~((sq.norm(sd=5) + 2) * 2)
-~(-sq.lognorm(0.1, 1) * sq.pareto(1) / 10)
-
-# You can change the CI from 90% (default) to 80%
-sq.norm(1, 3, credibility=80)
-
-# You can clip
-sq.norm(0, 3, lclip=0, rclip=5) # Sample norm with a 90% CI from 0-3, but anything lower than 0 gets clipped to 0 and anything higher than 5 gets clipped to 5.
-
-# You can also clip with a function, and use pipes
-sq.norm(0, 3) >> sq.clip(0, 5)
-
-# You can correlate continuous distributions
-a, b = sq.uniform(-1, 1), sq.to(0, 3)
-a, b = sq.correlate((a, b), 0.5)  # Correlate a and b with a correlation of 0.5
-# You can even pass your own correlation matrix!
-a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]])
-
    
-
    
-
    
-
    Example: Rolling a Die#
    
-
    An example of how to use distributions to build tools:
    
-
    import squigglepy as sq
-
-def roll_die(sides, n=1):
-    return sq.discrete(list(range(1, sides + 1))) @ n if sides > 0 else None
-
-roll_die(sides=6, n=10)
-# [2, 6, 5, 2, 6, 2, 3, 1, 5, 2]
-
    
-
    
-
    This is already included standard in the utils of this package. Use
-sq.roll_die.
    
-
    
-
    
-
    
-
    Bayesian inference#
    
-
    1% of women at age forty who participate in routine screening have
-breast cancer. 80% of women with breast cancer will get positive
-mammographies. 9.6% of women without breast cancer will also get
-positive mammographies.
    
-
    A woman in this age group had a positive mammography in a routine
-screening. What is the probability that she actually has breast cancer?
    
-
    We can approximate the answer with a Bayesian network (uses rejection
-sampling):
    
-
    import squigglepy as sq
-from squigglepy import bayes
-from squigglepy.numbers import M
-
-def mammography(has_cancer):
-    return sq.event(0.8 if has_cancer else 0.096)
-
-def define_event():
-    cancer = ~sq.bernoulli(0.01)
-    return({'mammography': mammography(cancer),
-            'cancer': cancer})
-
-bayes.bayesnet(define_event,
-               find=lambda e: e['cancer'],
-               conditional_on=lambda e: e['mammography'],
-               n=1*M)
-# 0.07723995880535531
-
    
-
    
-
    Or if we have the information immediately on hand, we can directly
-calculate it. Though this doesn’t work for very complex stuff.
    
-
    from squigglepy import bayes
-bayes.simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096)
-# 0.07763975155279504
-
    
-
    
-
    You can also make distributions and update them:
    
-
    import matplotlib.pyplot as plt
-import squigglepy as sq
-from squigglepy import bayes
-from squigglepy.numbers import K
-import numpy as np
-
-print('Prior')
-prior = sq.norm(1,5)
-prior_samples = prior @ (10*K)
-plt.hist(prior_samples, bins = 200)
-plt.show()
-print(sq.get_percentiles(prior_samples))
-print('Prior Mean: {} SD: {}'.format(np.mean(prior_samples), np.std(prior_samples)))
-print('-')
-
-print('Evidence')
-evidence = sq.norm(2,3)
-evidence_samples = evidence @ (10*K)
-plt.hist(evidence_samples, bins = 200)
-plt.show()
-print(sq.get_percentiles(evidence_samples))
-print('Evidence Mean: {} SD: {}'.format(np.mean(evidence_samples), np.std(evidence_samples)))
-print('-')
-
-print('Posterior')
-posterior = bayes.update(prior, evidence)
-posterior_samples = posterior @ (10*K)
-plt.hist(posterior_samples, bins = 200)
-plt.show()
-print(sq.get_percentiles(posterior_samples))
-print('Posterior Mean: {} SD: {}'.format(np.mean(posterior_samples), np.std(posterior_samples)))
-
-print('Average')
-average = bayes.average(prior, evidence)
-average_samples = average @ (10*K)
-plt.hist(average_samples, bins = 200)
-plt.show()
-print(sq.get_percentiles(average_samples))
-print('Average Mean: {} SD: {}'.format(np.mean(average_samples), np.std(average_samples)))
-
    
-
    
-
    
-
    Example: Alarm net#
    
-
    This is the alarm network from Bayesian Artificial Intelligence -
-Section
-2.5.1:
    
-
    
-
    Assume your house has an alarm system against burglary.
    
-
    You live in the seismically active area and the alarm system can get
-occasionally set off by an earthquake.
    
-
    You have two neighbors, Mary and John, who do not know each other. If
-they hear the alarm they call you, but this is not guaranteed.
    
-
    The chance of a burglary on a particular day is 0.1%. The chance of
-an earthquake on a particular day is 0.2%.
    
-
    The alarm will go off 95% of the time with both a burglary and an
-earthquake, 94% of the time with just a burglary, 29% of the time
-with just an earthquake, and 0.1% of the time with nothing (total
-false alarm).
    
-
    John will call you 90% of the time when the alarm goes off. But on 5%
-of the days, John will just call to say “hi”. Mary will call you 70%
-of the time when the alarm goes off. But on 1% of the days, Mary will
-just call to say “hi”.
    
-
    
-
    import squigglepy as sq
-from squigglepy import bayes
-from squigglepy.numbers import M
-
-def p_alarm_goes_off(burglary, earthquake):
-    if burglary and earthquake:
-        return 0.95
-    elif burglary and not earthquake:
-        return 0.94
-    elif not burglary and earthquake:
-        return 0.29
-    elif not burglary and not earthquake:
-        return 0.001
-
-def p_john_calls(alarm_goes_off):
-    return 0.9 if alarm_goes_off else 0.05
-
-def p_mary_calls(alarm_goes_off):
-    return 0.7 if alarm_goes_off else 0.01
-
-def define_event():
-    burglary_happens = sq.event(p=0.001)
-    earthquake_happens = sq.event(p=0.002)
-    alarm_goes_off = sq.event(p_alarm_goes_off(burglary_happens, earthquake_happens))
-    john_calls = sq.event(p_john_calls(alarm_goes_off))
-    mary_calls = sq.event(p_mary_calls(alarm_goes_off))
-    return {'burglary': burglary_happens,
-            'earthquake': earthquake_happens,
-            'alarm_goes_off': alarm_goes_off,
-            'john_calls': john_calls,
-            'mary_calls': mary_calls}
-
-# What are the chances that both John and Mary call if an earthquake happens?
-bayes.bayesnet(define_event,
-               n=1*M,
-               find=lambda e: (e['mary_calls'] and e['john_calls']),
-               conditional_on=lambda e: e['earthquake'])
-# Result will be ~0.19, though it varies because it is based on a random sample.
-# This also may take a minute to run.
-
-# If both John and Mary call, what is the chance there's been a burglary?
-bayes.bayesnet(define_event,
-               n=1*M,
-               find=lambda e: e['burglary'],
-               conditional_on=lambda e: (e['mary_calls'] and e['john_calls']))
-# Result will be ~0.27, though it varies because it is based on a random sample.
-# This will run quickly because there is a built-in cache.
-# Use `cache=False` to not build a cache and `reload_cache=True` to recalculate the cache.
-
    
-
    
-
    Note that the amount of Bayesian analysis that squigglepy can do is
-pretty limited. For more complex bayesian analysis, consider
-sorobn,
-pomegranate,
-bnlearn, or
-pyMC.
    
-
    
-
    
-
    Example: A Demonstration of the Monty Hall Problem#
    
-
    import squigglepy as sq
-from squigglepy import bayes
-from squigglepy.numbers import K, M, B, T
-
-
-def monte_hall(door_picked, switch=False):
-    doors = ['A', 'B', 'C']
-    car_is_behind_door = ~sq.discrete(doors)
-    reveal_door = ~sq.discrete([d for d in doors if d != door_picked and d != car_is_behind_door])
-
-    if switch:
-        old_door_picked = door_picked
-        door_picked = [d for d in doors if d != old_door_picked and d != reveal_door][0]
-
-    won_car = (car_is_behind_door == door_picked)
-    return won_car
-
-
-def define_event():
-    door = ~sq.discrete(['A', 'B', 'C'])
-    switch = sq.event(0.5)
-    return {'won': monte_hall(door_picked=door, switch=switch),
-            'switched': switch}
-
-RUNS = 10*K
-r = bayes.bayesnet(define_event,
-                   find=lambda e: e['won'],
-                   conditional_on=lambda e: e['switched'],
-                   verbose=True,
-                   n=RUNS)
-print('Win {}% of the time when switching'.format(int(r * 100)))
-
-r = bayes.bayesnet(define_event,
-                   find=lambda e: e['won'],
-                   conditional_on=lambda e: not e['switched'],
-                   verbose=True,
-                   n=RUNS)
-print('Win {}% of the time when not switching'.format(int(r * 100)))
-
-# Win 66% of the time when switching
-# Win 34% of the time when not switching
-
    
-
    
-
    
-
    
-
    Example: More complex coin/dice interactions#
    
-
    
-
    Imagine that I flip a coin. If heads, I take a random die out of my
-blue bag. If tails, I take a random die out of my red bag. The blue
-bag contains only 6-sided dice. The red bag contains a 4-sided die, a
-6-sided die, a 10-sided die, and a 20-sided die. I then roll the
-random die I took. What is the chance that I roll a 6?
    
-
    
-
    import squigglepy as sq
-from squigglepy.numbers import K, M, B, T
-from squigglepy import bayes
-
-def define_event():
-    if sq.flip_coin() == 'heads': # Blue bag
-        return sq.roll_die(6)
-    else: # Red bag
-        return sq.discrete([4, 6, 10, 20]) >> sq.roll_die
-
-
-bayes.bayesnet(define_event,
-               find=lambda e: e == 6,
-               verbose=True,
-               n=100*K)
-# This run for me returned 0.12306 which is pretty close to the correct answer of 0.12292
-
    
-
    
-
    
-
    
-
    
-
    Kelly betting#
    
-
    You can use probability generated, combine with a bankroll to determine
-bet sizing using Kelly
-criterion.
    
-
    For example, if you want to Kelly bet and you’ve…
    
-
      
-
    • determined that your price (your probability of the event in question
-happening / the market in question resolving in your favor) is $0.70
-(70%)
      • 
-
    • see that the market is pricing at $0.65
      • 
-
    • you have a bankroll of $1000 that you are willing to bet
      • 
-
    
-
    You should bet as follows:
    
-
    import squigglepy as sq
-kelly_data = sq.kelly(my_price=0.70, market_price=0.65, bankroll=1000)
-kelly_data['kelly']  # What fraction of my bankroll should I bet on this?
-# 0.143
-kelly_data['target']  # How much money should be invested in this?
-# 142.86
-kelly_data['expected_roi']  # What is the expected ROI of this bet?
-# 0.077
-
    
-
    
-
    
-
    
-
    More examples#
    
-
    You can see more examples of squigglepy in action
-here.
    
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-    Created using Sphinx 7.2.6.
-    
    
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-      
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-  Built with the PyData Sphinx Theme 0.14.3.
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-    Squigglepy: Implementation of Squiggle in Python — Squigglepy  documentation
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    Squigglepy: Implementation of Squiggle in Python#
    
-
    Squiggle is a “simple
-programming language for intuitive probabilistic estimation”. It serves
-as its own standalone programming language with its own syntax, but it
-is implemented in JavaScript. I like the features of Squiggle and intend
-to use it frequently, but I also sometimes want to use similar
-functionalities in Python, especially alongside other Python statistical
-programming packages like Numpy, Pandas, and Matplotlib. The
-squigglepy package here implements many Squiggle-like
-functionalities in Python.
    
-
    
-
    Contents
    
-
-
    
-
    
-
    Disclaimers#
    
-
    This package is unofficial and supported by Peter Wildeford and Rethink
-Priorities. It is not affiliated with or associated with the Quantified
-Uncertainty Research Institute, which maintains the Squiggle language
-(in JavaScript).
    
-
    This package is also new and not yet in a stable production version, so
-you may encounter bugs and other errors. Please report those so they can
-be fixed. It’s also possible that future versions of the package may
-introduce breaking changes.
    
-
    This package is available under an MIT License.
    
-
    
-
    
-
    Acknowledgements#
    
-
      
-
    • The primary author of this package is Peter Wildeford. Agustín
-Covarrubias and Bernardo Baron contributed several key features and
-developments.
      • 
-
    • Thanks to Ozzie Gooen and the Quantified Uncertainty Research
-Institute for creating and maintaining the original Squiggle
-language.
      • 
-
    • Thanks to Dawn Drescher for helping me implement math between
-distributions.
      • 
-
    • Thanks to Dawn Drescher for coming up with the idea to use ~ as a
-shorthand for sample, as well as helping me implement it.
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-
    
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-
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    squigglepy.bayes module#
    
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    This modules includes functions for Bayesian inference.
    
-
    
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-squigglepy.bayes.average(prior, evidence, weights=[0.5, 0.5], relative_weights=None)[source]#
    
-
    Average two distributions.
    
-
    
-
    Parameters:
    
-
    
-
    priorDistribution
    The prior distribution.
    
-
    
-
    evidenceDistribution
    The distribution used to average with the prior.
    
-
    
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    weightslist or np.array or float
    How much weight to put on prior versus evidence when averaging? If
-only one weight is passed, the other weight will be inferred to make the
-total weights sum to 1. Defaults to 50-50 weights.
    
-
    
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    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
-to sum to 1.
    
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    Returns:
    
-
    
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    Distribution
    A mixture distribution that accords weights to prior and evidence.
    
-
    
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-
    
-
    Examples
    
-
    >> prior = sq.norm(1,5)
->> evidence = sq.norm(2,3)
->> bayes.average(prior, evidence)
-<Distribution> mixture
    
-
    
-
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-squigglepy.bayes.bayesnet(event_fn=None, n=1, find=None, conditional_on=None, reduce_fn=None, raw=False, memcache=True, memcache_load=True, memcache_save=True, reload_cache=False, dump_cache_file=None, load_cache_file=None, cache_file_primary=False, verbose=False, cores=1)[source]#
    
-
    Calculate a Bayesian network.
    
-
    Allows you to find conditional probabilities of custom events based on
-rejection sampling.
    
-
    
-
    Parameters:
    
-
    
-
    event_fnfunction
    A function that defines the bayesian network
    
-
    
-
    nint
    The number of samples to generate
    
-
    
-
    finda function or None
    What do we want to know the probability of?
    
-
    
-
    conditional_ona function or None
    When finding the probability, what do we want to condition on?
    
-
    
-
    reduce_fna function or None
    When taking all the results of the simulations, how do we aggregate them
-into a final answer? Defaults to np.mean.
    
-
    
-
    rawbool
    If True, just return the results of each simulation without aggregating.
    
-
    
-
    memcachebool
    If True, cache the results in-memory for future calculations. Each cache
-will be matched based on the event_fn. Default True.
    
-
    
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    memcache_loadbool
    If True, load cache from the in-memory. This will be true if memcache
-is True. Cache will be matched based on the event_fn. Default True.
    
-
    
-
    memcache_savebool
    If True, save results to an in-memory cache. This will be true if memcache
-is True. Cache will be matched based on the event_fn. Default True.
    
-
    
-
    reload_cachebool
    If True, any existing cache will be ignored and recalculated. Default False.
    
-
    
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    dump_cache_filestr or None
    If present, will write out the cache to a binary file with this path with
-.sqlcache appended to the file name.
    
-
    
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    load_cache_filestr or None
    If present, will first attempt to load and use a cache from a file with this
-path with .sqlcache appended to the file name.
    
-
    
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    cache_file_primarybool
    If both an in-memory cache and file cache are present, the file
-cache will be used for the cache if this is True, and the in-memory cache
-will be used otherwise. Defaults to False.
    
-
    
-
    verbosebool
    If True, will print out statements on computational progress.
    
-
    
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    coresint
    If 1, runs on a single core / process. If greater than 1, will run on a multiprocessing
-pool with that many cores / processes.
    
-
    
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    Returns:
    
-
    
-
    various
    The result of reduce_fn on n simulations of event_fn.
    
-
    
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-
    
-
    
-
    Examples
    
-
    # Cancer example: prior of having cancer is 1%, the likelihood of a positive
-# mammography given cancer is 80% (true positive rate), and the likelihood of
-# a positive mammography given no cancer is 9.6% (false positive rate).
-# Given this, what is the probability of cancer given a positive mammography?
->> def mammography(has_cancer):
->>    p = 0.8 if has_cancer else 0.096
->>    return bool(sq.sample(sq.bernoulli(p)))
->>
->> def define_event():
->>    cancer = sq.sample(sq.bernoulli(0.01))
->>    return({‘mammography’: mammography(cancer),
->>            ‘cancer’: cancer})
->>
->> bayes.bayesnet(define_event,
->>                find=lambda e: e[‘cancer’],
->>                conditional_on=lambda e: e[‘mammography’],
->>                n=1*M)
-0.07723995880535531
    
-
    
-
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-squigglepy.bayes.simple_bayes(likelihood_h, likelihood_not_h, prior)[source]#
    
-
    Calculate Bayes rule.
    
-
    p(h|e) = (p(e|h)*p(h)) / (p(e|h)*p(h) + p(e|~h)*(1-p(h)))
-p(h|e) is called posterior
-p(e|h) is called likelihood
-p(h) is called prior
    
-
    
-
    Parameters:
    
-
    
-
    likelihood_hfloat
    The likelihood (given that the hypothesis is true), aka p(e|h)
    
-
    
-
    likelihood_not_hfloat
    The likelihood given the hypothesis is not true, aka p(e|~h)
    
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    priorfloat
    The prior probability, aka p(h)
    
-
    
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    Returns:
    
-
    
-
    float
    The result of Bayes rule, aka p(h|e)
    
-
    
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-
    
-
    
-
    Examples
    
-
    # Cancer example: prior of having cancer is 1%, the likelihood of a positive
-# mammography given cancer is 80% (true positive rate), and the likelihood of
-# a positive mammography given no cancer is 9.6% (false positive rate).
-# Given this, what is the probability of cancer given a positive mammography?
->>> simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096)
-0.07763975155279504
    
-
    
-
-
    
-
    
-squigglepy.bayes.update(prior, evidence, evidence_weight=1)[source]#
    
-
    Update a distribution.
    
-
    Starting with a prior distribution, use Bayesian inference to perform an update,
-producing a posterior distribution from the evidence distribution.
    
-
    
-
    Parameters:
    
-
    
-
    priorDistribution
    The prior distribution. Currently must either be normal or beta type. Other
-types are not yet supported.
    
-
    
-
    evidenceDistribution
    The distribution used to update the prior. Currently must either be normal
-or beta type. Other types are not yet supported.
    
-
    
-
    evidence_weightfloat
    How much weight to put on the evidence distribution? Currently this only matters
-for normal distributions, where this should be equivalent to the sample weight.
    
-
    
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-
    Returns:
    
-
    
-
    Distribution
    The posterior distribution
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >> prior = sq.norm(1,5)
->> evidence = sq.norm(2,3)
->> bayes.update(prior, evidence)
-<Distribution> norm(mean=2.53, sd=0.29)
    
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    squigglepy.correlation module#
    
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-
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-
    
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-class squigglepy.correlation.CorrelationGroup(correlated_dists: tuple[OperableDistribution], correlation_matrix: NDArray[np.float64], correlation_tolerance: float | None = 0.05, min_unique_samples: int = 100)[source]#
    
-
    Bases: object
    
-
    An object that holds metadata for a group of correlated distributions.
-This object is not intended to be used directly by the user, but
-rather during sampling to induce correlations between distributions.
    
-
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-
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-
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    has_sufficient_sample_diversity(samples[, ...])
    Check if there is there are sufficient unique samples to work with in the data.
    induce_correlation(data)
    Induce a set of correlations on a column-wise dataset
    
-
    
-
    
-correlated_dists: tuple[OperableDistribution]#
    
-
    
-
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-
    
-correlation_matrix: NDArray[np.float64]#
    
-
    
-
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-
    
-correlation_tolerance: float | None = 0.05#
    
-
    
-
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-
    
-has_sufficient_sample_diversity(samples: ndarray[Any, dtype[float64]], relative_threshold: float = 0.7, absolute_threshold=None) → bool[source]#
    
-
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-
    
-
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-
    
-induce_correlation(data: ndarray[Any, dtype[float64]]) → ndarray[Any, dtype[float64]][source]#
    
-
    Induce a set of correlations on a column-wise dataset
    
-
    
-
    Parameters:
    
-
    
-
    data2d-array
    An m-by-n array where m is the number of samples and n is the
-number of independent variables, each column of the array corresponding
-to each variable
    
-
    
-
    corrmat2d-array
    An n-by-n array that defines the desired correlation coefficients
-(between -1 and 1). Note: the matrix must be symmetric and
-positive-definite in order to induce.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    new_data2d-array
    An m-by-n array that has the desired correlations.
    
-
    
-
    
-
    
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-
    
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-
    
-min_unique_samples: int = 100#
    
-
    
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-
    
-squigglepy.correlation.correlate(variables: tuple[OperableDistribution, ...], correlation: NDArray[np.float64] | list[list[float]] | np.float64 | float, tolerance: float | np.float64 | None = 0.05, _min_unique_samples: int = 100)[source]#
    
-
    Correlate a set of variables according to a rank correlation matrix.
    
-
    This employs the Iman-Conover method to induce the correlation while
-preserving the original marginal distributions.
    
-
    This method works on a best-effort basis, and may fail to induce the desired
-correlation depending on the distributions provided. An exception will be raised
-if that’s the case.
    
-
    
-
    Parameters:
    
-
    
-
    variablestuple of distributions
    The variables to correlate as a tuple of distributions.
    
-
    The distributions must be able to produce enough unique samples for the method
-to be able to induce the desired correlation by shuffling the samples.
    
-
    Discrete distributions are notably hard to correlate this way,
-as it’s common for them to result in very few unique samples.
    
-
    
-
    correlation2d-array or float
    An n-by-n array that defines the desired Spearman rank correlation coefficients.
-This matrix must be symmetric and positive semi-definite; and must not be confused with
-a covariance matrix.
    
-
    Correlation parameters can only be between -1 and 1, exclusive
-(including extremely close approximations).
    
-
    If a float is provided, all variables will be correlated with the same coefficient.
    
-
    
-
    tolerancefloat, optional
    If provided, overrides the absolute tolerance used to check if the resulting
-correlation matrix matches the desired correlation matrix. Defaults to 0.05.
    
-
    Checking can also be disabled by passing None.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    correlated_variablestuple of distributions
    The correlated variables as a tuple of distributions in the same order as
-the input variables.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    Suppose we want to correlate two variables with a correlation coefficient of 0.65:
->>> solar_radiation, temperature = sq.gamma(300, 100), sq.to(22, 28)
->>> solar_radiation, temperature = sq.correlate((solar_radiation, temperature), 0.7)
->>> print(np.corrcoef(solar_radiation @ 1000, temperature @ 1000)[0, 1])
-0.6975960649767123
    
-
    Or you could pass a correlation matrix:
    
-
    >>> funding_gap, cost_per_delivery, effect_size = (
-        sq.to(20_000, 80_000), sq.to(30, 80), sq.beta(2, 5)
-    )
->>> funding_gap, cost_per_delivery, effect_size = sq.correlate(
-        (funding_gap, cost_per_delivery, effect_size),
-        [[1, 0.6, -0.5], [0.6, 1, -0.2], [-0.5, -0.2, 1]]
-    )
->>> print(np.corrcoef(funding_gap @ 1000, cost_per_delivery @ 1000, effect_size @ 1000))
-array([[ 1.      ,  0.580520  , -0.480149],
-       [ 0.580962,  1.        , -0.187831],
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-    squigglepy.distributions module — Squigglepy  documentation
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    squigglepy.distributions module#
    
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    A collection of probability distributions and functions to operate on them.
    
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-class squigglepy.distributions.BaseDistribution[source]#
    
-
    Bases: ABC
    
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-class squigglepy.distributions.BernoulliDistribution(p)[source]#
    
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    Bases: DiscreteDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.BetaDistribution(a, b)[source]#
    
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    Bases: ContinuousDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.BinomialDistribution(n, p)[source]#
    
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    Bases: DiscreteDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.CategoricalDistribution(items)[source]#
    
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    Bases: DiscreteDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.ChiSquareDistribution(df)[source]#
    
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    Bases: ContinuousDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.ComplexDistribution(left, right=None, fn=<built-in function add>, fn_str='+', infix=True)[source]#
    
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    Bases: CompositeDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.CompositeDistribution[source]#
    
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    Bases: OperableDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.ConstantDistribution(x)[source]#
    
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    Bases: DiscreteDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.ContinuousDistribution[source]#
    
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    Bases: OperableDistribution, ABC
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.DiscreteDistribution[source]#
    
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    Bases: OperableDistribution, ABC
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.ExponentialDistribution(scale, lclip=None, rclip=None)[source]#
    
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    Bases: ContinuousDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.GammaDistribution(shape, scale=1, lclip=None, rclip=None)[source]#
    
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    Bases: ContinuousDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.GeometricDistribution(p)[source]#
    
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    Bases: OperableDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.LogTDistribution(x=None, y=None, t=1, credibility=90, lclip=None, rclip=None)[source]#
    
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    Bases: ContinuousDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.LognormalDistribution(x=None, y=None, norm_mean=None, norm_sd=None, lognorm_mean=None, lognorm_sd=None, credibility=90, lclip=None, rclip=None)[source]#
    
-
    Bases: ContinuousDistribution
    
-
    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.MixtureDistribution(dists, weights=None, relative_weights=None, lclip=None, rclip=None)[source]#
    
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    Bases: CompositeDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.NormalDistribution(x=None, y=None, mean=None, sd=None, credibility=90, lclip=None, rclip=None)[source]#
    
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    Bases: ContinuousDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
-
    
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-class squigglepy.distributions.OperableDistribution[source]#
    
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    Bases: BaseDistribution
    
-
    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-plot(num_samples=None, bins=None)[source]#
    
-
    Plot a histogram of the samples.
    
-
    
-
    Parameters:
    
-
    
-
    num_samplesint
    The number of samples to draw for plotting. Defaults to 1000 if not set.
    
-
    
-
    binsint
    The number of bins to plot. Defaults to 200 if not set.
    
-
    
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    Examples
    
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    >>> sq.norm(5, 10).plot()
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-class squigglepy.distributions.PERTDistribution(left, mode, right, lam=4, lclip=None, rclip=None)[source]#
    
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    Bases: ContinuousDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.ParetoDistribution(shape)[source]#
    
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    Bases: ContinuousDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.PoissonDistribution(lam, lclip=None, rclip=None)[source]#
    
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    Bases: DiscreteDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.TDistribution(x=None, y=None, t=20, credibility=90, lclip=None, rclip=None)[source]#
    
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    Bases: ContinuousDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
-
    
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-class squigglepy.distributions.TriangularDistribution(left, mode, right)[source]#
    
-
    Bases: ContinuousDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-class squigglepy.distributions.UniformDistribution(x, y)[source]#
    
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    Bases: ContinuousDistribution
    
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    Methods
    
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    plot([num_samples, bins])
    Plot a histogram of the samples.
    
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-squigglepy.distributions.bernoulli(p)[source]#
    
-
    Initialize a Bernoulli distribution.
    
-
    
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    Parameters:
    
-
    
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    pfloat
    The probability of the binary event. Must be between 0 and 1.
    
-
    
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    Returns:
    
-
    
-
    BernoulliDistribution
    
-
    
-
    
-
    
-
    Examples
    
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    >>> bernoulli(0.1)
-<Distribution> bernoulli(p=0.1)
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-squigglepy.distributions.beta(a, b)[source]#
    
-
    Initialize a beta distribution.
    
-
    
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    Parameters:
    
-
    
-
    afloat
    The alpha shape value of the distribution. Typically takes the value of the
-number of trials that resulted in a success.
    
-
    
-
    bfloat
    The beta shape value of the distribution. Typically takes the value of the
-number of trials that resulted in a failure.
    
-
    
-
    
-
    
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    Returns:
    
-
    
-
    BetaDistribution
    
-
    
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-
    Examples
    
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    >>> beta(1, 2)
-<Distribution> beta(1, 2)
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-squigglepy.distributions.binomial(n, p)[source]#
    
-
    Initialize a binomial distribution.
    
-
    
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    Parameters:
    
-
    
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    nint
    The number of trials.
    
-
    
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    pfloat
    The probability of success for each trial. Must be between 0 and 1.
    
-
    
-
    
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    Returns:
    
-
    
-
    BinomialDistribution
    
-
    
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-
    
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    Examples
    
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    >>> binomial(1, 0.1)
-<Distribution> binomial(1, 0.1)
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-squigglepy.distributions.chisquare(df)[source]#
    
-
    Initialize a chi-square distribution.
    
-
    
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    Parameters:
    
-
    
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    dffloat
    The degrees of freedom. Must be positive.
    
-
    
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-
    
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    Returns:
    
-
    
-
    ChiSquareDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> chisquare(2)
-<Distribution> chiaquare(2)
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-squigglepy.distributions.clip(dist1, left, right=None)[source]#
    
-
    Initialize the clipping/bounding of the output of the distribution.
    
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    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters:
    
-
    
-
    dist1Distribution or function
    The distribution to clip. If this is a funciton, it will return a partial that will
-be suitable for use in piping.
    
-
    
-
    leftint or float or None
    The value to use as the lower bound for clipping.
    
-
    
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    rightint or float or None
    The value to use as the upper bound for clipping.
    
-
    
-
    
-
    
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    Returns:
    
-
    
-
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> clip(norm(0, 1), 0.5, 0.9)
-<Distribution> rclip(lclip(norm(mean=0.5, sd=0.3), 0.5), 0.9)
-
    
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-squigglepy.distributions.const(x)[source]#
    
-
    Initialize a constant distribution.
    
-
    Constant distributions always return the same value no matter what.
    
-
    
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    Parameters:
    
-
    
-
    xanything
    The value the constant distribution should always return.
    
-
    
-
    
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    Returns:
    
-
    
-
    ConstantDistribution
    
-
    
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-
    
-
    Examples
    
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    >>> const(1)
-<Distribution> const(1)
-
    
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-squigglepy.distributions.discrete(items)[source]#
    
-
    Initialize a discrete distribution (aka categorical distribution).
    
-
    
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    Parameters:
    
-
    
-
    itemslist or dict
    The values that the discrete distribution will return and their associated
-weights (or likelihoods of being returned when sampled).
    
-
    
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    Returns:
    
-
    
-
    CategoricalDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> discrete({0: 0.1, 1: 0.9})  # 10% chance of returning 0, 90% chance of returning 1
-<Distribution> categorical({0: 0.1, 1: 0.9})
->>> discrete([[0.1, 0], [0.9, 1]])  # Different notation for the same thing.
-<Distribution> categorical([[0.1, 0], [0.9, 1]])
->>> discrete([0, 1, 2])  # When no weights are given, all have equal chance of happening.
-<Distribution> categorical([0, 1, 2])
->>> discrete({'a': 0.1, 'b': 0.9})  # Values do not have to be numbers.
-<Distribution> categorical({'a': 0.1, 'b': 0.9})
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-squigglepy.distributions.dist_ceil(dist1)[source]#
    
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    Initialize the ceiling rounding of the output of the distribution.
    
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    The function won’t be applied until the distribution is sampled.
    
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    Parameters:
    
-
    
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    dist1Distribution
    The distribution to sample and then ceiling round.
    
-
    
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    Returns:
    
-
    
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    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
-
    
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    Examples
    
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    >>> dist_ceil(norm(0, 1))
-<Distribution> ceil(norm(mean=0.5, sd=0.3))
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-squigglepy.distributions.dist_exp(dist1)[source]#
    
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    Initialize the exp of the output of the distribution.
    
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    The function won’t be applied until the distribution is sampled.
    
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    Parameters:
    
-
    
-
    dist1Distribution
    The distribution to sample and then take the exp of.
    
-
    
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    Returns:
    
-
    
-
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
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    Examples
    
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    >>> dist_exp(norm(0, 1))
-<Distribution> exp(norm(mean=0.5, sd=0.3))
-
    
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-squigglepy.distributions.dist_floor(dist1)[source]#
    
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    Initialize the floor rounding of the output of the distribution.
    
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    The function won’t be applied until the distribution is sampled.
    
-
    
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    Parameters:
    
-
    
-
    dist1Distribution
    The distribution to sample and then floor round.
    
-
    
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    Returns:
    
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    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
-
    
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    Examples
    
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    >>> dist_floor(norm(0, 1))
-<Distribution> floor(norm(mean=0.5, sd=0.3))
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-squigglepy.distributions.dist_fn(dist1, dist2=None, fn=None, name=None)[source]#
    
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    Initialize a distribution that has a custom function applied to the result.
    
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    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters:
    
-
    
-
    dist1Distribution or function or list
    Typically, the distribution to apply the function to. Could also be a function
-or list of functions if dist_fn is being used in a pipe.
    
-
    
-
    dist2Distribution or function or list or None
    Typically, the second distribution to apply the function to if the function takes
-two arguments. Could also be a function or list of functions if dist_fn is
-being used in a pipe.
    
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    fnfunction or None
    The function to apply to the distribution(s).
    
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    namestr or None
    By default, fn.__name__ will be used to name the function. But you can pass
-a custom name.
    
-
    
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    Returns:
    
-
    
-
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
-when it is sampled.
    
-
    
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-
    Examples
    
-
    >>> def double(x):
->>>     return x * 2
->>> dist_fn(norm(0, 1), double)
-<Distribution> double(norm(mean=0.5, sd=0.3))
->>> norm(0, 1) >> dist_fn(double)
-<Distribution> double(norm(mean=0.5, sd=0.3))
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-squigglepy.distributions.dist_log(dist1, base=2.718281828459045)[source]#
    
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    Initialize the log of the output of the distribution.
    
-
    The function won’t be applied until the distribution is sampled.
    
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-
    Parameters:
    
-
    
-
    dist1Distribution
    The distribution to sample and then take the log of.
    
-
    
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-
    
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    Returns:
    
-
    
-
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
-
    
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    Examples
    
-
    >>> dist_log(norm(0, 1), 10)
-<Distribution> log(norm(mean=0.5, sd=0.3), const(10))
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-squigglepy.distributions.dist_max(dist1, dist2=None)[source]#
    
-
    Initialize the calculation of the maximum value of two distributions.
    
-
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters:
    
-
    
-
    dist1Distribution
    The distribution to sample and determine the max of.
    
-
    
-
    dist2Distribution
    The second distribution to sample and determine the max of.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
-when it is sampled.
    
-
    
-
    
-
    
-
    
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    Examples
    
-
    >>> dist_max(norm(0, 1), norm(1, 2))
-<Distribution> max(norm(mean=0.5, sd=0.3), norm(mean=1.5, sd=0.3))
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.dist_min(dist1, dist2=None)[source]#
    
-
    Initialize the calculation of the minimum value of two distributions.
    
-
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters:
    
-
    
-
    dist1Distribution
    The distribution to sample and determine the min of.
    
-
    
-
    dist2Distribution
    The second distribution to sample and determine the min of.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> dist_min(norm(0, 1), norm(1, 2))
-<Distribution> min(norm(mean=0.5, sd=0.3), norm(mean=1.5, sd=0.3))
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.dist_round(dist1, digits=0)[source]#
    
-
    Initialize the rounding of the output of the distribution.
    
-
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters:
    
-
    
-
    dist1Distribution
    The distribution to sample and then round.
    
-
    
-
    digitsint
    The number of digits to round to.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> dist_round(norm(0, 1))
-<Distribution> round(norm(mean=0.5, sd=0.3), 0)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.exponential(scale, lclip=None, rclip=None)[source]#
    
-
    Initialize an exponential distribution.
    
-
    
-
    Parameters:
    
-
    
-
    scalefloat
    The scale value of the exponential distribution (> 0)
    
-
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
-
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    ExponentialDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> exponential(1)
-<Distribution> exponential(1)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.gamma(shape, scale=1, lclip=None, rclip=None)[source]#
    
-
    Initialize a gamma distribution.
    
-
    
-
    Parameters:
    
-
    
-
    shapefloat
    The shape value of the gamma distribution.
    
-
    
-
    scalefloat
    The scale value of the gamma distribution. Defaults to 1.
    
-
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
-
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    GammaDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> gamma(10, 1)
-<Distribution> gamma(shape=10, scale=1)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.geometric(p)[source]#
    
-
    Initialize a geometric distribution.
    
-
    
-
    Parameters:
    
-
    
-
    pfloat
    The probability of success of an individual trial. Must be between 0 and 1.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    GeometricDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> geometric(0.1)
-<Distribution> geometric(0.1)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.inf0(p_zero, dist)[source]#
    
-
    Initialize an arbitrary zero-inflated distribution.
    
-
    Alias for zero_inflated.
    
-
    
-
    Parameters:
    
-
    
-
    p_zerofloat
    The chance of the distribution returning zero
    
-
    
-
    distDistribution
    The distribution to sample from when not zero
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    MixtureDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> inf0(0.6, norm(1, 2))
-<Distribution> mixture
- - 0
- - <Distribution> norm(mean=1.5, sd=0.3)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.lclip(dist1, val=None)[source]#
    
-
    Initialize the clipping/bounding of the output of the distribution by the lower value.
    
-
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters:
    
-
    
-
    dist1Distribution or function
    The distribution to clip. If this is a funciton, it will return a partial that will
-be suitable for use in piping.
    
-
    
-
    valint or float or None
    The value to use as the lower bound for clipping.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> lclip(norm(0, 1), 0.5)
-<Distribution> lclip(norm(mean=0.5, sd=0.3), 0.5)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.log_tdist(x=None, y=None, t=1, credibility=90, lclip=None, rclip=None)[source]#
    
-
    Initialize a log t-distribution, which is a t-distribution in log-space.
    
-
    Is defined either via a loose credible interval from x to y (use credibility or
-it will default to being a 90% CI). Unlike the normal and lognormal distributions, this
-credible interval is an approximation and is not precisely defined.
    
-
    If x and y are not defined, can just return a classic t-distribution defined via
-t as the number of degrees of freedom, but in log-space.
    
-
    
-
    Parameters:
    
-
    
-
    xfloat or None
    The low value of a credible interval defined by credibility. Must be greater than 0.
-Defaults to a 90% CI.
    
-
    
-
    yfloat or None
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
-
    
-
    tfloat
    The number of degrees of freedom of the t-distribution. Defaults to 1.
    
-
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
-
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
-
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    LogTDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> log_tdist(0, 1, 2)
-<Distribution> log_tdist(x=0, y=1, t=2)
->>> log_tdist()
-<Distribution> log_tdist(t=1)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.lognorm(x=None, y=None, credibility=90, norm_mean=None, norm_sd=None, lognorm_mean=None, lognorm_sd=None, lclip=None, rclip=None)[source]#
    
-
    Initialize a lognormal distribution.
    
-
    Can be defined either via a credible interval from x to y (use credibility or
-it will default to being a 90% CI) or defined via mean and sd.
    
-
    
-
    Parameters:
    
-
    
-
    xfloat
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
-Must be a value greater than 0.
    
-
    
-
    yfloat
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
-Must be a value greater than 0.
    
-
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90. Ignored if the distribution is
-defined instead by mean and sd.
    
-
    
-
    norm_meanfloat or None
    The mean of the underlying normal distribution. If not defined, defaults to 0.
    
-
    
-
    norm_sdfloat
    The standard deviation of the underlying normal distribution.
    
-
    
-
    lognorm_meanfloat or None
    The mean of the lognormal distribution. If not defined, defaults to 1.
    
-
    
-
    lognorm_sdfloat
    The standard deviation of the lognormal distribution.
    
-
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
-
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    LognormalDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> lognorm(1, 10)
-<Distribution> lognorm(lognorm_mean=4.04, lognorm_sd=3.21, norm_mean=1.15, norm_sd=0.7)
->>> lognorm(norm_mean=1, norm_sd=2)
-<Distribution> lognorm(lognorm_mean=20.09, lognorm_sd=147.05, norm_mean=1, norm_sd=2)
->>> lognorm(lognorm_mean=1, lognorm_sd=2)
-<Distribution> lognorm(lognorm_mean=1, lognorm_sd=2, norm_mean=-0.8, norm_sd=1.27)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.mixture(dists, weights=None, relative_weights=None, lclip=None, rclip=None)[source]#
    
-
    Initialize a mixture distribution, which is a combination of different distributions.
    
-
    
-
    Parameters:
    
-
    
-
    distslist or dict
    The distributions to mix. Can also be defined as a list of weights and distributions.
    
-
    
-
    weightslist or None
    The weights for each distribution.
    
-
    
-
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
-to sum to 1.
    
-
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
-
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    MixtureDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> mixture([norm(1, 2), norm(3, 4)], weights=[0.1, 0.9])
-<Distribution> mixture
- - <Distribution> norm(mean=1.5, sd=0.3)
- - <Distribution> norm(mean=3.5, sd=0.3)
->>> mixture([[0.1, norm(1, 2)], [0.9, norm(3, 4)]])  # Different notation for the same thing.
-<Distribution> mixture
- - <Distribution> norm(mean=1.5, sd=0.3)
- - <Distribution> norm(mean=3.5, sd=0.3)
->>> mixture([norm(1, 2), norm(3, 4)])  # When no weights are given, all have equal chance
->>>                                    # of happening.
-<Distribution> mixture
- - <Distribution> norm(mean=1.5, sd=0.3)
- - <Distribution> norm(mean=3.5, sd=0.3)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.norm(x=None, y=None, credibility=90, mean=None, sd=None, lclip=None, rclip=None) → NormalDistribution[source]#
    
-
    Initialize a normal distribution.
    
-
    Can be defined either via a credible interval from x to y (use credibility or
-it will default to being a 90% CI) or defined via mean and sd.
    
-
    
-
    Parameters:
    
-
    
-
    xfloat
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
    
-
    
-
    yfloat
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
-
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90. Ignored if the distribution is
-defined instead by mean and sd.
    
-
    
-
    meanfloat or None
    The mean of the normal distribution. If not defined, defaults to 0.
    
-
    
-
    sdfloat
    The standard deviation of the normal distribution.
    
-
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
-
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    NormalDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> norm(0, 1)
-<Distribution> norm(mean=0.5, sd=0.3)
->>> norm(mean=1, sd=2)
-<Distribution> norm(mean=1, sd=2)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.pareto(shape)[source]#
    
-
    Initialize a pareto distribution.
    
-
    
-
    Parameters:
    
-
    
-
    shapefloat
    The shape value of the pareto distribution.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    ParetoDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> pareto(1)
-<Distribution> pareto(1)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.pert(left, mode, right, lam=4, lclip=None, rclip=None)[source]#
    
-
    Initialize a PERT distribution.
    
-
    
-
    Parameters:
    
-
    
-
    leftfloat
    The smallest value of the PERT distribution.
    
-
    
-
    modefloat
    The most common value of the PERT distribution.
    
-
    
-
    rightfloat
    The largest value of the PERT distribution.
    
-
    
-
    lamfloat
    The lambda value of the PERT distribution. Defaults to 4.
    
-
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
-
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    PERTDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> pert(1, 2, 3)
-<Distribution> PERT(1, 2, 3)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.poisson(lam, lclip=None, rclip=None)[source]#
    
-
    Initialize a poisson distribution.
    
-
    
-
    Parameters:
    
-
    
-
    lamfloat
    The lambda value of the poisson distribution.
    
-
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
-
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    PoissonDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> poisson(1)
-<Distribution> poisson(1)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.rclip(dist1, val=None)[source]#
    
-
    Initialize the clipping/bounding of the output of the distribution by the upper value.
    
-
    The function won’t be applied until the distribution is sampled.
    
-
    
-
    Parameters:
    
-
    
-
    dist1Distribution or function
    The distribution to clip. If this is a funciton, it will return a partial that will
-be suitable for use in piping.
    
-
    
-
    valint or float or None
    The value to use as the upper bound for clipping.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    ComplexDistribution or function
    This will be a lazy evaluation of the desired function that will then be calculated
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> rclip(norm(0, 1), 0.5)
-<Distribution> rclip(norm(mean=0.5, sd=0.3), 0.5)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.tdist(x=None, y=None, t=20, credibility=90, lclip=None, rclip=None)[source]#
    
-
    Initialize a t-distribution.
    
-
    Is defined either via a loose credible interval from x to y (use credibility or
-it will default to being a 90% CI). Unlike the normal and lognormal distributions, this
-credible interval is an approximation and is not precisely defined.
    
-
    If x and y are not defined, can just return a classic t-distribution defined via
-t as the number of degrees of freedom.
    
-
    
-
    Parameters:
    
-
    
-
    xfloat or None
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
    
-
    
-
    yfloat or None
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
-
    
-
    tfloat
    The number of degrees of freedom of the t-distribution. Defaults to 20.
    
-
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
-
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
-
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    TDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> tdist(0, 1, 2)
-<Distribution> tdist(x=0, y=1, t=2)
->>> tdist()
-<Distribution> tdist(t=1)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.to(x, y, credibility=90, lclip=None, rclip=None) → LognormalDistribution | NormalDistribution[source]#
    
-
    Initialize a distribution from x to y.
    
-
    The distribution will be lognormal by default, unless x is less than or equal to 0,
-in which case it will become a normal distribution.
    
-
    The distribution will default to be a 90% credible interval between x and y unless
-credibility is passed.
    
-
    
-
    Parameters:
    
-
    
-
    xfloat
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
    
-
    
-
    yfloat
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
-
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
-
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
-
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    LognormalDistribution if x > 0, otherwise a NormalDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> to(1, 10)
-<Distribution> lognorm(mean=1.15, sd=0.7)
->>> to(-10, 10)
-<Distribution> norm(mean=0.0, sd=6.08)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.triangular(left, mode, right, lclip=None, rclip=None)[source]#
    
-
    Initialize a triangular distribution.
    
-
    
-
    Parameters:
    
-
    
-
    leftfloat
    The smallest value of the triangular distribution.
    
-
    
-
    modefloat
    The most common value of the triangular distribution.
    
-
    
-
    rightfloat
    The largest value of the triangular distribution.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    TriangularDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> triangular(1, 2, 3)
-<Distribution> triangular(1, 2, 3)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.uniform(x, y)[source]#
    
-
    Initialize a uniform random distribution.
    
-
    
-
    Parameters:
    
-
    
-
    xfloat
    The smallest value the uniform distribution will return.
    
-
    
-
    yfloat
    The largest value the uniform distribution will return.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    UniformDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> uniform(0, 1)
-<Distribution> uniform(0, 1)
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.distributions.zero_inflated(p_zero, dist)[source]#
    
-
    Initialize an arbitrary zero-inflated distribution.
    
-
    
-
    Parameters:
    
-
    
-
    p_zerofloat
    The chance of the distribution returning zero
    
-
    
-
    distDistribution
    The distribution to sample from when not zero
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    MixtureDistribution
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> zero_inflated(0.6, norm(1, 2))
-<Distribution> mixture
- - 0
- - <Distribution> norm(mean=1.5, sd=0.3)
-
    
-
    
-
    
-
-
    
-
-
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-  
    
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-     On this page
-  
    
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-       Show Source
-    
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-              
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-  
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-  
-    
    
-      
-        
    
-  
    
-    
-      © Copyright 2023, Peter Wildeford.
-      
    
-    
-  
    
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-    Created using Sphinx 7.2.6.
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    The RNG used internally.
    
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-squigglepy.samplers.bernoulli_sample(p, samples=1)[source]#
    
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    The probability of success. Must be between 0 and 1.
    
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->>> bernoulli_sample(0.5)
-0
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-squigglepy.samplers.beta_sample(a, b, samples=1)[source]#
    
-
    Sample a random number according to a beta distribution.
    
-
    
-
    Parameters:
    
-
    
-
    afloat
    The alpha shape value of the distribution. Typically takes the value of the
-number of trials that resulted in a success.
    
-
    
-
    bfloat
    The beta shape value of the distribution. Typically takes the value of the
-number of trials that resulted in a failure.
    
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    The number of samples to return.
    
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-
    
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    float
    A random number sampled from a beta distribution defined by
-a and b.
    
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    Examples
    
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->>> beta_sample(1, 1)
-0.22145847498048798
-
    
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-
    Sample a random number according to a binomial distribution.
    
-
    
-
    Parameters:
    
-
    
-
    nint
    The number of trials.
    
-
    
-
    pfloat
    The probability of success for each trial. Must be between 0 and 1.
    
-
    
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    samplesint
    The number of samples to return.
    
-
    
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    Returns:
    
-
    
-
    int
    A random number sampled from a binomial distribution defined by
-n and p. The random number should be between 0 and n.
    
-
    
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    Examples
    
-
    >>> set_seed(42)
->>> binomial_sample(10, 0.1)
-2
-
    
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-squigglepy.samplers.chi_square_sample(df, samples=1)[source]#
    
-
    Sample a random number according to a chi-square distribution.
    
-
    
-
    Parameters:
    
-
    
-
    dffloat
    The number of degrees of freedom
    
-
    
-
    samplesint
    The number of samples to return.
    
-
    
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-
    Returns:
    
-
    
-
    float
    A random number sampled from a chi-square distribution.
    
-
    
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    Examples
    
-
    >>> set_seed(42)
->>> chi_square_sample(2)
-4.808417207931989
-
    
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-squigglepy.samplers.discrete_sample(items, samples=1, verbose=False, _multicore_tqdm_n=1, _multicore_tqdm_cores=1)[source]#
    
-
    Sample a random value from a discrete distribution (aka categorical distribution).
    
-
    
-
    Parameters:
    
-
    
-
    itemslist or dict
    The values that the discrete distribution will return and their associated
-weights (or likelihoods of being returned when sampled).
    
-
    
-
    samplesint
    The number of samples to return.
    
-
    
-
    verbosebool
    If True, will print out statements on computational progress.
    
-
    
-
    _multicore_tqdm_nint
    The total number of samples to use for printing tqdm’s interface. This is meant to only
-be used internally by squigglepy to make the progress bar printing work well for
-multicore. This parameter can be safely ignored by the user.
    
-
    
-
    _multicore_tqdm_coresint
    The total number of cores to use for printing tqdm’s interface. This is meant to only
-be used internally by squigglepy to make the progress bar printing work well for
-multicore. This parameter can be safely ignored by the user.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    Various, based on items in items
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> # 10% chance of returning 0, 90% chance of returning 1
->>> discrete_sample({0: 0.1, 1: 0.9})
-1
->>> discrete_sample([[0.1, 0], [0.9, 1]])  # Different notation for the same thing.
-1
->>> # When no weights are given, all have equal chance of happening.
->>> discrete_sample([0, 1, 2])
-2
->>> discrete_sample({'a': 0.1, 'b': 0.9})  # Values do not have to be numbers.
-'b'
-
    
-
    
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-squigglepy.samplers.exponential_sample(scale, samples=1)[source]#
    
-
    Sample a random number according to an exponential distribution.
    
-
    
-
    Parameters:
    
-
    
-
    scalefloat
    The scale value of the exponential distribution.
    
-
    
-
    samplesint
    The number of samples to return.
    
-
    
-
    
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-
    Returns:
    
-
    
-
    int
    A random number sampled from an exponential distribution.
    
-
    
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    Examples
    
-
    >>> set_seed(42)
->>> exponential_sample(10)
-24.042086039659946
-
    
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-
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-
    
-squigglepy.samplers.gamma_sample(shape, scale, samples=1)[source]#
    
-
    Sample a random number according to a gamma distribution.
    
-
    
-
    Parameters:
    
-
    
-
    shapefloat
    The shape value of the gamma distribution.
    
-
    
-
    scalefloat
    The scale value of the gamma distribution. Defaults to 1.
    
-
    
-
    samplesint
    The number of samples to return.
    
-
    
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-
    Returns:
    
-
    
-
    int
    A random number sampled from an gamma distribution.
    
-
    
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    Examples
    
-
    >>> set_seed(42)
->>> gamma_sample(10, 2)
-21.290716894247602
-
    
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-
    Sample a random number according to a geometric distribution.
    
-
    
-
    Parameters:
    
-
    
-
    pfloat
    The probability of success of an individual trial. Must be between 0 and 1.
    
-
    
-
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    The number of samples to return.
    
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    Returns:
    
-
    
-
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-
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->>> geometric_sample(0.1)
-2
-
    
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-squigglepy.samplers.log_t_sample(low=None, high=None, t=20, samples=1, credibility=90)[source]#
    
-
    Sample a random number according to a log-t-distribution.
    
-
    The log-t-distribution is a t-distribution in log-space. It is defined with
-degrees of freedom via the t parameter. Additionally, a loose credibility
-interval can be defined via the t-distribution using the low and high
-values. This will be a 90% CI by default unless you change credibility.
-Unlike the normal and lognormal samplers, this credible interval is an
-approximation and is not precisely defined.
    
-
    
-
    Parameters:
    
-
    
-
    lowfloat or None
    The low value of a credible interval defined by credibility.
-Must be greater than 0. Defaults to a 90% CI.
    
-
    
-
    highfloat or None
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
-
    
-
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    The number of degrees of freedom of the t-distribution. Defaults to 20.
    
-
    
-
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    The number of samples to return.
    
-
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
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    A random number sampled from a lognormal distribution defined by
-mean and sd.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> log_t_sample(1, 2, t=4)
-2.052949773846356
-
    
-
    
-
    
-
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-squigglepy.samplers.lognormal_sample(mean, sd, samples=1)[source]#
    
-
    Sample a random number according to a lognormal distribution.
    
-
    
-
    Parameters:
    
-
    
-
    meanfloat
    The mean of the lognormal distribution that is being sampled.
    
-
    
-
    sdfloat
    The standard deviation of the lognormal distribution that is being sampled.
    
-
    
-
    samplesint
    The number of samples to return.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    float
    A random number sampled from a lognormal distribution defined by
-mean and sd.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> lognormal_sample(0, 1)
-1.3562412406168636
-
    
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-
    
-
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-squigglepy.samplers.mixture_sample(values, weights=None, relative_weights=None, samples=1, verbose=False, _multicore_tqdm_n=1, _multicore_tqdm_cores=1)[source]#
    
-
    Sample a ranom number from a mixture distribution.
    
-
    
-
    Parameters:
    
-
    
-
    valueslist or dict
    The distributions to mix. Can also be defined as a list of weights and distributions.
    
-
    
-
    weightslist or None
    The weights for each distribution.
    
-
    
-
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
-to sum to 1.
    
-
    
-
    samplesint
    The number of samples to return.
    
-
    
-
    verbosebool
    If True, will print out statements on computational progress.
    
-
    
-
    _multicore_tqdm_nint
    The total number of samples to use for printing tqdm’s interface. This is meant to only
-be used internally by squigglepy to make the progress bar printing work well for
-multicore. This parameter can be safely ignored by the user.
    
-
    
-
    _multicore_tqdm_coresint
    The total number of cores to use for printing tqdm’s interface. This is meant to only
-be used internally by squigglepy to make the progress bar printing work well for
-multicore. This parameter can be safely ignored by the user.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    Various, based on items in values
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> mixture_sample([norm(1, 2), norm(3, 4)], weights=[0.1, 0.9])
-3.183867278765718
->>> # Different notation for the same thing.
->>> mixture_sample([[0.1, norm(1, 2)], [0.9, norm(3, 4)]])
-3.7859113725925972
->>> # When no weights are given, all have equal chance of happening.
->>> mixture_sample([norm(1, 2), norm(3, 4)])
-1.1041655362137777
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.samplers.normal_sample(mean, sd, samples=1)[source]#
    
-
    Sample a random number according to a normal distribution.
    
-
    
-
    Parameters:
    
-
    
-
    meanfloat
    The mean of the normal distribution that is being sampled.
    
-
    
-
    sdfloat
    The standard deviation of the normal distribution that is being sampled.
    
-
    
-
    samplesint
    The number of samples to return.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    float
    A random number sampled from a normal distribution defined by
-mean and sd.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> normal_sample(0, 1)
-0.30471707975443135
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.samplers.pareto_sample(shape, samples=1)[source]#
    
-
    Sample a random number according to a pareto distribution.
    
-
    
-
    Parameters:
    
-
    
-
    shapefloat
    The shape value of the pareto distribution.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    int
    A random number sampled from an pareto distribution.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> pareto_sample(1)
-10.069666324736094
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.samplers.pert_sample(left, mode, right, lam, samples=1)[source]#
    
-
    Sample a random number according to a PERT distribution.
    
-
    
-
    Parameters:
    
-
    
-
    leftfloat
    The smallest value of the PERT distribution.
    
-
    
-
    modefloat
    The most common value of the PERT distribution.
    
-
    
-
    rightfloat
    The largest value of the PERT distribution.
    
-
    
-
    lamfloat
    The lambda of the PERT distribution.
    
-
    
-
    samplesint
    The number of samples to return.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    float
    A random number sampled from a PERT distribution.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> pert_sample(1, 2, 3, 4)
-2.327625176788963
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.samplers.poisson_sample(lam, samples=1)[source]#
    
-
    Sample a random number according to a poisson distribution.
    
-
    
-
    Parameters:
    
-
    
-
    lamfloat
    The lambda value of the poisson distribution.
    
-
    
-
    samplesint
    The number of samples to return.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    int
    A random number sampled from a poisson distribution.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> poisson_sample(10)
-13
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.samplers.sample(dist=None, n=1, lclip=None, rclip=None, memcache=False, reload_cache=False, dump_cache_file=None, load_cache_file=None, cache_file_primary=False, verbose=None, cores=1, _multicore_tqdm_n=1, _multicore_tqdm_cores=1, _correlate_if_needed=True)[source]#
    
-
    Sample random numbers from a given distribution.
    
-
    
-
    Parameters:
    
-
    
-
    distDistribution
    The distribution to sample random number from.
    
-
    
-
    nint
    The number of random numbers to sample from the distribution. Default to 1.
    
-
    
-
    lclipfloat or None
    If not None, any value below lclip will be coerced to lclip.
    
-
    
-
    rclipfloat or None
    If not None, any value below rclip will be coerced to rclip.
    
-
    
-
    memcachebool
    If True, will attempt to load the results in-memory for future calculations if
-a cache is present. Otherwise will save the results to an in-memory cache. Each cache
-will be matched based on dist. Default False.
    
-
    
-
    reload_cachebool
    If True, any existing cache will be ignored and recalculated. Default False.
    
-
    
-
    dump_cache_filestr or None
    If present, will write out the cache to a numpy file with this path with
-.sqlcache.npy appended to the file name.
    
-
    
-
    load_cache_filestr or None
    If present, will first attempt to load and use a cache from a file with this
-path with .sqlcache.npy appended to the file name.
    
-
    
-
    cache_file_primarybool
    If both an in-memory cache and file cache are present, the file
-cache will be used for the cache if this is True, and the in-memory cache
-will be used otherwise. Defaults to False.
    
-
    
-
    verbosebool
    If True, will print out statements on computational progress. If False, will not.
-If None (default), will be True when n is greater than or equal to 1M.
    
-
    
-
    coresint
    If 1, runs on a single core / process. If greater than 1, will run on a multiprocessing
-pool with that many cores / processes.
    
-
    
-
    _multicore_tqdm_nint
    The total number of samples to use for printing tqdm’s interface. This is meant to only
-be used internally by squigglepy to make the progress bar printing work well for
-multicore. This parameter can be safely ignored by the user.
    
-
    
-
    _multicore_tqdm_coresint
    The total number of cores to use for printing tqdm’s interface. This is meant to only
-be used internally by squigglepy to make the progress bar printing work well for
-multicore. This parameter can be safely ignored by the user.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    Various, based on dist.
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> sample(norm(1, 2))
-1.592627415218455
->>> sample(mixture([norm(1, 2), norm(3, 4)]))
-1.7281209657534462
->>> sample(lognorm(1, 10), n=5, lclip=3)
-array([6.10817361, 3.        , 3.        , 3.45828454, 3.        ])
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.samplers.sample_correlated_group(requested_dist: BaseDistribution, n: int, verbose=False) → ndarray[Any, dtype[float64]][source]#
    
-
    Samples a correlated distribution, alongside
-all other correlated distributions in the same group.
    
-
    The samples for other variables are stored in the distributions themselves
-(in _correlated_samples).
    
-
    This is necessary, because the sampling needs to happen all at once, regardless
-of where the distributions are used in the binary tree of operations.
    
-
    
-
-
    
-
    
-squigglepy.samplers.t_sample(low=None, high=None, t=20, samples=1, credibility=90)[source]#
    
-
    Sample a random number according to a t-distribution.
    
-
    The t-distribution is defined with degrees of freedom via the t
-parameter. Additionally, a loose credibility interval can be defined
-via the t-distribution using the low and high values. This will be a
-90% CI by default unless you change credibility. Unlike the normal and
-lognormal samplers, this credible interval is an approximation and is
-not precisely defined.
    
-
    
-
    Parameters:
    
-
    
-
    lowfloat or None
    The low value of a credible interval defined by credibility. Defaults to a 90% CI.
    
-
    
-
    highfloat or None
    The high value of a credible interval defined by credibility. Defaults to a 90% CI.
    
-
    
-
    tfloat
    The number of degrees of freedom of the t-distribution. Defaults to 20.
    
-
    
-
    samplesint
    The number of samples to return.
    
-
    
-
    credibilityfloat
    The range of the credibility interval. Defaults to 90.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    float
    A random number sampled from a lognormal distribution defined by
-mean and sd.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> t_sample(1, 2, t=4)
-2.7887113716855985
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.samplers.triangular_sample(left, mode, right, samples=1)[source]#
    
-
    Sample a random number according to a triangular distribution.
    
-
    
-
    Parameters:
    
-
    
-
    leftfloat
    The smallest value of the triangular distribution.
    
-
    
-
    modefloat
    The most common value of the triangular distribution.
    
-
    
-
    rightfloat
    The largest value of the triangular distribution.
    
-
    
-
    samplesint
    The number of samples to return.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    float
    A random number sampled from a triangular distribution.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> triangular_sample(1, 2, 3)
-2.327625176788963
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.samplers.uniform_sample(low, high, samples=1)[source]#
    
-
    Sample a random number according to a uniform distribution.
    
-
    
-
    Parameters:
    
-
    
-
    lowfloat
    The smallest value the uniform distribution will return.
    
-
    
-
    highfloat
    The largest value the uniform distribution will return.
    
-
    
-
    samplesint
    The number of samples to return.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    float
    A random number sampled from a uniform distribution between
-`low` and `high`.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> uniform_sample(0, 1)
-0.7739560485559633
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-
    squigglepy.utils module#
    
-
    
-
    
-squigglepy.utils.doubling_time_to_growth_rate(doubling_time)[source]#
    
-
    Convert a doubling time to a growth rate.
    
-
    Doubling time is expressed as a number, numpy array or distribution in any
-time unit. Growth rate is set where e.g. 0.05 means +5%. The time unit remains the
-same, so if we’ve got a doubling time of 2 years, the returned value is the annual
-growth rate.
    
-
    NOTE: This only works works for numbers, arrays and distributions where all numbers
-are above 0. (Otherwise it makes no sense to talk about doubling times.)
    
-
    
-
    Parameters:
    
-
    
-
    doubling_timefloat or np.array or BaseDistribution
    The doubling time expressed in any time unit.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    float or np.array or ComplexDistribution
    Returns the growth rate expressed as a fraction (the percentage divided by 100).
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> doubling_time_to_growth_rate(12)
-0.05946309435929531
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.event(p)[source]#
    
-
    Return True with probability p and False with probability 1 - p.
    
-
    Alias for event_occurs.
    
-
    
-
    Parameters:
    
-
    
-
    pfloat
    The probability of returning True. Must be between 0 and 1.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    bool
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> event(p=0.5)
-False
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.event_happens(p)[source]#
    
-
    Return True with probability p and False with probability 1 - p.
    
-
    Alias for event_occurs.
    
-
    
-
    Parameters:
    
-
    
-
    pfloat
    The probability of returning True. Must be between 0 and 1.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> event_happens(p=0.5)
-False
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.event_occurs(p)[source]#
    
-
    Return True with probability p and False with probability 1 - p.
    
-
    
-
    Parameters:
    
-
    
-
    pfloat
    The probability of returning True. Must be between 0 and 1.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> event_occurs(p=0.5)
-False
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.extremize(p, e)[source]#
    
-
    Extremize a prediction.
    
-
    
-
    Parameters:
    
-
    
-
    pfloat
    The prediction to extremize. Must be within 0-1.
    
-
    
-
    efloat
    The extremization factor.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    float
    The extremized prediction
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> # Extremizing of 1.73 per https://arxiv.org/abs/2111.03153
->>> extremize(p=0.7, e=1.73)
-0.875428191155692
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.flip_coin(n=1)[source]#
    
-
    Flip a coin.
    
-
    
-
    Parameters:
    
-
    
-
    nint
    The number of coins to be flipped.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    str or list
    Returns the value of each coin flip, as either “heads” or “tails”
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> flip_coin()
-'heads'
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.full_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0)[source]#
    
-
    Alias for kelly where deference is 0.
    
-
    
-
    Parameters:
    
-
    
-
    my_pricefloat
    The price (or probability) you give for the given event.
    
-
    
-
    market_pricefloat
    The price the market is giving for that event.
    
-
    
-
    bankrollfloat
    How much money do you have to bet? Defaults to 1.
    
-
    
-
    resolve_datestr or None
    When will the event happen, the market resolve, and you get your money back? Used for
-calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
-ARR is not calculated.
    
-
    
-
    currentfloat
    How much do you already have invested in this event? Used for calculating the
-additional amount you should invest. Defaults to 0.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    dict
    
-
    A dict of values specifying:
      
-
    • my_price
      • 
-
    • market_price
      • 
-
    • deference
      • 
-
    • adj_price : an adjustment to my_price once deference is taken
-into account.
      • 
-
    • delta_price : the absolute difference between my_price and market_price.
      • 
-
    • adj_delta_price : the absolute difference between adj_price and
-market_price.
      • 
-
    • kelly : the kelly criterion indicating the percentage of bankroll
-you should bet.
      • 
-
    • target : the target amount of money you should have invested
      • 
-
    • current
      • 
-
    • delta : the amount of money you should invest given what you already
-have invested
      • 
-
    • max_gain : the amount of money you would gain if you win
      • 
-
    • modeled_gain : the expected value you would win given adj_price
      • 
-
    • expected_roi : the expected return on investment
      • 
-
    • expected_arr : the expected ARR given resolve_date
      • 
-
    • resolve_date
      • 
-
    
-
    
-
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> full_kelly(my_price=0.7, market_price=0.4, bankroll=100)
-{'my_price': 0.7, 'market_price': 0.4, 'deference': 0, 'adj_price': 0.7,
- 'delta_price': 0.3, 'adj_delta_price': 0.3, 'kelly': 0.5, 'target': 50.0,
- 'current': 0, 'delta': 50.0, 'max_gain': 125.0, 'modeled_gain': 72.5,
- 'expected_roi': 0.75, 'expected_arr': None, 'resolve_date': None}
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.geomean(a, weights=None, relative_weights=None, drop_na=True)[source]#
    
-
    Calculate the geometric mean.
    
-
    
-
    Parameters:
    
-
    
-
    alist or np.array
    The values to calculate the geometric mean of.
    
-
    
-
    weightslist or None
    The weights, if a weighted geometric mean is desired.
    
-
    
-
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
-to sum to 1.
    
-
    
-
    drop_naboolean
    Should NA-like values be dropped when calculating the geomean?
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    float
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> geomean([1, 3, 10])
-3.1072325059538595
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.geomean_odds(a, weights=None, relative_weights=None, drop_na=True)[source]#
    
-
    Calculate the geometric mean of odds.
    
-
    
-
    Parameters:
    
-
    
-
    alist or np.array
    The probabilities to calculate the geometric mean of. These are converted to odds
-before the geometric mean is taken..
    
-
    
-
    weightslist or None
    The weights, if a weighted geometric mean is desired.
    
-
    
-
    relative_weightslist or None
    Relative weights, which if given will be weights that are normalized
-to sum to 1.
    
-
    
-
    drop_naboolean
    Should NA-like values be dropped when calculating the geomean?
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    float
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> geomean_odds([0.1, 0.3, 0.9])
-0.42985748800076845
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.get_log_percentiles(data, percentiles=[1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99], reverse=False, display=True, digits=1)[source]#
    
-
    Print the log (base 10) of the percentiles of the data.
    
-
    
-
    Parameters:
    
-
    
-
    datalist or np.array
    The data to calculate percentiles for.
    
-
    
-
    percentileslist
    A list of percentiles to calculate. Must be values between 0 and 100.
    
-
    
-
    reversebool
    If True, the percentile values are reversed (e.g., 95th and 5th percentile
-swap values.)
    
-
    
-
    displaybool
    If True, the function returns an easy to read display.
    
-
    
-
    digitsint or None
    The number of digits to display (using rounding).
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    dict
    A dictionary of the given percentiles. If display is true, will be str values.
-Otherwise will be float values. 10 to the power of the value gives the true percentile.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> get_percentiles(range(100), percentiles=[25, 50, 75])
-{25: 24.75, 50: 49.5, 75: 74.25}
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.get_mean_and_ci(data, credibility=90, digits=None)[source]#
    
-
    Return the mean and percentiles of the data.
    
-
    
-
    Parameters:
    
-
    
-
    datalist or np.array
    The data to calculate the mean and CI for.
    
-
    
-
    credibilityfloat
    The credibility of the interval. Must be values between 0 and 100. Default 90 for 90% CI.
    
-
    
-
    digitsint or None
    The number of digits to display (using rounding).
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    dict
    A dictionary with the mean and CI.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> get_mean_and_ci(range(100))
-{'mean': 49.5, 'ci_low': 4.95, 'ci_high': 94.05}
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.get_median_and_ci(data, credibility=90, digits=None)[source]#
    
-
    Return the median and percentiles of the data.
    
-
    
-
    Parameters:
    
-
    
-
    datalist or np.array
    The data to calculate the mean and CI for.
    
-
    
-
    credibilityfloat
    The credibility of the interval. Must be values between 0 and 100. Default 90 for 90% CI.
    
-
    
-
    digitsint or None
    The number of digits to display (using rounding).
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    dict
    A dictionary with the median and CI.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> get_median_and_ci(range(100))
-{'mean': 49.5, 'ci_low': 4.95, 'ci_high': 94.05}
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.get_percentiles(data, percentiles=[1, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99], reverse=False, digits=None)[source]#
    
-
    Print the percentiles of the data.
    
-
    
-
    Parameters:
    
-
    
-
    datalist or np.array
    The data to calculate percentiles for.
    
-
    
-
    percentileslist
    A list of percentiles to calculate. Must be values between 0 and 100.
    
-
    
-
    reversebool
    If True, the percentile values are reversed (e.g., 95th and 5th percentile
-swap values.)
    
-
    
-
    digitsint or None
    The number of digits to display (using rounding).
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    dict
    A dictionary of the given percentiles.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> get_percentiles(range(100), percentiles=[25, 50, 75])
-{25: 24.75, 50: 49.5, 75: 74.25}
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.growth_rate_to_doubling_time(growth_rate)[source]#
    
-
    Convert a positive growth rate to a doubling rate.
    
-
    Growth rate must be expressed as a number, numpy array or distribution
-where 0.05 means +5% to a doubling time. The time unit remains the same, so if we’ve
-got +5% annual growth, the returned value is the doubling time in years.
    
-
    NOTE: This only works works for numbers, arrays and distributions where all numbers
-are above 0. (Otherwise it makes no sense to talk about doubling times.)
    
-
    
-
    Parameters:
    
-
    
-
    growth_ratefloat or np.array or BaseDistribution
    The growth rate expressed as a fraction (the percentage divided by 100).
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    float or np.array or ComplexDistribution
    Returns the doubling time.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> growth_rate_to_doubling_time(0.01)
-69.66071689357483
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.half_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0)[source]#
    
-
    Alias for kelly where deference is 0.5.
    
-
    
-
    Parameters:
    
-
    
-
    my_pricefloat
    The price (or probability) you give for the given event.
    
-
    
-
    market_pricefloat
    The price the market is giving for that event.
    
-
    
-
    bankrollfloat
    How much money do you have to bet? Defaults to 1.
    
-
    
-
    resolve_datestr or None
    When will the event happen, the market resolve, and you get your money back? Used for
-calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
-ARR is not calculated.
    
-
    
-
    currentfloat
    How much do you already have invested in this event? Used for calculating the
-additional amount you should invest. Defaults to 0.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    dict
    
-
    A dict of values specifying:
      
-
    • my_price
      • 
-
    • market_price
      • 
-
    • deference
      • 
-
    • adj_price : an adjustment to my_price once deference is taken
-into account.
      • 
-
    • delta_price : the absolute difference between my_price and market_price.
      • 
-
    • adj_delta_price : the absolute difference between adj_price and
-market_price.
      • 
-
    • kelly : the kelly criterion indicating the percentage of bankroll
-you should bet.
      • 
-
    • target : the target amount of money you should have invested
      • 
-
    • current
      • 
-
    • delta : the amount of money you should invest given what you already
-have invested
      • 
-
    • max_gain : the amount of money you would gain if you win
      • 
-
    • modeled_gain : the expected value you would win given adj_price
      • 
-
    • expected_roi : the expected return on investment
      • 
-
    • expected_arr : the expected ARR given resolve_date
      • 
-
    • resolve_date
      • 
-
    
-
    
-
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> half_kelly(my_price=0.7, market_price=0.4, bankroll=100)
-{'my_price': 0.7, 'market_price': 0.4, 'deference': 0.5, 'adj_price': 0.55,
- 'delta_price': 0.3, 'adj_delta_price': 0.15, 'kelly': 0.25, 'target': 25.0,
- 'current': 0, 'delta': 25.0, 'max_gain': 62.5, 'modeled_gain': 23.13,
- 'expected_roi': 0.375, 'expected_arr': None, 'resolve_date': None}
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.is_continuous_dist(obj)[source]#
    
-
    
-
-
    
-
    
-squigglepy.utils.is_dist(obj)[source]#
    
-
    Test if a given object is a Squigglepy distribution.
    
-
    
-
    Parameters:
    
-
    
-
    objobject
    The object to test.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    bool
    True, if the object is a distribution. False if not.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> is_dist(norm(0, 1))
-True
->>> is_dist(0)
-False
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.is_sampleable(obj)[source]#
    
-
    Test if a given object can be sampled from.
    
-
    This includes distributions, integers, floats, None,
-strings, and callables.
    
-
    
-
    Parameters:
    
-
    
-
    objobject
    The object to test.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    bool
    True, if the object can be sampled from. False if not.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> is_sampleable(norm(0, 1))
-True
->>> is_sampleable(0)
-True
->>> is_sampleable([0, 1])
-False
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.kelly(my_price, market_price, deference=0, bankroll=1, resolve_date=None, current=0)[source]#
    
-
    Calculate the Kelly criterion.
    
-
    
-
    Parameters:
    
-
    
-
    my_pricefloat
    The price (or probability) you give for the given event.
    
-
    
-
    market_pricefloat
    The price the market is giving for that event.
    
-
    
-
    deferencefloat
    How much deference (or weight) do you give the market price? Use 0.5 for half Kelly
-and 0.75 for quarter Kelly. Defaults to 0, which is full Kelly.
    
-
    
-
    bankrollfloat
    How much money do you have to bet? Defaults to 1.
    
-
    
-
    resolve_datestr or None
    When will the event happen, the market resolve, and you get your money back? Used for
-calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
-ARR is not calculated.
    
-
    
-
    currentfloat
    How much do you already have invested in this event? Used for calculating the
-additional amount you should invest. Defaults to 0.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    dict
    
-
    A dict of values specifying:
      
-
    • my_price
      • 
-
    • market_price
      • 
-
    • deference
      • 
-
    • adj_price : an adjustment to my_price once deference is taken
-into account.
      • 
-
    • delta_price : the absolute difference between my_price and market_price.
      • 
-
    • adj_delta_price : the absolute difference between adj_price and
-market_price.
      • 
-
    • kelly : the kelly criterion indicating the percentage of bankroll
-you should bet.
      • 
-
    • target : the target amount of money you should have invested
      • 
-
    • current
      • 
-
    • delta : the amount of money you should invest given what you already
-have invested
      • 
-
    • max_gain : the amount of money you would gain if you win
      • 
-
    • modeled_gain : the expected value you would win given adj_price
      • 
-
    • expected_roi : the expected return on investment
      • 
-
    • expected_arr : the expected ARR given resolve_date
      • 
-
    • resolve_date
      • 
-
    
-
    
-
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> kelly(my_price=0.7, market_price=0.4, deference=0.5, bankroll=100)
-{'my_price': 0.7, 'market_price': 0.4, 'deference': 0.5, 'adj_price': 0.55,
- 'delta_price': 0.3, 'adj_delta_price': 0.15, 'kelly': 0.25, 'target': 25.0,
- 'current': 0, 'delta': 25.0, 'max_gain': 62.5, 'modeled_gain': 23.13,
- 'expected_roi': 0.375, 'expected_arr': None, 'resolve_date': None}
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.laplace(s, n=None, time_passed=None, time_remaining=None, time_fixed=False)[source]#
    
-
    Return probability of success on next trial given Laplace’s law of succession.
    
-
    Also can be used to calculate a time-invariant version defined in
-https://www.lesswrong.com/posts/wE7SK8w8AixqknArs/a-time-invariant-version-of-laplace-s-rule
    
-
    
-
    Parameters:
    
-
    
-
    sint
    The number of successes among n past trials or among time_passed amount of time.
    
-
    
-
    nint or None
    The number of trials that contain the successes (and/or failures). Leave as None if
-time-invariant mode is desired.
    
-
    
-
    time_passedfloat or None
    The amount of time that has passed when the successes (and/or failures) occured for
-calculating a time-invariant Laplace.
    
-
    
-
    time_remainingfloat or None
    We are calculating the likelihood of observing at least one success over this time
-period.
    
-
    
-
    time_fixedbool
    This should be False if the time period is variable - that is, if the time period
-was chosen specifically to include the most recent success. Otherwise the time period
-is fixed and this should be True. Defaults to False.
    
-
    
-
    
-
    
-
    Returns:
    
-
    
-
    float
    The probability of at least one success in the next trial or time_remaining amount
-of time.
    
-
    
-
    
-
    
-
    
-
    Examples
    
-
    >>> # The sun has risen the past 100,000 days. What are the odds it rises again tomorrow?
->>> laplace(s=100*K, n=100*K)
-0.999990000199996
->>> # The last time a nuke was used in war was 77 years ago. What are the odds a nuke
->>> # is used in the next year, not considering any information other than this naive prior?
->>> laplace(s=1, time_passed=77, time_remaining=1, time_fixed=False)
-0.012820512820512664
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.normalize(lst)[source]#
    
-
    Normalize a list to sum to 1.
    
-
    
-
    Parameters:
    
-
    
-
    lstlist
    The list to normalize.
    
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    Returns:
    
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    list
    A list where each value is normalized such that the list sums to 1.
    
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    Examples
    
-
    >>> normalize([0.1, 0.2, 0.2])
-[0.2, 0.4, 0.4]
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-squigglepy.utils.odds_to_p(odds)[source]#
    
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    Calculate the probability from given decimal odds.
    
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    Parameters:
    
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    oddsfloat
    The decimal odds to calculate the probability for.
    
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    Returns:
    
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    float
    Probability
    
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    Examples
    
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    >>> odds_to_p(0.1)
-0.09090909090909091
-
    
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-squigglepy.utils.one_in(p, digits=0, verbose=True)[source]#
    
-
    Convert a probability into “1 in X” notation.
    
-
    
-
    Parameters:
    
-
    
-
    pfloat
    The probability to convert.
    
-
    
-
    digitsint
    The number of digits to round the result to. Defaults to 0. If digits
-is 0, the result will be converted to int instead of float.
    
-
    
-
    verboselogical
    If True, will return a string with “1 in X”. If False, will just return X.
    
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    Returns:
    
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    str if verbose is True. Otherwise, int if digits is 0 or float if digits > 0.
    
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    Examples
    
-
    >>> one_in(0.1)
-"1 in 10"
-
    
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-squigglepy.utils.p_to_odds(p)[source]#
    
-
    Calculate the decimal odds from a given probability.
    
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    Parameters:
    
-
    
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    pfloat
    The probability to calculate decimal odds for. Must be between 0 and 1.
    
-
    
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    Returns:
    
-
    
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    float
    Decimal odds
    
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    Examples
    
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    >>> p_to_odds(0.1)
-0.1111111111111111
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-squigglepy.utils.quarter_kelly(my_price, market_price, bankroll=1, resolve_date=None, current=0)[source]#
    
-
    Alias for kelly where deference is 0.75.
    
-
    
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    Parameters:
    
-
    
-
    my_pricefloat
    The price (or probability) you give for the given event.
    
-
    
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    market_pricefloat
    The price the market is giving for that event.
    
-
    
-
    bankrollfloat
    How much money do you have to bet? Defaults to 1.
    
-
    
-
    resolve_datestr or None
    When will the event happen, the market resolve, and you get your money back? Used for
-calculating expected ARR. Give in YYYY-MM-DD format. Defaults to None, which means
-ARR is not calculated.
    
-
    
-
    currentfloat
    How much do you already have invested in this event? Used for calculating the
-additional amount you should invest. Defaults to 0.
    
-
    
-
    
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    Returns:
    
-
    
-
    dict
    
-
    A dict of values specifying:
      
-
    • my_price
      • 
-
    • market_price
      • 
-
    • deference
      • 
-
    • adj_price : an adjustment to my_price once deference is taken
-into account.
      • 
-
    • delta_price : the absolute difference between my_price and market_price.
      • 
-
    • adj_delta_price : the absolute difference between adj_price and
-market_price.
      • 
-
    • kelly : the kelly criterion indicating the percentage of bankroll
-you should bet.
      • 
-
    • target : the target amount of money you should have invested
      • 
-
    • current
      • 
-
    • delta : the amount of money you should invest given what you already
-have invested
      • 
-
    • max_gain : the amount of money you would gain if you win
      • 
-
    • modeled_gain : the expected value you would win given adj_price
      • 
-
    • expected_roi : the expected return on investment
      • 
-
    • expected_arr : the expected ARR given resolve_date
      • 
-
    • resolve_date
      • 
-
    
-
    
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-
    
-
    
-
    Examples
    
-
    >>> quarter_kelly(my_price=0.7, market_price=0.4, bankroll=100)
-{'my_price': 0.7, 'market_price': 0.4, 'deference': 0.75, 'adj_price': 0.48,
- 'delta_price': 0.3, 'adj_delta_price': 0.08, 'kelly': 0.125, 'target': 12.5,
- 'current': 0, 'delta': 12.5, 'max_gain': 31.25, 'modeled_gain': 8.28,
- 'expected_roi': 0.188, 'expected_arr': None, 'resolve_date': None}
-
    
-
    
-
    
-
-
    
-
    
-squigglepy.utils.roll_die(sides, n=1)[source]#
    
-
    Roll a die.
    
-
    
-
    Parameters:
    
-
    
-
    sidesint
    The number of sides of the die that is rolled.
    
-
    
-
    nint
    The number of dice to be rolled.
    
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-
    
-
    Returns:
    
-
    
-
    int or list
    Returns the value of each die roll.
    
-
    
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-
    
-
    Examples
    
-
    >>> set_seed(42)
->>> roll_die(6)
-5
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diff --git a/doc/build/html/reference/squigglepy.version.html b/doc/build/html/reference/squigglepy.version.html
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-      © Copyright 2023, Peter Wildeford.
-      
    
-    
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-
    
-      
-        
    
-  
    
-    Created using Sphinx 7.2.6.
-    
    
-  
    
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-      
-    
    
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-      
-        
    
-  Built with the PyData Sphinx Theme 0.14.3.
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diff --git a/doc/build/html/search.html b/doc/build/html/search.html
deleted file mode 100644
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--- a/doc/build/html/search.html
+++ /dev/null
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-
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-
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-  
-    
-    Search - Squigglepy  documentation
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    Search
    
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-  
-  
-  
-
-
-  
    
-
    
-  
-    
    
-      
-        
    
-  
    
-    
-      © Copyright 2023, Peter Wildeford.
-      
    
-    
-  
    
-
    
-      
-        
    
-  
    
-    Created using Sphinx 7.2.6.
-    
    
-  
    
-
    
-      
-    
    
-  
-  
-  
-    
    
-      
-        
    
-  Built with the PyData Sphinx Theme 0.14.3.
-
    
-      
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diff --git a/doc/build/html/searchindex.js b/doc/build/html/searchindex.js
deleted file mode 100644
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--- a/doc/build/html/searchindex.js
+++ /dev/null
@@ -1 +0,0 @@
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    Examples#
    
-
    
-
    Piano tuners example#
    
-
    Here’s the Squigglepy implementation of the example from Squiggle
-Docs:
    
-
    import squigglepy as sq
-import numpy as np
-import matplotlib.pyplot as plt
-from squigglepy.numbers import K, M
-from pprint import pprint
-
-pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)  # This means that you're 90% confident the value is between 8.1 and 8.4 Million.
-pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01  # We assume there are almost no people with multiple pianos
-pianos_per_piano_tuner = sq.to(2*K, 50*K)
-piano_tuners_per_piano = 1 / pianos_per_piano_tuner
-total_tuners_in_2022 = pop_of_ny_2022 * pct_of_pop_w_pianos * piano_tuners_per_piano
-samples = total_tuners_in_2022 @ 1000  # Note: `@ 1000` is shorthand to get 1000 samples
-
-# Get mean and SD
-print('Mean: {}, SD: {}'.format(round(np.mean(samples), 2),
-                                round(np.std(samples), 2)))
-
-# Get percentiles
-pprint(sq.get_percentiles(samples, digits=0))
-
-# Histogram
-plt.hist(samples, bins=200)
-plt.show()
-
-# Shorter histogram
-total_tuners_in_2022.plot()
-
    
-
    
-
    And the version from the Squiggle doc that incorporates time:
    
-
    import squigglepy as sq
-from squigglepy.numbers import K, M
-
-pop_of_ny_2022 = sq.to(8.1*M, 8.4*M)
-pct_of_pop_w_pianos = sq.to(0.2, 1) * 0.01
-pianos_per_piano_tuner = sq.to(2*K, 50*K)
-piano_tuners_per_piano = 1 / pianos_per_piano_tuner
-
-def pop_at_time(t):  # t = Time in years after 2022
-    avg_yearly_pct_change = sq.to(-0.01, 0.05)  # We're expecting NYC to continuously grow with an mean of roughly between -1% and +4% per year
-    return pop_of_ny_2022 * ((avg_yearly_pct_change + 1) ** t)
-
-def total_tuners_at_time(t):
-    return pop_at_time(t) * pct_of_pop_w_pianos * piano_tuners_per_piano
-
-# Get total piano tuners at 2030
-sq.get_percentiles(total_tuners_at_time(2030-2022) @ 1000)
-
    
-
    
-
    WARNING: Be careful about dividing by K, M, etc. 1/2*K =
-500 in Python. Use 1/(2*K) instead to get the expected outcome.
    
-
    WARNING: Be careful about using K to get sample counts. Use
-sq.norm(2, 3) @ (2*K)… sq.norm(2, 3) @ 2*K will return only
-two samples, multiplied by 1000.
    
-
    
-
    
-
    Distributions#
    
-
    import squigglepy as sq
-
-# Normal distribution
-sq.norm(1, 3)  # 90% interval from 1 to 3
-
-# Distribution can be sampled with mean and sd too
-sq.norm(mean=0, sd=1)
-
-# Shorthand to get one sample
-~sq.norm(1, 3)
-
-# Shorthand to get more than one sample
-sq.norm(1, 3) @ 100
-
-# Longhand version to get more than one sample
-sq.sample(sq.norm(1, 3), n=100)
-
-# Nice progress reporter
-sq.sample(sq.norm(1, 3), n=1000, verbose=True)
-
-# Other distributions exist
-sq.lognorm(1, 10)
-sq.tdist(1, 10, t=5)
-sq.triangular(1, 2, 3)
-sq.pert(1, 2, 3, lam=2)
-sq.binomial(p=0.5, n=5)
-sq.beta(a=1, b=2)
-sq.bernoulli(p=0.5)
-sq.poisson(10)
-sq.chisquare(2)
-sq.gamma(3, 2)
-sq.pareto(1)
-sq.exponential(scale=1)
-sq.geometric(p=0.5)
-
-# Discrete sampling
-sq.discrete({'A': 0.1, 'B': 0.9})
-
-# Can return integers
-sq.discrete({0: 0.1, 1: 0.3, 2: 0.3, 3: 0.15, 4: 0.15})
-
-# Alternate format (also can be used to return more complex objects)
-sq.discrete([[0.1,  0],
-             [0.3,  1],
-             [0.3,  2],
-             [0.15, 3],
-             [0.15, 4]])
-
-sq.discrete([0, 1, 2]) # No weights assumes equal weights
-
-# You can mix distributions together
-sq.mixture([sq.norm(1, 3),
-            sq.norm(4, 10),
-            sq.lognorm(1, 10)],  # Distributions to mix
-           [0.3, 0.3, 0.4])     # These are the weights on each distribution
-
-# This is equivalent to the above, just a different way of doing the notation
-sq.mixture([[0.3, sq.norm(1,3)],
-            [0.3, sq.norm(4,10)],
-            [0.4, sq.lognorm(1,10)]])
-
-# Make a zero-inflated distribution
-# 60% chance of returning 0, 40% chance of sampling from `norm(1, 2)`.
-sq.zero_inflated(0.6, sq.norm(1, 2))
-
    
-
    
-
    
-
    
-
    Additional features#
    
-
    import squigglepy as sq
-
-# You can add and subtract distributions
-(sq.norm(1,3) + sq.norm(4,5)) @ 100
-(sq.norm(1,3) - sq.norm(4,5)) @ 100
-(sq.norm(1,3) * sq.norm(4,5)) @ 100
-(sq.norm(1,3) / sq.norm(4,5)) @ 100
-
-# You can also do math with numbers
-~((sq.norm(sd=5) + 2) * 2)
-~(-sq.lognorm(0.1, 1) * sq.pareto(1) / 10)
-
-# You can change the CI from 90% (default) to 80%
-sq.norm(1, 3, credibility=80)
-
-# You can clip
-sq.norm(0, 3, lclip=0, rclip=5) # Sample norm with a 90% CI from 0-3, but anything lower than 0 gets clipped to 0 and anything higher than 5 gets clipped to 5.
-
-# You can also clip with a function, and use pipes
-sq.norm(0, 3) >> sq.clip(0, 5)
-
-# You can correlate continuous distributions
-a, b = sq.uniform(-1, 1), sq.to(0, 3)
-a, b = sq.correlate((a, b), 0.5)  # Correlate a and b with a correlation of 0.5
-# You can even pass your own correlation matrix!
-a, b = sq.correlate((a, b), [[1, 0.5], [0.5, 1]])
-
    
-
    
-
    
-
    Example: Rolling a die#
    
-
    An example of how to use distributions to build tools:
    
-
    import squigglepy as sq
-
-def roll_die(sides, n=1):
-    return sq.discrete(list(range(1, sides + 1))) @ n if sides > 0 else None
-
-roll_die(sides=6, n=10)
-# [2, 6, 5, 2, 6, 2, 3, 1, 5, 2]
-
    
-
    
-
    This is already included standard in the utils of this package. Use
-sq.roll_die.
    
-
    
-
    
-
    
-
    Bayesian inference#
    
-
    1% of women at age forty who participate in routine screening have
-breast cancer. 80% of women with breast cancer will get positive
-mammographies. 9.6% of women without breast cancer will also get
-positive mammographies.
    
-
    A woman in this age group had a positive mammography in a routine
-screening. What is the probability that she actually has breast cancer?
    
-
    We can approximate the answer with a Bayesian network (uses rejection
-sampling):
    
-
    import squigglepy as sq
-from squigglepy import bayes
-from squigglepy.numbers import M
-
-def mammography(has_cancer):
-    return sq.event(0.8 if has_cancer else 0.096)
-
-def define_event():
-    cancer = ~sq.bernoulli(0.01)
-    return({'mammography': mammography(cancer),
-            'cancer': cancer})
-
-bayes.bayesnet(define_event,
-               find=lambda e: e['cancer'],
-               conditional_on=lambda e: e['mammography'],
-               n=1*M)
-# 0.07723995880535531
-
    
-
    
-
    Or if we have the information immediately on hand, we can directly
-calculate it. Though this doesn’t work for very complex stuff.
    
-
    from squigglepy import bayes
-bayes.simple_bayes(prior=0.01, likelihood_h=0.8, likelihood_not_h=0.096)
-# 0.07763975155279504
-
    
-
    
-
    You can also make distributions and update them:
    
-
    import matplotlib.pyplot as plt
-import squigglepy as sq
-from squigglepy import bayes
-from squigglepy.numbers import K
-import numpy as np
-
-print('Prior')
-prior = sq.norm(1,5)
-prior_samples = prior @ (10*K)
-plt.hist(prior_samples, bins = 200)
-plt.show()
-print(sq.get_percentiles(prior_samples))
-print('Prior Mean: {} SD: {}'.format(np.mean(prior_samples), np.std(prior_samples)))
-print('-')
-
-print('Evidence')
-evidence = sq.norm(2,3)
-evidence_samples = evidence @ (10*K)
-plt.hist(evidence_samples, bins = 200)
-plt.show()
-print(sq.get_percentiles(evidence_samples))
-print('Evidence Mean: {} SD: {}'.format(np.mean(evidence_samples), np.std(evidence_samples)))
-print('-')
-
-print('Posterior')
-posterior = bayes.update(prior, evidence)
-posterior_samples = posterior @ (10*K)
-plt.hist(posterior_samples, bins = 200)
-plt.show()
-print(sq.get_percentiles(posterior_samples))
-print('Posterior Mean: {} SD: {}'.format(np.mean(posterior_samples), np.std(posterior_samples)))
-
-print('Average')
-average = bayes.average(prior, evidence)
-average_samples = average @ (10*K)
-plt.hist(average_samples, bins = 200)
-plt.show()
-print(sq.get_percentiles(average_samples))
-print('Average Mean: {} SD: {}'.format(np.mean(average_samples), np.std(average_samples)))
-
    
-
    
-
    
-
    Example: Alarm net#
    
-
    This is the alarm network from Bayesian Artificial Intelligence -
-Section
-2.5.1:
    
-
    
-
    Assume your house has an alarm system against burglary.
    
-
    You live in the seismically active area and the alarm system can get
-occasionally set off by an earthquake.
    
-
    You have two neighbors, Mary and John, who do not know each other. If
-they hear the alarm they call you, but this is not guaranteed.
    
-
    The chance of a burglary on a particular day is 0.1%. The chance of
-an earthquake on a particular day is 0.2%.
    
-
    The alarm will go off 95% of the time with both a burglary and an
-earthquake, 94% of the time with just a burglary, 29% of the time
-with just an earthquake, and 0.1% of the time with nothing (total
-false alarm).
    
-
    John will call you 90% of the time when the alarm goes off. But on 5%
-of the days, John will just call to say “hi”. Mary will call you 70%
-of the time when the alarm goes off. But on 1% of the days, Mary will
-just call to say “hi”.
    
-
    
-
    import squigglepy as sq
-from squigglepy import bayes
-from squigglepy.numbers import M
-
-def p_alarm_goes_off(burglary, earthquake):
-    if burglary and earthquake:
-        return 0.95
-    elif burglary and not earthquake:
-        return 0.94
-    elif not burglary and earthquake:
-        return 0.29
-    elif not burglary and not earthquake:
-        return 0.001
-
-def p_john_calls(alarm_goes_off):
-    return 0.9 if alarm_goes_off else 0.05
-
-def p_mary_calls(alarm_goes_off):
-    return 0.7 if alarm_goes_off else 0.01
-
-def define_event():
-    burglary_happens = sq.event(p=0.001)
-    earthquake_happens = sq.event(p=0.002)
-    alarm_goes_off = sq.event(p_alarm_goes_off(burglary_happens, earthquake_happens))
-    john_calls = sq.event(p_john_calls(alarm_goes_off))
-    mary_calls = sq.event(p_mary_calls(alarm_goes_off))
-    return {'burglary': burglary_happens,
-            'earthquake': earthquake_happens,
-            'alarm_goes_off': alarm_goes_off,
-            'john_calls': john_calls,
-            'mary_calls': mary_calls}
-
-# What are the chances that both John and Mary call if an earthquake happens?
-bayes.bayesnet(define_event,
-               n=1*M,
-               find=lambda e: (e['mary_calls'] and e['john_calls']),
-               conditional_on=lambda e: e['earthquake'])
-# Result will be ~0.19, though it varies because it is based on a random sample.
-# This also may take a minute to run.
-
-# If both John and Mary call, what is the chance there's been a burglary?
-bayes.bayesnet(define_event,
-               n=1*M,
-               find=lambda e: e['burglary'],
-               conditional_on=lambda e: (e['mary_calls'] and e['john_calls']))
-# Result will be ~0.27, though it varies because it is based on a random sample.
-# This will run quickly because there is a built-in cache.
-# Use `cache=False` to not build a cache and `reload_cache=True` to recalculate the cache.
-
    
-
    
-
    Note that the amount of Bayesian analysis that squigglepy can do is
-pretty limited. For more complex bayesian analysis, consider
-sorobn,
-pomegranate,
-bnlearn, or
-pyMC.
    
-
    
-
    
-
    Example: A demonstration of the Monty Hall Problem#
    
-
    import squigglepy as sq
-from squigglepy import bayes
-from squigglepy.numbers import K, M, B, T
-
-
-def monte_hall(door_picked, switch=False):
-    doors = ['A', 'B', 'C']
-    car_is_behind_door = ~sq.discrete(doors)
-    reveal_door = ~sq.discrete([d for d in doors if d != door_picked and d != car_is_behind_door])
-
-    if switch:
-        old_door_picked = door_picked
-        door_picked = [d for d in doors if d != old_door_picked and d != reveal_door][0]
-
-    won_car = (car_is_behind_door == door_picked)
-    return won_car
-
-
-def define_event():
-    door = ~sq.discrete(['A', 'B', 'C'])
-    switch = sq.event(0.5)
-    return {'won': monte_hall(door_picked=door, switch=switch),
-            'switched': switch}
-
-RUNS = 10*K
-r = bayes.bayesnet(define_event,
-                   find=lambda e: e['won'],
-                   conditional_on=lambda e: e['switched'],
-                   verbose=True,
-                   n=RUNS)
-print('Win {}% of the time when switching'.format(int(r * 100)))
-
-r = bayes.bayesnet(define_event,
-                   find=lambda e: e['won'],
-                   conditional_on=lambda e: not e['switched'],
-                   verbose=True,
-                   n=RUNS)
-print('Win {}% of the time when not switching'.format(int(r * 100)))
-
-# Win 66% of the time when switching
-# Win 34% of the time when not switching
-
    
-
    
-
    
-
    
-
    Example: More complex coin/dice interactions#
    
-
    
-
    Imagine that I flip a coin. If heads, I take a random die out of my
-blue bag. If tails, I take a random die out of my red bag. The blue
-bag contains only 6-sided dice. The red bag contains a 4-sided die, a
-6-sided die, a 10-sided die, and a 20-sided die. I then roll the
-random die I took. What is the chance that I roll a 6?
    
-
    
-
    import squigglepy as sq
-from squigglepy.numbers import K, M, B, T
-from squigglepy import bayes
-
-def define_event():
-    if sq.flip_coin() == 'heads': # Blue bag
-        return sq.roll_die(6)
-    else: # Red bag
-        return sq.discrete([4, 6, 10, 20]) >> sq.roll_die
-
-
-bayes.bayesnet(define_event,
-               find=lambda e: e == 6,
-               verbose=True,
-               n=100*K)
-# This run for me returned 0.12306 which is pretty close to the correct answer of 0.12292
-
    
-
    
-
    
-
    
-
    
-
    Kelly betting#
    
-
    You can use probability generated, combine with a bankroll to determine
-bet sizing using Kelly
-criterion.
    
-
    For example, if you want to Kelly bet and you’ve…
    
-
      
-
    • determined that your price (your probability of the event in question
-happening / the market in question resolving in your favor) is $0.70
-(70%)
      • 
-
    • see that the market is pricing at $0.65
      • 
-
    • you have a bankroll of $1000 that you are willing to bet
      • 
-
    
-
    You should bet as follows:
    
-
    import squigglepy as sq
-kelly_data = sq.kelly(my_price=0.70, market_price=0.65, bankroll=1000)
-kelly_data['kelly']  # What fraction of my bankroll should I bet on this?
-# 0.143
-kelly_data['target']  # How much money should be invested in this?
-# 142.86
-kelly_data['expected_roi']  # What is the expected ROI of this bet?
-# 0.077
-
    
-
    
-
    
-
    
-
    More examples#
    
-
    You can see more examples of squigglepy in action
-here.
    
-
    Use black . for formatting.
    
-
    Run
-ruff check . && pytest && pip3 install . && python3 tests/integration.py
    
-
    
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