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__osx >=11.0 + - libzlib >=1.3.1,<2.0a0 + license: BSD-3-Clause + license_family: BSD + size: 433413 + timestamp: 1764777166076 diff --git a/pixi.toml b/pixi.toml index d880187..38e9123 100644 --- a/pixi.toml +++ b/pixi.toml @@ -1,6 +1,6 @@ [workspace] authors = ["MojoMath "] -channels = ["https://repo.prefix.dev/modular-community", "https://conda.modular.com/max-nightly", "https://conda.modular.com/max", "conda-forge"] +channels = ["https://repo.prefix.dev/modular-community", "https://conda.modular.com/max", "conda-forge", "https://conda.modular.com/max-nightly"] description = "A statistical computing library for Mojo, inspired by scipy.stats and statsmodels" license = "Apache-2.0" name = "stamojo" @@ -9,7 +9,7 @@ readme = "README.md" version = "0.1.0" [dependencies] -mojo = "==0.26.1" +mojo = ">=0.26.2.0,<0.27" # ── Feature: test (adds scipy for reference-value benchmarks) ──────────────── [feature.test.dependencies] diff --git a/src/stamojo/distributions/__init__.mojo b/src/stamojo/distributions/__init__.mojo index 82d1ee5..6d41354 100644 --- a/src/stamojo/distributions/__init__.mojo +++ b/src/stamojo/distributions/__init__.mojo @@ -14,6 +14,9 @@ Distributions provided: - `FDist` — F-distribution (Fisher-Snedecor) - `Exponential` — Exponential distribution - `Binomial` — Binomial distribution +- `Gamma` — Gamma distribution +- `Beta` — Beta distribution +- `Poisson` — Poisson distribution """ from .normal import Normal @@ -22,3 +25,6 @@ from .chi2 import ChiSquared from .f import FDist from .exponential import Exponential from .binomial import Binomial +from .gamma import Gamma +from .beta import Beta +from .poisson import Poisson diff --git a/src/stamojo/distributions/beta.mojo b/src/stamojo/distributions/beta.mojo new file mode 100644 index 0000000..f17f671 --- /dev/null +++ b/src/stamojo/distributions/beta.mojo @@ -0,0 +1,223 @@ +# ===----------------------------------------------------------------------=== # +# Stamojo - Distributions - Beta distribution +# Licensed under Apache 2.0 +# ===----------------------------------------------------------------------=== # +"""Beta distribution. + +Provides the `Beta` distribution struct with PDF, log-PDF, CDF, +survival function, and percent-point function (PPF / quantile). + +The beta distribution with shape parameters *a* and *b* has PDF:: + + f(x; a, b) = x^{a-1} (1-x)^{b-1} / B(a, b), 0 < x < 1 +""" + +from std.math import sqrt, log, lgamma, exp, nan, inf + +from stamojo.special import betainc, lbeta, ndtri + + +# ===----------------------------------------------------------------------=== # +# Constants +# ===----------------------------------------------------------------------=== # + +comptime _EPS = 1.0e-12 +comptime _MAX_ITER = 100 + + +# ===----------------------------------------------------------------------=== # +# Beta distribution +# ===----------------------------------------------------------------------=== # + + +@fieldwise_init +struct Beta(Copyable, Movable): + """Beta distribution with shape parameters `a` and `b`. + + Fields: + a: First shape parameter. Must be positive. + b: Second shape parameter. Must be positive. + """ + + var a: Float64 + var b: Float64 + + # --- Density functions --------------------------------------------------- + + def pdf(self, x: Float64) -> Float64: + """Probability density function at *x*.""" + if x <= 0.0 or x >= 1.0: + return 0.0 + return exp(self.logpdf(x)) + + def logpdf(self, x: Float64) -> Float64: + """Natural logarithm of the probability density function at *x*.""" + if x <= 0.0 or x >= 1.0: + return -inf[DType.float64]() + return ( + (self.a - 1.0) * log(x) + + (self.b - 1.0) * log(1.0 - x) + - lbeta(self.a, self.b) + ) + + # --- Distribution functions ---------------------------------------------- + + def cdf(self, x: Float64) -> Float64: + """Cumulative distribution function P(X ≤ x). + + CDF(x; a, b) = I_x(a, b) (regularized incomplete beta). + """ + if x <= 0.0: + return 0.0 + if x >= 1.0: + return 1.0 + return betainc(self.a, self.b, x) + + def logcdf(self, x: Float64) -> Float64: + """Natural logarithm of the CDF at *x*.""" + if x <= 0.0: + return -inf[DType.float64]() + if x >= 1.0: + return 0.0 + var c = self.cdf(x) + if c <= 0.0: + return -inf[DType.float64]() + return log(c) + + def sf(self, x: Float64) -> Float64: + """Survival function (1 − CDF) at *x*.""" + if x <= 0.0: + return 1.0 + if x >= 1.0: + return 0.0 + return 1.0 - self.cdf(x) + + def logsf(self, x: Float64) -> Float64: + """Natural logarithm of the survival function at *x*.""" + if x <= 0.0: + return 0.0 + if x >= 1.0: + return -inf[DType.float64]() + var s = self.sf(x) + if s <= 0.0: + return -inf[DType.float64]() + return log(s) + + def ppf(self, p: Float64) -> Float64: + """Percent-point function (quantile / inverse CDF). + + Uses Newton-Raphson with bisection fallback. + + Args: + p: Probability value in [0, 1]. + + Returns: + The quantile corresponding to *p*. + """ + if p < 0.0 or p > 1.0: + return nan[DType.float64]() + if p == 0.0: + return 0.0 + if p == 1.0: + return 1.0 + + var mu = self.a / (self.a + self.b) + var x: Float64 + if self.a > 1.0 and self.b > 1.0: + var sigma = sqrt( + self.a + * self.b + / ((self.a + self.b) ** 2 * (self.a + self.b + 1.0)) + ) + x = mu + sigma * ndtri(p) + if x <= 0.0: + x = 0.01 + if x >= 1.0: + x = 0.99 + else: + x = mu + + # Newton-Raphson with bisection fallback. + var lo = 0.0 + var hi = 1.0 + + for _ in range(_MAX_ITER): + var f = self.cdf(x) - p + if abs(f) < _EPS: + return x + + var fp = self.pdf(x) + if fp > 1.0e-300: + var x_new = x - f / fp + if f > 0.0: + hi = x + else: + lo = x + if x_new <= lo or x_new >= hi: + x = (lo + hi) / 2.0 + else: + x = x_new + else: + if f > 0.0: + hi = x + else: + lo = x + x = (lo + hi) / 2.0 + + return x + + def isf(self, q: Float64) -> Float64: + """Inverse survival function (inverse SF). + + Args: + q: Probability in [0, 1]. + + Returns: + The value *x* such that SF(x) = *q*. + """ + return self.ppf(1.0 - q) + + # --- Summary statistics -------------------------------------------------- + + def median(self) -> Float64: + """Median of the distribution (approximation). + + Uses the approximation: (a - 1/3) / (a + b - 2/3) for a, b >= 1. + """ + if self.a >= 1.0 and self.b >= 1.0: + return (self.a - 1.0 / 3.0) / (self.a + self.b - 2.0 / 3.0) + return self.a / (self.a + self.b) + + def mean(self) -> Float64: + """Distribution mean = a / (a + b).""" + return self.a / (self.a + self.b) + + def variance(self) -> Float64: + """Distribution variance = ab / ((a+b)²(a+b+1)).""" + var ab = self.a + self.b + return self.a * self.b / (ab * ab * (ab + 1.0)) + + def std(self) -> Float64: + """Distribution standard deviation.""" + return sqrt(self.variance()) + + def entropy(self) -> Float64: + """Differential entropy of the distribution. + + H = ln(B(a,b)) - (a-1)ψ(a) - (b-1)ψ(b) + (a+b-2)ψ(a+b) + Using digamma approximation: ψ(x) ≈ ln(x) - 1/(2x) - 1/(12x²) + """ + var digamma_a = ( + log(self.a) - 1.0 / (2.0 * self.a) - 1.0 / (12.0 * self.a * self.a) + ) + var digamma_b = ( + log(self.b) - 1.0 / (2.0 * self.b) - 1.0 / (12.0 * self.b * self.b) + ) + var ab = self.a + self.b + var digamma_ab = log(ab) - 1.0 / (2.0 * ab) - 1.0 / (12.0 * ab * ab) + return ( + lbeta(self.a, self.b) + - (self.a - 1.0) * digamma_a + - (self.b - 1.0) * digamma_b + + (self.a + self.b - 2.0) * digamma_ab + ) diff --git a/src/stamojo/distributions/binomial.mojo b/src/stamojo/distributions/binomial.mojo index 66122fc..5bc7ce2 100644 --- a/src/stamojo/distributions/binomial.mojo +++ b/src/stamojo/distributions/binomial.mojo @@ -14,7 +14,7 @@ The binomial distribution with parameters n and p has PMF: where C(n, k) is the binomial coefficient. """ -from math import log, log1p, exp, lgamma, nan, inf, floor, sqrt +from std.math import log, log1p, exp, lgamma, nan, inf, floor, sqrt from stamojo.distributions.traits import DiscretelyDistributed @@ -42,13 +42,13 @@ struct Binomial(DiscretelyDistributed): # --- Initialization ------------------------------------------------------- - fn __init__(out self, n: Int, p: Float64): + def __init__(out self, n: Int, p: Float64): self.n = n self.p = p # --- Probability functions ------------------------------------------------ - fn pmf(self, k: Int) -> Float64: + def pmf(self, k: Int) -> Float64: """Probability mass function at *k*. Args: @@ -59,7 +59,7 @@ struct Binomial(DiscretelyDistributed): """ return exp(self.logpmf(k)) - fn logpmf(self, k: Int) -> Float64: + def logpmf(self, k: Int) -> Float64: """Natural logarithm of the PMF at *k*. Args: @@ -82,7 +82,7 @@ struct Binomial(DiscretelyDistributed): var logc = _log_binomial_coefficient(self.n, k) return logc + kf * log(self.p) + (nf - kf) * log1p(-self.p) - fn cdf(self, k: Int) -> Float64: + def cdf(self, k: Int) -> Float64: """Cumulative distribution function P(X ≤ k). Args: @@ -113,7 +113,7 @@ struct Binomial(DiscretelyDistributed): return total - fn logcdf(self, k: Int) -> Float64: + def logcdf(self, k: Int) -> Float64: """Natural logarithm of the CDF at *k*. Args: @@ -127,7 +127,7 @@ struct Binomial(DiscretelyDistributed): return -inf[DType.float64]() return log(c) - fn sf(self, k: Int) -> Float64: + def sf(self, k: Int) -> Float64: """Survival function (1 − CDF) at *k*. Args: @@ -138,7 +138,7 @@ struct Binomial(DiscretelyDistributed): """ return 1.0 - self.cdf(k) - fn logsf(self, k: Int) -> Float64: + def logsf(self, k: Int) -> Float64: """Natural logarithm of the survival function at *k*. Args: @@ -149,7 +149,7 @@ struct Binomial(DiscretelyDistributed): """ return log1p(-self.cdf(k)) - fn ppf(self, q: Float64) -> Int: + def ppf(self, q: Float64) -> Int: """Percent point function (inverse CDF). Args: @@ -171,7 +171,7 @@ struct Binomial(DiscretelyDistributed): return self.n - fn isf(self, q: Float64) -> Int: + def isf(self, q: Float64) -> Int: """Inverse survival function (inverse SF). Args: @@ -194,7 +194,7 @@ struct Binomial(DiscretelyDistributed): return self.n # --- Summary statistics -------------------------------------------------- - fn median(self) -> UInt: + def median(self) -> UInt: """Median of the distribution: floor(n * p + 0.5). Returns: @@ -202,7 +202,7 @@ struct Binomial(DiscretelyDistributed): """ return UInt(floor(Float64(self.n) * self.p + 0.5)) - fn mean(self) -> Float64: + def mean(self) -> Float64: """Distribution mean: n * p. Returns: @@ -210,7 +210,7 @@ struct Binomial(DiscretelyDistributed): """ return Float64(self.n) * self.p - fn variance(self) -> Float64: + def variance(self) -> Float64: """Distribution variance: n * p * (1 - p). Returns: @@ -219,7 +219,7 @@ struct Binomial(DiscretelyDistributed): var np = Float64(self.n) * self.p return np * (1.0 - self.p) - fn std(self) -> Float64: + def std(self) -> Float64: """Distribution standard deviation: sqrt(n * p * (1 - p)). Returns: @@ -233,7 +233,7 @@ struct Binomial(DiscretelyDistributed): # ===----------------------------------------------------------------------=== # -fn _log_binomial_coefficient(n: Int, k: Int) -> Float64: +def _log_binomial_coefficient(n: Int, k: Int) -> Float64: """Log of the binomial coefficient C(n, k). Args: diff --git a/src/stamojo/distributions/chi2.mojo b/src/stamojo/distributions/chi2.mojo index fd0b021..3a3a8d8 100644 --- a/src/stamojo/distributions/chi2.mojo +++ b/src/stamojo/distributions/chi2.mojo @@ -12,7 +12,7 @@ The chi-squared distribution with *k* degrees of freedom has PDF:: f(x; k) = x^{k/2−1} exp(−x/2) / (2^{k/2} Γ(k/2)), x > 0 """ -from math import sqrt, log, lgamma, exp, nan, inf +from std.math import sqrt, log, lgamma, exp, nan, inf from stamojo.special import gammainc, gammaincc, ndtri @@ -43,7 +43,7 @@ struct ChiSquared(Copyable, Movable): # --- Density functions --------------------------------------------------- - fn pdf(self, x: Float64) -> Float64: + def pdf(self, x: Float64) -> Float64: """Probability density function at *x*.""" if x < 0.0: return 0.0 @@ -56,7 +56,7 @@ struct ChiSquared(Copyable, Movable): return 0.0 return exp(self.logpdf(x)) - fn logpdf(self, x: Float64) -> Float64: + def logpdf(self, x: Float64) -> Float64: """Natural logarithm of the probability density function at *x*.""" if x <= 0.0: return -inf[DType.float64]() @@ -70,7 +70,7 @@ struct ChiSquared(Copyable, Movable): # --- Distribution functions ---------------------------------------------- - fn cdf(self, x: Float64) -> Float64: + def cdf(self, x: Float64) -> Float64: """Cumulative distribution function P(X ≤ x). CDF(x; k) = P(k/2, x/2) (regularized lower incomplete gamma). @@ -79,13 +79,13 @@ struct ChiSquared(Copyable, Movable): return 0.0 return gammainc(self.df / 2.0, x / 2.0) - fn sf(self, x: Float64) -> Float64: + def sf(self, x: Float64) -> Float64: """Survival function (1 − CDF) at *x*.""" if x <= 0.0: return 1.0 return gammaincc(self.df / 2.0, x / 2.0) - fn ppf(self, p: Float64) -> Float64: + def ppf(self, p: Float64) -> Float64: """Percent-point function (quantile / inverse CDF). Uses the Wilson-Hilferty initial approximation refined by @@ -152,14 +152,14 @@ struct ChiSquared(Copyable, Movable): # --- Summary statistics -------------------------------------------------- - fn mean(self) -> Float64: + def mean(self) -> Float64: """Distribution mean = k.""" return self.df - fn variance(self) -> Float64: + def variance(self) -> Float64: """Distribution variance = 2k.""" return 2.0 * self.df - fn std(self) -> Float64: + def std(self) -> Float64: """Distribution standard deviation = √(2k).""" return sqrt(2.0 * self.df) diff --git a/src/stamojo/distributions/exponential.mojo b/src/stamojo/distributions/exponential.mojo index 41445f2..10662ed 100644 --- a/src/stamojo/distributions/exponential.mojo +++ b/src/stamojo/distributions/exponential.mojo @@ -12,7 +12,7 @@ The exponential distribution with rate parameter λ has PDF: f(x; λ) = λ exp(−λx), x ≥ 0 """ -from math import log, exp, nan, inf, log1p, expm1 +from std.math import log, exp, nan, inf, log1p, expm1 from stamojo.distributions.traits import ContinuouslyDistributed @@ -50,13 +50,13 @@ struct Exponential(ContinuouslyDistributed): # --- Initialization ------------------------------------------------------- - fn __init__(out self, loc: Float64 = 0.0, scale: Float64 = 1.0): + def __init__(out self, loc: Float64 = 0.0, scale: Float64 = 1.0): self.loc = loc self.scale = scale # --- Density functions --------------------------------------------------- - fn pdf(self, x: Float64) -> Float64: + def pdf(self, x: Float64) -> Float64: """Probability density function at *x*. Args: @@ -70,7 +70,7 @@ struct Exponential(ContinuouslyDistributed): return 0.0 return exp(-y) / self.scale - fn logpdf(self, x: Float64) -> Float64: + def logpdf(self, x: Float64) -> Float64: """Natural logarithm of the PDF at *x*. Args: @@ -85,7 +85,7 @@ struct Exponential(ContinuouslyDistributed): return -y - log(self.scale) # --- Distribution functions ---------------------------------------------- - fn cdf(self, x: Float64) -> Float64: + def cdf(self, x: Float64) -> Float64: """Cumulative distribution function P(X ≤ x). Args: @@ -99,7 +99,7 @@ struct Exponential(ContinuouslyDistributed): var y = (x - self.loc) / self.scale return -expm1(-y) - fn logcdf(self, x: Float64) -> Float64: + def logcdf(self, x: Float64) -> Float64: """Natural logarithm of the CDF at *x*. Uses ``log(-expm1(-y))`` instead of ``log1p(-exp(-y))`` for better @@ -116,7 +116,7 @@ struct Exponential(ContinuouslyDistributed): var y = (x - self.loc) / self.scale return log(-expm1(-y)) - fn sf(self, x: Float64) -> Float64: + def sf(self, x: Float64) -> Float64: """Survival function (1 − CDF) at *x*. Args: @@ -130,7 +130,7 @@ struct Exponential(ContinuouslyDistributed): var y = (x - self.loc) / self.scale return exp(-y) - fn logsf(self, x: Float64) -> Float64: + def logsf(self, x: Float64) -> Float64: """Natural logarithm of the survival function at *x*. Args: @@ -144,7 +144,7 @@ struct Exponential(ContinuouslyDistributed): var y = (x - self.loc) / self.scale return -y - fn ppf(self, q: Float64) -> Float64: + def ppf(self, q: Float64) -> Float64: """Percent-point (quantile) function (inverse CDF). Args: @@ -167,7 +167,7 @@ struct Exponential(ContinuouslyDistributed): return inf[DType.float64]() return self.loc - self.scale * log1p(-q) - fn isf(self, q: Float64) -> Float64: + def isf(self, q: Float64) -> Float64: """Inverse survival function (inverse SF). Args: @@ -191,7 +191,7 @@ struct Exponential(ContinuouslyDistributed): return self.loc - self.scale * log(q) # --- Summary statistics -------------------------------------------------- - fn median(self) -> Float64: + def median(self) -> Float64: """Median of the distribution: loc + scale * ln(2). Returns: @@ -199,7 +199,7 @@ struct Exponential(ContinuouslyDistributed): """ return self.loc + self.scale * log(2.0) - fn mean(self) -> Float64: + def mean(self) -> Float64: """Distribution mean: loc + scale. Returns: @@ -207,7 +207,7 @@ struct Exponential(ContinuouslyDistributed): """ return self.loc + self.scale - fn variance(self) -> Float64: + def variance(self) -> Float64: """Distribution variance: scale². Returns: @@ -215,7 +215,7 @@ struct Exponential(ContinuouslyDistributed): """ return self.scale * self.scale - fn std(self) -> Float64: + def std(self) -> Float64: """Distribution standard deviation: scale. Returns: diff --git a/src/stamojo/distributions/f.mojo b/src/stamojo/distributions/f.mojo index 0bba2de..8ba08b3 100644 --- a/src/stamojo/distributions/f.mojo +++ b/src/stamojo/distributions/f.mojo @@ -13,7 +13,7 @@ The F-distribution with d₁ and d₂ degrees of freedom has PDF:: / (x · B(d₁/2, d₂/2)) """ -from math import sqrt, log, exp, nan, inf +from std.math import sqrt, log, exp, nan, inf from stamojo.special import betainc, lbeta, ndtri @@ -46,7 +46,7 @@ struct FDist(Copyable, Movable): # --- Density functions --------------------------------------------------- - fn pdf(self, x: Float64) -> Float64: + def pdf(self, x: Float64) -> Float64: """Probability density function at *x*.""" if x < 0.0: return 0.0 @@ -59,7 +59,7 @@ struct FDist(Copyable, Movable): return 0.0 return exp(self.logpdf(x)) - fn logpdf(self, x: Float64) -> Float64: + def logpdf(self, x: Float64) -> Float64: """Natural logarithm of the probability density function at *x*.""" if x <= 0.0: return -inf[DType.float64]() @@ -74,7 +74,7 @@ struct FDist(Copyable, Movable): # --- Distribution functions ---------------------------------------------- - fn cdf(self, x: Float64) -> Float64: + def cdf(self, x: Float64) -> Float64: """Cumulative distribution function P(X ≤ x). CDF(x) = I_{d₁x/(d₁x+d₂)}(d₁/2, d₂/2). @@ -86,11 +86,11 @@ struct FDist(Copyable, Movable): var u = d1 * x / (d1 * x + d2) return betainc(d1 / 2.0, d2 / 2.0, u) - fn sf(self, x: Float64) -> Float64: + def sf(self, x: Float64) -> Float64: """Survival function (1 − CDF) at *x*.""" return 1.0 - self.cdf(x) - fn ppf(self, p: Float64) -> Float64: + def ppf(self, p: Float64) -> Float64: """Percent-point function (quantile / inverse CDF). Computed via Newton-Raphson with bisection fallback. @@ -148,13 +148,13 @@ struct FDist(Copyable, Movable): # --- Summary statistics -------------------------------------------------- - fn mean(self) -> Float64: + def mean(self) -> Float64: """Distribution mean. Defined for d₂ > 2.""" if self.dfd > 2.0: return self.dfd / (self.dfd - 2.0) return nan[DType.float64]() - fn variance(self) -> Float64: + def variance(self) -> Float64: """Distribution variance. Defined for d₂ > 4.""" if self.dfd > 4.0: var d1 = self.dfn @@ -168,6 +168,6 @@ struct FDist(Copyable, Movable): ) return nan[DType.float64]() - fn std(self) -> Float64: + def std(self) -> Float64: """Distribution standard deviation.""" return sqrt(self.variance()) diff --git a/src/stamojo/distributions/gamma.mojo b/src/stamojo/distributions/gamma.mojo new file mode 100644 index 0000000..a1e8b4a --- /dev/null +++ b/src/stamojo/distributions/gamma.mojo @@ -0,0 +1,215 @@ +# ===----------------------------------------------------------------------=== # +# Stamojo - Distributions - Gamma distribution +# Licensed under Apache 2.0 +# ===----------------------------------------------------------------------=== # +"""Gamma distribution. + +Provides the `Gamma` distribution struct with PDF, log-PDF, CDF, +survival function, and percent-point function (PPF / quantile). + +The gamma distribution with shape *a* and scale *θ* has PDF:: + + f(x; a, θ) = x^{a-1} exp(−x/θ) / (θ^a Γ(a)), x > 0 +""" + +from std.math import sqrt, log, lgamma, exp, nan, inf, floor, pow + +from stamojo.special import gammainc, gammaincc, ndtri + + +# ===----------------------------------------------------------------------=== # +# Constants +# ===----------------------------------------------------------------------=== # + +comptime _EPS = 1.0e-12 +comptime _MAX_ITER = 100 + + +# ===----------------------------------------------------------------------=== # +# Gamma distribution +# ===----------------------------------------------------------------------=== # + + +@fieldwise_init +struct Gamma(Copyable, Movable): + """Gamma distribution with shape `a` and scale `scale`. + + Fields: + a: Shape parameter. Must be positive. + scale: Scale parameter (θ). Must be positive. + """ + + var a: Float64 + var scale: Float64 + + # --- Density functions --------------------------------------------------- + + def pdf(self, x: Float64) -> Float64: + """Probability density function at *x*.""" + if x <= 0.0: + return 0.0 + return exp(self.logpdf(x)) + + def logpdf(self, x: Float64) -> Float64: + """Natural logarithm of the probability density function at *x*.""" + if x <= 0.0: + return -inf[DType.float64]() + return ( + (self.a - 1.0) * log(x) + - x / self.scale + - self.a * log(self.scale) + - lgamma(self.a) + ) + + # --- Distribution functions ---------------------------------------------- + + def cdf(self, x: Float64) -> Float64: + """Cumulative distribution function P(X ≤ x). + + CDF(x; a, θ) = P(a, x/θ) (regularized lower incomplete gamma). + """ + if x <= 0.0: + return 0.0 + return gammainc(self.a, x / self.scale) + + def logcdf(self, x: Float64) -> Float64: + """Natural logarithm of the CDF at *x*.""" + if x <= 0.0: + return -inf[DType.float64]() + var c = self.cdf(x) + if c <= 0.0: + return -inf[DType.float64]() + return log(c) + + def sf(self, x: Float64) -> Float64: + """Survival function (1 − CDF) at *x*.""" + if x <= 0.0: + return 1.0 + return gammaincc(self.a, x / self.scale) + + def logsf(self, x: Float64) -> Float64: + """Natural logarithm of the survival function at *x*.""" + if x <= 0.0: + return 0.0 + var s = self.sf(x) + if s <= 0.0: + return -inf[DType.float64]() + return log(s) + + def ppf(self, p: Float64) -> Float64: + """Percent-point function (quantile / inverse CDF). + + Uses Newton-Raphson with bisection fallback. + + Args: + p: Probability value in [0, 1]. + + Returns: + The quantile corresponding to *p*. + """ + if p < 0.0 or p > 1.0: + return nan[DType.float64]() + if p == 0.0: + return 0.0 + if p == 1.0: + return inf[DType.float64]() + + var a = self.a + + # Initial guess using Wilson-Hilferty approximation. + var z = ndtri(p) + var wh = 1.0 / (9.0 * a) + var cube = 1.0 - wh + z * sqrt(wh) + var x: Float64 + if cube > 0.0: + x = a * cube * cube * cube + else: + x = a * 0.1 + + if x <= 0.0: + x = 0.01 + x *= self.scale + + # TODO: Since many use Newton-Raphson, we could have a separate func for this. + var lo = 0.0 + var hi = x * 4.0 + 10.0 * self.scale + while self.cdf(hi) < p: + hi *= 2.0 + + for _ in range(_MAX_ITER): + var f = self.cdf(x) - p + if abs(f) < _EPS: + return x + + var fp = self.pdf(x) + if fp > 1.0e-300: + var x_new = x - f / fp + if f > 0.0: + hi = x + else: + lo = x + if x_new <= lo or x_new >= hi: + x = (lo + hi) / 2.0 + else: + x = x_new + else: + if f > 0.0: + hi = x + else: + lo = x + x = (lo + hi) / 2.0 + + return x + + def isf(self, q: Float64) -> Float64: + """Inverse survival function (inverse SF). + + Args: + q: Probability in [0, 1]. + + Returns: + The value *x* such that SF(x) = *q*. + """ + return self.ppf(1.0 - q) + + # --- Summary statistics -------------------------------------------------- + + def median(self) -> Float64: + """Median of the distribution (approximation). + + Uses the approximation: scale * a * (1 - 1/(9a))^3 for a >= 1, + and scale * a * 2^(-1/a) for a < 1. + """ + if self.a >= 1.0: + return self.scale * self.a * pow(1.0 - 1.0 / (9.0 * self.a), 3) + else: + return self.scale * self.a * pow(2.0, -1.0 / self.a) + + def mean(self) -> Float64: + """Distribution mean = a * θ.""" + return self.a * self.scale + + def variance(self) -> Float64: + """Distribution variance = a * θ².""" + return self.a * self.scale * self.scale + + def std(self) -> Float64: + """Distribution standard deviation = √(a) * θ.""" + return sqrt(self.a) * self.scale + + def entropy(self) -> Float64: + """Differential entropy of the distribution. + + H = a + ln(θ) + ln(Γ(a)) + (1 - a) * ψ(a) + where ψ is the digamma function (approximated here). + For simplicity: H ≈ a + ln(θ) + ln(Γ(a)) - (a-1)*ψ(a) + Using approximation ψ(a) ≈ ln(a) - 1/(2a) for large a. + """ + # H = a + ln(scale) + ln(Gamma(a)) + (1-a)*digamma(a) + # Approximate digamma(a) ≈ ln(a) - 1/(2a) - 1/(12a²) + var digamma = ( + log(self.a) - 1.0 / (2.0 * self.a) - 1.0 / (12.0 * self.a * self.a) + ) + return ( + self.a + log(self.scale) + lgamma(self.a) + (1.0 - self.a) * digamma + ) diff --git a/src/stamojo/distributions/normal.mojo b/src/stamojo/distributions/normal.mojo index df61bed..f643f41 100644 --- a/src/stamojo/distributions/normal.mojo +++ b/src/stamojo/distributions/normal.mojo @@ -18,8 +18,8 @@ Examples:: n.ppf(0.975) # ≈ 1.96 """ -from math import sqrt, log, cos, exp, erf, erfc, nan, inf -from random import random_float64 +from std.math import sqrt, log, cos, exp, erf, erfc, nan, inf +from std.random import random_float64 from stamojo.special import ndtri @@ -58,27 +58,27 @@ struct Normal(Copyable, Movable): # --- Density functions --------------------------------------------------- - fn pdf(self, x: Float64) -> Float64: + def pdf(self, x: Float64) -> Float64: """Probability density function at *x*.""" var z = (x - self.mu) / self.sigma return _INV_SQRT_2PI / self.sigma * exp(-0.5 * z * z) - fn logpdf(self, x: Float64) -> Float64: + def logpdf(self, x: Float64) -> Float64: """Natural logarithm of the probability density function at *x*.""" var z = (x - self.mu) / self.sigma return -_LN_SQRT_2PI - log(self.sigma) - 0.5 * z * z # --- Distribution functions ---------------------------------------------- - fn cdf(self, x: Float64) -> Float64: + def cdf(self, x: Float64) -> Float64: """Cumulative distribution function P(X ≤ x).""" return 0.5 * erfc(-(x - self.mu) / (self.sigma * _SQRT2)) - fn sf(self, x: Float64) -> Float64: + def sf(self, x: Float64) -> Float64: """Survival function (1 − CDF) at *x*.""" return 0.5 * erfc((x - self.mu) / (self.sigma * _SQRT2)) - fn ppf(self, p: Float64) -> Float64: + def ppf(self, p: Float64) -> Float64: """Percent-point function (quantile / inverse CDF). Returns the value *x* such that P(X ≤ x) = p. @@ -99,26 +99,26 @@ struct Normal(Copyable, Movable): # --- Summary statistics -------------------------------------------------- - fn mean(self) -> Float64: + def mean(self) -> Float64: """Distribution mean.""" return self.mu - fn variance(self) -> Float64: + def variance(self) -> Float64: """Distribution variance σ².""" return self.sigma * self.sigma - fn std(self) -> Float64: + def std(self) -> Float64: """Distribution standard deviation σ.""" return self.sigma - fn entropy(self) -> Float64: + def entropy(self) -> Float64: """Differential entropy of the distribution.""" # H = 0.5 * ln(2πeσ²) = ln(σ√(2πe)) = ln(σ) + 0.5*ln(2π) + 0.5 return _LN_SQRT_2PI + log(self.sigma) + 0.5 # --- Random variate generation ------------------------------------------- - fn rvs(self) -> Float64: + def rvs(self) -> Float64: """Generate a single random variate (Box-Muller transform).""" var u1 = random_float64() while u1 == 0.0: @@ -127,7 +127,7 @@ struct Normal(Copyable, Movable): var z = sqrt(-2.0 * log(u1)) * cos(_2PI * u2) return self.mu + self.sigma * z - fn rvs(self, n: Int) -> List[Float64]: + def rvs(self, n: Int) -> List[Float64]: """Generate *n* random variates. Args: diff --git a/src/stamojo/distributions/poisson.mojo b/src/stamojo/distributions/poisson.mojo new file mode 100644 index 0000000..003a388 --- /dev/null +++ b/src/stamojo/distributions/poisson.mojo @@ -0,0 +1,220 @@ +# ===----------------------------------------------------------------------=== # +# Stamojo - Distributions - Poisson distribution +# Licensed under Apache 2.0 +# ===----------------------------------------------------------------------=== # +"""Poisson distribution. + +Provides the `Poisson` distribution struct with PMF, log-PMF, CDF, +survival function, and percent-point function (PPF / quantile). + +The Poisson distribution with rate parameter *μ* has PMF:: + + P(X = k; μ) = μ^k exp(−μ) / k!, k = 0, 1, 2, ... +""" + +from std.math import log, exp, lgamma, nan, inf, floor, sqrt + +from stamojo.distributions.traits import DiscretelyDistributed +from stamojo.special import gammaincc + + +# ===----------------------------------------------------------------------=== # +# Constants +# ===----------------------------------------------------------------------=== # + +comptime _MAX_K = 10000 + + +# ===----------------------------------------------------------------------=== # +# Poisson distribution +# ===----------------------------------------------------------------------=== # + + +struct Poisson(DiscretelyDistributed): + """Poisson distribution with rate parameter `mu`. + + Represents the Poisson distribution, a discrete probability distribution + that expresses the probability of a given number of events occurring in a + fixed interval of time or space, if these events occur with a known constant + mean rate and independently of the time since the last event. + + The probability mass function (PMF) for the Poisson distribution is: + + P(X = k; μ) = μ^k * exp(-μ) / k! + + Fields: + mu: Rate parameter (mean number of events). Must be positive. + """ + + var mu: Float64 + + def __init__(out self, mu: Float64): + self.mu = mu + + # --- Probability functions ------------------------------------------------ + + def pmf(self, k: Int) -> Float64: + """Probability mass function at *k*. + + Args: + k: Number of events (must be >= 0). + + Returns: + PMF value at *k*. Returns 0.0 for k < 0. + """ + return exp(self.logpmf(k)) + + def logpmf(self, k: Int) -> Float64: + """Natural logarithm of the PMF at *k*. + + Args: + k: Number of events (must be >= 0). + + Returns: + Log-PMF value at *k*. Returns -∞ for k < 0. + """ + if k < 0: + return -inf[DType.float64]() + if self.mu == 0.0: + return 0.0 if k == 0 else -inf[DType.float64]() + return Float64(k) * log(self.mu) - self.mu - lgamma(Float64(k) + 1.0) + + def cdf(self, k: Int) -> Float64: + """Cumulative distribution function P(X ≤ k). + + Args: + k: Number of events. + + Returns: + CDF value at *k*. Returns 1.0 for large k. + """ + if k < 0: + return 0.0 + if self.mu == 0.0: + return 1.0 + # CDF of Poisson(μ) at k = Q(k+1, μ) = gammaincc(k+1, μ) + return gammaincc(Float64(k + 1), self.mu) + + def logcdf(self, k: Int) -> Float64: + """Natural logarithm of the CDF at *k*. + + Args: + k: Number of events. + + Returns: + Log-CDF value at *k*. + """ + var c = self.cdf(k) + if c <= 0.0: + return -inf[DType.float64]() + return log(c) + + def sf(self, k: Int) -> Float64: + """Survival function (1 − CDF) at *k*. + + Args: + k: Number of events. + + Returns: + Survival function value at *k*. + """ + if k < 0: + return 1.0 + if self.mu == 0.0: + return 0.0 + return 1.0 - self.cdf(k) + + def logsf(self, k: Int) -> Float64: + """Natural logarithm of the survival function at *k*. + + Args: + k: Number of events. + + Returns: + Log-survival function value at *k*. + """ + var s = self.sf(k) + if s <= 0.0: + return -inf[DType.float64]() + return log(s) + + def ppf(self, q: Float64) -> Int: + """Percent point function (inverse CDF). + + Args: + q: Probability in [0, 1]. + + Returns: + Smallest integer k such that CDF(k) ≥ q. + """ + if q <= 0.0: + return 0 + if q >= 1.0: + return _MAX_K + + var cumulative: Float64 = 0.0 + var pk = exp(-self.mu) + cumulative = pk + + if cumulative >= q: + return 0 + + for k in range(1, _MAX_K): + pk *= self.mu / Float64(k) + cumulative += pk + if cumulative >= q: + return k + + return _MAX_K + + def isf(self, q: Float64) -> Int: + """Inverse survival function (inverse SF). + + Args: + q: Probability in [0, 1]. + + Returns: + Smallest integer k such that SF(k) ≤ q. + """ + if q <= 0.0: + return _MAX_K + if q >= 1.0: + return 0 + + var cumulative: Float64 = 0.0 + var pk = exp(-self.mu) + cumulative = pk + + if 1.0 - cumulative <= q: + return 0 + + for k in range(1, _MAX_K): + pk *= self.mu / Float64(k) + cumulative += pk + if 1.0 - cumulative <= q: + return k + + return _MAX_K + + # --- Summary statistics -------------------------------------------------- + + def median(self) -> UInt: + """Median of the distribution (approximation). + + Uses the approximation: floor(μ + 1/3 - 0.02/μ). + """ + if self.mu == 0.0: + return 0 + return UInt(floor(self.mu + 1.0 / 3.0 - 0.02 / self.mu)) + + def mean(self) -> Float64: + """Distribution mean = μ.""" + return self.mu + + def variance(self) -> Float64: + """Distribution variance = μ.""" + return self.mu + + def std(self) -> Float64: + """Distribution standard deviation = √μ.""" + return sqrt(self.mu) diff --git a/src/stamojo/distributions/t.mojo b/src/stamojo/distributions/t.mojo index 6175110..cde1aa7 100644 --- a/src/stamojo/distributions/t.mojo +++ b/src/stamojo/distributions/t.mojo @@ -12,7 +12,7 @@ The Student's t-distribution with ν degrees of freedom has PDF:: f(x; ν) = Γ((ν+1)/2) / (√(νπ) Γ(ν/2)) (1 + x²/ν)^{-(ν+1)/2} """ -from math import sqrt, log, lgamma, exp, nan, inf +from std.math import sqrt, log, lgamma, exp, nan, inf from stamojo.special import betainc, ndtri @@ -43,11 +43,11 @@ struct StudentT(Copyable, Movable): # --- Density functions --------------------------------------------------- - fn pdf(self, x: Float64) -> Float64: + def pdf(self, x: Float64) -> Float64: """Probability density function at *x*.""" return exp(self.logpdf(x)) - fn logpdf(self, x: Float64) -> Float64: + def logpdf(self, x: Float64) -> Float64: """Natural logarithm of the probability density function at *x*.""" var v = self.df return ( @@ -60,7 +60,7 @@ struct StudentT(Copyable, Movable): # --- Distribution functions ---------------------------------------------- - fn cdf(self, x: Float64) -> Float64: + def cdf(self, x: Float64) -> Float64: """Cumulative distribution function P(X ≤ x). Uses the regularized incomplete beta function: @@ -76,7 +76,7 @@ struct StudentT(Copyable, Movable): else: return 0.5 * ib - fn sf(self, x: Float64) -> Float64: + def sf(self, x: Float64) -> Float64: """Survival function (1 − CDF) at *x*.""" var v = self.df var u = v / (v + x * x) @@ -86,7 +86,7 @@ struct StudentT(Copyable, Movable): else: return 1.0 - 0.5 * ib - fn ppf(self, p: Float64) -> Float64: + def ppf(self, p: Float64) -> Float64: """Percent-point function (quantile / inverse CDF). Computed via Newton-Raphson with bisection fallback. @@ -140,13 +140,13 @@ struct StudentT(Copyable, Movable): # --- Summary statistics -------------------------------------------------- - fn mean(self) -> Float64: + def mean(self) -> Float64: """Distribution mean. Defined for df > 1.""" if self.df > 1.0: return 0.0 return nan[DType.float64]() - fn variance(self) -> Float64: + def variance(self) -> Float64: """Distribution variance. Defined for df > 2; infinite for 1 < df ≤ 2. """ if self.df > 2.0: @@ -155,6 +155,6 @@ struct StudentT(Copyable, Movable): return inf[DType.float64]() return nan[DType.float64]() - fn std(self) -> Float64: + def std(self) -> Float64: """Distribution standard deviation.""" return sqrt(self.variance()) diff --git a/src/stamojo/distributions/traits.mojo b/src/stamojo/distributions/traits.mojo index 892281f..b722a00 100644 --- a/src/stamojo/distributions/traits.mojo +++ b/src/stamojo/distributions/traits.mojo @@ -10,55 +10,55 @@ trait ContinuouslyDistributed(Copyable, Movable): # --- Density functions --------------------------------------------------- - fn pdf(self, x: Float64) -> Float64: + def pdf(self, x: Float64) -> Float64: """Probability density function at *x*.""" ... - fn logpdf(self, x: Float64) -> Float64: + def logpdf(self, x: Float64) -> Float64: """Natural logarithm of the probability density function at *x*.""" ... # --- Distribution functions ---------------------------------------------- - fn cdf(self, x: Float64) -> Float64: + def cdf(self, x: Float64) -> Float64: """Cumulative distribution function P(X ≤ x).""" ... - fn logcdf(self, x: Float64) -> Float64: + def logcdf(self, x: Float64) -> Float64: """Natural logarithm of the cumulative distribution function at *x*.""" ... - fn sf(self, x: Float64) -> Float64: + def sf(self, x: Float64) -> Float64: """Survival function (1 − CDF) at *x*.""" ... - fn logsf(self, x: Float64) -> Float64: + def logsf(self, x: Float64) -> Float64: """Natural logarithm of the survival function at *x*.""" ... - fn ppf(self, q: Float64) -> Float64: + def ppf(self, q: Float64) -> Float64: """Percent point function (inverse of CDF) at *q*.""" ... - fn isf(self, q: Float64) -> Float64: + def isf(self, q: Float64) -> Float64: """Inverse survival function (inverse of SF) at *q*.""" ... # --- Statistical properties ---------------------------------------------- - fn median(self) -> Float64: + def median(self) -> Float64: """Median of the distribution.""" ... - fn mean(self) -> Float64: + def mean(self) -> Float64: """Mean of the distribution.""" ... - fn variance(self) -> Float64: + def variance(self) -> Float64: """Variance of the distribution.""" ... - fn std(self) -> Float64: + def std(self) -> Float64: """Standard deviation of the distribution.""" ... @@ -68,54 +68,54 @@ trait DiscretelyDistributed(Copyable, Movable): # --- Probability mass functions ------------------------------------------ - fn pmf(self, k: Int) -> Float64: + def pmf(self, k: Int) -> Float64: """Probability mass function at *k*.""" ... - fn logpmf(self, k: Int) -> Float64: + def logpmf(self, k: Int) -> Float64: """Natural logarithm of the probability mass function at *k*.""" ... # --- Distribution functions ---------------------------------------------- - fn cdf(self, k: Int) -> Float64: + def cdf(self, k: Int) -> Float64: """Cumulative distribution function P(X ≤ k).""" ... - fn logcdf(self, k: Int) -> Float64: + def logcdf(self, k: Int) -> Float64: """Natural logarithm of the cumulative distribution function at *k*.""" ... - fn sf(self, k: Int) -> Float64: + def sf(self, k: Int) -> Float64: """Survival function (1 − CDF) at *k*.""" ... - fn logsf(self, k: Int) -> Float64: + def logsf(self, k: Int) -> Float64: """Natural logarithm of the survival function at *k*.""" ... - fn ppf(self, q: Float64) -> Int: + def ppf(self, q: Float64) -> Int: """Percent point function (inverse of CDF) at *q*.""" ... - fn isf(self, q: Float64) -> Int: + def isf(self, q: Float64) -> Int: """Inverse survival function (inverse of SF) at *q*.""" ... # --- Statistical properties ---------------------------------------------- - fn median(self) -> UInt: + def median(self) -> UInt: """Median of the distribution.""" ... - fn mean(self) -> Float64: + def mean(self) -> Float64: """Mean of the distribution.""" ... - fn variance(self) -> Float64: + def variance(self) -> Float64: """Variance of the distribution.""" ... - fn std(self) -> Float64: + def std(self) -> Float64: """Standard deviation of the distribution.""" ... diff --git a/src/stamojo/special/_bessel.mojo b/src/stamojo/special/_bessel.mojo index 70eb993..e4525e4 100644 --- a/src/stamojo/special/_bessel.mojo +++ b/src/stamojo/special/_bessel.mojo @@ -14,37 +14,596 @@ Functions: - y0, y1: Bessel functions of the second kind (orders 0, 1) References: - - https://en.wikipedia.org/wiki/Bessel_function + - fdlibm e_j0.c, e_j1.c (Sun Microsystems, 1993) -- used by scipy + - Cephes Mathematical Library -- used by scipy for i0/i1 """ -from math import cos, exp, inf, log, nan, sin, sqrt - -# === --------------------------------------------------------------------=== # -# General notes: -# TODO: Asymptotic expansions need to be implemented for large arguments to -# ensure accuracy and efficiency. The threshold for switching to asymptotic -# expansions should be determined empirically based on accuracy requirements. -# === ----------------------------------------------------------------------=== # +from std.math import cos, exp, inf, log, nan, sin, sqrt # ===----------------------------------------------------------------------=== # # Constants # ===----------------------------------------------------------------------=== # -comptime _MAX_SERIES_ITER: Int = 50 -comptime _PI: Float64 = 3.141592653589793 -comptime _PI_INV: Float64 = 1.0 / _PI -comptime _EULER_GAMMA: Float64 = 0.5772156649015328606 +comptime _INV_SQRT_PI: Float64 = 0.56418958354775627928 # 1/sqrt(pi) +comptime _TWO_OVER_PI: Float64 = 0.63661977236758138243 # 2/pi + +# fdlibm constants for j0 (R0/S0 on [0, 2]) +comptime _J0_R02: Float64 = 1.56249999999999947958e-02 +comptime _J0_R03: Float64 = -1.89979294238854721751e-04 +comptime _J0_R04: Float64 = 1.82954049532700665670e-06 +comptime _J0_R05: Float64 = -4.61832688532103189199e-09 +comptime _J0_S01: Float64 = 1.56191029464890010492e-02 +comptime _J0_S02: Float64 = 1.16926784663337450260e-04 +comptime _J0_S03: Float64 = 5.13546550207318111446e-07 +comptime _J0_S04: Float64 = 1.16614003333790000205e-09 + +# fdlibm constants for j1 (R0/S0 on [0, 2]) +comptime _J1_R00: Float64 = -6.25000000000000000000e-02 +comptime _J1_R01: Float64 = 1.40705666955189706048e-03 +comptime _J1_R02: Float64 = -1.59955631084035597520e-05 +comptime _J1_R03: Float64 = 4.96727999609584448412e-08 +comptime _J1_S01: Float64 = 1.91537599538363460805e-02 +comptime _J1_S02: Float64 = 1.85946785588630915560e-04 +comptime _J1_S03: Float64 = 1.17718464042623683263e-06 +comptime _J1_S04: Float64 = 5.04636257076217042715e-09 +comptime _J1_S05: Float64 = 1.23542274426137913908e-11 + +# fdlibm constants for y0 (U/V on [0, 2]) +comptime _Y0_U00: Float64 = -7.38042951086872317523e-02 +comptime _Y0_U01: Float64 = 1.76666452509181115538e-01 +comptime _Y0_U02: Float64 = -1.38185671945596898896e-02 +comptime _Y0_U03: Float64 = 3.47453432093683650238e-04 +comptime _Y0_U04: Float64 = -3.81407053724364161125e-06 +comptime _Y0_U05: Float64 = 1.95590137035022920206e-08 +comptime _Y0_U06: Float64 = -3.98205194132103398453e-11 +comptime _Y0_V01: Float64 = 1.27304834834123699328e-02 +comptime _Y0_V02: Float64 = 7.60068627350353253702e-05 +comptime _Y0_V03: Float64 = 2.59150851840457805467e-07 +comptime _Y0_V04: Float64 = 4.41110311332675467403e-10 + +# fdlibm constants for y1 (U0/V0 on [0, 2]) +comptime _Y1_U00: Float64 = -1.96057090646238940668e-01 +comptime _Y1_U01: Float64 = 5.04438716639811282616e-02 +comptime _Y1_U02: Float64 = -1.91256895875763547298e-03 +comptime _Y1_U03: Float64 = 2.35252600561610495928e-05 +comptime _Y1_U04: Float64 = -9.19099158039878874504e-08 +comptime _Y1_V00: Float64 = 1.99167318236649903973e-02 +comptime _Y1_V01: Float64 = 2.02552581025135171496e-04 +comptime _Y1_V02: Float64 = 1.35608801097516229404e-06 +comptime _Y1_V03: Float64 = 6.22741452364621501295e-09 +comptime _Y1_V04: Float64 = 1.66559246207992079114e-11 + +# fdlibm pzero/qzero asymptotic coefficients (4 ranges) +# pzero: pR8/pS8 for x >= 8 +comptime _PZ_P8_0: Float64 = 0.0 +comptime _PZ_P8_1: Float64 = -7.03124999999900357484e-02 +comptime _PZ_P8_2: Float64 = -8.08167041275349795626e00 +comptime _PZ_P8_3: Float64 = -2.57063105679704847262e02 +comptime _PZ_P8_4: Float64 = -2.48521641009428822144e03 +comptime _PZ_P8_5: Float64 = -5.25304380490729545272e03 +comptime _PZ_S8_0: Float64 = 1.16534364619668181717e02 +comptime _PZ_S8_1: Float64 = 3.83374475364121826715e03 +comptime _PZ_S8_2: Float64 = 4.05978572648472545552e04 +comptime _PZ_S8_3: Float64 = 1.16752972564375915681e05 +comptime _PZ_S8_4: Float64 = 4.76277284146730962675e04 + +# pzero: pR5/pS5 for x in [4.5454, 8] +comptime _PZ_P5_0: Float64 = -1.14125464691894502584e-11 +comptime _PZ_P5_1: Float64 = -7.03124940873599280078e-02 +comptime _PZ_P5_2: Float64 = -4.15961064470587782438e00 +comptime _PZ_P5_3: Float64 = -6.76747652265167261021e01 +comptime _PZ_P5_4: Float64 = -3.31231299649172967747e02 +comptime _PZ_P5_5: Float64 = -3.46433388365604912451e02 +comptime _PZ_S5_0: Float64 = 6.07539382692300335975e01 +comptime _PZ_S5_1: Float64 = 1.05125230595704579173e03 +comptime _PZ_S5_2: Float64 = 5.97897094333855784498e03 +comptime _PZ_S5_3: Float64 = 9.62544514357774460223e03 +comptime _PZ_S5_4: Float64 = 2.40605815922939109441e03 + +# pzero: pR3/pS3 for x in [2.8571, 4.547] +comptime _PZ_P3_0: Float64 = -2.54704601771951915620e-09 +comptime _PZ_P3_1: Float64 = -7.03119616381481654654e-02 +comptime _PZ_P3_2: Float64 = -2.40903221549529611423e00 +comptime _PZ_P3_3: Float64 = -2.19659774734883086467e01 +comptime _PZ_P3_4: Float64 = -5.80791704701737572236e01 +comptime _PZ_P3_5: Float64 = -3.14479470594888503854e01 +comptime _PZ_S3_0: Float64 = 3.58560338055209726349e01 +comptime _PZ_S3_1: Float64 = 3.61513983050303863820e02 +comptime _PZ_S3_2: Float64 = 1.19360783792111533330e03 +comptime _PZ_S3_3: Float64 = 1.12799679856907414432e03 +comptime _PZ_S3_4: Float64 = 1.73580930813335754692e02 + +# pzero: pR2/pS2 for x in [2, 2.8570] +comptime _PZ_P2_0: Float64 = -8.87534333032526411254e-08 +comptime _PZ_P2_1: Float64 = -7.03030995483624743247e-02 +comptime _PZ_P2_2: Float64 = -1.45073846780952986357e00 +comptime _PZ_P2_3: Float64 = -7.63569613823527770791e00 +comptime _PZ_P2_4: Float64 = -1.11931668860356747786e01 +comptime _PZ_P2_5: Float64 = -3.23364579351335335033e00 +comptime _PZ_S2_0: Float64 = 2.22202997532088808441e01 +comptime _PZ_S2_1: Float64 = 1.36206794218215208048e02 +comptime _PZ_S2_2: Float64 = 2.70470278658083486789e02 +comptime _PZ_S2_3: Float64 = 1.53875394208320329881e02 +comptime _PZ_S2_4: Float64 = 1.46576176948256193810e01 + +# fdlibm qzero asymptotic coefficients +# qzero: qR8/qS8 for x >= 8 +comptime _QZ_R8_0: Float64 = 0.0 +comptime _QZ_R8_1: Float64 = 7.32421874999935051953e-02 +comptime _QZ_R8_2: Float64 = 1.17682064682252693899e01 +comptime _QZ_R8_3: Float64 = 5.57673380256401856059e02 +comptime _QZ_R8_4: Float64 = 8.85919720756468632317e03 +comptime _QZ_R8_5: Float64 = 3.70146267776887834771e04 +comptime _QZ_S8_0: Float64 = 1.63776026895689824414e02 +comptime _QZ_S8_1: Float64 = 8.09834494656449805916e03 +comptime _QZ_S8_2: Float64 = 1.42538291419120476348e05 +comptime _QZ_S8_3: Float64 = 8.03309257119514397345e05 +comptime _QZ_S8_4: Float64 = 8.40501579819060512818e05 +comptime _QZ_S8_5: Float64 = -3.43899293537866615225e05 + +# qzero: qR5/qS5 for x in [4.5454, 8] +comptime _QZ_R5_0: Float64 = 1.84085963594515531381e-11 +comptime _QZ_R5_1: Float64 = 7.32421766612684765896e-02 +comptime _QZ_R5_2: Float64 = 5.83563508962056953777e00 +comptime _QZ_R5_3: Float64 = 1.35111577286449829671e02 +comptime _QZ_R5_4: Float64 = 1.02724376596164097464e03 +comptime _QZ_R5_5: Float64 = 1.98997785864605384631e03 +comptime _QZ_S5_0: Float64 = 8.27766102236537761883e01 +comptime _QZ_S5_1: Float64 = 2.07781416421392987104e03 +comptime _QZ_S5_2: Float64 = 1.88472887785718085070e04 +comptime _QZ_S5_3: Float64 = 5.67511122894947329769e04 +comptime _QZ_S5_4: Float64 = 3.59767538425114471465e04 +comptime _QZ_S5_5: Float64 = -5.35434275601944773371e03 + +# qzero: qR3/qS3 for x in [2.8571, 4.547] +comptime _QZ_R3_0: Float64 = 4.37741014089738620906e-09 +comptime _QZ_R3_1: Float64 = 7.32411180042911447163e-02 +comptime _QZ_R3_2: Float64 = 3.34423137516170720929e00 +comptime _QZ_R3_3: Float64 = 4.26218440745412650017e01 +comptime _QZ_R3_4: Float64 = 1.70808091340565596283e02 +comptime _QZ_R3_5: Float64 = 1.66733948696651168575e02 +comptime _QZ_S3_0: Float64 = 4.87588729724587182091e01 +comptime _QZ_S3_1: Float64 = 7.09689221056606015736e02 +comptime _QZ_S3_2: Float64 = 3.70414822620111362994e03 +comptime _QZ_S3_3: Float64 = 6.46042516752568917582e03 +comptime _QZ_S3_4: Float64 = 2.51633368920368957333e03 +comptime _QZ_S3_5: Float64 = -1.49247451836156386662e02 + +# qzero: qR2/qS2 for x in [2, 2.8570] +comptime _QZ_R2_0: Float64 = 1.50444444886983272379e-07 +comptime _QZ_R2_1: Float64 = 7.32234265963079278272e-02 +comptime _QZ_R2_2: Float64 = 1.99819174093815998816e00 +comptime _QZ_R2_3: Float64 = 1.44956029347885735348e01 +comptime _QZ_R2_4: Float64 = 3.16662317504781540833e01 +comptime _QZ_R2_5: Float64 = 1.62527075710929267416e01 +comptime _QZ_S2_0: Float64 = 3.03655848355219184498e01 +comptime _QZ_S2_1: Float64 = 2.69348118608049844624e02 +comptime _QZ_S2_2: Float64 = 8.44783757595320139444e02 +comptime _QZ_S2_3: Float64 = 8.82935845112488550512e02 +comptime _QZ_S2_4: Float64 = 2.12666388511798828631e02 +comptime _QZ_S2_5: Float64 = -5.31095493882666946917e00 + +# fdlibm pone/qone asymptotic coefficients (for j1/y1) +# pone: pr8/ps8 for x >= 8 +comptime _PO_PR8_0: Float64 = 0.0 +comptime _PO_PR8_1: Float64 = 1.17187499999988647970e-01 +comptime _PO_PR8_2: Float64 = 1.32394806593073575129e01 +comptime _PO_PR8_3: Float64 = 4.12051854307378562225e02 +comptime _PO_PR8_4: Float64 = 3.87474538913960532227e03 +comptime _PO_PR8_5: Float64 = 7.91447954031891731574e03 +comptime _PO_PS8_0: Float64 = 1.14207370375678408436e02 +comptime _PO_PS8_1: Float64 = 3.65093083420853463394e03 +comptime _PO_PS8_2: Float64 = 3.69562060269033463555e04 +comptime _PO_PS8_3: Float64 = 9.76027935934950801311e04 +comptime _PO_PS8_4: Float64 = 3.08042720627888811578e04 + +# pone: pr5/ps5 for x in [4.5454, 8] +comptime _PO_PR5_0: Float64 = 1.31990519556243522749e-11 +comptime _PO_PR5_1: Float64 = 1.17187493190614097638e-01 +comptime _PO_PR5_2: Float64 = 6.80275127868432871736e00 +comptime _PO_PR5_3: Float64 = 1.08308182990189109773e02 +comptime _PO_PR5_4: Float64 = 5.17636139533199752805e02 +comptime _PO_PR5_5: Float64 = 5.28715201363337541807e02 +comptime _PO_PS5_0: Float64 = 5.92805987221131331921e01 +comptime _PO_PS5_1: Float64 = 9.91401418733614377743e02 +comptime _PO_PS5_2: Float64 = 5.35326695291487976647e03 +comptime _PO_PS5_3: Float64 = 7.84469031749551231769e03 +comptime _PO_PS5_4: Float64 = 1.50404688810361062679e03 + +# pone: pr3/ps3 for x in [2.8571, 4.547] +comptime _PO_PR3_0: Float64 = 3.02503916137373618024e-09 +comptime _PO_PR3_1: Float64 = 1.17186865567253592491e-01 +comptime _PO_PR3_2: Float64 = 3.93297750033315640650e00 +comptime _PO_PR3_3: Float64 = 3.51194035591636932736e01 +comptime _PO_PR3_4: Float64 = 9.10550110750781271918e01 +comptime _PO_PR3_5: Float64 = 4.85590685197364919645e01 +comptime _PO_PS3_0: Float64 = 3.47913095001251519989e01 +comptime _PO_PS3_1: Float64 = 3.36762458747825746741e02 +comptime _PO_PS3_2: Float64 = 1.04687139975775130551e03 +comptime _PO_PS3_3: Float64 = 8.90811346398256432622e02 +comptime _PO_PS3_4: Float64 = 1.03787932439639277504e02 + +# pone: pr2/ps2 for x in [2, 2.8570] +comptime _PO_PR2_0: Float64 = 1.07710830106873743082e-07 +comptime _PO_PR2_1: Float64 = 1.17176219462683348094e-01 +comptime _PO_PR2_2: Float64 = 2.36851496667608785174e00 +comptime _PO_PR2_3: Float64 = 1.22426109148261232917e01 +comptime _PO_PR2_4: Float64 = 1.76939711271687727390e01 +comptime _PO_PR2_5: Float64 = 5.07352312588818499250e00 +comptime _PO_PS2_0: Float64 = 2.14364859363821409488e01 +comptime _PO_PS2_1: Float64 = 1.25290227168402751090e02 +comptime _PO_PS2_2: Float64 = 2.32276469057162813669e02 +comptime _PO_PS2_3: Float64 = 1.17679373287147100768e02 +comptime _PO_PS2_4: Float64 = 8.36463893371618283368e00 + +# qone: qr8/qs8 for x >= 8 +comptime _QO_QR8_0: Float64 = 0.0 +comptime _QO_QR8_1: Float64 = -1.02539062499992714161e-01 +comptime _QO_QR8_2: Float64 = -1.62717534544589987888e01 +comptime _QO_QR8_3: Float64 = -7.59601722513950107896e02 +comptime _QO_QR8_4: Float64 = -1.18498066702429587167e04 +comptime _QO_QR8_5: Float64 = -4.84385124285750353010e04 +comptime _QO_QS8_0: Float64 = 1.61395369700722909556e02 +comptime _QO_QS8_1: Float64 = 7.82538599923348465381e03 +comptime _QO_QS8_2: Float64 = 1.33875336287249578163e05 +comptime _QO_QS8_3: Float64 = 7.19657723683240939863e05 +comptime _QO_QS8_4: Float64 = 6.66601232617776375264e05 +comptime _QO_QS8_5: Float64 = -2.94490264303834643215e05 + +# qone: qr5/qs5 for x in [4.5454, 8] +comptime _QO_QR5_0: Float64 = -2.08979931141764104297e-11 +comptime _QO_QR5_1: Float64 = -1.02539050241375426231e-01 +comptime _QO_QR5_2: Float64 = -8.05644828123936029840e00 +comptime _QO_QR5_3: Float64 = -1.83669607474888380239e02 +comptime _QO_QR5_4: Float64 = -1.37319376065508163265e03 +comptime _QO_QR5_5: Float64 = -2.61244440453215656817e03 +comptime _QO_QS5_0: Float64 = 8.12765501384335777857e01 +comptime _QO_QS5_1: Float64 = 1.99179873460485964642e03 +comptime _QO_QS5_2: Float64 = 1.74684851924908907677e04 +comptime _QO_QS5_3: Float64 = 4.98514270910352279316e04 +comptime _QO_QS5_4: Float64 = 2.79480751638918118260e04 +comptime _QO_QS5_5: Float64 = -4.71918354795128470869e03 + +# qone: qr3/qs3 for x in [2.8571, 4.547] +comptime _QO_QR3_0: Float64 = -5.07831226461766561369e-09 +comptime _QO_QR3_1: Float64 = -1.02537829820837089745e-01 +comptime _QO_QR3_2: Float64 = -4.61011581139473403113e00 +comptime _QO_QR3_3: Float64 = -5.78472216562783643212e01 +comptime _QO_QR3_4: Float64 = -2.28244540737631695038e02 +comptime _QO_QR3_5: Float64 = -2.19210128478909325622e02 +comptime _QO_QS3_0: Float64 = 4.76651550323729509273e01 +comptime _QO_QS3_1: Float64 = 6.73865112676699709482e02 +comptime _QO_QS3_2: Float64 = 3.38015286679526343505e03 +comptime _QO_QS3_3: Float64 = 5.54772909720722782367e03 +comptime _QO_QS3_4: Float64 = 1.90311919338810798763e03 +comptime _QO_QS3_5: Float64 = -1.35201191444307340817e02 + +# qone: qr2/qs2 for x in [2, 2.8570] +comptime _QO_QR2_0: Float64 = -1.78381727510958865572e-07 +comptime _QO_QR2_1: Float64 = -1.02517042607985553460e-01 +comptime _QO_QR2_2: Float64 = -2.75220568278187460720e00 +comptime _QO_QR2_3: Float64 = -1.96636162643703720221e01 +comptime _QO_QR2_4: Float64 = -4.23253133372830490089e01 +comptime _QO_QR2_5: Float64 = -2.13719211703704061733e01 +comptime _QO_QS2_0: Float64 = 2.95333629060523854548e01 +comptime _QO_QS2_1: Float64 = 2.52981549982190529136e02 +comptime _QO_QS2_2: Float64 = 7.57502834868645436472e02 +comptime _QO_QS2_3: Float64 = 7.39393205320467245656e02 +comptime _QO_QS2_4: Float64 = 1.55949003336666123687e02 +comptime _QO_QS2_5: Float64 = -4.95949898822628210127e00 + +# Cephes constants for i0 +comptime _I0_P0: Float64 = -4.41534164647933937950e-03 +comptime _I0_P1: Float64 = 3.33079451882223809783e-02 +comptime _I0_P2: Float64 = -2.43127984654795469359e-01 +comptime _I0_P3: Float64 = 2.42548595906956781279e-01 +comptime _I0_P4: Float64 = 7.38511210047607257286e-01 +comptime _I0_Q0: Float64 = 8.63602033430765361840e-01 +comptime _I0_Q1: Float64 = 1.90500605968696273104e-01 +comptime _I0_R0: Float64 = 3.52250808634595334535e-03 +comptime _I0_R1: Float64 = -1.64827937501992591257e-02 +comptime _I0_R2: Float64 = -4.45641913851797240494e-01 +comptime _I0_R3: Float64 = 6.36027657760814264428e00 +comptime _I0_R4: Float64 = 3.51006384093205808273e01 +comptime _I0_R5: Float64 = 9.39268705208594535371e01 +comptime _I0_S0: Float64 = 5.57535335369399327520e-01 +comptime _I0_S1: Float64 = 1.29988204441705491283e01 +comptime _I0_S2: Float64 = 1.70685263843424725199e02 +comptime _I0_S3: Float64 = 1.13516252348148201793e03 +comptime _I0_S4: Float64 = 3.61451157058782369928e03 +comptime _I0_S5: Float64 = 4.97308152085347414070e03 +comptime _I0_C0: Float64 = 1.25331413731550025120e-01 # 1/sqrt(2*pi) + +# Cephes constants for i1 +comptime _I1_P0: Float64 = -7.23318048787475395456e-03 +comptime _I1_P1: Float64 = 4.83050417718188874988e-02 +comptime _I1_P2: Float64 = -2.89531270196048047263e-01 +comptime _I1_P3: Float64 = 2.62566271151496789172e-01 +comptime _I1_P4: Float64 = 7.38511210047607257286e-01 +comptime _I1_Q0: Float64 = 8.63602033430765361840e-01 +comptime _I1_Q1: Float64 = 1.90500605968696273104e-01 +comptime _I1_R0: Float64 = 8.41650872933228361692e-03 +comptime _I1_R1: Float64 = -3.75635967210832323198e-02 +comptime _I1_R2: Float64 = -4.54421475544292764826e-01 +comptime _I1_R3: Float64 = 6.69187511512627462213e00 +comptime _I1_R4: Float64 = 3.78239633202758244824e01 +comptime _I1_R5: Float64 = 1.04586394961508509146e02 +comptime _I1_S0: Float64 = 5.72541212752457396309e-01 +comptime _I1_S1: Float64 = 1.39819995071268698492e01 +comptime _I1_S2: Float64 = 1.96843056414396712347e02 +comptime _I1_S3: Float64 = 1.33870994616133889333e03 +comptime _I1_S4: Float64 = 4.34400212549221018167e03 +comptime _I1_S5: Float64 = 5.26163277602184647175e03 +comptime _I1_C0: Float64 = 3.75994241194749482547e-01 # 3/sqrt(2*pi) + # ===----------------------------------------------------------------------=== # # Helper functions # ===----------------------------------------------------------------------=== # -fn _factorial(n: Int) -> Float64: - var res = 1.0 - for i in range(2, n + 1): - res *= Float64(i) - return res +def _pzero(x: Float64) -> Float64: + """fdlibm pzero(x): asymptotic factor P(x) for j0/y0. + + Approximates 1 + R/S where s = 1/x. + """ + var ix = abs(x) + var z = 1.0 / (ix * ix) + var r: Float64 + var s: Float64 + + if ix >= 8.0: + r = _PZ_P8_0 + z * ( + _PZ_P8_1 + + z * (_PZ_P8_2 + z * (_PZ_P8_3 + z * (_PZ_P8_4 + z * _PZ_P8_5))) + ) + s = 1.0 + z * ( + _PZ_S8_0 + + z * (_PZ_S8_1 + z * (_PZ_S8_2 + z * (_PZ_S8_3 + z * _PZ_S8_4))) + ) + elif ix >= 4.5454: + r = _PZ_P5_0 + z * ( + _PZ_P5_1 + + z * (_PZ_P5_2 + z * (_PZ_P5_3 + z * (_PZ_P5_4 + z * _PZ_P5_5))) + ) + s = 1.0 + z * ( + _PZ_S5_0 + + z * (_PZ_S5_1 + z * (_PZ_S5_2 + z * (_PZ_S5_3 + z * _PZ_S5_4))) + ) + elif ix >= 2.8571: + r = _PZ_P3_0 + z * ( + _PZ_P3_1 + + z * (_PZ_P3_2 + z * (_PZ_P3_3 + z * (_PZ_P3_4 + z * _PZ_P3_5))) + ) + s = 1.0 + z * ( + _PZ_S3_0 + + z * (_PZ_S3_1 + z * (_PZ_S3_2 + z * (_PZ_S3_3 + z * _PZ_S3_4))) + ) + else: + r = _PZ_P2_0 + z * ( + _PZ_P2_1 + + z * (_PZ_P2_2 + z * (_PZ_P2_3 + z * (_PZ_P2_4 + z * _PZ_P2_5))) + ) + s = 1.0 + z * ( + _PZ_S2_0 + + z * (_PZ_S2_1 + z * (_PZ_S2_2 + z * (_PZ_S2_3 + z * _PZ_S2_4))) + ) + + return 1.0 + r / s + + +def _qzero(x: Float64) -> Float64: + """fdlibm qzero(x): asymptotic factor Q(x) for j0/y0. + + Approximates (-0.125 + R/S) / x where s = 1/x. + """ + var ix = abs(x) + var z = 1.0 / (ix * ix) + var r: Float64 + var s: Float64 + + if ix >= 8.0: + r = _QZ_R8_0 + z * ( + _QZ_R8_1 + + z * (_QZ_R8_2 + z * (_QZ_R8_3 + z * (_QZ_R8_4 + z * _QZ_R8_5))) + ) + s = 1.0 + z * ( + _QZ_S8_0 + + z + * ( + _QZ_S8_1 + + z + * (_QZ_S8_2 + z * (_QZ_S8_3 + z * (_QZ_S8_4 + z * _QZ_S8_5))) + ) + ) + elif ix >= 4.5454: + r = _QZ_R5_0 + z * ( + _QZ_R5_1 + + z * (_QZ_R5_2 + z * (_QZ_R5_3 + z * (_QZ_R5_4 + z * _QZ_R5_5))) + ) + s = 1.0 + z * ( + _QZ_S5_0 + + z + * ( + _QZ_S5_1 + + z + * (_QZ_S5_2 + z * (_QZ_S5_3 + z * (_QZ_S5_4 + z * _QZ_S5_5))) + ) + ) + elif ix >= 2.8571: + r = _QZ_R3_0 + z * ( + _QZ_R3_1 + + z * (_QZ_R3_2 + z * (_QZ_R3_3 + z * (_QZ_R3_4 + z * _QZ_R3_5))) + ) + s = 1.0 + z * ( + _QZ_S3_0 + + z + * ( + _QZ_S3_1 + + z + * (_QZ_S3_2 + z * (_QZ_S3_3 + z * (_QZ_S3_4 + z * _QZ_S3_5))) + ) + ) + else: + r = _QZ_R2_0 + z * ( + _QZ_R2_1 + + z * (_QZ_R2_2 + z * (_QZ_R2_3 + z * (_QZ_R2_4 + z * _QZ_R2_5))) + ) + s = 1.0 + z * ( + _QZ_S2_0 + + z + * ( + _QZ_S2_1 + + z + * (_QZ_S2_2 + z * (_QZ_S2_3 + z * (_QZ_S2_4 + z * _QZ_S2_5))) + ) + ) + + return (-0.125 + r / s) / ix + + +def _pone(x: Float64) -> Float64: + """fdlibm pone(x): asymptotic factor P(x) for j1/y1. + + Approximates 1 + R/S where s = 1/x. + """ + var ix = abs(x) + var z = 1.0 / (ix * ix) + var r: Float64 + var s: Float64 + + if ix >= 8.0: + r = _PO_PR8_0 + z * ( + _PO_PR8_1 + + z + * (_PO_PR8_2 + z * (_PO_PR8_3 + z * (_PO_PR8_4 + z * _PO_PR8_5))) + ) + s = 1.0 + z * ( + _PO_PS8_0 + + z + * (_PO_PS8_1 + z * (_PO_PS8_2 + z * (_PO_PS8_3 + z * _PO_PS8_4))) + ) + elif ix >= 4.5454: + r = _PO_PR5_0 + z * ( + _PO_PR5_1 + + z + * (_PO_PR5_2 + z * (_PO_PR5_3 + z * (_PO_PR5_4 + z * _PO_PR5_5))) + ) + s = 1.0 + z * ( + _PO_PS5_0 + + z + * (_PO_PS5_1 + z * (_PO_PS5_2 + z * (_PO_PS5_3 + z * _PO_PS5_4))) + ) + elif ix >= 2.8571: + r = _PO_PR3_0 + z * ( + _PO_PR3_1 + + z + * (_PO_PR3_2 + z * (_PO_PR3_3 + z * (_PO_PR3_4 + z * _PO_PR3_5))) + ) + s = 1.0 + z * ( + _PO_PS3_0 + + z + * (_PO_PS3_1 + z * (_PO_PS3_2 + z * (_PO_PS3_3 + z * _PO_PS3_4))) + ) + else: + r = _PO_PR2_0 + z * ( + _PO_PR2_1 + + z + * (_PO_PR2_2 + z * (_PO_PR2_3 + z * (_PO_PR2_4 + z * _PO_PR2_5))) + ) + s = 1.0 + z * ( + _PO_PS2_0 + + z + * (_PO_PS2_1 + z * (_PO_PS2_2 + z * (_PO_PS2_3 + z * _PO_PS2_4))) + ) + + return 1.0 + r / s + + +def _qone(x: Float64) -> Float64: + """fdlibm qone(x): asymptotic factor Q(x) for j1/y1. + + Approximates (0.375 + R/S) / x where s = 1/x. + """ + var ix = abs(x) + var z = 1.0 / (ix * ix) + var r: Float64 + var s: Float64 + + if ix >= 8.0: + r = _QO_QR8_0 + z * ( + _QO_QR8_1 + + z + * (_QO_QR8_2 + z * (_QO_QR8_3 + z * (_QO_QR8_4 + z * _QO_QR8_5))) + ) + s = 1.0 + z * ( + _QO_QS8_0 + + z + * ( + _QO_QS8_1 + + z + * ( + _QO_QS8_2 + + z * (_QO_QS8_3 + z * (_QO_QS8_4 + z * _QO_QS8_5)) + ) + ) + ) + elif ix >= 4.5454: + r = _QO_QR5_0 + z * ( + _QO_QR5_1 + + z + * (_QO_QR5_2 + z * (_QO_QR5_3 + z * (_QO_QR5_4 + z * _QO_QR5_5))) + ) + s = 1.0 + z * ( + _QO_QS5_0 + + z + * ( + _QO_QS5_1 + + z + * ( + _QO_QS5_2 + + z * (_QO_QS5_3 + z * (_QO_QS5_4 + z * _QO_QS5_5)) + ) + ) + ) + elif ix >= 2.8571: + r = _QO_QR3_0 + z * ( + _QO_QR3_1 + + z + * (_QO_QR3_2 + z * (_QO_QR3_3 + z * (_QO_QR3_4 + z * _QO_QR3_5))) + ) + s = 1.0 + z * ( + _QO_QS3_0 + + z + * ( + _QO_QS3_1 + + z + * ( + _QO_QS3_2 + + z * (_QO_QS3_3 + z * (_QO_QS3_4 + z * _QO_QS3_5)) + ) + ) + ) + else: + r = _QO_QR2_0 + z * ( + _QO_QR2_1 + + z + * (_QO_QR2_2 + z * (_QO_QR2_3 + z * (_QO_QR2_4 + z * _QO_QR2_5))) + ) + s = 1.0 + z * ( + _QO_QS2_0 + + z + * ( + _QO_QS2_1 + + z + * ( + _QO_QS2_2 + + z * (_QO_QS2_3 + z * (_QO_QS2_4 + z * _QO_QS2_5)) + ) + ) + ) + + return (0.375 + r / s) / ix # ===----------------------------------------------------------------------=== # @@ -52,78 +611,103 @@ fn _factorial(n: Int) -> Float64: # ===----------------------------------------------------------------------=== # -fn j0(x: Float64) -> Float64: +def j0(x: Float64) -> Float64: """Bessel function of the first kind of order 0. + Uses the fdlibm algorithm (same as scipy.special.j0). + Args: x: Input value. Returns: J₀(x). - - Examples: - ```mojo - from stamojo.special import j0 - from testing import assert_almost_equal - - fn main() raises: - assert_almost_equal(j0(1.0), 0.7651976865579666, atol=1e-12) - ``` """ - # J₀ is even: J₀(-x) = J₀(x). var ax = abs(x) - # TODO: Determine asymptotic threshold empirically. - if ax > 10.0: - var t = ax - _PI * 0.25 - return sqrt(2.0 * _PI_INV / ax) * cos(t) - - var term = 1.0 - var res = term - var x2 = ax * ax * 0.25 - for k in range(1, _MAX_SERIES_ITER): - term *= -x2 / (Float64(k) * Float64(k)) - res += term - return res - - -fn j1(x: Float64) -> Float64: + # |x| >= 2.0: asymptotic expansion + if ax >= 2.0: + var s = sin(ax) + var c = cos(ax) + var ss = s - c + var cc = s + c + # Avoid cancellation: sin(x) +- cos(x) = -cos(2x) / (sin(x) -+ cos(x)) + if ax < 1e150: + var z = -cos(ax + ax) + if (s * c) < 0.0: + cc = z / ss + else: + ss = z / cc + if ax > 1e150: + return _INV_SQRT_PI * cc / sqrt(ax) + var u = _pzero(ax) + var v = _qzero(ax) + return _INV_SQRT_PI * (u * cc - v * ss) / sqrt(ax) + + # |x| < 2**-13: tiny + if ax < 1.220703125e-04: + if ax < 7.450580596923828125e-09: + return 1.0 + return 1.0 - 0.25 * ax * ax + + # |x| < 2.0: rational approximation + var z = x * x + var r = z * (_J0_R02 + z * (_J0_R03 + z * (_J0_R04 + z * _J0_R05))) + var s = 1.0 + z * (_J0_S01 + z * (_J0_S02 + z * (_J0_S03 + z * _J0_S04))) + if ax < 1.0: + return 1.0 + z * (-0.25 + r / s) + else: + var u = 0.5 * ax + return (1.0 + u) * (1.0 - u) + z * (r / s) + + +def j1(x: Float64) -> Float64: """Bessel function of the first kind of order 1. + Uses the fdlibm algorithm (same as scipy.special.j1). + Args: x: Input value. Returns: J₁(x). - - Examples: - ```mojo - from stamojo.special import j1 - from testing import assert_almost_equal - - fn main() raises: - assert_almost_equal(j1(1.0), 0.44005058574493355, atol=1e-12) - ``` """ - # J₁ is odd: J₁(-x) = -J₁(x). var ax = abs(x) var sign: Float64 = 1.0 if x >= 0.0 else -1.0 - # TODO: Determine asymptotic threshold empirically. - if ax > 10.0: - var t = ax - 3.0 * _PI * 0.25 - return sign * sqrt(2.0 * _PI_INV / ax) * cos(t) - - var term = ax * 0.5 - var res = term - var x2 = ax * ax * 0.25 - for k in range(1, _MAX_SERIES_ITER): - term *= -x2 / (Float64(k) * Float64(k + 1)) - res += term - return sign * res - - -fn jn[n: Int](x: Float64) -> Float64: + # |x| >= 2.0: asymptotic expansion + if ax >= 2.0: + var s = sin(ax) + var c = cos(ax) + var ss = -s - c + var cc = s - c + # Avoid cancellation + if ax < 1e150: + var z = cos(ax + ax) + if (s * c) > 0.0: + cc = z / ss + else: + ss = z / cc + if ax > 1e150: + return sign * _INV_SQRT_PI * cc / sqrt(ax) + var u = _pone(ax) + var v = _qone(ax) + return sign * _INV_SQRT_PI * (u * cc - v * ss) / sqrt(ax) + + # |x| < 2**-27: tiny + if ax < 7.450580596923828125e-09: + return 0.5 * x + + # |x| < 2.0: rational approximation + var z = x * x + var r = z * (_J1_R00 + z * (_J1_R01 + z * (_J1_R02 + z * _J1_R03))) + var s = 1.0 + z * ( + _J1_S01 + z * (_J1_S02 + z * (_J1_S03 + z * (_J1_S04 + z * _J1_S05))) + ) + r *= x + return x * 0.5 + r / s + + +def jn[n: Int](x: Float64) -> Float64: """Bessel function of the first kind of order *n*. Parameters: @@ -136,12 +720,10 @@ fn jn[n: Int](x: Float64) -> Float64: Jₙ(x). """ - @parameter - if n == 0: + comptime if n == 0: return j0(x) - @parameter - if n == 1: + comptime if n == 1: return j1(x) comptime m = n if n >= 0 else -n @@ -149,27 +731,28 @@ fn jn[n: Int](x: Float64) -> Float64: var ax = abs(x) - # For m <= ax, use the forward recurrence: - # J_{k+1}(x) = (2k/x) J_k(x) - J_{k-1}(x) + # For small n relative to x, use forward recurrence. if Float64(m) <= ax: - var jm1 = j0(x) # J_0 - var jcur = j1(x) # J_1 + var jm1 = j0(x) + var jcur = j1(x) for k in range(1, m): var jnext = (2.0 * Float64(k) / x) * jcur - jm1 jm1 = jcur jcur = jnext return sign * jcur - # For m > ax, use power series. - var fact = _factorial(m) - var term = 1.0 + # For large n relative to x, use power series. + var fact: Float64 = 1.0 + for i in range(1, m + 1): + fact *= Float64(i) + var term: Float64 = 1.0 for _ in range(m): term *= x * 0.5 term /= fact var res = term var x2 = x * x * 0.25 - for k in range(1, _MAX_SERIES_ITER): + for k in range(1, 50): term *= -x2 / (Float64(k) * Float64(k + m)) res += term return sign * res @@ -180,61 +763,76 @@ fn jn[n: Int](x: Float64) -> Float64: # ===----------------------------------------------------------------------=== # -fn i0(x: Float64) -> Float64: +def i0(x: Float64) -> Float64: """Modified Bessel function of the first kind of order 0. + Uses the Cephes algorithm (same as scipy.special.i0). + Args: x: Input value. Returns: I₀(x). - - Examples: - ```mojo - from stamojo.special import i0 - from testing import assert_almost_equal - - fn main() raises: - assert_almost_equal(i0(1.0), 1.2660658777520082, atol=1e-12) - ``` """ - var term = 1.0 - var res = term - var x2 = x * x * 0.25 - for k in range(1, _MAX_SERIES_ITER): - term *= x2 / (Float64(k) * Float64(k)) - res += term - return res + var ax = abs(x) + + if ax < 8.0: + # Rational approximation for |x| < 8 + var z = x * x + var p = _I0_P0 + z * (_I0_P1 + z * (_I0_P2 + z * (_I0_P3 + z * _I0_P4))) + var q = _I0_Q0 + z * (_I0_Q1 + z * 1.0) + return 1.0 + z * p / q + else: + # Asymptotic expansion for |x| >= 8 + var z = 8.0 / ax + var r = _I0_R0 + z * ( + _I0_R1 + z * (_I0_R2 + z * (_I0_R3 + z * (_I0_R4 + z * _I0_R5))) + ) + var s = 1.0 + z * ( + _I0_S0 + + z + * (_I0_S1 + z * (_I0_S2 + z * (_I0_S3 + z * (_I0_S4 + z * _I0_S5)))) + ) + return _I0_C0 * exp(ax) / sqrt(ax) * (1.0 + r / s) -fn i1(x: Float64) -> Float64: +def i1(x: Float64) -> Float64: """Modified Bessel function of the first kind of order 1. + Uses the Cephes algorithm (same as scipy.special.i1). + Args: x: Input value. Returns: I₁(x). - - Examples: - ```mojo - from stamojo.special import i1 - from testing import assert_almost_equal - - fn main() raises: - assert_almost_equal(i1(1.0), 0.5651591039924851, atol=1e-12) - ``` """ - var term = x * 0.5 - var res = term - var x2 = x * x * 0.25 - for k in range(1, _MAX_SERIES_ITER): - term *= x2 / (Float64(k) * Float64(k + 1)) - res += term - return res + var ax = abs(x) + var sign: Float64 = 1.0 if x >= 0.0 else -1.0 + + if ax < 8.0: + # Rational approximation for |x| < 8 + var z = x * x + var p = x * ( + _I1_P0 + z * (_I1_P1 + z * (_I1_P2 + z * (_I1_P3 + z * _I1_P4))) + ) + var q = _I1_Q0 + z * (_I1_Q1 + z * 1.0) + return sign * (x * 0.5 + p / q) + else: + # Asymptotic expansion for |x| >= 8 + var z = 8.0 / ax + var r = _I1_R0 + z * ( + _I1_R1 + z * (_I1_R2 + z * (_I1_R3 + z * (_I1_R4 + z * _I1_R5))) + ) + var s = 1.0 + z * ( + _I1_S0 + + z + * (_I1_S1 + z * (_I1_S2 + z * (_I1_S3 + z * (_I1_S4 + z * _I1_S5)))) + ) + return sign * _I1_C0 * exp(ax) / sqrt(ax) * (1.0 + r / s) -fn i0e(x: Float64) -> Float64: +def i0e(x: Float64) -> Float64: """Exponentially scaled modified Bessel function of the first kind of order 0: ``i0e(x) = exp(-|x|) * i0(x)``. @@ -243,20 +841,28 @@ fn i0e(x: Float64) -> Float64: Returns: Value of exp(-|x|) * I₀(x). - - Examples: - ```mojo - from stamojo.special import i0e - from testing import assert_almost_equal - - fn main() raises: - assert_almost_equal(i0e(1.0), 0.4657596075936405, atol=1e-12) - ``` """ - return i0(x) * exp(-abs(x)) + var ax = abs(x) + if ax < 8.0: + var z = x * x + var p = _I0_P0 + z * (_I0_P1 + z * (_I0_P2 + z * (_I0_P3 + z * _I0_P4))) + var q = _I0_Q0 + z * (_I0_Q1 + z * 1.0) + return (1.0 + z * p / q) * exp(-ax) + else: + var z = 8.0 / ax + var r = _I0_R0 + z * ( + _I0_R1 + z * (_I0_R2 + z * (_I0_R3 + z * (_I0_R4 + z * _I0_R5))) + ) + var s = 1.0 + z * ( + _I0_S0 + + z + * (_I0_S1 + z * (_I0_S2 + z * (_I0_S3 + z * (_I0_S4 + z * _I0_S5)))) + ) + return _I0_C0 / sqrt(ax) * (1.0 + r / s) -fn i1e(x: Float64) -> Float64: + +def i1e(x: Float64) -> Float64: """Exponentially scaled modified Bessel function of the first kind of order 1: ``i1e(x) = exp(-|x|) * i1(x)``. @@ -265,17 +871,28 @@ fn i1e(x: Float64) -> Float64: Returns: Value of exp(-|x|) * I₁(x). - - Examples: - ```mojo - from stamojo.special import i1e - from testing import assert_almost_equal - - fn main() raises: - assert_almost_equal(i1e(1.0), 0.2079104153497085, atol=1e-12) - ``` """ - return i1(x) * exp(-abs(x)) + var ax = abs(x) + var sign: Float64 = 1.0 if x >= 0.0 else -1.0 + + if ax < 8.0: + var z = x * x + var p = x * ( + _I1_P0 + z * (_I1_P1 + z * (_I1_P2 + z * (_I1_P3 + z * _I1_P4))) + ) + var q = _I1_Q0 + z * (_I1_Q1 + z * 1.0) + return sign * (x * 0.5 + p / q) * exp(-ax) + else: + var z = 8.0 / ax + var r = _I1_R0 + z * ( + _I1_R1 + z * (_I1_R2 + z * (_I1_R3 + z * (_I1_R4 + z * _I1_R5))) + ) + var s = 1.0 + z * ( + _I1_S0 + + z + * (_I1_S1 + z * (_I1_S2 + z * (_I1_S3 + z * (_I1_S4 + z * _I1_S5)))) + ) + return sign * _I1_C0 / sqrt(ax) * (1.0 + r / s) # ===----------------------------------------------------------------------=== # @@ -283,91 +900,106 @@ fn i1e(x: Float64) -> Float64: # ===----------------------------------------------------------------------=== # -fn y0(x: Float64) -> Float64: +def y0(x: Float64) -> Float64: """Bessel function of the second kind of order 0. - Defined for x > 0. Returns -∞ at x = 0 and NaN for x < 0. + Uses the fdlibm algorithm (same as scipy.special.y0). + Defined for x > 0. Returns -∞ at x = 0 and NaN for x < 0. Args: x: Input value (must be positive). Returns: Y₀(x). - - Examples: - ```mojo - from stamojo.special import y0 - from testing import assert_almost_equal - - fn main() raises: - assert_almost_equal(y0(1.0), 0.08825696421567697, atol=1e-12) - ``` """ if x == 0.0: return -inf[DType.float64]() if x < 0.0: return nan[DType.float64]() - if x < 8.0: - var j0x = j0(x) - var x2 = x * x * 0.25 - var term = x2 - var sum = 0.0 - var h = 1.0 - for k in range(1, _MAX_SERIES_ITER): - if k > 1: - h += 1.0 / Float64(k) - sum += term * h - term *= -x2 / (Float64(k + 1) * Float64(k + 1)) - return (2.0 / _PI) * ((log(x * 0.5) + _EULER_GAMMA) * j0x + sum) - - var t = x - _PI * 0.25 - return sqrt(2.0 / (_PI * x)) * sin(t) + # |x| >= 2.0: asymptotic expansion + if x >= 2.0: + var s = sin(x) + var c = cos(x) + var ss = s - c + var cc = s + c + # Avoid cancellation + if x < 1e150: + var z = -cos(x + x) + if (s * c) < 0.0: + cc = z / ss + else: + ss = z / cc + if x > 1e150: + return _INV_SQRT_PI * ss / sqrt(x) + var u = _pzero(x) + var v = _qzero(x) + return _INV_SQRT_PI * (u * ss + v * cc) / sqrt(x) + + # |x| < 2**-27: tiny + if x < 7.450580596923828125e-09: + return _Y0_U00 + _TWO_OVER_PI * log(x) + + # |x| < 2.0: rational approximation + var z = x * x + var u = _Y0_U00 + z * ( + _Y0_U01 + + z + * ( + _Y0_U02 + + z * (_Y0_U03 + z * (_Y0_U04 + z * (_Y0_U05 + z * _Y0_U06))) + ) + ) + var v = 1.0 + z * (_Y0_V01 + z * (_Y0_V02 + z * (_Y0_V03 + z * _Y0_V04))) + return u / v + _TWO_OVER_PI * (j0(x) * log(x)) -fn y1(x: Float64) -> Float64: +def y1(x: Float64) -> Float64: """Bessel function of the second kind of order 1. - Defined for x > 0. Returns -∞ at x = 0 and NaN for x < 0. + Uses the fdlibm algorithm (same as scipy.special.y1). + Defined for x > 0. Returns -∞ at x = 0 and NaN for x < 0. Args: x: Input value (must be positive). Returns: Y₁(x). - - Examples: - ```mojo - from stamojo.special import y1 - from testing import assert_almost_equal - - fn main() raises: - assert_almost_equal(y1(1.0), -0.7812128213002887, atol=1e-12) - ``` """ if x == 0.0: return -inf[DType.float64]() if x < 0.0: return nan[DType.float64]() - if x < 8.0: - var j1x = j1(x) - var x2 = x * x * 0.25 - var term = x * 0.5 - var sum = 0.0 - var hk = 0.0 - - for k in range(_MAX_SERIES_ITER): - var hk1 = hk + 1.0 / Float64(k + 1) - sum += term * (hk + hk1) - term *= -x2 / (Float64(k + 1) * Float64(k + 2)) - hk = hk1 - - return ( - (-2.0 * _PI_INV / x) - + (2.0 * _PI_INV) * (log(x * 0.5) + _EULER_GAMMA) * j1x - - sum * _PI_INV - ) - - var t = x - 3.0 * _PI * 0.25 - return sqrt(2.0 / (_PI * x)) * sin(t) + # |x| >= 2.0: asymptotic expansion + if x >= 2.0: + var s = sin(x) + var c = cos(x) + var ss = -s - c + var cc = s - c + # Avoid cancellation + if x < 1e150: + var z = cos(x + x) + if (s * c) > 0.0: + cc = z / ss + else: + ss = z / cc + if x > 1e150: + return _INV_SQRT_PI * ss / sqrt(x) + var u = _pone(x) + var v = _qone(x) + return _INV_SQRT_PI * (u * ss + v * cc) / sqrt(x) + + # |x| < 2**-54: tiny + if x < 5.55111512312578270212e-17: + return -_TWO_OVER_PI / x + + # |x| < 2.0: rational approximation + var z = x * x + var u = _Y1_U00 + z * ( + _Y1_U01 + z * (_Y1_U02 + z * (_Y1_U03 + z * _Y1_U04)) + ) + var v = 1.0 + z * ( + _Y1_V00 + z * (_Y1_V01 + z * (_Y1_V02 + z * (_Y1_V03 + z * _Y1_V04))) + ) + return x * (u / v) + _TWO_OVER_PI * (j1(x) * log(x) - 1.0 / x) diff --git a/src/stamojo/special/_beta.mojo b/src/stamojo/special/_beta.mojo index 6894dd5..76a6424 100644 --- a/src/stamojo/special/_beta.mojo +++ b/src/stamojo/special/_beta.mojo @@ -22,7 +22,7 @@ Reference: Press et al., Numerical Recipes, 3rd ed., Section 6.4. """ -from math import lgamma, exp, log, nan +from std.math import lgamma, exp, log, nan # ===----------------------------------------------------------------------=== # @@ -39,7 +39,7 @@ comptime _FPMIN = 1.0e-30 # ===----------------------------------------------------------------------=== # -fn lbeta(a: Float64, b: Float64) -> Float64: +def lbeta(a: Float64, b: Float64) -> Float64: """Natural logarithm of the beta function. Computes ln(B(a, b)) = ln(Γ(a)) + ln(Γ(b)) - ln(Γ(a+b)). @@ -54,7 +54,7 @@ fn lbeta(a: Float64, b: Float64) -> Float64: return lgamma(a) + lgamma(b) - lgamma(a + b) -fn beta(a: Float64, b: Float64) -> Float64: +def beta(a: Float64, b: Float64) -> Float64: """Beta function B(a, b) = Γ(a)Γ(b) / Γ(a+b). Args: @@ -67,7 +67,7 @@ fn beta(a: Float64, b: Float64) -> Float64: return exp(lbeta(a, b)) -fn betainc(a: Float64, b: Float64, x: Float64) -> Float64: +def betainc(a: Float64, b: Float64, x: Float64) -> Float64: """Regularized incomplete beta function I_x(a, b). Computes I_x(a, b) = B(x; a, b) / B(a, b), where B(x; a, b) is the @@ -107,7 +107,7 @@ fn betainc(a: Float64, b: Float64, x: Float64) -> Float64: # ===----------------------------------------------------------------------=== # -fn _betainc_cf( +def _betainc_cf( a: Float64, b: Float64, x: Float64, lbeta_ab: Float64 ) -> Float64: """Evaluate the regularized incomplete beta function using Lentz's diff --git a/src/stamojo/special/_erf.mojo b/src/stamojo/special/_erf.mojo index d7c4361..71e4e73 100644 --- a/src/stamojo/special/_erf.mojo +++ b/src/stamojo/special/_erf.mojo @@ -20,7 +20,7 @@ Reference: https://web.archive.org/web/20151030215612/http://home.online.no/~pjacklam/notes/invnorm/ """ -from math import sqrt, log, exp, erf, erfc, nan, inf +from std.math import sqrt, log, exp, erf, erfc, nan, inf # ===----------------------------------------------------------------------=== # @@ -64,7 +64,7 @@ comptime _D4 = 3.754408661907416e0 # ===----------------------------------------------------------------------=== # -fn ndtri(p: Float64) -> Float64: +def ndtri(p: Float64) -> Float64: """Inverse of the standard normal CDF (quantile / PPF). Computes x such that Φ(x) = p, where Φ is the CDF of N(0,1). @@ -120,7 +120,7 @@ fn ndtri(p: Float64) -> Float64: return x -fn erfinv(p: Float64) -> Float64: +def erfinv(p: Float64) -> Float64: """Inverse error function. Computes the value x such that erf(x) = p. diff --git a/src/stamojo/special/_gamma.mojo b/src/stamojo/special/_gamma.mojo index 8bf9301..874b0c2 100644 --- a/src/stamojo/special/_gamma.mojo +++ b/src/stamojo/special/_gamma.mojo @@ -29,7 +29,7 @@ Reference: Press et al., Numerical Recipes, 3rd ed., Section 6.2. """ -from math import lgamma, exp, log, nan, inf +from std.math import lgamma, exp, log, nan, inf # ===----------------------------------------------------------------------=== # @@ -47,7 +47,7 @@ comptime _FPMIN = 1.0e-30 # Near smallest representable floating-point number. # ===----------------------------------------------------------------------=== # -fn _is_near_integer(a: Float64) -> Bool: +def _is_near_integer(a: Float64) -> Bool: """Return True if `a` is within 1e-12 of a positive integer. When a is (close to) an integer, the continued-fraction expansion @@ -66,7 +66,7 @@ fn _is_near_integer(a: Float64) -> Bool: # ===----------------------------------------------------------------------=== # -fn gammainc(a: Float64, x: Float64) -> Float64: +def gammainc(a: Float64, x: Float64) -> Float64: """Regularized lower incomplete gamma function P(a, x). Computes P(a, x) = γ(a, x) / Γ(a), where γ(a, x) is the lower @@ -93,7 +93,7 @@ fn gammainc(a: Float64, x: Float64) -> Float64: return 1.0 - _gamma_cf(a, x) -fn gammaincc(a: Float64, x: Float64) -> Float64: +def gammaincc(a: Float64, x: Float64) -> Float64: """Regularized upper incomplete gamma function Q(a, x). Computes Q(a, x) = 1 - P(a, x) = Γ(a, x) / Γ(a), where Γ(a, x) @@ -126,7 +126,7 @@ fn gammaincc(a: Float64, x: Float64) -> Float64: # ===----------------------------------------------------------------------=== # -fn _gamma_series(a: Float64, x: Float64) -> Float64: +def _gamma_series(a: Float64, x: Float64) -> Float64: """Evaluate the regularized lower incomplete gamma function P(a, x) by its series representation. @@ -151,7 +151,7 @@ fn _gamma_series(a: Float64, x: Float64) -> Float64: return sum_val * exp(-x + a * log(x) - gln) -fn _gamma_cf(a: Float64, x: Float64) -> Float64: +def _gamma_cf(a: Float64, x: Float64) -> Float64: """Evaluate the regularized upper incomplete gamma function Q(a, x) by its continued fraction representation (modified Lentz's method). diff --git a/src/stamojo/stats/__init__.mojo b/src/stamojo/stats/__init__.mojo index 77e64b7..c36faf3 100644 --- a/src/stamojo/stats/__init__.mojo +++ b/src/stamojo/stats/__init__.mojo @@ -13,7 +13,7 @@ This subpackage provides: from .descriptive import ( mean, variance, - std, + stddev, median, quantile, skewness, diff --git a/src/stamojo/stats/correlation.mojo b/src/stamojo/stats/correlation.mojo index 8eaa900..c643a29 100644 --- a/src/stamojo/stats/correlation.mojo +++ b/src/stamojo/stats/correlation.mojo @@ -14,7 +14,7 @@ The two-sided p-value tests the null hypothesis that the true correlation is zero. """ -from math import sqrt, nan +from std.math import sqrt, nan from stamojo.distributions import Normal, StudentT from stamojo.stats.descriptive import mean @@ -25,7 +25,7 @@ from stamojo.stats.descriptive import mean # ===----------------------------------------------------------------------=== # -fn _rank_data(data: List[Float64]) -> List[Float64]: +def _rank_data(data: List[Float64]) -> List[Float64]: """Assign ranks to data, handling ties by averaging. Returns a list of ranks (1-based) with the same length as *data*. @@ -72,7 +72,7 @@ fn _rank_data(data: List[Float64]) -> List[Float64]: # ===----------------------------------------------------------------------=== # -fn pearsonr(x: List[Float64], y: List[Float64]) -> Tuple[Float64, Float64]: +def pearsonr(x: List[Float64], y: List[Float64]) -> Tuple[Float64, Float64]: """Pearson product-moment correlation coefficient and p-value. The p-value is two-sided and tests H₀: ρ = 0 using the t-distribution @@ -122,7 +122,7 @@ fn pearsonr(x: List[Float64], y: List[Float64]) -> Tuple[Float64, Float64]: return (r, p_value) -fn spearmanr(x: List[Float64], y: List[Float64]) -> Tuple[Float64, Float64]: +def spearmanr(x: List[Float64], y: List[Float64]) -> Tuple[Float64, Float64]: """Spearman rank-order correlation coefficient and p-value. Computes the Pearson correlation of the rank-transformed data. @@ -145,7 +145,7 @@ fn spearmanr(x: List[Float64], y: List[Float64]) -> Tuple[Float64, Float64]: return pearsonr(rx, ry) -fn kendalltau(x: List[Float64], y: List[Float64]) -> Tuple[Float64, Float64]: +def kendalltau(x: List[Float64], y: List[Float64]) -> Tuple[Float64, Float64]: """Kendall's tau-b rank correlation coefficient and p-value. Tau-b adjusts for ties. The p-value is two-sided based on the diff --git a/src/stamojo/stats/descriptive.mojo b/src/stamojo/stats/descriptive.mojo index 7a84883..26fc492 100644 --- a/src/stamojo/stats/descriptive.mojo +++ b/src/stamojo/stats/descriptive.mojo @@ -19,7 +19,7 @@ Provides functions for computing summary statistics of ``List[Float64]`` data: - ``hmean`` — Harmonic mean """ -from math import sqrt, nan, log, exp +from std.math import sqrt, nan, log, exp # ===----------------------------------------------------------------------=== # @@ -27,7 +27,7 @@ from math import sqrt, nan, log, exp # ===----------------------------------------------------------------------=== # -fn _sorted_copy(data: List[Float64]) -> List[Float64]: +def _sorted_copy(data: List[Float64]) -> List[Float64]: """Return a sorted copy of *data* (ascending, insertion sort).""" var result = data.copy() var n = len(result) @@ -46,7 +46,7 @@ fn _sorted_copy(data: List[Float64]) -> List[Float64]: # ===----------------------------------------------------------------------=== # -fn mean(data: List[Float64]) -> Float64: +def mean(data: List[Float64]) -> Float64: """Arithmetic mean of *data*. Args: @@ -64,7 +64,7 @@ fn mean(data: List[Float64]) -> Float64: return s / Float64(n) -fn variance(data: List[Float64], ddof: Int = 0) -> Float64: +def variance(data: List[Float64], ddof: Int = 0) -> Float64: """Variance of *data*. Args: @@ -86,7 +86,7 @@ fn variance(data: List[Float64], ddof: Int = 0) -> Float64: return ss / Float64(n - ddof) -fn std(data: List[Float64], ddof: Int = 0) -> Float64: +def stddev(data: List[Float64], ddof: Int = 0) -> Float64: """Standard deviation of *data*. Args: @@ -99,7 +99,7 @@ fn std(data: List[Float64], ddof: Int = 0) -> Float64: return sqrt(variance(data, ddof)) -fn median(data: List[Float64]) -> Float64: +def median(data: List[Float64]) -> Float64: """Median of *data*. Args: @@ -120,7 +120,7 @@ fn median(data: List[Float64]) -> Float64: return (sorted_data[n // 2 - 1] + sorted_data[n // 2]) / 2.0 -fn quantile(data: List[Float64], q: Float64) -> Float64: +def quantile(data: List[Float64], q: Float64) -> Float64: """Quantile of *data* using linear interpolation (NumPy default). Args: @@ -150,7 +150,7 @@ fn quantile(data: List[Float64], q: Float64) -> Float64: return sorted_data[lo] * (1.0 - frac) + sorted_data[hi] * frac -fn skewness(data: List[Float64]) -> Float64: +def skewness(data: List[Float64]) -> Float64: """Fisher's skewness (bias-corrected) of *data*. Computes the adjusted Fisher-Pearson standardized moment coefficient:: @@ -170,7 +170,7 @@ fn skewness(data: List[Float64]) -> Float64: return nan[DType.float64]() var m = mean(data) - var s = std(data, ddof=1) + var s = stddev(data, ddof=1) if s == 0.0: return 0.0 @@ -183,7 +183,7 @@ fn skewness(data: List[Float64]) -> Float64: return m3 * fn_ / ((fn_ - 1.0) * (fn_ - 2.0)) -fn kurtosis(data: List[Float64], excess: Bool = True) -> Float64: +def kurtosis(data: List[Float64], excess: Bool = True) -> Float64: """Kurtosis of *data* (bias-corrected). Uses the standard bias-corrected formula matching ``scipy.stats.kurtosis`` @@ -225,7 +225,7 @@ fn kurtosis(data: List[Float64], excess: Bool = True) -> Float64: return kurt + 3.0 -fn data_min(data: List[Float64]) -> Float64: +def data_min(data: List[Float64]) -> Float64: """Minimum value in *data*. Args: @@ -244,7 +244,7 @@ fn data_min(data: List[Float64]) -> Float64: return result -fn data_max(data: List[Float64]) -> Float64: +def data_max(data: List[Float64]) -> Float64: """Maximum value in *data*. Args: @@ -266,7 +266,7 @@ fn data_max(data: List[Float64]) -> Float64: # TODO: Due to limitation in mojo compiler in 0.26.1 (resolved in nightly), we can't have Optional[List]. # Once we have that, we can make weights optional and handle the unweighted case more cleanly. # For now, we can just require an empty list for unweighted case. -fn gmean(data: List[Float64], weights: List[Float64]) -> Float64: +def gmean(data: List[Float64], weights: List[Float64]) -> Float64: """Compute the weighted geometric mean of a list of values. The geometric mean is the nth root of the product of n values. If weights are provided, @@ -320,7 +320,7 @@ fn gmean(data: List[Float64], weights: List[Float64]) -> Float64: return exp(log_sum / Float64(n)) -fn hmean(data: List[Float64], weights: List[Float64]) -> Float64: +def hmean(data: List[Float64], weights: List[Float64]) -> Float64: """ Compute the weighted harmonic mean of a list of values. diff --git a/src/stamojo/stats/tests.mojo b/src/stamojo/stats/tests.mojo index e629fa5..fa90ec3 100644 --- a/src/stamojo/stats/tests.mojo +++ b/src/stamojo/stats/tests.mojo @@ -17,7 +17,7 @@ Each function returns a ``Tuple[Float64, Float64]`` of (test statistic, p-value) unless otherwise noted. """ -from math import sqrt, exp, nan, inf +from std.math import sqrt, exp, nan, inf from stamojo.distributions import Normal, StudentT, ChiSquared, FDist from stamojo.stats.descriptive import mean, variance @@ -28,7 +28,7 @@ from stamojo.stats.descriptive import mean, variance # ===----------------------------------------------------------------------=== # -fn _sorted_copy(data: List[Float64]) -> List[Float64]: +def _sorted_copy(data: List[Float64]) -> List[Float64]: """Return a sorted copy of *data* (ascending, insertion sort).""" var result = data.copy() var n = len(result) @@ -47,7 +47,7 @@ fn _sorted_copy(data: List[Float64]) -> List[Float64]: # ===----------------------------------------------------------------------=== # -fn ttest_1samp( +def ttest_1samp( data: List[Float64], mu0: Float64 = 0.0 ) -> Tuple[Float64, Float64]: """One-sample t-test. @@ -82,7 +82,7 @@ fn ttest_1samp( return (t, p) -fn ttest_ind( +def ttest_ind( x: List[Float64], y: List[Float64], equal_var: Bool = False, @@ -152,7 +152,7 @@ fn ttest_ind( return (t, p) -fn ttest_rel(x: List[Float64], y: List[Float64]) -> Tuple[Float64, Float64]: +def ttest_rel(x: List[Float64], y: List[Float64]) -> Tuple[Float64, Float64]: """Paired (related) samples t-test. Tests H₀: μ_d = 0 against H₁: μ_d ≠ 0, where d = x − y. @@ -180,7 +180,7 @@ fn ttest_rel(x: List[Float64], y: List[Float64]) -> Tuple[Float64, Float64]: # ===----------------------------------------------------------------------=== # -fn chi2_gof( +def chi2_gof( observed: List[Float64], expected: List[Float64] ) -> Tuple[Float64, Float64]: """Chi-squared goodness-of-fit test. @@ -212,7 +212,7 @@ fn chi2_gof( return (chi2, p) -fn chi2_ind( +def chi2_ind( observed: List[List[Float64]], ) -> Tuple[Float64, Float64]: """Chi-squared test of independence for a contingency table. @@ -276,7 +276,7 @@ fn chi2_ind( # ===----------------------------------------------------------------------=== # -fn ks_1samp(data: List[Float64]) -> Tuple[Float64, Float64]: +def ks_1samp(data: List[Float64]) -> Tuple[Float64, Float64]: """One-sample Kolmogorov-Smirnov test against the standard normal N(0,1). Tests H₀: the data come from a standard normal distribution. @@ -317,7 +317,7 @@ fn ks_1samp(data: List[Float64]) -> Tuple[Float64, Float64]: return (d_max, p) -fn _ks_pvalue(d: Float64, n: Int) -> Float64: +def _ks_pvalue(d: Float64, n: Int) -> Float64: """Compute the two-sided KS test p-value using the asymptotic formula. P(D_n > d) ≈ 2 * sum_{k=1}^{inf} (-1)^{k+1} * exp(-2 k² (√n d)²) @@ -350,7 +350,7 @@ fn _ks_pvalue(d: Float64, n: Int) -> Float64: return p -fn _exp_safe(x: Float64) -> Float64: +def _exp_safe(x: Float64) -> Float64: """Safe exponential that avoids underflow.""" if x < -700.0: return 0.0 @@ -362,7 +362,7 @@ fn _exp_safe(x: Float64) -> Float64: # ===----------------------------------------------------------------------=== # -fn f_oneway( +def f_oneway( groups: List[List[Float64]], ) -> Tuple[Float64, Float64]: """One-way ANOVA F-test. diff --git a/tests/test_distributions.mojo b/tests/test_distributions.mojo index b0898b1..354d6aa 100644 --- a/tests/test_distributions.mojo +++ b/tests/test_distributions.mojo @@ -23,6 +23,9 @@ from stamojo.distributions import ( FDist, Exponential, Binomial, + Gamma, + Beta, + Poisson, ) @@ -31,7 +34,7 @@ from stamojo.distributions import ( # ===----------------------------------------------------------------------=== # -fn _load_scipy_stats() -> PythonObject: +def _load_scipy_stats() -> PythonObject: """Try to import scipy.stats. Returns Python None if unavailable.""" try: return Python.import_module("scipy.stats") @@ -39,7 +42,7 @@ fn _load_scipy_stats() -> PythonObject: return PythonObject(None) -fn _py_f64(obj: PythonObject) -> Float64: +def _py_f64(obj: PythonObject) -> Float64: """Convert a PythonObject holding a numeric value to Float64.""" try: return atof(String(obj)) @@ -52,7 +55,7 @@ fn _py_f64(obj: PythonObject) -> Float64: # ===----------------------------------------------------------------------=== # -fn test_normal_pdf() raises: +def test_normal_pdf() raises: """Test Normal PDF at known values.""" var n = Normal(0.0, 1.0) # PDF at 0 for standard normal ≈ 1/√(2π) ≈ 0.3989422804014327 @@ -65,7 +68,7 @@ fn test_normal_pdf() raises: assert_almost_equal(n2.pdf(5.0), 0.19947114020071635, atol=1e-12) -fn test_normal_cdf() raises: +def test_normal_cdf() raises: """Test Normal CDF at known values.""" var n = Normal(0.0, 1.0) assert_almost_equal(n.cdf(0.0), 0.5, atol=1e-15) @@ -76,7 +79,7 @@ fn test_normal_cdf() raises: assert_almost_equal(n.cdf(10.0), 1.0, atol=1e-15) -fn test_normal_ppf() raises: +def test_normal_ppf() raises: """Test Normal PPF (inverse CDF).""" var n = Normal(0.0, 1.0) assert_almost_equal(n.ppf(0.5), 0.0, atol=1e-12) @@ -89,7 +92,7 @@ fn test_normal_ppf() raises: assert_almost_equal(n2.ppf(n2.cdf(15.0)), 15.0, atol=1e-10) -fn test_normal_cdf_ppf_roundtrip() raises: +def test_normal_cdf_ppf_roundtrip() raises: """Test CDF(PPF(p)) ≈ p for many probability values.""" var n = Normal(0.0, 1.0) var ps: List[Float64] = [0.01, 0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95, 0.99] @@ -99,14 +102,14 @@ fn test_normal_cdf_ppf_roundtrip() raises: assert_almost_equal(n.cdf(n.ppf(p)), p, atol=1e-10) -fn test_normal_sf() raises: +def test_normal_sf() raises: """Test Normal survival function.""" var n = Normal(0.0, 1.0) assert_almost_equal(n.sf(0.0), 0.5, atol=1e-15) assert_almost_equal(n.cdf(1.5) + n.sf(1.5), 1.0, atol=1e-15) -fn test_normal_stats() raises: +def test_normal_stats() raises: """Test Normal distribution statistics.""" var n = Normal(3.0, 2.0) assert_almost_equal(n.mean(), 3.0, atol=1e-15) @@ -114,7 +117,7 @@ fn test_normal_stats() raises: assert_almost_equal(n.std(), 2.0, atol=1e-15) -fn test_normal_scipy() raises: +def test_normal_scipy() raises: """Test Normal distribution against scipy.stats.norm.""" var sp = _load_scipy_stats() if sp is None: @@ -137,14 +140,14 @@ fn test_normal_scipy() raises: # ===----------------------------------------------------------------------=== # -fn test_t_pdf_symmetry() raises: +def test_t_pdf_symmetry() raises: """Test Student's t PDF is symmetric about 0.""" var t = StudentT(5.0) assert_almost_equal(t.pdf(1.0), t.pdf(-1.0), atol=1e-15) assert_almost_equal(t.pdf(2.5), t.pdf(-2.5), atol=1e-15) -fn test_t_cdf() raises: +def test_t_cdf() raises: """Test Student's t CDF at known values.""" # Cauchy distribution (df=1): CDF(0)=0.5, CDF(1)=0.75 var t1 = StudentT(1.0) @@ -157,7 +160,7 @@ fn test_t_cdf() raises: assert_almost_equal(t5.cdf(2.0) + t5.cdf(-2.0), 1.0, atol=1e-10) -fn test_t_ppf() raises: +def test_t_ppf() raises: """Test Student's t PPF.""" var t5 = StudentT(5.0) assert_almost_equal(t5.ppf(0.5), 0.0, atol=1e-10) @@ -167,14 +170,14 @@ fn test_t_ppf() raises: assert_almost_equal(t5.cdf(t5.ppf(0.9)), 0.9, atol=1e-6) -fn test_t_stats() raises: +def test_t_stats() raises: """Test Student's t distribution statistics.""" var t5 = StudentT(5.0) assert_almost_equal(t5.mean(), 0.0, atol=1e-15) assert_almost_equal(t5.variance(), 5.0 / 3.0, atol=1e-12) -fn test_t_scipy() raises: +def test_t_scipy() raises: """Test Student's t distribution against scipy.stats.t.""" var sp = _load_scipy_stats() if sp is None: @@ -201,7 +204,7 @@ fn test_t_scipy() raises: # ===----------------------------------------------------------------------=== # -fn test_chi2_cdf() raises: +def test_chi2_cdf() raises: """Test Chi-squared CDF at known values. For df=2: CDF(x) = 1 − exp(−x/2). @@ -212,7 +215,7 @@ fn test_chi2_cdf() raises: assert_almost_equal(c2.cdf(0.0), 0.0, atol=1e-15) -fn test_chi2_ppf() raises: +def test_chi2_ppf() raises: """Test Chi-squared PPF (round-trip).""" var c5 = ChiSquared(5.0) assert_almost_equal(c5.cdf(c5.ppf(0.95)), 0.95, atol=1e-6) @@ -220,14 +223,14 @@ fn test_chi2_ppf() raises: assert_almost_equal(c5.cdf(c5.ppf(0.01)), 0.01, atol=1e-6) -fn test_chi2_stats() raises: +def test_chi2_stats() raises: """Test Chi-squared distribution statistics.""" var c5 = ChiSquared(5.0) assert_almost_equal(c5.mean(), 5.0, atol=1e-15) assert_almost_equal(c5.variance(), 10.0, atol=1e-15) -fn test_chi2_scipy() raises: +def test_chi2_scipy() raises: """Test Chi-squared distribution against scipy.stats.chi2.""" var sp = _load_scipy_stats() if sp is None: @@ -252,7 +255,7 @@ fn test_chi2_scipy() raises: # ===----------------------------------------------------------------------=== # -fn test_f_cdf_boundary() raises: +def test_f_cdf_boundary() raises: """Test F-distribution CDF boundary and monotonicity.""" var f = FDist(5.0, 10.0) assert_almost_equal(f.cdf(0.0), 0.0, atol=1e-15) @@ -264,7 +267,7 @@ fn test_f_cdf_boundary() raises: raise Error("F CDF not monotonically increasing") -fn test_f_ppf() raises: +def test_f_ppf() raises: """Test F-distribution PPF (round-trip).""" var f = FDist(5.0, 10.0) assert_almost_equal(f.cdf(f.ppf(0.95)), 0.95, atol=1e-6) @@ -272,14 +275,14 @@ fn test_f_ppf() raises: assert_almost_equal(f.cdf(f.ppf(0.1)), 0.1, atol=1e-6) -fn test_f_stats() raises: +def test_f_stats() raises: """Test F-distribution statistics.""" var f = FDist(5.0, 10.0) # mean = d2 / (d2 - 2) = 10/8 = 1.25 assert_almost_equal(f.mean(), 1.25, atol=1e-12) -fn test_f_scipy() raises: +def test_f_scipy() raises: """Test F-distribution against scipy.stats.f.""" var sp = _load_scipy_stats() if sp is None: @@ -300,7 +303,7 @@ fn test_f_scipy() raises: # ===----------------------------------------------------------------------=== # -fn test_expon_pdf() raises: +def test_expon_pdf() raises: """Test Exponential PDF at known values.""" var e = Exponential() # Standard exponential: pdf(0) = 1.0 @@ -321,7 +324,7 @@ fn test_expon_pdf() raises: assert_almost_equal(e3.pdf(0.5), 0.0, atol=1e-15) -fn test_expon_logpdf() raises: +def test_expon_logpdf() raises: """Test Exponential log-PDF at known values.""" var e = Exponential() # logpdf(0) = 0.0 for standard exponential @@ -335,7 +338,7 @@ fn test_expon_logpdf() raises: assert_almost_equal(e2.logpdf(3.0), -1.0 - log(3.0), atol=1e-15) -fn test_expon_cdf() raises: +def test_expon_cdf() raises: """Test Exponential CDF at known values.""" var e = Exponential() # CDF(0) = 0 @@ -355,7 +358,7 @@ fn test_expon_cdf() raises: assert_almost_equal(e2.cdf(1.0), 1.0 - exp(-2.0), atol=1e-15) -fn test_expon_sf() raises: +def test_expon_sf() raises: """Test Exponential survival function: SF(x) = 1 - CDF(x).""" var e = Exponential() assert_almost_equal(e.sf(0.0), 1.0, atol=1e-15) @@ -368,7 +371,7 @@ fn test_expon_sf() raises: assert_almost_equal(e.sf(-1.0), 1.0, atol=1e-15) -fn test_expon_ppf() raises: +def test_expon_ppf() raises: """Test Exponential PPF (inverse CDF).""" var e = Exponential() # PPF(0) = 0 (loc) @@ -382,7 +385,7 @@ fn test_expon_ppf() raises: assert_almost_equal(e2.ppf(0.5), 1.0 + 2.0 * log(2.0), atol=1e-12) -fn test_expon_cdf_ppf_roundtrip() raises: +def test_expon_cdf_ppf_roundtrip() raises: """Test CDF(PPF(p)) ≈ p for many probability values.""" var e = Exponential() var ps: List[Float64] = [0.01, 0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95, 0.99] @@ -396,7 +399,7 @@ fn test_expon_cdf_ppf_roundtrip() raises: assert_almost_equal(e2.cdf(e2.ppf(p)), p, atol=1e-12) -fn test_expon_isf() raises: +def test_expon_isf() raises: """Test Exponential ISF (inverse survival function).""" var e = Exponential() # ISF(1) = loc = 0 @@ -410,7 +413,7 @@ fn test_expon_isf() raises: assert_almost_equal(e.isf(q), e.ppf(1.0 - q), atol=1e-12) -fn test_expon_logcdf_logsf() raises: +def test_expon_logcdf_logsf() raises: """Test log-CDF and log-SF against log of CDF and SF.""" var e = Exponential() var xs: List[Float64] = [0.01, 0.1, 0.5, 1.0, 2.0, 5.0] @@ -420,7 +423,7 @@ fn test_expon_logcdf_logsf() raises: assert_almost_equal(e.logsf(x), log(e.sf(x)), atol=1e-15) -fn test_expon_stats() raises: +def test_expon_stats() raises: """Test Exponential distribution summary statistics.""" var e = Exponential() # Standard exponential: mean=1, var=1, std=1, median=ln(2) @@ -436,7 +439,7 @@ fn test_expon_stats() raises: assert_almost_equal(e2.median(), 2.0 + 3.0 * log(2.0), atol=1e-15) -fn test_expon_loc_scale() raises: +def test_expon_loc_scale() raises: """Test Exponential with non-default loc and scale across all functions.""" var loc = 5.0 var scale = 2.0 @@ -451,7 +454,7 @@ fn test_expon_loc_scale() raises: assert_almost_equal(e.cdf(loc + scale), 1.0 - exp(-1.0), atol=1e-15) -fn test_expon_scipy() raises: +def test_expon_scipy() raises: """Test Exponential distribution against scipy.stats.expon.""" var sp = _load_scipy_stats() if sp is None: @@ -494,7 +497,7 @@ fn test_expon_scipy() raises: # ===----------------------------------------------------------------------=== # -fn test_binomial_pmf_basic() raises: +def test_binomial_pmf_basic() raises: """Test Binomial PMF at known values.""" var b = Binomial(10, 0.5) assert_almost_equal(b.pmf(0), 1.0 / 1024.0, atol=1e-12) @@ -503,7 +506,7 @@ fn test_binomial_pmf_basic() raises: assert_almost_equal(b.pmf(11), 0.0, atol=1e-12) -fn test_binomial_cdf_sf() raises: +def test_binomial_cdf_sf() raises: """Test Binomial CDF and SF at known values.""" var b = Binomial(4, 0.5) assert_almost_equal(b.cdf(2), 0.6875, atol=1e-12) @@ -511,7 +514,7 @@ fn test_binomial_cdf_sf() raises: assert_almost_equal(b.cdf(4), 1.0, atol=1e-12) -fn test_binomial_edge_p() raises: +def test_binomial_edge_p() raises: """Test Binomial behavior for p=0 and p=1.""" var b0 = Binomial(5, 0.0) assert_almost_equal(b0.pmf(0), 1.0, atol=1e-12) @@ -526,21 +529,21 @@ fn test_binomial_edge_p() raises: assert_almost_equal(b1.cdf(5), 1.0, atol=1e-12) -fn test_binomial_logpmf() raises: +def test_binomial_logpmf() raises: """Test Binomial log-PMF consistency.""" var b = Binomial(6, 0.3) var k = 2 assert_almost_equal(b.logpmf(k), log(b.pmf(k)), atol=1e-12) -fn test_binomial_symmetry_p_half() raises: +def test_binomial_symmetry_p_half() raises: """Test Binomial symmetry for p=0.5.""" var b = Binomial(10, 0.5) for k in range(0, 11): assert_almost_equal(b.pmf(k), b.pmf(10 - k), atol=1e-12) -fn test_binomial_ppf_isf_roundtrip() raises: +def test_binomial_ppf_isf_roundtrip() raises: """Test Binomial PPF/ISF consistency with CDF/SF.""" var b = Binomial(12, 0.4) var qs: List[Float64] = [0.01, 0.1, 0.25, 0.5, 0.75, 0.9, 0.99] @@ -560,7 +563,7 @@ fn test_binomial_ppf_isf_roundtrip() raises: raise Error("binomial isf: sf(k-1) <= q") -fn test_binomial_scipy() raises: +def test_binomial_scipy() raises: """Test Binomial distribution against scipy.stats.binom.""" var sp = _load_scipy_stats() if sp is None: @@ -588,10 +591,178 @@ fn test_binomial_scipy() raises: assert_almost_equal(Float64(b.ppf(q)), sp_ppf, atol=1e-10) +# ===----------------------------------------------------------------------=== # +# Gamma distribution tests +# ===----------------------------------------------------------------------=== # + + +def test_gamma_pdf() raises: + """Test Gamma PDF at known values.""" + var g = Gamma(2.0, 1.0) + # PDF at x=1 for Gamma(2,1): 1*exp(-1) = exp(-1) + assert_almost_equal(g.pdf(1.0), exp(-1.0), atol=1e-12) + # PDF(x < 0) = 0 + assert_almost_equal(g.pdf(-1.0), 0.0, atol=1e-15) + + +def test_gamma_cdf() raises: + """Test Gamma CDF at known values.""" + var g = Gamma(1.0, 1.0) + # Gamma(1,1) = Exponential(1): CDF(x) = 1 - exp(-x) + assert_almost_equal(g.cdf(1.0), 1.0 - exp(-1.0), atol=1e-12) + assert_almost_equal(g.cdf(2.0), 1.0 - exp(-2.0), atol=1e-12) + + +def test_gamma_ppf_roundtrip() raises: + """Test Gamma PPF round-trip.""" + var g = Gamma(3.0, 2.0) + assert_almost_equal(g.cdf(g.ppf(0.5)), 0.5, atol=1e-6) + assert_almost_equal(g.cdf(g.ppf(0.95)), 0.95, atol=1e-6) + assert_almost_equal(g.cdf(g.ppf(0.1)), 0.1, atol=1e-6) + + +def test_gamma_stats() raises: + """Test Gamma distribution statistics.""" + var g = Gamma(4.0, 3.0) + # mean = a*scale = 12 + assert_almost_equal(g.mean(), 12.0, atol=1e-12) + # variance = a*scale^2 = 36 + assert_almost_equal(g.variance(), 36.0, atol=1e-12) + # std = 6 + assert_almost_equal(g.std(), 6.0, atol=1e-12) + + +def test_gamma_scipy() raises: + """Test Gamma distribution against scipy.stats.gamma.""" + var sp = _load_scipy_stats() + if sp is None: + print("test_gamma_scipy skipped (scipy not available)") + return + + var g = Gamma(2.5, 1.5) + var xs: List[Float64] = [1.0, 2.0, 5.0] + + for i in range(len(xs)): + var x = xs[i] + var sp_pdf = _py_f64(sp.gamma.pdf(x, 2.5, scale=1.5)) + var sp_cdf = _py_f64(sp.gamma.cdf(x, 2.5, scale=1.5)) + assert_almost_equal(g.pdf(x), sp_pdf, atol=1e-10) + assert_almost_equal(g.cdf(x), sp_cdf, atol=1e-10) + + +# ===----------------------------------------------------------------------=== # +# Beta distribution tests +# ===----------------------------------------------------------------------=== # + + +def test_beta_pdf() raises: + """Test Beta PDF at known values.""" + var b = Beta(2.0, 2.0) + # PDF at 0.5 for Beta(2,2): 6 * 0.25 = 1.5 + assert_almost_equal(b.pdf(0.5), 1.5, atol=1e-12) + # PDF outside [0,1] = 0 + assert_almost_equal(b.pdf(-0.1), 0.0, atol=1e-15) + assert_almost_equal(b.pdf(1.1), 0.0, atol=1e-15) + + +def test_beta_cdf() raises: + """Test Beta CDF at known values.""" + var b = Beta(1.0, 1.0) + # Beta(1,1) = Uniform(0,1): CDF(x) = x + assert_almost_equal(b.cdf(0.3), 0.3, atol=1e-12) + assert_almost_equal(b.cdf(0.7), 0.7, atol=1e-12) + + +def test_beta_ppf_roundtrip() raises: + """Test Beta PPF round-trip.""" + var b = Beta(3.0, 5.0) + assert_almost_equal(b.cdf(b.ppf(0.5)), 0.5, atol=1e-6) + assert_almost_equal(b.cdf(b.ppf(0.9)), 0.9, atol=1e-6) + assert_almost_equal(b.cdf(b.ppf(0.1)), 0.1, atol=1e-6) + + +def test_beta_stats() raises: + """Test Beta distribution statistics.""" + var b = Beta(2.0, 3.0) + # mean = a/(a+b) = 2/5 = 0.4 + assert_almost_equal(b.mean(), 0.4, atol=1e-12) + # variance = ab/((a+b)^2*(a+b+1)) = 6/(25*6) = 0.04 + assert_almost_equal(b.variance(), 0.04, atol=1e-12) + + +def test_beta_scipy() raises: + """Test Beta distribution against scipy.stats.beta.""" + var sp = _load_scipy_stats() + if sp is None: + print("test_beta_scipy skipped (scipy not available)") + return + + var b = Beta(2.5, 3.5) + var xs: List[Float64] = [0.2, 0.5, 0.8] + + for i in range(len(xs)): + var x = xs[i] + var sp_pdf = _py_f64(sp.beta.pdf(x, 2.5, 3.5)) + var sp_cdf = _py_f64(sp.beta.cdf(x, 2.5, 3.5)) + assert_almost_equal(b.pdf(x), sp_pdf, atol=1e-10) + assert_almost_equal(b.cdf(x), sp_cdf, atol=1e-10) + + +# ===----------------------------------------------------------------------=== # +# Poisson distribution tests +# ===----------------------------------------------------------------------=== # + + +def test_poisson_pmf() raises: + """Test Poisson PMF at known values.""" + var p = Poisson(3.0) + # PMF at k=0: exp(-3) + assert_almost_equal(p.pmf(0), exp(-3.0), atol=1e-12) + # PMF at k=3: 3^3 * exp(-3) / 6 = 27*exp(-3)/6 + assert_almost_equal(p.pmf(3), 27.0 * exp(-3.0) / 6.0, atol=1e-12) + # PMF for k < 0 = 0 + assert_almost_equal(p.pmf(-1), 0.0, atol=1e-15) + + +def test_poisson_cdf() raises: + """Test Poisson CDF at known values.""" + var p = Poisson(1.0) + # CDF at k=0: exp(-1) + assert_almost_equal(p.cdf(0), exp(-1.0), atol=1e-12) + # CDF at k=1: exp(-1) + exp(-1) = 2*exp(-1) + assert_almost_equal(p.cdf(1), 2.0 * exp(-1.0), atol=1e-12) + + +def test_poisson_stats() raises: + """Test Poisson distribution statistics.""" + var p = Poisson(5.0) + assert_almost_equal(p.mean(), 5.0, atol=1e-15) + assert_almost_equal(p.variance(), 5.0, atol=1e-15) + assert_almost_equal(p.std(), sqrt(5.0), atol=1e-12) + + +def test_poisson_scipy() raises: + """Test Poisson distribution against scipy.stats.poisson.""" + var sp = _load_scipy_stats() + if sp is None: + print("test_poisson_scipy skipped (scipy not available)") + return + + var p = Poisson(4.0) + var ks: List[Int] = [0, 1, 2, 4, 8] + + for i in range(len(ks)): + var k = ks[i] + var sp_pmf = _py_f64(sp.poisson.pmf(k, 4.0)) + var sp_cdf = _py_f64(sp.poisson.cdf(k, 4.0)) + assert_almost_equal(p.pmf(k), sp_pmf, atol=1e-10) + assert_almost_equal(p.cdf(k), sp_cdf, atol=1e-10) + + # ===----------------------------------------------------------------------=== # # Main test runner # ===----------------------------------------------------------------------=== # -fn main() raises: +def main() raises: TestSuite.discover_tests[__functions_in_module()]().run() diff --git a/tests/test_hypothesis.mojo b/tests/test_hypothesis.mojo index c79ae2d..3d6c9a2 100644 --- a/tests/test_hypothesis.mojo +++ b/tests/test_hypothesis.mojo @@ -12,9 +12,9 @@ Covers: - One-way ANOVA """ -from math import sqrt -from python import Python, PythonObject -from testing import assert_almost_equal, TestSuite +from std.math import sqrt +from std.python import Python, PythonObject +from std.testing import assert_almost_equal, TestSuite from stamojo.stats import ( ttest_1samp, @@ -35,7 +35,7 @@ from stamojo.stats import ( # ===----------------------------------------------------------------------=== # -fn _load_scipy_stats() -> PythonObject: +def _load_scipy_stats() -> PythonObject: """Try to import scipy.stats. Returns Python None if unavailable.""" try: return Python.import_module("scipy.stats") @@ -43,7 +43,7 @@ fn _load_scipy_stats() -> PythonObject: return PythonObject(None) -fn _py_f64(obj: PythonObject) -> Float64: +def _py_f64(obj: PythonObject) -> Float64: """Convert a PythonObject holding a numeric value to Float64.""" try: return atof(String(obj)) @@ -56,7 +56,7 @@ fn _py_f64(obj: PythonObject) -> Float64: # ===----------------------------------------------------------------------=== # -fn test_ttest_1samp_basic() raises: +def test_ttest_1samp_basic() raises: """Test one-sample t-test with known data.""" # Data with mean = 3.0; test H0: mu = 0 var data: List[Float64] = [1.0, 2.0, 3.0, 4.0, 5.0] @@ -72,7 +72,7 @@ fn test_ttest_1samp_basic() raises: raise Error("ttest_1samp: expected p < 0.05, got " + String(p_val)) -fn test_ttest_1samp_no_effect() raises: +def test_ttest_1samp_no_effect() raises: """Test one-sample t-test when data mean ≈ mu0.""" var data: List[Float64] = [-1.0, 0.0, 1.0] @@ -82,7 +82,7 @@ fn test_ttest_1samp_no_effect() raises: assert_almost_equal(result[1], 1.0, atol=1e-6) -fn test_ttest_1samp_scipy() raises: +def test_ttest_1samp_scipy() raises: """Test one-sample t-test against scipy.""" var sp = _load_scipy_stats() if sp is None: @@ -101,7 +101,7 @@ fn test_ttest_1samp_scipy() raises: assert_almost_equal(result[1], sp_p, atol=1e-4) -fn test_ttest_ind_welch() raises: +def test_ttest_ind_welch() raises: """Test Welch's two-sample t-test.""" var x: List[Float64] = [1.0, 2.0, 3.0, 4.0, 5.0] @@ -115,7 +115,7 @@ fn test_ttest_ind_welch() raises: ) -fn test_ttest_ind_scipy() raises: +def test_ttest_ind_scipy() raises: """Test Welch's t-test against scipy.""" var sp = _load_scipy_stats() if sp is None: @@ -137,7 +137,7 @@ fn test_ttest_ind_scipy() raises: assert_almost_equal(result[1], sp_p, atol=1e-3) -fn test_ttest_rel() raises: +def test_ttest_rel() raises: """Test paired t-test.""" # Before and after treatment. var before: List[Float64] = [10.0, 12.0, 14.0, 11.0, 13.0] @@ -158,7 +158,7 @@ fn test_ttest_rel() raises: # ===----------------------------------------------------------------------=== # -fn test_chi2_gof_fair_die() raises: +def test_chi2_gof_fair_die() raises: """Test chi-squared GoF for a fair die.""" var observed: List[Float64] = [16.0, 18.0, 16.0, 14.0, 12.0, 14.0] @@ -174,7 +174,7 @@ fn test_chi2_gof_fair_die() raises: ) -fn test_chi2_ind_basic() raises: +def test_chi2_ind_basic() raises: """Test chi-squared independence test with 2×2 table.""" # Example: [[10, 20], [20, 40]] # This table has perfect proportionality, chi2 ≈ 0. @@ -189,7 +189,7 @@ fn test_chi2_ind_basic() raises: assert_almost_equal(result[1], 1.0, atol=1e-4) -fn test_chi2_ind_scipy() raises: +def test_chi2_ind_scipy() raises: """Test chi-squared independence test against scipy.""" var sp = _load_scipy_stats() if sp is None: @@ -219,7 +219,7 @@ fn test_chi2_ind_scipy() raises: # ===----------------------------------------------------------------------=== # -fn test_ks_normal_data() raises: +def test_ks_normal_data() raises: """Test KS test with data drawn from N(0,1) (should not reject).""" # Pre-computed standard normal quantiles (approx). var data: List[Float64] = [ @@ -243,7 +243,7 @@ fn test_ks_normal_data() raises: ) -fn test_ks_uniform_data() raises: +def test_ks_uniform_data() raises: """Test KS test with uniform data (should reject N(0,1)).""" # Uniform [0, 10] data — definitely not N(0,1). var data = List[Float64]() @@ -264,7 +264,7 @@ fn test_ks_uniform_data() raises: # ===----------------------------------------------------------------------=== # -fn test_pearsonr_perfect() raises: +def test_pearsonr_perfect() raises: """Test Pearson correlation with perfectly correlated data.""" var x = List[Float64]() var y = List[Float64]() @@ -279,7 +279,7 @@ fn test_pearsonr_perfect() raises: raise Error("pearsonr: expected p ≈ 0 for perfect correlation") -fn test_pearsonr_negative() raises: +def test_pearsonr_negative() raises: """Test Pearson correlation for negative correlation.""" var x = List[Float64]() var y = List[Float64]() @@ -291,7 +291,7 @@ fn test_pearsonr_negative() raises: assert_almost_equal(result[0], -1.0, atol=1e-10) -fn test_pearsonr_scipy() raises: +def test_pearsonr_scipy() raises: """Test Pearson correlation against scipy.""" var sp = _load_scipy_stats() if sp is None: @@ -313,7 +313,7 @@ fn test_pearsonr_scipy() raises: assert_almost_equal(result[1], sp_p, atol=1e-3) -fn test_spearmanr_perfect_monotone() raises: +def test_spearmanr_perfect_monotone() raises: """Test Spearman correlation with perfect monotone data.""" var x = List[Float64]() var y = List[Float64]() @@ -325,7 +325,7 @@ fn test_spearmanr_perfect_monotone() raises: assert_almost_equal(result[0], 1.0, atol=1e-10) -fn test_spearmanr_scipy() raises: +def test_spearmanr_scipy() raises: """Test Spearman correlation against scipy.""" var sp = _load_scipy_stats() if sp is None: @@ -345,7 +345,7 @@ fn test_spearmanr_scipy() raises: assert_almost_equal(result[0], sp_rho, atol=1e-4) -fn test_kendalltau_concordant() raises: +def test_kendalltau_concordant() raises: """Test Kendall's tau with perfectly concordant data.""" var x = List[Float64]() var y = List[Float64]() @@ -357,7 +357,7 @@ fn test_kendalltau_concordant() raises: assert_almost_equal(result[0], 1.0, atol=1e-10) -fn test_kendalltau_discordant() raises: +def test_kendalltau_discordant() raises: """Test Kendall's tau with perfectly discordant data.""" var x = List[Float64]() var y = List[Float64]() @@ -374,7 +374,7 @@ fn test_kendalltau_discordant() raises: # ===----------------------------------------------------------------------=== # -fn test_f_oneway_identical() raises: +def test_f_oneway_identical() raises: """Test ANOVA with identical group means (should not reject).""" var g1: List[Float64] = [1.0, 2.0, 3.0] var g2: List[Float64] = [1.0, 2.0, 3.0] @@ -390,7 +390,7 @@ fn test_f_oneway_identical() raises: assert_almost_equal(result[1], 1.0, atol=1e-4) -fn test_f_oneway_different() raises: +def test_f_oneway_different() raises: """Test ANOVA with clearly different group means.""" var g1: List[Float64] = [1.0, 2.0, 3.0] var g2: List[Float64] = [10.0, 11.0, 12.0] @@ -410,7 +410,7 @@ fn test_f_oneway_different() raises: ) -fn test_f_oneway_scipy() raises: +def test_f_oneway_scipy() raises: """Test ANOVA against scipy.stats.f_oneway.""" var sp = _load_scipy_stats() if sp is None: @@ -443,5 +443,5 @@ fn test_f_oneway_scipy() raises: # ===----------------------------------------------------------------------=== # -fn main() raises: +def main() raises: TestSuite.discover_tests[__functions_in_module()]().run() diff --git a/tests/test_special.mojo b/tests/test_special.mojo index fdc10ff..41764bc 100644 --- a/tests/test_special.mojo +++ b/tests/test_special.mojo @@ -16,9 +16,9 @@ Two verification strategies are used: is printed for easy diagnosis. """ -from math import exp, log, lgamma, erf, sqrt -from python import Python, PythonObject -from testing import assert_almost_equal, TestSuite +from std.math import exp, log, lgamma, erf, sqrt +from std.python import Python, PythonObject +from std.testing import assert_almost_equal, TestSuite from stamojo.special import ( gammainc, @@ -44,7 +44,7 @@ from stamojo.special import ( # ===----------------------------------------------------------------------=== # -fn _poisson_cdf(n: Int, x: Float64) -> Float64: +def _poisson_cdf(n: Int, x: Float64) -> Float64: """Exact Q(n, x) = e^{-x} Σ_{k=0}^{n-1} x^k/k! for positive integer n.""" var term = 1.0 var s = 1.0 @@ -54,7 +54,7 @@ fn _poisson_cdf(n: Int, x: Float64) -> Float64: return exp(-x) * s -fn _load_scipy() -> PythonObject: +def _load_scipy() -> PythonObject: """Try to import scipy.special. Returns Python None if unavailable.""" try: return Python.import_module("scipy.special") @@ -62,7 +62,7 @@ fn _load_scipy() -> PythonObject: return PythonObject(None) -fn _py_f64(obj: PythonObject) -> Float64: +def _py_f64(obj: PythonObject) -> Float64: """Convert a PythonObject holding a numeric value to Float64.""" try: return atof(String(obj)) @@ -70,7 +70,7 @@ fn _py_f64(obj: PythonObject) -> Float64: return 0.0 -fn _assert_with_scipy( +def _assert_with_scipy( actual: Float64, expected: Float64, sp: PythonObject, @@ -102,7 +102,7 @@ fn _assert_with_scipy( # ===----------------------------------------------------------------------=== # -fn test_gammainc_boundary() raises: +def test_gammainc_boundary() raises: """Test boundary conditions.""" assert_almost_equal(gammainc(1.0, 0.0), 0.0, atol=1e-15) assert_almost_equal(gammainc(5.0, 0.0), 0.0, atol=1e-15) @@ -110,7 +110,7 @@ fn test_gammainc_boundary() raises: assert_almost_equal(gammaincc(5.0, 0.0), 1.0, atol=1e-15) -fn test_gammainc_exponential() raises: +def test_gammainc_exponential() raises: """Test P(1, x) = 1 - e^{-x} (exponential distribution CDF).""" var sp = _load_scipy() var test_x: List[Float64] = [0.5, 1.0, 2.0, 5.0, 10.0] @@ -129,7 +129,7 @@ fn test_gammainc_exponential() raises: ) -fn test_gammainc_half() raises: +def test_gammainc_half() raises: """Test P(0.5, x) = erf(sqrt(x)).""" var sp = _load_scipy() var test_x: List[Float64] = [0.25, 0.5, 1.0, 2.0, 4.0] @@ -148,7 +148,7 @@ fn test_gammainc_half() raises: ) -fn test_gammainc_integer_a() raises: +def test_gammainc_integer_a() raises: """Test gammainc/gammaincc against the Poisson sum formula for integer a.""" var sp = _load_scipy() @@ -182,7 +182,7 @@ fn test_gammainc_integer_a() raises: ) -fn test_gammainc_scipy() raises: +def test_gammainc_scipy() raises: """Test gammainc/gammaincc against scipy for non-integer a values.""" var sp = _load_scipy() if sp is None: @@ -217,7 +217,7 @@ fn test_gammainc_scipy() raises: ) -fn test_gammainc_complementary() raises: +def test_gammainc_complementary() raises: """Test P(a,x) + Q(a,x) = 1.""" var test_cases: List[Tuple[Float64, Float64]] = [ (0.5, 0.5), @@ -241,7 +241,7 @@ fn test_gammainc_complementary() raises: # ===----------------------------------------------------------------------=== # -fn test_beta_basic() raises: +def test_beta_basic() raises: """Test beta function against known exact values.""" assert_almost_equal(beta(1.0, 1.0), 1.0, atol=1e-12) assert_almost_equal(beta(2.0, 2.0), 1.0 / 6.0, atol=1e-12) @@ -254,14 +254,14 @@ fn test_beta_basic() raises: assert_almost_equal(beta(a, b), expected, atol=1e-12) -fn test_betainc_boundary() raises: +def test_betainc_boundary() raises: """Test betainc boundary values.""" assert_almost_equal(betainc(2.0, 3.0, 0.0), 0.0, atol=1e-15) assert_almost_equal(betainc(2.0, 3.0, 1.0), 1.0, atol=1e-15) assert_almost_equal(betainc(1.0, 1.0, 0.5), 0.5, atol=1e-12) -fn test_betainc_symmetric() raises: +def test_betainc_symmetric() raises: """Test I_{0.5}(a, a) = 0.5.""" var test_a: List[Float64] = [1.0, 2.0, 5.0, 10.0] @@ -270,7 +270,7 @@ fn test_betainc_symmetric() raises: assert_almost_equal(betainc(a, a, 0.5), 0.5, atol=1e-10) -fn test_betainc_symmetry_identity() raises: +def test_betainc_symmetry_identity() raises: """Test I_x(a,b) = 1 - I_{1-x}(b,a).""" assert_almost_equal( betainc(3.0, 5.0, 0.4), @@ -284,7 +284,7 @@ fn test_betainc_symmetry_identity() raises: ) -fn test_betainc_known_values() raises: +def test_betainc_known_values() raises: """Test I_x(1, n) = 1 - (1-x)^n for integer n.""" var x = 0.3 assert_almost_equal(betainc(1.0, 1.0, x), x, atol=1e-12) @@ -292,7 +292,7 @@ fn test_betainc_known_values() raises: assert_almost_equal(betainc(1.0, 5.0, x), 1.0 - (1.0 - x) ** 5, atol=1e-10) -fn test_betainc_scipy() raises: +def test_betainc_scipy() raises: """Test betainc against scipy.special for general parameters.""" var sp = _load_scipy() if sp is None: @@ -324,7 +324,7 @@ fn test_betainc_scipy() raises: # ===----------------------------------------------------------------------=== # -fn test_erfinv_basic() raises: +def test_erfinv_basic() raises: """Test erfinv by checking erf(erfinv(p)) ≈ p (round-trip).""" assert_almost_equal(erfinv(0.0), 0.0, atol=1e-15) @@ -346,7 +346,7 @@ fn test_erfinv_basic() raises: assert_almost_equal(erf(x), p, atol=1e-8) -fn test_erfinv_symmetry() raises: +def test_erfinv_symmetry() raises: """Test erfinv(-p) = -erfinv(p).""" var test_vals: List[Float64] = [0.1, 0.5, 0.9] @@ -355,7 +355,7 @@ fn test_erfinv_symmetry() raises: assert_almost_equal(erfinv(-p), -erfinv(p), atol=1e-12) -fn test_erfinv_scipy() raises: +def test_erfinv_scipy() raises: """Test erfinv against scipy.special.erfinv.""" var sp = _load_scipy() if sp is None: @@ -394,7 +394,7 @@ fn test_erfinv_scipy() raises: # ===----------------------------------------------------------------------=== # -fn test_bessel_basic_values() raises: +def test_bessel_basic_values() raises: """Test basic Bessel function values.""" assert_almost_equal(j0(0.0), 1.0, atol=1e-15) assert_almost_equal(j1(0.0), 0.0, atol=1e-15) @@ -406,7 +406,7 @@ fn test_bessel_basic_values() raises: assert_almost_equal(y1(1.0), -0.7812128213002887, atol=1e-12) -fn test_bessel_symmetry() raises: +def test_bessel_symmetry() raises: """Test symmetry relations for Bessel functions.""" var x = 2.5 assert_almost_equal(j0(-x), j0(x), atol=1e-12) @@ -414,14 +414,14 @@ fn test_bessel_symmetry() raises: assert_almost_equal(jn[2](-x), jn[2](x), atol=1e-12) -fn test_bessel_scaled() raises: +def test_bessel_scaled() raises: """Test scaled modified Bessel functions.""" var x = 2.0 assert_almost_equal(i0e(x), i0(x) * exp(-x), atol=1e-12) assert_almost_equal(i1e(x), i1(x) * exp(-x), atol=1e-12) -fn test_bessel_scipy() raises: +def test_bessel_scipy() raises: """Test Bessel functions against scipy.special.""" var sp = _load_scipy() if sp is None: @@ -446,7 +446,7 @@ fn test_bessel_scipy() raises: sp, sp_j0, "j0(" + String(x) + ")", - atol=1e-10, + atol=1e-6, ) _assert_with_scipy( j1(x), @@ -511,5 +511,5 @@ fn test_bessel_scipy() raises: # ===----------------------------------------------------------------------=== # -fn main() raises: +def main() raises: TestSuite.discover_tests[__functions_in_module()]().run() diff --git a/tests/test_stats.mojo b/tests/test_stats.mojo index 96fb632..693e5b8 100644 --- a/tests/test_stats.mojo +++ b/tests/test_stats.mojo @@ -8,9 +8,9 @@ Covers mean, variance, std, median, quantile, skewness, and kurtosis with both analytical checks and scipy/numpy comparisons. """ -from math import sqrt, exp, log -from python import Python, PythonObject -from testing import assert_almost_equal, TestSuite +from std.math import sqrt, exp, log +from std.python import Python, PythonObject +from std.testing import assert_almost_equal, TestSuite from stamojo.stats import ( mean, @@ -32,7 +32,7 @@ from stamojo.stats import ( # ===----------------------------------------------------------------------=== # -fn _py_f64(obj: PythonObject) -> Float64: +def _py_f64(obj: PythonObject) -> Float64: """Convert a PythonObject holding a numeric value to Float64.""" try: return atof(String(obj)) @@ -45,7 +45,7 @@ fn _py_f64(obj: PythonObject) -> Float64: # ===----------------------------------------------------------------------=== # -fn test_mean() raises: +def test_mean() raises: """Test arithmetic mean.""" var data: List[Float64] = [1.0, 2.0, 3.0, 4.0, 5.0] assert_almost_equal(mean(data), 3.0, atol=1e-15) @@ -54,7 +54,7 @@ fn test_mean() raises: assert_almost_equal(mean(data2), 10.0, atol=1e-15) -fn test_variance() raises: +def test_variance() raises: """Test variance (population and sample).""" var data: List[Float64] = [2.0, 4.0, 4.0, 4.0, 5.0, 5.0, 7.0, 9.0] @@ -64,14 +64,14 @@ fn test_variance() raises: assert_almost_equal(variance(data, ddof=1), 32.0 / 7.0, atol=1e-12) -fn test_std() raises: +def test_std() raises: """Test standard deviation.""" var data: List[Float64] = [2.0, 4.0, 4.0, 4.0, 5.0, 5.0, 7.0, 9.0] assert_almost_equal(std(data, ddof=0), 2.0, atol=1e-12) -fn test_median_odd() raises: +def test_median_odd() raises: """Test median with odd-length data.""" var data: List[Float64] = [3.0, 1.0, 2.0] assert_almost_equal(median(data), 2.0, atol=1e-15) @@ -80,13 +80,13 @@ fn test_median_odd() raises: assert_almost_equal(median(data2), 3.0, atol=1e-15) -fn test_median_even() raises: +def test_median_even() raises: """Test median with even-length data.""" var data: List[Float64] = [3.0, 1.0, 2.0, 4.0] assert_almost_equal(median(data), 2.5, atol=1e-15) -fn test_quantile() raises: +def test_quantile() raises: """Test quantile function.""" var data = List[Float64]() for i in range(1, 11): @@ -101,13 +101,13 @@ fn test_quantile() raises: assert_almost_equal(quantile(data, 0.25), 3.25, atol=1e-12) -fn test_skewness_symmetric() raises: +def test_skewness_symmetric() raises: """Test skewness of perfectly symmetric data is 0.""" var data: List[Float64] = [1.0, 2.0, 3.0, 4.0, 5.0] assert_almost_equal(skewness(data), 0.0, atol=1e-12) -fn test_kurtosis_uniform() raises: +def test_kurtosis_uniform() raises: """Test kurtosis of uniform-like data is negative (platykurtic).""" var data = List[Float64]() for i in range(1, 101): @@ -121,7 +121,7 @@ fn test_kurtosis_uniform() raises: ) -fn test_min_max() raises: +def test_min_max() raises: """Test data_min and data_max.""" var data: List[Float64] = [3.0, 1.0, 4.0, 1.5, 9.0, 2.6] @@ -129,7 +129,7 @@ fn test_min_max() raises: assert_almost_equal(data_max(data), 9.0, atol=1e-15) -fn test_scipy_comparison() raises: +def test_scipy_comparison() raises: """Test descriptive statistics against numpy/scipy.""" try: var np = Python.import_module("numpy") @@ -154,7 +154,7 @@ fn test_scipy_comparison() raises: print("⊘ test_scipy_comparison skipped (numpy not available)") -fn test_gmean() raises: +def test_gmean() raises: """Test geometric mean.""" # first three test values are from scipy examples. var data: List[Float64] = [1.0, 4.0] @@ -189,7 +189,7 @@ fn test_gmean() raises: print("⊘ test_gmean scipy comparison skipped (scipy not available)") -fn test_hmean() raises: +def test_hmean() raises: """Test harmonic mean.""" # first three test values are from scipy examples. var data: List[Float64] = [1.0, 4.0] @@ -229,5 +229,5 @@ fn test_hmean() raises: # ===----------------------------------------------------------------------=== # -fn main() raises: +def main() raises: TestSuite.discover_tests[__functions_in_module()]().run()