feat: add transplanted 1D quadrature maps, docs, tests, and QBX example by xywei · Pull Request #159 · inducer/modepy

xywei · 2026-02-24T02:24:25Z

Summary

Add modepy.quadrature.transplanted with transplanted 1D quadrature support:
- map functions: identity, generic sausage_d{odd}, strip, and kte / kosloff_tal_ezer
- dispatcher: map_trefethen_transplant
- quadrature classes: Transplanted1DQuadrature and TransplantedLegendreGaussQuadrature
Export transplanted quadrature classes from package init modules.
Expand quadrature docs with dedicated transplanted sections:
- map-by-map subsections and usage guidance
- parameter notes (strip_rho, kte_rho, kte_alpha)
- references for Hale–Trefethen (2008) and Kosloff–Tal-Ezer (1993)
Add a 2D QBX comparison example:
- examples/plot-qbx-transplanted-vs-gauss.py
- compares Gauss, KTE, strip, sausage d5/d9 on the circle with frozen centers/targets
- sample plot:
Add transplanted quadrature tests:
- map-name dispatch and direct-map consistency
- strip-map endpoint rejection
- KTE parameter validation and alias coverage
- generic sausage degree parsing/validation

Validation

python examples/plot-qbx-transplanted-vs-gauss.py
pytest modepy/test/test_quadrature.py -k transplanted

inducer · 2026-02-24T15:23:00Z

Thanks! Could you look at those linter failures? The biggest one is probably adding types.

inducer · 2026-02-24T15:23:16Z

(I can help if there's an issue.)

inducer · 2026-02-24T15:23:32Z

cc @ShawnL00

Copilot

Pull request overview

Adds transplanted 1D quadrature rules/maps (Hale–Trefethen and Kosloff–Tal-Ezer) to modepy, with accompanying docs, tests, and a QBX comparison example.

Changes:

Introduces modepy.quadrature.transplanted with transplant maps, a dispatcher, and transplanted quadrature classes.
Exports transplanted quadrature classes through package init modules (modepy.quadrature and top-level modepy).
Adds docs + tests for map dispatch/validation and includes a 2D QBX comparison example script.

Reviewed changes

Copilot reviewed 6 out of 6 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
`modepy/quadrature/transplanted.py`	New transplanted-map implementations and transplanted quadrature classes.
`modepy/quadrature/__init__.py`	Re-exports transplanted quadrature classes from the quadrature package.
`modepy/__init__.py`	Exposes transplanted quadrature classes at the top-level `modepy` API.
`modepy/test/test_quadrature.py`	Adds unit tests for transplanted quadrature mapping/validation behavior.
`examples/plot-qbx-transplanted-vs-gauss.py`	New QBX comparison example for Gauss vs transplanted rules.
`doc/quadrature.rst`	Adds documentation section describing transplanted quadrature usage and references.

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Copilot · 2026-02-24T17:21:44Z

examples/plot-qbx-transplanted-vs-gauss.py

+OUT = "/tmp/qbx-transplanted-vs-gauss-2d.png"
+


The example writes output to a hard-coded /tmp/... path, which will fail on non-POSIX platforms (e.g. Windows) and can be surprising for users.

Consider using tempfile.gettempdir()/pathlib.Path, saving relative to the current working directory, or making the output path a CLI argument.

Copilot · 2026-02-24T17:21:44Z

modepy/quadrature/transplanted.py

+        mapped_nodes, jacobian = map_trefethen_transplant(
+            nodes_1d,
+            map_name=map_name,
+            strip_rho=strip_rho,
+            kte_rho=kte_rho,
+            kte_alpha=kte_alpha,
+        )
+        mapped_weights = quadrature.weights * jacobian
+
+        if force_dim_axis:
+            mapped_nodes = np.reshape(mapped_nodes, (1, mapped_nodes.shape[0]))
+
+        super().__init__(mapped_nodes, mapped_weights)
+


Transplanted1DQuadrature drops the base rule's exact_to information even when map_name="identity" (and similarly for identity-equivalent maps like sausage_d1). That makes q.exact_to raise AttributeError despite the transplanted rule being identical to the base rule in that case.

Consider preserving exact_to when the map is exactly the identity, while leaving it unset for non-identity maps where polynomial exactness in x is generally not preserved.

modepy/quadrature/transplanted.py

alexfikl

Very nifty! 😁

I took a quick look and left some nitpicks and questions.

alexfikl · 2026-02-24T18:42:24Z

doc/quadrature.rst

    :members:
    :show-inheritance:

+Transplanted quadrature in one dimension


I don't feel particularly strongly about this, but I haven't heard the term "transplanted" used very often, so it sounds a bit unintuitive to me. Maybe call this mapped or conformal mapped? Maybe just transformed? Although we already have a Transformed1DQuadrature that just does linear transformations.

For context, I'm mostly familiar with stuff like this from Kress' Numerical Analysis, e.g. Chapter 9.6 and some of the cited references, so it might just be a different tradition.

(Same for other places where the term is used, depending on what's decided.)

alexfikl · 2026-02-24T18:47:41Z

doc/quadrature.rst

+
+* N. Hale and L. N. Trefethen, *New Quadrature Formulas from Conformal
+  Maps*, ``SIAM Journal on Numerical Analysis`` 46(2), 930-948 (2008),
+  doi:10.1137/07068607X.


Suggested change

doi:10.1137/07068607X.

`doi:10.1137/07068607X <https://doi.org/10.1137/07068607X>`__.

? Same in other places. Also as far as formatting goes, it looks a bit weird to put the journal in code mode (?).

alexfikl · 2026-02-24T18:48:13Z

doc/quadrature.rst

+  Maps*, ``SIAM Journal on Numerical Analysis`` 46(2), 930-948 (2008),
+  doi:10.1137/07068607X.
+* D. Kosloff and H. Tal-Ezer, *A Modified Chebyshev Pseudospectral Method
+  with an O(N^{-1}) Time Step Restriction*,


Suggested change

with an O(N^{-1}) Time Step Restriction*,

with an :math:`O(N^{-1})` Time Step Restriction*,

? I haven't actually checked how this renders.

alexfikl · 2026-02-24T18:50:29Z

examples/plot-qbx-transplanted-vs-gauss.py

@@ -0,0 +1,292 @@
+from __future__ import annotations


This example is pretty awesome, but I'm wondering if it's too big for modepy? Maybe better to just put it in pytential once this gets in?

For modepy, I would appreciate just a little example from the paper, e.g. Figure 7.1 or similar (doesn't need to be all those functions).

alexfikl · 2026-02-24T18:53:19Z

modepy/quadrature/transplanted.py

+Transplanted quadrature applies a smooth map :math:`x=g(s)` to an existing
+one-dimensional rule on :math:`[-1,1]`.
+
+Given base nodes/weights :math:`(s_i, w_i)`, the transplanted rule is


Suggested change

Given base nodes/weights :math:`(s_i, w_i)`, the transplanted rule is

Given base nodes/weights :math:`(s_i, w_i')`, the transplanted rule is

? (add a little prime to w or use \omega? to avoid confusion)

alexfikl · 2026-02-24T19:10:50Z

modepy/quadrature/transplanted.py

+    sausage_degree = _sausage_degree_from_map_name(map_name)
+    if sausage_degree is not None:
+        return map_sausage(s, sausage_degree)


Hm, would it be clearer to just add a sausage_degree parameter and let the map name be sausage? Similar to how the other maps have their kte_rho etc parameters in here.

It avoids the need to parse the int from the name at least.

alexfikl · 2026-02-24T19:12:19Z

modepy/quadrature/transplanted.py

+    if map_name == "strip":
+        return map_strip(s, rho=strip_rho)


I don't imagine we'll be calling these in a hot loop, so the order probably doesn't matter, but would it make sense to put the strip first? My understanding is that it's the latest and the greatest, so likely to be the most used in practice.

alexfikl · 2026-02-24T19:13:02Z

modepy/quadrature/transplanted.py

+    Reference:
+        N. Hale and L. N. Trefethen, "New Quadrature Formulas from
+        Conformal Maps," SIAM Journal on Numerical Analysis 46(2),
+        930-948 (2008),
+        doi:10.1137/07068607X.
+
+        D. Kosloff and H. Tal-Ezer, "A Modified Chebyshev Pseudospectral
+        Method with an O(N^{-1}) Time Step Restriction," Journal of
+        Computational Physics 104(2), 457-469 (1993),
+        doi:10.1006/jcph.1993.1044.


Same, just put these references in a central place.

alexfikl · 2026-02-24T19:17:40Z

modepy/quadrature/transplanted.py

+    )
+
+
+class Transplanted1DQuadrature(Quadrature):


Does this need to be a separate quadrature class? I would expect map_trefethen_transplant (or a small wrapper) to just take a Quadrature and return a Quadrature with custom nodes + weights?

I don't feel particularly strongly about that though, since it's mostly all the same. I guess if we have Transformed1DQuadrature, this makes sense too.

alexfikl · 2026-02-24T19:19:42Z

modepy/quadrature/__init__.py

+from modepy.quadrature.transplanted import (
+    Transplanted1DQuadrature as Transplanted1DQuadrature,
+    TransplantedLegendreGaussQuadrature as TransplantedLegendreGaussQuadrature,
+)


Should be fine to let these just be imported from quadrature.transplanted? The other quadrature rules also just have a shortcut in modepy.__init__.

feat: add transplanted 1d quadrature

9e132f4

xywei added 4 commits February 24, 2026 09:58

fix: unblock CI

f9884a8

fix: less strict checking for the qbx example script

5f2d7a9

fix: add typing to transplanted.py

3efe064

fix: add typing to test_quadrature.py

0b90d2f

inducer requested a review from Copilot February 24, 2026 17:15

Copilot started reviewing on behalf of inducer February 24, 2026 17:16 View session

Copilot AI reviewed Feb 24, 2026

View reviewed changes

fix: address copilot reviews

dc4f215

alexfikl reviewed Feb 24, 2026

View reviewed changes

	doi:10.1137/07068607X.
	`doi:10.1137/07068607X <https://doi.org/10.1137/07068607X>`__.

	with an O(N^{-1}) Time Step Restriction*,
	with an :math:`O(N^{-1})` Time Step Restriction*,

	Given base nodes/weights :math:`(s_i, w_i)`, the transplanted rule is
	Given base nodes/weights :math:`(s_i, w_i')`, the transplanted rule is

		OUT = "/tmp/qbx-transplanted-vs-gauss-2d.png"

		)


		class Transplanted1DQuadrature(Quadrature):

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xywei commented Feb 24, 2026

Summary

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inducer commented Feb 24, 2026

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alexfikl Feb 24, 2026 • edited Loading Uh oh! There was an error while loading. Please reload this page.

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alexfikl Feb 24, 2026 •

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