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:triangular_ruler: Orthogonal polynomials in all shapes and sizes.

python mathematics engineering physics chemistry quadrature polynomials zernike-polynomials legendre-polynomials chebyshev-polynomials

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orthopy's Issues

unify standardizations in triangle orth

ball

Section 5.1 in

Orthogonal polynomials of several variables
Y. Xu, ‎2017,
https://arxiv.org/pdf/1701.02709.pdf.

Implement Stieltjes procedure

Described by, e.g., Gautschi in On generating orthogonal polynomials.

For higher-dimensional polynomials, the fitting data structure for each level would be a numpy.array of shape (n, n, ...), but only the lower (or upper) triangle of (n,n) is used. Perhaps even more fitting would be to address the entries in "barycentric" coordinates, such that the indices sum up to L. Check with the product scheme and, perhaps, ndim.

implement (modified) Chebyshev algo

See, e.g., Gautschi's "On orthogonal polynomials".

product scheme for enr

compute linear combination of polynomials efficiently (like clenshaw)

The Clenshaw algorithm allows the efficient computation of linear combination of recurrence-scheme polynomials. It'd be nice if this could be extended to all of the polynomials classes in orthopy.

(Suggestion by Rob Kirby.)

No setup.py

setup.py was removed in a recent commit. However, this makes it quite cumbersome to install the package by downloading the package and doing it manually (which is what I am doing).

I.e.

Download from here
Extract
Do python setup.py install would fail.
Then I found out that you are doing: python3 -m pep517.build --source --binary .

While pep517 may have gotten traction I would hope that you would re-enable the setup.py since it is quite convenient until pep517 has stabilized (the pep517.build documentation clearly states that this is not the final placement).

If you want a minimal setup.py you could do with:

#!/usr/bin/env python
from setuptools import setup

setup(use_scm_version=True)

and then amend your setup.cfg with

setup_requires =
    setuptools >= 41.2
    setuptools_scm

The reason is that I can't figure out how to customize --prefix with the pep517 command. And this is really necessary when trying to install in non-standard locations.

Basically I cannot do:

python3 -m pep517.build --source . --prefix=<>

Do you know of any other way?

PS. This issue would also apply to quadpy ;)

fix hermite polynomials

The scaling (monic, classical, normal) is orthogonal on the standardization (probabilist, physicist).

allow mpmath computation of classical Gaussian schemes

collect explicit recurrence coefficients for a number of weight functions

Aim to make Stroud/Secrest's book of Gaussian tables obsolete.

unify sympy/numpy computation

See bugs

Generate recursion coefficients from points, weights

For generating the recursion coefficients from the points and weights, refer to

Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules

and the reference

A survey of matrix inverse eigenvalue problems by Boley and Golub.

The latter describes one method (3.2. Method 2 – orthogonal reduction) that should be rather easy to implement once scipy/scipy#7775 has been resolved.

separate associated legendre and spherical harmonics

The trees have the same algrebraic structure, can be shared in tools.

tetrahedra

Singularity-free evaluation of collapsed-coordinate orthogonal polynomials, Robert C. Kirby, Texas Tech University
https://cpb-us-w2.wpmucdn.com/sites.baylor.edu/dist/6/32/files/2015/01/dubrec-1dzeylu.pdf

All versions except 0.9.6 removed from pypi

Is this expected behavior from PYPI? We were using an older version of orthopy and we can no longer install it via pip.

Hard dependency on matplotlib / tk?

It would be good if orthopy was usable in environments where matplotlib and/or tk is not installed. Currently it will attempt to import matplotlib, which attempts to set up the tkagg backend, failing to do so because I'm using a Python that was not compiled with tk. It seems a little counterintuitive that I need to have a GUI library compiled with Python for generating quadrature rules (via quadpy).

In the meantime I've had to lift the parts I need out of quadpy into my own modules. This is fine but not ideal. Please consider making the dependency on matplotlib optional.

plot function on sphere

Some tests are not passing (unexpected keyword argument 'colorspace')

Hi, from last friday the test were passing, but today when install I have this message. Thanks in advance for support. This is the full log.

===================================================================================== FAILURES ======================================================================================
_________________________________________________________________________________ code block check __________________________________________________________________________________
line 246, line 246:

import orthopy

orthopy.u3.write_tree("u3.vtk", 5, "quantum mechanic")


get_srgb1() got an unexpected keyword argument 'colorspace'
_________________________________________________________________________________ test_write_single _________________________________________________________________________________

n = 5, r = 3

    def test_write_single(n=5, r=3):
>       orthopy.u3.write_single(f"sph{n}{r}.vtk", n, r, "quantum mechanic")

tests/test_u3.py:142: 
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

filename = 'sph53.vtk', n = 5, r = 3, scaling = 'quantum mechanic', res = 20

    def write_single(filename, n, r, scaling, res=20):
        """This function creates a sphere mesh with "srgb1" values. Can be views in ParaView
        by disabling "Map Scalars".
        """
        import cplot
        import meshio
        import meshzoo
    
        points, cells = meshzoo.icosa_sphere(res)
    
        evaluator = EvalCartesian(points.T, scaling, complex_valued=True)
        vals = next(itertools.islice(evaluator, n, None))[r]
    
>       srgb1_vals = cplot.get_srgb1(vals, colorspace="cam16")
E       TypeError: get_srgb1() got an unexpected keyword argument 'colorspace'

tmp_install/usr/lib/python3.10/site-packages/orthopy/u3/tools.py:21: TypeError
__________________________________________________________________________________ test_write_tree __________________________________________________________________________________

n = 2

    def test_write_tree(n=2):
>       orthopy.u3.write_tree(f"sph{n}.vtk", n, "quantum mechanic")

tests/test_u3.py:146: 
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

filename = 'sph2.vtk', n = 2, scaling = 'quantum mechanic', res = 20

    def write_tree(filename, n, scaling, res=20):
        import cplot
        import meshio
        import meshzoo
    
        points, cells = meshzoo.icosa_sphere(res)
    
        evaluator = EvalCartesian(points.T, scaling, complex_valued=True)
        meshes = []
        for L, level in enumerate(itertools.islice(evaluator, n)):
            for k, vals in enumerate(level):
>               srgb1_vals = cplot.get_srgb1(vals, colorspace="cam16")
E               TypeError: get_srgb1() got an unexpected keyword argument 'colorspace'

tmp_install/usr/lib/python3.10/site-packages/orthopy/u3/tools.py:39: TypeError
================================================================================= warnings summary ==================================================================================
tests/test_cn.py::test_show_tree[2]
tests/test_cn.py::test_show_tree[2]
  /tmp/makepkg/python-orthopy/src/orthopy-0.9.5/tmp_install/usr/lib/python3.10/site-packages/orthopy/cn/tools.py:73: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
    plt.colorbar()

tests/test_enr2.py::test_show_tree[2]
tests/test_enr2.py::test_show_tree[2]
  /tmp/makepkg/python-orthopy/src/orthopy-0.9.5/tmp_install/usr/lib/python3.10/site-packages/orthopy/enr2/tools.py:80: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
    plt.colorbar()

tests/test_t2.py::test_show_tree
tests/test_t2.py::test_show_tree
  /tmp/makepkg/python-orthopy/src/orthopy-0.9.5/tmp_install/usr/lib/python3.10/site-packages/orthopy/t2/tools.py:112: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
    plt.colorbar()

tests/test_s2/test_xu.py::test_show[degrees0]
tests/test_s2/test_xu.py::test_show[degrees0]
tests/test_s2/test_zernike.py::test_show[degrees0]
tests/test_s2/test_zernike2.py::test_show[degrees0]
  /tmp/makepkg/python-orthopy/src/orthopy-0.9.5/tmp_install/usr/lib/python3.10/site-packages/orthopy/s2/tools.py:32: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
    plt.colorbar()

tests/test_s2/test_xu.py::test_show_tree[2]
tests/test_s2/test_xu.py::test_show_tree[2]
tests/test_s2/test_zernike.py::test_show_tree[2]
tests/test_s2/test_zernike.py::test_show_tree[2]
tests/test_s2/test_zernike2.py::test_show_tree[2]
tests/test_s2/test_zernike2.py::test_show_tree[2]
  /tmp/makepkg/python-orthopy/src/orthopy-0.9.5/tmp_install/usr/lib/python3.10/site-packages/orthopy/s2/tools.py:108: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
    plt.colorbar()

-- Docs: https://docs.pytest.org/en/stable/how-to/capture-warnings.html
============================================================================== short test summary info ==============================================================================
FAILED README.md::line 246
FAILED tests/test_u3.py::test_write_single - TypeError: get_srgb1() got an unexpected keyword argument 'colorspace'
FAILED tests/test_u3.py::test_write_tree - TypeError: get_srgb1() got an unexpected keyword argument 'colorspace'
========================================================= 3 failed, 237 passed, 10 skipped, 16 warnings in 65.79s (0:01:05) =========================================================

make symbolic="auto" the default for Eval

Understanding outputs of the functions

I have a doubt about the inputs/outputs of the software. When I write:

x = np.linspace(-1,1,101)
evaluator = orthopy.c1.legendre.Eval(x, "classical")
for _ in range(5):
     print(next(evaluator))

what I get is the function legendre evaluated at x.
However, when I write:

x = [0.1, -0.3]
evaluator = orthopy.s2.zernike.Eval(x, "normal")
for _ in range(5):
     print(next(evaluator))

What am I getting here?

provide iterators for all domains

inverse eigenvalue problem

More details by Meurant (http://www.math.hkbu.edu.hk/ICM/LecturesAndSeminars/08OctMaterials/2/Slide2.pdf).

show depends on matplotx

import orthopy

orthopy.c1.jacobi.show(5, "normal", 0.0, 0.0)

gives,
ModuleNotFoundError: No module named 'matplotx'

matplotx is not installed by default when installing orthopy.

Laguerre polynomials of several variables.

Section 5.4 in

Orthogonal polynomials of several variables
Y. Xu, ‎2017,
https://arxiv.org/pdf/1701.02709.pdf.

use svg images in readme (as far as possible)

rename `||p**2||=1|` to `normal`

remove line_evaluate

vectorize Rational

This will allow for faster computation in numpy. Depends on sympy/sympy#13618.

plot "trees" in the readme

simplify norm2 in triangle recurrence

See https://groups.google.com/forum/?utm_medium=email&utm_source=footer#!topic/sympy/J2pjEQZnSsc.

assert orthonormality in tests

Zernike polynomials

https://en.wikipedia.org/wiki/Zernike_polynomials

faster tests

Explicit polynomial integration helps, see, e.g., the e1r tests.

rename standardization to scaling?

Zernike cosine polynomials should have switched sign

The polynomials generated by orthopy are not in accordance to the formal definition of the zernikes.

For example, $Z_{1}^{1} $ should be $2 \rho \cos \phi $ but the orthopy generated polynomial looks like $-2\rho \cos \phi $.

This is an issue with all polynomials with azimuthal degree $m > 0$. Sadly, I do not fully understand the source code, so I can not easily spot the mistake.

An easy fix could be multiplying every output polynomial where $m > 0 $ by $-1 $ where $m $ can be calculated from the OSA/ANSI index $j $ (which I believe to be self.L in the zernike.py) by

n = int(sqrt(2*j+1) - 0.5)
m = int(2*j - n*(n+2))