ENH Add N-D fitting and evaluation methods to the chebyshev.py and polynomial.py library #6071

pbrod · Jul 13, 2015

Currently there are no functions in chebyshev.py/ polynomial.py that do

N-dimensional fitting for N>1
N-dimensional evaluation for N>3
Construct Vandermonde matrix for N>3

This submission is a first implementation to fill the above mentioned gap.
Functions added to chebyshev.py and polynomial.py are:
chebvalnd, chebgridnd, chebfitnd, chebfitfunc, chebvandernd
polyvalnd, polygridnd, polyfitnd, polyfitfunc, polyvandernd
and supporting tests

Examples on use

>>> import numpy as np
>>> import numpy.polynomial.chebyshev as cheb
>>> import matplotlib.pyplot as plt
>>> n = 51
>>> xorder, yorder = n-1, n-1
>>> x = cheb.chebpts1(n)
>>> xgrid, ygrid = np.meshgrid(x, x)
>>> def f(x, y): return np.exp(-x**2-6*y**2)
>>> zgrid = f(xgrid, ygrid)
>>> dcoeff2 = cheb.chebfitnd((xgrid, ygrid), zgrid, [xorder,yorder])
>>> dcoeff = cheb.chebfitfunc(f, n=(xorder+1,yorder+1))
>>> np.allclose(dcoeff2, dcoeff)
True

Visualize the significant coefficients

>>> plt.figure()
>>> plt.spy(np.abs(dcoeff)>1e-13)
>>> plt.title('Coefficients > 10^-13')

Evaluate on finer grid

>>> xi = np.linspace(-1, 1, 151)
>>> Xi,Yi = np.meshgrid(xi, xi)
>>> Zi = f(Xi, Yi)

Compute residuals

>>> zzi = cheb.chebvalnd(dcoeff, Xi, Yi)
>>> devi = Zi - zzi

>>> zz = cheb.chebvalnd(dcoeff, xgrid, ygrid)
>>> dev = zgrid - zz

and plot them

>>> plt.figure() 
>>> plt.contourf(xgrid, ygrid, np.abs(dev))
>>> plt.colorbar()
>>> plt.title('Error at the chebfitnd-points')

>>> plt.figure()
>>> plt.contourf(Xi, Yi, np.abs(devi))
>>> plt.colorbar()
>>> plt.title('Error on a fine grid')
>>> plt.show('hold')

charris · Jul 18, 2015

You should squash the commits and follow the guidelines in doc/source/dev/gitwash/development_workflow.rst for the messages. Also, doc/source/reference/routines.polynomials.chebyshev.rst will need an update before this is merged, and perhaps the doc/release/1.10.0-notes.rst also if this is merged before the 1.10.0 branch.

charris · Jul 18, 2015

numpy/polynomial/chebyshev.py

@@ -1411,6 +1412,111 @@ def chebgrid3d(x, y, z, c):
    return c



Need to add the new functions to __all__.

And also in the module documentation.

Ok. This is done. I have updated the files to according to your comments.

charris · Jul 18, 2015

I like this in general. The tests are a bit skimpy and some of my style comments apply more generally. Once this is settled, it should be extended to the remaining polynomials, although power series will be a bit of an exception.

I've thought a bit about making classes for some of this similar to the Polynomial etc. classes but with fewer features. Two other generalization that might be useful in practice are vector valued functions and gradients and Jacobians. If you have any thoughts along those lines I'd like to hear them.

charris · Jul 20, 2015

I'm curious if you actually have a use case for the > 3d case?

charris · Oct 1, 2015

The second commit should be a bit more specific and begin with DOC:, or you could just squash it into the first...

Now begins the drudgery. We try to keep all 6 polynomials in sync, so functions added to one also need to be added to the remaining 5 and tested. Yep, it's a PITA ;)

charris · Oct 1, 2015

If this goes in, it will also need a mention in doc/release/1.11.0-notes.rst.

charris · Oct 1, 2015

numpy/polynomial/chebyshev.py

+    If `c` has fewer than N dimensions, ones are implicitly appended to its
+    shape to make it N-D. The shape of the result will be c.shape[3:] +
+    x1.shape.
+


Needs .. versionadded:: 1.11.0 here, followed by a blank line.

Grep for other examples.

pbrod · Oct 1, 2015

Added .. versionadded:: 1.11.0. and updated doc/release/1.11.0-notes.rst

seberg · Oct 1, 2015

@pbrod, I think you have to update your master and rebase, it seems to me you created a new 1.11 release notes file. This already exists.

pbrod · Oct 1, 2015

Ok. Thanks.

Added: chebvalnd, chebgridnd, chebfitnd, chebfitfunc, chebvandernd polvalnd, polygridnd, polyfitnd, polyfitfunc, polyvandernd Also added supporting tests

homu · Nov 16, 2015

☔ The latest upstream changes (presumably #6688) made this pull request unmergeable. Please resolve the merge conflicts.

homu · Jun 12, 2016

☔ The latest upstream changes (presumably #7735) made this pull request unmergeable. Please resolve the merge conflicts.

woodscn · Sep 22, 2016

For what it's worth, I was just thinking about trying to implement something like this. I'm also interested in evaluation for N>3, i.e. x,y,z,t; or state spaces, etc.

What is the current status of this PR?

charris · Sep 22, 2016

IIRC, it was in decent shape. I was thinking of taking a further look at it in the next few days.

woodscn · Sep 22, 2016

Looking at this more closely, I'm not sure if it does what I'm looking for. Essentially, I'm after something like a MultiVariatePolynomial helper class, with things like derivatives, integrals, +, *, etc.

charris · Sep 25, 2018

@pbrod This is old but I still think this is useful. Want to pursue this?

charris · Sep 25, 2018

@woodscn I agree that that would be useful. If you are motivated in that direction you may want to put together a PR.

Qiyu8 · Jun 8, 2020

@pbrod Are you still working on this? looks valuable if you can solve the confict 😄

rossbar · Jun 8, 2020

There is another attempt at expanding polynomial fitting to ND in #14151

scratchmex · Dec 2, 2021

ping @pbrod. I think this is very valuable. Do you have any opinion or comments about the difference between this and #14151 as mentioned by rossbar? To not repeat efforts

pbrod · Dec 3, 2021

I am closing this as #14151 does the same and more.

Currently there are no functions in chebyshev.py that do N-dimensional fitting for N>1 This submission is a attempt to fill the above mentioned gap and complements the efforts in numpy#14151. The multidimensional interpolation method implemented here uses the 1D Discrete Cosine Transform (DCT) instead of the vandermonde method. This is a reimplementation of the chebfitfunc function found in numpy#6071. The accuracy of the new interpolation method is better than the old one especially for polynomials of high degrees. Also added domain as input to chebinterpolate in order to interpolate the function over any input domain. Added test_2d_approximation for testing interpolation of a 2D function. Replaced all references to the missing chebfromfunction with chebinterpolate.

Currently there are no functions in chebyshev.py that do N-dimensional fitting for N>1 This submission is a attempt to fill the above mentioned gap and complements the efforts in numpy#14151. The multidimensional interpolation method implemented here uses the 1D Discrete Cosine Transform (DCT) instead of the vandermonde method. This is a reimplementation of the chebfitfunc function found in numpy#6071. The accuracy of the new interpolation method is better than the old one especially for polynomials of high degrees. Also added domain as input to chebinterpolate in order to interpolate the function over any input domain. Added test_2d_approximation for testing interpolation of a 2D function. Replaced all references to the missing chebfromfunction with chebinterpolate. Made doctest of chebinterpolate more robust.

charris reviewed Jul 18, 2015
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rgommers added 01 - Enhancement component: numpy.polynomial labels Jul 26, 2015

pbrod force-pushed the ENH_chebyshev branch 3 times, most recently from 105c7e7 to 125cbcc Compare September 30, 2015 14:04

charris mentioned this pull request Oct 1, 2015

ENH: Allow specification of terms to fit in polynomial fitting functions #6360

Merged

charris reviewed Oct 1, 2015
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pbrod force-pushed the ENH_chebyshev branch 4 times, most recently from 2caf7d5 to 0bf9fb3 Compare October 1, 2015 09:37

pbrod force-pushed the ENH_chebyshev branch 2 times, most recently from f7b3b43 to a4ad7b5 Compare October 1, 2015 14:29

pbrod force-pushed the ENH_chebyshev branch from a4ad7b5 to 0c23ad2 Compare October 1, 2015 15:22

ENH: Added N-D fitting and evaluation methods:

f195ee8

Added: chebvalnd, chebgridnd, chebfitnd, chebfitfunc, chebvandernd polvalnd, polygridnd, polyfitnd, polyfitfunc, polyvandernd Also added supporting tests

pbrod force-pushed the ENH_chebyshev branch from 0c23ad2 to f195ee8 Compare October 1, 2015 15:31

pbrod changed the title ~~ENH Add N-D fitting and evaluation methods to the chebyshev.py library~~ ENH Add N-D fitting and evaluation methods to the chebyshev.py and polynomial.py library Oct 1, 2015

charris mentioned this pull request Jun 9, 2017

ENH: add interpolation API for all polynomial classes #9198

Closed

charris added the 25 - WIP label Sep 25, 2018

charris mentioned this pull request Mar 3, 2019

MAINT: deduplicate fromroots in np.polynomial #13078

Merged

Qiyu8 added the 61 - Stale label Jun 8, 2020

Base automatically changed from master to main March 4, 2021 02:03

seberg requested a review from charris September 8, 2021 16:36

pbrod closed this Dec 3, 2021

pbrod mentioned this pull request Dec 7, 2021

ENH: Extended chebinterpolate to interpolate a multidimensional function #20529

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ENH Add N-D fitting and evaluation methods to the chebyshev.py and polynomial.py library #6071

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pbrod commented Jul 13, 2015

Examples on use

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