ENH: Add polynomial features and extra basis functions to scipy.interpolate.rbf #7157

evanlimanto · 2017-03-11T09:59:16Z

See section 2.1 of this paper.

evanlimanto · 2017-03-11T10:03:23Z

Surface plot of sample data with degree = 2:

import numpy as np
from scipy.interpolate import Rbf
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from matplotlib import cm

fig = plt.figure()
ax = fig.gca(projection='3d')
X, Y, Z = axes3d.get_test_data(0.05)
X, Y, Z = X[60:100], Y[60:100], Z[60:100]
ax.plot_surface(X, Y, Z, rstride=8, cstride=8, alpha=0.3, color='red')

x = np.linspace(np.min(X), np.max(X), 30)
y = np.linspace(np.min(Y), np.max(Y), 30)
xv, yv = np.meshgrid(x, y)
rbfi = Rbf(X, Y, Z, degree=2)
di = rbfi(xv.flatten(), yv.flatten())
ax.plot_surface(xv, yv, di.reshape(xv.shape[0], xv.shape[1]), rstride=8, cstride=8, alpha=0.5, cmap=cm.coolwarm)
plt.show()

ev-br · 2017-03-12T21:57:02Z

This now needs a rebase, as it crossed with gh-7161.

You can either do a rebase yourself, or grab the rebased branch: https://github.com/ev-br/scipy/commits/pr/7157

ev-br · 2017-03-12T22:07:44Z

scipy/interpolate/rbf.py

        self.A = self._init_function(r) - np.eye(self.N)*self.smooth
-        self.nodes = linalg.solve(self.A, self.di)
+        self.A_aug = self._generate_augmented_matrix(self.xi.T)


This should not be stored on the instance: the matrix is only used once and can be large. If really needs be, it can be made into a property, or just discarded.

ev-br · 2017-03-12T22:19:34Z

scipy/interpolate/rbf.py

+        combs = combinations(n_dims, deg)
+        for i, c in enumerate(combs):
+            POLY[:, i] = xi[:, c].prod(axis=1)
+        return bmat([[self.A, POLY], [POLY.T, None]], format='csr')


Style nitpick: This function is a bit confusing: it receives xi as an argument, and is being called with self.xi; it also uses self.degree which it reads off the instance; it attaches self.n_features but returns self.A_aug. This could probably be combined into def _compute_nodes(self): which computes self.nodes and discards all local variables, e.g. A_aug.

Fixed all the above.

ev-br · 2017-03-12T22:19:54Z

scipy/interpolate/rbf.py

+        n_points, n_dims = xi.shape
+        # closed-form formula for number of polynomial coefficients
+        deg = self.degree if self.degree else -1
+        self.n_features = int(comb(deg + n_dims, n_dims))


What are features?

features are the generated polynomial coefficients. Updated the variable name and description.

ev-br · 2017-03-12T22:23:16Z

It would be helpful to explain a bit what is going on here. Also references should be added to the docstring.

It would also be helpful to explain a connection to the suggestions in
#4523 (comment).

ev-br · 2017-03-17T20:28:20Z

Oops, something went wrong on the git side. Don't merge master, please rebase on master instead, yhen force-push (the latter is key). Do you need help untangling this?

evanlimanto · 2017-03-17T20:40:12Z

Yeah @ev-br trying to fix this now, but how do I rebase all the previous commits and keep my latest ones?

ev-br · 2017-03-17T20:55:23Z

You squashed your work into this single commit, dbb346c
Then it's probably easiest to cherry-pick it into a new branch and force-push:

$ git co master
$ git co new-branch
$ git cherry-pick dbb346c56d43c9e949d0b24b52e735e61777cca8
$ git push origin new-branch:rbf-polynomials --force     # assuming your scipy fork is named "origin"

This will replace the the current contents of this PR by that single commit.

evanlimanto · 2017-03-17T20:57:45Z

Done, thanks! Just couldn't figure out the new-branch:rbf-polynomials part.

stefanv · 2017-03-23T06:41:38Z

scipy/interpolate/rbf.py


        If callable, then it must take 2 arguments (self, r).  The epsilon
        parameter will be available as self.epsilon.  Other keyword
        arguments passed in will be available as well.
-
+    degree : integer, optional


This description needs to be clarified.

Also "adjustable constant" reads a bit oddly.

stefanv · 2017-03-23T06:42:18Z

scipy/interpolate/rbf.py

    epsilon : float, optional
        Adjustable constant for gaussian or multiquadrics functions
        - defaults to approximate average distance between nodes (which is
        a good start).
+    m : float, optional
+        Adjustable constant for polyharmonic splines.


Again, what is m, how do you adjust it? Guidelines here would be helpful to the user.

I see how this works now. Perhaps something like "A parameter used to construct polyharmonic splines. Large m yields ... Typical values lie between ... and ..."

Updated. I specified that m refers to the degree of the polyharmonic spline.

stefanv · 2017-03-23T06:42:35Z

scipy/interpolate/rbf.py

+    m : float, optional
+        Adjustable constant for polyharmonic splines.
+    p : float, optional
+        Adjustable constant for bessel functions.


Same as above.

stefanv · 2017-03-23T06:45:45Z

scipy/interpolate/rbf.py

+    def _compute_nodes(self):
+        """
+        First, we generate all possible combinations of the input over all
+        dimensions for the polynomial features. Then, these are stacked to


"polynomial features"?

Changed to powers of input dimensions.

stefanv · 2017-03-23T06:46:18Z

scipy/interpolate/rbf.py

+          |C.T| 0 |
+          ---------
+
+        where C is a matrix of size (n, num_coeffs) generated from the


More detail is needed to understand what happens here

stefanv · 2017-11-02T04:57:36Z

@treverhines I just came across your RBF work at https://github.com/treverhines/RBF

I was wondering if you could take a look at this pull-request, and consider whether we could work together to include your existing work into SciPy?

Thanks!

ev-br · 2022-04-29T20:44:11Z

@evanlimanto very sorry for this PR slipping under the radar. I don't think we will be merging this in the end, now that the RBFInterpolator is in. Your work is much appreciated regardless!

What is the status here, is there something from this PR to be ported to the RBFInterpolator interface? @treverhines @segasai @stefanv @evanlimanto

stefanv · 2022-04-30T01:26:41Z

It would be good to ask @treverhines that question. (Woops, see you already did :) ).

ev-br · 2022-06-23T21:48:04Z

Ok, let's close this. If there's something to port to the current RBF framework, we can always reopen or cherry-pick. Thank you very much @evanlimanto , your work is much appreciated regardless!

evanlimanto force-pushed the rbf-polynomials branch from 34b44f2 to 482cd5e Compare March 11, 2017 10:14

evanlimanto changed the title ~~ENH: Add polynomials and basis functions to scipy.interpolate.rbf~~ ENH: Add polynomials and extra basis functions to scipy.interpolate.rbf Mar 11, 2017

evanlimanto changed the title ~~ENH: Add polynomials and extra basis functions to scipy.interpolate.rbf~~ ENH: Add polynomial features and extra basis functions to scipy.interpolate.rbf Mar 11, 2017

ev-br reviewed Mar 12, 2017

View reviewed changes

ev-br added enhancement A new feature or improvement needs-work Items that are pending response from the author scipy.interpolate labels Mar 12, 2017

stefanv mentioned this pull request Mar 17, 2017

Evan's weekly updates machine-shop/updates#110

Merged

evanlimanto force-pushed the rbf-polynomials branch from 482cd5e to a8a8488 Compare March 17, 2017 18:47

evanlimanto force-pushed the rbf-polynomials branch from 3b0eef8 to dbb346c Compare March 17, 2017 20:42

evanlimanto force-pushed the rbf-polynomials branch from dbb346c to c64d285 Compare March 17, 2017 20:57

evanlimanto force-pushed the rbf-polynomials branch 3 times, most recently from c291427 to 5b9252f Compare March 23, 2017 06:44

stefanv requested changes Mar 23, 2017

View reviewed changes

Implement polynomials and add basis functions to rbf interpolation

f5fb436

evanlimanto force-pushed the rbf-polynomials branch from 5b9252f to f5fb436 Compare March 23, 2017 21:57

pv removed the needs-work Items that are pending response from the author label Jul 30, 2017

Jwink3101 mentioned this pull request Dec 12, 2019

Improved Radial Basis Function Interpolation #11212

Closed

ev-br added this to N-D scattered in scipy.interpolate Apr 29, 2022

ev-br moved this from N-D scattered to In progress in scipy.interpolate Apr 30, 2022

ev-br moved this from In progress to triaged, waiting-for-contributor in scipy.interpolate May 5, 2022

ev-br closed this Jun 23, 2022

scipy.interpolate automation moved this from triaged, waiting-for-contributor to Abandoned / rejected Jun 23, 2022

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

ENH: Add polynomial features and extra basis functions to scipy.interpolate.rbf #7157

ENH: Add polynomial features and extra basis functions to scipy.interpolate.rbf #7157

evanlimanto commented Mar 11, 2017 •

edited

Loading

evanlimanto commented Mar 11, 2017

ev-br commented Mar 12, 2017

ev-br Mar 12, 2017

evanlimanto Mar 17, 2017

ev-br Mar 12, 2017

evanlimanto Mar 17, 2017

ev-br Mar 12, 2017

evanlimanto Mar 17, 2017

ev-br commented Mar 12, 2017

ev-br commented Mar 17, 2017

evanlimanto commented Mar 17, 2017

ev-br commented Mar 17, 2017

evanlimanto commented Mar 17, 2017

stefanv Mar 23, 2017

stefanv Mar 23, 2017

evanlimanto Mar 23, 2017

stefanv Mar 23, 2017

stefanv Mar 23, 2017

evanlimanto Mar 23, 2017

stefanv Mar 23, 2017

evanlimanto Mar 23, 2017

stefanv Mar 23, 2017

evanlimanto Mar 23, 2017

stefanv Mar 23, 2017

evanlimanto Mar 23, 2017

stefanv commented Nov 2, 2017

ev-br commented Apr 29, 2022

stefanv commented Apr 30, 2022 •

edited

Loading

ev-br commented Jun 23, 2022

ENH: Add polynomial features and extra basis functions to scipy.interpolate.rbf #7157

ENH: Add polynomial features and extra basis functions to scipy.interpolate.rbf #7157

Conversation

evanlimanto commented Mar 11, 2017 • edited Loading

evanlimanto commented Mar 11, 2017

ev-br commented Mar 12, 2017

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

ev-br commented Mar 12, 2017

ev-br commented Mar 17, 2017

evanlimanto commented Mar 17, 2017

ev-br commented Mar 17, 2017

evanlimanto commented Mar 17, 2017

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

stefanv commented Nov 2, 2017

ev-br commented Apr 29, 2022

stefanv commented Apr 30, 2022 • edited Loading

ev-br commented Jun 23, 2022

evanlimanto commented Mar 11, 2017 •

edited

Loading

stefanv commented Apr 30, 2022 •

edited

Loading