ENH: Rbf interpolation of large multi-dimensional data

[jrsassen]

So far, scipy.interpolate.Rbf could only be used to interpolate one-dimensional functions, I added the capability to also interpolate multi-dimensional functions.
Furthermore, I changed the way the norm is computed in Rbf to exploit the much faster implementations from scipy.spatial.distance.
Lastly, I also aligned the interface of Rbf to other interpolations in scipy.interpolate such as griddata or LinearNDInterpolator.

Example usage:

>>> from scipy.interpolate import Rbf
>>> x = np.random.rand(50,)*4-2
>>> y = np.random.rand(50,)*4-2
>>> z0 = x*np.exp(-x**2-1j*y**2)
>>> z1 = y*np.exp(-y**2-1j*x**2)
>>> z = np.vstack([z0, z1]).T
>>> rbf = Rbf((x, y), z, epsilon=2)
>>> zi = rbf((x, y))
>>> zi.shape
(50, 2)

[rgommers]

Thanks @jrsassen.

So far, scipy.interpolate.Rbf could only be used to interpolate one-dimensional functions, I added the capability to also interpolate multi-dimensional functions.

sounds good

Furthermore, I changed the way the norm is computed in Rbf to exploit the much faster implementations from scipy.spatial.distance.

yes that makes sense

Lastly, I also aligned the interface of Rbf to other interpolations in scipy.interpolate such as griddata or LinearNDInterpolator.

Unfortunately we cannot do this - it will break Rbf for all current users. Could you undo this change?

[jrsassen]

Thanks for the feedback, @rgommers

Unfortunately we cannot do this - it will break Rbf for all current users. Could you undo this change?

Yes, you're right, that was a bit extreme. At first I thought it would be necessary, but I was mistaken. I have removed this change.

[rgommers]

@jrsassen if you don't mind, could you open a separate PR for just the performance improvement with spatial.distance? That can be merged very quickly, and then this one is a bit easier to review (squash and rebase on top of the merged one).

[rgommers]

typo, plus use backticks to create a link: `scipy.spatial.distance.cdist`

[rgommers]

CI failure is unrelated

[rgommers]

Sorry, not awake yet - CI failure is in Rbf. Looks like this should keep working:

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

# 2-d tests - setup scattered data
x = np.random.rand(100)*4.0-2.0
y = np.random.rand(100)*4.0-2.0
z = x*np.exp(-x**2-y**2)
ti = np.linspace(-2.0, 2.0, 100)
XI, YI = np.meshgrid(ti, ti)

# use RBF
rbf = Rbf(x, y, z, epsilon=2)
ZI = rbf(XI, YI)

# plot the result
plt.subplot(1, 1, 1)
plt.pcolor(XI, YI, ZI, cmap=cm.jet)
plt.scatter(x, y, 100, z, cmap=cm.jet)
plt.title('RBF interpolation - multiquadrics')
plt.xlim(-2, 2)
plt.ylim(-2, 2)
plt.colorbar()

[jrsassen]

I have opened a separate PR #9222 for the 'spatial.distance' part as requested.

I also understand the problem CI turns up, the interface (esp. the return value of __call__) before my multidimensional changes was a bit different than it is now. I will try to come up with compatible way for this.

[rgommers]

gh-9222 is merged, this can now be rebased on master

[jrsassen]

Finally got around to it, also fixed the problem that CI reported before.
Let me know if anything else is needed.

[rgommers]

Thanks @jrsassen. I just opened gh-9283 to document what are public attributes, needed that to help figure out what's ok/nok here.

[rgommers]

This looks like a backwards compatibility break, in two ways:

• di is public, and you're changing its shape for >1-D input
• you're using di.ndim as an indication that the interpolation should now be multi-dimensional.

This should be avoided. I suspect that there's no better way than adding a new keyword argument (e.g. flatten=True or `mode='1-D') that preserves backwards compat but allows the user to enable multi-dim interpolation.

[ev-br]

Needs a rebase again

[jrsassen]

Hey, I rebased and introduced mode as keyword argument, which determines whether we would like one-dim or multi-dim interpolation.

[ev-br]

Looks good. Let's get this in before it needs one more rebase. Sorry it took so long @jrsassen, and thanks!