interpolate 3D volume with numpy and or scipy

Question

I am extremely frustrated because after several hours I can't seem to be able to do a seemingly easy 3D interpolation in python. In Matlab all I had to do was

Vi = interp3(x,y,z,V,xi,yi,zi) 

What is the exact equivalent of this using scipy's ndimage.map_coordinate or other numpy methods?

Thanks

Answer 1

In scipy 0.14 or later, there is a new function scipy.interpolate.RegularGridInterpolator which closely resembles interp3.

The MATLAB command Vi = interp3(x,y,z,V,xi,yi,zi) would translate to something like:

from numpy import array from scipy.interpolate import RegularGridInterpolator as rgi my_interpolating_function = rgi((x,y,z), V) Vi = my_interpolating_function(array([xi,yi,zi]).T) 

Here is a full example demonstrating both; it will help you understand the exact differences...

MATLAB CODE:

x = linspace(1,4,11); y = linspace(4,7,22); z = linspace(7,9,33); V = zeros(22,11,33); for i=1:11     for j=1:22         for k=1:33             V(j,i,k) = 100*x(i) + 10*y(j) + z(k);         end     end end xq = [2,3]; yq = [6,5]; zq = [8,7]; Vi = interp3(x,y,z,V,xq,yq,zq); 

The result is Vi=[268 357] which is indeed the value at those two points (2,6,8) and (3,5,7).

SCIPY CODE:

from scipy.interpolate import RegularGridInterpolator from numpy import linspace, zeros, array x = linspace(1,4,11) y = linspace(4,7,22) z = linspace(7,9,33) V = zeros((11,22,33)) for i in range(11):     for j in range(22):         for k in range(33):             V[i,j,k] = 100*x[i] + 10*y[j] + z[k] fn = RegularGridInterpolator((x,y,z), V) pts = array([[2,6,8],[3,5,7]]) print(fn(pts)) 

Again it's [268,357]. So you see some slight differences: Scipy uses x,y,z index order while MATLAB uses y,x,z (strangely); In Scipy you define a function in a separate step and when you call it, the coordinates are grouped like (x1,y1,z1),(x2,y2,z2),... while matlab uses (x1,x2,...),(y1,y2,...),(z1,z2,...).

Other than that, the two are similar and equally easy to use.

Answer 2

The exact equivalent to MATLAB's interp3 would be using scipy's interpn for one-off interpolation:

import numpy as np from scipy.interpolate import interpn  Vi = interpn((x,y,z), V, np.array([xi,yi,zi]).T) 

The default method for both MATLAB and scipy is linear interpolation, and this can be changed with the method argument. Note that only linear and nearest-neighbor interpolation is supported by interpn for 3 dimensions and above, unlike MATLAB which supports cubic and spline interpolation as well.

When making multiple interpolation calls on the same grid it is preferable to use the interpolation object RegularGridInterpolator, as in the accepted answer above. interpn uses RegularGridInterpolator internally.