Multidimensional Convolution in python

Question

I'm trying to convolve a 3 dimensional values array of shape (10, 100, 100) with a gaussian of shape (10, 100, 100). When I use the convolve function I get a Value error.

def gaussian(x, mu, sigma):
    g = (1./ (sigma * sqrt(2*pi))) * exp(-(x - mu)**2 / sigma**2)
    return g

gauss_I = gaussian( values, mean(values), std(values) ) 

import numpy as np 
np.convolve( values, gauss_I)

convolve(values, gauss_I)

Traceback (most recent call last):

File "", line 1, in convolve(values, gauss_I)

  File "/Users/Me/Applications/anaconda/lib/python3.5/site-packages/numpy/core/numeric.py", line 1013, in convolve
    return multiarray.correlate(a, v[::-1], mode)

ValueError: object too deep for desired array

I've also used the correlate function but that gives me the same error.

Please supply the entire error message: the trace-back is important to people who know innards of the support packages. — Prune
– Prune, Commented Mar 30, 2017 at 16:31
The docs for np.convolve say: convolution of two one-dimensional sequences. — hpaulj
– hpaulj, Commented Mar 30, 2017 at 16:38
Full stack won't help here. convolve calls core.multiarray.correlate right away, and that is built-in (i.e. compiled). This is a usage error - wrong dimensions for the inputs. — hpaulj
– hpaulj, Commented Mar 30, 2017 at 16:40
I've just been looking into that but it makes my kernel crash repeatedly — Oh_canada
– Oh_canada, Commented Mar 30, 2017 at 17:34

Marco Molari · Accepted Answer · 2018-05-31 13:23:42Z

I have been having the same problem for some time. As already mentioned in the comments the function np.convolve supports only 1-dimensional convolution. One alternative I found is the scipy function scipy.signal.fftconvolve which works for N-dimensional arrays.

For example here I test the convolution for 3D arrays with shape (100,100,100)

import numpy as np
import matplotlib.pyplot as plt
import scipy.signal as sps

# create 3D meshgrid and function cos(x+y)
bins = np.linspace(-10,10,100)
x, y, z = np.meshgrid(bins, bins, bins)
cos = np.cos(x+y)
print(cos.shape) # (100, 100, 100)

# plot projection of function on x-y plane
plt.title(r'$\cos(x+y)$')
plt.contourf(x[:,:,0], y[:,:,0], np.sum(cos,axis=2))
plt.colorbar()
plt.xlabel(r'$x$')
plt.ylabel(r'$y$')
plt.show()

# perform convolution of function with itself
conv = sps.fftconvolve(cos, cos, mode='same')

print(conv.shape) # (100, 100, 100)

# plot projection of convolution on x-y plane
plt.title('numerical convolution')
plt.contourf(x[:,:,0], y[:,:,0], np.sum(conv,axis=2))
plt.colorbar()
plt.xlabel(r'$x$')
plt.ylabel(r'$y$')
plt.show()

I obtain the following images:

Hope it is helpful!

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