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    <p>For the particular case of sums, you could use <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.filters.convolve.html" rel="nofollow">ndimage.convolve</a>:</p> <pre><code>In [42]: import numpy as np In [43]: a = np.zeros((6,6), dtype=np.int) a[1:5, 1:5] = 1; a[3,3] = 0; a[2,2] = 2 In [48]: s = ndimage.generate_binary_structure(2,2) # Binary structure In [49]: ndimage.convolve(a,s) Out[49]: array([[1, 2, 3, 3, 2, 1], [2, 5, 7, 7, 4, 2], [3, 7, 9, 9, 5, 3], [3, 7, 9, 9, 5, 3], [2, 4, 5, 5, 3, 2], [1, 2, 3, 3, 2, 1]]) </code></pre> <p>For the particular case of products, you could use the fact that <code>log(a*b) = log(a)+log(b)</code> to convert the problem back to one involving sums. For example, if we wanted to "product-convolve" <code>b</code>:</p> <pre><code>b = a[1:-1, 1:-1] print(b) # [[1 1 1 1] # [1 2 1 1] # [1 1 0 1] # [1 1 1 1]] </code></pre> <p>we could compute:</p> <pre><code>print(np.exp(ndimage.convolve(np.log(b), s, mode = 'constant'))) # [[ 2. 2. 2. 1.] # [ 2. 0. 0. 0.] # [ 2. 0. 0. 0.] # [ 1. 0. 0. 0.]] </code></pre> <p>The situation becomes more complicated if <code>b</code> includes negative values:</p> <pre><code>b[0,1] = -1 print(b) # [[ 1 -1 1 1] # [ 1 2 1 1] # [ 1 1 0 1] # [ 1 1 1 1]] </code></pre> <p>but not impossible:</p> <pre><code>logb = np.log(b.astype('complex')) real, imag = logb.real, logb.imag print(np.real_if_close( np.exp( sum(j * ndimage.convolve(x, s, mode = 'constant') for x,j in zip((real, imag),(1,1j)))))) # [[-2. -2. -2. 1.] # [-2. -0. -0. 0.] # [ 2. 0. 0. 0.] # [ 1. 0. 0. 0.]] </code></pre>
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    1. POIterate with binary structure over numpy array to get cell sums
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    1. POIterate with binary structure over numpy array to get cell sums
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    1. CO+1 Nice lateral thinking using a logarithm.
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    2. COthanks for providing some examples. However the function sum is just an example. I want to apply various functions to the cell vicinity values (even custom made ones). How does convolve work? Does it apply the function x to each cell value? I need something which returns all values for the cells vicinity to work on (so for cell 1,2 it should work on [0,1,1,2,1,1,0,0,1]
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    3. COThink of `s` as defining a patch or a mask indicating which cells to add together. So for each cell in `a`, the patch is placed over that cell, the neighboring cells are selected, and summed. `convolve` returns an array composed of those summed values. You can also apply different weights to the cells using the `weight` parameter. But `convolve` is always going to perform a sum. I do not know of any `scipy` function which allows you to perform a calculation like `convolve` except with an arbitrary function.
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