Loop over a matrix for mean value of a matrix slice Python

Question

I have a large matrix with floats (250x112) like this:

import numpy as np
data = np.arange(1, 28001).reshape((250, 112))

What is the elegant way to calculate the mean value of a 3x3 matrix slice that goes over the large matrix and loops over all the cells? It is also important that the slice matrix becomes a 2x3 matrix in the fringe area and respectively a 2x2 matrix in the corners.

This looks like a signal convolve: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.convolve2d.html — Willem Van Onsem, Sep 23 '19 at 18:10
Iterate over indices, by 3, in both directions select the slice and take the mean? — wwii, Sep 23 '19 at 18:15
no, that won't work. I need it the mean value for every cell — dani_bandita, Sep 23 '19 at 18:17

score 1 · Answer 1 · edited Sep 24 '19 at 16:42

As suggested in the comments, it works with signal convolve:

from scipy import signal
kernel = np.array([[1,1,1],[1,1,1],[1,1,1]])
grad = signal.convolve2d(data, kernel, 'same')
grad  = grad/9

then you divide the matrix by the number of elements in the kernel matrix, for a 3x3 matrix you divide by 9. It works with smaller and larger matrixes.

More theory here, it helped my a lot to understand the convolute function: machinelearninguru.com

If you don't want to use scipy, it will work also with numpy only: NumPy Example

If the means for the corners and edges need to reflect just the cell and its neighbors a divisor for the convolve2d result can be constructed as:

corners = (np.array([0,0,-1,-1], dtype=np.int32),np.array([0,-1,0,-1], dtype=np.int32))
edges = np.ones(data.shape, dtype=np.bool)
edges[1:-1,1:-1] = False
edges[corners] = False
divisor = np.ones(data.shape) * 9
divisor[corners] = 4
divisor[edges] = 6

grad = signal.convolve2d(data, kernel, 'same')
grad = grad / divisor

For an initial array of data = np.arange(1, (5*3)+1).reshape((5, 3)) this results in:

In [35]: data
Out[35]: 
array([[ 1,  2,  3],
       [ 4,  5,  6],
       [ 7,  8,  9],
       [10, 11, 12],
       [13, 14, 15]])

In [36]: divisor
Out[36]: 
array([[ 4.,  6.,  4.],
       [ 6.,  9.,  6.],
       [ 6.,  9.,  6.],
       [ 6.,  9.,  6.],
       [ 4.,  6.,  4.]])

In [37]: grad
Out[37]: 
array([[  3. ,   3.5,   4. ],
       [  4.5,   5. ,   5.5],
       [  7.5,   8. ,   8.5],
       [ 10.5,  11. ,  11.5],
       [ 12. ,  12.5,  13. ]])

no, I don't. The mean value in the corners and in the fringe area are not correct, but that works for me because of the size of my matrix. The division coefficient for the corner and fringe area should be 4 and 6. — dani_bandita, Sep 24 '19 at 07:12

Loop over a matrix for mean value of a matrix slice Python

1 Answers1