Summing partly overlapping matrices

Question

I have 3x3 matrices which can have different positions on a 5x5 matrix, so that those 3x3 matrices overlap partially or fully. Finally I want to sum those matrices together, to get a final 5x5 matrix. Here is a toy example:

import numpy as np
# I have 3 matrices which partly overlap, defined by their center index
mat1 = np.arange(9).reshape(3,3)
mat2 = np.arange(9).reshape(3,3)+2
mat3 = np.arange(9).reshape(3,3)*2.+1
# I construct 3 empty 5x5 matrices and store my 3x3 matrices there
A = np.zeros((3,5,5))
A[0,0:3,0:3]=mat1
A[1,2:5,2:5]=mat2
A[2,1:4,0:3]=mat3
# Finally I sum the matrices
output = A.sum(0)

In my opinion I waste a lot of memory space and time by constructing the matrix A, if the number of the 3x3 matrices becomes large. I am looking for another way, to add those partly overlapping 3x3 matrices together. Note, that the positions (indices) of the 3x3 matrices are known.

Answer 1

You can avoid the temporary (3,5,5) using add.at and as_strided :

>>> out = np.zeros((5, 5))
>>> oas = np.lib.stride_tricks.as_strided(out, (3,3,3,3), 2*out.strides)
>>> at = [0,2,1], [0,2,0]
>>> np.add.at(oas, at, (mat1, mat2, mat3))
>>> out
array([[ 0.,  1.,  2.,  0.,  0.],
       [ 4.,  7., 10.,  0.,  0.],
       [13., 16., 21.,  3.,  4.],
       [13., 15., 22.,  6.,  7.],
       [ 0.,  0.,  8.,  9., 10.]])

Answer 2

If, for each matrice, you have a tuple (offrow, offcol) , you could create your output directly by iterating over all your matrices:

output = np.zeros((5,5))
matrices = [mat1, mat2, mat3]
offsets = [(0, 0), (2, 2), (1, 0)]
for m, o in zip(matrices, offsets):
    for i in range(3):
       for j in range(3):
           output[i + o[0], j + o[1]] += m[i,j]

This avoids to create temporary 5x5 matrices, created from the 3x3 matrices. This will consume less memory but it might not be faster.