MATLAB: Output of the function conv2 is not the size I expected

Question

Hello,

I am trying to use the conv2 function to convolute a matrix with a filter for the creation of a convolutional neural network. Take the following 3 by 3 matrix:

A = [1 2 3; 4 5 6; 7 8 9];

and the filter:

B = [1 0; 0 1];

For a stride of 1, my understanding of convolution from the examples I have seen is that the output should be (1*1) + (0*2) + (0*4) + (5*1) = 6 for the first element in the resulting matrix and (1*2) + (0*3) + (0*5) + (1*6) = 8 for the second element and so on until the filter reaches the bottom lower half of A for a final result of

ans = [6 8; 12 14];

when I use the conv2 function my results is:

conv2(A,B) = [1     2     3     0
             4     6     8     3
             7    12    14     6
             0     7     8     9];

where my expected answer is in the middle of the output. Where do these extra numbers come from?

Answer 1

Reverse the order of the arguments (so that the smaller size matrix is first), then use the 'same' shape argument:

C = conv2(B,A,'same')

produces:

C =
     6     8
    12    14