How can I mutiply every elements in a matrix by another given kernel matrix and then superpose them accodingly?

Hi !

I have a matrix A and a matrix B （they are all square matrixs but may be different in size), I want to superpose B with the weights and position of each elements in A (the Bs will overlap with each other) to get C. How can I do this efficently? (this process looks like a convolution in someways..?But I haven't figure out how to rewrite it to be a conventional convolution..)

And here is my code where I use for-loops and some examples that describes the function I am looking forward to:

A=[1,0,0;0,0,0;0,0,0];
B=[1,2,3;4,5,6;7,8,9];
temp=zeros(5);
for m = 1:1:3
    for n = 1:1:3
        temp(m:1:m+2,n:1:n+2)=temp(m:1:m+2,n:1:n+2)+A(m,n).*B;
    end
end
C=temp(2:1:4,2:1:4)

Examples:

%Some examples:
input1:
A =

     1     0     0
     0     0     0
     0     0     0


B =

     1     2     3
     4     5     6
     7     8     9

output1:

C =

     5     6     0
     8     9     0
     0     0     0

----------------------------------

input2:
A =

     0     0     0
     0     0     0
     0     0     1


B =

     1     2     3
     4     5     6
     7     8     9

output2:
C =

     0     0     0
     0     1     2
     0     4     5

------------------------------------------------
input3:
A =

     1     0     0
     0     0     0
     0     0     1


B =

     1     2     3
     4     5     6
     7     8     9

output3
C =

     5     6     0
     8    10     2
     0     4     5

This problem has a Physics backgroud that I have a LED array and each LED bulb projects a set of rings onto a wall in front of the LED array, and I want to know that what the wall looks like when all LEDs are turned on. The matrix A above is the LEDs and the matrix B means the effect that single LED bulb would have on the wall. The matrix C I want to calculate is the summarized effect of all LEDs described in A.

Thank you

Answer 1

[David Hill]

I think this would work as long as you specify that the square matrix is odd sized.

C=conv2(A,B);
a=size(A,1);
C=C((a+1)/2:end-(a-1)/2,(a+1)/2:end-(a-1)/2);

[Zhang Gene]

Thanks ! :)

And I found that conv2(A,B,'same') works well, too .