MATLAB: Add some elements of one matrix with another

Question

Hello,

I need to add some elements of several ‘n’ square matrices in a particular fashion and append zeros in the rest of the elements.

Let’s say for example, there are 4 2 x 2 square matrices,

1st matrix = [1 2; 3 4]

2nd matrix = [5 6; 7 8]

3rd matrix = [9 10; 11 12]

4th matrix = [13 14; 15 16]

Then resultant matrix should be (5×5),

R = [1 2   0     0       0; 
     3 4+5 0+6   0       0; 
     0 0+7 0+8+9 0+10    0; 
     0 0   0+11  0+12+13 0+14; 
     0 0   0     0+15    0+16]

But if there are three 4 x 4 input matrices,

1st matrix = [1 2 3 4; 5 6 7 8; 9 10 11 12; 13 14 15 16]

2nd matrix = [a b c d; e f g h; i j k l; m n o p]

3rd matrix = [A B C D; E F G H; I J K L; M N O P]

Then resultant matrix should be (8×8),

[1  2  3    4    0   0   0   0;
 5  6  7    8    0   0   0   0;
 9  10 11+a 12+b 0+c 0+d 0   0;
 13 14 15+e 16+f 0+g 0+h 0   0;
 0  0  i    j    k+A l+B 0+C 0+D;
 0  0  m    n    o+E p+F 0+G 0+H;
 0  0  0    0    0+I 0+J 0+K 0+L;
 0  0  0    0    0+M 0+N 0+O 0+P]

So now it will go forward by 2 elements between the matrices and for 6*6 matrices, it will go forward by 3 elements between the matrices and so on.

The step for n matrices of size 2*2 is n+1 and 4*4 is 2(n+1) and 6*6 is 3(n+1) and so on.

So is there any way by which I can compute this resultant matrix for ‘n’ even square matrices?

Thanks in advance.

Answer 1

Using a straightforward loop:

C = {[1,2;3,4],[5,6;7,8],[9,10;11,12],[13,14;15,16]};
A = cat(3,C{:}); % not strictly required, but ensures same size matrices.
S = size(A);
N = S(3)+S(2)-1; % adjust to suit step, etc.
B = zeros(N,N,S(3));
for k = 1:S(3)
    V = k:k+S(1)-1;
    B(V,V,k) = A(:,:,k);
end
Z = sum(B,3)

Giving:

Z =
    1    2    0    0    0
    3    9    6    0    0
    0    7   17   10    0
    0    0   11   25   14
    0    0    0   15   16