When mapping smaller arrays to a bigger array, how do I have overlapping elements be added?

So I am working with stiffness matrices and I am trying to make a global stiffness matrix. I am trying to map each stiffness matrix into a portion of the global stiffness matrix, and wherever the individual matrices overlap, I need the elements to be added. To explain better:

Say I have 2 4x4 matrices:

A = [1 1 1 1;

1 1 1 1;

1 1 1 1;

1 1 1 1]

B = [1 1 1 1;

1 1 1 1;

1 1 1 1;

1 1 1 1]

and I want to map it to one larger 6x6 matrix:

C = [1 1 1 1 0 0;

1 1 1 1 0 0;

1 1 2 2 1 1;

1 1 2 2 1 1;

0 0 1 1 1 1;

0 0 1 1 1 1]

where A and B overlap at C(3:4,3:4), and everywhere that A and B are not is filled up with 0s.

I know that I can map A and B to C by writing:

C(1:4,1:4) = A

C(3:6,3:6) = B

but how do I get C(3:4,3:4) to automatically add the corresponding elements in A and B?

Answer 1

[Stephen23]

A = ones(4,4);
B = ones(4,4);
C = blkdiag(A,0,0)+blkdiag(0,0,B)

C = 6×6

1 1 1 1 0 0 1 1 1 1 0 0 1 1 2 2 1 1 1 1 2 2 1 1 0 0 1 1 1 1 0 0 1 1 1 1

Answer 2

[Sachin]

Hi @Anivartin Anand,

Referring the following information might be of good help to you.

C = zeros(6,6);
A = [1 1 1 1; 
       1 1 1 1; 
       1 1 1 1; 
       1 1 1 1];
B = [1 1 1 1; 
       1 1 1 1; 
       1 1 1 1; 
       1 1 1 1];

C(1:length(A),1:length(A)) = A;
rowidx = 6-length(A)+1;  % row index where overlapping starts
colidx = 6-length(A)+1;  % col index where overlapping starts
C(rowidx:6,colidx:6) = C(rowidx:6,colidx:6) + B;
C

C = 6×6

1 1 1 1 0 0 1 1 1 1 0 0 1 1 2 2 1 1 1 1 2 2 1 1 0 0 1 1 1 1 0 0 1 1 1 1

This solution can be used for any size square matrix.

Regards

Sachin