Adding Matrices to make Bigger Matrix

Hello

I have a problem related to FEM. I want to add two stiffness matrices. Such as

A  = [ 1 -1;
      -1  1];

and

B = [ 2 -2;
     -2  2];

The result which I should get is

 C = [1 -1   0;
     -1  3  -2;
      0 -2   2];

C is a 3x3 matrix and A is a 2x2 matrix, B is also a 2x2 matrix

Does anybody know how to do it in a loop and how to expand it to more matrices, such as if I have 3 or 4 matrices instead of 2 and I want to add them this way.

Answer 1

[the cyclist]

Here is a straightforward way to do it with a for loop:

A{1}  = [ 1 -1;
         -1  1];

A{2} = [ 2 -2;
        -2  2];

A{3} = [ 3 -3;
        -3  3];

numberMatrices = size(A,2);

output = zeros(numberMatrices+1);

for na = 1:numberMatrices
    output(na:na+1,na:na+1) = output(na:na+1,na:na+1) + A{na};
end

It relies on having stored your input arrays sensibly in a cell array, rather than as variables named A,B,C,..., Z.

[Chris Dan]

Hey,

Thanks for the answer, but I donot understand this line

"It relies on having stored your input arrays sensibly in a cell array, rather than as variables named A,B,C,..., Z."

Also, will this method also work for sparse matrices or bigger matrices like 3x3 or nxn matrices?

[Stephen23]

"It relies on having stored your input arrays sensibly in a cell array..."

Because accessing those arrays within a cell array is simple and very efficient using indexing.

"... rather than as variables named A,B,C,..., Z."

What you showed in your question uses different variable names for each matrix. Accessing variable names dynamically is slow, complex, buggy, and hard to debug.

[the cyclist]

Yes, what Stephen wrote. Although you can still make my solution work, if you do

B  = [ 1 -1;
      -1  1];
C = [ 2 -2;
     -2  2];
D = [ 3 -3;
     -3  3];

A = {B,C,D};

before using my algorithm.

[Walter Roberson]

For larger matrices you need to define whether the offset to add them at is down by 1 diagonally each time, or the the rule is to overlap just the last entry.

Answer 2

[Walter Roberson]

It is probably easiest to intialize C to zeros() and then loop over a cell array {A, B, third, fourth} adding them into the appropriate section of C cumulatively.

There are other options, but they are not nearly as clear.