Adding Matrices to make Bigger Matrix

Question

Chris Dan 2019-11-6

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评论： Walter Roberson 2019-11-7

采纳的回答： the cyclist

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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.

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Answer 1

the cyclist 2019-11-6

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编辑：the cyclist 2019-11-6

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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.

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the cyclist 2019-11-7

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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 2019-11-7

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.

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Answer 2

Walter Roberson 2019-11-7

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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.