Matrix Sum

Hi!

I have a question I think it's pretty basic, but I can´t seem to find the answer!

I have 'n' 3x3 matrices (B), and I want to construct another 3x3 matrix (A) in which each entry is the sum of the similar entries of the initial 3x3 B matrices:

A(ij) = Bij (1) + Bij (2) + ... + Bij (n)

The in brackets numbers are the corresponding B matrices.

The way i tried to solve this was by making two 'for' loops - one for i and another for j. The problem I'm having is with the summation itself. I can work pass that if I code the summation 'by hand', that is, explicitating each member of the sum - the way I wrote it above. This could be a sollution if I had only 2 or 3 matrices. But I have 20 or 30 B matrices, which makes it very boring (and very very bad programming) to write all explicitly.

I know this is a very basic situation, but I'm reletively new at MatLab, so any help is really appreciated!

SB

Answer 1

[Jan]

Store the B matrices in a CELL instead of using different names:

n = 30;
B = call(1, n);
for i = 1:n
  B{i} = rand(3, 3);
end

Now the sum:

B2 = cat(3, B{:});
A  = sum(B2, 3);

Answer 2

[bym]

just add the B matricies. For example:

A = ones(3) + eye(3) + magic(3);

Answer 3

[Sven]

You can (and possibly should, depending on what you want to do next) turn your N 3-by-3 matrices into a single 3-by-3-by-N matrix.

Then you could just write:

A = sum(B,3);

The above will make A as the sum of B along the 3rd dimension. There are lots of neat things you can do in MATLAB once you work with matrices like this.

To get B as a 3-by-3-by-N matrix you can do many things... one of them is to concatenate in the 3rd dimension as follows:

B = cat(3, rand(3,3), ones(3,3), zeros(3,3), rand(3,3))

Another way to get B would be in a loop over each of the N layers:

B = zeros(3,3,N); % This is called "preallocation". A good idea for big matrices.
for i = 1:N
  B(:,:,i) = your3by3(N); % Put in this slice of B
end

Answer 4

[Walter Roberson]

Do not use 20 or 30 B matrices.

See http://matlab.wikia.com/wiki/FAQ#How_can_I_create_variables_A1.2C_A2.2C....2CA10_in_a_loop.3F