How to multiply two matrices

Hello,

For example I would like to multiply the following two matrices:

A = rand([10,10,10]);
B = rand([10,10,10]);

defined by:

for i=1:size(A,3)
C(:,:,i)= A(:,:,i)*B(:,:,i);
end

The question is: is this possible without the use of a for loop? Kind regards, Carlas

[umar siyab]

no its not possible without the use of loop because u have to multiply every element in the matrix with other matrix..

[Jan]

What are the real dimensions in your problem? It matters if size(A, 3) is much larger or much smaller than size(A, 1) and size(A, 2).

Answer 1

[Andrei Bobrov]

[m n p]= size(A);
o1 = ones(p,1));
out = cell2mat(cellfun(@mtimes,mat2cell(A,m,n,o1),mat2cell(B,m,n,o1),'un',0));

ADD

[m,n,p] = size(A);
out0 = bsxfun(@times,reshape(A,m,[]),reshape(permute(B,[1 3 2]),1,[],n));
out = reshape(sum(reshape(permute(out0,[1 3 2]),m,m,n,[]),3),m,n,[]);

or for out

out = permute(blockproc(out0,[m n],@(block_struct)sum(block_struct.data,2)),[1 3 2]);

Answer 2

[Titus Edelhofer]

Hi Carlas,

probably yes. But in this case probably the loop is not your worst option, as long as you initialize

C = zeros(size(A,2), size(B,1), size(A,3));

before the loop.

Titus

[Jan]

I do not completely agree with you, Titus: Instead of "not the worst" I'd claim, it is at least "very good". +1

James Tursa's MTIMESX (http://www.mathworks.com/matlabcentral/fileexchange/25977-mtimesx-fast-matrix-multiply-with-multi-dimensional-support ) can handle such tasks efficiently.

Answer 3

[carlas]

A = rand([10,10,10]);
[m n p]= size(A);
tic
    o1 = ones(p,1);
    out = cell2mat(cellfun(@mtimes,mat2cell(A,m,n,o1),mat2cell(A,m,n,o1),'un',0));
t1 = toc;

tic
C = zeros([10,10,10]);
for i=1:size(A,3)
   C(:,:,i) = A(:,:,i)'*A(:,:,i);
end
t2 = toc;

xFaster = t2/t1

xFaster =

    0.5072

The for loop is faster. Based on the above answers I assume that the for loop is the most optimal implementation if the final matrix is initialized. However, it is possible to do without.

[Jan]

I definitely prefer the loop. Especially for large inputs it has a much smaller memory footprint than the CELL method. For A=rand(100,100,1000) the loop is 3 times faster.

Answer 4

[carlas]

Thanks Titus and Andrei!