How to multiply two matrices

Question

carlas 2011-11-24

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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

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umar siyab 2011-11-24

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

Jan 2011-11-24

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).

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Answer 1

Andrei Bobrov 2011-11-24

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[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]);

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Answer 2

Titus Edelhofer 2011-11-24

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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

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Jan 2011-11-24

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.

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Answer 3

carlas 2011-11-24

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https://ww2.mathworks.cn/matlabcentral/answers/22145-how-to-multiply-two-matrices#answer_29154

在 MATLAB Online 中打开

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.

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Jan 2011-11-24

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.

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