Fast way for vector/array multiplication in Matlab

Question

I am looking for a fast and flexible way to compute the following in Matlab without using a loop:

c = 1:5;
A = reshape(1:5^3,5,5,5);
res= c(1)*A(:,:,1)+...+c(5)*A(:,:,5)

I think, working with

sum(A,3)

could be a nice way as long as I am able to perform the multiplication along the third dimension. One solution (but with loops) would be:

val = zeros(length(c),length(c))
for i = 1:length(c)
    val = val+c(i)*A(:,:,i)
end

I am just wondering if this can be done in a simpler (and more elegant) way avoiding the loop.

Clarify a liitle bit better your question . you want to multiple what? — 16per9
– 16per9, Commented Apr 20, 2016 at 8:43
I want to obtain res at the end of the day.. So in other words, I would like to multiply the whole Matrix A(:,:,1) with the scalar c(1), the whole Matrix A(:,:,2) with the scalar c(2) and so on...at the end I want to sum up each of those five matrices, such that res is a matrix. — Stefan Voigt
– Stefan Voigt, Commented Apr 20, 2016 at 8:45

Community · Accepted Answer · 2017-05-23 11:52:40Z

6

You can reshape A from 3D to 2D, use the very efficient matrix-multiplication, which will give you a 1D array and finally reshape back to 2D for the final output, like so -

res = reshape(reshape(A,[],size(A,3))*c(:),size(A,1),[])

edited May 23, 2017 at 11:52

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answered Apr 20, 2016 at 9:32

Divakar

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Comments

hbaderts · Accepted Answer · 2016-04-20 08:57:37Z

4

Yes, this is a perfect job for bsxfun and permute:

res = sum(bsxfun(@times,A,permute(c,[3,1,2])),3)

You send c to the third dimension using permute(c,[3,1,2]). Then, by calling bsxfun, each of the matrices in A is multiplied by the corresponding (permuted) c. Finally, you can do a sum over the third dimension.

answered Apr 20, 2016 at 8:57

hbaderts

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