Efficient matrix operation: how to avoid for loop

Hi all,

I need to speed up a matrix operation and don't know how.

Here's a toy example of what I need to do:

A = randi(10,[4,10])

A =

     3     8     8     5     1     1     9     9     4     2
     8     9     4     3     4    10     5     8     8     7
     4     1     2    10     1     5     2     6     1     2
     1     7     1     5     4     7     3    10     1     4
     
B = randi(10,[2,10])

B =

     3     3     4    10     3     7     5     6     8     8
     8     1     4     8     8     6    10     5     8     5
     

C = zeros(size(A,1),size(B,1),size(B,2));
for i = 1:size(B,2)
    C(:,:,i) = A(:,i).*B(:,i)';
end

C(:,:,1)

ans =

     9    24
    24    64
    12    32
     3     8

In other words C is a 3 dimensional tensor and C(:,:,i) is a matrix in which the column k is A(:,i)*C(k,i).

How can I compute C (or compute and store the same informations of C in some other way) in a more efficient way, possibly avoiding the for loop?

Thanks

Answer 1

[Allen]

Roberto, this should help with consolidating your code as well as improving the overall performance. Benchtests that I ran were orders of magnitude faster when comparing to size(A) = [4, 1e+6] and size(B) = [2, 1e+6].

C = reshape(A,[size(A,1),1,size(A,2)]).*reshape(B,[1,size(B)]);

[Roberto]

Thank you!