vector to repeated matrix multiplication

Hi all.

Just wanted to find a non loop way of computing the following operation.

A = [1 2; 3 4], V = [ 1 2 3]

compute Y = 1*A + 2*A + 3*A = 1*[1 2; 3 4] + 2*[1 2; 3 4] + 3*[1 2; 3 4] = [6 12; 18 24]

i.e. each element of V times A then sum up each of these matrices

many thanks!

Answer 1

[Matt Fig]

One approach:

sum(bsxfun(@times,A,reshape(V,1,1,3)),3)

[Fred]

Thank you Matt! Works out!

Answer 2

[Matt Tearle]

Not being able to think up a more elegant solution off the top of my head, how about

reshape(repmat(A(:),1,3)*(V'),2,2)

Or, more generally and cryptically,

reshape(repmat(A(:),size(V))*(V'),size(A))

[Fred]

Hi Matt, Many Thanks! Seems like for than one way to skin a cat.

Answer 3

[Bruno Luong]

v1 = [1 2 3]
v2 = [4 5 6]
A = [1 2; 3 4]

v2(2,:) = -1
P=sum(bsxfun(@times,v1,v2),2)

P(1)+P(2)*A % *Not* polynomial of A

Answer 4

[Fred]

OK, one last one which is just an extension of this one.

suppose I have v1 = [1 2 3], v2 = [4 5 6], and A = [1 2; 3 4]

I want to eliminate a loop, bottleneck in my code of course :) so want to from the following

1*(4 - A) + 2*(5 - A) + 3*(6 - A) = [26 20; 14 8]

many thanks!

Cheers, Fred

Answer 5

[Fred]

actually, figured it out. Thank you both again for your help!

A1 = bsxfun(@minus,reshape(v2,1,1,3),A);

sum(bsxfun(@times,reshape(v1,1,1,3),A1),3);

a similar method can be used with the repmat command like matt posted above. BTW, which is faster? repmat bs bsxfun?

Cheers, Fred

[Paulo Silva]

You can find that out using tic and toc

[Matt Fig]

I suspect the BSXFUN method will be faster for smaller arrays, and REPMAT will be faster for larger arrays. For even more speed, indexing instead of REPMATing can often work magic.

[Fred]

Hi Matt, can you give an example of indexing for this problem? I am not familiar with it.

[Matt Fig]

Sure, see below.

Answer 6

[Matt Fig]

On my machine, this outputs: 3.1 2.2 1

function [] = compare_bsx()
% Compare BSXFUN, REPMAT and indexing.
T = [0 0 0];
N = 40; % The array sizes.  Change this to see if the fastest changes 
% with array size.  It will.

for ii = 1:300

      mA = ceil(rand*N); % Make the arrays up to size N.
      nA = ceil(rand*N);
      nV = ceil(rand*N);
      A = round(rand(mA,nA)*100);
      V = round(rand(1,nV)*100);
      tic
      E = sum(bsxfun(@times,A,reshape(V,1,1,length(V))),3);
      T(1) = T(1) + toc;
      tic
      E2 = reshape(repmat(A(:),size(V))*(V'),size(A));
      T(2) = T(2) + toc;
      tic
      E3 = A(:);
      E3 = E3(:,ones(length(V),1,'single'));
      E3 = reshape(E3*(V.'),size(A));
      T(3) = T(3) + toc;
end

T/min(T)  % The 1 is the quickest

[Fred]

wow! 2 or 3x's faster! I'll give it a go. Many thanks again!