Multiply each element in a matrix by each element in a vector

2
votes

I have an mxn matrix, M, and a vector, b, (length c). Is there a way of multiplying each element of M by each element of vector to get an mxnxc result, i.e. result(1, 1, :) is M(1, 1) .* b?

For vectors, using the element-wise operators works. E.g. if m = [a; b] and n = [c d] then a .* b gives

a*c  a*d
b*c  b*d

but for matrices, this will perform the element-wise operation column-wise or row-wise on the matrix, depending on whether n is a column or row vector. E.g. if m = [ a b; c d ] and n = [ e f ] then m .* n gives

a*e  b*f
c*e  d*f

while the result I'm looking for would be result(:, :, 1) =

a*e  b*e
c*e  d*e

and result(:, :, 2) =

a*f  b*f
c*f  d*f

I know this can be achieved using a loop,

result = zeros(m, n, c);
for i = 1:b
  result(:, :, i) = M .* b(i); 
end

but I'm wondering if there is a simpler, i.e. moreMATLAB/Octave (usually more readable and performant) way, of doing it.

1
arraysmatlabmatrixoctave

1 Answers

4
votes

You only need to permute/reshape b along the third dimension, and let implicit expansion do its work:

result = M.*reshape(b,1,1,[]);

For older Matlab versions use bsxfun:

result = bsxfun(@times, M, reshape(b,1,1,[]));