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matlabmatrixvectorizationbsxfun

Matlab: multiplying rows of a matrix by vector elements

Let v be a row vector (1 x n matrix) and M be a n x m matrix. I use the following piece of code to create a "weighted vector" (I hope the comments explain what it's supposed to be doing):

weighted_M = bsxfun(@times,v',M);
%creates a matrix with the i-th row of M being weighted (multiplied) by the i-th element of v
weighted_v = sum(weighted_M);
%sums the columns of weighted_M

Now the actual question: I have to do the same calculation for a lot of input vectors v. So instead I would like to input a matrix V that contains the vectors v as rows and output a matrix that contains the weighted vectors as rows. Is there any way to do this without using for loops?

Solution

  • If V is of size [k,n] and M is of size [n,m], and you're looking for the k weighted vectors, then you might simply need

    weighted_vs = V*M;

    an element of which is equal to

    weighted_vs_ij = (V*M)ij = sum_l V_il * M_lj

    First you multiply each row of M with a corresponding element of V (V_il * M_lj above for a fix i), then sum up as a function of the first index.

    The result are the k weighted row vectors, each of length m.