Element wise multiplication by a vector

Given a vector V, I can define an element-wise multiplication on another vector W as V.*W. I'd like to be able to likewise multiply the rows or columns of a matrix by a vector V in the same sense. In other words, given a vector with components V(i) and a matrix with components M(i,j), I'd like to output a new matrix W(i,j) whose elements are W(i,j)= V(j) M(i,j).

One way to achieve that, just to demonstrate what I mean, is by using a loop:

for r=1:N
W(r,:)= V.*M(r,:)
end

But, it would be nicer to vectorize that -- I have to use this type of operation many times and the multiple nested loops slow the code down. Attempting something like

W(1:N,:)= V.*M(1:N,:)

does not work, though it really should if you think about both sides as a collection of vectors parametrized by the index 1:N. Any way to accomplish that with a valid Matlab syntax?

This is an example of more general issue, of attempting to vectorize nested loops. A single iterator is usually fairly easy to replace by an index of a matrix, harder to replace nested loops by multiple indices. General advice would be appreciated.

Answer 1

[James Tursa]

W = bsxfun(@times,V,M)

If V is a row vector you will get V element-wise times each row of M. Similarly if V is a column vector.

Answer 2

[nanren888]

I guess it is the definition of matrix multiply that is getting in your way.

Maybe have a look at diag(V).

It will cost you some space & do a lot of multiplies by zero, but will look neat in code.

Answer 3

[Youssef Khmou]

hi,

Im not sure about your expectations but try Kronecker product :

 T=rand(4);
 V=1:4;
 G=kron(T,V);