# Element wise multiplication by a vector

241 views (last 30 days)
Moshe on 7 Mar 2013
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.

James Tursa on 7 Mar 2013
Edited: James Tursa on 7 Mar 2013
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.

nanren888 on 7 Mar 2013
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.

Youssef Khmou on 7 Mar 2013
hi,
T=rand(4);
V=1:4;
G=kron(T,V);