Thread Subject: use vectorization instead of loops (how to speed the current program?)

Dear all,

I have written a code as below, using two loops. Is there a smart way to use vectorization instead of using loops to speed it? I mean, without loops or only one loop? Since the current code is inside some main program and it does substantially impose the computation burden when I run the whole program each time.

The code is to solve the following problem:
to express a matrix D_{ni} where the subscript {ni} means the nth row, the ith column element in matrix D. D is a N*N matrix. D must satisfy the following condition (the writing follows the format of Latex):
D_{ni}=\sum_{j=1}^{N} y_{nij} * b_{j} * {\min_{m=1,2, ..., N} [c_{m}*K_{nm}*L_{mj}]}

where D, K, L are N*N matrix. b and c are N*1 vector. y is N*N*N (3-dimension). Suppose b, c, K, L are given. We know y_{nij}=0 if i~=m and y_{nij}=1 if i==m. I mean, if i is the index which minimizes the last part (inside the \min symbol), then this y_{nij}=1. If there are more than one index to minimize the last part, we evenly give the weight to each index. Therefore, ultimately, we have \sum_{i} y_{nij}=1
i, j, n, m are all indexes which is taken from 1 to N. Now we need to express this D matrix. We can know that we only need to consider when i (in D_{ni}) equals the index m (i.e., the index which can minimize the last part) and all other D_{ni}=0

My code is as below.
y=zeros(N,N,N);
D=zeros(N);
for n=1:N
    for j=1:N
        val=c.*K(n,:)'.*L(:,j);
        minval=min(val);
        minj=find(val==minval);
        y(n,minj,j)=1/length(minj);
        D(n,minj)=D(n,minj)+minval*b(j)/length(minj);
    end
end

If the two loops above can be vectorized, that would be a great help to my program! I hope someone can help me out. Many thanks in advance!

All my best,
Yao (Amber)

Sorry for the repeated message following this one. I didn't know it was sent twice. I don't know how to delete the repeated one. So please read this message as the main thread.

Your description says that you require y, but it is not used in the code.

"Darren Rowland" <darrenjremovethisrowland@hotmail.com> wrote in message <h7271b$47t$1@fred.mathworks.com>...
> Your description says that you require y, but it is not used in the code.

It doesn't matter since all other y =0 and only y_{n,minj,j) matters. When constructing D, we only need to construct D(n,minj) that's why y does not appear there. Please see below.
        y(n,minj,j)=1/length(minj);
        D(n,minj)=D(n,minj)+minval*b(j)/length(minj);

Or you can write as this: D(n,minj)=D(n,minj)+minval*b(j)*y(n,minj,j);