Matlab for循环的矢量化

Question

I am looking for proper vectorization of following matlab function to eliminate for-loop and gain speed by multithreading.

size(A) = N -by- N , where 30 <= N <= 60

1e4 <= numIter <= 1e6

function val=permApproxStochSquare(A,numIter)
%// A       ... input square non-negative matrix
%// numIter ... number of interations

N=size(A,1);

alpha=zeros(numIter,1);
for curIter=1:numIter
    U=randn(N,N);
    B=U.*sqrt(A);
    alpha(curIter)=det(B)^2;
end

val=mean(alpha);
end

Answer 1

To summarize the discussion in the comment to two versions of the code which slightly improve the performance:

Using multiple ideas from the comments, the code needs roughly 1/3 less time:

N=size(A,1);
%precompute sqrt(A)
sA=sqrt(A);
alpha=zeros(numIter,1);
parfor curIter=1:numIter
    %vectorizing rand did not improve the performance because it increased communitcation when combined with parfor
    U=randn(N,N);
    B=U.*sA;
    alpha(curIter)=det(B);
end
%moved calculation out of the loop to vectorize
val=mean(alpha.^2);

Another approach, vectorize as far as possible using a for loop only did small improvemens to the perfrmance:

N=size(A,1);
%precompute sqrt(A)
sA=sqrt(A);
alpha=zeros(numIter,1);
%using a for, a vectorized rand outside the loop is faster.
U=randn(N,N,numIter);
B=bsxfun(@times,U,sA);
for curIter=1:numIter
    alpha(curIter)=det(B(:,:,curIter));
end
val=mean(alpha.^2);