Matlab for循環的矢量化

Question

我正在尋找適當的以下matlab函數向量化，以消除多線程的for循環並提高速度。

size(A) = N - N ，其中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

總結注釋中對兩個版本的代碼的討論，這些版本會稍微改善性能：

使用注釋中的多個想法，代碼大約需要減少1/3的時間：

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);

另一種方法是使用for循環盡可能地矢量化，這僅對性能產生了很小的改善：

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);