Accelerate nested bsxfun double loop?

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andrej
andrej 2013-10-7
编辑： Matt J 2013-10-8
I have a simple double loop that requires multiple 'repmat' tasks in each iteration. I'm currently using bsxfun to avoid repmats, but have found it to be only a little faster than repmat/elementwise multiplication.
Any suggestions on speeding this up?
n = 200;
U = rand(n);
M = zeros(n); % preallocate matrix
a = rand(1,n);
b = rand(1,n);
SZI = bsxfun(@times,a,b');
for j = 1 : n
j
for i = 1 : n
if i ~= j
plusvec = U(j,:).^2 - U(i,:).*U(j,:);
timesvec = U(i,:) - U(j,:);
M(i,j) = sum(sum(SZI.*(bsxfun(@plus,bsxfun(@times,U,timesvec),plusvec))));
end
end
end

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回答（2 个）

Sean de Wolski
Sean de Wolski 2013-10-7
编辑：Sean de Wolski 2013-10-7
Usually two dimensional:
bsxfun(@times
Can be replaced with matrix multiplication:
SZC = b'*a;
isequal(SZC,SZI)
ans =
1
More Being a fan of "ez" speedups, I turned the outer for-loop into a parfor-loop:
With two for-loops:
timeit(@()A89455(200),0)
ans =
6.3238
With the outer loop being a parfor-loop with four local workers:
timeit(@()A89455(200),0)
ans =
3.7519
A89455 is your code in a function taking n as an input.
Matt J
Matt J 2013-10-7
编辑：Matt J 2013-10-8
Without loops:
tic;
a=a(:);
Ut=U.';
S=U*spdiags(a,0,n,n)*Ut;
S=bsxfun(@minus,diag(S).',S)*sum(b);
c=(b*U)*bsxfun(@times,Ut,a);
T=bsxfun(@minus,c(:),c);
M=S+T;
toc;
%Elapsed time is 0.002864 seconds.

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