How to vectorize this code to eliminate nested For loops

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DaveF
DaveF 2013-1-18
Would like to know how this code be vectorized:
X=zeros(nn);
for i=1:nn
for j=1:nn
X(i,j)=x(i)-x(j);
end
end

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回答（5 个）

Sean de Wolski
Sean de Wolski 2013-1-18
X = bsxfun(@minus,x(1:nn).',x(1:nn));
Jan
Jan 2013-1-18
编辑：Jan 2013-1-19
This cannot compete with the BSXFUN approach, but it is 32% faster than the original loop:
nn = numel(x);
X = zeros(nn);
for i = 1:nn
for j = i+1:nn
a = x(i) - x(j);
X(i,j) = a;
X(j,i) = -a;
end
end
Using a temporary variable for x(i), which is updated in the outer loop only, is slightly slower.
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Jan
Jan 2013-1-19
编辑：Jan 2013-1-19
@Cedric: When you post this as an answer, you get my vote.
Your version does not exploit the symmetry as the other approaches. But this modification is much slower:
X=zeros(nn);
for ii = 1:nn
a = x(ii:nn) - x(ii);
X(ii:nn, ii) = a;
X(ii, ii:nn) = -a;
end
Obviously the overhead for explicit indexing is too high.
Cedric
Cedric 2013-1-19
@Jan : thank you! Knowing that I would get your vote is enough, so I'll keep that as a comment ;-)
I just profiled your last version and it is very interesting indeed, because I would never have expected such an overhead. It might even lead me to review my code in a few projects, so thank you for the comment!

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Jan
Jan 2013-1-19
And a C-Mex, which has the same speed as BSXFUN for a [1 x 1e3] vector under Matlab R2009a/64, Win7, MSVC 2008:
#include "mex.h"
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
double *X, *Y;
mwSize i, j, n;
n = mxGetNumberOfElements(prhs[0]);
X = mxGetPr(prhs[0]);
plhs[0] = mxCreateDoubleMatrix(n, n, mxREAL);
Y = mxGetPr(plhs[0]);
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
*Y++ = X[i] - X[j];
}
}
}
Azzi Abdelmalek
Azzi Abdelmalek 2013-1-18
编辑：Azzi Abdelmalek 2013-1-18
x=[1 3 4 10 20 30];
X=cell2mat(arrayfun(@(y) y-x,x','un',0))
%or
X=bsxfun(@minus,repmat(x',1,numel(x)),x)
  2 个评论
Cedric
Cedric 2013-1-18
编辑：Cedric 2013-1-18
Or
[X, Xt] = meshgrid(x, x) ; Xt-X
More efficient than cell2mat/arrayfun and less efficient than bsxfun. So the latter (bsxfun) should be the winner ;) But Sean's version without repmat beats them all.
Sean de Wolski
Sean de Wolski 2013-1-18
Well the for-loops will smoke arrayfun/cell2mat like a Lambo would smoke bicycle...
bsxfun will be faster than the for-loops some of the time; meshgrid will only be faster if you need to reuse the gridded matrices.

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Matt J
Matt J 2013-1-19
y=exp(x(1:nn));
X=log( y * (1./y.') );

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