Reduce computation time by using vectorization in MATLAB instead of multiple for loops

Question

I have a long MATLAB code which takes a lot of time due to numerous for loops. I try to eliminate them but it looks like I do not understand the vectorization concept. To be more specific, consider the following simple example with two vectors with different sizes:

a1=[1 2];
a2=[1 2 3];

I want to computea1/a2 in a "piece-wise" sense. For that, I use the following for loops

div=0;
for i=1:size(a1,2)
 for j=1:size(a2,2)
  div=div+a1(i)/a2(j);
 end
end

How can I vectorize such two for loops? Many thanks!

chappjc · Accepted Answer · 2014-03-15 05:49:14Z

1

Two good options: bsxfun and ndgrid. Given two row vectors:

a1=[1 2];
a2=[1 2 3];

bsxfun

The old-school way is with two repmat calls. Virtual replication can now be done with bsxfun:

divM = bsxfun(@rdivide,a1,a2');
div = sum(divM(:))

Faster and more memory-efficient than repmat.

ndgrid

When you think "all combinations", think ndgrid.

[ii,jj] = ndgrid(1:numel(a2),1:numel(a1))
divM = a1(jj)./a2(ii);
div = sum(divM(:))

answered Mar 15, 2014 at 5:49

chappjc

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1 Comment

chappjc Over a year ago

@LuisMendo You're right! Ah, curse you! Why didn't i think to just invert a2?

Luis Mendo · Accepted Answer · 2014-03-15 17:05:08Z

1

You can do it with just matrix multiplication: a column vector times a row vector gives a matrix with all combinations of element-wise products:

divs = a1(:) * (1./a2(:)).';
div = sum(divs(:));

answered Mar 15, 2014 at 17:05

Luis Mendo

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Comments

Anoop · Accepted Answer · 2014-03-15 04:35:01Z

0

This would work for you.

a1=[1 2];
a2=[1 2 3];
div_matrix = a1' ./ repmat(a2, [size(a1,2), 1])
sum(div_matrix(:))

edited Mar 15, 2014 at 4:35

answered Mar 15, 2014 at 4:24

Anoop

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