How would you remove the loop from this matlab code

Question

Given that we have:

x is 2d matrix with size [numSamples x numFeatures]
A is 2d square matrix with size [numFeatures x numFeatures]
B is a 1d vector with size [1 x numFeatures]

I would like to evaluate the following code without a loop: (or in a way faster way)

out = zeros(1,numSamples);
for i = 1:numSamples
    res = sum(repmat(B - x(i,:), numSamples, 1)*A.*(x - repmat(x(i,:), numSamples, 1)), 2).^2;
    out(i) = var(res);
end

If you have other suggestions on a faster improvement of the above, it is also more than welcome.

Let's take a step back. How fast is this code when you run it on your test data? Are you not happy with the time? — rayryeng
– rayryeng, Commented Oct 28, 2015 at 19:32
Unfortunately no. For a large number of samples it becomes very slow. — user2324712
– user2324712, Commented Oct 28, 2015 at 19:45
In addition to the comment above, is there a particular formula you try to implement? — usεr11852
– usεr11852, Commented Oct 28, 2015 at 19:46
Nothing famous. This is a simplified part of the whole formula, the rest is normalization expressions and I felt that including them will only complicate things. I feel that if you can help me with this simplified expression I am certain that I can extrapolate to the more general expression. — user2324712
– user2324712, Commented Oct 28, 2015 at 19:50

Divakar · Accepted Answer · 2015-10-28 20:31:24Z

7

You can bsxfun those piece-by-piece for a vectorized solution -

P1 = bsxfun(@minus,B,x)*A;
P2 = bsxfun(@minus,x,permute(x,[3 2 1]));
out = var(squeeze(sum(bsxfun(@times,P1,P2),2)).^2.');

Partially vectorized approach -

P = (bsxfun(@minus,B,x)*A).';  %//'
out = zeros(1,numSamples);
for i = 1:numSamples
    out(i) = var((bsxfun(@minus,x,x(i,:))*P(:,i)).^2);
end

edited Oct 28, 2015 at 20:31

answered Oct 28, 2015 at 19:47

Divakar

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6 Comments

user2324712 Over a year ago

thank you for the reply, let me verify that this works :)

Divakar Over a year ago

@user2324712 Damn, I see some disbelief there! ;)

Divakar Over a year ago

@user2324712 Sure, that's the best way to do it!

user2324712 Over a year ago

That sure solves it. On my aging laptop, the jit solution in matlab makes the original implementation faster. But I am quite sure that for big data on a gpu your solution takes the cake. Thank you!

Divakar Over a year ago

@user2324712 bsxfun loves cake aka memory, so feed it good ;) Just be careful, because with huge data, the memory transfers, rather than the actual computations might slow it down. But, all those would depend a lot on the GPU and the associated hardware.

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