# Fast 2D distance calculation

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Neuropragmatist on 29 Jul 2019
Commented: Neuropragmatist on 3 Aug 2019
Hi all,
Many of the codes I am currently using depend on a simple calculation: the distance between a single point and a set of other points.
In one example, using the matlab profiler I see that this single calculation takes 50% of the total function time, so I would like to optimise it as far as possible.
I have looked around and haven't found anything more optimal than:
p1 = rand(1,2); % single point
pn = rand(1000000,2); % random points
tic
d = sqrt(sum((p1-pn).^2,2)); % calculate the distance between these
toc
Does anyone else have a clever idea that would optimise this - even just by a tiny fraction? Is there any way to speed these calculations up on the GPU or using a mex? I would be really happy to see any suggestions.
I suspect this might be already be as mathematically simple as possible, but I'm frustrated because I need to calculate this a lot.
I have already vectrorised my code as far as possible.
Thanks for any help,
R.
Neuropragmatist on 3 Aug 2019
I have run the following code several times and I get slightly different results:
xi = 1:.5:8;
t1 = NaN(1,8);
t2 = NaN(1,8);
for p = 1:length(xi)
p1 = rand(1,2);
pn = rand(ceil(10^xi(p)),2);
tic;
d1 = sqrt(sum((pn-p1).^2,2));
t1(p) = toc;
tic;
d2 = pdist2(p1,pn);
t2(p) = toc;
end
figure
plot(xi,t1,'r',xi,t2,'b');
legend({'Manual','Pdist2'})
Which probably suggests that any differences in time between pdist2 and manual calculation are negligible and more dependent on the current background state of the CPU.
However, generally the manual calculation is slightly faster or both methods are the same.

Matt J on 29 Jul 2019
Edited: Matt J on 29 Jul 2019
If you have the Parallel Computing Toolbox, you can execute the computations on the GPU just by building p1 and pn as gpuArrays. That should definitely speed things up.
gd=gpuDevice;
p1 = gpuArray.rand(1,2);
pn = gpuArray.rand(1000000,2);
tic
d = sqrt(sum((p1-pn).^2,2));
wait(gd);
toc %Elapsed time is 0.001429 seconds.
##### 2 CommentsShowHide 1 older comment
Matt J on 29 Jul 2019
Well, I don't think the question can be taken any further until we know what parallel computing resources you do have, or can remote connect to. I think you are at the limits of performance already with standard Matlab.

Joss Knight on 3 Aug 2019
pdist2 is the usual way to do this, if you have Statistics and Machine Learning Toolbox.
##### 2 CommentsShowHide 1 older comment
Joss Knight on 3 Aug 2019
But pdist2 does that. Input x is a 1-by-2 vector, and input y is an N-by-2 array of N points.
You may be right that it is no faster than implementing it manually.

R2018a

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