# Fast 2D distance calculation

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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.

### Answers (2)

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 Comments

Matt J
on 29 Jul 2019

Joss Knight
on 3 Aug 2019

pdist2 is the usual way to do this, if you have Statistics and Machine Learning Toolbox.

##### 2 Comments

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.

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