Speed-up special case euclidean distance in MATLAB

Question

I want to optimize the following code example:

%Example definition
A = rand(40,10000,250);
B = rand(40,10000,250);

%Euclidean
seuc = sum((A-B).^2, 3);

Do you have any idea how to speed this up? Or is it already optimized for MATLAB?

I guess this is as good as you can get.. It takes around 0.43 s (using `timeit`) on my computer (r2016a, 16GB RAM) — ammportal, Aug 01 '17 at 10:52

score 0 · Accepted Answer · answered Aug 01 '17 at 13:33

You can speed it up further by using 2D matrix operations as follows:

reshape(sum((reshape(A, [], size(A, 3))-reshape(B, [], size(A, 3))).^2, 2), size(A, 1), size(A, 2))

This reduces the execution time from ~0.5s to ~0.3s.

Approach

I first converted both input matrices into 2D matrices using reshape (taking first and second dimension together):

reshape(A, [], size(A, 3))
reshape(B, [], size(A, 3))

At the end, I reshaped the outcome of the sum (a 1D vector) back into the desired 2D vector:

reshape(..., size(A, 1), size(A, 2))

Why is this faster?

I don't know for sure. I guess MATLAB more often used with 2D matrices than 3D matrices and therefore better optimised for it.

1 Answers1