How to generate all pairs from two vectors in MATLAB using vectorised code?

matlab combinations
Brendan picture Brendan · Sep 16, 2011 · Viewed 52.6k times · Source

More than once now I have needed to generate all possible pairs of two vectors in MATLAB which I do with for loops which take up a fair few lines of code i.e.

vec1 = 1:4;
vec2 = 1:3;
i = 0;
pairs = zeros([4*3 2]);
for val1 = vec1
    for val2 = vec2
         i = i + 1;
         pairs(i,1) = val1;
         pairs(i,2) = val2;
    end
end

Generates ...

1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
4 1 
4 2
4 3

There must be a better way to do this which is more MATLAB'esque?

n.b. nchoosek does not do the reversed pairs which is what I need (i.e. 2 1 as well as 1 2), I can't just reverse and append the nchoosek output because the symmetric pairs will be included twice.

Answer

Lambdageek picture Lambdageek · Sep 16, 2011

Try

[p,q] = meshgrid(vec1, vec2);
pairs = [p(:) q(:)];

See the MESHGRID documentation. Although this is not exactly what that function is for, but if you squint at it funny, what you are asking for is exactly what it does.

Related questions

Generate a matrix containing all combinations of elements taken from n vectors

This question pops up quite often in one form or another (see for example here or here). So I thought I'd present it in a general form, and provide an answer which might serve for future reference. Given an arbitrary …

Read More
Generating all combinations with repetition using MATLAB

How do I create all k-combinations with repetitions of a given set (also called k-multicombinations or multisubsets) using MATLAB? This is similar to the cartesian product, but two rows that only differ by their sorting should be considered the same (…

Read More
Read .mat files in Python

Is it possible to read binary MATLAB .mat files in Python? I've seen that SciPy has alleged support for reading .mat files, but I'm unsuccessful with it. I installed SciPy version 0.7.0, and I can't find the loadmat() method.

Read More