How to generate all pairs of two vectors in MATLAB using vectorized code?

Question

More than once I had to generate all possible pairs of two vectors in MATLAB, which I do for loops that occupy several lines of code ie

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 

Creates ...

 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?

nb nchoosek does not execute the inverse pairs that I need (i.e. 2 1 , as well as 1 2 ), I cannot just cancel and add the nchoosek output because the symmetric pairs will be included twice.

Answer 1

Try

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

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

Answer 2

you can use

 a = 1:4; b = 1:3; result = combvec(a,b); result = result' 

Answer 3

You can do this by replicating matrices using repmat , and then turning the result into a column vector using reshape .

 a = 1:4; b = 1:3; c = reshape( repmat(a, numel(b), 1), numel(a) * numel(b), 1 ); d = repmat(b(:), length(a), 1); e = [cd] e = 1 1 1 2 1 3 2 1 2 2 2 3 3 1 3 2 3 3 4 1 4 2 4 3 

Of course, you can get rid of all the intermediate variables from the above example.

Answer 4

Another collection solution:

 [idx2, idx1] = find(true(numel(vec2),numel(vec1))); pairs = [reshape(vec1(idx1), [], 1), reshape(vec2(idx2), [], 1)]; 

Answer 5

You can use simple old matrix operations, for example. at

 x = [3,2,1]; y = [11,22,33,44,55]; v = [(ones(length(y),1) * x)(:), (ones(length(x), 1) * y)'(:)] 

Edit: this is Octave syntax, MATLAB will look like this:

 x = [3,2,1]; y = [11,22,33,44,55]; A = ones(length(y),1) * x; B = (ones(length(x), 1) * y)'; v = [A(:) B(:)] 

in both cases the result will be

 v = 3 11 3 22 3 33 3 44 3 55 2 11 2 22 2 33 2 44 2 55 1 11 1 22 1 33 1 44 1 55 

Answer 6

Here's more MATLAB'esque way to find combinations. It can also be easily expanded to more than 2 vectors (as well as non-numerical combinations):

 v1 = 1: 1: 3; v2 = 11: 11: 44; v3 = 111:111:555; dimensions = cellfun(@numel, {v1,v2,v3}); [i1,i2,i3] = ind2sub(dimensions, 1:prod(dimensions)); combinations = [v1(i1); v2(i2); v3(i3)]' 

Answer 7

Starting with version R2015a, you can do this with repelem and repmat :

 >> vec1 = 1:4; >> vec2 = 1:3; >> pairs = [repelem(vec1(:), numel(vec2)) ... repmat(vec2(:), numel(vec1), 1)] pairs = 1 1 1 2 1 3 2 1 2 2 2 3 3 1 3 2 3 3 4 1 4 2 4 3 

This type of solution avoids the additional intermediate variables necessary for some other solutions (for example, based on meshgrid ), which can lead to memory problems for large vectors.

Answer 8

What you are looking for is a Cartesian product.

cartprod is a function that implements it. You can find it in a linear algebra package, so you will need to do:

  >> pkg install -forge linear-algebra >> pkg load linear-algebra >> sortrows(cartprod(1:4,1:3)) ans = 1 1 1 2 1 3 2 1 2 2 2 3 3 1 3 2 3 3 4 1 4 2 4 3