matrix nchoosk for column HELP

Suppose I have

A=[a1 a2 a3; b1 b2 b3; c1 c2 c3; d1 d2 d3];

I want to be able to generate all the possible vectors [a b c d]'

For example [a1 b1 c1 d1] is one but so is [a2 b1 c1 d2] and [a3 b1 c2 d3]

There are many combinations and depending on the number of rows and columns it will get explosive fast.

But how do I do this? Can it be extended to a matrix with an arbitrary number of rows and columns?

Answer 1

[Jan]

You can create the indices for each single column by:

http://www.mathworks.com/matlabcentral/fileexchange/26242-vchoosekro

To get the linear index related to the matrix, add (0:size(A,1):numel(A)-1) to the created array - you will need BSXFUN for that.

Answer 2

[Matt Fig]

This file should do what you want.

http://www.mathworks.com/matlabcentral/fileexchange/10064-allcomb

[Jos (10584)]

Indeed, just feed the rows of A to allcomb

R = allcomb(A(1,:), A(2,:), A(3,:), A(4,:))

For a little more flexibility you can create cell array and use comma-separated list expansion:

C = mat2cell(A, ones(1,size(A,1))) ;

R2 = allcomb(C{:})