All combinations of matrix elements?

Hello,

I'd like to find all combinations of 2 elements in a matrix.

For example, a = [1:4; 5:8; 9:12]', the result should be [1*1 1*2 1*3 1*4 1*5 ... 1*12 2*2 2*3 ... 2*12 3*3 ... 12*11 12*12]';

Thanks for your help!

[Stephen23]

Continued here:

http://www.mathworks.com/matlabcentral/answers/304525-all-combination-for-a-cell-structure

Answer 1

[Stephen23]

Method One: matrix multiply and tril:

You can use a simple matrix multiply to do this:

 >> z = a(:) * a(:)'

and use tril to get the triangular lower portion:

 >> z(tril(true(size(z))))

Method Two: FEX submission combinator:

>> prod(a(combinator(numel(a),2,'c','r')),2)

[Xiaohan Du]

Hi Stephen,

This is awesome! Thanks!

What if a is made of row vectors of the same length rather than constants? For example, a = [a1 a2 a3; a4 a5 a6]', where a1-a6 are 3 by 1 column vectors.

[Stephen23]

@Xiaohan Du: can you please post a numeric example for your last question.

[Xiaohan Du]

@Stephen a numerical example:

var = rand(20, 3);
no = 5;
numcell = mat2cell(var, size(var, 1)/no*ones(1, no), ones(1, 3));

result in a 5 by 3 cell 'numcell' which contains 4 by 1 double for each cell.

Now for numcell, I'd like the same effort as

z = numcell(:) * numcell(:)';

But MATLAB gives me error: Undefined operator '*' for input arguments of type 'cell'.

[Stephen23]

@Xiaohan Du: cell arrays are containers for other data classes. They cannot have mathematical operations applied to them. Whatever you want to do (it is not clear to me) needs to be applied to a numeric array, not a cell array.

[James Tursa]

@Xiaohan Du: It is unclear what solution you really want from your original post. Stephen's answer does the entire outer product, which does not match your example result which appears to be only one triangular portion of the outer product. Andrei's answer does this triangular portion which matches your original post example result. What is it you really want? (The accepted answer does not match the question example result)

Answer 2

[Andrei Bobrov]

b = a(:)*a(:).';
out = b(tril(true(size(b))));

[Xiaohan Du]

Thanks buddy!