All combinations of matrix elements?

2016 9 23
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更新时间：2016 9 27
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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!

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Stephen23
Stephen23 2016-9-23
编辑：Stephen23 2016-9-27

2 个投票

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)

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Xiaohan Du
Xiaohan Du 2016-9-23
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
Stephen23 2016-9-23
@Xiaohan Du: can you please post a numeric example for your last question.
Xiaohan Du
Xiaohan Du 2016-9-26
编辑：Xiaohan Du 2016-9-26
@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
Stephen23 2016-9-26
@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
James Tursa 2016-9-26
@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)

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