MATLAB: Combination calculations and matrix manipulation

combinationgroupsmatrix manipulation

Hello, I am working on a matrix (m x n) and I want to pick up different groups of m elements which have to be non dependent. Practically speaking I need (n-1)*m+2. For n = 4 and m = 3 I need 11 groups and an example of matrix is: [1 2 3 4, 5 6 7 8, 9 10 11 12] and the groups might be
(1 5 9),(1 5 10),(1 5 11),(1 5 12) 4
(1 6 9),(1 7 9),(1 8 9) 3
(2 5 9),(3 5 9),(4 5 9) 3
(2 6 9) 1
I have the matrix written, do you have any suggestion how to write this problem assuming that n and m are completely random and the first group has to be composed by the first column.
Thank you very much Antonio

Best Answer

Here is how to get all of them using NPERMUTEK
A = [1 2 3 4; 
     5 6 7 8; 
     9 10 11 12];
[m,n] = size(A);
I = npermutek(1:n,m);
J = cumsum(ones(size(I)),2);
R = A(J+(I-1)*m)  % Look at each row.
If you find that NPERMUTEK gives you too many samplings, you could try one of the lesser combinatorial samplings found in this file: COMBINATOR
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