# How can I Store all the possible combinations of columns of a matrix?

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samad khansari on 25 Jul 2014
Commented: Chenyang Zhang on 12 May 2020
for example I have : [1 2 3; 4 5 6; 7 8 9] as 3x3 matrix. Now I want : [2 1 3; 5 4 6; 8 7 9] and every other combination of it. in other word I want all nchoosek(n,2) of columns of a nxn matrix.

José-Luis on 25 Jul 2014
I would recommend that you only save the indices, if you really need to. Sure, you only have a small matrix, but the amount of required memory can become a problem really fast in combinatorial problems.
a = [1 2 3; 4 5 6; 7 8 9];
idx = perms(1:size(a,2));
for ii = idx'
your_mat = a(:,ii)
end
Chenyang Zhang on 12 May 2020
In this case how do you get a 18x3 matrix as a result? Thank you

Ben11 on 25 Jul 2014
As a starting point you could store the output of the function 'perms' is a cell array, in which the kth cell cell contains all the possible permutations of the kth column. Eg:
clear all
clc
A= [1 2 3;4 5 6;7 8 9];
P = cell(1,size(A,1));
for k = 1:size(A,1)
P{k} = perms(A(:,k))'; % Notice the transpose of the output.
end
disp('P{1}')
disp(P{1})
disp('P{2}')
disp(P{2})
disp('P{3}')
disp(P{3})
which gives this:
P{1}
7 7 4 4 1 1
4 1 7 1 4 7
1 4 1 7 7 4
P{2}
8 8 5 5 2 2
5 2 8 2 5 8
2 5 2 8 8 5
P{3}
9 9 6 6 3 3
6 3 9 3 6 9
3 6 3 9 9 6
Then you could implement a loop in which you take every column of say P{1} and get the possible combinations with the columns from P{2}, P{3} and so on. There is probably a built-in function for this but I don't know it sorry. I hope that helps!
##### 2 CommentsShowHide 1 older comment
Ben11 on 25 Jul 2014
Oh shoot sorry then I guess I misunderstood the question! :)

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