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

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.

Answer 1

[José-Luis]

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

[samad khansari]

Thank you very much. This was the answer I expected. Now, what permutations are there if we want n-2 columnc be the same and just 2 columns swap. Here is an example of what I mean: a=[1 2 3 4;5 6 7 8;9 10 11 12;13 14 15 16] then indices would be (1,2,3,4) now I want to know how can I implement (2,1,3,4) (3,2,1,4) (4,2,3,1) (1,3,2,4) (1,4,3,2) (1,2,4,3) as you see at any permutation just 2 indices are swaping and the rest are the same as in (1,2,3,4) Thank you in advance

[Chenyang Zhang]

how to store all the your_mat value from every loop into one matrix? Thanks in advance

[Chenyang Zhang]

In this case how do you get a 18x3 matrix as a result? Thank you

Answer 2

[Ben11]

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!

[samad khansari]

Thank you very much but not helping :)

[Ben11]

Oh shoot sorry then I guess I misunderstood the question! :)