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

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samad khansari 2014-7-25

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评论： Chenyang Zhang 2020-5-12

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.

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Answer 1

José-Luis 2014-7-25

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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

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Chenyang Zhang 2020-5-12

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

Chenyang Zhang 2020-5-12

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

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Answer 2

Ben11 2014-7-25

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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     4     4     1     1
   1     7     1     4     7
   4     1     7     7     4
P{2}
   8     5     5     2     2
   2     8     2     5     8
   5     2     8     8     5
P{3}
   9     6     6     3     3
   3     9     3     6     9
   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!