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How to create a matrix out of all the possible combinations of a vector

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Hi !
I want to fill a vector with specifice numbers of 1's and -1's, and the rest are zeros. And get all possible combinations in each row of a matrix.
For example, if I have a vector of length 12 and I want to have 5 elements = +1 and 4 elements = -1
Then, the results should be like:
M=[1 1 1 1 1 -1 -1 -1 -1 0 0 0; 0 0 0 1 1 1 1 1 -1 -1 -1 -1; -1 1 1 1 1 1 -1 -1 -1 0 0 0; .....]
and every other distinct combination of the three numbers.

Accepted Answer

Andrei Bobrov
Andrei Bobrov on 23 Jul 2019
Edited: Andrei Bobrov on 23 Jul 2019
Please see answer by Roger Stafford.
In your case:
a = 3:5;
v = [0,-1,1];
n = cumsum(a,'reverse');
C1 = nchoosek(1:n(1),a(1)); % Here are the two calls on 'nchoosek'
C2 = nchoosek(1:n(2),a(2));
M = ones(size(C1,1)*size(C2,1),n(1)); % First, fill M with all 1's
k1 = 0;
for k2 = 1:size(C1,1)
p1 = C1(k2,:); % Use C1 to generate indices for inserting 0's
q1 = 1:n(1);
q1(p1) = []; % These indices will point to -1 and 1 locations
for k3 = 1:size(C2,1)
p2 = C2(k3,:); % Use C2 to generate indices for inserting -1's
k1 = k1 + 1; % Advance the row index of M
M(k1,p1) = v(1); % Insert 0's
M(k1,q1(p2)) = v(2); % and -1's
end
end
  2 Comments
Rik
Rik on 23 Jul 2019
Just out of curiosity (and because I can't test myself because I'm on mobile): does this code allow longer vectors? And if so, why? What makes this approach fundamentally different from perms()?

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More Answers (1)

Rik
Rik on 23 Jul 2019
https://www.mathworks.com/help/matlab/ref/perms.html
  2 Comments
Nora Khaled
Nora Khaled on 23 Jul 2019
Edited: Nora Khaled on 23 Jul 2019
Thank you for your answer!
This works for small numbers like in the example total of 10.
but it does not work with my actual implmentation it does not.
I get error msg:
Maximum variable size allowed by the program is exceeded.
Rik
Rik on 23 Jul 2019
All combinations will result in a huge matrix if you have a large number of elements. As the documentation warns: this is only practical for a small number of elements. This is a fundamental problem that you need to solve separately.

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