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

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Nora Khaled on 23 Jul 2019
Edited: Andrei Bobrov on 23 Jul 2019
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.

Andrei Bobrov on 23 Jul 2019
Edited: Andrei Bobrov on 23 Jul 2019
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
Nora Khaled on 23 Jul 2019
Thank you !
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()?

Rik on 23 Jul 2019
https://www.mathworks.com/help/matlab/ref/perms.html
Nora Khaled on 23 Jul 2019
Edited: Nora Khaled on 23 Jul 2019
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 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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