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

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.

Answer 1

[Andrei Bobrov]

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

[Nora Khaled]

Thank you !

[Rik]

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()?

Answer 2

[Rik]

https://www.mathworks.com/help/matlab/ref/perms.html

[Nora Khaled]

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]

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.