Generation of all possible vectors with constraints

Hi

I want to create all possible vectors comprised of 0, 1 or/and -1 such that length of each vector is 7 and it contains exactly 3 zeros. Finally the result should be in a matrix form in which each row is an aforsaid type vector.

e.g. M= 1 0 1 -1 0 -1 0

0 0 -1 0 1 1 1

-1 -1 -1 0 -1 0 0

:::::::::::::::::::::::

Thank you!

[Sheet]

Yes.

Answer 1

[Naren]

Hello,

To generate all possible vectors of length 7 that contains exactly 3 zeros and each of the remaining elements being either 1 or -1, and then to represent these vectors in a matrix form with each row being one of these vectors in MATLAB, you can use the following code:

n = 7;
zp = combnk(1:n, 3); % Positions for zeros
s = size(zp, 1) * 2^(n-3); % Total number of vectors with 3 zeros and the rest being either 1 or -1
M = zeros(s, n);
c = 1;

for i = 1:size(zp, 1)
    non_zero_combinations = dec2bin(0:15) - '0';
    non_zero_combinations(non_zero_combinations == 0) = -1;
    
    % Insert zeros and non-zeros into the vectors
    for j = 1:size(non_zero_combinations, 1)
        v = ones(1, n);
        % Set the three chosen positions to zero
        v(zp(i, :)) = 0;
        % Fill the remaining positions with current combination of 1s and -1s
        non_zp = setdiff(1:n, zp(i, :));
        for k = 1:length(non_zp)
            v(non_zp(k)) = non_zero_combinations(j, k);
        end
        % Add the v to the matrix
        M(c, :) = v;
        c = c + 1;
    end
end

Regards.

[Sheet]

Thank you Naren!

It worked.

[Sheet]

Hi Naren,

I just wanted to understand the code. In line 7 "non_zero_combinations = dec2bin(0:15)" why did you use 15? Is it related to some calculations in previous lines? Could you please enlighten me?

[Dyuman Joshi]

@Sheet, The 0:15 i.e. 16 values comes from 2^4 non-zeros combinations (2 values for 7-3 = 4 spaces) for a particular set of placementof elements in 7 spaces.

[Sheet]

Thank you Dyuman! I got it।