Generation of all possible vectors with constraints
2 views (last 30 days)
Show older comments
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!
Accepted Answer
Naren
on 7 May 2024
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.
4 Comments
Dyuman Joshi
on 9 May 2024
Edited: Dyuman Joshi
on 9 May 2024
@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.
More Answers (0)
See Also
Categories
Find more on Logical in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!