solving memory problem for this code

I run this code for X that has size 42*12

if size(X,2)==1
    M=0;
end
    n = size(X, 1);
    
    rank_X = rank(X);
    for d = 1:(n-1)
        newn = n - d;
        indices_matrix = combnk(1:n, newn);
        Mset = 0;  % for breaking the loop need to define initial value
        for j = 1:size(indices_matrix, 1)
            indices = indices_matrix(j, :);
            X_minus_d = X(indices, :);
            rank_X_minus_d = rank(X_minus_d);
            if (rank_X_minus_d < rank_X)
                dstar = d;
                M = n - dstar;
                Mset = 1;
                break
            end
        end
        if Mset == 1 % breaking from first loop
            break
        end
    end

And gives this error

Out of memory.

How can I fix this problem?

Answer 1

[Walter Roberson]

You cannot fix that. combnk(1:n,newn) takes all combinations of 1:n, newn at a time, where your n is 42, and newn is 41 down to 1. The maximum number of combinations is 538257874440 when newn = 21 . For that, each entry would be length 21 doubles, 8 bytes per double, so you would need 538257874440 * 21 * 8 = 90427322905920 bytes, which is about 83 terabytes of memory. Do you have that much RAM in your system?: