Creating random integer row array each element different upper limit and sum of elements add up to a number

I am looking for a intutuve code to generate 1x6 array where each element is random integer (with in specific upper limit) and sums to a given number.

For example a random array where element lower limit [ 0 0 0 0 0 0] and upper limit [ 9 12 25 6 14 7]. The sum of the random integer number adds up to 24, e.g.

[4 3 8 1 3 4 1]

Answer 1

[Ameer Hamza]

See this excellent FEX package by John: https://www.mathworks.com/matlabcentral/fileexchange/49795-randfixedlinearcombination. However, It generates fractional numbers. Following code proposes one modification. I don't know how it will change the probability distribution.

lb = [0 0 0 0 0 0];
ub = [9 12 25 6 14 7];
n = numel(lb);

s = 24;

x = round(randFixedLinearCombination(1, s, [1 1 1 1 1 1], lb, ub));
k = sum(x) - s;

if k > 0
    idx = find(x >= (lb+1));
    idx = idx(randperm(numel(idx), k));
    x(idx) = x(idx) - 1;
else
    idx = find(x <= (ub-1));
    idx = idx(randperm(numel(idx), -k));
    x(idx) = x(idx) + 1;
end

[Biswanath Mahanty]

The logic is very intutive, however the there is no inbuild function named "randFixedLinearCombination()" in Matlab 2020. The randFixedLinearCombination() is user contributed is available in Matlab central and must be placed in the matlab path.

I though a segmented iterative approach shared here

[Bruno Luong]

I believe it must have a minus in the second if-branch

idx = randperm(n, -k)

[John D'Errico]

You download randFixedLinearCombination from the File Exchange. It is part of MATLAB, in the sense that you need do nothing more than download it. NO cost. Ameer gave you the link.

[Ameer Hamza]

John: Thanks for the comment.

Bruno: Thanks for pointing out. You are correct. It should be -k.

Biswanath: As John mentioned, download this package from the link and place it in MATLAB's path: https://www.mathworks.com/help/matlab/matlab_env/add-remove-or-reorder-folders-on-the-search-path.html

[Bruno Luong]

The rounding method is still flawed. The results might get out of bound once they are added by +/-1. You have to select the subset more careful than randperm.

[Ameer Hamza]

Yes, thanks for pointing out the issue. I have updated the code. I am not sure if there still are some cases where it will fail to meet the constraint.

[Bruno Luong]

I think you can do better if you replace the first filtering with <= >= tests rather than strict inequality.

It still not perfect though.

[Ameer Hamza]

Yes, I guess this will fail when the bounds are very tight in accordance with the sum constraints. The point about inequality is also valid. For the given bounds, the method does not seem to fail.