You should try to restructure your problem to make it fit the tools you already have.
If we figure out a way to generate an order, we can use randfixedsum to generate the actual values.
If you have m=5,N=2,S=10, then you can first list all possible permutations:
m = 5;N = 2;S = 10;
rng(0) % fix random seed to make this example the same each time
A = rand;B = rand;
[A A A A B];
[A A A B B];
[A A B B B];
[A B B B B];
A and B must each occur at least once, so we only need to generate a list for the m-N remaining elements.
remaining_elements = randi(N,1,m-N)
Now we can count how often each element is selected:
Occurences_per_value = 1+histcounts(remaining_elements,0.5:(0.5+N))
Now let's actually generate some random numbers:
x = randfixedsum(N,1,S,0,S).'
You will notice, this only results in N numbers, not m. The trick is to divide these numbers and replicate them:
x./Occurences_per_value
We can use repelem to replicate the numbers as often as we need them:
repelem('AB',Occurences_per_value)
RandomData = repelem(x./Occurences_per_value,Occurences_per_value)
But we have a last problem: these values are not randomly ordered. Once last call to randperm will fix that:
RandomData = RandomData(randperm(end))
All in one compact (uncommented) block:
Occurences_per_value = 1+histcounts(randi(N,1,m-N),0.5:(0.5+N))
RandomData = repelem((randfixedsum(N,1,S,0,S).')./Occurences_per_value,Occurences_per_value)
RandomData = RandomData(randperm(end))
function [x,v] = randfixedsum(n,m,s,a,b)
% https://www.mathworks.com/matlabcentral/fileexchange/9700-random-vectors-with-fixed-sum
end
