How to generate repeatable random multiple vectors with Specific Number of Values and Fixed Sum?

Hello everybody,

I want to create repeatable random multiple vectors with Specific Number of Values and Fixed Sum.

for example, in case of Specific Number of Values 3 and Fixed Sum 10,

If m row is 5, the random number can be [1; 2; 2; 4; 1], 1+2+2+4+1 =10 and Number of Values 3 (1,2 and 4 used)

or [1.1; 2.1; 2.1; 3.6; 1.1]. 1.1+2.1+2.1+3.6+1.1 =10 and Number of Values 3 (1.1, 2.1 and 3.6 used)

in case of Specific Number of Values 2 and Fixed Sum 10,

If m row is 4, the random number can be [2; 3; 3; 2], 2+3+3+2 =10 and Number of Values 2 (2 and 3 used)

or [1.5; 3.5; 3.5; 1.5]. 1.5+3.5+3.5+1.5 =10 and Number of Values 2 (1.5 and 3.5 used)

in case of Specific Number of Values 1 and Fixed Sum 10,

If m row is 4, the random number can be [2.5; 2.5; 2.5; 2.5]. 2.5+2.5+2.5+2.5 =10 and Number of Values 1 (2.5 only used)

Specific Number of Values 1 means only one value can be used,

I found the randfixedsum code provided by Roger Stafford. It is wonderful code, but it generate all random numers

without Specific Number of Values.

Please give me some help how to make the code for it.

Answer 1

[Rik]

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)

remaining_elements = 1×3

1 2 2

Now we can count how often each element is selected:

Occurences_per_value = 1+histcounts(remaining_elements,0.5:(0.5+N))

Occurences_per_value = 1×2

2 3

Now let's actually generate some random numbers:

x = randfixedsum(N,1,S,0,S).'

x = 1×2

6.3925 3.6075

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

ans = 1×2

3.1962 1.2025

We can use repelem to replicate the numbers as often as we need them:

repelem('AB',Occurences_per_value)

ans = 'AABBB'

RandomData = repelem(x./Occurences_per_value,Occurences_per_value)

RandomData = 1×5

3.1962 3.1962 1.2025 1.2025 1.2025

But we have a last problem: these values are not randomly ordered. Once last call to randperm will fix that:

RandomData = RandomData(randperm(end))

RandomData = 1×5

3.1962 1.2025 1.2025 3.1962 1.2025

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

[Smithy]

Wow... thank you very mcuh. I really really appreciate with it. It works perfect.

Answer 2

[Bruno Luong]

Just split randomly at most m times on top of randfixedsum output

m=5;
nvalues=3;
starget=10;

n=diff([0 sort(randperm(m-1,nvalues-1)) m]); % nvalues integers sum to m
r=randfixedsum(nvalues,1,starget,0,10); % nvalues positive numbers sum to starget
r=repelem(r./n',n)

r = 5×1

2.3823 2.3823 1.2863 1.9745 1.9745

[Smithy]

Thank you very for your answer, It is really wonderful. It works really well.

[Bruno Luong]

This code generate a slightly different statistics property. The difference between vallues has probably smaller rms than my forst code, if such difference is important for whatever simulation you do.

m=5;
nvalues=3;
starget=10;

i = sort(randperm(m-1,nvalues-1));
n = diff([0 i m]);                   % nvalues integers sum to m
r = randfixedsum(m,1,starget,0,10)';    % m positive numbers sum to starget
c = cumsum(r);
r = diff([0 c(i) starget]);             % nvalues integers sum to starget 
r = repelem(r./n, n)

r = 1×5

1.6626 1.6626 1.4038 2.6355 2.6355