Matlab function for creating random number satisfying constraints

Question

As an input I have two number x and y. x>y. I want to create exactly y non-zero random number which their sum will be equal to x. I know randi([min max]) function . Can you help me?

just recalled it might be a possible duplicate of [Random numbers that add to 100: Matlab](http://stackoverflow.com/questions/8064629/random-numbers-that-add-to-100-matlab) — bla, Jan 04 '13 at 23:07

score 4 · Accepted Answer · answered Jan 04 '13 at 22:24

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If I got it right, you want something like this:

data = rand(1,y);
data = data * x / sum(data);

data will contain exactly y positive uniformly distributed numbers which sum equals to x.

answered Jan 04 '13 at 22:24

Leonid Beschastny

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score 2 · Answer 2 · answered Jan 04 '13 at 22:19

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Check out the file random vectors generator with fixed sum in Matlab FEX. I believe this will answer your question.

answered Jan 04 '13 at 22:19

bla

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Thanks I will check it just one thing all the y numbers should be non zero. – Sara Jan 04 '13 at 22:21

score 0 · Answer 3 · edited Feb 20 '13 at 19:19

Leonid's approach will certainly generate a set of random numbers that have the correct sum, but it won't select uniformly over the allowed space. If this is important, an approach that will work is the following:

(with x = 1):

Generate Y-1 random numbers uniformly over [0,1].
Sort the Y-1 numbers from smallest to largest. Call these {y1,...,y_{N-1}}
Take as the Y random numbers the set {y_1-0 ,y_2-y1,...,1-y_{N-1}} == {n_1,... n_Y}.

These n_i clearly sum to one. It is easy to prove uniformity by considering the probability for a given realization of the n_i.

Matlab function for creating random number satisfying constraints

3 Answers3