How to generate matrix with mean equal to a specific number?

How can I generate a random matrix A with

(for example A is 10x10) mean(A(:)) = 0.5 or says sum(sum(A)) / (10*10) = 0.5

Every element in matrix randomly from 0 to 1.

Thanks

Kai

[Thorsten]

It is not possible to meet your conditions: If every element must be picked randomly between 0 and 1, it can be easily > 0.5, invalidating your condition that the sum must be equal to 0.5. Likewise, if the sum must be 0.5, the first element r(1) can be picked from [0, 0.5], the second element r(2) from [0, 0.5-sum(r)], and so on, until the final element which is not random at all but must be 0.5-sum(r), all invalidating your condition that the number must be randomly between 0 and 1. So what do you actually want to do?

[Roger Stafford]

What you are saying, Thorsten, would only be true if one assumes that all number selections must be statistically mutually independent of one another, but Kai stated no such requirement. In the example I gave here of choosing three random variables, each between 0 and 1, whose sum is 3/2, the random variables can be so selected that the planar two-dimensional hexagon of number triples which satisfy all these conditions is uniformly distributed area-wise. It is my opinion that this satisfies Kai's requirements for randomness, but obviously the three random variables would not be mutually independent.

Answer 1

[Roger Stafford]

You are asking for the sum of n = 100 random numbers with values between 0 and 1 to have a sum of exactly 50. That is just what the File Exchange routine randfixedsum is designed to accomplish.

Also with multiple solutions it will produce a statistically uniform distribution on the (n-1)-dimensional polytope which satisfies this sum condition. For example, if your n were equal to 3, it would produce a uniform distribution within the two-dimensional hexagon x+y+z=3/2 with x, y, and z all bounded between 0 and 1 (similar to the image shown in the above site.)

[Jan]

@Roger: Thanks for the clarification. I've delete my answer, because I obviously had misinterpreted the term "randomly from 0 to 1".

[Kai]

Thanks, Roger. It works well