Random positive numbers with constant sum

How to form a matrix such that every time the numbers add up to be the same

z=0.4
minimum z= 0.2
maximum z= 0.6
R is a random number between 0.2 and 0.6
a 1x10 R matrix is generated but the sum must be equal to (0.4 x 10 = 4)

I tried running the following using randn but it gives negatives numbers and the sums are not constant

z=0.4
zmax=1.5*z;
zmin=0.5*z;
R=zmin+randn(1,10)*(zmax-zmin);

Eg. Desired random number R matrix
[0.35 0.27 0.43 0.51 0.54 0.44 0.37 0.29 0.59 0.21]
sum(R)=4 < must be consistent for every matrix generated

Answer 1

[John D'Errico]

First of all, there is no such thing as a random positive number. If you don't define the distribution, then it is meaningless to talk about a random number.

And you can't have a uniform random number on the interval (0,inf].

You CAN define a uniform random number on A BOUNDED SET. So, the interval[0,1]. But if you want to constrain the sum to be constant, then be careful. This question gets asked over and over again, and people answer it thinking you can solve it trivially. They generate a vector of numbers, and then scale them so the sum is the desired value. WRONG. This generates a distribution that is not in fact uniform.

So use a tool like randfixedsum , as found on the file exchange, or my own randFixedLinearCombination , also on the file exchange.

The latter tool is more capable for some problems, but for long vectors that sum to a constant, it will be inefficient. It probably won't work well in more than about 6 dimensions. But randfixedsum is fine beyond that point.

So to generate a set of 10 numbers that sum to 4, where each element in the vector is in the interval [.2, .6], is as simple as:

S = randfixedsum(10,1,4,.2,.6)
S =
    0.4354
    0.5535
    0.2221
    0.3235
    0.4106
    0.5368
    0.3963
    0.2636
    0.4705
    0.3877

sum(S)
ans =
    4.0000

Again, DON'T use a rescaling scheme. Randfixedsum is perfect for the problem.

[Joseph Lee]

Thanks for the detailed response

[Joseph Lee]

Does the sum only work for columns? Im trying to get the sum for rows to be constant not the column

eg.
  randfixedsum(10,1300,4,.2,.6)
  Error using randfixedsum (line 46)
  Inequalities n*a <= s <= n*b and a < b must hold.

[John D'Errico]

Be serious. Surely it cannot be difficult to transpose the result?

R = randfixedsum(10,1300,4,.2,.6)';
size(R)
ans =
      1300          10

sum(R(1,:))
ans =
     4

[Joseph Lee]

my mistake, it was not related to that, just that the formula i input for the sum was wrong which caused that error. Thanks a lot

Answer 2

[Torsten]

https://de.mathworks.com/matlabcentral/fileexchange/9700-random-vectors-with-fixed-sum

Best wishes

Torsten.