Randomly initializing a N-element vector

[jalex]

I need to randomly initialize a N-element vector such that

 (a) every element is between 0 and 1
 (b) the sum of all elements is 1

I find that uniformly sampling the space carved out by those
requirements a bit tricky.  The first thing I tried was to generate a
vector in the N-dimensional cube---since it is easy to do so without
bias---and then throw the vector away if it doesn't fall within the
space I'm interested in.  I.e., something like:

    float sum;
    int i;
    BOOL in_simplex = NO;
    do {
      sum = 0.0;
      for (i=0; i<11; i++) {
        initialStateVector[i] = 
          [uniformDblRand getDoubleWithMin: 0.0 withMax: 1.0];
        sum += initialStateVector[i];
      }

      if (sum <= 1.0) in_simplex = YES;
    } while (in_simplex == NO);

Of course, if I had thought for a little longer before hammering out
this code, I would have realized that the space I'm interested in
takes up so little volume in the N-dimensional cube that I'll have to
wait too long to get a valid point. 

Since this probably is a well-known problem, I'd appreciate any
pointers, references, etc. on how to handle this.  


Thanks,

Jason Alexander
Logic & Philosophy of Science
University of California, Irvine


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