
Re: Generate random numbers with fixed sum and different constraints
Posted:
Nov 20, 2012 2:17 AM


"Roger Stafford" wrote in message <k8ens1$kfr$1@newscl01ah.mathworks.com>... > "David Epstein" <David.Epstein.spam@remove.warwick.ac.uk> wrote in message <k8d1g1$4gr$1@newscl01ah.mathworks.com>... > > @Roger: what were your reasons for rejecting this approach in your randfixedsum package on FEX? >           > I think you will find that as n increases the acceptance rate in such a procedure shrinks toward zero altogether too rapidly, thereby restricting one in practice to a rather small range for n. > > To get a feeling for this, consider an ndimensional hypersphere of radius 1/2 enclosed in an ndimensional cube with unitlength sides. The ndimensional volume of the cube is 1 whereas that of the hypersphere for even n is (pi/4)^(n/2)/(n/2)! (See http://en.wikipedia.org/wiki/Nsphere.) For n = 50 this would be 1.53E28, a small acceptance rate indeed.
IMHO, the difficulty is in the same order than solving linear programing with the constraints A*y <= b, which have to find accurately the vertices without ambiguity. At least for the convex part.
I have little experience in Delaunay in high dimensional space. But I could imagine it 's challenging too.
Bruno

