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Topic: Generate random numbers with fixed sum and different constraints
Replies: 25   Last Post: Sep 17, 2013 2:28 AM

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 Bruno Luong Posts: 9,822 Registered: 7/26/08
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 n-dimensional hypersphere of radius 1/2 enclosed in an n-dimensional cube with unit-length sides. The n-dimensional 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/N-sphere.) For n = 50 this would be 1.53E-28, 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

Date Subject Author
11/14/12 Dmitrey Yershov
11/17/12 Greg Heath
11/17/12 Roger Stafford
11/17/12 Bruno Luong
11/17/12 Roger Stafford
11/18/12 Dmitrey Yershov
11/18/12 Bruno Luong
11/19/12 Bruno Luong
11/19/12 Dmitrey Yershov
11/19/12 Bruno Luong
11/19/12 Dmitrey Yershov
11/19/12 Bruno Luong
11/19/12 Bruno Luong
11/19/12 Roger Stafford
11/20/12 Bruno Luong
11/20/12 Bruno Luong
11/20/12 Roger Stafford
11/21/12 Bruno Luong
11/21/12 james bejon
11/20/12 james bejon
9/17/13 JS Hong
9/17/13 JS Hong
11/19/12 David Epstein
11/19/12 Roger Stafford
11/20/12 Bruno Luong
11/17/12 Greg Heath