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From: oliver@athena.mit.edu (James D. Oliver III)
Newsgroups: comp.lang.fortran
Subject: Re: Random Number Functions--Generate versus Input
Message-ID: <1990Nov13.053812.19914@athena.mit.edu>
Date: 13 Nov 90 05:38:12 GMT
References: <1990Nov8.170334.24579@athena.mit.edu> <1990Nov8.215752.7075@athena.mit.edu> <108474@convex.convex.com>
Sender: daemon@athena.mit.edu (Mr Background)
Reply-To: oliver@athena.mit.edu (James D. Oliver III)
Organization: Massachusetts Institute of Technology
Lines: 41

In article <108474@convex.convex.com>, dodson@convex.COM (Dave Dodson) writes:
>	real x(n),y(n),z(n),r(n)
>	integer indx(n)
>	do 10 i = 1, n
>	    x(i) = 2.0 * ranf() - 1.0
>	    y(i) = 2.0 * ranf() - 1.0
>	    z(i) = 2.0 * ranf() - 1.0
>	    r(i) = x(i)**2 + y(i)**2 + z(i)**2
>   10	continue
>	call whenflt (n,r,1,1.0,indx,nindx)
>cdir$	appropriate compiler directive to ignore dependencies in the loop.
>	do 20 i = 1, nindx
>	    j = indx(i)
>	    t = 1.0 / sqrt(r(j))
>	    x(i) = t * x(j)
>	    y(i) = t * y(j)
>	    z(i) = t * z(j)
>   20	continue

Your algorithm is the same as the original scheme proposed by von Neumann
for generating random vectors.  It's efficiency is given by the area of a
unit cube divided by a unit sphere, so 18/pi=5.73 random numbers plus a
square root must be generated for each vector, as opposed to the 2.55 plus
a square root for the Marsaglia method I posted in a recent follow-up

>You are using one of our competitors' machines, so I haven't tried this,
>but I believe it will all vectorize on a Cray, as it does on a Convex.  

Hey, offer me a price, my code knows no loyalty! :-)

>P.S.  I don't think you can calculate z from x and y and get a truly uniform
>distribution of unit vectors.  You have to generate x, y, and z independently
>and reject those outside the unit sphere to get uniformity.

As I said, Marsaglia devised a clever way around this; see a more recent
posting. 
--
____________________________
	Jim Oliver   
	oliver@athena.mit.edu /	joliver@hstbme.mit.edu
	oliver%mitwccf.BITNET@MITVMA.MIT.EDU