[R] Random unit vectors in R^{n}

[Thomas Lumley]

On 26 Aug 2002, A.J. Rossini wrote:

> >>>>> "tom" == Tom Richards <Richards> writes:
>
>     tom> Hello: Can you tell me if there's a simple way to generate in
>     tom> R random vectors on the unit sphere in R^{n}?  Additionally,
>     tom> are there references for this question?  Thanks in advance.
>
>
> I suspect that you can generate them in R^n and then scale?  (i.e.
> use (x/|x|) ).

If you use a spherically symmetric distribution to generate them from, eg
making the coordinates independent standard Normals rather than
independent uniform[-1,1]  or, say, Cauchy

eg
    x<-matrix(rnorm(n*nsamples),nrow=nsamples)
    r<-x/sqrt(rowSums(x*x))
works.


	-thomas

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