Re: [R] power of a matrix

From: Peter Dalgaard <p.dalgaard_at_biostat.ku.dk>
Date: Thu 18 Aug 2005 - 17:44:02 EST

Gabor Grothendieck <ggrothendieck@gmail.com> writes:

> Its expm.

Doh. I had even looked up its help page...  

>
> On 8/17/05, Spencer Graves <spencer.graves@pdf.com> wrote:
> > Hi, Peter:
> >
> > I couldn't find "mexp" in the Matrix package, but I did find it in
> > fMultivar and in Lindsey's rmutil. These are different functions, but
> > produced essentially the same answer for mexp(array(1:4, dim=c(2,2))).
> > While hunting for that, I also also found reference by Doug Bates in a
> > previous interchange on r-help to "a classic paper ... I would recommend
> > reading":
> >
> > Moler C., van Loan C., (2003); _Nineteen dubious ways to compute
> > the exponential of a matrix, twenty-five years later_, SIAM
> > Review 45, 3-49.
> >
> > This paper was cited in the help page for mexp in fMultivar but not
> > in rmutil.

As far as I remember, that's because rmutil is using one of the more dubious methods, namely eigendecomposition. It breaks down if there are eigenvalues with multiplicity greater than 1, which does happen (systematically) in some statistical models.

> > spencer graves
> >
> > Peter Dalgaard wrote:
> >
> > > "Rau, Roland" <Rau@demogr.mpg.de> writes:
> > >
> > >
> > >>Thank you very much! Thanks also to the authors of this function,
> > >>Vincente Canto Cassola and Martin Maechler!
> > >>
> > >>This is exactly what I hoped for.
> > >
> > > ....
> > >
> > >>>look at function ?mtx.exp() in the Malmig package, e.g.,
> > >
> > >
> > > Also, there is mexp() in the Matrix package. I'm not sure about the
> > > relative merits. mexp() is one of the less dubious implementations of
> > > matrix exponentials, but it does require to and from class "Matrix".
> > > mtx.exp is a bit unfortunately named as it appears to calculate matrix
> > > *powers* (which in this case is what you need).
> > >
> >
> > --
> > Spencer Graves, PhD
> > Senior Development Engineer
> > PDF Solutions, Inc.
> > 333 West San Carlos Street Suite 700
> > San Jose, CA 95110, USA
> >
> > spencer.graves@pdf.com
> > www.pdf.com <http://www.pdf.com>
> > Tel: 408-938-4420
> > Fax: 408-280-7915
> >
> > ______________________________________________
> > R-help@stat.math.ethz.ch mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
> >
>

-- 
   O__  ---- Peter Dalgaard             ุster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk)                  FAX: (+45) 35327907

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Received on Fri Aug 19 20:32:10 2005

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