From: Dimitris Rizopoulos <dimitris.rizopoulos_at_med.kuleuven.be>

Date: Wed 17 Aug 2005 - 21:38:16 EST

library(Malmig)

Dimitris Rizopoulos

Ph.D. Student

Biostatistical Centre

School of Public Health

Catholic University of Leuven

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 Received on Wed Aug 17 21:41:18 2005

Date: Wed 17 Aug 2005 - 21:38:16 EST

look at function ?mtx.exp() in the Malmig package, e.g.,

A <- matrix(c(0,1,5, 0.3,0,0, 0,0.5,0), ncol=3, byrow=TRUE) n.zero <- c(1,0,0)

##################

library(Malmig)

all.equal(A %*% (A %*% n.zero), mtx.exp(A, 2) %*% n.zero) all.equal(A %*% (A %*% (A %*% n.zero)), mtx.exp(A, 3) %*% n.zero)

mtx.exp(A, 15) %*% n.zero

I hope it helps.

Best,

Dimitris

Dimitris Rizopoulos

Ph.D. Student

Biostatistical Centre

School of Public Health

Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium

Tel: +32/16/336899 Fax: +32/16/337015 Web: http://www.med.kuleuven.be/biostat/ http://www.student.kuleuven.be/~m0390867/dimitris.htm

- Original Message ----- From: "Rau, Roland" <Rau@demogr.mpg.de> To: "R-Help" <r-help@stat.math.ethz.ch> Sent: Wednesday, August 17, 2005 12:15 PM Subject: [R] power of a matrix

> Dear all,

*>
**> I have a population with three age-classes, at time t=0 the
**> population
**> is:
**> n.zero <- c(1,0,0)
**> I have a transition matrix A which denotes "fertility" and
**> "survival":
**>
**> A <- matrix(c(0,1,5, 0.3,0,0, 0,0.5,0), ncol=3, byrow=TRUE)
**>
**> To obtain the population at t=1, I calculate:
**> A %*% n.zero
**>
**> To obtain the population t=2, I calculate:
**> A %*% (A %*% n.zero)
**>
**> ... and so on ...
**>
**> I thought now to obtain the population at time x, I should simply
**> do:
**> A^x %*% n.zero
**>
**> But this, of course, does not work since the following two
**> statements
**> are not equivalent for matrices:
**> A %*% A
**> A * A
**>
**> Is there something like a "powermatrix"-function?
**>
**> Thanks,
**> Roland
**>
**> P.S. The example is taken from:
**> Example 3.1 ("A linear, time-invariant model") from Keyfitz/Caswell:
**> "Applied Mathematical Demography", 3rd Edition, 2005, p. 52f
**>
**>
**> +++++
**> This mail has been sent through the MPI for Demographic
**> Rese...{{dropped}}
**>
**> ______________________________________________
**> 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
**>
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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 Received on Wed Aug 17 21:41:18 2005

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