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
+++++
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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 at demogr.mpg.de>
To: "R-Help" <r-help at 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 at 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
>
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. Best, Roland> -----Original Message----- > From: Dimitris Rizopoulos > [mailto:dimitris.rizopoulos at med.kuleuven.be] > Sent: Wednesday, August 17, 2005 1:38 PM > To: Rau, Roland > Cc: r-help at stat.math.ethz.ch > Subject: Re: [R] power of a matrix > > 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 at demogr.mpg.de> > To: "R-Help" <r-help at 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 at 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 > > > >+++++ This mail has been sent through the MPI for Demographic Rese...{{dropped}}