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
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