On Sun, 27 Sep 2009, Douglas Bates wrote:
There is a logm function in the expm package in the expm project on
R-forge. See http://expm.R-forge.R-project.org/
Martin was the person who added that function so I will defer to his
explanations of what it does. I know he has been traveling and it may
be a day or two before he can get to this thread.
Douglas,
Thanks for this note.
The logm() function in the expm package does the trick.
It seems to properly handle block structures for non-diagonalizable
matrices:
require(expm)
M <- matrix(c(0,1,0,0),2)
expm(M)
[,1] [,2]
[1,] 1 0
[2,] 1 1
logm(expm(M))
[,1] [,2]
[1,] 0 0
[2,] 1 0
And thanks to Vincent, Martin, et al for this package!
:-)
Chuck
On Sun, Sep 27, 2009 at 11:44 AM, Charles C. Berry <cbe...@tajo.ucsd.edu> wrote:
On Sat, 26 Sep 2009, spencerg wrote:
Sylvester's formula
(http://en.wikipedia.org/wiki/Sylvester%27s_formula) applies to a square
matrix A = S L solve(S), where L = a diagonal matrix and S = matrix of
eigenvectors. Let "f" be an analytic function [for which f(A) is well
defined]. Then f(A) = S f(L) solve(S).
We can code this as follows:
sylvester <- function(x, f){
n <- nrow(x)
eig <- eigen(x)
vi <- solve(eig$vectors)
with(eig, (vectors * rep(f(values), each=n)) %*% vi)
}
logm <- function(x)sylvester(x, log)
Example:
A <- matrix(1:4, 2)
eA <- expm(A)
logm(eA)
With Chuck Berry's example, we get the following:
M <- matrix( c(0,1,0,0), 2 )
sylvester(M, log)
The case I gave would be
sylvester( as.matrix( expm( M ) ), log )
for which the perfectly sensible answer is M, not what appears here:
Error in solve.default(eig$vectors) :
system is computationally singular: reciprocal condition number =
1.00208e-292
This is a perfectly sensible answer in this case. We get the
same result from "sylvester(M, exp)", though "expm(M)" works fine.
A better algorithm for this could be obtains by studying the code
for "expm" in the Matrix package and the references in the associated help
page.
I doubt that code already in R will handle cases requiring Jordan blocks for
evaluation of the matrix logarithm (which cases arise in the context of
discrete state, continuous time Markov chains) without requiring one to
built that code more or less from scratch.
I'd be happy to hear that this is not so.
HTH,
Chuck
Hope this helps. Spencer
Gabor Grothendieck wrote:
Often one uses matrix logarithms on symmetric positive definite
matrices so the assumption of being symmetric is sufficient in many
cases.
On Sat, Sep 26, 2009 at 7:28 PM, Charles C. Berry <cbe...@tajo.ucsd.edu>
wrote:
On Sat, 26 Sep 2009, Gabor Grothendieck wrote:
OK. Try this:
library(Matrix)
M <- matrix(c(2, 1, 1, 2), 2); M
[,1] [,2]
[1,] 2 1
[2,] 1 2
Right. expm( M ) is diagonalizable.
But for
M <- matrix( c(0,1,0,0), 2 )
you get the wrong result.
Maybe I should have added that I do not see the machinery in R for >
dealing
with Jordan blocks.
HTH,
Chuck
# log of expm(M) is original matrix M
with(eigen(expm(M)), vectors %*% diag(log(values)) %*% t(vectors))
[,1] [,2]
[1,] 2 1
[2,] 1 2
On Sat, Sep 26, 2009 at 6:24 PM, Charles C. Berry > >
<cbe...@tajo.ucsd.edu>
wrote:
On Sat, 26 Sep 2009, Gabor Grothendieck wrote:
Try:
expm( - M)
Mimosa probably meant say 'the inverse function'.
I do not see one in R.
Chuck
On Sat, Sep 26, 2009 at 5:06 PM, Mimosa Zeus
<mimosa1...@yahoo.fr>
wrote:
Dear R users,
Does anyone has implemented the inverse of the
matrix > > > > > exponential (expm
in the package Matrix)?
In Matlab, there're logm and expm, there's only expm
in R.
Cheers
Mimosa
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Dept of Family/Preventive
Medicine
E mailto:cbe...@tajo.ucsd.edu UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego >
92093-0901
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PLEASE do read the posting guide
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Charles C. Berry (858) 534-2098
Dept of Family/Preventive
Medicine
E mailto:cbe...@tajo.ucsd.edu UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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Dept of Family/Preventive Medicine
E mailto:cbe...@tajo.ucsd.edu UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901
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