Re: [R] implementation of matrix logarithm (inverse of matrix exponential)
DB == Douglas Bates ba...@stat.wisc.edu
on Sun, 27 Sep 2009 17:25:39 -0500 writes:
DB There is a logm function in the expm package in the expm project on
DB R-forge. See http://expm.R-forge.R-project.org/
DB Martin was the person who added that function so I will defer to his
DB explanations of what it does. I know he has been traveling and it may
DB be a day or two before he can get to this thread.
Indeed, thank you, Doug.
Yes, I'd strongly recommend using the expm package's logm().
Computing Matrix Exponentials and Logs (and more) reliably is actually a
quite a science.
The recent addition of expm::logm() actually happened based on
a master thesis done here at ETH, and that itself was based
on *THE* reference on these topics,
Higham, N.~J. (2008). _Functions of Matrices: Theory and
Computation_; Society for Industrial and Applied Mathematics,
Philadelphia, PA, USA.
and so is are part of latest methods for the matrix exponential,
expm().
One reason that I haven't released 'expm' to CRAN yet,
has been that it hasn't been entirely clear to me what the
default 'method' should be.
The (currently only one) method, uses in Matrix::expm() is
no longer state of the art (and yes, I had plans to also
update that).
An interesting side-question is actually how to deal with such
issues, of active research rendering the state of the art to
a moving target.
In Matlab, I see they just provide the current method, so are
not bug-back-compatible with previous versions of itself.
In R, I'd at least want to provide an optional 'method' argument
and keep former methods available.
The question still remain if it's okay to change the default
method, as the state of the art advances.
For the matrix functions expm(), logm(), etc., I'd say yes,
the default should be allowed to change.
Martin Maechler, ETH Zurich
DB 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
Re: [R] implementation of matrix logarithm (inverse of matrix exponential)
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,]21
[2,]12
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,]21
[2,]12
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
[[alternative HTML version deleted]]
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible
code.
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
--
Re: [R] implementation of matrix logarithm (inverse of matrix exponential)
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.
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
[[alternative HTML
version deleted]]
__
r-h...@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible
code.
__
r-h...@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible
code.
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
__
r-h...@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Charles C. Berry
Re: [R] implementation of matrix logarithm (inverse of matrix exponential)
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,]10
[2,]11
logm(expm(M))
[,1] [,2]
[1,]00
[2,]10
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
[[alternative HTML
version deleted]]
__
r-h...@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible
code.
__
r-h...@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible
code.
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
__
r-h...@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Charles C. Berry (858) 534-2098
Re: [R] implementation of matrix logarithm (inverse of matrix exponential)
Try: expm( - M) 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 [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] implementation of matrix logarithm (inverse of matrix exponential)
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 [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. 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 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] implementation of matrix logarithm (inverse of matrix exponential)
OK. Try this: library(Matrix) M - matrix(c(2, 1, 1, 2), 2); M [,1] [,2] [1,]21 [2,]12 # log of expm(M) is original matrix M with(eigen(expm(M)), vectors %*% diag(log(values)) %*% t(vectors)) [,1] [,2] [1,]21 [2,]12 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 [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. 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 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] implementation of matrix logarithm (inverse of matrix exponential)
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,]21 [2,]12 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,]21 [2,]12 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 [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. 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 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. 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 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] implementation of matrix logarithm (inverse of matrix exponential)
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 [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. 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 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. 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 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] implementation of matrix logarithm (inverse of matrix exponential)
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$vectors)
with(eig, (vectors * rep(f(values), each=n)) %*% vi)
}
logm - function(x)sylvester(x, log)
Example:
A - matrix(1:4, 2)
eA - expm(A)
logm(eA)
With Chuck Berry's example, we get the following:
M - matrix( c(0,1,0,0), 2 )
sylvester(M, log)
Error in solve.default(eig$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.
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,]21
[2,]12
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,]21
[2,]12
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
[[alternative HTML version deleted]]
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
--
Spencer Graves, PE, PhD
President and Chief Operating Officer
Structure Inspection and Monitoring, Inc.
751 Emerson Ct.
San José, CA 95126
ph: 408-655-4567
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
