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 (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. >>> >>> >> >> >> -- >> 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. >> >> > > 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. > > ______________________________________________ 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.
