A question, a comment, and an alternative answer to matrix^(-1/2):
QUESTION:
What's the status of the "expm" package, mentioned in the email you
cited from Martin Maechler, dated Apr 5 19:52:09 CEST 2008? I tried both
install.packages('expm') and
install.packages("expm",repos="http://R-Forge.R-project.org";), and got
"package 'expm' is not available" in both cases.
COMMENT:
The solution proposed by Venables rests on Sylvester's matrix theorem,
which essentially says that if a matrix A is diagonalizable with
eigenvalue decomposition eigA <- eigen(A) and f: D → C with D ⊂ C be a
function for which f(A) is well defined
(http://en.wikipedia.org/wiki/Sylvester%27s_matrix_theorem), then f(A) =
with(eigA, vectors %*% diag(f(values)) %*% solve(vectors)). Maechler and
others have noted that this can be one of the least accurate and most
computationally expensive ways to compute f(A).
ALTERNATIVE ANSWER:
For A^(-1/2), if A is symmetric and nonnegative definite, then
solve(chol(A)) would be a very good way to compute it.
Hope this helps,
Spencer
David Winsemius wrote:
On Oct 31, 2009, at 9:33 PM, David Winsemius wrote:
On Oct 31, 2009, at 4:39 PM, Kajan Saied wrote:
Dear R-Help Team,
as a R novice I have a (maybe for you very simple question), how do
I get
the following solved in R:
Let R be a n x n matrix:
\mid R\mid^{-\frac{1}{2}}
solve(A) gives me the inverse of the matrix R, however not the
^(-1/2) of
the matrix...
GIYF: (and Bill Venables if friendly, too.)
http://www.lmgtfy.com/?q=powers+of+matrix+r-project
I had assumed that the first hit I got:
https://stat.ethz.ch/pipermail/r-help/2008-April/160662.html
... would be the first hit anybody got, but that's not necessarily
true now and especially for the future. And further searching within
the results produced this more recent Maechler posting:
https://stat.ethz.ch/pipermail/r-devel/2008-April/048969.html
For the Mac users, there appears to be no binary, but the source
compiles without error on a 64-bit version of R 2.10.0:
install.packages("expm",repos="http://R-Forge.R-project.org";,
type="source")
#The suggested code throws an error, so my very minor revision would be:
library(expm)
?"%^%"
--
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
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