matrix^(-1/2)

 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 Jos?, CA 95126
ph:  408-655-4567