matrix^(-1/2)

On Sun, 1 Nov 2009, spencerg wrote:

 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.

Try

    http://r-forge.r-project.org/projects/expm/

HTH,

Chuck

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)
 ?"%^%"

Charles C. Berry                            (858) 534-2098
                                            Dept of Family/Preventive 
Medicine
E mailto:cberry at tajo.ucsd.edu                UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 
92093-0901