[R] matrix^(-1/2)

[Charles C. Berry]

On Sun, 1 Nov 2009, David Winsemius wrote:

>
> On Nov 1, 2009, at 1:46 PM, spencerg wrote:
>
>> Hi, Chuck:
>>
>>     Thanks very much, but why do I get "package 'expm' is not available"
>>     from install.packages("expm",repos="http://R-Forge.R-project.org")?
>
> In my case I think it was it is because there is no 2.10 branch to either 
> the:
>
> http: //r-forge.r-project.org/bin/macosx/leopard/contrib/    ... or the
> http: //r-forge.r-project.org/bin/macosx/universal/contrib/    ...trees.
>
> I tried a variety of stems for the installer but got these messages:
> Warning: unable to access index for repository
> http://r-forge.r-project.org/bin/macosx/universal/contrib/latest/bin/macosx/leopard/contrib/2.10
> Warning: unable to access index for repository
> http://r-forge.r-project.org/bin/macosx/universal/contrib/bin/macosx/leopard/contrib/2.10
> Warning: unable to access index for repository
> http://r-forge.r-project.org/bin/macosx/leopard/contrib/2.10
>
> So I wonder if the package installers' expectations for the r-forge 
> repository are matching up with the tree structures.

Right. FWIW, the source install works OK on my linux box:

> sessionInfo()
R version 2.10.0 (2009-10-26)
x86_64-pc-linux-gnu

[output truncated]


>
> I should also note that the matpow or "%^%" functions in expm would not 
> address the OP's question since they require that the exponent be positive.
>

Roger that.

If solve(chol(A)) isn't good enough a symmetric inverse square root is 
available from expm as 'solve( sqrtm( A ) )'

Chuck


> -- 
> David.
>
>>
>>     Best Wishes,
>>     Spencer Graves
>> 
>> 
>> Charles C. Berry wrote:
>> > 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)
>> > > > ?"%^%"
>> > > 
>> > > ______________________________________________
>> > > R-help at 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:cberry at tajo.ucsd.edu                UC San Diego
>> > http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 
>> > 92093-0901
>> 
>
> David Winsemius, MD
> Heritage Laboratories
> West Hartford, CT
>
>

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