[R] matrix^(-1/2)

[Charles C. Berry]

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)
>>  ?"%^%"
>> 
>
>
> -- 
> 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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>

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