[R] matrix^(-1/2)

[David Winsemius]

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.

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.

-- 
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_the 
>>> orem), 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