[R] matrix^(-1/2)

[spencerg]

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")? 


      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)
>>>  ?"%^%"
>>
>> ______________________________________________
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>> 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