matrix^(-1/2)

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)
     ?"%^%"
David Winsemius, MD
Heritage Laboratories
West Hartford, CT
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.

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
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 Jos?, CA 95126
ph:  408-655-4567

 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 Jos?, CA 95126
ph:  408-655-4567

______________________________________________
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
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
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

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

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

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:
snipped details
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
Yes, as I said, I had already succeeded in a source compilation using:
install.packages("expm",repos="http://R-Forge.R-project.org",  
type="source")

(I am not quite sure why R was able to navigate the tree, but suspect  
my issues may stem from generally using the 64-bit Mac version of R.)

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 ) )'
I (as a noobisher matrix mechanic)  have discovered that the symmetric  
part is essential. Experiments with non-symmetric examples have come  
to a "singularly bad end". The OP did offer a symmetric example, so he  
probably was more matrix-savvy than I.  I am not sufficiently  
knowledgeable to design the error checking. I think a useful addition  
to %^% would be properly designed negative fractional matrix powers  
with more informative error messages for the matrix klutzes among us.  
I hope I am correct in thinking that M %^% (-1/integer) has meaning  
for integers other than 2, correct?  And noticing that the current  
version of %^% rounds the exponent, I think that raises the question  
(given that the matrix argument were symmetric), would one round the 1/ 
<negative-exponent>? And if so, Up or down?
David.

>
> 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
>

David Winsemius, MD
Heritage Laboratories
West Hartford, CT