On 22-04-2012, at 21:08, Jonathan Greenberg wrote:
> Thanks all (particularly to you, Berend) -- I'll push forward with these
> solutions and integrate them into my code. I did come across geigen while
> rooting around in the CCA code but its not formally documented (it just says
> "for internal use" or something along those lines) and as you found out
> above, it does not produce the same solution as the dggev. It would be nice
> to have a more complete set of formal packages for doing LA in R (rather than
> having to hand-write .Fortran calls) but I'll leave that to someone with more
> expertise in linear algebra than me. Something that perhaps matches the
> SciPy set of functions (both in terms of input and output):
>
> http://docs.scipy.org/doc/scipy/reference/linalg.html
>
> Some of these are already implemented, but clearly not all of them.
Package CCA has package fda as dependency.
And package fda defines a function geigen.
The first 14 lines of this function are
geigen <- function(Amat, Bmat, Cmat)
{
# solve the generalized eigenanalysis problem
#
# max {tr L'AM / sqrt[tr L'BL tr M'CM] w.r.t. L and M
#
# Arguments:
# AMAT ... p by q matrix
# BMAT ... order p symmetric positive definite matrix
# CMAT ... order q symmetric positive definite matrix
# Returns:
# VALUES ... vector of length s = min(p,q) of eigenvalues
# LMAT ... p by s matrix L
# MMAT ... q by s matrix M
It's not clear to me how it is used and exactly what it is doing and how that
compares with Lapack.
Berend
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