[R] highest eigenvalues of a matrix
ba208 at exeter.ac.uk
Thu Jun 19 16:12:50 CEST 2008
Thank you for the suggestions and pointers. It looks like I'll need
to do some interface with Fortran/C code. The igraph package seems to
provide an interface with ARPACK, albeit not with the options I need,
so it could be a good starting point.
On 19 Jun 2008, at 10:50, Katharine Mullen wrote:
> On Thu, 19 Jun 2008, Simon Wood wrote:
>>> I happily use eigen() to compute the eigenvalues and eigenvectors of
>>> a fairly large matrix (200x200, say), but it seems over-killed as
>>> rank is limited to typically 2 or 3. I sort of remember being taught
>>> that numerical techniques can find iteratively decreasing
>>> and corresponding orthogonal eigenvectors, which would provide a
>>> alternative (once I have the first 3, say, I stop the search).
>> Lanczos iteration will do this efficiently (see e.g. Golub & van
>> Loan "Matrix
>> Computations"), but I don't think that there are any such routines
>> built into
>> R or LAPACK (although I haven't checked the latest LAPACK
>> release). When I
>> looked it seemed that the LAPACK options that allow you to select
>> eigen-values/vectors still depend on an initial O(n^3)
>> decomposition of the
>> matrix, rather than the O(n^2) that a Lanczos based method would
> ARPACK (http://www.caam.rice.edu/software/ARPACK/) uses a Lanczos
> for symmetric matrics; otherwise it uses an Arnoldi iteration.
> Development of an R interface to ARPACK would be a nice project (but
> unfortunately one I don't have time for for a while). Maybe one of
> maintainers of a package for sparse matrices would be interested.
>> My `mgcv' package (see cran) uses Lanczos iteration for setting up
>> low rank
>> bases for smoothing. The source code is in mgcv/src/
>> matrix.c:lanczos_spd, but
>> I'm afraid that there is no direct R interface, although it would
>> not be too
>> hard to write a suitable wrapper. It requires the matrix to be
>>> Looking at the R source code for eigen and some posts on this list,
>>> it seems that the function uses a LAPACK routine, but obviously all
>>> the options are not available through the R wrapper. I'm not
>>> experienced enough to try and make my own interface with Fortran
>>> code, so here are two questions:
>>> - is this option (choosing a desired number of eigenvectors) already
>>> implemented in some function / package that I missed?
>> --- In the symmetric case you can use `svd' which lets you select
>> you'd need to fix up the signs of the singular values to get eigen-
>> values if
>> the matrix is not +ve definite). But this answer is pretty useless
>> as it will
>> be slower than using `eigen' and getting the full decomposition.
>> Of course if you know that your matrix is low rank because it's a
>> product of
>> non-square matrices then there's usually some way of getting at the
>> eigen-decomposition efficiently. E.g. if A=B'B where B is 3 by
>> 1000, then the
>> cost can easily be kept down to O(1000^2) in R...
>>> - is the "range of indices" option in DSYEVR.f < http://
>>> www.netlib.org/lapack/double/dsyevr.f > what I think, the indices of
>>> the desired eigenvalues ordered from the highest to lowest?
> dsyevr.f will work with symmetric real matrices only. When the range
> argument of dysevr is set to 'I', arguments il and iu seem to
> specify the
> range of eigenvalue indices you want in ascending order (lowest to
> highest, not highest to lowest). If you look at
> https://svn.r-project.org/R/trunk/src/modules/lapack/Lapack.c you
> see that
> range is always set to 'A'.
>>> Many thanks in advance for any piece of advice,
>>> dummy example if needed:
>>> test <- matrix(c(1, 2, 0, 4, 5, 6, 1.00001, 2, 0), ncol=3)
>>> Baptiste Auguié
>>> Physics Department
>>> University of Exeter
>>> Stocker Road,
>>> Exeter, Devon,
>>> EX4 4QL, UK
>>> Phone: +44 1392 264187
>>> R-help at r-project.org mailing list
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html and provide
>>> commented, minimal,
>>> self-contained, reproducible code.
>>> Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2
>>> 7AY UK
>>> +44 1225 386603 www.maths.bath.ac.uk/~sw283
>> R-help at r-project.org mailing list
>> PLEASE do read the posting guide http://www.R-project.org/posting-
>> and provide commented, minimal, self-contained, reproducible code.
> R-help at r-project.org mailing list
> PLEASE do read the posting guide http://www.R-project.org/posting-
> and provide commented, minimal, self-contained, reproducible code.
University of Exeter
EX4 4QL, UK
Phone: +44 1392 264187
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