> > I happily use eigen() to compute the eigenvalues and eigenvectors of > a fairly large matrix (200x200, say), but it seems over-killed as its > rank is limited to typically 2 or 3. I sort of remember being taught > that numerical techniques can find iteratively decreasing eigenvalues > and corresponding orthogonal eigenvectors, which would provide a nice > 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 require. 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 symmetric. > 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 (although 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... best, Simon > - 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? > > Many thanks in advance for any piece of advice, > > Sincerely, > > Baptiste > > dummy example if needed: > > test <- matrix(c(1, 2, 0, 4, 5, 6, 1.00001, 2, 0), ncol=3) > eigen(test) > > > > > _____________________________ > > Baptiste Auguié > > Physics Department > University of Exeter > Stocker Road, > Exeter, Devon, > EX4 4QL, UK > > Phone: +44 1392 264187 > > http://newton.ex.ac.uk/research/emag > http://projects.ex.ac.uk/atto > > ______________________________________________ > R-help@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. -- > Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK > +44 1225 386603 www.maths.bath.ac.uk/~sw283 ______________________________________________ R-help@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.