I want to compute the Generalized Singular Value Decomposition (GSVD) for sparse matrices A and B. Therefore I am looking for an implementation that is capable of using a special data structure for sparse matrices.
The only implementation I found (here) is part of the LAPACK package which is written in Fortran 77.
It works quite good, but unfortunately it can't handle sparse matrices.
MATLAB's gsvd accepts sparse matrices. I believe Octave (freely available) supports gsvd as well.
I asked the same question on Scicomp and got good answers. The post can be found here.
Related
I am currently trying to reconstruct some of the function of R's kappa condition number estimation function, which estimates the condition number of a matrix X by:
Working out the QR decomposition of X.
Calling to LAPACK's dtrcon or LINPACK's dtrco (depending on what the underlying dependencies on the users system are), and calculating the condition number of R, the upper triangular matrix which should have the same condition number as X (see here).
I have been trying to understand what the LAPACK and LINPACK algorithms do as it may be extremely useful for my own coding.
I have managed to find the algorithm that LINPACK uses, which was described here, but have had no luck finding the origin of LAPACK's algorithm. The comments in R's kappa function suggest that these are using different algorithms (see here) but I am unsure...
Long story short, my question is:
Does anyone know if LAPACK's dtrcon and LINPACK's dtrco are using the same algorithm and if not, what algorithm is LAPACK's dtrcon using?
Thank you in advance!
I have a mathematical optimization which I wish to solve in R consider this system/problem:
How Can I solve this problem in R?
In this model Budget, p_l for all l and mu_target are fixed constants while muis a given m-dimensional vector and R is a given n by m matrix.
I have looked into constrOptim and lp but I don't have the imagination to implement the constraints
Those functions require that I have a "constraint" matrix but my problem is that I simply don't know how to design that constraint matrix. There are not many examples with decision variables on both sides of the equations.
Have a look on the nloptr package. It has quite extensive documentation with examples. Lots of algorithms to choose from, depending what problem you are trying to resolve.
NLoptr link
How do I find generalized Eigen Values, Vectors using Eigen3 library?
In octave, matlab, the eigen value function is of the form: [V, lambda] = eig (A, B).
I could only find this Class in Eigen3 lib but was not helpful in validating the results from above matlab/octave code.
You'll want to use the EigenSolver class which is located in the Eigen/Eigenvalues header. Either use the EigenSolver constructor that takes a matrix parameter or of or call the compute method with a matrix and it will solve for that matrix's eigenvalues and eigenvectors. Then you can use the eigenvalues() and eigenvectors() methods to retrieve the eigenvalues and eigenvectors.
This question is old. Anyway, if someone here is looking for it, they should consider the GeneralizedEigenSolver (http://eigen.tuxfamily.org/dox-devel/classEigen_1_1GeneralizedEigenSolver.html) that is available in the Eigen library. Although, at this time, as far as I know, it is not completely ready.
In most applications (esp. statistical ones) the thin SVD suffices. However, on occasion one needs the full SVD in order to obtain an orthobasis of the null space of a matrix (and its conjugate). It seems that svd() in R only returns the thin version. Is it possible to produce the full version? Are there alternatives?
library(sos)
> findFn("svd NULL space")
found 47 matches; retrieving 3 pages
This looks on point:
MSBVAR null.space Find the null space of a matrix
As does this function in MASS.
R Core uses the routines from Linpack, Lapack, ... that it needs.
If you need something different, you probably need to either get yourself other Linpack etc routines, or connect to a library providing more.
Doug Bates just wrapped the Eigen library in the RcppEigen package which may have something for you. Eigen appear to be both powerful and fairly featureful while being highly optimised.
There are at least two sparse matrix packages for R. I'm looking into these because I'm working with datasets that are too big and sparse to fit in memory with a dense representation. I want basic linear algebra routines, plus the ability to easily write C code to operate on them. Which library is the most mature and best to use?
So far I've found
Matrix which has many reverse dependencies, implying it's the most used one.
SparseM which doesn't have as many reverse deps.
Various graph libraries probably have their own (implicit) versions of this; e.g. igraph and network (the latter is part of statnet). These are too specialized for my needs.
Anyone have experience with this?
From searching around RSeek.org a little bit, the Matrix package seems the most commonly mentioned one. I often think of CRAN Task Views as fairly authoritative, and the Multivariate Task View mentions Matrix and SparseM.
Matrix is the most common and has also just been accepted R standard installation (as of 2.9.0), so should be broadly available.
Matrix in base:
https://stat.ethz.ch/pipermail/r-announce/2009/000499.html
In my experience, Matrix is the best supported and most mature of the packages you mention. Its C architecture should also be fairly well-exposed and relatively straightforward to work with.
log(x) on a sparse matrix is a bad idea since log(0) isn't defined and most elements of a sparse matrix are zero.
If you would just like to get the log of the non-zero elements, try converting to a triplet sparse representation and taking a log of those values.