Chetan, I completely agree that (rank-revealing) QR should be the first choice. As a side note, from what he has said, his matrix is actually dense.
If his matrix was sparse, I am not sure how much sparsity would be lost by the column pivoting inherent in a rank-revealing QR. I know that the MUMPS group is either working on or has finished a sparse QR, but I don't know any details about their approach to pivoting (though I would be very interested!). Hopefully it could simply reuse the threshold approach used for sparse LU and LDL. Jack On Mon, Dec 19, 2011 at 1:38 PM, Chetan Jhurani <chetan.jhurani at gmail.com>wrote: > > It can be further optimized using the Woodbury identity for two cases ?* > *** > > > rank <= size or rank >= size to reduce the size of auxiliary internal > Cholesky solve.**** > > ** ** > > Sorry, that?s wrong. I meant rank <= size/2 or rank >= size/2. Size here > **** > > refers to square matrix size, but this analysis can be done for rectangular > **** > > case too.**** > > ** ** > > Chetan**** > > ** ** > > *From:* Chetan Jhurani [mailto:chetan.jhurani at gmail.com] > *Sent:* Monday, December 19, 2011 11:35 AM > *To:* 'PETSc users list' > *Subject:* RE: [petsc-users] Pseudoinverse of a large matrix**** > > ** ** > > ** ** > > Couple of optimizations not there currently.**** > > ** ** > > **1. **It can be changed to use sparse RRQR factorization for sparse > input matrix.**** > > **2. **It can be further optimized using the Woodbury identity for two > cases ?**** > > rank <= size or rank >= size to reduce the size of auxiliary internal > Cholesky solve.**** > > ** ** > > Chetan**** > > ** ** > > ** ** > > *From:* petsc-users-bounces at mcs.anl.gov [ > mailto:petsc-users-bounces at mcs.anl.gov <petsc-users-bounces at > mcs.anl.gov>] > *On Behalf Of *Modhurita Mitra > *Sent:* Monday, December 19, 2011 11:01 AM > *To:* PETSc users list > *Subject:* Re: [petsc-users] Pseudoinverse of a large matrix**** > > ** ** > > I am trying to express the radiation pattern of an antenna in terms of > spherical harmonic basis functions. I have radiation pattern data at > N=324360 points. Therefore, my matrix is spherical harmonic basis functions > evaluated till order sqrt(N) (which makes up at total of N elements), > evaluated at N data points. So this is a linear least squares problem, and > I have been trying to solve it by finding its pseudoinverse which uses SVD. > The elements of the matrix are complex, and the matrix is non-sparse. I > have solved it in MATLAB using a subsample of the data, but MATLAB runs out > of memory while calculating the SVD at input matrix size 2500 X 2500. I > need to solve this problem using the entire data. > > > I was thinking of using SLEPc because I found a ready-to-use code which > computes the SVD of a complex-valued matrix ( > http://www.grycap.upv.es/slepc/documentation/current/src/svd/examples/tutorials/ex14.c.html). > I don't know how to use either PETSc or SLEPc (or Elemental) yet, so I > am trying to figure out where to start and what I should learn. > > Thanks, > Modhurita**** > > On Mon, Dec 19, 2011 at 12:31 PM, Matthew Knepley <knepley at gmail.com> > wrote:**** > > On Mon, Dec 19, 2011 at 12:21 PM, Modhurita Mitra <modhurita at gmail.com> > wrote:**** > > Hi, > > I have to compute the pseudoinverse of a 324360 X 324360 matrix. Can PETSc > compute the SVD of this matrix without parallelization? If parallelization > is needed, do I need to use SLEPc?**** > > ** ** > > With enough memory, yes. However, I am not sure you want to wait. I am not > sure how SLEPc would help here.**** > > From the very very little detail you have given, you would need parallel > linear algebra, like Elemental. However,**** > > I would start out from a more fundamental viewpoint. Such as replacing > "compute the psuedoinverse" with**** > > "solve a least-squares problem" if that is indeed the case.**** > > ** ** > > Matt**** > > **** > > > Thanks, > Modhurita**** > > > > **** > > ** ** > > -- > What most experimenters take for granted before they begin their > experiments is infinitely more interesting than any results to which their > experiments lead. > -- Norbert Wiener**** > > ** ** > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20111219/bd921e5e/attachment-0001.htm>
