[Trilinos-Users] hermitian banded matrix factorization

Phil Cummins phil.cummins at anu.edu.au
Wed Feb 24 15:13:25 MST 2010

Many thanks Bill and Mike, these were very useful replies! 
I will try it and see...

On 25/02/2010, at 2:08 AM, Heroux, Michael A wrote:

> Phil,
> To follow up on Bill’s comments, equivalent real formulations (ERFs) are not particularly well suited to complex symmetric, since there are commonly used special variants of BiCG for complex symmetric that don’t have a corresponding ERF formulation.  Also, we don’t take advantage of the potential storage reduction.  
> At the same time, casting your problem as an ERF allows you to use a lot of high powered real-based algorithms and software, and I don’t know of a scalable complex symmetric solver elsewhere, but there might be one.
> Mike
> On 2/24/10 8:36 AM, "Bill Spotz" <wfspotz at sandia.gov> wrote:
> Phil,
> I have attached a simple python script that uses Komplex, so you can 
> see what PyTrilinos code looks like.  It uses AztecOO, which is the 
> Trilinos iterative solver, to solve a complex diagonal linear system.  
> For LU factorization of a sparse matrix, you would want to use the 
> Amesos package.  There are (real, non-complex) examples for that, too.
> A quick primer:  The Epetra package provides (real, double precision) 
> linear algebra classes, such as Vector, MultiVector, Operator, a 
> variety of sparse matrices and a LinearProblem class, which 
> encapsulates a linear operator, an LHS vector and a RHS vector.  
> Different solver packages, such as AztecOO and Amesos, can take this 
> class or the individual components, and attempt to solve a linear 
> system.  The Komplex package provides a way to build an 
> Epetra.LinearProblem that is the equivalent real-valued representation 
> of a complex system.
> So for your problem, complex values are covered, sparsity is covered, 
> but I'm not sure if there is a sparse matrix class that takes 
> advantage of symmetry.
> On Feb 24, 2010, at 4:53 AM, Phil Cummins wrote:
> > Hello,
> >
> > I am new to Trilinos and am trying to answer the typical newbie 
> > question 'Is it worth my learning Trlinos?'
> >
> > I am a python user and have an application that requires the LU 
> > factorization of a banded Hermitian (i.e., complex, conjugate-
> > symmetric) matrix. For efficiency, I want something that will take 
> > advantage of the symmetry and sparseness of the matrix. Can anyone 
> > tell me if the Kcomplex package in Trilinos (which I hope to use via 
> > Pytrilinos) would be suitable for this?
> >
> > Many thanks,
> >
> > - Phil
> > _______________________________________________
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> > Trilinos-Users at software.sandia.gov
> > http://software.sandia.gov/mailman/listinfo/trilinos-users
> ** Bill Spotz                                              **
> ** Sandia National Laboratories  Voice: (505)845-0170      **
> ** P.O. Box 5800                 Fax:   (505)284-0154      **
> ** Albuquerque, NM 87185-0370    Email: wfspotz at sandia.gov **

Phil Cummins
Prof. Natural Hazards
Research School of Earth Sciences
Australian National University
Canberra, Australia

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