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Re: Symmetric Matrices: time and space efficient represenation

From: Michele Martone
Subject: Re: Symmetric Matrices: time and space efficient represenation
Date: Fri, 19 Feb 2016 14:46:50 +0100
User-agent: Mutt/1.5.24 (2015-08-30)

On address@hidden:34, JuanPi wrote:
> On Fri, Feb 19, 2016 at 2:25 PM, Michele Martone
> <address@hidden> wrote:
> > On address@hidden:11, JuanPi wrote:
> >> Hi all,
> >>
> >> I am looking for a library with a good representation for symmetric
> >> matrices. Does Octave has one? (in pkg mechanics there was a first
> >> attempt)
> >> Anybody knows a good C/C++ or Fortran library?
> >>
> >> Thanks
> >
> > Hi JuanPi,
> >
> > if you mean sparse symmetric matrices, possibly big ones, the sparsersb
> > package
> >
> > based on librsb could be of your interest.
> >
> Thank you Michele,
> >From what I can read this representation doesn't exploit the symmetry
> of the matrix. Does it?
> In general I am dealing with full symmetric matrices, which are fully
> represented by its upper or lower triangular matrix.
> Would you know some lib specific for these matrices?

Hi JuanPi,

It is a specialty of librsb to exploit the symmetry of matrices. 
Also having multiple right hand sides for multiplication is exploited;
you can see this poster for some benchmarks versus Intel's MKL:
If you have >1e6 nonzeroes sparse matrix I highly recommend librsb.
Being currently there are no special subcases for fully or partially
dense ones.

If I find an application area where matrices with substantially full
portions arise, I could think of implement such an extension, so to
adapt with a "dense/sparse" hybrid.
But I'm not aware of such application areas so far.

If you deal only with dense symmetric, the standard approach is

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