Re: Symmetric Matrices: time and space efficient represenation

[JuanPi]

On Fri, Feb 19, 2016 at 4:30 PM, JuanPi <address@hidden> wrote:
> On Fri, Feb 19, 2016 at 2:46 PM, Michele Martone
> <address@hidden> wrote:
>> 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
>>> >  http://octave.sourceforge.net/sparsersb/function/sparsersb.html
>>> > 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:
>>  http://home.rzg.mpg.de/~mima/exascale15-poster-a4.pdf
>> 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.
>>
> The area of application is all kernel regression methods (e.g.
> Guassian processes, Gaussian Bayesian estimation)
> The covariance matrices are symmetric and most of the time not sparse.
>
>> If you deal only with dense symmetric, the standard approach is
>> ATLAS/LAPACK & co.
> I will se what they have, but I did not see anything exploiting
> symmetry directly.
>
> Thanks
>
>
> --
> JuanPi Carbajal
> Public GnuPG key: 9C5B72BF
> -----
> The end of funding: "Many researchers were caught up in a web of
> increasing exaggeration."
> - Hans Moravec

Boost has a representation for the symm. matrix in packed format, but
I can't find efficient matrix-matrix and matrix-vector
multiplication...
It seems Eigen3 has many implemented, although is just a view of the
matrix, so I wonder if they save the memory of the other half.
http://www.boost.org/doc/libs/1_60_0/libs/numeric/ublas/doc/symmetric.html
http://eigen.tuxfamily.org/dox/group__QuickRefPage.html#title15


-- 
JuanPi Carbajal
Public GnuPG key: 9C5B72BF
-----
The end of funding: "Many researchers were caught up in a web of
increasing exaggeration."
- Hans Moravec