Re: Symmetric Matrices: time and space efficient represenation

[JuanPi]

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
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