Re: Symmetric Matrices: time and space efficient represenation

[Michele Martone]

On address@hidden:30, JuanPi wrote:
> ...
> 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

Assuming you want basic operations then the BLAS will suffice.
In the BLAS (and LAPACK as well, for that matters) symmetry is 
in the routine name; see the routines containing xSY in their names 
in here:
 http://www.netlib.org/blas/BLAS-snapshot.jpg
Same story for LAPACK:
 http://www.netlib.org/lapack/explore-html/de/d9e/group___d_y.html

e.g.:
 http://www.netlib.org/lapack/explore-html/d6/d0e/group__double_s_ysolve.html
 subroutine     dsysv (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
 DSYSV computes the solution to system of linear equations A * X = B for SY 
matrices More...
 ...