This is a standard problem in dense linear algebra.
The most established package to solve this problem is LAPACK.
There are newer packages, but this is a good reference point.
You first factor the matrix, DGETRF for a general matrix,
DSYTRF for a symmetric matrix, DPOTRF for a symmetric positive definite
matrix.
Then you call one of the functions: DGETRI, DSYTRI, DPOTRI, to do the rest.
DPOTRI is just a call to DTRTRI (inverse of the triangular factor),
and DLAUUM (triangular matrix multiply).
If you are on a multicore, MKL has that routine decently optimized.
If you are adventurous, you can try an academic package, such as PLASMA.
(May beat MKL on matrix inversion, but still requires MKL for BLAS.)
If you're going for the kill (performancewise), you can try GPU
acceleration with MAGMA.
My guess is that MAGMA will invert a 20K x 20K matrix for you in the matter
of seconds.
On Mon, Jan 21, 2013 at 1:12 AM, Colin Wang <colin.bin.wang.mahout@gmail.com
> wrote:
> Hi Koobas,
>
> I am trying on dense matrix in Hadoop, thousand times thousand square size.
> How do HPC guys to solve this problem? Any references?
>
> Thank you,
> Colin
>
> On Mon, Jan 21, 2013 at 11:49 AM, Koobas <koobas@gmail.com> wrote:
>
> > Colin,
> > I am more of an HPC guys.
> > I am a Mahout noob myself.
> > Are we talking about a dense matrix?
> > What size?
> >
> >
> > On Sun, Jan 20, 2013 at 9:34 PM, Colin Wang <
> > colin.bin.wang.mahout@gmail.com
> > > wrote:
> >
> > > Hi Koobas,
> > >
> > > I want the first one. Do you have any suggestions?
> > >
> > > Thank you,
> > > Colin
> > > On Fri, Jan 18, 2013 at 12:49 PM, Koobas <koobas@gmail.com> wrote:
> > >
> > > > Martix inversion
> > >
> >
>
