# [Trilinos-Users] Cholesky decomposition of a sparse distributed matrix

Heroux, Mike MHeroux at CSBSJU.EDU
Tue Dec 20 18:25:54 EST 2016

```Brian,

I assume you are looking for a solver that performs both the factorization and solve (the most common situation).

If I understand your question correctly, the kind of functionality you are looking for would be in the Amesos package.  Amesos provides uniform access to a variety of third-party sparse direct solvers.  If you have access to Pardiso (available in Intel MKL, for example), it is probably the best option.  I believe Pardiso can solve symmetric systems efficiently.

Amesos provides support for several other sparse direct solvers, but most are for unsymmetric systems.  These will work for your problem, but will not take advantage of symmetry.  Also, for symmetric problems, the LDL^T factorization is most common, since it can compute factorizations of matrices that are indefinite (often the case in structures).

Trilinos has a newer package Amesos2 that is based on the Tpetra package.  It has similar capabilities, but supports the newer Trilinos software stack.  Just FYI.

Trilinos does not have a random generator for Gaussian random variables.

I hope this helps.

Mike

On 12/19/16, 8:21 AM, "Trilinos-Users on behalf of Brian Staber" <trilinos-users-bounces at trilinos.org on behalf of brian.staber at u-pem.fr> wrote:

Hi Trilinos team,

I’m trying to implement the following problem in Trilinos but I didn’t find how to proceed. My problem is:

Solve Lv = z where

- L is the Cholesky decomposition of a symmetric, positive-definite and sparse matrix R (R = LL^T), stored as a Epetra_FECrsMatrix and distributed across n processors.
- z is a Epetra_Vector whose components are realizations of a Gaussian random variable.

Is there any method available in Trilinos that computes the distributed matrix L ? And also, is a random generator for Gaussian random variables available in the Trilinos package (I tried Stokhos but I didn’t find any method for this in the doxygen page).

Thanks a lot for your help.

Best regards,
Brian.
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