# Difference between revisions of "FSPAI"

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FSPAI is a preconditioner for large sparse and ill-conditioned symmetric positive <br> definite systems of linear equations. It is the factorized version of the SPAI <br> algorithm. FSPAI is inherently parallel and generates a preconditioner which <br> approximates the inverse of the Cholesky factor of the system matrix, i.e., | FSPAI is a preconditioner for large sparse and ill-conditioned symmetric positive <br> definite systems of linear equations. It is the factorized version of the SPAI <br> algorithm. FSPAI is inherently parallel and generates a preconditioner which <br> approximates the inverse of the Cholesky factor of the system matrix, i.e., | ||

− | : | + | http://www5.in.tum.de/pic/Fspai.png |

Based on an initial chosen sparsity structure, FSPAI automatically updates its <br> sparsity structure and improves an a current approximation. | Based on an initial chosen sparsity structure, FSPAI automatically updates its <br> sparsity structure and improves an a current approximation. |

## Revision as of 15:00, 15 July 2011

## Contents

__Factorized Sparse Approximate Inverses__

- This is a dummy text
**Latest release is 1.0**

We developed a sequential and highly scalable parallel C/C++ implementation
of the

known *FSPAI (Factorized SParse Approximate Inverses)* algorithm.

## Theory

FSPAI is a preconditioner for large sparse and ill-conditioned symmetric positive

definite systems of linear equations. It is the factorized version of the SPAI

algorithm. FSPAI is inherently parallel and generates a preconditioner which

approximates the inverse of the Cholesky factor of the system matrix, i.e.,

Based on an initial chosen sparsity structure, FSPAI automatically updates its

sparsity structure and improves an a current approximation.

## Features

- Single source providing
- highly scalable parallel implementation
- sequential (MPI free) implementation

- Support for real and complex valued problems
- PCG solver available using HYPRE package
- Arbitrary start patterns, i.e., possibility to compute a FSAI without

updating the pattern - Written in C/C++

We are currently working on a next release which will cover a highly scalable

block version of FSPAI, i.e., BFSPAI.

## Download

### FSPAI 1.0

- Source code tar ball: fspai-1.0.tar.gz.
- Manual: fspai-1.0.pdf.

- HTML documentation of source code: htmlonly-fspai-1.0.tar.gz.
- Source code and HTML documentation: fspai-1.0-html.tar.gz.

## Tested environments

- Shaheen from the KAUST Supercomputing Laboratory (KSL) at King

Abdullah University of Science and Technology (KAUST):- 65536 compute cores: 16 racks of Blue Gene/P, each containing

1024 quad-core, 32-bit 850 MHz PowerPC compute nodes - Architecture: PowerPC (PPC)
- Compiler version: IBM XL C/C++ Advanced Edition for Blue Gene/P, V9.0
- Libraries:
- Lapack 3.2.1
- MPI based on MPICH2
- HYPRE 2.7

- 65536 compute cores: 16 racks of Blue Gene/P, each containing

- InfiniBand-Cluster of the Lehrstuhl Rechnertechnik und Rechnerorganisation/

Parallelrechnerarchitektur of Technische Universtität München:- 128 compute cores: AMD Opteron™ Processor 850
- Architecture: x86_64
- Compiler version: gcc version 4.2.4 (Ubuntu 4.2.4-1ubuntu3)
- Libraries:
- Lapack 3.0
- MPI based on MPICH 1.2.7
- HYPRE 2.7.0b

- i686-pc-linux-gnu:
- Processor: Intel® Core™2 Duo CPU P8700 @ 2.53GHz
- Architecture: i686
- Compiler version: gcc version 4.3.4 (Gentoo 4.3.4 p1.1, pie-10.1.5)
- Libraries:
- Lapack 3.3.1
- HYPRE 2.7.0b

FSPAI is provided "as is", without warranty and support of any kind, express
or

implied, including but not limited to the warranties of merchantability,
fitness for a

particular purpose, title and non-infringement. In no event
shall the copyright holders

or anyone distributing FSPAI be liable for any
damages or other liability, whether in contract, tort or otherwise, arising
from, out of or in connection with FSPAI or the use

or other dealings in FSPAI.

## Some References

### Papers

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### Further

- Short summary on sparse approximate inverses with core reference list: summary.pdf
- Extended reference list: extended.pdf

## Authors

## License

FSPAI: Factorized Sparse Approximate Inverses

Copyright © 2010-2011, Matous Sedlacek

Research Unit Scientific Computing in Computer Science - Informatics V

Technische Universität München

This program is free software: you can redistribute it and/or modify
it under the

terms of the GNU Lesser General Public License as published by
the Free Software

Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY

WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR

A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License
along with

this program. If not, see http://www.gnu.org/licenses/.

If you obtain any results with FSPAI we would appreciate that you refer to FSPAI.

## Further work on Sparse Approximate Inverses

**SPAI**: Parallel Implementation on SPAI — Sparse Approximate Inverses:

http://www.computational.unibas.ch/software/spai/**MSPAI**: Parallel implementation of MSPAI — Modified Sparse Approximate Inverses:

http://www5.in.tum.de/wiki/index.php/MSPAI**PARASAILS**: Parallel Sparse Approximate Inverse (Least-Squares) Preconditioner:

https://computation.llnl.gov/casc/parasails/parasails.html**HYPRE**: Software on high performance preconditioners containing a PARASAILS module:

https://computation.llnl.gov/casc/linear_solvers/sls_hypre.html