FSPAI
Contents
Factorized Sparse Approximate Inverses
- This is a dummy textLatest release is 1.1
We developed a sequential and highly scalable parallel C/C++ implementation
of the
known FSPAI (Factorized SParse Approximate Inverses) algorithm.
Note that there is a scalable implementation of Modified Sparse Approximate
Inverses (MSPAI) as well.
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 on 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 - Support for sparse methods using CXSparse by Tim Davis
- Caching and Hashing approach to avoid redundant Cholesky decompositions
- 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 1.1
In contrast to FSPAI 1.0, FSPAI 1.1 additionally requires CXSparse and UFconfig.
If you are not going to use the Fspai Caching/Hashing or the
sparse methods,
you can use FSPAI 1.0 instead.
- Source code tar ball: fspai-1.1.tar.gz.
- Manual: fspai-1.1.pdf.
- Only the HTML documentation of source code: htmlonly-fspai-1.1.tar.gz
FSPAI 1.0
- Source code tar ball: fspai-1.0.tar.gz.
- Manual: fspai-1.0.pdf.
- Only the HTML documentation of source code: htmlonly-fspai-1.0.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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Thesis
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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 © 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