FSPAI: Difference between revisions

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We developed a sequential and highly scalable parallel C/C++ implementation  
We developed a sequential and highly scalable parallel C/C++ implementation  
of the known ''FSPAI (Factorized SParse Approximate Inverses)'' algorithm.
of the <br> known ''FSPAI (Factorized SParse Approximate Inverses)'' algorithm.




== Theory ==
== Theory ==
<!--


MSPAI is a preconditioner for large sparse and ill-conditioned systems of <br> linear equations. We extended the basic SPAI minimization
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 approximates the inverse of the cholesky factor of the system matrix, i.e.,


: [[Image:spai.jpg]]  
: [[/home/sedlacek/Fspai.pdf]]


to target form and further generalized it in order to add additional ''probing constraints'':
Based on an initial chosen sparsity structure, FSPAI automatically updates its <br> sparsity structure and improves an a current approximation.


: [[Image:mspai.jpg]]
For an overview of the versatile employment possibilities of our MSPAI formulation, <br>
see this [http://www5.in.tum.de/software/mspai/mspai_variants.pdf pdf] taken from [http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:91-diss-20071114-632977-1-5 here].
-->


== Implementation and Features ==
== Implementation and Features ==
Line 31: Line 25:
* Written in C/C++
* Written in C/C++


We are currently working on a next release which will cover
We are currently working on a next release which will cover a highly scalable <br> block version of FSPAI, i.e., BFSPAI.
a highly scalable block version of FSPAI.


== Download ==
== Download ==

Revision as of 11:03, 15 July 2011

Factorized Sparse Approximate Inverses

This is a dummy textLatest 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.,

/home/sedlacek/Fspai.pdf

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


Implementation and 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
  • 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

Tested environments

Some References

Papers

<pubsccs>nocaption=1&pubid=620&lang=en</pubsccs><pubsccs>nocaption=1&pubid=645&lang=en</pubsccs><pubsccs>nocaption=1&pubid=677&lang=en</pubsccs><pubsccs>nocaption=1&persid=53&utypid=2030&datum=2008&lang=en</pubsccs><pubsccs>nocaption=1&pubid=1140&lang=en</pubsccs>

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

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