SuperLU

Copyright and License

SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations on high performance machines. The library is written in C and is callable from either C or Fortran. The library routines will perform an LU decomposition with partial pivoting and triangular system solves through forward and back substitution. The LU factorization routines can handle non-square matrices but the triangular solves are performed only for square matrices. The matrix columns may be preordered (before factorization) either through library or user supplied routines. This preordering for sparsity is completely separate from the factorization. Working precision iterative refinement subroutines are provided for improved backward stability. Routines are also provided to equilibrate the system, estimate the condition number, calculate the relative backward error, and estimate error bounds for the refined solutions.

SuperLU package comes in three different flavors:

• SuperLU for sequential machines (code documentation in HTML)
• SuperLU_MT for shared memory parallel machines
• SuperLU_DIST for distributed memory

Referencing SuperLU in a publication.

The User Mailing List is used to announce changes, new releases, etc.

Please send me email if you have used any versions of the library. Also use this mailing address to report problems.

This is my survey article about sparse direct solvers of various flavours.

This project has been funded by DOE, NSF and DARPA.

Developers:
     Sherry Li
     Jim Demmel
     John Gilbert
     Laura Grigori

Other Contributors:
     Pietro Cicotti, UCSD
     Daniel Schreiber
     Jinqchong Teo
     Yu Wang
     Eric Zhang, Albany High

• Download software (V3.1) -- source code and documentation in a compressed tar file (~1.9 MB).
• Supports both real and complex data types, in single or double precision.
• The SIMAX paper describes the algorithms and performance on various machines.
  SuperLU has achieved up to 40% of the theoretical floating-point rate on a number of workstations, such as MIPS R8000 and IBM RS/6000. The megaflop rate usually increases with increasing ratio of floating-point operations count over the number of nonzeros in the L and U factors.
• These slides are from an up-to-date talk.
• Release note:
  • February 4, 1997 Version 1.0
  • November 15, 1997 Version 1.1
  • September 1, 1999   Version 2.0     (Last update: 06/03/03)
  • October 15, 2003   Version 3.0     (Last update: 01/02/06)
    • Included "symmetric mode"
  • August 1, 2008   Version 3.1
• Change Log

• Download software -- source code and documentation in a compressed tar file (~1.3 MB). There are parallel directives for several SMPs. In addition, we also provide the POSIX threads and OpenMP interfaces.
• The SIMAX paper describes the algorithms and performance on various machines.
  SuperLU_MT demonstrated 5--10 fold speedups on a range of commercially popular SMPs, and up to 2.5 Gigaflops factorization rate.
• These slides are from an up-to-date talk.
• Release note:
  • November 15, 1997 Version ALPHA
  • September 1, 1999    Version 1.0     (Last update: 5/24/05)
  • September 10, 2007    Version 2.0 (Last update: 01/15/08)
• Change Log

• Download software (V2.2) -- source code and documentation in a compressed tar file (~1.3 MB).
  MPI is used for interprocess communication.
• Supports both real and complex data types, in double precision.
• The SC98 paper describes our new GESP algorithm designed for large scale parallel machines.
  GESP stands for Gaussian Elimination with "Static Pivoting". Static pivoting is a technique that combines the numerical stability of partial pivoting with the scalability of no pivoting, to run accurately and efficiently on large numbers of processors.
• The SIAM PP99 paper improves the kernel performance -- 20% to 40% better than the SC98 paper.
  SuperLU_DIST demonstrated up to 100 fold speedup on the 512-PE Cray T3E at NERSC, and 10.2 Gigaflops factorization rate, using MPI.
  
• The SC01 paper describes the use of SuperLU_DIST to solve complex sparse linear systems up to order 2 million, for a quantum mechanics problem.
  The scientific result was reported earlier in the cover article of Science, Dec 24, 1999.
  
• The ACM TOMS paper (2003) discusses all the aspects of the SuperLU_DIST library.
  
• This talk was given in the Minisymposium on "Parallel Sparse Direct Solvers", the Ninth SIAM Conference on Parallel Processing and Scientific Computing, March 22-24, 1999.
• This table contains detailed numerical results of the GESP algorithm.
• The recent SIAM SISC paper (2007) describes the parallel algorithm and performance for symbolic factorization.
• Release note:
  • September 1, 1999   Version 1.0     (Last update: 2/18/03)
  • March 15, 2003   Version 2.0    (Last update: 01/02/06)
    • Included distributed input interface
  • November 1, 2007   Version 2.1    (Last update: 12/19/07)
    • Included parallel symbolic factorization
  • Feburary 20, 2008   Version 2.2  
    • Fixed memory leaks and a few other bugs in parallel symbolic factorization