SUPERLU_OPENMP
Sparse Linear Equation Solver with OpenMP

SUPERLU_OPENMP, FORTRAN90 programs which illustrate the use of the SUPERLU_OPENMP library, a version of SUPERLU compiled with the OpenMP parallel programming interface, for the fast direct solution of large sparse systems of linear equations.

SUPERLU_OPENMP contains a set of subroutines to solve a sparse linear system A*X=B. It uses Gaussian elimination with partial pivoting (GEPP). The columns of A may be preordered before factorization; the preordering for sparsity is completely separate from the factorization.

SUPERLU_OPENMP is implemented in ANSI C, and must be compiled with an ANSI C compiler. It provides functionality for both real and complex matrices, in both single and double precision. The initial letter of a routine name indicates the arithmetic type and precision:

• C, such as cgstrf, is for single precision complex arithmetic;
• D, such as dgstrf, is for double precision real arithmetic;
• S, such as sgstrf, is for single precision real arithmetic;
• Z, such as zgstrf, is for double precision complex arithmetic.

SUPERLU_OPENMP includes functions to read a sparse matrix from a file in the Harwell-Boeing sparse matrix format.

Licensing:

Copyright (c) 2003, The Regents of the University of California, through Lawrence Berkeley National Laboratory (subject to receipt of any required approvals from U.S. Dept. of Energy)

All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
3. Neither the name of Lawrence Berkeley National Laboratory, U.S. Dept. of Energy nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Languages:

SUPERLU_OPENMP is available in a C version and a C++ version and a FORTRAN90 version.

Related Data and Programs:

HB, a data directory which contains examples of Harwell Boeing (HB) files, a sparse matrix file format;

HB_IO, a FORTRAN90 library which reads and writes sparse linear systems stored in the Harwell Boeing (HB) format for sparse matrices.

JACOBI_OPENMP, a FORTRAN90 program which illustrates the use of the OpenMP application program interface to parallelize a Jacobi iteration solving A*x=b.

MGMRES, a FORTRAN90 library which applies the restarted GMRES algorithm to solve a sparse linear system, by Lili Ju.

OPENMP, FORTRAN90 programs which illustrate the use of the OpenMP application program interface for carrying out parallel computations in a shared memory environment.

OPENMP_RCC, FORTRAN90 programs which illustrate how a FORTRAN90 program, using OpenMP, can be compiled and run in batch mode on the FSU High Performance Computing (HPC) cluster operated by the Research Computing Center (RCC).

SPARSE_CC, a data directory which contains a description and examples of the CC format, ("compressed column") for storing a sparse matrix, including a way to write the matrix as a set of three files.

SUPERLU, FORTRAN90 programs which illustrate how to use the SUPERLU library, which applies a fast direct solution method to solve sparse linear systems, by James Demmel, John Gilbert, and Xiaoye Li.

Reference:

1. http://crd.lbl.gov/~xiaoye/SuperLU/ the SuperLU web site.
2. James Demmel, John Gilbert, Xiaoye Li,
   SuperLU Users's Guide.
3. James Demmel, Stanley Eisenstat, John Gilbert, Xiaoye Li, Joseph Liu
   A Supernodal Approach to Sparse Partial Pivoting,
   SIAM Journal on Matrix Analysis and Applications,
   Volume 20, Number 3, pages 720-755, 1999.

Examples and Tests:

Many of the examples read the matrix from a file, which uses the Harwell-Boeing sparse matrix format. These matrices include:

• cg20_cua.txt, a complex matrix in UA format;
• cmat_cua.txt, a complex matrix in UA format.
• g10_rua.txt, a real matrix in UA format;
• g20_rua.txt, a real matrix in UA format;

The FORTRAN77 examples must call a C interface routine. The C interface routine called depends on the precision and arithmetic used.

• c_bridge_pcgssv.c, the interface for single precision complex arithmetic.
• c_bridge_pdgssv.c, the interface for double precision real arithmetic.
• c_bridge_psgssv.c, the interface for single precision real arithmetic.
• c_bridge_pzgssv.c, the interface for double precision complex arithmetic.

C_HB uses CGSSV to solve a linear system one time. The program reads the matrix from the file cg20_cua.txt. Single precision complex arithmetic is used.

• c_hb.f, the calling program;
• c_hb.sh, commands to compile, link and run the calling program;
• c_hb_1.txt, the sample output using 1 processor.
• c_hb_4.txt, the sample output using 4 processors.

D_HB uses DGSSV to solve a linear system one time. The program reads the matrix from the file g20_rua.txt. Double precision real arithmetic is used.

• d_hb.f, the calling program;
• d_hb.sh, commands to compile, link and run the calling program;
• d_hb_1.txt, the sample output using 1 processor.
• d_hb_4.txt, the sample output using 4 processors.

S_HB uses SGSSV to solve a linear system one time. The program reads the matrix from the file g20_rua.txt. Single precision real arithmetic is used.

• s_hb.f, the calling program;
• s_hb.sh, commands to compile, link and run the calling program;
• s_hb_1.txt, the sample output using 1 processor.
• s_hb_4.txt, the sample output using 4 processors.

Z_HB uses ZGSSV to solve a linear system one time. The program reads the matrix from the file cg20_cua.txt. Double precision complex arithmetic is used.

• z_hb.f, the calling program;
• z_hb.sh, commands to compile, link and run the calling program;
• z_hb_1.txt, the sample output using 1 processor.
• z_hb_4.txt, the sample output using 4 processors.

You can go up one level to the FORTRAN77 source codes.