Lis (linear algebra library)

Stable release	2.1.7 / December 17, 2024
Operating system	Cross-platform
Available in	C, Fortran
Type	Software library
License	New BSD License
Website	www.ssisc.org/lis/

Lis (Library of Iterative Solvers for linear systems; pronounced lis]) is a scalable parallel software library to solve discretized linear equations and eigenvalue problems that mainly arise from the numerical solution of partial differential equations using iterative methods.^[1]^[2]^[3] Although it is designed for parallel computers, the library can be used without being conscious of parallel processing.

Features

Lis provides facilities for:

Automatic program configuration
NUMA aware hybrid implementation with MPI and OpenMP
Exchangeable dense and sparse matrix storage formats
Basic linear algebra operations for dense and sparse matrices
Parallel iterative methods for linear equations and eigenvalue problems
Parallel preconditioners for iterative methods
Quadruple precision floating point operations
Performance analysis
Command-line interface to solvers and benchmarks

Example

A C program to solve the linear equation $Ax=b$ is written as follows:

#include <stdio.h>
#include "lis_config.h"
#include "lis.h"

LIS_INT main(LIS_INT argc, char* argv[])
{
  LIS_MATRIX  A;
  LIS_VECTOR  b, x;
  LIS_SOLVER  solver;
  LIS_INT     iter;
  double      time;

  lis_initialize(&argc, &argv);

  lis_matrix_create(LIS_COMM_WORLD, &A);
  lis_vector_create(LIS_COMM_WORLD, &b);
  lis_vector_create(LIS_COMM_WORLD, &x);

  lis_input_matrix(A, argv[1]);
  lis_input_vector(b, argv[2]);
  lis_vector_duplicate(A, &x);

  lis_solver_create(&solver);
  lis_solver_set_optionC(solver);
  lis_solve(A, b, x, solver);

  lis_solver_get_iter(solver, &iter);
  lis_solver_get_time(solver, &time);
  printf("number of iterations = %d\n", iter);
  printf("elapsed time = %e\n", time);

  lis_output_vector(x, LIS_FMT_MM, argv[3]);

  lis_solver_destroy(solver);
  lis_matrix_destroy(A);
  lis_vector_destroy(b);
  lis_vector_destroy(x);

  lis_finalize();

  return 0;
}

System requirements

Installing Lis requires a C compiler. If you wish to use the Fortran interface, a Fortran compiler is needed, and the algebraic multigrid preconditioner requires a Fortran 90 compiler.^[4] For parallel computing environments, an OpenMP or MPI library is necessary. Lis supports both the Matrix Market and Harwell-Boeing formats for importing and exporting user data.

Packages that use Lis

References

^ Akira Nishida (2010). "Experience in Developing an Open Source Scalable Software Infrastructure in Japan". Computational Science and Its Applications – ICCSA 2010. Lecture Notes in Computer Science 6017. Vol. 6017. Springer. pp. 87–98. doi:10.1007/978-3-642-12165-4_36. ISBN 978-3-642-12164-7.
^ Hisashi Kotakemori; Hidehiko Hasegawa; Tamito Kajiyama; Akira Nukada; Reiji Suda & Akira Nishida (2008). "Performance Evaluation of Parallel Sparse Matrix-Vector Products on SGI Altix 3700". OpenMP Shared Memory Parallel Programming. Lecture Notes in Computer Science 4315. Springer. pp. 153–163. doi:10.1007/978-3-540-68555-5_13. ISBN 978-3-540-68554-8.
^ Hisashi Kotakemori; Hidehiko Hasegawa & Akira Nishida (2005). "Performance Evaluation of a Parallel Iterative Method Library using OpenMP". Proceedings of the 8th International Conference on High Performance Computing in Asia Pacific Region (HPC Asia 2005). IEEE. pp. 432–436. doi:10.1109/HPCASIA.2005.74. ISBN 0-7695-2486-9. S2CID 6402585.
^ Akihiro Fujii; Akira Nishida & Yoshio Oyanagi (2005). "Evaluation of Parallel Aggregate Creation Orders : Smoothed Aggregation Algebraic Multigrid Method". High Performance Computational Science and Engineering. Springer. pp. 99–122. doi:10.1007/0-387-24049-7_6. ISBN 1-4419-3684-X. S2CID 118053459.