Lis (linear algebra library)

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.

Stable release	2.1.7 / December 17, 2024 (2024-12-17)
Operating system	Cross-platform
Available in	C, Fortran
Type	Software library
License	New BSD License
Website	www.ssisc.org/lis/

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 ${\displaystyle Ax=b}$ 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

• Gerris
• OpenModelica
• OpenGeoSys
• SICOPOLIS
• STOMP
• Diablo
• Kiva
• Notus
• Solis
• GeMA
• openCFS
• numgeo
• freeCappuccino
• Andromeda
• Yelmo

See also

• Free and open-source software portal

• List of numerical libraries
• Conjugate gradient method
• Biconjugate gradient stabilized method (BiCGSTAB)
• Generalized minimal residual method (GMRES)
• Eigenvalue algorithm
• Lanczos algorithm
• Arnoldi iteration
• Krylov subspace
• Multigrid method