MGMRES
Restarted GMRES solver for sparse linear systems

MGMRES is a FORTRAN90 library which applies a simple restarted GMRES iteration to a sparse linear system stored in a simple format, by Lili Ju.

One matrix format used is the DSP or ST or "sparse triplet" format, which simply stores NZ_NUM, the number of nonzeros, and stores the K-th nonzero matrix entry as

• A(K), the value of the entry;
• IA(K), the row of the entry;
• JA(K), the column of the entry;

Another matrix format used is the CR or "sparse compressed row" format, which is similar to the sparse triplet format except that it the vector of row indices is compressed to a vector of length N+1 which points to the beginning of the set of entries for each row.

• A(1:NZ_NUM), the value of the entry;
• IA(1:N+1), row I values occur in entries IA(I) to IA(I+1)-1;
• JA(1:NZ_NUM), the column of the entry;

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

MGMRES is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CSPARSE, a C library which implements iterative methods for solving linear systems.

DLAP, a FORTRAN90 library which implements iterative methods for solving linear systems.

DSP, a file format which can be used to store a sparse matrix in a file.

FEM2D_POISSON_SPARSE, a FORTRAN90 program which solves the steady Poisson equation on a 2D triangulated region. The program uses a copy of MGMRES to solve the linear system.

HBSMC, a dataset directory which contains large sparse matrices stored in the Harwell-Boeing format.

LINPACK, a FORTRAN90 library which carries out direct methods for solving linear systems.

MM, a data directory which contains a description and examples of the Matrix Market format for storing matrices.

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.

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

SPARSEKIT, a FORTRAN90 library which implements operations on sparse matrices, including conversion between various formats.

ST, a data directory which contains a description and examples of the ST format for storing sparse matrices, which used by the C and C++ versions of MGMRES.

SUPER_LU, a C program which applies a fast direct solution method to a sparse linear system.

TEMPLATES, a FORTRAN90 library which carries out simple versions of various iterative solvers.

TEST_MAT, a FORTRAN90 library which defines test matrices.

Author:

Lili Ju,
Mathematics Department,
University of South Carolina.

Reference:

1. Richard Barrett, Michael Berry, Tony Chan, James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roidan Pozo, Charles Romine, Henk van der Vorst,
   Templates for the Solution of Linear Systems:
   Building Blocks for Iterative Methods,
   SIAM, 1994,
   ISBN: 0898714710,
   LC: QA297.8.T45.
2. Tim Kelley,
   Iterative Methods for Linear and Nonlinear Equations,
   SIAM, 2004,
   ISBN: 0898713528,
   LC: QA297.8.K45.
3. Yousef Saad,
   Iterative Methods for Sparse Linear Systems,
   Second Edition,
   SIAM, 20003,
   ISBN: 0898715342,
   LC: QA188.S17.

Source Code:

• mgmres.f90, the source code.
• mgmres.sh, commands to compile the source code.

Examples and Tests:

• mgmres_prb.f90, a sample calling program.
• mgmres_prb.sh, commands to compile and run the sample program.
• mgmres_prb_output.txt, the output file.

List of Routines:

• ATX_CR computes A'*x for a matrix stored in sparse compressed row form.
• ATX_ST computes A'*x for a matrix stored in sparset triplet form.
• AX_CR computes A*x for a matrix stored in sparse compressed row form.
• AX_ST computes A*x for a matrix stored in sparset triplet form.
• DIAGONAL_POINTER_CR finds diagonal entries in a sparse compressed row matrix.
• ILU_CR computes the incomplete LU factorization of a matrix.
• LUS_CR applies the incomplete LU preconditioner.
• MGMRES_ST applies restarted GMRES to a sparse triplet matrix.
• MULT_GIVENS applies a Givens rotation to two successive entries of a vector.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• REARRANGE_CR sorts a sparse compressed row matrix.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.