TEMPLATES
Iterative Solvers
for Linear Systems

TEMPLATES is a FORTRAN90 library which outlines the most common iterative methods of solving a linear system.

Languages:

TEMPLATES is available in a FORTRAN90 version and a MATLAB version

Related Data and Programs:

CG, a FORTRAN90 library which implements the conjugate gradient method for solving a positive definite sparse linear system A*x=b, using reverse communication.

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

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

JACOBI, a FORTRAN90 library which implements the Jacobi iteration for solving symmetric positive definite systems of linear equations.

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.

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

TEST_MAT, a FORTRAN90 library which defines test matrices.

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.
2. http://www.netlib.org/templates/index.html
   the TEMPLATES web site;

Source Code:

• templates.f90, the source code.

Examples and Tests:

JACOBI_GE is a calling program that uses dense GE format matrix storage, and the Jacobi iteration. Files you may copy include:

• jacobi_ge_test.f90, the sample calling program.
• jacobi_ge_test.txt, the output.

SOR_GE is a calling program that uses dense GE format matrix storage, and the Jacobi iteration. Files you may copy include:

• sor_ge_test.f90, the sample calling program.
• sor_ge_test.txt, the output.

List of Routines:

• APPROXRES approximates the residual using a Givens updating scheme.
• BICG implements the BiConjugate Gradient method.
• BICG_REVCOM is controlled by BICG using reverse communication.
• BICGSTAB implements the BiConjugate Gradient Stabilized method.
• BICGSTAB_REVCOM is controlled by BICGSTAB using reverse communication.
• CG implements the Conjugate Gradient method.
• CG_REVCOM is controlled by CG using reverse communication.
• CGS implements the Conjugate Gradient Squared method.
• CGS_GE implements the Conjugate Gradient Squared method for GE matrices.
• CGS_REVCOM is controlled by CGS using reverse communication.
• CHEBY implements the Chebyshev method.
• CHEBY_REVCOM is controlled by CHEBY using reverse communication.
• DIF returns the second difference matrix.
• ELEM_VEC constructs the I-th elementary vector E, scaled by ALPHA.
• GETBREAK is supposed to allow the user to set certain tolerances.
• GETEIG_GE computes the eigenvalues of the iteration matrix for the GE format.
• GIVENS_APPLY applies a sequence of Givens rotations to a column of H.
• GIVENS_SET computes Givens rotation parameters.
• GMRES implements the Generalized Minimal Residual method.
• GMRES_REVCOM is controlled by GMRES using reverse communication.
• JACOBI_GE implements the Jacobi method for a matrix in GE format.
• JACOBI_REVCOM is controlled by JACOBI using reverse communication.
• JACOBI_SPLIT_GE splits a GE matrix for the Jacobi algorithm.
• JACOBI_RECON_GE reconstitutes a split GE matrix for the Jacobi algorithm.
• MATVEC_GE computes Z := ALPHA * A * X + BETA * Y for a GE matrix.
• MATVEC_GB computes Z := ALPHA * A * X + BETA * Y for a GB matrix.
• MVGE is a version of the MATVEC routine which assumes that the
• ORTHOH constructs the I-th column of the upper Hessenberg matrix H
• PSOLVE calls the appropriate preconditioner solver.
• PSOLVE_JACOBI ??
• PSOLVE_JACOBI_TRANS solves the linear system Mx = b where matrix M is diagonal.
• PSOLVE_NONE is for the unpreconditioned version, i.e. just does
• PSOLVE_NONE_TRANS is for the unpreconditioned version, i.e. just does
• PSOLVE_Q is a solver for QMR which requires left preconditioning
• PSOLVE_T calls the appropriate solver.
• PSOLVE_T_Q is a solver for QMR which requires right preconditioning.
• QMR implements the Quasi-Minimal Residual method.
• QMR_REVCOM is controlled by QMR using reverse communication.
• RESID_GE computes the residual A*X-B when A is stored in GE format.
• ROTVEC applies a Givens rotation to a vector (X,Y).
• R4VEC_PRINT_SOME prints "some" of an R4VEC.
• SAMAX returns the maximum absolute value of the entries in a vector.
• SGB_TO_SGE converts a general band matrix to general matrix format.
• SGE_CHECK checks the dimensions of a general matrix.
• SLT_SL solves a lower triangular system.
• SNRM2 computes the Euclidean norm of a vector.
• SOR_GE implements the Successive Over-Relaxation method for a GE matrix.
• SOR_REVCOM is controlled by SOR using reverse communication.
• SOR_SPLIT_GE splits a GE matrix for the SOR algorithm.
• SOR_RECON_GE reconstructs the matrix A and right hand side B after splitting.
• STOPB computes the stopping criterion on B.
• STOPX computes the stopping criterion on X.
• SUT_MXV computes A * x, where A is an upper triangular matrix.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• UPDATE ??
• VECGEN generates a vector of all ones, zeros, or the row sum

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