TEMPLATES
Iterative Solvers
for Linear Systems

TEMPLATES is a FORTRAN77 library which outlines the most common iterative methods of solving a linear system.

Languages:

TEMPLATES is available in a FORTRAN77 version and a FORTRAN90 version and a MATLAB version

Related Data and Programs:

CG, a FORTRAN77 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.

LINPACK, a FORTRAN77 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.

MULTIGRID_POISSON_1D, a FORTRAN77 library which applies the multigrid method to a discretized version of the 1D Poisson equation.

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

TEMPLATED, a FORTRAN77 library which carries out simple versions of various iterative solvers. This is the double precision version.

TEST_MAT, a FORTRAN77 library which defines test matrices.

UMFPACK, a FORTRAN77 library which solves unsymmetric sparse linear systems, by Timothy Davis, Iain Duff.

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.f, the source code.
• templates.sh, commands to compile the source code.

Examples and Tests:

• templates_prb.f, a sample calling program.
• templates_prb.sh, commands to compile and run the sample program.
• test.data, a sample input file.
• test.results, the output file.

List of Routines:

• APPLYGIVENS
• APPROXRES
• BACKSOLVE
• BICG
• BICGREVCOM
• BICGSTAB
• BICGSTABREVCOM
• CG
• CGREVCOM
• CGS
• CGSREVCOM
• CHEBY
• CHEBYREVCOM
• COMP2DENSE
• ELEMVEC constructs the I-th elementary vector E, scaled by ALPHA.
• GEN57PT
• GETEIG computes the eigenvalues of a matrix.
• GETGIV
• GETSTEN
• GMRES
• GMRESREVCOM
• HENKDFUN
• HENKFUN
• ILAENV sets local environment parameters for LAPACK.
• ISAMAX finds the index of element having maximum absolute value.
• JACOBI
• JACOBIREVCOM
• JACSPLIT
• LSAME returns TRUE if CA is the same letter as CB regardless of case.
• LSAMEN is TRUE if the first N characters of two strings match.
• MATCOPY
• MATSPLIT
• MATVEC
• MATVECTRANS
• NEGONEFUN
• NEGTHOUSXFUN
• ONEFUN
• ORTHOH
• PSOLVE
• PSOLVEJAC
• PSOLVEJACTRANS
• PSOLVENONE
• PSOLVENONETRANS
• PSOLVEQ
• PSOLVETRANS
• PSOLVETRANSQ
• QMR
• QMRREVCOM
• ROTVEC
• SAXPY computes constant times a vector plus a vector.
• SCOPY copies a vector, x, to a vector, y.
• SDOT forms the dot product of two vectors.
• SET_E
• SGEMM adds a matrix product to a matrix.
• SGEMV adds a matrix-vector product to a vector.
• SGER performs a rank-one update of a matrix.
• SLAE2 computes the eigenvalues of a 2x2 symmetric matrix.
• SLAEV2 computes the eigen-decomposition of a 2x2 symmetric matrix.
• SLAMC1 determines machine parameters.
• SLAMC2 determines machine parameters.
• SLAMC3 determines machine parameters.
• SLAMC4 determines machine parameters.
• SLAMC5 determines machine parameters.
• SLAMCH determines machine parameters.
• SLANSY returns the norm of a real symmetric matrix.
• SLAPY2 computes sqrt ( x*x + y*y ).
• SLARAN returns a pseudorandom uniform value from [0,1].
• SLARFB
• SLARF
• SLARFG
• SLARFT
• SLARTG
• SLASR
• SLASSQ
• SLATRD
• SLAZRO
• SNRM2 returns the euclidean norm of a real vector.
• SOR solvea s linear system using the SOR iteration.
• SORG2L
• SORG2R
• SORGQL
• SORQGR
• SORGTR
• SORREVCOM
• SORSPLIT
• SROT applies a plane rotation.
• SROTG constructs a Givens plane rotation.
• SSCAL scales a vector by a constant.
• SSTEQR
• SSTERF
• SSWAP interchanges two vectors.
• SSYEV
• SSYMM
• SSYMV
• SSYR2K
• SSYTD2
• SSYTRD
• STOPTEST2
• STRMM
• STRMV
• STRSV
• TEN5X2FUN
• THOUSFUN
• THOUSXFUN
• UPDATE
• WATHEN
• XERBLA is an error handler.
• ZEROFUN evaluates f(x,y,z) = 0.

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