The SUNLinSol_SPTFQMR Module

The SPTFQMR (Scaled, Preconditioned, Transpose-Free Quasi-Minimum Residual [F1993]) implementation of the SUNLinearSolver module provided with SUNDIALS, SUNLinSol_SPTFQMR, is an iterative linear solver that is designed to be compatible with any N_Vector implementation (serial, threaded, parallel, and user-supplied) that supports a minimal subset of operations (N_VClone(), N_VDotProd(), N_VScale(), N_VLinearSum(), N_VProd(), N_VConst(), N_VDiv(), and N_VDestroy()). Unlike the SPGMR and SPFGMR algorithms, SPTFQMR requires a fixed amount of memory that does not increase with the number of allowed iterations.

SUNLinSol_SPTFQMR Usage

The header file to be included when using this module is sunlinsol/sunlinsol_sptfqmr.h. The SUNLinSol_SPTFQMR module is accessible from all SUNDIALS solvers without linking to the libsundials_sunlinsolsptfqmr module library.

The module SUNLinSol_SPTFQMR provides the following user-callable routines:

SUNLinearSolver SUNLinSol_SPTFQMR(N_Vector y, int pretype, int maxl)

This constructor function creates and allocates memory for a SPTFQMR SUNLinearSolver. Its arguments are an N_Vector, the desired type of preconditioning, and the number of linear iterations to allow.

This routine will perform consistency checks to ensure that it is called with a consistent N_Vector implementation (i.e. that it supplies the requisite vector operations). If y is incompatible, then this routine will return NULL.

A maxl argument that is \(\le0\) will result in the default value (5).

Allowable inputs for pretype are PREC_NONE (0), PREC_LEFT (1), PREC_RIGHT (2) and PREC_BOTH (3); any other integer input will result in the default (no preconditioning). We note that some SUNDIALS solvers are designed to only work with left preconditioning (IDA and IDAS) and others with only right preconditioning (KINSOL). While it is possible to configure a SUNLinSol_SPTFQMR object to use any of the preconditioning options with these solvers, this use mode is not supported and may result in inferior performance.

int SUNLinSol_SPTFQMRSetPrecType(SUNLinearSolver S, int pretype)

This function updates the type of preconditioning to use. Supported values are PREC_NONE (0), PREC_LEFT (1), PREC_RIGHT (2), and PREC_BOTH (3).

This routine will return with one of the error codes SUNLS_ILL_INPUT (illegal pretype), SUNLS_MEM_NULL (S is NULL), or SUNLS_SUCCESS.

int SUNLinSol_SPTFQMRSetMaxl(SUNLinearSolver S, int maxl)

This function updates the number of linear solver iterations to allow.

A maxl argument that is \(\le0\) will result in the default value (5).

This routine will return with one of the error codes SUNLS_MEM_NULL (S is NULL) or SUNLS_SUCCESS.

int SUNLinSolSetInfoFile_SPTFQMR(SUNLinearSolver LS, FILE* info_file)

The function SUNLinSolSetInfoFile_SPTFQMR() sets the output file where all informative (non-error) messages should be directed.

Arguments:
  • LS – a SUNLinSol object
  • info_file – pointer to output file (stdout by default);
    a NULL input will disable output
Return value:
  • SUNLS_SUCCESS if successful
  • SUNLS_MEM_NULL if the SUNLinearSolver memory was NULL
  • SUNLS_ILL_INPUT if SUNDIALS was not built with monitoring enabled

Notes: This function is intended for users that wish to monitor the linear solver progress. By default, the file pointer is set to stdout.

SUNDIALS must be built with the CMake option ``SUNDIALS_BUILD_WITH_MONITORING``, to utilize this function. See section Configuration options (Unix/Linux) for more information.

int SUNLinSolSetPrintLevel_SPTFQMR(SUNLinearSolver LS, int print_level)

The function SUNLinSolSetPrintLevel_SPTFQMR() specifies the level of verbosity of the output.

Arguments:
  • LS – a SUNLinSol object

  • print_level – flag indicating level of verbosity; must be one of:

    • 0, no information is printed (default)
    • 1, for each linear iteration the residual norm is printed
Return value:
  • SUNLS_SUCCESS if successful
  • SUNLS_MEM_NULL if the SUNLinearSolver memory was NULL
  • SUNLS_ILL_INPUT if SUNDIALS was not built with monitoring enabled, or if the print level value was invalid

Notes: This function is intended for users that wish to monitor the linear solver progress. By default, the print level is 0.

SUNDIALS must be built with the CMake option ``SUNDIALS_BUILD_WITH_MONITORING``, to utilize this function. See section Configuration options (Unix/Linux) for more information.

For backwards compatibility, we also provide the wrapper functions, each with identical input and output arguments to the routines that they wrap:

SUNLinearSolver SUNSPTFQMR(N_Vector y, int pretype, int maxl)

Wrapper function for SUNLinSol_SPTFQMR()

int SUNSPTFQMRSetPrecType(SUNLinearSolver S, int pretype)

Wrapper function for SUNLinSol_SPTFQMRSetPrecType()

int SUNSPTFQMRSetMaxl(SUNLinearSolver S, int maxl)

Wrapper function for SUNLinSol_SPTFQMRSetMaxl()

For solvers that include a Fortran interface module, the SUNLinSol_SPTFQMR module also includes the Fortran-callable function FSUNSPTFQMRInit() to initialize this SUNLinSol_SPTFQMR module for a given SUNDIALS solver.

subroutine FSUNSPTFQMRInit(CODE, PRETYPE, MAXL, IER)

Initializes a SPTFQMR SUNLinearSolver structure for use in a SUNDIALS package.

This routine must be called after the N_Vector object has been initialized.

Arguments:
  • CODE (int, input) – flag denoting the SUNDIALS solver this matrix will be used for: CVODE=1, IDA=2, KINSOL=3, ARKode=4.
  • PRETYPE (int, input) – flag denoting type of preconditioning to use: none=0, left=1, right=2, both=3.
  • MAXL (int, input) – number of SPTFQMR iterations to allow.
  • IER (int, output) – return flag (0 success, -1 for failure).

Additionally, when using ARKode with a non-identity mass matrix, the Fortran-callable function FSUNMassSPTFQMRInit() initializes this SUNLinSol_SPTFQMR module for solving mass matrix linear systems.

subroutine FSUNMassSPTFQMRInit(PRETYPE, MAXL, IER)

Initializes a SPTFQMR SUNLinearSolver structure for use in solving mass matrix systems in ARKode.

This routine must be called after the N_Vector object has been initialized.

Arguments:
  • PRETYPE (int, input) – flag denoting type of preconditioning to use: none=0, left=1, right=2, both=3.
  • MAXL (int, input) – number of SPTFQMR iterations to allow.
  • IER (int, output) – return flag (0 success, -1 for failure).

The SUNLinSol_SPTFQMRSetPrecType() and SUNLinSol_SPTFQMRSetMaxl() routines also support Fortran interfaces for the system and mass matrix solvers:

subroutine FSUNSPTFQMRSetPrecType(CODE, PRETYPE, IER)

Fortran interface to SUNLinSol_SPTFQMRSetPrecType() for system linear solvers.

This routine must be called after FSUNSPTFQMRInit() has been called.

Arguments: all should have type int, and have meanings identical to those listed above.

subroutine FSUNMassSPTFQMRSetPrecType(PRETYPE, IER)

Fortran interface to SUNLinSol_SPTFQMRSetPrecType() for mass matrix linear solvers in ARKode.

This routine must be called after FSUNMassSPTFQMRInit() has been called.

Arguments: all should have type int, and have meanings identical to those listed above.

subroutine FSUNSPTFQMRSetMaxl(CODE, MAXL, IER)

Fortran interface to SUNLinSol_SPTFQMRSetMaxl() for system linear solvers.

This routine must be called after FSUNSPTFQMRInit() has been called.

Arguments: all should have type int, and have meanings identical to those listed above.

subroutine FSUNMassSPTFQMRSetMaxl(MAXL, IER)

Fortran interface to SUNLinSol_SPTFQMRSetMaxl() for mass matrix linear solvers in ARKode.

This routine must be called after FSUNMassSPTFQMRInit() has been called.

Arguments: all should have type int, and have meanings identical to those listed above.

SUNLinSol_SPTFQMR Description

The SUNLinSol_SPTFQMR module defines the content field of a SUNLinearSolver to be the following structure:

struct _SUNLinearSolverContent_SPTFQMR {
  int maxl;
  int pretype;
  int numiters;
  realtype resnorm;
  int last_flag;
  ATimesFn ATimes;
  void* ATData;
  PSetupFn Psetup;
  PSolveFn Psolve;
  void* PData;
  N_Vector s1;
  N_Vector s2;
  N_Vector r_star;
  N_Vector q;
  N_Vector d;
  N_Vector v;
  N_Vector p;
  N_Vector *r;
  N_Vector u;
  N_Vector vtemp1;
  N_Vector vtemp2;
  N_Vector vtemp3;
  int      print_level;
  FILE*    info_file;
};

These entries of the content field contain the following information:

  • maxl - number of TFQMR iterations to allow (default is 5),
  • pretype - flag for type of preconditioning to employ (default is none),
  • numiters - number of iterations from the most-recent solve,
  • resnorm - final linear residual norm from the most-recent solve,
  • last_flag - last error return flag from an internal function,
  • ATimes - function pointer to perform \(Av\) product,
  • ATData - pointer to structure for ATimes,
  • Psetup - function pointer to preconditioner setup routine,
  • Psolve - function pointer to preconditioner solve routine,
  • PData - pointer to structure for Psetup and Psolve,
  • s1, s2 - vector pointers for supplied scaling matrices (default is NULL),
  • r_star - a N_Vector which holds the initial scaled, preconditioned linear system residual,
  • q, d, v, p, u - N_Vector used for workspace by the SPTFQMR algorithm,
  • r - array of two N_Vector used for workspace within the SPTFQMR algorithm,
  • vtemp1, vtemp2, vtemp3 - temporary vector storage.
  • print_level - controls the amount of information to be printed to the info file
  • info_file - the file where all informative (non-error) messages will be directed

This solver is constructed to perform the following operations:

  • During construction all N_Vector solver data is allocated, with vectors cloned from a template N_Vector that is input, and default solver parameters are set.
  • User-facing “set” routines may be called to modify default solver parameters.
  • Additional “set” routines are called by the SUNDIALS solver that interfaces with SUNLinSol_SPTFQMR to supply the ATimes, PSetup, and Psolve function pointers and s1 and s2 scaling vectors.
  • In the “initialize” call, the solver parameters are checked for validity.
  • In the “setup” call, any non-NULL PSetup function is called. Typically, this is provided by the SUNDIALS solver itself, that translates between the generic PSetup function and the solver-specific routine (solver-supplied or user-supplied).
  • In the “solve” call the TFQMR iteration is performed. This will include scaling and preconditioning if those options have been supplied.

The SUNLinSol_SPTFQMR module defines implementations of all “iterative” linear solver operations listed in the section The SUNLinearSolver API:

  • SUNLinSolGetType_SPTFQMR
  • SUNLinSolInitialize_SPTFQMR
  • SUNLinSolSetATimes_SPTFQMR
  • SUNLinSolSetPreconditioner_SPTFQMR
  • SUNLinSolSetScalingVectors_SPTFQMR
  • SUNLinSolSetup_SPTFQMR
  • SUNLinSolSolve_SPTFQMR
  • SUNLinSolNumIters_SPTFQMR
  • SUNLinSolResNorm_SPTFQMR
  • SUNLinSolResid_SPTFQMR
  • SUNLinSolLastFlag_SPTFQMR
  • SUNLinSolSpace_SPTFQMR
  • SUNLinSolFree_SPTFQMR