Abstract base class for iterative solver. More...

#include <solvers.hpp>

Inheritance diagram for mfem::IterativeSolver:

Collaboration diagram for mfem::IterativeSolver:

Classes
struct	PrintLevel
	Settings for the output behavior of the IterativeSolver. More...

Public Member Functions
	IterativeSolver ()

	IterativeSolver (MPI_Comm comm_)

virtual void	SetPreconditioner (Solver &pr)
	This should be called before SetOperator.

virtual void	SetOperator (const Operator &op) override
	Also calls SetOperator for the preconditioner if there is one.

void	SetMonitor (IterativeSolverMonitor &m)
	Set the iterative solver monitor.

MPI_Comm	GetComm () const
	Return the associated MPI communicator, or MPI_COMM_NULL if no communicator is set.

Convergence
Termination criteria for the iterative solvers. While the convergence criterion is solver specific, most of the provided iterative solvers use one of the following criteria \( \|\|r\|\|_X \leq tol_{rel}\|\|r_0\|\|_X \), \( \|\|r\|\|_X \leq tol_{abs} \), \( \|\|r\|\|_X \leq \max\{ tol_{abs}, tol_{rel} \|\|r_0\|\|_X \} \), where X denotes the space in which the norm is measured. The choice of X depends on the specific iterative solver.
void	SetRelTol (real_t rtol)

void	SetAbsTol (real_t atol)

void	SetMaxIter (int max_it)

Reporting
These options control the internal reporting behavior into mfem::out and mfem::err of the iterative solvers.
virtual void	SetPrintLevel (int print_lvl)
	Legacy method to set the level of verbosity of the solver output.

virtual void	SetPrintLevel (PrintLevel)
	Set the level of verbosity of the solver output.

Solver statistics.
These are valid after the call to Mult().
int	GetNumIterations () const
	Returns the number of iterations taken during the last call to Mult()

bool	GetConverged () const
	Returns true if the last call to Mult() converged successfully.

real_t	GetInitialNorm () const
	Returns the initial residual norm from the last call to Mult().

real_t	GetFinalNorm () const
	Returns the final residual norm after termination of the solver during the last call to Mult().

real_t	GetFinalRelNorm () const
	Returns the final residual norm after termination of the solver during the last call to Mult(), divided by the initial residual norm. Returns -1 if one of these norms is left undefined by the solver.

Public Member Functions inherited from mfem::Solver
	Solver (int s=0, bool iter_mode=false)
	Initialize a square Solver with size s.

	Solver (int h, int w, bool iter_mode=false)
	Initialize a Solver with height h and width w.

Public Member Functions inherited from mfem::Operator
void	InitTVectors (const Operator Po, const Operator Ri, const Operator *Pi, Vector &x, Vector &b, Vector &X, Vector &B) const
	Initializes memory for true vectors of linear system.

	Operator (int s=0)
	Construct a square Operator with given size s (default 0).

	Operator (int h, int w)
	Construct an Operator with the given height (output size) and width (input size).

int	Height () const
	Get the height (size of output) of the Operator. Synonym with NumRows().

int	NumRows () const
	Get the number of rows (size of output) of the Operator. Synonym with Height().

int	Width () const
	Get the width (size of input) of the Operator. Synonym with NumCols().

int	NumCols () const
	Get the number of columns (size of input) of the Operator. Synonym with Width().

virtual MemoryClass	GetMemoryClass () const
	Return the MemoryClass preferred by the Operator.

virtual void	Mult (const Vector &x, Vector &y) const =0
	Operator application: `y=A(x)`.

virtual void	MultTranspose (const Vector &x, Vector &y) const
	Action of the transpose operator: `y=A^t(x)`. The default behavior in class Operator is to generate an error.

virtual void	AddMult (const Vector &x, Vector &y, const real_t a=1.0) const
	Operator application: `y+=A(x)` (default) or `y+=a*A(x)`.

virtual void	AddMultTranspose (const Vector &x, Vector &y, const real_t a=1.0) const
	Operator transpose application: `y+=A^t(x)` (default) or `y+=a*A^t(x)`.

virtual void	ArrayMult (const Array< const Vector * > &X, Array< Vector * > &Y) const
	Operator application on a matrix: `Y=A(X)`.

virtual void	ArrayMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y) const
	Action of the transpose operator on a matrix: `Y=A^t(X)`.

virtual void	ArrayAddMult (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
	Operator application on a matrix: `Y+=A(X)` (default) or `Y+=a*A(X)`.

virtual void	ArrayAddMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
	Operator transpose application on a matrix: `Y+=A^t(X)` (default) or `Y+=a*A^t(X)`.

virtual Operator &	GetGradient (const Vector &x) const
	Evaluate the gradient operator at the point x. The default behavior in class Operator is to generate an error.

virtual void	AssembleDiagonal (Vector &diag) const
	Computes the diagonal entries into diag. Typically, this operation only makes sense for linear Operators. In some cases, only an approximation of the diagonal is computed.

virtual const Operator *	GetProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. `NULL` means identity.

virtual const Operator *	GetRestriction () const
	Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity.

virtual const Operator *	GetOutputProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. `NULL` means identity.

virtual const Operator *	GetOutputRestrictionTranspose () const
	Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators.

virtual const Operator *	GetOutputRestriction () const
	Restriction operator from output vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity.

void	FormLinearSystem (const Array< int > &ess_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B, int copy_interior=0)
	Form a constrained linear system using a matrix-free approach.

void	FormRectangularLinearSystem (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B)
	Form a column-constrained linear system using a matrix-free approach.

virtual void	RecoverFEMSolution (const Vector &X, const Vector &b, Vector &x)
	Reconstruct a solution vector x (e.g. a GridFunction) from the solution X of a constrained linear system obtained from Operator::FormLinearSystem() or Operator::FormRectangularLinearSystem().

void	FormSystemOperator (const Array< int > &ess_tdof_list, Operator *&A)
	Return in A a parallel (on truedofs) version of this square operator.

void	FormRectangularSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Operator *&A)
	Return in A a parallel (on truedofs) version of this rectangular operator (including constraints).

void	FormDiscreteOperator (Operator *&A)
	Return in A a parallel (on truedofs) version of this rectangular operator.

void	PrintMatlab (std::ostream &out, int n, int m=0) const
	Prints operator with input size n and output size m in Matlab format.

virtual void	PrintMatlab (std::ostream &out) const
	Prints operator in Matlab format.

virtual	~Operator ()
	Virtual destructor.

Type	GetType () const
	Return the type ID of the Operator class.

Protected Member Functions
virtual real_t	Dot (const Vector &x, const Vector &y) const
	Return the standard (l2, i.e., Euclidean) inner product of x and y.

real_t	Norm (const Vector &x) const
	Return the inner product norm of x, using the inner product defined by Dot()

void	Monitor (int it, real_t norm, const Vector &r, const Vector &x, bool final=false) const
	Monitor both the residual r and the solution x.

Protected Member Functions inherited from mfem::Operator
void	FormConstrainedSystemOperator (const Array< int > &ess_tdof_list, ConstrainedOperator *&Aout)
	see FormSystemOperator()

void	FormRectangularConstrainedSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, RectangularConstrainedOperator *&Aout)
	see FormRectangularSystemOperator()

Operator *	SetupRAP (const Operator Pi, const Operator Po)
	Returns RAP Operator of this, using input/output Prolongation matrices Pi corresponds to "P", Po corresponds to "Rt".

Protected Attributes
const Operator *	oper

Solver *	prec

IterativeSolverMonitor *	monitor = nullptr

Convergence (protected attributes)
int	max_iter
	Limit for the number of iterations the solver is allowed to do.

real_t	rel_tol
	Relative tolerance.

real_t	abs_tol
	Absolute tolerance.

Solver statistics (protected attributes)
Every IterativeSolver is expected to define these in its Mult() call.
int	final_iter = -1

bool	converged = false

real_t	initial_norm = -1.0

real_t	final_norm = -1.0

Protected Attributes inherited from mfem::Operator
int	height
	Dimension of the output / number of rows in the matrix.

int	width
	Dimension of the input / number of columns in the matrix.

Reporting (protected attributes and member functions)
int	print_level = -1
	(DEPRECATED) Legacy print level definition, which is left for compatibility with custom iterative solvers.

PrintLevel	print_options
	Output behavior for the iterative solver.

PrintLevel	FromLegacyPrintLevel (int)
	Convert a legacy print level integer to a PrintLevel object.

static int	GuessLegacyPrintLevel (PrintLevel)
	Use some heuristics to guess a legacy print level corresponding to the given PrintLevel.

Additional Inherited Members
Public Types inherited from mfem::Operator
enum	DiagonalPolicy { DIAG_ZERO , DIAG_ONE , DIAG_KEEP }
	Defines operator diagonal policy upon elimination of rows and/or columns. More...

enum	Type { ANY_TYPE , MFEM_SPARSEMAT , Hypre_ParCSR , PETSC_MATAIJ , PETSC_MATIS , PETSC_MATSHELL , PETSC_MATNEST , PETSC_MATHYPRE , PETSC_MATGENERIC , Complex_Operator , MFEM_ComplexSparseMat , Complex_Hypre_ParCSR , Complex_DenseMat , MFEM_Block_Matrix , MFEM_Block_Operator }
	Enumeration defining IDs for some classes derived from Operator. More...

Public Attributes inherited from mfem::Solver
bool	iterative_mode
	If true, use the second argument of Mult() as an initial guess.

Detailed Description

Abstract base class for iterative solver.

Definition at line 66 of file solvers.hpp.

Constructor & Destructor Documentation

◆ IterativeSolver() [1/2]

mfem::IterativeSolver::IterativeSolver ( )

Definition at line 28 of file solvers.cpp.

◆ IterativeSolver() [2/2]

mfem::IterativeSolver::IterativeSolver ( MPI_Comm comm_ )

Definition at line 42 of file solvers.cpp.

Member Function Documentation

◆ Dot()

real_t mfem::IterativeSolver::Dot	(	const Vector &	x,
		const Vector &	y ) const

protectedvirtual

Return the standard (l2, i.e., Euclidean) inner product of x and y.

Overriding this method in a derived class enables a custom inner product.

Definition at line 55 of file solvers.cpp.

◆ FromLegacyPrintLevel()

IterativeSolver::PrintLevel mfem::IterativeSolver::FromLegacyPrintLevel ( int print_level_ )

protected

Convert a legacy print level integer to a PrintLevel object.

Definition at line 114 of file solvers.cpp.

◆ GetComm()

MPI_Comm mfem::IterativeSolver::GetComm ( ) const

inline

Return the associated MPI communicator, or MPI_COMM_NULL if no communicator is set.

Definition at line 302 of file solvers.hpp.

◆ GetConverged()

bool mfem::IterativeSolver::GetConverged ( ) const

inline

Returns true if the last call to Mult() converged successfully.

Definition at line 262 of file solvers.hpp.

◆ GetFinalNorm()

real_t mfem::IterativeSolver::GetFinalNorm ( ) const

inline

Returns the final residual norm after termination of the solver during the last call to Mult().

This function returns the norm of the residual (or preconditioned residual, depending on the solver), corresponding to the returned solution.

Definition at line 275 of file solvers.hpp.

◆ GetFinalRelNorm()

real_t mfem::IterativeSolver::GetFinalRelNorm ( ) const

inline

Returns the final residual norm after termination of the solver during the last call to Mult(), divided by the initial residual norm. Returns -1 if one of these norms is left undefined by the solver.

See also: GetFinalNorm(), GetInitialNorm()

Definition at line 281 of file solvers.hpp.

◆ GetInitialNorm()

real_t mfem::IterativeSolver::GetInitialNorm ( ) const

inline

Returns the initial residual norm from the last call to Mult().

This function returns the norm of the residual (or preconditioned residual, depending on the solver), computed before the start of the iteration.

Definition at line 268 of file solvers.hpp.

◆ GetNumIterations()

int mfem::IterativeSolver::GetNumIterations ( ) const

inline

Returns the number of iterations taken during the last call to Mult()

Definition at line 260 of file solvers.hpp.

◆ GuessLegacyPrintLevel()

int mfem::IterativeSolver::GuessLegacyPrintLevel ( PrintLevel print_options_ )

staticprotected

Use some heuristics to guess a legacy print level corresponding to the given PrintLevel.

Definition at line 149 of file solvers.cpp.

◆ Monitor()

void mfem::IterativeSolver::Monitor	(	int	it,
		real_t	norm,
		const Vector &	r,
		const Vector &	x,
		bool	final = false ) const

protected

Monitor both the residual r and the solution x.

Definition at line 190 of file solvers.cpp.

◆ Norm()

real_t mfem::IterativeSolver::Norm ( const Vector & x ) const

inlineprotected

Return the inner product norm of x, using the inner product defined by Dot()

Definition at line 180 of file solvers.hpp.

◆ SetAbsTol()

void mfem::IterativeSolver::SetAbsTol ( real_t atol )

inline

Definition at line 210 of file solvers.hpp.

◆ SetMaxIter()

void mfem::IterativeSolver::SetMaxIter ( int max_it )

inline

Definition at line 211 of file solvers.hpp.

◆ SetMonitor()

void mfem::IterativeSolver::SetMonitor ( IterativeSolverMonitor & m )

inline

Set the iterative solver monitor.

Definition at line 296 of file solvers.hpp.

◆ SetOperator()

void mfem::IterativeSolver::SetOperator ( const Operator & op )

overridevirtual

Also calls SetOperator for the preconditioner if there is one.

Implements mfem::Solver.

Reimplemented in mfem::BiCGSTABSolver, mfem::blocksolvers::BPCGSolver, mfem::CGSolver, mfem::ConstrainedSolver, mfem::EliminationSolver, mfem::KINSolver, mfem::LBFGSSolver, mfem::MINRESSolver, mfem::NewtonSolver, mfem::OptimizationSolver, mfem::PenaltyConstrainedSolver, and mfem::SLISolver.

Definition at line 179 of file solvers.cpp.

◆ SetPreconditioner()

void mfem::IterativeSolver::SetPreconditioner ( Solver & pr )

virtual

This should be called before SetOperator.

Reimplemented in mfem::blocksolvers::BPCGSolver, mfem::EliminationSolver, mfem::KINSolver, mfem::LBFGSSolver, mfem::MINRESSolver, mfem::OptimizationSolver, mfem::PenaltyConstrainedSolver, and mfem::TMOPNewtonSolver.

Definition at line 173 of file solvers.cpp.

◆ SetPrintLevel() [1/2]

void mfem::IterativeSolver::SetPrintLevel ( int print_lvl )

virtual

Legacy method to set the level of verbosity of the solver output.

This is the old way to control what information will be printed to mfem::out and mfem::err. The behavior for the print level for all iterative solvers is:

-1: Suppress all outputs.
0: Print information about all detected issues (e.g. no convergence).
1: Same as level 0, but with detailed information about each iteration.
2: Print detected issues and a summary when the solver terminates.
3: Same as 2, but print also the first and last iterations.
>3: Custom print options which are dependent on the specific solver.

In parallel, only rank 0 produces output.

Note: It is recommended to use SetPrintLevel(PrintLevel) instead.; Some derived classes, like KINSolver, redefine this method and use their own set of print level constants.

Reimplemented in mfem::KINSolver.

Definition at line 71 of file solvers.cpp.

◆ SetPrintLevel() [2/2]

void mfem::IterativeSolver::SetPrintLevel ( PrintLevel options )

virtual

Set the level of verbosity of the solver output.

In parallel, only rank 0 produces outputs. Errors are output to mfem::err and all other information to mfem::out.

Note: Not all subclasses of IterativeSolver support all possible options.; Some derived classes, like KINSolver, disable this method in favor of SetPrintLevel(int).

See also: PrintLevel for possible options.

Reimplemented in mfem::KINSolver.

Definition at line 92 of file solvers.cpp.

◆ SetRelTol()

void mfem::IterativeSolver::SetRelTol ( real_t rtol )

inline

Definition at line 209 of file solvers.hpp.

Member Data Documentation

◆ abs_tol

real_t mfem::IterativeSolver::abs_tol

protected

Absolute tolerance.

Definition at line 158 of file solvers.hpp.

◆ converged

bool mfem::IterativeSolver::converged = false

mutableprotected

Definition at line 167 of file solvers.hpp.

◆ final_iter

int mfem::IterativeSolver::final_iter = -1

mutableprotected

Definition at line 166 of file solvers.hpp.

◆ final_norm

real_t mfem::IterativeSolver::final_norm = -1.0

protected

Definition at line 168 of file solvers.hpp.

◆ initial_norm

real_t mfem::IterativeSolver::initial_norm = -1.0

mutableprotected

Definition at line 168 of file solvers.hpp.

◆ max_iter

int mfem::IterativeSolver::max_iter

protected

Limit for the number of iterations the solver is allowed to do.

Definition at line 152 of file solvers.hpp.

◆ monitor

IterativeSolverMonitor* mfem::IterativeSolver::monitor = nullptr

protected

Definition at line 123 of file solvers.hpp.

◆ oper

const Operator* mfem::IterativeSolver::oper

protected

Definition at line 121 of file solvers.hpp.

◆ prec

Solver* mfem::IterativeSolver::prec

protected

Definition at line 122 of file solvers.hpp.

◆ print_level

int mfem::IterativeSolver::print_level = -1

protected

(DEPRECATED) Legacy print level definition, which is left for compatibility with custom iterative solvers.

Deprecated: print_options should be used instead.

Definition at line 131 of file solvers.hpp.

◆ print_options

PrintLevel mfem::IterativeSolver::print_options

protected

Output behavior for the iterative solver.

This primarily controls the output behavior of the iterative solvers provided by this library. This member must be synchronized with print_level to ensure compatibility with custom iterative solvers.

Definition at line 138 of file solvers.hpp.

◆ rel_tol

real_t mfem::IterativeSolver::rel_tol

protected

Relative tolerance.

Definition at line 155 of file solvers.hpp.

The documentation for this class was generated from the following files:

linalg/solvers.hpp
linalg/solvers.cpp

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Reporting (protected attributes and member functions)

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ IterativeSolver() [1/2]

◆ IterativeSolver() [2/2]

Member Function Documentation

◆ Dot()

◆ FromLegacyPrintLevel()

◆ GetComm()

◆ GetConverged()

◆ GetFinalNorm()

◆ GetFinalRelNorm()

◆ GetInitialNorm()

◆ GetNumIterations()

◆ GuessLegacyPrintLevel()

◆ Monitor()

◆ Norm()

◆ SetAbsTol()

◆ SetMaxIter()

◆ SetMonitor()

◆ SetOperator()

◆ SetPreconditioner()

◆ SetPrintLevel() [1/2]

◆ SetPrintLevel() [2/2]

◆ SetRelTol()

Member Data Documentation

◆ abs_tol

◆ converged

◆ final_iter

◆ final_norm

◆ initial_norm

◆ max_iter

◆ monitor

◆ oper

◆ prec

◆ print_level

◆ print_options

◆ rel_tol