Jacobi-type diagonal smoother of a sparse matrix. More...

#include <sparsesmoothers.hpp>

Inheritance diagram for mfem::DSmoother:

Collaboration diagram for mfem::DSmoother:

Public Types
enum	JacobiType { JACOBI , L1_JACOBI , LUMPED_JACOBI }

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 Member Functions
	DSmoother (JacobiType t=JACOBI, real_t s=1., int it=1)
	Create a Jacobi smoother. SetOperator() will need to be called with a SparseMatrix before first use.

	DSmoother (const SparseMatrix &a, JacobiType t=JACOBI, real_t s=1., int it=1)
	Create a Jacobi smoother using the SparseMatrix a.

	DSmoother (int t, real_t s=1., int it=1)
	Same as DSmoother(JacobiType,real_t,int), for backwards compatibility.

	DSmoother (const SparseMatrix &a, int t, real_t s=1., int it=1)
	Same as DSmoother(const SparseMatrix&,JacobiType,real_t,int), for backwards compatibility.

void	SetPositiveDiagonal (bool pos_diag=true)
	Replace diagonal entries with their absolute values. Relevant only with JacobiType::JACOBI.

void	Mult (const Vector &x, Vector &y) const override
	Apply the Jacobi smoother.

void	MultTranspose (const Vector &x, Vector &y) const override
	Apply the transpose of the Jacobi smoother.

Public Member Functions inherited from mfem::SparseSmoother
	SparseSmoother ()=default

	SparseSmoother (const SparseMatrix &a)

void	SetOperator (const Operator &a) override
	Sets the underlying matrix. a must be a SparseMatrix.

Public Member Functions inherited from mfem::MatrixInverse
	MatrixInverse ()

	MatrixInverse (const Matrix &mat)
	Creates approximation of the inverse of square matrix.

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	AbsMult (const Vector &x, Vector &y) const
	Action of the absolute-value operator: `y=\|A\|(x)`. The default behavior in class Operator is to generate an error. If the Operator is a composition of several operators, the composition unfold into a product of absolute-value operators too.

virtual void	AbsMultTranspose (const Vector &x, Vector &y) const
	Action of the transpose absolute-value 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 void	MultMV (const MultiVector &x, MultiVector &y) const
	Operator application, y = A(x), where the input x and the output y are MultiVector objects, i.e. they generally use non-contiguous memory representation.

virtual void	MultTransposeMV (const MultiVector &x, MultiVector &y) const
	Action of the transpose operator, y = A^t(x), where the input x and the output y are MultiVector objects, i.e. they generally use non-contiguous memory representation.

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 Operator &	GetGradientMV (const MultiVector &x) const
	Evaluate the gradient operator at the point x. The input x is provided as a MultiVector, i.e. it generally uses non-contiguous memory representation.

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
void	Mult_ (const SparseMatrix &A, const Vector &x, Vector &y) const
	Apply the Jacobi smoother (used internally by Mult() and MultTranspose())

Protected Member Functions inherited from mfem::SparseSmoother
void	EnsureTranspose () const
	Ensure that the transpose is set.

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
JacobiType	type
	Type of diagonal scaling, see DSmoother::JacobiType.

real_t	scale
	Scaling (damping) factor.

int	iterations
	Number of stationary iterations to perform.

bool	use_abs_diag = false
	Uses abs values of the diagonal entries. Relevant only with type JacobiType::JACOBI.

Vector	z
	Temporary work vector.

Protected Attributes inherited from mfem::SparseSmoother
const SparseMatrix *	oper = nullptr
	The underlying matrix.

const SparseMatrix *	oper_T = nullptr

std::unique_ptr< SparseMatrix >	At
	Transpose of A, if needed.

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.

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

Detailed Description

Jacobi-type diagonal smoother of a sparse matrix.

Definition at line 98 of file sparsesmoothers.hpp.

Member Enumeration Documentation

◆ JacobiType

enum mfem::DSmoother::JacobiType

Enumerator
JACOBI	Scale by the diagonal of the matrix.
L1_JACOBI	Scale by the l1-norm of the rows.
LUMPED_JACOBI	Scale by the sum of the rows.

Definition at line 101 of file sparsesmoothers.hpp.

Constructor & Destructor Documentation

◆ DSmoother() [1/4]

mfem::DSmoother::DSmoother	(	JacobiType	t = JACOBI,
		real_t	s = 1.,
		int	it = 1 )

inline

Create a Jacobi smoother. SetOperator() will need to be called with a SparseMatrix before first use.

Parameters

[in]	t	Type of Jacobi smoother (see DSmoother::JacobiType)
[in]	s	Scaling factor
[in]	it	Number of stationary iterations to perform

Definition at line 128 of file sparsesmoothers.hpp.

◆ DSmoother() [2/4]

mfem::DSmoother::DSmoother	(	const SparseMatrix &	a,
		JacobiType	t = JACOBI,
		real_t	s = 1.,
		int	it = 1 )

inline

Create a Jacobi smoother using the SparseMatrix a.

Parameters

[in]	a	The underlying SparseMatrix
[in]	t	Type of Jacobi smoother (see DSmoother::JacobiType)
[in]	s	Scaling factor
[in]	it	Number of stationary iterations to perform

Definition at line 137 of file sparsesmoothers.hpp.

◆ DSmoother() [3/4]

mfem::DSmoother::DSmoother	(	int	t,
		real_t	s = 1.,
		int	it = 1 )

inline

Same as DSmoother(JacobiType,real_t,int), for backwards compatibility.

Definition at line 141 of file sparsesmoothers.hpp.

◆ DSmoother() [4/4]

mfem::DSmoother::DSmoother	(	const SparseMatrix &	a,
		int	t,
		real_t	s = 1.,
		int	it = 1 )

inline

Same as DSmoother(const SparseMatrix&,JacobiType,real_t,int), for backwards compatibility.

Definition at line 146 of file sparsesmoothers.hpp.

Member Function Documentation

◆ Mult()

void mfem::DSmoother::Mult	(	const Vector &	x,
		Vector &	y ) const

overridevirtual

Apply the Jacobi smoother.

Applies a stationary iteration with diagonal scaling. If Solver::iterative_mode is true, then y is used as the initial guess (and the diagonal scaling is applied to the residual \(x - Ay\), giving \(D^{-1}(x - Ay)\)).

By default, Solver::iterative_mode is false and only one iteration is performed, corresponding to \(y = D^{-1}x\).

Implements mfem::Operator.

Definition at line 139 of file sparsesmoothers.cpp.

◆ Mult_()

void mfem::DSmoother::Mult_	(	const SparseMatrix &	A,
		const Vector &	x,
		Vector &	y ) const

protected

Apply the Jacobi smoother (used internally by Mult() and MultTranspose())

Definition at line 92 of file sparsesmoothers.cpp.

◆ MultTranspose()

void mfem::DSmoother::MultTranspose	(	const Vector &	x,
		Vector &	y ) const

overridevirtual

Apply the transpose of the Jacobi smoother.

If the underlying matrix is symmetric, or if only one iteration is performed with zero initial guess (Solver::iterative_mode is false), then this is the same as Mult(). For non-symmetric matrices with iteration count greater than one, only JacobiType::JACOBI is supported.

Reimplemented from mfem::Operator.

Definition at line 144 of file sparsesmoothers.cpp.

◆ SetPositiveDiagonal()

void mfem::DSmoother::SetPositiveDiagonal ( bool pos_diag = true )

inline

Replace diagonal entries with their absolute values. Relevant only with JacobiType::JACOBI.

Definition at line 151 of file sparsesmoothers.hpp.

Member Data Documentation

◆ iterations

int mfem::DSmoother::iterations

protected

Number of stationary iterations to perform.

Definition at line 110 of file sparsesmoothers.hpp.

◆ scale

real_t mfem::DSmoother::scale

protected

Scaling (damping) factor.

Definition at line 109 of file sparsesmoothers.hpp.

◆ type

JacobiType mfem::DSmoother::type

protected

Type of diagonal scaling, see DSmoother::JacobiType.

Definition at line 108 of file sparsesmoothers.hpp.

◆ use_abs_diag

bool mfem::DSmoother::use_abs_diag = false

protected

Uses abs values of the diagonal entries. Relevant only with type JacobiType::JACOBI.

Definition at line 114 of file sparsesmoothers.hpp.

◆ z

Vector mfem::DSmoother::z

mutableprotected

Temporary work vector.

Definition at line 116 of file sparsesmoothers.hpp.

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

linalg/sparsesmoothers.hpp
linalg/sparsesmoothers.cpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

◆ JacobiType

Constructor & Destructor Documentation

◆ DSmoother() [1/4]

◆ DSmoother() [2/4]

◆ DSmoother() [3/4]

◆ DSmoother() [4/4]

Member Function Documentation

◆ Mult()

◆ Mult_()

◆ MultTranspose()

◆ SetPositiveDiagonal()

Member Data Documentation

◆ iterations

◆ scale

◆ type

◆ use_abs_diag

◆ z