Inner product weighted by operators, X and Y. The method Eval() computes the inner product of two vectors, x and y, weighted by the operators, X and Y, as (Y(y),X(x)). More...

#include <solvers.hpp>

Inheritance diagram for mfem::WeightedInnerProduct:

[legend]

Collaboration diagram for mfem::WeightedInnerProduct:

[legend]

Public Member Functions
	WeightedInnerProduct (MPI_Comm comm_)
	Constructor from MPI communicator.

	WeightedInnerProduct (Operator X, Operator Y)
	Constructor from weighting operators.

void	SetOperator (Operator X, Operator Y)
	Set/update the weighting operators (not owned) for each term.

void	SetOperator (Operator *XY)
	Set/update the same weighting operator (not owned) for both terms.

virtual real_t	Eval (const Vector &x, const Vector &y) override
	Compute the inner product (Y(y),X(x)) of vectors x and y, weighted by the operators X and Y.

virtual void	Mult (const Vector &x, Vector &y) const override
	Apply the weighting operator to vector x and return in y=Y(X(x)).

Public Member Functions inherited from mfem::InnerProductOperator
	InnerProductOperator (MPI_Comm comm_)

	InnerProductOperator ()
	Create an operator of size 1 (scalar).

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	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	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 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 Attributes
Operator *	operX = nullptr

Operator *	operY = nullptr
	Weighting operator for x.

Vector	wx
	Weighting operator for y.

Vector	wy

MemoryClass	mem_class
	Weighted vectors.

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 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...

Protected Member Functions inherited from mfem::InnerProductOperator
virtual real_t	Dot (const Vector &x, const Vector &y) const
	Standard global/local \(\ell_2\) inner product.

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".

Detailed Description

Inner product weighted by operators, X and Y. The method Eval() computes the inner product of two vectors, x and y, weighted by the operators, X and Y, as (Y(y),X(x)).

Definition at line 382 of file solvers.hpp.

Constructor & Destructor Documentation

◆ WeightedInnerProduct() [1/2]

mfem::WeightedInnerProduct::WeightedInnerProduct ( MPI_Comm comm_ )

inline

Constructor from MPI communicator.

Definition at line 393 of file solvers.hpp.

◆ WeightedInnerProduct() [2/2]

mfem::WeightedInnerProduct::WeightedInnerProduct	(	Operator *	X,
		Operator *	Y )

inline

Constructor from weighting operators.

Definition at line 396 of file solvers.hpp.

Member Function Documentation

◆ Eval()

real_t mfem::WeightedInnerProduct::Eval	(	const Vector &	x,
		const Vector &	y )

overridevirtual

Compute the inner product (Y(y),X(x)) of vectors x and y, weighted by the operators X and Y.

Note: Either (but not both) operator, X or Y, can be set as null, in which case the corresponding vector is unmodified (i.e. the operator acts as an identity operator).

Implements mfem::InnerProductOperator.

Definition at line 283 of file solvers.cpp.

◆ Mult()

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

overridevirtual

Apply the weighting operator to vector x and return in y=Y(X(x)).

Reimplemented from mfem::InnerProductOperator.

Definition at line 304 of file solvers.cpp.

◆ SetOperator() [1/2]

void mfem::WeightedInnerProduct::SetOperator	(	Operator *	X,
		Operator *	Y )

Set/update the weighting operators (not owned) for each term.

Definition at line 254 of file solvers.cpp.

◆ SetOperator() [2/2]

void mfem::WeightedInnerProduct::SetOperator ( Operator * XY )

inline

Set/update the same weighting operator (not owned) for both terms.

Definition at line 403 of file solvers.hpp.

Member Data Documentation

◆ mem_class

MemoryClass mfem::WeightedInnerProduct::mem_class

protected

Weighted vectors.

Definition at line 388 of file solvers.hpp.

◆ operX

Operator* mfem::WeightedInnerProduct::operX = nullptr

protected

Definition at line 385 of file solvers.hpp.

◆ operY

Operator* mfem::WeightedInnerProduct::operY = nullptr

protected

Weighting operator for x.

Definition at line 386 of file solvers.hpp.

◆ wx

Vector mfem::WeightedInnerProduct::wx

mutableprotected

Weighting operator for y.

Definition at line 387 of file solvers.hpp.

◆ wy

Vector mfem::WeightedInnerProduct::wy

protected

Definition at line 387 of file solvers.hpp.

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

linalg/solvers.hpp
linalg/solvers.cpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ WeightedInnerProduct() [1/2]

◆ WeightedInnerProduct() [2/2]

Member Function Documentation

◆ Eval()

◆ Mult()

◆ SetOperator() [1/2]

◆ SetOperator() [2/2]

Member Data Documentation

◆ mem_class

◆ operX

◆ operY

◆ wx

◆ wy