Mimic the action of a complex operator using two real operators. More...

#include <complex_operator.hpp>

Inheritance diagram for mfem::ComplexOperator:

Collaboration diagram for mfem::ComplexOperator:

Public Types
enum	Convention { HERMITIAN , BLOCK_SYMMETRIC }

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
	ComplexOperator (Operator Op_Real, Operator Op_Imag, bool ownReal, bool ownImag, Convention convention=HERMITIAN)
	Constructs complex operator object.

virtual	~ComplexOperator ()

bool	hasRealPart () const
	Check for existence of real or imaginary part of the operator.

bool	hasImagPart () const

virtual Operator &	real ()
	Real or imaginary part accessor methods.

virtual Operator &	imag ()

virtual const Operator &	real () const

virtual const Operator &	imag () const

virtual void	Mult (const Vector &x, Vector &y) const
	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 Type	GetType () const

Convention	GetConvention () const

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	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
void	Mult (const Vector &x_r, const Vector &x_i, Vector &y_r, Vector &y_i) const

void	MultTranspose (const Vector &x_r, const Vector &x_i, Vector &y_r, Vector &y_i) const

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
Operator *	Op_Real_

Operator *	Op_Imag_

bool	ownReal_

bool	ownImag_

Convention	convention_

Vector	x_r_

Vector	x_i_

Vector	y_r_

Vector	y_i_

Vector *	u_

Vector *	v_

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.

Detailed Description

Mimic the action of a complex operator using two real operators.

This operator requires vectors that are twice the length of its internally stored real operators, Op_Real and Op_Imag. It is assumed that these vectors store the real part of the vector first followed by its imaginary part.

ComplexOperator allows one to choose a convention upon construction, which facilitates symmetry.

If we let (y_r + i y_i) = (Op_r + i Op_i)(x_r + i x_i) then Matrix-vector products are computed as:

When Convention::HERMITIAN is used (default) / y_r \ / Op_r -Op_i \ / x_r \ | | = | | | | \ y_i / \ Op_i Op_r / \ x_i /
When Convention::BLOCK_SYMMETRIC is used / y_r \ / Op_r -Op_i \ / x_r \ | | = | | | | -y_i / -Op_i -Op_r / \ x_i / In other words, Matrix-vector products with Convention::BLOCK_SYMMETRIC compute the complex conjugate of Op*x.

Either convention can be used with a given complex operator, however, each of them may be best suited for different classes of problems. For example:

Convention::HERMITIAN, is well suited for Hermitian operators, i.e., operators where the real part is symmetric and the imaginary part of the operator is anti-symmetric, hence the name. In such cases the resulting 2 x 2 operator will be symmetric.
Convention::BLOCK_SYMMETRIC, is well suited for operators where both the real and imaginary parts are symmetric. In this case the resulting 2 x 2 operator will also be symmetric. Such operators are common when studying damped oscillations, for example.

Note: this class cannot be used to represent a general nonlinear complex operator.

Definition at line 68 of file complex_operator.hpp.

Member Enumeration Documentation

◆ Convention

enum mfem::ComplexOperator::Convention

Enumerator
HERMITIAN	Native convention for Hermitian operators.
BLOCK_SYMMETRIC	Alternate convention for damping operators.

Definition at line 71 of file complex_operator.hpp.

Constructor & Destructor Documentation

◆ ComplexOperator()

mfem::ComplexOperator::ComplexOperator	(	Operator *	Op_Real,
		Operator *	Op_Imag,
		bool	ownReal,
		bool	ownImag,
		Convention	convention = HERMITIAN )

Constructs complex operator object.

Note that either Op_Real or Op_Imag can be NULL, thus eliminating their action (see documentation of the class for more details).

In case ownership of the passed operator is transferred to this class through ownReal and ownImag, the operators will be explicitly destroyed at the end of the life of this object.

Definition at line 19 of file complex_operator.cpp.

◆ ~ComplexOperator()

mfem::ComplexOperator::~ComplexOperator ( )

virtual

Definition at line 37 of file complex_operator.cpp.

Member Function Documentation

◆ GetConvention()

Convention mfem::ComplexOperator::GetConvention ( ) const

inline

Definition at line 119 of file complex_operator.hpp.

◆ GetType()

virtual Type mfem::ComplexOperator::GetType ( ) const

inlinevirtual

Reimplemented in mfem::ComplexDenseMatrix, mfem::ComplexHypreParMatrix, and mfem::ComplexSparseMatrix.

Definition at line 117 of file complex_operator.hpp.

◆ hasImagPart()

bool mfem::ComplexOperator::hasImagPart ( ) const

inline

Definition at line 98 of file complex_operator.hpp.

◆ hasRealPart()

bool mfem::ComplexOperator::hasRealPart ( ) const

inline

Check for existence of real or imaginary part of the operator.

These methods do not check that the operators are non-zero but only that the operators have been set.

Definition at line 97 of file complex_operator.hpp.

◆ imag() [1/2]

Operator & mfem::ComplexOperator::imag ( )

virtual

Reimplemented in mfem::ComplexDenseMatrix, mfem::ComplexHypreParMatrix, and mfem::ComplexSparseMatrix.

Definition at line 51 of file complex_operator.cpp.

◆ imag() [2/2]

const Operator & mfem::ComplexOperator::imag ( ) const

virtual

Reimplemented in mfem::ComplexDenseMatrix, mfem::ComplexHypreParMatrix, and mfem::ComplexSparseMatrix.

Definition at line 63 of file complex_operator.cpp.

◆ Mult() [1/2]

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

virtual

Operator application: y=A(x).

Implements mfem::Operator.

Definition at line 69 of file complex_operator.cpp.

◆ Mult() [2/2]

void mfem::ComplexOperator::Mult	(	const Vector &	x_r,
		const Vector &	x_i,
		Vector &	y_r,
		Vector &	y_i ) const

protected

Definition at line 86 of file complex_operator.cpp.

◆ MultTranspose() [1/2]

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

virtual

Action of the transpose operator: y=A^t(x). The default behavior in class Operator is to generate an error.

Reimplemented from mfem::Operator.

Definition at line 118 of file complex_operator.cpp.

◆ MultTranspose() [2/2]

void mfem::ComplexOperator::MultTranspose	(	const Vector &	x_r,
		const Vector &	x_i,
		Vector &	y_r,
		Vector &	y_i ) const

protected

Definition at line 135 of file complex_operator.cpp.

◆ real() [1/2]

Operator & mfem::ComplexOperator::real ( )

virtual

Real or imaginary part accessor methods.

The following accessor methods should only be called if the requested part of the operator is known to exist. This can be checked with hasRealPart() or hasImagPart().

Reimplemented in mfem::ComplexDenseMatrix, mfem::ComplexHypreParMatrix, and mfem::ComplexSparseMatrix.

Definition at line 45 of file complex_operator.cpp.

◆ real() [2/2]

const Operator & mfem::ComplexOperator::real ( ) const

virtual

Reimplemented in mfem::ComplexDenseMatrix, mfem::ComplexHypreParMatrix, and mfem::ComplexSparseMatrix.

Definition at line 57 of file complex_operator.cpp.

Member Data Documentation

◆ convention_

Convention mfem::ComplexOperator::convention_

protected

Definition at line 136 of file complex_operator.hpp.

◆ Op_Imag_

Operator* mfem::ComplexOperator::Op_Imag_

protected

Definition at line 131 of file complex_operator.hpp.

◆ Op_Real_

Operator* mfem::ComplexOperator::Op_Real_

protected

Definition at line 130 of file complex_operator.hpp.

◆ ownImag_

bool mfem::ComplexOperator::ownImag_

protected

Definition at line 134 of file complex_operator.hpp.

◆ ownReal_

bool mfem::ComplexOperator::ownReal_

protected

Definition at line 133 of file complex_operator.hpp.

◆ u_

Vector* mfem::ComplexOperator::u_

mutableprotected

Definition at line 139 of file complex_operator.hpp.

◆ v_

Vector * mfem::ComplexOperator::v_

protected

Definition at line 139 of file complex_operator.hpp.

◆ x_i_

Vector mfem::ComplexOperator::x_i_

protected

Definition at line 138 of file complex_operator.hpp.

◆ x_r_

Vector mfem::ComplexOperator::x_r_

mutableprotected

Definition at line 138 of file complex_operator.hpp.

◆ y_i_

Vector mfem::ComplexOperator::y_i_

protected

Definition at line 138 of file complex_operator.hpp.

◆ y_r_

Vector mfem::ComplexOperator::y_r_

protected

Definition at line 138 of file complex_operator.hpp.

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

linalg/complex_operator.hpp
linalg/complex_operator.cpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Enumeration Documentation

◆ Convention

Constructor & Destructor Documentation

◆ ComplexOperator()

◆ ~ComplexOperator()

Member Function Documentation

◆ GetConvention()

◆ GetType()

◆ hasImagPart()

◆ hasRealPart()

◆ imag() [1/2]

◆ imag() [2/2]

◆ Mult() [1/2]

◆ Mult() [2/2]

◆ MultTranspose() [1/2]

◆ MultTranspose() [2/2]

◆ real() [1/2]

◆ real() [2/2]

Member Data Documentation

◆ convention_

◆ Op_Imag_

◆ Op_Real_

◆ ownImag_

◆ ownReal_

◆ u_

◆ v_

◆ x_i_

◆ x_r_

◆ y_i_

◆ y_r_