#include <densemat.hpp>

Inheritance diagram for mfem::DenseMatrixInverse:

Collaboration diagram for mfem::DenseMatrixInverse:

Public Member Functions
	DenseMatrixInverse (bool spd_=false)
	Default constructor.

	DenseMatrixInverse (const DenseMatrix &mat, bool spd_=false)

	DenseMatrixInverse (const DenseMatrix *mat, bool spd_=false)
	Same as above but does not factorize the matrix.

int	Size () const
	Get the size of the inverse matrix.

void	Factor ()
	Factor the current DenseMatrix, *a.

void	Factor (const DenseMatrix &mat)
	Factor a new DenseMatrix of the same size.

virtual void	SetOperator (const Operator &op)
	Set/update the solver for the given operator.

void	Mult (const real_t x, real_t y) const
	Matrix vector multiplication with the inverse of dense matrix.

virtual void	Mult (const Vector &x, Vector &y) const
	Matrix vector multiplication with the inverse of dense matrix.

void	Mult (const DenseMatrix &B, DenseMatrix &X) const
	Multiply the inverse matrix by another matrix: X = A^{-1} B.

void	Mult (DenseMatrix &X) const
	Multiply the inverse matrix by another matrix: X <- A^{-1} X.

void	GetInverseMatrix (DenseMatrix &Ainv) const
	Compute and return the inverse matrix in Ainv.

real_t	Det () const
	Compute the determinant of the original DenseMatrix using the LU factors.

void	TestInversion ()
	Print the numerical conditioning of the inversion: \|\|A^{-1} A - I\|\|.

virtual	~DenseMatrixInverse ()
	Destroys dense inverse matrix.

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	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.

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.

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 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

Data type for inverse of square dense matrix. Stores matrix factors, i.e., Cholesky factors if the matrix is SPD, LU otherwise.

Definition at line 829 of file densemat.hpp.

Constructor & Destructor Documentation

◆ DenseMatrixInverse() [1/3]

mfem::DenseMatrixInverse::DenseMatrixInverse ( bool spd_ = false )

inline

Default constructor.

Definition at line 840 of file densemat.hpp.

◆ DenseMatrixInverse() [2/3]

mfem::DenseMatrixInverse::DenseMatrixInverse	(	const DenseMatrix &	mat,
		bool	spd_ = false )

Creates square dense matrix. Computes factorization of mat and stores its factors.

Definition at line 4168 of file densemat.cpp.

◆ DenseMatrixInverse() [3/3]

mfem::DenseMatrixInverse::DenseMatrixInverse	(	const DenseMatrix *	mat,
		bool	spd_ = false )

Same as above but does not factorize the matrix.

Definition at line 4177 of file densemat.cpp.

◆ ~DenseMatrixInverse()

mfem::DenseMatrixInverse::~DenseMatrixInverse ( )

virtual

Destroys dense inverse matrix.

Definition at line 4263 of file densemat.cpp.

Member Function Documentation

◆ Det()

real_t mfem::DenseMatrixInverse::Det ( ) const

inline

Compute the determinant of the original DenseMatrix using the LU factors.

Definition at line 878 of file densemat.hpp.

◆ Factor() [1/2]

void mfem::DenseMatrixInverse::Factor ( )

Factor the current DenseMatrix, *a.

Definition at line 4185 of file densemat.cpp.

◆ Factor() [2/2]

void mfem::DenseMatrixInverse::Factor ( const DenseMatrix & mat )

Factor a new DenseMatrix of the same size.

Definition at line 4203 of file densemat.cpp.

◆ GetInverseMatrix()

void mfem::DenseMatrixInverse::GetInverseMatrix ( DenseMatrix & Ainv ) const

Compute and return the inverse matrix in Ainv.

Definition at line 4197 of file densemat.cpp.

◆ Mult() [1/4]

void mfem::DenseMatrixInverse::Mult	(	const DenseMatrix &	B,
		DenseMatrix &	X ) const

Multiply the inverse matrix by another matrix: X = A^{-1} B.

Definition at line 4246 of file densemat.cpp.

◆ Mult() [2/4]

void mfem::DenseMatrixInverse::Mult	(	const real_t *	x,
		real_t *	y ) const

Matrix vector multiplication with the inverse of dense matrix.

Definition at line 4231 of file densemat.cpp.

◆ Mult() [3/4]

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

virtual

Matrix vector multiplication with the inverse of dense matrix.

Implements mfem::Operator.

Definition at line 4240 of file densemat.cpp.

◆ Mult() [4/4]

void mfem::DenseMatrixInverse::Mult ( DenseMatrix & X ) const

inline

Multiply the inverse matrix by another matrix: X <- A^{-1} X.

Definition at line 870 of file densemat.hpp.

◆ SetOperator()

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

virtual

Set/update the solver for the given operator.

Implements mfem::Solver.

Definition at line 4224 of file densemat.cpp.

◆ Size()

int mfem::DenseMatrixInverse::Size ( ) const

inline

Get the size of the inverse matrix.

Definition at line 850 of file densemat.hpp.

◆ TestInversion()

void mfem::DenseMatrixInverse::TestInversion ( )

Print the numerical conditioning of the inversion: ||A^{-1} A - I||.

Definition at line 4252 of file densemat.cpp.

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

linalg/densemat.hpp
linalg/densemat.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DenseMatrixInverse() [1/3]

◆ DenseMatrixInverse() [2/3]

◆ DenseMatrixInverse() [3/3]

◆ ~DenseMatrixInverse()

Member Function Documentation

◆ Det()

◆ Factor() [1/2]

◆ Factor() [2/2]

◆ GetInverseMatrix()

◆ Mult() [1/4]

◆ Mult() [2/4]

◆ Mult() [3/4]

◆ Mult() [4/4]

◆ SetOperator()

◆ Size()

◆ TestInversion()