Abstract data type for sparse matrices. More...

#include <matrix.hpp>

Inheritance diagram for mfem::AbstractSparseMatrix:

Collaboration diagram for mfem::AbstractSparseMatrix:

Public Member Functions
	AbstractSparseMatrix (int s=0)
	Creates a square matrix of the given size.

	AbstractSparseMatrix (int h, int w)
	Creates a matrix of the given height and width.

virtual int	NumNonZeroElems () const =0
	Returns the number of non-zeros in a matrix.

virtual int	GetRow (const int row, Array< int > &cols, Vector &srow) const =0
	Gets the columns indexes and values for row row.

virtual void	EliminateZeroRows (const real_t threshold=1e-12)=0
	If the matrix is square, this method will place 1 on the diagonal (i,i) if row i has "almost" zero l1-norm.

virtual void	Mult (const Vector &x, Vector &y) const =0
	Matrix-Vector Multiplication y = A*x.

virtual void	AddMult (const Vector &x, Vector &y, const real_t val=1.) const =0
	Matrix-Vector Multiplication y = y + valAx.

virtual void	MultTranspose (const Vector &x, Vector &y) const =0
	MatrixTranspose-Vector Multiplication y = A'*x.

virtual void	AddMultTranspose (const Vector &x, Vector &y, const real_t val=1.) const =0
	MatrixTranspose-Vector Multiplication y = y + valA'x.

virtual	~AbstractSparseMatrix ()
	Destroys AbstractSparseMatrix.

Public Member Functions inherited from mfem::Matrix
	Matrix (int s)
	Creates a square matrix of size s.

	Matrix (int h, int w)
	Creates a matrix of the given height and width.

bool	IsSquare () const
	Returns whether the matrix is a square matrix.

virtual real_t &	Elem (int i, int j)=0
	Returns reference to a_{ij}.

virtual const real_t &	Elem (int i, int j) const =0
	Returns constant reference to a_{ij}.

virtual MatrixInverse *	Inverse () const =0
	Returns a pointer to (an approximation) of the matrix inverse.

virtual void	Finalize (int)
	Finalizes the matrix initialization.

virtual void	Print (std::ostream &out=mfem::out, int width_=4) const
	Prints matrix to stream out.

virtual	~Matrix ()
	Destroys matrix.

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	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...

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

Abstract data type for sparse matrices.

Definition at line 73 of file matrix.hpp.

Constructor & Destructor Documentation

◆ AbstractSparseMatrix() [1/2]

mfem::AbstractSparseMatrix::AbstractSparseMatrix ( int s = 0 )

inlineexplicit

Creates a square matrix of the given size.

Definition at line 77 of file matrix.hpp.

◆ AbstractSparseMatrix() [2/2]

mfem::AbstractSparseMatrix::AbstractSparseMatrix	(	int	h,
		int	w )

inlineexplicit

Creates a matrix of the given height and width.

Definition at line 80 of file matrix.hpp.

◆ ~AbstractSparseMatrix()

virtual mfem::AbstractSparseMatrix::~AbstractSparseMatrix ( )

inlinevirtual

Destroys AbstractSparseMatrix.

Definition at line 110 of file matrix.hpp.

Member Function Documentation

◆ AddMult()

virtual void mfem::AbstractSparseMatrix::AddMult	(	const Vector &	x,
		Vector &	y,
		const real_t	val = 1. ) const

pure virtual

Matrix-Vector Multiplication y = y + val*A*x.

Reimplemented from mfem::Operator.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

◆ AddMultTranspose()

virtual void mfem::AbstractSparseMatrix::AddMultTranspose	(	const Vector &	x,
		Vector &	y,
		const real_t	val = 1. ) const

pure virtual

MatrixTranspose-Vector Multiplication y = y + val*A'*x.

Reimplemented from mfem::Operator.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

◆ EliminateZeroRows()

virtual void mfem::AbstractSparseMatrix::EliminateZeroRows ( const real_t threshold = 1e-12 )

pure virtual

If the matrix is square, this method will place 1 on the diagonal (i,i) if row i has "almost" zero l1-norm.

If entry (i,i) does not belong to the sparsity pattern of A, then an error will occur.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

◆ GetRow()

virtual int mfem::AbstractSparseMatrix::GetRow	(	const int	row,
		Array< int > &	cols,
		Vector &	srow ) const

pure virtual

Gets the columns indexes and values for row row.

Returns:

0 if cols and srow are copies of the values in the matrix.
1 if cols and srow are views of the values in the matrix.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

◆ Mult()

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

pure virtual

Matrix-Vector Multiplication y = A*x.

Implements mfem::Operator.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

◆ MultTranspose()

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

pure virtual

MatrixTranspose-Vector Multiplication y = A'*x.

Reimplemented from mfem::Operator.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

◆ NumNonZeroElems()

virtual int mfem::AbstractSparseMatrix::NumNonZeroElems ( ) const

pure virtual

Returns the number of non-zeros in a matrix.

Implemented in mfem::BlockMatrix, and mfem::SparseMatrix.

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

linalg/matrix.hpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ AbstractSparseMatrix() [1/2]

◆ AbstractSparseMatrix() [2/2]

◆ ~AbstractSparseMatrix()

Member Function Documentation

◆ AddMult()

◆ AddMultTranspose()

◆ EliminateZeroRows()

◆ GetRow()

◆ Mult()

◆ MultTranspose()

◆ NumNonZeroElems()