Data type sparse matrix. More...

#include <sparsemat.hpp>

Inheritance diagram for mfem::SparseMatrix:

Collaboration diagram for mfem::SparseMatrix:

Public Member Functions
	SparseMatrix ()
	Create an empty SparseMatrix. More...

	SparseMatrix (int nrows, int ncols=-1)
	Create a sparse matrix with flexible sparsity structure using a row-wise linked list (LIL) format. More...

	SparseMatrix (int i, int j, double *data, int m, int n)
	Create a sparse matrix in CSR format. Ownership of i, j, and data is transferred to the SparseMatrix. More...

	SparseMatrix (int i, int j, double *data, int m, int n, bool ownij, bool owna, bool issorted)
	Create a sparse matrix in CSR format. Ownership of i, j, and data is optionally transferred to the SparseMatrix. More...

	SparseMatrix (int nrows, int ncols, int rowsize)
	Create a sparse matrix in CSR format where each row has space allocated for exactly rowsize entries. More...

	SparseMatrix (const SparseMatrix &mat, bool copy_graph=true)
	Copy constructor (deep copy). More...

SparseMatrix &	operator= (const SparseMatrix &rhs)
	Assignment operator: deep copy. More...

void	MakeRef (const SparseMatrix &master)
	Clear the contents of the SparseMatrix and make it a reference to master. More...

int	Size () const
	For backward compatibility, define Size() to be synonym of Height(). More...

void	Clear ()
	Clear the contents of the SparseMatrix. More...

bool	Empty () const
	Check if the SparseMatrix is empty. More...

int *	GetI () const
	Return the array I. More...

int *	GetJ () const
	Return the array J. More...

double *	GetData () const
	Return element data, i.e. array A. More...

int	RowSize (const int i) const
	Returns the number of elements in row i. More...

int	MaxRowSize () const
	Returns the maximum number of elements among all rows. More...

int *	GetRowColumns (const int row)
	Return a pointer to the column indices in a row. More...

const int *	GetRowColumns (const int row) const

double *	GetRowEntries (const int row)
	Return a pointer to the entries in a row. More...

const double *	GetRowEntries (const int row) const

void	SetWidth (int width_=-1)
	Change the width of a SparseMatrix. More...

int	ActualWidth ()
	Returns the actual Width of the matrix. More...

void	SortColumnIndices ()
	Sort the column indices corresponding to each row. More...

void	MoveDiagonalFirst ()
	Move the diagonal entry to the first position in each row, preserving the order of the rest of the columns. More...

virtual double &	Elem (int i, int j)
	Returns reference to a_{ij}. More...

virtual const double &	Elem (int i, int j) const
	Returns constant reference to a_{ij}. More...

double &	operator() (int i, int j)
	Returns reference to A[i][j]. More...

const double &	operator() (int i, int j) const
	Returns reference to A[i][j]. More...

void	GetDiag (Vector &d) const
	Returns the Diagonal of A. More...

virtual void	Mult (const Vector &x, Vector &y) const
	Matrix vector multiplication. More...

void	AddMult (const Vector &x, Vector &y, const double a=1.0) const
	y += A * x (default) or y += a * A * x More...

void	MultTranspose (const Vector &x, Vector &y) const
	Multiply a vector with the transposed matrix. y = At * x. More...

void	AddMultTranspose (const Vector &x, Vector &y, const double a=1.0) const
	y += At * x (default) or y += a * At * x More...

void	PartMult (const Array< int > &rows, const Vector &x, Vector &y) const

void	PartAddMult (const Array< int > &rows, const Vector &x, Vector &y, const double a=1.0) const

void	BooleanMult (const Array< int > &x, Array< int > &y) const
	y = A * x, but treat all elements as booleans (zero=false, nonzero=true). More...

void	BooleanMultTranspose (const Array< int > &x, Array< int > &y) const
	y = At * x, but treat all elements as booleans (zero=false, nonzero=true). More...

double	InnerProduct (const Vector &x, const Vector &y) const
	Compute y^t A x. More...

void	GetRowSums (Vector &x) const
	For all i compute \( x_i = \sum_j A_{ij} \). More...

double	GetRowNorml1 (int irow) const
	For i = irow compute \( x_i = \sum_j \| A_{i, j} \| \). More...

virtual MatrixInverse *	Inverse () const
	This virtual method is not supported: it always returns NULL. More...

void	EliminateRow (int row, const double sol, Vector &rhs)
	Eliminates a column from the transpose matrix. More...

void	EliminateRow (int row, DiagonalPolicy dpolicy=DIAG_ZERO)
	Eliminates a row from the matrix. More...

void	EliminateCol (int col, DiagonalPolicy dpolicy=DIAG_ZERO)
	Eliminates the column col from the matrix. More...

void	EliminateCols (const Array< int > &cols, const Vector x=NULL, Vector b=NULL)
	Eliminate all columns i for which cols[i] != 0. More...

void	EliminateRowCol (int rc, const double sol, Vector &rhs, DiagonalPolicy dpolicy=DIAG_ONE)
	Eliminate row rc and column rc and modify the rhs using sol. More...

void	EliminateRowColMultipleRHS (int rc, const Vector &sol, DenseMatrix &rhs, DiagonalPolicy dpolicy=DIAG_ONE)
	Similar to EliminateRowCol(int, const double, Vector &, DiagonalPolicy), but multiple values for eliminated unknowns are accepted, and accordingly multiple right-hand-sides are used. More...

void	EliminateRowColDiag (int rc, double value)
	Perform elimination and set the diagonal entry to the given value. More...

void	EliminateRowCol (int rc, DiagonalPolicy dpolicy=DIAG_ONE)
	Eliminate row rc and column rc. More...

void	EliminateRowCol (int rc, SparseMatrix &Ae, DiagonalPolicy dpolicy=DIAG_ONE)
	Similar to EliminateRowCol(int, DiagonalPolicy) + save the eliminated entries into Ae so that (*this) + Ae is equal to the original matrix. More...

void	SetDiagIdentity ()
	If a row contains only one diag entry of zero, set it to 1. More...

virtual void	EliminateZeroRows (const double threshold=1e-12)
	If a row contains only zeros, set its diagonal to 1. More...

void	Gauss_Seidel_forw (const Vector &x, Vector &y) const
	Gauss-Seidel forward and backward iterations over a vector x. More...

void	Gauss_Seidel_back (const Vector &x, Vector &y) const

double	GetJacobiScaling () const
	Determine appropriate scaling for Jacobi iteration. More...

void	Jacobi (const Vector &b, const Vector &x0, Vector &x1, double sc) const

void	DiagScale (const Vector &b, Vector &x, double sc=1.0) const

void	Jacobi2 (const Vector &b, const Vector &x0, Vector &x1, double sc=1.0) const

void	Jacobi3 (const Vector &b, const Vector &x0, Vector &x1, double sc=1.0) const

virtual void	Finalize (int skip_zeros=1)
	Finalize the matrix initialization, switching the storage format from LIL to CSR. More...

void	Finalize (int skip_zeros, bool fix_empty_rows)
	A slightly more general version of the Finalize(int) method. More...

bool	Finalized () const

bool	areColumnsSorted () const

void	GetBlocks (Array2D< SparseMatrix * > &blocks) const

void	GetSubMatrix (const Array< int > &rows, const Array< int > &cols, DenseMatrix &subm) const

void	SetColPtr (const int row) const

void	ClearColPtr () const

double &	SearchRow (const int col)

void	_Add_ (const int col, const double a)

void	_Set_ (const int col, const double a)

double	_Get_ (const int col) const

double &	SearchRow (const int row, const int col)

void	_Add_ (const int row, const int col, const double a)

void	_Set_ (const int row, const int col, const double a)

void	Set (const int i, const int j, const double a)

void	Add (const int i, const int j, const double a)

void	SetSubMatrix (const Array< int > &rows, const Array< int > &cols, const DenseMatrix &subm, int skip_zeros=1)

void	SetSubMatrixTranspose (const Array< int > &rows, const Array< int > &cols, const DenseMatrix &subm, int skip_zeros=1)

void	AddSubMatrix (const Array< int > &rows, const Array< int > &cols, const DenseMatrix &subm, int skip_zeros=1)

bool	RowIsEmpty (const int row) const

virtual int	GetRow (const int row, Array< int > &cols, Vector &srow) const
	Extract all column indices and values from a given row. More...

void	SetRow (const int row, const Array< int > &cols, const Vector &srow)

void	AddRow (const int row, const Array< int > &cols, const Vector &srow)

void	ScaleRow (const int row, const double scale)

void	ScaleRows (const Vector &sl)

void	ScaleColumns (const Vector &sr)

SparseMatrix &	operator+= (const SparseMatrix &B)

void	Add (const double a, const SparseMatrix &B)

SparseMatrix &	operator= (double a)

SparseMatrix &	operator*= (double a)

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

void	PrintMatlab (std::ostream &out=mfem::out) const
	Prints matrix in matlab format. More...

void	PrintMM (std::ostream &out=mfem::out) const
	Prints matrix in Matrix Market sparse format. More...

void	PrintCSR (std::ostream &out) const
	Prints matrix to stream out in hypre_CSRMatrix format. More...

void	PrintCSR2 (std::ostream &out) const
	Prints a sparse matrix to stream out in CSR format. More...

void	PrintInfo (std::ostream &out) const
	Print various sparse matrix staticstics. More...

int	Walk (int &i, int &j, double &a)
	Walks the sparse matrix. More...

double	IsSymmetric () const
	Returns max_{i,j} \|(i,j)-(j,i)\| for a finalized matrix. More...

void	Symmetrize ()
	(this) = 1/2 ((this) + (*this)^t) More...

virtual int	NumNonZeroElems () const
	Returns the number of the nonzero elements in the matrix. More...

double	MaxNorm () const

int	CountSmallElems (double tol) const
	Count the number of entries with \|a_ij\| <= tol. More...

int	CheckFinite () const
	Count the number of entries that are NOT finite, i.e. Inf or Nan. More...

void	SetGraphOwner (bool ownij)
	Set the graph ownership flag (I and J arrays). More...

void	SetDataOwner (bool owna)
	Set the data ownership flag (A array). More...

bool	OwnsGraph () const
	Get the graph ownership flag (I and J arrays). More...

bool	OwnsData () const
	Get the data ownership flag (A array). More...

void	LoseData ()
	Lose the ownership of the graph (I, J) and data (A) arrays. More...

void	Swap (SparseMatrix &other)

virtual	~SparseMatrix ()
	Destroys sparse matrix. More...

Type	GetType () const

Public Member Functions inherited from mfem::AbstractSparseMatrix
	AbstractSparseMatrix (int s=0)
	Creates a square matrix of the given size. More...

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

virtual	~AbstractSparseMatrix ()
	Destroys AbstractSparseMatrix. More...

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

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

virtual	~Matrix ()
	Destroys matrix. More...

Public Member Functions inherited from mfem::Operator
	Operator (int s=0)
	Construct a square Operator with given size s (default 0). More...

	Operator (int h, int w)
	Construct an Operator with the given height (output size) and width (input size). More...

int	Height () const
	Get the height (size of output) of the Operator. Synonym with NumRows(). More...

int	NumRows () const
	Get the number of rows (size of output) of the Operator. Synonym with Height(). More...

int	Width () const
	Get the width (size of input) of the Operator. Synonym with NumCols(). More...

int	NumCols () const
	Get the number of columns (size of input) of the Operator. Synonym with Width(). More...

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. More...

virtual const Operator *	GetProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. `NULL` means identity. More...

virtual const Operator *	GetRestriction () const
	Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity. More...

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. More...

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(). More...

void	PrintMatlab (std::ostream &out, int n=0, int m=0) const
	Prints operator with input size n and output size m in Matlab format. More...

virtual	~Operator ()
	Virtual destructor. More...

Type	GetType () const
	Return the type ID of the Operator class. More...

Protected Types
typedef MemAlloc< RowNode, 1024 >	RowNodeAlloc

Protected Member Functions
void	Destroy ()

void	SetEmpty ()

Protected Attributes
RowNode **	Rows
	Array of linked lists, one for every row. This array represents the linked list (LIL) storage format. More...

int	current_row

int *	ColPtrJ

RowNode **	ColPtrNode

RowNodeAlloc *	NodesMem

bool	ownGraph
	Say whether we own the pointers for I and J (should we free them?). More...

bool	ownData
	Say whether we own the pointers for A (should we free them?). More...

bool	isSorted
	Are the columns sorted already. More...

Arrays used by the CSR storage format.
int *	I
	Array with size (height+1) containing the row offsets. More...

int *	J
	Array with size I[height], containing the column indices for all matrix entries, as indexed by the I array. More...

double *	A
	Array with size I[height], containing the actual entries of the sparse matrix, as indexed by the I array. More...

Protected Attributes inherited from mfem::Operator
int	height
	Dimension of the output / number of rows in the matrix. More...

int	width
	Dimension of the input / number of columns in the matrix. More...

Additional Inherited Members
Public Types inherited from mfem::Matrix
enum	DiagonalPolicy { DIAG_ZERO, DIAG_ONE, DIAG_KEEP }

Public Types inherited from mfem::Operator
enum	Type { ANY_TYPE, MFEM_SPARSEMAT, Hypre_ParCSR, PETSC_MATAIJ, PETSC_MATIS, PETSC_MATSHELL, PETSC_MATNEST, PETSC_MATHYPRE, PETSC_MATGENERIC }
	Enumeration defining IDs for some classes derived from Operator. More...

Detailed Description

Data type sparse matrix.

Definition at line 38 of file sparsemat.hpp.

Member Typedef Documentation

typedef MemAlloc<RowNode, 1024> mfem::SparseMatrix::RowNodeAlloc

protected

Definition at line 68 of file sparsemat.hpp.

Constructor & Destructor Documentation

mfem::SparseMatrix::SparseMatrix ( )

inline

Create an empty SparseMatrix.

Definition at line 85 of file sparsemat.hpp.

mfem::SparseMatrix::SparseMatrix	(	int	nrows,
		int	ncols = `-1`
	)

explicit

Create a sparse matrix with flexible sparsity structure using a row-wise linked list (LIL) format.

New entries are added as needed by methods like AddSubMatrix(), SetSubMatrix(), etc. Calling Finalize() will convert the SparseMatrix to the more compact compressed sparse row (CSR) format.

Definition at line 30 of file sparsemat.cpp.

mfem::SparseMatrix::SparseMatrix	(	int *	i,
		int *	j,
		double *	data,
		int	m,
		int	n
	)

Create a sparse matrix in CSR format. Ownership of i, j, and data is transferred to the SparseMatrix.

Definition at line 53 of file sparsemat.cpp.

mfem::SparseMatrix::SparseMatrix	(	int *	i,
		int *	j,
		double *	data,
		int	m,
		int	n,
		bool	ownij,
		bool	owna,
		bool	issorted
	)

Create a sparse matrix in CSR format. Ownership of i, j, and data is optionally transferred to the SparseMatrix.

Definition at line 70 of file sparsemat.cpp.

mfem::SparseMatrix::SparseMatrix	(	int	nrows,
		int	ncols,
		int	rowsize
	)

Create a sparse matrix in CSR format where each row has space allocated for exactly rowsize entries.

SetRow() can then be called or the I, J, A arrays can be used directly.

Definition at line 99 of file sparsemat.cpp.

mfem::SparseMatrix::SparseMatrix	(	const SparseMatrix &	mat,
		bool	copy_graph = `true`
	)

Copy constructor (deep copy).

If mat is finalized and copy_graph is false, the I and J arrays will use a shallow copy (copy the pointers only) without transferring ownership.

Definition at line 121 of file sparsemat.cpp.

virtual mfem::SparseMatrix::~SparseMatrix ( )

inlinevirtual

Destroys sparse matrix.

Definition at line 433 of file sparsemat.hpp.

Member Function Documentation

void mfem::SparseMatrix::_Add_	(	const int	col,
		const double	a
	)

inline

Definition at line 324 of file sparsemat.hpp.

void mfem::SparseMatrix::_Add_	(	const int	row,
		const int	col,
		const double	a
	)

inline

Definition at line 331 of file sparsemat.hpp.

double mfem::SparseMatrix::_Get_ ( const int col ) const

inline

Definition at line 569 of file sparsemat.hpp.

void mfem::SparseMatrix::_Set_	(	const int	col,
		const double	a
	)

inline

Definition at line 326 of file sparsemat.hpp.

void mfem::SparseMatrix::_Set_	(	const int	row,
		const int	col,
		const double	a
	)

inline

Definition at line 333 of file sparsemat.hpp.

int mfem::SparseMatrix::ActualWidth ( )

Returns the actual Width of the matrix.

This method can be called for matrices finalized or not.

Definition at line 2696 of file sparsemat.cpp.

void mfem::SparseMatrix::Add	(	const int	i,
		const int	j,
		const double	a
	)

Definition at line 2035 of file sparsemat.cpp.

void mfem::SparseMatrix::Add	(	const double	a,
		const SparseMatrix &	B
	)

Add the sparse matrix 'B' scaled by the scalar 'a' into '*this'. Only entries in the sparsity pattern of '*this' are added.

Definition at line 2407 of file sparsemat.cpp.

void mfem::SparseMatrix::AddMult	(	const Vector &	x,
		Vector &	y,
		const double	a = `1.0`
	)		const

virtual

y += A * x (default) or y += a * A * x

Implements mfem::AbstractSparseMatrix.

Definition at line 492 of file sparsemat.cpp.

void mfem::SparseMatrix::AddMultTranspose	(	const Vector &	x,
		Vector &	y,
		const double	a = `1.0`
	)		const

virtual

y += At * x (default) or y += a * At * x

Implements mfem::AbstractSparseMatrix.

Definition at line 569 of file sparsemat.cpp.

void mfem::SparseMatrix::AddRow	(	const int	row,
		const Array< int > &	cols,
		const Vector &	srow
	)

Definition at line 2258 of file sparsemat.cpp.

void mfem::SparseMatrix::AddSubMatrix	(	const Array< int > &	rows,
		const Array< int > &	cols,
		const DenseMatrix &	subm,
		int	skip_zeros = `1`
	)

Definition at line 1978 of file sparsemat.cpp.

bool mfem::SparseMatrix::areColumnsSorted ( ) const

inline

Definition at line 311 of file sparsemat.hpp.

void mfem::SparseMatrix::BooleanMult	(	const Array< int > &	x,
		Array< int > &	y
	)		const

y = A * x, but treat all elements as booleans (zero=false, nonzero=true).

Definition at line 644 of file sparsemat.cpp.

void mfem::SparseMatrix::BooleanMultTranspose	(	const Array< int > &	x,
		Array< int > &	y
	)		const

y = At * x, but treat all elements as booleans (zero=false, nonzero=true).

Definition at line 667 of file sparsemat.cpp.

int mfem::SparseMatrix::CheckFinite ( ) const

Count the number of entries that are NOT finite, i.e. Inf or Nan.

Definition at line 1056 of file sparsemat.cpp.

void mfem::SparseMatrix::Clear ( )

inline

Clear the contents of the SparseMatrix.

Definition at line 128 of file sparsemat.hpp.

void mfem::SparseMatrix::ClearColPtr ( ) const

inline

Definition at line 527 of file sparsemat.hpp.

int mfem::SparseMatrix::CountSmallElems ( double tol ) const

Count the number of entries with |a_ij| <= tol.

Definition at line 1028 of file sparsemat.cpp.

void mfem::SparseMatrix::Destroy ( )

protected

Definition at line 2648 of file sparsemat.cpp.

void mfem::SparseMatrix::DiagScale	(	const Vector &	b,
		Vector &	x,
		double	sc = `1.0`
	)		const

Definition at line 1898 of file sparsemat.cpp.

double & mfem::SparseMatrix::Elem	(	int	i,
		int	j
	)

virtual

Returns reference to a_{ij}.

Implements mfem::Matrix.

Definition at line 390 of file sparsemat.cpp.

const double & mfem::SparseMatrix::Elem	(	int	i,
		int	j
	)		const

virtual

Returns constant reference to a_{ij}.

Implements mfem::Matrix.

Definition at line 395 of file sparsemat.cpp.

void mfem::SparseMatrix::EliminateCol	(	int	col,
		DiagonalPolicy	dpolicy = `DIAG_ZERO`
	)

Eliminates the column col from the matrix.

If dpolicy = DIAG_ZERO, all entries in the column will be set to 0.
If dpolicy = DIAG_ONE (matrix must be square), the diagonal entry will be set equal to 1 and all other entries in the column to 0.
The policy DIAG_KEEP is not supported.

Definition at line 1133 of file sparsemat.cpp.

void mfem::SparseMatrix::EliminateCols	(	const Array< int > &	cols,
		const Vector *	x = `NULL`,
		Vector *	b = `NULL`
	)

Eliminate all columns i for which cols[i] != 0.

Elimination of a column means that all entries in the column are set to zero. In addition, if the pointers x and b are not NULL, the eliminated matrix entries are multiplied by the corresponding solution value in *x and subtracted from the r.h.s. vector, *b.

Definition at line 1173 of file sparsemat.cpp.

void mfem::SparseMatrix::EliminateRow	(	int	row,
		const double	sol,
		Vector &	rhs
	)

Eliminates a column from the transpose matrix.

Definition at line 1085 of file sparsemat.cpp.

void mfem::SparseMatrix::EliminateRow	(	int	row,
		DiagonalPolicy	dpolicy = `DIAG_ZERO`
	)

Eliminates a row from the matrix.

If dpolicy = DIAG_ZERO, all the entries in the row will be set to 0.
If dpolicy = DIAG_ONE (matrix must be square), the diagonal entry will be set equal to 1 and all other entries in the row to 0.
The policy DIAG_KEEP is not supported.

Definition at line 1101 of file sparsemat.cpp.

void mfem::SparseMatrix::EliminateRowCol	(	int	rc,
		const double	sol,
		Vector &	rhs,
		DiagonalPolicy	dpolicy = `DIAG_ONE`
	)

Eliminate row rc and column rc and modify the rhs using sol.

Eliminates the column rc to the rhs, deletes the row rc and replaces the element (rc,rc) with 1.0; assumes that element (i,rc) is assembled if and only if the element (rc,i) is assembled. By default, elements (rc,rc) are set to 1.0, although this behavior can be adjusted by changing the dpolicy parameter.

Definition at line 1204 of file sparsemat.cpp.

void mfem::SparseMatrix::EliminateRowCol	(	int	rc,
		DiagonalPolicy	dpolicy = `DIAG_ONE`
	)

Eliminate row rc and column rc.

Definition at line 1424 of file sparsemat.cpp.

void mfem::SparseMatrix::EliminateRowCol	(	int	rc,
		SparseMatrix &	Ae,
		DiagonalPolicy	dpolicy = `DIAG_ONE`
	)

Similar to EliminateRowCol(int, DiagonalPolicy) + save the eliminated entries into Ae so that (*this) + Ae is equal to the original matrix.

Definition at line 1554 of file sparsemat.cpp.

void mfem::SparseMatrix::EliminateRowColDiag	(	int	rc,
		double	value
	)

Perform elimination and set the diagonal entry to the given value.

Definition at line 1497 of file sparsemat.cpp.

void mfem::SparseMatrix::EliminateRowColMultipleRHS	(	int	rc,
		const Vector &	sol,
		DenseMatrix &	rhs,
		DiagonalPolicy	dpolicy = `DIAG_ONE`
	)

Similar to EliminateRowCol(int, const double, Vector &, DiagonalPolicy), but multiple values for eliminated unknowns are accepted, and accordingly multiple right-hand-sides are used.

Definition at line 1300 of file sparsemat.cpp.

void mfem::SparseMatrix::EliminateZeroRows ( const double threshold = 1e-12 )

virtual

If a row contains only zeros, set its diagonal to 1.

Implements mfem::AbstractSparseMatrix.

Definition at line 1657 of file sparsemat.cpp.

bool mfem::SparseMatrix::Empty ( ) const

inline

Check if the SparseMatrix is empty.

Definition at line 131 of file sparsemat.hpp.

virtual void mfem::SparseMatrix::Finalize ( int skip_zeros = 1 )

inlinevirtual

Finalize the matrix initialization, switching the storage format from LIL to CSR.

This method should be called once, after the matrix has been initialized. Internally, this method converts the matrix from row-wise linked list (LIL) format into CSR (compressed sparse row) format.

Reimplemented from mfem::Matrix.

Definition at line 305 of file sparsemat.hpp.

void mfem::SparseMatrix::Finalize	(	int	skip_zeros,
		bool	fix_empty_rows
	)

A slightly more general version of the Finalize(int) method.

Definition at line 755 of file sparsemat.cpp.

bool mfem::SparseMatrix::Finalized ( ) const

inline

Definition at line 310 of file sparsemat.hpp.

void mfem::SparseMatrix::Gauss_Seidel_back	(	const Vector &	x,
		Vector &	y
	)		const

Definition at line 1759 of file sparsemat.cpp.

void mfem::SparseMatrix::Gauss_Seidel_forw	(	const Vector &	x,
		Vector &	y
	)		const

Gauss-Seidel forward and backward iterations over a vector x.

Definition at line 1684 of file sparsemat.cpp.

void mfem::SparseMatrix::GetBlocks ( Array2D< SparseMatrix * > & blocks ) const

Split the matrix into M x N blocks of sparse matrices in CSR format. The 'blocks' array is M x N (i.e. M and N are determined by its dimensions) and its entries are overwritten by the new blocks.

Definition at line 836 of file sparsemat.cpp.

double* mfem::SparseMatrix::GetData ( ) const

inline

Return element data, i.e. array A.

Definition at line 138 of file sparsemat.hpp.

void mfem::SparseMatrix::GetDiag ( Vector & d ) const

Returns the Diagonal of A.

Definition at line 458 of file sparsemat.cpp.

int* mfem::SparseMatrix::GetI ( ) const

inline

Return the array I.

Definition at line 134 of file sparsemat.hpp.

int* mfem::SparseMatrix::GetJ ( ) const

inline

Return the array J.

Definition at line 136 of file sparsemat.hpp.

double mfem::SparseMatrix::GetJacobiScaling ( ) const

Determine appropriate scaling for Jacobi iteration.

Definition at line 1834 of file sparsemat.cpp.

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

virtual

Extract all column indices and values from a given row.

If the matrix is finalized (i.e. in CSR format), cols and srow will simply be references to the specific portion of the J and A arrays. As required by the AbstractSparseMatrix interface this method returns:

0, if cols and srow are copies of the values in the matrix, i.e. when the matrix is open.
1, if cols and srow are views of the values in the matrix, i.e. when the matrix is finalized.

Implements mfem::AbstractSparseMatrix.

Definition at line 2171 of file sparsemat.cpp.

int * mfem::SparseMatrix::GetRowColumns ( const int row )

Return a pointer to the column indices in a row.

Definition at line 271 of file sparsemat.cpp.

const int * mfem::SparseMatrix::GetRowColumns ( const int row ) const

Definition at line 278 of file sparsemat.cpp.

double * mfem::SparseMatrix::GetRowEntries ( const int row )

Return a pointer to the entries in a row.

Definition at line 285 of file sparsemat.cpp.

const double * mfem::SparseMatrix::GetRowEntries ( const int row ) const

Definition at line 292 of file sparsemat.cpp.

double mfem::SparseMatrix::GetRowNorml1 ( int irow ) const

For i = irow compute \( x_i = \sum_j | A_{i, j} | \).

Definition at line 735 of file sparsemat.cpp.

void mfem::SparseMatrix::GetRowSums ( Vector & x ) const

For all i compute \( x_i = \sum_j A_{ij} \).

Definition at line 716 of file sparsemat.cpp.

void mfem::SparseMatrix::GetSubMatrix	(	const Array< int > &	rows,
		const Array< int > &	cols,
		DenseMatrix &	subm
	)		const

Definition at line 2122 of file sparsemat.cpp.

Type mfem::SparseMatrix::GetType ( ) const

inline

Definition at line 435 of file sparsemat.hpp.

double mfem::SparseMatrix::InnerProduct	(	const Vector &	x,
		const Vector &	y
	)		const

Compute y^t A x.

Definition at line 690 of file sparsemat.cpp.

MatrixInverse * mfem::SparseMatrix::Inverse ( ) const

virtual

This virtual method is not supported: it always returns NULL.

Implements mfem::Matrix.

Definition at line 1080 of file sparsemat.cpp.

double mfem::SparseMatrix::IsSymmetric ( ) const

Returns max_{i,j} |(i,j)-(j,i)| for a finalized matrix.

Definition at line 926 of file sparsemat.cpp.

void mfem::SparseMatrix::Jacobi	(	const Vector &	b,
		const Vector &	x0,
		Vector &	x1,
		double	sc
	)		const

One scaled Jacobi iteration for the system A x = b. x1 = x0 + sc D^{-1} (b - A x0) where D is the diag of A.

Definition at line 1867 of file sparsemat.cpp.

void mfem::SparseMatrix::Jacobi2	(	const Vector &	b,
		const Vector &	x0,
		Vector &	x1,
		double	sc = `1.0`
	)		const

x1 = x0 + sc D^{-1} (b - A x0) where \( D_{ii} = \sum_j |A_{ij}| \).

Definition at line 1930 of file sparsemat.cpp.

void mfem::SparseMatrix::Jacobi3	(	const Vector &	b,
		const Vector &	x0,
		Vector &	x1,
		double	sc = `1.0`
	)		const

x1 = x0 + sc D^{-1} (b - A x0) where \( D_{ii} = \sum_j A_{ij} \).

Definition at line 1954 of file sparsemat.cpp.

void mfem::SparseMatrix::LoseData ( )

inline

Lose the ownership of the graph (I, J) and data (A) arrays.

Definition at line 428 of file sparsemat.hpp.

void mfem::SparseMatrix::MakeRef ( const SparseMatrix & master )

Clear the contents of the SparseMatrix and make it a reference to master.

After this call, the matrix will point to the same data as master but it will not own its data. The master must be finalized.

Definition at line 197 of file sparsemat.cpp.

double mfem::SparseMatrix::MaxNorm ( ) const

Definition at line 1005 of file sparsemat.cpp.

int mfem::SparseMatrix::MaxRowSize ( ) const

Returns the maximum number of elements among all rows.

Definition at line 247 of file sparsemat.cpp.

void mfem::SparseMatrix::MoveDiagonalFirst ( )

Move the diagonal entry to the first position in each row, preserving the order of the rest of the columns.

Definition at line 366 of file sparsemat.cpp.

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

virtual

Matrix vector multiplication.

Implements mfem::AbstractSparseMatrix.

Definition at line 486 of file sparsemat.cpp.

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

virtual

Multiply a vector with the transposed matrix. y = At * x.

Implements mfem::AbstractSparseMatrix.

Definition at line 563 of file sparsemat.cpp.

int mfem::SparseMatrix::NumNonZeroElems ( ) const

virtual

Returns the number of the nonzero elements in the matrix.

Implements mfem::AbstractSparseMatrix.

Definition at line 983 of file sparsemat.cpp.

double & mfem::SparseMatrix::operator()	(	int	i,
		int	j
	)

Returns reference to A[i][j].

Definition at line 400 of file sparsemat.cpp.

const double & mfem::SparseMatrix::operator()	(	int	i,
		int	j
	)		const

Returns reference to A[i][j].

Definition at line 423 of file sparsemat.cpp.

SparseMatrix & mfem::SparseMatrix::operator*= ( double a )

Definition at line 2448 of file sparsemat.cpp.

SparseMatrix & mfem::SparseMatrix::operator+= ( const SparseMatrix & B )

Add the sparse matrix 'B' to '*this'. This operation will cause an error if '*this' is finalized and 'B' has larger sparsity pattern.

Definition at line 2377 of file sparsemat.cpp.

SparseMatrix & mfem::SparseMatrix::operator= ( const SparseMatrix & rhs )

Assignment operator: deep copy.

Definition at line 187 of file sparsemat.cpp.

SparseMatrix & mfem::SparseMatrix::operator= ( double a )

Definition at line 2430 of file sparsemat.cpp.

bool mfem::SparseMatrix::OwnsData ( ) const

inline

Get the data ownership flag (A array).

Definition at line 426 of file sparsemat.hpp.

bool mfem::SparseMatrix::OwnsGraph ( ) const

inline

Get the graph ownership flag (I and J arrays).

Definition at line 424 of file sparsemat.hpp.

void mfem::SparseMatrix::PartAddMult	(	const Array< int > &	rows,
		const Vector &	x,
		Vector &	y,
		const double	a = `1.0`
	)		const

Definition at line 626 of file sparsemat.cpp.

void mfem::SparseMatrix::PartMult	(	const Array< int > &	rows,
		const Vector &	x,
		Vector &	y
	)		const

Definition at line 608 of file sparsemat.cpp.

void mfem::SparseMatrix::Print	(	std::ostream &	out = `mfem::out`,
		int	width_ = `4`
	)		const

virtual

Prints matrix to stream out.

Reimplemented from mfem::Matrix.

Definition at line 2466 of file sparsemat.cpp.

void mfem::SparseMatrix::PrintCSR ( std::ostream & out ) const

Prints matrix to stream out in hypre_CSRMatrix format.

Definition at line 2548 of file sparsemat.cpp.

void mfem::SparseMatrix::PrintCSR2 ( std::ostream & out ) const

Prints a sparse matrix to stream out in CSR format.

Definition at line 2572 of file sparsemat.cpp.

void mfem::SparseMatrix::PrintInfo ( std::ostream & out ) const

Print various sparse matrix staticstics.

Definition at line 2597 of file sparsemat.cpp.

void mfem::SparseMatrix::PrintMatlab ( std::ostream & out = mfem::out ) const

Prints matrix in matlab format.

Definition at line 2510 of file sparsemat.cpp.

void mfem::SparseMatrix::PrintMM ( std::ostream & out = mfem::out ) const

Prints matrix in Matrix Market sparse format.

Definition at line 2528 of file sparsemat.cpp.

bool mfem::SparseMatrix::RowIsEmpty ( const int row ) const

Definition at line 2150 of file sparsemat.cpp.

int mfem::SparseMatrix::RowSize ( const int i ) const

Returns the number of elements in row i.

Definition at line 224 of file sparsemat.cpp.

void mfem::SparseMatrix::ScaleColumns ( const Vector & sr )

Definition at line 2349 of file sparsemat.cpp.

void mfem::SparseMatrix::ScaleRow	(	const int	row,
		const double	scale
	)

Definition at line 2290 of file sparsemat.cpp.

void mfem::SparseMatrix::ScaleRows ( const Vector & sl )

Definition at line 2318 of file sparsemat.cpp.

double & mfem::SparseMatrix::SearchRow ( const int col )

inline

Definition at line 542 of file sparsemat.hpp.

double & mfem::SparseMatrix::SearchRow	(	const int	row,
		const int	col
	)

inline

Definition at line 583 of file sparsemat.hpp.

void mfem::SparseMatrix::Set	(	const int	i,
		const int	j,
		const double	a
	)

Definition at line 2016 of file sparsemat.cpp.

void mfem::SparseMatrix::SetColPtr ( const int row ) const

inline

Definition at line 492 of file sparsemat.hpp.

void mfem::SparseMatrix::SetDataOwner ( bool owna )

inline

Set the data ownership flag (A array).

Definition at line 422 of file sparsemat.hpp.

void mfem::SparseMatrix::SetDiagIdentity ( )

If a row contains only one diag entry of zero, set it to 1.

Definition at line 1648 of file sparsemat.cpp.

void mfem::SparseMatrix::SetEmpty ( )

protected

Definition at line 209 of file sparsemat.cpp.

void mfem::SparseMatrix::SetGraphOwner ( bool ownij )

inline

Set the graph ownership flag (I and J arrays).

Definition at line 420 of file sparsemat.hpp.

void mfem::SparseMatrix::SetRow	(	const int	row,
		const Array< int > &	cols,
		const Vector &	srow
	)

Definition at line 2210 of file sparsemat.cpp.

void mfem::SparseMatrix::SetSubMatrix	(	const Array< int > &	rows,
		const Array< int > &	cols,
		const DenseMatrix &	subm,
		int	skip_zeros = `1`
	)

Definition at line 2054 of file sparsemat.cpp.

void mfem::SparseMatrix::SetSubMatrixTranspose	(	const Array< int > &	rows,
		const Array< int > &	cols,
		const DenseMatrix &	subm,
		int	skip_zeros = `1`
	)

Definition at line 2087 of file sparsemat.cpp.

void mfem::SparseMatrix::SetWidth ( int width_ = -1 )

Change the width of a SparseMatrix.

If width_ = -1 (DEFAULT), this routine will set the new width to the actual Width of the matrix awidth = max(J) + 1. Values 0 <= width_ < awidth are not allowed (error check in Debug Mode only)

This method can be called for matrices finalized or not.

Definition at line 299 of file sparsemat.cpp.

int mfem::SparseMatrix::Size ( ) const

inline

For backward compatibility, define Size() to be synonym of Height().

Definition at line 125 of file sparsemat.hpp.

void mfem::SparseMatrix::SortColumnIndices ( )

Sort the column indices corresponding to each row.

Definition at line 337 of file sparsemat.cpp.

void mfem::SparseMatrix::Swap ( SparseMatrix & other )

Definition at line 3260 of file sparsemat.cpp.

void mfem::SparseMatrix::Symmetrize ( )

(*this) = 1/2 ((*this) + (*this)^t)

Definition at line 968 of file sparsemat.cpp.

int mfem::SparseMatrix::Walk	(	int &	i,
		int &	j,
		double &	a
	)

Walks the sparse matrix.

Member Data Documentation

double* mfem::SparseMatrix::A

protected

Array with size I[height], containing the actual entries of the sparse matrix, as indexed by the I array.

Definition at line 56 of file sparsemat.hpp.

int* mfem::SparseMatrix::ColPtrJ

mutableprotected

Definition at line 64 of file sparsemat.hpp.

RowNode** mfem::SparseMatrix::ColPtrNode

mutableprotected

Definition at line 65 of file sparsemat.hpp.

int mfem::SparseMatrix::current_row

mutableprotected

Definition at line 63 of file sparsemat.hpp.

int* mfem::SparseMatrix::I

protected

Array with size (height+1) containing the row offsets.

The data for row r, 0 <= r < height, is at offsets j, I[r] <= j < I[r+1]. The offsets, j, are indices in the J and A arrays. The first entry in this array is always zero, I[0] = 0, and the last entry, I[height], gives the total number of entries stored (at a minimum, all nonzeros must be represented) in the sparse matrix.

Definition at line 50 of file sparsemat.hpp.

bool mfem::SparseMatrix::isSorted

protected

Are the columns sorted already.

Definition at line 78 of file sparsemat.hpp.

int* mfem::SparseMatrix::J

protected

Array with size I[height], containing the column indices for all matrix entries, as indexed by the I array.

Definition at line 53 of file sparsemat.hpp.

RowNodeAlloc* mfem::SparseMatrix::NodesMem

protected

Definition at line 69 of file sparsemat.hpp.

bool mfem::SparseMatrix::ownData

protected

Say whether we own the pointers for A (should we free them?).

Definition at line 75 of file sparsemat.hpp.

bool mfem::SparseMatrix::ownGraph

protected

Say whether we own the pointers for I and J (should we free them?).

Definition at line 73 of file sparsemat.hpp.

RowNode** mfem::SparseMatrix::Rows

protected

Array of linked lists, one for every row. This array represents the linked list (LIL) storage format.

Definition at line 61 of file sparsemat.hpp.

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

linalg/sparsemat.hpp
linalg/sparsemat.cpp

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation