DMatrix Class Template Reference
[Vector and Matrix]

#include <DMatrix.h>

Inheritance diagram for DMatrix:

List of all members.

---

Detailed Description

template<class T_>
class OFELI::DMatrix< T_ >

To store dense matrices.

This class enables storing and manipulating general dense matrices. Matrices can be square or rectangle ones.

Template Argument :

• T_ data type (double, float, int, ...)

Public Member Functions
void	Add (size_t i, size_t j, const T_ &x)
	Add constant x to entry (i,j) of the matrix.
void	Assembly (const Side *sd, const DMatrix< T_ > &a)
	Assembly of side matrix into global matrix.
void	Assembly (const Side *sd, T_ *a)
	Assembly of side matrix into global matrix.
void	Assembly (const Element *el, const DMatrix< T_ > &a)
	Assembly of element matrix into global matrix.
void	Assembly (const Element *el, T_ *a)
	Assembly of element matrix into global matrix.
	DMatrix (const DMatrix< T_ > &m)
	Copy Constructor.
	DMatrix (Vect< T_ > &v)
	Constructor that uses a Vect instance.
	DMatrix (size_t nr, size_t nc)
	Constructor for a matrix with nr rows and nc columns.
	DMatrix (size_t nr)
	Constructor for a matrix with nr rows and nr columns.
	DMatrix ()
	Default constructor. Initializes a zero-dimension matrix.
int	Factor ()
	Factorize matrix (LU factorization).
int	FactorAndSolve (Vect< T_ > &b)
	Factorize matrix and solve the linear system.
T_ *	getArray () const
	Return matrix as C-Array.
size_t	getColInd (size_t i) const
	Return storage information.
Vect< T_ >	getColumn (size_t j) const
	Get j-th column vector.
T_	getDiag (size_t k) const
	Return k-th diagonal entry of A.
T_	getEntry (size_t i, size_t j) const
	Return entry (i,j) of matrix.
unsigned long	getLength () const
	Return number of stored terms in matrix.
size_t	getNbColumns () const
	Return number of columns.
size_t	getNbRows () const
	Return number of rows.
void	getPrintView (size_t &rmin, size_t &rmax, size_t &cmin, size_t &cmax) const
	Return window data for matrix printing.
Vect< T_ >	getRow (size_t i) const
	Get i-th row vector.
virtual size_t	getRowPtr (size_t i) const
	Return Row pointer for row i (See the description for class SpMatrix).
size_t	getSize () const
	Return matrix dimension (Number of rows and columns).
bool	isDiagonal () const
	Say if matrix is diagonal or not.
bool	isFactorized () const
	Say if matrix is factorized or not.
void	Mult (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector x and save result in y.
void	MultAdd (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector x and add result to y.
void	MultAdd (T_ a, const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector a*x and add result to y.
const T_	operator() (size_t i) const
	Operator () with one argument (Constant version).
T_ &	operator() (size_t i, size_t j)
	Operator () (Non constant version).
T_	operator() (size_t i, size_t j) const
	Operator () (Constant version).
DMatrix &	operator*= (const T_ &x)
	Operator *=.
Matrix &	operator+= (const Matrix< T_ > &m)
	Operator +=.
DMatrix &	operator+= (const T_ &x)
	Operator +=.
DMatrix &	operator+= (const DMatrix< T_ > &m)
	Operator +=.
Matrix &	operator-= (const Matrix< T_ > &m)
	Operator -=.
DMatrix &	operator-= (const T_ &x)
	Operator -=.
DMatrix &	operator-= (const DMatrix< T_ > &m)
	Operator -=.
DMatrix &	operator= (const T_ &x)
	Operator =.
DMatrix &	operator= (DMatrix< T_ > &m)
	Operator =.
T_	operator[] (size_t k) const
	Operator [] (Constant version).
T_ &	operator[] (size_t k)
	Operator [] (Non constant version).
void	Prescribe (size_t dof, const class Mesh &mesh, Vect< T_ > &b, const Vect< T_ > &u, int flag=0)
	Impose by a penalty method an essential boundary condition when only one DOF is treated.
void	Prescribe (const class Mesh &mesh, Vect< T_ > &b, int flag=0)
	Impose by a penalty method a homegeneous (=0) essential boundary condition.
void	Prescribe (const class Mesh &mesh, Vect< T_ > &b, const Vect< T_ > &u, int flag=0)
	Impose by a penalty method an essential boundary condition.
void	PrescribeSide (const class Mesh &mesh)
	Impose by a penalty method an essential boundary condition when DOFs are supported by sides.
void	Resize (size_t nr, size_t nc)
	Set size (number of rows and columns) of matrix.
void	Resize (size_t size)
	Set size (number of rows) of matrix.
void	Set (size_t i, size_t j, const T_ &x)
	Assign a constant value x to an entry of the matrix.
void	setDiag ()
	Store diagonal entries in a separate internal vector.
void	setDiagonal (const class Mesh &mesh)
	Initialize matrix storage in the case where only diagonal terms are stored.
void	setPenal (double p)
	Set Penalty Parameter (For boundary condition prescription).
void	setPrintView (size_t rmin, size_t rmax, size_t cmin, size_t cmax)
	set a window for matrix printing
int	Solve (const Vect< T_ > &b, Vect< T_ > &x)
	Solve system with factorized matrix (forward and back substitution).
int	Solve (Vect< T_ > &b)
	Solve system with factorized matrix (forward and back substitution).
void	TMult (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply transpose of matrix by vector x and add result in y.
	~DMatrix ()
	Destructor.

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Constructor & Destructor Documentation

DMatrix

(

size_t

nr

)

Constructor for a matrix with nr rows and nr columns.

Matrix entries are set to 0.

References DMatrix::Resize().

DMatrix	(	size_t	nr,
		size_t	nc
	)

Constructor for a matrix with nr rows and nc columns.

Matrix entries are set to 0.

References DMatrix::Resize().

DMatrix

(

Vect< T_ > &

v

)

Constructor that uses a Vect instance.

The class uses the memory space occupied by this vector.

Parameters:

[in]

v

Vector to copy

References Vect::getSize().

DMatrix

(

const DMatrix< T_ > &

m

)

Copy Constructor.

Parameters:

[in]

m

Matrix to copy

References DMatrix::_fact, and DMatrix::Resize().

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Member Function Documentation

void Add	(	size_t	i,
		size_t	j,
		const T_ &	x
	)			[virtual]

Add constant x to entry (i,j) of the matrix.

Parameters:

[in]	i	row index
[in]	j	column index
[in]	x	Constant to add

Implements Matrix.

void Assembly	(	const Side *	sd,
		const DMatrix< T_ > &	a
	)			[inherited]

Assembly of side matrix into global matrix.

Case where side matrix is given by a DMatrix instance.

Parameters:

[in]	sd	Pointer to side instance
[in]	a	Side matrix as a DMatrix instance

References Matrix::Add(), Node::getDOF(), Node::getNbDOF(), Side::getNbNodes(), and Side::getPtrNode().

void Assembly	(	const Side *	sd,
		T_ *	a
	)			[inherited]

Assembly of side matrix into global matrix.

Case where side matrix is given by a C-array.

Parameters:

[in]	sd	Pointer to side instance
[in]	a	Side matrix as a C-array instance

References Matrix::Add(), Node::getDOF(), Node::getNbDOF(), Side::getNbNodes(), and Side::getPtrNode().

void Assembly	(	const Element *	el,
		const DMatrix< T_ > &	a
	)			[inherited]

Assembly of element matrix into global matrix.

Case where element matrix is given by a DMatrix instance.

Parameters:

[in]	el	Pointer to element instance
[in]	a	Element matrix as a DMatrix instance

References Matrix::Add(), Node::getDOF(), Node::getNbDOF(), Element::getNbNodes(), and Element::getPtrNode().

void Assembly	(	const Element *	el,
		T_ *	a
	)			[inherited]

Assembly of element matrix into global matrix.

Case where element matrix is given by a C-array.

Parameters:

[in]	el	Pointer to element instance
[in]	a	Element matrix as a C-array

References Matrix::Add(), Node::getDOF(), Node::getNbDOF(), Element::getNbNodes(), and Element::getPtrNode().

int Factor

(

)

[virtual]

Factorize matrix (LU factorization).

Return values:

ret

0 if factorization was normally performed, n if the n-th pivot is null.

Implements Matrix.

References OFELI::Abs(), and OFELI_TOLERANCE.

int FactorAndSolve

(

Vect< T_ > &

b

)

[inherited]

Factorize matrix and solve the linear system.

This is available only if the storage class enables it.

References Matrix::Factor(), and Matrix::Solve().

T_ * getArray

(

)

const

Return matrix as C-Array.

Matrix is stored row by row.

T_ getDiag

(

size_t

k

)

const [inherited]

Return k-th diagonal entry of A.

First entry is given by GetDiag(1).

void getPrintView	(	size_t &	rmin,
		size_t &	rmax,
		size_t &	cmin,
		size_t &	cmax
	)			const [inherited]

Return window data for matrix printing.

Parameters:

[out]	rmin	first row index to view
[out]	rmax	last row index to view
[out]	cmin	first column index to view
[out]	cmax	last column index to view

Referenced by OFELI::operator<<().

bool isFactorized

(

)

const [inherited]

Say if matrix is factorized or not.

If the matrix was not factorized, the class does not allow solving by a direct solver.

void Mult	(	const Vect< T_ > &	x,
		Vect< T_ > &	y
	)			const [virtual]

Multiply matrix by vector x and save result in y.

Parameters:

[in]	x	Vector to add to y
[out]	y	Result.

Implements Matrix.

References OFELI::Clear(), and DMatrix::MultAdd().

void MultAdd	(	const Vect< T_ > &	x,
		Vect< T_ > &	y
	)			const [virtual]

Multiply matrix by vector x and add result to y.

Parameters:

[in]	x	Vector to add to y
[in,out]	y	on input, vector to add to. On output, result.

Implements Matrix.

void MultAdd	(	T_	a,
		const Vect< T_ > &	x,
		Vect< T_ > &	y
	)			const [virtual]

Multiply matrix by vector a*x and add result to y.

Parameters:

[in]	a	constant to multiply by
[in]	x	Vector to multiply by a
[in,out]	y	on input, vector to add to. On output, result.

Implements Matrix.

Referenced by DMatrix::Mult().

const T_ operator()

(

size_t

i

)

const [virtual]

Operator () with one argument (Constant version).

Returns i-th position in the array storing matrix entries. The first entry is at location 1. Entries are stored row by row.

Parameters:

[in]

i

entry index

Implements Matrix.

T_ & operator()	(	size_t	i,
		size_t	j
	)			[virtual]

Operator () (Non constant version).

Return a(i,j)

Parameters:

[in]	i	row index
[in]	j	column index

Implements Matrix.

T_ operator()	(	size_t	i,
		size_t	j
	)			const [virtual]

Operator () (Constant version).

Return a(i,j)

Parameters:

[in]	i	row index
[in]	j	column index

Implements Matrix.

DMatrix< T_ > & operator*=

(

const T_ &

x

)

Operator *=.

Premultiply matrix entries by constant value x.

Reimplemented from Matrix.

Matrix< T_ > & operator+=

(

const Matrix< T_ > &

m

)

[inherited]

Operator +=.

Add matrix m to current matrix instance.

DMatrix< T_ > & operator+=

(

const T_ &

x

)

Operator +=.

Add constant value x to matrix entries.

Reimplemented from Matrix.

DMatrix< T_ > & operator+=

(

const DMatrix< T_ > &

m

)

Operator +=.

Add matrix m to current matrix instance.

Matrix< T_ > & operator-=

(

const Matrix< T_ > &

m

)

[inherited]

Operator -=.

Subtract matrix m from current matrix instance.

DMatrix< T_ > & operator-=

(

const T_ &

x

)

Operator -=.

Subtract constant value x from matrix entries.

Reimplemented from Matrix.

DMatrix< T_ > & operator-=

(

const DMatrix< T_ > &

m

)

Operator -=.

Subtract matrix m from current matrix instance.

DMatrix< T_ > & operator=

(

const T_ &

x

)

Operator =.

Assign constant value x to all matrix entries.

Reimplemented from Matrix.

DMatrix< T_ > & operator=

(

DMatrix< T_ > &

m

)

Operator =.

Copy matrix m to current matrix instance.

T_ operator[]

(

size_t

k

)

const [inherited]

Operator [] (Constant version).

Returns k-th stored element in matrix Index k starts at 0.

Reimplemented in SpMatrix, and SpMatrix< double >.

T_& operator[]

(

size_t

k

)

[inherited]

Operator [] (Non constant version).

Returns k-th stored element in matrix Index k starts at 0.

void Prescribe	(	size_t	dof,
		const class Mesh &	mesh,
		Vect< T_ > &	b,
		const Vect< T_ > &	u,
		int	flag = 0
	)			[inherited]

Impose by a penalty method an essential boundary condition when only one DOF is treated.

This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. This gunction is to be used if only one DOF per node is treated in the linear system. The penalty parameter is by default equal to 1.e20. It can be modified by member function setPenal.

Parameters:

[in]	dof	Label of the concerned degree of freedom (DOF).
[in]	mesh	Mesh instance from which information is extracted.
[in,out]	b	Vect instance that contains right-hand side.
[in]	u	Vect instance that conatins imposed valued at DOFs where they are to be imposed.
[in]	flag	Parameter to determine whether only the right-hand side is to be modified (dof>0) or both matrix and right-hand side (dof=0, default value).

References Node::getCode(), Matrix::getEntry(), Node::getLabel(), Mesh::getNode(), Matrix::Set(), and Mesh::topNode().

void Prescribe	(	const class Mesh &	mesh,
		Vect< T_ > &	b,
		int	flag = 0
	)			[inherited]

Impose by a penalty method a homegeneous (=0) essential boundary condition.

This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).

Parameters:

[in]	mesh	Mesh instance from which information is extracted.
[in,out]	b	Vect instance that contains right-hand side.
[in]	flag	Parameter to determine whether only the right-hand side is to be modified (dof>0) or both matrix and right-hand side (dof=0, default value).

References Node::getCode(), Node::getDOF(), Matrix::getEntry(), Node::getNbDOF(), Mesh::getNode(), Matrix::Set(), and Mesh::topNode().

void Prescribe	(	const class Mesh &	mesh,
		Vect< T_ > &	b,
		const Vect< T_ > &	u,
		int	flag = 0
	)			[inherited]

Impose by a penalty method an essential boundary condition.

This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).

Parameters:

[in]	mesh	Mesh instance from which information is extracted.
[in,out]	b	Vect instance that contains right-hand side.
[in]	u	Vect instance that conatins imposed valued at DOFs where they are to be imposed.
[in]	flag	Parameter to determine whether only the right-hand side is to be modified (dof>0) or both matrix and right-hand side (dof=0, default value).

References Node::getCode(), Node::getDOF(), Matrix::getEntry(), Node::getNbDOF(), Mesh::getNode(), Matrix::Set(), and Mesh::topNode().

void PrescribeSide

(

const class Mesh &

mesh

)

[inherited]

Impose by a penalty method an essential boundary condition when DOFs are supported by sides.

This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).

Parameters:

[in]

mesh

Mesh instance from which information is extracted.

References Side::getCode(), Side::getDOF(), Matrix::getEntry(), Side::getNbDOF(), Mesh::getSide(), Matrix::Set(), and Mesh::topSide().

void Resize	(	size_t	nr,
		size_t	nc
	)

Set size (number of rows and columns) of matrix.

Parameters:

[in]	nr	Number of rows.
[in]	nc	Number of columns.

References OFELI::Clear().

void Resize

(

size_t

size

)

Set size (number of rows) of matrix.

Parameters:

[in]

size

Number of rows and columns.

References OFELI::Clear().

Referenced by DMatrix::DMatrix().

void Set	(	size_t	i,
		size_t	j,
		const T_ &	x
	)			[virtual]

Assign a constant value x to an entry of the matrix.

Parameters:

[in]	i	row index of matrix
[in]	j	column index of matrix
[in]	x	Value to assign to a(i,j).

Implements Matrix.

void setDiagonal

(

const class Mesh &

mesh

)

[inherited]

Initialize matrix storage in the case where only diagonal terms are stored.

This member function is to be used for explicit time integration schemes

References OFELI::Clear(), and Mesh::getNbEq().

void setPrintView	(	size_t	rmin,
		size_t	rmax,
		size_t	cmin,
		size_t	cmax
	)

set a window for matrix printing

Parameters:

[in]	rmin	first row index to view
[in]	rmax	last row index to view
[in]	cmin	first column index to view
[in]	cmax	last column index to view

Reimplemented from Matrix.

int Solve	(	const Vect< T_ > &	b,
		Vect< T_ > &	x
	)

Solve system with factorized matrix (forward and back substitution).

Parameters:

[in]	b	Vect instance that contains right-hand side
[out]	x	Vect instance that contains solution

Return values:

ret

= 0 if solution was normally performed, n if the n-th pivot is null. Solution is performed only is factorization has previouly been invoked.

Reimplemented from Matrix.

References DMatrix::Solve().

int Solve

(

Vect< T_ > &

b

)

[virtual]

Solve system with factorized matrix (forward and back substitution).

Parameters:

[in,out]

b

Vect instance that contains right-hand side on input and solution on output.

Return values:

ret

= 0 if solution was normally performed, n if the n-th pivot is null. Solution is performed only is factorization has previouly been invoked.

Implements Matrix.

References OFELI::Abs(), and OFELI_TOLERANCE.

Referenced by DMatrix::Solve().

void TMult	(	const Vect< T_ > &	x,
		Vect< T_ > &	y
	)			const [virtual]

Multiply transpose of matrix by vector x and add result in y.

Parameters:

[in]	x	Vector to add to y
[in,out]	y	on input, vector to add to. On output, result.

Implements Matrix.