SkMatrix Class Template Reference
[Vector and Matrix]

#include <SkMatrix.h>

Inheritance diagram for SkMatrix:

List of all members.

---

Detailed Description

template<class T_>
class OFELI::SkMatrix< T_ >

To handle square matrices in skyline storage format.

This template class allows storing and manipulating a matrix in skyline storage format.

Template Argument :

• T_ data type (double, float, ...)

Public Member Functions
void	Add (size_t i, size_t j, const T_ &x)
	Add a constant value to an entry ofthe 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.
void	DiagPrescribe (const class Mesh &mesh, Vect< T_ > &b, const Vect< T_ > &u, int flag=0)
	Impose an essential boundary condition.
int	Factor ()
	Factorize matrix (LU factorization).
int	FactorAndSolve (Vect< T_ > &b)
	Factorize matrix and solve the linear system.
T_ *	getArray () const
	Return C-Array.
size_t	getColHeight (size_t i) const
	Return column height.
virtual size_t	getColInd (size_t i) const
	Return Column index for column i (See the description for class SpMatrix).
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 if this one is stored, 0 else.
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.
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 in y.
void	MultAdd (T_ a, const Vect< T_ > &v, Vect< T_ > &w) const
	Multiply matrix by a vector and add to another one.
void	MultAdd (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector x and add to y.
T_ &	operator() (size_t i, size_t j)
	Operator () (Non constant version).
T_	operator() (size_t i, size_t j) const
	Operator () (Constant version).
const T_	operator() (size_t i) const
	Operator () with one argument (Constant version).
SkMatrix< T_ > &	operator*= (const T_ &x)
	Operator *=.
Matrix &	operator+= (const Matrix< T_ > &m)
	Operator +=.
SkMatrix< T_ > &	operator+= (const T_ &x)
	Operator +=.
SkMatrix< T_ > &	operator+= (const SkMatrix< T_ > &m)
	Operator +=.
Matrix &	operator-= (const T_ &x)
	Operator -=.
Matrix &	operator-= (const Matrix< T_ > &m)
	Operator -=.
SkMatrix< T_ > &	operator= (const T_ &x)
	Operator =.
SkMatrix< T_ > &	operator= (const SkMatrix< 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	Set (size_t i, size_t j, const T_ &x)
	Assign a value to an entry ofthe 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	setDOF (size_t i)
	Choose DOF to activate.
virtual void	setMesh (const class Mesh &mesh, size_t dof=0, size_t type=0)
	Determine mesh graph and initialize matrix.
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
void	setSkyline (const class Mesh &mesh)
	Determine matrix structure.
	SkMatrix (const SkMatrix< T_ > &m)
	Copy Constructor.
	SkMatrix (const Vect< size_t > &ColHt)
	Constructor that initializes skyline structure of matrix using vector of column heights.
	SkMatrix (size_t size)
	Constructor that initializes current instance as a dense matrix.
	SkMatrix (const class Mesh &mesh, size_t dof=0)
	Constructor using mesh to initialize skyline structure of matrix.
	SkMatrix ()
	Default constructor. Initializes a zero-dimension matrix.
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 save in y.
void	TMultAdd (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply transpose of matrix by vector x and add to y.
	~SkMatrix ()
	Destructor.

---

Constructor & Destructor Documentation

SkMatrix	(	const class Mesh &	mesh,
		size_t	dof = 0
	)

Constructor using mesh to initialize skyline structure of matrix.

Parameters:

[in]	mesh	Mesh instance for which matrix graph is determined.
[in]	dof	Option parameter, with default value 0 dof=1 means that only one degree of freedom for each node (or element or side) is taken to determine matrix structure. The value dof=0 means that matrix structure is determined using all DOFs. Matrix entries are set to 0.

References SkMatrix::setMesh().

SkMatrix

(

size_t

size

)

Constructor that initializes current instance as a dense matrix.

Normally, for a dense matrix this is not the right class.

Parameters:

[in]

size

Number of matrix rows (and columns). Matrix entries are set to 0.

References OFELI::Clear().

SkMatrix

(

const Vect< size_t > &

ColHt

)

Constructor that initializes skyline structure of matrix using vector of column heights.

Parameters:

[in]

ColHt

Vect instance that contains rows lengths of matrix. Matrix entries are set to 0.

References OFELI::Clear().

---

Member Function Documentation

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

Add a constant value to an entry ofthe matrix.

Parameters:

[in]	i	Row index
[in]	j	Column index
[in]	x	Constant value to add to a(i,j)

Implements Matrix.

Referenced by OFELI::Assembly(), and OFELI::SideAssembly().

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().

void DiagPrescribe	(	const class Mesh &	mesh,
		Vect< T_ > &	b,
		const Vect< T_ > &	u,
		int	flag = 0
	)

Impose 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. It can be modified by member function setPenal(..).

Parameters:

[in]	mesh	Mesh instance from which information is extracted.
[in]	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(), Node::getNbDOF(), Mesh::getNode(), and Mesh::topNode().

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 C-Array.

Skyline of matrix is stored row by row.

size_t getColHeight

(

size_t

i

)

const

Return column height.

Column height at entry i is returned.

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 in y.

Parameters:

[in]	x	Vector to multiply by matrix
[out]	y	Vector that contains on output the result.

Implements Matrix.

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

void MultAdd	(	T_	a,
		const Vect< T_ > &	v,
		Vect< T_ > &	w
	)			const [virtual]

Multiply matrix by a vector and add to another one.

Parameters:

[in]	a	Constant to multiply by matrix
[in]	v	Vector to multiply by matrix
[in,out]	w	Vector to add to the result. y contains on output the result.

Implements Matrix.

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

Multiply matrix by vector x and add to y.

Parameters:

[in]	x	Vector to multiply by matrix
[in,out]	y	Vector to add to the result. y contains on output the result.

Implements Matrix.

Referenced by SkMatrix::Mult().

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

Operator () (Non constant version).

Parameters:

[in]	i	Row index
[in]	j	Column index

Implements Matrix.

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

Operator () (Constant version).

Parameters:

[in]	i	Row index
[in]	j	Column index

Implements Matrix.

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.

Implements Matrix.

SkMatrix< 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.

SkMatrix< T_ > & operator+=

(

const T_ &

x

)

Operator +=.

Add constant value x to matrix entries.

Reimplemented from Matrix.

SkMatrix< T_ > & operator+=

(

const SkMatrix< T_ > &

m

)

Operator +=.

Add matrix m to current matrix instance.

Matrix< T_ > & operator-=

(

const T_ &

x

)

[inherited]

Operator -=.

Subtract constant value x from all matrix entries.

Reimplemented in DMatrix, and DMatrix< double >.

Matrix< T_ > & operator-=

(

const Matrix< T_ > &

m

)

[inherited]

Operator -=.

Subtract matrix m from current matrix instance.

SkMatrix< T_ > & operator=

(

const T_ &

x

)

Operator =.

Assign constant value x to all matrix entries.

Reimplemented from Matrix.

SkMatrix< T_ > & operator=

(

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

Assign a value to an entry ofthe matrix.

Parameters:

[in]	i	Row index
[in]	j	Column index
[in]	x	Value to assign to entry 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 setDOF

(

size_t

i

)

Choose DOF to activate.

This function is available only if variable dof is equal to 1 in the constructor

void setMesh	(	const class Mesh &	mesh,
		size_t	dof = 0,
		size_t	type = 0
	)			[virtual]

Determine mesh graph and initialize matrix.

This member function is called by constructor with the same arguments

Parameters:

[in]	mesh	Mesh instance for which matrix graph is determined.
[in]	dof	Option parameter, with default value 0. dof=1 means that only one degree of freedom for each node (or element or side) is taken to determine matrix structure. The value dof=0 means that matrix structure is determined using all DOFs.
[in]	type	Unused Matrix entries are set to 0.

References OFELI::Clear().

Referenced by SkMatrix::SkMatrix().

void setPrintView	(	size_t	rmin,
		size_t	rmax,
		size_t	cmin,
		size_t	cmax
	)			[inherited]

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 in DMatrix, DSMatrix, and DMatrix< double >.

void setSkyline

(

const class Mesh &

mesh

)

Determine matrix structure.

This member function calculates matrix structure using a Mesh instance.

Parameters:

[in]

mesh

Mesh instance

References OFELI::Clear(), Mesh::ElementsAreDOF(), Mesh::getNbEq(), Mesh::getNbNodes(), Mesh::getNbSides(), Mesh::NodesAreDOF(), and Mesh::SidesAreDOF().

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 SkMatrix::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 SkMatrix::Solve().

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

Multiply transpose of matrix by vector x and save in y.

Parameters:

[in]	x	Vector to multiply by matrix
[out]	y	Vector that contains on output the result.

Implements Matrix.

References OFELI::Clear(), and SkMatrix::TMultAdd().

void TMultAdd	(	const Vect< T_ > &	x,
		Vect< T_ > &	y
	)			const

Multiply transpose of matrix by vector x and add to y.

Parameters:

[in]	x	Vector to multiply by matrix
[in,out]	y	Vector to add to the result. y contains on output the result.

Referenced by SkMatrix::TMult().