DSMatrix< T_ > Class Template Reference

To handle symmetric dense matrices. More...

Inheritance diagram for DSMatrix< T_ >:

List of all members.

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

---

Detailed Description

template<class T_>
class OFELI::DSMatrix< T_ >

To handle symmetric dense matrices.

This class enables storing and manipulating symmetric dense matrices.

Template Parameters:

<T_>	Data type (double, float, complex<double>, ...)

---

Constructor & Destructor Documentation

DSMatrix

(

size_t

dim

)

Constructor that for a ymmetric matrix with given number of rows. Assigns 0 to all matrix entries.

Parameters:

[in]

dim

Number of rows

DSMatrix

(

const DSMatrix< T_ > &

m

)

Copy Constructor.

Parameters:

[in]

m

DSMatrix instance to copy

---

Member Function Documentation

void Resize

(

size_t

dim

)

Set size (number of rows) of matrix.

Parameters:

[in]

dim

Number of rows and columns.

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

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

Parameters:

[in]	i	row index
[in]	j	column index
[in]	x	value to assign to a(i,j)

Implements Matrix< T_ >.

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

Add constant to an entry ofthe matrix.

Parameters:

[in]	i	row index
[in]	j	column index
[in]	x	value to add to a(i,j)

Implements Matrix< T_ >.

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

Operator () (Constant version).

Parameters:

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

Implements Matrix< T_ >.

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_ >.

int Factor

(

)

[virtual]

Factorize matrix (LDLt).

Returns:

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

Implements Matrix< T_ >.

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

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

Parameters:

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

Implements Matrix< T_ >.

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< T_ >.

void Axpy	(	T_	a,
		const DSMatrix< T_ > &	x
	)

Add to matrix the product of a matrix by a scalar.

Parameters:

[in]	a	Scalar to premultiply
[in]	x	Matrix by which a is multiplied. The result is added to current instance

void Axpy	(	T_	a,
		const Matrix< T_ > *	x
	)		[virtual]

Add to matrix the product of a matrix by a scalar.

Parameters:

[in]	a	Scalar to premultiply
[in]	x	Matrix by which a is multiplied. The result is added to current instance

Implements Matrix< T_ >.

int Solve

(

Vect< T_ > &

b

)

[virtual]

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

Parameters:

[in]

b

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

Returns:

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

Implements Matrix< T_ >.

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
[in]	x	Vect instance that contains solution

Returns:

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

Reimplemented from Matrix< T_ >.

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< T_ >.

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

T_ getDiag

(

size_t

k

)

const [inherited]

Return k-th diagonal entry of matrix.

First entry is given by getDiag(1).

void Assembly	(	const class 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

void Assembly	(	const class 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

void Assembly	(	const class 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

void Assembly	(	const class 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

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).

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

Impose by a penalty method an essential boundary condition, using the Mesh instance provided by the constructor.

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,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).

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).

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

Impose by a penalty method a homegeneous (=0) essential boundary condition, using the Mesh instance provided by the constructor.

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,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).

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).

void Prescribe	(	size_t	dof,
		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 uses the Mesh instance provided by the constructor.
It 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,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).

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 uses the Mesh instance provided by the constructor
It 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(..).

void PrescribeSide

(

)

[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(..).

int FactorAndSolve

(

Vect< T_ > &

b

)

[inherited]

Factorize matrix and solve the linear system.

This is available only if the storage class enables it.

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.

T_ operator()

(

size_t

i

)

const [inherited]

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

Reimplemented in SpMatrix< T_ >.

T_& operator()

(

size_t

i

)

[inherited]

Operator () with one argument (Non 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

T_& operator[]

(

size_t

k

)

[inherited]

Operator [] (Non constant version).

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

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< T_ >.

Matrix< T_ > & operator+=

(

const Matrix< T_ > &

m

)

[inherited]

Operator +=.

Add matrix m to current matrix instance.

Matrix< T_ > & operator+=

(

const T_ &

x

)

[inherited]

Operator +=.

Add constant value x to all matrix entries.

Reimplemented in SkMatrix< T_ >, DMatrix< T_ >, and BMatrix< T_ >.

Matrix< T_ > & operator-=

(

const Matrix< T_ > &

m

)

[inherited]

Operator -=.

Subtract matrix m from current matrix instance.

Matrix< T_ > & operator-=

(

const T_ &

x

)

[inherited]

Operator -=.

Subtract constant value x from all matrix entries.

Reimplemented in DMatrix< T_ >.

Matrix< T_ > & operator*=

(

const T_ &

x

)

[inherited]

Operator *=.

Premultiply matrix entries by constant value x.

Reimplemented in SkMatrix< T_ >, SkSMatrix< T_ >, DMatrix< T_ >, BMatrix< T_ >, and TrMatrix< T_ >.

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