SpMatrix< T_ > Class Template Reference

To handle matrices in sparse storage format. More...

Inheritance diagram for SpMatrix< T_ >:

List of all members.

Public Member Functions
	SpMatrix ()
	Default constructor.
	SpMatrix (size_t nr, size_t nc)
	Constructor that initializes current instance as a dense matrix.
	SpMatrix (size_t size, bool is_diagonal=false)
	Constructor that initializes current instance as a dense matrix.
	SpMatrix (class Mesh &mesh, size_t dof=0, bool is_diagonal=false)
	Constructor using a Mesh instance.
	SpMatrix (const class Vect< std::pair< size_t, size_t > > &I, int opt=1)
	Constructor for a square matrix using non zero row and column indices.
	SpMatrix (const class Vect< std::pair< size_t, size_t > > &I, const class Vect< T_ > &a, int opt=1)
	Constructor for a square matrix using non zero row and column indices.
	SpMatrix (size_t nr, size_t nc, const class Vect< size_t > &row_ptr, const class Vect< size_t > &col_ind)
	Constructor for a rectangle matrix.
	SpMatrix (size_t nr, size_t nc, const class Vect< size_t > &row_ptr, const class Vect< size_t > &col_ind, const class Vect< T_ > &a)
	Constructor for a rectangle matrix.
	SpMatrix (const class Vect< size_t > &row_ptr, const class Vect< size_t > &col_ind)
	Constructor for a rectangle matrix. Matrix entries are set to 0.
	SpMatrix (const class Vect< size_t > &row_ptr, const class Vect< size_t > &col_ind, const class Vect< T_ > &a)
	Constructor for a rectangle matrix.
	SpMatrix (const SpMatrix &m)
	Copy constructor.
	~SpMatrix (void)
	Destructor.
virtual void	setMesh (class Mesh &mesh, size_t dof=0)
	Determine mesh graph and initialize matrix.
void	setOneDOF ()
	Activate 1-DOF per node option.
void	setSides ()
	Activate Sides option.
void	setDiag ()
	Store diagonal entries in a separate internal vector.
Vect< T_ >	getColumn (size_t j) const
	Get j-th column vector.
void	DiagPrescribe (class Mesh &mesh, Vect< T_ > &b, const class Vect< T_ > &u)
	Impose by a diagonal method an essential boundary condition.
void	DiagPrescribe (Vect< T_ > &b, const class Vect< T_ > &u)
	Impose by a diagonal method an essential boundary condition using the Mesh instance provided by the constructor.
void	Resize (size_t size)
	Set size of matrix (case where it's a square matrix).
void	Resize (size_t nr, size_t nc)
	Set size (number of rows) of matrix.
void	setGraph (const Vect< std::pair< size_t, size_t > > &I, int opt=1)
	Set graph of matrix by giving a vector of its nonzero entries.
Vect< T_ >	getRow (size_t i) const
	Get i-th row vector.
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).
const T_	operator[] (size_t i) const
	Operator [] (Constant version).
void	getMesh (class Mesh &mesh)
	Get mesh instance whose reference will be stored in current instance of SpMatrix.
void	Mult (const class Vect< T_ > &v, class Vect< T_ > &w) const
	Multiply matrix by vector and save in another one.
void	MultAdd (const class Vect< T_ > &v, class Vect< T_ > &w) const
	Multiply matrix by vector v and add to w.
void	MultAdd (T_ a, const class Vect< T_ > &v, class Vect< T_ > &w) const
	Multiply matrix by vector a*v and add to w.
void	TMult (const class Vect< T_ > &v, class Vect< T_ > &w) const
	Multiply transpose of matrix by vector v and save in w.
void	Axpy (T_ a, const SpMatrix< 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.
void	set (size_t i, size_t j, const T_ &x)
	Assign a value to an entry of the matrix.
void	Add (size_t i, size_t j, const T_ &x)
	Add a value to an entry of the matrix.
void	operator= (const T_ &x)
	Operator =.
size_t	getColInd (size_t i) const
	Return storage information.
size_t	getRowPtr (size_t i) const
	Return Row pointer at position i.
int	Solve (class Vect< T_ > &b)
	Solve the linear system of equations.
int	Solve (const class Vect< T_ > &b, class Vect< T_ > &x)
	Solve the linear system of equations.
void	setSolver (Iteration solver=CG_SOLVER, Preconditioner prec=DIAG_PREC, int max_it=1000, double toler=1.e-8)
	Choose solver and preconditioner for an iterative procedure.
T_ *	getArray () const
	Return C-Array.
T_	getEntry (size_t i, size_t j) const
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).
virtual void	MultAdd (const Vect< T_ > &x, Vect< T_ > &y) const =0
	Multiply matrix by vector x and add to y.
virtual void	MultAdd (T_ a, const Vect< T_ > &v, Vect< T_ > &w) const =0
	Multiply matrix by vector a*x and add to y.
virtual void	Mult (const Vect< T_ > &x, Vect< T_ > &y) const =0
	Multiply matrix by vector x and save in y.
virtual void	TMult (const Vect< T_ > &v, Vect< T_ > &w) const =0
	Multiply transpose of matrix by vector x and save in y.
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.
virtual int	Factor ()=0
	Factorize matrix. Available only if the storage class enables it.
int	Solve (const Vect< T_ > &b, Vect< T_ > &x)
	Solve system with factorized matrix (forward and back substitution).
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.
T_ &	operator() (size_t i)
	Operator () with one argument (Non Constant version).
T_ &	operator[] (size_t k)
	Operator [] (Non 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	setPrintView (size_t rmin, size_t rmax, size_t cmin, size_t cmax)
	Set a window for matrix printing.
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::SpMatrix< T_ >

To handle matrices in sparse storage format.

This template class enables to store and manipulate a sparse matrix, i.e. only nonzero terms are stored. Internally, the matrix is stored as a vector instance and uses for the definition of its graph a Vect<size_t> instance row_ptr and a Vect<size_t> instance col_ind that contains respectively addresses of first element of each row and column indices.

To illustrate this, consider the matrix

            1   2   0
            3   4   0
            0   5   0
   

Such a matrix is stored in the valarray<double> instance {1,2,3,4,5}. The vectors row_ptr and col_ind are respectively: {1,3,5,6}, {1,2,1,2,2}

Template Parameters:

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

---

Constructor & Destructor Documentation

SpMatrix

(

)

Default constructor.

Initialize a zero-dimension matrix

SpMatrix	(	size_t	nr,
		size_t	nc
	)

Constructor that initializes current instance as a dense matrix.

Normally, for a dense matrix this is not the right class. Matrix entries are set to 0.

Parameters:

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

SpMatrix	(	size_t	size,
		bool	is_diagonal = false
	)

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).
[in]	is_diagonal	Boolean argument to say is the matrix is actually a diagonal matrix or not. Matrix entries are set to 0.

SpMatrix	(	class Mesh &	mesh,
		size_t	dof = 0,
		bool	is_diagonal = false
	)

Constructor using a Mesh instance.

Parameters:

[in]	mesh	Mesh instance from which matrix graph is extracted.
[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]	is_diagonal	Boolean argument to say is the matrix is actually a diagonal matrix or not. Matrix entries are set to 0.

SpMatrix	(	const class Vect< std::pair< size_t, size_t > > &	I,
		int	opt = 1
	)

Constructor for a square matrix using non zero row and column indices.

Parameters:

[in]	I	Vector containing pairs of row and column indices
[in]	opt	Flag indicating if vectors I is cleaned and ordered (opt=1) or not (opt=0). In the latter case, this vector can have the same contents more than once and are not necessarily ordered

SpMatrix	(	const class Vect< std::pair< size_t, size_t > > &	I,
		const class Vect< T_ > &	a,
		int	opt = 1
	)

Constructor for a square matrix using non zero row and column indices.

Parameters:

[in]	I	Vector containing pairs of row and column indices
[in]	a	Vector containing matrix entries in the same order than the one given by I
[in]	opt	Flag indicating if vector I is cleaned and ordered (opt=1: default) or not (opt=0). In the latter case, this vector can have the same contents more than once and are not necessarily ordered

SpMatrix	(	size_t	nr,
		size_t	nc,
		const class Vect< size_t > &	row_ptr,
		const class Vect< size_t > &	col_ind
	)

Constructor for a rectangle matrix.

Parameters:

[in]	nr	Number of rows
[in]	nc	Number of columns
[in]	row_ptr	Vector of row pointers (See the above description of this class).
[in]	col_ind	Vector of column indices (See the above description of this class). Matrix entries are set to 0.

SpMatrix	(	size_t	nr,
		size_t	nc,
		const class Vect< size_t > &	row_ptr,
		const class Vect< size_t > &	col_ind,
		const class Vect< T_ > &	a
	)

Constructor for a rectangle matrix.

Parameters:

[in]	nr	Number of rows
[in]	nc	Number of columns
[in]	row_ptr	Vector of row pointers (See the above description of this class).
[in]	col_ind	Vector of column indices (See the above description of this class).
[in]	a	C-Array containing matrix entries stored columnwise

SpMatrix	(	const class Vect< size_t > &	row_ptr,
		const class Vect< size_t > &	col_ind
	)

Constructor for a rectangle matrix. Matrix entries are set to 0.

Parameters:

[in]	row_ptr	Vector of row pointers (See the above description of this class).
[in]	col_ind	Vector of column indices (See the above description of this class).

SpMatrix	(	const class Vect< size_t > &	row_ptr,
		const class Vect< size_t > &	col_ind,
		const class Vect< T_ > &	a
	)

Constructor for a rectangle matrix.

Parameters:

[in]	row_ptr	Vector of row pointers (See the above description of this class).
[in]	col_ind	Vector of column indices (See the above description of this class).
[in]	a	Vect instance that contain matrix entries stored row by row. Number of rows is extracted from vector row_ptr.

---

Member Function Documentation

virtual void setMesh	(	class Mesh &	mesh,
		size_t	dof = 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. Matrix entries are set to 0.

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

Impose by a diagonal 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.

void DiagPrescribe	(	Vect< T_ > &	b,
		const class Vect< T_ > &	u
	)

Impose by a diagonal 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.

void Resize

(

size_t

size

)

Set size of matrix (case where it's a square matrix).

Parameters:

[in]

size

Number of rows and columns.

void Resize	(	size_t	nr,
		size_t	nc
	)

Set size (number of rows) of matrix.

Parameters:

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

void setGraph	(	const Vect< std::pair< size_t, size_t > > &	I,
		int	opt = 1
	)

Set graph of matrix by giving a vector of its nonzero entries.

Parameters:

[in]	I	Vector containing pairs of row and column indices
[in]	opt	Flag indicating if vector I is cleaned and ordered (opt=1: default) or not (opt=0). In the latter case, this vector can have the same contents more than once and are not necessarily ordered

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_ >.

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_ >.

const T_ operator()

(

size_t

i

)

const

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.

Reimplemented from Matrix< T_ >.

const T_ operator[]

(

size_t

i

)

const

Operator [] (Constant version).

Returns i-th position in the array storing matrix entries. The first entry is at location 0. Entries are stored row by row.

Reimplemented from Matrix< T_ >.

void Mult	(	const class Vect< T_ > &	v,
		class Vect< T_ > &	w
	)		const

Multiply matrix by vector and save in another one.

Parameters:

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

void MultAdd	(	const class Vect< T_ > &	v,
		class Vect< T_ > &	w
	)		const

Multiply matrix by vector v and add to w.

Parameters:

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

void MultAdd	(	T_	a,
		const class Vect< T_ > &	v,
		class Vect< T_ > &	w
	)		const

Multiply matrix by vector a*v and add to w.

Parameters:

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

void TMult	(	const class Vect< T_ > &	v,
		class Vect< T_ > &	w
	)		const

Multiply transpose of matrix by vector v and save in w.

Parameters:

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

void Axpy	(	T_	a,
		const SpMatrix< 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	Pointer to Matrix by which a is multiplied. The result is added to current instance

Implements Matrix< T_ >.

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

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

Parameters:

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

Implements Matrix< T_ >.

void operator=

(

const T_ &

x

)

Operator =.

Assign constant value x to all matrix entries.

Reimplemented from Matrix< T_ >.

size_t getColInd

(

size_t

i

)

const [virtual]

Return storage information.

Returns:

Column index of the i-th stored element in matrix

Reimplemented from Matrix< T_ >.

int Solve

(

class Vect< T_ > &

b

)

[virtual]

Solve the linear system of equations.

The default parameters are:

• CG_SOLVER for solver
• DIAG_PREC for preconditioner
• Max. Nb. of iterations is 1000
• Tolerance is 1.e-8 To change these values, call function setSolver before this function

  Parameters:

  [in,out]

  b

  Vector that contains right-hand side on input and solution on output

  Returns:

  Number of actual performed iterations

Implements Matrix< T_ >.

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

Solve the linear system of equations.

The default parameters are:

• CG_SOLVER for solver
• DIAG_PREC for preconditioner
• Max. Nb. of iterations is 1000
• Tolerance is 1.e-8 To change these values, call function setSolver before this function

  Parameters:

  [in]	b	Vector that contains right-hand side
  [out]	x	Vector that contains the obtained solution

  Returns:

  Number of actual performed iterations

void setSolver	(	Iteration	solver = CG_SOLVER,
		Preconditioner	prec = DIAG_PREC,
		int	max_it = 1000,
		double	toler = 1.e-8
	)

Choose solver and preconditioner for an iterative procedure.

Parameters:

[in]	solver	Option to choose iterative solver in an enumerated variable CG_SOLVER : Conjugate Gradient [default] CGS_SOLVER : Squared conjugate gradient BICG_SOLVER : Biconjugate gradient BICG_STAB_SOLVER : Biconjugate gradient stabilized GMRES_SOLVER : Generalized Minimal Residual QMR_SOLVER : Quasi-Minimal Residual Default value is CG_SOLVER
[in]	prec	Option to choose preconditioner in an enumerated variable IDENT_PREC : Identity preconditioner (no preconditioning) DIAG_PREC : Diagonal preconditioner [default] ILU_PREC : ILU (Incomplete factorization) preconditioner Default value is DIAG_PREC
[in]	max_it	Maximum number of allowed iterations. Default value is 1000.
[in]	toler	Tolerance for convergence. Default value is 1.e-8

T_* getArray

(

)

const

Return C-Array.

Non zero terms of matrix is stored row by row.

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

Return entry (i,j) of matrix if this one is stored, 0 otherwise

Implements 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 Solve	(	const Vect< T_ > &	b,
		Vect< T_ > &	x
	)		[inherited]

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

Returns:

- 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 in SkMatrix< T_ >, SkSMatrix< T_ >, DMatrix< T_ >, and DSMatrix< T_ >.

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

)

[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.

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 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< T_ >, and DSMatrix< 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