TrMatrix< T_ > Class Template Reference

To handle tridiagonal matrices. More...

#include <TrMatrix.h>

Inheritance diagram for TrMatrix< T_ >:

Public Member Functions
	TrMatrix ()
	Default constructor.
	TrMatrix (size_t size)
	Constructor for a tridiagonal matrix with size rows.
	TrMatrix (const TrMatrix &m)
	Copy Constructor.
	~TrMatrix ()
	Destructor.
void	Identity ()
	Define matrix as identity matrix.
void	Diagonal ()
	Define matrix as a diagonal one.
void	Diagonal (const T_ &a)
	Define matrix as a diagona one and assign value a to all diagonal entries.
void	Laplace1D (real_t h)
	Define matrix as the one of 3-point finite difference discretization of the second derivative.
void	setSize (size_t size)
	Set size (number of rows) of matrix.
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.
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 save result in y.
void	Axpy (T_ a, const TrMatrix< T_ > &m)
	Add to matrix the product of a matrix by a scalar.
void	Axpy (T_ a, const Matrix< T_ > *m)
	Add to matrix the product of a matrix by a scalar.
void	set (size_t i, size_t j, const T_ &val)
	Assign constant val to an entry (i,j) of the matrix.
void	add (size_t i, size_t j, const T_ &val)
	Add constant val value to an entry (i,j) of the matrix.
void	add (size_t i, const T_ &val)
	Add val to entry i.
T_	at (size_t i, size_t j)
	Return a value of a matrix entry.
T_	operator() (size_t i, size_t j) const
	Operator () (Constant version).
T_ &	operator() (size_t i, size_t j)
	Operator () (Non constant version).
TrMatrix< T_ > &	operator= (const TrMatrix< T_ > &m)
	Operator =.
TrMatrix< T_ > &	operator= (const T_ &x)
	Operator = Assign matrix to identity times x.
TrMatrix< T_ > &	operator*= (const T_ &x)
	Operator *=.
int	solve (Vect< T_ > &b, bool fact=true)
	Solve a linear system with current matrix (forward and back substitution).
int	solve (const Vect< T_ > &b, Vect< T_ > &x, bool fact=false)
	Solve a linear system with current matrix (forward and back substitution).
T_ *	get () const
	Return C-Array.
T_	get (size_t i, size_t j) const
	Return entry (i,j) of matrix.
Public Member Functions inherited from Matrix< T_ >
	Matrix ()
	Default constructor.
	Matrix (const Matrix< T_ > &m)
	Copy Constructor.
virtual	~Matrix ()
	Destructor.
virtual void	reset ()
	Set matrix to 0 and reset factorization parameter.
size_t	getNbRows () const
	Return number of rows.
size_t	getNbColumns () const
	Return number of columns.
string	getName () const
	Return name of matrix.
MatrixSize	getMatrixSize () const
	Return storage type.
void	setPenal (real_t p)
	Set Penalty Parameter (For boundary condition prescription).
void	setDiagonal ()
	Set the matrix as diagonal.
T_	getDiag (size_t k) const
	Return k-th diagonal entry of matrix.
size_t	size () const
	Return matrix dimension (Number of rows and columns).
void	setDiagonal (Mesh &mesh)
	Initialize matrix storage in the case where only diagonal terms are stored.
virtual void	clear ()
	brief Set all matrix entries to zero
void	Assembly (const Element &el, T_ *a)
	Assembly of element matrix into global matrix.
void	Assembly (const Side &sd, T_ *a)
	Assembly of side matrix into global matrix.
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 (int dof, int code, Vect< T_ > &b, const Vect< T_ > &u, int flag=0)
	Impose by a penalty method an essential boundary condition to a given degree of freedom for a given code.
void	Prescribe (Vect< T_ > &b, int flag=0)
	Impose by a penalty method a homegeneous (=0) essential boundary condition.
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 ()
	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	FactorAndSolve (Vect< T_ > &b)
	Factorize matrix and solve the linear system.
int	FactorAndSolve (const Vect< T_ > &b, Vect< T_ > &x)
	Factorize matrix and solve the linear system.
size_t	getLength () const
	Return number of stored terms in matrix.
int	isDiagonal () const
	Say if matrix is diagonal or not.
int	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= (Matrix< T_ > &m)
	Operator =.
Matrix &	operator+= (const Matrix< T_ > &m)
	Operator +=.
Matrix &	operator-= (const Matrix< T_ > &m)
	Operator -=.
Matrix &	operator= (const T_ &x)
	Operator =.
Matrix &	operator*= (const T_ &x)
	Operator *=.
Matrix &	operator+= (const T_ &x)
	Operator +=.
Matrix &	operator-= (const T_ &x)
	Operator -=.

Detailed Description

template<class T_>
class OFELI::TrMatrix< T_ >

To handle tridiagonal matrices.

This class enables storing and manipulating tridiagonal matrices. The template parameter is the type of matrix entries. Any matrix entry can be accessed by the () operator: For instance, if A is an instance of this class, A(i,j) stands for the entry at the i-th row and j-th column, i and j starting from 1. If is difference from i-1, i or i+1, the returned value is 0. Entries of A can be assigned a value by the same operator. Only nonzero entries can be assigned.

Template Parameters

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

Author

Rachid Touzani

Copyright

GNU Lesser Public License