SpMatrix< T_ > Class Template Reference

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

#include <SpMatrix.h>

Inheritance diagram for SpMatrix< T_ >:

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, int is_diagonal=false)
	Constructor that initializes current instance as a dense matrix.
	SpMatrix (Mesh &mesh, size_t dof=0, int is_diagonal=false)
	Constructor using a Mesh instance.
	SpMatrix (const vector< RC > &I, int opt=1)
	Constructor for a square matrix using non zero row and column indices.
	SpMatrix (const vector< RC > &I, const 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 vector< size_t > &row_ptr, const vector< size_t > &col_ind)
	Constructor for a rectangle matrix.
	SpMatrix (size_t nr, size_t nc, const vector< size_t > &row_ptr, const vector< size_t > &col_ind, const vector< T_ > &a)
	Constructor for a rectangle matrix.
	SpMatrix (const vector< size_t > &row_ptr, const vector< size_t > &col_ind)
	Constructor for a rectangle matrix.
	SpMatrix (const vector< size_t > &row_ptr, const vector< size_t > &col_ind, const vector< T_ > &a)
	Constructor for a rectangle matrix.
	SpMatrix (const SpMatrix &m)
	Copy constructor.
	~SpMatrix ()
	Destructor.
void	Identity ()
	Define matrix as identity.
void	Dense ()
	Define matrix as a dense one.
void	Diagonal ()
	Define matrix as a diagonal one.
void	Diagonal (const T_ &a)
	Define matrix as a diagonal one with diagonal entries equal to a
void	Laplace1D (size_t n, real_t h)
	Sets the matrix as the one for the Laplace equation in 1-D.
void	Laplace2D (size_t nx, size_t ny)
	Sets the matrix as the one for the Laplace equation in 2-D.
void	setMesh (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.
void	DiagPrescribe (Mesh &mesh, Vect< T_ > &b, const Vect< T_ > &u)
	Impose by a diagonal method an essential boundary condition.
void	DiagPrescribe (Vect< T_ > &b, const Vect< T_ > &u)
	Impose by a diagonal method an essential boundary condition using the Mesh instance provided by the constructor.
void	setSize (size_t size)
	Set size of matrix (case where it's a square matrix).
void	setSize (size_t nr, size_t nc)
	Set size (number of rows) of matrix.
void	setGraph (const vector< RC > &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.
Vect< T_ >	getColumn (size_t j) const
	Get j-th column vector.
T_	at (size_t i, size_t j)
	Return a value of a matrix entry.
T_ &	operator() (size_t i, size_t j)
	Operator () (Non constant version)
T_	operator() (size_t i, size_t j) const
	Operator () (Constant version)
T_	operator() (size_t i) const
	Operator () with one argument (Constant version)
T_	operator[] (size_t i) const
	Operator [] (Constant version).
Vect< T_ >	operator* (const Vect< T_ > &x) const
	Operator * to multiply matrix by a vector.
SpMatrix< T_ > &	operator*= (const T_ &a)
	Operator *= to premultiply matrix by a constant.
void	getMesh (Mesh &mesh)
	Get mesh instance whose reference will be stored in current instance of SpMatrix.
void	Mult (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector and save in another one.
void	MultAdd (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector x and add 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	TMult (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply transpose of matrix by vector x and save in y.
void	Axpy (T_ a, const SpMatrix< 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 a value to an entry of the matrix.
void	add (size_t i, size_t j, const T_ &val)
	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 (const Vect< T_ > &b, Vect< T_ > &x, bool fact=false)
	Solve the linear system of equations.
void	setSolver (Iteration solver=CG_SOLVER, Preconditioner prec=DIAG_PREC, int max_it=1000, real_t toler=1.e-8)
	Choose solver and preconditioner for an iterative procedure.
void	clear ()
	brief Set all matrix entries to zero
T_ *	get () const
	Return C-Array.
T_	get (size_t i, size_t j) const
	Return entry (i,j) of matrix if this one is stored, 0 otherwise.
void	add (size_t i, const T_ &val)
	Add val to entry i.
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.
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.
virtual int	solve (Vect< T_ > &b, bool fact=true)=0
	Solve the linear system.
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.
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::SpMatrix< T_ >

To handle matrices in sparse storage format.

This template class enables storing and manipulating 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 vector<real_t> instance {1,2,3,4,5}. The vectors row_ptr and col_ind are respectively: {0,2,4,5}, {1,2,1,2,2}

When the library eigen is used in conjunction with OFELI, the class uses the sparse matrix class of eigen and enables then access to specific solvers (see class LinearSolver)

Template Parameters

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

Author

Rachid Touzani

Copyright

GNU Lesser Public License