OFELI's Logo

An Object Oriented Finite Element Library

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. More...
 
 SpMatrix (size_t nr, size_t nc)
 Constructor that initializes current instance as a dense matrix. More...
 
 SpMatrix (size_t size, int is_diagonal=false)
 Constructor that initializes current instance as a dense matrix. More...
 
 SpMatrix (Mesh &mesh, size_t dof=0, int is_diagonal=false)
 Constructor using a Mesh instance. More...
 
 SpMatrix (const Vect< RC > &I, int opt=1)
 Constructor for a square matrix using non zero row and column indices. More...
 
 SpMatrix (const Vect< RC > &I, const Vect< T_ > &a, int opt=1)
 Constructor for a square matrix using non zero row and column indices. More...
 
 SpMatrix (size_t nr, size_t nc, const vector< size_t > &row_ptr, const vector< size_t > &col_ind)
 Constructor for a rectangle matrix. More...
 
 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. More...
 
 SpMatrix (const vector< size_t > &row_ptr, const vector< size_t > &col_ind)
 Constructor for a rectangle matrix. More...
 
 SpMatrix (const vector< size_t > &row_ptr, const vector< size_t > &col_ind, const vector< T_ > &a)
 Constructor for a rectangle matrix. More...
 
 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. More...
 
void Laplace2D (size_t nx, size_t ny)
 Sets the matrix as the one for the Laplace equation in 2-D. More...
 
void setMesh (Mesh &mesh, size_t dof=0)
 Determine mesh graph and initialize matrix. More...
 
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. More...
 
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. More...
 
void setSize (size_t size)
 Set size of matrix (case where it's a square matrix). More...
 
void setSize (size_t nr, size_t nc)
 Set size (number of rows) of matrix. More...
 
void setGraph (const Vect< RC > &I, int opt=1)
 Set graph of matrix by giving a vector of its nonzero entries. More...
 
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_ & operator() (size_t i, size_t j)
 Operator () (Non constant version) More...
 
T_ operator() (size_t i, size_t j) const
 Operator () (Constant version) More...
 
T_ operator() (size_t i) const
 Operator () with one argument (Constant version) More...
 
T_ operator[] (size_t i) const
 Operator [] (Constant version). More...
 
Vect< T_ > operator* (const Vect< T_ > &x) const
 Operator * to multiply matrix by a vector. More...
 
SpMatrix< T_ > & operator*= (const T_ &a)
 Operator *= to premultiply matrix by a constant. More...
 
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. More...
 
void MultAdd (const Vect< T_ > &x, Vect< T_ > &y) const
 Multiply matrix by vector x and add to y. More...
 
void MultAdd (T_ a, const Vect< T_ > &x, Vect< T_ > &y) const
 Multiply matrix by vector a*x and add to y. More...
 
void TMult (const Vect< T_ > &x, Vect< T_ > &y) const
 Multiply transpose of matrix by vector x and save in y. More...
 
void Axpy (T_ a, const SpMatrix< T_ > &m)
 Add to matrix the product of a matrix by a scalar. More...
 
void Axpy (T_ a, const Matrix< T_ > *m)
 Add to matrix the product of a matrix by a scalar. More...
 
void set (size_t i, size_t j, const T_ &val)
 Assign a value to an entry of the matrix. More...
 
void add (size_t i, size_t j, const T_ &val)
 Add a value to an entry of the matrix. More...
 
void operator= (const T_ &x)
 Operator =. More...
 
size_t getColInd (size_t i) const
 Return storage information. More...
 
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. More...
 
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. More...
 
void clear ()
 brief Set all matrix entries to zero
 
T_ * get () const
 Return C-Array. More...
 
T_ get (size_t i, size_t j) const
 Return entry (i,j) of matrix if this one is stored, 0 otherwise. More...
 
- Public Member Functions inherited from Matrix< T_ >
 Matrix ()
 Default constructor. More...
 
 Matrix (const Matrix< T_ > &m)
 Copy Constructor.
 
virtual ~Matrix ()
 Destructor.
 
virtual void reset ()
 Set matrix to 0 and reset factorization parameter. More...
 
size_t getNbRows () const
 Return number of rows.
 
size_t getNbColumns () const
 Return number of columns.
 
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. More...
 
size_t size () 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_ > &x, Vect< T_ > &y) 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
 
virtual void Axpy (T_ a, const Matrix< T_ > *x)=0
 Add to matrix the product of a matrix by a scalar. More...
 
void setDiagonal (Mesh &mesh)
 Initialize matrix storage in the case where only diagonal terms are stored. More...
 
virtual void clear ()
 brief Set all matrix entries to zero
 
void Assembly (const Element &el, T_ *a)
 Assembly of element matrix into global matrix. More...
 
void Assembly (const Side &sd, T_ *a)
 Assembly of side matrix into global matrix. More...
 
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. More...
 
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. More...
 
void Prescribe (Vect< T_ > &b, int flag=0)
 Impose by a penalty method a homegeneous (=0) essential boundary condition. More...
 
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. More...
 
void PrescribeSide ()
 Impose by a penalty method an essential boundary condition when DOFs are supported by sides. More...
 
virtual void add (size_t i, size_t j, const T_ &val)=0
 Add val to entry (i,j).
 
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. More...
 
virtual int solve (const Vect< T_ > &b, Vect< T_ > &x, bool fact=true)=0
 Solve the linear system. More...
 
int FactorAndSolve (Vect< T_ > &b)
 Factorize matrix and solve the linear system. More...
 
int FactorAndSolve (const Vect< T_ > &b, Vect< T_ > &x)
 Factorize matrix and solve the linear system. More...
 
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. More...
 
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).
 
virtual void set (size_t i, size_t j, const T_ &val)=0
 Assign a value to an entry of the matrix. More...
 
virtual T_ & operator() (size_t i, size_t j)=0
 Operator () (Non constant version). More...
 
virtual T_ operator() (size_t i, size_t j) const =0
 Operator () (Non constant version). More...
 
T_ operator() (size_t i) const
 Operator () with one argument (Constant version). More...
 
T_ & operator() (size_t i)
 Operator () with one argument (Non Constant version). More...
 
T_ & operator[] (size_t k)
 Operator [] (Non constant version). More...
 
T_ operator[] (size_t k) const
 Operator [] (Constant version). More...
 
Matrixoperator= (Matrix< T_ > &m)
 Operator =. More...
 
Matrixoperator+= (const Matrix< T_ > &m)
 Operator +=. More...
 
Matrixoperator-= (const Matrix< T_ > &m)
 Operator -=. More...
 
Matrixoperator= (const T_ &x)
 Operator =. More...
 
Matrixoperator*= (const T_ &x)
 Operator *=. More...
 
Matrixoperator+= (const T_ &x)
 Operator +=. More...
 
Matrixoperator-= (const T_ &x)
 Operator -=. More...
 
virtual T_ get (size_t i, size_t j) const =0
 Return entry (i,j) of matrix if this one is stored, 0 else.
 

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 © 1998-2022 Rachid Touzani