To handle band matrices. More...

#include <BMatrix.h>

Inheritance diagram for BMatrix< T_ >:

Public Member Functions
	BMatrix ()
	Default constructor.

	BMatrix (size_t size, int ld, int ud)
	Constructor that for a band matrix with given size and bandwidth.

	BMatrix (const BMatrix &m)
	Copy Constructor.

	~BMatrix ()
	Destructor.

void	setSize (size_t size, int ld, int ud)
	Set size (number of rows) and storage 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 BMatrix< 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_ &val)
	Add 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.

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).

BMatrix< T_ > &	operator= (const BMatrix< T_ > &m)
	Operator =.

BMatrix< T_ > &	operator= (const T_ &x)
	Operator = Assign matrix to identity times `x`.

BMatrix< T_ > &	operator*= (const T_ &x)
	Operator *=.

BMatrix< T_ > &	operator+= (const T_ &x)
	Operator +=.

int	setLU ()
	Factorize the matrix (LU factorization)

int	solve (Vect< T_ > &b, bool fact=false)
	Solve linear system.

int	solve (const Vect< T_ > &b, Vect< T_ > &x, bool fact=false)
	Solve linear system.

T_ *	get () const
	Return C-Array.

T_	get (size_t i, size_t j) const
	Return entry `(i,j)` of matrix.

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.

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::BMatrix< T_ >

To handle band matrices.

This class enables storing and manipulating band matrices. The matrix can have different numbers of lower and upper co-diagonals

Template Parameters

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

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Constructor & Destructor Documentation

◆ BMatrix() [1/2]

template<class T_ >

BMatrix ( )

Default constructor.

Initialize a zero dimension band matrix

◆ BMatrix() [2/2]

template<class T_ >

BMatrix	(	size_t	size,
		int	ld,
		int	ud
	)

Constructor that for a band matrix with given size and bandwidth.

Assign 0 to all matrix entries.

Parameters

[in]	size	Number of rows and columns
[in]	ld	Number of lower co-diagonals (must be >= 0)
[in]	ud	Number of upper co-diagonals (must be >= 0)

Remarks: Works only if ud+ld+1 <= size

Member Function Documentation

◆ at()

template<class T_ >

T_ at	(	size_t	i,
		size_t	j
	)

virtual

Return a value of a matrix entry.

Parameters

[in]	i	Row index (starts at 1)
[in]	j	Column index (starts at 1)

Implements Matrix< T_ >.

◆ Axpy() [1/2]

template<class T_ >

void Axpy	(	T_	a,
		const BMatrix< 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

◆ Axpy() [2/2]

template<class T_ >

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_ >.

◆ operator()() [1/2]

template<class 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_ >.

◆ operator()() [2/2]

template<class 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_ >.

◆ operator*=()

template<class T_ >

BMatrix< T_ > & operator*= ( const T_ & x )

Operator *=.

Premultiply matrix entries by constant value x

◆ operator+=()

template<class T_ >

BMatrix< T_ > & operator+= ( const T_ & x )

Operator +=.

Add constant x to matrix entries.

◆ operator=()

template<class T_ >

BMatrix< T_ > & operator= ( const BMatrix< T_ > & m )

Operator =.

Copy matrix m to current matrix instance.

◆ setLU()

template<class T_ >

int setLU ( )

Factorize the matrix (LU factorization)

LU factorization of the matrix is realized. Note that since this is an in place factorization, the contents of the matrix are modified.

Returns

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

Remarks: A flag in this class indicates after factorization that this one has been realized, so that, if the member function solve is called after this no further factorization is done.

◆ setSize()

template<class T_ >

void setSize	(	size_t	size,
		int	ld,
		int	ud
	)

Set size (number of rows) and storage of matrix.

Parameters

[in]	size	Number of rows and columns
[in]	ld	Number of lower co-diagonals (must be > 0)
[in]	ud	Number of upper co-diagonals (must be > 0)

◆ solve() [1/2]

template<class T_ >

int solve	(	const Vect< T_ > &	b,
		Vect< T_ > &	x,
		bool	fact = `false`
	)

virtual

Solve linear system.

The linear system having the current instance as a matrix is solved by using the LU decomposition. Solution is thus realized after a factorization step and a forward/backward substitution step. The factorization step is realized only if this was not already done.
Note that this function modifies the matrix contents is a factorization is performed. Naturally, if the the matrix has been modified after using this function, the user has to refactorize it using the function setLU. This is because the class has no non-expensive way to detect if the matrix has been modified. The function setLU realizes the factorization step only.

Parameters

[in]	b	Vect instance that contains right-hand side.
[out]	x	Vect instance that contains solution
[in]	fact	Unused argument

Returns

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

Implements Matrix< T_ >.

◆ solve() [2/2]

template<class T_ >

int solve	(	Vect< T_ > &	b,
		bool	fact = `false`
	)

virtual

Solve linear system.

The linear system having the current instance as a matrix is solved by using the LU decomposition. Solution is thus realized after a factorization step and a forward/backward substitution step. The factorization step is realized only if this was not already done.
Note that this function modifies the matrix contents is a factorization is performed. Naturally, if the the matrix has been modified after using this function, the user has to refactorize it using the function setLU. This is because the class has no non-expensive way to detect if the matrix has been modified. The function setLU realizes the factorization step only.

Parameters

[in,out]	b	Vect instance that contains right-hand side on input and solution on output.
[in]	fact	Unused argument

Returns

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

Implements Matrix< T_ >.

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ BMatrix() [1/2]

◆ BMatrix() [2/2]

Member Function Documentation

◆ at()

◆ Axpy() [1/2]

◆ Axpy() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=()

◆ operator+=()

◆ operator=()

◆ setLU()

◆ setSize()

◆ solve() [1/2]

◆ solve() [2/2]