To handle symmetric dense matrices. More...

#include <DSMatrix.h>

Inheritance diagram for DSMatrix< T_ >:

Public Member Functions
	DSMatrix ()
	Default constructor.

	DSMatrix (size_t dim)
	Constructor that for a symmetric matrix with given number of r‡qows.

	DSMatrix (const DSMatrix< T_ > &m)
	Copy Constructor.

	DSMatrix (Mesh &mesh, size_t dof=0, int is_diagonal=false)
	Constructor using mesh to initialize matrix.

	~DSMatrix ()
	Destructor.

void	setDiag ()
	Store diagonal entries in a separate internal vector.

void	setSize (size_t dim)
	Set size (number of rows) of matrix.

void	set (size_t i, size_t j, const T_ &val)
	Assign constant to entry `(i,j)` of the matrix.

void	getColumn (size_t j, Vect< T_ > &v) const
	Get `j`-th column vector.

Vect< T_ >	getColumn (size_t j) const
	Get `j`-th column vector.

void	getRow (size_t i, Vect< T_ > &v) const
	Get `i`-th row vector.

Vect< T_ >	getRow (size_t i) const
	Get `i`-th row vector.

void	setRow (size_t i, const Vect< T_ > &v)
	Copy a given vector to a prescribed row in the matrix.

void	setColumn (size_t j, const Vect< T_ > &v)
	Copy a given vector to a prescribed column in the matrix.

void	setDiag (const T_ &a)
	Set matrix as diagonal and assign its diagonal entries as a constant.

void	setDiag (const vector< T_ > &d)
	Set matrix as diagonal and assign its diagonal entries.

void	add (size_t i, size_t j, const T_ &val)
	Add constant to an entry ofthe 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).

DSMatrix< T_ > &	operator= (const DSMatrix< T_ > &m)
	Operator `=` Copy matrix `m` to current matrix instance.

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

DSMatrix &	operator+= (const T_ &x)
	Operator +=.

DSMatrix &	operator-= (const T_ &x)
	Operator -=.

int	setLDLt ()
	Factorize matrix (`LDL^T`)

void	MultAdd (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector `a*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 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 add result in `y`.

void	Axpy (T_ a, const DSMatrix< T_ > &m)
	Add to matrix the product of a matrix by a scalar.

void	add (size_t i, const T_ &val)
	Add `val` to entry `i`.

void	Axpy (T_ a, const Matrix< T_ > *m)
	Add to matrix the product of a matrix by a scalar.

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

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

const T_ *	getArray ()
	Return matrix as C-Array. Matrix is stored row by row. Only lower triangle is stored.

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::DSMatrix< T_ >

To handle symmetric dense matrices.

This class enables storing and manipulating symmetric dense matrices.

Template Parameters

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

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Constructor & Destructor Documentation

◆ DSMatrix() [1/3]

template<class T_ >

DSMatrix ( size_t dim )

Constructor that for a symmetric matrix with given number of r‡qows.

Parameters

[in] dim Number of rows

◆ DSMatrix() [2/3]

template<class T_ >

DSMatrix ( const DSMatrix< T_ > & m )

Copy Constructor.

Parameters

[in] m DSMatrix instance to copy

◆ DSMatrix() [3/3]

template<class T_ >

DSMatrix	(	Mesh &	mesh,
		size_t	dof = `0`,
		int	is_diagonal = `false`
	)

Constructor using mesh to initialize matrix.

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.
[in]	is_diagonal	Boolean argument to say is the matrix is actually a diagonal matrix or not.

Member Function Documentation

◆ add()

template<class T_ >

void add	(	size_t	i,
		size_t	j,
		const T_ &	val
	)

virtual

Add constant to an entry ofthe matrix.

Parameters

[in]	i	row index
[in]	j	column index
[in]	val	value to add to `a(i,j)`

Implements Matrix< T_ >.

◆ 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 DSMatrix< T_ > &	m
	)

Add to matrix the product of a matrix by a scalar.

Parameters

[in]	a	Scalar to premultiply
[in]	m	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_ > *	m
	)

virtual

Add to matrix the product of a matrix by a scalar.

Parameters

[in]	a	Scalar to premultiply
[in]	m	Matrix by which `a` is multiplied. The result is added to current instance

Implements Matrix< T_ >.

◆ getColumn() [1/2]

template<class T_ >

Vect< T_ > getColumn ( size_t j ) const

Get j-th column vector.

Parameters

[in] j Index of column to extract

Returns: Vect instance where the column is stored

Remarks: Vector v does not need to be sized before. It is resized in the function

◆ getColumn() [2/2]

template<class T_ >

void getColumn	(	size_t	j,
		Vect< T_ > &	v
	)		const

Get j-th column vector.

Parameters

[in]	j	Index of column to extract
[out]	v	Reference to Vect instance where the column is stored

Remarks: Vector v does not need to be sized before. It is resized in the function

◆ getRow() [1/2]

template<class T_ >

Vect< T_ > getRow ( size_t i ) const

Get i-th row vector.

Parameters

[in] i Index of row to extract

Returns: Vect instance where the row is stored

Remarks: Vector v does not need to be sized before. It is resized in the function

◆ getRow() [2/2]

template<class T_ >

void getRow	(	size_t	i,
		Vect< T_ > &	v
	)		const

Get i-th row vector.

Parameters

[in]	i	Index of row to extract
[out]	v	Reference to Vect instance where the row is stored

Remarks: Vector v does not need to be sized before. It is resized in the function

◆ MultAdd()

template<class T_ >

void MultAdd	(	T_	a,
		const Vect< T_ > &	x,
		Vect< T_ > &	y
	)		const

virtual

Multiply matrix by vector a*x and add to y.

Parameters

[in]	a	Constant to multiply by matrix
[in]	x	Vector to multiply by matrix
[in,out]	y	Vector to add to the result. `y` contains on output the result.

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

Warning: To modify a value of an entry of the matrix it is safer not to modify both lower and upper triangles. Otherwise, wrong values will be assigned. If not sure, use the member functions set or add.

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_ >

DSMatrix & operator+= ( const T_ & x )

Operator +=.

Add constant value x to all matrix entries.

◆ operator-=()

template<class T_ >

DSMatrix & operator-= ( const T_ & x )

Operator -=.

Subtract constant value x from to all matrix entries.

◆ set()

template<class T_ >

void set	(	size_t	i,
		size_t	j,
		const T_ &	val
	)

virtual

Assign constant to entry (i,j) of the matrix.

Parameters

[in]	i	row index
[in]	j	column index
[in]	val	value to assign to `a(i,j)`

Implements Matrix< T_ >.

◆ setColumn()

template<class T_ >

void setColumn	(	size_t	j,
		const Vect< T_ > &	v
	)

Copy a given vector to a prescribed column in the matrix.

Parameters

[in]	j	column index to be assigned
[in]	v	Vect instance to copy

◆ setDiag() [1/2]

template<class T_ >

void setDiag ( const T_ & a )

Set matrix as diagonal and assign its diagonal entries as a constant.

Parameters

[in] a Value to assign to all diagonal entries

◆ setDiag() [2/2]

template<class T_ >

void setDiag ( const vector< T_ > & d )

Set matrix as diagonal and assign its diagonal entries.

Parameters

[in] d Vector entries to assign to matrix diagonal entries

◆ setLDLt()

template<class T_ >

int setLDLt ( )

Factorize matrix (LDL^T)

Returns

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

◆ setRow()

template<class T_ >

void setRow	(	size_t	i,
		const Vect< T_ > &	v
	)

Copy a given vector to a prescribed row in the matrix.

Parameters

[in]	i	row index to be assigned
[in]	v	Vect instance to copy

◆ setSize()

template<class T_ >

void setSize ( size_t dim )

Set size (number of rows) of matrix.

Parameters

[in] dim Number of rows and columns.

◆ solve() [1/2]

template<class T_ >

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

virtual

Solve linear system.

The matrix is factorized using the LDLt (Crout) decomposition. If this one is already factorized, no further factorization is performed. If the matrix has been modified the user has to refactorize it using the function setLDLt.

Parameters

[in]	b	Vect instance that contains right-hand side.
[out]	x	Vect instance that contains solution
[in]	fact	Set true if matrix is to be factorized (Default value), false if not

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 = `true`
	)

virtual

Solve linear system.

The matrix is factorized using the LDLt (Crout) decomposition. If this one is already factorized, no further factorization is performed. If the matrix has been modified the user has to refactorize it using the function setLDLt.

Parameters

[in,out]	b	Vect instance that contains right-hand side on input and solution on output.
[in]	fact	Set true if matrix is to be factorized (Default value), false if not

Returns

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

Implements Matrix< T_ >.

◆ TMult()

template<class T_ >

void TMult	(	const Vect< T_ > &	x,
		Vect< T_ > &	y
	)		const

virtual

Multiply transpose of matrix by vector x and add result in y.

Parameters

[in]	x	Vector to add to `y`
[in,out]	y	on input, vector to add to. On output, result.

Implements Matrix< T_ >.

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ DSMatrix() [1/3]

◆ DSMatrix() [2/3]

◆ DSMatrix() [3/3]

Member Function Documentation

◆ add()

◆ at()

◆ Axpy() [1/2]

◆ Axpy() [2/2]

◆ getColumn() [1/2]

◆ getColumn() [2/2]

◆ getRow() [1/2]

◆ getRow() [2/2]

◆ MultAdd()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator+=()

◆ operator-=()

◆ set()

◆ setColumn()

◆ setDiag() [1/2]

◆ setDiag() [2/2]

◆ setLDLt()

◆ setRow()

◆ setSize()

◆ solve() [1/2]

◆ solve() [2/2]

◆ TMult()