To handle square matrices in skyline storage format. More...

#include <SkMatrix.h>

Inheritance diagram for SkMatrix< T_ >:

Public Member Functions
	SkMatrix ()
	Default constructor.

	SkMatrix (size_t size, int is_diagonal=false)
	Constructor that initializes a dense symmetric matrix.

	SkMatrix (Mesh &mesh, size_t dof=0, int is_diagonal=false)
	Constructor using mesh to initialize skyline structure of matrix.

	SkMatrix (const vector< size_t > &ColHt)
	Constructor that initializes skyline structure of matrix using vector of column heights.

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

	~SkMatrix ()
	Destructor.

void	setMesh (Mesh &mesh, size_t dof=0)
	Determine mesh graph and initialize matrix.

void	setSkyline (Mesh &mesh)
	Determine matrix structure.

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

void	setDOF (size_t i)
	Choose DOF to activate.

void	set (size_t i, size_t j, const T_ &val)
	Assign a value to an entry ofthe matrix.

void	Axpy (T_ a, const SkMatrix< 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	MultAdd (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector `x` and add to `y`.

void	TMultAdd (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply transpose of matrix by vector `x` and add to `y`.

void	MultAdd (T_ a, const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by a vector and add to another one.

void	Mult (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply matrix by vector `x` and save in `y`.

void	TMult (const Vect< T_ > &x, Vect< T_ > &y) const
	Multiply transpose of matrix by vector `x` and save in `y`.

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

size_t	getColHeight (size_t i) const
	Return column height.

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).

void	DiagPrescribe (Mesh &mesh, Vect< T_ > &b, const Vect< T_ > &u, int flag=0)
	Impose an essential boundary condition.

void	DiagPrescribe (Vect< T_ > &b, const Vect< T_ > &u, int flag=0)
	Impose an essential boundary condition using the Mesh instance provided by the constructor.

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

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

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

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

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

int	setLU ()
	Factorize the matrix (LU factorization)

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.

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 else.

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::SkMatrix< T_ >

To handle square matrices in skyline storage format.

This template class allows storing and manipulating a matrix in skyline storage format.

The matrix entries are stored in 2 vectors column by column as in the following example:

/                    \        /                       \ 
| l0            .    |        | u0   u1    0   0   u7 |
| l1  l2        .    |        |      u2   u3   0   u8 |
|  0  l3  l4    .    |        | ...       u4  u5   u9 |
|  0   0  l5  l6     |        |               u6  u10 |
| l7  l8  l9 l10 l11 |        |                   u11 |
\                    /        \                       /

Template Parameters

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

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Constructor & Destructor Documentation

◆ SkMatrix() [1/4]

template<class T_ >

SkMatrix ( )

Default constructor.

Initializes a zero-dimension matrix

◆ SkMatrix() [2/4]

template<class T_ >

SkMatrix	(	size_t	size,
		int	is_diagonal = `false`
	)

Constructor that initializes a dense symmetric matrix.

Normally, for a dense matrix this is not the right class.

Parameters

[in]	size	Number of matrix rows (and columns).
[in]	is_diagonal	Boolean to select if the matrix is diagonal or not [Default: false]

◆ SkMatrix() [3/4]

template<class T_ >

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

Constructor using mesh to initialize skyline structure of 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.

◆ SkMatrix() [4/4]

template<class T_ >

SkMatrix ( const vector< size_t > & ColHt )

Constructor that initializes skyline structure of matrix using vector of column heights.

Parameters

[in] ColHt Vect instance that contains rows lengths of matrix.

Member Function Documentation

◆ add()

template<class T_ >

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

virtual

Add a constant value to an entry ofthe matrix.

Parameters

[in]	i	Row index
[in]	j	Column index
[in]	val	Constant 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 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_ >.

◆ Axpy() [2/2]

template<class T_ >

void Axpy	(	T_	a,
		const SkMatrix< 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

◆ DiagPrescribe() [1/2]

template<class T_ >

void DiagPrescribe	(	Mesh &	mesh,
		Vect< T_ > &	b,
		const Vect< T_ > &	u,
		int	flag = `0`
	)

Impose an essential boundary condition.

This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. It can be modified by member function setPenal(..).

Parameters

[in]	mesh	Mesh instance from which information is extracted.
[in]	b	Vect instance that contains right-hand side.
[in]	u	Vect instance that conatins imposed valued at DOFs where they are to be imposed.
[in]	flag	Parameter to determine whether only the right-hand side is to be modified (`dof>0`) or both matrix and right-hand side (`dof=0`, default value).

◆ DiagPrescribe() [2/2]

template<class T_ >

void DiagPrescribe	(	Vect< T_ > &	b,
		const Vect< T_ > &	u,
		int	flag = `0`
	)

Impose an essential boundary condition using the Mesh instance provided by the constructor.

This member function modifies diagonal terms in matrix and terms in vector that correspond to degrees of freedom with nonzero code in order to impose a boundary condition. It can be modified by member function setPenal(..).

Parameters

[in]	b	Vect instance that contains right-hand side.
[in]	u	Vect instance that conatins imposed valued at DOFs where they are to be imposed.
[in]	flag	Parameter to determine whether only the right-hand side is to be modified (`dof>0`) or both matrix and right-hand side (`dof=0`, default value).

◆ get()

template<class T_ >

T_ * get ( ) const

Return C-Array.

Skyline of matrix is stored row by row.

◆ getColHeight()

template<class T_ >

size_t getColHeight ( size_t i ) const

Return column height.

Column height at entry i is returned.

◆ Mult()

template<class T_ >

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

virtual

Multiply matrix by vector x and save in y.

Parameters

[in]	x	Vector to multiply by matrix
[out]	y	Vector that contains on output the result.

Implements Matrix< T_ >.

◆ MultAdd() [1/2]

template<class T_ >

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

virtual

Multiply matrix by vector x and add to y.

Parameters

[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_ >.

◆ MultAdd() [2/2]

template<class T_ >

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

virtual

Multiply matrix by a vector and add to another one.

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

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_ >

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

Operator *=.

Premultiply matrix entries by constant value x.

◆ operator+=() [1/2]

template<class T_ >

SkMatrix< T_ > & operator+= ( const SkMatrix< T_ > & m )

Operator +=.

Add matrix m to current matrix instance.

◆ operator+=() [2/2]

template<class T_ >

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

Operator +=.

Add constant value x to matrix entries.

◆ operator=() [1/2]

template<class T_ >

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

Operator =.

Copy matrix m to current matrix instance.

◆ operator=() [2/2]

template<class T_ >

SkMatrix< T_ > & operator= ( const T_ & x )

Operator =.

define the matrix as a diagonal one with all diagonal entries equal to x.

◆ set()

template<class T_ >

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

virtual

Assign a value to an entry ofthe matrix.

Parameters

[in]	i	Row index (starting at `i=1`)
[in]	j	Column index (starting at `i=1`)
[in]	val	Value to assign to entry `a(i,j)`

Implements Matrix< T_ >.

◆ setDOF()

template<class T_ >

void setDOF ( size_t i )

Choose DOF to activate.

This function is available only if variable dof is equal to 1 in the constructor

Parameters

[in] i Index of the DOF

◆ 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.

◆ setMesh()

template<class T_ >

void setMesh	(	Mesh &	mesh,
		size_t	dof = `0`
	)

Determine mesh graph and initialize matrix.

This member function is called by constructor with the same arguments

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.

◆ setSkyline()

template<class T_ >

void setSkyline ( Mesh & mesh )

Determine matrix structure.

This member function calculates matrix structure using a Mesh instance.

Parameters

[in] mesh Mesh instance

◆ solve() [1/2]

template<class T_ >

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

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	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 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	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 save in y.

Parameters

[in]	x	Vector to multiply by matrix
[out]	y	Vector that contains on output the result.

Implements Matrix< T_ >.

◆ TMultAdd()

template<class T_ >

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

Multiply transpose of matrix by vector x and add to y.

Parameters

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

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ SkMatrix() [1/4]

◆ SkMatrix() [2/4]

◆ SkMatrix() [3/4]

◆ SkMatrix() [4/4]

Member Function Documentation

◆ add()

◆ at()

◆ Axpy() [1/2]

◆ Axpy() [2/2]

◆ DiagPrescribe() [1/2]

◆ DiagPrescribe() [2/2]

◆ get()

◆ getColHeight()

◆ Mult()

◆ MultAdd() [1/2]

◆ MultAdd() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ set()

◆ setDOF()

◆ setLU()

◆ setMesh()

◆ setSkyline()

◆ solve() [1/2]

◆ solve() [2/2]

◆ TMult()

◆ TMultAdd()