Matrix< T_ > Class Template Reference

Virtual class to handle matrices for all storage formats. More...

Inheritance diagram for Matrix< T_ >:

Public Member Functions
	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.
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. 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 void	add (size_t i, const T_ &val)=0
	Add val to entry i.
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_	at (size_t i, size_t j)=0
	Return a value of a matrix entry. 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...
Matrix &	operator= (Matrix< T_ > &m)
	Operator =. More...
Matrix &	operator+= (const Matrix< T_ > &m)
	Operator +=. More...
Matrix &	operator-= (const Matrix< T_ > &m)
	Operator -=. More...
Matrix &	operator= (const T_ &x)
	Operator =. More...
Matrix &	operator*= (const T_ &x)
	Operator *=. More...
Matrix &	operator+= (const T_ &x)
	Operator +=. More...
Matrix &	operator-= (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::Matrix< T_ >

Virtual class to handle matrices for all storage formats.

This class enables storing and manipulating dense matrices. The template parameter is the type of matrix entries. Any matrix entry can be accessed by the () operator: For instance, if A is an instance of this class, A(i,j) stands for the entry at the i-th row and j-th column, i and j starting from 1. Entries of A can be assigned a value by the same operator.

Template Parameters

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

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Constructor & Destructor Documentation

Matrix()

Matrix

(

)

Default constructor.

Initializes a zero-size matrix.

Member Function Documentation

Assembly() [1/2]

void Assembly	(	const Element &	el,
		T_ *	a
	)

Assembly of element matrix into global matrix.

Case where element matrix is given by a C-array.

Parameters

[in]	el	Pointer to element instance
[in]	a	Element matrix as a C-array

Assembly() [2/2]

void Assembly	(	const Side &	sd,
		T_ *	a
	)

Assembly of side matrix into global matrix.

Case where side matrix is given by a C-array.

Parameters

[in]	sd	Pointer to side instance
[in]	a	Side matrix as a C-array instance

at()

virtual T_ at ( size_t  i, size_t  j  )

pure virtual

Return a value of a matrix entry.

Parameters

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

Implemented in SpMatrix< T_ >, SpMatrix< real_t >, DMatrix< T_ >, DMatrix< real_t >, SkSMatrix< T_ >, SkMatrix< T_ >, DSMatrix< T_ >, DSMatrix< real_t >, TrMatrix< T_ >, BMatrix< T_ >, and BMatrix< real_t >.

Axpy()

virtual void Axpy ( T_  a, const Matrix< T_ > *  x  )

pure 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

Implemented in SpMatrix< T_ >, SpMatrix< real_t >, DSMatrix< T_ >, DSMatrix< real_t >, DMatrix< T_ >, DMatrix< real_t >, SkSMatrix< T_ >, SkMatrix< T_ >, TrMatrix< T_ >, BMatrix< T_ >, and BMatrix< real_t >.

FactorAndSolve() [1/2]

int FactorAndSolve

(

Vect< T_ > &

b

)

Factorize matrix and solve the linear system.

This is available only if the storage cass enables it.

Parameters

[in,out]

b

Vect instance that contains right-hand side on input and solution on output

FactorAndSolve() [2/2]

int FactorAndSolve	(	const Vect< T_ > &	b,
		Vect< T_ > &	x
	)

Factorize matrix and solve the linear system.

This is available only if the storage class enables it.

Parameters

[in]	b	Vect instance that contains right-hand side
[out]	x	Vect instance that contains solution

Returns

• 0 if solution was normally performed
• n if the n-th pivot is nul

getDiag()

T_ getDiag

(

size_t

k

)

const

Return k-th diagonal entry of matrix.

First entry is given by getDiag(1).

isFactorized()

int isFactorized

(

)

const

Say if matrix is factorized or not.

If the matrix was not factorized, the class does not allow solving by a direct solver.

operator()() [1/4]

virtual T_& operator() ( size_t  i, size_t  j  )

pure virtual

Operator () (Non constant version).

Returns the (i,j) entry of the matrix.

Parameters

[in]	i	Row index
[in]	j	Column index

Implemented in SpMatrix< T_ >, SpMatrix< real_t >, DMatrix< T_ >, DMatrix< real_t >, SkSMatrix< T_ >, SkMatrix< T_ >, DSMatrix< T_ >, DSMatrix< real_t >, TrMatrix< T_ >, BMatrix< T_ >, and BMatrix< real_t >.

operator()() [2/4]

virtual T_ operator() ( size_t  i, size_t  j  ) const

pure virtual

Operator () (Non constant version).

Returns the (i,j) entry of the matrix.

Parameters

[in]	i	Row index
[in]	j	Column index

Implemented in SpMatrix< T_ >, SpMatrix< real_t >, DMatrix< T_ >, DMatrix< real_t >, SkSMatrix< T_ >, SkMatrix< T_ >, DSMatrix< T_ >, DSMatrix< real_t >, TrMatrix< T_ >, BMatrix< T_ >, and BMatrix< real_t >.

operator()() [3/4]

T_ operator()

(

size_t

i

)

const

Operator () with one argument (Constant version).

Returns i-th position in the array storing matrix entries. The first entry is at location 1. Entries are stored row by row.

Parameters

[in]

i

entry index

operator()() [4/4]

T_& operator()

(

size_t

i

)

Operator () with one argument (Non Constant version).

Returns i-th position in the array storing matrix entries. The first entry is at location 1. Entries are stored row by row.

Parameters

[in]

i

entry index

operator*=()

Matrix& operator*=

(

const T_ &

x

)

Operator *=.

Premultiply matrix entries by constant value x

operator+=() [1/2]

Matrix& operator+=

(

const Matrix< T_ > &

m

)

Operator +=.

Add matrix m to current matrix instance.

operator+=() [2/2]

Matrix& operator+=

(

const T_ &

x

)

Operator +=.

Add constant value x to all matrix entries.

operator-=() [1/2]

Matrix& operator-=

(

const Matrix< T_ > &

m

)

Operator -=.

Subtract matrix m from current matrix instance.

operator-=() [2/2]

Matrix& operator-=

(

const T_ &

x

)

Operator -=.

Subtract constant value x from all matrix entries.

operator=() [1/2]

Matrix& operator=

(

Matrix< T_ > &

m

)

Operator =.

Copy matrix m to current matrix instance.

operator=() [2/2]

Matrix& operator=

(

const T_ &

x

)

Operator =.

Assign constant value x to all matrix entries.

operator[]() [1/2]

T_& operator[]

(

size_t

k

)

Operator [] (Non constant version).

Returns k-th stored element in matrix Index k starts at 0.

operator[]() [2/2]

T_ operator[]

(

size_t

k

)

const

Operator [] (Constant version).

Returns k-th stored element in matrix Index k starts at 0.

Prescribe() [1/4]

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.

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. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).

Parameters

[in,out]	b	Vect instance that contains right-hand side.
[in]	u	Vect instance that contains 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).

Prescribe() [2/4]

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.

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. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).

Parameters

[in]	dof	Degree of freedom for which a boundary condition is to be enforced
[in]	code	Code for which a boundary condition is to be enforced
[in,out]	b	Vect instance that contains right-hand side.
[in]	u	Vect instance that contains 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).

Prescribe() [3/4]

void Prescribe	(	Vect< T_ > &	b,
		int	flag = 0
	)

Impose by a penalty method a homegeneous (=0) 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. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).

Parameters

[in,out]	b	Vect instance that contains right-hand side.
[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).

Prescribe() [4/4]

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.

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. This gunction is to be used if only one DOF per node is treated in the linear system. The penalty parameter is by default equal to 1.e20. It can be modified by member function setPenal.

Parameters

[in]	dof	Label of the concerned degree of freedom (DOF).
[in,out]	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).

PrescribeSide()

void PrescribeSide

(

)

Impose by a penalty method an essential boundary condition when DOFs are supported by sides.

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. The penalty parameter is defined by default equal to 1.e20. It can be modified by member function setPenal(..).

reset()

virtual void reset ( )

virtual

Set matrix to 0 and reset factorization parameter.

Warning

This function must be used if after a factorization, the matrix has been modified

Reimplemented in DMatrix< T_ >, and DMatrix< real_t >.

set()

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

pure virtual

Assign a value to an entry of the matrix.

Parameters

[in]	i	Row index
[in]	j	Column index
[in]	val	Value to assign

Implemented in SpMatrix< T_ >, SpMatrix< real_t >, SkSMatrix< T_ >, DMatrix< T_ >, DMatrix< real_t >, SkMatrix< T_ >, TrMatrix< T_ >, BMatrix< T_ >, BMatrix< real_t >, DSMatrix< T_ >, and DSMatrix< real_t >.

setDiagonal()

void setDiagonal

(

Mesh &

mesh

)

Initialize matrix storage in the case where only diagonal terms are stored.

This member function is to be used for explicit time integration schemes

solve() [1/2]

virtual int solve ( Vect< T_ > &  b, bool  fact = true  )

pure virtual

Solve the linear system.

If the inherited class is SpMatrix, the function uses an iterative method once this one has been chosen. Otherwise, the method solves the linear system by factorization.

Implemented in DMatrix< T_ >, DMatrix< real_t >, SkSMatrix< T_ >, SkMatrix< T_ >, DSMatrix< T_ >, DSMatrix< real_t >, BMatrix< T_ >, BMatrix< real_t >, and TrMatrix< T_ >.

solve() [2/2]

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

pure virtual

Solve the linear system.

If the inherited class is SpMatrix, the function uses an iterative method once this one has been chosen. Otherwise, the method solves the linear system by factorization.

Parameters

[in]	b	Vect instance that contains right-hand side
[out]	x	Vect instance that contains solution
[in]	fact	Set to true if factorization is to be performed, false if not. [Default: true]

Returns

• 0 if solution was normally performed
• n if the n-th pivot is null
  Solution is performed only is factorization has previouly been invoked.

Implemented in SpMatrix< T_ >, SpMatrix< real_t >, DMatrix< T_ >, DMatrix< real_t >, SkSMatrix< T_ >, SkMatrix< T_ >, DSMatrix< T_ >, DSMatrix< real_t >, BMatrix< T_ >, BMatrix< real_t >, and TrMatrix< T_ >.