Handles small size matrices like element matrices, with a priori known size. More...

Public Member Functions
	LocalMatrix ()
	Default constructor. More...

	LocalMatrix (const LocalMatrix< T_, NR_, NC_ > &m)
	Copy constructor.

	LocalMatrix (Element *el, const SpMatrix< T_ > &a)
	Constructor of a local matrix associated to element from a SpMatrix. More...

	LocalMatrix (Element *el, const SkMatrix< T_ > &a)
	Constructor of a local matrix associated to element from a SkMatrix. More...

	LocalMatrix (Element *el, const SkSMatrix< T_ > &a)
	Constructor of a local matrix associated to element from a SkSMatrix. More...

	~LocalMatrix ()
	Destructor.

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...

void	Localize (Element *el, const SpMatrix< T_ > &a)
	Initialize matrix as element matrix from global SpMatrix. More...

void	Localize (Element *el, const SkMatrix< T_ > &a)
	Initialize matrix as element matrix from global SkMatrix. More...

void	Localize (Element *el, const SkSMatrix< T_ > &a)
	Initialize matrix as element matrix from global SkSMatrix. More...

LocalMatrix< T_, NR_, NC_ > &	operator= (const LocalMatrix< T_, NR_, NC_ > &m)
	Operator `=` More...

void	clear ()
	Clear matrix. More...

LocalMatrix< T_, NR_, NC_ > &	operator= (const T_ &x)
	Operator `=` More...

LocalMatrix< T_, NR_, NC_ > &	operator+= (const LocalMatrix< T_, NR_, NC_ > &m)
	Operator `+=` More...

LocalMatrix< T_, NR_, NC_ > &	operator-= (const LocalMatrix< T_, NR_, NC_ > &m)
	Operator `-=` More...

LocalVect< T_, NR_ >	operator* (LocalVect< T_, NC_ > &x)
	Operator `*` More...

LocalMatrix< T_, NR_, NC_ > &	operator+= (const T_ &x)
	Operator `+=` More...

LocalMatrix< T_, NR_, NC_ > &	operator-= (const T_ &x)
	Operator `-=` More...

LocalMatrix< T_, NR_, NC_ > &	operator*= (const T_ &x)
	Operator `*=` More...

LocalMatrix< T_, NR_, NC_ > &	operator/= (const T_ &x)
	Operator `/=` More...

void	MultAdd (const LocalVect< T_, NC_ > &x, LocalVect< T_, NR_ > &y)
	Multiply matrix by vector and add result to vector. More...

void	MultAddScal (const T_ &a, const LocalVect< T_, NC_ > &x, LocalVect< T_, NR_ > &y)
	Multiply matrix by scaled vector and add result to vector. More...

void	Mult (const LocalVect< T_, NC_ > &x, LocalVect< T_, NR_ > &y)
	Multiply matrix by vector. More...

void	Symmetrize ()
	Symmetrize matrix. More...

int	Factor ()
	Factorize matrix. More...

int	solve (LocalVect< T_, NR_ > &b)
	Forward and backsubstitute to solve a linear system. More...

int	FactorAndSolve (LocalVect< T_, NR_ > &b)
	Factorize matrix and solve linear system. More...

void	Invert (LocalMatrix< T_, NR_, NC_ > &A)
	Calculate inverse of matrix. More...

T_	getInnerProduct (const LocalVect< T_, NC_ > &x, const LocalVect< T_, NR_ > &y)
	Calculate inner product witrh respect to matrix. More...

T_ *	get ()
	Return pointer to matrix as a C-array.

Detailed Description

template<class T_, size_t NR_, size_t NC_>
class OFELI::LocalMatrix< T_, NR_, NC_ >

Handles small size matrices like element matrices, with a priori known size.

The template class LocalMatrix treats small size matrices. Typically, this class is recommended to store element and side arrays.
Internally, no dynamic storage is used.

Template Parameters

T_	Data type (double, float, complex<double>, ...)
NR_	number of rows of matrix
NC_	number of columns of matrix

Author: Rachid Touzani

Copyright: GNU Lesser Public License

Constructor & Destructor Documentation

◆ LocalMatrix() [1/4]

LocalMatrix ( )

Default constructor.

Constructs a matrix with 0 rows and 0 columns

◆ LocalMatrix() [2/4]

LocalMatrix	(	Element *	el,
		const SpMatrix< T_ > &	a
	)

Constructor of a local matrix associated to element from a SpMatrix.

Parameters

[in]	el	Pointer to Element
[in]	a	Global matrix as instance of class SpMatrix.

◆ LocalMatrix() [3/4]

LocalMatrix	(	Element *	el,
		const SkMatrix< T_ > &	a
	)

Constructor of a local matrix associated to element from a SkMatrix.

Parameters

[in]	el	Pointer to Element
[in]	a	Global matrix as instance of class SkMatrix.

◆ LocalMatrix() [4/4]

LocalMatrix	(	Element *	el,
		const SkSMatrix< T_ > &	a
	)

Constructor of a local matrix associated to element from a SkSMatrix.

Parameters

[in]	el	Pointer to Element
[in]	a	Global matrix as instance of class SkSMatrix.

Member Function Documentation

◆ clear()

void clear ( )

Clear matrix.

Set all matrix entries to zero

◆ Factor()

int Factor ( )

Factorize matrix.

Performs a LU factorization.

Returns

0: Factorization has ended normally,
n: n-th pivot was zero.

◆ FactorAndSolve()

int FactorAndSolve ( LocalVect< T_, NR_ > & b )

Factorize matrix and solve linear system.

Parameters

[in,out] b Right-hand side in input and solution vector in output.

Returns: 0 if solution was performed normally. n if n-th pivot is zero. This function simply calls Factor() then Solve(b).

◆ getInnerProduct()

T_ getInnerProduct	(	const LocalVect< T_, NC_ > &	x,
		const LocalVect< T_, NR_ > &	y
	)

Calculate inner product witrh respect to matrix.

Returns the product x^TAy

Parameters

[in]	x	Left vector
[in]	y	Right vector

Returns: Resulting product

◆ Invert()

void Invert ( LocalMatrix< T_, NR_, NC_ > & A )

Calculate inverse of matrix.

Parameters

[out] A Inverse of matrix

◆ Localize() [1/3]

void Localize	(	Element *	el,
		const SpMatrix< T_ > &	a
	)

Initialize matrix as element matrix from global SpMatrix.

Parameters

[in]	el	Pointer to Element
[in]	a	Global matrix as instance of class SpMatrix. This function is called by its corresponding constructor.

◆ Localize() [2/3]

void Localize	(	Element *	el,
		const SkMatrix< T_ > &	a
	)

Initialize matrix as element matrix from global SkMatrix.

Parameters

[in]	el	Pointer to Element
[in]	a	Global matrix as instance of class SkMatrix. This function is called by its corresponding constructor.

◆ Localize() [3/3]

void Localize	(	Element *	el,
		const SkSMatrix< T_ > &	a
	)

Initialize matrix as element matrix from global SkSMatrix.

Parameters

[in]	el	Pointer to Element
[in]	a	Global matrix as instance of class SkSMatrix. This function is called by its corresponding constructor.

◆ Mult()

void Mult	(	const LocalVect< T_, NC_ > &	x,
		LocalVect< T_, NR_ > &	y
	)

Multiply matrix by vector.

Parameters

[in]	x	Vector to multiply matrix by.
[out]	y	Resulting vector.

◆ MultAdd()

void MultAdd	(	const LocalVect< T_, NC_ > &	x,
		LocalVect< T_, NR_ > &	y
	)

Multiply matrix by vector and add result to vector.

Parameters

[in]	x	Vector to multiply matrix by.
[out]	y	Resulting vector (`y += a * x`)

◆ MultAddScal()

void MultAddScal	(	const T_ &	a,
		const LocalVect< T_, NC_ > &	x,
		LocalVect< T_, NR_ > &	y
	)

Multiply matrix by scaled vector and add result to vector.

Parameters

[in]	a	Constant to premultiply by vector `x`.
[in]	x	(Scaled) vector to multiply matrix by.
[out]	y	Resulting vector (`y += a * x`)

◆ operator()() [1/2]

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

Operator () (Non constant version)

Returns entry at row i and column j.

◆ operator()() [2/2]

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

Operator () (Constant version)

Returns entry at row i and column j.

◆ operator*()

LocalVect<T_,NR_> operator* ( LocalVect< T_, NC_ > & x )

Operator *

Return a Vect instance as product of current matrix by vector x.

◆ operator*=()

LocalMatrix<T_,NR_,NC_>& operator*= ( const T_ & x )

Operator *=

Multiply matrix entries by constant x.

◆ operator+=() [1/2]

LocalMatrix<T_,NR_,NC_>& operator+= ( const LocalMatrix< T_, NR_, NC_ > & m )

Operator +=

Add m to current matrix.

◆ operator+=() [2/2]

LocalMatrix<T_,NR_,NC_>& operator+= ( const T_ & x )

Operator +=

Add constant x to current matrix entries.

◆ operator-=() [1/2]

LocalMatrix<T_,NR_,NC_>& operator-= ( const LocalMatrix< T_, NR_, NC_ > & m )

Operator -=

Subtract m from current matrix.

◆ operator-=() [2/2]

LocalMatrix<T_,NR_,NC_>& operator-= ( const T_ & x )

Operator -=

Subtract x from current matrix entries.

◆ operator/=()

LocalMatrix<T_,NR_,NC_>& operator/= ( const T_ & x )

Operator /=

Divide by x current matrix entries.

◆ operator=() [1/2]

LocalMatrix<T_,NR_,NC_>& operator= ( const LocalMatrix< T_, NR_, NC_ > & m )

Operator =

Copy instance m into current instance.

◆ operator=() [2/2]

LocalMatrix<T_,NR_,NC_>& operator= ( const T_ & x )

Operator =

Assign matrix to identity times x

◆ solve()

int solve ( LocalVect< T_, NR_ > & b )

Forward and backsubstitute to solve a linear system.

Parameters

[in] b Right-hand side in input and solution vector in output.

Returns

0: Solution was performed normally.
n: n-th pivot is zero.

Note: Matrix must have been factorized at first.

◆ Symmetrize()

void Symmetrize ( )

Symmetrize matrix.

Fill upper triangle to form a symmetric matrix.

Public Member Functions

Detailed Description

template<class T_, size_t NR_, size_t NC_> class OFELI::LocalMatrix< T_, NR_, NC_ >

Constructor & Destructor Documentation

◆ LocalMatrix() [1/4]

◆ LocalMatrix() [2/4]

◆ LocalMatrix() [3/4]

◆ LocalMatrix() [4/4]

Member Function Documentation

◆ clear()

◆ Factor()

◆ FactorAndSolve()

◆ getInnerProduct()

◆ Invert()

◆ Localize() [1/3]

◆ Localize() [2/3]

◆ Localize() [3/3]

◆ Mult()

◆ MultAdd()

◆ MultAddScal()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*()

◆ operator*=()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ solve()

◆ Symmetrize()

template<class T_, size_t NR_, size_t NC_>
class OFELI::LocalMatrix< T_, NR_, NC_ >