LocalMatrix< T_, NR_, NC_ > Class Template Reference

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

#include <LocalMatrix.h>

Public Member Functions
	LocalMatrix ()
	Default constructor.
	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.
	LocalMatrix (Element *el, const SkMatrix< T_ > &a)
	Constructor of a local matrix associated to element from a SkMatrix.
	LocalMatrix (Element *el, const SkSMatrix< T_ > &a)
	Constructor of a local matrix associated to element from a SkSMatrix.
	~LocalMatrix ()
	Destructor.
T_ &	operator() (size_t i, size_t j)
	Operator () (Non constant version)
T_	operator() (size_t i, size_t j) const
	Operator () (Constant version)
void	Localize (Element *el, const SpMatrix< T_ > &a)
	Initialize matrix as element matrix from global SpMatrix.
void	Localize (Element *el, const SkMatrix< T_ > &a)
	Initialize matrix as element matrix from global SkMatrix.
void	Localize (Element *el, const SkSMatrix< T_ > &a)
	Initialize matrix as element matrix from global SkSMatrix.
LocalMatrix< T_, NR_, NC_ > &	operator= (const LocalMatrix< T_, NR_, NC_ > &m)
	Operator =
void	clear ()
	Clear matrix.
LocalMatrix< T_, NR_, NC_ > &	operator= (const T_ &x)
	Operator =
LocalMatrix< T_, NR_, NC_ > &	operator+= (const LocalMatrix< T_, NR_, NC_ > &m)
	Operator +=
LocalMatrix< T_, NR_, NC_ > &	operator-= (const LocalMatrix< T_, NR_, NC_ > &m)
	Operator -=
LocalVect< T_, NR_ >	operator* (LocalVect< T_, NC_ > &x)
	Operator *
LocalMatrix< T_, NR_, NC_ > &	operator+= (const T_ &x)
	Operator +=
LocalMatrix< T_, NR_, NC_ > &	operator-= (const T_ &x)
	Operator -=
LocalMatrix< T_, NR_, NC_ > &	operator*= (const T_ &x)
	Operator *=
LocalMatrix< T_, NR_, NC_ > &	operator/= (const T_ &x)
	Operator /=
void	MultAdd (const LocalVect< T_, NC_ > &x, LocalVect< T_, NR_ > &y)
	Multiply matrix by vector and add result to vector.
void	MultAddScal (const T_ &a, const LocalVect< T_, NC_ > &x, LocalVect< T_, NR_ > &y)
	Multiply matrix by scaled vector and add result to vector.
void	Mult (const LocalVect< T_, NC_ > &x, LocalVect< T_, NR_ > &y)
	Multiply matrix by vector.
void	Symmetrize ()
	Symmetrize matrix.
int	Factor ()
	Factorize matrix.
int	solve (LocalVect< T_, NR_ > &b)
	Forward and backsubstitute to solve a linear system.
int	FactorAndSolve (LocalVect< T_, NR_ > &b)
	Factorize matrix and solve linear system.
void	Invert (LocalMatrix< T_, NR_, NC_ > &A)
	Calculate inverse of matrix.
T_	getInnerProduct (const LocalVect< T_, NC_ > &x, const LocalVect< T_, NR_ > &y)
	Calculate inner product witrh respect to matrix.
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]

template<class T_ , size_t NR_, size_t NC_>

LocalMatrix

(

)

Default constructor.

Constructs a matrix with 0 rows and 0 columns

LocalMatrix() [2/4]

template<class T_ , size_t NR_, size_t NC_>

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]

template<class T_ , size_t NR_, size_t NC_>

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]

template<class T_ , size_t NR_, size_t NC_>

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()

template<class T_ , size_t NR_, size_t NC_>

void clear

(

)

Clear matrix.

Set all matrix entries to zero

Factor()

template<class T_ , size_t NR_, size_t NC_>

int Factor

(

)

Factorize matrix.

Performs a LU factorization.

Returns

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

FactorAndSolve()

template<class T_ , size_t NR_, size_t NC_>

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()

template<class T_ , size_t NR_, size_t NC_>

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

Calculate inner product witrh respect to matrix.

Returns the product xTAy

Parameters

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

Returns

Resulting product

Invert()

template<class T_ , size_t NR_, size_t NC_>

void Invert

(

LocalMatrix< T_, NR_, NC_ > &

A

)

Calculate inverse of matrix.

Parameters

[out]

A

Inverse of matrix

Localize() [1/3]

template<class T_ , size_t NR_, size_t NC_>

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() [2/3]

template<class T_ , size_t NR_, size_t NC_>

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.

Localize() [3/3]

template<class T_ , size_t NR_, size_t NC_>

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.

Mult()

template<class T_ , size_t NR_, size_t NC_>

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()

template<class T_ , size_t NR_, size_t NC_>

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()

template<class T_ , size_t NR_, size_t NC_>

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]

template<class T_ , size_t NR_, size_t NC_>

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

Operator () (Non constant version)

Returns entry at row i and column j.

operator()() [2/2]

template<class T_ , size_t NR_, size_t NC_>

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

Operator () (Constant version)

Returns entry at row i and column j.

operator*()

template<class T_ , size_t NR_, size_t NC_>

LocalVect< T_, NR_ > operator*

(

LocalVect< T_, NC_ > &

x

)

Operator *

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

operator*=()

template<class T_ , size_t NR_, size_t NC_>

LocalMatrix< T_, NR_, NC_ > & operator*=

(

const T_ &

x

)

Operator *=

Multiply matrix entries by constant x.

operator+=() [1/2]

template<class T_ , size_t NR_, size_t NC_>

LocalMatrix< T_, NR_, NC_ > & operator+=

(

const LocalMatrix< T_, NR_, NC_ > &

m

)

Operator +=

Add m to current matrix.

operator+=() [2/2]

template<class T_ , size_t NR_, size_t NC_>

LocalMatrix< T_, NR_, NC_ > & operator+=

(

const T_ &

x

)

Operator +=

Add constant x to current matrix entries.

operator-=() [1/2]

template<class T_ , size_t NR_, size_t NC_>

LocalMatrix< T_, NR_, NC_ > & operator-=

(

const LocalMatrix< T_, NR_, NC_ > &

m

)

Operator -=

Subtract m from current matrix.

operator-=() [2/2]

template<class T_ , size_t NR_, size_t NC_>

LocalMatrix< T_, NR_, NC_ > & operator-=

(

const T_ &

x

)

Operator -=

Subtract x from current matrix entries.

operator/=()

template<class T_ , size_t NR_, size_t NC_>

LocalMatrix< T_, NR_, NC_ > & operator/=

(

const T_ &

x

)

Operator /=

Divide by x current matrix entries.

operator=() [1/2]

template<class T_ , size_t NR_, size_t NC_>

LocalMatrix< T_, NR_, NC_ > & operator=

(

const LocalMatrix< T_, NR_, NC_ > &

m

)

Operator =

Copy instance m into current instance.

operator=() [2/2]

template<class T_ , size_t NR_, size_t NC_>

LocalMatrix< T_, NR_, NC_ > & operator=

(

const T_ &

x

)

Operator =

Assign matrix to identity times x

solve()

template<class T_ , size_t NR_, size_t NC_>

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()

template<class T_ , size_t NR_, size_t NC_>

void Symmetrize

(

)

Symmetrize matrix.

Fill upper triangle to form a symmetric matrix.