LocalMatrix< T_, NR_, NC_ > Class Template Reference

Handles small size matrices like element matrices. More...

List of all members.

Public Member Functions
	LocalMatrix ()
	Default constructor.
	LocalMatrix (const LocalMatrix< T_, NR_, NC_ > &m)
	Copy constructor.
	LocalMatrix (class Element *el, const class SpMatrix< T_ > &a)
	Constructor of a local matrix associated to element from a SpMatrix.
	LocalMatrix (class Element *el, const class SkMatrix< T_ > &a)
	Constructor of a local matrix associated to element from a SkMatrix.
	LocalMatrix (class Element *el, const class 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 (class Element *el, const class SpMatrix< T_ > &a)
	Initialize matrix as element matrix from global SpMatrix.
void	Localize (class Element *el, const class SkMatrix< T_ > &a)
	Initialize matrix as element matrix from global SkMatrix.
void	Localize (class Element *el, const class SkSMatrix< T_ > &a)
	Initialize matrix as element matrix from global SkSMatrix.
LocalMatrix< T_, NR_, NC_ > &	operator= (const LocalMatrix< T_, NR_, NC_ > &m)
	Operator =.
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* (class 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 class LocalVect< T_, NC_ > &x, class LocalVect< T_, NR_ > &y)
	Multiply matrix by vector and add result to vector.
void	MultAddScal (const T_ &a, const class LocalVect< T_, NC_ > &x, class LocalVect< T_, NR_ > &y)
	Multiply matrix by scaled vector and add result to vector.
void	Mult (const class LocalVect< T_, NC_ > &x, class LocalVect< T_, NR_ > &y)
	Multiply matrix by vector.
void	Symmetrize ()
	Symmetrize matrix.
int	Factor ()
	Factorize matrix.
int	Solve (class LocalVect< T_, NR_ > &b)
	Forward and backsubstitute to solve a linear system.
int	FactorAndSolve (class LocalVect< T_, NR_ > &b)
	Factorize matrix and solve linear system.
void	Invert (LocalMatrix< T_, NR_, NC_ > &A)
	Calculate inverse of matrix.
T_	getInnerProduct (const class LocalVect< T_, NC_ > &x, const class LocalVect< T_, NR_ > &y)
T_ *	getArray ()
	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.

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

---

Constructor & Destructor Documentation

LocalMatrix

(

)

Default constructor.

Initialize matrix entries to zero.

LocalMatrix	(	class Element *	el,
		const class 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	(	class Element *	el,
		const class 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	(	class Element *	el,
		const class 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

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

Operator () (Non constant version).

Returns entry at row i and column j.

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

Operator () (Constant version).

Returns entry at row i and column j.

void Localize	(	class Element *	el,
		const class 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.

void Localize	(	class Element *	el,
		const class 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.

void Localize	(	class Element *	el,
		const class 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.

LocalMatrix< T_, NR_, NC_ > & operator=

(

const LocalMatrix< T_, NR_, NC_ > &

m

)

Operator =.

Copy instance m into current instance.

LocalMatrix< T_, NR_, NC_ > & operator=

(

const T_ &

x

)

Operator =.

Assign x to matrix entries.

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

(

const LocalMatrix< T_, NR_, NC_ > &

m

)

Operator +=.

Add m to current matrix.

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

(

const LocalMatrix< T_, NR_, NC_ > &

m

)

Operator -=.

Subtract m from current matrix.

LocalVect< T_, NR_ > operator*

(

class LocalVect< T_, NC_ > &

x

)

Operator *.

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

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

(

const T_ &

x

)

Operator +=.

Add constant x to current matrix entries.

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

(

const T_ &

x

)

Operator -=.

Subtract x from current matrix entries.

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

(

const T_ &

x

)

Operator *=.

Multiply matrix entries by constant x.

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

(

const T_ &

x

)

Operator /=.

Divide by x current matrix entries.

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

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

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

Multiply matrix by vector.

Parameters:

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

void Symmetrize

(

)

Symmetrize matrix.

Fill upper triangle to form a symmetric matrix.

int Factor

(

)

Factorize matrix.

Performs a LU factorization.

Returns:

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

int Solve

(

class 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.

int FactorAndSolve

(

class 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).

void Invert

(

LocalMatrix< T_, NR_, NC_ > &

A

)

Calculate inverse of matrix.

Parameters:

[out]

A

Inverse of matrix

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

Calculate inner product witrh respect to matrix. Returns the product x^T*A*y

Parameters:

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

Returns:

Resulting product