Vector and Matrix

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Detailed Description

A module that groups vector and matrix related classes.

Classes
class	AbsVect
	This is a template abstract class from which inherit finite element oriented vectors. More...
class	BCVect
	To treat vectors that contain imposed boundary conditions. More...
class	DMatrix
	To store dense matrices. More...
class	DSMatrix
	To store symmetric dense matrices. More...
class	EdgeVect
	Defines an edgewise vector. More...
class	ElementVect
	Defines an elementwise vector. More...
class	LocalMatrix
	Handles small size matrices like element matrices. More...
class	LocalVect
	Handles small size vectors like element vectors. More...
class	NodeVect
	Defines a nodewise vector. More...
class	SideVect
	Defines a sidewise vector. More...
class	SkMatrix
	To handle square matrices in skyline storage format. More...
class	SkSMatrix
	To handle symmetric matrices in skyline storage format. More...
class	SpMatrix
	To handle matrices in sparse storage format. More...
class	TrMatrix
	To store tridiagonal matrices. More...
class	Vect
	To handle general purpose vectors. More...
Functions
template<class T_, size_t N_>
void	Axpy (T_ a, const LocalVect< T_, N_ > &x, LocalVect< T_, N_ > &y)
	Add a*x to vector y.
template<class T_, size_t N_>
void	Copy (const LocalVect< T_, N_ > &x, LocalVect< T_, N_ > &y)
	Copy vector x into vector y.
template<class T_>
T_	Dot (const Vect< T_ > &x, const Vect< T_ > &y)
	Calculate dot product of two vectors.
template<class T_, size_t N_>
double	Dot (const LocalVect< T_, N_ > &a, const LocalVect< T_, N_ > &b)
	Calculate dot product of 2 vectors (instances of class LocalVect).
template<class T_>
Vect< T_ >	operator* (T_ a, const Vect< T_ > &x)
	Operator * (Multiplication of vector by constant).
template<class T_>
TrMatrix< T_ >	operator* (T_ a, const TrMatrix< T_ > &A)
	Operator * (Premultiplication of matrix by constant).
template<class T_, size_t N_>
LocalVect< T_, N_ >	operator* (T_ a, const LocalVect< T_, N_ > &x)
	Operator * (Premultiplication of vector by constant).
template<class T_, size_t NR_, size_t NC_>
LocalMatrix< T_, NR_, NC_ >	operator* (T_ a, const LocalMatrix< T_, NR_, NC_ > &x)
	Operator * (Multiply matrix x by scalar a).
template<class T_>
Vect< T_ >	operator+ (const Vect< T_ > &x, const Vect< T_ > &y)
	Operator + (Addition of two instances of class Vect).
template<class T_, size_t N_>
LocalVect< T_, N_ >	operator+ (const LocalVect< T_, N_ > &x, const LocalVect< T_, N_ > &y)
	Operator + (Add two vectors).
template<class T_, size_t NR_, size_t NC_>
LocalMatrix< T_, NR_, NC_ >	operator+ (const LocalMatrix< T_, NR_, NC_ > &x, const LocalMatrix< T_, NR_, NC_ > &y)
	Operator + (Add matrix x to y).
template<class T_>
Vect< T_ >	operator- (const Vect< T_ > &x, const Vect< T_ > &y)
	Operator - (Difference between two instances of class Vect).
template<class T_, size_t N_>
LocalVect< T_, N_ >	operator- (const LocalVect< T_, N_ > &x, const LocalVect< T_, N_ > &y)
	Operator - (Subtract two vectors).
template<class T_, size_t NR_, size_t NC_>
LocalMatrix< T_, NR_, NC_ >	operator- (const LocalMatrix< T_, NR_, NC_ > &x, const LocalMatrix< T_, NR_, NC_ > &y)
	Operator - (Subtract matrix y from x).
template<class T_, size_t N_>
LocalVect< T_, N_ >	operator/ (T_ a, const LocalVect< T_, N_ > &x)
	Operator / (Division of vector by constant).
template<class T_, size_t NR_, size_t NC_>
LocalMatrix< T_, NR_, NC_ >	operator/ (T_ a, const LocalMatrix< T_, NR_, NC_ > &x)
	Operator / (Divide matrix x by scalar a).
template<class T_>
ostream &	operator<< (ostream &s, const Vect< T_ > &v)
	Output vector in output stream.
template<class T_>
ostream &	operator<< (ostream &s, const TrMatrix< T_ > &a)
	Output matrix in output stream.
template<class T_>
ostream &	operator<< (ostream &s, const SpMatrix< T_ > &a)
	Output matrix in output stream.
template<class T_>
ostream &	operator<< (ostream &s, const SkSMatrix< T_ > &a)
	Output matrix in output stream.
template<class T_>
ostream &	operator<< (ostream &s, const SkMatrix< T_ > &a)
	Output matrix in output stream.
template<class T_>
ostream &	operator<< (ostream &s, const SideVect< T_ > &v)
	Output vector in output stream.
template<class T_>
ostream &	operator<< (ostream &s, const NodeVect< T_ > &v)
	Output vector in output stream.
template<class T_, size_t N_>
ostream &	operator<< (ostream &s, const LocalVect< T_, N_ > &v)
	Output vector in output stream.
template<class T_, size_t NR_, size_t NC_>
ostream &	operator<< (ostream &s, const LocalMatrix< T_, NR_, NC_ > &a)
	Output vector in output stream.
template<class T_>
ostream &	operator<< (ostream &s, const ElementVect< T_ > &v)
	Output vector in output stream.
template<class T_>
ostream &	operator<< (ostream &s, const EdgeVect< T_ > &a)
	Output vector.
template<class T_>
ostream &	operator<< (ostream &s, const DSMatrix< T_ > &a)
	Output matrix in output stream.
template<class T_>
ostream &	operator<< (ostream &s, const DMatrix< T_ > &a)
	Output matrix in output stream.
template<class T_>
istream &	operator>> (istream &s, Vect< T_ > &a)
	Read vector from input stream.
template<class T_>
istream &	operator>> (istream &s, SideVect< T_ > &v)
	Read vector from an input stream.
template<class T_>
istream &	operator>> (istream &s, NodeVect< T_ > &v)
	Read vector from input stream.
template<class T_>
istream &	operator>> (istream &s, ElementVect< T_ > &v)
	Read vector from an input stream.
template<class T_>
istream &	operator>> (istream &s, EdgeVect< T_ > &a)
	Read vector from an input stream.
template<class T_, size_t N_>
void	Scale (T_ a, LocalVect< T_, N_ > &x)
	Multiply vector x by constant a and store result in x.
template<class T_, size_t N_>
void	Scale (T_ a, const LocalVect< T_, N_ > &x, LocalVect< T_, N_ > &y)
	Multiply vector x by constant a and store result in y.
template<class T_, size_t N_>
void	SideAssembly (const Element &e, const LocalMatrix< T_, N_, N_ > &ae, SpMatrix< T_ > &a)
	Side assembly of local matrix into global matrix (as instance of class SpMatrix).

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Function Documentation

Axpy	(	T_	a,
		const LocalVect< T_, N_ > &	x,
		LocalVect< T_, N_ > &	y
	)

Add a*x to vector y.

void Copy	(	const LocalVect< T_, N_ > &	x,
		LocalVect< T_, N_ > &	y
	)

Copy vector x into vector y.

T_ Dot	(	const Vect< T_ > &	x,
		const Vect< T_ > &	y
	)

Calculate dot product of two vectors.

Return values:

Dot

(inner or scalar) product Calculate dot (scalar) product of two vectors

Referenced by OFELI::BiCG(), OFELI::BiCGStab(), OFELI::CG(), OFELI::CGS(), OFELI::GMRes(), OFELI::Nrm2(), and OFELI::QMR().

double Dot	(	const LocalVect< T_, N_ > &	a,
		const LocalVect< T_, N_ > &	b
	)

Calculate dot product of 2 vectors (instances of class LocalVect).

Return values:

Dot

product

Vect< T_ > operator*	(	T_	a,
		const Vect< T_ > &	x
	)

Operator * (Multiplication of vector by constant).

Return values:

a*x

TrMatrix< T_ > operator*	(	T_	a,
		const TrMatrix< T_ > &	A
	)

Operator * (Premultiplication of matrix by constant).

Return values:

a*A

References Matrix::getLength().

LocalVect< T_, N_ > operator*	(	T_	a,
		const LocalVect< T_, N_ > &	x
	)

Operator * (Premultiplication of vector by constant).

Return values:

a*x

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

Operator * (Multiply matrix x by scalar a).

Return values:

a*x

Vect< T_ > operator+	(	const Vect< T_ > &	x,
		const Vect< T_ > &	y
	)

Operator + (Addition of two instances of class Vect).

Return values:

\a

x + y

LocalVect< T_, N_ > operator+	(	const LocalVect< T_, N_ > &	x,
		const LocalVect< T_, N_ > &	y
	)

Operator + (Add two vectors).

Return values:

x+y

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

Operator + (Add matrix x to y).

Return values:

x+y

Vect< T_ > operator-	(	const Vect< T_ > &	x,
		const Vect< T_ > &	y
	)

Operator - (Difference between two instances of class Vect).

Return values:

x

- y

LocalVect< T_, N_ > operator-	(	const LocalVect< T_, N_ > &	x,
		const LocalVect< T_, N_ > &	y
	)

Operator - (Subtract two vectors).

Return values:

x-y

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

Operator - (Subtract matrix y from x).

Return values:

x-y

LocalVect< T_, N_ > operator/	(	T_	a,
		const LocalVect< T_, N_ > &	x
	)

Operator / (Division of vector by constant).

Return values:

x/a

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

Operator / (Divide matrix x by scalar a).

Return values:

x/a

ostream & operator<<	(	ostream &	s,
		const SideVect< T_ > &	v
	)

Output vector in output stream.

References Side::getLabel(), and AbsVect::getName().

void Scale	(	T_	a,
		LocalVect< T_, N_ > &	x
	)

Multiply vector x by constant a and store result in x.

void Scale	(	T_	a,
		const LocalVect< T_, N_ > &	x,
		LocalVect< T_, N_ > &	y
	)

Multiply vector x by constant a and store result in y.

void SideAssembly	(	const Element &	e,
		const LocalMatrix< T_, N_, N_ > &	ae,
		SpMatrix< T_ > &	a
	)

Side assembly of local matrix into global matrix (as instance of class SpMatrix).

Parameters:

[in]	e	Reference to local Element
[in]	ae	Local matrix
[in,out]	a	Global matrix

References SpMatrix::Add(), Side::getDOF(), Side::getNbDOF(), Element::getNbSides(), and Element::getPtrSide().