MathTL::PeriodicQuasiStationaryMatrix< C > Class Template Reference

#include <qs_matrix.h>

List of all members.

Public Types
typedef Vector< C >::size_type	size_type
Public Member Functions
	PeriodicQuasiStationaryMatrix (const int j0, const int offset, const Array1D< C > &band, const double factor=1.0)
PeriodicQuasiStationaryMatrix < C > &	operator= (const PeriodicQuasiStationaryMatrix< C > &M)
	assignment
const size_type	row_dimension () const
const size_type	column_dimension () const
void	set_level (const int j) const
const C	get_entry (const size_type row, const size_type column) const
void	to_sparse (SparseMatrix< C > &S) const
template<class VECTOR >
void	apply (const VECTOR &x, VECTOR &Mx, const size_type x_offset=0, const size_type Mx_offset=0, const bool add_to=false) const
template<class VECTOR >
void	apply_transposed (const VECTOR &x, VECTOR &Mtx, const size_type x_offset=0, const size_type Mtx_offset=0, const bool add_to=false) const
void	print (std::ostream &os, const unsigned int tabwidth=8, const unsigned int precision=3) const
Protected Attributes
int	j0_
int	offset_
int	j_
Array1D< C >	band_
double	factor_

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Detailed Description

template<class C>
class MathTL::PeriodicQuasiStationaryMatrix< C >

This class models quasi-stationary matrices like M_{j,0}, M_{j,1} or their dual counterparts for periodic bases. The dimensions are hence always 2^{j+1} times 2^j. Internally, we assume at the moment that the corresponding non-periodic filter (a_k) has a nonpositive offset (starting index) and a length < 2^(j0+1), which is the case for the primal and dual CDF generator and wavelet filters.

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Member Typedef Documentation

template<class C>

typedef Vector<C>::size_type MathTL::PeriodicQuasiStationaryMatrix< C >::size_type

type of indexes and size type (cf. STL containers)

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Constructor & Destructor Documentation

template<class C >

MathTL::PeriodicQuasiStationaryMatrix< C >::PeriodicQuasiStationaryMatrix	(	const int	j0,
		const int	offset,
		const Array1D< C > &	band,
		const double	factor = 1.0
	)

constructor from the matrix ingredients j0 : coarsest level offset : offset for the band, i.e., band[i] corresponds to a(i+offset) band : band (will be (2^j)-periodized internally factor : constant pre-factor

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Member Function Documentation

template<class C >

template<class VECTOR >

void MathTL::PeriodicQuasiStationaryMatrix< C >::apply	(	const VECTOR &	x,
		VECTOR &	Mx,
		const size_type	x_offset = 0,
		const size_type	Mx_offset = 0,
		const bool	add_to = false
	)		const

matrix-vector multiplication Mx = (*this) * x; it is possible to specify an offset which parts of the vectors shall be used, thus enabling in-place algorithms, the flag "add_to" toggles whether the result is added to Mx (true) or Mx is overwritten (false)

template<class C >

template<class VECTOR >

void MathTL::PeriodicQuasiStationaryMatrix< C >::apply_transposed	(	const VECTOR &	x,
		VECTOR &	Mtx,
		const size_type	x_offset = 0,
		const size_type	Mtx_offset = 0,
		const bool	add_to = false
	)		const

transposed matrix-vector multiplication Mtx = (*this)^T * x; again potentially with offsets for both input and output vector and with an "add_to" flag

template<class C>

const size_type MathTL::PeriodicQuasiStationaryMatrix< C >::column_dimension

(

)

const [inline]

column dimension

template<class C >

const C MathTL::PeriodicQuasiStationaryMatrix< C >::get_entry	(	const size_type	row,
		const size_type	column
	)		const

read-only access to a single matrix entry

template<class C >

void MathTL::PeriodicQuasiStationaryMatrix< C >::print	(	std::ostream &	os,
		const unsigned int	tabwidth = 8,
		const unsigned int	precision = 3
	)		const

stream output with user-defined tabwidth and precision (cf. deal.II)

template<class C>

const size_type MathTL::PeriodicQuasiStationaryMatrix< C >::row_dimension

(

)

const [inline]

row dimension

template<class C >

void MathTL::PeriodicQuasiStationaryMatrix< C >::set_level

(

const int

j

)

const

set level j

template<class C >

void MathTL::PeriodicQuasiStationaryMatrix< C >::to_sparse

(

SparseMatrix< C > &

S

)

const

construct a sparse matrix

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The documentation for this class was generated from the following files:

• algebra/qs_matrix.h
• algebra/qs_matrix.cpp