LatMRG::KorobovLattice< Int, Dbl > Class Template Reference

This class implements lattice bases built from a Korobov lattice rule. More...

#include <latmrg/KorobovLattice.h>

Inheritance diagram for LatMRG::KorobovLattice< Int, Dbl >:

Public Member Functions
	KorobovLattice (const Int &n, const Int &a, int maxDim, LatticeTester::NormType norm=LatticeTester::L2NORM)
	Constructs a Korobov lattice with \(n\) points, maximal dimension maxDim using the norm norm. More...
	KorobovLattice (const Int &n, const Int &a, int dim, int t, LatticeTester::NormType norm=LatticeTester::L2NORM)
	Constructor. More...
	KorobovLattice (const KorobovLattice &Lat)
	Copy constructor. More...
	~KorobovLattice ()
	Destructor. More...
void	buildBasis (int d)
	Builds the basis in dimension \(d\). More...
void	incDim ()
	Increments the dimension of the basis by 1. More...
void	incDimSlow ()
	Increments the dimension of the basis by 1 by rebuilding the basis from scratch. More...
KorobovLattice &	operator= (const KorobovLattice &Lat)
	Assigns Lat to this object. More...
std::string	toStringCoef () const
	Returns the multiplier \(a\) as a string. More...

Protected Member Functions
void	init ()
	Initialization. More...

Protected Attributes
Int	m_a
	The multiplier of the Korobov lattice rule. More...
int	m_shift
	The shift applied to the lattice rule. More...

Private Types
typedef NTL::matrix< Int >	IntMat

Detailed Description

template<typename Int, typename Dbl>
class LatMRG::KorobovLattice< Int, Dbl >

This class implements lattice bases built from a Korobov lattice rule.

For a given \(a\), a Korobov lattice basis is formed as follows:

\[ \mathbf{b_1} = (1, a, a^2, …, a^{d-1}),\quad \mathbf{b_2} = (0, n, 0, …, 0),\quad…,\quad \mathbf{b_d} = (0, …, 0, n). \]

Remarks

Pierre: Reprogrammer incDim de façon efficace comme dans MRGLattice

Member Typedef Documentation

IntMat

template<typename Int , typename Dbl >

typedef NTL::matrix<Int> LatMRG::KorobovLattice< Int, Dbl >::IntMat

private

Constructor & Destructor Documentation

KorobovLattice() [1/3]

template<typename Int , typename Dbl >

LatMRG::KorobovLattice< Int, Dbl >::KorobovLattice	(	const Int &	n,
		const Int &	a,
		int	maxDim,
		LatticeTester::NormType	norm = LatticeTester::L2NORM
	)

Constructs a Korobov lattice with \(n\) points, maximal dimension maxDim using the norm norm.

KorobovLattice() [2/3]

template<typename Int , typename Dbl >

LatMRG::KorobovLattice< Int, Dbl >::KorobovLattice	(	const Int &	n,
		const Int &	a,
		int	dim,
		int	t,
		LatticeTester::NormType	norm = LatticeTester::L2NORM
	)

Constructor.

Same as above, except the lattice is formed as follow:

\[ \mathbf{b_1} = (a^t, a^{t+1}, a^{t+2}, …, a^{t+d-1}),\qquad \mathbf{b_2} = (0, n, 0, …, 0),\qquad…,\qquad \mathbf{b_d} = (0, …, 0, n). \]

KorobovLattice() [3/3]

template<typename Int , typename Dbl >

LatMRG::KorobovLattice< Int, Dbl >::KorobovLattice

(

const KorobovLattice< Int, Dbl > &

Lat

)

Copy constructor.

~KorobovLattice()

template<typename Int , typename Dbl >

LatMRG::KorobovLattice< Int, Dbl >::~KorobovLattice

(

)

Destructor.

Member Function Documentation

buildBasis()

template<typename Int , typename Dbl >

void LatMRG::KorobovLattice< Int, Dbl >::buildBasis

(

int

d

)

Builds the basis in dimension \(d\).

incDim()

template<typename Int , typename Dbl >

void LatMRG::KorobovLattice< Int, Dbl >::incDim

(

)

Increments the dimension of the basis by 1.

incDimSlow()

template<typename Int , typename Dbl >

void LatMRG::KorobovLattice< Int, Dbl >::incDimSlow

(

)

Increments the dimension of the basis by 1 by rebuilding the basis from scratch.

This is very slow. It can be used for verification of the fast incDim method above.

init()

template<typename Int , typename Dbl >

void LatMRG::KorobovLattice< Int, Dbl >::init ( )

protected

Initialization.

operator=()

template<typename Int , typename Dbl >

KorobovLattice< Int, Dbl > & LatMRG::KorobovLattice< Int, Dbl >::operator=

(

const KorobovLattice< Int, Dbl > &

Lat

)

Assigns Lat to this object.

toStringCoef()

template<typename Int , typename Dbl >

std::string LatMRG::KorobovLattice< Int, Dbl >::toStringCoef

(

)

const

Returns the multiplier \(a\) as a string.

Member Data Documentation

m_a

template<typename Int , typename Dbl >

Int LatMRG::KorobovLattice< Int, Dbl >::m_a

protected

The multiplier of the Korobov lattice rule.

m_shift

template<typename Int , typename Dbl >

int LatMRG::KorobovLattice< Int, Dbl >::m_shift

protected

The shift applied to the lattice rule.

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

• include/latmrg/KorobovLattice.h