LatCommon::KorobovLattice Class Reference

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

#include <KorobovLattice.h>

Inherits LatCommon::IntLattice.

Public Member Functions
	KorobovLattice (const MScal &n, const MScal &a, int maxDim, NormType norm=L2NORM)
	Constructs a Korobov lattice with \(n\) points, maximal dimension maxDim using the norm norm.
	KorobovLattice (const MScal &n, const MScal &a, int dim, int t, NormType norm=L2NORM)
	Constructor. More...
	KorobovLattice (const KorobovLattice &Lat)
	Copy constructor.
KorobovLattice &	operator= (const KorobovLattice &Lat)
	Assigns Lat to this object.
	~KorobovLattice ()
	Destructor.
std::string	toStringCoef () const
	Returns the multiplier \(a\) as a string.
void	buildBasis (int d)
	Builds the basis in dimension \(d\).
void	incDim ()
	Increments the dimension of the basis by 1.
void	incDimSlow ()
	Increments the dimension of the basis by 1 by rebuilding the basis from scratch. More...
Public Member Functions inherited from LatCommon::IntLattice
	IntLattice (const MScal &m, int k, int maxDim, NormType norm=L2NORM)
	Constructor. More...
	IntLattice (const IntLattice &Lat)
	Copy constructor. More...
IntLattice &	operator= (const IntLattice &Lat)
	Assigns Lat to this object. More...
virtual	~IntLattice ()
	Destructor.
void	copy (const IntLattice &lattice)
	Same as assignment operator above.
int	getDim () const
	Returns actual dimension Dim.
void	setDim (int d)
	Sets actual dimension to \(d\).
int	getMaxDim () const
	Returns the maximal dimension of the lattice.
NormType	getNorm () const
	Returns the norm used by the lattice.
MScal	getM () const
	Returns the value of the modulus \(m\) of the recurrence (the number of points of the lattice).
NScal	getM2 () const
	Returns the square number of points in the lattice.
int	getOrder () const
	Returns the order.
Normalizer *	getNormalizer (NormaType norma, int alpha)
	Creates and returns the normalizer corresponding to criterion norma. More...
Base &	getPrimalBasis ()
	Returns the primal basis V.
Base &	getDualBasis ()
	Returns the dual basis W.
void	calcLgVolDual2 (bool dualF)
	Computes the logarithm of the normalization factor m_lgVolDual2 for the merit in all dimensions % \(\le \) maxDim for the dual lattice if dualF is true, and for the primal lattice if dualF is false.
double	getLgVolDual2 (int i) const
bool	getXX (int i) const
void	setXX (bool val, int i)
void	sort (int d)
	Sorts the basis vectors with indices from \(d+1\) to the dimension of the basis by increasing length. More...
void	permute (int i, int j)
	Exchanges vectors \(i\) and \(j\) in the basis and in the dual basis.
void	write (const char *filename) const
	Writes this basis in file named filename.
void	trace (char *msg)
	For debugging purposes.
void	write (int flag)
	Writes this basis on standard output. More...
void	dualize ()
	Exchanges basis \(V\) and its dual \(W\).
bool	checkDuality ()
	Checks that the bases satisfy the duality relation \(V[i]\cdot W[j] = m\,\delta_{ij}\). More...
bool	baseEquivalence (IntLattice &Lat)
	Checks that Lat's basis and this basis are equivalent. More...
void	buildProjection (IntLattice *lattice, const Coordinates &proj)
	Builds the basis (and dual basis) of the projection proj for this lattice. More...

Protected Member Functions
void	init ()
	Initialization.
Protected Member Functions inherited from LatCommon::IntLattice
void	init ()
void	kill ()
	Cleans and releases all the memory allocated for this lattice.

Protected Attributes
MScal	m_a
	The multiplier of the Korobov lattice rule.
int	m_shift
	The shift applied to the lattice rule.
Protected Attributes inherited from LatCommon::IntLattice
int	m_order
	The order of the basis.
MScal	m_m
	Number of points per unit volume (m_m) and its square (m_m2).
NScal	m_m2
double	m_lgm2
	The logarithm \(\log_2 (m^2)\).
Base	m_v
	Primal basis of the lattice.
Base	m_w
	Dual basis of the lattice.
double *	m_lgVolDual2
bool *	m_xx
	Work variables.
MScal	m_t1
MScal	m_t2
MScal	m_t3
BMat	m_vSI
Base	m_vTemp

Detailed Description

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

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

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

Note

Pierre: Reprogrammer incDim de facon efficace comme dans MRGLattice

Constructor & Destructor Documentation

LatCommon::KorobovLattice::KorobovLattice	(	const MScal &	n,
		const MScal &	a,
		int	dim,
		int	t,
		NormType	norm = L2NORM
	)

Constructor.

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

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

Member Function Documentation

void LatCommon::KorobovLattice::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.

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

• latcommon/include/latcommon/KorobovLattice.h