LatCommon::IntLattice Class Reference

This class offers tools to manipulate lattice bases. More...

#include <IntLattice.h>

Inherited by LatCommon::KorobovLattice, and LatCommon::Rank1Lattice.

Public Member Functions
	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.
virtual void	incDim ()
	Increases dimension Dim by 1.
virtual void	buildBasis (int d)
	Builds the basis for the lattice in dimension d.
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...
virtual std::string	toStringCoef () const
	Returns the vector of multipliers (or coefficients) \(A\) as a string.
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 ()
void	kill ()
	Cleans and releases all the memory allocated for this lattice.

Protected Attributes
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 offers tools to manipulate lattice bases.

Each lattice is represented by a basis \(V\) and its dual \(W\). It is sometimes possible, as in the case of lattices associated with LCGs (linear congruential generators) or MRGs (multiple recursive generators), to multiply a lattice (and its dual) by a constant factor \(m\) in such a way that they are included in \(\mathbb{Z}^t\), allowing exact representation of basis vector coordinates. The duality relation will then read \(V_i\cdot W_j = m\delta_{ij}\) for some integer constant { \(m\)}.

Constructor & Destructor Documentation

LatCommon::IntLattice::IntLattice	(	const MScal &	m,
		int	k,
		int	maxDim,
		NormType	norm = L2NORM
	)

Constructor.

The modulus is initialized to \(m\), the maximal dimension of the bases is set to maxDim, and the order is set to \(k\).

LatCommon::IntLattice::IntLattice

(

const IntLattice &

Lat

)

Copy constructor.

The maximal dimension of the created basis is set equal to Lat's current dimension.

Member Function Documentation

bool LatCommon::IntLattice::baseEquivalence

(

IntLattice &

Lat

)

Checks that Lat's basis and this basis are equivalent.

If so, returns true, otherwise returns false.

void LatCommon::IntLattice::buildProjection	(	IntLattice *	lattice,
		const Coordinates &	proj
	)

Builds the basis (and dual basis) of the projection proj for this lattice.

The result is placed in the lattice lattice. The basis is triangularized to form a proper basis.

bool LatCommon::IntLattice::checkDuality

(

)

Checks that the bases satisfy the duality relation \(V[i]\cdot W[j] = m\,\delta_{ij}\).

If so, returns true, otherwise returns false.

Normalizer* LatCommon::IntLattice::getNormalizer	(	NormaType	norma,
		int	alpha
	)

Creates and returns the normalizer corresponding to criterion norma.

In the case of the \(P_\alpha\) test, the argument alpha = \(\alpha\). In all other cases, it is unused.

IntLattice& LatCommon::IntLattice::operator=

(

const IntLattice &

Lat

)

Assigns Lat to this object.

The maximal dimension of this basis is set equal to Lat's current dimension.

void LatCommon::IntLattice::sort

(

int

d

)

Sorts the basis vectors with indices from \(d+1\) to the dimension of the basis by increasing length.

The dual vectors are permuted accordingly. Assumes that the lengths of the corresponding basis vectors % VV and WW are up to date.

void LatCommon::IntLattice::write

(

int

flag

)

Writes this basis on standard output.

If flag \( > 0\), the norm of the basis vectors will be recomputed; otherwise not.

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

• latcommon/include/latcommon/IntLattice.h