LatticeTester::NormaBestLat Class Reference

This Normalizer class implements upper bounds on the length of the shortest nonzero vector in a lattice. More...

#include <latticetester/NormaBestLat.h>

Inheritance diagram for LatticeTester::NormaBestLat:

Public Member Functions
	NormaBestLat (double logm, int64_t k, int64_t maxDim)
	This constructor assumes that the rescaled primal lattice has scaling factor \(m\) and order \(k\), so its density is \(m^{k-t}\) for \(t\geq k\), and cannot exceed 1 for projections in \(s < k\) dimensions.
	NormaBestLat (double logDensity, int64_t maxDim)
	Constructs a NormaBestLat for up to maxDim dimensions, by assuming that the log density is logDensity in all dimensions and the lattice was not rescaled.
	NormaBestLat (int64_t maxDim)
	Constructs a NormaBestLat for up to maxDim dimensions, without computing the bounds.
double	getGamma (int64_t j) const
	Returns the value of the bound on the Hermite's constant \(\gamma_j\) in dimension \(j\).
Public Member Functions inherited from LatticeTester::Normalizer
	Normalizer (double logm, int64_t k, int64_t maxDim, std::string name="", NormType norm=L2NORM)
	This is the preferred constructor in all the subclasses.
	Normalizer (double logDensity, int64_t maxDim, std::string name="", NormType norm=L2NORM)
	***** DEPRECATED *****
	Normalizer (int64_t maxDim, std::string name, NormType norm=L2NORM)
	This constructor creates a Normalizer object without computing any bounds.
virtual	~Normalizer ()
	Destructor.
virtual void	computeBounds (double logDensity)
	This method is rarely applicable! It computes bounds by assuming that the log density is logDensity for all dimensions up to the maximal dimension maxDim.
void	computeBounds (double logm, int64_t k)
	This method is called by the constructors of subclasses, in which the constants gamma_t are known.
std::string	toString () const
	Returns a string that describes this object.
NormType	getNorm () const
	Returns the norm associated with this object.
int64_t	getMaxDim () const
	Returns the maximal dimension for this object.
virtual double *	getBounds () const
	Returns the array that contains the bounds on the lengths of the shortest nonzero vectors.
virtual double	getBound (int64_t j) const
	Returns the bound on the length of the shortest nonzero vector in j dimensions.

Additional Inherited Members
Static Public Attributes inherited from LatticeTester::Normalizer
static const int64_t	MAX_DIM = 48
	The maximum dimension of the lattices for which this class can give an upper bound.
Protected Attributes inherited from LatticeTester::Normalizer
std::string	m_name
	Name of the normalizer.
NormType	m_norm
	Norm type associated with this object.
int64_t	m_maxDim
	Maximum dimension.
double *	m_bounds
	Contains the bounds on the length of the shortest nonzero vector in the lattice in each dimension up to maxDim.

Detailed Description

This Normalizer class implements upper bounds on the length of the shortest nonzero vector in a lattice.

The Hermite constants \(\gamma_s\) are approximated by using the largest known density values for lattices [2]. These approximations are stored in a table accessible via the getGamma(int) const method. In [2], Table I.1(a) gives the center density \(\delta_s\) of the densest known packings in dimension \(s\). We then have that

\[ \gamma_s = 4 \delta_s^{2/s}. \]

This class is to be used with the L2NORM (the Euclidian norm) exclusively.

Constructor & Destructor Documentation

NormaBestLat() [1/3]

LatticeTester::NormaBestLat::NormaBestLat	(	double	logm,
		int64_t	k,
		int64_t	maxDim )

This constructor assumes that the rescaled primal lattice has scaling factor \(m\) and order \(k\), so its density is \(m^{k-t}\) for \(t\geq k\), and cannot exceed 1 for projections in \(s < k\) dimensions.

NormaBestLat() [2/3]

LatticeTester::NormaBestLat::NormaBestLat	(	double	logDensity,
		int64_t	maxDim )

Constructs a NormaBestLat for up to maxDim dimensions, by assuming that the log density is logDensity in all dimensions and the lattice was not rescaled.

Restriction: maxDim \( \le 48\).

NormaBestLat() [3/3]

LatticeTester::NormaBestLat::NormaBestLat

(

int64_t

maxDim

)

Constructs a NormaBestLat for up to maxDim dimensions, without computing the bounds.

Restriction: maxDim \( \le 48\).

Member Function Documentation

getGamma()

double LatticeTester::NormaBestLat::getGamma ( int64_t j ) const

inlinevirtual

Returns the value of the bound on the Hermite's constant \(\gamma_j\) in dimension \(j\).

Reimplemented from LatticeTester::Normalizer.

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

• include/latticetester/NormaBestLat.h