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

#include <latticetester/NormaLaminated.h>

Inheritance diagram for LatticeTester::NormaLaminated:

Public Member Functions
	NormaLaminated (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.

	NormaLaminated (double logDensity, int64_t maxDim)
	Constructs a `NormaLaminated` for up to `maxDim` dimensions, by assuming that the log density is `logDensity` in all dimensions and the lattice was not rescaled.

	NormaLaminated (int64_t maxDim)
	Constructs a `NormaLaminated` 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 values that correspond to the laminated lattices [2]. These lattices are not always the densest lattices available, but they are intuitive constructions dense lattices. In [2], Table 6.1 gives the determinant \(\lambda_s\) that can be used to recover the center density \(\delta_s = \lambda_s^{-1/2}\) of the densest laminated lattice in dimension \(s\). From there, we get

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

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

Constructor & Destructor Documentation

◆ NormaLaminated() [1/3]

LatticeTester::NormaLaminated::NormaLaminated	(	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.

◆ NormaLaminated() [2/3]

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

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

Restriction: maxDim \( \le 48\).

◆ NormaLaminated() [3/3]

LatticeTester::NormaLaminated::NormaLaminated ( int64_t maxDim )

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

Restriction: maxDim \( \le 48\).

Member Function Documentation

◆ getGamma()

double LatticeTester::NormaLaminated::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.

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

include/latticetester/NormaLaminated.h

Public Member Functions