LatticeTester::NormaMinkowski< RedDbl > Class Template Reference

This class implements Minkowski’s theoretical LOWER bound on the length of the shortest non-zero vector in a lattice. More...

#include <NormaMinkowski.h>

Inherits LatticeTester::Normalizer< RedDbl >.

Public Member Functions
	NormaMinkowski (RedDbl &logDensity, int t, double beta=1)
	Constructor for the bounds obtained for Minkowski lattices.
double	getGamma (int j) const
	Returns the value of the lattice constant \(\gamma_j\) in dimension \(j\).
Public Member Functions inherited from LatticeTester::Normalizer< RedDbl >
	Normalizer (RedDbl &logDensity, int t, std::string Name, NormType norm=L2NORM, double beta=1)
	Complete constructor for a Normalizer.
	Normalizer (int t, std::string Name, NormType norm=L2NORM, double beta=1)
	Constructor that does not take the density as an argument.
virtual	~Normalizer ()
	Destructor.
virtual void	init (RedDbl &logDensity, double beta)
	This is a method that will initialize the bounds this normalizer can return.
std::string	ToString () const
	Returns a string that describes this object.
NormType	getNorm () const
	Returns the norm associated with this object.
void	setLogDensity (RedDbl logDensity)
	Sets the log-density associated with this object to logDensity.
RedDbl	getLogDensity () const
	Returns the logDensity associated with this object.
void	setNorm (NormType norm)
	Sets the norm associated with this object to norm.
int	getDim () const
	Returns the maximal dimension for this object.
double	getPreComputedBound (int j) const
	Returns the bound for dimension j as computed in Normalizer::init().
virtual RedDbl	getBound (int j) const
	Calculates and returns the bound on the length of the shortest nonzero vector in dimension j.

Additional Inherited Members
Static Public Attributes inherited from LatticeTester::Normalizer< RedDbl >
static const int	MAX_DIM = 48
	The maximum dimension of the lattices for which this class can give an upper bound.
Protected Attributes inherited from LatticeTester::Normalizer< RedDbl >
std::string	m_name
	Name of the normalizer.
NormType	m_norm
	Norm associated with this object.
RedDbl	m_logDensity
	log of the density, ie log of the number of points of the lattice per unit of volume.
int	m_maxDim
	Only elements 1 to m_maxDim (inclusive) of m_bounds bellow will be pre-computed.
double	m_beta
	Beta factor used to give more or less importance to some of the dimensions.
double *	m_bounds
	Contains the bounds on the length of the shortest nonzero vector in the lattice in each dimension.

Detailed Description

template<typename RedDbl>
class LatticeTester::NormaMinkowski< RedDbl >

This class implements Minkowski’s theoretical LOWER bound on the length of the shortest non-zero vector in a lattice.

The length of a vector is computed using the \({\mathcal{L}}_2\) norm. The bounding lengths, for a lattice containing \(n\) points per unit volume in dimension \(t\), are given by \(\ell_t^* = \gamma_t^{1/2} n^{-1/t}\), where the \(\gamma_t\) are the Minkowski lattice constants.

Constructor & Destructor Documentation

NormaMinkowski()

template<typename RedDbl>

LatticeTester::NormaMinkowski< RedDbl >::NormaMinkowski	(	RedDbl &	logDensity,
		int	t,
		double	beta = 1 )

Constructor for the bounds obtained for Minkowski lattices.

The lattices have \(n\) points per unit volume, in all dimensions \(\le t\). The bias factor beta \(= \beta\) gives more weight to some of the dimensions. Note this class stores the log value of the density to handle larger values. Restriction: \(t \le48\).

References LatticeTester::Normalizer< RedDbl >::init(), LatticeTester::Normalizer< RedDbl >::MAX_DIM, and LatticeTester::Normalizer< RedDbl >::Normalizer().

Member Function Documentation

getGamma()

template<typename RedDbl>

double LatticeTester::NormaMinkowski< RedDbl >::getGamma ( int j ) const

inlinevirtual

Returns the value of the lattice constant \(\gamma_j\) in dimension \(j\).

Reimplemented from LatticeTester::Normalizer< RedDbl >.

References LatticeTester::Normalizer< RedDbl >::MAX_DIM.

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

• latticetester/include/latticetester/NormaMinkowski.h