LatticeTester::Normalizer< RedDbl > Class Template Reference

Classes which inherit from this base class are used in implementing bounds on the length of the shortest nonzero vector in a lattice [3] . More...

#include <Normalizer.h>

Inherited by LatticeTester::NormaBestLat< RedDbl >, LatticeTester::NormaLaminated< RedDbl >, LatticeTester::NormaMinkL1< RedDbl >, LatticeTester::NormaMinkowski< RedDbl >, LatticeTester::NormaPalpha< Int, RedDbl >, and LatticeTester::NormaRogers< RedDbl >.

Public Member Functions
	Normalizer (RedDbl &logDensity, int t, std::string Name, NormType norm=L2NORM, double beta=1)
	Constructor for the bounds. More...
	Normalizer (int t, std::string Name, NormType norm=L2NORM, double beta=1)
	Constructor only used by the NormaPalpha class. More...
virtual	~Normalizer ()
	Destructor.
virtual void	init (RedDbl &logDensity, double beta)
	Initializes the bounds on the length of the shortest vector. More...
std::string	ToString () const
	Returns this object as a string.
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 on the length of the shortest nonzero vector in dimension \(j\) as computed in Normalizer::init.
double	getBound (int j) const
	Calculates and returns the bound on the length of the shortest nonzero vector in dimension \(j\).
virtual double	getGamma (int j) const
	Returns the value of the lattice constant \(\gamma_j\) in dimension \(j\). More...

Static Public Attributes
static const int	MAX_DIM = 48

Protected Attributes
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 arrays are defined.
double	m_beta
	Beta factor.
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::Normalizer< RedDbl >

Classes which inherit from this base class are used in implementing bounds on the length of the shortest nonzero vector in a lattice [3] .

These bounds are used to normalize the length of the shortest vectors. Tight lower bounds are available for all dimensions for many important cases. In most cases, the \({\mathcal{L}}_2\) norm is used to compute the length of vectors.

For some figures of merit, no useful bounds are known to normalize the length of the shortest vector. In these cases, this base class will be used as normalizer since it simply sets all normalization constants to 1. This is necessary because the tests compare the normalized values of the merit when searching for good lattices.

Constructor & Destructor Documentation

Normalizer() [1/2]

template<typename RedDbl >

LatticeTester::Normalizer< RedDbl >::Normalizer	(	RedDbl &	logDensity,
		int	t,
		std::string	Name,
		NormType	norm = L2NORM,
		double	beta = 1
	)

Constructor for the bounds.

Deals with lattices having \(n\) points per unit volume, in all dimensions \(\le t\). Name is the name of the Normalizer. The bias factor beta \(= \beta\) gives more weight to some of the dimensions: taking \(\beta< 1\) inflates the figure of merit by \((1/\beta)^t\), thus weakening the requirements for large \(t\) in a worst-case figure of merit. One normally uses \(\beta= 1\). Note that the log value of the density is stored (instead of the density itself) so it is easier to manipulate really large values of density.

Remarks

Richard: Je crois que ce facteur beta devrait disparaître car des poids beaucoup plus généraux sont maintenant implantés dans les classes *Weights.

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

Normalizer() [2/2]

template<typename RedDbl >

LatticeTester::Normalizer< RedDbl >::Normalizer	(	int	t,
		std::string	Name,
		NormType	norm = L2NORM,
		double	beta = 1
	)

Constructor only used by the NormaPalpha class.

It doesn't take any log density argument. This only works for rank1 lattices, having m points per unit of volume (m being a prime number), normalized with NormaPalpha.

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

Member Function Documentation

getGamma()

template<typename RedDbl >

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

virtual

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

For this base class, always returns 1.

Reimplemented in LatticeTester::NormaMinkL1< RedDbl >, LatticeTester::NormaRogers< RedDbl >, LatticeTester::NormaBestLat< RedDbl >, LatticeTester::NormaLaminated< RedDbl >, and LatticeTester::NormaMinkowski< RedDbl >.

init()

template<typename RedDbl >

void LatticeTester::Normalizer< RedDbl >::init ( RedDbl &  logDensity, double  beta  )

virtual

Initializes the bounds on the length of the shortest vector.

The lattices have \(Density\) points per unit volume and the bias factor is beta for all dimensions \(j\le\) maxDim.

Referenced by LatticeTester::NormaBestLat< RedDbl >::NormaBestLat(), LatticeTester::NormaLaminated< RedDbl >::NormaLaminated(), LatticeTester::NormaMinkL1< RedDbl >::NormaMinkL1(), LatticeTester::NormaMinkowski< RedDbl >::NormaMinkowski(), and LatticeTester::NormaRogers< RedDbl >::NormaRogers().

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

• latticetester/include/latticetester/Normalizer.h