This class is a skeleton for the implementation of different types of lattices of arbitrary rank. More...

#include <IntLattice.h>

Inherits LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >.

Inherited by LatticeTester::Rank1Lattice< Int, BasInt, Dbl, RedDbl >.

Public Member Functions
	IntLattice (Int modulo, int k, int maxDim, NormType norm=L2NORM)
	Constructor initializing the primal and the dual basis with the identity matrix. More...

	IntLattice (const IntLattice< Int, BasInt, Dbl, RedDbl > &Lat)
	Copy constructor that makes a copy of `Lat`. More...

void	copy (const IntLattice< Int, BasInt, Dbl, RedDbl > &lattice)
	Copies `lattice` into this object. More...

virtual	~IntLattice ()
	Destructor.

void	init ()
	Allocates space to vectors used internally. More...

int	getOrder () const
	This is the order of the underlying MRG. More...

virtual void	incDim ()
	Increments the dimension of the basis and dual basis vectors by one. More...

void	calcLgVolDual2 (double lgm2)
	Computes the logarithm of the normalization factor (`m_lgVolDual2`) in all dimensions \(\leq\) `MaxDim` for the lattice. More...

double	getLgVolDual2 (int i) const
	Gives the log of m^(2i) if i < order, else gives the log of m^(2i)

void	dualize ()
	Exchange the primal basis and the dual basis.

void	fixLatticeNormalization (bool dualF)
	This function is called to fix the normalization constants to get the normalized merit from the shortest distance in the lattice. More...

void	buildProjection (IntLattice< Int, BasInt, Dbl, RedDbl > *lattice, const Coordinates &proj)
	Builds the basis (and dual basis) of the projection `proj` for this lattice. More...

virtual void	buildBasis (int d)
	Builds the basis for the lattice in dimension `d`. More...

LatticeTester::Normalizer< RedDbl > *	getNormalizer (NormaType norma, int alpha, bool dualF)
	Creates and returns the normalizer corresponding to criterion `norma`. More...

virtual void	setLac (const Lacunary< BasInt > &)
	Does nothing is this base class.

virtual std::string	toStringCoef () const
	Returns the vector of multipliers (or coefficients) \(A\) as a string.

Public Member Functions inherited from LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >
	IntLatticeBasis (const int dim, NormType norm=L2NORM)
	Constructor initializing the primal basis with the identity matrix. More...

	IntLatticeBasis (const BasIntMat basis, const int dim, NormType norm=L2NORM)
	Constructor taking all three needed component of an IntLatticeBasis. More...

	IntLatticeBasis (const BasIntMat primalbasis, const BasIntMat dualbasis, const Int modulo, const int dim, NormType norm=L2NORM)
	Complete constructor. More...

	IntLatticeBasis (const IntLatticeBasis< Int, BasInt, Dbl, RedDbl > &Lat)
	Copy constructor. More...

	~IntLatticeBasis ()
	Destructor.

void	kill ()
	Cleans and releases all the memory allocated to this lattice.

void	copyBasis (const IntLatticeBasis< Int, BasInt, Dbl, RedDbl > &lat)
	Copy the lattice `lat`, except it's NormType and dimension, into this object. More...

void	copyBasis (const IntLatticeBasis< Int, BasInt, Dbl, RedDbl > &lat, int n)
	Copy the n first elements of the basis of the lattice `lat` into this object. More...

void	initVecNorm ()
	Initializes a vector containing the norms of the basis vectors to -1 at all components.

BasIntMat &	getBasis ()
	Returns the basis represented in a matrix.

BasIntMat &	getDualBasis ()
	Returns the dual basis represented in a matrix.

int	getDim () const
	Returns the dimension of the lattice. More...

NormType	getNorm () const
	Returns the NormType used by this lattice.

Dbl	getVecNorm (const int &i)
	Returns the norm of the i-th vector of the basis.

DblVec	getVecNorm () const
	Returns the norm of each vector of the basis in a vector.

Dbl	getDualVecNorm (const int &i)
	Returns the norm of the i-th vector of the dual basis.

DblVec	getDualVecNorm () const
	Returns the norm of each vector of the dual basis in a vector.

Int	getModulo () const
	Returns the `m` used for rescaling if it has been defined. More...

void	setDim (const int &d)
	Sets the dimension of the basis to `d`. More...

void	setNorm (const NormType &norm)
	Sets the NormType used by this lattice to `norm`.

void	setVecNorm (const Dbl &value, const int &i)
	Sets the norm of the `i`-th component of the basis to `value`. More...

void	setDualVecNorm (const Dbl &value, const int &i)
	Sets the norm of the `i`-th component of the dual basis to `value`. More...

bool	withDual ()
	Returns `true` if a dual has been defined and `false` otherwise.

void	setDualFlag (bool flag)
	Sets the `withDual` flag to `flag`. More...

bool	getXX (int i) const
	Gets whether or not there is a component at the `i`-th position in the basis. More...

void	setXX (bool val, int i)
	Sets `value` at the `i`-th position in the array xx.

void	setNegativeNorm ()
	Sets all the values in the array containing the norms of the basis vectors to -1.

void	setNegativeNorm (const int &i)
	Sets the value of the `i`-th component in the array containing the norms of the basis vectors to -1.

void	setDualNegativeNorm ()
	Sets all the values in the array containing the norms of the dual basis vectors to -1.

void	setDualNegativeNorm (const int &i)
	Sets the value of the `i`-th component in the array containing the norms of the dual basis vectors to -1.

void	updateVecNorm ()
	Updates the array containing the basis vectors norms by recomputing them.

void	updateVecNorm (const int &d)
	Updates the array containing the basis vectors norms from the `d`-th component to the last by recomputing them.

void	updateDualVecNorm ()
	Updates the array containing the dual basis vectors norms by recomputing them.

void	updateDualVecNorm (const int &d)
	Updates the array containing the dual basis vectors norms from the `d`-th component to the last by recomputing them.

void	updateScalL2Norm (const int i)
	Updates the `i`-th value of the array containing the norms of the basis vectors by recomputing it using the `L2NORM`.

void	updateScalL2Norm (const int k1, const int k2)
	Updates the `k1`-th to the `k2-1`-th values of the array containing the norms of the basis vectors by recomputing them using the `L2NORM`.

void	updateDualScalL2Norm (const int i)
	Updates the `i`-th value of the array containing the norms of the dual basis vectors by recomputing it using the `L2NORM`.

void	updateDualScalL2Norm (const int k1, const int k2)
	Updates the `k1`-th to the `k2-1`-th values of the array containing the norms of the dual basis vectors by recomputing them using the `L2NORM`.

void	permute (int i, int j)
	Exchanges vectors `i` and `j` in the basis. More...

bool	checkDuality ()
	Returns `true` if the dual basis contained in the object really is the dual of the basis, and `false` otherwise. More...

void	sort (int d)
	Sorts the basis vectors with indices greater of equal to \(d\) by increasing length. More...

std::string	toStringBasis () const
	Returns a string with the primal basis and its norms.

std::string	toStringDualBasis () const
	Returns a string with the dual basis and its norms.

void	write () const
	Writes the lattice and its parameters on standard output. More...

Protected Member Functions
virtual void	kill ()
	The components of the lattice when it is built out of more than one component. More...

Protected Attributes
int	m_order
	The order of the basis.

double *	m_lgVolDual2
	Represente sur dual along the diagonal?? ERWAN.

double	m_lgm2
	The logarithm \(\log_2 (m^2)\).

BasIntMat	m_wSI
	Use to save the dual basis and the basis in some works.

BasIntMat	m_vSI

Int	m_t1
	Working Variables use in MRGLattice.h.

Int	m_t2

Int	m_t3

Protected Attributes inherited from LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >
BasIntMat	m_basis
	Each row of this matrix represents a vector in the basis of the lattice.

BasIntMat	m_dualbasis
	Each row of this matrix represents a vector in the dual basis of the lattice.

int	m_dim
	The dimension of the lattice. More...

NormType	m_norm
	The NormType used in the reduction and for this lattice.

DblVec	m_vecNorm
	The norm of each vector in the basis.

DblVec	m_dualvecNorm
	The norm of each vector in the dual basis.

Int	m_modulo
	The `m` used for rescaling the lattice.

bool	m_withDual
	If m_withDual is `true` a dual basis has been specified, otherwise it is `false`.

bool *	m_xx
	This table is used in the Minkowski reduction, but it's usage is quite obscure.

Detailed Description

template<typename Int, typename BasInt, typename Dbl, typename RedDbl>
class LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >

This class is a skeleton for the implementation of different types of lattices of arbitrary rank.

This class contains a method to compute lattices of projections of \(\{x_i\}_{ 0 \leq i}\), a method to exchange the basis and the dual basis, and a virtual method that can be implemented in subclasses to recompute the basis for different dimensions.

A lattice of rank \(k\) with integer vectors modulo \(m\) contains \(m^k\) distinct vectors. This number, the density, can then be used to compute bounds on the spectral test. This class implements methods to compute \( \log_2(m^{2i}) \) for \( 1 \leq i \leq k \) to help with the computation of such bounds.

Constructor & Destructor Documentation

◆ IntLattice() [1/2]

template<typename Int , typename BasInt , typename Dbl , typename RedDbl >

LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::IntLattice	(	Int	modulo,
		int	k,
		int	maxDim,
		NormType	norm = `L2NORM`
	)

Constructor initializing the primal and the dual basis with the identity matrix.

The dimension of the lattice is set to maxDim and the norm used for reduction to norm.

Parameters

modulo	The modulo of the integer coordinates
k	The rank of the lattice to be constructed
maxDim	The maximal dimension for which this lattice can be expanded/tested (?)
norm	The norm to use in for reduction

◆ IntLattice() [2/2]

template<typename Int , typename BasInt , typename Dbl , typename RedDbl >

LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::IntLattice ( const IntLattice< Int, BasInt, Dbl, RedDbl > & Lat )

Copy constructor that makes a copy of Lat.

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

References LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::init(), LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::m_order, LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::m_withDual, LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::m_wSI, and LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::setDualNegativeNorm().

Member Function Documentation

◆ buildBasis()

template<typename Int , typename BasInt , typename Dbl , typename RedDbl >

void LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::buildBasis ( int d )

virtual

Builds the basis for the lattice in dimension d.

This fonction is implemented in subclasses

Reimplemented in LatticeTester::Rank1Lattice< Int, BasInt, Dbl, RedDbl >.

References LatticeTester::MyExit().

◆ buildProjection()

template<typename Int , typename BasInt , typename Dbl , typename RedDbl >

void LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::buildProjection	(	IntLattice< Int, BasInt, Dbl, RedDbl > *	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.

References LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::m_basis, LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::m_dualbasis, LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::m_order, LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::setDim(), LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::setDualNegativeNorm(), and LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::setNegativeNorm().

◆ calcLgVolDual2()

template<typename Int , typename BasInt , typename Dbl , typename RedDbl >

void LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::calcLgVolDual2 ( double lgm2 )

Computes the logarithm of the normalization factor (m_lgVolDual2) in all dimensions \(\leq\) MaxDim for the lattice.

lgm2 is the logarithm in base 2 of \(m^2\).

◆ copy()

template<typename Int , typename BasInt , typename Dbl , typename RedDbl >

void LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::copy ( const IntLattice< Int, BasInt, Dbl, RedDbl > & lattice )

Copies lattice into this object.

This should be equivalent to the creation of a new IntLattice using the copy constructor with lattice as an argument.

References LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::getDim(), LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::getOrder(), LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::getXX(), LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::m_basis, LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::m_dualbasis, and LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::m_modulo.

◆ fixLatticeNormalization()

template<typename Int , typename BasInt , typename Dbl , typename RedDbl >

void LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::fixLatticeNormalization ( bool dualF )

This function is called to fix the normalization constants to get the normalized merit from the shortest distance in the lattice.

If dualF is true, the normalization constant is reset for the dual lattice, otherwise it is reset for the primal lattice.

◆ getNormalizer()

template<typename Int , typename BasInt , typename Dbl , typename RedDbl >

Normalizer< RedDbl > * LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::getNormalizer	(	NormaType	norma,
		int	alpha,
		bool	dualF
	)

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.

◆ getOrder()

template<typename Int, typename BasInt, typename Dbl, typename RedDbl>

int LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::getOrder ( ) const

inline

This is the order of the underlying MRG.

The problem is that the lattice is not necessarily associated with a MRG anymore. The solution probably is to change this so that it is now the rank because a MRG of order k spans a lattice of rank k. (See the lattice construction in Pierre's book)

References LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::m_order.

Referenced by LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::copy().

◆ incDim()

template<typename Int , typename BasInt , typename Dbl , typename RedDbl >

void LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::incDim ( )

virtual

Increments the dimension of the basis and dual basis vectors by one.

This initializes the added components to 0 and does not compute the value taken by the added components and vector. It also resets vectors containing the norms. The implementation in this class is meant to be overriden by subclasses and probably should not be used.

Reimplemented in LatticeTester::Rank1Lattice< Int, BasInt, Dbl, RedDbl >.

References LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::m_basis, LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::m_dualbasis, LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::m_dualvecNorm, and LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::m_vecNorm.

◆ init()

template<typename Int , typename BasInt , typename Dbl , typename RedDbl >

void LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::init ( )

Allocates space to vectors used internally.

This should probably be private or protected because it should not be needed to call it directly (the constructors and copy already call it.

References NTL::conv(), LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::initVecNorm(), and LatticeTester::Lg().

Referenced by LatticeTester::Rank1Lattice< Int, BasInt, Dbl, RedDbl >::init(), and LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::IntLattice().

◆ kill()

template<typename Int , typename BasInt , typename Dbl , typename RedDbl >

void LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::kill ( )

protectedvirtual

The components of the lattice when it is built out of more than one component.

When there is only one component, it is unused as the parameters are the same as above. Cleans and releases all the memory allocated to this lattice.

References LatticeTester::IntLatticeBasis< Int, BasInt, Dbl, RedDbl >::kill().

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

latticetester/include/latticetester/IntLattice.h

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<typename Int, typename BasInt, typename Dbl, typename RedDbl> class LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >

Constructor & Destructor Documentation

◆ IntLattice() [1/2]

◆ IntLattice() [2/2]

Member Function Documentation

◆ buildBasis()

◆ buildProjection()

◆ calcLgVolDual2()

◆ copy()

◆ fixLatticeNormalization()

◆ getNormalizer()

◆ getOrder()

◆ incDim()

◆ init()

◆ kill()

template<typename Int, typename BasInt, typename Dbl, typename RedDbl>
class LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >