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

#include <latticetester/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, bool withDual, 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. More...

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

int	getOrder () const
	This returns the rank of the lattice. 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) More...

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

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...

virtual 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 > &)
	A utility method to store a vector of indices with lacunary values in subclasses of this one. More...

virtual std::string	toString () const
	Returns a string describing the lattice. More...

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. More...

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

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, long 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. More...

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

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

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

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

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

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

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

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

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`. More...

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 () const
	Returns `true` if a dual has been defined and `false` otherwise. More...

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

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

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. More...

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

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. More...

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

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

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

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. More...

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`. More...

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`. More...

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`. More...

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`. More...

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

void	permuteNoDual (int i, int j)
	Exchanges vectors `i` and `j` in the basis without changing the dual. 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...

void	sortNoDual (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. More...

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

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

Protected Member Functions
virtual void	kill ()
	Cleans and releases all the memory allocated to this lattice. More...

Protected Attributes
int	m_order
	The order of the basis. More...

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

double	m_lgm2
	The logarithm \(\log (m^2)\). More...

BasIntMat	m_wSI
	The dual basis of the current projection. More...

BasIntMat	m_vSI
	The primal basis of the current projection. More...

Int	m_t1
	Working Variables used in MRGLattice.h. More...

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. More...

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

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

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

DblVec	m_vecNorm
	The norm of each vector in the basis. More...

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

BasInt	m_modulo
	The `m` used for rescaling the lattice. More...

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

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.

This class is not really intended to be used directly, hence the lack of constructor allowing the specification of a basis.

This class can store a lattice with or without dual and contains a few virtual methods to perform common computations on lattices. 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,
		bool	withDual,
		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 (?)
withDual	Specifies wether this object contains a dual or not
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.

◆ ~IntLattice()

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

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

virtual

Destructor.

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 function is not implemented for this class. The general basis construction for a lattice such as this one is located in BasisConstruction.

◆ 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
	)

virtual

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.

◆ 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.

◆ dualize()

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

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

Exchange the primal basis and the dual basis.

◆ 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.

◆ getLgVolDual2()

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

double LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::getLgVolDual2 ( int i ) const

inline

Gives the log of m^(2*i) if i < order, else gives the log of m^(2*i)

◆ 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 returns the rank of the lattice.

◆ 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 >.

◆ 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).

◆ kill()

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

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

protectedvirtual

Cleans and releases all the memory allocated to this lattice.

◆ setLac()

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

virtual void LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::setLac ( const Lacunary< BasInt > & )

inlinevirtual

A utility method to store a vector of indices with lacunary values in subclasses of this one.

This method has no implementation in this base class.

◆ toString()

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

std::string LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::toString ( ) const

virtual

Returns a string describing the lattice.

Member Data Documentation

◆ m_lgm2

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

double LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::m_lgm2

protected

The logarithm \(\log (m^2)\).

◆ m_lgVolDual2

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

double* LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::m_lgVolDual2

protected

Represente sur dual along the diagonal?? ERWAN.

◆ m_order

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

int LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::m_order

protected

The order of the basis.

◆ m_t1

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

Int LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::m_t1

protected

Working Variables used in MRGLattice.h.

◆ m_vSI

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

BasIntMat LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::m_vSI

protected

The primal basis of the current projection.

◆ m_wSI

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

BasIntMat LatticeTester::IntLattice< Int, BasInt, Dbl, RedDbl >::m_wSI

protected

The dual basis of the current projection.

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

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]

◆ ~IntLattice()

Member Function Documentation

◆ buildBasis()

◆ buildProjection()

◆ calcLgVolDual2()

◆ copy()

◆ dualize()

◆ fixLatticeNormalization()

◆ getLgVolDual2()

◆ getNormalizer()

◆ getOrder()

◆ incDim()

◆ init()

◆ kill()

◆ setLac()

◆ toString()

Member Data Documentation

◆ m_lgm2

◆ m_lgVolDual2

◆ m_order

◆ m_t1

◆ m_vSI

◆ m_wSI

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