This subclass of MRGLattice constructs and handles lattice bases built from MRGs as in MRGLattice, but with arbitrary lacunary indices that can be spaced very far apart. More...

Inheritance diagram for LatMRG::MRGLatticeLac< Int, Real >:

Public Member Functions
	MRGLatticeLac (const Int &m, const IntVec &aa, int64_t maxDim, IntVec &lac, NormType norm=L2NORM)
	Constructor with modulus of congruence \(m\), order of the recurrence \(k\), multipliers in aa, and maximal dimension maxDim.
	MRGLatticeLac (const MRGLatticeLac< Int, Real > &Lat)
	Copy constructor.
MRGLatticeLac &	operator= (const MRGLatticeLac< Int, Real > &Lat)
	Assigns Lat to this object.
virtual	~MRGLatticeLac ()
	Destructor.
void	setLac (const IntVec &lac, bool buildBasisCopy=true)
	Sets the lacunary indices for this lattice to lac.
void	setaa (const IntVec &lac, bool buildBasisCopy=true)
	Sets the generating vector to aa.
Int &	getLac (int j)
	Returns the \(j\)-th lacunary index.
Public Member Functions inherited from LatMRG::MRGLattice< Int, Real >
	MRGLattice (const Int &m, const IntVec &aa, int64_t maxDim, NormType norm=L2NORM)
	This constructor takes as input the modulus m, the vector of multipliers aa, and the norm used to measure the vector lengths.
	MRGLattice (const MRGLattice< Int, Real > &Lat)
MRGLattice &	operator= (const MRGLattice< Int, Real > &Lat)
	Assigns Lat to this object.
	~MRGLattice ()
	Destructor.
virtual void	setaa (const IntVec &aa)
	Sets the vector of multipliers.
void	buildBasis (int64_t dim)
	Builds a basis in dim dimensions.
void	buildDualBasis (int64_t dim)
	Builds the m-dual lower triangular basis directly in dim dimensions.
void	incDimBasis ()
	Increases the current dimension of the primal basis by 1 and updates the basis.
void	incDimDualBasis ()
	Increases the current dimension of the m-dual basis by 1.
void	buildProjection (IntLattice< Int, Real > &projLattice, const Coordinates &proj) override
	This method overrides its namesake in IntLattice.
void	buildProjectionDual (IntLattice< Int, Real > &projLattice, const Coordinates &proj) override
	Overrides the same function from IntLattice.
std::string	toStringCoef () const
	Returns the first dim components of the generating vector \(\ba\) as a string, where dim is the current lattice dimension.

Protected Member Functions
void	buildBasis0 (IntMat &basis, int64_t d) override
	This function overrides the correpsonding protected function in 'MRGLattice'.
void	buildDualBasis0 (IntMat &basis, int64_t d) override
	This functions overrides the corresponding protected function in 'MRGLattice', which is necessary because the entire copy of the primal basis is build upon creation of the object.
void	incDimBasis0 (IntMat &basis, int64_t d) override
	This function overrides the correpsonding protected function in 'MRGLattice'.
void	incDimDualBasis0 (IntMat &basis, int64_t d) override
	This function overrides the correpsonding protected function in 'MRGLattice'.
bool	buildProjection0 (IntMat &basis, int64_t dimbasis, IntMat &pbasis, const Coordinates &proj) override
	This function overrides the correpsonding protected function in 'MRGLattice'.
void	polyToColumn (IntVec &col, typename FlexModInt< Int >::PolE &pcol)
	Takes the polynomial pcol and returns in col the corresponding column in the matrix of generating vectors.

Protected Attributes
IntVec	m_lac
	Stores the lacunary indices.
IntMat	m_copy_primal_basis
	If we want to increase the dimension of the dual basis with the polynomial approach we also need a copy of the primal and the dual basis.
IntMat	m_copy_dual_basis
Protected Attributes inherited from LatMRG::MRGLattice< Int, Real >
IntMat	m_genTemp
	This auxiliary matrix is used to store the generating vectors of a projections before reducing them into a triangular basis.
IntMat	m_copy_primal_basis
	For generating the dual basis or increasing its dimension, we need a copy of the the primal basis if we use polynomial arithmetic.
int	m_order
IntVec	m_aCoeff
	The coefficients \(a_1, ..., a_k\) of the MRG recurrence, a_j stored in m_aCoeff[j].

Detailed Description

template<typename Int, typename Real>
class LatMRG::MRGLatticeLac< Int, Real >

This subclass of MRGLattice constructs and handles lattice bases built from MRGs as in MRGLattice, but with arbitrary lacunary indices that can be spaced very far apart.

A special case of this is when they are regularly spaced by packets of the same size.

To construct or increment the basis in that case, we proceed as described in Section 3.1.9 of the guide. First, \(P(z)\) must be set as the polynomial modulus in NTL. Then for each lacunary index \(\nu = i_j\), we compute the corresponding column by computing \(z^{\nu-1} \bmod P(z)\) using power from polE in NTL, then transforming its vector of coefficients into the vector \((y_{\nu+k-2},\dots,y_{\nu-1})\) with the function polyToColumn. This gives a set of generating vectors, which can be reduced to a basis, as in MRGLattice. Under certain conditions, it is already a basis.

Constructor & Destructor Documentation

◆ MRGLatticeLac() [1/2]

template<typename Int, typename Real>

LatMRG::MRGLatticeLac< Int, Real >::MRGLatticeLac	(	const Int &	m,
		const IntVec &	aa,
		int64_t	maxDim,
		IntVec &	lac,
		NormType	norm = L2NORM )

Constructor with modulus of congruence \(m\), order of the recurrence \(k\), multipliers in aa, and maximal dimension maxDim.

The length of basis vectors is computed with norm. The basis is built for the lacunary indices in lac. The vector aa must have k+1 components with a[j]= \(a_j\).

◆ MRGLatticeLac() [2/2]

template<typename Int, typename Real>

LatMRG::MRGLatticeLac< Int, Real >::MRGLatticeLac ( const MRGLatticeLac< Int, Real > & Lat )

Copy constructor.

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

◆ ~MRGLatticeLac()

template<typename Int, typename Real>

virtual LatMRG::MRGLatticeLac< Int, Real >::~MRGLatticeLac ( )

inlinevirtual

Destructor.

Member Function Documentation

◆ operator=()

template<typename Int, typename Real>

MRGLatticeLac< Int, Real > & LatMRG::MRGLatticeLac< Int, Real >::operator= ( const MRGLatticeLac< Int, Real > & Lat )

Assigns Lat to this object.

The maximal dimension of this basis is set to Lat’s current dimension.

◆ setLac()

template<typename Int, typename Real>

void LatMRG::MRGLatticeLac< Int, Real >::setLac	(	const IntVec &	lac,
		bool	buildBasisCopy = true )

Sets the lacunary indices for this lattice to lac.

If 'buildBasisCopy' is set to true, then 'm_copy_primal_basis' and 'm_dual_copy_basis' are updated according to the new lacunary indices.

◆ setaa()

template<typename Int, typename Real>

void LatMRG::MRGLatticeLac< Int, Real >::setaa	(	const IntVec &	lac,
		bool	buildBasisCopy = true )

Sets the generating vector to aa.

If 'buildBasisCopy' is set to true, then 'm_copy_primal_basis' and 'm_dual_copy_basis' are updated according to the new generator vector.

◆ getLac()

template<typename Int, typename Real>

Int & LatMRG::MRGLatticeLac< Int, Real >::getLac ( int j )

inline

Returns the \(j\)-th lacunary index.

◆ buildBasis0()

template<typename Int, typename Real>

void LatMRG::MRGLatticeLac< Int, Real >::buildBasis0	(	IntMat &	basis,
		int64_t	d )

overrideprotectedvirtual

This function overrides the correpsonding protected function in 'MRGLattice'.

It Builds a basis directly in d dimensions, as explained in Section 3.1.9 of the LatMRG guide. Must have d <= m_maxdim. The basis matrix is taken as a parameter.

Reimplemented from LatMRG::MRGLattice< Int, Real >.

◆ buildDualBasis0()

template<typename Int, typename Real>

void LatMRG::MRGLatticeLac< Int, Real >::buildDualBasis0	(	IntMat &	basis,
		int64_t	d )

overrideprotectedvirtual

This functions overrides the corresponding protected function in 'MRGLattice', which is necessary because the entire copy of the primal basis is build upon creation of the object.

Reimplemented from LatMRG::MRGLattice< Int, Real >.

◆ incDimBasis0()

template<typename Int, typename Real>

void LatMRG::MRGLatticeLac< Int, Real >::incDimBasis0	(	IntMat &	basis,
		int64_t	d )

overrideprotectedvirtual

This function overrides the correpsonding protected function in 'MRGLattice'.

It increases the dimension of the given basis from d-1 to d dimensions. One new column is calclated using the algorithm from the guide.

Reimplemented from LatMRG::MRGLattice< Int, Real >.

◆ incDimDualBasis0()

template<typename Int, typename Real>

void LatMRG::MRGLatticeLac< Int, Real >::incDimDualBasis0	(	IntMat &	basis,
		int64_t	d )

overrideprotectedvirtual

This function overrides the correpsonding protected function in 'MRGLattice'.

It increases the dimension of a given dual basis from d-1 to d dimensions. One new column is calclated using the polynomial representation.

Reimplemented from LatMRG::MRGLattice< Int, Real >.

◆ buildProjection0()

template<typename Int, typename Real>

bool LatMRG::MRGLatticeLac< Int, Real >::buildProjection0	(	IntMat &	basis,
		int64_t	dimbasis,
		IntMat &	pbasis,
		const Coordinates &	proj )

overrideprotectedvirtual

This function overrides the correpsonding protected function in 'MRGLattice'.

It builds a projection for the primal basis.

Reimplemented from LatMRG::MRGLattice< Int, Real >.

◆ polyToColumn()

template<typename Int, typename Real>

void LatMRG::MRGLatticeLac< Int, Real >::polyToColumn	(	IntVec &	col,
		typename FlexModInt< Int >::PolE &	pcol )

protected

Takes the polynomial pcol and returns in col the corresponding column in the matrix of generating vectors.

Member Data Documentation

◆ m_lac

template<typename Int, typename Real>

IntVec LatMRG::MRGLatticeLac< Int, Real >::m_lac

protected

Stores the lacunary indices.

◆ m_copy_primal_basis

template<typename Int, typename Real>

IntMat LatMRG::MRGLatticeLac< Int, Real >::m_copy_primal_basis

protected

If we want to increase the dimension of the dual basis with the polynomial approach we also need a copy of the primal and the dual basis.

◆ m_copy_dual_basis

template<typename Int, typename Real>

IntMat LatMRG::MRGLatticeLac< Int, Real >::m_copy_dual_basis

protected

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

include/latmrg/MRGLatticeLac.h

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MRGLatticeLac() [1/2]

◆ MRGLatticeLac() [2/2]

◆ ~MRGLatticeLac()

Member Function Documentation

◆ operator=()

◆ setLac()

◆ setaa()

◆ getLac()

◆ buildBasis0()

◆ buildDualBasis0()

◆ incDimBasis0()

◆ incDimDualBasis0()

◆ buildProjection0()

◆ polyToColumn()

Member Data Documentation

◆ m_lac

◆ m_copy_primal_basis

◆ m_copy_dual_basis