This subclass of IntLatticeExt defines an MRG lattice and is similar to Rank1Lattice, but constructs lattices associated with multiple recursive generators (MRGs) with modulus m, order k, and vector of multipliers a = (a_1, . More...

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

Public Member Functions
	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
virtual void	buildBasis0 (IntMat &basis, int64_t d)
	The following protected functions take the basis as a parameter for more flexibility.
virtual void	buildDualBasis0 (IntMat &basis, int64_t d)
virtual void	incDimBasis0 (IntMat &basis, int64_t d)
virtual void	incDimDualBasis0 (IntMat &basis, int64_t d)
virtual bool	buildProjection0 (IntMat &basis, int64_t dimbasis, IntMat &pbasis, const Coordinates &proj)

Protected Attributes
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::MRGLattice< Int, Real >

This subclass of IntLatticeExt defines an MRG lattice and is similar to Rank1Lattice, but constructs lattices associated with multiple recursive generators (MRGs) with modulus m, order k, and vector of multipliers a = (a_1, .

. . , a_k).

The functions buildBasis and incDimBasis always build and update the primal basis. To build the m-dual, use buildDualBasis.

Constructor & Destructor Documentation

◆ MRGLattice() [1/2]

template<typename Int, typename Real>

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.

The vector aa must have length k+1, with \(a_j\) in aa[j]. The maximal dimension maxDim will be the maximal dimension of the basis. This constructor does not build the basis, so we can build it for a smaller number of dimensions or only for selected projections.

◆ MRGLattice() [2/2]

template<typename Int, typename Real>

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

◆ ~MRGLattice()

template<typename Int, typename Real>

LatMRG::MRGLattice< Int, Real >::~MRGLattice ( )

Destructor.

Member Function Documentation

◆ operator=()

template<typename Int, typename Real>

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

Assigns Lat to this object.

◆ setaa()

template<typename Int, typename Real>

void LatMRG::MRGLattice< Int, Real >::setaa ( const IntVec & aa )

virtual

Sets the vector of multipliers.

Sets the generating vector to aa.

The order k of the lattice is set equal to the length of this vector, minus 1. aa[j] must contain \(a_j\) for j=1,...,k.

◆ buildBasis()

template<typename Int, typename Real>

void LatMRG::MRGLattice< Int, Real >::buildBasis ( int64_t dim )

Builds a basis in dim dimensions.

This dim must not exceed this->maxDim(). This initial primal basis will be upper triangular - based on V^{(0)} or V^{(p)} depending on which approach is chosen by the user.

◆ buildDualBasis()

template<typename Int, typename Real>

void LatMRG::MRGLattice< Int, Real >::buildDualBasis ( int64_t dim )

Builds the m-dual lower triangular basis directly in dim dimensions.

This dim must not exceed maxDim. In order to build the m-dual basis, the primal basis is needed, even if it has not been built yet. Therefore, a copy of the basis matrix is always created upon building the m-dual basis. It is stored in the variable 'm_copy_primal_basis'.

◆ incDimBasis()

template<typename Int, typename Real>

void LatMRG::MRGLattice< Int, Real >::incDimBasis ( )

Increases the current dimension of the primal basis by 1 and updates the basis.

The new increased dimension must not exceed maxDim.

◆ incDimDualBasis()

template<typename Int, typename Real>

void LatMRG::MRGLattice< Int, Real >::incDimDualBasis ( )

Increases the current dimension of the m-dual basis by 1.

The new increased dimension must not exceed maxDim. This function uses the simplified method for MRG lattices given in the lattice tester guide. It requires to increase the dimension of 'm_copy_primal_basis' as well.

◆ buildProjection()

template<typename Int, typename Real>

void LatMRG::MRGLattice< Int, Real >::buildProjection	(	IntLattice< Int, Real > &	projLattice,
		const Coordinates &	proj )

override

This method overrides its namesake in IntLattice.

A basis for the projection of this MRGLattice over the coordinates in proj is returned in projLattice. The implementation used here exploits the rank-k lattice structure and it is faster than the general one. See Section 3.1.7 of the LatMRG guide.

◆ buildProjectionDual()

template<typename Int, typename Real>

void LatMRG::MRGLattice< Int, Real >::buildProjectionDual	(	IntLattice< Int, Real > &	projLattice,
		const Coordinates &	proj )

override

Overrides the same function from IntLattice.

When all the first k coordinates {1,...,k} belong to the projection, both the primal and m-dual constructions are direct, just by selecting the rows and columns whose indices are in proj. Otherwise an upper triangular basis is constructed for the basis and a lower-triangular basis for the m-dual.

◆ toStringCoef()

template<typename Int, typename Real>

std::string LatMRG::MRGLattice< Int, Real >::toStringCoef ( ) const

Returns the first dim components of the generating vector \(\ba\) as a string, where dim is the current lattice dimension.

◆ buildBasis0()

template<typename Int, typename Real>

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

protectedvirtual

The following protected functions take the basis as a parameter for more flexibility.

They are used inside buildBasis, buildBasisDual, incDimBasis, etc. For building the basis either the standard approach or the polynomial approach can be chosen. The polynomial approach is implemented in those functions ending with Pol

Reimplemented in LatMRG::MRGLatticeLac< Int, Real >.

◆ buildDualBasis0()

template<typename Int, typename Real>

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

protectedvirtual

Reimplemented in LatMRG::MRGLatticeLac< Int, Real >.

◆ incDimBasis0()

template<typename Int, typename Real>

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

protectedvirtual

Reimplemented in LatMRG::MRGLatticeLac< Int, Real >.

◆ incDimDualBasis0()

template<typename Int, typename Real>

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

protectedvirtual

Reimplemented in LatMRG::MRGLatticeLac< Int, Real >.

◆ buildProjection0()

template<typename Int, typename Real>

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

protectedvirtual

Reimplemented in LatMRG::MRGLatticeLac< Int, Real >.

Member Data Documentation

◆ m_genTemp

template<typename Int, typename Real>

IntMat LatMRG::MRGLattice< Int, Real >::m_genTemp

protected

This auxiliary matrix is used to store the generating vectors of a projections before reducing them into a triangular basis.

◆ m_copy_primal_basis

template<typename Int, typename Real>

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

protected

For generating the dual basis or increasing its dimension, we need a copy of the the primal basis if we use polynomial arithmetic.

Otherwise we just need to keep the first m_order rows of the matrix and save it here.

◆ m_order

template<typename Int, typename Real>

int LatMRG::MRGLattice< Int, Real >::m_order

protected

◆ m_aCoeff

template<typename Int, typename Real>

IntVec LatMRG::MRGLattice< Int, Real >::m_aCoeff

protected

The coefficients \(a_1, ..., a_k\) of the MRG recurrence, a_j stored in m_aCoeff[j].

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

include/latmrg/MRGLattice.h

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MRGLattice() [1/2]

◆ MRGLattice() [2/2]

◆ ~MRGLattice()

Member Function Documentation

◆ operator=()

◆ setaa()

◆ buildBasis()

◆ buildDualBasis()

◆ incDimBasis()

◆ incDimDualBasis()

◆ buildProjection()

◆ buildProjectionDual()

◆ toStringCoef()

◆ buildBasis0()

◆ buildDualBasis0()

◆ incDimBasis0()

◆ incDimDualBasis0()

◆ buildProjection0()

Member Data Documentation

◆ m_genTemp

◆ m_copy_primal_basis

◆ m_order

◆ m_aCoeff