This subclass of IntLatticeExt defines an MRG lattice. More...

Inheritance diagram for LatticeTester::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 ()
	Destructor.

void	setaa (const IntVec &aa)
	Sets the vector of multipliers.

void	buildBasis (int64_t dim)
	Builds a primal basis in `dim` dimensions.

void	buildDualBasis (int64_t dim)
	Builds an 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 \(\mathbf{a}\) as a string, where `dim` is the current lattice dimension.

Public Member Functions inherited from LatticeTester::IntLatticeExt< Int, Real >
	IntLatticeExt (Int m, int64_t maxDim, NormType norm=L2NORM)
	A constructor that reserves the space for the primal and m-dual bases and vector lengths, but does not initialize them.

virtual	~IntLatticeExt ()
	Destructor.

Public Member Functions inherited from LatticeTester::IntLattice< Int, Real >
	IntLattice (const Int m, const int64_t maxDim, NormType norm=L2NORM)
	Constructs a lattice whose basis is uninitialized, in `maxDim` dimensions, with the scaling factor `m` and specified norm type.

	IntLattice (const IntMat basis, const Int m, const int64_t maxDim, NormType norm=L2NORM)
	Similar to the previous constructor, except that the primal basis is given in `basis`, which must be an `IntMat` object of size `maxDim` by `maxDim`.

	IntLattice (const IntMat primalbasis, const IntMat dualbasis, const Int m, const int64_t maxDim, NormType norm=L2NORM)
	Constructs a lattice with the given basis and given m-dual basis for the given `m`, in `maxDim` dimensions, and with the specified norm type.

virtual	~IntLattice ()
	Destructor.

virtual void	buildProjectionLLL (IntLattice< Int, Real > &projLattice, const Coordinates &proj, double delta=0.5)
	Constructs a set of generating vectors for the projection of the present lattice, over the set of coordinates determined by `proj`, and builds a basis for that projection using an LLL procedure from `BasisConstruction`.

IntMat &	getBasis ()
	Returns the `IntMat` object that contains the basis of this lattice.

void	setBasis (const IntMat basis, const Int m, const int64_t dim, NormType norm=L2NORM)
	Changes the basis to 'basis', the modulus to 'm', and the current dimension to 'dim'.

void	setBasis (const IntMat basis, const int64_t dim)
	Changes only the 'basis' and the current dimension to 'dim'.

IntMat &	getDualBasis ()
	Returns the m-dual basis represented in a matrix.

int64_t	getMaxDim () const
	Returns the maximal dimension for this lattice.

int64_t	getDim () const
	Returns the current dimension of the primal lattice, which should be the dimension of the basis vectors and also the number of independent vectors in the basis.

int64_t	getDimDual () const
	Returns the current dimension of the m-dual lattice.

NormType	getNormType () const
	Returns the `NormType` used by this lattice.

Real	getVecNorm (const int64_t &i)
	Returns the norm (squared in case of the L^2 norm) of the i-th vector of the basis, with the index i starting at 0.

RealVec	getVecNorm () const
	Returns the norm (squared in case of the L^2 norm) of each basis vector, in a vector.

Real	getDualVecNorm (const int64_t &i)
	Returns the norm (squared in case of the L^2 norm) of the i-th vector of the m-dual basis.

RealVec	getDualVecNorm () const
	Returns the norm (squared in case of the L^2 norm) of each vector of the m-dual basis, in a vector.

Int	getModulus () const
	Returns the scaling factor `m`.

void	setDim (const int64_t dim)
	Sets the dimension of the primal basis to `dim`.

void	setDimDual (const int64_t dim)
	Sets the dimension of the m-dual basis to `dim`.

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

void	setVecNorm (const Real &value, const int64_t &i)
	Sets the norm of the `i`-th component of the basis to `value`, which is assumed to be the correct value.

void	setDualVecNorm (const Real &value, const int64_t &i)
	Sets the norm of the `i`-th component of the m-dual basis to `value`, which is assumed to be the correct value.

void	setNegativeNorm ()
	Sets to -1 the first `dim` values in the array containing the norms of the basis vectors, where `dim` is the current dimension of the lattice.

void	setNegativeNorm (const int64_t &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, to indicate that these norms are no longer up to date.

void	setDualNegativeNorm (const int64_t &i)
	Sets the value of the `i`-th component in the array containing the norms of the m-dual basis vectors to -1.

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

void	updateVecNorm (const int64_t &d)
	Updates the array containing the norm of the basis vectors from the `d`-th component to the last, by recomputing them.

void	updateSingleVecNorm (const int64_t &d, const int64_t &c)
	Updates the 'd'-th entry of the array containing the basis vectors norms.

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

void	updateSingleDualVecNorm (const int64_t &d, const int64_t &c)
	Updates the 'd'-th entry of the array containing the m-dual basis vectors norms.

void	updateDualVecNorm (const int64_t &d)
	Updates the array containing the m-dual basis vectors norms from the `d`-th component to the last by recomputing them.

void	updateDualVecNorm (const int64_t &d, const int64_t &c)
	Updates the array containing the m-dual basis vectors norms from the `d`-th component to the last by recomputing them.

void	updateScalL2Norm (const int64_t i)
	Updates the `i`-th value of the array containing the square norms of the basis vectors by recomputing it using the `L2NORM`.

void	updateScalL2Norm (const int64_t k1, const int64_t k2)
	Updates the `k1`-th to the `k2-1`-th values of the array containing the square norms of the basis vectors by recomputing them using the `L2NORM`.

void	updateDualScalL2Norm (const int64_t i)
	Updates the `i`-th value of the array containing the square norms of the m-dual basis vectors by recomputing it using the `L2NORM`.

void	updateDualScalL2Norm (const int64_t k1, const int64_t k2)
	Updates the `k1`-th to the `k2-1`-th values of the array containing the square norms of the m-dual basis vectors by recomputing them using the `L2NORM`.

void	permute (int64_t i, int64_t j)
	Exchanges vectors `i` and `j` in the basis.

void	permuteDual (int64_t i, int64_t j)
	Exchanges vectors `i` and `j` in the `m`-dual basis without changing the primal.

void	dualize ()
	Exchanges the primal and m-dual bases, their dimensions, and vector norms.

bool	checkDuality ()
	Returns `true` iff the m-dual basis contained in the object really is the m-dual of the current primal basis.

void	sortBasis (int64_t d)
	Sorts the primal basis vectors with indices greater of equal to `d` by increasing length.

void	sortDualBasis (int64_t d)
	Sorts the `m`-dual basis vectors with indices greater of equal to `d` by increasing length.

std::string	toStringBasis () const
	Returns a string that contains the primal basis vectors and their norms.

std::string	toStringDualBasis () const
	Returns a string with the `m`-dual basis vectors and their norms.

std::string	toString () const
	Returns a string that represents this lattice and its parameters.

Public Attributes
int	m_order

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

Protected Member Functions
void	buildBasis0 (IntMat &basis, int64_t d)
	The following protected functions take the basis as a parameter for more flexibility.

void	incDimBasis0 (IntMat &basis, int64_t d)

bool	buildProjection0 (IntMat &basis, int64_t dimbasis, IntMat &pbasis, const Coordinates &proj)

Protected Member Functions inherited from LatticeTester::IntLatticeExt< Int, Real >
virtual void	kill ()

Protected Attributes
IntMat	m_basis0
	This matrix contains the initial basis V for the MRG lattice as defined in Section 4.1 of the LatMRG guide.

int64_t	m_dim0 = 0
	The current dimension of `m_basis0`.

IntVec	m_y
	A vector to store \(y_0, y_1, ..., y_{t+k-2}\) used in the matrix V^{(p)}.

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

Protected Attributes inherited from LatticeTester::IntLattice< Int, Real >
Int	m_modulo
	The scaling factor `m` used for rescaling the lattice.

int64_t	m_maxDim
	The maximal dimension for this lattice.

int64_t	m_dim
	The current dimension of the primal basis, which is the number of (independent) vectors in it.

int64_t	m_dimdual
	The current dimension of the m-dual basis, which is the number of (independent) vectors in its basis.

IntMat	m_basis
	The rows of the m_dim x m_dim upper left corner of this matrix are the primal basis vectors.

IntMat	m_dualbasis
	The rows of the m_dim x m_dim upper left corner this matrix are the m-dual basis vectors.

NormType	m_norm
	The NormType used to measure the vector lengths for this lattice.

RealVec	m_vecNorm
	A vector that stores the norm of each basis vector.

RealVec	m_dualvecNorm
	Similar to vecNorm, but for the m-dual basis.

Detailed Description

template<typename Int, typename Real>
class LatticeTester::MRGLattice< Int, Real >

This subclass of IntLatticeExt defines an MRG lattice.

It is similar to Rank1Lattice, but constructs lattices associated with multiple recursive generators (MRGs) with modulus \(m\), order \(k\), and vector of multipliers \(\mathbf{a} = (a_1, . . . , a_k)\). The functions buildBasis and incDimBasis always build and update the primal basis. To build the m-dual, use buildDualBasis.

Constructor & Destructor Documentation

◆ MRGLattice()

template<typename Int , typename Real >

LatticeTester::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()

template<typename Int , typename Real >

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

Destructor.

Member Function Documentation

◆ setaa()

template<typename Int , typename Real >

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

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

virtual

Builds a primal basis in dim dimensions.

This dim must not exceed this->maxDim(). This initial primal basis will be upper triangular.

Reimplemented from LatticeTester::IntLatticeExt< Int, Real >.

◆ buildDualBasis()

template<typename Int , typename Real >

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

virtual

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

This dim must not exceed maxDim. This function uses the existing primal basis if it has at least dim dimensions, otherwise it also computes it in dim dimensions.

Reimplemented from LatticeTester::IntLatticeExt< Int, Real >.

◆ incDimBasis()

template<typename Int , typename Real >

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

virtual

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

The new increased dimension must not exceed maxDim.

Reimplemented from LatticeTester::IntLatticeExt< Int, Real >.

◆ incDimDualBasis()

template<typename Int , typename Real >

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

virtual

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 the original primal basis to update the m-dual, so if the dimension of the primal is smaller than the new dimension of the m-dual, the dimension of the primal will also be increased to that new dimension.

Reimplemented from LatticeTester::IntLatticeExt< Int, Real >.

◆ buildProjection()

template<typename Int , typename Real >

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

overridevirtual

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 5.5 of the LatMRG guide.

Reimplemented from LatticeTester::IntLattice< Int, Real >.

◆ buildProjectionDual()

template<typename Int , typename Real >

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

overridevirtual

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.

Reimplemented from LatticeTester::IntLattice< Int, Real >.

◆ toStringCoef()

template<typename Int , typename Real >

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

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

◆ buildBasis0()

template<typename Int , typename Real >

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

protected

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

They are used inside buildBasis, buildBasisDual, incDimBasis, etc., with either m_basis or m_basis0.

◆ incDimBasis0()

template<typename Int , typename Real >

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

protected

◆ buildProjection0()

template<typename Int , typename Real >

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

protected

Member Data Documentation

◆ m_order

template<typename Int , typename Real >

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

◆ m_aCoeff

template<typename Int , typename Real >

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

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

◆ m_basis0

template<typename Int , typename Real >

IntMat LatticeTester::MRGLattice< Int, Real >::m_basis0

protected

This matrix contains the initial basis V for the MRG lattice as defined in Section 4.1 of the LatMRG guide.

It is used only to calculate or update the m-dual basis. Its dimension is enlarged whenever needed and never reduced.

◆ m_dim0

template<typename Int , typename Real >

int64_t LatticeTester::MRGLattice< Int, Real >::m_dim0 = 0

protected

The current dimension of m_basis0.

◆ m_y

template<typename Int , typename Real >

IntVec LatticeTester::MRGLattice< Int, Real >::m_y

protected

A vector to store \(y_0, y_1, ..., y_{t+k-2}\) used in the matrix V^{(p)}.

◆ m_genTemp

template<typename Int , typename Real >

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

protected

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

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

include/latticetester/MRGLattice.h

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MRGLattice()

◆ ~MRGLattice()

Member Function Documentation

◆ setaa()

◆ buildBasis()

◆ buildDualBasis()

◆ incDimBasis()

◆ incDimDualBasis()

◆ buildProjection()

◆ buildProjectionDual()

◆ toStringCoef()

◆ buildBasis0()

◆ incDimBasis0()

◆ buildProjection0()

Member Data Documentation

◆ m_order

◆ m_aCoeff

◆ m_basis0

◆ m_dim0

◆ m_y

◆ m_genTemp