An IntLattice object is an integral lattice, with its basis or its m-dual basis, or both. More...

Inheritance diagram for LatticeTester::IntLattice< Int, Real >:

Public Member Functions
	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`.

virtual void	buildProjection (IntLattice< Int, Real > &projLattice, const Coordinates &proj)
	Builds a basis for the projection of the present lattice over the set of coordinates determined by `proj`.

virtual void	buildProjectionDual (IntLattice< Int, Real > &projLattice, const Coordinates &proj)
	Similar to `buildProjection`, except that it builds an upper-triangular basis for the primal and a lower-triangular basis for the $m$-dual of the projection, both in `projLattice`.

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.

Protected Attributes
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::IntLattice< Int, Real >

An IntLattice object is an integral lattice, with its basis or its m-dual basis, or both.

There are tools to perform simple manipulations on those lattice bases, to compute and store the vector lengths, etc. It is assumed that the value of m is chosen so that all coordinates of the basis and of its m-dual are integers. These coordinates are then represented exactly on the computer. This property is typically achieved by rescaling the primal lattice by the appropriate factor m, as explained in the guide.

The dimension dim of the lattice is the number of independent vectors that form a basis. In general, these basis vectors could have more than dim coordinates, but in this software we assume that the number of coordinates is always equal to the lattice dimension, and that the vectors $m \mathbf{e}_i$, which are $m$ times the unit vectors, all belong to the lattice. The basis and/or the m-dual basis are stored in IntMat arrays (from NTL) of sizes maxDim x maxDim, where maxDim is usually fixed to a value as large as the largest dim that we want to handle. We use only the upper-left dim x dim corner of each array to store the actual basis. These arrays can then be allocated only once and never have to be resized, which improves speed. There are internal variables for the dimensions of the primal and m-dual basis. For the basis that is not maintained, that variable should be set to 0.

Methods are offered to compute and store the norms of the basis and/or the m-dual basis vectors, to permute these vectors, sort them by length, etc. Some quantities are stored in protected variables. A norm must be chosen to measure the vector lengths in the (rescaled) primal lattice and its m-dual; by default it is the Euclidean norm. For better efficiency, we should avoid creating many IntLattice objects, for example when making searches for good lattices. We should try to reuse the same one as much as we can.

Often, we want to assess the quality of projections of the lattice over subsets of coordinates. The method buildProjection computes a basis for the lattice defined as the projection of the full lattice on a subset $I$ of coordinates indices defined by a Coordinates object. When computing figures of merit, one may want to recompute a basis for a large number of different projections, which can be specified by a CoordinateSets object.

The class IntLatticeExt extends this class and contains additional virtual methods that depend on the specific lattice type that is considered. These methods must be defined in subclasses.

Constructor & Destructor Documentation

◆ IntLattice() [1/3]

template<typename Int , typename Real >

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() [2/3]

template<typename Int , typename Real >

LatticeTester::IntLattice< Int, Real >::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() [3/3]

template<typename Int , typename Real >

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

The two IntMat objects must be of size maxDim by maxDim.

◆ ~IntLattice()

template<typename Int , typename Real >

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

virtual

Destructor.

Member Function Documentation

◆ buildProjectionLLL()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::buildProjectionLLL	(	IntLattice< Int, Real > &	projLattice,
		const Coordinates &	proj,
		double	delta = 0.5 )

virtual

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.

It is assumed that a basis for the present lattice is already available and contains all the coordinates in proj. The maxDim of the projLattice object must be large enough so it can holds the projection. The modulus m is assumed to be the same for projLattice and for the current object. This function can be called several times with the same projLattice object to examine several different projections. Note that representing each projection as an IntLattice object is required when we want to call Reducer::shortestVector for several projections. This function can be overridden by more efficient ones in subclasses.

◆ buildProjection()

template<typename Int , typename Real >

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

virtual

Builds a basis for the projection of the present lattice over the set of coordinates determined by proj.

This becomes the basis in projLattice. By default, it uses an upper-triangular construction, but it can be overridden in subclasses. It is assumed that a basis for the present lattice is already available and contains all the coordinates in proj.

Reimplemented in LatticeTester::MRGLattice< Int, Real >, and LatticeTester::Rank1Lattice< Int, Real >.

◆ buildProjectionDual()

template<typename Int , typename Real >

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

virtual

Similar to buildProjection, except that it builds an upper-triangular basis for the primal and a lower-triangular basis for the $m$-dual of the projection, both in projLattice.

The dimensions in the latter are updated. We should use this function when we need a basis for the $m$-dual of the projection.

Reimplemented in LatticeTester::MRGLattice< Int, Real >, and LatticeTester::Rank1Lattice< Int, Real >.

◆ getBasis()

template<typename Int , typename Real >

IntMat & LatticeTester::IntLattice< Int, Real >::getBasis ( )

inline

Returns the IntMat object that contains the basis of this lattice.

◆ setBasis() [1/2]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::setBasis	(	const IntMat	basis,
		const Int	m,
		const int64_t	dim,
		NormType	norm = L2NORM )

inline

Changes the basis to 'basis', the modulus to 'm', and the current dimension to 'dim'.

Does not change maxDim.

◆ setBasis() [2/2]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::setBasis	(	const IntMat	basis,
		const int64_t	dim )

inline

Changes only the 'basis' and the current dimension to 'dim'.

Does not change m and maxDim.

◆ getDualBasis()

template<typename Int , typename Real >

IntMat & LatticeTester::IntLattice< Int, Real >::getDualBasis ( )

inline

Returns the m-dual basis represented in a matrix.

◆ getMaxDim()

template<typename Int , typename Real >

int64_t LatticeTester::IntLattice< Int, Real >::getMaxDim ( ) const

inline

Returns the maximal dimension for this lattice.

◆ getDim()

template<typename Int , typename Real >

int64_t LatticeTester::IntLattice< Int, Real >::getDim ( ) const

inline

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.

◆ getDimDual()

template<typename Int , typename Real >

int64_t LatticeTester::IntLattice< Int, Real >::getDimDual ( ) const

inline

Returns the current dimension of the m-dual lattice.

◆ getNormType()

template<typename Int , typename Real >

NormType LatticeTester::IntLattice< Int, Real >::getNormType ( ) const

inline

Returns the NormType used by this lattice.

◆ getVecNorm() [1/2]

template<typename Int , typename Real >

Real LatticeTester::IntLattice< Int, Real >::getVecNorm ( const int64_t & i )

inline

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.

◆ getVecNorm() [2/2]

template<typename Int , typename Real >

RealVec LatticeTester::IntLattice< Int, Real >::getVecNorm ( ) const

inline

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

◆ getDualVecNorm() [1/2]

template<typename Int , typename Real >

Real LatticeTester::IntLattice< Int, Real >::getDualVecNorm ( const int64_t & i )

inline

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

The index i starts at 0.

◆ getDualVecNorm() [2/2]

template<typename Int , typename Real >

RealVec LatticeTester::IntLattice< Int, Real >::getDualVecNorm ( ) const

inline

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

◆ getModulus()

template<typename Int , typename Real >

Int LatticeTester::IntLattice< Int, Real >::getModulus ( ) const

inline

Returns the scaling factor m.

◆ setDim()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::setDim ( const int64_t dim )

inline

Sets the dimension of the primal basis to dim.

This does not change maxDim nor any of the basis vectors, but only the dimension variable.

◆ setDimDual()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::setDimDual ( const int64_t dim )

inline

Sets the dimension of the m-dual basis to dim.

This does not change maxDim nor any of the basis vectors, but only the dimension variable.

◆ setNormType()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::setNormType ( const NormType & norm )

inline

Sets the NormType used by this lattice to norm.

◆ setVecNorm()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::setVecNorm	(	const Real &	value,
		const int64_t &	i )

inline

Sets the norm of the i-th component of the basis to value, which is assumed to be the correct value.

To recompute the norm, use updateVecNorm(const int64_t&) instead.

◆ setDualVecNorm()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::setDualVecNorm	(	const Real &	value,
		const int64_t &	i )

inline

Sets the norm of the i-th component of the m-dual basis to value, which is assumed to be the correct value.

To recompute the norm, use updateDualVecNorm(const int64_t&) instead.

◆ setNegativeNorm() [1/2]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::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.

This means that these norms are no longer up to date.

◆ setNegativeNorm() [2/2]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::setNegativeNorm ( const int64_t & i )

inline

Sets the value of the i-th component in the array containing the norms of the basis vectors to -1.

◆ setDualNegativeNorm() [1/2]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::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.

◆ setDualNegativeNorm() [2/2]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::setDualNegativeNorm ( const int64_t & i )

inline

Sets the value of the i-th component in the array containing the norms of the m-dual basis vectors to -1.

◆ updateVecNorm() [1/2]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::updateVecNorm ( )

Updates the array containing the norms of the basis vectors by recomputing them.

We could also return the index of the vector that is shortest!

◆ updateVecNorm() [2/2]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::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.

Putting d=0 recomputes all the norms.

◆ updateSingleVecNorm()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::updateSingleVecNorm	(	const int64_t &	d,
		const int64_t &	c )

Updates the 'd'-th entry of the array containing the basis vectors norms.

Only the first c components are used for calculating the norm.

◆ updateDualVecNorm() [1/3]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::updateDualVecNorm ( )

Updates the array containing the m-dual basis vectors norms by recomputing them.

Assumes that the dual basis is available.

◆ updateSingleDualVecNorm()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::updateSingleDualVecNorm	(	const int64_t &	d,
		const int64_t &	c )

Updates the 'd'-th entry of the array containing the m-dual basis vectors norms.

Only the first c components are used for calculating the norm.

◆ updateDualVecNorm() [2/3]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::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.

◆ updateDualVecNorm() [3/3]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::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.

Only the first c components are used for calculating the norm

◆ updateScalL2Norm() [1/2]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::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.

◆ updateScalL2Norm() [2/2]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::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.

◆ updateDualScalL2Norm() [1/2]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::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.

◆ updateDualScalL2Norm() [2/2]

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::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.

◆ permute()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::permute	(	int64_t	i,
		int64_t	j )

Exchanges vectors i and j in the basis.

Also exchanges secondary information about these two vectors (like the norms).

◆ permuteDual()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::permuteDual	(	int64_t	i,
		int64_t	j )

Exchanges vectors i and j in the m-dual basis without changing the primal.

◆ dualize()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::dualize ( )

Exchanges the primal and m-dual bases, their dimensions, and vector norms.

◆ checkDuality()

template<typename Int , typename Real >

bool LatticeTester::IntLattice< Int, Real >::checkDuality ( )

Returns true iff the m-dual basis contained in the object really is the m-dual of the current primal basis.

Otherwise, it returns false.

◆ sortBasis()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::sortBasis ( int64_t d )

Sorts the primal basis vectors with indices greater of equal to d by increasing length.

The m-dual vectors are permuted accordingly. Assumes that the lengths (norms) of the corresponding basis vectors are up to date. The dual basis vectors are not permuted.

◆ sortDualBasis()

template<typename Int , typename Real >

void LatticeTester::IntLattice< Int, Real >::sortDualBasis ( int64_t d )

Sorts the m-dual basis vectors with indices greater of equal to d by increasing length.

The primal basis vectors are not permuted.

◆ toStringBasis()

template<typename Int , typename Real >

std::string LatticeTester::IntLattice< Int, Real >::toStringBasis ( ) const

Returns a string that contains the primal basis vectors and their norms.

◆ toStringDualBasis()

template<typename Int , typename Real >

std::string LatticeTester::IntLattice< Int, Real >::toStringDualBasis ( ) const

Returns a string with the m-dual basis vectors and their norms.

◆ toString()

template<typename Int , typename Real >

std::string LatticeTester::IntLattice< Int, Real >::toString ( ) const

Returns a string that represents this lattice and its parameters.

It contains the dimension, the norm used, the basis and m-dual basis vectors and the basis and dual basis vector norms.

Member Data Documentation

◆ m_modulo

template<typename Int , typename Real >

Int LatticeTester::IntLattice< Int, Real >::m_modulo

protected

The scaling factor m used for rescaling the lattice.

◆ m_maxDim

template<typename Int , typename Real >

int64_t LatticeTester::IntLattice< Int, Real >::m_maxDim

protected

The maximal dimension for this lattice.

It should correspond to the size of the IntMat objects that contain the basis and/or its m-dual.

◆ m_dim

template<typename Int , typename Real >

int64_t LatticeTester::IntLattice< Int, Real >::m_dim

protected

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

It cannot exceed the number of coordinates in those vectors. It also cannot exceed m_maxDim.

◆ m_dimdual

template<typename Int , typename Real >

int64_t LatticeTester::IntLattice< Int, Real >::m_dimdual

protected

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

It cannot exceed the number of coordinates in those vectors. It also cannot exceed m_maxDim.

◆ m_basis

template<typename Int , typename Real >

IntMat LatticeTester::IntLattice< Int, Real >::m_basis

protected

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

◆ m_dualbasis

template<typename Int , typename Real >

IntMat LatticeTester::IntLattice< Int, Real >::m_dualbasis

protected

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

May not be initialized.

◆ m_norm

template<typename Int , typename Real >

NormType LatticeTester::IntLattice< Int, Real >::m_norm

protected

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

It is used for the basis reduction and compute a shortest vector, for example.

◆ m_vecNorm

template<typename Int , typename Real >

RealVec LatticeTester::IntLattice< Int, Real >::m_vecNorm

protected

A vector that stores the norm of each basis vector.

In case of the L_2 norm, it contains the square norm instead. A value of -1 means that the norm is not up to date.

◆ m_dualvecNorm

template<typename Int , typename Real >

RealVec LatticeTester::IntLattice< Int, Real >::m_dualvecNorm

protected

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

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

include/latticetester/IntLattice.h

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ IntLattice() [1/3]

◆ IntLattice() [2/3]

◆ IntLattice() [3/3]

◆ ~IntLattice()

Member Function Documentation

◆ buildProjectionLLL()

◆ buildProjection()

◆ buildProjectionDual()

◆ getBasis()

◆ setBasis() [1/2]

◆ setBasis() [2/2]

◆ getDualBasis()

◆ getMaxDim()

◆ getDim()

◆ getDimDual()

◆ getNormType()

◆ getVecNorm() [1/2]

◆ getVecNorm() [2/2]

◆ getDualVecNorm() [1/2]

◆ getDualVecNorm() [2/2]

◆ getModulus()

◆ setDim()

◆ setDimDual()

◆ setNormType()

◆ setVecNorm()

◆ setDualVecNorm()

◆ setNegativeNorm() [1/2]

◆ setNegativeNorm() [2/2]

◆ setDualNegativeNorm() [1/2]

◆ setDualNegativeNorm() [2/2]

◆ updateVecNorm() [1/2]

◆ updateVecNorm() [2/2]

◆ updateSingleVecNorm()

◆ updateDualVecNorm() [1/3]

◆ updateSingleDualVecNorm()

◆ updateDualVecNorm() [2/3]

◆ updateDualVecNorm() [3/3]

◆ updateScalL2Norm() [1/2]

◆ updateScalL2Norm() [2/2]

◆ updateDualScalL2Norm() [1/2]

◆ updateDualScalL2Norm() [2/2]

◆ permute()

◆ permuteDual()

◆ dualize()

◆ checkDuality()

◆ sortBasis()

◆ sortDualBasis()

◆ toStringBasis()

◆ toStringDualBasis()

◆ toString()

Member Data Documentation

◆ m_modulo

◆ m_maxDim

◆ m_dim

◆ m_dimdual

◆ m_basis

◆ m_dualbasis

◆ m_norm

◆ m_vecNorm

◆ m_dualvecNorm