This class implements lattice basis built from multiple recursive linear congruential generators (MRGs). More...

#include <latmrg/MRGLattice.h>

Inheritance diagram for LatMRG::MRGLattice< Integ, Float >:

Public Types
typedef Float	Dbl

typedef Integ	Int

typedef NTL::matrix< Int >	IntMat

typedef NTL::vector< Int >	IntVec

Public Member Functions
	MRGLattice (const Int &m, const IntVec &a, int maxDim, int k, LatticeType latt, LatticeTester::NormType norm=LatticeTester::L2NORM)
	Constructor with modulus of congruence \(m\), order of the recurrence \(k\), multipliers \(a\), maximal dimension `MaxDim`, and lattice type `Latt`. More...

	MRGLattice (const Int &m, const Int &a, int maxDim, LatticeType latt, LatticeTester::NormType norm=LatticeTester::L2NORM)
	Alternative constructor for a LCG. More...

	MRGLattice (const Int &m, const IntVec &a, int maxDim, int k, IntVec &lac, LatticeType latt, LatticeTester::NormType norm=LatticeTester::L2NORM)
	As in the constructor above but the basis is built for the lacunary indices `lac`. More...

	MRGLattice (const MRGLattice< Int, Dbl > &Lat)
	Copy constructor. More...

	~MRGLattice ()
	Destructor. More...

virtual void	buildBasis (int d)
	Builds the basis in dimension \(d\). More...

Int &	getLac (int j)
	Returns the \(j\)-th lacunary index. More...

virtual void	incDim ()
	Increments the dimension of the basis by 1 by calling either `incDimBasis` or `incDimLaBasis`. More...

bool	isLacunary () const
	Returns `true` for the case of lacunary indices, returns `false` for non-lacunary indices. More...

void	kill ()
	Cleans and releases memory used by this object. More...

MRGLattice< Int, Dbl > &	operator= (const MRGLattice< Int, Dbl > &Lat)
	Assigns `Lat` to this object. More...

virtual void	setLac (const LatticeTester::Lacunary< Int > &lat)
	Sets the lacunary indices for this lattice to `lat`. More...

Protected Attributes
IntVec	m_aCoef
	The coefficients of the recurrence. More...

bool *	m_ip
	When the flag `m_ip[i]` is `true`, the \(i\)-th diagonal element of matrix `m_sta` is non-zero (modulo \(m\)) and divides \(m\). More...

LatticeTester::Lacunary< Int >	m_lac
	Contains the lacunary indices when `LacunaryFlag` is `true`, otherwise is undefined. More...

bool	m_lacunaryFlag
	Is `true` in the case of lacunary indices, `false` otherwise. More...

LatticeType	m_latType
	Indicates which lattice or sublattice is analyzed. More...

IntMat	m_sta
	Matrix that contains the vectors that can be used to generate the basis for an arbitrary dimension. More...

Used for the calculation of a combined MRG.
Int	m_lossRho

Int	m_rho


Int	m_t4
	Work variables. More...

Int	m_t5

Int	m_t6

Int	m_t7

Int	m_t8

Int	m_e

IntVec	m_xi

Private Attributes
std::vector< IntVec >	m_pow2_exp
	The powers of 2 used if this generator has power of 2 coefficients. More...

bool	m_power2
	Indicates this generator is built using coefficients that are power of 2 combinations. More...

Sets and gets the values of <tt>m_rho</tt> and <tt>m_lossRho</tt>.
Int	getRho () const

Int	getLossRho () const

void	setRho (const Int &val)

void	setLossRho (const Int &val)

const IntVec &	getCoef () const
	Returns a non-mutable copy of the multipliers (coefficients) of the MRG. More...

virtual std::string	toStringCoef () const
	Returns the vector of multipliers \(A\) as a string. More...

std::string	toString () const override
	Returns the vector of multipliers \(A\) as a string. More...

void	setPower2 (std::vector< IntVec > &coeffs)
	Sets `m_power2` to true and sets `m_pow2_exp to`coeffs`. More...

void	buildProjection (LatticeTester::IntLattice< Int, Int, Dbl, Dbl > *lattice, const LatticeTester::Coordinates &proj) override
	Builds a projection for this lattice on the set in indices in `proj`. More...

void	initStates ()
	Initializes a square matrix of order \(k\). More...

void	init ()
	Initializes some of the local variables. More...

void	initOrbit ()
	Initializes this object when the lattice type is `ORBIT`. More...

void	insertion (IntVec &Sta)

void	lemme2 (IntVec &Sta)

void	trace (char *msg, int d)
	For debugging purposes. More...

virtual void	incDimBasis ()
	Increments the basis by 1 in case of non-lacunary indices. More...

void	incDimLaBasis (int)
	Increments the basis by 1 in case of lacunary indices. More...

void	buildNaBasis (int d)
	Builds the basis of the MRG recurrence in case of non-lacunary indices. More...

void	buildLaBasis (int d)
	Builds the basis of the MRG recurrence in case of lacunary indices. More...

Detailed Description

template<typename Integ, typename Float>
class LatMRG::MRGLattice< Integ, Float >

This class implements lattice basis built from multiple recursive linear congruential generators (MRGs).

One must first call the constructor with a given congruence modulus \(m\), order \(k\) for the recurrence, and maximal dimension for the basis. One must then build the lattice basis associated to a vector of multipliers for a given dimension. Each MRG is defined by a vector of multipliers \(A\), where \(A[i-1]\) represents \(a_i\). This MRG satisfies the recurrence

\[ x_n = (a_1 x_{n-1} + \cdots+ a_k x_{n-k}) \mod m. \]

Member Typedef Documentation

◆ Dbl

template<typename Integ, typename Float>

typedef Float LatMRG::MRGLattice< Integ, Float >::Dbl

◆ Int

template<typename Integ, typename Float>

typedef Integ LatMRG::MRGLattice< Integ, Float >::Int

◆ IntMat

template<typename Integ, typename Float>

typedef NTL::matrix<Int> LatMRG::MRGLattice< Integ, Float >::IntMat

◆ IntVec

template<typename Integ, typename Float>

typedef NTL::vector<Int> LatMRG::MRGLattice< Integ, Float >::IntVec

Constructor & Destructor Documentation

◆ MRGLattice() [1/4]

template<typename Int , typename Dbl >

LatMRG::MRGLattice< Int, Dbl >::MRGLattice	(	const Int &	m,
		const IntVec &	a,
		int	maxDim,
		int	k,
		LatticeType	latt,
		LatticeTester::NormType	norm = `LatticeTester::L2NORM`
	)

Constructor with modulus of congruence \(m\), order of the recurrence \(k\), multipliers \(a\), maximal dimension MaxDim, and lattice type Latt.

a has to be a vector of k+1 components with a[i]= \(a_i\) for compatibility with other classes. Vectors and (square) matrices of the basis have maximal dimension maxDim, and the indices of vectors and matrices vary from dimension 1 to maxDim. The norm to be used for the basis vectors is norm.

◆ MRGLattice() [2/4]

template<typename Int , typename Dbl >

LatMRG::MRGLattice< Int, Dbl >::MRGLattice	(	const Int &	m,
		const Int &	a,
		int	maxDim,
		LatticeType	latt,
		LatticeTester::NormType	norm = `LatticeTester::L2NORM`
	)

Alternative constructor for a LCG.

In this case, k is 1 and a is a single number.

◆ MRGLattice() [3/4]

template<typename Int , typename Dbl >

LatMRG::MRGLattice< Int, Dbl >::MRGLattice	(	const Int &	m,
		const IntVec &	a,
		int	maxDim,
		int	k,
		IntVec &	lac,
		LatticeType	latt,
		LatticeTester::NormType	norm = `LatticeTester::L2NORM`
	)

As in the constructor above but the basis is built for the lacunary indices lac.

a has to be a vector of k+1 components with a[i]= \(a_i\) for compatibility with other classes.

◆ MRGLattice() [4/4]

template<typename Int , typename Dbl >

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

Copy constructor.

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

◆ ~MRGLattice()

template<typename Int , typename Dbl >

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

Destructor.

Member Function Documentation

◆ buildBasis()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::buildBasis ( int d )

virtual

Builds the basis in dimension \(d\).

◆ buildLaBasis()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::buildLaBasis ( int d )

protected

Builds the basis of the MRG recurrence in case of lacunary indices.

◆ buildNaBasis()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::buildNaBasis ( int d )

protected

Builds the basis of the MRG recurrence in case of non-lacunary indices.

◆ buildProjection()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::buildProjection	(	LatticeTester::IntLattice< Int, Int, Dbl, Dbl > *	lattice,
		const LatticeTester::Coordinates &	proj
	)

override

Builds a projection for this lattice on the set in indices in proj.

This differs from the original implementation in IntLattice because it does not compute a dual lattice basis. lattice has to be initialized with the right dimension beforehand.

◆ getCoef()

template<typename Integ, typename Float>

const IntVec& LatMRG::MRGLattice< Integ, Float >::getCoef ( ) const

inline

Returns a non-mutable copy of the multipliers (coefficients) of the MRG.

◆ getLac()

template<typename Int , typename Dbl >

Int & LatMRG::MRGLattice< Int, Dbl >::getLac ( int j )

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

◆ getLossRho()

template<typename Integ, typename Float>

Int LatMRG::MRGLattice< Integ, Float >::getLossRho ( ) const

inline

◆ getRho()

template<typename Integ, typename Float>

Int LatMRG::MRGLattice< Integ, Float >::getRho ( ) const

inline

◆ incDim()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::incDim ( )

virtual

Increments the dimension of the basis by 1 by calling either incDimBasis or incDimLaBasis.

◆ incDimBasis()

template<typename Int , typename Dbl >

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

protectedvirtual

Increments the basis by 1 in case of non-lacunary indices.

◆ incDimLaBasis()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::incDimLaBasis ( int IMax )

protected

Increments the basis by 1 in case of lacunary indices.

Uses the method described in the article: P. L'Ecuyer and R. Couture, "An Implementation of the Lattice and Spectral Tests for Multiple Recursive Linear Random Number Generators", INFORMS Journal on Computing, 9, 2 (1997), page 206–217. Section 3, "Lacunary indices".

◆ init()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::init ( )

protected

Initializes some of the local variables.

◆ initOrbit()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::initOrbit ( )

protected

Initializes this object when the lattice type is ORBIT.

◆ initStates()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::initStates ( )

protected

Initializes a square matrix of order \(k\).

This initial matrix contains a system of generators for the given group of states.

◆ insertion()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::insertion ( IntVec & Sta )

protected

◆ isLacunary()

template<typename Integ, typename Float>

bool LatMRG::MRGLattice< Integ, Float >::isLacunary ( ) const

inline

Returns true for the case of lacunary indices, returns false for non-lacunary indices.

◆ kill()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::kill ( )

Cleans and releases memory used by this object.

◆ lemme2()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::lemme2 ( IntVec & Sta )

protected

◆ operator=()

template<typename Int , typename Dbl >

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

Assigns Lat to this object.

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

◆ setLac()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::setLac ( const LatticeTester::Lacunary< Int > & lat )

virtual

Sets the lacunary indices for this lattice to lat.

◆ setLossRho()

template<typename Integ, typename Float>

void LatMRG::MRGLattice< Integ, Float >::setLossRho ( const Int & val )

inline

◆ setPower2()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::setPower2 ( std::vector< IntVec > & coeffs )

Sets m_power2 to true and sets m_pow2_exp tocoeffs`.

◆ setRho()

template<typename Integ, typename Float>

void LatMRG::MRGLattice< Integ, Float >::setRho ( const Int & val )

inline

◆ toString()

template<typename Int , typename Dbl >

std::string LatMRG::MRGLattice< Int, Dbl >::toString ( ) const

override

Returns the vector of multipliers \(A\) as a string.

◆ toStringCoef()

template<typename Int , typename Dbl >

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

virtual

Returns the vector of multipliers \(A\) as a string.

Reimplemented in LatMRG::MWCLattice< Int, Dbl >, and LatMRG::AWCSWBLattice< Int, Dbl >.

◆ trace()

template<typename Int , typename Dbl >

void LatMRG::MRGLattice< Int, Dbl >::trace	(	char *	msg,
		int	d
	)

protected

For debugging purposes.

Member Data Documentation

◆ m_aCoef

template<typename Integ, typename Float>

IntVec LatMRG::MRGLattice< Integ, Float >::m_aCoef

protected

The coefficients of the recurrence.

◆ m_e

template<typename Integ, typename Float>

Int LatMRG::MRGLattice< Integ, Float >::m_e

protected

◆ m_ip

template<typename Integ, typename Float>

bool* LatMRG::MRGLattice< Integ, Float >::m_ip

protected

When the flag m_ip[i] is true, the \(i\)-th diagonal element of matrix m_sta is non-zero (modulo \(m\)) and divides \(m\).

Otherwise (when m_ip[i] is false), the \(i\)-th line of matrix m_sta is identically 0.

◆ m_lac

template<typename Integ, typename Float>

LatticeTester::Lacunary<Int> LatMRG::MRGLattice< Integ, Float >::m_lac

protected

Contains the lacunary indices when LacunaryFlag is true, otherwise is undefined.

◆ m_lacunaryFlag

template<typename Integ, typename Float>

bool LatMRG::MRGLattice< Integ, Float >::m_lacunaryFlag

protected

Is true in the case of lacunary indices, false otherwise.

◆ m_latType

template<typename Integ, typename Float>

LatticeType LatMRG::MRGLattice< Integ, Float >::m_latType

protected

Indicates which lattice or sublattice is analyzed.

◆ m_lossRho

template<typename Integ, typename Float>

Int LatMRG::MRGLattice< Integ, Float >::m_lossRho

protected

◆ m_pow2_exp

template<typename Integ, typename Float>

std::vector<IntVec> LatMRG::MRGLattice< Integ, Float >::m_pow2_exp

private

The powers of 2 used if this generator has power of 2 coefficients.

◆ m_power2

template<typename Integ, typename Float>

bool LatMRG::MRGLattice< Integ, Float >::m_power2

private

Indicates this generator is built using coefficients that are power of 2 combinations.

◆ m_rho

template<typename Integ, typename Float>

Int LatMRG::MRGLattice< Integ, Float >::m_rho

protected

◆ m_sta

template<typename Integ, typename Float>

IntMat LatMRG::MRGLattice< Integ, Float >::m_sta

protected

Matrix that contains the vectors that can be used to generate the basis for an arbitrary dimension.

This matrix is of order k and if we want to build the full lattice, this matrix is the identity matrix. Marc-Antoine This matrix is different in some way that I don't quite understand if we use lacunary indices.

◆ m_t4

template<typename Integ, typename Float>

Int LatMRG::MRGLattice< Integ, Float >::m_t4

protected

Work variables.

◆ m_t5

template<typename Integ, typename Float>

Int LatMRG::MRGLattice< Integ, Float >::m_t5

protected

◆ m_t6

template<typename Integ, typename Float>

Int LatMRG::MRGLattice< Integ, Float >::m_t6

protected

◆ m_t7

template<typename Integ, typename Float>

Int LatMRG::MRGLattice< Integ, Float >::m_t7

protected

◆ m_t8

template<typename Integ, typename Float>

Int LatMRG::MRGLattice< Integ, Float >::m_t8

protected

◆ m_xi

template<typename Integ, typename Float>

IntVec LatMRG::MRGLattice< Integ, Float >::m_xi

protected

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

include/latmrg/MRGLattice.h

Public Types

Public Member Functions

Protected Attributes

Private Attributes

Sets and gets the values of <tt>m_rho</tt> and <tt>m_lossRho</tt>.

Detailed Description

template<typename Integ, typename Float> class LatMRG::MRGLattice< Integ, Float >

Member Typedef Documentation

◆ Dbl

◆ Int

◆ IntMat

◆ IntVec

Constructor & Destructor Documentation

◆ MRGLattice() [1/4]

◆ MRGLattice() [2/4]

◆ MRGLattice() [3/4]

◆ MRGLattice() [4/4]

◆ ~MRGLattice()

Member Function Documentation

◆ buildBasis()

◆ buildLaBasis()

◆ buildNaBasis()

◆ buildProjection()

◆ getCoef()

◆ getLac()

◆ getLossRho()

◆ getRho()

◆ incDim()

◆ incDimBasis()

◆ incDimLaBasis()

◆ init()

◆ initOrbit()

◆ initStates()

◆ insertion()

◆ isLacunary()

◆ kill()

◆ lemme2()

◆ operator=()

◆ setLac()

◆ setLossRho()

◆ setPower2()

◆ setRho()

◆ toString()

◆ toStringCoef()

◆ trace()

Member Data Documentation

◆ m_aCoef

◆ m_e

◆ m_ip

◆ m_lac

◆ m_lacunaryFlag

◆ m_latType

◆ m_lossRho

◆ m_pow2_exp

◆ m_power2

◆ m_rho

◆ m_sta

◆ m_t4

◆ m_t5

◆ m_t6

◆ m_t7

◆ m_t8

◆ m_xi

template<typename Integ, typename Float>
class LatMRG::MRGLattice< Integ, Float >