LatBuilder Namespace Reference

LatBuilder namespace. More...

Namespaces
namespace	Functor
	Various functors.
namespace	GenSeq
	Sequences of generator values.
namespace	IndexedIterator
	Immutable indexed iterators.
namespace	Interlaced
	Features used for interlaced digital nets.
namespace	Kernel
	Kernels for coordinate-uniform figures of merit.
namespace	LatSeq
	Sequences of Lattices.
namespace	MeritCombiner
	Combiner functors for merit values.
namespace	MeritSeq
	Sequences of merit values.
namespace	Norm
	Normalizations and bounds.
namespace	Parser
	String parsing facilities for LatBuilder objects.
namespace	ProjDepMerit
	Projection-dependent figures of merit.
namespace	Task
	Standard tasks that can be performed by LatBuilder.
namespace	TextStream
	Overloaded stream operators.
namespace	Traversal
	Traversal types for indexable sequences.
namespace	Vectorize
	Helpers to vectorize simple operations.

Classes
class	Accumulator
	Accumulator template class. More...
struct	BasicMeritFilter
	Abstract base class for filters. More...
class	BasicMeritFilterList
	Container class for merit filters. More...
class	BasicSizeParam
	Abstract CRTP base class for lattice size parameter. More...
class	BasicStorage
	Base class for storage types. More...
class	BridgeIteratorCached
	Bridge iterator with cached value. More...
class	BridgeIteratorCachedPtr
	Bridge iterator with cached value accessible through a pointer. More...
class	BridgeIteratorDynamic
	Bridge iterator with dynamically computed value. More...
class	BridgeSeq
	Bridge CRTP class for sequence based on another type of sequence, with elements computed by the derived class. More...
class	CachedSeq
	Cached sequence wrapper. More...
class	CartesianProduct
	Iterator incrementing policy that traverses unidimensional sequences sequentially. More...
class	ClonePtr
	Copyable alternative to std::unique_ptr<> for cloneable objects. More...
class	CombinedWeights
	Combined weights. More...
struct	CompressTraits
	Compression types for vectors and matrices. More...
struct	CompressTraits< Compress::NONE >
	No compression. More...
struct	CompressTraits< Compress::SYMMETRIC >
	Symmetric compression. More...
class	CoordUniformFigureOfMerit
	Base base class for coordinate-uniform figures of merit. More...
struct	defaultPerLevelOrder
	default per level value depending on the lattice (ordinary/polynomial) and the lattice type (ordinary/embedded). More...
struct	defaultPerLevelOrder< LatticeType::DIGITAL, EmbeddingType::MULTILEVEL >
struct	defaultPerLevelOrder< LatticeType::DIGITAL, EmbeddingType::UNILEVEL >
struct	defaultPerLevelOrder< LatticeType::ORDINARY, EmbeddingType::MULTILEVEL >
struct	defaultPerLevelOrder< LatticeType::ORDINARY, EmbeddingType::UNILEVEL >
struct	defaultPerLevelOrder< LatticeType::POLYNOMIAL, EmbeddingType::MULTILEVEL >
struct	defaultPerLevelOrder< LatticeType::POLYNOMIAL, EmbeddingType::UNILEVEL >
class	Digits
	Vector of digits representing a number in an arbitrary base. More...
class	FigureOfMerit
	Abstract base class for figures of merit. More...
class	IndexMap
	Permutation of vector indices. More...
class	LatDef
	Definition of a rank-1 lattice. More...
struct	LatticeRejectedException
	Exception raised by filters upon rejection of a candidate lattice rule. More...
struct	LatticeTraits
	Lattice traits. More...
struct	LatticeTraits< LatticeType::DIGITAL >
	Lattice traits for digital lattice rule. More...
struct	LatticeTraits< LatticeType::ORDINARY >
	Lattice traits for ordinary lattice rule. More...
struct	LatticeTraits< LatticeType::POLYNOMIAL >
	Lattice traits for polynomial lattice rule. More...
class	LFSR113
	LFSR113 pseudo-random generator by L'Ecuyer. More...
class	LFSR258
	LFSR258 pseudo-random generator by L'Ecuyer. More...
class	MeritFilter
	Generic filter wrapper for merit values. More...
class	MeritFilterList
	List of filters for merit values. More...
class	MeritFilterListPolicy
	Policy class template for MeritFilterList. More...
class	MeritFilterListPolicy< LR, EmbeddingType::MULTILEVEL >
	Specialization of MeritFilterListPolicy for embedded lattices. More...
class	MeritFilterListPolicy< LR, EmbeddingType::UNILEVEL >
	Specialization of MeritFilterListPolicy for ordinary lattices. More...
struct	MeritFilterTraits
	Traits class template for filters of merit values. More...
struct	MeritFilterTraits< EmbeddingType::MULTILEVEL >
struct	MeritFilterTraits< EmbeddingType::UNILEVEL >
struct	PerLevelOrderTraits
struct	PerLevelOrderTraits< PerLevelOrder::BASIC, LatticeType::DIGITAL, COMPRESS >
struct	PerLevelOrderTraits< PerLevelOrder::BASIC, LR, COMPRESS >
struct	PerLevelOrderTraits< PerLevelOrder::CYCLIC, LR, COMPRESS >
class	SeqCombiner
	Multidimensional sequence composed of unidimensional sequences. More...
class	SizeParam
	Lattice size parameter. More...
class	SizeParam< LR, EmbeddingType::MULTILEVEL >
	Lattice size type for embedded lattices.
class	SizeParam< LR, EmbeddingType::UNILEVEL >
	Ordinary lattice size parameter.
struct	SizeParamTraits
	SizeParam traits. More...
struct	SizeParamTraits< SizeParam< LatticeType::DIGITAL, ET > >
	SizeParam traits for digital lattice rule. More...
struct	SizeParamTraits< SizeParam< LatticeType::ORDINARY, ET > >
	SizeParam traits for ordinary lattice rule. More...
struct	SizeParamTraits< SizeParam< LatticeType::POLYNOMIAL, ET > >
	SizeParam traits for polynomial lattice rule. More...
class	Storage
	Storage policy. More...
class	Storage< LR, EmbeddingType::MULTILEVEL, COMPRESS, PLO >
	Vector permutation for embedded lattices.
class	Storage< LR, EmbeddingType::UNILEVEL, COMPRESS, PLO >
	Storage class for flat vectors.
struct	StorageTraits
	Storage traits. More...
struct	StorageTraits< Storage< LatticeType::DIGITAL, EmbeddingType::MULTILEVEL, COMPRESS > >
struct	StorageTraits< Storage< LatticeType::DIGITAL, EmbeddingType::UNILEVEL, COMPRESS > >
struct	StorageTraits< Storage< LR, EmbeddingType::MULTILEVEL, COMPRESS, PLO > >
struct	StorageTraits< Storage< LR, EmbeddingType::UNILEVEL, COMPRESS > >
struct	TypeInfo
	Framework to specify a human-readable name for data types. More...
struct	TypeInfo< boost::accumulators::tag::max >
struct	TypeInfo< boost::accumulators::tag::sum >
class	UniformUIntDistribution
class	WeightedFigureOfMerit
	Weighted figure of merit. More...
class	WeightedFigureOfMeritEvaluator
	Evaluator for WeightedFigureOfMerit. More...
class	WeightsDispatcher
class	Zip
	Iterator incrementing policy that traverses unidimensional sequences in parallel. More...

Typedefs
typedef unsigned long	uInteger
	Scalar unsigned integer .
typedef double	Real
	Scalar floating-point type.
typedef boost::numeric::ublas::vector< Real >	RealVector
	Vector of floating-point values.
typedef RealVector::size_type	Level
	Scalar integer type for level of embedding.
typedef size_t	Dimension
	Scalar integer type for dimension.
typedef NTL::polynomial	Polynomial
	polynomial over Z/2Z type. This is just a wrapper over NTL::GF2X. See ntlwrap.h.

Enumerations
enum class	LatticeType { ORDINARY , POLYNOMIAL , DIGITAL }
	Lattices supported: ordinary lattice rules amd polynomial lattice rules.
enum class	EmbeddingType { UNILEVEL , MULTILEVEL }
	Simple lattice / a sequence of embedded lattices.
enum class	Compress { NONE , SYMMETRIC }
	Types of compression.
enum class	PerLevelOrder { BASIC , CYCLIC }

Functions
template<LatticeType LR, Compress COMPRESS, PerLevelOrder PLO, class E>
Storage< LR, EmbeddingType::UNILEVEL, COMPRESS, PLO >::MeritValue	compressedSum (const Storage< LR, EmbeddingType::UNILEVEL, COMPRESS, PLO > &storage, const boost::numeric::ublas::vector_expression< E > &e)
	Sum of all the elements of a (possibly compressed) vector.
template<LatticeType LR, Compress COMPRESS, PerLevelOrder PLO, class E>
Storage< LR, EmbeddingType::MULTILEVEL, COMPRESS, PLO >::MeritValue	compressedSum (const Storage< LR, EmbeddingType::MULTILEVEL, COMPRESS, PLO > &storage, const boost::numeric::ublas::vector_expression< E > &e)
	Returns the per-level sums of the elements of the compressed multilevel vector expression e.
template<typename INT>
std::ostream &	operator<< (std::ostream &os, Digits< INT > &digits)
std::ostream &	operator<< (std::ostream &os, const FigureOfMerit &merit)
	Formats merit and outputs it on os.
template<typename VEC, typename MAP>
boost::numeric::ublas::vector_indirect< VEC, IndexMap< MAP > >	permuteVector (VEC &vec, MAP mapper)
	Returns a vector proxy whose elements are a permutation of another vector.
int	main (int argc, const char *argv[])
template<EmbeddingType ET>
std::ostream &	operator<< (std::ostream &os, const LatDef< LatticeType::ORDINARY, ET > &lat)
	Formats lat and outputs it to os.
template<EmbeddingType ET>
std::ostream &	operator<< (std::ostream &os, const LatDef< LatticeType::POLYNOMIAL, ET > &lat)
template<LatticeType LR, EmbeddingType ET>
LatDef< LR, ET >	createLatDef (SizeParam< LR, ET > sizeParam=SizeParam< LR, ET >(), typename LatDef< LR, ET >::GeneratingVector gen=typename LatDef< LR, ET >::GeneratingVector())
	Returns a lattice definition instance with the proper type of size parameter.
template<LatticeType LR>
std::ostream &	operator<< (std::ostream &, const BasicMeritFilterList< LR, EmbeddingType::UNILEVEL > &)
	Formats and outputs filters to os.
template<LatticeType LR>
std::ostream &	operator<< (std::ostream &, const BasicMeritFilterList< LR, EmbeddingType::MULTILEVEL > &)
template<LatticeType LR>
std::ostream &	operator<< (std::ostream &os, const MeritFilterList< LR, EmbeddingType::UNILEVEL > &filters)
	Formats and outputs filters to os.
template<LatticeType LR>
std::ostream &	operator<< (std::ostream &os, const MeritFilterList< LR, EmbeddingType::MULTILEVEL > &filters)
template<class D>
std::ostream &	operator<< (std::ostream &os, const BasicSizeParam< D > &sizeParam)
	DECLARE_TYPEINFO (float)
	DECLARE_TYPEINFO (double)
	DECLARE_TYPEINFO (int)
	DECLARE_TYPEINFO (unsigned int)
	DECLARE_TYPEINFO (long)
	DECLARE_TYPEINFO (unsigned long)
	DECLARE_TYPEINFO (long long)
	DECLARE_TYPEINFO (unsigned long long)
std::ostream &	operator<< (std::ostream &os, EmbeddingType latType)
template<typename T>
T	intPow (T base, unsigned long exponent)
	Integer exponentiation.
Polynomial	PolynomialFromInt (uInteger x)
	convert Integer to polynomial
uInteger	IndexOfPolynomial (Polynomial P)
	convert polynomial to integer
template<typename T>
T	modularPow (T base, uInteger exponent, T modulus)
	Modular exponentiation.
std::vector< uInteger >	primeFactors (uInteger n, bool raise=false)
	Prime factorization using the naive "trial division" algorithm.
std::map< uInteger, uInteger >	primeFactorsMap (uInteger n)
	Prime factorization using the naive "trial division" algorithm.
std::pair< long long, long long >	egcd (uInteger a, uInteger b)
	Extended Euclidian algorithm.
uInteger	Vm (const Polynomial &h, const Polynomial &P)
	computes The integer \(2^{\deg(P)}\nu_m(\frac{h} {p}) \) where \(\nu_{m}\) is the mapping \(\nu_{m} : \mathbb{L}_{2} \rightarrow \mathbb{R} \)
uInteger	log2Int (unsigned int n)
std::string	getDefaultPolynomial (unsigned int degree)
	Returns a default polynomial of degree degree.
std::string	to_string (LatticeType LT)

Variables
const int	LENGTH_UINTEGER = 64

Detailed Description

LatBuilder namespace.

Class and type definitions that are specific to LatBuilder.

Function Documentation

compressedSum()

template<LatticeType LR, Compress COMPRESS, PerLevelOrder PLO, class E>

Storage< LR, EmbeddingType::UNILEVEL, COMPRESS, PLO >::MeritValue LatBuilder::compressedSum	(	const Storage< LR, EmbeddingType::UNILEVEL, COMPRESS, PLO > &	storage,
		const boost::numeric::ublas::vector_expression< E > &	e )

Sum of all the elements of a (possibly compressed) vector.

In an compressed vector some elements are implicitly repeated.

Referenced by LatBuilder::ProjDepMerit::Evaluator< CoordUniform< KERNEL >, LR, ET, COMPRESS, PLO >::operator()().

egcd()

std::pair< long long, long long > LatBuilder::egcd	(	uInteger	a,
		uInteger	b )

Extended Euclidian algorithm.

Source: http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Iterative_method_2

Referenced by LatBuilder::GenSeq::CoprimeIntegers< COMPRESS, TRAV >::CoprimeIntegers().

getDefaultPolynomial()

std::string LatBuilder::getDefaultPolynomial

(

unsigned int

degree

)

Returns a default polynomial of degree degree.

Polynomials will be primitive and irreducible for degree superior to \(2\), irreducible for degree \(1\) and equal to \(1\) for degree \(0\). The current default list goes up to degree 32. Modify data/default_poly.csv to change the default polynomials.

Parameters

degree

Degree of the default polynomial.

IndexOfPolynomial()

uInteger LatBuilder::IndexOfPolynomial

(

Polynomial

P

)

convert polynomial to integer

the polyomial \( \sum a_iz^i\) is converted to \(\sum a_i2^i\)

intPow()

template<typename T>

T LatBuilder::intPow	(	T	base,
		unsigned long	exponent )

Integer exponentiation.

Source: http://en.wikipedia.org/wiki/Exponentiation_by_squaring#Computation_by_powers_of_2

Examples

tutorial/GenSeqExtend.cc.

Referenced by LatBuilder::GenSeq::CoprimeIntegers< COMPRESS, TRAV >::CoprimeIntegers(), LatBuilder::GenSeq::PowerSeq< SEQ >::element(), LatBuilder::Functor::IAAlpha::IAAlpha(), LatBuilder::Functor::IB::IB(), LatBuilder::Functor::ICAlpha::ICAlpha(), NetBuilder::AbstractDigitalNet::numPoints(), LatBuilder::Functor::IAAlpha::operator()(), LatBuilder::Functor::IB::operator()(), LatBuilder::Functor::ICAlpha::operator()(), NetBuilder::JoeKuo::Combiner< q >::operator()(), and NetBuilder::AbstractDigitalNet::size().

modularPow()

template<typename T>

T LatBuilder::modularPow	(	T	base,
		uInteger	exponent,
		T	modulus )

Modular exponentiation.

Source: http://en.wikipedia.org/wiki/Modular_exponentiation#Right-to-left_binary_method Note : to use this fonction an operator %
BASE operator% (BASE, MODULUS) has to be implemented

Referenced by LatBuilder::GenSeq::PowerSeq< SEQ >::element().

permuteVector()

template<typename VEC, typename MAP>

boost::numeric::ublas::vector_indirect< VEC, IndexMap< MAP > > LatBuilder::permuteVector	(	VEC &	vec,
		MAP	mapper )

Returns a vector proxy whose elements are a permutation of another vector.

Parameters

vec	Original vector.
mapper	Object that defines a permutation of vector indices through the definition of its member operator().

To use this function, first define a mapper class, say MyMapper, that defines the type size_type, that implements size() whose return value is number of elements in the permutation, and that implements operator() that maps an input index (the operator argument) to an output index, e.g.:

class MyMapper {
public:
   typedef unsigned size_type;
   size_type size() const { return ...; }
   size_type operator() (size_type i) const { return ...; }
};

Next, simply instantiate a Boost uBLAS vector vec and obtain a permutation pvec:

boost::numeric::ublas::vector<unsigned> vec(10);
auto pvec = LatBuilder::permuteVector(vec, MyMapper());

PolynomialFromInt()

Polynomial LatBuilder::PolynomialFromInt

(

uInteger

x

)

convert Integer to polynomial

the integer \(\sum a_i2^i\) is converted to \( \sum a_iz^i\) Note that the input integer must be < 2^64

Examples

tutorial/GenSeqCyclicGroup.cc, tutorial/GenSeqExtend.cc, tutorial/GenSeqGeneratingValues.cc, tutorial/GenSeqVector.cc, tutorial/LatDef.cc, tutorial/LatSeqCBC.cc, tutorial/LatSeqCBC1.cc, tutorial/LatSeqExhaustive.cc, tutorial/LatSeqKorobov.cc, tutorial/LatSeqRandom.cc, tutorial/NetDef.cc, tutorial/NetSearchCBC.cc, and tutorial/Storage.cc.

primeFactors()

std::vector< uInteger > LatBuilder::primeFactors	(	uInteger	n,
		bool	raise = false )

Prime factorization using the naive "trial division" algorithm.

Returns a list of prime factors, without their multiplicity if raise is false, or raised to their multiplicity if it is true.

primeFactorsMap()

std::map< uInteger, uInteger > LatBuilder::primeFactorsMap

(

uInteger

n

)

Prime factorization using the naive "trial division" algorithm.

Returns a map of (factor, multiplicity) pairs.

Referenced by LatBuilder::GenSeq::CoprimeIntegers< COMPRESS, TRAV >::CoprimeIntegers().

Vm()

uInteger LatBuilder::Vm	(	const Polynomial &	h,
		const Polynomial &	P )

computes The integer \(2^{\deg(P)}\nu_m(\frac{h} {p}) \)
where \(\nu_{m}\) is the mapping \(\nu_{m} : \mathbb{L}_{2} \rightarrow \mathbb{R} \)

\[ \nu_{m}(\sum_{l=\omega}^{\infty} x_{l} z^{-l}) = \sum_{l=\max(\omega,1)}^{m} x_{l} 2^{-l} \]

reference : https://people.cs.kuleuven.be/~dirk.nuyens/phdthesis/thesis.pdf page 153