Namespace in which all linbox code resides. More...

Namespaces
namespace	MatrixHom
	Limited doc so far. Used in RationalSolver.

namespace	IndexedTags
	limited doc so far

namespace	RingCategories
	some basic information about each field or ring.

namespace	Protected
	This is the namespace all LinBox internal code is in.

namespace	GetEntryTags
	limited doc so far.

namespace	TraceTags
	undocumented

namespace	VectorWrapper
	limited doc so far.

Data Structures
class	BlackboxBlockContainerBase
	A base class for BlackboxBlockContainer. More...

class	BlackboxBlockContainer
	no doc. More...

class	BlackboxBlockContainerRecord
	no doc. More...

class	BlackboxContainerBase
	A base class for BlackboxContainer. More...

class	BlackboxContainerSymmetric
	See base class for doc. More...

class	BlackboxContainerSymmetrize
	Symmetrizing iterator (for rank computations). More...

class	BlackboxContainer
	Limited doc so far. More...

class	BlasMatrixDomainInv< MultiModDouble, BlasMatrix< MultiModDouble > >
	specialisation for MultiModDouble. More...

class	BlasMatrixDomainSubin
	C -= A. More...

class	BlasMatrixDomainAddin
	C += A. More...

class	BlasMatrixDomain
	Interface for all functionnalities provided for BlasMatrix. More...

class	BlockLanczosSolver
	Block Lanczos iteration. More...

class	BlockMasseyDomain
	Compute the linear generator of a sequence of matrices. More...

struct	ChineseRemainderSeq
	No doc. More...

struct	ChineseRemainder
	Wrapper around OMP/SEQ version of ChineseRemainderXXX<CRABase>. More...

struct	EarlyMultipCRA
	NO DOC. More...

struct	EarlySingleCRA
	NO DOC. More...

struct	FullMultipFixedCRA
	Chinese Remaindering Algorithm for multiple residues. More...

struct	FullMultipBlasMatCRA
	NO DOC. More...

struct	FullMultipCRA
	NO DOC... More...

struct	GivaroRnsFixedCRA
	NO DOC... More...

class	DenseContainer
	Limited doc so far. More...

class	DiophantineSolver
	DiophantineSolver<QSolver> creates a diophantine solver using a QSolver to generate rational solutions. More...

class	EchelonFormDomain
	Echelon form domain. More...

class	Eliminator
	Elimination system. More...

class	GaussDomain
	Repository of functions for rank by elimination on sparse matrices. More...

class	LABlockLanczosSolver
	Biorthogonalising block Lanczos iteration. More...

class	LanczosSolver
	Solve a linear system using the conjugate Lanczos iteration. More...

class	LastInvariantFactor
	This is used in a Smith Form algorithm. More...

class	latticeMethod
	NTL methods. More...

class	DixonLiftingContainer
	Dixon Lifting Container. More...

class	WiedemannLiftingContainer
	Wiedemann LiftingContianer. More...

class	BlockWiedemannLiftingContainer
	Block Wiedemann LiftingContianer. More...

class	BlockHankelLiftingContainer
	Block Hankel LiftingContianer. More...

class	SparseLULiftingContainer
	SparseLULiftingContainer. More...

struct	LinBoxTag
	Structure for tags. More...

class	MasseyDomain
	Berlekamp/Massey algorithm. More...

class	MatrixRank
	Compute the rank of an integer matrix in place over a finite field by Gaussian elimination. More...

class	MGBlockLanczosSolver
	Block Lanczos iteration. More...

class	OneInvariantFactor
	Limited doc so far. More...

struct	RationalRemainder
	Chinese remainder of rationals. More...

struct	RationalRemainder2
	Chinese remainder of rationals. More...

class	RationalReconstruction
	Limited doc so far. More...

class	RationalSolver
	Interface for the different specialization of p-adic lifting based solvers. More...

class	RationalSolver< Ring, Field, RandomPrime, WiedemannTraits >
	Partial specialization of p-adic based solver with Wiedemann algorithm. More...

class	RationalSolver< Ring, Field, RandomPrime, BlockWiedemannTraits >
	partial specialization of p-adic based solver with block Wiedemann algorithm. More...

class	RationalSolver< Ring, Field, RandomPrime, DixonTraits >
	partial specialization of p-adic based solver with Dixon algorithm. More...

class	RationalSolver< Ring, Field, RandomPrime, BlockHankelTraits >
	Block Hankel. More...

class	RationalSolver< Ring, Field, RandomPrime, SparseEliminationTraits >
	Sparse LU. More...

class	RationalSolver< Ring, Field, RandomPrime, WanTraits >
	solver using a hybrid Numeric/Symbolic computation. More...

class	RNS
	RNS. More...

class	TernaryLattice
	NO DOC. More...

class	LargeDouble
	NO DOC. More...

class	SigmaBasis
	implementation of $\sigma$ -basis (minimal basis). More...

class	SmithFormBinary
	Compute Smith form. More...

class	SmithFormIliopoulos
	This is Iliopoulos' algorithm do diagonalize. More...

class	SmithFormLocal
	Smith normal form (invariant factors) of a matrix over a local ring. More...

class	PowerGaussDomain
	Repository of functions for rank modulo a prime power by elimination on sparse matrices. More...

class	PowerGaussDomainPowerOfTwo
	Repository of functions for rank modulo a prime power by elimination on sparse matrices. More...

class	VectorFraction
	VectorFraction<Domain> is a vector of rational elements with common reduced denominator. More...

class	WiedemannSolver
	Linear system solvers based on Wiedemann's method. More...

class	BlackboxArchetype
	showing the member functions provided by all blackbox matrix classes. More...

class	Butterfly
	Switching Network based BlackBox Matrix. More...

struct	Companion
	Companion matrix of a monic polynomial. More...

class	Compose
	Blackbox of a product: , i.e $Cx \gets A(Bx)$ . More...

class	ComposeOwner
	Blackbox of a product: , i.e $Cx \gets A(Bx)$ . More...

class	Compose< _Blackbox, _Blackbox >
	specialization for _Blackbox1 = _Blackbox2 More...

class	ComposeTraits
	used in ..., for example More...

class	ComposeTraits< BlasMatrix< Field > >
	used in smith-binary, for example More...

class	Diagonal
	Random diagonal matrices are used heavily as preconditioners. More...

class	Diagonal< _Field, VectorCategories::DenseVectorTag >
	Specialization of Diagonal for application to dense vectors. More...

class	Diagonal< _Field, VectorCategories::SparseSequenceVectorTag >
	Specialization of Diagonal for application to sparse sequence vectors. More...

class	Diagonal< _Field, VectorCategories::SparseAssociativeVectorTag >
	Specialization of Diagonal for application to sparse associative vectors. More...

class	Dif
	Blackbox of a difference: `C := A - B`, i.e `Cx = Ax - Bx`. More...

class	DirectSum
	If C = DirectSum(A, B) and y = xA and z = wB, then (y,z) = (x,w)C. More...

class	BlackboxFactory
	A tool for computations with integer and rational matrices. More...

class	Hilbert_JIT_Entry
	The object needed to build a Hilbert matrix as a JIT matrix. More...

class	Hilbert
	Example of a blackbox that is space efficient, though not time efficient. More...

class	Inverse
	A Blackbox for the inverse. More...

class	JIT_Matrix
	Example of a blackbox that is space efficient, though not time efficient. More...

class	MatrixBlackbox
	Matrix black box. More...

class	MoorePenrose
	Generalized inverse of a blackbox. More...

class	Sylvester
	This is a representation of the Sylvester matrix of two polynomials. More...

class	NullMatrix
	This is a representation of the 0 by 0 empty matrix which does not occupy memory. More...

class	Permutation
	size is n. More...

class	PolynomialBB
	represent the matrix P(A) where A is a blackbox and P a polynomial More...

class	PolynomialBBOwner
	represent the matrix P(A) where A is a blackbox and P a polynomial More...

class	ZeroOne
	Time and space efficient representation of sparse {0,1}-matrices. More...

class	ScalarMatrix
	Blackbox for `aI`. More...

class	ZOQuad
	A class of striped or block-decomposed zero-one matrices. More...

class	SparseMatrix
	vector of sparse rows. More...

class	SparseMatrixFactory
	Sparse matrix factory This class inherits BlackboxFactory and provides a method for using a SparseMatrixBase object with integer or rational data type as input to the high-level integer and rational solutions functions. More...

class	Squarize
	transpose matrix without copying. More...

class	Submatrix
	leading principal minor of existing matrix without copying. More...

class	Submatrix< Blackbox, VectorCategories::DenseVectorTag >
	Specialization for dense vectors. More...

class	Submatrix< Blackbox, VectorCategories::DenseZeroOneVectorTag >
	Specialization for dense ZeroOne vectors. More...

class	Submatrix< BlasMatrix< _Field >, VectorCategories::DenseVectorTag >
	Specialization for BlasMatrix. More...

class	SubmatrixOwner< Blackbox, VectorCategories::DenseVectorTag >
	Specialization for dense vectors. More...

class	Sum
	blackbox of a matrix sum without copying. More...

class	SumOwner
	blackbox of a matrix sum without copying. More...

class	Toeplitz
	This is the blackbox representation of a Toeplitz matrix. More...

class	Toeplitz< typename _PField::CoeffField, _PField >
	Specialization for when the field of matrix elements is the same as the coefficient field of the polynomial field. More...

class	Transpose
	transpose matrix without copying. More...

class	TransposeOwner
	transpose matrix without copying. More...

class	TriplesBB
	wrapper for NAG Sparse Matrix format. More...

class	ZeroOne< GF2 >
	Time and space efficient representation of sparse matrices over GF2. More...

class	ElementAbstract
	Abstract element base class, a technicality. More...

class	ElementArchetype
	Field and Ring element interface specification and archetypical instance class. More...

class	RingEnvelope
	implement the ring archetype to minimize code bloat. More...

class	FieldEnvelope
	Derived class used to implement the field archetypeHelps to minimize code bloat. More...

class	RandIterEnvelope
	Random field base element generator. More...

class	ElementEnvelope
	Adaptor from archetypical interface to abstract interface, a technicality. More...

class	GMPRationalElement
	elements of GMP_Rationals. More...

class	FieldAbstract
	field base class. More...

class	FieldArchetype
	field specification and archetypical instance. More...

class	BlockRing
	Elements are wrapped BlasMatrix objects. More...

class	FieldInterface
	This field base class exists solely to aid documentation organization. More...

struct	ClassifyRing
	Default ring category. More...

struct	FieldTraits
	FieldTrait. More...

class	GivaroExtension
	This template class is defined to be in phase with the LinBox archetype. More...

class	GivaroExtension< LinBox::GivaroGfq >
	This template class is define just to be in phase with the LinBox archetype. More...

class	Hom< BaseField, GivaroExtension< BaseField > >
	NO DOC. More...

struct	GivaroField< LinBox::GF2 >
	give LinBox fields an allure of Givaro FieldsThis class adds the necessary requirements allowing the construction of an extension of a LinBox field. More...

struct	GivaroField
	give LinBox fields an allure of Givaro FieldsThis class adds the necessary requirements allowing the construction of an extension of a LinBox field or a givaro polynomial of a LinBox field ... More...

class	GivaroGfq
	Wrapper of Givaro's GFqDom<int32_t> class. More...

class	GivaroMontg
	wrapper of Givaro's Givaro::Montgomery< Givaro::Std32>. More...

class	FieldAXPY
	FieldAXPY object. More...

class	GivaroZpz
	wrapper of Givaro's ZpzDom. More...

class	NoHomError
	Error object for attempt to establish a Hom that cannot exist. More...

class	Hom
	map element of source ring(field) to target ringAn instance of Hom is a homomorphism from a ring of type Source to a ring (usually field) of type Target. More...

class	LidiaGfq
	defines the Galois Field GF(p^k). More...

struct	Local2_32
	Fast arithmetic mod 2^32, including gcd. More...

class	ModularBalanced< double >
	Centered representation of $\mathbf{Z}/m\mathbf{Z}$ . More...

class	FieldAXPY< ModularBalanced< double > >
	Specialization of FieldAXPY. More...

class	DotProductDomain< ModularBalanced< double > >
	Specialization of DotProductDomain. More...

class	ModularBalancedRandIter
	Random field base element generator. More...

class	NonzeroRandIter
	Random iterator for nonzero random numbers. More...

class	Modular
	Prime fields of positive characteristic implemented directly in LinBox. More...

class	ModularRandIter
	Random field base element generator. More...

class	MVProductDomain
	Helper class to allow specializations of certain matrix-vector products. More...

class	Modular< int8_t >
	Specialization of Modular to signed 8 bit element type with efficient dot product. More...

class	Modular< double >
	Standard representation of $\mathbf{Z}/m\mathbf{Z}$ . More...

class	Modular< int32_t >
	Specialization of Modular to int32_t element type with efficient dot product. More...

class	Modular< int64_t >
	Specialization of Modular to int64_t element type with efficient dot product. More...

class	Modular< int16_t >
	Specialization of Modular to short element type with efficient dot product. More...

class	Modular< uint8_t >
	Allows compact storage when the modulus is less than 2^8. More...

class	FieldAXPY< Modular< uint8_t > >
	Specialization of FieldAXPY for uint8_t modular field. More...

class	DotProductDomain< Modular< uint8_t > >
	Specialization of DotProductDomain for unsigned short modular field. More...

class	MVProductDomain< Modular< uint8_t > >
	Specialization of MVProductDomain for uint8_t modular field. More...

class	Modular< uint16_t >
	Specialization of class Modular for uint16_t element type. More...

class	FieldAXPY< Modular< uint16_t > >
	Specialization of FieldAXPY for uint16_t modular field. More...

class	DotProductDomain< Modular< uint16_t > >
	Specialization of DotProductDomain for unsigned short modular field. More...

class	MVProductDomain< Modular< uint16_t > >
	Specialization of MVProductDomain for uint16_t modular field. More...

class	Modular< uint32_t >
	Specialization of class Modular for uint32_t element type. More...

class	FieldAXPY< Modular< uint32_t > >
	Specialization of FieldAXPY for unsigned short modular field. More...

class	DotProductDomain< Modular< uint32_t > >
	Specialization of DotProductDomain for uint32_t modular field. More...

class	MVProductDomain< Modular< uint32_t > >
	Specialization of MVProductDomain for uint32_t modular field. More...

class	FieldAXPY< Modular< _Element > >
	Specialization of FieldAXPY for parameterized modular field. More...

struct	NTL_zz_p
	long ints modulo a positive integer. More...

class	NTL_zz_pE_Initialiser
	use ZZ_pEBak mechanism too ? More...

class	NTL_zz_pE
	zz_pE Define a parameterized class to easily handle UnparametricField<NTL::zz_pE> field More...

class	NTL_zz_pX
	Ring (in fact, a unique factorization domain) of polynomial with coefficients in class NTL_zz_p (integers mod a wordsize prime). More...

class	NTL_ZZ
	the integer ring. More...

struct	NTL_ZZ_p
	Wrapper of zz_p from NTL. More...

class	UnparametricRandIter< NTL::ZZ_p >
	Constructor for random field element generator. More...

class	NTL_ZZ_pE
	Wrapper of ZZ_pE from NTL Define a parameterized class to handle easily UnparametricField<NTL::ZZ_pE> field. More...

class	NTL_ZZ_pX
	Ring (in fact, a unique factorization domain) of polynomial with coefficients in class NTL_ZZ_p (integers mod a wordsize prime). More...

class	ParamFuzzy
	Abstract parameterized field of "fuzzy" doubles. More...

class	PID_double
	NO DOC. More...

class	PID_integer
	Domain for integer operations. More...

struct	NTL_PID_zz_p
	extend Wrapper of zz_p from NTL. More...

class	PIR_ntl_ZZ_p
	extend Wrapper of ZZ_p from NTL. More...

struct	Rebind
	used in support of Hom, MatrixHom More...

class	FieldAXPY< UnparametricField< integer > >
	NO DOc. More...

class	MatrixArchetype
	Directly-represented matrix archetype. More...

class	BlasMatrix< MultiModDouble >
	No Doc. More...

class	BlasSubmatrix
	Dense Submatrix representation. More...

class	BlasMatrix
	Dense matrix representation. More...

class	TriangularBlasMatrix
	Triangular BLAS matrix. More...

class	indexDomain
	Class used for permuting indices. More...

class	TransposedBlasMatrix
	TransposedBlasMatrix. More...

class	TransposedBlasMatrix< TransposedBlasMatrix< Matrix > >
	TransposedBlasMatrix. More...

class	DenseRowsMatrix
	Dense row-wise matrix container. More...

class	LQUPMatrix
	LQUP factorisation. More...

class	MatrixDomain< GF2 >
	Specialization of MatrixDomain for GF2. More...

struct	MatrixCategories
	For specializing matrix arithmetic. More...

class	MatrixDomain
	Class of matrix arithmetic functions. More...

class	MatrixPermutation
	Permutation classique. More...

class	BlasPermutation
	Lapack-style permutation. More...

struct	RankBuilder
	random method for constructing rank More...

class	RandomDenseMatrix
	Random Dense Matrix builder. More...

class	InvalidMatrixInput
	Exception class for invalid matrix input. More...

class	FieldIO
	Dummy field for conceptually unclear io. More...

class	SparseMatrixBase
	Sparse matrix container This class acts as a generic row-wise container for sparse matrices. More...

class	TransposeMatrix
	Matrix transpose. More...

class	RandIterAbstract
	Random field element generator. More...

class	RandIterArchetype
	Random field element generator archetype. More...

class	GmpRandomPrime
	generating random prime integers, using the gmp library. More...

class	ModularCrookedRandIter
	Random field base element generator. More...

class	RandomIntegerIterator
	Random Prime Generator. More...

class	RandomIntegerIter
	Random Integer Iterator. More...

class	RandomPrimeIterator
	Random Prime Generator. More...

class	RandomPrimeIter
	Random Prime Iterator. More...

class	UnparametricRandIter
	Unparameterized random field element generator template. More...

class	RingAbstract
	Abstract ring base class. More...

class	RingArchetype
	specification and archetypic instance for the ring interfaceThe RingArchetype and its encapsulated element class contain pointers to the RingAbstract and its encapsulated ring element, respectively. More...

class	GivPolynomialRing
	Polynomials. More...

class	PowerOfTwoModular
	Ring of elements modulo some power of two. More...

class	RingInterface
	This ring base class exists solely to aid documentation organization. More...

struct	HybridSpecifier
	HybridSpecifier. More...

struct	BlackboxSpecifier
	BlackboxSpecifier. More...

struct	EliminationSpecifier
	EliminationSpecifier. More...

struct	CRASpecifier
	CRASpecifier. More...

struct	IMLTraits
	IML wrapper. More...

struct	Method
	Method specifiers for controlling algorithm choice. More...

struct	CRATraits
	Solve using CRA (iterations uses SolveMethod) More...

struct	SolverTraits
	Solver traits. More...

class	SolveFailed
	Exception thrown when the computed solution vector is not a true solution to the system, but none of the problems cited below exist. More...

class	InconsistentSystem
	Exception thrown when the system to be solved is inconsistent. More...

class	BooleanSwitch
	Boolean switch object. More...

class	BooleanSwitchFactory
	Boolean switch factory. More...

class	CekstvSwitchFactory
	Cekstv switch factory. More...

class	CekstvSwitch
	Butterfly switch object from preconditioner paper. More...

class	Commentator
	Give information to user during runtime. More...

class	PreconditionFailed
	A precondition failed. More...

class	Exception
	This is the exception class in LinBox. More...

class	algoException
	Algorithmic exception. More...

class	NotImplementedYetException
	Not implemented yet. More...

class	IrrecuperableException
	Something bad an unexpected happened. More...

class	BadInputException
	The input is not as expected. More...

class	LinboxError
	base class for execption handling in LinBox More...

class	MatrixStream
	MatrixStream. More...

class	MatrixStreamReader
	An abstract base class to represent readers for specific formats. More...

class	PrimeStream
	Prime number stream. More...

class	BitVector
	Binary constant defined both for 32 and 64 bits. More...

class	ReverseVector
	Reverse vector class This class wraps an existing vector type and reverses its direction. More...

class	Sparse_Vector
	vector< Pair<T,I> > and actualsize More...

class	VectorStream
	Vector factory. More...

class	ConstantVectorStream
	Constant vector factory. More...

class	RandomDenseStream
	Random dense vector stream. More...

class	RandomDenseStream< Field, _Vector, RandIter, VectorCategories::DenseVectorTag >
	Specialization of random dense stream for dense vectors. More...

class	RandomSparseStream
	Random sparse vector stream. More...

class	RandomSparseStream< Field, _Vector, RandIter, VectorCategories::DenseVectorTag >
	Specialization of RandomSparseStream for dense vectors. More...

class	RandomSparseStream< Field, _Vector, RandIter, VectorCategories::SparseSequenceVectorTag >
	Specialization of RandomSparseStream for sparse sequence vectors. More...

class	RandomSparseStream< Field, _Vector, RandIter, VectorCategories::SparseAssociativeVectorTag >
	Specialization of RandomSparseStream for sparse associative vectors. More...

class	RandomSparseStream< Field, _Vector, RandIter, VectorCategories::SparseParallelVectorTag >
	Specialization of RandomSparseStream for sparse parallel vectors. More...

class	StandardBasisStream
	Stream for $e_1,\cdots,e_n$ . More...

class	StandardBasisStream< Field, _Vector, VectorCategories::DenseVectorTag >
	Specialization of standard basis stream for dense vectors. More...

class	StandardBasisStream< Field, _Vector, VectorCategories::SparseSequenceVectorTag >
	Specialization of standard basis stream for sparse sequence vectors. More...

class	StandardBasisStream< Field, _Vector, VectorCategories::SparseAssociativeVectorTag >
	Specialization of standard basis stream for sparse associative vectors. More...

class	StandardBasisStream< Field, _Vector, VectorCategories::SparseParallelVectorTag >
	Specialization of standard basis stream for sparse parallel vectors. More...

class	Subiterator
	Subvector iterator class provides striding iterators. More...

class	Subvector
	Dense subvectorThis class provides a statically sized subvector of a random access container (such as std::vector, deque). More...

struct	VectorCategories
	List of vector categories. More...

struct	VectorTraits
	Vector traits template structure. More...

struct	RawVector
	Canonical vector types. More...

struct	Vector
	Vector ?? More...

struct	Rebind< std::vector< T >, U >
	Rebind. More...

class	PlotStyle
	Represents a table of values to plot. More...

class	PlotData
	The raw data to plot. More...

class	PlotGraph
	The graph. More...

Typedefs
typedef Givaro::Integer	integer
	Integers in LinBox. More...

Enumerations
enum	SolveResult
	Enumeration for results of next solver. More...

enum	SNSolverReturnStatus
	define the possible return status of the solver's computation.

enum	SolverReturnStatus
	define the different return status of the p-adic based solver's computation.

enum	SolverLevel
	Define the different strategy which can be used in the p-adic based solver. More...

enum	FileFormatTag
	tags for SparseMatrixBase::read() and write()

Functions
template<class Field , class Vector , class Blackbox >
WiedemannSolver< Field > ::ReturnStatus	solve (const Blackbox &A, Vector &x, const Vector &b, Vector &u, const Field &F, const WiedemannTraits &traits=WiedemannTraits())
	Solve Ax=b over field F using Wiedemann's method, with inconsistency certificate. More...

template<class Field , class Vector , class Blackbox >
Vector &	solve (const Blackbox &A, Vector &x, const Vector &b, const Field &F, const WiedemannTraits &traits=WiedemannTraits())
	Solve Ax=b over field F using the Wiedemann method. More...

template<class Field , class Vector , class Blackbox >
Vector &	solve (const Blackbox &A, Vector &x, const Vector &b, const Field &F, const LanczosTraits &traits)
	Solve Ax=b over field F using the Lanczos method. More...

template<class Field , class Vector , class Blackbox >
Vector &	solve (const Blackbox &A, Vector &x, const Vector &b, const Field &F, const BlockLanczosTraits &traits)
	Solve Ax=b over field F using the block Lanczos method. More...

template<class Field , class Matrix , class Vector >
Vector &	solve (const Matrix &A, Vector &x, const Vector &b, const Field &F, const BlasEliminationTraits &traits)
	Solve Ax=b over field F using Gaussian elimination. More...

template<class Field , class Blackbox , class Vector , class MethodTraits >
SolveResult	solve (const Blackbox &A, Vector &x, const Vector &b, const Field &F, Vector &u, const MethodTraits &traits=MethodTraits())
	Solve Ax=b over field F, returning consistency indicator. More...

template<class Polynomial , class Blackbox >
Polynomial &	cia (Polynomial &P, const Blackbox &A, const Method::BlasElimination &M)
	Algorithm computing the integer characteristic polynomial of a dense matrix. More...

template<class Field >
size_t	NullSpaceBasis (const Field &F, const LinBoxTag::Side Side, const size_t &m, const size_t &n, typename Field::Element A, const size_t &lda, typename Field::Element &Ker, size_t &ldk, size_t &kerdim)
	Computes the kernel of a dense matrix using `LQUP`. More...

template<class Field >
size_t &	NullSpaceBasis (const Field &F, const LinBoxTag::Side Side, BlasMatrix< typename Field::Element > &A, BlasMatrix< typename Field::Element > &Ker, size_t &kerdim)
	Nullspace of a dense matrix on a finite field. More...

template<class Field >
size_t &	NullSpaceBasis (const Field &F, const LinBoxTag::Side Side, const BlasMatrix< typename Field::Element > &A, BlasMatrix< typename Field::Element > &Ker, size_t &kerdim)
	Nullspace of a dense matrix on a finite field. More...

template<class Field >
void	Zero (const Field &F, typename Field::Element *Z, const size_t ldZ, const size_t lig1, const size_t col1, const size_t lig2, const size_t col2)

template<class Field >
void	Identity (const Field &F, typename Field::Element *Id, const size_t ldI, const size_t lig1, const size_t col1, const size_t lig2, const size_t col2)
	Creates identity matrix in `F` of size `dim1` `x` `dim2`. More...

template<class Field >
Field::Element *	RightNullspaceDirect (const Field &F, typename Field::Element *A, const size_t &M, const size_t &N, const size_t &lda, size_t &ker_dim)
	The right or left nullspace (kernel or cokernel) of a matrix A We use the LU decomposition. More...

template<class Ring >
int	dyadicToRational (const Ring &Z, typename Ring::Element &a, typename Ring::Element &b, const typename Ring::Element &n, const typename Ring::Element &d, const typename Ring::Element &B)
	Rational reconstruction of a/b from n/d with denominator bound B. More...

template<class Ring >
bool	partial_hegcd (Ring &Z, typename Ring::Element &e, typename Ring::Element &b, const typename Ring::Element &n, const typename Ring::Element &d, const typename Ring::Element &denBound)
	partial_hegcd() sets e, b from the remainder sequence of n,d. More...

template<class Blackbox , class MyMethod >
Blackbox::Field::Element &	lif_cra_det (typename Blackbox::Field::Element &d, const Blackbox &A, const RingCategories::IntegerTag &tag, const MyMethod &M)
	Compute the determinant of A over the integers. More...

template<class Ring , class ItMatrix >
void	SpecialBound (const Ring &R, typename Ring::Element &H_col_sqr, typename Ring::Element &short_col_sqr, const ItMatrix &A)
	BoundBlackbox. More...

template<class Ring , class ItMatrix >
void	ApplyBound (const Ring &R, typename Ring::Element &bound_A, const ItMatrix &A)
	ApplyBound. More...

template<class Prime >
bool	checkBlasPrime (const Prime p)
	NO DOC ! More...

int	large_double_division (integer &x, const integer &y, const integer &z)
	NO DOC.

template<class Domain >
void	reduceIn (Domain &D, std::pair< typename Domain::Element, typename Domain::Element > &frac)
	utility function to reduce a rational pair to lowest form

template<class Domain , class Vector >
void	vectorGcdIn (typename Domain::Element &result, Domain &D, Vector &v)
	utility function to gcd-in a vector of elements over a domain

template<class Domain , class Vector >
Domain::Element	vectorGcd (Domain &D, Vector &v)
	utility function, returns gcd of a vector of elements over a domain

template<class Domain , class IMatrix >
void	create_MatrixQadic (const Domain &D, const IMatrix &Mat, double *chunks, size_t num_chunks, const integer shift)
	split an integer matrix into a padic chunk representation More...

template<class Domain , class Vector >
void	create_VectorQadic (const Domain &D, const Vector &V, double *chunks, size_t num_chunks)
	split an integer vector into a padic chunk representation More...

template<class Domain , class Vector >
void	create_VectorQadic_32 (const Domain &D, const Vector &V, double *chunks, size_t num_chunks)
	split an integer vector into a padic chunk representation More...

double	naturallog (const Givaro::Integer &a)
	Natural logarithm (ln). More...

template<class T >
std::ostream &	operator<< (std::ostream &o, const BlasMatrix< T > &Mat)
	Write a matrix to a stream. More...

template<class T >
std::ostream &	operator<< (std::ostream &o, const BlasSubmatrix< T > &Mat)
	Write a matrix to a stream. More...

void	RandomBlasPermutation (BlasPermutation< size_t > &P)

template<class Blackbox , class Polynomial , class MyMethod >
Polynomial &	charpoly (Polynomial &P, const Blackbox &A, const MyMethod &M)
	...using an optional Method parameter More...

template<class Blackbox , class Polynomial >
Polynomial &	charpoly (Polynomial &P, const Blackbox &A)
	...using default method

template<class Polynomial , class Blackbox >
Polynomial &	charpoly (Polynomial &P, const Blackbox &A, const RingCategories::ModularTag &tag, const Method::BlasElimination &M)
	Compute the characteristic polynomial over $\mathbf{Z}_p$ . More...

template<class Polynomial , class Blackbox >
Polynomial &	charpoly (Polynomial &P, const Blackbox &A, const RingCategories::ModularTag &tag, const Method::Blackbox &M)
	Compute the characteristic polynomial over $\mathbf{Z}_p$ . More...

template<class Blackbox , class DetMethod , class DomainCategory >
Blackbox::Field::Element &	det (typename Blackbox::Field::Element &d, const Blackbox &A, const DomainCategory &tag, const DetMethod &Meth)
	Compute the determinant of A. More...

template<class Field >
Field::Element &	detin (typename Field::Element &d, BlasMatrix< Field > &A)
	Rank of Blackbox `A`. More...

template<class BB >
BB::Field::Element &	getEntry (typename BB::Field::Element &x, const BB &A, const size_t i, const size_t j)
	Getting the i,j entry of the blackbox.

template<class BB , class Method >
BB::Field::Element &	getEntry (typename BB::Field::Element &x, const BB &A, const size_t i, const size_t j, Method &m)
	To ignore methods.

template<class Blackbox , class MyMethod >
bool	isPositiveDefinite (const Blackbox &A, const MyMethod &M)
	Compute the isPositiveDefinite of A. More...

template<class Blackbox , class MyMethod >
bool	isPositiveSemiDefinite (const Blackbox &A, const MyMethod &M)
	Compute the isPositiveSemiDefinite of A. More...

template<class Polynomial , class Blackbox >
Polynomial &	minpoly (Polynomial &P, const Blackbox &A)
	...using default Method

template<class Blackbox , class Method , class DomainCategory >
unsigned long &	rank (unsigned long &r, const Blackbox &A, const DomainCategory &tag, const Method &M)
	Compute the rank of a linear transform A over a field by selected method. More...

template<class Blackbox >
unsigned long &	rank (unsigned long &r, const Blackbox &A)
	Compute the rank of a linear transform A over a field. More...

template<class Matrix >
unsigned long &	rankin (unsigned long &r, Matrix &A)
	Rank of `A`. More...

template<class Blackbox , class Method >
unsigned long &	rank (unsigned long &r, const Blackbox &A, const Method &M)
	Compute the rank of a linear transform A over a field. More...

template<class Blackbox >
unsigned long &	rank (unsigned long &res, const Blackbox &A, const RingCategories::ModularTag &tag, const Method::Wiedemann &M)
	M may be `Method::Wiedemann()`.

template<class Field >
unsigned long &	rank (unsigned long &r, const SparseMatrix< Field, typename LinBox::Vector< Field >::SparseSeq > &A, const RingCategories::ModularTag &tag, const Method::SparseElimination &M)
	M may be `Method::SparseElimination()`.

unsigned long &	rankin (unsigned long &r, GaussDomain< GF2 >::Matrix &A, const Method::SparseElimination &)
	specialization to $\mathbf{F}_2$

unsigned long &	rankin (unsigned long &r, GaussDomain< GF2 >::Matrix &A, const RingCategories::ModularTag &, const Method::SparseElimination &M)
	specialization to $\mathbf{F}_2$

template<class Field >
unsigned long &	rankin (unsigned long &r, BlasMatrix< Field > &A, const RingCategories::ModularTag &tag, const Method::BlasElimination &M)
	A is modified.

template<class Output , class Blackbox , class MyMethod >
Output &	smithForm (Output &S, const Blackbox &A, const MyMethod &M)
	Compute the Smith form of A. More...

template<class Vector , class Blackbox , class SolveMethod >
Vector &	solve (Vector &x, const Blackbox &A, const Vector &b, const SolveMethod &M)
	Solve Ax = b, for x. More...

template<class Vector , class Blackbox >
Vector &	solve (Vector &x, const Blackbox &A, const Vector &b)
	the solve with default method.

template<class BB >
BB::Field::Element &	trace (typename BB::Field::Element &t, const BB &A)
	Sum of the eigenvalues. More...

template<class Blackbox , class MyMethod >
Blackbox::Field::Element &	valence (typename Blackbox::Field::Element &v, const Blackbox &A, const MyMethod &M)
	Compute the valence of A. More...

template<class Field , class Vector >
Vector	randomVector (Field &F, size_t n, typename Field::RandIter &r)
	Random vector generator This templated function takes a field and a random field element generator and returns a vector of random field elements. More...

Butterfly
Butterfly preconditioner and supporting function
std::vector< bool >	setButterfly (const std::vector< bool > &x, size_t j=0)
	A function used with Butterfly Blackbox Matrices. More...


template<class T >
bool	isPositive (const T &x)
	Positiveness of an integer. More...

template<>
bool	isPositive (const uint8_t &)
	Positiveness of an integer. More...

template<>
bool	isPositive (const uint16_t &)
	Positiveness of an integer. More...

template<>
bool	isPositive (const uint32_t &)
	Positiveness of an integer. More...

template<>
bool	isPositive (const uint64_t &)
	Positiveness of an integer. More...


template<class Vector , class BB >
Vector &	solve (Vector &x, typename BB::Field::Element &d, const BB &A, const Vector &b)
	2nd integer solver API : solution is a formed by a common denominator and a vector of integer numerator solution is num/d BB: why not a struct RatVector2 { IntVector _n ; Int _d } ; ?

template<class Vector , class BB , class MethodTraits >
Vector &	solve (Vector &x, typename BB::Field::Element &d, const BB &A, const Vector &b, const MethodTraits &m)
	2nd integer solver API : solution is a formed by a common denominator and a vector of integer numerator solution is num/d BB: why not a struct RatVector2 { IntVector _n ; Int _d } ; ?

template<class Vector , class BB >
Vector &	solve (Vector &x, typename BB::Field::Element &d, const BB &A, const Vector &b, const RingCategories::IntegerTag &tag, const Method::BlasElimination &m)
	2nd integer solver API : solution is a formed by a common denominator and a vector of integer numerator solution is num/d BB: why not a struct RatVector2 { IntVector _n ; Int _d } ; ?

template<class Vector , class Ring >
Vector &	solve (Vector &x, typename Ring::Element &d, const BlasMatrix< Ring > &A, const Vector &b, const RingCategories::IntegerTag &tag, const Method::BlasElimination &m)

template<class Vect , class Ring >
Vect &	solve (Vect &x, typename Ring::Element &d, const SparseMatrix< Ring, typename Vector< Ring >::SparseSeq > &A, const Vect &b, const RingCategories::IntegerTag &tag, const Method::SparseElimination &m)
	2nd integer solver API : solution is a formed by a common denominator and a vector of integer numerator solution is num/d BB: why not a struct RatVector2 { IntVector _n ; Int _d } ; ?

template<class Vector , class Ring >
Vector &	solve (Vector &x, typename Ring::Element &d, const BlasMatrix< Ring > &A, const Vector &b, const RingCategories::IntegerTag tag, Method::Dixon &m)
	solver specialization with the 2nd API and DixonTraits over integer (no copying)

template<class Vect , class Ring >
Vect &	solve (Vect &x, typename Ring::Element &d, const SparseMatrix< Ring, typename Vector< Ring >::SparseSeq > &A, const Vect &b, const RingCategories::IntegerTag tag, Method::Dixon &m)
	solver specialization with the 2nd API and DixonTraits over integer (no copying)

Detailed Description

Namespace in which all linbox code resides.

The subdirectories of linbox/ contain the template source code for all the LinBox functionality. See the Modules list for the documentation of the main parts of linbox.

Warning: The timer comes from Givaro and lives in its anonymous namespace.

Enumeration Type Documentation

enum SolveResult

Enumeration for results of next solver.

SOLVE_SUCCESSFUL - System solution was succesful, x holds the solution vector SOLVE_INCONSISTENT - System was inconsistent, u holds the certificate of inconsistency and x is untouched SOLVE_FAILED - Neither a system solution nor a certificate of inconsistency could be obtained before the maximum number of trials elapsed. Both x and u are untouched.

Function Documentation

WiedemannSolver<Field>::ReturnStatus LinBox::solve	(	const Blackbox &	A,
		Vector &	x,
		const Vector &	b,
		Vector &	u,
		const Field &	F,
		const WiedemannTraits &	traits = `WiedemannTraits ()`
	)

Solve Ax=b over field F using Wiedemann's method, with inconsistency certificate.

This is a general interface for the linear system solving capabilities of LinBox. If the system is nonsingular, it returns the unique solution, storing it in the vector x. If the system is consistent and singular, it returns a random solution. Repeated calls to this function can give a complete description of the solution manifold. If the system is inconsistent and the SolverTraits structure supplied requests certification of inconsistency, it fills in the certificate of inconsistency. Otherwise, it runs through the number of iterations specified in traits and throws a SolveFailed exception if it cannot find a solution.

This specialization uses Wiedemann's algorithm and is the default.

Parameters

A	Black box matrix of the system
x	Place to store solution vector
b	Right-hand side
u	Vector in which to store certificate of inconsistency, if required
F	Field over which to perform computations
traits	SolverTraits structure with user-specified parameters

Returns: Reference to solution vector

Examples:: examples/checksolve.C, and examples/solve.C.

Vector& LinBox::solve	(	const Blackbox &	A,
		Vector &	x,
		const Vector &	b,
		const Field &	F,
		const WiedemannTraits &	traits = `WiedemannTraits ()`
	)

Solve Ax=b over field F using the Wiedemann method.

This version differs from the one above in that there is no extra parameter for the certificate of inconsistency, and it throws exceptions if the solution fails. It also returns a reference to the solution vector.

Vector& LinBox::solve	(	const Blackbox &	A,
		Vector &	x,
		const Vector &	b,
		const Field &	F,
		const LanczosTraits &	traits
	)

Solve Ax=b over field F using the Lanczos method.

This is a general interface for the linear system solving capabilities of LinBox. If the system is nonsingular, it returns the unique solution, storing it in the vector x. If the system is consistent and singular, it returns a random solution. Repeated calls to this function can give a complete description of the solution manifold. If the system is inconsistent and the SolverTraits structure has result checking turned on, it runs through the number of iterations specified in traits and throws a SolveFailed exception if it cannot find a solution.

This specialization uses the Lanczos algorithm.

Parameters

A	Black box matrix of the system
x	Place to store solution vector
b	Right-hand side
F	Field over which to perform computations
traits	SolverTraits structure with user-specified parameters

Returns: Reference to solution vector

Vector& LinBox::solve	(	const Blackbox &	A,
		Vector &	x,
		const Vector &	b,
		const Field &	F,
		const BlockLanczosTraits &	traits
	)

Solve Ax=b over field F using the block Lanczos method.

This is a general interface for the linear system solving capabilities of LinBox. If the system is nonsingular, it returns the unique solution, storing it in the vector x. If the system is consistent and singular, it returns a random solution. Repeated calls to this function can give a complete description of the solution manifold. If the system is inconsistent and the SolverTraits structure has result checking turned on, it runs through the number of iterations specified in traits and throws a SolveFailed exception if it cannot find a solution.

This specialization uses the block Lanczos algorithm.

Parameters

A	Black box matrix of the system
x	Place to store solution vector
b	Right-hand side
F	Field over which to perform computations
traits	SolverTraits structure with user-specified parameters

Returns: Reference to solution vector

Vector& LinBox::solve	(	const Matrix &	A,
		Vector &	x,
		const Vector &	b,
		const Field &	F,
		const BlasEliminationTraits &	traits
	)

Solve Ax=b over field F using Gaussian elimination.

This is a general interface for the linear system solving capabilities of LinBox. If the system is nonsingular, it returns the unique solution, storing it in the vector x. If the system is consistent and singular, it returns a random solution. Repeated calls to this function can give a complete description of the solution manifold. If the system is inconsistent and the SolverTraits structure supplied requests certification of inconsistency, it throws an InconsistentSystem exception, which includes a certificate of inconsistency. Otherwise, it runs through the number of iterations specified in traits and throws a SolveFailed exception if it cannot find a solution.

Parameters

A	Black box matrix of the system
x	Place to store solution vector
b	Right-hand side
F	Field over which to perform computations
traits	SolverTraits structure with user-specified parameters

Returns: Reference to solution vector

SolveResult LinBox::solve	(	const Blackbox &	A,
		Vector &	x,
		const Vector &	b,
		const Field &	F,
		Vector &	u,
		const MethodTraits &	traits = `MethodTraits ()`
	)

Solve Ax=b over field F, returning consistency indicator.

This is a variant of solve that does not throw any exceptions unless the user makes an error. It returns a SolveResult enum indicating whether the solve operation was successful, the system was inconsistent, or the solve operation failed. The certificate of inconsistency, if requested, is stored in a reference parameter supplied to this variant.

Parameters

A	Black box matrix of the system
x	Place to store solution vector
b	Right-hand side
u	Place to store certificate of inconsistency
F	Field over which to perform computations
traits	SolverTraits structure with user-specified parameters

Returns: SolveResult indicating whether the solve operation was successful

size_t NullSpaceBasis	(	const Field &	F,
		const LinBoxTag::Side	Side,
		const size_t &	m,
		const size_t &	n,
		typename Field::Element *	A,
		const size_t &	lda,
		typename Field::Element *&	Ker,
		size_t &	ldk,
		size_t &	kerdim
	)

Computes the kernel of a dense matrix using LQUP.

Acccording to the dimensions of the input matrix, we chose different methods.

Warning: timings may vary and these choices were made on an experimental basis.

Parameters

F	Field
Side	left or right from `LinBox::SideTag`
m	rows
n	cols
A	input matrix
lda	leading dimension of A
Ker	Kernel. `NULL` if `kerdim==0`
ldk	leading dimension of the kernel.
kerdim	dimension of the kernel.

Returns: dimension of the kernel.

Warning: A is modified.

size_t & NullSpaceBasis	(	const Field &	F,
		const LinBoxTag::Side	Side,
		BlasMatrix< typename Field::Element > &	A,
		BlasMatrix< typename Field::Element > &	Ker,
		size_t &	kerdim
	)

Nullspace of a dense matrix on a finite field.

  A is modified.

Parameters

	F	field
	Side	`SideTag::Left` or `SideTag::Right` nullspace.
[in,out]	A	Input matrix
[out]	Ker	Nullspace of the matrix (Allocated in the routine)
[out]	kerdim	rank of the kernel

Returns: kerdim

Todo:: this is slow : use a constructor from Ker ?

Todo:: this is slow : use a constructor from Ker ?

size_t& LinBox::NullSpaceBasis	(	const Field &	F,
		const LinBoxTag::Side	Side,
		const BlasMatrix< typename Field::Element > &	A,
		BlasMatrix< typename Field::Element > &	Ker,
		size_t &	kerdim
	)

Nullspace of a dense matrix on a finite field.

  A is preserved.

Parameters

	F	field
	Side	`SideTag::Left` or `SideTag::Right` nullspace.
[in]	A	Input matrix
[out]	Ker	Nullspace of the matrix (Allocated in the routine)
[out]	kerdim	rank of the kernel

Returns: kerdim

void LinBox::Zero	(	const Field &	F,
		typename Field::Element *	Z,
		const size_t	ldZ,
		const size_t	lig1,
		const size_t	col1,
		const size_t	lig2,
		const size_t	col2
	)

Parameters

F
Z
ldZ
lig1
col1
lig2
col2

void LinBox::Identity	(	const Field &	F,
		typename Field::Element *	Id,
		const size_t	ldI,
		const size_t	lig1,
		const size_t	col1,
		const size_t	lig2,
		const size_t	col2
	)

Creates identity matrix in F of size dim1 x dim2.

Warning: diag_num peut être < 0 !

Bug:: long et size_t ne cohabitent pas bien.

Field::Element* LinBox::RightNullspaceDirect	(	const Field &	F,
		typename Field::Element *	A,
		const size_t &	M,
		const size_t &	N,
		const size_t &	lda,
		size_t &	ker_dim
	)

The right or left nullspace (kernel or cokernel) of a matrix A We use the LU decomposition.

Parameters

F	the field in which `A` lives
A	is a matrix whose nullspace we look for.
M	number of lines in `A`
N	number of column of `A`
lda	the leading dimension of matrix `A`
ker_dim	the dimension of the kernel

Template Parameters

Field -

Returns: a matrix of leading dimension ker_dim whose column vectors span the nullspace of A. Returns NULL (and not $\mathbf{0}$ ) if ker_dim == 0 .

int LinBox::dyadicToRational	(	const Ring &	Z,
		typename Ring::Element &	a,
		typename Ring::Element &	b,
		const typename Ring::Element &	n,
		const typename Ring::Element &	d,
		const typename Ring::Element &	B
	)

Rational reconstruction of a/b from n/d with denominator bound B.

We give a/b, the continued fraction approximant of n/d that satisfies |a/b - n/d| < 1/2d (well approximated) and 0 < b <= B. Return value is 0, if no such approximant exists. Return value is 1, if either (i) a second well approximated rational with denominator bounded by B may exist, or (ii) the well approximated condition is not met for a/b. In these cases, a/b may be used speculatively. Return value is 2, if the approximant is guaranteed (because bB <= d).

If no fraction is well approximated the last b <= B in the remainder sequence of n,d is given.

If d = 2^k and n = sum_i=l to k n_i 2^i, then * n/d = sum_{i=l down to 0} n_i/2^{k-i} is a {dyadic rational}. Numbers of this form are produced for example by numeric-symbolic iterations.

If it is known that n/d is the most accurate approximation with denominator d to a/b, and that the denominator b is bounded by B, i.e. b <= B, then such a/b is uniquely determined, provided d >= bB. ...in that case, such a/b is returned by dyadicToRational(). This follows from two facts: First, by definition, n/d is an accurate approximation to a/b with b <= d when |n/d - a/b| < 1/2d. Otherwise (n-1)/d or (n+1)/d would be a better approximation. Second, if a/b and a'/b' are distinct rationals, then |a/b - a'/b'| >= 1/bb'. Thus if a'/b' is another rational accurately approximated by n/d, we have 1/bb' <= |a/b - a'/b'| <= |a/b - n/d| + |n/d - a'/b'| <= 1/2d + 1/2d = 1/d. So bb' > d >= bB, thus b' > B.

In summary: If it exists, the unique a/b is given such that n/d approximates a/b to within 1/2d and b <= B. Otherwise a plausible a/b is given or failure is signaled.

"Symbolic-Numeric Exact Rational Linear System Solver" by Saunders, Wood, Youse. describes the construction.

bool LinBox::partial_hegcd	(	Ring &	Z,
		typename Ring::Element &	e,
		typename Ring::Element &	b,
		const typename Ring::Element &	n,
		const typename Ring::Element &	d,
		const typename Ring::Element &	denBound
	)

partial_hegcd() sets e, b from the remainder sequence of n,d.

It requires positive n and d. It sets e to the first r_i (remainder) and b to the corresponding q_i (coefficient of n) such that 2r_i < |q_i| and |q_i| <= B (the given denominator bound). True is returned iff such e, b exist.

If not, b is the largest q_i such that |q_i| <= B, and e is the corresponding remainder. In this case b is the denominator of a plausibly approximated but not well approximated rational. It can be used speculatively.

void LinBox::SpecialBound	(	const Ring &	R,
		typename Ring::Element &	H_col_sqr,
		typename Ring::Element &	short_col_sqr,
		const ItMatrix &	A
	)

BoundBlackbox.

BoundBlackbox: Sets H_col_sqr <- H_col(A)^2, short_col_sqr <- short_col(A)^2 where H_col(A) is prod_j sqrt(sum_i a_ij^2) ('Hadamard column bound') short_col(A) is min_j sqrt(sum_i a_ij^2) ('shortest column')

Note: H_col is not actually a norm! but it is what we need for lifting bound computation

void LinBox::ApplyBound	(	const Ring &	R,
		typename Ring::Element &	bound_A,
		const ItMatrix &	A
	)

ApplyBound.

ApplyBound computes bound_A <- max_i(max(sum_{j|a_ij > 0} a_ij, sum_{j|a_ij < 0} |a_ij|)) this is useful because for all u, v >= 0: [b has all entries in -u..v] => [each entry of A.b is at most (u+v)*bound_A in absolute value]

bool LinBox::checkBlasPrime ( const Prime p )

inline

NO DOC !

Bug:: why is this hard coded ?

void create_MatrixQadic	(	const Domain &	D,
		const IMatrix &	Mat,
		double *	chunks,
		size_t	num_chunks,
		const integer	shift
	)

split an integer matrix into a padic chunk representation

void LinBox::create_VectorQadic	(	const Domain &	D,
		const Vector &	V,
		double *	chunks,
		size_t	num_chunks
	)

split an integer vector into a padic chunk representation

void LinBox::create_VectorQadic_32	(	const Domain &	D,
		const Vector &	V,
		double *	chunks,
		size_t	num_chunks
	)

split an integer vector into a padic chunk representation

std::vector<bool> LinBox::setButterfly	(	const std::vector< bool > &	x,
		size_t	j = `0`
	)

inline

A function used with Butterfly Blackbox Matrices.

This function takes an STL vector x of booleans, and returns a vector y of booleans such that setting the switches marked by true flags in y to be on (or to swap elements) the true elements x will be switched to a given contiguous block through the use of a Butterfly switching network. The integer parameter j marks where this block is to begin. If x has r true elements, the Butterfly switching network will place these elements in a contiguous block starting at j and ending at j + r - 1. Wrap around shall be considered to preserve contiguity. The value of j is defaulted to be zero, and it is only allowed to be non-zero is the size of x is a power of 2.

Returns: vector of booleans for setting switches

Parameters

x	vector of booleans marking elements to switch into contiguous block
j	offset of contiguous block

double LinBox::naturallog ( const Givaro::Integer & a )

inline

Natural logarithm (ln).

log(2) being close to 0.69314718055994531

Parameters

a integer.

Returns: ln(a).

bool LinBox::isPositive ( const T & x )

inline

Positiveness of an integer.

  Essentially usefull in debug mode to avoid compiler warnings
  about comparison always true for some unsigned type.

Parameters

x integer

Returns: true iff x>=0.

bool LinBox::isPositive ( const uint8_t & )

inline

Positiveness of an integer.

  Essentially usefull in debug mode to avoid compiler warnings
  about comparison always true for some unsigned type.

Parameters

x integer

Returns: true iff x>=0.

bool LinBox::isPositive ( const uint16_t & )

inline

Positiveness of an integer.

  Essentially usefull in debug mode to avoid compiler warnings
  about comparison always true for some unsigned type.

Parameters

x integer

Returns: true iff x>=0.

bool LinBox::isPositive ( const uint32_t & )

inline

Positiveness of an integer.

  Essentially usefull in debug mode to avoid compiler warnings
  about comparison always true for some unsigned type.

Parameters

x integer

Returns: true iff x>=0.

bool LinBox::isPositive ( const uint64_t & )

inline

Positiveness of an integer.

  Essentially usefull in debug mode to avoid compiler warnings
  about comparison always true for some unsigned type.

Parameters

x integer

Returns: true iff x>=0.

std::ostream& LinBox::operator<<	(	std::ostream &	o,
		const BlasMatrix< T > &	Mat
	)

Write a matrix to a stream.

  The \c C++ way using <code>operator<<</code>

Parameters

o	output stream
Mat	matrix to write.

std::ostream& LinBox::operator<<	(	std::ostream &	o,
		const BlasSubmatrix< T > &	Mat
	)

Write a matrix to a stream.

  The C++ way using <code>operator<<</code>

Parameters

o	output stream
Mat	matrix to write.

void RandomBlasPermutation ( BlasPermutation< size_t > & P )

Todo:: To be factorized.

Polynomial& LinBox::charpoly	(	Polynomial &	P,
		const Blackbox &	A,
		const MyMethod &	M
	)

...using an optional Method parameter

Parameters

P	- the output characteristic polynomial. If the polynomial is of degree d, this random access container has size d+1, the 0-th entry is the constant coefficient and the d-th is 1 since the charpoly is monic.
A	- a blackbox matrix Optional
M	- the method object. Generally, the default object suffices and the algorithm used is determined by the class of M. Basic methods are Method::Blackbox, Method::Elimination, and Method::Hybrid (the default). See methods.h for more options.

Returns: a reference to P.

Polynomial& LinBox::charpoly	(	Polynomial &	P,
		const Blackbox &	A,
		const RingCategories::ModularTag &	tag,
		const Method::BlasElimination &	M
	)

Compute the characteristic polynomial over $\mathbf{Z}_p$ .

Compute the characteristic polynomial of a matrix using dense elimination methods

Parameters

P	Polynomial where to store the result
A	Blackbox representing the matrix
tag
M

Polynomial& LinBox::charpoly	(	Polynomial &	P,
		const Blackbox &	A,
		const RingCategories::ModularTag &	tag,
		const Method::Blackbox &	M
	)

Compute the characteristic polynomial over $\mathbf{Z}_p$ .

Compute the characteristic polynomial of a matrix, represented via a blackBox.

Parameters

P	Polynomial where to store the result
A	Blackbox representing the matrix
tag
M

bool LinBox::isPositiveDefinite	(	const Blackbox &	A,
		const MyMethod &	M
	)

Compute the isPositiveDefinite of A.

The isPositiveDefinite of a linear operator A, represented as a black box, is computed over the ring or field of A.

Parameters

A	Black box of which to compute the isPositiveDefinite
M	may be a Method::Hybrid (default), Method::Blackbox, Method::Elimination, or of other method type.

bool LinBox::isPositiveSemiDefinite	(	const Blackbox &	A,
		const MyMethod &	M
	)

Compute the isPositiveSemiDefinite of A.

The isPositiveSemiDefinite of a linear operator A, represented as a black box, is computed over the ring or field of A.

Parameters

A	Black box of which to compute the isPositiveSemiDefinite
M	may be a Method::Hybrid (SemiDefault), Method::Blackbox, Method::Elimination, or of other method type.

unsigned long& LinBox::rankin	(	unsigned long &	r,
		Matrix &	A
	)

inline

Rank of A.

A may be modified

Parameters

A	matrix
r	rank

Examples:: examples/rank.C, and examples/smithvalence.h.

Vector& LinBox::solve	(	Vector &	x,
		const Blackbox &	A,
		const Vector &	b,
		const SolveMethod &	M
	)

Solve Ax = b, for x.

Vector x such that Ax = b is returned. In the case of a singular matrix A, if the system is consistent, a random solution is returned by default. The method parameter may contain an indication that an arbitrary element of the solution space is acceptable, which can be faster to compute. If the system is inconsistent the zero vector is returned.

Warning: no doc for when using what method

Parameters

[out]	x	solution
[in]	A	matrix
[in]	b	target
[in]	M	method to use (

See Also: solutions/method.h)

Returns: reference to x

Vector& LinBox::solve	(	Vector &	x,
		typename Ring::Element &	d,
		const BlasMatrix< Ring > &	A,
		const Vector &	b,
		const RingCategories::IntegerTag &	tag,
		const Method::BlasElimination &	m
	)

Bug:: check we don't copy

BB::Field::Element& LinBox::trace	(	typename BB::Field::Element &	t,
		const BB &	A
	)

Sum of the eigenvalues.

Also it is the sum of the diagonal entries.

Runtime on n by n matrix is n times the cost of getEntry(). This is linear in n for those classes where getEntry is constant time (eg DenseMatrix and SparseMatrix). Trace is constant time when the diagonal is necessarily constant, eg. for ScalarMatrix and Toeplitz. Worst case time is cost of n blackbox applies (matrix vector products), and apply cost typically ranges between O(n) and O(n^2).

Vector LinBox::randomVector	(	Field &	F,
		size_t	n,
		typename Field::RandIter &	r
	)

inline

Random vector generator This templated function takes a field and a random field element generator and returns a vector of random field elements.

The vector is dense in the field elements, even if the vector is a sparse LinBox vector. The funtion is templatized by the field and the vector types being used. This function calls another function by the same name with an additional parameter of the vector category of the vector it is called with. This mechanism is used because functions cannot have partial template specializations like classes can. This new, extended function can be specialized for specific fields and vectors to allow for better performance.

Returns: v vector of random field elements

Parameters

F	Field in which arithmetic is done
n	integer number of elements in vector
r	Random field element generator

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Data Structures

Typedefs

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Functions

Detailed Description

Enumeration Type Documentation

Function Documentation