RationalSolver< Ring, Field, RandomPrime, WiedemannTraits > Class Template Reference

#include <rational-solver.h>

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Detailed Description

template<class Ring, class Field, class RandomPrime>
class LinBox::RationalSolver< Ring, Field, RandomPrime, WiedemannTraits >

partial specialization of p-adic based solver with Wiedemann algorithm

See the following reference for details on this algorithm:

• Douglas H. Wiedemann: Solving sparse linear equations over finite fields. IEEE Transaction on Information Theory, 32(1), pages 54-62, 1986.

• Erich Kaltofen and B. David Saunders: On Wiedemann's method of solving sparse linear systems. In Applied Algebra, Algebraic Algorithms and Error Correcting Codes - AAECC'91, volume 539 of Lecture Notes in Computer Sciences, pages 29-38, 1991.

Public Types
typedef Ring	RingType
typedef Ring::Element	Integer
typedef Field::Element	Element
typedef RandomPrime::Prime_Type	Prime
typedef std::vector< Element >	FPolynomial
Public Member Functions
	RationalSolver (const Ring &r=Ring(), const RandomPrime &rp=RandomPrime(DEFAULT_PRIMESIZE), const WiedemannTraits &traits=WiedemannTraits())
	RationalSolver (const Prime &p, const Ring &r=Ring(), const RandomPrime &rp=RandomPrime(DEFAULT_PRIMESIZE), const WiedemannTraits &traits=WiedemannTraits())
template<class IMatrix, class Vector1, class Vector2> SolverReturnStatus	solve (Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, const bool, int maxPrimes=DEFAULT_MAXPRIMES) const
template<class IMatrix, class Vector1, class Vector2> SolverReturnStatus	solveNonsingular (Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, int maxPrimes=DEFAULT_MAXPRIMES) const
template<class IMatrix, class Vector1, class Vector2> SolverReturnStatus	solveSingular (Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, int maxPrimes=DEFAULT_MAXPRIMES) const
template<class IMatrix, class FMatrix, class IVector> void	sparseprecondition (const Field &, const IMatrix *, Compose< LambdaSparseMatrix< Ring >, Compose< IMatrix, LambdaSparseMatrix< Ring > > > *&, const FMatrix *, Compose< LambdaSparseMatrix< Field >, Compose< FMatrix, LambdaSparseMatrix< Field > > > *&, const IVector &, IVector &, LambdaSparseMatrix< Ring > *&, LambdaSparseMatrix< Ring > *&, LambdaSparseMatrix< Field > *&, LambdaSparseMatrix< Field > *&) const
Protected Attributes
Ring	_R
RandomPrime	_genprime
Prime	_prime
WiedemannTraits	_traits

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Member Typedef Documentation

typedef Ring RingType

typedef Ring::Element Integer

typedef Field::Element Element

typedef RandomPrime::Prime_Type Prime

typedef std::vector<Element> FPolynomial

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Member Function Documentation

RationalSolver (  const Ring &  r = Ring(), const RandomPrime &  rp = RandomPrime(DEFAULT_PRIMESIZE), const WiedemannTraits &  traits = WiedemannTraits() )  [inline]

Constructor Parameters: r,a  Ring, set by default rp,a  RandomPrime generator, set by default

RationalSolver (  const Prime &  p, const Ring &  r = Ring(), const RandomPrime &  rp = RandomPrime(DEFAULT_PRIMESIZE), const WiedemannTraits &  traits = WiedemannTraits() )  [inline]

Constructor with a prime Parameters: p,a  Prime r,a  Ring, set by default rp,a  RandomPrime generator, set by default

SolverReturnStatus solve (  Vector1 &  num, Integer &  den, const IMatrix &  A, const Vector2 &  b, const  bool, int  maxPrimes = DEFAULT_MAXPRIMES )  const

SolverReturnStatus solveNonsingular (  Vector1 &  num, Integer &  den, const IMatrix &  A, const Vector2 &  b, int  maxPrimes = DEFAULT_MAXPRIMES )  const

SolverReturnStatus solveSingular (  Vector1 &  num, Integer &  den, const IMatrix &  A, const Vector2 &  b, int  maxPrimes = DEFAULT_MAXPRIMES )  const

void sparseprecondition (  const Field &  , const IMatrix *  , Compose< LambdaSparseMatrix< Ring >, Compose< IMatrix, LambdaSparseMatrix< Ring > > > *&  , const FMatrix *  , Compose< LambdaSparseMatrix< Field >, Compose< FMatrix, LambdaSparseMatrix< Field > > > *&  , const IVector &  , IVector &  , LambdaSparseMatrix< Ring > *&  , LambdaSparseMatrix< Ring > *&  , LambdaSparseMatrix< Field > *&  , LambdaSparseMatrix< Field > *&  )  const

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Field Documentation

Ring _R [protected]

RandomPrime _genprime [protected]

Prime _prime [mutable, protected]

WiedemannTraits _traits [protected]

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