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

partial specialization of p-adic based solver with Dixon algorithm More...

#include <rational-solver.h>

List of all members.

Public Member Functions
	RationalSolver (const Ring &r=Ring(), const RandomPrime &rp=RandomPrime(DEFAULT_PRIMESIZE))
	RationalSolver (const Prime &p, const Ring &r=Ring(), const RandomPrime &rp=RandomPrime(DEFAULT_PRIMESIZE))
template<class IMatrix , class Vector1 , class Vector2 >
SolverReturnStatus	solve (Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, const bool=false, const int maxPrimes=DEFAULT_MAXPRIMES, const SolverLevel level=SL_DEFAULT) const
template<class IMatrix , class Vector1 , class Vector2 >
SolverReturnStatus	solve (Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, const int maxPrimes, const SolverLevel level=SL_DEFAULT) const
template<class IMatrix , class Vector1 , class Vector2 >
SolverReturnStatus	solveNonsingular (Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, bool=false, 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 SolverLevel level=SL_DEFAULT) const
template<class IMatrix , class Vector1 , class Vector2 >
SolverReturnStatus	findRandomSolution (Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, int maxPrimes=DEFAULT_MAXPRIMES, const SolverLevel level=SL_DEFAULT) const
template<class IMatrix , class Vector1 , class Vector2 >
SolverReturnStatus	monolithicSolve (Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, bool makeMinDenomCert, bool randomSolution, int maxPrimes=DEFAULT_MAXPRIMES, const SolverLevel level=SL_DEFAULT) const

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Detailed Description

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

partial specialization of p-adic based solver with Dixon algorithm

See the following reference for details on this algorithm:

• John D. Dixon: Exact Solution of linear equations using p-adic expansions. Numerische Mathematik, volume 40, pages 137-141, 1982.

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Constructor & Destructor Documentation

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

Constructor, trying the prime p first

Parameters:

	p,a	Prime
	r,a	Ring, set by default
	rp,a	RandomPrime generator, set by default

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Member Function Documentation

SolverReturnStatus solve	(	Vector1 &	num,
		Integer &	den,
		const IMatrix &	A,
		const Vector2 &	b,
		const	bool = false,
		const int	maxPrimes = DEFAULT_MAXPRIMES,
		const SolverLevel	level = SL_DEFAULT
	)			const [inline]

Solve a linear system Ax=b over quotient field of a ring

Parameters:

	num,Vector	of numerators of the solution
	den,The	common denominator. 1/den * num is the rational solution of Ax = b.
	A,Matrix	of linear system
	b,Right-hand	side of system
	maxPrimes,maximum	number of moduli to try
	level,level	of certification to be used

Returns:

status of solution. if (return != SS_FAILED), and (level >= SL_LASVEGAS), solution is guaranteed correct. SS_FAILED - all primes used were bad SS_OK - solution found. SS_INCONSISTENT - system appreared inconsistent. certificate is in lastCertificate if (level >= SL_CERTIFIED)

SolverReturnStatus solve	(	Vector1 &	num,
		Integer &	den,
		const IMatrix &	A,
		const Vector2 &	b,
		const int	maxPrimes,
		const SolverLevel	level = SL_DEFAULT
	)			const [inline]

overload so that the bool 'oldMatrix' argument is not accidentally set to true

SolverReturnStatus solveNonsingular	(	Vector1 &	num,
		Integer &	den,
		const IMatrix &	A,
		const Vector2 &	b,
		bool	= false,
		int	maxPrimes = DEFAULT_MAXPRIMES
	)			const [inline]

Solve a nonsingular, square linear system Ax=b over quotient field of a ring

Parameters:

	num,Vector	of numerators of the solution
	den,The	common denominator. 1/den * num is the rational solution of Ax = b.
	A,Matrix	of linear system (it must be square)
	b,Right-hand	side of system
	maxPrimes,maximum	number of moduli to try

Returns:

status of solution. SS_FAILED - all primes used were bad SS_OK - solution found, guaranteed correct. SS_SINGULAR - system appreared singular mod all primes.

SolverReturnStatus solveSingular	(	Vector1 &	num,
		Integer &	den,
		const IMatrix &	A,
		const Vector2 &	b,
		int	maxPrimes = DEFAULT_MAXPRIMES,
		const SolverLevel	level = SL_DEFAULT
	)			const [inline]

Solve a general rectangular linear system Ax=b over quotient field of a ring. If A is known to be square and nonsingular, calling solveNonsingular is more efficient.

Parameters:

	num,Vector	of numerators of the solution
	den,The	common denominator. 1/den * num is the rational solution of Ax = b.
	A,Matrix	of linear system
	b,Right-hand	side of system
	maxPrimes,maximum	number of moduli to try
	level,level	of certification to be used

Returns:

status of solution. if (return != SS_FAILED), and (level >= SL_LASVEGAS), solution is guaranteed correct. SS_FAILED - all primes used were bad SS_OK - solution found. SS_INCONSISTENT - system appreared inconsistent. certificate is in lastCertificate if (level >= SL_CERTIFIED)

SolverReturnStatus findRandomSolution	(	Vector1 &	num,
		Integer &	den,
		const IMatrix &	A,
		const Vector2 &	b,
		int	maxPrimes = DEFAULT_MAXPRIMES,
		const SolverLevel	level = SL_DEFAULT
	)			const [inline]

Find a random solution of the general linear system Ax=b over quotient field of a ring.

Parameters:

	num,Vector	of numerators of the solution
	den,The	common denominator. 1/den * num is the rational solution of Ax = b.
	A,Matrix	of linear system
	b,Right-hand	side of system
	maxPrimes,maximum	number of moduli to try
	level,level	of certification to be used

Returns:

status of solution. if (return != SS_FAILED), and (level >= SL_LASVEGAS), solution is guaranteed correct. SS_FAILED - all primes used were bad SS_OK - solution found. SS_INCONSISTENT - system appreared inconsistent. certificate is in lastCertificate if (level >= SL_CERTIFIED)

SolverReturnStatus monolithicSolve	(	Vector1 &	num,
		Integer &	den,
		const IMatrix &	A,
		const Vector2 &	b,
		bool	makeMinDenomCert,
		bool	randomSolution,
		int	maxPrimes = DEFAULT_MAXPRIMES,
		const SolverLevel	level = SL_DEFAULT
	)			const [inline]

Big solving routine to perform random solving and certificate generation. Same arguments and return as findRandomSolution, except

Parameters:

	num,Vector	of numerators of the solution
	den,The	common denominator. 1/den * num is the rational solution of Ax = b.
	randomSolution,parameter	to determine whether to randomize or not (since solveSingular calls this function as well)
	makeMinDenomCert,determines	whether a partial certificate for the minimal denominator of a rational solution is made

When (randomSolution == true && makeMinDenomCert == true), If (level == SL_MONTECARLO) this function has the same effect as calling findRandomSolution. If (level >= SL_LASVEGAS && return == SS_OK), lastCertifiedDenFactor contains a certified factor of the min-solution's denominator. If (level >= SL_CERTIFIED && return == SS_OK), lastZBNumer and lastCertificate are updated as well.

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

• /build/buildd/linbox-1.1.6~rc0/linbox/algorithms/rational-solver.h