PolynomialSolver< _Scalar, 1 > Class Template Reference

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Detailed Description

template<typename _Scalar>
class PolynomialSolver< _Scalar, 1 >

Definition at line 379 of file Polynomials.

Inheritance diagram for PolynomialSolver< _Scalar, 1 >:

List of all members.

Public Types
typedef PolynomialSolverBase < _Scalar, 1 >	PS_Base
typedef _Scalar	Scalar
typedef NumTraits< Scalar >::Real	RealScalar
typedef std::complex< RealScalar >	RootType
typedef Matrix< RootType, _Deg, 1 >	RootsType
typedef DenseIndex	Index
Public Member Functions
template<typename OtherPolynomial >
void	compute (const OtherPolynomial &poly)
	Computes the complex roots of a new polynomial.
const RootsType &	roots () const
void	realRoots (Stl_back_insertion_sequence &bi_seq, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const
	Clear and fills the back insertion sequence with the real roots of the polynomial i.e.
const RootType &	greatestRoot () const
const RootType &	smallestRoot () const
const RealScalar &	absGreatestRealRoot (bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const
const RealScalar &	absSmallestRealRoot (bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const
const RealScalar &	greatestRealRoot (bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const
const RealScalar &	smallestRealRoot (bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const
Protected Member Functions
void	setPolynomial (const OtherPolynomial &poly)
const RootType &	selectComplexRoot_withRespectToNorm (squaredNormBinaryPredicate &pred) const
const RealScalar &	selectRealRoot_withRespectToAbsRealPart (squaredRealPartBinaryPredicate &pred, bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const
const RealScalar &	selectRealRoot_withRespectToRealPart (RealPartBinaryPredicate &pred, bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const
Protected Attributes
RootsType	m_roots

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Member Typedef Documentation

typedef DenseIndex PolynomialSolverBase< _Scalar, _Deg >::Index [inherited]

Definition at line 53 of file Polynomials.

template<typename _Scalar >

typedef PolynomialSolverBase<_Scalar,1> PolynomialSolver< _Scalar, 1 >::PS_Base

Definition at line 382 of file Polynomials.

typedef NumTraits<Scalar>::Real PolynomialSolverBase< _Scalar, _Deg >::RealScalar [inherited]

Definition at line 49 of file Polynomials.

typedef Matrix<RootType,_Deg,1> PolynomialSolverBase< _Scalar, _Deg >::RootsType [inherited]

Definition at line 51 of file Polynomials.

typedef std::complex<RealScalar> PolynomialSolverBase< _Scalar, _Deg >::RootType [inherited]

Definition at line 50 of file Polynomials.

typedef _Scalar PolynomialSolverBase< _Scalar, _Deg >::Scalar [inherited]

Definition at line 48 of file Polynomials.

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Member Function Documentation

const RealScalar& PolynomialSolverBase< _Scalar, _Deg >::absGreatestRealRoot	(	bool &	hasArealRoot,
		const RealScalar &	absImaginaryThreshold = NumTraits<Scalar>::dummy_precision()
	)		const [inline, inherited]

Returns:

a real root with greatest absolute magnitude. A real root is defined as the real part of a complex root with absolute imaginary part smallest than absImaginaryThreshold. absImaginaryThreshold takes the dummy_precision associated with the _Scalar template parameter of the PolynomialSolver class as the default value. If no real root is found the boolean hasArealRoot is set to false and the real part of the root with smallest absolute imaginary part is returned instead.

Parameters:

[out]	hasArealRoot	: boolean true if a real root is found according to the absImaginaryThreshold criterion, false otherwise.
[in]	absImaginaryThreshold	: threshold on the absolute imaginary part to decide whether or not a root is real.

Definition at line 223 of file Polynomials.

const RealScalar& PolynomialSolverBase< _Scalar, _Deg >::absSmallestRealRoot	(	bool &	hasArealRoot,
		const RealScalar &	absImaginaryThreshold = NumTraits<Scalar>::dummy_precision()
	)		const [inline, inherited]

Returns:

a real root with smallest absolute magnitude. A real root is defined as the real part of a complex root with absolute imaginary part smallest than absImaginaryThreshold. absImaginaryThreshold takes the dummy_precision associated with the _Scalar template parameter of the PolynomialSolver class as the default value. If no real root is found the boolean hasArealRoot is set to false and the real part of the root with smallest absolute imaginary part is returned instead.

Parameters:

[out]	hasArealRoot	: boolean true if a real root is found according to the absImaginaryThreshold criterion, false otherwise.
[in]	absImaginaryThreshold	: threshold on the absolute imaginary part to decide whether or not a root is real.

Definition at line 246 of file Polynomials.

template<typename _Scalar >

template<typename OtherPolynomial >

void PolynomialSolver< _Scalar, 1 >::compute

(

const OtherPolynomial &

poly

)

[inline]

Computes the complex roots of a new polynomial.

Definition at line 388 of file Polynomials.

const RealScalar& PolynomialSolverBase< _Scalar, _Deg >::greatestRealRoot	(	bool &	hasArealRoot,
		const RealScalar &	absImaginaryThreshold = NumTraits<Scalar>::dummy_precision()
	)		const [inline, inherited]

Returns:

the real root with greatest value. A real root is defined as the real part of a complex root with absolute imaginary part smallest than absImaginaryThreshold. absImaginaryThreshold takes the dummy_precision associated with the _Scalar template parameter of the PolynomialSolver class as the default value. If no real root is found the boolean hasArealRoot is set to false and the real part of the root with smallest absolute imaginary part is returned instead.

Parameters:

[out]	hasArealRoot	: boolean true if a real root is found according to the absImaginaryThreshold criterion, false otherwise.
[in]	absImaginaryThreshold	: threshold on the absolute imaginary part to decide whether or not a root is real.

Definition at line 269 of file Polynomials.

const RootType& PolynomialSolverBase< _Scalar, _Deg >::greatestRoot

(

)

const [inline, inherited]

Returns:

the complex root with greatest norm.

Definition at line 113 of file Polynomials.

void PolynomialSolverBase< _Scalar, _Deg >::realRoots	(	Stl_back_insertion_sequence &	bi_seq,
		const RealScalar &	absImaginaryThreshold = NumTraits<Scalar>::dummy_precision()
	)		const [inline, inherited]

Clear and fills the back insertion sequence with the real roots of the polynomial i.e.

the real part of the complex roots that have an imaginary part which absolute value is smaller than absImaginaryThreshold. absImaginaryThreshold takes the dummy_precision associated with the _Scalar template parameter of the PolynomialSolver class as the default value.

Parameters:

[out]	bi_seq	: the back insertion sequence (stl concept)
[in]	absImaginaryThreshold	: the maximum bound of the imaginary part of a complex number that is considered as real.

Definition at line 83 of file Polynomials.

const RootsType& PolynomialSolverBase< _Scalar, _Deg >::roots

(

)

const [inline, inherited]

Returns:

the complex roots of the polynomial

Definition at line 69 of file Polynomials.

const RootType& PolynomialSolverBase< _Scalar, _Deg >::selectComplexRoot_withRespectToNorm

(

squaredNormBinaryPredicate &

pred

)

const [inline, protected, inherited]

Definition at line 96 of file Polynomials.

const RealScalar& PolynomialSolverBase< _Scalar, _Deg >::selectRealRoot_withRespectToAbsRealPart	(	squaredRealPartBinaryPredicate &	pred,
		bool &	hasArealRoot,
		const RealScalar &	absImaginaryThreshold = NumTraits<Scalar>::dummy_precision()
	)		const [inline, protected, inherited]

Definition at line 130 of file Polynomials.

const RealScalar& PolynomialSolverBase< _Scalar, _Deg >::selectRealRoot_withRespectToRealPart	(	RealPartBinaryPredicate &	pred,
		bool &	hasArealRoot,
		const RealScalar &	absImaginaryThreshold = NumTraits<Scalar>::dummy_precision()
	)		const [inline, protected, inherited]

Definition at line 170 of file Polynomials.

void PolynomialSolverBase< _Scalar, _Deg >::setPolynomial

(

const OtherPolynomial &

poly

)

[inline, protected, inherited]

Definition at line 57 of file Polynomials.

const RealScalar& PolynomialSolverBase< _Scalar, _Deg >::smallestRealRoot	(	bool &	hasArealRoot,
		const RealScalar &	absImaginaryThreshold = NumTraits<Scalar>::dummy_precision()
	)		const [inline, inherited]

Returns:

the real root with smallest value. A real root is defined as the real part of a complex root with absolute imaginary part smallest than absImaginaryThreshold. absImaginaryThreshold takes the dummy_precision associated with the _Scalar template parameter of the PolynomialSolver class as the default value. If no real root is found the boolean hasArealRoot is set to false and the real part of the root with smallest absolute imaginary part is returned instead.

Parameters:

[out]	hasArealRoot	: boolean true if a real root is found according to the absImaginaryThreshold criterion, false otherwise.
[in]	absImaginaryThreshold	: threshold on the absolute imaginary part to decide whether or not a root is real.

Definition at line 292 of file Polynomials.

const RootType& PolynomialSolverBase< _Scalar, _Deg >::smallestRoot

(

)

const [inline, inherited]

Returns:

the complex root with smallest norm.

Definition at line 122 of file Polynomials.

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Member Data Documentation

RootsType PolynomialSolverBase< _Scalar, _Deg >::m_roots [protected, inherited]

Definition at line 301 of file Polynomials.