Defined to be inherited by polynomial solvers: it provides convenient methods such as. More...

#include <PolynomialSolver.h>

Inheritance diagram for Eigen::PolynomialSolverBase< _Scalar, _Deg >:

Public Types
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 >
	PolynomialSolverBase (const OtherPolynomial &poly)

	PolynomialSolverBase ()

const RootsType &	roots () const

template<typename Stl_back_insertion_sequence >
void	realRoots (Stl_back_insertion_sequence &bi_seq, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const

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
template<typename OtherPolynomial >
void	setPolynomial (const OtherPolynomial &poly)

template<typename squaredNormBinaryPredicate >
const RootType &	selectComplexRoot_withRespectToNorm (squaredNormBinaryPredicate &pred) const

template<typename squaredRealPartBinaryPredicate >
const RealScalar &	selectRealRoot_withRespectToAbsRealPart (squaredRealPartBinaryPredicate &pred, bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const

template<typename RealPartBinaryPredicate >
const RealScalar &	selectRealRoot_withRespectToRealPart (RealPartBinaryPredicate &pred, bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const

Protected Attributes
RootsType	m_roots

Detailed Description

template<typename _Scalar, int _Deg>
class Eigen::PolynomialSolverBase< _Scalar, _Deg >

Defined to be inherited by polynomial solvers: it provides convenient methods such as.

real roots,
greatest, smallest complex roots,
real roots with greatest, smallest absolute real value,
greatest, smallest real roots.

It stores the set of roots as a vector of complexes.

Member Typedef Documentation

◆ Index

template<typename _Scalar , int _Deg>

typedef DenseIndex Eigen::PolynomialSolverBase< _Scalar, _Deg >::Index

◆ RealScalar

template<typename _Scalar , int _Deg>

typedef NumTraits<Scalar>::Real Eigen::PolynomialSolverBase< _Scalar, _Deg >::RealScalar

◆ RootsType

template<typename _Scalar , int _Deg>

typedef Matrix<RootType,_Deg,1> Eigen::PolynomialSolverBase< _Scalar, _Deg >::RootsType

◆ RootType

template<typename _Scalar , int _Deg>

typedef std::complex<RealScalar> Eigen::PolynomialSolverBase< _Scalar, _Deg >::RootType

◆ Scalar

template<typename _Scalar , int _Deg>

typedef _Scalar Eigen::PolynomialSolverBase< _Scalar, _Deg >::Scalar

Constructor & Destructor Documentation

◆ PolynomialSolverBase() [1/2]

template<typename _Scalar , int _Deg>

template<typename OtherPolynomial >

Eigen::PolynomialSolverBase< _Scalar, _Deg >::PolynomialSolverBase ( const OtherPolynomial & poly )

inline

◆ PolynomialSolverBase() [2/2]

template<typename _Scalar , int _Deg>

Eigen::PolynomialSolverBase< _Scalar, _Deg >::PolynomialSolverBase ( )

inline

Member Function Documentation

◆ absGreatestRealRoot()

template<typename _Scalar , int _Deg>

const RealScalar & Eigen::PolynomialSolverBase< _Scalar, _Deg >::absGreatestRealRoot	(	bool &	hasArealRoot,
		const RealScalar &	absImaginaryThreshold = `NumTraits<Scalar>::dummy_precision()`
	)		const

inline

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.

◆ absSmallestRealRoot()

template<typename _Scalar , int _Deg>

const RealScalar & Eigen::PolynomialSolverBase< _Scalar, _Deg >::absSmallestRealRoot	(	bool &	hasArealRoot,
		const RealScalar &	absImaginaryThreshold = `NumTraits<Scalar>::dummy_precision()`
	)		const

inline

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.

◆ greatestRealRoot()

template<typename _Scalar , int _Deg>

const RealScalar & Eigen::PolynomialSolverBase< _Scalar, _Deg >::greatestRealRoot	(	bool &	hasArealRoot,
		const RealScalar &	absImaginaryThreshold = `NumTraits<Scalar>::dummy_precision()`
	)		const

inline

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.

◆ greatestRoot()

template<typename _Scalar , int _Deg>

const RootType & Eigen::PolynomialSolverBase< _Scalar, _Deg >::greatestRoot ( ) const

inline

Returns: the complex root with greatest norm.

◆ realRoots()

template<typename _Scalar , int _Deg>

template<typename Stl_back_insertion_sequence >

void Eigen::PolynomialSolverBase< _Scalar, _Deg >::realRoots	(	Stl_back_insertion_sequence &	bi_seq,
		const RealScalar &	absImaginaryThreshold = `NumTraits<Scalar>::dummy_precision()`
	)		const

inline

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.

◆ roots()

template<typename _Scalar , int _Deg>

const RootsType & Eigen::PolynomialSolverBase< _Scalar, _Deg >::roots ( ) const

inline

Returns: the complex roots of the polynomial

◆ selectComplexRoot_withRespectToNorm()

template<typename _Scalar , int _Deg>

template<typename squaredNormBinaryPredicate >

const RootType & Eigen::PolynomialSolverBase< _Scalar, _Deg >::selectComplexRoot_withRespectToNorm ( squaredNormBinaryPredicate & pred ) const

inlineprotected

◆ selectRealRoot_withRespectToAbsRealPart()

template<typename _Scalar , int _Deg>

template<typename squaredRealPartBinaryPredicate >

const RealScalar & Eigen::PolynomialSolverBase< _Scalar, _Deg >::selectRealRoot_withRespectToAbsRealPart	(	squaredRealPartBinaryPredicate &	pred,
		bool &	hasArealRoot,
		const RealScalar &	absImaginaryThreshold = `NumTraits<Scalar>::dummy_precision()`
	)		const

inlineprotected

◆ selectRealRoot_withRespectToRealPart()

template<typename _Scalar , int _Deg>

template<typename RealPartBinaryPredicate >

const RealScalar & Eigen::PolynomialSolverBase< _Scalar, _Deg >::selectRealRoot_withRespectToRealPart	(	RealPartBinaryPredicate &	pred,
		bool &	hasArealRoot,
		const RealScalar &	absImaginaryThreshold = `NumTraits<Scalar>::dummy_precision()`
	)		const

inlineprotected

◆ setPolynomial()

template<typename _Scalar , int _Deg>

template<typename OtherPolynomial >

void Eigen::PolynomialSolverBase< _Scalar, _Deg >::setPolynomial ( const OtherPolynomial & poly )

inlineprotected

◆ smallestRealRoot()

template<typename _Scalar , int _Deg>

const RealScalar & Eigen::PolynomialSolverBase< _Scalar, _Deg >::smallestRealRoot	(	bool &	hasArealRoot,
		const RealScalar &	absImaginaryThreshold = `NumTraits<Scalar>::dummy_precision()`
	)		const

inline

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.

◆ smallestRoot()

template<typename _Scalar , int _Deg>

const RootType & Eigen::PolynomialSolverBase< _Scalar, _Deg >::smallestRoot ( ) const

inline

Returns: the complex root with smallest norm.

Member Data Documentation

◆ m_roots

template<typename _Scalar , int _Deg>

RootsType Eigen::PolynomialSolverBase< _Scalar, _Deg >::m_roots

protected

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

core/util/algorithms/eigen-3.4.0/unsupported/Eigen/src/Polynomials/PolynomialSolver.h

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Index

◆ RealScalar

◆ RootsType

◆ RootType

◆ Scalar

Constructor & Destructor Documentation

◆ PolynomialSolverBase() [1/2]

◆ PolynomialSolverBase() [2/2]

Member Function Documentation

◆ absGreatestRealRoot()

◆ absSmallestRealRoot()

◆ greatestRealRoot()

◆ greatestRoot()

◆ realRoots()

◆ roots()

◆ selectComplexRoot_withRespectToNorm()

◆ selectRealRoot_withRespectToAbsRealPart()

◆ selectRealRoot_withRespectToRealPart()

◆ setPolynomial()

◆ smallestRealRoot()

◆ smallestRoot()

Member Data Documentation

◆ m_roots