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 DenseIndex	Index

typedef NumTraits< Scalar >::Real	RealScalar

typedef Matrix< RootType, _Deg, 1 >	RootsType

typedef std::complex< RealScalar >	RootType

typedef _Scalar	Scalar

Public Member Functions
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 RootType &	greatestRoot () const

template<typename OtherPolynomial >
	PolynomialSolverBase (const OtherPolynomial &poly)

	PolynomialSolverBase ()

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

const RootsType &	roots () const

const RealScalar &	smallestRealRoot (bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const

const RootType &	smallestRoot () const

Protected Member Functions
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

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

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.

Definition at line 29 of file PolynomialSolver.h.

Member Typedef Documentation

◆ Index

template<typename _Scalar, int _Deg>

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

Definition at line 39 of file PolynomialSolver.h.

◆ RealScalar

template<typename _Scalar, int _Deg>

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

Definition at line 35 of file PolynomialSolver.h.

◆ RootsType

template<typename _Scalar, int _Deg>

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

Definition at line 37 of file PolynomialSolver.h.

◆ RootType

template<typename _Scalar, int _Deg>

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

Definition at line 36 of file PolynomialSolver.h.

◆ Scalar

template<typename _Scalar, int _Deg>

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

Definition at line 34 of file PolynomialSolver.h.

Constructor & Destructor Documentation

◆ PolynomialSolverBase() [1/2]

template<typename _Scalar, int _Deg>

template<typename OtherPolynomial >

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

inline

Definition at line 48 of file PolynomialSolver.h.

◆ PolynomialSolverBase() [2/2]

template<typename _Scalar, int _Deg>

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

inline

Definition at line 51 of file PolynomialSolver.h.

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.

Definition at line 212 of file PolynomialSolver.h.

◆ 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.

Definition at line 235 of file PolynomialSolver.h.

◆ 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.

Definition at line 258 of file PolynomialSolver.h.

◆ greatestRoot()

template<typename _Scalar, int _Deg>

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

inline

Returns: the complex root with greatest norm.

Definition at line 100 of file PolynomialSolver.h.

◆ 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.

Definition at line 69 of file PolynomialSolver.h.

◆ roots()

template<typename _Scalar, int _Deg>

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

inline

Returns: the complex roots of the polynomial

Definition at line 55 of file PolynomialSolver.h.

◆ selectComplexRoot_withRespectToNorm()

template<typename _Scalar, int _Deg>

template<typename squaredNormBinaryPredicate >

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

inlineprotected

Definition at line 83 of file PolynomialSolver.h.

◆ 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

Definition at line 117 of file PolynomialSolver.h.

◆ 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

Definition at line 158 of file PolynomialSolver.h.

◆ setPolynomial()

template<typename _Scalar, int _Deg>

template<typename OtherPolynomial >

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

inlineprotected

Definition at line 43 of file PolynomialSolver.h.

◆ 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.

Definition at line 281 of file PolynomialSolver.h.

◆ smallestRoot()

template<typename _Scalar, int _Deg>

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

inline

Returns: the complex root with smallest norm.

Definition at line 109 of file PolynomialSolver.h.

Member Data Documentation

◆ m_roots

template<typename _Scalar, int _Deg>

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

protected

Definition at line 290 of file PolynomialSolver.h.

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

PolynomialSolver.h

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

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

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

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