PolynomialSolverBase< _Scalar, _Deg > Class Template Reference

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

#include <PolynomialSolver.h>

Inheritance diagram for PolynomialSolverBase< _Scalar, _Deg >:

List of all members.

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 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 42 of file PolynomialSolver.h.

---

Member Typedef Documentation

template<typename _Scalar, int _Deg>

typedef DenseIndex PolynomialSolverBase< _Scalar, _Deg >::Index

Definition at line 52 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

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

Definition at line 48 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

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

Definition at line 50 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

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

Definition at line 49 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

typedef _Scalar PolynomialSolverBase< _Scalar, _Deg >::Scalar

Definition at line 47 of file PolynomialSolver.h.

---

Constructor & Destructor Documentation

template<typename _Scalar, int _Deg>

template<typename OtherPolynomial >

PolynomialSolverBase< _Scalar, _Deg >::PolynomialSolverBase

(

const OtherPolynomial &

poly

)

[inline]

Definition at line 61 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

PolynomialSolverBase< _Scalar, _Deg >::PolynomialSolverBase

(

)

[inline]

Definition at line 64 of file PolynomialSolver.h.

---

Member Function Documentation

template<typename _Scalar, int _Deg>

const RealScalar& 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 222 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

const RealScalar& 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 245 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

const RealScalar& 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 268 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

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

(

)

const [inline]

Returns:

the complex root with greatest norm.

Definition at line 112 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

template<typename Stl_back_insertion_sequence >

void 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 82 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

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

(

)

const [inline]

Returns:

the complex roots of the polynomial

Definition at line 68 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

template<typename squaredNormBinaryPredicate >

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

(

squaredNormBinaryPredicate &

pred

)

const [inline, protected]

Definition at line 95 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

template<typename squaredRealPartBinaryPredicate >

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

Definition at line 129 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

template<typename RealPartBinaryPredicate >

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

Definition at line 169 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

template<typename OtherPolynomial >

void PolynomialSolverBase< _Scalar, _Deg >::setPolynomial

(

const OtherPolynomial &

poly

)

[inline, protected]

Definition at line 56 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

const RealScalar& 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 291 of file PolynomialSolver.h.

template<typename _Scalar, int _Deg>

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

(

)

const [inline]

Returns:

the complex root with smallest norm.

Definition at line 121 of file PolynomialSolver.h.

---

Member Data Documentation

template<typename _Scalar, int _Deg>

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

Definition at line 300 of file PolynomialSolver.h.

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

• PolynomialSolver.h