PolynomialSolverBase< _Scalar, _Deg > Class Template Reference
[Polynomials module]

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

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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)
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

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


Member Function Documentation

const RealScalar& 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.
const RealScalar& 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.
const RealScalar& 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.
const RootType& greatestRoot (  )  const [inline]
Returns:
the complex root with greatest norm.
void 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.
const RootsType& roots (  )  const [inline]
Returns:
the complex roots of the polynomial
const RealScalar& 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.
const RootType& smallestRoot (  )  const [inline]
Returns:
the complex root with smallest norm.

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

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