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Eigen::PolynomialSolver< _Scalar, _Deg > Class Template Reference

Detailed Description

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

A polynomial solver.

Computes the complex roots of a real polynomial.

Parameters
_Scalarthe scalar type, i.e., the type of the polynomial coefficients
_Degthe degree of the polynomial, can be a compile time value or Dynamic. Notice that the number of polynomial coefficients is _Deg+1.

This class implements a polynomial solver and provides convenient methods such as

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

WARNING: this polynomial solver is experimental, part of the unsupported Eigen modules.

Currently a QR algorithm is used to compute the eigenvalues of the companion matrix of the polynomial to compute its roots. This supposes that the complex moduli of the roots are all distinct: e.g. there should be no multiple roots or conjugate roots for instance. With 32bit (float) floating types this problem shows up frequently. However, almost always, correct accuracy is reached even in these cases for 64bit (double) floating types and small polynomial degree (<20).

+ Inheritance diagram for Eigen::PolynomialSolver< _Scalar, _Deg >:

Public Member Functions

template<typename OtherPolynomial >
void compute (const OtherPolynomial &poly)
 
- Public Member Functions inherited from Eigen::PolynomialSolverBase< _Scalar, _Deg >
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 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
 

Member Function Documentation

template<typename _Scalar , int _Deg>
template<typename OtherPolynomial >
void Eigen::PolynomialSolver< _Scalar, _Deg >::compute ( const OtherPolynomial &  poly)
inline

Computes the complex roots of a new polynomial.


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