#include <PolynomialSolver.h>
Inheritance diagram for Eigen::PolynomialSolver< _Scalar, _Deg >:
Public Types | |
| typedef Matrix< Scalar, _Deg, _Deg > | CompanionMatrixType |
| typedef internal::conditional< NumTraits< Scalar >::IsComplex, Scalar, std::complex< Scalar > >::type | ComplexScalar |
| typedef internal::conditional< NumTraits< Scalar >::IsComplex, ComplexEigenSolver< CompanionMatrixType >, EigenSolver< CompanionMatrixType > >::type | EigenSolverType |
| typedef PolynomialSolverBase< _Scalar, _Deg > | PS_Base |
 Public Types inherited from Eigen::PolynomialSolverBase< _Scalar, _Deg > | |
| 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 | |
| template<typename OtherPolynomial > | |
| void | compute (const OtherPolynomial &poly) |
| PolynomialSolver () | |
| template<typename OtherPolynomial > | |
| PolynomialSolver (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 |
| PolynomialSolverBase () | |
| 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 Attributes | |
| EigenSolverType | m_eigenSolver |
| RootsType | m_roots |
| Protected Attributes inherited from Eigen::PolynomialSolverBase< _Scalar, _Deg > | |
| RootsType | m_roots |
Additional Inherited Members | |
| Protected Member Functions inherited from Eigen::PolynomialSolverBase< _Scalar, _Deg > | |
| 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) |
Detailed Description
template<typename _Scalar, int _Deg>
class Eigen::PolynomialSolver< _Scalar, _Deg >
A polynomial solver.
Computes the complex roots of a real polynomial.
- Parameters
-
_Scalar the scalar type, i.e., the type of the polynomial coefficients _Deg the 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).
Definition at line 331 of file PolynomialSolver.h.
Member Typedef Documentation
◆ CompanionMatrixType
template<typename _Scalar , int _Deg>
| typedef Matrix<Scalar,_Deg,_Deg> Eigen::PolynomialSolver< _Scalar, _Deg >::CompanionMatrixType |
Definition at line 339 of file PolynomialSolver.h.
◆ ComplexScalar
template<typename _Scalar , int _Deg>
| typedef internal::conditional<NumTraits<Scalar>::IsComplex, Scalar, std::complex<Scalar> >::type Eigen::PolynomialSolver< _Scalar, _Deg >::ComplexScalar |
Definition at line 343 of file PolynomialSolver.h.
◆ EigenSolverType
template<typename _Scalar , int _Deg>
| typedef internal::conditional<NumTraits<Scalar>::IsComplex, ComplexEigenSolver<CompanionMatrixType>, EigenSolver<CompanionMatrixType> >::type Eigen::PolynomialSolver< _Scalar, _Deg >::EigenSolverType |
Definition at line 342 of file PolynomialSolver.h.
◆ PS_Base
template<typename _Scalar , int _Deg>
| typedef PolynomialSolverBase<_Scalar,_Deg> Eigen::PolynomialSolver< _Scalar, _Deg >::PS_Base |
Definition at line 336 of file PolynomialSolver.h.
Constructor & Destructor Documentation
◆ PolynomialSolver() [1/2]
template<typename _Scalar , int _Deg>
template<typename OtherPolynomial >
|
inline |
Definition at line 387 of file PolynomialSolver.h.
◆ PolynomialSolver() [2/2]
template<typename _Scalar , int _Deg>
|
inline |
Definition at line 390 of file PolynomialSolver.h.
Member Function Documentation
◆ compute()
template<typename _Scalar , int _Deg>
template<typename OtherPolynomial >
|
inline |
Computes the complex roots of a new polynomial.
Definition at line 348 of file PolynomialSolver.h.
Member Data Documentation
◆ m_eigenSolver
template<typename _Scalar , int _Deg>
|
protected |
Definition at line 394 of file PolynomialSolver.h.
◆ m_roots
template<typename _Scalar , int _Deg>
|
protected |
Definition at line 290 of file PolynomialSolver.h.
The documentation for this class was generated from the following file: