A polynomial solver. More...
#include <PolynomialSolver.h>
Public Types | |
| typedef Matrix< Scalar, _Deg, _Deg > | CompanionMatrixType |
| typedef EigenSolver< CompanionMatrixType > | 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) |
| template<typename OtherPolynomial > | |
| PolynomialSolver (const OtherPolynomial &poly) | |
| PolynomialSolver () | |
| 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 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 Attributes | |
| EigenSolverType | m_eigenSolver |
| 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 unsuported 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
| typedef Matrix<Scalar,_Deg,_Deg> Eigen::PolynomialSolver< _Scalar, _Deg >::CompanionMatrixType |
Definition at line 339 of file PolynomialSolver.h.
| typedef EigenSolver<CompanionMatrixType> Eigen::PolynomialSolver< _Scalar, _Deg >::EigenSolverType |
Definition at line 340 of file PolynomialSolver.h.
| typedef PolynomialSolverBase<_Scalar,_Deg> Eigen::PolynomialSolver< _Scalar, _Deg >::PS_Base |
Definition at line 336 of file PolynomialSolver.h.
Constructor & Destructor Documentation
|
inline |
Definition at line 356 of file PolynomialSolver.h.
|
inline |
Definition at line 359 of file PolynomialSolver.h.
Member Function Documentation
|
inline |
Computes the complex roots of a new polynomial.
Definition at line 345 of file PolynomialSolver.h.
Member Data Documentation
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protected |
Definition at line 363 of file PolynomialSolver.h.
The documentation for this class was generated from the following file: