A polynomial solver. More...

#include <PolynomialSolver.h>

Inheritance diagram for PolynomialSolver< _Scalar, _Deg >:

Public Types
typedef Matrix< Scalar, _Deg, _Deg >	CompanionMatrixType
typedef EigenSolver < CompanionMatrixType >	EigenSolverType
typedef PolynomialSolverBase < _Scalar, _Deg >	PS_Base
Public Member Functions
template<typename OtherPolynomial >
void	compute (const OtherPolynomial &poly)
template<typename OtherPolynomial >
	PolynomialSolver (const OtherPolynomial &poly)
	PolynomialSolver ()
Protected Attributes
EigenSolverType	m_eigenSolver

Detailed Description

template<typename _Scalar, int _Deg>
class 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 341 of file PolynomialSolver.h.