Polynomials_Module

Collaboration diagram for Polynomials_Module:

Classes
class	PolynomialSolver< _Scalar, _Deg >
	A polynomial solver. More...
class	PolynomialSolverBase< _Scalar, _Deg >
	Defined to be inherited by polynomial solvers: it provides convenient methods such as. More...
Functions
template<typename Polynomial >
NumTraits< typename Polynomial::Scalar >::Real	cauchy_max_bound (const Polynomial &poly)
template<typename Polynomial >
NumTraits< typename Polynomial::Scalar >::Real	cauchy_min_bound (const Polynomial &poly)
template<typename Polynomials , typename T >
T	poly_eval (const Polynomials &poly, const T &x)
template<typename Polynomials , typename T >
T	poly_eval_horner (const Polynomials &poly, const T &x)
template<typename RootVector , typename Polynomial >
void	roots_to_monicPolynomial (const RootVector &rv, Polynomial &poly)

---

Function Documentation

template<typename Polynomial >

NumTraits<typename Polynomial::Scalar>::Real cauchy_max_bound

(

const Polynomial &

poly

)

[inline]

Returns:

a maximum bound for the absolute value of any root of the polynomial.

Parameters:

[in]

poly

: the vector of coefficients of the polynomial ordered by degrees i.e. poly[i] is the coefficient of degree i of the polynomial e.g. is stored as a vector .

Precondition: the leading coefficient of the input polynomial poly must be non zero

Definition at line 88 of file PolynomialUtils.h.

template<typename Polynomial >

NumTraits<typename Polynomial::Scalar>::Real cauchy_min_bound

(

const Polynomial &

poly

)

[inline]

Returns:

a minimum bound for the absolute value of any non zero root of the polynomial.

Parameters:

[in]

poly

: the vector of coefficients of the polynomial ordered by degrees i.e. poly[i] is the coefficient of degree i of the polynomial e.g. is stored as a vector .

Definition at line 110 of file PolynomialUtils.h.

template<typename Polynomials , typename T >

T poly_eval	(	const Polynomials &	poly,
		const T &	x
	)		[inline]

Returns:

the evaluation of the polynomial at x using stabilized Horner algorithm.

Parameters:

[in]	poly	: the vector of coefficients of the polynomial ordered by degrees i.e. poly[i] is the coefficient of degree i of the polynomial e.g. is stored as a vector .
[in]	x	: the value to evaluate the polynomial at.

Definition at line 59 of file PolynomialUtils.h.

template<typename Polynomials , typename T >

T poly_eval_horner	(	const Polynomials &	poly,
		const T &	x
	)		[inline]

Returns:

the evaluation of the polynomial at x using Horner algorithm.

Parameters:

[in]	poly	: the vector of coefficients of the polynomial ordered by degrees i.e. poly[i] is the coefficient of degree i of the polynomial e.g. is stored as a vector .
[in]	x	: the value to evaluate the polynomial at.

Note for stability:

Definition at line 41 of file PolynomialUtils.h.

template<typename RootVector , typename Polynomial >

void roots_to_monicPolynomial	(	const RootVector &	rv,
		Polynomial &	poly
	)

Given the roots of a polynomial compute the coefficients in the monomial basis of the monic polynomial with same roots and minimal degree. If RootVector is a vector of complexes, Polynomial should also be a vector of complexes.

Parameters:

[in]	rv	: a vector containing the roots of a polynomial.
[out]	poly	: the vector of coefficients of the polynomial ordered by degrees i.e. poly[i] is the coefficient of degree i of the polynomial e.g. is stored as a vector .

Definition at line 138 of file PolynomialUtils.h.