Classes | Functions
Polynomials_Module
Unsupported modules
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. $ 1 + 3x^2 $ is stored as a vector $ [ 1, 0, 3 ] $.

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. $ 1 + 3x^2 $ is stored as a vector $ [ 1, 0, 3 ] $.

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. $ 1 + 3x^2 $ is stored as a vector $ [ 1, 0, 3 ] $.
[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. $ 1 + 3x^2 $ is stored as a vector $ [ 1, 0, 3 ] $.
[in]x: the value to evaluate the polynomial at.

Note for stability: $ |x| \le 1 $

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. $ 3 + x^2 $ is stored as a vector $ [ 3, 0, 1 ] $.

Definition at line 138 of file PolynomialUtils.h.



libicr
Author(s): Robert Krug
autogenerated on Mon Jan 6 2014 11:34:09