This module provides a QR based polynomial solver.
To use this module, add
#include <unsupported/Eigen/Polynomials>
at the start of your source file.
◆ cauchy_max_bound()
template<typename Polynomial >
NumTraits< typenamePolynomial::Scalar >::Real Eigen::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
◆ cauchy_min_bound()
template<typename Polynomial >
NumTraits< typenamePolynomial::Scalar >::Real Eigen::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 \( [ 1, 0, 3 ] \). |
◆ poly_eval()
template<typename Polynomials , typename T >
T Eigen::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. |
◆ poly_eval_horner()
template<typename Polynomials , typename T >
T Eigen::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: \( |x| \le 1 \)
◆ roots_to_monicPolynomial()
template<typename RootVector , typename Polynomial >
void Eigen::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 \( [ 3, 0, 1 ] \). |