Polynomial class. More...

#include <Poly.hh>

Inherits Eigen::Vector< Real, Eigen::Dynamic >.

Public Types
using	Vector

Public Member Functions
	Poly ()
	Class constructor from a vector.
	Poly (Integer order)
	Class constructor from a vector.
	Poly (const Poly &c)
	Class constructor from a vector.
	Poly (const Vector &c)
	Class constructor from a vector.
const Vector &	to_eigen () const
	Access to the Eigen const class.
void	set_order (Integer order)
	Set the order of the polynomial.
void	set_degree (Integer degree)
	Set the degree of the polynomial.
Poly &	set_scalar (Real s)
	Set the polynomial to a scalar value.
Poly &	set_monomial (Real a)
	Set the polynomial to a monomial with a given coefficient.
Vector	coeffs () const
	Get the coefficients of the polynomial.
Integer	degree () const
	Get the degree of the polynomial.
Integer	order () const
	Get the order of the polynomial.
std::string	to_string () const
	Convert the polynomial to a string representation.
Real	evaluate (Real x) const
	Evaluate the polynomial at a given point.
Real	evaluate_derivative (Real x) const
	Evaluate the derivative of the polynomial at a given point.
void	evaluate (Real x, Real &p, Real &Dp) const
	Evaluate the polynomial and its derivative at a given point.
Real	leading_coeff () const
	Get the leading coefficient of the polynomial.
void	derivative (Poly &res) const
	Compute the derivative of the polynomial.
void	integral (Poly &res) const
	Compute the integral of the polynomial.
void	integral (Poly &res, Real c) const
	Compute the integral of the polynomial with a given constant.
Real	normalize ()
	Normalize the polynomial.
void	purge (const Real eps)
	Purge small coefficients.
void	adjust_degree ()
	Adjust the degree of the polynomial and remove leading zeros.
Integer	sign_variations () const
	Count the number of sign variations.
void	make_monic ()
	Normalize the polynomial to monic form.
Poly &	operator= (const Poly &p)
	Define the assignment with another polynomial.
Poly	operator- ()
	Define the negation of the polynomial.
Poly &	operator+= (const Poly &p)
	Define the addition with another polynomial.
Poly &	operator-= (const Poly &p)
	Define the subtraction with another polynomial.
Poly &	operator*= (const Poly &p)
	Define the multiplication with another polynomial.
Poly &	operator+= (Real s)
	Define the addition with a scalar.
Poly &	operator-= (Real s)
	Define the subtraction with a scalar.
Poly &	operator*= (Real s)
	Define the multiplication with a scalar.

Static Public Attributes
static constexpr const Real	EPSILON

Private Member Functions
Vector &	to_eigen ()
	Access to the Eigen class.

Private Attributes
Integer	m_order

Detailed Description

template<typename Real>
class Sturm::Poly< Real >

This class implements a polynomial of the form \( p(x) = \sum_{i=0}^n a_i x^i \).

Template Parameters

Real	Scalar number type.

Member Typedef Documentation

◆ Vector

template<typename Real>

using Sturm::Poly< Real >::Vector

Initial value:

Eigen::Vector<Real, Eigen::Dynamic>

Vector of real numbers.

Constructor & Destructor Documentation

◆ Poly() [1/4]

template<typename Real>

Sturm::Poly< Real >::Poly ( )

inline

◆ Poly() [2/4]

template<typename Real>

Sturm::Poly< Real >::Poly ( Integer order )

inlineexplicit

Parameters

[in] order Order of the polynomial.

◆ Poly() [3/4]

template<typename Real>

Sturm::Poly< Real >::Poly ( const Poly< Real > & c )

inline

Parameters

[in] c Vector of coefficients.

◆ Poly() [4/4]

template<typename Real>

Sturm::Poly< Real >::Poly ( const Vector & c )

inlineexplicit

Parameters

[in] c Vector of coefficients.

Member Function Documentation

◆ adjust_degree()

template<typename Real>

void Sturm::Poly< Real >::adjust_degree ( )

inline

Adjust the degree of the polynomial to ensure the leading coefficient is non-zero.

◆ coeffs()

template<typename Real>

Vector Sturm::Poly< Real >::coeffs ( ) const

inline

Returns: Coefficients at the given index.

◆ degree()

template<typename Real>

Integer Sturm::Poly< Real >::degree ( ) const

inline

Returns: Degree of the polynomial.

◆ derivative()

template<typename Real>

void Sturm::Poly< Real >::derivative ( Poly< Real > & res ) const

inline

Parameters

[out] res Polynomial representing the derivative.

◆ evaluate() [1/2]

template<typename Real>

Real Sturm::Poly< Real >::evaluate ( Real x ) const

inline

Parameters

[in] x Point at which to evaluate the polynomial.

Returns: Value of the polynomial at the given point.

◆ evaluate() [2/2]

template<typename Real>

void Sturm::Poly< Real >::evaluate	(	Real	x,
		Real &	p,
		Real &	Dp ) const

inline

Parameters

[in]	x	Point at which to evaluate.
[out]	p	Value of the polynomial at the given point.
[out]	Dp	Value of the derivative at the given point.

◆ evaluate_derivative()

template<typename Real>

Real Sturm::Poly< Real >::evaluate_derivative ( Real x ) const

inline

Parameters

[in] x Point at which to evaluate the derivative.

Returns: Value of the derivative at the given point.

◆ integral() [1/2]

template<typename Real>

void Sturm::Poly< Real >::integral ( Poly< Real > & res ) const

inline

Parameters

[out] res Polynomial representing the integral.

◆ integral() [2/2]

template<typename Real>

void Sturm::Poly< Real >::integral	(	Poly< Real > &	res,
		Real	c ) const

inline

Parameters

[out]	res	Polynomial representing the integral.
[in]	c	Constant value for the integral.

◆ leading_coeff()

template<typename Real>

Real Sturm::Poly< Real >::leading_coeff ( ) const

inline

Returns: Leading coefficient.

◆ make_monic()

template<typename Real>

void Sturm::Poly< Real >::make_monic ( )

inline

Scales all coefficients such that the leading coefficient becomes 1. After this operation, the polynomial satisfies \( p(x) = x^n + \sum_{i=0}^{n-1} a_i x^i \), where \( n \) is the polynomial degree.

Precondition: The leading coefficient must be non-zero.

◆ normalize()

template<typename Real>

Real Sturm::Poly< Real >::normalize ( )

inline

Normalize the polynomial such that the maximum absolute coefficient is 1.

Returns: Scaling value used for normalization.

◆ operator*=() [1/2]

template<typename Real>

Poly & Sturm::Poly< Real >::operator*= ( const Poly< Real > & p )

inline

Parameters

[in] p Polynomial to multiply.

Returns: Reference to the polynomial.

◆ operator*=() [2/2]

template<typename Real>

Poly & Sturm::Poly< Real >::operator*= ( Real s )

inline

Parameters

[in] s Scalar to multiply.

Returns: Reference to the polynomial.

◆ operator+=() [1/2]

template<typename Real>

Poly & Sturm::Poly< Real >::operator+= ( const Poly< Real > & p )

inline

Parameters

[in] p Polynomial to add.

Returns: Reference to the polynomial.

◆ operator+=() [2/2]

template<typename Real>

Poly & Sturm::Poly< Real >::operator+= ( Real s )

inline

Parameters

[in] s Scalar to add.

Returns: Reference to the polynomial.

◆ operator-()

template<typename Real>

Poly Sturm::Poly< Real >::operator- ( )

inline

Returns: Negated polynomial.

◆ operator-=() [1/2]

template<typename Real>

Poly & Sturm::Poly< Real >::operator-= ( const Poly< Real > & p )

inline

Parameters

[in] p Polynomial to subtract.

Returns: Reference to the polynomial.

◆ operator-=() [2/2]

template<typename Real>

Poly & Sturm::Poly< Real >::operator-= ( Real s )

inline

Parameters

[in] s Scalar to subtract.

Returns: Reference to the polynomial.

◆ operator=()

template<typename Real>

Poly & Sturm::Poly< Real >::operator= ( const Poly< Real > & p )

inline

Parameters

[in] p Polynomial to assign from.

Returns: Reference to the polynomial.

◆ order()

template<typename Real>

Integer Sturm::Poly< Real >::order ( ) const

inline

Returns: Order of the polynomial.

◆ purge()

template<typename Real>

void Sturm::Poly< Real >::purge ( const Real eps )

inline

Purge (set to 0) coefficients that are smaller than or equal to a given epsilon.

Parameters

[in] eps Epsilon value for purging coefficients.

◆ set_degree()

template<typename Real>

void Sturm::Poly< Real >::set_degree ( Integer degree )

inline

Parameters

[in] degree Degree of the polynomial.

◆ set_monomial()

template<typename Real>

Poly & Sturm::Poly< Real >::set_monomial ( Real a )

inline

Parameters

[in] a Coefficient of the monomial.

Returns: Reference to the polynomial.

◆ set_order()

template<typename Real>

void Sturm::Poly< Real >::set_order ( Integer order )

inline

Parameters

[in] order Order of the polynomial.

◆ set_scalar()

template<typename Real>

Poly & Sturm::Poly< Real >::set_scalar ( Real s )

inline

Parameters

[in] s Scalar value.

Returns: Reference to the polynomial.

◆ sign_variations()

template<typename Real>

Integer Sturm::Poly< Real >::sign_variations ( ) const

inline

Count the number of sign variations in the polynomial coefficients.

Returns: Number of sign variations.

◆ to_eigen() [1/2]

template<typename Real>

Vector & Sturm::Poly< Real >::to_eigen ( )

inlineprivate

Returns: The Eigen class.

◆ to_eigen() [2/2]

template<typename Real>

const Vector & Sturm::Poly< Real >::to_eigen ( ) const

inline

Returns: The Eigen const class.

◆ to_string()

template<typename Real>

std::string Sturm::Poly< Real >::to_string ( ) const

inline

Returns: String representation of the polynomial.

Member Data Documentation

◆ EPSILON

template<typename Real>

const Real Sturm::Poly< Real >::EPSILON

staticconstexpr

Initial value:

{

std::numeric_limits<Real>::epsilon()}

Machine epsilon.

◆ m_order

template<typename Real>

Integer Sturm::Poly< Real >::m_order

private

Polynomial order.

The documentation for this class was generated from the following file:

core/include/Sturm/Poly.hh

Public Types

Public Member Functions

Static Public Attributes

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ Vector

Constructor & Destructor Documentation

◆ Poly() [1/4]

◆ Poly() [2/4]

◆ Poly() [3/4]

◆ Poly() [4/4]

Member Function Documentation

◆ adjust_degree()

◆ coeffs()

◆ degree()

◆ derivative()

◆ evaluate() [1/2]

◆ evaluate() [2/2]

◆ evaluate_derivative()

◆ integral() [1/2]

◆ integral() [2/2]

◆ leading_coeff()

◆ make_monic()

◆ normalize()

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-()

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator=()

◆ order()

◆ purge()

◆ set_degree()

◆ set_monomial()

◆ set_order()

◆ set_scalar()

◆ sign_variations()

◆ to_eigen() [1/2]

◆ to_eigen() [2/2]

◆ to_string()

Member Data Documentation

◆ EPSILON

◆ m_order