rl::math::Polynomial< T > Class Template Reference

A vector-valued polynomial function from Real -> T. More...

#include <Polynomial.h>

Inheritance diagram for rl::math::Polynomial< T >:

Public Member Functions
	Polynomial (const ::std::size_t &degree)
virtual	~Polynomial ()
Polynomial *	clone () const
T &	coefficient (const ::std::size_t &i)
const T &	coefficient (const ::std::size_t &i) const
::std::size_t	degree () const
Polynomial	derivative () const
T	getAbsoluteMaximum () const
	Returns the array of the maximum function values of each dimension within the definition range, not regarding the sign of the function values. More...
Polynomial	integral () const
T	operator() (const Real &x, const ::std::size_t &derivative=0) const
	Evaluates the function or a derivative thereof for a given value x. More...
Polynomial	operator+ (const Polynomial &rhs) const
Polynomial &	operator+= (const T &rhs)
Polynomial &	operator+= (const Polynomial &rhs)
Polynomial	operator- () const
Polynomial	operator- (const Polynomial &rhs) const
Polynomial &	operator-= (const T &rhs)
Polynomial &	operator-= (const Polynomial &rhs)
Polynomial &	operator*= (const Real &rhs)
Polynomial &	operator/= (const Real &rhs)
static ::std::vector< Real >	realRoots (const ::std::vector< Real > &c)
	Calculates the real roots (or, zeros) for given polynomial coefficients. More...
Polynomial	scaledX (const Real &factor) const
	Stretches the x-axis of a polynomial by a given factor. More...
Polynomial	translatedX (const Real &translation) const
	Translates a polynomial along the x-axis by a given parameter translation. More...
Public Member Functions inherited from rl::math::Function< T >
	Function ()
virtual	~Function ()
Real	duration () const
Real &	lower ()
const Real &	lower () const
Real &	upper ()
const Real &	upper () const

Static Public Member Functions
static Polynomial	CubicFirst (const T &y0, const T &y1, const T &yd0, const T &yd1, const Real &x1=1)
static Polynomial	CubicSecond (const T &y0, const T &y1, const T &ydd0, const T &ydd1, const Real &x1=1)
static Polynomial	Linear (const T &y0, const T &y1, const Real &x1=1)
static Polynomial	Quadratic (const T &y0, const T &y1, const T &yd0, const Real &x1=1)
static Polynomial	QuarticFirstSecond (const T &y0, const T &y1, const T &yd0, const T &yd1, const T &ydd0, const Real &x1=1)
static Polynomial	QuinticFirstSecond (const T &y0, const T &y1, const T &yd0, const T &yd1, const T &ydd0, const T &ydd1, const Real &x1=1)
static Polynomial	SepticFirstSecondThird (const T &y0, const T &y1, const T &yd0, const T &yd1, const T &ydd0, const T &ydd1, const T &yddd0, const T &yddd1, const Real &x1=1)
static Polynomial	SexticFirstSecondThird (const T &y0, const T &y1, const T &yd0, const T &yd1, const T &ydd0, const T &ydd1, const T &yddd0, const Real &x1=1)

Protected Attributes
::std::vector< T >	c
Protected Attributes inherited from rl::math::Function< T >
Real	x0
Real	x1

Friends
Polynomial	operator+ (const T &lhs, const Polynomial &rhs)
Polynomial	operator+ (const Polynomial &lhs, const T &rhs)
Polynomial	operator- (const T &lhs, const Polynomial &rhs)
Polynomial	operator- (const Polynomial &lhs, const T &rhs)
Polynomial	operator* (const Real &lhs, const Polynomial &rhs)
Polynomial	operator* (const Polynomial &lhs, const Real &rhs)
Polynomial	operator/ (const Real &lhs, const Polynomial &rhs)
Polynomial	operator/ (const Polynomial &lhs, const Real &rhs)

Detailed Description

template<typename T>
class rl::math::Polynomial< T >

A vector-valued polynomial function from Real -> T.

A Polynomial is indefinitely often differentiable and can be evaluated efficiently.

Constructor & Destructor Documentation

Polynomial()

template<typename T >

rl::math::Polynomial< T >::Polynomial ( const ::std::size_t &  degree )

inline

~Polynomial()

template<typename T >

virtual rl::math::Polynomial< T >::~Polynomial ( )

inlinevirtual

Member Function Documentation

clone()

template<typename T >

Polynomial* rl::math::Polynomial< T >::clone ( ) const

inlinevirtual

Implements rl::math::Function< T >.

coefficient() [1/2]

template<typename T >

T& rl::math::Polynomial< T >::coefficient ( const ::std::size_t &  i )

inline

coefficient() [2/2]

template<typename T >

const T& rl::math::Polynomial< T >::coefficient ( const ::std::size_t &  i ) const

inline

CubicFirst()

template<typename T >

static Polynomial rl::math::Polynomial< T >::CubicFirst ( const T &  y0, const T &  y1, const T &  yd0, const T &  yd1, const Real &  x1 = 1  )

inlinestatic

CubicSecond()

template<typename T >

static Polynomial rl::math::Polynomial< T >::CubicSecond ( const T &  y0, const T &  y1, const T &  ydd0, const T &  ydd1, const Real &  x1 = 1  )

inlinestatic

degree()

template<typename T >

::std::size_t rl::math::Polynomial< T >::degree ( ) const

inline

derivative()

template<typename T >

Polynomial rl::math::Polynomial< T >::derivative ( ) const

inline

getAbsoluteMaximum()

template<typename T >

T rl::math::Polynomial< T >::getAbsoluteMaximum ( ) const

inline

Returns the array of the maximum function values of each dimension within the definition range, not regarding the sign of the function values.

For polynomials higher than cubics, Eigen::PolynomialSolver is required and calculations become iterative, without guaranteeing convergence. A common use case is to verify speed limits with the comparison (trajectory.derivate().getAbsoluteMaximum() < maximumSpeed).all()

integral()

template<typename T >

Polynomial rl::math::Polynomial< T >::integral ( ) const

inline

Linear()

template<typename T >

static Polynomial rl::math::Polynomial< T >::Linear ( const T &  y0, const T &  y1, const Real &  x1 = 1  )

inlinestatic

operator()()

template<typename T >

T rl::math::Polynomial< T >::operator() ( const Real &  x, const ::std::size_t &  derivative = 0  ) const

inlinevirtual

Evaluates the function or a derivative thereof for a given value x.

Some functions are only defined in the interval [lower(), upper()], and fail to evaluate outside of [lower() - FUNCTION_BOUNDARY, upper() + FUNCTION_BOUNDARY]. In Debug mode, this is signaled by failing asserts. In Release mode, the function is evaluated if algebraically possible, or will return an empty ArrayX otherwise. Some functions are not indefinitely often differentiable, and will return a NaN array for all higher orders.

Parameters

[in]	x	Input value of the function or derivative
[in]	derivative	Order of the derivative to be evaluated

Implements rl::math::Function< T >.

operator*=()

template<typename T >

Polynomial& rl::math::Polynomial< T >::operator*= ( const Real &  rhs )

inline

operator+()

template<typename T >

Polynomial rl::math::Polynomial< T >::operator+ ( const Polynomial< T > &  rhs ) const

inline

operator+=() [1/2]

template<typename T >

Polynomial& rl::math::Polynomial< T >::operator+= ( const Polynomial< T > &  rhs )

inline

operator+=() [2/2]

template<typename T >

Polynomial& rl::math::Polynomial< T >::operator+= ( const T &  rhs )

inline

operator-() [1/2]

template<typename T >

Polynomial rl::math::Polynomial< T >::operator- ( ) const

inline

operator-() [2/2]

template<typename T >

Polynomial rl::math::Polynomial< T >::operator- ( const Polynomial< T > &  rhs ) const

inline

operator-=() [1/2]

template<typename T >

Polynomial& rl::math::Polynomial< T >::operator-= ( const Polynomial< T > &  rhs )

inline

operator-=() [2/2]

template<typename T >

Polynomial& rl::math::Polynomial< T >::operator-= ( const T &  rhs )

inline

operator/=()

template<typename T >

Polynomial& rl::math::Polynomial< T >::operator/= ( const Real &  rhs )

inline

Quadratic()

template<typename T >

static Polynomial rl::math::Polynomial< T >::Quadratic ( const T &  y0, const T &  y1, const T &  yd0, const Real &  x1 = 1  )

inlinestatic

QuarticFirstSecond()

template<typename T >

static Polynomial rl::math::Polynomial< T >::QuarticFirstSecond ( const T &  y0, const T &  y1, const T &  yd0, const T &  yd1, const T &  ydd0, const Real &  x1 = 1  )

inlinestatic

QuinticFirstSecond()

template<typename T >

static Polynomial rl::math::Polynomial< T >::QuinticFirstSecond ( const T &  y0, const T &  y1, const T &  yd0, const T &  yd1, const T &  ydd0, const T &  ydd1, const Real &  x1 = 1  )

inlinestatic

realRoots()

template<typename T >

static ::std::vector<Real> rl::math::Polynomial< T >::realRoots ( const ::std::vector< Real > &  c )

inline

Calculates the real roots (or, zeros) for given polynomial coefficients.

For degrees higher than 3, Eigen::PolynomialSolver is required and calculations become iterative, without guaranteeing convergence.

scaledX()

template<typename T >

Polynomial rl::math::Polynomial< T >::scaledX ( const Real &  factor ) const

inline

Stretches the x-axis of a polynomial by a given factor.

The returned, scaled polynomial p' of a given polynomial p fulfills p'(x * factor) = p(x), and p'.duration() = factor * p.duration(). This is done by recalculating the underlying polynomial coefficients.

SepticFirstSecondThird()

template<typename T >

static Polynomial rl::math::Polynomial< T >::SepticFirstSecondThird ( const T &  y0, const T &  y1, const T &  yd0, const T &  yd1, const T &  ydd0, const T &  ydd1, const T &  yddd0, const T &  yddd1, const Real &  x1 = 1  )

inlinestatic

SexticFirstSecondThird()

template<typename T >

static Polynomial rl::math::Polynomial< T >::SexticFirstSecondThird ( const T &  y0, const T &  y1, const T &  yd0, const T &  yd1, const T &  ydd0, const T &  ydd1, const T &  yddd0, const Real &  x1 = 1  )

inlinestatic

translatedX()

template<typename T >

Polynomial rl::math::Polynomial< T >::translatedX ( const Real &  translation ) const

inline

Translates a polynomial along the x-axis by a given parameter translation.

The returned polynomial p' for a given polynomial p fulfills p'(x - translation) = p(x) This is done by recalculating the underlying polynomial coefficients.

Friends And Related Function Documentation

operator* [1/2]

template<typename T >

Polynomial operator* ( const Polynomial< T > &  lhs, const Real &  rhs  )

friend

operator* [2/2]

template<typename T >

Polynomial operator* ( const Real &  lhs, const Polynomial< T > &  rhs  )

friend

operator+ [1/2]

template<typename T >

Polynomial operator+ ( const Polynomial< T > &  lhs, const T &  rhs  )

friend

operator+ [2/2]

template<typename T >

Polynomial operator+ ( const T &  lhs, const Polynomial< T > &  rhs  )

friend

operator- [1/2]

template<typename T >

Polynomial operator- ( const Polynomial< T > &  lhs, const T &  rhs  )

friend

operator- [2/2]

template<typename T >

Polynomial operator- ( const T &  lhs, const Polynomial< T > &  rhs  )

friend

operator/ [1/2]

template<typename T >

Polynomial operator/ ( const Polynomial< T > &  lhs, const Real &  rhs  )

friend

operator/ [2/2]

template<typename T >

Polynomial operator/ ( const Real &  lhs, const Polynomial< T > &  rhs  )

friend

Member Data Documentation

c

template<typename T >

::std::vector<T> rl::math::Polynomial< T >::c

protected

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

• rl/math/Polynomial.h