Representation of an ordinary polynomial with scalar coefficients (that can be both real and complex). More...

#include <Polynomial.hpp>

Inherits PolynomialND< double, double >.

Public Member Functions
	Polynomial (std::size_t order)
	Create polynomial with coefficients initialized to zero. More...

	Polynomial (const std::vector< T > &coefficients)
	Create polynomial from vector. More...

	Polynomial (const Polynomial< T > &p)
	Create polynomial from other polynomial. More...

	Polynomial (const PolynomialND< T, T > &p)
	Create polynomial from other polynomial. More...

virtual	~Polynomial ()
	Destructor.

T	evaluate (const T &x) const
	Evaluate the polynomial using Horner's Method. More...

template<typename ErrT = T>
T	evaluate (const T &x, ErrT &err) const
	Evaluate the polynomial using Horner's Method. More...

std::vector< T >	evaluateDerivatives (const T &x, std::size_t n=1) const
	Evaluate the first n derivatives of the polynomial using Horner's Method. More...

template<typename ErrT = T>
std::vector< T >	evaluateDerivatives (const T &x, std::vector< ErrT > &err, std::size_t n=1) const
	Evaluate the first n derivatives of the polynomial using Horner's Method. More...

Polynomial< T >	deflate (const T &x) const
	Perform deflation of polynomial. More...

Polynomial< T >	derivative (std::size_t n=1) const
	Get the derivative polynomial. More...

const Polynomial< T >	operator- () const
	Negate coefficients. More...

bool	operator== (const Polynomial< T > &b) const
	Check if polynomials are equal. More...

template<class Q >
const Polynomial< Q >	cast ()
	Cast to other type. More...

Arithmetic operators between polynomials.
Operators used to do arithmetic between two polynomials.
const Polynomial< T >	operator- (const Polynomial< T > &b) const
	Polynomial subtraction. More...

Polynomial< T > &	operator-= (const Polynomial< T > &b)
	Polynomial subtraction. More...

const Polynomial< T >	operator+ (const Polynomial< T > &b) const
	Polynomial addition. More...

Polynomial< T > &	operator+= (const Polynomial< T > &b)
	Polynomial addition. More...

void	operator= (const Polynomial< T > &b)
	Assignment. More...

Public Member Functions inherited from PolynomialND< double, double >
	PolynomialND (std::size_t order)
	Create polynomial with uninitialized coefficients. More...

	PolynomialND (const std::vector< double > &coefficients)
	Create polynomial from vector. More...

	PolynomialND (const PolynomialND< double, double > &p)
	Create polynomial from other polynomial. More...

virtual	~PolynomialND ()
	Destructor.

std::size_t	order () const
	Get the order of the polynomial (the highest power). More...

void	increaseOrder (std::size_t increase, const double &value)
	Increase the order of this polynomial. More...

void	increaseOrder (std::size_t increase=1)
	Increase the order of this polynomial. More...

double	evaluate (const double &x) const
	Evaluate the polynomial using Horner's Method. More...

std::vector< double >	evaluateDerivatives (const double &x, std::size_t n=1) const
	Evaluate the first n derivatives of the polynomial using Horner's Method. More...

PolynomialND< double, double >	deflate (const double &x) const
	Perform deflation of polynomial. More...

PolynomialND< double, double >	derivative (std::size_t n=1) const
	Get the derivative polynomial. More...

const PolynomialND< double, double >	operator- () const
	Negate coefficients. More...

bool	operator== (const PolynomialND< double, double > &b) const
	Check if polynomials are equal. More...

const double &	operator() (std::size_t i) const
	Get specific coefficient. More...

double &	operator() (size_t i)
	Get specific coefficient. More...

const double &	operator[] (size_t i) const
	Get specific coefficient. More...

double &	operator[] (size_t i)
	Get specific coefficient. More...

const PolynomialND< double, double >	operator- (const PolynomialND< double, double > &b) const
	Polynomial subtraction. More...

PolynomialND< double, double > &	operator-= (const PolynomialND< double, double > &b)
	Polynomial subtraction. More...

const PolynomialND< double, double >	operator+ (const PolynomialND< double, double > &b) const
	Polynomial addition. More...

PolynomialND< double, double > &	operator+= (const PolynomialND< double, double > &b)
	Polynomial addition. More...

PolynomialND< OutCoef, double >	multiply (const PolynomialND< Coef2, double > &b) const
	Polynomial multiplication. More...

PolynomialND< OutCoef, double >	multiply (const Coef2 &b) const
	Multiply with a coefficient. More...

void	operator= (const PolynomialND< double, double > &b)
	Assignment. More...

const PolynomialND< double, double >	operator* (double s) const
	Scalar multiplication. More...

const PolynomialND< double, double >	operator/ (double s) const
	Scalar division. More...

PolynomialND< double, double > &	operator*= (double s)
	Scalar multiplication. More...

PolynomialND< double, double > &	operator/= (double s)
	Scalar division. More...

Friends
std::ostream &	operator<< (std::ostream &out, const Polynomial< T > &p)
	Printing polynomial to stream. More...

Related Functions
(Note that these are not member functions.)
template<>
void	write (const rw::math::Polynomial< double > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	write (const rw::math::Polynomial< float > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	read (rw::math::Polynomial< double > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

template<>
void	read (rw::math::Polynomial< float > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

Arithmetic operators between polynomial and scalars.
Operators used to do arithmetic with scalars.
const Polynomial< T >	operator+ (T s) const
	Scalar addition. More...

const Polynomial< T >	operator- (T s) const
	Scalar subtraction. More...

const Polynomial< T >	operator* (T s) const
	Scalar multiplication. More...

const Polynomial< T >	operator* (const Polynomial< T > &polynomial) const
	Polynomial multiplication. More...

PolynomialND< Eigen::Matrix< T, 3, 1 >, T >	operator* (const PolynomialND< Eigen::Matrix< T, 3, 1 >, T > &polynomial) const
	Multiply polynomial with scalar coefficients with a 3D polynomial vector. More...

PolynomialND< Eigen::Matrix< T, 1, 3 >, T >	operator* (const PolynomialND< Eigen::Matrix< T, 1, 3 >, T > &polynomial) const
	Multiply polynomial with scalar coefficients with a 3D polynomial vector. More...

PolynomialND< Eigen::Matrix< T, 3, 3 >, T >	operator* (const PolynomialND< Eigen::Matrix< T, 3, 3 >, T > &polynomial) const
	Multiply polynomial with scalar coefficients with a 3D polynomial matrix. More...

PolynomialND< Eigen::Matrix< T, 3, 1 >, T >	operator* (const Eigen::Matrix< T, 3, 1 > &a) const
	Multiply polynomial with scalar coefficients with a vector. More...

PolynomialND< Eigen::Matrix< T, 1, 3 >, T >	operator* (const Eigen::Matrix< T, 1, 3 > &a) const
	Multiply polynomial with scalar coefficients with a vector. More...

PolynomialND< Eigen::Matrix< T, 3, 3 >, T >	operator* (const Eigen::Matrix< T, 3, 3 > &A) const
	Multiply polynomial with scalar coefficients with a matrix. More...

const Polynomial< T >	operator/ (T s) const
	Scalar division. More...

Polynomial< T > &	operator+= (T s)
	Scalar addition. More...

Polynomial< T > &	operator-= (T s)
	Scalar subtraction. More...

Polynomial< T > &	operator*= (T s)
	Scalar multiplication. More...

Polynomial< T > &	operator/= (T s)
	Scalar division. More...

const Polynomial< T >	operator* (T s, const Polynomial< T > &p)
	Scalar multiplication. More...

Additional Inherited Members
Protected Attributes inherited from PolynomialND< double, double >
std::vector< double >	_coef
	The coefficient vector.

Detailed Description

template<typename T = double>
class rw::math::Polynomial< T >

Representation of an ordinary polynomial with scalar coefficients (that can be both real and complex).

Representation of a polynomial of the following form:

\( f(x) = c_n x^n + c_(n-1) x^(n-1) + c_2 x^2 + c_1 x + c_0 \)

The polynomial is represented as a list of coefficients ordered from lowest-order term to highest-order term, \({c_0,c_1,...,c_n}\).

Constructor & Destructor Documentation

◆ Polynomial() [1/4]

Polynomial ( std::size_t order )

inlineexplicit

Create polynomial with coefficients initialized to zero.

Parameters

order [in] the order of the polynomial.

◆ Polynomial() [2/4]

Polynomial ( const std::vector< T > & coefficients )

inline

Create polynomial from vector.

Parameters

coefficients [in] the coefficients ordered from lowest-order term to highest-order term.

◆ Polynomial() [3/4]

Polynomial ( const Polynomial< T > & p )

inline

Create polynomial from other polynomial.

Parameters

p	[in] the polynomial to copy.

◆ Polynomial() [4/4]

Polynomial ( const PolynomialND< T, T > & p )

inline

Create polynomial from other polynomial.

Parameters

p	[in] the polynomial to copy.

Member Function Documentation

◆ cast()

const Polynomial<Q> cast ( )

inline

Cast to other type.

Returns: a new polynomial after cast to new type.

◆ deflate()

Polynomial<T> deflate ( const T & x ) const

inline

Perform deflation of polynomial.

Parameters

x	[in] a root of the polynomial.

Returns: a new polynomial of same order minus one.

Note: There is no check that the given root is in fact a root of the polynomial.

◆ derivative()

Polynomial<T> derivative ( std::size_t n = 1 ) const

inline

Get the derivative polynomial.

Parameters

n	[in] gives the n'th derivative (default is n=1).

Returns: a new polynomial of same order minus one.

Note: To evaluate derivatives use the evaluate derivative method which is more precise.

◆ evaluate() [1/2]

T evaluate ( const T & x ) const

inline

Evaluate the polynomial using Horner's Method.

Parameters

x	[in] the input parameter.

Returns: the value \( f(x)\).

◆ evaluate() [2/2]

T evaluate	(	const T &	x,
		ErrT &	err
	)		const

inline

Evaluate the polynomial using Horner's Method.

This function estimates the error of the result. For float or double types, the error type, ErrT, should be the same as the type T. For std::complex<float> or std::complex<double> types, the error type, ErrT, should be either float or double.

Parameters

x	[in] the input parameter.
err	[out] estimate of the absolute error.

Returns: the value \(f(x)\).

Note: Error is the absolute size of the interval where \(f(x)\) can be, assuming coefficients are exact.

◆ evaluateDerivatives() [1/2]

std::vector<T> evaluateDerivatives	(	const T &	x,
		std::size_t	n = `1`
	)		const

inline

Evaluate the first n derivatives of the polynomial using Horner's Method.

Parameters

x	[in] the input parameter.
n	[in] the number of derivatives to find (default is the first derivative only)

Returns: a vector of values \( {f(x),\dot{f}(x),\ddot{f}(x),\cdots}\).

◆ evaluateDerivatives() [2/2]

std::vector<T> evaluateDerivatives	(	const T &	x,
		std::vector< ErrT > &	err,
		std::size_t	n = `1`
	)		const

inline

Evaluate the first n derivatives of the polynomial using Horner's Method.

This function estimates the error of the result. For float or double types, the error type, ErrT, should be the same as the type T. For std::complex<float> or std::complex<double> types, the error type, ErrT, should be either float or double.

Parameters

x	[in] the input parameter.
err	[out] estimate of the absolute errors.
n	[in] the number of derivatives to find (default is the first derivative only)

Returns: the value \(\dot{f}(x)\).

Note: Error is the absolute size of the interval where \(f(x)\) can be, assuming coefficients are exact.

◆ operator*() [1/8]

PolynomialND<Eigen::Matrix<T, 1, 3>, T> operator* ( const Eigen::Matrix< T, 1, 3 > & a ) const

inline

Multiply polynomial with scalar coefficients with a vector.

Parameters

a	[in] vector to multiply with.

Returns: a 3D polynomial vector.

◆ operator*() [2/8]

PolynomialND<Eigen::Matrix<T, 3, 1>, T> operator* ( const Eigen::Matrix< T, 3, 1 > & a ) const

inline

Multiply polynomial with scalar coefficients with a vector.

Parameters

a	[in] vector to multiply with.

Returns: a 3D polynomial vector.

◆ operator*() [3/8]

PolynomialND<Eigen::Matrix<T, 3, 3>, T> operator* ( const Eigen::Matrix< T, 3, 3 > & A ) const

inline

Multiply polynomial with scalar coefficients with a matrix.

Parameters

A	[in] matrix to multiply with.

Returns: a 3D polynomial matrix.

◆ operator*() [4/8]

const Polynomial<T> operator* ( const Polynomial< T > & polynomial ) const

inline

Polynomial multiplication.

This multiplication functions uses a convolution of the coefficients. More efficient implementations are possible.

Parameters

polynomial [in] polynomial to multiply with.

Returns: new polynomial after multiplication.

◆ operator*() [5/8]

PolynomialND<Eigen::Matrix<T, 1, 3>, T> operator* ( const PolynomialND< Eigen::Matrix< T, 1, 3 >, T > & polynomial ) const

inline

Multiply polynomial with scalar coefficients with a 3D polynomial vector.

Parameters

polynomial [in] polynomial vector.

Returns: a 3D polynomial vector.

◆ operator*() [6/8]

PolynomialND<Eigen::Matrix<T, 3, 1>, T> operator* ( const PolynomialND< Eigen::Matrix< T, 3, 1 >, T > & polynomial ) const

inline

Multiply polynomial with scalar coefficients with a 3D polynomial vector.

Parameters

polynomial [in] polynomial vector.

Returns: a 3D polynomial vector.

◆ operator*() [7/8]

PolynomialND<Eigen::Matrix<T, 3, 3>, T> operator* ( const PolynomialND< Eigen::Matrix< T, 3, 3 >, T > & polynomial ) const

inline

Multiply polynomial with scalar coefficients with a 3D polynomial matrix.

Parameters

polynomial [in] polynomial matrix.

Returns: a 3D polynomial matrix.

◆ operator*() [8/8]

const Polynomial<T> operator* ( T s ) const

inline

Scalar multiplication.

Parameters

s	[in] scalar to multiply with.

Returns: new polynomial after multiplication.

◆ operator*=()

Polynomial<T>& operator*= ( T s )

inline

Scalar multiplication.

Parameters

s	[in] the scalar to multiply with.

Returns: reference to same polynomial with changed coefficients.

◆ operator+() [1/2]

const Polynomial<T> operator+ ( const Polynomial< T > & b ) const

inline

Polynomial addition.

Parameters

b	[in] polynomial to add.

Returns: new polynomial after addition.

◆ operator+() [2/2]

const Polynomial<T> operator+ ( T s ) const

inline

Scalar addition.

Parameters

s	[in] scalar to add.

Returns: new polynomial after addition.

◆ operator+=() [1/2]

Polynomial<T>& operator+= ( const Polynomial< T > & b )

inline

Polynomial addition.

Parameters

b	[in] polynomial to add.

Returns: same polynomial with different coefficients after addition.

◆ operator+=() [2/2]

Polynomial<T>& operator+= ( T s )

inline

Scalar addition.

Parameters

s	[in] scalar to add.

Returns: same polynomial with coefficients changed.

◆ operator-() [1/3]

const Polynomial<T> operator- ( ) const

inline

Negate coefficients.

Returns: new polynomial with coefficients negated.

◆ operator-() [2/3]

const Polynomial<T> operator- ( const Polynomial< T > & b ) const

inline

Polynomial subtraction.

Parameters

b	[in] polynomial of to subtract.

Returns: new polynomial after subtraction.

◆ operator-() [3/3]

const Polynomial<T> operator- ( T s ) const

inline

Scalar subtraction.

Parameters

s	[in] scalar to subtract.

Returns: new polynomial after subtraction.

◆ operator-=() [1/2]

Polynomial<T>& operator-= ( const Polynomial< T > & b )

inline

Polynomial subtraction.

Parameters

b	[in] polynomial to subtract.

Returns: same polynomial with different coefficients after subtraction.

◆ operator-=() [2/2]

Polynomial<T>& operator-= ( T s )

inline

Scalar subtraction.

Parameters

s	[in] scalar to subtract.

Returns: same polynomial with coefficients changed.

◆ operator/()

const Polynomial<T> operator/ ( T s ) const

inline

Scalar division.

Parameters

s	[in] scalar to divide with.

Returns: new polynomial after division.

◆ operator/=()

Polynomial<T>& operator/= ( T s )

inline

Scalar division.

Parameters

s	[in] the scalar to divide with.

Returns: reference to same polynomial with changed coefficients.

◆ operator=()

void operator= ( const Polynomial< T > & b )

inline

Assignment.

Parameters

b	[in] the polynomial to take coefficients from.

Returns: true if equal, false if not.

◆ operator==()

bool operator== ( const Polynomial< T > & b ) const

inline

Check if polynomials are equal.

Parameters

b	[in] the polynomial to compare with.

Returns: true if equal, false if not.

Friends And Related Function Documentation

◆ operator*

const Polynomial<T> operator*	(	T	s,
		const Polynomial< T > &	p
	)

friend

Scalar multiplication.

Parameters

s	[in] scalar to multiply with.
p	[in] polynomial to multiply with.

Returns: new polynomial after multiplication.

◆ operator<<

std::ostream& operator<<	(	std::ostream &	out,
		const Polynomial< T > &	p
	)

friend

Printing polynomial to stream.

Parameters

out	[in/out] the stream to write to.
p	[in] the polynomail to print.

Returns: the same ostream as out parameter.

◆ read() [1/2]

void read	(	rw::math::Polynomial< double > &	sobject,
		rw::common::InputArchive &	iarchive,
		const std::string &	id
	)

Parameters

sobject	[out] the object in which the data should be streamed into
iarchive	[in] the InputArchive from which to read data.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

◆ read() [2/2]

void read	(	rw::math::Polynomial< float > &	sobject,
		rw::common::InputArchive &	iarchive,
		const std::string &	id
	)

Parameters

sobject	[out] the object in which the data should be streamed into
iarchive	[in] the InputArchive from which to read data.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

◆ write() [1/2]

void write	(	const rw::math::Polynomial< double > &	sobject,
		rw::common::OutputArchive &	oarchive,
		const std::string &	id
	)

Parameters

sobject	[in] the object from which the data should be streamed.
oarchive	[out] the OutputArchive in which data should be written.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

◆ write() [2/2]

void write	(	const rw::math::Polynomial< float > &	sobject,
		rw::common::OutputArchive &	oarchive,
		const std::string &	id
	)

Parameters

sobject	[in] the object from which the data should be streamed.
oarchive	[out] the OutputArchive in which data should be written.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

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

core/math_fwd.hpp
Polynomial.hpp

Public Member Functions

Friends

Related Functions

Arithmetic operators between polynomial and scalars.

Additional Inherited Members

Detailed Description

template<typename T = double> class rw::math::Polynomial< T >

Constructor & Destructor Documentation

◆ Polynomial() [1/4]

◆ Polynomial() [2/4]

◆ Polynomial() [3/4]

◆ Polynomial() [4/4]

Member Function Documentation

◆ cast()

◆ deflate()

◆ derivative()

◆ evaluate() [1/2]

◆ evaluate() [2/2]

◆ evaluateDerivatives() [1/2]

◆ evaluateDerivatives() [2/2]

◆ operator*() [1/8]

◆ operator*() [2/8]

◆ operator*() [3/8]

◆ operator*() [4/8]

◆ operator*() [5/8]

◆ operator*() [6/8]

◆ operator*() [7/8]

◆ operator*() [8/8]

◆ operator*=()

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/()

◆ operator/=()

◆ operator=()

◆ operator==()

Friends And Related Function Documentation

◆ operator*

◆ operator<<

◆ read() [1/2]

◆ read() [2/2]

◆ write() [1/2]

◆ write() [2/2]

template<typename T = double>
class rw::math::Polynomial< T >