Representation of a polynomial that can have non-scalar coefficients (polynomial matrix). More...

#include <PolynomialND.hpp>

Inherited by Polynomial< std::complex< double > >.

Public Member Functions
	PolynomialND (std::size_t order)
	Create polynomial with uninitialized coefficients. More...

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

	PolynomialND (const PolynomialND< Coef, Scalar > &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 Coef &value)
	Increase the order of this polynomial. More...

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

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

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

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

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

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

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

Coefficient access operators.
Operators used to access coefficients.
const Coef &	operator() (std::size_t i) const
	Get specific coefficient. More...

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

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

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

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

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

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

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

template<typename OutCoef , typename Coef2 = Coef>
PolynomialND< OutCoef, Scalar >	multiply (const PolynomialND< Coef2, Scalar > &b) const
	Polynomial multiplication. More...

template<typename OutCoef , typename Coef2 = Coef>
PolynomialND< OutCoef, Scalar >	multiply (const Coef2 &b) const
	Multiply with a coefficient. More...

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

Protected Attributes
std::vector< Coef >	_coef
	The coefficient vector.

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

Arithmetic operators between polynomial and scalars.
Operators used to do arithmetic with scalars.
const PolynomialND< Coef, Scalar >	operator* (Scalar s) const
	Scalar multiplication. More...

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

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

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

const PolynomialND< Coef, Scalar >	operator* (Scalar s, const PolynomialND< Coef, Scalar > &p)
	Scalar multiplication. More...

Detailed Description

template<typename Coef, typename Scalar = double>
class rw::math::PolynomialND< Coef, Scalar >

Representation of a polynomial that can have non-scalar coefficients (polynomial matrix).

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

◆ PolynomialND() [1/3]

PolynomialND ( std::size_t order )

inlineexplicit

Create polynomial with uninitialized coefficients.

Parameters

order [in] the order of the polynomial.

◆ PolynomialND() [2/3]

PolynomialND ( const std::vector< Coef > & coefficients )

inline

Create polynomial from vector.

Parameters

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

◆ PolynomialND() [3/3]

PolynomialND ( const PolynomialND< Coef, Scalar > & p )

inline

Create polynomial from other polynomial.

Parameters

p	[in] the polynomial to copy.

Member Function Documentation

◆ deflate()

PolynomialND<Coef, Scalar> deflate ( const Scalar & 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()

PolynomialND<Coef, Scalar> 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()

Coef evaluate ( const Scalar & x ) const

inline

Evaluate the polynomial using Horner's Method.

Parameters

x	[in] the input parameter.

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

◆ evaluateDerivatives()

std::vector<Coef> evaluateDerivatives	(	const Scalar &	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 \( {f(x),\dot{f}(x),\ddot{f}(x),\cdots}\).

◆ increaseOrder() [1/2]

void increaseOrder	(	std::size_t	increase,
		const Coef &	value
	)

inline

Increase the order of this polynomial.

Parameters

increase	[in] how much to increase the order (default is 1).
value	[in] initialize new coefficients to this value.

◆ increaseOrder() [2/2]

void increaseOrder ( std::size_t increase = 1 )

inline

Increase the order of this polynomial.

Parameters

increase [in] how much to increase the order (default is 1).

See also: increaseOrder(std::size_t,const Coef&) for a version that initializes the new coefficients to a certain value.

◆ multiply() [1/2]

PolynomialND<OutCoef, Scalar> multiply ( const Coef2 & b ) const

inline

Multiply with a coefficient.

Each coefficient is post-multiplied with the given coefficient.

Parameters

b	[in] coefficient to multiply with. Post-multiplication is used - the dimensions must match.

Returns: new polynomial after multiplication.

◆ multiply() [2/2]

PolynomialND<OutCoef, Scalar> multiply ( const PolynomialND< Coef2, Scalar > & b ) const

inline

Polynomial multiplication.

A convolution of the coefficients is used. Notice that more efficient algorithms exist for polynomials with scalar coefficients.

Parameters

b	[in] polynomial to multiply. Post-multiplication is used - the dimensions must match.

Returns: new polynomial after multiplication.

◆ operator()() [1/2]

Coef& operator() ( size_t i )

inline

Get specific coefficient.

Parameters

i	[in] the power of the term to get coefficient for.

Returns: the coefficient.

◆ operator()() [2/2]

const Coef& operator() ( std::size_t i ) const

inline

Get specific coefficient.

Parameters

i	[in] the power of the term to get coefficient for.

Returns: the coefficient.

◆ operator*()

const PolynomialND<Coef, Scalar> operator* ( Scalar s ) const

inline

Scalar multiplication.

Parameters

s	[in] scalar to multiply with.

Returns: new polynomial after multiplication.

◆ operator*=()

PolynomialND<Coef, Scalar>& operator*= ( Scalar s )

inline

Scalar multiplication.

Parameters

s	[in] the scalar to multiply with.

Returns: reference to same polynomial with changed coefficients.

◆ operator+()

const PolynomialND<Coef, Scalar> operator+ ( const PolynomialND< Coef, Scalar > & b ) const

inline

Polynomial addition.

Parameters

b	[in] polynomial to add.

Returns: new polynomial after addition.

◆ operator+=()

PolynomialND<Coef, Scalar>& operator+= ( const PolynomialND< Coef, Scalar > & b )

inline

Polynomial addition.

Parameters

b	[in] polynomial to add.

Returns: same polynomial with different coefficients after addition.

◆ operator-() [1/2]

const PolynomialND<Coef, Scalar> operator- ( ) const

inline

Negate coefficients.

Returns: new polynomial with coefficients negated.

◆ operator-() [2/2]

const PolynomialND<Coef, Scalar> operator- ( const PolynomialND< Coef, Scalar > & b ) const

inline

Polynomial subtraction.

Parameters

b	[in] polynomial of to subtract.

Returns: new polynomial after subtraction.

◆ operator-=()

PolynomialND<Coef, Scalar>& operator-= ( const PolynomialND< Coef, Scalar > & b )

inline

Polynomial subtraction.

Parameters

b	[in] polynomial to subtract.

Returns: same polynomial with different coefficients after subtraction.

◆ operator/()

const PolynomialND<Coef, Scalar> operator/ ( Scalar s ) const

inline

Scalar division.

Parameters

s	[in] scalar to divide with.

Returns: new polynomial after division.

◆ operator/=()

PolynomialND<Coef, Scalar>& operator/= ( Scalar s )

inline

Scalar division.

Parameters

s	[in] the scalar to divide with.

Returns: reference to same polynomial with changed coefficients.

◆ operator=()

void operator= ( const PolynomialND< Coef, Scalar > & b )

inline

Assignment.

Parameters

b	[in] the polynomial to take coefficients from.

◆ operator==()

bool operator== ( const PolynomialND< Coef, Scalar > & b ) const

inline

Check if polynomials are equal.

Parameters

b	[in] the polynomial to compare with.

Returns: true if equal, false if not.

◆ operator[]() [1/2]

Coef& operator[] ( size_t i )

inline

Get specific coefficient.

Parameters

i	[in] the power of the term to get coefficient for.

Returns: the coefficient.

◆ operator[]() [2/2]

const Coef& operator[] ( size_t i ) const

inline

Get specific coefficient.

Parameters

i	[in] the power of the term to get coefficient for.

Returns: the coefficient.

◆ order()

std::size_t order ( ) const

inline

Get the order of the polynomial (the highest power).

Returns: the order.

Friends And Related Function Documentation

◆ operator*

const PolynomialND<Coef, Scalar> operator*	(	Scalar	s,
		const PolynomialND< Coef, Scalar > &	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 PolynomialND< Coef, Scalar > &	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.

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

PolynomialND.hpp

Public Member Functions

Protected Attributes

Friends

Arithmetic operators between polynomial and scalars.

Detailed Description

template<typename Coef, typename Scalar = double> class rw::math::PolynomialND< Coef, Scalar >

Constructor & Destructor Documentation

◆ PolynomialND() [1/3]

◆ PolynomialND() [2/3]

◆ PolynomialND() [3/3]

Member Function Documentation

◆ deflate()

◆ derivative()

◆ evaluate()

◆ evaluateDerivatives()

◆ increaseOrder() [1/2]

◆ increaseOrder() [2/2]

◆ multiply() [1/2]

◆ multiply() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*()

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator=()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ order()

Friends And Related Function Documentation

◆ operator*

◆ operator<<

template<typename Coef, typename Scalar = double>
class rw::math::PolynomialND< Coef, Scalar >