Approximation of scalar-valued functions by Chebyshev polynomial expansion. More...

#include <ChebyshevFit.h>

Inheritance diagram for pcl::GenericScalarChebyshevFit< Tx, Ty >:

Public Member Functions
	GenericScalarChebyshevFit ()=default

	GenericScalarChebyshevFit (const GenericScalarChebyshevFit &)=default

template<class F >
	GenericScalarChebyshevFit (F f, Tx x1, Tx x2, int n)

	GenericScalarChebyshevFit (GenericScalarChebyshevFit &&)=default

GenericScalarChebyshevFit	Derivative () const

Ty	Evaluate (Tx x) const

GenericScalarChebyshevFit	Integral () const

bool	IsTruncated () const

Ty	operator() (Tx x) const

GenericScalarChebyshevFit &	operator= (const GenericScalarChebyshevFit &)=default

GenericScalarChebyshevFit &	operator= (GenericScalarChebyshevFit &&)=default

int	TruncatedLength () const

Ty	TruncationError () const

Public Member Functions inherited from pcl::GenericChebyshevFit< Tx, Ty >
	GenericChebyshevFit ()=default

	GenericChebyshevFit (const coefficient_series &ck, Tx x1, Tx x2)

	GenericChebyshevFit (const GenericChebyshevFit &)=default

template<class F >
	GenericChebyshevFit (F f, Tx x1, Tx x2, int N, int n)

	GenericChebyshevFit (GenericChebyshevFit &&)=default

const coefficient_series &	Coefficients () const

GenericChebyshevFit	Derivative () const

function_value	Evaluate (Tx x) const

GenericChebyshevFit	Integral () const

bool	IsTruncated (int i=-1) const

bool	IsValid () const

int	Length (int i=0) const

Tx	LowerBound () const

int	NumberOfCoefficients () const

int	NumberOfComponents () const

int	NumberOfTruncatedCoefficients () const

function_value	operator() (Tx x) const

GenericChebyshevFit &	operator= (const GenericChebyshevFit &)=default

GenericChebyshevFit &	operator= (GenericChebyshevFit &&)=default

bool	Truncate (const coefficients &eps, int mmin=2)

bool	Truncate (Ty e, int mmin=2)

int	TruncatedLength (int i=-1) const

Ty	TruncationError (int i=-1) const

Tx	UpperBound () const

Additional Inherited Members
Public Types inherited from pcl::GenericChebyshevFit< Tx, Ty >
using	coefficient_series = GenericMultiVector< Ty >

using	coefficients = GenericVector< Ty >

using	function_value = GenericVector< Ty >

using	function_values = GenericMultiVector< Ty >

Detailed Description

template<typename Tx, typename Ty>
class pcl::GenericScalarChebyshevFit< Tx, Ty >

GenericScalarChebyshevFit approximates a smooth, scalar-valued function f(x) in a given interval [a,b] by expansion with a single truncated series of Chebyshev polynomials. GenericScalarChebyshevFit is a convenient specialization of GenericChebyshevFit for functions returning a single value; refer to the parent class for complete information.

Definition at line 651 of file ChebyshevFit.h.

Constructor & Destructor Documentation

◆ GenericScalarChebyshevFit() [1/4]

template<typename Tx , typename Ty >

template<class F >

pcl::GenericScalarChebyshevFit< Tx, Ty >::GenericScalarChebyshevFit	(	F	f,
		Tx	x1,
		Tx	x2,
		int	n
	)

inline

Constructs a truncated Chebyshev polynomial expansion with n coefficients to approximate the specified N-dimensional, scalar-valued function f in the interval [x1,x2] of the independent variable.

See GenericChebyshevFit::GenericChebyshevFit() for detailed information.

Definition at line 663 of file ChebyshevFit.h.

◆ GenericScalarChebyshevFit() [2/4]

template<typename Tx , typename Ty >

pcl::GenericScalarChebyshevFit< Tx, Ty >::GenericScalarChebyshevFit ( )

default

Default constructor.

Constructs an invalid, uninitialized object that cannot be used to perform function evaluations. A default-constructed GenericScalarChebyshevFit object should be assigned with an already initialized instance in order to become operative.

See also: IsValid()

◆ GenericScalarChebyshevFit() [3/4]

template<typename Tx , typename Ty >

pcl::GenericScalarChebyshevFit< Tx, Ty >::GenericScalarChebyshevFit ( const GenericScalarChebyshevFit< Tx, Ty > & )

default

Copy constructor.

◆ GenericScalarChebyshevFit() [4/4]

template<typename Tx , typename Ty >

pcl::GenericScalarChebyshevFit< Tx, Ty >::GenericScalarChebyshevFit ( GenericScalarChebyshevFit< Tx, Ty > && )

default

Move constructor.

Member Function Documentation

◆ Derivative()

template<typename Tx , typename Ty >

GenericScalarChebyshevFit pcl::GenericScalarChebyshevFit< Tx, Ty >::Derivative ( ) const

inline

Returns a GenericChebyshevFit object that approximates the derivative of the function fitted by this object.

See GenericChebyshevFit::Derivative() for detailed information.

See also: Integral()

Definition at line 760 of file ChebyshevFit.h.

References pcl::GenericChebyshevFit< Tx, Ty >::Derivative().

◆ Evaluate()

template<typename Tx , typename Ty >

Ty pcl::GenericScalarChebyshevFit< Tx, Ty >::Evaluate ( Tx x ) const

inline

Evaluates the truncated Chebyshev polynomial expansion for the specified value x of the independent variable, and returns the approximated function value.