Detailed Description

Approximate a function on a finite interval using a Chebyshev series:

$f(x) = \sum_n c_n T_n(x)$

where $T_n(x)=\cos(n \arccos x)$

See also the Chebyshev approximation example .

Idea for Future:: Move non-template functions to .cpp file.

Definition at line 52 of file cheb_approx.h.

Public Types
typedef boost::numeric::ublas::vector< double >	ubvector

Public Member Functions
	cheb_approx (const cheb_approx &gc)
	Copy constructor.

cheb_approx &	operator= (const cheb_approx &gc)
	Copy constructor.

Initialization methods
template<class func_t >
void	init (func_t &func, size_t ord, double a1, double b1)
	Initialize a Chebyshev approximation of the function `func` over the interval from `a1` to `b1`. More...

template<class vec_t >
void	init (double a1, double b1, size_t ord, vec_t &v)
	Create an approximation from a vector of coefficients.

template<class vec_t >
void	init_func_values (double a1, double b1, size_t ord, vec_t &fval)
	Create an approximation from a vector of function values.

Evaulation methods
double	eval (double x) const
	Evaluate the approximation.

double	operator() (double x) const
	Evaluate the approximation.

double	eval_n (size_t n, double x) const
	Evaluate the approximation to a specified order.

void	eval_err (double x, double &result, double &abserr)
	Evaluate the approximation and give the uncertainty.

void	eval_n_err (size_t n, double x, double &result, double &abserr)
	Evaluate the approximation to a specified order and give the uncertainty.

Maniupulating coefficients and endpoints
double	get_coefficient (size_t ix) const
	Get a coefficient. More...

void	set_coefficient (size_t ix, double co)
	Set a coefficient. More...

void	get_endpoints (double &la, double &lb)
	Return the endpoints of the approximation.

template<class vec_t >
void	get_coefficients (size_t n, vec_t &v) const
	Get the coefficients.

template<class vec_t >
void	set_coefficients (size_t n, const vec_t &v)
	Set the coefficients.

Derivatives and integrals
void	deriv (cheb_approx &gc) const
	Make `gc` an approximation to the derivative.

void	integ (cheb_approx &gc) const
	Make `gc` an approximation to the integral.

Protected Attributes
ubvector	c
	Coefficients.

size_t	order
	Order of the approximation.

double	a
	Lower end of the interval.

double	b
	Upper end of the interval.

size_t	order_sp
	Single precision order.

ubvector	f
	Function evaluated at Chebyshev points.

bool	init_called
	True if init has been called.

Member Function Documentation

◆ get_coefficient()

double o2scl::cheb_approx::get_coefficient ( size_t ix ) const

inline

Legal values of the argument are 0 to order (inclusive)

Definition at line 347 of file cheb_approx.h.

◆ init()

template<class func_t >

void o2scl::cheb_approx::init	(	func_t &	func,
		size_t	ord,
		double	a1,
		double	b1
	)

inline

The interval must be specified so that $ a < b $ , so a and b are swapped if this is not the case.

Definition at line 120 of file cheb_approx.h.

◆ set_coefficient()

void o2scl::cheb_approx::set_coefficient	(	size_t	ix,
		double	co
	)

inline

Legal values of the argument are 0 to order (inclusive)

Definition at line 361 of file cheb_approx.h.

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

/home/awsteiner/wcs/o2scl/src/other/cheb_approx.h

Detailed Description

Public Types

Public Member Functions

Protected Attributes

Member Function Documentation

◆ get_coefficient()

◆ init()

◆ set_coefficient()