Class implements the natural cubic spline interpolation. More...

#include <naturalCubicSpline.hpp>

Inheritance diagram for julian::NaturalCubicSpline:

Public Member Functions
virtual double	operator() (const std::vector< double > &, const std::vector< double > &, const double &) const
	Performs interpolation. More...

virtual NaturalCubicSpline *	clone () const
	Virtual copy constructor. More...

virtual unsigned int	getMinSize () const
	return the minimum number of points required by the interpolation More...

virtual std::string	info () const
	Name of a class. More...

Public Member Functions inherited from julian::Interpolation
	Interpolation ()
	Constructor. More...

virtual	~Interpolation ()
	Destructor. More...

Private Member Functions
template<class Archive >
void	serialize (Archive &, const unsigned int)
	interface used by Boost serialization library More...

Friends
class	boost::serialization::access

Detailed Description

Class implements the natural cubic spline interpolation.

A natural cubic spline is a non-local method of interpolation. The interpolant is a piecewise function build from cubic polynomial defined on each interval $(x_{i-1},x_{i})$ for $i = 0,1,..,n$ :

$f_{i}(x) = a_{i} x^{3} + b_{i} x^{2} + c_{i} x + d_{i} for x \in (x_{i-1}, x_{i})$

For a given tabulated points $(x_{i},y_{i})$ where $i = 0,1,..,n$ cubic functions $f_{j}$ where $j = 1,..,n$ satisfies the conditions:

$f_{i}(x_{i-1}) = y_{i-1}$ for
$f_{i}(x_{i}) = y_{i}$ for
$\frac{df_{i}(x)}{dx}|_{x=x_{i}} = \frac{df_{i+1}(x)}{dx}|_{x=x_{i}}$ for
$\frac{d^{2}f_{i}(x)}{dx^{2}}|_{x=x_{i}} = \frac{d^{2}f_{i+1}(x)}{dx^{2}}|_{x=x_{i}}$ for
$\frac{d^{2}f_{1}(x)}{dx^{2}}|_{x=x_{0}} = 0$
$\frac{d^{2}f_{n}(x)}{dx^{2}}|_{x=x_{n}} = 0$