A barycentric rational interpolation class. More...

#include <BarycentricRational.hpp>

Public Member Functions
	BarycentricRational (std::vector< double > x_values, std::vector< double > y_values, size_t order)

double	operator() (double x_to_interp_to) const

const std::vector< double > &	x_values () const

const std::vector< double > &	y_values () const

size_t	order () const

void	pup (PUP::er &p)

Detailed Description

A barycentric rational interpolation class.

The class builds a barycentric rational interpolant of a specified order using the x_values and y_values passed into the constructor. Barycentric interpolation requires $3 N$ storage, and costs $O (N d)$ to construct, where $N$ is the size of the x- and y-value vectors and $d$ is the order of the interpolant. The evaluation cost is $O (N)$ compared to $O (d)$ of a spline method, but constructing the barycentric interpolant does not require any derivatives of the function to be known.

The interpolation function is

$I (x) = \frac{\sum_{i = 0}^{N - 1} w_{i} y_{i} / (x - x_{i})}{\sum_{i = 0}^{N - 1} w_{i} / (x - x_{i})}$

where $w_{i}$ are the weights. The weights are computed using

$w_{k} = \sum_{i = k - d 0 \leq i < N - d}^{k} (- 1)^{i} \prod_{j = i j \neq k}^{i + d} \frac{1}{x_{k} - x_{j}}$

Requires: x_values.size() == y_values.size() and x_values_.size() >= order

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

src/NumericalAlgorithms/Interpolation/BarycentricRational.hpp

Public Member Functions

Detailed Description