net.finmath.analytic.interpolation

Class RationalFunctionInterpolation

java.lang.Object

net.finmath.analytic.interpolation.RationalFunctionInterpolation

public class RationalFunctionInterpolation
extends Object

This class provides methodologies to interpolate given sample points by rational functions, that is, given interpolation points (x_i,y_i) the class provides a continuous function y = f(x) where

• f(x_i) = y_i and
• for x_i < x < x_i+1 the function is a fraction of two polynomes f(x) = (sum a_j x^j) / (sum b_k x^k).

This setup comprises linear interpolation (for which the function is C⁰) and cubic spline interpolation (for which the function is C¹).

Version:

1.3

Author:

Christian Fries

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	RationalFunctionInterpolation.ExtrapolationMethod
static class	RationalFunctionInterpolation.InterpolationMethod

Constructor Summary

Constructors

Constructor and Description
RationalFunctionInterpolation(double[] points, RandomVariable[] values) Generate a rational function interpolation from a given set of points.
RationalFunctionInterpolation(double[] points, RandomVariable[] values, RationalFunctionInterpolation.InterpolationMethod interpolationMethod, RationalFunctionInterpolation.ExtrapolationMethod extrapolationMethod) Generate a rational function interpolation from a given set of points using the specified interpolation and extrapolation method.

Method Summary

Modifier and Type	Method and Description
RationalFunctionInterpolation.InterpolationMethod	getInterpolationMethod() Returns the interpolation method used.
RandomVariable	getValue(double x) Get an interpolated value for a given argument x.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

RationalFunctionInterpolation

public RationalFunctionInterpolation(double[] points,
                                     RandomVariable[] values)

Generate a rational function interpolation from a given set of points.

Parameters:

points - The array of the x_i sample points of a function y=f(x).

values - The corresponding array of the y_i sample values to the sample points x_i.

RationalFunctionInterpolation

public RationalFunctionInterpolation(double[] points,
                                     RandomVariable[] values,
                                     RationalFunctionInterpolation.InterpolationMethod interpolationMethod,
                                     RationalFunctionInterpolation.ExtrapolationMethod extrapolationMethod)

Generate a rational function interpolation from a given set of points using the specified interpolation and extrapolation method.

Parameters:

points - The array of the x_i sample points of a function y=f(x).

values - The corresponding array of the y_i sample values to the sample points x_i.

interpolationMethod - The interpolation method to be used.

extrapolationMethod - The extrapolation method to be used.

Method Detail

getInterpolationMethod

public RationalFunctionInterpolation.InterpolationMethod getInterpolationMethod()

Returns the interpolation method used.

Returns:

Returns the interpolationMethod.

getValue

public RandomVariable getValue(double x)

Get an interpolated value for a given argument x.

Parameters:

x - The abscissa at which the interpolation should be performed.

Returns:

The interpolated value (ordinate).