smile.interpolation

Class ShepardInterpolation1D

java.lang.Object

smile.interpolation.ShepardInterpolation1D

All Implemented Interfaces:

Interpolation

public class ShepardInterpolation1D
extends java.lang.Object
implements Interpolation

Shepard interplation is a special case of normalized radial basis function interpolation if the function φ(r) goes to infinity as r → 0, and is finite for r > 0. In this case, the weights w_i are just equal to the respective function values y_i. So we need not solve linear equations and thus it works for very large N.

An example of such φ is φ(r) = r^-p with (typically) 1 < p ≤ 3.

Shepard interpolation is rarely as accurate as the well-tuned application of other radial basis functions. However, it is simple, fast, and often jut the thing for quick and dirty applications.

Constructor Summary

Constructors

Constructor and Description
ShepardInterpolation1D(double[] x, double[] y) Constructor.
ShepardInterpolation1D(double[] x, double[] y, double p) Constructor.

Method Summary

Modifier and Type	Method and Description
double	interpolate(double x) Given a value x, return an interploated value.

Methods inherited from class java.lang.Object

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

Constructor Detail

ShepardInterpolation1D

public ShepardInterpolation1D(double[] x,
                              double[] y)

Constructor. By default p = 2.

Parameters:

x - the point set.

y - the function values at given points.

ShepardInterpolation1D

public ShepardInterpolation1D(double[] x,
                              double[] y,
                              double p)

Constructor.

Parameters:

x - the point set.

y - the function values at given points.

p - the parameter in the radial basis function φ(r) = r^-p.

Method Detail

interpolate

public double interpolate(double x)

Description copied from interface: Interpolation

Given a value x, return an interploated value.

Specified by:

interpolate in interface Interpolation