smile.interpolation

Class ShepardInterpolation

java.lang.Object

smile.interpolation.ShepardInterpolation

public class ShepardInterpolation
extends java.lang.Object

Shepard interpolation 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 just the thing for quick and dirty applications.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
double	interpolate(double... x) Interpolate the function at given point.

Methods inherited from class java.lang.Object

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

Constructor Detail

ShepardInterpolation

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

Constructor. By default p = 2.

Parameters:

x - the point set.

y - the function values at given points.

ShepardInterpolation

public ShepardInterpolation(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)

Interpolate the function at given point.