Package smile.interpolation

Class ShepardInterpolation

java.lang.Object

smile.interpolation.ShepardInterpolation

public class ShepardInterpolation
extends 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	Description
ShepardInterpolation(double[][] x, double[] y)	Constructor.
ShepardInterpolation(double[][] x, double[] y, double p)	Constructor.

Method Summary

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

Methods inherited from class java.lang.Object

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

Constructor Details

ShepardInterpolation

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

Constructor. By default p = 2.

Parameters:

x - the data points.

y - the function values at x.

ShepardInterpolation

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

Constructor.

Parameters:

x - the data points.

y - the function values at x.

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

Method Details

interpolate

public double interpolate(double... x)

Interpolate the function at given point.

Parameters:

x - a point.

Returns:

the interpolated function value.

toString

public String toString()

Overrides:

toString in class Object