Package smile.interpolation

Class ShepardInterpolation1D

java.lang.Object

smile.interpolation.ShepardInterpolation1D

All Implemented Interfaces:

Serializable, Interpolation

public class ShepardInterpolation1D
extends Object
implements Interpolation

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 jut the thing for quick and dirty applications.

See Also:

• Serialized Form

Constructor Summary

Constructors

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

Method Summary

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

Methods inherited from class java.lang.Object

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

Constructor Details

ShepardInterpolation1D

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

Constructor. By default p = 2.

Parameters:

x - the tabulated points.

y - the function values at x.

ShepardInterpolation1D

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

Constructor.

Parameters:

x - the tabulated 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)

Description copied from interface: Interpolation

Given a value x, return an interpolated value.

Specified by:

interpolate in interface Interpolation

Parameters:

x - a real number.

Returns:

the interpolated function value.

toString

public String toString()

Overrides:

toString in class Object