smile.math.rbf

Class ThinPlateRadialBasis

java.lang.Object

smile.math.rbf.ThinPlateRadialBasis

All Implemented Interfaces:

java.io.Serializable, Function, RadialBasisFunction

public class ThinPlateRadialBasis
extends java.lang.Object
implements RadialBasisFunction, java.io.Serializable

Thin plate RBF. φ(r) = r² log(r / r₀) with the limiting value φ(0)=0 assumed, where r₀ is a scale factor. This function has some physical justification in the energy minimization problem associated with warping a thin elastic plate. However, there is no indication that it is generally better than multiquadric or inverse multiquadric function.

In general, r₀ should be larger than the typical separation of points but smaller than the "outer scale" or feature size of the function to interplate. There can be several orders of magnitude difference between the interpolation accuracy with a good choice for r₀, versus a poor choice, so it is definitely worth some experimentation. One way to experiment is to construct an RBF interpolator omitting one data point at a time and measuring the interpolation error at the omitted point.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
ThinPlateRadialBasis() Constructor.
ThinPlateRadialBasis(double scale) Constructor.

Method Summary

Modifier and Type	Method and Description
double	f(double r) Compute the value of the function at x.
java.lang.String	toString()

Methods inherited from class java.lang.Object

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

Constructor Detail

ThinPlateRadialBasis

public ThinPlateRadialBasis()

Constructor.

ThinPlateRadialBasis

public ThinPlateRadialBasis(double scale)

Constructor.

Method Detail

f

public double f(double r)

Description copied from interface: Function

Compute the value of the function at x.

Specified by:

f in interface Function

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object