smile.math.rbf

Class InverseMultiquadricRadialBasis

java.lang.Object

smile.math.rbf.InverseMultiquadricRadialBasis

All Implemented Interfaces:

java.io.Serializable, Function, RadialBasisFunction

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

Inverse multiquadric RBF. φ(r) = (r² + r²₀)^-1/2 where r₀ is a scale factor. Although it sounds odd, the inverse multiquadric gives results that are comparable to the multiquadric, sometimes better. The reason is what really matters is smoothness, and certain properties of the function's Fourier transform that are not very different between the multiquadric and its reciprocal. The fact that one increases monotonically and the other decreases turns out to be almost irrelevant. Besides, inverse multiquadric will extrapolate any function to zero far from the data.

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
InverseMultiquadricRadialBasis()
InverseMultiquadricRadialBasis(double scale)

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

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

Constructor Detail

InverseMultiquadricRadialBasis

public InverseMultiquadricRadialBasis()

InverseMultiquadricRadialBasis

public InverseMultiquadricRadialBasis(double scale)

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