Package smile.math.rbf

Class InverseMultiquadricRadialBasis

java.lang.Object
smile.math.rbf.InverseMultiquadricRadialBasis
All Implemented Interfaces:
Serializable, Function, RadialBasisFunction
public class InverseMultiquadricRadialBasis extends Object implements RadialBasisFunction
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:

  • Constructor Details

    • InverseMultiquadricRadialBasis

      public InverseMultiquadricRadialBasis()
      Constructor. The default scale is 1.0.

    • InverseMultiquadricRadialBasis

      public InverseMultiquadricRadialBasis(double scale)
      Constructor.
      Parameters:
      scale - the scale parameter.

  • Method Details

    • f

      public double f(double r)
      Description copied from interface: Function
      Computes the value of the function at x.
      Specified by:
      f in interface Function
      Parameters:
      r - a real number.
      Returns:
      the function value.

    • toString

      public String toString()
      Overrides:
      toString in class Object