Package smile.math.rbf

Class MultiquadricRadialBasis

java.lang.Object
smile.math.rbf.MultiquadricRadialBasis
All Implemented Interfaces:
Serializable, Function, RadialBasisFunction
public class MultiquadricRadialBasis extends Object implements RadialBasisFunction
Multiquadric RBF. φ(r) = (r2 + r20)1/2 where r0 is a scale factor. Multiquadrics are said to be less sensitive to the choice of r0 than som other functional forms.

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

    • MultiquadricRadialBasis

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

    • MultiquadricRadialBasis

      public MultiquadricRadialBasis(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