Class InverseQuadraticRadialBasis

java.lang.Object
smile.math.rbf.InverseQuadraticRadialBasis
All Implemented Interfaces:
Serializable, RadialBasisFunction, Function
public class InverseQuadraticRadialBasis extends Object implements RadialBasisFunction
Inverse quadratic RBF.

φ(r) = 1 / (1 + (r / r0)2)

where r0 is a scale factor. The inverse quadratic is a completely monotone function, making it a valid positive-definite kernel. Unlike the Gaussian, it has heavier tails, which can be advantageous for capturing long-range correlations. It also has the property that φ(0) = 1 and φ(r) → 0 as r → ∞.

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 interpolate.

See Also:

  • Constructor Details

    • InverseQuadraticRadialBasis

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

    • InverseQuadraticRadialBasis

      public InverseQuadraticRadialBasis(double scale)
      Constructor.
      Parameters:
      scale - the scale parameter. Must be positive.

  • Method Details

    • scale

      public double scale()
      Returns the scale factor r0.
      Returns:
      the scale factor.

    • 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