smile.interpolation.variogram

Class PowerVariogram

java.lang.Object

smile.interpolation.variogram.PowerVariogram

All Implemented Interfaces:

Variogram, Function

public class PowerVariogram
extends java.lang.Object
implements Variogram

Power variogram

v(r) = c + α r^β

where β is fixed and α is fitted by unweighted least squares over all pairs of data points. The value of β should be in the range 1 ≤ β < 2. A good general choice is 1.5, but for functions with a strong linear trend, we may experiment with values as large as 1.99.

The parameter c is the so-called nugget effect. Though the value of the variogram for h = 0 is strictly 0, several factors, such as sampling error and short scale variability, may cause sample values separated by extremely small distances to be quite dissimilar. This causes a discontinuity at the origin of the variogram. The vertical jump from the value of 0 at the origin to the value of the variogram at extremely small separation distances is called the nugget effect.

Constructor Summary

Constructors

Constructor and Description
PowerVariogram(double[][] x, double[] y) Constructor.
PowerVariogram(double[][] x, double[] y, double beta) Constructor.
PowerVariogram(double[][] x, double[] y, double beta, double nugget) 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

PowerVariogram

public PowerVariogram(double[][] x,
                      double[] y)

Constructor. No nugget effect and β = 1.5 and α will be estimated from x and y.

PowerVariogram

public PowerVariogram(double[][] x,
                      double[] y,
                      double beta)

Constructor. No nugget effect and α will be estimated from x and y.

PowerVariogram

public PowerVariogram(double[][] x,
                      double[] y,
                      double beta,
                      double nugget)

Constructor. α will be estimated from x and y.

Parameters:

nugget - the nugget effect parameter. The height of the jump of the variogram at the discontinuity at the origin.

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