smile.interpolation.variogram

Class SphericalVariogram

java.lang.Object

smile.interpolation.variogram.SphericalVariogram

All Implemented Interfaces:

Variogram, Function

public class SphericalVariogram
extends java.lang.Object
implements Variogram

Spherical variogram.

v(r) = c + b * (1.5 * r / a - 0.5 * (r / a)³) for 0 ≤ r ≤ a

or

v(r) = c + b for a ≤ r

where a is the range parameter and b is sill paramter. The distance of two pairs increase, the variogram of those two pairs also increase. Eventually, the increase of the distance can not cause the variogram increase. The distance which cause the variogram reach plateau is called range. The sill parameter b is the maximum variogram value (by default, we set c = 0).

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
SphericalVariogram(double a, double b) Constructor.
SphericalVariogram(double a, double b, double c) 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

SphericalVariogram

public SphericalVariogram(double a,
                          double b)

Constructor. No nugget effect.

Parameters:

a - the range parameter.

b - the sill parameter.

SphericalVariogram

public SphericalVariogram(double a,
                          double b,
                          double c)

Constructor.

Parameters:

a - the range parameter.

b - the sill parameter.

c - the nugget effect parameter.

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