Class PowerVariogram

java.lang.Object

smile.interpolation.variogram.PowerVariogram

All Implemented Interfaces:

Serializable, Variogram, Function

public class PowerVariogram
extends 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.

See Also:

• Serialized Form

Field Summary

Fields inherited from interface Function

logger

Constructor Summary

Constructors

Constructor	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	Description
double	f(double r)	Computes the value of the function at x.
String	toString()

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface Function

apply, inv, root

Constructor Details

PowerVariogram

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

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

Parameters:

x - the training data.

y - the responsible variable.

PowerVariogram

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

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

Parameters:

x - the training data.

y - the responsible variable.

beta - the beta parameter 1 <= β < 2.

PowerVariogram

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

Constructor. α will be estimated from x and y.

Parameters:

x - the training data.

y - the responsible variable.

beta - the beta parameter 1 <= β < 2.

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

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