Class KrigingInterpolation
Kriging can be either an interpolation method or a fitting method. The distinction between the two is whether the fitted/interpolated function goes exactly through all the input data points (interpolation), or whether it allows measurement errors to be specified and then "smooths" to get a statistically better predictor that does not generally go through the data points.
The aim of kriging is to estimate the value of an unknown realvalued function, f, at a point, x, given the values of the function at some other points, x_{1},…, x_{n}. Kriging computes the best linear unbiased estimator based on a stochastic model of the spatial dependence quantified either by the variogram γ(x,y) or by expectation μ(x) = E[f(x)] and the covariance function c(x,y) of the random field. A kriging estimator is a linear combination that may be written as
ƒ(x) = Σ λ_{i}(x) f(x_{i})
The weights λ_{i} are solutions of a system of linear equations which is obtained by assuming that f is a samplepath of a random process F(x), and that the error of prediction
ε(x) = F(x)  Σ λ_{i}(x) F(x_{i})
is to be minimized in some sense.
Depending on the stochastic properties of the random field different types of kriging apply. The type of kriging determines the linear constraint on the weights λ_{i} implied by the unbiasedness condition; i.e. the linear constraint, and hence the method for calculating the weights, depends upon the type of kriging.
This class implements ordinary kriging, which is the most commonly used type of kriging. The typical assumptions for the practical application of ordinary kriging are:
 Intrinsic stationarity or wide sense stationarity of the field
 enough observations to estimate the variogram.
 The mean E[f(x)] = μ is unknown but constant
 The variogram γ(x,y) = E[(f(x)  f(y))^{2}] of f(x) is known.

Constructor Summary
ConstructorDescriptionKrigingInterpolation
(double[][] x, double[] y) Constructor.KrigingInterpolation
(double[][] x, double[] y, Variogram variogram, double[] error) Constructor. 
Method Summary
Modifier and TypeMethodDescriptiondouble
interpolate
(double... x) Interpolate the function at given point.toString()

Constructor Details

KrigingInterpolation
public KrigingInterpolation(double[][] x, double[] y) Constructor. The power variogram is employed. We assume no errors, i.e. we are doing interpolation rather fitting. Parameters:
x
 the data points.y
 the function values atx
.

KrigingInterpolation
Constructor. Parameters:
x
 the data points.y
 the function values atx
.variogram
 the variogram function of offset distance to estimate the mean square variation of function y(x).error
 the measure error associated with y. It is the sqrt of diagonal elements of covariance matrix.


Method Details