Simple Kriging Constraints

SK_constraints

In simple kriging, the error variance is minimized without any additional constraint. The kriging system is then:

$$\left\{\vphantom{ \begin{array}{l} Var \Big( \sum_{\alpha=1}^{n}... ... u})-m(\rm {\bf u})] \Big) \quad \textrm{is minimum} \\ \end{array} }\right.$$$$\begin{array}{l} Var \Big( \sum_{\alpha=1}^{n} \lambda_{\alpha} ... ...(\rm {\bf u})-m(\rm {\bf u})] \Big) \quad \textrm{is minimum} \\ \end{array}$$

or, if secondary variables are accounted for:

$$\left\{\vphantom{ \begin{array}{l} Var \Big( \sum_{\alpha=1}^{n}... ...- [Z(\rm {\bf u})-m] \Big) \quad \textrm{is minimum} \\ \end{array} }\right.$$$$\begin{array}{l} Var \Big( \sum_{\alpha=1}^{n} \lambda_{\alpha} ... ... \qquad - [Z(\rm {\bf u})-m] \Big) \quad \textrm{is minimum} \\ \end{array}$$

SK_constraints computes the kriging system size, resizes the kriging matrix and the second member, and returns the system size.

Where Defined

In header file <kriging.h>

Model of

Kriging Constraint

Type Requirements

See 2.4 for a thorough description of the requirements on the matrix library.

Members

• SK_constraints::SK_constraints()
  
  Default constructor.

• template<class InputIterator, class Location, class Matrix, class Vector>
  unsigned int
  SK_constraints::operator()(Matrix& A, Vector& b,
                             const Location& u
                             InputIterator first_neigh, InputIterator last_neigh)
  
  
  Function call operator. first_neigh,last_neigh) is a range of Neighborhood, and Location is a model of Location. A is the kriging matrix and b the right hand side of the kriging system. u is the location being estimated. The function returns the total number of neighbors, i.e. the sum of the number of neighbors in each neighborhoods. The requirements on concepts Matrix and Vector are fully described in 2.4.