Computational Resources

The KRIGE2D Procedure

Computational Resources

To generate a predicted value at a single grid point using N data points, PROC KRIGE2D must solve the following kriging system:

${C{\lambda}_0} = {C_0}$

where C is (N+1) ×(N+1), and the right-hand side vector C₀ is (N+1) ×1.

Holding the matrix and vector associated with this system in core requires approximately [(N²)/2] doubles (with typically eight bytes per double). The CPU time used in solving the system is proportional to N³. For large N, this time dominates the time to compute the [((N+1)(N+2))/2] elements of the covariance matrix C from the specified covariance or variogram model. This latter computation is proportional to N².

For local kriging, the kriging system is set up and solved for each grid point. Part of the set up process involves determining the neighborhood of each grid point. A fast K-D tree algorithm is used to determine neighborhoods. For G grid points, the dominant CPU time factor is setting up and solving the G kriging systems. The N in the preceding algorithm is the number of data points in a given neighborhood, and it can differ for each grid point.

In global kriging, the entire input data set and all grid points are used to set up and solve the single system

${C{\lambda}_0} = {C_0}$

Again C is (N+1) ×(N+1), but ${\lambda}_\mathbf{0}$ is now (N+1) ×G, where G is the number of grid points, and N is the number of nonmissing observations in the input data set. The right-hand side matrix C₀ is (N+1) ×G. Memory requirements are approximately [(N²)/2] + GN doubles. The CPU time used in solving the system is still dominated by the N³ factorization of the left-hand side.

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