The SIM2D Procedure

Computational Details

In the computation of bold-italic mu overTilde and bold upper Sigma described in the previous section, the inverse bold upper Sigma 22 Superscript negative 1 is never actually computed; an equation of the form

bold upper Sigma 22 bold upper A equals bold upper B

is solved for bold upper A by using a modified Gaussian elimination algorithm that takes advantage of the fact that bold upper Sigma 22 is symmetric with constant diagonal upper C Subscript z Baseline left-parenthesis 0 right-parenthesis that is larger than all off-diagonal elements. The SINGULAR= option pertains to this algorithm. The value specified for the SINGULAR= option is scaled by upper C Subscript z Baseline left-parenthesis 0 right-parenthesis before comparison with the pivot element.

Memory Usage

For conditional simulations, the largest matrix held in core memory at any one time depends on the number of grid points and data points. Using the previous notation, the data-data covariance matrix bold upper C 22 is n times n, where n is the number of nonmissing observations for the VAR= variable in the DATA= data set. The grid-data cross covariance bold upper C 12 is n times k, where k is the number of grid points. The grid-grid covariance bold upper C 11 is k times k. The maximum memory required at any one time for storing these matrices is

max left-parenthesis k left-parenthesis k plus 1 right-parenthesis comma n left-parenthesis n plus 1 right-parenthesis plus 2 left-parenthesis n times k right-parenthesis right-parenthesis times sizeof left-parenthesis double right-parenthesis

There are additional memory requirements that add to the total memory usage, but usually these matrix calculations dominate, especially when the number of grid points is large.

Last updated: December 09, 2022