RSICC CODE PACKAGE PSR-394

1. NAME AND TITLE

LHS: Code System to Generate Latin Hypercube & Random Samples.

2. CONTRIBUTOR

Sandia National Laboratories, Albuquerque, New Mexico.

3. CODING LANGUAGE AND COMPUTER

FORTRAN 77; DEC VAX8650; SUN SPARC60 (P00394SUN0500);

FORTRAN 77; PC (P00394/PC486/00).

4. NATURE OF PROBLEM SOLVED

LHS was written for the generation of multi variate samples either completely at random or by a constrained randomization termed Latin hypercube sampling (LHS). The generation of these samples is based on user-specified parameters which dictate the characteristics of the generated samples, such as type of sample (LHS or random), sample size, number of samples desired, correlation structure on input variables, and type of distribution specified on each variable. The following distributions are built into the program: normal, lognormal, uniform, loguniform, triangular, and beta. In addition, the samples from the uniform and loguniform distributions may be modified by changing the frequency of the sampling within subintervals, and a subroutine which can be modified by the user to generate samples from other distributions (including empirical data) is provided.

5. METHOD OF SOLUTION

The Latin hypercube technique employs a constrained sampling scheme, whereas random sampling corresponds to a simple Monte Carlo technique. The actual sampled values are used to form vectors of variables commonly used as input to computer models for sensitivity and uncertainty analyses studies.

6. RESTRICTIONS OR LIMITATIONS

Maxima of 1000 observations, 50 variables, 50 pairs of correlated variables, and 50 subintervals in the uniform and loguniform distributions. These restrictions are implemented through the FORTRAN 77 PARAMETER statement.

7. TYPICAL RUNNING TIME

Sample problems executed on the SUN ULTRASPARC 60 and the Pentium II 266 Mhz in less than 1 second.

8. COMPUTER HARDWARE REQUIREMENTS

VAX: 500,000 Kbytes virtual memory are required for execution.

PC 486: w/16 MB RAM

9. COMPUTER SOFTWARE REQUIREMENTS

VAX:VMS 4.3; VMS 4.5; SPARC: SUN OS 5.6; PC486:Windows 95/NT. The PC executable included in the package was created with Digital Visual Fortran 5.0.

10. REFERENCES

a) Included in the document:

R. L. Iman and M. J. Shortencarier, "A FORTRAN 77 Program and User's Guide for the Generation of Latin Hypercube and Random Samples for Use With Computer Models," NUREG/CR-3624 (SAND83-2365) (March 1984).

b) Background information:

R. L. Iman, J. M. Davenport, and D. K. Zeigler, "Latin Hypercube Sampling (Program User's Guide)," SAND79-1473 (January 1980).

11. CONTENTS OF CODE PACKAGE

Included are the referenced document in (10.a) and a 3.5" DOS diskette with a compressed UNIX tar file which contains source, sample input, and sample output files. The PC version includes an executable and is distributed in a DOS self-extracting compressed file.

12. DATE OF ABSTRACT

February 1999.

KEYWORD: RANDOM NUMBER GENERATOR