NESC1085 LHS-ESTSC.

1. NAME OR DESIGNATION OF PROGRAM:  LHS.

3. DESCRIPTION OF PROGRAM OR FUNCTION

LHS was written for the generation of multivariate 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 of 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.

4. 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.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Maxima of

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

6. TYPICAL RUNNING TIME

NESC executed each sample problem in 10 seconds on a DEC VAX11/785.

The test cases included in his package were executed by NEA-DB on a VAX-11/780 computer. The CPU times required were 57.3 seconds (case 1); 47.3 seconds (case 2).

7. UNUSUAL FEATURES OF THE PROGRAM

If the input correlation structure produces a correlation matrix that is not positive definite, a built-in iterative scheme attempts to adjust the input rank correlation matrix to make it positive definite.

8. RELATED AND AUXILIARY PROGRAMS

The present program replaces an earlier Latin hypercube sampling program developed at Sandia in 1980 by Iman, Davenport, and Zeigler. Subroutines from AMOSLIB were adapted for use in generating the beta distribution.

10. REFERENCES

- LHS, NESC No. 1085, LHS Tape Description,
  National Energy Software Center Note 87-100, September 21, 1987.
- R.L. Iman, J.M. Davenport, and D.K. Zeigler
  Latin Hypercube Sampling (Program User's Guide),
  SAND79-1473, January 1980.

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

11. MACHINE REQUIREMENTS

500,000 Kbytes of virtual memory are required for execution.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  VMS 4.3, 4.5.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

The LHS reference report contains information to assist in modifying the program for installation on other machines.

15. NAME AND ESTABLISHMENT OF AUTHORS

          R.L. Iman and M.J. Shortencarier
          Sandia National Laboratories, Albuquerque

File name	File description	Records
NESC1085_01.001	LHS Information file	96
NESC1085_01.002	LHS Source program	5499
NESC1085_01.003	LHS Sample problem n.1 Input data	22
NESC1085_01.004	LHS Sample problem n.2 Input data	24
NESC1085_01.005	LHS Sample problem n.1 Printed output	117
NESC1085_01.006	LHS Sample problem n.2 Printed output	71