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231. NEPROP: Subroutines for Numerical Propagation of
Uncertainties
by Ralph D. Nelson, Jr., and Mark R. Ellenberger, Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506 Several years ago, National Standards Reference Data System called for a computer system which could (1) read and store a number and its uncertainty, (2) permit the user to alter the uncertainty, (3) carry the uncertainties through to the results of the calculations, (4) deliver a number whose length is consistent with its uncertainty, and (5) deliver, on demand, the uncertainty of the computer result. In response to this need, this package of programs was developed to propagate the uncertainties and round the output to the proper number of places. It will also check on the validity of the assumptions used in the propagation process and find "weak links" in the experiment whose results are being computed. The package is based on a multivariate Taylor expansion which employs Stirling's method to compute partial derivatives and produces the statistical moments for the computed results. The major requirements for the use of NEPROP are that the uncertainties be essentially random in character and that they not be coupled. A mode flag 10, resettable at any time during a run, allows the user to select any one of four modes of operation. In mode 1, NEPROP propagates uncertainties and rounds the output. In mode 2, the contributions of each of the input parameters to the total uncertainty is printed out, validity checks are made on the numerical methods involved, and the output is rounded. In mode 3, uncertainties are propagated, but there is no roundoff; and in mode 4, neither uncertainty nor roundoff is done. The Monte Carlo and algebraic-root mean-square methods serve well for simple tests for many runs using the same program. They are not so easily generalized into subroutines, nor can the validity checks and partial contributions be so easily put in and removed as with NEPROP. FORTRAN IV (IBM 360) Lines of Code: 367 Recommended Citation:R. D. Nelson and M. R. Ellenberger, QCPE 11, 231 (1973). |