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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).
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