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Manuscript Title: Users manual for the OPTIME system.
Authors: P.H. Eberhard, W.O. Koellner
Program title: OPTIME SYSTEM
Catalogue identifier: AAYB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 5(1973)163
Programming language: Fortran.
Computer: CDC 6600.
Operating system: BKY.
RAM: 60K words
Word size: 60
Peripherals: magnetic tape, disc.
Keywords: General purpose, Nuclear physics, High energy, Fitting, Maximum likelihood, Least squares, Maximization, Estimator, Likelihood function, Chi square function, Expectation value, Reference function, Gram-schmidt Orthonormalization, Error matrix, Histogram, Monte carlo Event generation, Preferred frequency Distribution, General experiment.
Classification: 4.9, 17.4.

Nature of problem:
The OPTIME System is an assembly of subroutines for fitting theoretical expressions to statistical distributions, especially those arising in particle physics. The system also provides for calculating error matrices, performing integrations, and making histograms.

Solution method:
The program adjusts parameters of the theoretical expression by using various estimators and maximization techniques combined with special stepping procedures, some of which use approximations for the second derivative matrix. The quality of the fit should be judged by analysis of the printout, inspection of the error matrix, and inspection of histograms of the data with the fitted curve superposed.

Restrictions:
This program is usable for functions with any number of variable parameters subject only to available core space and running time. The user function of parameters |a| and variable |x| (whose value is either the data point |xi|k or the integration point |x|l) must be proportional to the expectation value of the distribution of data points at |x| for the true values of |a|. When integration points in the fit have weights Omega l, Sigma Omega ly(|x|l,|a|) must approximate the integral of y. If the Monte Carlo event generator in the OPTIME System is used, Omega l reconstitutes phase space, and the function y(|x|,|a|) corresponds to the square of the matrix element.

Unusual features:
The program allows for experimental data points to be weighted, for example, to allow for detection efficiencies in particle physics. Since the standard OPTIME System allocates blank COMMON dynamically during execution, only a minimal amount of blank COMMON is declared initially. Once the variable parameters and buffer sizes are specified, the necessary blank COMMON is allocated by a call to a SUBROUTINE OPTIME which adjusts the field length. This is fesible on the CDC machine because blank COMMON is located at the high end of the user's block of core. To disable this scheme check in the subroutines IMME, RAME, STORME, and COCHIS how much blank COMMON is required in each case, declare the maximum amount initially in the main program, and replace standard SUBROUTINE OPTIME by
 SUBROUTINE OPTIME                                                       
 RETURN                                                                  
 END
or eliminate the calls to this subroutine.

Running time:
The typical running time for fitting a function of three linear variable parameters, using 500 experimental data points and 3000 Monte Carlo integration points, with convergence in one step, is about 76 s of CP- time on a CDC-6600. This includes 46 s of CP-time to compile the complete program.