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Manuscript Title: MINUIT: a system for function minimization and analysis of the parameter errors and correlations.
Authors: F. James, M. Roos
Program title: MINUIT
Catalogue identifier: ACWH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 10(1975)343
Programming language: Fortran.
Computer: CDC 7600.
Operating system: SCOPE 2.1.2 OR 2.0.
RAM: 12K words
Word size: 60
Keywords: General purpose, Minimization, Fitting, Error analysis, Correlation, Simplex method, Variable metric method, Global minimum, Contours.
Classification: 4.9.

Revision history:
Type Tit le Reference
correction 000ACORRECTION 17/02/77 See below

Nature of problem:
The final stages of the analysis of experimental data often consists of determining(estimating)a certain number of physical parameters and establishing the errors (confidence regions) of these parameters. This in turn generally involves one or more stages of function minimization to determine the best parameter values and various techniques for investigating the shape of the function near the minimum to determine the errors. In this essentially statistical problem the function involved is usually a chisquare or negative log-likelihood function, however many other physical problems of a non-statistical nature, such as finding the minimum energy configuration of a molecule, can be treated using the same techniques.

Solution method:
We have chosen to offer the user a large number of different techniques which can be conveniently invoked by the use of command cards. For example, three different minimization algorithms are available (a Monte Carlo search, the simplex method of Nelder and Mead, and the variable metric method of Fletcher) and they may be "guided" by fixing and restoring variable parameters in between minimization commands, and by putting limits on the values allowed for different parameters. Similarly, error analysis may be carried out using the covariance matrix of the function, or by calculating exact MINOS confidence intervals, or by plotting function contours. If the function is suspected of having more than one local minimum, a global minimization can be attempted using a simplified version of the algorithm of Goldstein and Price.

The current version is dimensioned for a maximum of 30 function parameters, of which not more than 15 may be variable.

Unusual features:
MINUIT is not merely a minimization program, but is more properly a system for analysis of functions in the sense that its essential element is its structure rather than any of the algorithms that are actually implemented. This structure also allows in a very natural way the inclusion of global logic connecting the different algorithms, for example switching from one minimization method to another if the first does not converge rapidly enough.

Running time:
In most cases nearly all the actual running time is spent in the user- supplied subroutine FCN which is the function being analyzed by MINUIT. Typical applications usually require a few hundred or a few thousand function evaluations, which could in turn reqiure much less than a second or many minutes on the CDC 7600 depending on the complexity of FCN.

Manuscript Title: Unpublished correction to MINUIT: a system for function minimization and analysis of the parameter errors and correlations.
Authors: F. James, M. Roos
Program title: 000ACORRECTION 17/02/77
Catalogue identifier: ACWH_v1_0
Distribution format: gz
Classification: 4.9.