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Manuscript Title: Constrained nonlinear least squares fitting.
Authors: R. Shally
Program title: CNFIT
Catalogue identifier: AAXQ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 46(1987)437
Programming language: Fortran.
Computer: IBM 3090-200.
Operating system: VM/CMS, VMS, SJE.
Word size: 32
Keywords: General purpose, Particle physics, Track fitting, Least squares, Fitting, Lagrange multipliers, Inversion matrix.
Classification: 4.9.

Nature of problem:
Many high energy physics experiments require fitting of particle tracks. In particular, one often has to (e.g. OPAL at LEP) fit a curve to a set of points (xi,yi,zi),i=1,...,N each of which is a function of two measured independent quantities.

Solution method:
The method of least squares for the directly measurable uncorrelated quantities is used and the theoretical model is taken into account via the method of Lagrange multipliers. The resulting nonlinear equations are linearized and most of them are solved explicitly by partitioning the matrix and inverting the largest submatrix analytically. The result gives the parameters of the fit together with the error matrix as well as the theoretical expectations of the measured quantities. This is a rigorous and efficient method of solving the problem.

Running time:
A fit of N=18 points requires 0.3 sec (on VAX) or 0.01 sec (on IBM). In general (on VAX) an approximate formula for larger N (between 30 and 180) is T= -7.77+0.14N - 0.0005N**2 + 0.000026N**3 seconds.