110420     NONLIN: Nonlinear Least-Squares Curve Fitting Program
Version: October 1979
 
Author: Fred Wood, Standard Oil Company, Chicago, IL
 
Submitted by: David Zarnow, U.S. Naval Avionics Center, Indianapolis,
IN
 
Operating System: See note below  Source Language: See note below
Memory Required: 70K user partitioned  Keywords: Statistics
 
Abstract: This program allows the user to estimate the
coefficients of a nonlinear equation such as Y = A/(x
+ B)2 and Y = AxB = C_equations that are
nonlinear in the coefficients. An iterative technique is
used; the estimates at each iteration are obtained by
Marquardt's Maximum Neighborhood Method which combines
the Gauss (Taylor Series) Method and the Method of
Steepest Descent.
 
Since numerous forms of equations can be used, the user
must specify the form by providing a subroutine to
compute the values of the equation's coefficients. In
addition, the user must provide a control card, a format
card for reading data, and estimates of the starting
values of the coefficients.
 
The output of the program is a printed report which
includes a description of the problem, the starting
values of the coefficients, the size of the incremental
steps, a summary of each iteration, and a summary of the
final fit (in terms similar to those in the Linear
Least-Squares Curve Fitting Program, DECUS No. 11-419).
The statistics calculated include the number of
observations, the number of coefficients, the residual
degrees of freedom, the maximum and minimum value of the
dependent variable as well as its range, the standard
error and t-value for each coefficient, the residual sum
of squares, the residual mean square, and the residual
root mean square.
 
Provisions are made to run multiple programs as well as
different equations using the same data. The program as
dimensioned (70K) will handle up to 20 variables and 170
observations. Information is given in the program
listings on which dimensions to change in order to
reduce the overall dimensions or to increase either the
number of variables and/or the number of observations
which the program will handle.
 
Notes: Operating systems the program runs on are IAS V2.0+ with
support for PLAS
Directives, RSX-11M V3.0+.  Source language the program is written in
is
FORTRAN IV V2.04C or later with virtual array support.
 
Media (Service Charge Code): User's Manual (EA), 600' Magnetic Tape
(MA)  Format: FILES-11