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THE NLFIT PACKAGE
This subdirectory contains the routines in the non-linear least squares
fitting package NLFIT. NLFIT uses the Levenberg-Marquardt method to
to solve for the parameters of a user specified non-linear equation.
The user must supply two routines. The first routine evaluates the function
in terms of its parameters. The second routine evaluates the function and its
derivatives in terms of its parameters. The user must also supply initial
guesses for the parameters and parameter increments, the list of
parameters to be varied during the fitting processa, a fitting
tolerance and the maximum number of iterations.
The principal entry points into the NLFIT are listed below.
nlinit - Initialize the fitting routines
nlstati - Get the value of an integer NLFIT parameter
nlstat - Get the value of floating point NLFIT parameter
nlpget - Get the values of the fitted parameters
nlfree - Free memory allocated by nlinit
nlfit - Fit the function
nleval - Evaluate the curve at a given point
nlvector - Evaluate the curve at an array of points
nlerrors - Compute the fits statistics and errors in the parameters
The calling sequences for the above routines are listed below. The [ird]
stand for integer, real and double precision versions of each routine
respectively.
nlinit[rd] (nl, address(fnc), address(dfnc), params, dparams,
nparams, plist, nfparams, tol, itmax)
ival = nlstati (nl, param)
[rd]val = nlstat[rd] (nl, param)
nlpget[rd] (nl, params, nparams)
nlfree[rd] (nl)
nlfit[rd] (nl, x, z, w, npts, nvars, wtflag, ier)
[rd]val = nleval[rd] (nl, x, nvars)
nlvector[rd] (nl, x, zfit, npts, nvars)
nlerrors[rd] (nl, z, zfit, wts, npts, variance, chisqr, errors)
The user supplied functions fnc and dfnc have the following calling
sequences.
fnc (x, nvars, params, nparams, zfit)
dfnc (x, nvars, params, dparams, nparams, zfit, derivs)
The address of the user supplied function can be determined with a
call to locpr as in
address = locpr (fnc)
The user definitions for the NLFIT package can be found in the file
lib$math/nlfit.h and can be made available to user applications programs
with the statement "include <math/nlfit.h>".
The permitted values for the param argument in nlstat[ird] are the following.
define NLNPARAMS integer # Number of parameters
define NLNFPARAMS integer # Number of fitted parameters
define NLITMAX integer # Maximum number of iterations
define NLITER integer # Current number of iterations
define NLNPTS integer # Number of points
define NLSUMSQ real/double # Current reduced chi-squared
define NLOLDSQ real/double # Previous reduced chi-squared
define NLLAMBDA real/double # Value of lambda factor
define NLTOL real/double # Fitting tolerance in %chi-squared
define NLSCATTER real/double # Mean scatter in the fit
The permitted values of the wtflag argument in nlfit[rd] are the following.
define WTS_USER # User enters weights
define WTS_UNIFORM # Equal weights
define WTS_CHISQ # Chi-squared weights
define WTS_SCATTER # Weights include scatter term
The permitted error values returned from nlfit[rd] are the following.
define DONE 0 # Solution converged
define SINGULAR 1 # Singular matrix
define NO_DEG_FREEDOM 2 # Too few points
define NOT_DONE 3 # Solution did not converge
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