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THE INLFIT PACKAGE
This subdirectory contains the routines of the interactive non-linear
least squares fitting package INLFIT. This package is layered on the NLFIT
package in MATH. NLFIT uses the Levenberg-Marquardt method 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 process, a fitting tolerance, and the maximum
number of iterations.
The entry points into the INLFIT package are listed below.
ininit - Initialize the fitting routines
inget - Get the value of an INLFIT parameter
input - Store the value of an INLFIT parameter
ingkey - Get the value of an INLFIT graphics/axis parameter
inpkey - Store the value of an INLFIT graphics/axis parameter
infit - Fit the function non-interactively
ingfit - Fit the function interactively
inerrors - Compute the errors of the fit
infree - Free memory allocated by ininit
The calling sequences for the above routines are listed below. The [iprd]
stand for integer, pointer, real and double precision versions of each
routine respectively. [str] stands for string.
in_init[rd] (in, address(func), address(dfunc), param, dparam,
nparams, plist, nfparams)
[irdp]val = in_get[irdp] (in, param)
in_gstr (in, params, str, maxch)
in_put[irdp] (in, param, val)
in_pstr (in, param, str)
in_gkey (in, key, axis, type, varnum)
in_pkey (in, key, axis, type, varnum)
in_fit[rd] (in, nl, x, y, wts, npts, nvars, wtflag, stat)
ing_fit[rd] (in, gp, cursor, gt, nl, x, y, wts, names, npts,
nvars, len_names, wtflag, stat)
in_errors[rd] (in, nl, x, y, wts, npts, nvars, variance,
chisqr, scatter, rms, errors)
in_free[rd] (in)
The user supplied functions fnc and dfnc have the following calling
sequences.
fnc (x, nvars, nparams, nparams, zfit)
dfnc (x, nvars, params, dparams, nparams, zfit, derivs)
The addresses of the user supplied functions can be obtained with a call
to locpr as follows.
address = locpr (fnc)
The user definition for the INLFIT package can be found in the file
lib$pkg/inlfit.h and can be made available to user applications programs
with the statement "include <pkg/inlfit.h>".
The permitted values for the param argument are the following.
# Integer valued parameters (in_geti, in_puti)
define INLFUNCTION # Fitting function
define INLDERIVATIVE # Fitting function derivatives
define INLNPARAMS # Total number of parameters
define INLNFPARAMS # Number of fitting parameters
define INLNVARS # Number of variables
define INLNPTS # Number of variables
define INLMAXITER # Max. number of iterations
define INLNREJECT # Number of rejection iterations
define INLNREJPTS # Number of rejected points
define INLUAXES # User plot function
define INLUCOLON # User colon function
define INLUFIT # User fit function
define INLOVERPLOT # Overplot next plot ?
define INLPLOTFIT # Overplot fit ?
define INLFITERROR # Error fit code
define INLGKEY # Graph key
# Real/double valued parameters (in_get[rd], in_put[rd])
define INLTOLERANCE # Tolerance of convergence
define INLLOW # Low rejection value
define INLHIGH # High rejection value
define INLGROW # Rejection growing radius
# Pointer valued parameters (in_getp, in_getp)
define INLNL # NLFIT descriptor
define INLPARAM # Parameter vector
define INLDPARAM # Parameter change vector
define INLPLIST # Parameter list
define INLREJPTS # Rejected points
define INLXMIN # Minimum value for curve
define INLXMAX # Maximum value for curve
define INLSFLOAT # Floating point substructure
define INLSGAXES # Graphics substructure
# String valued parameters (in_gstr, in_pstr)
define INLLABELS # standard axis labels
define INLUNITS # standard axis units
define INLFLABELS # Function labels
define INLFUNITS # Function units
define INLPLABELS # Parameter labels
define INLPUNITS # Parameter units
define INLVLABELS # Variable labels
define INLVUNITS # Variable units
define INLUSERLABELS # User plot labels
define INLUSERUNITS # User plot units
define INLHELP # Help file name
define INLPROMPT # Help prompt
The permitted values for the key argument are the following.
# in_gkey, in_pkey
define KEY_FUNCTION # Function
define KEY_FIT # Fit
define KEY_RESIDUALS # Residuals
define KEY_RATIO # Ratio
define KEY_NONLINEAR # Non-linear part
define KEY_VARIABLE # Variable (user or default)
define KEY_UAXIS # User plot function
define KEY_MIN # Min. key type
define KEY_MAX # Max. key type
The permitted values for the axis argument are the following.
# in_gkey, in_pkey
define INLXAXIS # X axis
define INLYAXIS # Y axis
The permitted values of the weights flag argument wtflag input to
in_fit[rd] or in_gfit[rd], and the stat argument returned by in_fit[rd]
or in_gfit[rd] are defined in lib$math/nlfit.h. They can be included in
the user's application with the statement "include <math/nlfit.h>".
The values are listed below.
# Permitted values for wtflag
define WTS_USER # User supplied weights
define WTS_UNIFORM # Uniform weighting
define WTS_CHISQ # Chi-squared weighting
define WTS_SCATTER # Weights include computed scatter term
# Permitted values for stat
define DONE # Solution converged
define SINGULAR # Singular solution
define NO_DEG_FREEDOM # Too few points
define NOT_DONE # Solution did not converge.
Note the pointer to the NLFIT structure nl is returned by the in_fit[rd]
and in_gfit[rd] routines and input to the in_errors[rd] routine. This
pointer must be freed separately with a call to nl_free when the fitting
process terminates.
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