|o||A good guess improves the probability of convergence and the quality of the fit.|
|o||Increasing the number of free parameters decreases the quality and convergence speed.|
|o||Make sure that there are no correlated parameters such as in a + b * e^(c+x). (The example can be rewritten as a + b * e^c * e^x in which c and b are basically equivalent parameters.|
The formula should be a string that can be parsed by Math::Symbolic.
Alternatively, it can be an existing Math::Symbolic tree.
Please refer to the documentation of that module for the syntax.
Evaluation of the formula for a specific value of the variable (X-Data) and the parameters (see below) should yield the associated Y-Data value in case of perfect fit.
|variable||The variable is the variable in the formula that will be replaced with the X-Data points for evaluation. If omitted in the call to curve_fit, the name x is default. (Hence xdata.)|
The parameters are the symbols in the formula whose value is varied by the
algorithm to find the best fit of the curve to the data. There may be
one or more parameters, but please keep in mind that the number of parameters
not only increases processing time, but also decreases the quality of the fit.
The value of this options should be an anonymous array. This array should hold one anonymous array for each parameter. That array should hold (in order) a parameter name, an initial guess, and optionally an accuracy measure.
The accuracy measure means that if the change of parameters from one iteration to the next is below each accuracy measure for each parameter, convergence is assumed and the algorithm stops iterating.
In order to prevent looping forever, you are strongly encouraged to make use of the accuracy measure (see also: maximum_iterations).
|xdata||This should be an array reference to an array holding the data for the variable of the function. (Which defaults to x.)|
|ydata||This should be an array reference to an array holding the function values corresponding to the x-values in xdata.|
|maximum_iterations||Optional parameter to make the process stop after a given number of iterations. Using the accuracy measure and this option together is encouraged to prevent the algorithm from going into an endless loop in some cases.|
None by default, but you may choose to export curve_fit using the standard Exporter semantics.
This is a list of public subroutines
curve_fit This subroutine implements the curve fitting as explained in DESCRIPTION above.
o When computing the derivative symbolically using Math::Symbolic, the formula simplification algorithm can sometimes fail to find the equivalent of (x-x_0)/(x-x_0). Typically, these would be hidden in a more complex product. The effect is that for x -> x_0, the evaluation of the derivative becomes undefined.
Since version 1.05, we fall back to numeric differentiation using five-point stencil in such cases. This should help with one of the primary complaints about the reliability of the module.
o This module is NOT fast. For slightly better performance, the formulas are compiled to Perl code if possible.
The algorithm implemented in this module was taken from:
Eric W. Weisstein. Nonlinear Least Squares Fitting. From MathWorldA Wolfram Web Resource. http://mathworld.wolfram.com/NonlinearLeastSquaresFitting.html
New versions of this module can be found on http://steffen-mueller.net or CPAN.
Steffen Mueller, <email@example.com<gt>
Copyright (C) 2005-2010 by Steffen Mueller
This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.6 or, at your option, any later version of Perl 5 you may have available.
|perl v5.20.3||ALGORITHM::CURVEFIT (3)||2016-03-17|