Nonlinear Least Squares Fitting

'Algorithm::CurveFit' implements a nonlinear least squares curve fitting algorithm. That means, it fits a curve of known form (sine-like, exponential, polynomial of degree n, etc.) to a given set of data points. For details about the algorithm and its capabilities and flaws, you're encouraged to read the MathWorld page referenced below. Note, however, that it is an iterative algorithm that improves the fit with each iteration until it converges. The following rule of thumb usually holds true: The curve fitting algorithm is accessed via the 'curve_fit' subroutine. It requires the following parameters as 'key => value' pairs: * formula 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'.) * params 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. Example: $params = [ ['parameter1', 5, 0.00001], ['parameter2', 12, 0.0001 ], ... ]; Then later: curve_fit( ... params => $params, ... ); 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). The final set of parameters is *not* returned from the subroutine but the parameters are modified in-place. That means the original data structure will hold the best estimate of the parameters. * 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. The subroutine returns the sum of square residuals after the final iteration as a measure for the quality of the fit.

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