Algorithm::CurveFit Algorithm::CurveFit - Nonlinear Least Squares Fitting.
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Algorithm::CurveFit Tags

Perl module least Nonlinear Least Squares Fitting Nonlinear

Algorithm::CurveFit Description

Algorithm::CurveFit - Nonlinear Least Squares Fitting. Algorithm::CurveFit - Nonlinear Least Squares Fitting.SYNOPSISuse Algorithm::CurveFit; # Known form of the formula my $formula = 'c + a * x^2'; my $variable = 'x'; my @xdata = read_file('xdata'); # The data corresponsing to $variable my @ydata = read_file('ydata'); # The data on the other axis my @parameters = ( # Name Guess Accuracy , # If an iteration introduces smaller , # changes that the accuracy, end. ); my $max_iter = 100; # maximum iterations my $square_residual = Algorithm::CurveFit->curve_fit( formula => $formula, # may be a Math::Symbolic tree instead params => @parameters, variable => $variable, xdata => @xdata, ydata => @ydata, maximum_iterations => $max_iter, ); use Data::Dumper; print Dumper @parameters; # Prints # $VAR1 = , # # ]; # # Real values of the parameters (as demonstrated by noisy input data): # a = 0.2 # c = 2Algorithm::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:A good guess improves the probability of convergence and the quality of the fit.Increasing the number of free parameters decreases the quality and convergence speed.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 curve fitting algorithm is accessed via the 'curve_fit' subroutine. It requires the following parameters as 'key => value' pairs:formulaThe 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.variableThe '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'.)paramsThe 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 = , , ... ]; 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.xdataThis should be an array reference to an array holding the data for the variable of the function. (Which defaults to 'x'.)ydataThis should be an array reference to an array holding the function values corresponding to the x-values in 'xdata'.maximum_iterationsOptional 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.Requirements:· Perl Requirements: · Perl

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