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NAME
    Algorithm::CurveFit - Nonlinear Least Squares Fitting

SYNOPSIS
      use 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
          ['a',     0.9,    0.00001],  # If an iteration introduces smaller
          ['c',     20,     0.00005],  # 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 = [
      #          [
      #            'a',
      #            '0.201366784209602',
      #            '1e-05'
      #          ],
      #          [
      #            'c',
      #            '1.94690440147554',
      #            '5e-05'
      #          ]
      #        ];
      #
      # Real values of the parameters (as demonstrated by noisy input data):
      # a = 0.2
      # c = 2

DESCRIPTION
    "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:

    * 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:

    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