Linfit(t)      User Contributed Perl Documentation      Linfit(t)



NAME
       PDL::Fit::Linfit - routines for fitting data with linear
       combinations of functions.

DESCRIPTION
       This module contains routines to perform general curve-
       fits to a set (linear combination) of specified functions.

       Given a set of Data:

         (y0, y1, y2, y3, y4, y5, ...ynoPoints-1)

       The fit routine tries to model y as:

         y' = beta0*x0 + beta1*x1 + ... beta_noCoefs*x_noCoefs

       Where x0, x1, ... x_noCoefs, is a set of functions
       (curves) that the are combined linearly using the beta
       coefs to yield an approximation of the input data.

       The Sum-Sq error is reduced to a minimum in this curve
       fit.

       Inputs:

       $data
        This is your data you are trying to fit. Size=n

       $functions
        2D array. size (n, noCoefs). Row 0 is the evaluation of
        function x0 at all the points in y. Row 1 is the evalua-
        tion of of function x1 at all the points in y, ... etc.

        Example of $functions array Structure:

        $data is a set of 10 points that we are trying to model
        using the linear combination of 3 functions.

         $functions = ( [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],  # Constant Term
                        [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ],  # Linear Slope Term
                        [ 0, 2, 4, 9, 16, 25, 36, 49, 64, 81] # quadradic term
                    )


SYNOPSIS
           $yfit = linfit1d $data, $funcs


FUNCTIONS
       linfit1d

       1D Fit linear combination of supplied functions to data
       using min chi^2 (least squares).

        Usage: ($yfit, [$coeffs]) = linfit1d [$xdata], $data, $fitFuncs, [Options...]

       Signature: (xdata(a); ydata(a); $fitFuncs(n,order);
       [o]yfit(t); [o]coeffs(s))

       Uses a standard matrix inversion method to do a least
       squares/min chi^2 fit to data.

       Returns the fitted data and optionally the coefficients.

       One can thread over extra dimensions to do multiple fits
       (except the order can not be threaded over - i.e. it must
       be one fixed set of fit functions "fitFuncs".

       The data is normalised internally to avoid overflows
       (using the mean of the abs value) which are common in
       large polynomial series but the returned fit, coeffs are
       in unnormalised units.

         # Generate data from a set of functions
         $xvalues = sequence(e);
         $data = 3*$xvalues + 2*cos($xvalues) + 3*sin($xvalues*2);

         # Make the fit Functions
         $fitFuncs = cat $xvalues, cos($xvalues), sin($xvalues*2);

         # Now fit the data, Coefs should be the coefs in the linear combination
         #   above: 3,2,3
         ($yfit, $coeffs) = linfit1d $data,$fitFuncs;

         Options:
            Weights    Weights to use in fit, e.g. 1/$sigma**2 (default=1)




perl v5.6.1                 2000-12-06                  Linfit(t)