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Linfit(3)	      User Contributed Perl Documentation	     Linfit(3)

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 evaluation 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(n); ydata(n); $fitFuncs(n,order); [o]yfit(n); [o]coeffs(order))

       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(100);
	 $data = 3*$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 v5.32.1			  2018-05-05			     Linfit(3)

NAME | DESCRIPTION | SYNOPSIS | FUNCTIONS

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