pdl::linfit(3) [redhat man page]

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 v5.8.0							    2000-12-06								 Linfit(3)

GRDTREND(l)															       GRDTREND(l)

NAME

       grdtrend - Fit and/or remove a polynomial trend in a grd file

SYNOPSIS

       grdtrend grdfile -Nn_model[r] [ -Ddiff.grd ] [ -Ttrend.grd ] [ -V ] [ -Wweight.grd ]

DESCRIPTION

       grdtrend  reads	a  2-D	gridded file and fits a low-order polynomial trend to these data by [optionally weighted] least-squares. The trend
       surface is defined by:

       m1 + m2*x + m3*y + m4*x*y + m5*x*x + m6*y*y + m7*x*x*x + m8*x*x*y + m9*x*y*y + m10*y*y*y.

       The user must specify -Nn_model, the number of model parameters to use; thus, -N4 fits a bilinear trend, -N6 a quadratic  surface,  and	so
       on.  Optionally, append r to the -N option to perform a robust fit. In this case, the program will iteratively reweight the data based on a
       robust scale estimate, in order to converge to a solution insensitive to outliers.  This may be handy when separating  a  "regional"  field
       from a "residual" which should have non-zero mean, such as a local mountain on a regional surface.

       If data file has values set to NaN, these will be ignored during fitting; if output files are written, these will also have NaN in the same
       locations.

       No space between the option flag and the associated arguments.

       grdfile
	      The name of a 2-D binary grd file.

       -N     [r]n_model sets the number of model parameters to fit. Prepend r for robust fit.

OPTIONS

       No space between the option flag and the associated arguments.

       -D     Write the difference (input data - trend) to the file diff.grd.

       -T     Write the fitted trend to the file trend.grd.

       -V     Selects verbose mode, which will send progress reports to stderr [Default runs "silently"].

       -W     If weight.grd exists, it will be read and used to solve a weighted least-squares problem. [Default: Ordinary least-squares fit.]	If
	      the robust option has been selected, the weights used in the robust fit will be written to weight.grd.

REMARKS

       The  domain  of	x  and	y  will be shifted and scaled to [-1, 1] and the basis functions are built from Legendre polynomials. These have a
       numerical advantage in the form of the matrix which must be inverted and allow more accurate solutions. NOTE: The model	parameters  listed
       with  -V are Legendre polynomial coefficients; they are not numerically equivalent to the m#s in the equation described above. The descrip-
       tion above is to allow the user to match -N with the order of the polynomial surface.

EXAMPLES

       To remove a planar trend from hawaii_topo.grd and write result in hawaii_residual.grd, try

       grdtrend hawaii_topo.grd -N3 -Dhawaii_residual.grd

       To do a robust  fit  of	a  bicubic  surface  to  hawaii_topo.grd,  writing  the  result  in  hawaii_trend.grd  and  the  weights  used	in
       hawaii_weight.grd, and reporting the progress, try

       grdtrend hawaii_topo.grd -Nr10 -Thawaii_trend.grd -Whawaii_weight.grd -V

SEE ALSO

       gmt(1gmt), grdfft(1gmt), grdfilter(1gmt)

								    1 Jan 2004							       GRDTREND(l)