#======================================================================

#                    . L M F I T . P O L Y 

#                    doc: Wed Feb 24 09:40:06 1999

#                    dlm: Fri Jul 28 13:35:50 2006

#                    (c) 1999 A.M. Thurnherr

#                    uE-Info: 28 41 NIL 0 0 72 2 2 4 NIL ofnI

#======================================================================

# What you need to provide if you wanna fit a different

# model function to your data:

#	- a number of global variables to be set during loading

#	- a number of subs to perform admin tasks (usage, init, ...)

#	- a sub to evaluate the model function which is to be fitted using

#	  a number of pararams which are all stored in @A (beginning at

#	  A[1]!!!). You also need to return the partial derivatives of

#	  the model function wrt all params.

#	- the interface is documented between +++++++ lines

# fit polynomial (sum of A_i x^i) to data

# NB:

# HISTORY:

#	Feb 25, 1999: - created

#	Mar 14, 1999: - cosmetic changes

#	Jul 31, 1999: - argument typechecking

#   Mar 17, 2001: - param->arg

#	Jan 12, 2006: - specify order with -o as in [.lsfit.poly]

#	Jul 28, 2006: - Version 3.3 [HISTORY]

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

#

# THE FOLLOWING VARIABLES MUST BE SET GLOBALLY (i.e. during loading)

#

#	$modelOpts			string of allowed options

#	$modelOptsUsage		usage information string for options

#	$modelMinArgs		min # of arguments of model

#	$modelArgsUsage		usage information string for arguments

#

# The following variables may be set later but not after &modelInit()

#

#	$modelNFit			number of params to fit in model

#	@nameA				symbolic names of model parameters

#

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

$modelOpts = "o:";

$modelOptsUsage = "-o)rder <n>";

$modelMinArgs = 0;

$modelArgsUsage = "[c0 [c1 [...]]]";

&antsInfo("non-linear method deprecated; use `lsfit' instead");

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

#

# &modelUsage()		mangle parameters; NB: there may be `infinite' # of

#					filenames after model arguments; this usually sets

#					@A (the model parameters) but these can later be

#					calculated heuristically during &modelInit()

#

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

sub modelUsage()

{

	my($c);

	die("$0 (.lmfit.poly): ERROR! -o required\n")	# order of polynomial

		unless (defined($opt_o) && $opt_o >= 0);

	$modelNFit = &antsCardOpt($opt_o)+1;			

	for ($c=0; $c<$modelNFit; $c++) {				# init coefficients

		if ($#ARGV >= 0 && ! -r $ARGV[0]) {

			$A[$c+1] = &antsFloatArg();

		} else {

			$A[$c+1] = nan;

		}

		$nameA[$c+1] = "c$c";						# and names

	}

	&antsUsageError() unless ($#ARGV < 0 || -r $ARGV[0]);

}

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

#

# &modelInit()		initializes model after reading of data

#

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

sub modelInit()

{

	my($c);

	for ($c=0; $c<$modelNFit; $c++) {				# init coefficients

		$A[$c+1] = 10**-$c unless (numberp($A[$c+1]));

	}

}

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

#

# &modelEvaluate(x,A,dyda)	evaluate polynomial and derivatives

#		x					x value (NOT xfnr)

#		A					reference to @A

#		dyda				reference to array for partial derivatives

#							(wrt individaul params in @A)

#		<ret val>			y value

#

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

sub modelEvaluate($$$)

{

	my($x,$AR,$dydaR) = @_;

	my($i);

	my($pow) = 1;

	my($y) = 0;

	for ($i=1; $i<=$modelNFit; $i++) {

		$y += $AR->[$i]*$pow;

		$dydaR->[$i] = $pow;

		$pow *= $x;

	}

	return $y;

}

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

# &modelCleanup()	cleans up after fitting but before output

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

sub modelCleanup()

{

}