#======================================================================
#                    . 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()
{
}