#======================================================================
#                    . L M F I T . N O R M A L 
#                    doc: Wed Feb 24 09:40:06 1999
#                    dlm: Fri Jul 28 13:35:24 2006
#                    (c) 1999 A.M. Thurnherr
#                    uE-Info: 34 51 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

# check if a given distribution is normal
# NB:
#	- fitting is based on gauss curve fitting [.lmfit.gauss]
#	- heuristics are taken from there and scaled for the normal
#	  parameter choices
#	- simplified, e.g. y-shift is removed (does not make sense for
#	  distribution)
#	- added chi^2 significance testing to &modelCleanup() on -x

# HISTORY:
#	Oct 04, 1999: - created from [.lmfit.gauss]
#	Oct 05, 1999: - added chi^2 significance test
#				  - removed -y
#				  - improved heuristics
#   Mar 17, 2001: - param->arg
#	Jul 28, 2006: - Version 3.3 [HISTORY]; &isnan()

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# 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 = "x";
$modelOptsUsage = "[-x chi^2 test]";
$modelMinArgs = 0;
$modelArgsUsage = "[area guess [mean guess [sigma guess]]]";
$modelNFit = 3;			
$nameA[1] = "area";
$nameA[2] = "mean";		
$nameA[3] = "sigma";	

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# &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()
{
	$A[1] = nan; $A[2] = nan; $A[3] = nan;				# usage
	$A[1] = &antsFloatArg() if ($#ARGV >= 0 && ! -r $ARGV[0]);
	$A[2] = &antsFloatArg() if ($#ARGV >= 0 && ! -r $ARGV[0]);
	$A[3] = &antsFloatArg() if ($#ARGV >= 0 && ! -r $ARGV[0]);
	&antsUsageError() unless ($#ARGV < 0 || -r $ARGV[0]);
}

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# &modelInit()		initializes model after reading of data
#
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

sub modelInit()
{
	my($i,$j,$ymin,$ymax,$xatymax);

#	--------------------------------------------------
#	heuristics for initial model param values
#	--------------------------------------------------

	$ymin = 1e33, $ymax = -1e33, $xatymax = 0;
	for ($i=0; $i<=$#ants_; $i++) {
		next if ($antsFlagged[$i]);
		$ymin = $ants_[$i][$yfnr]
			if ($ants_[$i][$yfnr] < $ymin);
		$ymax = $ants_[$i][$yfnr], $xatymax = $ants_[$i][$xfnr]
			if ($ants_[$i][$yfnr] > $ymax);
	}
	$A[1] = $ymax - $ymin if isnan($A[1]);			# peak guess
	$A[2] = $xatymax if isnan($A[2]);				# mean guess
	if (isnan($A[3])) {								# e-scale guess
		for ($i=1;
			 $i<=$#ants_ && !$antsFlagged[$i]
						 && $ants_[$i][$yfnr]-$ymin<0.36*$A[1];
			 $i++) {}
		for ($j=$#ants_;
			 $j>=1 && !$antsFlagged[$i]
				   && $ants_[$j][$yfnr]-$ymin < 0.36*$A[1];
			 $j--) {}
		$A[3] = abs($ants_[$i][$xfnr]-$ants_[$j][$xfnr]) / 2.0;
		if ($A[3] == 0.0) {
			&antsInfo("$model: sigma heuristic failed (set to 1)!");
			$A[3] = 1.0;
	    }
	}

	$A[1] *= 1.77 * $A[3]							# gauss -> normal
		unless (isnan($A[1]) || isnan($A[3]));
	$A[3] *= 0.71 unless isnan($A[3]);
}

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# &modelEvaluate(x,A,dyda)	evaluate Normal distribution curve at x
#		x					x value (NOT xfnr)
#		A					reference to @A
#		dyda				reference to array for partial derivatives
#							(wrt individual params in @A)
#		<ret val>			y value
#
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

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

	my($peak) = $AR->[1] / (2.506628274631 * $AR->[3]);
	my($dx  ) = $x - $AR->[2];
	my($sig2) = $AR->[3] * $AR->[3];
	my($expo) = exp(-$dx*$dx/(2*$sig2));
	my($norm) = $peak * $expo;

	if (defined($dydaR)) {
		$dydaR->[1] = $norm / $AR->[1];
		$dydaR->[2] = $norm * $dx / $sig2;
	    $dydaR->[3] = $norm/$AR->[3] * ($dx*$dx/$sig2 - 1);
	}

	return $norm;
}

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

sub modelCleanup()
{
	return unless ($opt_x);

	require "$ANTS/libfuns.pl";
	my($chisq) = 0;
	my($nval,$prob,$sign);

	for ($i=0; $i<=$#ants_; $i++) {
		next if ($antsFlagged[$i]);
#		next if ($ants_[$i][$yfnr] <= 1);	# IGNORE TAIL HEURISTICS
		$nval = &modelEvaluate($ants_[$i][$xfnr],\@A);
		$chisq += ($ants_[$i][$yfnr] - $nval)**2 / $nval;
	}
	$prob = &gammq(($ndata-3)/2,$chisq/2);
	$sign = int($prob*100);
	&antsInfo("$model: normal-distr. hypothesis disproved at $sign%% sign. level");
}