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+#======================================================================
+# . 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");
+}