#======================================================================
#                    . L M F I T . E X P 
#                    doc: Wed Feb 24 09:40:06 1999
#                    dlm: Fri Jul 28 13:40:56 2006
#                    (c) 1999 A.M. Thurnherr
#                    uE-Info: 30 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 exponential A[3]+A[2]*exp(A[1]*x) to data
#
# NOTES:
#	- initial parameter estimates are crucial
#	- there is currently no heuristics

# HISTORY:
#	Mar 11, 1999: - created from [./.mfit.poly] & [./.mfit.gauss]
#	Jul 31, 1999: - typecheck usage
#   Mar 17, 2001: - param->arg
#	Jan 16, 2006: - added notes
#	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 = "";
$modelOptsUsage = "";
$modelMinArgs = 0;
$modelArgsUsage = "[exp [mul [add guess]]]";
$modelNFit = 3;
$nameA[1] = "exp";
$nameA[2] = "mul";		
$nameA[3] = "add";	

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# &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()
{
	$A[1] = 1 unless (numberp($A[1]));
	$A[2] = 1 unless (numberp($A[2]));
	$A[3] = 0 unless (numberp($A[3]));
}

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# &modelEvaluate(x,A,dyda)	evaluate polynom 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($$$)					# y = A[3]+A[2]*exp(A[1]*x)
{
	my($x,$AR,$dydaR) = @_;
	my($e) = exp($AR->[1]*$x);

	$dydaR->[1] = $AR->[2]*$x*$e;
	$dydaR->[2] = $e;
	$dydaR->[3] = 1;					# partial derivatives

	return $AR->[3] + $AR->[2]*$e;
}

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

sub modelCleanup()
{
}