#======================================================================
#                    . L M F I T . S Q R T 
#                    doc: Fri Oct 10 15:50:42 2014
#                    dlm: Sat Oct 11 09:30:48 2014
#                    (c) 2014 A.M. Thurnherr
#                    uE-Info: 27 32 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 square root A[1]*sqrt(x) to data
#
# NOTES:
#	- initial parameter estimates may be important
#	- there is currently no heuristics

# HISTORY:
#	Oct 10, 2014: - created from [.lmfit.exp]
#	Oct 11, 2014: - made it work

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# 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 = "[scale guess]";
$modelNFit = 1;
$nameA[1] = "scale";

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# &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; 			
	$A[1] = &antsFloatArg() if ($#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]));		# scale
}

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# &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[1]*sqrt(*x)
{										
	my($x,$AR,$dydaR) = @_;
	my($v) = sqrt($x);

	$dydaR->[1] = $v;					# dy/dA[1] = sqrt(x)
	return $AR->[1]*$v;
}

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

sub modelCleanup()
{
}