#======================================================================

#                    . 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()

{

}