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

#                    L F I T . P L 

#                    doc: Sat Jul 31 11:24:47 1999

#                    dlm: Mon May 18 10:07:47 2015

#                    (c) 1999 A.M. Thurnherr

#                    uE-Info: 20 61 NIL 0 0 72 2 2 4 NIL ofnI

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

# LFIT routine from Numerical Recipes adapted to ANTS

# HISTORY:

#	Jul 31, 1999: - manually converted from c-source

#	Aug 01, 1999: - changed funcs() interface

#	Sep 26, 1999: - made sure right version of covsrt is used

#	Jun 28, 2001: - re-added commented out code 'cause it's required

#					on some perl versions

#	Jan  5, 2012: - BUG: non-numeric x/y were not handled correctly;

#						 this was only easily apparent when the last

#						 record contained non-numeric values

#	May 18, 2015: - added firstRec, lastRec parameters (V6.1)

# Notes:

#   - x,y,sig are field numbers for data in $ants_

#	- funcs is passed the current index & xfnr instead of the x-value

#   - if sig is a negative number, -sig is used as constant input stddev

#   - @a, @ia, @covar, &funcs passed as refs

#	- chi square is returned

require "$ANTS/nrutil.pl";

require "$ANTS/covsrt.pl";

require "$ANTS/gaussj.pl";

sub lfit(@)

{

	my($xfnr,$yfnr,$sig,$aR,$iaR,$covarR,$funcsR,$firstRec,$lastRec) = @_;

	$firstRec = 0 unless defined($firstRec);

	$lastRec = $#ants_ unless defined($lastRec);

	my($i,$j,$k,$l,$m,$mfit);			# int

	my($ym,$wt,$sum,$sig2i,$chisq);		# float

	my(@beta,@afunc);					# float[]

	&matrix(\@beta,1,$#{$aR},1,1);

	&vector(\@afunc,1,$#{$aR});

	for ($j=1; $j<=$#{$aR}; $j++) {

		$mfit++ if ($iaR->[$j]);

	}

	croak("lfit: no parameters to be fitted") if ($mfit == 0);

	for ($j=1; $j<=$mfit; $j++) {		# REQUIRED FOR SOME PERL VERSIONS!!!

		for ($k=1;$ k<=$mfit; $k++) {

			$covarR->[$j][$k] = 0;

		}

		$beta[$j][1] = 0;

	}

	for ($i=$firstRec; $i<=$lastRec; $i++) {

		next if ($antsFlagged[$i]);

		next unless numberp($ants_[$i][$xfnr]) && numberp($ants_[$i][$yfnr]);

		&$funcsR($i,$xfnr,\@afunc);

		$ym = $ants_[$i][$yfnr];

		if ($mfit < $#{$aR}) {

			for ($j=1; $j<=$#{$aR}; $j++) {

				$ym -= $aR->[$j]*$afunc[$j] if (!$iaR->[$j]);

			}

		}

        if ($sig > 0) {                                 # field number

            $sig2i = 1.0/($ants_[$i][$sig]*$ants_[$i][$sig]);

        } else {                                        # const value

            $sig2i = 1.0/($sig*$sig);

        }

		for ($j=0,$l=1; $l<=$#{$aR}; $l++) {

			if ($iaR->[$l]) {

				$wt = $afunc[$l]*$sig2i;

				for ($j++,$k=0,$m=1; $m<=$l; $m++) {

					$covarR->[$j][++$k] += $wt*$afunc[$m] if ($iaR->[$m]);

				}

				$beta[$j][1] += $ym*$wt;

			}

		}

	}

	for ($j=2; $j<=$mfit; $j++) {

		for ($k=1;$k<$j;$k++) {

			$covarR->[$k][$j] = $covarR->[$j][$k];

#			print(STDERR "covarR[$k][$j] = $covarR->[$k][$j]\n");

		}

	}

	&gaussj($covarR,\@beta);

	for ($j=0,$l=1;$l<=$#{$aR};$l++) {

		$aR->[$l]=$beta[++$j][1] if ($iaR->[$l]);

	}

	for ($i=$firstRec; $i<=$lastRec; $i++) {

		next if ($antsFlagged[$i]);

		next unless numberp($ants_[$i][$xfnr]) && numberp($ants_[$i][$yfnr]);

		&$funcsR($i,$xfnr,\@afunc);

		for ($sum=0,$j=1; $j<=$#{$aR}; $j++) {

			$sum += $aR->[$j]*$afunc[$j];

		}

		my($tmpval) = ($sig > 0) ?

			($ants_[$i][$yfnr] - $sum) / $ants_[$i][$sig] :

			($ants_[$i][$yfnr] - $sum) / -$sig;

		$chisq += $tmpval * $tmpval;

	}

	&covsrt($covarR,$iaR);

	return $chisq;

}