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

#                    . N M I N T E R P . S P L I N E 

#                    doc: Wed Nov 22 21:01:09 2000

#                    dlm: Fri Sep 23 16:52:31 2011

#                    (c) 2000 A.M. Thurnherr

#                    uE-Info: 19 50 NIL 0 0 72 2 2 4 NIL ofnI

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

# spline interpolation for [fillgaps]

# HISTORY:

#	Apr  3, 2006: - created from [.interp.spline]

#	Jul 28, 2006: - made to work

#	Jul 30, 2006: - added max-gap support

#				  - BUG: extended interpolation into last interval

#				  - BUG: assertions made it incompatible with decreasing data

#	Aug  8, 2008: - renamed

#	Sep 23, 2011: - removed $xv from interpolate() args

#				  - added error when xf<0 (%RECNO)

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

#

# THE FOLLOWING VARIABLES MUST BE SET GLOBALLY (i.e. during loading)

#

#	$ISOpts				string of allowed options

#	$ISOptsUsage		usage information string for options

#

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

$ISOpts = '';

$ISOptsUsage = '';

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

#

# &ISUsage() 	mangle parameters (options, really)

#

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

sub ISUsage() {}

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

#

# &ISInit(f,xf)				init interpolation of field f

#       f					field number

#		xf					x field number

#       <ret val>           none

#

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

my(@y2);

sub ISInit($$) {

	my($f,$xf) = @_;

	my($k,$i,$p,$qn,$sig,$un,@u);

	croak(".nminterp.spline: cannot use %RECNO as x-field (implementation restriction)\n")

		unless ($xf >= 0);

	my($pi,$ppi,$li);				# find idx of first 3 & last valid recs

	for (my($r)=0; $r<=$#ants_; $r++) {

		if (numberp($ants_[$r][$f])) {

			unless (defined($ppi)) {

				$ppi = $pi; $pi = $i; $i = $r;

			}

			$li = $r;

		}

	}

	unless (defined($ppi)) {

		&antsInfo("WARNING: not enough <$antsLayout[$f]> data for spline interpolation");

		return;

	}

	my($fpi) = $pi;

	$y2[$pi][$f] = $u[$pi] = 0;

	for (; $i<=$li; $i++) {

		next unless numberp($ants_[$i][$f]);

		$sig = ($ants_[$pi][$xf]-$ants_[$ppi][$xf]) /

				($ants_[$i][$xf]-$ants_[$ppi][$xf]);

		$p = $sig*$y2[$pi][$f] + 2;

		$y2[$i][$f] = ($sig-1)/$p;

		$u[$i] = ($ants_[$i][$f]-$ants_[$pi][$f]) /

					($ants_[$i][$xf]-$ants_[$pi][$xf])

						- ($ants_[$pi][$f]-$ants_[$ppi][$f]) /

							($ants_[$pi][$xf]-$ants_[$ppi][$xf]);

		$u[$i] = (6*$u[$i]/($ants_[$i][$xf]-$ants_[$ppi][$xf]) -

					$sig * $u[$pi]) / $p;

		$ppi = $pi; $pi = $i;

	}

	$qn = $un = 0;

	$y2[$li][$f] = ($un-$qn*$u[$pi]) / ($qn*$y2[$pi][$f]+1);

	my($pk) = $li;

	for ($k=$pi; $k>=$fpi; $k--) {

		next unless numberp($ants_[$k][$f]);

		$y2[$k][$f] = $y2[$k][$f] * $y2[$pk][$f] + $u[$k];

		$pk = $k;

	}

}

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

#

# &interpolate(xf,mg,f,lvr,cr)	interpolate field f

#		xf							x field

#		mg							max allowed x gap

#		f							field number to interpolate

#		lvr							last record with valid y val

#		cr							current record

#		<ret val>					interpolated value

#

# NB:

#	- handle f == xf

#	- return undef if interpolation cannot be carried out

#	- x VALUES MAY NOT BE MONOTONIC

#

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

sub interpolate($$$$$$)

{

	my($xf,$mg,$f,$lvr,$cr) = @_;

	return $ants_[$cr][$xf] if ($xf == $f);

	return $ants_[$lvr][$f]							# edge values are ok

		if equal($ants_[$cr][$xf],$ants_[$lvr][$xf]);

	my($nvr1) = $cr + 1;							# find next

	while ($nvr1 <= $#y2 && !numberp($y2[$nvr1][$f])) { $nvr1++; }

	return undef									# none or gap too large

		if ($nvr1>$#ants_ || abs($ants_[$nvr1][$xf]-$ants_[$lvr][$xf])>$mg);

	return $ants_[$nvr1][$f]						# edge values are ok

		if equal($ants_[$cr][$xf],$ants_[$nvr1][$xf]);

	my($nvr2) = $nvr1 + 1;

	while ($nvr2 <= $#y2 && !numberp($y2[$nvr2][$f])) { $nvr2++; }

	my($h) = $ants_[$nvr1][$xf] - $ants_[$lvr][$xf];

	my($a) = ($ants_[$nvr1][$xf] - $ants_[$cr][$xf]) / $h;

	my($b) = ($ants_[$cr][$xf] - $ants_[$lvr][$xf]) / $h;

	return $a*$ants_[$lvr][$f] + $b*$ants_[$nvr1][$f] +

			(($a*$a*$a-$a) * $y2[$nvr1][$f] +

			 ($b*$b*$b-$b) * $y2[$nvr2][$f]) *

			 	($h*$h)/6;

}

#----------------------------------------------------------------------

1;