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

#                    S V D C M P . P L 

#                    doc: Sun Aug  1 09:51:37 1999

#                    dlm: Wed Mar 11 16:54:26 2015

#                    (c) 1999 A.M. Thurnherr

#                    uE-Info: 188 1 NIL 0 0 72 10 2 4 NIL ofnI

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

# SVDCMP routine from Numerical Recipes adapted to ANTS

# HISTORY:

#	Aug 01, 1999: - manually converted from c-source

#	Jul 19, 2001: - done *something* (message only?)

#	Mar 11, 2015: - picked up this never-used code because of need to fit circles

# Notes:

#   - everything passed as refs

require "$ANTS/nrutil.pl";

require "$ANTS/pythag.pl";

use strict;

sub svdcmp($$$)

{	

	my($aR,$wR,$vR) = @_;							# params

	my($flag,$i,$its,$j,$jj,$k,$l,$nm);				# int 

	my($anorm,$c,$f,$g,$h,$s,$scale,$x,$y,$z);		# float

	my(@rv1);										# float[]

	vector(\@rv1,1,$#{$vR});

	$g = $scale = $anorm = 0;

	for ($i=1; $i<=$#{$vR}; $i++) {

		$l = $i+1;

		$rv1[$i] = $scale*$g;

		$g = $s = $scale = 0;

		if ($i <= $#{$aR}) {

			for ($k=$i; $k<=$#{$aR}; $k++) {

				$scale += abs($aR->[$k][$i]);

			}

			if ($scale) {

				for ($k=$i; $k<=$#{$aR}; $k++) {

					$aR->[$k][$i] /= $scale;

					$s += $aR->[$k][$i]*$aR->[$k][$i];

				}

				$f = $aR->[$i][$i];

				$g = -&SIGN(sqrt($s),$f);

				$h = $f*$g-$s;

				$aR->[$i][$i] = $f-$g;

				for ($j=$l; $j<=$#{$vR}; $j++) {

					for ($s=0,$k=$i; $k<=$#{$aR}; $k++) {

						$s += $aR->[$k][$i]*$aR->[$k][$j];

					}

					$f = $s/$h;

					for ($k=$i; $k<=$#{$aR}; $k++) {

						$aR->[$k][$j] += $f*$aR->[$k][$i];

					}

				}

				for ($k=$i; $k<=$#{$aR}; $k++) {

					$aR->[$k][$i] *= $scale;

				}

			}

		}

		$wR->[$i] = $scale * $g;

		$g = 0; $s = 0; $scale = 0;

		if ($i <= $#{$aR} && $i != $#{$vR}) {

			for ($k=$l; $k<=$#{$vR}; $k++) {

				$scale += abs($aR->[$i][$k]);

			}

			if ($scale) {

				for ($k=$l; $k<=$#{$vR}; $k++) {

					$aR->[$i][$k] /= $scale;

					$s += $aR->[$i][$k]*$aR->[$i][$k];

				}

				$f = $aR->[$i][$l];

				$g = -&SIGN(sqrt($s),$f);

				$h = $f*$g-$s;

				$aR->[$i][$l] = $f-$g;

				for ($k=$l; $k<=$#{$vR}; $k++) {

					$rv1[$k] = $aR->[$i][$k]/$h;

				}

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

					for ($s=0,$k=$l; $k<=$#{$vR}; $k++) {

						$s += $aR->[$j][$k]*$aR->[$i][$k];

					}

					for ($k=$l; $k<=$#{$vR}; $k++) {

						$aR->[$j][$k] += $s*$rv1[$k];

					}

				}

				for ($k=$l; $k<=$#{$vR}; $k++) {

					$aR->[$i][$k] *= $scale;

				}

			}

		}

		$anorm = MAX($anorm,(abs($wR->[$i])+abs($rv1[$i])));

	}

	for ($i=$#{$vR}; $i>=1; $i--) {

		if ($i < $#{$vR}) {

			if ($g) {

				for ($j=$l; $j<=$#{$vR}; $j++) {

					$vR->[$j][$i] = ($aR->[$i][$j]/$aR->[$i][$l])/$g;

				}

				for ($j=$l; $j<=$#{$vR}; $j++) {

					for ($s=0,$k=$l; $k<=$#{$vR}; $k++) {

						$s += $aR->[$i][$k]*$vR->[$k][$j];

					}

					for ($k=$l; $k<=$#{$vR}; $k++) {

						$vR->[$k][$j] += $s*$vR->[$k][$i];

					}

				}

			}

			for ($j=$l; $j<=$#{$vR}; $j++) {

				$vR->[$i][$j] = 0; $vR->[$j][$i] = 0;

			}

		}

		$vR->[$i][$i] = 1;

		$g = $rv1[$i];

		$l = $i;

	}

	for ($i=MIN($#{$aR},$#{$vR}); $i>=1; $i--) {

		$l = $i+1;

		$g = $wR->[$i];

		for ($j=$l; $j<=$#{$vR}; $j++) {

			$aR->[$i][$j] = 0;

		}

		if ($g) {

			$g = 1/$g;

			for ($j=$l; $j<=$#{$vR}; $j++) {

				for ($s=0,$k=$l; $k<=$#{$aR}; $k++) {

					$s += $aR->[$k][$i]*$aR->[$k][$j];

				}

				$f = ($s/$aR->[$i][$i])*$g;

				for ($k=$i; $k<=$#{$aR}; $k++) {

					$aR->[$k][$j] += $f*$aR->[$k][$i];

				}

			}

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

				$aR->[$j][$i] *= $g;

			}

		} else {

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

				$aR->[$j][$i] = 0;

			}

		}

		++$aR->[$i][$i];

	}

	for ($k=$#{$vR}; $k>=1; $k--) {

		for ($its=1; $its<=30; $its++) {

			$flag = 1;

			for ($l=$k; $l>=1; $l--) {

				$nm = $l-1;

				if ((abs($rv1[$l])+$anorm) == $anorm) {

					$flag = 0;

					last;

				}

				last if ($nm == 0) || ((abs($wR->[$nm])+$anorm) == $anorm);	## $nm == 0 test not in original code

			}

			if ($flag) {

				$c = 0;

				$s = 1;

				for ($i=$l; $i<=$k; $i++) {

					$f = $s*$rv1[$i];

					$rv1[$i] = $c*$rv1[$i];

					last if ((abs($f)+$anorm) == $anorm);

					$g = $wR->[$i];

					$h = &pythag($f,$g);

					$wR->[$i] = $h;

					$h = 1/$h;

					$c = $g*$h;

					$s = -$f*$h;

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

						$y = $aR->[$j][$nm];

						$z = $aR->[$j][$i];

						$aR->[$j][$nm] = $y*$c+$z*$s;

						$aR->[$j][$i] = $z*$c-$y*$s;

					}

				}

			}

			$z = $wR->[$k];

			if ($l == $k) {

				if ($z < 0) {

					$wR->[$k] = -$z;

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

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

					}

				}

#				print(STDERR "its($k) = $its\n");

				last;

			}

			croak("no convergence in 30 svdcmp iterations\n") if ($its == 30);

			$x = $wR->[$l];

			$nm = $k-1;

			$y = $wR->[$nm];

			$g = $rv1[$nm];

			$h = $rv1[$k];

			$f = (($y-$z)*($y+$z)+($g-$h)*($g+$h))/(2.0*$h*$y);

			$g = &pythag($f,1);

			$f = (($x-$z)*($x+$z)+$h*(($y/($f+&SIGN($g,$f)))-$h))/$x;

			$c = 1; $s = 1;

			for ($j=$l; $j<=$nm; $j++) {

				$i = $j+1;

				$g = $rv1[$i];

				$y = $wR->[$i];

				$h = $s*$g;

				$g = $c*$g;

				$z = &pythag($f,$h);

				$rv1[$j] = $z;

				$c = $f/$z;

				$s = $h/$z;

				$f = $x*$c+$g*$s;

				$g = $g*$c-$x*$s;

				$h = $y*$s;

				$y *= $c;

				for ($jj=1; $jj<=$#{$vR}; $jj++) {

					$x = $vR->[$jj][$j];

					$z = $vR->[$jj][$i];

					$vR->[$jj][$j] = $x*$c+$z*$s;

					$vR->[$jj][$i] = $z*$c-$x*$s;

				}

				$z = &pythag($f,$h);

				$wR->[$j] = $z;

				if ($z) {

					$z = 1/$z;

					$c = $f*$z;

					$s = $h*$z;

				}

				$f = $c*$g+$s*$y;

				$x = $c*$y-$s*$g;

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

					$y = $aR->[$jj][$j];

					$z = $aR->[$jj][$i];

					$aR->[$jj][$j] = $y*$c+$z*$s;

					$aR->[$jj][$i] = $z*$c-$y*$s;

				}

			}

			$rv1[$l] = 0;

			$rv1[$k] = $f;

			$wR->[$k] = $x;

		}

	}

}