#------------------------------------------------------------------------------
#$Author: antanas $
#$Date: 2019-11-15 18:13:46 +0200 (Fri, 15 Nov 2019) $ 
#$Revision: 7412 $
#$URL: svn://www.crystallography.net/cod-tools/tags/v2.11/src/lib/perl5/COD/Cell/Niggli/KG76.pm $
#------------------------------------------------------------------------------
#*

# Implements cell reduction to a Niggli reduced cell using the Křivý
# & Gruber algorithm of 1976, as described in:

# Křivý, I. & Gruber, B. A unified algorithm for determining the
# reduced (Niggli) cell Acta Crystallographica Section A, 1976, 32,
# 297-298, http://dx.doi.org/10.1107/S0567739476000636

# with corrections and stability-increasing modifications from:

# Grosse-Kunstleve, R. W.; Sauter, N. K. & Adams, P. D. Numerically
# Stable Algorithms for the Computation of Reduced Unit Cells Acta
# Crystallographica. Section A, Foundations of Crystallography, 2004,
# 60, 1-6, http://dx.doi.org/10.1107/S010876730302186X

# To test, run in trunk/:

# PERL5LIB=src/lib/perl5/ perl -MCOD::Cell::Niggli::KG76 -e 'COD::Cell::Niggli::KG76::reduce(3,5.196,2,103+55/60,109+28/60,134+53/60)'

#**

package COD::Cell::Niggli::KG76;

use strict;
use warnings;
use COD::Spacegroups::Symop::Algebra qw( symop_mul );

require Exporter;
our @ISA = qw( Exporter );
our @EXPORT_OK = qw(
    reduce
);

my $PI = 4 * atan2(1,1);
my $EPSILON = 1E-2;

$COD::Cell::Niggli::KG76::debug = 1;

sub reduce
{
    my @cell = @_;

    my $eps = @cell > 6 ? pop(@cell) : $EPSILON;

    my ($a, $b, $c, $alpha, $beta, $gamma ) =
        (@cell[0..2], map { $PI * $_ / 180 }  @cell[3..5]);

    my ($ca, $cb, $cg) = map {cos} ($alpha, $beta, $gamma);

    my ($A, $B, $C, $ksi, $eta, $dzeta) =
        ( $a*$a, $b*$b, $c*$c, 2*$b*$c*$ca, 2*$a*$c*$cb, 2*$a*$b*$cg );

    # The Change-of-Basis matrix, initially unity:
    my $CoB = [ [1,0,0], [0,1,0], [0,0,1] ];

    local $, = " ";
    local $\ = "\n";

    my $max_n = 1000;
    my $n = 1;
    while(1) {
        if( ++$n > $max_n ) {
            die 'ERROR, reduce() subroutine could not reduce cell in '
              . "$max_n steps\n";
        }
        # 1.
        if( $A - $eps > $B or
            (abs($A-$B) < $eps && abs($ksi) - $eps > abs($eta)) ) {
            printf "%s  %6.2f %6.2f %6.2f %6.2f %6.2f %6.2f [[%s]]\n",
            "1.", $A, $B, $C, $ksi, $eta, $dzeta,
            join("], [", map {join(",", @$_)} @$CoB)
                if $COD::Cell::Niggli::KG76::debug;
            my $Cm = [ [0,-1,0], [-1,0,0], [0,0,-1] ];
            $CoB = symop_mul( $CoB, $Cm );
            my ($tmp1, $tmp2) = ($A, $ksi);
            ($A, $ksi) = ($B, $eta);
            ($B, $eta) = ($tmp1, $tmp2);
        }
        # 2.
        if( $B - $eps > $C or
            (abs($B-$C) < $eps && abs($eta) - $eps > abs($dzeta)) ) {
            printf "%s  %6.2f %6.2f %6.2f %6.2f %6.2f %6.2f [[%s]]\n",
            "2.", $A, $B, $C, $ksi, $eta, $dzeta,
            join("], [", map {join(",", @$_)} @$CoB)
                if $COD::Cell::Niggli::KG76::debug;
            my $Cm = [ [-1,0,0], [0,0,-1], [0,-1,0] ];
            $CoB = symop_mul( $CoB, $Cm );
            my ($tmp1, $tmp2) = ($B, $eta);
            ($B, $eta) = ($C, $dzeta);
            ($C, $dzeta) = ($tmp1, $tmp2);
            next
        }
        # 3.
        if( $ksi * $eta * $dzeta - $eps > 0 ) {
            printf "%s  %6.2f %6.2f %6.2f %6.2f %6.2f %6.2f [[%s]]\n",
            "3.", $A, $B, $C, $ksi, $eta, $dzeta,
            join("], [", map {join(",", @$_)} @$CoB)
                if $COD::Cell::Niggli::KG76::debug;
            my $i = ($ksi   < 0) ? -1 : 1;
            my $j = ($eta   < 0) ? -1 : 1;
            my $k = ($dzeta < 0) ? -1 : 1;
            my $Cm = [ [$i,0,0], [0,$j,0], [0,0,$k] ];
            $CoB = symop_mul( $CoB, $Cm );
            ($ksi, $eta, $dzeta) = map {abs} ($ksi, $eta, $dzeta);
        }
        # 4.
        if( !($ksi * $eta * $dzeta - $eps > 0) ) {
            printf "%s  %6.2f %6.2f %6.2f %6.2f %6.2f %6.2f [[%s]]\n",
            "4.", $A, $B, $C, $ksi, $eta, $dzeta,
            join("], [", map {join(",", @$_)} @$CoB)
                if $COD::Cell::Niggli::KG76::debug;
            my $i = ($ksi   > $eps) ? -1 : 1;
            my $j = ($eta   > $eps) ? -1 : 1;
            my $k = ($dzeta > $eps) ? -1 : 1;
            if( $i * $j * $k == -1 ) {
                $i = -1 if abs($ksi)   < $eps;
                $j = -1 if abs($eta)   < $eps;
                $k = -1 if abs($dzeta) < $eps;
            }
            my $Cm = [ [$i,0,0], [0,$j,0], [0,0,$k] ];
            $CoB = symop_mul( $CoB, $Cm );
            ($ksi, $eta, $dzeta) = map {-abs($_)} ($ksi, $eta, $dzeta);
        }
        # 5.
        ## print "5:", abs($ksi-$B) - $eps;
        if( abs($ksi) - $eps > $B or 
            (abs($ksi-$B) < $eps && 2 * $eta < $dzeta - $eps) or
            (abs($ksi+$B) < $eps && $dzeta < -$eps) ) {
            printf "%s  %6.2f %6.2f %6.2f %6.2f %6.2f %6.2f [[%s]]\n",
            "5.", $A, $B, $C, $ksi, $eta, $dzeta,
            join("], [", map {join(",", @$_)} @$CoB)
                if $COD::Cell::Niggli::KG76::debug;
            my $sign_ksi = $ksi > 0 ? 1 : -1;
            my $Cm = [ [1,0,0], [0,1,-$sign_ksi], [0,0,1] ];
            $CoB = symop_mul( $CoB, $Cm );
            $C = $B + $C - $ksi * $sign_ksi;
            $eta -= $dzeta * $sign_ksi;
            $ksi -= 2 * $B * $sign_ksi;
            next
        }
        # 6.
        if( abs($eta) - $eps > $A or
            (abs($eta-$A) < $eps && 2 * $ksi < $dzeta - $eps) or
            (abs($eta+$A) < $eps && $dzeta < -$eps) ) {
            printf "%s  %6.2f %6.2f %6.2f %6.2f %6.2f %6.2f [[%s]]\n",
            "6.", $A, $B, $C, $ksi, $eta, $dzeta,
            join("], [", map {join(",", @$_)} @$CoB)
                if $COD::Cell::Niggli::KG76::debug;
            my $sign_eta = $eta > 0 ? 1 : -1;
            my $Cm = [ [1,0,-$sign_eta], [0,1,0], [0,0,1] ];
            $CoB = symop_mul( $CoB, $Cm );
            $C = $A + $C - $eta * $sign_eta;
            $ksi -= $dzeta * $sign_eta;
            $eta -= 2 * $A * $sign_eta;
            next
        }
        # 7.
        ## print "7:", abs($dzeta+$A);
        if( abs($dzeta) - $eps > $A or
            (abs($dzeta-$A) < $eps && 2 * $ksi < $eta - $eps) or
            (abs($dzeta+$A) < $eps && $eta < -$eps) ) {
            printf "%s  %6.2f %6.2f %6.2f %6.2f %6.2f %6.2f [[%s]]\n",
            "7.", $A, $B, $C, $ksi, $eta, $dzeta,
            join("], [", map {join(",", @$_)} @$CoB)
                if $COD::Cell::Niggli::KG76::debug;
            my $sign_dzeta = $dzeta > 0 ? 1 : -1;
            my $Cm = [ [1,-$sign_dzeta,0], [0,1,0], [0,0,1] ];
            $CoB = symop_mul( $CoB, $Cm );
            $B = $A + $B - $dzeta * $sign_dzeta;
            $ksi -= $eta * $sign_dzeta;
            $dzeta -= 2 * $A * $sign_dzeta;
            next;
        }
        # 8.
        if( $ksi + $eta + $dzeta + $A + $B < -$eps or
            (abs($ksi + $eta + $dzeta + $A + $B) < $eps && 
             2*($A+$eta) + $dzeta - $eps > 0) ) {
            printf "%s  %6.2f %6.2f %6.2f %6.2f %6.2f %6.2f [[%s]]\n",
            "8.", $A, $B, $C, $ksi, $eta, $dzeta,
            join("], [", map {join(",", @$_)} @$CoB)
                if $COD::Cell::Niggli::KG76::debug;
            my $Cm = [ [1,0,1], [0,1,1], [0,0,1] ];
            $CoB = symop_mul( $CoB, $Cm );
            $C = $A + $B + $C + $ksi + $eta + $dzeta;
            $ksi = 2*$B + $ksi + $dzeta;
            $eta = 2*$A + $eta + $dzeta;
            next;
        }
        last
    }
    if( $COD::Cell::Niggli::KG76::debug ) {
        use POSIX;
        printf "%s  %6.2f %6.2f %6.2f %6.2f %6.2f %6.2f [[%s]]\n", 
        "  ", $A, $B, $C, $ksi, $eta, $dzeta,
        join("], [", map {join(",", @$_)} @$CoB)
            if $COD::Cell::Niggli::KG76::debug;
        print "CELL", sqrt($A), sqrt($B), sqrt($C),
        180*acos($ksi/(2*sqrt($B)*sqrt($C)))/$PI,
        180*acos($eta/(2*sqrt($A)*sqrt($C)))/$PI,
        180*acos($dzeta/(2*sqrt($A)*sqrt($B)))/$PI;
        print "COB", @{$CoB->[0]};
        print "COB", @{$CoB->[1]};
        print "COB", @{$CoB->[2]};
    }
    return (sqrt($A), sqrt($B), sqrt($C),
            180*acos($ksi/(2*sqrt($B)*sqrt($C)))/$PI,
            180*acos($eta/(2*sqrt($A)*sqrt($C)))/$PI,
            180*acos($dzeta/(2*sqrt($A)*sqrt($B)))/$PI,
            $CoB);
}

1;
