#===============================================
# Vector
#===============================================
package Vector;
use Exporter;
use Math::Vector::Real;
use Math::MatrixReal;
@ISA = qw(Exporter Math::Vector::Real Math::MatrixReal);

#公開したいサブルーチン
#@EXPORT = qw(V);

#our $VERSION = '0.17';

use strict;
use Sci qw($todeg $torad);

#my $u = V(3, 3, 0);
#$p = $u * $v;       # dot product
#$f = 1.4 * $u + $v; # scalar product and vector addition
#$c = $u x $v;       # cross product, only defined for 3D vectors
#+ * /
#- (both unary and binary)
#x (cross product for 3D vectors)
#+= -= *= /= x=
#== !=
#"" (stringfication)
#abs (returns the norm)
#atan2 (returns the angle between two vectors)

#use Math::MatrixReal;
#my $a = Math::MatrixReal->new_random(5, 5);
#my $matrix = Math::MatrixReal->new_from_cols( [ [1,2], [3,4] ] );
#my $matrix = Math::MatrixReal->new_from_rows( [ [1,2], [3,4] ] );
#my $b = $a->new_random(10, 30, { symmetric=>1, bounded_by=>[-1,1] });
#my $c = $b * $a ** 3;
#my $d = $b->new_from_rows( [ [ 5, 3 ,4], [3, 4, 5], [ 2, 4, 1 ] ] );
#print $a;
#my $row = ($a * $b)->row(3);
#my $col = (5*$c)->col(2);
#my $transpose = ~$c;
#my $transpose = $c->transpose;
#my $inverse = $a->inverse;
#my $inverse = 1/$a;
#my $inverse = $a ** -1;
#my $determinant= $a->det;


#sub V { bless [@_] }
#sub new {
#    my $class = shift;
#    bless [@_], $class
#}

sub new
{
	my ($module) = @_;
	my $this = {};
	bless $this, $module;

#$v = Math::Vector::Real->new(@components)

	return $this;
}

sub DESTROY
{
	my $this = shift;
}

sub zero
{
	my ($dim) = @_;
	return Math::Vector::Real->zero($dim);
}

sub unit
{
	my ($v) = @_;

#$v / abs($v) = $v->versor();
	return $v / abs($v);
}

sub UnitVectors
{
#V(@components) = Math::Vector::Real->new(@components)
	my $e1 = V(1.0, 0.0, 0.0);
	my $e2 = V(0.0, 1.0, 0.0);
	my $e3 = V(0.0, 0.0, 1.0);
	return ($e1, $e2, $e3);
}

sub Angle
{
	my ($pa, $pb, $UseDeg) = @_;
	my $a2 = &InnerProduct(@$pa, @$pa);
	my $b2 = &InnerProduct(@$pb, @$pb);
	my $ab = &InnerProduct(@$pa, @$pb);
	my $cosQ = $ab / sqrt($a2 * $b2);
	return Sci::acos($cosQ) if(!$UseDeg);
	return Sci::acos($cosQ) * $todeg;
}

sub OuterProduct
{
	my (@a) = @_;
	my $dim = 3;
	return ($a[1]*$a[2+$dim]-$a[2]*$a[1+$dim], $a[2]*$a[0+$dim]-$a[0]*$a[2+$dim], $a[0]*$a[1+$dim]-$a[1]*$a[0+$dim]);
}

sub InnerProduct
{
	my (@a) = @_;
	my $dim = scalar @a / 2;
#print "dim=$dim\n";
	my $c = 0.0;
	for(my $i = 0 ; $i < $dim ; $i++) {
		$c += $a[$i] * $a[$i+$dim];
	}
	return $c;
}

sub Difference
{
	my (@a) = @_;
	my $dim = scalar @a / 2;
#print "dim=$dim\n";
	my @c;
	for(my $i = 0 ; $i < $dim ; $i++) {
		$c[$i] = $a[$i] - $a[$i+$dim];
	}
	return @c;
}

1;