package QStuff;
use strict;
use Exporter;
use Math::MatrixReal;
use Quantum::Entanglement;
our @ISA = qw/Quantum::Entanglement Exporter/;
our @EXPORT_OK = qw/entangle/;

sub entangle {bless Quantum::Entanglement::entangle(@_)}

# args($entangle) returns values passed to entangle()
sub args { map {@{$_}} @{${$_[0]->[0]}} }

# $entange->probs returns probs only
sub probs { 
	my @ar = args(shift);
	return map {@ar[$_*2]} 0..(int($#ar/2));
}

# $entange->states return states only
sub states { 
	my @ar = args(shift);
	return map {@ar[$_*2+1]} 0..(int($#ar/2));
}

# $a->cmpquanta($b) sees if 2 quanta the same
sub cmpquanta {
	return 0 unless $_[0]->cmpstates($_[1]);
	my @probs0 = $_[0]->probs;
	my @probs1 = $_[1]->probs;
	for(0..$#probs0){return 0 unless abs($probs0[$_] - $probs1[$_]) < 0.000001}
	return 1;
}

# $a->cmpstates($b) sees if $a & $b have the same state space
sub cmpstates {
	my @a = $_[0]->states;
	my @b = $_[1]->states;
	return 0 if $#a != $#b;
	for (0..$#a) {return 0 if $a[$_] != $b[$_]};
	return 1;
}

# project $a onto the subspace of $b
sub proj {
	my ($a, $b) = @_;
	# checking states compatability to be implemented
	my @bstates = $b->states;
	my ($I, $prob, $Pb, $measure, $norm, $measure);
	$b = Math::MatrixReal->new_from_cols([[$b->probs]]);
	$a = Math::MatrixReal->new_from_cols([[$a->probs]]);
	$I = Math::MatrixReal->new_diag( [1, 1] );

	$prob = (~$a * $b * ~$b * $a)->element(1,1);
	$Pb = rand(1) < $prob ? $b * ~$b : ($I - $b * ~$b ); # quantum thing
	$measure = $Pb * $a;
	$norm = sqrt((~($measure) * $measure)->element(1,1));
	$measure = $Pb * $a * (1/$norm);
	bless QStuff::entangle(
		map {$measure->element($_+1, 1) => $bstates[$_]} 0..$#bstates
	);
}

1;