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);

has objective_function_value => (
    is  => 'lazy',
    isa => Str,
);

has number_of_rows => (
    is       => 'lazy',
    isa      => Int,
    init_arg => undef,
);

has number_of_columns => (
    is       => 'lazy',
    isa      => Int,
    init_arg => undef,
);

has number_of_pivots_made => (
    is      => 'rw',
    isa     => Int,
    default => sub { 0 },
);

has EPSILON => (
    is      => 'rw',
    isa     => Num,
    default => sub { 1e-13 },
);

has MAXIMUM_PIVOTS => (
    is      => 'rw',
    isa     => Int,
    default => sub { 200 },
);

has x_variables => (
    is  => 'lazy',
    isa => ArrayRef [ HashRef [Str] ],
);
has 'y_variables' => (
    is  => 'lazy',
    isa => ArrayRef [ HashRef [Str] ],
);
has u_variables => (
    is  => 'lazy',
    isa => ArrayRef [ HashRef [Str] ],
);
has v_variables => (
    is  => 'lazy',
    isa => ArrayRef [ HashRef [Str] ],
);

=head1 Name

Algorithm::Simplex - Simplex Algorithm Implementation using Tucker Tableaux

=head1 Synopsis

Given a linear program formulated as a Tucker tableau, a 2D matrix or 
ArrayRef[ArrayRef] in Perl, seek an optimal solution.

    use Algorithm::Simplex::Rational;
    my $matrix = [
        [ 5,  2,  30],
        [ 3,  4,  20],
        [10,  8,   0],
    ];
    my $tableau = Algorithm::Simplex::Rational->new( tableau => $matrix );
    $tableau->solve;
    my ($primal_solution, $dual_solution) = $tableau->current_solution;

=head1 Methods

=head2 _build_number_of_rows 

Set the number of rows.
This number represent the number of rows of the
coefficient matrix.  It is one less than the full tableau.

=cut

sub _build_number_of_rows {
    my $self = shift;

    return scalar @{ $self->tableau } - 1;
}

=head2 _build_number_of_columns 

Set the number of columns given the tableau matrix.
This number represent the number of columns of the
coefficient matrix.

=cut

sub _build_number_of_columns {
    my $self = shift;

    return scalar @{ $self->tableau->[0] } - 1;
}

=head2 _build_x_variables

Set x variable names for the given tableau, x1, x2 ... xn
These are the decision variables of the maximization problem.
The maximization problem is read horizontally in a Tucker tableau.

=cut

sub _build_x_variables {
    my $self = shift;

    my $x_vars;
    for my $j (0 .. $self->number_of_columns - 1) {
        my $x_index = $j + 1;
        $x_vars->[$j]->{'generic'} = 'x' . $x_index;
    }
    return $x_vars;
}