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package Algorithm::Simplex::PDL; |
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use Moo; |
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use MooX::Types::MooseLike::Base qw( ArrayRef Str ); |
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extends 'Algorithm::Simplex'; |
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with 'Algorithm::Simplex::Role::Solve'; |
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use PDL::Lite; |
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use namespace::clean; |
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=head1 Name |
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Algorithm::Simplex::PDL - PDL model of the Simplex Algorithm |
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=cut |
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# TODO: Probably need EPSILON for zero approximation check like in Float model. |
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has '+tableau' => ( |
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isa => sub { $_[0]->isa('PDL') }, |
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coerce => sub { PDL->pdl($_[0]) }, |
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); |
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has '+display_tableau' => ( |
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isa => ArrayRef [ ArrayRef [Str] ], |
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coerce => sub { &display_piddle($_[0]) }, |
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); |
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=head1 Methods |
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=head2 _build_number_of_rows |
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Set the number of rows. This is actually for the A matrix in Ax <= y. |
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So the number is one less than the total number of rows in the tableau. |
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The same holds for number of columns. |
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=cut |
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sub _build_number_of_rows { |
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my $self = shift; |
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my ($number_of_columns, $number_of_rows) = ($self->tableau->dims); |
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return $number_of_rows - 1; |
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} |
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=head2 _build_number_of_columns |
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set the number of columns given the tableau matrix |
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=cut |
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sub _build_number_of_columns { |
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my $self = shift; |
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my ($number_of_columns, $number_of_rows) = ($self->tableau->dims); |
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return $number_of_columns - 1; |
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} |
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=head2 pivot |
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Do the algebra of a Tucker/Bland pivot. i.e. Traverse from one node to and |
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adjacent node along the Simplex of feasible solutions. This pivot method |
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is particular to this PDL model. |
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=cut |
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sub pivot { |
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my $self = shift; |
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my $pivot_row_number = shift; |
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my $pivot_column_number = shift; |
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my $pdl_A = $self->tableau; |
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my $neg_one = PDL->zeroes(1); |
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$neg_one -= 1; |
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my $scale_copy = |
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$pdl_A->slice("($pivot_column_number),($pivot_row_number)")->copy; |
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my $scale = $pdl_A->slice("($pivot_column_number),($pivot_row_number)"); |
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my $pivot_row = $pdl_A->slice(":,($pivot_row_number)"); |
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$pivot_row /= $scale_copy; |
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$scale /= $scale_copy; |
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# peform pivot algebra in non-pivot rows |
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for my $i (0 .. $self->number_of_rows) { |
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if ($i != $pivot_row_number) { |
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my $a_ic_copy = $pdl_A->slice("($pivot_column_number),($i)")->copy; |
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my $a_ic = $pdl_A->slice("($pivot_column_number),($i)"); |
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my $change_row = $pdl_A->slice(":,($i)"); |
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my $diff_term = $a_ic x $pivot_row; |
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$change_row -= $diff_term; |
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my $tmp = $neg_one x $a_ic_copy; |
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$a_ic .= $tmp; # $scale_copy; |
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$a_ic /= $scale_copy; |
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} |
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} |
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return $pdl_A; |
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} |
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# Count pivots made |
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after 'pivot' => sub { |
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my $self = shift; |
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$self->number_of_pivots_made($self->number_of_pivots_made + 1); |
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return; |
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}; |
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103
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=head2 is_optimal |
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105
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Return 1 if the current solution is optimal, 0 otherwise. |
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107
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=cut |
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109
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sub is_optimal { |
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my $self = shift; |
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my $T_pdl = $self->tableau; |
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113
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# Look at basement row to see if no positive entries exists. |
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my $n_cols_A = $self->number_of_columns - 1; |
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my $number_of_rows = $self->number_of_rows; |
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my $basement_row = $T_pdl->slice("0:$n_cols_A,($number_of_rows)"); |
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my @basement_row = $basement_row->list; |
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foreach my $profit_coefficient (@basement_row) { |
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if ($profit_coefficient > 0) { |
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return 0; |
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} |
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} |
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return 1; |
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} |
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=head2 determine_simplex_pivot_columns |
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Look at the basement row to see where positive entries exists. |
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Columns with positive entries in the basement row are pivot column candidates. |
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Should run optimality test, is_optimal, first to insure |
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at least one positive entry exists in the basement row which then |
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means we can increase the objective value for the maximization problem. |
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136
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=cut |
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138
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sub determine_simplex_pivot_columns { |
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my $self = shift; |
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my @simplex_pivot_column_numbers; |
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my $n_cols_A = $self->number_of_columns - 1; |
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my $number_of_rows = $self->number_of_rows; |
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my $basement_row = $self->tableau->slice("0:$n_cols_A,($number_of_rows)"); |
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my @basement_row = $basement_row->list; |
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my $column_number = 0; |
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foreach my $profit_coefficient (@basement_row) { |
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if ($profit_coefficient > 0) { |
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push @simplex_pivot_column_numbers, $column_number; |
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} |
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$column_number++; |
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} |
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return @simplex_pivot_column_numbers; |
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} |
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=head2 determine_positive_ratios |
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160
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Starting with the pivot column find the entry that yields the lowest |
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positive b to entry ratio that has lowest bland number in the event of ties. |
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163
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=cut |
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sub determine_positive_ratios { |
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my $self = shift; |
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my $pivot_column_number = shift; |
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my $n_rows_A = $self->number_of_rows - 1; |
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my $number_of_columns = $self->number_of_columns; |
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my $pivot_column = |
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$self->tableau->slice("($pivot_column_number),0:$n_rows_A"); |
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my @pivot_column = $pivot_column->list; |
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my $constant_column = |
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$self->tableau->slice("($number_of_columns),0:$n_rows_A"); |
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my @constant_column = $constant_column->list; |
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my $row_number = 0; |
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my @positive_ratio_row_numbers; |
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my @positive_ratios; |
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foreach my $i (0 .. $n_rows_A) { |
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if ($pivot_column[$i] > 0) { |
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push @positive_ratios, ($constant_column[$i] / $pivot_column[$i]); |
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push @positive_ratio_row_numbers, $i; |
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} |
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} |
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return (\@positive_ratios, \@positive_ratio_row_numbers); |
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} |
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=head2 display_pdl |
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192
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Given a Piddle return it as a string in a Matrix like format. |
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194
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=cut |
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196
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sub display_pdl { |
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my $self = shift; |
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my $pdl = $self->tableau; |
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my $output = "$pdl"; |
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return $output; |
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} |
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203
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=head2 current_solution |
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205
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Return both the primal (max) and dual (min) solutions for the tableau. |
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207
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=cut |
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209
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sub current_solution { |
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0
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0
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1
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my $self = shift; |
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212
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# Report the Current Solution as primal dependents and dual dependents. |
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my @y = @{ $self->y_variables }; |
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my @u = @{ $self->u_variables }; |
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215
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216
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# Dependent Primal Variables |
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my $n_rows_A = $self->number_of_rows - 1; |
218
|
0
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|
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|
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|
my $number_of_columns = $self->number_of_columns; |
219
|
0
|
|
|
|
|
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my $constant_column = |
220
|
|
|
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|
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$self->tableau->slice("($number_of_columns),0:$n_rows_A"); |
221
|
0
|
|
|
|
|
|
my @constant_column = $constant_column->list; |
222
|
0
|
|
|
|
|
|
my %primal_solution; |
223
|
0
|
|
|
|
|
|
for my $i (0 .. $#y) { |
224
|
0
|
|
|
|
|
|
$primal_solution{ $y[$i]->{generic} } = $constant_column[$i]; |
225
|
|
|
|
|
|
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} |
226
|
|
|
|
|
|
|
|
227
|
|
|
|
|
|
|
# Dependent Dual Variables |
228
|
0
|
|
|
|
|
|
my $n_cols_A = $self->number_of_columns - 1; |
229
|
0
|
|
|
|
|
|
my $number_of_rows = $self->number_of_rows; |
230
|
0
|
|
|
|
|
|
my $basement_row = $self->tableau->slice("0:$n_cols_A,($number_of_rows)"); |
231
|
0
|
|
|
|
|
|
my @basement_row = $basement_row->list; |
232
|
0
|
|
|
|
|
|
my %dual_solution; |
233
|
0
|
|
|
|
|
|
for my $j (0 .. $#u) { |
234
|
0
|
|
|
|
|
|
$dual_solution{ $u[$j]->{generic} } = $basement_row[$j] * (-1); |
235
|
|
|
|
|
|
|
} |
236
|
|
|
|
|
|
|
|
237
|
0
|
|
|
|
|
|
return (\%primal_solution, \%dual_solution); |
238
|
|
|
|
|
|
|
} |
239
|
|
|
|
|
|
|
|
240
|
|
|
|
|
|
|
=head2 display_piddle |
241
|
|
|
|
|
|
|
|
242
|
|
|
|
|
|
|
Coercion: convert a PDL into an ArrayRef[ArrayRef[Num]] |
243
|
|
|
|
|
|
|
|
244
|
|
|
|
|
|
|
=cut |
245
|
|
|
|
|
|
|
|
246
|
|
|
|
|
|
|
sub display_piddle { |
247
|
0
|
|
|
0
|
1
|
|
my $piddle_tableau = shift; |
248
|
|
|
|
|
|
|
|
249
|
0
|
|
|
|
|
|
my @display_tableau; |
250
|
0
|
|
|
|
|
|
my ($number_of_columns, $number_of_rows) = ($piddle_tableau->dims); |
251
|
0
|
|
|
|
|
|
my $number_of_zero_based_rows = $number_of_rows - 1; |
252
|
0
|
|
|
|
|
|
my $number_of_zero_based_columns = $number_of_columns - 1; |
253
|
0
|
|
|
|
|
|
for my $i (0 .. $number_of_zero_based_rows) { |
254
|
0
|
|
|
|
|
|
my $row = |
255
|
|
|
|
|
|
|
$piddle_tableau->slice("0:$number_of_zero_based_columns,($i)"); |
256
|
0
|
|
|
|
|
|
my @row = $row->list; |
257
|
0
|
|
|
|
|
|
push @display_tableau, \@row; |
258
|
|
|
|
|
|
|
} |
259
|
|
|
|
|
|
|
|
260
|
0
|
|
|
|
|
|
return \@display_tableau; |
261
|
|
|
|
|
|
|
} |
262
|
|
|
|
|
|
|
|
263
|
|
|
|
|
|
|
1; |