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<?php |
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declare(strict_types=1); |
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namespace Ctefan\Kiwi; |
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use Ctefan\Kiwi\Exception\DuplicateConstraintException; |
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use Ctefan\Kiwi\Exception\DuplicateEditVariableException; |
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use Ctefan\Kiwi\Exception\InternalSolverException; |
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use Ctefan\Kiwi\Exception\RequiredFailureException; |
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use Ctefan\Kiwi\Exception\UnknownConstraintException; |
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use Ctefan\Kiwi\Exception\UnknownEditVariableException; |
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use Ctefan\Kiwi\Exception\UnsatisfiableConstraintException; |
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/** |
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* The constraint solver. |
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*/ |
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class Solver |
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{ |
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/** |
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* @var \SplObjectStorage<Constraint, Tag> |
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*/ |
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protected $constraints; |
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/** |
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* @var \SplObjectStorage<Symbol, Row> |
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*/ |
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protected $rows; |
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/** |
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* @var \SplObjectStorage<Variable, Symbol> |
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*/ |
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protected $variables; |
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/** |
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* @var \SplObjectStorage<Variable, EditInfo> |
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*/ |
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protected $edits; |
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/** |
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* @var array<Symbol> |
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*/ |
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protected $infeasibleRows; |
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/** |
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* @var Row |
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*/ |
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protected $objective; |
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/** |
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* @var Row |
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*/ |
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protected $artificial; |
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/** |
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* Solver constructor. |
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*/ |
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public function __construct() |
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{ |
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$this->constraints = new \SplObjectStorage(); |
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$this->rows = new \SplObjectStorage(); |
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$this->variables = new \SplObjectStorage(); |
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$this->edits = new \SplObjectStorage(); |
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$this->infeasibleRows = []; |
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$this->objective = new Row(); |
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} |
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/** |
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* Add a constraint to the solver. |
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* |
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* @param Constraint $constraint |
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* @throws DuplicateConstraintException The given constraint has already been added to the solver. |
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* @throws UnsatisfiableConstraintException The given constraint is required and cannot be satisfied. |
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* @throws InternalSolverException |
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*/ |
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public function addConstraint(Constraint $constraint): void |
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{ |
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if (true === $this->constraints->contains($constraint)) { |
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throw new DuplicateConstraintException($constraint); |
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} |
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// Creating a row causes symbols to reserved for the variables in the constraint. |
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// If this method exits with an exception, then its possible those variables will linger in the var map. |
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// Since its likely that those variables will be used in other constraints and since exceptional conditions are uncommon, |
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// I'm not too worried about aggressive cleanup of the var map. |
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$tag = new Tag(); |
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$row = $this->createRow($constraint, $tag); |
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$subject = $this->chooseSubject($row, $tag); |
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// If chooseSubject() could find a valid entering symbol, one last option is available if the entire row is composed of dummy variables. |
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// If the constant of the row is zero, then this represents redundant constraints and the new dummy marker can enter the basis. |
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// If the constant is non-zero, then it represents an unsatisfiable constraint. |
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if ($subject->getType() === Symbol::INVALID && true === $this->allDummies($row)) { |
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if (false === Util::isNearZero($row->getConstant())) { |
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throw new UnsatisfiableConstraintException($constraint); |
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} else { |
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$subject = $tag->getMarker(); |
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} |
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} |
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// If an entering symbol still isn't found, then the row must be added using an artificial variable. |
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// If that fails, then the row represents an unsatisfiable constraint. |
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if ($subject->getType() === Symbol::INVALID) { |
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if (false === $this->addWithArtificialVariable($row)) { |
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throw new UnsatisfiableConstraintException($constraint); |
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} |
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} else { |
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$row->solveForSymbol($subject); |
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$this->substitute($subject, $row); |
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$this->rows->attach($subject, $row); |
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} |
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$this->constraints->attach($constraint, $tag); |
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// Optimizing after each constraint is added performs less aggregate work due to a smaller average system size. |
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// It also ensures the solver remains in a consistent state. |
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$this->optimize($this->objective); |
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} |
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/** |
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* Remove a constraint from the solver. |
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* |
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* @param Constraint $constraint |
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* @throws UnknownConstraintException The given constraint has not been added to the solver. |
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* @throws InternalSolverException |
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*/ |
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public function removeConstraint(Constraint $constraint): void |
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{ |
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if (false === $this->constraints->contains($constraint)) { |
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throw new UnknownConstraintException($constraint); |
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} |
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$tag = $this->constraints->offsetGet($constraint); |
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$this->constraints->offsetUnset($constraint); |
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// Remove the error effects from the objective function before pivoting, |
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// or substitutions into the objective will lead to incorrect solver results. |
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$this->removeConstraintEffects($constraint, $tag); |
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// If the marker is basic, simply drop the row. Otherwise, pivot the marker into the basis and then drop the row. |
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if (true === $this->rows->contains($tag->getMarker())) { |
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$this->rows->offsetUnset($tag->getMarker()); |
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} else { |
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$leaving = $this->getMarkerLeavingSymbol($tag->getMarker()); |
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if ($leaving->getType() === Symbol::INVALID) { |
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throw new InternalSolverException('Internal solver error'); |
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} |
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$row = $this->rows->offsetGet($leaving); |
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$this->rows->offsetUnset($leaving); |
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$row->solveForSymbols($leaving, $tag->getMarker()); |
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$this->substitute($tag->getMarker(), $row); |
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} |
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// Optimizing after each constraint is removed ensures that the solver remains consistent. |
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// It makes the solver API easier to use at a small tradeoff for speed. |
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$this->optimize($this->objective); |
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} |
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/** |
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* Test whether a constraint has been added to the solver. |
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* |
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* @param Constraint $constraint |
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* @return bool |
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*/ |
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public function hasConstraint(Constraint $constraint): bool |
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{ |
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return $this->constraints->contains($constraint); |
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} |
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/** |
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* Add an edit variable to the solver. |
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* |
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* This method should be called before the 'suggestValue' method is used to supply a suggested value |
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* for the given edit variable. |
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* |
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* @param Variable $variable |
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* @param float $strength |
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* @throws DuplicateEditVariableException The given edit variable has already been added to the solver. |
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* @throws RequiredFailureException The given strength is >= required. |
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* @throws InternalSolverException |
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*/ |
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public function addEditVariable(Variable $variable, float $strength): void |
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{ |
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if ($this->edits->contains($variable)) { |
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throw new DuplicateEditVariableException(); |
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} |
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$strength = Strength::clip($strength); |
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if (Strength::required() === $strength) { |
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throw new RequiredFailureException(); |
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} |
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$terms = []; |
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$terms[] = new Term($variable); |
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$constraint = new Constraint(new Expression($terms), RelationalOperator::EQ, $strength); |
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try { |
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$this->addConstraint($constraint); |
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} catch (DuplicateConstraintException $e) { |
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// TODO log |
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} catch (UnsatisfiableConstraintException $e) { |
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// TODO log |
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} |
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$info = new EditInfo($constraint, $this->constraints->offsetGet($constraint), 0.0); |
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$this->edits->attach($variable, $info); |
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} |
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/** |
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* Remove an edit variable from the solver. |
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* |
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* @param Variable $variable |
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* @throws UnknownEditVariableException The given edit variable has not been added to the solver. |
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* @throws InternalSolverException |
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*/ |
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public function removeEditVariable(Variable $variable): void |
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{ |
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if (false === $this->edits->contains($variable)) { |
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throw new UnknownEditVariableException(); |
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} |
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$info = $this->edits->offsetGet($variable); |
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try { |
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$this->removeConstraint($info->getConstraint()); |
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} catch (UnknownConstraintException $e) { |
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// TODO log |
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} |
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$this->edits->offsetUnset($variable); |
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} |
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/** |
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* Test whether an edit variable has been added to the solver. |
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* |
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* @param Variable $variable |
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* @return bool |
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*/ |
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public function hasEditVariable(Variable $variable): bool |
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{ |
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return $this->edits->contains($variable); |
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} |
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/** |
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* Suggest a value for the given edit variable. |
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* |
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* This method should be used after an edit variable as been added to the solver |
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* in order to suggest the value for that variable. |
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* |
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* @param Variable $variable |
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* @param float $value |
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* @throws UnknownEditVariableException The given edit variable has not been added to the solver. |
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* @throws InternalSolverException |
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254
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*/ |
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public function suggestValue(Variable $variable, float $value): void |
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{ |
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if (false === $this->edits->contains($variable)) { |
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throw new UnknownEditVariableException(); |
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} |
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260
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$info = $this->edits->offsetGet($variable); |
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$delta = $value - $info->getConstant(); |
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$info->setContant($value); |
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264
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265
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// Check first if the positive error variable is basic. |
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if (true === $this->rows->contains($info->getTag()->getMarker())) { |
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267
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$row = $this->rows->offsetGet($info->getTag()->getMarker()); |
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268
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if (0.0 > $row->add(-$delta)) { |
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$this->infeasibleRows[] = $info->getTag()->getMarker(); |
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} |
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271
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$this->dualOptimize(); |
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return; |
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273
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} |
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274
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275
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// Check next if the negative error variable is basic. |
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276
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if (true === $this->rows->contains($info->getTag()->getOther())) { |
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277
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$row = $this->rows->offsetGet($info->getTag()->getOther()); |
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278
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if (0.0 > $row->add($delta)) { |
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279
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$this->infeasibleRows[] = $info->getTag()->getOther(); |
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280
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} |
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281
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$this->dualOptimize(); |
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282
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return; |
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283
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} |
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284
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285
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// Otherwise update each row where the error variables exist. |
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286
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foreach ($this->rows as $symbol) { |
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287
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$currentRow = $this->rows->offsetGet($symbol); |
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288
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$coefficient = $currentRow->getCoefficientForSymbol($info->getTag()->getMarker()); |
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289
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if (0.0 !== $coefficient && 0.0 > $currentRow->add($delta * $coefficient) && Symbol::EXTERNAL !== $symbol->getType()) { |
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290
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$this->infeasibleRows[] = $symbol; |
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291
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} |
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292
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} |
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293
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294
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$this->dualOptimize(); |
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295
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} |
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296
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297
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/** |
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298
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* Update the values of the external solver variables. |
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299
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*/ |
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300
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18 |
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public function updateVariables(): void |
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301
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{ |
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302
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18 |
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foreach ($this->variables as $variable) { |
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303
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18 |
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$symbol = $this->variables->offsetGet($variable); |
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304
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18 |
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if (false === $this->rows->contains($symbol)) { |
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305
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1 |
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$variable->setValue(0.0); |
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306
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} else { |
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307
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18 |
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$row = $this->rows->offsetGet($symbol); |
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308
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18 |
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$variable->setValue($row->getConstant()); |
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309
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} |
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310
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} |
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311
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18 |
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} |
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312
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313
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/** |
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314
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* Remove the effects of a constraint on the objective function. |
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315
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* |
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316
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* @param Constraint $constraint |
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317
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* @param Tag $tag |
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318
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*/ |
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319
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2 |
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protected function removeConstraintEffects(Constraint $constraint, Tag $tag): void |
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320
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{ |
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321
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2 |
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if ($tag->getMarker()->getType() === Symbol::ERROR) { |
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322
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$this->removeMarkerEffects($tag->getMarker(), $constraint->getStrength()); |
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323
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2 |
|
} elseif ($tag->getOther()->getType() === Symbol::ERROR) { |
|
324
|
|
|
$this->removeMarkerEffects($tag->getOther(), $constraint->getStrength()); |
|
325
|
|
|
} |
|
326
|
2 |
|
} |
|
327
|
|
|
|
|
328
|
|
|
/** |
|
329
|
|
|
* Remove the effects of an error marker on the objective function. |
|
330
|
|
|
* |
|
331
|
|
|
* @param Symbol $marker |
|
332
|
|
|
* @param float $strength |
|
333
|
|
|
*/ |
|
334
|
|
|
protected function removeMarkerEffects(Symbol $marker, float $strength): void |
|
335
|
|
|
{ |
|
336
|
|
|
if (true === $this->rows->contains($marker)) { |
|
337
|
|
|
$row = $this->rows->offsetGet($marker); |
|
338
|
|
|
$this->objective->insertSymbol($row, -$strength); |
|
339
|
|
|
} else { |
|
340
|
|
|
$this->objective->insertSymbol($marker, -$strength); |
|
341
|
|
|
} |
|
342
|
|
|
} |
|
343
|
|
|
|
|
344
|
|
|
/** |
|
345
|
|
|
* Compute the leaving symbol for a marker variable. |
|
346
|
|
|
* |
|
347
|
|
|
* This method will return a symbol corresponding to a basic row which holds the given marker variable. |
|
348
|
|
|
* The row will be chosen according to the following precedence: |
|
349
|
|
|
* 1) The row with a restricted basic varible and a negative coefficient for the marker with the smallest ratio of -constant / coefficient. |
|
350
|
|
|
* 2) The row with a restricted basic variable and the smallest ratio of constant / coefficient. |
|
351
|
|
|
* 3) The last unrestricted row which contains the marker. |
|
352
|
|
|
* If the marker does not exist in any row, an invalid symbol will be returned. |
|
353
|
|
|
* This indicates an internal solver error since the marker should exist somewhere in the tableau. |
|
354
|
|
|
* |
|
355
|
|
|
* @param Symbol $marker |
|
356
|
|
|
* @return Symbol |
|
357
|
|
|
*/ |
|
358
|
2 |
|
protected function getMarkerLeavingSymbol(Symbol $marker): Symbol |
|
359
|
|
|
{ |
|
360
|
2 |
|
$max = PHP_FLOAT_MAX; |
|
361
|
2 |
|
$ratio1 = $max; |
|
362
|
2 |
|
$ratio2 = $max; |
|
363
|
|
|
|
|
364
|
2 |
|
$first = new Symbol(); |
|
365
|
2 |
|
$second = new Symbol(); |
|
366
|
2 |
|
$third = new Symbol(); |
|
367
|
|
|
|
|
368
|
2 |
|
foreach ($this->rows as $symbol) { |
|
369
|
2 |
|
$candidateRow = $this->rows->offsetGet($symbol); |
|
370
|
2 |
|
$coefficient = $candidateRow->getCoefficientForSymbol($marker); |
|
371
|
2 |
|
if (0.0 === $coefficient) { |
|
372
|
1 |
|
continue; |
|
373
|
|
|
} |
|
374
|
2 |
|
if ($symbol->getType() === Symbol::EXTERNAL) { |
|
375
|
2 |
|
$third = $symbol; |
|
376
|
2 |
|
} elseif (0.0 > $coefficient) { |
|
377
|
|
|
$ratio = -$candidateRow->getConstant() / $coefficient; |
|
378
|
|
|
if ($ratio < $ratio1) { |
|
379
|
|
|
$ratio1 = $ratio; |
|
380
|
|
|
$first = $symbol; |
|
381
|
|
|
} |
|
382
|
|
|
} else { |
|
383
|
2 |
|
$ratio = $candidateRow->getConstant() / $coefficient; |
|
384
|
2 |
|
if ($ratio < $ratio2) { |
|
385
|
2 |
|
$ratio2 = $ratio; |
|
386
|
2 |
|
$second = $symbol; |
|
387
|
|
|
} |
|
388
|
|
|
} |
|
389
|
|
|
} |
|
390
|
|
|
|
|
391
|
2 |
|
if ($first->getType() !== Symbol::INVALID) { |
|
392
|
|
|
return $first; |
|
393
|
|
|
} |
|
394
|
2 |
|
if ($second->getType() !== Symbol::INVALID) { |
|
395
|
2 |
|
return $second; |
|
396
|
|
|
} |
|
397
|
|
|
return $third; |
|
398
|
|
|
} |
|
399
|
|
|
|
|
400
|
|
|
/** |
|
401
|
|
|
* Create a new Row object for the given constraint. |
|
402
|
|
|
* |
|
403
|
|
|
* The terms in the constraint will be converted to cells in the row. |
|
404
|
|
|
* Any term in the constraint with a coefficient of zero is ignored. |
|
405
|
|
|
* This method uses the 'getVarSymbol' method to get the symbol for the variables added to the row. |
|
406
|
|
|
* If the symbol for a given cell variable is basic, the cell variable will be substituted with the basic row. |
|
407
|
|
|
* The necessary slack and error variables will be added to the row. |
|
408
|
|
|
* If the constant for the row is negative, the sign for the row will be inverted so the constant becomes positive. |
|
409
|
|
|
* The tag will be updated with the marker and error symbols to use for tracking the movement of the constraint in the tableau. |
|
410
|
|
|
* |
|
411
|
|
|
* @param Constraint $constraint |
|
412
|
|
|
* @param Tag $tag |
|
413
|
|
|
* @return Row |
|
414
|
|
|
*/ |
|
415
|
21 |
|
protected function createRow(Constraint $constraint, Tag $tag): Row |
|
416
|
|
|
{ |
|
417
|
21 |
|
$expression = $constraint->getExpression(); |
|
418
|
21 |
|
$row = new Row($expression->getConstant()); |
|
419
|
|
|
|
|
420
|
|
|
// Substitute the current basic variables into the row. |
|
421
|
21 |
|
foreach ($expression->getTerms() as $term) { |
|
422
|
21 |
|
if (false === Util::isNearZero($term->getCoefficient())) { |
|
423
|
21 |
|
$symbol = $this->getVariableSymbol($term->getVariable()); |
|
424
|
21 |
|
if (false === $this->rows->contains($symbol)) { |
|
425
|
21 |
|
$row->insertSymbol($symbol, $term->getCoefficient()); |
|
426
|
|
|
} else { |
|
427
|
19 |
|
$otherRow = $this->rows->offsetGet($symbol); |
|
428
|
21 |
|
$row->insertRow($otherRow, $term->getCoefficient()); |
|
429
|
|
|
} |
|
430
|
|
|
|
|
431
|
|
|
} |
|
432
|
|
|
} |
|
433
|
|
|
|
|
434
|
|
|
// Add the necessary slack, error, and dummy variables. |
|
435
|
21 |
|
switch ($constraint->getOperator()) { |
|
436
|
21 |
|
case RelationalOperator::LE: |
|
437
|
20 |
|
case RelationalOperator::GE: |
|
438
|
17 |
|
$coefficient = $constraint->getOperator() === RelationalOperator::LE ? 1.0 : -1.0; |
|
439
|
17 |
|
$slack = new Symbol(Symbol::SLACK); |
|
440
|
17 |
|
$tag->setMarker($slack); |
|
441
|
17 |
|
$row->insertSymbol($slack, $coefficient); |
|
442
|
17 |
|
if ($constraint->getStrength() < Strength::required()) { |
|
443
|
1 |
|
$error = new Symbol(Symbol::ERROR); |
|
444
|
1 |
|
$tag->setOther($error); |
|
445
|
1 |
|
$row->insertSymbol($error, -$coefficient); |
|
446
|
1 |
|
$this->objective->insertSymbol($error, $constraint->getStrength()); |
|
447
|
|
|
} |
|
448
|
17 |
|
break; |
|
449
|
18 |
|
case RelationalOperator::EQ: |
|
450
|
18 |
|
if ($constraint->getStrength() < Strength::required()) { |
|
451
|
2 |
|
$errPlus = new Symbol(Symbol::ERROR); |
|
452
|
2 |
|
$errMinus = new Symbol(Symbol::ERROR); |
|
453
|
2 |
|
$tag->setMarker($errPlus); |
|
454
|
2 |
|
$tag->setOther($errMinus); |
|
455
|
2 |
|
$row->insertSymbol($errPlus, -1.0); |
|
456
|
2 |
|
$row->insertSymbol($errMinus, 1.0); |
|
457
|
2 |
|
$this->objective->insertSymbol($errPlus, $constraint->getStrength()); |
|
458
|
2 |
|
$this->objective->insertSymbol($errMinus, $constraint->getStrength()); |
|
459
|
|
|
} else { |
|
460
|
18 |
|
$dummy = new Symbol(Symbol::DUMMY); |
|
461
|
18 |
|
$tag->setMarker($dummy); |
|
462
|
18 |
|
$row->insertSymbol($dummy); |
|
463
|
|
|
} |
|
464
|
18 |
|
break; |
|
465
|
|
|
} |
|
466
|
|
|
|
|
467
|
|
|
// Ensure the row as a positive constant. |
|
468
|
21 |
|
if ($row->getConstant() < 0.0) { |
|
469
|
16 |
|
$row->reverseSign(); |
|
470
|
|
|
} |
|
471
|
|
|
|
|
472
|
21 |
|
return $row; |
|
473
|
|
|
} |
|
474
|
|
|
|
|
475
|
|
|
/** |
|
476
|
|
|
* Choose the subject for solving for the row. |
|
477
|
|
|
* |
|
478
|
|
|
* This method will choose the best subject for using as the solve target for the row. |
|
479
|
|
|
* An invalid symbol will be returned if there is no valid target. |
|
480
|
|
|
* The symbols are chosen according to the following precedence: |
|
481
|
|
|
* 1) The first symbol representing an external variable. |
|
482
|
|
|
* 2) A negative slack or error tag variable. |
|
483
|
|
|
* If a subject cannot be found, an invalid symbol will be returned. |
|
484
|
|
|
* |
|
485
|
|
|
* @param Row $row |
|
486
|
|
|
* @param Tag $tag |
|
487
|
|
|
* @return Symbol |
|
488
|
|
|
*/ |
|
489
|
21 |
|
protected function chooseSubject(Row $row, Tag $tag): Symbol |
|
490
|
|
|
{ |
|
491
|
21 |
|
foreach ($row->getCells() as $symbol) { |
|
492
|
21 |
|
if ($symbol->getType() === Symbol::EXTERNAL) { |
|
493
|
21 |
|
return $symbol; |
|
494
|
|
|
} |
|
495
|
19 |
|
if ($tag->getMarker()->getType() === Symbol::SLACK || $tag->getMarker()->getType() === Symbol::ERROR) { |
|
496
|
5 |
|
if ($row->getCoefficientForSymbol($tag->getMarker()) < 0.0) { |
|
497
|
4 |
|
return $tag->getMarker(); |
|
498
|
|
|
} |
|
499
|
|
|
} |
|
500
|
19 |
|
if ($tag->getOther() !== null && ($tag->getOther()->getType() === Symbol::SLACK || $tag->getOther()->getType() === Symbol::ERROR)) { |
|
501
|
|
|
if ($row->getCoefficientForSymbol($tag->getOther()) < 0.0) { |
|
502
|
19 |
|
return $tag->getOther(); |
|
503
|
|
|
} |
|
504
|
|
|
} |
|
505
|
|
|
} |
|
506
|
18 |
|
return new Symbol(); |
|
507
|
|
|
} |
|
508
|
|
|
|
|
509
|
|
|
/** |
|
510
|
|
|
* Add the row to the tableau using an artificial variable. |
|
511
|
|
|
* |
|
512
|
|
|
* This will return false if the constraint cannot be satisfied. |
|
513
|
|
|
* |
|
514
|
|
|
* @param Row $row |
|
515
|
|
|
* @return bool |
|
516
|
|
|
* @throws InternalSolverException |
|
517
|
|
|
*/ |
|
518
|
17 |
|
protected function addWithArtificialVariable(Row $row): bool |
|
519
|
|
|
{ |
|
520
|
|
|
// Create and add the artificial variable to the tableau. |
|
521
|
17 |
|
$artificial = new Symbol(Symbol::SLACK); |
|
522
|
17 |
|
$this->rows->attach($artificial, Row::createFromRow($row)); |
|
523
|
|
|
|
|
524
|
17 |
|
$this->artificial = Row::createFromRow($row); |
|
525
|
|
|
|
|
526
|
|
|
// Optimize the artificial objective. |
|
527
|
|
|
// This is successful only if the artificial objective is optimized to zero. |
|
528
|
17 |
|
$this->optimize($this->artificial); |
|
529
|
17 |
|
$success = Util::isNearZero($this->artificial->getConstant()); |
|
530
|
17 |
|
$this->artificial = null; |
|
531
|
|
|
|
|
532
|
|
|
// If the artificial variable is basic, pivot the row so that it becomes non-basic. |
|
533
|
|
|
// If the row is constant, exit early. |
|
534
|
17 |
|
if (true === $this->rows->contains($artificial)) { |
|
535
|
17 |
|
$rowPointer = $this->rows->offsetGet($artificial); |
|
536
|
|
|
|
|
537
|
17 |
|
$deleteQueue = []; |
|
538
|
17 |
|
foreach ($this->rows as $symbol) { |
|
539
|
17 |
|
if ($this->rows->offsetGet($symbol) === $rowPointer) { |
|
540
|
17 |
|
$deleteQueue[] = $symbol; |
|
541
|
|
|
} |
|
542
|
|
|
} |
|
543
|
17 |
|
while (false === empty($deleteQueue)) { |
|
544
|
17 |
|
$this->rows->offsetUnset(array_pop($deleteQueue)); |
|
545
|
|
|
} |
|
546
|
|
|
|
|
547
|
17 |
|
if (0 === $rowPointer->getCells()->count()) { |
|
548
|
|
|
return $success; |
|
549
|
|
|
} |
|
550
|
|
|
|
|
551
|
17 |
|
$entering = $this->anyPivotableSymbol($rowPointer); |
|
552
|
17 |
|
if ($entering->getType() === Symbol::INVALID) { |
|
553
|
|
|
return false; |
|
554
|
|
|
} |
|
555
|
|
|
|
|
556
|
17 |
|
$rowPointer->solveForSymbols($artificial, $entering); |
|
557
|
17 |
|
$this->substitute($entering, $rowPointer); |
|
558
|
17 |
|
$this->rows->attach($entering, $rowPointer); |
|
559
|
|
|
} |
|
560
|
|
|
|
|
561
|
|
|
// Remove the artificial variable from the tableau. |
|
562
|
17 |
|
foreach ($this->rows as $symbol) { |
|
563
|
17 |
|
$rowEntry = $this->rows->offsetGet($symbol); |
|
564
|
17 |
|
$rowEntry->remove($artificial); |
|
565
|
|
|
} |
|
566
|
|
|
|
|
567
|
17 |
|
$this->objective->remove($artificial); |
|
568
|
|
|
|
|
569
|
17 |
|
return $success; |
|
570
|
|
|
} |
|
571
|
|
|
|
|
572
|
|
|
/** |
|
573
|
|
|
* Substitute the parametric symbol with the given row. |
|
574
|
|
|
* |
|
575
|
|
|
* This method will substitute all instances of the parametric symbol in the tableau |
|
576
|
|
|
* and the objective function with the given row. |
|
577
|
|
|
* |
|
578
|
|
|
* @param Symbol $symbol |
|
579
|
|
|
* @param Row $row |
|
580
|
|
|
*/ |
|
581
|
21 |
|
protected function substitute(Symbol $symbol, Row $row): void |
|
582
|
|
|
{ |
|
583
|
21 |
|
foreach ($this->rows as $currentSymbol) { |
|
584
|
18 |
|
$currentRow = $this->rows->offsetGet($currentSymbol); |
|
585
|
18 |
|
$currentRow->substitute($symbol, $row); |
|
586
|
18 |
|
if ($currentSymbol->getType() !== Symbol::EXTERNAL && $currentRow->getConstant() < 0.0) { |
|
587
|
18 |
|
$this->infeasibleRows[] = $currentSymbol; |
|
588
|
|
|
} |
|
589
|
|
|
} |
|
590
|
|
|
|
|
591
|
21 |
|
$this->objective->substitute($symbol, $row); |
|
592
|
|
|
|
|
593
|
21 |
|
if (null !== $this->artificial) { |
|
594
|
9 |
|
$this->artificial->substitute($symbol, $row); |
|
595
|
|
|
} |
|
596
|
21 |
|
} |
|
597
|
|
|
|
|
598
|
|
|
/** |
|
599
|
|
|
* Optimize the system for the given objective function. |
|
600
|
|
|
* This method performs iterations of Phase 2 of the simplex method until the objective function reaches a minimum. |
|
601
|
|
|
* |
|
602
|
|
|
* @param Row $objective |
|
603
|
|
|
* @throws InternalSolverException The value of the objective function is unbounded. |
|
604
|
|
|
*/ |
|
605
|
21 |
|
protected function optimize(Row $objective): void |
|
606
|
|
|
{ |
|
607
|
21 |
|
while (true) { |
|
608
|
21 |
|
$entering = $this->getEnteringSymbol($objective); |
|
609
|
21 |
|
if ($entering->getType() === Symbol::INVALID) { |
|
610
|
21 |
|
return; |
|
611
|
|
|
} |
|
612
|
|
|
|
|
613
|
9 |
|
$leaving = $this->getLeavingSymbol($entering); |
|
614
|
9 |
|
if ($leaving->getType() === Symbol::INVALID) { |
|
615
|
|
|
throw new InternalSolverException('The objective is unbounded.'); |
|
616
|
|
|
} |
|
617
|
|
|
|
|
618
|
|
|
// Pivot the entering symbol into the basis. |
|
619
|
9 |
|
$row = $this->rows->offsetGet($leaving); |
|
620
|
9 |
|
$this->rows->offsetUnset($leaving); |
|
621
|
9 |
|
$row->solveForSymbols($leaving, $entering); |
|
622
|
9 |
|
$this->rows->attach($entering, $row); |
|
623
|
9 |
|
$this->substitute($entering, $row); |
|
624
|
|
|
} |
|
625
|
|
|
} |
|
626
|
|
|
|
|
627
|
|
|
/** |
|
628
|
|
|
* Optimize the system using the dual of the simplex method. |
|
629
|
|
|
* |
|
630
|
|
|
* The current state of the system should be such that the objective function is optimal, but not feasible. |
|
631
|
|
|
* This method will perform an iteration of the dual simplex method to make the solution both optimal and feasible. |
|
632
|
|
|
* |
|
633
|
|
|
* @throws InternalSolverException The system cannot be dual optimized. |
|
634
|
|
|
*/ |
|
635
|
|
|
protected function dualOptimize(): void |
|
636
|
|
|
{ |
|
637
|
|
|
while (false === empty($this->infeasibleRows)) { |
|
638
|
|
|
$leaving = array_shift($this->infeasibleRows); |
|
639
|
|
|
if ($this->rows->contains($leaving)) { |
|
640
|
|
|
$row = $this->rows->offsetGet($leaving); |
|
641
|
|
|
if ($row->getConstant() < 0.0) { |
|
642
|
|
|
$entering = $this->getDualEnteringSymbol($row); |
|
643
|
|
|
if ($entering->getType() === Symbol::INVALID) { |
|
644
|
|
|
throw new InternalSolverException('Internal solver error'); |
|
645
|
|
|
} |
|
646
|
|
|
// Pivot the entering symbol into the basis. |
|
647
|
|
|
$this->rows->offsetUnset($leaving); |
|
648
|
|
|
$row->solveForSymbols($leaving, $entering); |
|
649
|
|
|
$this->substitute($entering, $row); |
|
650
|
|
|
$this->rows->attach($entering, $row); |
|
651
|
|
|
} |
|
652
|
|
|
} |
|
653
|
|
|
|
|
654
|
|
|
} |
|
655
|
|
|
} |
|
656
|
|
|
|
|
657
|
|
|
/** |
|
658
|
|
|
* Compute the entering variable for a pivot operation. |
|
659
|
|
|
* |
|
660
|
|
|
* This method will return first symbol in the objective function which is non-dummy and has a coefficient less than zero. |
|
661
|
|
|
* If no symbol meets the criteria, it means the objective function is at a minimum, and an invalid symbol is returned. |
|
662
|
|
|
* |
|
663
|
|
|
* @param Row $objective |
|
664
|
|
|
* @return Symbol |
|
665
|
|
|
*/ |
|
666
|
21 |
|
protected function getEnteringSymbol(Row $objective): Symbol |
|
667
|
|
|
{ |
|
668
|
21 |
|
foreach ($objective->getCells() as $symbol) { |
|
669
|
17 |
|
$coefficient = $objective->getCells()->offsetGet($symbol); |
|
670
|
17 |
|
if ($symbol->getType() !== Symbol::DUMMY && 0.0 > $coefficient) { |
|
671
|
17 |
|
return $symbol; |
|
672
|
|
|
} |
|
673
|
|
|
} |
|
674
|
21 |
|
return new Symbol(); |
|
675
|
|
|
} |
|
676
|
|
|
|
|
677
|
|
|
/** |
|
678
|
|
|
* Compute the entering symbol for the dual optimize operation. |
|
679
|
|
|
* |
|
680
|
|
|
* This method will return the symbol in the row which has a positive coefficient |
|
681
|
|
|
* and yields the minimum ratio for its respective symbol in the objective function. |
|
682
|
|
|
* The provided row must be infeasible. |
|
683
|
|
|
* If no symbol is found which meets the criteria, an invalid symbol is returned. |
|
684
|
|
|
* |
|
685
|
|
|
* @param Row $row |
|
686
|
|
|
* @return Symbol |
|
687
|
|
|
*/ |
|
688
|
|
|
protected function getDualEnteringSymbol(Row $row): Symbol |
|
689
|
|
|
{ |
|
690
|
|
|
$entering = new Symbol(); |
|
691
|
|
|
$ratio = PHP_FLOAT_MAX; |
|
692
|
|
|
|
|
693
|
|
|
foreach ($row->getCells() as $symbol) { |
|
694
|
|
|
if ($symbol->getType() !== Symbol::DUMMY) { |
|
695
|
|
|
$currentCoefficient = $row->getCells()->offsetGet($symbol); |
|
696
|
|
|
if (0.0 > $currentCoefficient) { |
|
697
|
|
|
$coefficient = $this->objective->getCoefficientForSymbol($symbol); |
|
698
|
|
|
$currentRatio = $coefficient / $currentCoefficient; |
|
699
|
|
|
if ($currentRatio < $ratio) { |
|
700
|
|
|
$ratio = $currentRatio; |
|
701
|
|
|
$entering = $symbol; |
|
702
|
|
|
} |
|
703
|
|
|
} |
|
704
|
|
|
} |
|
705
|
|
|
} |
|
706
|
|
|
|
|
707
|
|
|
return $entering; |
|
708
|
|
|
} |
|
709
|
|
|
|
|
710
|
|
|
/** |
|
711
|
|
|
* Get the first Slack or Error symbol in the row. |
|
712
|
|
|
* |
|
713
|
|
|
* If no such symbol is present, an Invalid symbol will be returned. |
|
714
|
|
|
* |
|
715
|
|
|
* @param Row $row |
|
716
|
|
|
* @return Symbol |
|
717
|
|
|
*/ |
|
718
|
17 |
|
protected function anyPivotableSymbol(Row $row): Symbol |
|
719
|
|
|
{ |
|
720
|
17 |
|
$symbol = new Symbol(); |
|
721
|
17 |
|
foreach ($row->getCells() as $_symbol) { |
|
722
|
17 |
|
if ($_symbol->getType() === Symbol::SLACK || $_symbol->getType() === Symbol::ERROR) { |
|
723
|
17 |
|
$symbol = $_symbol; |
|
724
|
|
|
} |
|
725
|
|
|
} |
|
726
|
17 |
|
return $symbol; |
|
727
|
|
|
} |
|
728
|
|
|
|
|
729
|
|
|
/** |
|
730
|
|
|
* Compute the symbol for pivot exit row. |
|
731
|
|
|
* |
|
732
|
|
|
* This method will return the symbol for the exit row in the row map. |
|
733
|
|
|
* If no appropriate exit symbol is found, an invalid symbol will be returned. |
|
734
|
|
|
* This indicates that the objective function is unbounded. |
|
735
|
|
|
* |
|
736
|
|
|
* @param Symbol $entering |
|
737
|
|
|
* @return Symbol |
|
738
|
|
|
*/ |
|
739
|
9 |
|
protected function getLeavingSymbol(Symbol $entering): Symbol |
|
740
|
|
|
{ |
|
741
|
9 |
|
$ratio = PHP_FLOAT_MAX; |
|
742
|
9 |
|
$symbol = new Symbol(); |
|
743
|
|
|
|
|
744
|
9 |
|
foreach ($this->rows as $currentSymbol) { |
|
745
|
9 |
|
if ($currentSymbol->getType() === Symbol::EXTERNAL) { |
|
746
|
9 |
|
continue; |
|
747
|
|
|
} |
|
748
|
9 |
|
$currentRow = $this->rows->offsetGet($currentSymbol); |
|
749
|
9 |
|
$temp = $currentRow->getCoefficientForSymbol($entering); |
|
750
|
9 |
|
if (0.0 > $temp) { |
|
751
|
9 |
|
$tempRatio = -$currentRow->getConstant() / $temp; |
|
752
|
9 |
|
if ($tempRatio < $ratio) { |
|
753
|
9 |
|
$ratio = $tempRatio; |
|
754
|
9 |
|
$symbol = $currentSymbol; |
|
755
|
|
|
} |
|
756
|
|
|
} |
|
757
|
|
|
} |
|
758
|
|
|
|
|
759
|
9 |
|
return $symbol; |
|
760
|
|
|
} |
|
761
|
|
|
|
|
762
|
|
|
/** |
|
763
|
|
|
* Get the symbol for the given variable. |
|
764
|
|
|
* |
|
765
|
|
|
* If a symbol does not exist for the variable, one will be created. |
|
766
|
|
|
* |
|
767
|
|
|
* @param Variable $variable |
|
768
|
|
|
* @return Symbol |
|
769
|
|
|
*/ |
|
770
|
21 |
|
protected function getVariableSymbol(Variable $variable): Symbol |
|
771
|
|
|
{ |
|
772
|
21 |
|
if (true === $this->variables->contains($variable)) { |
|
773
|
19 |
|
$symbol = $this->variables->offsetGet($variable); |
|
774
|
|
|
} else { |
|
775
|
21 |
|
$symbol = new Symbol(Symbol::EXTERNAL); |
|
776
|
21 |
|
$this->variables->attach($variable, $symbol); |
|
777
|
|
|
} |
|
778
|
21 |
|
return $symbol; |
|
779
|
|
|
} |
|
780
|
|
|
|
|
781
|
|
|
/** |
|
782
|
|
|
* Test whether a row is composed of all dummy variables. |
|
783
|
|
|
* |
|
784
|
|
|
* @param Row $row |
|
785
|
|
|
* @return bool |
|
786
|
|
|
*/ |
|
787
|
18 |
|
protected function allDummies(Row $row): bool |
|
788
|
|
|
{ |
|
789
|
18 |
|
foreach ($row->getCells() as $symbol) { |
|
790
|
18 |
|
if ($symbol->getType() !== Symbol::DUMMY) { |
|
791
|
18 |
|
return false; |
|
792
|
|
|
} |
|
793
|
|
|
} |
|
794
|
1 |
|
return true; |
|
795
|
|
|
} |
|
796
|
|
|
} |