| 1 |  |  | <?php | 
            
                                                                                                            
                            
            
                                    
            
            
                | 2 |  |  | declare(strict_types=1); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 3 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 4 |  |  | namespace Ctefan\Kiwi; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 5 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 6 |  |  | use Ctefan\Kiwi\Exception\DuplicateConstraintException; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 7 |  |  | use Ctefan\Kiwi\Exception\DuplicateEditVariableException; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 8 |  |  | use Ctefan\Kiwi\Exception\InternalSolverException; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 9 |  |  | use Ctefan\Kiwi\Exception\RequiredFailureException; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 10 |  |  | use Ctefan\Kiwi\Exception\UnknownConstraintException; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 11 |  |  | use Ctefan\Kiwi\Exception\UnknownEditVariableException; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 12 |  |  | use Ctefan\Kiwi\Exception\UnsatisfiableConstraintException; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 13 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 14 |  |  | /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 15 |  |  |  * The constraint solver. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 16 |  |  |  */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 17 |  |  | class Solver | 
            
                                                                                                            
                            
            
                                    
            
            
                | 18 |  |  | { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 19 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 20 |  |  |      * @var \SplObjectStorage<Constraint, Tag> | 
            
                                                                                                            
                            
            
                                    
            
            
                | 21 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 22 |  |  |     protected $constraints; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 23 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 24 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 25 |  |  |      * @var \SplObjectStorage<Symbol, Row> | 
            
                                                                                                            
                            
            
                                    
            
            
                | 26 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 27 |  |  |     protected $rows; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 28 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 29 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 30 |  |  |      * @var \SplObjectStorage<Variable, Symbol> | 
            
                                                                                                            
                            
            
                                    
            
            
                | 31 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 32 |  |  |     protected $variables; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 33 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 34 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 35 |  |  |      * @var \SplObjectStorage<Variable, EditInfo> | 
            
                                                                                                            
                            
            
                                    
            
            
                | 36 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 37 |  |  |     protected $edits; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 38 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 39 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 40 |  |  |      * @var array<Symbol> | 
            
                                                                                                            
                            
            
                                    
            
            
                | 41 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 42 |  |  |     protected $infeasibleRows; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 43 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 44 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 45 |  |  |      * @var Row | 
            
                                                                                                            
                            
            
                                    
            
            
                | 46 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 47 |  |  |     protected $objective; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 48 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 49 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 50 |  |  |      * @var Row | 
            
                                                                                                            
                            
            
                                    
            
            
                | 51 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 52 |  |  |     protected $artificial; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 53 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 54 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 55 |  |  |      * Solver constructor. | 
            
                                                                                                            
                                                                
            
                                    
            
            
                | 56 |  |  |      */ | 
            
                                                                        
                            
            
                                    
            
            
                | 57 | 21 |  |     public function __construct() | 
            
                                                                        
                            
            
                                    
            
            
                | 58 |  |  |     { | 
            
                                                                        
                            
            
                                    
            
            
                | 59 | 21 |  |         $this->constraints = new \SplObjectStorage(); | 
            
                                                                        
                            
            
                                    
            
            
                | 60 | 21 |  |         $this->rows = new \SplObjectStorage(); | 
            
                                                                        
                            
            
                                    
            
            
                | 61 | 21 |  |         $this->variables = new \SplObjectStorage(); | 
            
                                                                        
                            
            
                                    
            
            
                | 62 | 21 |  |         $this->edits = new \SplObjectStorage(); | 
            
                                                                        
                            
            
                                    
            
            
                | 63 | 21 |  |         $this->infeasibleRows = []; | 
            
                                                                        
                            
            
                                    
            
            
                | 64 | 21 |  |         $this->objective = new Row(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 65 | 21 |  |     } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 66 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 67 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 68 |  |  |      * Add a constraint to the solver. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 69 |  |  |      * | 
            
                                                                                                            
                            
            
                                    
            
            
                | 70 |  |  |      * @param Constraint $constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 71 |  |  |      * @throws DuplicateConstraintException The given constraint has already been added to the solver. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 72 |  |  |      * @throws UnsatisfiableConstraintException The given constraint is required and cannot be satisfied. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 73 |  |  |      * @throws InternalSolverException | 
            
                                                                                                            
                            
            
                                    
            
            
                | 74 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 75 | 21 |  |     public function addConstraint(Constraint $constraint): void | 
            
                                                                                                            
                            
            
                                    
            
            
                | 76 |  |  |     { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 77 | 21 |  |         if (true === $this->constraints->contains($constraint)) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 78 |  |  |             throw new DuplicateConstraintException($constraint); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 79 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 80 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 81 |  |  |         // Creating a row causes symbols to reserved for the variables in the constraint. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 82 |  |  |         // If this method exits with an exception, then its possible those variables will linger in the var map. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 83 |  |  |         // Since its likely that those variables will be used in other constraints and since exceptional conditions are uncommon, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 84 |  |  |         // I'm not too worried about aggressive cleanup of the var map. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 85 | 21 |  |         $tag = new Tag(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 86 | 21 |  |         $row = $this->createRow($constraint, $tag); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 87 | 21 |  |         $subject = $this->chooseSubject($row, $tag); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 88 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 89 |  |  |         // If chooseSubject() could find a valid entering symbol, one last option is available if the entire row is composed of dummy variables. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 90 |  |  |         // If the constant of the row is zero, then this represents redundant constraints and the new dummy marker can enter the basis. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 91 |  |  |         // If the constant is non-zero, then it represents an unsatisfiable constraint. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 92 | 21 |  |         if ($subject->getType() === Symbol::INVALID && true === $this->allDummies($row)) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 93 | 1 |  |             if (false === Util::isNearZero($row->getConstant())) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 94 | 1 |  |                 throw new UnsatisfiableConstraintException($constraint); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 95 |  |  |             } else { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 96 |  |  |                 $subject = $tag->getMarker(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 97 |  |  |             } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 98 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 99 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 100 |  |  |         // If an entering symbol still isn't found, then the row must be added using an artificial variable. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 101 |  |  |         // If that fails, then the row represents an unsatisfiable constraint. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 102 | 21 |  |         if ($subject->getType() === Symbol::INVALID) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 103 | 17 |  |             if (false === $this->addWithArtificialVariable($row)) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 104 | 17 |  |                 throw new UnsatisfiableConstraintException($constraint); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 105 |  |  |             } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 106 |  |  |         } else { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 107 | 21 |  |             $row->solveForSymbol($subject); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 108 | 21 |  |             $this->substitute($subject, $row); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 109 | 21 |  |             $this->rows->attach($subject, $row); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 110 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 111 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 112 | 21 |  |         $this->constraints->attach($constraint, $tag); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 113 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 114 |  |  |         // Optimizing after each constraint is added performs less aggregate work due to a smaller average system size. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 115 |  |  |         // It also ensures the solver remains in a consistent state. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 116 | 21 |  |         $this->optimize($this->objective); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 117 | 21 |  |     } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 118 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 119 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 120 |  |  |      * Remove a constraint from the solver. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 121 |  |  |      * | 
            
                                                                                                            
                            
            
                                    
            
            
                | 122 |  |  |      * @param Constraint $constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 123 |  |  |      * @throws UnknownConstraintException The given constraint has not been added to the solver. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 124 |  |  |      * @throws InternalSolverException | 
            
                                                                                                            
                            
            
                                    
            
            
                | 125 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 126 | 2 |  |     public function removeConstraint(Constraint $constraint): void | 
            
                                                                                                            
                            
            
                                    
            
            
                | 127 |  |  |     { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 128 | 2 |  |         if (false === $this->constraints->contains($constraint)) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 129 |  |  |             throw new UnknownConstraintException($constraint); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 130 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 131 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 132 | 2 |  |         $tag = $this->constraints->offsetGet($constraint); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 133 | 2 |  |         $this->constraints->offsetUnset($constraint); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 134 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 135 |  |  |         // Remove the error effects from the objective function before pivoting, | 
            
                                                                                                            
                            
            
                                    
            
            
                | 136 |  |  |         // or substitutions into the objective will lead to incorrect solver results. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 137 | 2 |  |         $this->removeConstraintEffects($constraint, $tag); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 138 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 139 |  |  |         // If the marker is basic, simply drop the row. Otherwise, pivot the marker into the basis and then drop the row. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 140 | 2 |  |         if (true === $this->rows->contains($tag->getMarker())) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 141 | 1 |  |             $this->rows->offsetUnset($tag->getMarker()); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 142 |  |  |         } else { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 143 | 2 |  |             $leaving = $this->getMarkerLeavingSymbol($tag->getMarker()); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 144 | 2 |  |             if ($leaving->getType() === Symbol::INVALID) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 145 |  |  |                 throw new InternalSolverException('Internal solver error'); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 146 |  |  |             } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 147 | 2 |  |             $row = $this->rows->offsetGet($leaving); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 148 | 2 |  |             $this->rows->offsetUnset($leaving); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 149 | 2 |  |             $row->solveForSymbols($leaving, $tag->getMarker()); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 150 | 2 |  |             $this->substitute($tag->getMarker(), $row); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 151 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 152 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 153 |  |  |         // Optimizing after each constraint is removed ensures that the solver remains consistent. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 154 |  |  |         // It makes the solver API easier to use at a small tradeoff for speed. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 155 | 2 |  |         $this->optimize($this->objective); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 156 | 2 |  |     } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 157 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 158 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 159 |  |  |      * Test whether a constraint has been added to the solver. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 160 |  |  |      * | 
            
                                                                                                            
                            
            
                                    
            
            
                | 161 |  |  |      * @param Constraint $constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 162 |  |  |      * @return bool | 
            
                                                                                                            
                            
            
                                    
            
            
                | 163 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 164 |  |  |     public function hasConstraint(Constraint $constraint): bool | 
            
                                                                                                            
                            
            
                                    
            
            
                | 165 |  |  |     { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 166 |  |  |         return $this->constraints->contains($constraint); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 167 |  |  |     } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 168 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 169 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 170 |  |  |      * Add an edit variable to the solver. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 171 |  |  |      * | 
            
                                                                                                            
                            
            
                                    
            
            
                | 172 |  |  |      * This method should be called before the 'suggestValue' method is used to supply a suggested value | 
            
                                                                                                            
                            
            
                                    
            
            
                | 173 |  |  |      * for the given edit variable. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 174 |  |  |      * | 
            
                                                                                                            
                            
            
                                    
            
            
                | 175 |  |  |      * @param Variable $variable | 
            
                                                                                                            
                            
            
                                    
            
            
                | 176 |  |  |      * @param float $strength | 
            
                                                                                                            
                            
            
                                    
            
            
                | 177 |  |  |      * @throws DuplicateEditVariableException The given edit variable has already been added to the solver. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 178 |  |  |      * @throws RequiredFailureException The given strength is >= required. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 179 |  |  |      * @throws InternalSolverException | 
            
                                                                                                            
                            
            
                                    
            
            
                | 180 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 181 |  |  |     public function addEditVariable(Variable $variable, float $strength): void | 
            
                                                                                                            
                            
            
                                    
            
            
                | 182 |  |  |     { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 183 |  |  |         if ($this->edits->contains($variable)) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 184 |  |  |             throw new DuplicateEditVariableException(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 185 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 186 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 187 |  |  |         $strength = Strength::clip($strength); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 188 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 189 |  |  |         if (Strength::required() === $strength) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 190 |  |  |             throw new RequiredFailureException(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 191 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 192 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 193 |  |  |         $terms = []; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 194 |  |  |         $terms[] = new Term($variable); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 195 |  |  |         $constraint = new Constraint(new Expression($terms), RelationalOperator::EQ, $strength); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 196 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 197 |  |  |         try { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 198 |  |  |             $this->addConstraint($constraint); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 199 |  |  |         } catch (DuplicateConstraintException $e) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 200 |  |  |             // TODO log | 
            
                                                                                                            
                            
            
                                    
            
            
                | 201 |  |  |         } catch (UnsatisfiableConstraintException $e) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 202 |  |  |             // TODO log | 
            
                                                                                                            
                            
            
                                    
            
            
                | 203 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 204 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 205 |  |  |         $info = new EditInfo($constraint, $this->constraints->offsetGet($constraint), 0.0); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 206 |  |  |         $this->edits->attach($variable, $info); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 207 |  |  |     } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 208 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 209 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 210 |  |  |      * Remove an edit variable from the solver. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 211 |  |  |      * | 
            
                                                                                                            
                            
            
                                    
            
            
                | 212 |  |  |      * @param Variable $variable | 
            
                                                                                                            
                            
            
                                    
            
            
                | 213 |  |  |      * @throws UnknownEditVariableException The given edit variable has not been added to the solver. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 214 |  |  |      * @throws InternalSolverException | 
            
                                                                                                            
                            
            
                                    
            
            
                | 215 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 216 |  |  |     public function removeEditVariable(Variable $variable): void | 
            
                                                                                                            
                            
            
                                    
            
            
                | 217 |  |  |     { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 218 |  |  |         if (false === $this->edits->contains($variable)) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 219 |  |  |             throw new UnknownEditVariableException(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 220 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 221 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 222 |  |  |         $info = $this->edits->offsetGet($variable); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 223 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 224 |  |  |         try { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 225 |  |  |             $this->removeConstraint($info->getConstraint()); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 226 |  |  |         } catch (UnknownConstraintException $e) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 227 |  |  |             // TODO log | 
            
                                                                                                            
                            
            
                                    
            
            
                | 228 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 229 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 230 |  |  |         $this->edits->offsetUnset($variable); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 231 |  |  |     } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 232 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 233 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 234 |  |  |      * Test whether an edit variable has been added to the solver. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 235 |  |  |      * | 
            
                                                                                                            
                            
            
                                    
            
            
                | 236 |  |  |      * @param Variable $variable | 
            
                                                                                                            
                            
            
                                    
            
            
                | 237 |  |  |      * @return bool | 
            
                                                                                                            
                            
            
                                    
            
            
                | 238 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 239 |  |  |     public function hasEditVariable(Variable $variable): bool | 
            
                                                                                                            
                            
            
                                    
            
            
                | 240 |  |  |     { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 241 |  |  |         return $this->edits->contains($variable); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 242 |  |  |     } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 243 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 244 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 245 |  |  |      * Suggest a value for the given edit variable. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 246 |  |  |      * | 
            
                                                                                                            
                            
            
                                    
            
            
                | 247 |  |  |      * This method should be used after an edit variable as been added to the solver | 
            
                                                                                                            
                            
            
                                    
            
            
                | 248 |  |  |      * in order to suggest the value for that variable. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 249 |  |  |      * | 
            
                                                                                                            
                            
            
                                    
            
            
                | 250 |  |  |      * @param Variable $variable | 
            
                                                                                                            
                            
            
                                    
            
            
                | 251 |  |  |      * @param float $value | 
            
                                                                                                            
                            
            
                                    
            
            
                | 252 |  |  |      * @throws UnknownEditVariableException The given edit variable has not been added to the solver. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 253 |  |  |      * @throws InternalSolverException | 
            
                                                                                                            
                            
            
                                    
            
            
                | 254 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 255 |  |  |     public function suggestValue(Variable $variable, float $value): void | 
            
                                                                                                            
                            
            
                                    
            
            
                | 256 |  |  |     { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 257 |  |  |         if (false === $this->edits->contains($variable)) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 258 |  |  |             throw new UnknownEditVariableException(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 259 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 260 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 261 |  |  |         $info = $this->edits->offsetGet($variable); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 262 |  |  |         $delta = $value - $info->getConstant(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 263 |  |  |         $info->setContant($value); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 264 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 265 |  |  |         // Check first if the positive error variable is basic. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 266 |  |  |         if (true === $this->rows->contains($info->getTag()->getMarker())) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 267 |  |  |             $row = $this->rows->offsetGet($info->getTag()->getMarker()); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 268 |  |  |             if (0.0 > $row->add(-$delta)) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 269 |  |  |                 $this->infeasibleRows[] = $info->getTag()->getMarker(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 270 |  |  |             } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 271 |  |  |             $this->dualOptimize(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 272 |  |  |             return; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 273 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 274 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 275 |  |  |         // Check next if the negative error variable is basic. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 276 |  |  |         if (true === $this->rows->contains($info->getTag()->getOther())) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 277 |  |  |             $row = $this->rows->offsetGet($info->getTag()->getOther()); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 278 |  |  |             if (0.0 > $row->add($delta)) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 279 |  |  |                 $this->infeasibleRows[] = $info->getTag()->getOther(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 280 |  |  |             } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 281 |  |  |             $this->dualOptimize(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 282 |  |  |             return; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 283 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 284 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 285 |  |  |         // Otherwise update each row where the error variables exist. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 286 |  |  |         foreach ($this->rows as $symbol) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 287 |  |  |             $currentRow = $this->rows->offsetGet($symbol); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 288 |  |  |             $coefficient = $currentRow->getCoefficientForSymbol($info->getTag()->getMarker()); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 289 |  |  |             if (0.0 !== $coefficient && 0.0 > $currentRow->add($delta * $coefficient) && Symbol::EXTERNAL !== $symbol->getType()) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 290 |  |  |                 $this->infeasibleRows[] = $symbol; | 
            
                                                                                                            
                            
            
                                    
            
            
                | 291 |  |  |             } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 292 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 293 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 294 |  |  |         $this->dualOptimize(); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 295 |  |  |     } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 296 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 297 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 298 |  |  |      * Update the values of the external solver variables. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 299 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 300 | 18 |  |     public function updateVariables(): void | 
            
                                                                                                            
                            
            
                                    
            
            
                | 301 |  |  |     { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 302 | 18 |  |         foreach ($this->variables as $variable) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 303 | 18 |  |             $symbol = $this->variables->offsetGet($variable); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 304 | 18 |  |             if (false === $this->rows->contains($symbol)) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 305 | 1 |  |                 $variable->setValue(0.0); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 306 |  |  |             } else { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 307 | 18 |  |                 $row = $this->rows->offsetGet($symbol); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 308 | 18 |  |                 $variable->setValue($row->getConstant()); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 309 |  |  |             } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 310 |  |  |         } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 311 | 18 |  |     } | 
            
                                                                                                            
                            
            
                                    
            
            
                | 312 |  |  |  | 
            
                                                                                                            
                            
            
                                    
            
            
                | 313 |  |  |     /** | 
            
                                                                                                            
                            
            
                                    
            
            
                | 314 |  |  |      * Remove the effects of a constraint on the objective function. | 
            
                                                                                                            
                            
            
                                    
            
            
                | 315 |  |  |      * | 
            
                                                                                                            
                            
            
                                    
            
            
                | 316 |  |  |      * @param Constraint $constraint | 
            
                                                                                                            
                            
            
                                    
            
            
                | 317 |  |  |      * @param Tag $tag | 
            
                                                                                                            
                            
            
                                    
            
            
                | 318 |  |  |      */ | 
            
                                                                                                            
                            
            
                                    
            
            
                | 319 | 2 |  |     protected function removeConstraintEffects(Constraint $constraint, Tag $tag): void | 
            
                                                                                                            
                            
            
                                    
            
            
                | 320 |  |  |     { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 321 | 2 |  |         if ($tag->getMarker()->getType() === Symbol::ERROR) { | 
            
                                                                                                            
                            
            
                                    
            
            
                | 322 |  |  |             $this->removeMarkerEffects($tag->getMarker(), $constraint->getStrength()); | 
            
                                                                                                            
                            
            
                                    
            
            
                | 323 | 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 |  |  | } |