private static function createPlayerTeamAssignmentMatrix(&$teamAssignmentsList, $totalPlayers)
 {
     // The team assignment matrix is often referred to as the "A" matrix. It's a matrix whose rows represent the players
     // and the columns represent teams. At Matrix[row, column] represents that player[row] is on team[col]
     // Positive values represent an assignment and a negative value means that we subtract the value of the next
     // team since we're dealing with pairs. This means that this matrix always has teams - 1 columns.
     // The only other tricky thing is that values represent the play percentage.
     // For example, consider a 3 team game where team1 is just player1, team 2 is player 2 and player 3, and
     // team3 is just player 4. Furthermore, player 2 and player 3 on team 2 played 25% and 75% of the time
     // (e.g. partial play), the A matrix would be:
     // A = this 4x2 matrix:
     // |  1.00  0.00 |
     // | -0.25  0.25 |
     // | -0.75  0.75 |
     // |  0.00 -1.00 |
     $playerAssignments = array();
     $totalPreviousPlayers = 0;
     $teamAssignmentsListCount = count($teamAssignmentsList);
     $currentColumn = 0;
     for ($i = 0; $i < $teamAssignmentsListCount - 1; $i++) {
         $currentTeam = $teamAssignmentsList[$i];
         // Need to add in 0's for all the previous players, since they're not
         // on this team
         $playerAssignments[$currentColumn] = $totalPreviousPlayers > 0 ? \array_fill(0, $totalPreviousPlayers, 0) : array();
         foreach ($currentTeam->getAllPlayers() as $currentPlayer) {
             $playerAssignments[$currentColumn][] = PartialPlay::getPartialPlayPercentage($currentPlayer);
             // indicates the player is on the team
             $totalPreviousPlayers++;
         }
         $rowsRemaining = $totalPlayers - $totalPreviousPlayers;
         $nextTeam = $teamAssignmentsList[$i + 1];
         foreach ($nextTeam->getAllPlayers() as $nextTeamPlayer) {
             // Add a -1 * playing time to represent the difference
             $playerAssignments[$currentColumn][] = -1 * PartialPlay::getPartialPlayPercentage($nextTeamPlayer);
             $rowsRemaining--;
         }
         for ($ixAdditionalRow = 0; $ixAdditionalRow < $rowsRemaining; $ixAdditionalRow++) {
             // Pad with zeros
             $playerAssignments[$currentColumn][] = 0;
         }
         $currentColumn++;
     }
     $playerTeamAssignmentsMatrix = Matrix::fromColumnValues($totalPlayers, $teamAssignmentsListCount - 1, $playerAssignments);
     return $playerTeamAssignmentsMatrix;
 }
Beispiel #2
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 public function testInverse()
 {
     // see http://www.mathwords.com/i/inverse_of_a_matrix.htm
     $a = new SquareMatrix(4, 3, 3, 2);
     $b = new SquareMatrix(-2, 3, 3, -4);
     $aInverse = $a->getInverse();
     $this->assertTrue($b->equals($aInverse));
     $identity2x2 = new IdentityMatrix(2);
     $aaInverse = Matrix::multiply($a, $aInverse);
     $this->assertTrue($identity2x2->equals($aaInverse));
     $c = new SquareMatrix(1, 2, 3, 0, 4, 5, 1, 0, 6);
     $cInverse = $c->getInverse();
     $d = Matrix::scalarMultiply(1.0 / 22, new SquareMatrix(24, -12, -2, 5, 3, -5, -4, 2, 4));
     $this->assertTrue($d->equals($cInverse));
     $identity3x3 = new IdentityMatrix(3);
     $ccInverse = Matrix::multiply($c, $cInverse);
     $this->assertTrue($identity3x3->equals($ccInverse));
 }