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;
}
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));
}