/**
* Constructor: Generate LU decomposition of the matrix.
*
* @param matrix matrix to get the lu decomposition of
* @return vector permutation
*/
public function __construct(&$matrix)
{
new Assertion($matrix instanceof Matrix, 'Given matrix not of class Matrix.');
new Assertion($matrix->isSquare(), 'Matrix is not quadratic.');
$this->_permutation = new Vector($matrix->rows());
$this->_matrix = $matrix->copy();
for ($j = 0; $j < $this->_matrix->rows(); $j++) {
$pivot = $j;
for ($i = $j + 1; $i < $this->_matrix->rows(); $i++) {
if (abs($this->_matrix->get($i, $j)) > abs($this->_matrix->get($pivot, $j))) {
$pivot = $i;
}
}
$this->_permutation->set($j, $pivot);
$this->_matrix->swapRows($j, $pivot);
for ($i = $j + 1; $i < $this->_matrix->columns(); $i++) {
$this->_matrix->set($i, $j, $this->_matrix->get($i, $j) / $this->_matrix->get($j, $j));
for ($k = $j + 1; $k < $this->_matrix->columns(); $k++) {
$this->_matrix->set($i, $k, $this->_matrix->get($i, $k) - $this->_matrix->get($i, $j) * $this->_matrix->get($j, $k));
}
}
}
}
