/**
* Constructor: Get the qr decomposition of the given matrix using householder transformations.
* The single householder matrizes are stores within the matrix.
*
* @param matrix matrix to get the composition of
*/
public function __construct(&$matrix)
{
new Assertion($matrix instanceof Matrix, 'Given matrix not of class Matrix.');
$this->_tau = new Vector($matrix->columns());
$this->_matrix = $matrix->copy();
for ($j = 0; $j < $this->_matrix->columns(); $j++) {
$norm = 0.0;
for ($i = $j; $i < $this->_matrix->rows(); $i++) {
$norm += pow($this->_matrix->get($i, $j), 2);
}
$norm = sqrt($norm);
$sign = 1.0;
if ($this->_matrix->get($j, $j) < 0) {
$sign = -1.0;
}
$v1 = $this->_matrix->get($j, $j) + $sign * $norm;
$scalar = 1;
for ($i = $j + 1; $i < $this->_matrix->rows(); $i++) {
$this->_matrix->set($i, $j, $this->_matrix->get($i, $j) / $v1);
$scalar += pow($this->_matrix->get($i, $j), 2);
}
$this->_tau->set($j, 2.0 / $scalar);
$w = new Vector($this->_matrix->columns());
$w->setAll(0.0);
// First calculate w = v_j^T * A.
for ($i = $j; $i < $this->_matrix->columns(); $i++) {
$w->set($i, $this->_matrix->get($j, $i));
for ($k = $j + 1; $k < $this->_matrix->rows(); $k++) {
if ($i == $j) {
$w->set($i, $w->get($i) + $this->_matrix->get($k, $j) * $this->_matrix->get($k, $i) * $v1);
} else {
$w->set($i, $w->get($i) + $this->_matrix->get($k, $j) * $this->_matrix->get($k, $i));
}
}
$this->_matrix->set($j, $i, $this->_matrix->get($j, $i) - $this->_tau->get($j) * $w->get($i));
for ($k = $j + 1; $k < $this->_matrix->rows(); $k++) {
if ($i > $j) {
$this->_matrix->set($k, $i, $this->_matrix->get($k, $i) - $this->_tau->get($j) * $this->_matrix->get($k, $j) * $w->get($i));
}
}
}
// Assemble v for trace.
$v = new Vector($this->_matrix->rows() - $j);
$v->set(0, 1);
for ($i = 1; $i < $v->size(); $i++) {
$v->set($i, $this->_matrix->get($i, $j));
}
$this->_trace[$j] = array('v' => $v, 'matrix' => $this->_matrix->copy());
}
}
public function removing()
{
$v = new Vector();
$o = new String('one');
$v->add($o);
$r = $v->remove(0);
$this->assertEquals(0, $v->size());
$this->assertEquals($o, $r);
}
