/**
* Assembles Q using the single givens rotations.
*
* @return matrix Q
*/
public function getQ()
{
// Q is an m x m matrix if m is the maximum of the number of rows and thenumber of columns.
$m = max($this->_matrix->columns(), $this->_matrix->rows());
$Q = new Matrix($m, $m);
$Q->setAll(0.0);
// Begin with the identity matrix.
for ($i = 0; $i < min($Q->rows(), $Q->columns()); $i++) {
$Q->set($i, $i, 1.0);
}
// Got backwards through all householder transformations and apply them on
for ($k = $this->_matrix->columns() - 1; $k >= 0; $k--) {
for ($j = $k; $j < $Q->columns(); $j++) {
// First compute w^T(j) = v^T * Q(j) where Q(j) is the j-th column of Q.
$w = $Q->get($k, $j) * 1.0;
for ($i = $k + 1; $i < $Q->rows(); $i++) {
$w += $this->_matrix->get($i, $k) * $Q->get($i, $j);
}
// Now : Q(i,j) = Q(i,j) - tau(k)*v(i)*w(j).
$Q->set($k, $j, $Q->get($k, $j) - $this->_tau->get($k) * 1.0 * $w);
for ($i = $k + 1; $i < $Q->rows(); $i++) {
$Q->set($i, $j, $Q->get($i, $j) - $this->_tau->get($k) * $this->_matrix->get($i, $k) * $w);
}
}
}
return $Q;
}
/**
* Calculate the determinant of the matrix with the given lu decomposition.
*
* @param matrix lu decomposition
* @param vector permutation vector of the lu decomposition
*/
public function getDeterminant()
{
// Calculate number of swapped rows.
$swapped = 0;
for ($i = 0; $i < $this->_permutation->size(); $i++) {
if ($this->_permutation->get($i) != $i) {
$swapped++;
}
}
$determinant = pow(-1, $swapped);
for ($i = 0; $i < $this->_matrix->rows(); $i++) {
$determinant *= $this->_matrix->get($i, $i);
}
return $determinant;
}
/**
* Build the inner product of two vectors.
*
* @param vector $a
* @param vector $b
* @return vector inner product
*/
public static function inner($a, $b)
{
new Assertion($a instanceof Vector, 'Given first vector not of class Vector.');
new Assertion($b instanceof Vector, 'Given second vector not of class Vector.');
new Assertion($a->size() == $b->size(), 'Dimensions do not match.');
$size = $a->size();
$result = 0;
for ($i = 0; $i < $size; $i++) {
$result += $a->get($i) * $b->get($i);
}
return $result;
}
