/**
* 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;
}
