/**
* 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));
}
}
}
}
}
/**
* Constructor: Generate cholesky deocmposition of given matrix.
*
* @param matrix
*/
public function __construct(&$matrix)
{
new Assertion($matrix instanceof Matrix, 'Given matrix not of class Matrix.');
new Assertion($matrix->isSquare(), 'Given matrix is not square.');
$this->_matrix = $matrix->copy();
for ($j = 0; $j < $this->_matrix->columns(); $j++) {
$d = $this->_matrix->get($j, $j);
for ($k = 0; $k < $j; $k++) {
$d -= pow($this->_matrix->get($j, $k), 2) * $this->_matrix->get($k, $k);
}
// Test if symmetric and positive definite can be guaranteed.
new Assertion($d > Cholesky::TOLERANCE * (double) $this->_matrix->get($j, $j), 'Symmetric and positive definite can not be guaranteed: ' . $d . ' > ' . Cholesky::TOLERANCE * (double) $this->_matrix->get($j, $j));
$this->_matrix->set($j, $j, $d);
for ($i = $j + 1; $i < $this->_matrix->rows(); $i++) {
$this->_matrix->set($i, $j, $this->_matrix->get($i, $j));
for ($k = 0; $k < $j; $k++) {
$this->_matrix->set($i, $j, $this->_matrix->get($i, $j) - $this->_matrix->get($i, $k) * $this->_matrix->get($k, $k) * $this->_matrix->get($j, $k));
}
$this->_matrix->set($i, $j, $this->_matrix->get($i, $j) / (double) $this->_matrix->get($j, $j));
}
}
}
/**
* Constructor: Generate LU decomposition of the matrix.
*
* @param matrix matrix to get the lu decomposition of
* @return vector permutation
*/
public function __construct(&$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, $k));
}
}
}
}
/**
* Constructor: Get the qr decomposition of the given matrix using givens rotations.
* The single givens rotations are stored within the matrix.
*
* @param matrix matrix to get the qr decomposition of
*/
public function __construct(&$matrix)
{
new Assertion($matrix instanceof Matrix, 'Given matrix not of class Matrix.');
$this->_matrix = $matrix->copy();
// Check in all columns except the n-th one for entries to eliminate.
for ($j = 0; $j < $this->_matrix->columns() - 1; $j++) {
for ($i = $j + 1; $i < $this->_matrix->rows(); $i++) {
// If the entry is zero it can be skipped.
if ($this->_matrix->get($i, $j) != 0) {
$r = sqrt(pow($this->_matrix->get($j, $j), 2) + pow($this->_matrix->get($i, $j), 2));
if ($this->_matrix->get($i, $j) < 0) {
$r = -$r;
}
$s = $this->_matrix->get($i, $j) / $r;
$c = $this->_matrix->get($j, $j) / $r;
// Apply the givens rotation:
for ($k = $j; $k < $this->_matrix->columns(); $k++) {
$jk = $this->_matrix->get($j, $k);
$ik = $this->_matrix->get($i, $k);
$this->_matrix->set($j, $k, $c * $jk + $s * $ik);
$this->_matrix->set($i, $k, -$s * $jk + $c * $ik);
}
// c and s can be stored in one matrix entry:
if ($c == 0) {
$this->_matrix->set($i, $j, 1);
} else {
if (abs($s) < abs($c)) {
if ($c < 0) {
$this->_matrix->set($i, $j, -0.5 * $s);
} else {
$this->_matrix->set($i, $j, 0.5 * $s);
}
} else {
$this->_matrix->set($i, $j, 2.0 / $c);
}
}
}
}
}
}
