/**
* Return LUP-factorization P*A=L*U
*
* @see http://en.wikipedia.org/wiki/LUP_decomposition
* @see Introduction to Algorithms by Thomas H. Cormen and other
* @static
* @param Matrix $A
* @return array($C, $P, $singular, $even) - C = L + U - E, $singular === true for singular matrix, $even - for det
*/
public static function LUP($A)
{
if (!Matrix::isMatrix($A)) {
throw new InvalidArgumentException('Matrix needed. Given' . gettype($A));
}
if (!$A->isSquare()) {
throw new InvalidArgumentException("Matrix must be square");
}
$size = $A->getRowsCount();
$C = clone $A;
$P = array();
for ($i = 0; $i < $size; $i++) {
$P[$i] = $i;
}
$singular = false;
$even = true;
for ($i = 0; $i < $size; $i++) {
//поиск опорного элемента
$pivotValue = 0;
$pivot = -1;
for ($row = $i; $row < $size; $row++) {
if (abs($C->getElem($row, $i)) > $pivotValue) {
$pivotValue = abs($C->getElem($row, $i));
$pivot = $row;
}
}
if ($pivotValue == 0) {
$singular = true;
break;
}
//меняем местами i-ю строку и строку с опорным элементом
if ($pivot !== $i) {
list($P[$i], $P[$pivot]) = array($P[$pivot], $P[$i]);
$C->swapRows($pivot, $i);
$even = !$even;
}
for ($j = $i + 1; $j < $size; $j++) {
$temp = $C->getElem($j, $i) / $C->getElem($i, $i);
$C->setElem($j, $i, $temp);
for ($k = $i + 1; $k < $size; $k++) {
$temp = $C->getElem($j, $k) - $C->getElem($j, $i) * $C->getElem($i, $k);
$C->setElem($j, $k, $temp);
}
}
}
return array($C, $P, $singular, $even);
}
public function testIsMatrix()
{
$matrix = MatrixFactory::identityMatrix(3);
$this->assertTrue(Matrix::isMatrix($matrix));
$not_matrix = array(1, 2, 3);
$this->assertTrue(!Matrix::isMatrix($not_matrix));
$not_matrix = new stdClass();
$this->assertTrue(!Matrix::isMatrix($not_matrix));
}
/**
* Return true if matrices is equals
*
* @param Matrix $matrix
* @param float $eps
* @return bool
* @throws InvalidArgumentException
*/
public function equals($matrix, $eps = 0.0)
{
if (!Matrix::isMatrix($matrix)) {
throw new InvalidArgumentException('Matrix needed. Given' . gettype($matrix));
}
if ($eps === 0) {
return $this->getArray() == $matrix->getArray();
} else {
$sub = $this->sub($matrix);
return $sub->EuclideanNorm() < $eps;
}
}