/**
* Calculates lower triangular matrix L of given symmetric positive definite matrix
*
* @param NumArray $squareMatrix symmetric positive definite matrix
*
* @return NumArray
*
* @throws InvalidArgumentException will be thrown, when `$squareMatrix` is not positive definite
* @throws NoSquareMatrixException will be thrown, when `$squareMatrix` is not square
* @throws NoSymmetricMatrixException will be thrown, when `$squareMatrix` is not symmetric
*
* @since 1.0.2
*/
public static function cholesky(NumArray $squareMatrix)
{
if (!Helper::isSquareMatrix($squareMatrix)) {
throw new NoSquareMatrixException(sprintf("Matrix with shape (%s) given, matrix has to be square", implode(', ', $squareMatrix->getShape())));
}
$shape = $squareMatrix->getShape();
$size = $shape[0];
$aMatrix = clone $squareMatrix;
$lMatrix = NumPHP::zerosLike($aMatrix);
for ($k = 0; $k < $size; $k++) {
$diaElem = $aMatrix->get($k, $k)->getData();
if ($diaElem <= 0) {
throw new InvalidArgumentException("Matrix is not positive definite");
}
$diaElem = sqrt($diaElem);
$lMatrix->set($k, $k, $diaElem);
for ($i = $k + 1; $i < $size; $i++) {
if ($squareMatrix->get($i, $k) != $squareMatrix->get($k, $i)) {
throw new NoSymmetricMatrixException("Matrix is not symmetric");
}
$lMatrix->set($i, $k, $aMatrix->get($i, $k)->div($diaElem));
for ($j = $k + 1; $j <= $i; $j++) {
$aMatrix->set($i, $j, $aMatrix->get($i, $j)->sub($lMatrix->get($i, $k)->mult($lMatrix->get($j, $k))));
}
}
}
return $lMatrix;
}
/**
* Calculates the determinant of a matrix
*
* @param mixed $matrix matrix
*
* @throws NoSquareMatrixException will be thrown, if given array is no square matrix
*
* @api
* @since 1.0.0
*
* @return float
*/
public static function det($matrix)
{
if (!$matrix instanceof NumArray) {
$matrix = new NumArray($matrix);
} elseif ($matrix->inCache(self::CACHE_KEY_DETERMINANT)) {
return $matrix->getCache(self::CACHE_KEY_DETERMINANT);
}
if (!Helper::isSquareMatrix($matrix)) {
throw new NoSquareMatrixException(sprintf("Matrix with shape (%s) given, matrix has to be square", implode(', ', $matrix->getShape())));
}
$shape = $matrix->getShape();
$lud = self::lud($matrix);
/**
* Upper triangular matrix
*
* @var NumArray $uMatrix
*/
$uMatrix = $lud[2];
$det = 1;
for ($i = 0; $i < $shape[0]; $i++) {
$det *= $uMatrix->get($i, $i)->getData();
}
$matrix->setCache(self::CACHE_KEY_DETERMINANT, $det);
return $det;
}
/**
* Tests if Helper::isSquareMatrix works with invalid square matrix
*/
public function testCheckSquareMatrixInvalid()
{
$numArray = NumPHP::ones(2, 3);
$this->assertFalse(Helper::isSquareMatrix($numArray));
}
