Returns a NumArray with the same size, but filled with 0
|
public static zerosLike ( |
||
| $numArray | given NumArray | |
| return | ||
/**
* 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;
}
/**
* Tests NumPHP::zerosLike with 2x3 matrix
*/
public function testZerosLike()
{
$numArray = new NumArray([[1, 2, 3], [4, 5, 6]]);
$expectedNumArray = NumPHP::zeros(2, 3);
$this->assertNumArrayEquals($expectedNumArray, NumPHP::zerosLike($numArray));
}
/**
* Back Substitution solves a linear system with a upper triangular matrix of
* size n*n and a vector of size n or a matrix of size n*m
*
* @param NumArray $uMatrix upper triangular matrix of size n*n
* @param NumArray $numArray vector of size n or matrix of size n*m
*
* @return NumArray
*
* @since 1.0.0
*/
protected static function backSubstitution(NumArray $uMatrix, NumArray $numArray)
{
$shape = $numArray->getShape();
if (Helper::isVector($numArray)) {
$xVector = NumPHP::zerosLike($numArray);
for ($i = $shape[0] - 1; $i >= 0; $i--) {
$slice = sprintf("%d:%d", $i + 1, $shape[0]);
$sum = $uMatrix->get($i, $slice)->dot($xVector->get($slice));
$xVector->set($i, $numArray->get($i)->sub($sum)->div($uMatrix->get($i, $i)));
}
return $xVector;
}
// $numArray is a matrix
$copy = clone $numArray;
for ($i = 0; $i < $shape[1]; $i++) {
$copy->set(':', $i, self::backSubstitution($uMatrix, $copy->get(':', $i)));
}
return $copy;
}
