/**
* Tests if Helper::isVector works with invalid vector
*/
public function testCheckVectorInvalid()
{
$numArray = NumPHP::ones(3, 2);
$this->assertFalse(Helper::isVector($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;
}
