






'''simple docstring'''

import math






def 	_UpperCAmelCase    (  a		:	float						,			a		:	float							)			->			float:





						"""simple docstring"""
						if (
						    not isinstance(a						,			(int, float)							)
						    or power_factor < -1
						    or power_factor > 1
						):
												raise ValueError('power_factor must be a valid float value between -1 and 1.'							)
						return apparent_power * power_factor






def 	_UpperCAmelCase    (  a		:	float						,			a		:	float							)			->			float:





						"""simple docstring"""
						if (
						    not isinstance(a						,			(int, float)							)
						    or power_factor < -1
						    or power_factor > 1
						):
												raise ValueError('power_factor must be a valid float value between -1 and 1.'							)
						return apparent_power * math.sqrt(1 - power_factor**2							)


if __name__ == "__main__":
						import doctest

						doctest.testmod()








'''simple docstring'''

def 	_UpperCAmelCase    (  a		:	str						,			a		:	str							)			->			float:





						"""simple docstring"""

						def get_matched_characters(a		:	str						,			a		:	str							) -> str:
												lowercase_      :   Union[str, Any]        =			[]
												lowercase_      :   Tuple        =			min(len(_stra							)						,			len(_stra							)							) // 2
												for i, l in enumerate(_stra							):
																		lowercase_      :   Optional[int]        =			int(max(0						,			i - limit							)							)
																		lowercase_      :   Union[str, Any]        =			int(min(i + limit + 1						,			len(_stra							)							)							)
																		if l in _stra[left:right]:
																								matched.append(a							)
																								lowercase_      :   Union[str, Any]        =			f"{_stra[0:_stra.index(a							)]} {_stra[_stra.index(a							) + 1:]}"

												return "".join(a							)

						# matching characters
						lowercase_      :   Union[str, Any]        =			get_matched_characters(a						,			a							)
						lowercase_      :   Optional[Any]        =			get_matched_characters(a						,			a							)
						lowercase_      :   Optional[int]        =			len(a							)

						# transposition
						lowercase_      :   Dict        =			(
						    len([(ca, ca) for ca, ca in zip(a						,			a							) if ca != ca]							) // 2
						)

						if not match_count:
												lowercase_      :   List[str]        =			0.0
						else:
												lowercase_      :   Any        =			(
												    1
												    / 3
												    * (
												        match_count / len(a							)
												        + match_count / len(a							)
												        + (match_count - transpositions) / match_count
												    )
												)

						# common prefix up to 4 characters
						lowercase_      :   Optional[Any]        =			0
						for ca, ca in zip(stra[:4]						,			stra[:4]							):
												if ca == ca:
																		prefix_len += 1
												else:
																		break

						return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						print(jaro_winkler("hello", "world"))
