



def 					__snake_case     (      _UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase       ,			):
				__a							=    [redshift, radiation_density, matter_density, dark_energy]
				if any(p < 0 for p in parameters    ):
								raise ValueError('''All input parameters must be positive'''    )

				if any(p > 1 for p in parameters[1:4]    ):
								raise ValueError('''Relative densities cannot be greater than one'''    )
				else:
								__a							=    1 - (matter_density + radiation_density + dark_energy)

								__a							=    (
								    radiation_density * (redshift + 1) ** 4
								    + matter_density * (redshift + 1) ** 3
								    + curvature * (redshift + 1) ** 2
								    + dark_energy
								)

								__a							=    hubble_constant * e_a ** (1 / 2)
								return hubble


if __name__ == "__main__":
	import doctest

	# run doctest
	doctest.testmod()

	# demo LCDM approximation
	__snake_case						:Union[str, Any]						=					0.3

	print(
	    hubble_parameter(
	        hubble_constant=68.3,
	        radiation_density=1E-4,
	        matter_density=matter_density,
	        dark_energy=1 - matter_density,
	        redshift=0,
	    )
	)










def 					__snake_case     (      _UpperCAmelCase       ,			_UpperCAmelCase    ):

    def get_matched_characters(_UpperCAmelCase       ,			_UpperCAmelCase    ) -> str:
        __a							=    []
        __a							=    min(len(_stra    )       ,			len(_stra    )    ) // 2
        for i, l in enumerate(_stra    ):
            __a							=    int(max(0       ,			i - limit    )    )
            __a							=    int(min(i + limit + 1       ,			len(_stra    )    )    )
            if l in _stra[left:right]:
                matched.append(_UpperCAmelCase    )
                __a							=    f'{_stra[0:_stra.index(_UpperCAmelCase    )]} {_stra[_stra.index(_UpperCAmelCase    ) + 1:]}'

        return "".join(_UpperCAmelCase    )

    # matching characters
    __a							=    get_matched_characters(_UpperCAmelCase       ,			_UpperCAmelCase    )
    __a							=    get_matched_characters(_UpperCAmelCase       ,			_UpperCAmelCase    )
    __a							=    len(_UpperCAmelCase    )

    # transposition
    __a							=    (
        len([(ca, ca) for ca, ca in zip(_UpperCAmelCase       ,			_UpperCAmelCase    ) if ca != ca]    ) // 2
    )

    if not match_count:
        __a							=    0.0
    else:
        __a							=    (
            1
            / 3
            * (
                match_count / len(_UpperCAmelCase    )
                + match_count / len(_UpperCAmelCase    )
                + (match_count - transpositions) / match_count
            )
        )

    # common prefix up to 4 characters
    __a							=    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'''))





