




"""simple docstring"""

from dataclasses import dataclass, field
from typing import TYPE_CHECKING, Any, ClassVar, Dict, List, Optional, Union

import pyarrow as pa


if TYPE_CHECKING:
		from .features import FeatureType

@dataclass
class        lowercase      :

				'''simple docstring'''





				__lowerCAmelCase    :    List[str]
				__lowerCAmelCase    :    Optional[str]         =   None
				# Automatically constructed
				__lowerCAmelCase    :    ClassVar[str]         =   "dict"
				__lowerCAmelCase    :    ClassVar[Any]         =   None
				__lowerCAmelCase    :    str         =   field(default="""Translation"""     ,	init=__lowercase     ,	repr=__lowercase)







				def __call__(							self   :					Union[str, Any]       ):



					"""simple docstring"""

					return pa.struct({lang: pa.string() for lang in sorted(self.languages       )}       )







				def 					a_  (							self   :					Optional[int]       ):



					"""simple docstring"""

					from .features import Value

					return {k: Value('''string'''       ) for k in sorted(self.languages       )}

@dataclass
class        lowercase      :

				'''simple docstring'''





				__lowerCAmelCase    :    Optional[List]         =   None
				__lowerCAmelCase    :    Optional[int]         =   None
				__lowerCAmelCase    :    Optional[str]         =   None
				# Automatically constructed
				__lowerCAmelCase    :    ClassVar[str]         =   "dict"
				__lowerCAmelCase    :    ClassVar[Any]         =   None
				__lowerCAmelCase    :    str         =   field(default="""TranslationVariableLanguages"""     ,	init=__lowercase     ,	repr=__lowercase)







				def 					a_  (							self   :					Optional[int]       ):



					"""simple docstring"""

					A_  :				Tuple	   =		sorted(set(self.languages       )       ) if self.languages else None
					A_  :				List[Any]	   =		len(self.languages       ) if self.languages else None







				def __call__(							self   :					Optional[Any]       ):



					"""simple docstring"""

					return pa.struct({'''language''': pa.list_(pa.string()       ), '''translation''': pa.list_(pa.string()       )}       )







				def 					a_  (							self   :					Optional[int]      ,     _lowerCamelCase   :					List[Any]       ):



					"""simple docstring"""

					A_  :				str	   =		set(self.languages       )
					if self.languages and set(__a       ) - lang_set:
						raise ValueError(
						    F"""Some languages in example ({', '.join(sorted(set(__a       ) - lang_set       )       )}) are not in valid set ({', '.join(__a       )})."""       )

					# Convert dictionary into tuples, splitting out cases where there are
					# multiple translations for a single language.
					A_  :				Any	   =		[]
					for lang, text in translation_dict.items():
						if isinstance(__a      ,     __a       ):
							translation_tuples.append((lang, text)       )
						else:
							translation_tuples.extend([(lang, el) for el in text]       )

        # Ensure translations are in ascending order by language code.
					A_  :				Tuple	   =		zip(*sorted(__a       )       )

					return {"language": languages, "translation": translations}







				def 					a_  (							self   :					Tuple       ):



					"""simple docstring"""

					from .features import Sequence, Value

					return {
					    "language": Sequence(Value('''string'''       )       ),
					    "translation": Sequence(Value('''string'''       )       ),
					}











"""simple docstring"""

from typing import Any

import numpy as np

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	return np.array_equal(_UpperCAmelCase  ,      matrix.conjugate().T	)

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	A_  :				Tuple	   =		v.conjugate().T
	A_  :				Tuple	   =		v_star.dot(_UpperCAmelCase	)
	assert isinstance(_UpperCAmelCase  ,      np.ndarray	)
	return (v_star_dot.dot(_UpperCAmelCase	)) / (v_star.dot(_UpperCAmelCase	))

def 		lowercase_      (		):




	"""simple docstring"""






	A_  :				Optional[Any]	   =		np.array([[2, 2 + 1J, 4], [2 - 1J, 3, 1J], [4, -1J, 1]]	)
	A_  :				str	   =		np.array([[1], [2], [3]]	)
	assert is_hermitian(_UpperCAmelCase	), f"""{a} is not hermitian."""
	print(rayleigh_quotient(_UpperCAmelCase  ,      _UpperCAmelCase	)	)

	A_  :				int	   =		np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]	)
	assert is_hermitian(_UpperCAmelCase	), f"""{a} is not hermitian."""
	assert rayleigh_quotient(_UpperCAmelCase  ,      _UpperCAmelCase	) == float(3	)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		tests()





