





'''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  UpperCAmelCase     :
      _lowercase:			List[str]
      _lowercase:			Optional[str]						     =   None
      # Automatically constructed
      _lowercase:			ClassVar[str]						     =   "dict"
      _lowercase:			ClassVar[Any]						     =   None
      _lowercase:			str						     =   field(default='''Translation'''							,		init=snake_case_							,		repr=snake_case_   )




      def __call__(			self			: Optional[int]  )				->      Optional[int]:
            return pa.struct({lang: pa.string() for lang in sorted(self.languages  )}  )




      def 				lowercase__    (			self			: Union[str, Any]  )				->      Union["FeatureType", Dict[str, "FeatureType"]]:
            from .features import Value

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




@dataclass
class  UpperCAmelCase     :
      _lowercase:			Optional[List]						     =   None
      _lowercase:			Optional[int]						     =   None
      _lowercase:			Optional[str]						     =   None
      # Automatically constructed
      _lowercase:			ClassVar[str]						     =   "dict"
      _lowercase:			ClassVar[Any]						     =   None
      _lowercase:			str						     =   field(default='''TranslationVariableLanguages'''							,		init=snake_case_							,		repr=snake_case_   )




      def 				lowercase__    (			self			: Any  )				->      Optional[Any]:
            _lowerCAmelCase							     =							sorted(set(self.languages  )  ) if self.languages else None
            _lowerCAmelCase							     =							len(self.languages  ) if self.languages else None




      def __call__(			self			: List[str]  )				->      Optional[Any]:
            return pa.struct({"""language""": pa.list_(pa.string()  ), """translation""": pa.list_(pa.string()  )}  )




      def 				lowercase__    (			self			: Optional[Any]			,			__snake_case			: Tuple  )				->      Any:
            _lowerCAmelCase							     =							set(self.languages  )
            if self.languages and set(__snake_case  ) - lang_set:
                  raise ValueError(
                      f"Some languages in example ({', '.join(sorted(set(__snake_case  ) - lang_set  )  )}) are not in valid set ({', '.join(__snake_case  )})."  )

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

        # Ensure translations are in ascending order by language code.
            _lowerCAmelCase     ,							_lowerCAmelCase							     =							zip(*sorted(__snake_case  )  )

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




      def 				lowercase__    (			self			: str  )				->      Union["FeatureType", Dict[str, "FeatureType"]]:
            from .features import Sequence, Value

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














"""simple docstring"""




import unittest

import numpy as np

def 			lowerCAmelCase__     (     UpperCamelCase__     ,   UpperCamelCase__     ,   UpperCamelCase__     ,   UpperCamelCase__ = None     ,   ):



  '''simple docstring'''
  _a  :       List[Any]             =	np.shape(UpperCamelCase__				)
  _a  :       Any             =	np.shape(UpperCamelCase__				)
  _a  :       Union[str, Any]             =	np.shape(UpperCamelCase__				)

  if shape_a[0] != shape_b[0]:
    _a  :       int             =	(
        """Expected the same number of rows for A and B. """
        F"""Instead found A of size {shape_a} and B of size {shape_b}"""
    )
    raise ValueError(UpperCamelCase__				)

  if shape_b[1] != shape_c[1]:
    _a  :       Tuple             =	(
        """Expected the same number of columns for B and C. """
        F"""Instead found B of size {shape_b} and C of size {shape_c}"""
    )
    raise ValueError(UpperCamelCase__				)

  _a  :       int             =	pseudo_inv
  if a_inv is None:
    try:
      _a  :       Optional[int]             =	np.linalg.inv(UpperCamelCase__				)
    except np.linalg.LinAlgError:
      raise ValueError(
          """Input matrix A is not invertible. Cannot compute Schur complement."""				)

  return mat_c - mat_b.T @ a_inv @ mat_b






class        UpperCamelCase			(	unittest.TestCase      ):


 def _lowercase	(     self		:						int							)					->       None:
   _a  :       str             =	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
   _a  :       Tuple             =	np.array([[0, 3], [3, 0], [2, 3]]							)
   _a  :       Optional[int]             =	np.array([[2, 1], [6, 3]]							)

   _a  :       Optional[Any]             =	schur_complement(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)

   _a  :       Union[str, Any]             =	np.block([[a, b], [b.T, c]]							)

   _a  :       int             =	np.linalg.det(UpperCAmelCase__							)
   _a  :       Union[str, Any]             =	np.linalg.det(UpperCAmelCase__							)
   _a  :       List[Any]             =	np.linalg.det(UpperCAmelCase__							)

   self.assertAlmostEqual(UpperCAmelCase__							,						det_a * det_s							)


 def _lowercase	(     self		:						int							)					->       None:
   _a  :       Optional[int]             =	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
   _a  :       Optional[int]             =	np.array([[0, 3], [3, 0], [2, 3]]							)
   _a  :       Union[str, Any]             =	np.array([[2, 1], [6, 3]]							)

   with self.assertRaises(UpperCAmelCase__							):
     schur_complement(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)







 def _lowercase	(     self		:						List[Any]							)					->       None:
   _a  :       Any             =	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
   _a  :       Dict             =	np.array([[0, 3], [3, 0], [2, 3]]							)
   _a  :       List[Any]             =	np.array([[2, 1, 3], [6, 3, 5]]							)

   with self.assertRaises(UpperCAmelCase__							):
     schur_complement(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 unittest.main()

