




import unittest

import numpy as np


def    A						(__A   :    np.ndarray   ,				__A   :    np.ndarray   ,				__A   :    np.ndarray   ,				__A   :    np.ndarray | None = None   ,				)   ->      np.ndarray:







     """simple docstring"""


     UpperCAmelCase_          =							np.shape(__A       )
     UpperCAmelCase_          =							np.shape(__A       )
     UpperCAmelCase_          =							np.shape(__A       )

     if shape_a[0] != shape_b[0]:
          UpperCAmelCase_          =							(
              '''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(__A       )

     if shape_b[1] != shape_c[1]:
          UpperCAmelCase_          =							(
              '''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(__A       )

     UpperCAmelCase_          =							pseudo_inv
     if a_inv is None:
          try:
               UpperCAmelCase_          =							np.linalg.inv(__A       )
          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 __snake_case			(			unittest.TestCase		):







   def lowerCamelCase						(      self		:						Any):

        """simple docstring"""


        UpperCAmelCase_          =							np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]])
        UpperCAmelCase_          =							np.array([[0, 3], [3, 0], [2, 3]])
        UpperCAmelCase_          =							np.array([[2, 1], [6, 3]])

        UpperCAmelCase_          =							schur_complement(_snake_case					,						_snake_case					,						_snake_case)

        UpperCAmelCase_          =							np.block([[a, b], [b.T, c]])

        UpperCAmelCase_          =							np.linalg.det(_snake_case)
        UpperCAmelCase_          =							np.linalg.det(_snake_case)
        UpperCAmelCase_          =							np.linalg.det(_snake_case)

        self.assertAlmostEqual(_snake_case					,						det_a * det_s)







   def lowerCamelCase						(      self		:						List[str]):

        """simple docstring"""


        UpperCAmelCase_          =							np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]])
        UpperCAmelCase_          =							np.array([[0, 3], [3, 0], [2, 3]])
        UpperCAmelCase_          =							np.array([[2, 1], [6, 3]])

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







   def lowerCamelCase						(      self		:						List[str]):

        """simple docstring"""


        UpperCAmelCase_          =							np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]])
        UpperCAmelCase_          =							np.array([[0, 3], [3, 0], [2, 3]])
        UpperCAmelCase_          =							np.array([[2, 1, 3], [6, 3, 5]])

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    unittest.main()










'''simple docstring'''
from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCamelCase__    					=      {
    '''configuration_distilbert''': [
        '''DISTILBERT_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''DistilBertConfig''',
        '''DistilBertOnnxConfig''',
    ],
    '''tokenization_distilbert''': ['''DistilBertTokenizer'''],
}

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCamelCase__    					=      ['''DistilBertTokenizerFast''']

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCamelCase__    					=      [
      '''DISTILBERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
      '''DistilBertForMaskedLM''',
      '''DistilBertForMultipleChoice''',
      '''DistilBertForQuestionAnswering''',
      '''DistilBertForSequenceClassification''',
      '''DistilBertForTokenClassification''',
      '''DistilBertModel''',
      '''DistilBertPreTrainedModel''',
  ]

try:
  if not is_tf_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCamelCase__    					=      [
      '''TF_DISTILBERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
      '''TFDistilBertForMaskedLM''',
      '''TFDistilBertForMultipleChoice''',
      '''TFDistilBertForQuestionAnswering''',
      '''TFDistilBertForSequenceClassification''',
      '''TFDistilBertForTokenClassification''',
      '''TFDistilBertMainLayer''',
      '''TFDistilBertModel''',
      '''TFDistilBertPreTrainedModel''',
  ]

try:
  if not is_flax_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCamelCase__    					=      [
      '''FlaxDistilBertForMaskedLM''',
      '''FlaxDistilBertForMultipleChoice''',
      '''FlaxDistilBertForQuestionAnswering''',
      '''FlaxDistilBertForSequenceClassification''',
      '''FlaxDistilBertForTokenClassification''',
      '''FlaxDistilBertModel''',
      '''FlaxDistilBertPreTrainedModel''',
  ]


if TYPE_CHECKING:
  from .configuration_distilbert import (
      DISTILBERT_PRETRAINED_CONFIG_ARCHIVE_MAP,
      DistilBertConfig,
      DistilBertOnnxConfig,
  )
  from .tokenization_distilbert import DistilBertTokenizer

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_distilbert_fast import DistilBertTokenizerFast

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_distilbert import (
        DISTILBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
        DistilBertForMaskedLM,
        DistilBertForMultipleChoice,
        DistilBertForQuestionAnswering,
        DistilBertForSequenceClassification,
        DistilBertForTokenClassification,
        DistilBertModel,
        DistilBertPreTrainedModel,
    )

  try:
    if not is_tf_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_tf_distilbert import (
        TF_DISTILBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
        TFDistilBertForMaskedLM,
        TFDistilBertForMultipleChoice,
        TFDistilBertForQuestionAnswering,
        TFDistilBertForSequenceClassification,
        TFDistilBertForTokenClassification,
        TFDistilBertMainLayer,
        TFDistilBertModel,
        TFDistilBertPreTrainedModel,
    )

  try:
    if not is_flax_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_flax_distilbert import (
        FlaxDistilBertForMaskedLM,
        FlaxDistilBertForMultipleChoice,
        FlaxDistilBertForQuestionAnswering,
        FlaxDistilBertForSequenceClassification,
        FlaxDistilBertForTokenClassification,
        FlaxDistilBertModel,
        FlaxDistilBertPreTrainedModel,
    )

else:
  import sys

  UpperCamelCase__    					=      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)
