
import unittest

import numpy as np

def a__    (       A_,     A_,     A_,     A_ = None,     ):






  '''simple docstring'''





  __magic_name__				     =       np.shape(A_					)
  __magic_name__				     =       np.shape(A_					)
  __magic_name__				     =       np.shape(A_					)

  if shape_a[0] != shape_b[0]:
    __magic_name__				     =       (
        """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]:
    __magic_name__				     =       (
        """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_					)

  __magic_name__				     =       pseudo_inv
  if a_inv is None:
    try:
      __magic_name__				     =       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        UpperCAmelCase_			( unittest.TestCase     ):


  '''simple docstring'''







  def 							_lowercase							( self			: int    )			->	None:







    """simple docstring"""






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

    __magic_name__				     =       schur_complement(UpperCamelCase__			,							UpperCamelCase__			,							UpperCamelCase__    )

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

    __magic_name__				     =       np.linalg.det(UpperCamelCase__    )
    __magic_name__				     =       np.linalg.det(UpperCamelCase__    )
    __magic_name__				     =       np.linalg.det(UpperCamelCase__    )

    self.assertAlmostEqual(UpperCamelCase__			,							det_a * det_s    )
  def 							_lowercase							( self			: List[Any]    )			->	None:







    """simple docstring"""






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

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





  def 							_lowercase							( self			: int    )			->	None:







    """simple docstring"""






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



from typing import TYPE_CHECKING

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


__lowerCAmelCase			:     str           =   {
    'configuration_funnel': ['FUNNEL_PRETRAINED_CONFIG_ARCHIVE_MAP', 'FunnelConfig'],
    'convert_funnel_original_tf_checkpoint_to_pytorch': [],
    'tokenization_funnel': ['FunnelTokenizer'],
}

try:
    if not is_tokenizers_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCAmelCase			:     Any           =   ['FunnelTokenizerFast']

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCAmelCase			:     Optional[int]           =   [
        'FUNNEL_PRETRAINED_MODEL_ARCHIVE_LIST',
        'FunnelBaseModel',
        'FunnelForMaskedLM',
        'FunnelForMultipleChoice',
        'FunnelForPreTraining',
        'FunnelForQuestionAnswering',
        'FunnelForSequenceClassification',
        'FunnelForTokenClassification',
        'FunnelModel',
        'FunnelPreTrainedModel',
        'load_tf_weights_in_funnel',
    ]

try:
    if not is_tf_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCAmelCase			:     Tuple           =   [
        'TF_FUNNEL_PRETRAINED_MODEL_ARCHIVE_LIST',
        'TFFunnelBaseModel',
        'TFFunnelForMaskedLM',
        'TFFunnelForMultipleChoice',
        'TFFunnelForPreTraining',
        'TFFunnelForQuestionAnswering',
        'TFFunnelForSequenceClassification',
        'TFFunnelForTokenClassification',
        'TFFunnelModel',
        'TFFunnelPreTrainedModel',
    ]


if TYPE_CHECKING:
    from .configuration_funnel import FUNNEL_PRETRAINED_CONFIG_ARCHIVE_MAP, FunnelConfig
    from .tokenization_funnel import FunnelTokenizer

    try:
        if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_funnel_fast import FunnelTokenizerFast

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_funnel import (
            FUNNEL_PRETRAINED_MODEL_ARCHIVE_LIST,
            FunnelBaseModel,
            FunnelForMaskedLM,
            FunnelForMultipleChoice,
            FunnelForPreTraining,
            FunnelForQuestionAnswering,
            FunnelForSequenceClassification,
            FunnelForTokenClassification,
            FunnelModel,
            FunnelPreTrainedModel,
            load_tf_weights_in_funnel,
        )

    try:
        if not is_tf_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_tf_funnel import (
            TF_FUNNEL_PRETRAINED_MODEL_ARCHIVE_LIST,
            TFFunnelBaseModel,
            TFFunnelForMaskedLM,
            TFFunnelForMultipleChoice,
            TFFunnelForPreTraining,
            TFFunnelForQuestionAnswering,
            TFFunnelForSequenceClassification,
            TFFunnelForTokenClassification,
            TFFunnelModel,
            TFFunnelPreTrainedModel,
        )

else:
    import sys

    __lowerCAmelCase			:     List[Any]           =   _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)

