



"""simple docstring"""




import unittest

import numpy as np

def 						__snake_case						(				SCREAMING_SNAKE_CASE__     :						np.ndarray						,  SCREAMING_SNAKE_CASE__     :						np.ndarray						,  SCREAMING_SNAKE_CASE__     :						np.ndarray						,  SCREAMING_SNAKE_CASE__     :						np.ndarray | None = None						,  )  ->       np.ndarray:





     '''simple docstring'''

     _UpperCAmelCase      :     List[Any]        =   np.shape(SCREAMING_SNAKE_CASE__    )
     _UpperCAmelCase      :     List[str]        =   np.shape(SCREAMING_SNAKE_CASE__    )
     _UpperCAmelCase      :     Optional[Any]        =   np.shape(SCREAMING_SNAKE_CASE__    )

     if shape_a[0] != shape_b[0]:
          _UpperCAmelCase      :     Any        =   (
              "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(SCREAMING_SNAKE_CASE__    )

     if shape_b[1] != shape_c[1]:
          _UpperCAmelCase      :     Any        =   (
              "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(SCREAMING_SNAKE_CASE__    )

     _UpperCAmelCase      :     List[str]        =   pseudo_inv
     if a_inv is None:
          try:
               _UpperCAmelCase      :     Any        =   np.linalg.inv(SCREAMING_SNAKE_CASE__    )
          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 						snake_case_ (					self					:     List[str]						):
           _UpperCAmelCase      :     Optional[Any]        =   np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]						)
           _UpperCAmelCase      :     Any        =   np.array([[0, 3], [3, 0], [2, 3]]						)
           _UpperCAmelCase      :     Any        =   np.array([[2, 1], [6, 3]]						)

           _UpperCAmelCase      :     List[Any]        =   schur_complement(A					,     A					,     A						)

           _UpperCAmelCase      :     Optional[Any]        =   np.block([[a, b], [b.T, c]]						)

           _UpperCAmelCase      :     Tuple        =   np.linalg.det(A						)
           _UpperCAmelCase      :     Optional[int]        =   np.linalg.det(A						)
           _UpperCAmelCase      :     Union[str, Any]        =   np.linalg.det(A						)

           self.assertAlmostEqual(A					,     det_a * det_s						)



      def 						snake_case_ (					self					:     Dict						):
           _UpperCAmelCase      :     Tuple        =   np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]						)
           _UpperCAmelCase      :     str        =   np.array([[0, 3], [3, 0], [2, 3]]						)
           _UpperCAmelCase      :     Any        =   np.array([[2, 1], [6, 3]]						)

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



      def 						snake_case_ (					self					:     List[Any]						):
           _UpperCAmelCase      :     Optional[int]        =   np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]						)
           _UpperCAmelCase      :     Dict        =   np.array([[0, 3], [3, 0], [2, 3]]						)
           _UpperCAmelCase      :     str        =   np.array([[2, 1, 3], [6, 3, 5]]						)

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


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,
)


_lowerCAmelCase    : Union[str, Any]							=							{
    "configuration_roformer": ["ROFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP", "RoFormerConfig", "RoFormerOnnxConfig"],
    "tokenization_roformer": ["RoFormerTokenizer"],
}

try:
 if not is_tokenizers_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCAmelCase    : Any							=							["RoFormerTokenizerFast"]

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCAmelCase    : Any							=							[
     "ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
     "RoFormerForCausalLM",
     "RoFormerForMaskedLM",
     "RoFormerForMultipleChoice",
     "RoFormerForQuestionAnswering",
     "RoFormerForSequenceClassification",
     "RoFormerForTokenClassification",
     "RoFormerLayer",
     "RoFormerModel",
     "RoFormerPreTrainedModel",
     "load_tf_weights_in_roformer",
 ]


try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCAmelCase    : Optional[int]							=							[
     "TF_ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
     "TFRoFormerForCausalLM",
     "TFRoFormerForMaskedLM",
     "TFRoFormerForMultipleChoice",
     "TFRoFormerForQuestionAnswering",
     "TFRoFormerForSequenceClassification",
     "TFRoFormerForTokenClassification",
     "TFRoFormerLayer",
     "TFRoFormerModel",
     "TFRoFormerPreTrainedModel",
 ]


try:
 if not is_flax_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCAmelCase    : List[str]							=							[
     "FLAX_ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
     "FlaxRoFormerForMaskedLM",
     "FlaxRoFormerForMultipleChoice",
     "FlaxRoFormerForQuestionAnswering",
     "FlaxRoFormerForSequenceClassification",
     "FlaxRoFormerForTokenClassification",
     "FlaxRoFormerModel",
     "FlaxRoFormerPreTrainedModel",
 ]


if TYPE_CHECKING:
 from .configuration_roformer import ROFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, RoFormerConfig, RoFormerOnnxConfig
 from .tokenization_roformer import RoFormerTokenizer

 try:
  if not is_tokenizers_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_roformer_fast import RoFormerTokenizerFast

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_roformer import (
      ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
      RoFormerForCausalLM,
      RoFormerForMaskedLM,
      RoFormerForMultipleChoice,
      RoFormerForQuestionAnswering,
      RoFormerForSequenceClassification,
      RoFormerForTokenClassification,
      RoFormerLayer,
      RoFormerModel,
      RoFormerPreTrainedModel,
      load_tf_weights_in_roformer,
  )

 try:
  if not is_tf_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_tf_roformer import (
      TF_ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
      TFRoFormerForCausalLM,
      TFRoFormerForMaskedLM,
      TFRoFormerForMultipleChoice,
      TFRoFormerForQuestionAnswering,
      TFRoFormerForSequenceClassification,
      TFRoFormerForTokenClassification,
      TFRoFormerLayer,
      TFRoFormerModel,
      TFRoFormerPreTrainedModel,
  )

 try:
  if not is_flax_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_flax_roformer import (
      FLAX_ROFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
      FlaxRoFormerForMaskedLM,
      FlaxRoFormerForMultipleChoice,
      FlaxRoFormerForQuestionAnswering,
      FlaxRoFormerForSequenceClassification,
      FlaxRoFormerForTokenClassification,
      FlaxRoFormerModel,
      FlaxRoFormerPreTrainedModel,
  )


else:
 import sys

 _lowerCAmelCase    : List[str]							=							_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)
