
import unittest

import numpy as np

def 		UpperCamelCase						(   lowercase_			,			lowercase_			,			lowercase_			,			lowercase_ = None			,			)		->						np.ndarray:


  '''simple docstring'''






  lowercase__	: Tuple     		=   np.shape(lowercase_ )
  lowercase__	: Tuple     		=   np.shape(lowercase_ )
  lowercase__	: Optional[int]     		=   np.shape(lowercase_ )

  if shape_a[0] != shape_b[0]:
    lowercase__	: List[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(lowercase_ )

  if shape_b[1] != shape_c[1]:
    lowercase__	: 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(lowercase_ )

  lowercase__	: List[str]     		=   pseudo_inv
  if a_inv is None:
    try:
      lowercase__	: List[str]     		=   np.linalg.inv(lowercase_ )
    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   lowercase__  (       self):


   '''simple docstring'''




   lowercase__	: List[str]     		=   np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]])
   lowercase__	: List[str]     		=   np.array([[0, 3], [3, 0], [2, 3]])
   lowercase__	: Tuple     		=   np.array([[2, 1], [6, 3]])

   lowercase__	: List[Any]     		=   schur_complement(SCREAMING_SNAKE_CASE_       ,	SCREAMING_SNAKE_CASE_       ,	SCREAMING_SNAKE_CASE_)

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

   lowercase__	: List[Any]     		=   np.linalg.det(SCREAMING_SNAKE_CASE_)
   lowercase__	: List[Any]     		=   np.linalg.det(SCREAMING_SNAKE_CASE_)
   lowercase__	: int     		=   np.linalg.det(SCREAMING_SNAKE_CASE_)

   self.assertAlmostEqual(SCREAMING_SNAKE_CASE_       ,	det_a * det_s)


 def   lowercase__  (       self):


   '''simple docstring'''




   lowercase__	: Optional[Any]     		=   np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]])
   lowercase__	: Dict     		=   np.array([[0, 3], [3, 0], [2, 3]])
   lowercase__	: int     		=   np.array([[2, 1], [6, 3]])

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



 def   lowercase__  (       self):


   '''simple docstring'''




   lowercase__	: Tuple     		=   np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]])
   lowercase__	: Union[str, Any]     		=   np.array([[0, 3], [3, 0], [2, 3]])
   lowercase__	: str     		=   np.array([[2, 1, 3], [6, 3, 5]])

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


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     unittest.main()










"""simple docstring"""


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


A	:  Union[str, Any]            =     {
    "configuration_timesformer": ["TIMESFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP", "TimesformerConfig"],
}

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	A	:  Optional[int]            =     [
	    "TIMESFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
	    "TimesformerModel",
	    "TimesformerForVideoClassification",
	    "TimesformerPreTrainedModel",
	]

if TYPE_CHECKING:
	from .configuration_timesformer import TIMESFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, TimesformerConfig

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_timesformer import (
		    TIMESFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
		    TimesformerForVideoClassification,
		    TimesformerModel,
		    TimesformerPreTrainedModel,
		)

else:
	import sys

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




