


"""simple docstring"""


from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_speech_available,
    is_torch_available,
)


A	:  Any            =     {
    "configuration_trocr": ["TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP", "TrOCRConfig"],
    "processing_trocr": ["TrOCRProcessor"],
}


try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	A	:  Optional[Any]            =     [
	    "TROCR_PRETRAINED_MODEL_ARCHIVE_LIST",
	    "TrOCRForCausalLM",
	    "TrOCRPreTrainedModel",
	]


if TYPE_CHECKING:
	from .configuration_trocr import TROCR_PRETRAINED_CONFIG_ARCHIVE_MAP, TrOCRConfig
	from .processing_trocr import TrOCRProcessor

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_trocr import TROCR_PRETRAINED_MODEL_ARCHIVE_LIST, TrOCRForCausalLM, TrOCRPreTrainedModel

else:
	import sys

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








'''simple docstring'''


import unittest

import numpy as np


def 		_lowercase (SCREAMING_SNAKE_CASE       ,					SCREAMING_SNAKE_CASE       ,					SCREAMING_SNAKE_CASE       ,					SCREAMING_SNAKE_CASE = None       ,					):




     '''simple docstring'''





     __A	:       List[Any]      =							np.shape(SCREAMING_SNAKE_CASE							)
     __A	:       List[str]      =							np.shape(SCREAMING_SNAKE_CASE							)
     __A	:       Dict      =							np.shape(SCREAMING_SNAKE_CASE							)

     if shape_a[0] != shape_b[0]:
          __A	:       Tuple      =							(
              "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]:
          __A	:       Optional[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							)

     __A	:       Tuple      =							pseudo_inv
     if a_inv is None:
          try:
               __A	:       Optional[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 							__magic_name__	(       unittest.TestCase ):

     """simple docstring"""






     def lowerCAmelCase__  (   self		):


          '''simple docstring'''





          __A	:       Any      =							np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]		)
          __A	:       Tuple      =							np.array([[0, 3], [3, 0], [2, 3]]		)
          __A	:       Tuple      =							np.array([[2, 1], [6, 3]]		)

          __A	:       Optional[Any]      =							schur_complement(lowerCamelCase			,     lowerCamelCase			,     lowerCamelCase		)

          __A	:       int      =							np.block([[a, b], [b.T, c]]		)

          __A	:       int      =							np.linalg.det(lowerCamelCase		)
          __A	:       List[str]      =							np.linalg.det(lowerCamelCase		)
          __A	:       Any      =							np.linalg.det(lowerCamelCase		)

          self.assertAlmostEqual(lowerCamelCase			,     det_a * det_s		)


     def lowerCAmelCase__  (   self		):


          '''simple docstring'''





          __A	:       Optional[int]      =							np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]		)
          __A	:       List[Any]      =							np.array([[0, 3], [3, 0], [2, 3]]		)
          __A	:       List[str]      =							np.array([[2, 1], [6, 3]]		)

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


     def lowerCAmelCase__  (   self		):


          '''simple docstring'''





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

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


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      unittest.main()

