






import unittest

import numpy as np

def 	lowerCAmelCase__			(      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 		__a				(    unittest.TestCase      ):
		def      UpperCAmelCase__    (      self						)			->	None:




									"""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(_SCREAMING_SNAKE_CASE      ,   _SCREAMING_SNAKE_CASE      ,   _SCREAMING_SNAKE_CASE						)

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

									_UpperCAmelCase					=      np.linalg.det(_SCREAMING_SNAKE_CASE						)
									_UpperCAmelCase					=      np.linalg.det(_SCREAMING_SNAKE_CASE						)
									_UpperCAmelCase					=      np.linalg.det(_SCREAMING_SNAKE_CASE						)

									self.assertAlmostEqual(_SCREAMING_SNAKE_CASE      ,   det_a * det_s						)
		def      UpperCAmelCase__    (      self						)			->	None:




									"""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(_SCREAMING_SNAKE_CASE						):
																schur_complement(_SCREAMING_SNAKE_CASE      ,   _SCREAMING_SNAKE_CASE      ,   _SCREAMING_SNAKE_CASE						)






		def      UpperCAmelCase__    (      self						)			->	None:




									"""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(_SCREAMING_SNAKE_CASE						):
																schur_complement(_SCREAMING_SNAKE_CASE      ,   _SCREAMING_SNAKE_CASE      ,   _SCREAMING_SNAKE_CASE						)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		unittest.main()




from typing import TYPE_CHECKING

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


lowerCAmelCase__  :Any             =							{'''configuration_xglm''': ['''XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''XGLMConfig''']}

try:
		if not is_sentencepiece_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowerCAmelCase__  :Optional[Any]             =							['''XGLMTokenizer''']

try:
		if not is_tokenizers_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowerCAmelCase__  :str             =							['''XGLMTokenizerFast''']

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowerCAmelCase__  :List[str]             =							[
		    '''XGLM_PRETRAINED_MODEL_ARCHIVE_LIST''',
		    '''XGLMForCausalLM''',
		    '''XGLMModel''',
		    '''XGLMPreTrainedModel''',
		]


try:
		if not is_flax_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowerCAmelCase__  :str             =							[
		    '''FlaxXGLMForCausalLM''',
		    '''FlaxXGLMModel''',
		    '''FlaxXGLMPreTrainedModel''',
		]


try:
		if not is_tf_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowerCAmelCase__  :List[Any]             =							[
		    '''TF_XGLM_PRETRAINED_MODEL_ARCHIVE_LIST''',
		    '''TFXGLMForCausalLM''',
		    '''TFXGLMModel''',
		    '''TFXGLMPreTrainedModel''',
		]


if TYPE_CHECKING:
		from .configuration_xglm import XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP, XGLMConfig

		try:
				if not is_sentencepiece_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .tokenization_xglm import XGLMTokenizer

		try:
				if not is_tokenizers_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .tokenization_xglm_fast import XGLMTokenizerFast

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_xglm import XGLM_PRETRAINED_MODEL_ARCHIVE_LIST, XGLMForCausalLM, XGLMModel, XGLMPreTrainedModel

		try:
				if not is_flax_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_flax_xglm import FlaxXGLMForCausalLM, FlaxXGLMModel, FlaxXGLMPreTrainedModel

		try:
				if not is_tf_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_tf_xglm import (
				    TF_XGLM_PRETRAINED_MODEL_ARCHIVE_LIST,
				    TFXGLMForCausalLM,
				    TFXGLMModel,
				    TFXGLMPreTrainedModel,
				)


else:
		import sys

		lowerCAmelCase__  :Any             =							_LazyModule(__name__, globals()['''__file__'''], _import_structure)
