"""simple docstring"""




from typing import TYPE_CHECKING

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


__lowerCamelCase									=	{
    'configuration_camembert': ['CAMEMBERT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'CamembertConfig', 'CamembertOnnxConfig'],
}

try:
				if not is_sentencepiece_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__lowerCamelCase									=	['CamembertTokenizer']

try:
				if not is_tokenizers_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__lowerCamelCase									=	['CamembertTokenizerFast']

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__lowerCamelCase									=	[
				    'CAMEMBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
				    'CamembertForCausalLM',
				    'CamembertForMaskedLM',
				    'CamembertForMultipleChoice',
				    'CamembertForQuestionAnswering',
				    'CamembertForSequenceClassification',
				    'CamembertForTokenClassification',
				    'CamembertModel',
				    'CamembertPreTrainedModel',
				]

try:
				if not is_tf_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				__lowerCamelCase									=	[
				    'TF_CAMEMBERT_PRETRAINED_MODEL_ARCHIVE_LIST',
				    'TFCamembertForCausalLM',
				    'TFCamembertForMaskedLM',
				    'TFCamembertForMultipleChoice',
				    'TFCamembertForQuestionAnswering',
				    'TFCamembertForSequenceClassification',
				    'TFCamembertForTokenClassification',
				    'TFCamembertModel',
				    'TFCamembertPreTrainedModel',
				]


if TYPE_CHECKING:
				from .configuration_camembert import CAMEMBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, CamembertConfig, CamembertOnnxConfig

				try:
								if not is_sentencepiece_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .tokenization_camembert import CamembertTokenizer

				try:
								if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .tokenization_camembert_fast import CamembertTokenizerFast

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_camembert import (
								    CAMEMBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
								    CamembertForCausalLM,
								    CamembertForMaskedLM,
								    CamembertForMultipleChoice,
								    CamembertForQuestionAnswering,
								    CamembertForSequenceClassification,
								    CamembertForTokenClassification,
								    CamembertModel,
								    CamembertPreTrainedModel,
								)

				try:
								if not is_tf_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_tf_camembert import (
								    TF_CAMEMBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
								    TFCamembertForCausalLM,
								    TFCamembertForMaskedLM,
								    TFCamembertForMultipleChoice,
								    TFCamembertForQuestionAnswering,
								    TFCamembertForSequenceClassification,
								    TFCamembertForTokenClassification,
								    TFCamembertModel,
								    TFCamembertPreTrainedModel,
								)

else:
				import sys

				__lowerCamelCase									=	_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)









from typing import Any

import numpy as np






def  _UpperCAmelCase						( __lowerCamelCase							)		->bool:


 '''simple docstring'''
 assert np.shape(__lowerCamelCase							)[0] == np.shape(__lowerCamelCase							)[1]

 # If matrix not symmetric, exit right away.
 if np.allclose(__lowerCamelCase			,  matrix.T							) is False:
  return False

 # Get eigenvalues and eignevectors for a symmetric matrix.
 snake_case	,       snake_case :			int							=   np.linalg.eigh(__lowerCamelCase							)

 # Check sign of all eigenvalues.
 # np.all returns a value of type np.bool_
 return bool(np.all(eigen_values > 0							)							)






def  _UpperCAmelCase						( __lowerCamelCase							)		->Any:


 '''simple docstring'''
 snake_case :			Dict							=   np.random.randn(__lowerCamelCase			,  __lowerCamelCase							)
 snake_case :			List[Any]							=   np.dot(__lowerCamelCase			,  random_matrix.T							)
 assert _is_matrix_spd(__lowerCamelCase							)
 return spd_matrix






def  _UpperCAmelCase						( __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase = 1000			,  __lowerCamelCase = 1E-8			,  )		->Any:


 '''simple docstring'''
 assert np.shape(__lowerCamelCase							)[0] == np.shape(__lowerCamelCase							)[1]
 assert np.shape(__lowerCamelCase							)[0] == np.shape(__lowerCamelCase							)[0]
 assert _is_matrix_spd(__lowerCamelCase							)

 # Initialize solution guess, residual, search direction.
 snake_case :			Any							=   np.zeros((np.shape(__lowerCamelCase							)[0], 1)							)
 snake_case :			Optional[int]							=   np.copy(__lowerCamelCase							)
 snake_case :			Optional[Any]							=   np.copy(__lowerCamelCase							)

 # Set initial errors in solution guess and residual.
 snake_case :			Optional[Any]							=   1E9
 snake_case :			List[Any]							=   1E9
 snake_case :			List[str]							=   1E9

 # Set iteration counter to threshold number of iterations.
 snake_case :			List[str]							=   0

 while error > tol:
  # Save this value so we only calculate the matrix-vector product once.
  snake_case :			str							=   np.dot(__lowerCamelCase			,  __lowerCamelCase							)

  # The main algorithm.

  # Update search direction magnitude.
  snake_case :			List[str]							=   np.dot(ra.T			,  __lowerCamelCase							) / np.dot(pa.T			,  __lowerCamelCase							)
  # Update solution guess.
  snake_case :			Optional[int]							=   xa + alpha * pa
  # Calculate new residual.
  snake_case :			str							=   ra - alpha * w
  # Calculate new Krylov subspace scale.
  snake_case :			List[str]							=   np.dot(r.T			,  __lowerCamelCase							) / np.dot(ra.T			,  __lowerCamelCase							)
  # Calculate new A conjuage search direction.
  snake_case :			List[Any]							=   r + beta * pa

  # Calculate errors.
  snake_case :			List[Any]							=   np.linalg.norm(r - ra							)
  snake_case :			Any							=   np.linalg.norm(x - xa							)
  snake_case :			str							=   np.maximum(__lowerCamelCase			,  __lowerCamelCase							)

  # Update variables.
  snake_case :			Tuple							=   np.copy(__lowerCamelCase							)
  snake_case :			Tuple							=   np.copy(__lowerCamelCase							)
  snake_case :			List[str]							=   np.copy(__lowerCamelCase							)

  # Update number of iterations.
  iterations += 1
  if iterations > max_iterations:
   break

 return x






def  _UpperCAmelCase						( )		->None:


 '''simple docstring'''
 snake_case :			str							=   3
 snake_case :			Dict							=   _create_spd_matrix(__lowerCamelCase							)
 snake_case :			str							=   np.random.randn(__lowerCamelCase			,  1							)
 snake_case :			str							=   np.dot(__lowerCamelCase			,  __lowerCamelCase							)

 # Numpy solution.
 snake_case :			Any							=   np.linalg.solve(__lowerCamelCase			,  __lowerCamelCase							)

 # Our implementation.
 snake_case :			List[str]							=   conjugate_gradient(__lowerCamelCase			,  __lowerCamelCase							)

 # Ensure both solutions are close to x_true (and therefore one another).
 assert np.linalg.norm(x_numpy - x_true							) <= 1E-6
 assert np.linalg.norm(x_conjugate_gradient - x_true							) <= 1E-6


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  test_conjugate_gradient()






