


from typing import TYPE_CHECKING

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


SCREAMING_SNAKE_CASE		:Optional[int]											=       {
    '''configuration_bart''': ['''BART_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''BartConfig''', '''BartOnnxConfig'''],
    '''tokenization_bart''': ['''BartTokenizer'''],
}

try:
			if not is_tokenizers_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			SCREAMING_SNAKE_CASE		:List[str]											=       ['''BartTokenizerFast''']

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			SCREAMING_SNAKE_CASE		:str											=       [
			    '''BART_PRETRAINED_MODEL_ARCHIVE_LIST''',
			    '''BartForCausalLM''',
			    '''BartForConditionalGeneration''',
			    '''BartForQuestionAnswering''',
			    '''BartForSequenceClassification''',
			    '''BartModel''',
			    '''BartPretrainedModel''',
			    '''PretrainedBartModel''',
			]

try:
			if not is_tf_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			SCREAMING_SNAKE_CASE		:Union[str, Any]											=       [
			    '''TFBartForConditionalGeneration''',
			    '''TFBartForSequenceClassification''',
			    '''TFBartModel''',
			    '''TFBartPretrainedModel''',
			]

try:
			if not is_flax_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			SCREAMING_SNAKE_CASE		:Tuple											=       [
			    '''FlaxBartDecoderPreTrainedModel''',
			    '''FlaxBartForCausalLM''',
			    '''FlaxBartForConditionalGeneration''',
			    '''FlaxBartForQuestionAnswering''',
			    '''FlaxBartForSequenceClassification''',
			    '''FlaxBartModel''',
			    '''FlaxBartPreTrainedModel''',
			]

if TYPE_CHECKING:
			from .configuration_bart import BART_PRETRAINED_CONFIG_ARCHIVE_MAP, BartConfig, BartOnnxConfig
			from .tokenization_bart import BartTokenizer

			try:
						if not is_tokenizers_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .tokenization_bart_fast import BartTokenizerFast

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_bart import (
						    BART_PRETRAINED_MODEL_ARCHIVE_LIST,
						    BartForCausalLM,
						    BartForConditionalGeneration,
						    BartForQuestionAnswering,
						    BartForSequenceClassification,
						    BartModel,
						    BartPretrainedModel,
						    PretrainedBartModel,
						)

			try:
						if not is_tf_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_tf_bart import (
						    TFBartForConditionalGeneration,
						    TFBartForSequenceClassification,
						    TFBartModel,
						    TFBartPretrainedModel,
						)

			try:
						if not is_flax_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_flax_bart import (
						    FlaxBartDecoderPreTrainedModel,
						    FlaxBartForCausalLM,
						    FlaxBartForConditionalGeneration,
						    FlaxBartForQuestionAnswering,
						    FlaxBartForSequenceClassification,
						    FlaxBartModel,
						    FlaxBartPreTrainedModel,
						)

else:
			import sys

			SCREAMING_SNAKE_CASE		:int											=       _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)








from typing import Any

import numpy as np



def      _lowerCAmelCase  (							lowerCAmelCase_							:np.ndarray							)->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_         =   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      _lowerCAmelCase  (							lowerCAmelCase_							:int							)->Any:
   '''simple docstring'''






   snake_case_         =   np.random.randn(lowerCAmelCase_						,  lowerCAmelCase_							)
   snake_case_         =   np.dot(lowerCAmelCase_						,  random_matrix.T							)
   assert _is_matrix_spd(lowerCAmelCase_							)
   return spd_matrix



def      _lowerCAmelCase  (							lowerCAmelCase_							:np.ndarray						,  lowerCAmelCase_							:np.ndarray						,  lowerCAmelCase_							:int = 1_000						,  lowerCAmelCase_							:float = 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_         =   np.zeros((np.shape(lowerCAmelCase_							)[0], 1)							)
   snake_case_         =   np.copy(lowerCAmelCase_							)
   snake_case_         =   np.copy(lowerCAmelCase_							)

   # Set initial errors in solution guess and residual.
   snake_case_         =   1e9
   snake_case_         =   1e9
   snake_case_         =   1e9

   # Set iteration counter to threshold number of iterations.
   snake_case_         =   0

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

      # The main algorithm.

      # Update search direction magnitude.
      snake_case_         =   np.dot(ra.T						,  lowerCAmelCase_							) / np.dot(pa.T						,  lowerCAmelCase_							)
      # Update solution guess.
      snake_case_         =   xa + alpha * pa
      # Calculate new residual.
      snake_case_         =   ra - alpha * w
      # Calculate new Krylov subspace scale.
      snake_case_         =   np.dot(r.T						,  lowerCAmelCase_							) / np.dot(ra.T						,  lowerCAmelCase_							)
      # Calculate new A conjuage search direction.
      snake_case_         =   r + beta * pa

      # Calculate errors.
      snake_case_         =   np.linalg.norm(r - ra							)
      snake_case_         =   np.linalg.norm(x - xa							)
      snake_case_         =   np.maximum(lowerCAmelCase_						,  lowerCAmelCase_							)

      # Update variables.
      snake_case_         =   np.copy(lowerCAmelCase_							)
      snake_case_         =   np.copy(lowerCAmelCase_							)
      snake_case_         =   np.copy(lowerCAmelCase_							)

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

   return x



def      _lowerCAmelCase  (							)->None:
   '''simple docstring'''






   snake_case_         =   3
   snake_case_         =   _create_spd_matrix(lowerCAmelCase_							)
   snake_case_         =   np.random.randn(lowerCAmelCase_						,  1							)
   snake_case_         =   np.dot(lowerCAmelCase_						,  lowerCAmelCase_							)

   # Numpy solution.
   snake_case_         =   np.linalg.solve(lowerCAmelCase_						,  lowerCAmelCase_							)

   # Our implementation.
   snake_case_         =   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()




