
'''simple docstring'''





from typing import Any

import numpy as np
def 	snake_case_							(				_a  :				np.ndarray      ):
      assert np.shape(_a      )[0] == np.shape(_a      )[1]

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

      # Get eigenvalues and eignevectors for a symmetric matrix.
      snake_case_							,						snake_case_    							=				np.linalg.eigh(_a      )

      # Check sign of all eigenvalues.
      # np.all returns a value of type np.bool_
      return bool(np.all(eigen_values > 0      )      )
def 	snake_case_							(				_a  :				int      ):
      snake_case_    							=				np.random.randn(_a			,       _a      )
      snake_case_    							=				np.dot(_a			,       random_matrix.T      )
      assert _is_matrix_spd(_a      )
      return spd_matrix
def 	snake_case_							(				_a  :				np.ndarray			,       _a  :				np.ndarray			,       _a  :				int = 1_000			,       _a  :				float = 1E-8			,       ):
      assert np.shape(_a      )[0] == np.shape(_a      )[1]
      assert np.shape(_a      )[0] == np.shape(_a      )[0]
      assert _is_matrix_spd(_a      )

      # Initialize solution guess, residual, search direction.
      snake_case_    							=				np.zeros((np.shape(_a      )[0], 1)      )
      snake_case_    							=				np.copy(_a      )
      snake_case_    							=				np.copy(_a      )

      # 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(_a			,       _a      )

            # The main algorithm.

            # Update search direction magnitude.
            snake_case_    							=				np.dot(ra.T			,       _a      ) / np.dot(pa.T			,       _a      )
            # 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			,       _a      ) / np.dot(ra.T			,       _a      )
            # 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(_a			,       _a      )

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

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

      return x
def 	snake_case_							(				):
      snake_case_    							=				3
      snake_case_    							=				_create_spd_matrix(_a      )
      snake_case_    							=				np.random.randn(_a			,       1      )
      snake_case_    							=				np.dot(_a			,       _a      )

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

      # Our implementation.
      snake_case_    							=				conjugate_gradient(_a			,       _a      )

      # 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()









'''simple docstring'''





from typing import TYPE_CHECKING

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


__A				:				Union[str, Any]					=		{
    """configuration_gpt2""": ["""GPT2_PRETRAINED_CONFIG_ARCHIVE_MAP""", """GPT2Config""", """GPT2OnnxConfig"""],
    """tokenization_gpt2""": ["""GPT2Tokenizer"""],
}

try:
 if not is_tokenizers_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __A				:				Tuple					=		["""GPT2TokenizerFast"""]

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __A				:				Optional[int]					=		[
     """GPT2_PRETRAINED_MODEL_ARCHIVE_LIST""",
     """GPT2DoubleHeadsModel""",
     """GPT2ForQuestionAnswering""",
     """GPT2ForSequenceClassification""",
     """GPT2ForTokenClassification""",
     """GPT2LMHeadModel""",
     """GPT2Model""",
     """GPT2PreTrainedModel""",
     """load_tf_weights_in_gpt2""",
 ]

try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __A				:				Optional[Any]					=		[
     """TF_GPT2_PRETRAINED_MODEL_ARCHIVE_LIST""",
     """TFGPT2DoubleHeadsModel""",
     """TFGPT2ForSequenceClassification""",
     """TFGPT2LMHeadModel""",
     """TFGPT2MainLayer""",
     """TFGPT2Model""",
     """TFGPT2PreTrainedModel""",
 ]

try:
 if not is_keras_nlp_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __A				:				Any					=		["""TFGPT2Tokenizer"""]

try:
 if not is_flax_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __A				:				Tuple					=		["""FlaxGPT2LMHeadModel""", """FlaxGPT2Model""", """FlaxGPT2PreTrainedModel"""]

if TYPE_CHECKING:
 from .configuration_gpta import GPT2_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTaConfig, GPTaOnnxConfig
 from .tokenization_gpta import GPTaTokenizer

 try:
  if not is_tokenizers_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_gpta_fast import GPTaTokenizerFast

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_gpta import (
      GPT2_PRETRAINED_MODEL_ARCHIVE_LIST,
      GPTaDoubleHeadsModel,
      GPTaForQuestionAnswering,
      GPTaForSequenceClassification,
      GPTaForTokenClassification,
      GPTaLMHeadModel,
      GPTaModel,
      GPTaPreTrainedModel,
      load_tf_weights_in_gpta,
  )

 try:
  if not is_tf_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_tf_gpta import (
      TF_GPT2_PRETRAINED_MODEL_ARCHIVE_LIST,
      TFGPTaDoubleHeadsModel,
      TFGPTaForSequenceClassification,
      TFGPTaLMHeadModel,
      TFGPTaMainLayer,
      TFGPTaModel,
      TFGPTaPreTrainedModel,
  )

 try:
  if not is_keras_nlp_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_gpta_tf import TFGPTaTokenizer

 try:
  if not is_flax_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_flax_gpta import FlaxGPTaLMHeadModel, FlaxGPTaModel, FlaxGPTaPreTrainedModel

else:
 import sys

 __A				:				Tuple					=		_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)

