


from typing import Any

import numpy as np
def     UpperCAmelCase_ (							__snake_case						)					->      bool:







 """simple docstring"""


 assert np.shape(snake_case__						)[0] == np.shape(snake_case__						)[1]

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

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

 # Check sign of all eigenvalues.
 # np.all returns a value of type np.bool_
 return bool(np.all(eigen_values > 0						)						)
def     UpperCAmelCase_ (							__snake_case						)					->      Any:







 """simple docstring"""


 _lowercase											=np.random.randn(snake_case__					,						snake_case__						)
 _lowercase											=np.dot(snake_case__					,						random_matrix.T						)
 assert _is_matrix_spd(snake_case__						)
 return spd_matrix
def     UpperCAmelCase_ (							__snake_case					,						__snake_case					,						__snake_case = 1000					,						__snake_case = 1e-8					,						)					->      Any:







 """simple docstring"""


 assert np.shape(snake_case__						)[0] == np.shape(snake_case__						)[1]
 assert np.shape(snake_case__						)[0] == np.shape(snake_case__						)[0]
 assert _is_matrix_spd(snake_case__						)

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

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

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

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

  # The main algorithm.

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

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

  # Update variables.
  _lowercase											=np.copy(snake_case__						)
  _lowercase											=np.copy(snake_case__						)
  _lowercase											=np.copy(snake_case__						)

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

 return x
def     UpperCAmelCase_ (							)					->      None:







 """simple docstring"""


 _lowercase											=3
 _lowercase											=_create_spd_matrix(snake_case__						)
 _lowercase											=np.random.randn(snake_case__					,						1						)
 _lowercase											=np.dot(snake_case__					,						snake_case__						)

 # Numpy solution.
 _lowercase											=np.linalg.solve(snake_case__					,						snake_case__						)

 # Our implementation.
 _lowercase											=conjugate_gradient(snake_case__					,						snake_case__						)

 # 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()





from ...configuration_utils import PretrainedConfig
from ...utils import logging


UpperCAmelCase__            =							logging.get_logger(__name__)

UpperCAmelCase__            =							{
    '''bert-base-uncased''': '''https://huggingface.co/bert-base-uncased/resolve/main/config.json''',
    # QDQBERT models can be loaded from any BERT checkpoint, available at https://huggingface.co/models?filter=bert
}







class 				lowerCamelCase__       (	lowerCAmelCase):
     SCREAMING_SNAKE_CASE__				      =      '''qdqbert'''





     def __init__(self		,					UpperCAmelCase=3_0_5_2_2		,					UpperCAmelCase=7_6_8		,					UpperCAmelCase=1_2		,					UpperCAmelCase=1_2		,					UpperCAmelCase=3_0_7_2		,					UpperCAmelCase="gelu"		,					UpperCAmelCase=0.1		,					UpperCAmelCase=0.1		,					UpperCAmelCase=5_1_2		,					UpperCAmelCase=2		,					UpperCAmelCase=0.02		,					UpperCAmelCase=1e-12		,					UpperCAmelCase=True		,					UpperCAmelCase=1		,					UpperCAmelCase=0		,					UpperCAmelCase=2		,					**UpperCAmelCase		,					)					->       str:
      super().__init__(pad_token_id=UpperCAmelCase		,					bos_token_id=UpperCAmelCase		,					eos_token_id=UpperCAmelCase		,					**UpperCAmelCase	)

      _lowercase											=vocab_size
      _lowercase											=max_position_embeddings
      _lowercase											=hidden_size
      _lowercase											=num_hidden_layers
      _lowercase											=num_attention_heads
      _lowercase											=intermediate_size
      _lowercase											=hidden_act
      _lowercase											=hidden_dropout_prob
      _lowercase											=attention_probs_dropout_prob
      _lowercase											=initializer_range
      _lowercase											=type_vocab_size
      _lowercase											=layer_norm_eps
      _lowercase											=use_cache

