import numpy as np




def    lowerCAmelCase_  (		lowercase:				np.ndarray	,       lowercase:				np.ndarray	,       lowercase:				float = 1E-12	,       lowercase:				int = 100	,       )     ->					tuple[float, np.ndarray]:







 '''simple docstring'''
 assert np.shape(lowercase		)[0] == np.shape(lowercase		)[1]
 # Ensure proper dimensionality.
 assert np.shape(lowercase		)[0] == np.shape(lowercase		)[0]
 # Ensure inputs are either both complex or both real
 assert np.iscomplexobj(lowercase		) == np.iscomplexobj(lowercase		)
 _UpperCamelCase:  Optional[int]    						=			np.iscomplexobj(lowercase		)
 if is_complex:
  # Ensure complex input_matrix is Hermitian
  assert np.array_equal(lowercase	,       input_matrix.conj().T		)

 # Set convergence to False. Will define convergence when we exceed max_iterations
 # or when we have small changes from one iteration to next.

 _UpperCamelCase:  List[str]    						=			False
 _UpperCamelCase:  str    						=			0
 _UpperCamelCase:  Optional[int]    						=			0
 _UpperCamelCase:  Optional[Any]    						=			1E12

 while not convergence:
  # Multiple matrix by the vector.
  _UpperCamelCase:  Any    						=			np.dot(lowercase	,       lowercase		)
  # Normalize the resulting output vector.
  _UpperCamelCase:  Union[str, Any]    						=			w / np.linalg.norm(lowercase		)
  # Find rayleigh quotient
  # (faster than usual b/c we know vector is normalized already)
  _UpperCamelCase:  Optional[Any]    						=			vector.conj().T if is_complex else vector.T
  _UpperCamelCase:  List[Any]    						=			np.dot(lowercase	,       np.dot(lowercase	,       lowercase		)		)

  # Check convergence.
  _UpperCamelCase:  Optional[Any]    						=			np.abs(lambda_ - lambda_previous		) / lambda_
  iterations += 1

  if error <= error_tol or iterations >= max_iterations:
   _UpperCamelCase:  List[str]    						=			True

  _UpperCamelCase:  Optional[int]    						=			lambda_

 if is_complex:
  _UpperCamelCase:  Optional[Any]    						=			np.real(lambda_		)

 return lambda_, vector




def    lowerCAmelCase_  (		)     ->					None:







 '''simple docstring'''
 _UpperCamelCase:  Any    						=			np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]		)
 _UpperCamelCase:  Optional[int]    						=			np.array([41, 4, 20]		)
 _UpperCamelCase:  List[str]    						=			real_input_matrix.astype(np.complexaaa		)
 _UpperCamelCase:  Union[str, Any]    						=			np.triu(1j * complex_input_matrix	,       1		)
 complex_input_matrix += imag_matrix
 complex_input_matrix += -1 * imag_matrix.T
 _UpperCamelCase:  Optional[Any]    						=			np.array([41, 4, 20]		).astype(np.complexaaa		)

 for problem_type in ["real", "complex"]:
  if problem_type == "real":
   _UpperCamelCase:  Dict    						=			real_input_matrix
   _UpperCamelCase:  Any    						=			real_vector
  elif problem_type == "complex":
   _UpperCamelCase:  Optional[int]    						=			complex_input_matrix
   _UpperCamelCase:  Optional[Any]    						=			complex_vector

  # Our implementation.
  _UpperCamelCase						,				_UpperCamelCase:  List[str]    						=			power_iteration(lowercase	,       lowercase		)

  # Numpy implementation.

  # Get eigenvalues and eigenvectors using built-in numpy
  # eigh (eigh used for symmetric or hermetian matrices).
  _UpperCamelCase						,				_UpperCamelCase:  List[str]    						=			np.linalg.eigh(lowercase		)
  # Last eigenvalue is the maximum one.
  _UpperCamelCase:  Tuple    						=			eigen_values[-1]
  # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
  _UpperCamelCase:  Optional[Any]    						=			eigen_vectors[:, -1]

  # Check our implementation and numpy gives close answers.
  assert np.abs(eigen_value - eigen_value_max		) <= 1E-6
  # Take absolute values element wise of each eigenvector.
  # as they are only unique to a minus sign.
  assert np.linalg.norm(np.abs(lowercase		) - np.abs(lowercase		)		) <= 1E-6


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  test_power_iteration()
import unittest

import numpy as np

from transformers import BertConfig, is_flax_available
from transformers.testing_utils import require_flax, slow

from ...test_modeling_flax_common import FlaxModelTesterMixin, floats_tensor, ids_tensor, random_attention_mask


if is_flax_available():
  from transformers.models.bert.modeling_flax_bert import (
      FlaxBertForMaskedLM,
      FlaxBertForMultipleChoice,
      FlaxBertForNextSentencePrediction,
      FlaxBertForPreTraining,
      FlaxBertForQuestionAnswering,
      FlaxBertForSequenceClassification,
      FlaxBertForTokenClassification,
      FlaxBertModel,
  )




class 			__magic_name__	(		unittest.TestCase     ):





   """simple docstring"""




   def __init__(						self       :	Tuple		,	_lowercase       :	List[str]		,	_lowercase       :	Dict=13		,	_lowercase       :	Any=7		,	_lowercase       :	List[str]=True		,	_lowercase       :	Any=True		,	_lowercase       :	Optional[int]=True		,	_lowercase       :	int=True		,	_lowercase       :	str=99		,	_lowercase       :	Union[str, Any]=32		,	_lowercase       :	Any=5		,	_lowercase       :	Dict=4		,	_lowercase       :	Tuple=37		,	_lowercase       :	Optional[Any]="gelu"		,	_lowercase       :	Optional[int]=0.1		,	_lowercase       :	Any=0.1		,	_lowercase       :	Union[str, Any]=512		,	_lowercase       :	Dict=16		,	_lowercase       :	int=2		,	_lowercase       :	Union[str, Any]=0.02		,	_lowercase       :	Dict=4		,	):



    """simple docstring"""



    _UpperCamelCase:  List[str]    						=			parent
    _UpperCamelCase:  Optional[int]    						=			batch_size
    _UpperCamelCase:  Any    						=			seq_length
    _UpperCamelCase:  List[str]    						=			is_training
    _UpperCamelCase:  Union[str, Any]    						=			use_attention_mask
    _UpperCamelCase:  Union[str, Any]    						=			use_token_type_ids
    _UpperCamelCase:  str    						=			use_labels
    _UpperCamelCase:  List[str]    						=			vocab_size
    _UpperCamelCase:  Dict    						=			hidden_size
    _UpperCamelCase:  List[Any]    						=			num_hidden_layers
    _UpperCamelCase:  List[Any]    						=			num_attention_heads
    _UpperCamelCase:  Tuple    						=			intermediate_size
    _UpperCamelCase:  Optional[Any]    						=			hidden_act
    _UpperCamelCase:  Any    						=			hidden_dropout_prob
    _UpperCamelCase:  int    						=			attention_probs_dropout_prob
    _UpperCamelCase:  Optional[int]    						=			max_position_embeddings
    _UpperCamelCase:  List[Any]    						=			type_vocab_size
    _UpperCamelCase:  List[Any]    						=			type_sequence_label_size
    _UpperCamelCase:  List[Any]    						=			initializer_range
    _UpperCamelCase:  Optional[int]    						=			num_choices



   def 	lowerCAmelCase    (						self       :	Optional[Any]				):



    """simple docstring"""



    _UpperCamelCase:  int    						=			ids_tensor([self.batch_size, self.seq_length]		,	self.vocab_size				)

    _UpperCamelCase:  Optional[int]    						=			None
    if self.use_attention_mask:
     _UpperCamelCase:  List[str]    						=			random_attention_mask([self.batch_size, self.seq_length]				)

    _UpperCamelCase:  Optional[int]    						=			None
    if self.use_token_type_ids:
     _UpperCamelCase:  Tuple    						=			ids_tensor([self.batch_size, self.seq_length]		,	self.type_vocab_size				)

    _UpperCamelCase:  str    						=			BertConfig(
        vocab_size=self.vocab_size		,	hidden_size=self.hidden_size		,	num_hidden_layers=self.num_hidden_layers		,	num_attention_heads=self.num_attention_heads		,	intermediate_size=self.intermediate_size		,	hidden_act=self.hidden_act		,	hidden_dropout_prob=self.hidden_dropout_prob		,	attention_probs_dropout_prob=self.attention_probs_dropout_prob		,	max_position_embeddings=self.max_position_embeddings		,	type_vocab_size=self.type_vocab_size		,	is_decoder=_lowercase		,	initializer_range=self.initializer_range		,	)

    return config, input_ids, token_type_ids, attention_mask



   def 	lowerCAmelCase    (						self       :	Optional[Any]				):



    """simple docstring"""



    _UpperCamelCase:  Optional[Any]    						=			self.prepare_config_and_inputs()
    _UpperCamelCase						,				_UpperCamelCase						,				_UpperCamelCase						,				_UpperCamelCase:  Any    						=			config_and_inputs
    _UpperCamelCase:  List[Any]    						=			{'''input_ids''': input_ids, '''token_type_ids''': token_type_ids, '''attention_mask''': attention_mask}
    return config, inputs_dict



   def 	lowerCAmelCase    (						self       :	Dict				):



    """simple docstring"""



    _UpperCamelCase:  Any    						=			self.prepare_config_and_inputs()
    _UpperCamelCase						,				_UpperCamelCase						,				_UpperCamelCase						,				_UpperCamelCase:  str    						=			config_and_inputs

    _UpperCamelCase:  int    						=			True
    _UpperCamelCase:  Optional[Any]    						=			floats_tensor([self.batch_size, self.seq_length, self.hidden_size]				)
    _UpperCamelCase:  Optional[Any]    						=			ids_tensor([self.batch_size, self.seq_length]		,	vocab_size=2				)

    return (
        config,
        input_ids,
        attention_mask,
        encoder_hidden_states,
        encoder_attention_mask,
    )




@require_flax
class 			__magic_name__	(		__a   ,						unittest.TestCase     ):





   """simple docstring"""




   lowerCAmelCase   :     Dict	      = True

   lowerCAmelCase   :     List[Any]	      = (
       (
           FlaxBertModel,
           FlaxBertForPreTraining,
           FlaxBertForMaskedLM,
           FlaxBertForMultipleChoice,
           FlaxBertForQuestionAnswering,
           FlaxBertForNextSentencePrediction,
           FlaxBertForSequenceClassification,
           FlaxBertForTokenClassification,
           FlaxBertForQuestionAnswering,
       )
       if is_flax_available()
       else ()
   )



   def 	lowerCAmelCase    (						self       :	Dict				):



    """simple docstring"""



    _UpperCamelCase:  Dict    						=			FlaxBertModelTester(self				)



   @slow
   def 	lowerCAmelCase    (						self       :	Tuple				):



    """simple docstring"""



    _UpperCamelCase:  Dict    						=			FlaxBertModel.from_pretrained('''bert-base-cased'''				)
    _UpperCamelCase:  int    						=			model(np.ones((1, 1)				)				)
    self.assertIsNotNone(_lowercase				)