





import numpy as np





def 					lowerCAmelCase_			(	__a     ,   __a     ,   __a = 1e-12     ,   __a = 100     ,   )					->		tuple[float, np.ndarray]:







  """simple docstring"""





  assert np.shape(__a		)[0] == np.shape(__a		)[1]
  # Ensure proper dimensionality.
  assert np.shape(__a		)[0] == np.shape(__a		)[0]
  # Ensure inputs are either both complex or both real
  assert np.iscomplexobj(__a		) == np.iscomplexobj(__a		)
  lowerCamelCase__:				str        =np.iscomplexobj(__a		)
  if is_complex:
    # Ensure complex input_matrix is Hermitian
    assert np.array_equal(__a     ,   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.

  lowerCamelCase__:				int        =False
  lowerCamelCase__:				List[str]        =0
  lowerCamelCase__:				int        =0
  lowerCamelCase__:				int        =1e12

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

    # Check convergence.
    lowerCamelCase__:				Tuple        =np.abs(lambda_ - lambda_previous		) / lambda_
    iterations += 1

    if error <= error_tol or iterations >= max_iterations:
      lowerCamelCase__:				Any        =True

    lowerCamelCase__:				List[Any]        =lambda_

  if is_complex:
    lowerCamelCase__:				Dict        =np.real(lambda_		)

  return lambda_, vector





def 					lowerCAmelCase_			(	)					->		None:







  """simple docstring"""





  lowerCamelCase__:				Union[str, Any]        =np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]		)
  lowerCamelCase__:				Dict        =np.array([41, 4, 20]		)
  lowerCamelCase__:				Any        =real_input_matrix.astype(np.complexaaa		)
  lowerCamelCase__:				int        =np.triu(1J * complex_input_matrix     ,   1		)
  complex_input_matrix += imag_matrix
  complex_input_matrix += -1 * imag_matrix.T
  lowerCamelCase__:				List[Any]        =np.array([41, 4, 20]		).astype(np.complexaaa		)

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

    # Our implementation.
    lowerCamelCase__:				str        =power_iteration(__a     ,   __a		)

    # Numpy implementation.

    # Get eigenvalues and eigenvectors using built-in numpy
    # eigh (eigh used for symmetric or hermetian matrices).
    lowerCamelCase__:				int        =np.linalg.eigh(__a		)
    # Last eigenvalue is the maximum one.
    lowerCamelCase__:				Any        =eigen_values[-1]
    # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
    lowerCamelCase__:				Tuple        =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(__a		) - np.abs(__a		)		) <= 1e-6


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     test_power_iteration()








import json
import os
import unittest

from transformers.models.ctrl.tokenization_ctrl import VOCAB_FILES_NAMES, CTRLTokenizer

from ...test_tokenization_common import TokenizerTesterMixin



class        _SCREAMING_SNAKE_CASE						(     __SCREAMING_SNAKE_CASE   ,							unittest.TestCase   ):







 '''simple docstring'''
 lowercase_		=      CTRLTokenizer
 lowercase_		=      False
 lowercase_		=      False

 def 							SCREAMING_SNAKE_CASE_ (self    :       str)	->Union[str, Any]:



   '''simple docstring'''



   super().setUp()

   # Adapted from Sennrich et al. 2015 and https://github.com/rsennrich/subword-nmt
   lowerCamelCase__:				Optional[Any]        =["adapt", "re@@", "a@@", "apt", "c@@", "t", "<unk>"]
   lowerCamelCase__:				Optional[Any]        =dict(zip(UpperCAmelCase_	,			range(len(UpperCAmelCase_))))
   lowerCamelCase__:				Union[str, Any]        =["#version: 0.2", "a p", "ap t</w>", "r e", "a d", "ad apt</w>", ""]
   lowerCamelCase__:				Union[str, Any]        ={"unk_token": "<unk>"}

   lowerCamelCase__:				Union[str, Any]        =os.path.join(self.tmpdirname	,			VOCAB_FILES_NAMES["vocab_file"])
   lowerCamelCase__:				Optional[Any]        =os.path.join(self.tmpdirname	,			VOCAB_FILES_NAMES["merges_file"])
   with open(self.vocab_file	,			"w"	,			encoding="utf-8") as fp:
     fp.write(json.dumps(UpperCAmelCase_) + "\n")
   with open(self.merges_file	,			"w"	,			encoding="utf-8") as fp:
     fp.write("\n".join(UpperCAmelCase_))

 def 							SCREAMING_SNAKE_CASE_ (self    :       List[str]	,			**UpperCAmelCase_    :       str)	->List[Any]:



   '''simple docstring'''



   kwargs.update(self.special_tokens_map)
   return CTRLTokenizer.from_pretrained(self.tmpdirname	,			**UpperCAmelCase_)

 def 							SCREAMING_SNAKE_CASE_ (self    :       List[Any]	,			UpperCAmelCase_    :       Optional[int])	->Optional[int]:



   '''simple docstring'''



   lowerCamelCase__:				int        ="adapt react readapt apt"
   lowerCamelCase__:				int        ="adapt react readapt apt"
   return input_text, output_text







 def 							SCREAMING_SNAKE_CASE_ (self    :       str)	->Union[str, Any]:



   '''simple docstring'''



   lowerCamelCase__:				List[str]        =CTRLTokenizer(self.vocab_file	,			self.merges_file	,			**self.special_tokens_map)
   lowerCamelCase__:				Union[str, Any]        ="adapt react readapt apt"
   lowerCamelCase__:				Tuple        ="adapt re@@ a@@ c@@ t re@@ adapt apt".split()
   lowerCamelCase__:				Dict        =tokenizer.tokenize(UpperCAmelCase_)
   self.assertListEqual(UpperCAmelCase_	,			UpperCAmelCase_)

   lowerCamelCase__:				Optional[int]        =tokens + [tokenizer.unk_token]

   lowerCamelCase__:				List[str]        =[0, 1, 2, 4, 5, 1, 0, 3, 6]
   self.assertListEqual(tokenizer.convert_tokens_to_ids(UpperCAmelCase_)	,			UpperCAmelCase_)

