

'''simple docstring'''



import os
from collections import deque

import torch
from torch.utils.data import Dataset







class 						lowerCAmelCase__   (      a					):



 """simple docstring"""



 def __init__(		self					:       Optional[Any]					,							__SCREAMING_SNAKE_CASE					:       Any=""					,							__SCREAMING_SNAKE_CASE					:       List[str]="train"			)  -> List[Any]:


      """simple docstring"""




      assert os.path.isdir(__SCREAMING_SNAKE_CASE			)

      __SCREAMING_SNAKE_CASE     =      []
      __SCREAMING_SNAKE_CASE     =      os.listdir(__SCREAMING_SNAKE_CASE			)
      for story_filename in story_filenames_list:
           if "summary" in story_filename:
                continue
           __SCREAMING_SNAKE_CASE     =      os.path.join(__SCREAMING_SNAKE_CASE					,							__SCREAMING_SNAKE_CASE			)
           if not os.path.isfile(__SCREAMING_SNAKE_CASE			):
                continue
           self.documents.append(__SCREAMING_SNAKE_CASE			)
 def __len__(		self					:       Union[str, Any]			)  -> int:


      """simple docstring"""




      return len(self.documents			)


 def __getitem__(		self					:       Optional[Any]					,							__SCREAMING_SNAKE_CASE					:       Optional[int]			)  -> Any:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE     =      self.documents[idx]
      __SCREAMING_SNAKE_CASE     =      document_path.split("""/"""			)[-1]
      with open(__SCREAMING_SNAKE_CASE					,							encoding="""utf-8"""			) as source:
           __SCREAMING_SNAKE_CASE     =      source.read()
           __SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE     =      process_story(__SCREAMING_SNAKE_CASE			)
      return document_name, story_lines, summary_lines







def    a__       (  a__						):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      list(filter(lambda a__						: len(a__						) != 0      ,    [line.strip() for line in raw_story.split("""\n"""						)]						)						)

     # for some unknown reason some lines miss a period, add it
     __SCREAMING_SNAKE_CASE     =      [_add_missing_period(a__						) for line in nonempty_lines]

     # gather article lines
     __SCREAMING_SNAKE_CASE     =      []
     __SCREAMING_SNAKE_CASE     =      deque(a__						)
     while True:
          try:
               __SCREAMING_SNAKE_CASE     =      lines.popleft()
               if element.startswith("""@highlight"""						):
                    break
               story_lines.append(a__						)
          except IndexError:
               # if "@highlight" is absent from the file we pop
               # all elements until there is None, raising an exception.
               return story_lines, []

    # gather summary lines
     __SCREAMING_SNAKE_CASE     =      list(filter(lambda a__						: not t.startswith("""@highlight"""						)      ,    a__						)						)

     return story_lines, summary_lines







def    a__       (  a__						):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      [""".""", """!""", """?""", """...""", """'""", """`""", """\"""", """\u2019""", """\u2019""", """)"""]
     if line.startswith("""@highlight"""						):
          return line
     if line[-1] in END_TOKENS:
          return line
     return line + "."







def    a__       (  a__      ,    a__      ,    a__						):




     """simple docstring"""


     if len(a__						) > block_size:
          return sequence[:block_size]
     else:
          sequence.extend([pad_token_id] * (block_size - len(a__						))						)
          return sequence







def    a__       (  a__      ,    a__						):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      torch.ones_like(a__						)
     __SCREAMING_SNAKE_CASE     =      sequence == pad_token_id
     __SCREAMING_SNAKE_CASE     =      0
     return mask







def    a__       (  a__      ,    a__      ,    a__						):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      [tokenizer.encode(a__						) for line in story_lines]
     __SCREAMING_SNAKE_CASE     =      [token for sentence in story_lines_token_ids for token in sentence]
     __SCREAMING_SNAKE_CASE     =      [tokenizer.encode(a__						) for line in summary_lines]
     __SCREAMING_SNAKE_CASE     =      [token for sentence in summary_lines_token_ids for token in sentence]

     return story_token_ids, summary_token_ids







def    a__       (  a__      ,    a__						):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      []
     for sequence in batch:
          __SCREAMING_SNAKE_CASE     =      -1
          __SCREAMING_SNAKE_CASE     =      []
          for s in sequence:
               if s == separator_token_id:
                    sentence_num += 1
               embeddings.append(sentence_num % 2						)
          batch_embeddings.append(a__						)
     return torch.tensor(a__						)









'''simple docstring'''



import numpy as np







def    a__       (  a__      ,    a__      ,    a__ = 1E-1_2      ,    a__ = 1_00      ,    ):




     """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__						)
     __SCREAMING_SNAKE_CASE     =      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.

     __SCREAMING_SNAKE_CASE     =      False
     __SCREAMING_SNAKE_CASE     =      0
     __SCREAMING_SNAKE_CASE     =      0
     __SCREAMING_SNAKE_CASE     =      1E1_2

     while not convergence:
          # Multiple matrix by the vector.
          __SCREAMING_SNAKE_CASE     =      np.dot(a__      ,    a__						)
          # Normalize the resulting output vector.
          __SCREAMING_SNAKE_CASE     =      w / np.linalg.norm(a__						)
          # Find rayleigh quotient
          # (faster than usual b/c we know vector is normalized already)
          __SCREAMING_SNAKE_CASE     =      vector.conj().T if is_complex else vector.T
          __SCREAMING_SNAKE_CASE     =      np.dot(a__      ,    np.dot(a__      ,    a__						)						)

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

          if error <= error_tol or iterations >= max_iterations:
               __SCREAMING_SNAKE_CASE     =      True

          __SCREAMING_SNAKE_CASE     =      lambda_

     if is_complex:
          __SCREAMING_SNAKE_CASE     =      np.real(lambda_						)

     return lambda_, vector







def    a__       (  ):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]						)
     __SCREAMING_SNAKE_CASE     =      np.array([41, 4, 20]						)
     __SCREAMING_SNAKE_CASE     =      real_input_matrix.astype(np.complexaaa						)
     __SCREAMING_SNAKE_CASE     =      np.triu(1J * complex_input_matrix      ,    1						)
     complex_input_matrix += imag_matrix
     complex_input_matrix += -1 * imag_matrix.T
     __SCREAMING_SNAKE_CASE     =      np.array([41, 4, 20]						).astype(np.complexaaa						)

     for problem_type in ["real", "complex"]:
          if problem_type == "real":
               __SCREAMING_SNAKE_CASE     =      real_input_matrix
               __SCREAMING_SNAKE_CASE     =      real_vector
          elif problem_type == "complex":
               __SCREAMING_SNAKE_CASE     =      complex_input_matrix
               __SCREAMING_SNAKE_CASE     =      complex_vector

          # Our implementation.
          __SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE     =      power_iteration(a__      ,    a__						)

          # Numpy implementation.

          # Get eigenvalues and eigenvectors using built-in numpy
          # eigh (eigh used for symmetric or hermetian matrices).
          __SCREAMING_SNAKE_CASE   ,			__SCREAMING_SNAKE_CASE     =      np.linalg.eigh(a__						)
          # Last eigenvalue is the maximum one.
          __SCREAMING_SNAKE_CASE     =      eigen_values[-1]
          # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
          __SCREAMING_SNAKE_CASE     =      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()






