import numpy as np






def __lowerCAmelCase			(							UpperCamelCase__    ,  UpperCamelCase__    ,  UpperCamelCase__ = 1E-12    ,  UpperCamelCase__ = 1_00    ,  )     ->   tuple[float, np.ndarray]:
    assert np.shape(_lowerCAmelCase    )[0] == np.shape(_lowerCAmelCase    )[1]
    # Ensure proper dimensionality.
    assert np.shape(_lowerCAmelCase    )[0] == np.shape(_lowerCAmelCase    )[0]
    # Ensure inputs are either both complex or both real
    assert np.iscomplexobj(_lowerCAmelCase    ) == np.iscomplexobj(_lowerCAmelCase    )
    __lowerCamelCase          =  np.iscomplexobj(_lowerCAmelCase    )
    if is_complex:
        # Ensure complex input_matrix is Hermitian
        assert np.array_equal(_lowerCAmelCase    ,  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          =  False
    __lowerCamelCase          =  0
    __lowerCamelCase          =  0
    __lowerCamelCase          =  1E12

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

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

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

        __lowerCamelCase          =  lambda_

    if is_complex:
        __lowerCamelCase          =  np.real(lambda_    )

    return lambda_, vector






def __lowerCAmelCase			(							)     ->   None:
    __lowerCamelCase          =  np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]    )
    __lowerCamelCase          =  np.array([41, 4, 20]    )
    __lowerCamelCase          =  real_input_matrix.astype(np.complexaaa    )
    __lowerCamelCase          =  np.triu(1J * complex_input_matrix    ,  1    )
    complex_input_matrix += imag_matrix
    complex_input_matrix += -1 * imag_matrix.T
    __lowerCamelCase          =  np.array([41, 4, 20]    ).astype(np.complexaaa    )

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

        # Our implementation.
        __lowerCamelCase          =  power_iteration(_lowerCAmelCase    ,  _lowerCAmelCase    )

        # Numpy implementation.

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


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  test_power_iteration()

'''simple docstring'''




import os
import re
import warnings
from shutil import copyfile
from typing import List, Optional, Tuple

from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import is_sentencepiece_available, logging


if is_sentencepiece_available():
  from .tokenization_ta import TaTokenizer
else:
  __UpperCAmelCase												=None


__UpperCAmelCase												=logging.get_logger(__name__)

__UpperCAmelCase												={"vocab_file": "spiece.model", "tokenizer_file": "tokenizer.json"}

__UpperCAmelCase												={
    "vocab_file": {
        "t5-small": "https://huggingface.co/t5-small/resolve/main/spiece.model",
        "t5-base": "https://huggingface.co/t5-base/resolve/main/spiece.model",
        "t5-large": "https://huggingface.co/t5-large/resolve/main/spiece.model",
        "t5-3b": "https://huggingface.co/t5-3b/resolve/main/spiece.model",
        "t5-11b": "https://huggingface.co/t5-11b/resolve/main/spiece.model",
    },
    "tokenizer_file": {
        "t5-small": "https://huggingface.co/t5-small/resolve/main/tokenizer.json",
        "t5-base": "https://huggingface.co/t5-base/resolve/main/tokenizer.json",
        "t5-large": "https://huggingface.co/t5-large/resolve/main/tokenizer.json",
        "t5-3b": "https://huggingface.co/t5-3b/resolve/main/tokenizer.json",
        "t5-11b": "https://huggingface.co/t5-11b/resolve/main/tokenizer.json",
    },
}


# TODO(PVP) - this should be removed in Transformers v5
__UpperCAmelCase												={
    "t5-small": 5_1_2,
    "t5-base": 5_1_2,
    "t5-large": 5_1_2,
    "t5-3b": 5_1_2,
    "t5-11b": 5_1_2,
}




class    a__				(       UpperCAmelCase__			):
     lowerCamelCase  :					Dict							=VOCAB_FILES_NAMES
     lowerCamelCase  :					Optional[Any]							=PRETRAINED_VOCAB_FILES_MAP
     lowerCamelCase  :					Dict							=PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
     lowerCamelCase  :					int							=["input_ids", "attention_mask"]
     lowerCamelCase  :					Tuple							=TaTokenizer

     lowerCamelCase  :					List[int]							=[]






     def __init__(			self		:		int  ,    a		:		List[str]=None  ,    a		:		List[str]=None  ,    a		:		Dict="</s>"  ,    a		:		Optional[int]="<unk>"  ,    a		:		Any="<pad>"  ,    a		:		Optional[Any]=1_00  ,    a		:		List[Any]=None  ,    **a		:		Union[str, Any]  ,    ):





         """simple docstring"""



         if extra_ids > 0 and additional_special_tokens is None:
             __lowerCamelCase          =  [f"""<extra_id_{i}>""" for i in range(a   )]
         elif extra_ids > 0 and additional_special_tokens is not None:
             # Check that we have the right number of extra special tokens
             __lowerCamelCase          =  len(set(filter(lambda a   : bool('''extra_id_''' in str(a   )   )  ,    a   )   )   )
             if extra_tokens != extra_ids:
                 raise ValueError(
                     f"""Both extra_ids ({extra_ids}) and additional_special_tokens ({additional_special_tokens}) are"""
                     ''' provided to T5Tokenizer. In this case the additional_special_tokens must include the extra_ids'''
                     ''' tokens'''   )

         super().__init__(
             a  ,    tokenizer_file=a  ,    eos_token=a  ,    unk_token=a  ,    pad_token=a  ,    extra_ids=a  ,    additional_special_tokens=a  ,    **a  ,    )

         __lowerCamelCase          =  vocab_file
         __lowerCamelCase          =  False if not self.vocab_file else True
         __lowerCamelCase          =  extra_ids






     @staticmethod
     def        SCREAMING_SNAKE_CASE__       (			a		:		Optional[int]  ,    a		:		List[str]  ,    a		:		Union[str, Any]   ):





         """simple docstring"""



         if pretrained_model_name_or_path in TaTokenizerFast.max_model_input_sizes:
             __lowerCamelCase          =  TaTokenizerFast.max_model_input_sizes[pretrained_model_name_or_path]
             if init_max_model_length is not None and init_max_model_length != max_model_length:
                 return init_max_model_length
             elif init_max_model_length is None:
                 warnings.warn(
                     '''This tokenizer was incorrectly instantiated with a model max length of'''
                     f""" {deprecated_max_model_length} which will be corrected in Transformers v5.\nFor now, this"""
                     ''' behavior is kept to avoid breaking backwards compatibility when padding/encoding with'''
                     ''' `truncation is True`.\n- Be aware that you SHOULD NOT rely on'''
                     f""" {pretrained_model_name_or_path} automatically truncating your input to"""
                     f""" {deprecated_max_model_length} when padding/encoding.\n- If you want to encode/pad to sequences"""
                     f""" longer than {deprecated_max_model_length} you can either instantiate this tokenizer with"""
                     ''' `model_max_length` or pass `max_length` when encoding/padding.\n- To avoid this warning, please'''
                     ''' instantiate this tokenizer with `model_max_length` set to your preferred value.'''  ,    a  ,    )

         return max_model_length






     def        SCREAMING_SNAKE_CASE__       (			self		:		Tuple  ,    a		:		str  ,    a		:		Optional[str] = None   ):





         """simple docstring"""



         if not self.can_save_slow_tokenizer:
             raise ValueError(
                 '''Your fast tokenizer does not have the necessary information to save the vocabulary for a slow '''
                 '''tokenizer.'''   )

         if not os.path.isdir(a   ):
             logger.error(f"""Vocabulary path ({save_directory}) should be a directory"""   )
             return
         __lowerCamelCase          =  os.path.join(
             a  ,    (filename_prefix + '''-''' if filename_prefix else '''''') + VOCAB_FILES_NAMES['''vocab_file''']   )

         if os.path.abspath(self.vocab_file   ) != os.path.abspath(a   ):
             copyfile(self.vocab_file  ,    a   )
             logger.info(f"""Copy vocab file to {out_vocab_file}"""   )

         return (out_vocab_file,)






     def        SCREAMING_SNAKE_CASE__       (			self		:		int  ,    a		:		List[int]  ,    a		:		Optional[List[int]] = None   ):





         """simple docstring"""



         __lowerCamelCase          =  token_ids_a + [self.eos_token_id]
         if token_ids_a is None:
             return self.prefix_tokens + token_ids_a
         else:
             __lowerCamelCase          =  token_ids_a + [self.eos_token_id]
             return self.prefix_tokens + token_ids_a + token_ids_a






     def        SCREAMING_SNAKE_CASE__       (			self		:		List[Any]  ,    a		:		List[int]  ,    a		:		Optional[List[int]] = None   ):





         """simple docstring"""



         __lowerCamelCase          =  [self.eos_token_id]

         if token_ids_a is None:
             return len(token_ids_a + eos   ) * [0]
         return len(token_ids_a + eos + token_ids_a + eos   ) * [0]






     def        SCREAMING_SNAKE_CASE__       (			self		:		Any   ):





         """simple docstring"""



         return list(
             set(filter(lambda a   : bool(re.search(R'''<extra_id_\d+>'''  ,    a   )   ) is not None  ,    self.additional_special_tokens   )   )   )






     def        SCREAMING_SNAKE_CASE__       (			self		:		Union[str, Any]   ):





         """simple docstring"""



         return [self.convert_tokens_to_ids(a   ) for token in self.get_sentinel_tokens()]
