'''simple docstring'''

import collections
from typing import List, Optional, Union

from ...tokenization_utils_base import BatchEncoding
from ...utils import TensorType, add_end_docstrings, add_start_docstrings, logging
from ..bert.tokenization_bert import BertTokenizer


_A			:      Any					      =				logging.get_logger(__name__)

_A			:      List[Any]					      =				{'''vocab_file''': '''vocab.txt''', '''tokenizer_file''': '''tokenizer.json'''}

_A			:      Optional[Any]					      =				{
    '''vocab_file''': {
        '''facebook/dpr-ctx_encoder-single-nq-base''': (
            '''https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/vocab.txt'''
        ),
        '''facebook/dpr-ctx_encoder-multiset-base''': (
            '''https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/vocab.txt'''
        ),
    },
    '''tokenizer_file''': {
        '''facebook/dpr-ctx_encoder-single-nq-base''': (
            '''https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/tokenizer.json'''
        ),
        '''facebook/dpr-ctx_encoder-multiset-base''': (
            '''https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/tokenizer.json'''
        ),
    },
}
_A			:      Union[str, Any]					      =				{
    '''vocab_file''': {
        '''facebook/dpr-question_encoder-single-nq-base''': (
            '''https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/vocab.txt'''
        ),
        '''facebook/dpr-question_encoder-multiset-base''': (
            '''https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/vocab.txt'''
        ),
    },
    '''tokenizer_file''': {
        '''facebook/dpr-question_encoder-single-nq-base''': (
            '''https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/tokenizer.json'''
        ),
        '''facebook/dpr-question_encoder-multiset-base''': (
            '''https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/tokenizer.json'''
        ),
    },
}
_A			:      Optional[int]					      =				{
    '''vocab_file''': {
        '''facebook/dpr-reader-single-nq-base''': (
            '''https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/vocab.txt'''
        ),
        '''facebook/dpr-reader-multiset-base''': (
            '''https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/vocab.txt'''
        ),
    },
    '''tokenizer_file''': {
        '''facebook/dpr-reader-single-nq-base''': (
            '''https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/tokenizer.json'''
        ),
        '''facebook/dpr-reader-multiset-base''': (
            '''https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/tokenizer.json'''
        ),
    },
}

_A			:      str					      =				{
    '''facebook/dpr-ctx_encoder-single-nq-base''': 512,
    '''facebook/dpr-ctx_encoder-multiset-base''': 512,
}
_A			:      Any					      =				{
    '''facebook/dpr-question_encoder-single-nq-base''': 512,
    '''facebook/dpr-question_encoder-multiset-base''': 512,
}
_A			:      Optional[int]					      =				{
    '''facebook/dpr-reader-single-nq-base''': 512,
    '''facebook/dpr-reader-multiset-base''': 512,
}


_A			:      List[Any]					      =				{
    '''facebook/dpr-ctx_encoder-single-nq-base''': {'''do_lower_case''': True},
    '''facebook/dpr-ctx_encoder-multiset-base''': {'''do_lower_case''': True},
}
_A			:      Tuple					      =				{
    '''facebook/dpr-question_encoder-single-nq-base''': {'''do_lower_case''': True},
    '''facebook/dpr-question_encoder-multiset-base''': {'''do_lower_case''': True},
}
_A			:      int					      =				{
    '''facebook/dpr-reader-single-nq-base''': {'''do_lower_case''': True},
    '''facebook/dpr-reader-multiset-base''': {'''do_lower_case''': True},
}







class 				_lowercase     (				UpperCAmelCase__			):


 '''simple docstring'''






 _SCREAMING_SNAKE_CASE     :       Tuple      	=					VOCAB_FILES_NAMES
 _SCREAMING_SNAKE_CASE     :       int      	=					CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
 _SCREAMING_SNAKE_CASE     :       Optional[int]      	=					CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
 _SCREAMING_SNAKE_CASE     :       int      	=					CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION







class 				_lowercase     (				UpperCAmelCase__			):


 '''simple docstring'''






 _SCREAMING_SNAKE_CASE     :       List[Any]      	=					VOCAB_FILES_NAMES
 _SCREAMING_SNAKE_CASE     :       Tuple      	=					QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
 _SCREAMING_SNAKE_CASE     :       Dict      	=					QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
 _SCREAMING_SNAKE_CASE     :       int      	=					QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION







_A			:      List[str]					      =				collections.namedtuple(
    '''DPRSpanPrediction''', ['''span_score''', '''relevance_score''', '''doc_id''', '''start_index''', '''end_index''', '''text''']
)

_A			:      List[Any]					      =				collections.namedtuple('''DPRReaderOutput''', ['''start_logits''', '''end_logits''', '''relevance_logits'''])


_A			:      Union[str, Any]					      =				r'''
    Return a dictionary with the token ids of the input strings and other information to give to `.decode_best_spans`.
    It converts the strings of a question and different passages (title and text) in a sequence of IDs (integers),
    using the tokenizer and vocabulary. The resulting `input_ids` is a matrix of size `(n_passages, sequence_length)`
    with the format:

    ```
    [CLS] <question token ids> [SEP] <titles ids> [SEP] <texts ids>
    ```

    Args:
        questions (`str` or `List[str]`):
            The questions to be encoded. You can specify one question for many passages. In this case, the question
            will be duplicated like `[questions] * n_passages`. Otherwise you have to specify as many questions as in
            `titles` or `texts`.
        titles (`str` or `List[str]`):
            The passages titles to be encoded. This can be a string or a list of strings if there are several passages.
        texts (`str` or `List[str]`):
            The passages texts to be encoded. This can be a string or a list of strings if there are several passages.
        padding (`bool`, `str` or [`~utils.PaddingStrategy`], *optional*, defaults to `False`):
            Activates and controls padding. Accepts the following values:

            - `True` or `\'longest\'`: Pad to the longest sequence in the batch (or no padding if only a single sequence
              if provided).
            - `\'max_length\'`: Pad to a maximum length specified with the argument `max_length` or to the maximum
              acceptable input length for the model if that argument is not provided.
            - `False` or `\'do_not_pad\'` (default): No padding (i.e., can output a batch with sequences of different
              lengths).
        truncation (`bool`, `str` or [`~tokenization_utils_base.TruncationStrategy`], *optional*, defaults to `False`):
            Activates and controls truncation. Accepts the following values:

            - `True` or `\'longest_first\'`: Truncate to a maximum length specified with the argument `max_length` or to
              the maximum acceptable input length for the model if that argument is not provided. This will truncate
              token by token, removing a token from the longest sequence in the pair if a pair of sequences (or a batch
              of pairs) is provided.
            - `\'only_first\'`: Truncate to a maximum length specified with the argument `max_length` or to the maximum
              acceptable input length for the model if that argument is not provided. This will only truncate the first
              sequence of a pair if a pair of sequences (or a batch of pairs) is provided.
            - `\'only_second\'`: Truncate to a maximum length specified with the argument `max_length` or to the maximum
              acceptable input length for the model if that argument is not provided. This will only truncate the
              second sequence of a pair if a pair of sequences (or a batch of pairs) is provided.
            - `False` or `\'do_not_truncate\'` (default): No truncation (i.e., can output batch with sequence lengths
              greater than the model maximum admissible input size).
        max_length (`int`, *optional*):
                Controls the maximum length to use by one of the truncation/padding parameters.

                If left unset or set to `None`, this will use the predefined model maximum length if a maximum length
                is required by one of the truncation/padding parameters. If the model has no specific maximum input
                length (like XLNet) truncation/padding to a maximum length will be deactivated.
        return_tensors (`str` or [`~utils.TensorType`], *optional*):
                If set, will return tensors instead of list of python integers. Acceptable values are:

                - `\'tf\'`: Return TensorFlow `tf.constant` objects.
                - `\'pt\'`: Return PyTorch `torch.Tensor` objects.
                - `\'np\'`: Return Numpy `np.ndarray` objects.
        return_attention_mask (`bool`, *optional*):
            Whether or not to return the attention mask. If not set, will return the attention mask according to the
            specific tokenizer\'s default, defined by the `return_outputs` attribute.

            [What are attention masks?](../glossary#attention-mask)

    Returns:
        `Dict[str, List[List[int]]]`: A dictionary with the following keys:

        - `input_ids`: List of token ids to be fed to a model.
        - `attention_mask`: List of indices specifying which tokens should be attended to by the model.
    '''







@add_start_docstrings(UpperCAmelCase__			)
class 				_lowercase     :


 '''simple docstring'''






 def __call__(      self   :	Tuple      ,       SCREAMING_SNAKE_CASE__   :	Any      ,       SCREAMING_SNAKE_CASE__   :	Optional[str] = None      ,       SCREAMING_SNAKE_CASE__   :	Optional[str] = None      ,       SCREAMING_SNAKE_CASE__   :	Union[bool, str] = False      ,       SCREAMING_SNAKE_CASE__   :	Union[bool, str] = False      ,       SCREAMING_SNAKE_CASE__   :	Optional[int] = None      ,       SCREAMING_SNAKE_CASE__   :	Optional[Union[str, TensorType]] = None      ,       SCREAMING_SNAKE_CASE__   :	Optional[bool] = None      ,       **SCREAMING_SNAKE_CASE__   :	List[Any]      ,       )  ->    BatchEncoding:
  if titles is None and texts is None:
   return super().__call__(
       SCREAMING_SNAKE_CASE__      ,       padding=SCREAMING_SNAKE_CASE__      ,       truncation=SCREAMING_SNAKE_CASE__      ,       max_length=SCREAMING_SNAKE_CASE__      ,       return_tensors=SCREAMING_SNAKE_CASE__      ,       return_attention_mask=SCREAMING_SNAKE_CASE__      ,       **SCREAMING_SNAKE_CASE__      ,       )
  elif titles is None or texts is None:
   __lowerCAmelCase											=						titles if texts is None else texts
   return super().__call__(
       SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__      ,       padding=SCREAMING_SNAKE_CASE__      ,       truncation=SCREAMING_SNAKE_CASE__      ,       max_length=SCREAMING_SNAKE_CASE__      ,       return_tensors=SCREAMING_SNAKE_CASE__      ,       return_attention_mask=SCREAMING_SNAKE_CASE__      ,       **SCREAMING_SNAKE_CASE__      ,       )
  __lowerCAmelCase											=						titles if not isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							) else [titles]
  __lowerCAmelCase											=						texts if not isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							) else [texts]
  __lowerCAmelCase											=						len(SCREAMING_SNAKE_CASE__							)
  __lowerCAmelCase											=						questions if not isinstance(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							) else [questions] * n_passages
  if len(SCREAMING_SNAKE_CASE__							) != len(SCREAMING_SNAKE_CASE__							):
   raise ValueError(
       f"""There should be as many titles than texts but got {len(SCREAMING_SNAKE_CASE__							)} titles and {len(SCREAMING_SNAKE_CASE__							)} texts."""							)
  __lowerCAmelCase											=						super().__call__(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__      ,       padding=SCREAMING_SNAKE_CASE__      ,       truncation=SCREAMING_SNAKE_CASE__							)["""input_ids"""]
  __lowerCAmelCase											=						super().__call__(SCREAMING_SNAKE_CASE__      ,       add_special_tokens=SCREAMING_SNAKE_CASE__      ,       padding=SCREAMING_SNAKE_CASE__      ,       truncation=SCREAMING_SNAKE_CASE__							)["""input_ids"""]
  __lowerCAmelCase											=						{
      """input_ids""": [
          (encoded_question_and_title + encoded_text)[:max_length]
          if max_length is not None and truncation
          else encoded_question_and_title + encoded_text
          for encoded_question_and_title, encoded_text in zip(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							)
      ]
  }
  if return_attention_mask is not False:
   __lowerCAmelCase											=						[]
   for input_ids in encoded_inputs["input_ids"]:
    attention_mask.append([int(input_id != self.pad_token_id							) for input_id in input_ids]							)
   __lowerCAmelCase											=						attention_mask
  return self.pad(SCREAMING_SNAKE_CASE__      ,       padding=SCREAMING_SNAKE_CASE__      ,       max_length=SCREAMING_SNAKE_CASE__      ,       return_tensors=SCREAMING_SNAKE_CASE__							)
 def a					(      self   :	List[Any]      ,       SCREAMING_SNAKE_CASE__   :	BatchEncoding      ,       SCREAMING_SNAKE_CASE__   :	DPRReaderOutput      ,       SCREAMING_SNAKE_CASE__   :	int = 16      ,       SCREAMING_SNAKE_CASE__   :	int = 64      ,       SCREAMING_SNAKE_CASE__   :	int = 4      ,       )  ->    List[DPRSpanPrediction]:
  __lowerCAmelCase											=						reader_input["""input_ids"""]
  __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase											=						reader_output[:3]
  __lowerCAmelCase											=						len(SCREAMING_SNAKE_CASE__							)
  __lowerCAmelCase											=						sorted(range(SCREAMING_SNAKE_CASE__							)      ,       reverse=SCREAMING_SNAKE_CASE__      ,       key=relevance_logits.__getitem__							)
  __lowerCAmelCase											=						[]
  for doc_id in sorted_docs:
   __lowerCAmelCase											=						list(input_ids[doc_id]							)
   # assuming question & title information is at the beginning of the sequence
   __lowerCAmelCase											=						sequence_ids.index(self.sep_token_id      ,       2							) + 1  # second sep id
   if sequence_ids[-1] == self.pad_token_id:
    __lowerCAmelCase											=						sequence_ids.index(self.pad_token_id							)
   else:
    __lowerCAmelCase											=						len(SCREAMING_SNAKE_CASE__							)

   __lowerCAmelCase											=						self._get_best_spans(
       start_logits=start_logits[doc_id][passage_offset:sequence_len]      ,       end_logits=end_logits[doc_id][passage_offset:sequence_len]      ,       max_answer_length=SCREAMING_SNAKE_CASE__      ,       top_spans=SCREAMING_SNAKE_CASE__      ,       )
   for start_index, end_index in best_spans:
    start_index += passage_offset
    end_index += passage_offset
    nbest_spans_predictions.append(
        DPRSpanPrediction(
            span_score=start_logits[doc_id][start_index] + end_logits[doc_id][end_index]      ,       relevance_score=relevance_logits[doc_id]      ,       doc_id=SCREAMING_SNAKE_CASE__      ,       start_index=SCREAMING_SNAKE_CASE__      ,       end_index=SCREAMING_SNAKE_CASE__      ,       text=self.decode(sequence_ids[start_index : end_index + 1]							)      ,       )							)
   if len(SCREAMING_SNAKE_CASE__							) >= num_spans:
    break
  return nbest_spans_predictions[:num_spans]





 def a					(      self   :	Optional[int]      ,       SCREAMING_SNAKE_CASE__   :	List[int]      ,       SCREAMING_SNAKE_CASE__   :	List[int]      ,       SCREAMING_SNAKE_CASE__   :	int      ,       SCREAMING_SNAKE_CASE__   :	int      ,       )  ->    List[DPRSpanPrediction]:
  __lowerCAmelCase											=						[]
  for start_index, start_score in enumerate(SCREAMING_SNAKE_CASE__							):
   for answer_length, end_score in enumerate(end_logits[start_index : start_index + max_answer_length]							):
    scores.append(((start_index, start_index + answer_length), start_score + end_score)							)
  __lowerCAmelCase											=						sorted(SCREAMING_SNAKE_CASE__      ,       key=lambda SCREAMING_SNAKE_CASE__							: x[1]      ,       reverse=SCREAMING_SNAKE_CASE__							)
  __lowerCAmelCase											=						[]
  for (start_index, end_index), score in scores:
   if start_index > end_index:
    raise ValueError(f"""Wrong span indices: [{start_index}:{end_index}]"""							)
   __lowerCAmelCase											=						end_index - start_index + 1
   if length > max_answer_length:
    raise ValueError(f"""Span is too long: {length} > {max_answer_length}"""							)
   if any(
       start_index <= prev_start_index <= prev_end_index <= end_index
       or prev_start_index <= start_index <= end_index <= prev_end_index
       for (prev_start_index, prev_end_index) in chosen_span_intervals							):
    continue
   chosen_span_intervals.append((start_index, end_index)							)

   if len(SCREAMING_SNAKE_CASE__							) == top_spans:
    break
  return chosen_span_intervals







@add_end_docstrings(UpperCAmelCase__			)
class 				_lowercase     (				UpperCAmelCase__  ,							UpperCAmelCase__			):


 '''simple docstring'''






 _SCREAMING_SNAKE_CASE     :       Tuple      	=					VOCAB_FILES_NAMES
 _SCREAMING_SNAKE_CASE     :       List[str]      	=					READER_PRETRAINED_VOCAB_FILES_MAP
 _SCREAMING_SNAKE_CASE     :       Optional[Any]      	=					READER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
 _SCREAMING_SNAKE_CASE     :       Tuple      	=					READER_PRETRAINED_INIT_CONFIGURATION
 _SCREAMING_SNAKE_CASE     :       Optional[int]      	=					["""input_ids""", """attention_mask"""]







'''simple docstring'''

def      UpperCamelCase_						(					snake_case_       :       list[int]						,		snake_case_       :       list[int]      )					->     tuple[float, float]:






 '''simple docstring'''

 if not len(snake_case_      ) == len(snake_case_      ) == 3:
  raise ValueError("""Please enter a valid equation."""      )
 if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
  raise ValueError("""Both a & b of two equations can't be zero."""      )

 # Extract the coefficients
 __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase											=						equationa
 __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase											=						equationa

 # Calculate the determinants of the matrices
 __lowerCAmelCase											=						aa * ba - aa * ba
 __lowerCAmelCase											=						ca * ba - ca * ba
 __lowerCAmelCase											=						aa * ca - aa * ca

 # Check if the system of linear equations has a solution (using Cramer's rule)
 if determinant == 0:
  if determinant_x == determinant_y == 0:
   raise ValueError("""Infinite solutions. (Consistent system)"""      )
  else:
   raise ValueError("""No solution. (Inconsistent system)"""      )
 else:
  if determinant_x == determinant_y == 0:
   # Trivial solution (Inconsistent system)
   return (0.0, 0.0)
  else:
   __lowerCAmelCase											=						determinant_x / determinant
   __lowerCAmelCase											=						determinant_y / determinant
   # Non-Trivial Solution (Consistent system)
   return (x, y)






