from collections.abc import Callable

UpperCamelCase													=		Callable[[float], float]  # type alias for a real -> real function

def     lowercase_       (    _lowerCamelCase							: RealFunc	,			_lowerCamelCase							: RealFunc	,			_lowerCamelCase							: int	,			):
    lowercase__				:     Union[str, Any]					      =       float(_lowerCamelCase)
    while True:
        try:
            lowercase__				:     Union[str, Any]					      =       prev_guess - function(_lowerCamelCase) / derivative(_lowerCamelCase)
        except ZeroDivisionError:
            raise ZeroDivisionError("Could not find root") from None
        if abs(prev_guess - next_guess) < 10**-5:
            return next_guess
        lowercase__				:     List[Any]					      =       next_guess

def     lowercase_       (    _lowerCamelCase							: float):
    return (x**3) - (2 * x) - 5

def     lowercase_       (    _lowerCamelCase							: float):
    return 3 * (x**2) - 2


if __name__ == "__main__":
      print(newton(f, fa, 3))




import math
from typing import Optional

import torch
import torch.utils.checkpoint as checkpoint
from torch import nn

from ....modeling_utils import PreTrainedModel
from ....utils import add_start_docstrings, logging
from ...bert.modeling_bert import BertModel
from .configuration_retribert import RetriBertConfig


UpperCamelCase													=		logging.get_logger(__name__)

UpperCamelCase													=		[
    '''yjernite/retribert-base-uncased''',
    # See all RetriBert models at https://huggingface.co/models?filter=retribert
]



class 						snake_case_ (	__A ):
   __A			:	Optional[Any]        =       RetriBertConfig
   __A			:	str        =       None
   __A			:	Any        =       "retribert"






   def    __UpperCamelCase  (   self       :  Dict			,		lowercase_       :  List[Any]						)      ->		List[str]:
       if isinstance(lowercase_			,		nn.Linear						):
           module.weight.data.normal_(mean=0.0			,		std=self.config.initializer_range						)
           if module.bias is not None:
               module.bias.data.zero_()
       elif isinstance(lowercase_			,		nn.Embedding						):
           module.weight.data.normal_(mean=0.0			,		std=self.config.initializer_range						)
           if module.padding_idx is not None:
               module.weight.data[module.padding_idx].zero_()
       elif isinstance(lowercase_			,		nn.LayerNorm						):
           module.bias.data.zero_()
           module.weight.data.fill_(1.0						)



UpperCamelCase													=		R'''

    This model inherits from [`PreTrainedModel`]. Check the superclass documentation for the generic methods the
    library implements for all its model (such as downloading or saving, resizing the input embeddings, pruning heads
    etc.)

    This model is also a PyTorch [torch.nn.Module](https://pytorch.org/docs/stable/nn.html#torch.nn.Module) subclass.
    Use it as a regular PyTorch Module and refer to the PyTorch documentation for all matter related to general usage
    and behavior.

    Parameters:
        config ([`RetriBertConfig`]): Model configuration class with all the parameters of the model.
            Initializing with a config file does not load the weights associated with the model, only the
            configuration. Check out the [`~PreTrainedModel.from_pretrained`] method to load the model weights.
'''



@add_start_docstrings(
    "Bert Based model to embed queries or document for document retrieval."						,__A						,)
class 						snake_case_ (	__A ):






   def __init__(   self       :  Dict			,		lowercase_       :  RetriBertConfig						)      ->		None:
       super().__init__(lowercase_						)
       lowercase__				:     str					      =       config.projection_dim

       lowercase__				:     Optional[int]					      =       BertModel(lowercase_						)
       lowercase__				:     Union[str, Any]					      =       None if config.share_encoders else BertModel(lowercase_						)
       lowercase__				:     Tuple					      =       nn.Dropout(config.hidden_dropout_prob						)
       lowercase__				:     Any					      =       nn.Linear(config.hidden_size			,		config.projection_dim			,		bias=lowercase_						)
       lowercase__				:     str					      =       nn.Linear(config.hidden_size			,		config.projection_dim			,		bias=lowercase_						)

       lowercase__				:     Optional[Any]					      =       nn.CrossEntropyLoss(reduction="mean"						)

       # Initialize weights and apply final processing
       self.post_init()






   def    __UpperCamelCase  (   self       :  Dict			,		lowercase_       :  str			,		lowercase_       :  Optional[int]			,		lowercase_       :  Tuple			,		lowercase_       :  Optional[int]=-1			,		)      ->		List[str]:
       # reproduces BERT forward pass with checkpointing
       if checkpoint_batch_size < 0 or input_ids.shape[0] < checkpoint_batch_size:
           return sent_encoder(lowercase_			,		attention_mask=lowercase_						)[1]
       else:
           # prepare implicit variables
           lowercase__				:     Union[str, Any]					      =       input_ids.device
           lowercase__				:     Union[str, Any]					      =       input_ids.size()
           lowercase__				:     int					      =       torch.zeros(lowercase_			,		dtype=torch.long			,		device=lowercase_						)
           lowercase__				:     List[Any]					      =       [None] * sent_encoder.config.num_hidden_layers
           lowercase__				:     torch.Tensor					      =       sent_encoder.get_extended_attention_mask(
               lowercase_			,		lowercase_						)

           # define function for checkpointing
           def partial_encode(*lowercase_       :  int						):
               lowercase__				:     List[Any]					      =       sent_encoder.encoder(
                   inputs[0]			,		attention_mask=inputs[1]			,		head_mask=lowercase_			,		)
               lowercase__				:     Dict					      =       encoder_outputs[0]
               lowercase__				:     List[Any]					      =       sent_encoder.pooler(lowercase_						)
               return pooled_output

           # run embedding layer on everything at once
           lowercase__				:     Optional[int]					      =       sent_encoder.embeddings(
               input_ids=lowercase_			,		position_ids=lowercase_			,		token_type_ids=lowercase_			,		inputs_embeds=lowercase_						)
           # run encoding and pooling on one mini-batch at a time
           lowercase__				:     str					      =       []
           for b in range(math.ceil(input_ids.shape[0] / checkpoint_batch_size						)						):
               lowercase__				:     int					      =       embedding_output[b * checkpoint_batch_size : (b + 1) * checkpoint_batch_size]
               lowercase__				:     int					      =       extended_attention_mask[b * checkpoint_batch_size : (b + 1) * checkpoint_batch_size]
               lowercase__				:     int					      =       checkpoint.checkpoint(lowercase_			,		lowercase_			,		lowercase_						)
               pooled_output_list.append(lowercase_						)
           return torch.cat(lowercase_			,		dim=0						)






   def    __UpperCamelCase  (   self       :  Optional[Any]			,		lowercase_       :  Any			,		lowercase_       :  Any=None			,		lowercase_       :  Union[str, Any]=-1			,		)      ->		List[str]:
       lowercase__				:     Optional[Any]					      =       self.embed_sentences_checkpointed(
           lowercase_			,		lowercase_			,		self.bert_query			,		lowercase_			,		)
       return self.project_query(lowercase_						)






   def    __UpperCamelCase  (   self       :  Union[str, Any]			,		lowercase_       :  Optional[Any]			,		lowercase_       :  Union[str, Any]=None			,		lowercase_       :  Dict=-1			,		)      ->		Optional[int]:
       lowercase__				:     str					      =       self.embed_sentences_checkpointed(
           lowercase_			,		lowercase_			,		self.bert_query if self.bert_doc is None else self.bert_doc			,		lowercase_			,		)
       return self.project_doc(lowercase_						)







   def    __UpperCamelCase  (   self       :  str			,		lowercase_       :  torch.LongTensor			,		lowercase_       :  Optional[torch.FloatTensor]			,		lowercase_       :  torch.LongTensor			,		lowercase_       :  Optional[torch.FloatTensor]			,		lowercase_       :  int = -1			,		)      ->		torch.FloatTensor:
       lowercase__				:     Tuple					      =       input_ids_query.device
       lowercase__				:     str					      =       self.embed_questions(lowercase_			,		lowercase_			,		lowercase_						)
       lowercase__				:     Any					      =       self.embed_answers(lowercase_			,		lowercase_			,		lowercase_						)
       lowercase__				:     List[str]					      =       torch.mm(lowercase_			,		a_reps.t()						)
       lowercase__				:     Optional[int]					      =       self.ce_loss(lowercase_			,		torch.arange(compare_scores.shape[1]						).to(lowercase_						)						)
       lowercase__				:     str					      =       self.ce_loss(compare_scores.t()			,		torch.arange(compare_scores.shape[0]						).to(lowercase_						)						)
       lowercase__				:     Tuple					      =       (loss_qa + loss_aq) / 2
       return loss



