
'''simple docstring'''





import torch
import torch.nn as nn
from transformers.modeling_utils import ModuleUtilsMixin
from transformers.models.ta.modeling_ta import (
    TaBlock,
    TaConfig,
    TaLayerNorm,
)

from ...configuration_utils import ConfigMixin, register_to_config
from ...models import ModelMixin



class 			lowerCAmelCase__ (							UpperCamelCase       ,				UpperCamelCase       ,				UpperCamelCase							):



  '''simple docstring'''






  @register_to_config
  def __init__(self	:			int						,			lowerCAmelCase_	:			int						,			lowerCAmelCase_	:			int						,			lowerCAmelCase_	:			int						,			lowerCAmelCase_	:			float						,			lowerCAmelCase_	:			int						,			lowerCAmelCase_	:			int						,			lowerCAmelCase_	:			int						,			lowerCAmelCase_	:			int						,			lowerCAmelCase_	:			str						,			lowerCAmelCase_	:			bool = False						,			) ->							int:
        super().__init__()

        snake_case_    							=				nn.Linear(lowerCAmelCase_						,			lowerCAmelCase_						,			bias=lowerCAmelCase_     )

        snake_case_    							=				nn.Embedding(lowerCAmelCase_						,			lowerCAmelCase_     )
        snake_case_    							=				False

        snake_case_    							=				nn.Dropout(p=lowerCAmelCase_     )

        snake_case_    							=				TaConfig(
            d_model=lowerCAmelCase_						,			num_heads=lowerCAmelCase_						,			d_kv=lowerCAmelCase_						,			d_ff=lowerCAmelCase_						,			feed_forward_proj=lowerCAmelCase_						,			dropout_rate=lowerCAmelCase_						,			is_decoder=lowerCAmelCase_						,			is_encoder_decoder=lowerCAmelCase_						,			)
        snake_case_    							=				nn.ModuleList()
        for lyr_num in range(lowerCAmelCase_     ):
              snake_case_    							=				TaBlock(lowerCAmelCase_     )
              self.encoders.append(lowerCAmelCase_     )

        snake_case_    							=				TaLayerNorm(lowerCAmelCase_     )
        snake_case_    							=				nn.Dropout(p=lowerCAmelCase_     )


  def 		_lowerCamelCase						(self	:			Any						,			lowerCAmelCase_	:			Tuple						,			lowerCAmelCase_	:			Optional[Any]     ) ->							Optional[Any]:
        snake_case_    							=				self.input_proj(lowerCAmelCase_     )

        # terminal relative positional encodings
        snake_case_    							=				encoder_inputs.shape[1]
        snake_case_    							=				torch.arange(lowerCAmelCase_						,			device=encoder_inputs.device     )

        snake_case_    							=				encoder_inputs_mask.sum(-1     )
        snake_case_    							=				torch.roll(input_positions.unsqueeze(0     )						,			tuple(seq_lens.tolist()     )						,			dims=0     )
        x += self.position_encoding(lowerCAmelCase_     )

        snake_case_    							=				self.dropout_pre(lowerCAmelCase_     )

        # inverted the attention mask
        snake_case_    							=				encoder_inputs.size()
        snake_case_    							=				self.get_extended_attention_mask(lowerCAmelCase_						,			lowerCAmelCase_     )

        for lyr in self.encoders:
              snake_case_    							=				lyr(lowerCAmelCase_						,			lowerCAmelCase_     )[0]
        snake_case_    							=				self.layer_norm(lowerCAmelCase_     )

        return self.dropout_post(lowerCAmelCase_     ), encoder_inputs_mask



"""simple docstring"""






import math as m






def 		_snake_case			(      lowercase__						:    Any ,	lowercase__						:    Any ,	lowercase__						:    Optional[int]=0.001						)    ->							Tuple:


			'''simple docstring'''





			return (f(a + h						) - f(a - h						)) / (2 * h)






def 		_snake_case			(      lowercase__						:    Optional[Any] ,	lowercase__						:    List[str]=0 ,	lowercase__						:    Union[str, Any]=1_0_0 ,	lowercase__						:    Any=0.0001 ,	lowercase__						:    List[str]=1E-6 ,	lowercase__						:    str=False						)    ->							List[str]:


			'''simple docstring'''





			lowerCAmelCase_       :Dict     	=    xa  # set the initial guess
			lowerCAmelCase_       :int     	=    [a]
			lowerCAmelCase_       :int     	=    abs(f(lowercase__						)						)
			lowerCAmelCase_       :Optional[int]     	=    lambda lowercase__						: calc_derivative(lowercase__ ,	lowercase__ ,	h=lowercase__						)  # noqa: E731  Derivative of f(x)
			for _ in range(lowercase__						):
						if fa(lowercase__						) == 0:
									raise ValueError("""No converging solution found"""						)
						lowerCAmelCase_       :Tuple     	=    a - f(lowercase__						) / fa(lowercase__						)  # Calculate the next estimate
						if logsteps:
									steps.append(lowercase__						)
						if error < maxerror:
									break
			else:
						raise ValueError("""Iteration limit reached, no converging solution found"""						)
			if logsteps:
						# If logstep is true, then log intermediate steps
						return a, error, steps
			return a, error


if __name__ == "__main__":
				from matplotlib import pyplot as plt

				__UpperCAmelCase 					=    lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
				__UpperCAmelCase					,					__UpperCAmelCase					,					__UpperCAmelCase 					=    newton_raphson(
				    f, xa=10, maxiter=10_00, step=1e-6, logsteps=True
				)
				plt.plot([abs(f(x)) for x in steps])
				plt.xlabel('step')
				plt.ylabel('error')
				plt.show()
				print(F"""solution = {{{solution:f}}}, error = {{{error:f}}}""")






