


from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean







def     _lowercase							(  __lowerCamelCase      :       int      )	-> int:





     '''simple docstring'''





     def is_in_circle(__lowerCamelCase      :       float		,__lowerCamelCase      :       float      ) -> bool:
          UpperCamelCase__				:	Optional[int]										=  sqrt((x**2) + (y**2)      )
          # Our circle has a radius of 1, so a distance
          # greater than 1 would land outside the circle.
          return distance_from_centre <= 1

     # The proportion of guesses that landed in the circle
     UpperCamelCase__				:	int										=  mean(
         int(is_in_circle(uniform(-1.0		,1.0      )		,uniform(-1.0		,1.0      )      )      )
         for _ in range(UpperCamelCase__      )      )
     # The ratio of the area for circle to square is pi/4.
     UpperCamelCase__				:	Tuple										=  proportion * 4
     print(F'The estimated value of pi is {pi_estimate}'      )
     print(F'The numpy value of pi is {pi}'      )
     print(F'The total error is {abs(pi - pi_estimate      )}'      )







def     _lowercase							(  __lowerCamelCase      :       int		,__lowerCamelCase      :       Callable[[float], float]		,__lowerCamelCase      :       float = 0.0		,__lowerCamelCase      :       float = 1.0		,)	-> Optional[Any]:





     '''simple docstring'''





     return mean(
         function_to_integrate(uniform(UpperCamelCase__		,UpperCamelCase__      )      ) for _ in range(UpperCamelCase__      )      ) * (max_value - min_value)







def     _lowercase							(  __lowerCamelCase      :       int		,__lowerCamelCase      :       float = 0.0		,__lowerCamelCase      :       float = 1.0      )	-> Optional[Any]:





     '''simple docstring'''





     def identity_function(__lowerCamelCase      :       float      ) -> float:
          return x

     UpperCamelCase__				:	Dict										=  area_under_curve_estimator(
         UpperCamelCase__		,UpperCamelCase__		,UpperCamelCase__		,UpperCamelCase__      )
     UpperCamelCase__				:	Dict										=  (max_value * max_value - min_value * min_value) / 2

     print('''******************'''      )
     print(F'Estimating area under y=x where x varies from {min_value} to {max_value}'      )
     print(F'Estimated value is {estimated_value}'      )
     print(F'Expected value is {expected_value}'      )
     print(F'Total error is {abs(estimated_value - expected_value      )}'      )
     print('''******************'''      )







def     _lowercase							(  __lowerCamelCase      :       int      )	-> Union[str, Any]:





     '''simple docstring'''





     def function_to_integrate(__lowerCamelCase      :       float      ) -> float:
          return sqrt(4.0 - x * x      )

     UpperCamelCase__				:	int										=  area_under_curve_estimator(
         UpperCamelCase__		,UpperCamelCase__		,0.0		,2.0      )

     print('''******************'''      )
     print('''Estimating pi using area_under_curve_estimator'''      )
     print(F'Estimated value is {estimated_value}'      )
     print(F'Expected value is {pi}'      )
     print(F'Total error is {abs(estimated_value - pi      )}'      )
     print('''******************'''      )


if __name__ == "__main__":
   import doctest

   doctest.testmod()





'''simple docstring'''


import argparse

import pytorch_lightning as pl
import torch
from torch import nn

from transformers import LongformerForQuestionAnswering, LongformerModel






class     A ( pl.LightningModule ):





							def __init__(   self					:				Dict  ,		__a					:				List[str]						)				->						Tuple:
								super().__init__()
								__UpperCAmelCase      					=      model
								__UpperCAmelCase      					=      2
								__UpperCAmelCase      					=      nn.Linear(self.model.config.hidden_size  ,		self.num_labels						)






							def    snake_case__    (   self					:				int						)				->						int:
								pass





def    lowerCAmelCase       (		UpperCamelCase__					: str     ,       UpperCamelCase__					: str     ,       UpperCamelCase__					: str							):


	"""simple docstring"""
	# load longformer model from model identifier
	__UpperCAmelCase      					=      LongformerModel.from_pretrained(UpperCamelCase__							)
	__UpperCAmelCase      					=      LightningModel(UpperCamelCase__							)

	__UpperCAmelCase      					=      torch.load(UpperCamelCase__     ,       map_location=torch.device('''cpu'''							)							)
	lightning_model.load_state_dict(ckpt['''state_dict''']							)

	# init longformer question answering model
	__UpperCAmelCase      					=      LongformerForQuestionAnswering.from_pretrained(UpperCamelCase__							)

	# transfer weights
	longformer_for_qa.longformer.load_state_dict(lightning_model.model.state_dict()							)
	longformer_for_qa.qa_outputs.load_state_dict(lightning_model.qa_outputs.state_dict()							)
	longformer_for_qa.eval()

	# save model
	longformer_for_qa.save_pretrained(UpperCamelCase__							)

	print(f"""Conversion successful. Model saved under {pytorch_dump_folder_path}"""							)


if __name__ == "__main__":
					__lowerCAmelCase						:							Optional[Any]    							=						argparse.ArgumentParser()
					# Required parameters
					parser.add_argument(
					    "--longformer_model",
					    default=None,
					    type=str,
					    required=True,
					    help="model identifier of longformer. Should be either `longformer-base-4096` or `longformer-large-4096`.",
					)
					parser.add_argument(
					    "--longformer_question_answering_ckpt_path",
					    default=None,
					    type=str,
					    required=True,
					    help="Path the official PyTorch Lightning Checkpoint.",
					)
					parser.add_argument(
					    "--pytorch_dump_folder_path", default=None, type=str, required=True, help="Path to the output PyTorch model."
					)
					__lowerCAmelCase						:							List[str]    							=						parser.parse_args()
					convert_longformer_qa_checkpoint_to_pytorch(
					    args.longformer_model, args.longformer_question_answering_ckpt_path, args.pytorch_dump_folder_path
					)
