
"""simple docstring"""


import random







class 	lowerCamelCase__      :





			'''simple docstring'''



			def __init__(							self  ,  __UpperCAmelCase  ,  __UpperCAmelCase						)				->  None:
				_lowerCAmelCase			=x
				_lowerCAmelCase			=y



			def       _lowerCAmelCase	(							self						)				->  bool:
				return (self.x**2 + self.y**2) <= 1



			@classmethod
			def       _lowerCAmelCase	(							cls						)				->  int:
				return cls(x=random.random()  ,  y=random.random()						)







def 					_lowerCamelCase(__UpperCamelCase )       ->				float:
	if number_of_simulations < 1:
		raise ValueError("""At least one simulation is necessary to estimate PI.""" )

	_lowerCAmelCase			=0
	for _ in range(__UpperCamelCase ):
		_lowerCAmelCase			=Point.random_unit_square()

		if random_point.is_in_unit_circle():
			number_in_unit_circle += 1

	return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
			# import doctest

			# doctest.testmod()
			from math import pi

			__A 		= 'Please enter the desired number of Monte Carlo simulations: '
			__A 		= estimate_pi(int(input(prompt).strip()))
			print(F"""An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}""")





"""simple docstring"""


from typing import Dict, Optional, Tuple

import torch



def 					_lowerCamelCase(__UpperCamelCase )       ->				torch.Tensor:
	_lowerCAmelCase			=boundaries[1] - boundaries[0]
	_lowerCAmelCase			=boundaries + step / 2
	_lowerCAmelCase			=torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1 )]					,				dim=0 )
	return bin_centers



def 					_lowerCamelCase(__UpperCamelCase					,				__UpperCamelCase					,				)       ->				Tuple[torch.Tensor, torch.Tensor]:
	_lowerCAmelCase			=_calculate_bin_centers(__UpperCamelCase )
	return (
	    torch.sum(aligned_distance_error_probs * bin_centers					,				dim=-1 ),
	    bin_centers[-1],
	)



def 					_lowerCamelCase(__UpperCamelCase					,				__UpperCamelCase = 31					,				__UpperCamelCase = 64					,				**__UpperCamelCase					,				)       ->				Dict[str, torch.Tensor]:
	_lowerCAmelCase			=torch.linspace(0					,				__UpperCamelCase					,				steps=(no_bins - 1)					,				device=logits.device )

	_lowerCAmelCase			=torch.nn.functional.softmax(__UpperCamelCase					,				dim=-1 )
	_lowerCAmelCase		,							_lowerCAmelCase			=_calculate_expected_aligned_error(
	    alignment_confidence_breaks=__UpperCamelCase					,				aligned_distance_error_probs=__UpperCamelCase					,				)

	return {
	    "aligned_confidence_probs": aligned_confidence_probs,
	    "predicted_aligned_error": predicted_aligned_error,
	    "max_predicted_aligned_error": max_predicted_aligned_error,
	}



def 					_lowerCamelCase(__UpperCamelCase					,				__UpperCamelCase = None					,				__UpperCamelCase = 31					,				__UpperCamelCase = 64					,				__UpperCamelCase = 1E-8					,				**__UpperCamelCase					,				)       ->				torch.Tensor:
	if residue_weights is None:
		_lowerCAmelCase			=logits.new_ones(logits.shape[-2] )

	_lowerCAmelCase			=torch.linspace(0					,				__UpperCamelCase					,				steps=(no_bins - 1)					,				device=logits.device )

	_lowerCAmelCase			=_calculate_bin_centers(__UpperCamelCase )
	torch.sum(__UpperCamelCase )
	_lowerCAmelCase			=logits.shape[-2]
	_lowerCAmelCase			=max(__UpperCamelCase					,				19 )

	_lowerCAmelCase			=1.24 * (clipped_n - 15) ** (1.0 / 3) - 1.8

	_lowerCAmelCase			=torch.nn.functional.softmax(__UpperCamelCase					,				dim=-1 )

	_lowerCAmelCase			=1.0 / (1 + (bin_centers**2) / (da**2))
	_lowerCAmelCase			=torch.sum(probs * tm_per_bin					,				dim=-1 )

	_lowerCAmelCase			=residue_weights / (eps + residue_weights.sum())
	_lowerCAmelCase			=torch.sum(predicted_tm_term * normed_residue_mask					,				dim=-1 )

	_lowerCAmelCase			=per_alignment * residue_weights

	_lowerCAmelCase			=(weighted == torch.max(__UpperCamelCase )).nonzero()[0]
	return per_alignment[tuple(__UpperCamelCase )]



