



'''simple docstring'''

from typing import Dict, Optional, Tuple

import torch







def     __UpperCamelCase					(				_lowercase       )			->      torch.Tensor:
	_lowercase       :							Optional[Any]  	=		boundaries[1] - boundaries[0]
	_lowercase       :							int  	=		boundaries + step / 2
	_lowercase       :							Dict  	=		torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1       )],					dim=0       )
	return bin_centers







def     __UpperCamelCase					(				_lowercase,					_lowercase,					)			->      Tuple[torch.Tensor, torch.Tensor]:
	_lowercase       :							Union[str, Any]  	=		_calculate_bin_centers(SCREAMING_SNAKE_CASE_       )
	return (
	    torch.sum(aligned_distance_error_probs * bin_centers,					dim=-1       ),
	    bin_centers[-1],
	)







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

	_lowercase       :							Dict  	=		torch.nn.functional.softmax(SCREAMING_SNAKE_CASE_,					dim=-1       )
	_lowercase       :							str  	=		_calculate_expected_aligned_error(
	    alignment_confidence_breaks=SCREAMING_SNAKE_CASE_,					aligned_distance_error_probs=SCREAMING_SNAKE_CASE_,					)

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







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

	_lowercase       :							str  	=		torch.linspace(0,					SCREAMING_SNAKE_CASE_,					steps=(no_bins - 1),					device=logits.device       )

	_lowercase       :							Union[str, Any]  	=		_calculate_bin_centers(SCREAMING_SNAKE_CASE_       )
	torch.sum(SCREAMING_SNAKE_CASE_       )
	_lowercase       :							str  	=		logits.shape[-2]
	_lowercase       :							List[Any]  	=		max(SCREAMING_SNAKE_CASE_,					19       )

	_lowercase       :							Dict  	=		1.2_4 * (clipped_n - 15) ** (1.0 / 3) - 1.8

	_lowercase       :							Optional[Any]  	=		torch.nn.functional.softmax(SCREAMING_SNAKE_CASE_,					dim=-1       )

	_lowercase       :							Optional[Any]  	=		1.0 / (1 + (bin_centers**2) / (da**2))
	_lowercase       :							Union[str, Any]  	=		torch.sum(probs * tm_per_bin,					dim=-1       )

	_lowercase       :							Tuple  	=		residue_weights / (eps + residue_weights.sum())
	_lowercase       :							Any  	=		torch.sum(predicted_tm_term * normed_residue_mask,					dim=-1       )

	_lowercase       :							Tuple  	=		per_alignment * residue_weights

	_lowercase       :							Any  	=		(weighted == torch.max(SCREAMING_SNAKE_CASE_       )).nonzero()[0]
	return per_alignment[tuple(SCREAMING_SNAKE_CASE_       )]


lowerCamelCase__        =						[[0, 1, 1], [0, 0, 1], [1, 0, 0]]







class 	A__				:






				def __init__(		self   : Optional[int]       ,	a   : int  ):






							'''simple docstring'''







							lowerCAmelCase__ : List[str]   =						name
							lowerCAmelCase__ : List[Any]   =						[]
							lowerCAmelCase__ : int   =						[]






				def 				_lowerCamelCase						(		self   : List[str]       ,	a   : Union[str, Any]  ):






							'''simple docstring'''







							self.inbound.append(a  )






				def 				_lowerCamelCase						(		self   : Dict       ,	a   : Union[str, Any]  ):






							'''simple docstring'''







							self.outbound.append(a  )






				def __repr__(		self   : Tuple  ):






							'''simple docstring'''







							return f'''<node={self.name} inbound={self.inbound} outbound={self.outbound}>'''






def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_=3			,				SCREAMING_SNAKE_CASE_=0.85	)							->						Optional[Any]:
			lowerCAmelCase__ : Tuple   =						{}
			for node in nodes:
						lowerCAmelCase__ : Union[str, Any]   =						1

			lowerCAmelCase__ : List[str]   =						{}
			for node in nodes:
						lowerCAmelCase__ : str   =						len(node.outbound	)

			for i in range(SCREAMING_SNAKE_CASE_	):
						print(F'''======= Iteration {i + 1} ======='''	)
						for _, node in enumerate(SCREAMING_SNAKE_CASE_	):
									lowerCAmelCase__ : Optional[int]   =						(1 - d) + d * sum(
									    ranks[ib] / outbounds[ib] for ib in node.inbound	)
						print(SCREAMING_SNAKE_CASE_	)
def 					lowerCAmelCase__     (    )							->						Dict:
			lowerCAmelCase__ : List[Any]   =						list(input('Enter Names of the Nodes: '	).split()	)

			lowerCAmelCase__ : Union[str, Any]   =						[Node(SCREAMING_SNAKE_CASE_	) for name in names]

			for ri, row in enumerate(SCREAMING_SNAKE_CASE_	):
						for ci, col in enumerate(SCREAMING_SNAKE_CASE_	):
									if col == 1:
												nodes[ci].add_inbound(names[ri]	)
												nodes[ri].add_outbound(names[ci]	)

			print('======= Nodes ======='	)
			for node in nodes:
						print(SCREAMING_SNAKE_CASE_	)

			page_rank(SCREAMING_SNAKE_CASE_	)


if __name__ == "__main__":
					main()