
from typing import Dict, Optional, Tuple

import torch
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_	)							->						torch.Tensor:
			lowerCAmelCase__ : Optional[Any]   =						boundaries[1] - boundaries[0]
			lowerCAmelCase__ : int   =						boundaries + step / 2
			lowerCAmelCase__ : Dict   =						torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1	)]			,				dim=0	)
			return bin_centers
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				)							->						Tuple[torch.Tensor, torch.Tensor]:
			lowerCAmelCase__ : Union[str, Any]   =						_calculate_bin_centers(SCREAMING_SNAKE_CASE_	)
			return (
			    torch.sum(aligned_distance_error_probs * bin_centers			,				dim=-1	),
			    bin_centers[-1],
			)
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_ = 31			,				SCREAMING_SNAKE_CASE_ = 64			,				**SCREAMING_SNAKE_CASE_			,				)							->						Dict[str, torch.Tensor]:
			lowerCAmelCase__ : Optional[int]   =						torch.linspace(0			,				SCREAMING_SNAKE_CASE_			,				steps=(no_bins - 1)			,				device=logits.device	)

			lowerCAmelCase__ : Dict   =						torch.nn.functional.softmax(SCREAMING_SNAKE_CASE_			,				dim=-1	)
			lowerCAmelCase__ ,							lowerCAmelCase__ : 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 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_ = None			,				SCREAMING_SNAKE_CASE_ = 31			,				SCREAMING_SNAKE_CASE_ = 64			,				SCREAMING_SNAKE_CASE_ = 1e-8			,				**SCREAMING_SNAKE_CASE_			,				)							->						torch.Tensor:
			if residue_weights is None:
						lowerCAmelCase__ : str   =						logits.new_ones(logits.shape[-2]	)

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

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

			lowerCAmelCase__ : Dict   =						1.24 * (clipped_n - 15) ** (1.0 / 3) - 1.8

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

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

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

			lowerCAmelCase__ : Tuple   =						per_alignment * residue_weights

			lowerCAmelCase__ : 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()