


from typing import Dict, Optional, Tuple

import torch



def 			_a      (    __UpperCamelCase			):
     a_     :  Any				      =     boundaries[1] - boundaries[0]
     a_     :  List[Any]				      =     boundaries + step / 2
     a_     :  Tuple				      =     torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1			)]	,	dim=0			)
     return bin_centers



def 			_a      (    __UpperCamelCase	,	__UpperCamelCase	,	):
     a_     :  Union[str, Any]				      =     _calculate_bin_centers(__UpperCamelCase			)
     return (
         torch.sum(aligned_distance_error_probs * bin_centers	,	dim=-1			),
         bin_centers[-1],
     )



def 			_a      (    __UpperCamelCase	,	__UpperCamelCase = 3_1	,	__UpperCamelCase = 6_4	,	**__UpperCamelCase	,	):
     a_     :  Tuple				      =     torch.linspace(0	,	__UpperCamelCase	,	steps=(no_bins - 1)	,	device=logits.device			)

     a_     :  List[Any]				      =     torch.nn.functional.softmax(__UpperCamelCase	,	dim=-1			)
     a_      ,      a_     :  List[Any]				      =     _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 			_a      (    __UpperCamelCase	,	__UpperCamelCase = None	,	__UpperCamelCase = 3_1	,	__UpperCamelCase = 6_4	,	__UpperCamelCase = 1E-8	,	**__UpperCamelCase	,	):
     if residue_weights is None:
          a_     :  List[str]				      =     logits.new_ones(logits.shape[-2]			)

     a_     :  List[Any]				      =     torch.linspace(0	,	__UpperCamelCase	,	steps=(no_bins - 1)	,	device=logits.device			)

     a_     :  Dict				      =     _calculate_bin_centers(__UpperCamelCase			)
     torch.sum(__UpperCamelCase			)
     a_     :  Union[str, Any]				      =     logits.shape[-2]
     a_     :  Union[str, Any]				      =     max(__UpperCamelCase	,	1_9			)

     a_     :  List[str]				      =     1.24 * (clipped_n - 1_5) ** (1.0 / 3) - 1.8

     a_     :  Optional[int]				      =     torch.nn.functional.softmax(__UpperCamelCase	,	dim=-1			)

     a_     :  str				      =     1.0 / (1 + (bin_centers**2) / (da**2))
     a_     :  Dict				      =     torch.sum(probs * tm_per_bin	,	dim=-1			)

     a_     :  Optional[int]				      =     residue_weights / (eps + residue_weights.sum())
     a_     :  Optional[Any]				      =     torch.sum(predicted_tm_term * normed_residue_mask	,	dim=-1			)

     a_     :  str				      =     per_alignment * residue_weights

     a_     :  List[str]				      =     (weighted == torch.max(__UpperCamelCase			)).nonzero()[0]
     return per_alignment[tuple(__UpperCamelCase			)]








_lowercase:					Optional[Any]      =						[[0, 1, 1], [0, 0, 1], [1, 0, 0]]



class       _lowercase				:





	"""simple docstring"""




	def __init__(self						,			lowerCamelCase_						):
						"""simple docstring"""

						a   	=  name
						a   	=  []
						a   	=  []




	def 	UpperCamelCase_			(self						,			lowerCamelCase_						):
						"""simple docstring"""

						self.inbound.append(lowerCamelCase_						)




	def 	UpperCamelCase_			(self						,			lowerCamelCase_						):
						"""simple docstring"""

						self.outbound.append(lowerCamelCase_						)




	def __repr__(self						):
						"""simple docstring"""

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






def        a( A			:       Optional[Any]					,	A			:       Optional[int]=3					,	A			:       str=0.85			)						->			Optional[Any]:
					"""simple docstring"""





					a   	=  {}
					for node in nodes:
										a   	=  1

					a   	=  {}
					for node in nodes:
										a   	=  len(node.outbound			)

					for i in range(A			):
										print(f'''======= Iteration {i + 1} ======='''			)
										for _, node in enumerate(A			):
															a   	=  (1 - d) + d * sum(
															    ranks[ib] / outbounds[ib] for ib in node.inbound			)
										print(A			)






def        a( )						->			List[Any]:
					"""simple docstring"""





					a   	=  list(input("Enter Names of the Nodes: "			).split()			)

					a   	=  [Node(A			) for name in names]

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

					print("======= Nodes ======="			)
					for node in nodes:
										print(A			)

					page_rank(A			)


if __name__ == "__main__":
				main()
