





from typing import Dict, Optional, Tuple

import torch







def 			_SCREAMING_SNAKE_CASE    (       a  )				->				Dict:
     __A     :						int          =    boundaries[1] - boundaries[0]
     __A     :						List[Any]          =    boundaries + step / 2
     __A     :						int          =    torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1  )] ,						dim=0  )
     return bin_centers







def 			_SCREAMING_SNAKE_CASE    (       a ,						a ,						)				->				Union[str, Any]:
     __A     :						Tuple          =    _calculate_bin_centers(a  )
     return (
         torch.sum(aligned_distance_error_probs * bin_centers ,						dim=-1  ),
         bin_centers[-1],
     )







def 			_SCREAMING_SNAKE_CASE    (       a ,						a = 31 ,						a = 64 ,						**a ,						)				->				Optional[Any]:
     __A     :						Union[str, Any]          =    torch.linspace(0 ,						a ,						steps=(no_bins - 1) ,						device=logits.device  )

     __A     :						Optional[Any]          =    torch.nn.functional.softmax(a ,						dim=-1  )
     __A   ,    __A     :						Union[str, Any]          =    _calculate_expected_aligned_error(
         alignment_confidence_breaks=a ,						aligned_distance_error_probs=a ,						)

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







def 			_SCREAMING_SNAKE_CASE    (       a ,						a = None ,						a = 31 ,						a = 64 ,						a = 1e-8 ,						**a ,						)				->				Optional[int]:
     if residue_weights is None:
          __A     :						List[Any]          =    logits.new_ones(logits.shape[-2]  )

     __A     :						Any          =    torch.linspace(0 ,						a ,						steps=(no_bins - 1) ,						device=logits.device  )

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

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

     __A     :						Any          =    torch.nn.functional.softmax(a ,						dim=-1  )

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

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

     __A     :						str          =    per_alignment * residue_weights

     __A     :						Tuple          =    (weighted == torch.max(a  )).nonzero()[0]
     return per_alignment[tuple(a  )]











from __future__ import annotations

import math
import random







def 			_SCREAMING_SNAKE_CASE    (       a ,						a ,						a  )				->				list[int]:
					__A     :						int          =    d * e - 1
					__A     :						List[str]          =    0
					__A     :						Optional[Any]          =    0
					while p == 0:
										__A     :						List[Any]          =    random.randint(2 ,						n - 1  )
										__A     :						Optional[int]          =    k
										while True:
															if t % 2 == 0:
																				__A     :						Tuple          =    t // 2
																				__A     :						List[str]          =    (g**t) % n
																				__A     :						List[Any]          =    math.gcd(x - 1 ,						a  )
																				if x > 1 and y > 1:
																									__A     :						List[str]          =    y
																									__A     :						str          =    n // y
																									break  # find the correct factors
															else:
																				break  # t is not divisible by 2, break and choose another g
					return sorted([p, q]  )


if __name__ == "__main__":
				import doctest

				doctest.testmod()




