




from typing import Dict, Optional, Tuple

import torch




def      __magic_name__							(					A						:   torch.Tensor  ):






			'''simple docstring'''







			a       =     boundaries[1] - boundaries[0]
			a       =     boundaries + step / 2
			a       =     torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1  )],    dim=0  )
			return bin_centers




def      __magic_name__							(					A						:   torch.Tensor,    A						:   torch.Tensor,    ):






			'''simple docstring'''







			a       =     _calculate_bin_centers(_snake_case  )
			return (
			    torch.sum(aligned_distance_error_probs * bin_centers,    dim=-1  ),
			    bin_centers[-1],
			)




def      __magic_name__							(					A						:   torch.Tensor,    A						:   int = 31,    A						:   int = 64,    **A						:   Optional[Any],    ):






			'''simple docstring'''







			a       =     torch.linspace(0,    _snake_case,    steps=(no_bins - 1),    device=logits.device  )

			a       =     torch.nn.functional.softmax(_snake_case,    dim=-1  )
			a       =     _calculate_expected_aligned_error(
			    alignment_confidence_breaks=_snake_case,    aligned_distance_error_probs=_snake_case,    )

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






def      __magic_name__							(					A						:   torch.Tensor,    A						:   Optional[torch.Tensor] = None,    A						:   int = 31,    A						:   int = 64,    A						:   float = 1E-8,    **A						:   Tuple,    ):






			'''simple docstring'''







			if residue_weights is None:
						a       =     logits.new_ones(logits.shape[-2]  )

			a       =     torch.linspace(0,    _snake_case,    steps=(no_bins - 1),    device=logits.device  )

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

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

			a       =     torch.nn.functional.softmax(_snake_case,    dim=-1  )

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

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

			a       =     per_alignment * residue_weights

			a       =     (weighted == torch.max(_snake_case  )).nonzero()[0]
			return per_alignment[tuple(_snake_case  )]










"""simple docstring"""
from __future__ import annotations

import math
import random






def 						lowercase				(	_snake_case		: int	,  _snake_case		: int	,  _snake_case		: int	)	->list[int]:
	"""simple docstring"""





	__snake_case      :		Tuple         =							d * e - 1
	__snake_case      :		List[str]         =							0
	__snake_case      :		Dict         =							0
	while p == 0:
		__snake_case      :		str         =							random.randint(2	,  n - 1	)
		__snake_case      :		int         =							k
		while True:
			if t % 2 == 0:
				__snake_case      :		int         =							t // 2
				__snake_case      :		int         =							(g**t) % n
				__snake_case      :		Optional[Any]         =							math.gcd(x - 1	,  _snake_case	)
				if x > 1 and y > 1:
					__snake_case      :		Tuple         =							y
					__snake_case      :		int         =							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()





