from typing import Dict, Optional, Tuple

import torch


def SCREAMING_SNAKE_CASE					(  lowercase_:						Optional[int]					):
       _UpperCamelCase  :							str	    =	boundaries[1] - boundaries[0]
       _UpperCamelCase  :							Tuple	    =	boundaries + step / 2
       _UpperCamelCase  :							Any	    =	torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1					)]		,    dim=0					)
       return bin_centers


def SCREAMING_SNAKE_CASE					(  lowercase_:						Optional[Any]		,    lowercase_:						Optional[Any]		,    ):
       _UpperCamelCase  :							str	    =	_calculate_bin_centers(lowercase__					)
       return (
           torch.sum(aligned_distance_error_probs * bin_centers		,    dim=-1					),
           bin_centers[-1],
       )


def SCREAMING_SNAKE_CASE					(  lowercase_:						int		,    lowercase_:						Tuple = 31		,    lowercase_:						Optional[int] = 64		,    **lowercase_:						Any		,    ):
       _UpperCamelCase  :							List[Any]	    =	torch.linspace(0		,    lowercase__		,    steps=(no_bins - 1)		,    device=logits.device					)

       _UpperCamelCase  :							Any	    =	torch.nn.functional.softmax(lowercase__		,    dim=-1					)
       _UpperCamelCase    ,   _UpperCamelCase  :							Optional[int]	    =	_calculate_expected_aligned_error(
           alignment_confidence_breaks=lowercase__		,    aligned_distance_error_probs=lowercase__		,    )

       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					(  lowercase_:						Union[str, Any]		,    lowercase_:						Optional[int] = None		,    lowercase_:						List[str] = 31		,    lowercase_:						Dict = 64		,    lowercase_:						List[str] = 1e-8		,    **lowercase_:						Tuple		,    ):
       if residue_weights is None:
              _UpperCamelCase  :							Any	    =	logits.new_ones(logits.shape[-2]					)

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

       _UpperCamelCase  :							Optional[Any]	    =	_calculate_bin_centers(lowercase__					)
       torch.sum(lowercase__					)
       _UpperCamelCase  :							Optional[Any]	    =	logits.shape[-2]
       _UpperCamelCase  :							List[str]	    =	max(lowercase__		,    19					)

       _UpperCamelCase  :							Union[str, Any]	    =	1.24 * (clipped_n - 15) ** (1.0 / 3) - 1.8

       _UpperCamelCase  :							List[str]	    =	torch.nn.functional.softmax(lowercase__		,    dim=-1					)

       _UpperCamelCase  :							Any	    =	1.0 / (1 + (bin_centers**2) / (da**2))
       _UpperCamelCase  :							List[Any]	    =	torch.sum(probs * tm_per_bin		,    dim=-1					)

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

       _UpperCamelCase  :							List[str]	    =	per_alignment * residue_weights

       _UpperCamelCase  :							List[Any]	    =	(weighted == torch.max(lowercase__					)).nonzero()[0]
       return per_alignment[tuple(lowercase__					)]











'''simple docstring'''





from math import cos, sin






def  lowerCamelCase_  (     lowercase__):
 lowerCamelCase__	=  float(lowercase__)
 return [[scaling_factor * int(x == y) for x in range(2)] for y in range(2)]






def  lowerCamelCase_  (     lowercase__):
 lowerCamelCase__	,						lowerCamelCase__	=  cos(lowercase__), sin(lowercase__)
 return [[c, -s], [s, c]]






def  lowerCamelCase_  (     lowercase__):
 lowerCamelCase__	,						lowerCamelCase__	=  cos(lowercase__), sin(lowercase__)
 lowerCamelCase__	=  c * s
 return [[c * c, cs], [cs, s * s]]






def  lowerCamelCase_  (     lowercase__):
 lowerCamelCase__	,						lowerCamelCase__	=  cos(lowercase__), sin(lowercase__)
 lowerCamelCase__	=  c * s
 return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(F"""    {scaling(5) = }""")
print(F"""  {rotation(45) = }""")
print(F"""{projection(45) = }""")
print(F"""{reflection(45) = }""")

