

from typing import Dict, Optional, Tuple

import torch







def _a				( SCREAMING_SNAKE_CASE	:    torch.Tensor	)					->					torch.Tensor:

 """simple docstring"""






 __lowerCAmelCase:     List[str]     			=   boundaries[1] - boundaries[0]
 __lowerCAmelCase:     int     			=   boundaries + step / 2
 __lowerCAmelCase:     List[str]     			=   torch.cat([bin_centers, (bin_centers[-1] + step).unsqueeze(-1	)]					,      dim=0	)
 return bin_centers







def _a				( SCREAMING_SNAKE_CASE	:    torch.Tensor					,      SCREAMING_SNAKE_CASE	:    torch.Tensor					,      )					->					Tuple[torch.Tensor, torch.Tensor]:

 """simple docstring"""






 __lowerCAmelCase:     Tuple     			=   _calculate_bin_centers(SCREAMING_SNAKE_CASE	)
 return (
     torch.sum(aligned_distance_error_probs * bin_centers					,      dim=-1	),
     bin_centers[-1],
 )







def _a				( SCREAMING_SNAKE_CASE	:    torch.Tensor					,      SCREAMING_SNAKE_CASE	:    int = 31					,      SCREAMING_SNAKE_CASE	:    int = 64					,      **SCREAMING_SNAKE_CASE	:    Dict					,      )					->					Dict[str, torch.Tensor]:

 """simple docstring"""






 __lowerCAmelCase:     Tuple     			=   torch.linspace(0					,      SCREAMING_SNAKE_CASE					,      steps=(no_bins - 1)					,      device=logits.device	)

 __lowerCAmelCase:     Optional[int]     			=   torch.nn.functional.softmax(SCREAMING_SNAKE_CASE					,      dim=-1	)
 __lowerCAmelCase			,							__lowerCAmelCase:     List[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 _a				( SCREAMING_SNAKE_CASE	:    torch.Tensor					,      SCREAMING_SNAKE_CASE	:    Optional[torch.Tensor] = None					,      SCREAMING_SNAKE_CASE	:    int = 31					,      SCREAMING_SNAKE_CASE	:    int = 64					,      SCREAMING_SNAKE_CASE	:    float = 1E-8					,      **SCREAMING_SNAKE_CASE	:    List[Any]					,      )					->					torch.Tensor:

 """simple docstring"""






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

 __lowerCAmelCase:     Any     			=   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:     int     			=   logits.shape[-2]
 __lowerCAmelCase:     Any     			=   max(SCREAMING_SNAKE_CASE					,      19	)

 __lowerCAmelCase:     Any     			=   1.2_4 * (clipped_n - 15) ** (1.0 / 3) - 1.8

 __lowerCAmelCase:     int     			=   torch.nn.functional.softmax(SCREAMING_SNAKE_CASE					,      dim=-1	)

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

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

 __lowerCAmelCase:     int     			=   per_alignment * residue_weights

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








import math






class 							A_				:


     def __init__(							self    :	Any    ,						UpperCAmelCase    :	int    ,						UpperCAmelCase    :	int    ,						UpperCAmelCase    :	int    ,						UpperCAmelCase    :	Any      )							->			Any:
      __lowerCAmelCase:     Optional[Any]     			=   x
      __lowerCAmelCase:     Any     			=   y
      __lowerCAmelCase:     Tuple     			=   step_size
      __lowerCAmelCase:     Dict     			=   function_to_optimize


     def 						UpperCAmelCase						(							self    :	Dict      )							->			int:
      return self.function(self.x    ,						self.y      )


     def 						UpperCAmelCase						(							self    :	str      )							->			int:
      __lowerCAmelCase:     Union[str, Any]     			=   self.step_size
      return [
          SearchProblem(UpperCAmelCase    ,						UpperCAmelCase    ,						UpperCAmelCase    ,						self.function      )
          for x, y in (
              (self.x - step_size, self.y - step_size),
              (self.x - step_size, self.y),
              (self.x - step_size, self.y + step_size),
              (self.x, self.y - step_size),
              (self.x, self.y + step_size),
              (self.x + step_size, self.y - step_size),
              (self.x + step_size, self.y),
              (self.x + step_size, self.y + step_size),
          )
      ]


     def __hash__(							self    :	Optional[Any]      )							->			int:
      return hash(str(self      )      )


     def __eq__(							self    :	Dict    ,						UpperCAmelCase    :	Tuple      )							->			Any:
      if isinstance(UpperCAmelCase    ,						UpperCAmelCase      ):
       return hash(str(self      )      ) == hash(str(UpperCAmelCase      )      )
      return False


     def __str__(							self    :	Optional[Any]      )							->			Dict:
      return F'''x: {self.x} y: {self.y}'''







def _a				( SCREAMING_SNAKE_CASE	:    List[str]					,      SCREAMING_SNAKE_CASE	:    bool = True					,      SCREAMING_SNAKE_CASE	:    float = math.inf					,      SCREAMING_SNAKE_CASE	:    float = -math.inf					,      SCREAMING_SNAKE_CASE	:    float = math.inf					,      SCREAMING_SNAKE_CASE	:    float = -math.inf					,      SCREAMING_SNAKE_CASE	:    bool = False					,      SCREAMING_SNAKE_CASE	:    int = 1_00_00					,      )					->					SearchProblem:

 """simple docstring"""






 __lowerCAmelCase:     Dict     			=   search_prob
 __lowerCAmelCase:     str     			=   []  # list to store the current score at each iteration
 __lowerCAmelCase:     Optional[int]     			=   0
 __lowerCAmelCase:     int     			=   False
 __lowerCAmelCase:     Any     			=   set()
 while not solution_found and iterations < max_iter:
  visited.add(SCREAMING_SNAKE_CASE	)
  iterations += 1
  __lowerCAmelCase:     int     			=   current_state.score()
  scores.append(SCREAMING_SNAKE_CASE	)
  __lowerCAmelCase:     Any     			=   current_state.get_neighbors()
  __lowerCAmelCase:     Tuple     			=   -math.inf
  __lowerCAmelCase:     Any     			=   math.inf
  __lowerCAmelCase:     Dict     			=   None  # to hold the next best neighbor
  for neighbor in neighbors:
   if neighbor in visited:
    continue  # do not want to visit the same state again
   if (
       neighbor.x > max_x
       or neighbor.x < min_x
       or neighbor.y > max_y
       or neighbor.y < min_y
   ):
    continue  # neighbor outside our bounds
   __lowerCAmelCase:     List[str]     			=   neighbor.score() - current_score
   if find_max:  # finding max
    # going to direction with greatest ascent
    if change > max_change and change > 0:
     __lowerCAmelCase:     int     			=   change
     __lowerCAmelCase:     int     			=   neighbor
   else:  # finding min
    # to direction with greatest descent
    if change < min_change and change < 0:
     __lowerCAmelCase:     str     			=   change
     __lowerCAmelCase:     str     			=   neighbor
  if next_state is not None:
   # we found at least one neighbor which improved the current state
   __lowerCAmelCase:     Optional[Any]     			=   next_state
  else:
   # since we have no neighbor that improves the solution we stop the search
   __lowerCAmelCase:     Dict     			=   True

 if visualization:
  from matplotlib import pyplot as plt

  plt.plot(range(SCREAMING_SNAKE_CASE	)					,      SCREAMING_SNAKE_CASE	)
  plt.xlabel('Iterations'	)
  plt.ylabel('Function values'	)
  plt.show()

 return current_state


if __name__ == "__main__":
  import doctest

  doctest.testmod()







  def _a				( SCREAMING_SNAKE_CASE	:    List[str]					,      SCREAMING_SNAKE_CASE	:    List[str]	)					->					Optional[Any]:

   """simple docstring"""






   return (x**2) + (y**2)

  # starting the problem with initial coordinates (3, 4)
  _a	 =     SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  _a	 =     hill_climbing(prob, find_max=False)
  print(
      '''The minimum score for f(x, y) = x^2 + y^2 found via hill climbing: '''
      f"{local_min.score()}"
  )

  # starting the problem with initial coordinates (12, 47)
  _a	 =     SearchProblem(x=1_2, y=4_7, step_size=1, function_to_optimize=test_fa)
  _a	 =     hill_climbing(
      prob, find_max=False, max_x=1_0_0, min_x=5, max_y=5_0, min_y=-5, visualization=True
  )
  print(
      '''The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 '''
      f"and 50 > y > - 5 found via hill climbing: {local_min.score()}"
  )







  def _a				( SCREAMING_SNAKE_CASE	:    Tuple					,      SCREAMING_SNAKE_CASE	:    List[Any]	)					->					Dict:

   """simple docstring"""






   return (3 * x**2) - (6 * y)

  _a	 =     SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
  _a	 =     hill_climbing(prob, find_max=True)



  print(
      '''The maximum score for f(x, y) = x^2 + y^2 found via hill climbing: '''
      f"{local_min.score()}"
  )





