code: 
  
  
  
  
  """simple docstring"""
  
  
  
  import math
  
  
  
  
  class 			UpperCAmelCase_						:
  
  
  
  
      def __init__(					self		: Optional[int]			,				snake_case_		: int			,				snake_case_		: int			,				snake_case_		: int			,				snake_case_		: Tuple   )   ->							str:
  
  
  
  
       '''simple docstring'''
  
       A__ =       x
       A__ =       y
       A__ =       step_size
       A__ =       function_to_optimize
  
  
  
  
      def 							__magic_name__							(					self		: Optional[Any]   )   ->							int:
  
  
  
  
       '''simple docstring'''
  
       return self.function(self.x			,				self.y   )
  
  
  
  
      def 							__magic_name__							(					self		: List[str]   )   ->							Union[str, Any]:
  
  
  
  
       '''simple docstring'''
  
       A__ =       self.step_size
       return [
           SearchProblem(snake_case_			,				snake_case_			,				snake_case_			,				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]   )   ->							Tuple:
  
  
  
  
       '''simple docstring'''
  
       return hash(str(self   )   )
  
  
  
  
      def __eq__(					self		: Union[str, Any]			,				snake_case_		: Optional[Any]   )   ->							List[Any]:
  
  
  
  
       '''simple docstring'''
  
       if isinstance(snake_case_			,				snake_case_   ):
        return hash(str(self   )   ) == hash(str(snake_case_   )   )
       return False
  
  
  
  
      def __str__(					self		: str   )   ->							Any:
  
  
  
  
       '''simple docstring'''
  
       return F"""x: {self.x} y: {self.y}"""
  
  
  
  
  
  
  
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				lowercase_ = True    ,				lowercase_ = math.inf    ,				lowercase_ = -math.inf    ,				lowercase_ = math.inf    ,				lowercase_ = -math.inf    ,				lowercase_ = False    ,				lowercase_ = 1_00_00    ,				)		->	SearchProblem:
   A__ =       search_prob
   A__ =       []  # list to store the current score at each iteration
   A__ =       0
   A__ =       False
   A__ =       set()
   while not solution_found and iterations < max_iter:
    visited.add(lowercase_		)
    iterations += 1
    A__ =       current_state.score()
    scores.append(lowercase_		)
    A__ =       current_state.get_neighbors()
    A__ =       -math.inf
    A__ =       math.inf
    A__ =       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
     A__ =       neighbor.score() - current_score
     if find_max:  # finding max
      # going to direction with greatest ascent
      if change > max_change and change > 0:
       A__ =       change
       A__ =       neighbor
     else:  # finding min
      # to direction with greatest descent
      if change < min_change and change < 0:
       A__ =       change
       A__ =       neighbor
    if next_state is not None:
     # we found at least one neighbor which improved the current state
     A__ =       next_state
    else:
     # since we have no neighbor that improves the solution we stop the search
     A__ =       True
  
   if visualization:
    from matplotlib import pyplot as plt
  
    plt.plot(range(lowercase_		)    ,				lowercase_		)
    plt.xlabel("Iterations"		)
    plt.ylabel("Function values"		)
    plt.show()
  
   return current_state
  
  
  if __name__ == "__main__":
        import doctest
  
        doctest.testmod()
  
  
  
  
  
  
  
        def 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				lowercase_		)		->	Any:
         return (x**2) + (y**2)
  
        # starting the problem with initial coordinates (3, 4)
        SCREAMING_SNAKE_CASE       = SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
        SCREAMING_SNAKE_CASE       = 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)
        SCREAMING_SNAKE_CASE       = SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
        SCREAMING_SNAKE_CASE       = hill_climbing(
            prob, find_max=False, max_x=100, min_x=5, max_y=50, 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 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				lowercase_		)		->	str:
         return (3 * x**2) - (6 * y)
  
        SCREAMING_SNAKE_CASE       = SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
        SCREAMING_SNAKE_CASE       = 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()}'
        )
  
  
  
  
  
  
style_context: 
  
  
  
  
  """simple docstring"""
  
  
  
  from typing import Dict, Tuple, overload
  
  import torch
  import torch.types
  from torch import nn
  
  from . import residue_constants as rc
  from .rigid_utils import Rigid, Rotation
  from .tensor_utils import batched_gather
  
  
  
  
  
  
  
  @overload
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				lowercase_    ,				lowercase_		)		->	torch.Tensor:
   ...
  
  
  
  
  
  
  
  @overload
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				lowercase_    ,				lowercase_		)		->	Tuple[torch.Tensor, torch.Tensor]:
   ...
  
  
  
  
  
  
  
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				lowercase_    ,				lowercase_		)		->	Dict:
   A__ =       aatype == rc.restype_order["G"]
   A__ =       rc.atom_order["CA"]
   A__ =       rc.atom_order["CB"]
   A__ =       torch.where(
       is_gly[..., None].expand(*((-1,) * len(is_gly.shape		))    ,				3		)    ,				all_atom_positions[..., ca_idx, :]    ,				all_atom_positions[..., cb_idx, :]    ,				)
  
   if all_atom_masks is not None:
    A__ =       torch.where(
        lowercase_    ,				all_atom_masks[..., ca_idx]    ,				all_atom_masks[..., cb_idx]    ,				)
    return pseudo_beta, pseudo_beta_mask
   else:
    return pseudo_beta
  
  
  
  
  
  
  
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				lowercase_		)		->	torch.Tensor:
   A__ =       batched_gather(
       lowercase_    ,				batch["residx_atom37_to_atom14"]    ,				dim=-2    ,				no_batch_dims=len(atomaa.shape[:-2]		)    ,				)
  
   A__ =       atomaa_data * batch["atom37_atom_exists"][..., None]
  
   return atomaa_data
  
  
  
  
  
  
  
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_		)		->	torch.Tensor:
   A__ =       template_feats["template_aatype"]
   A__ =       template_feats["template_torsion_angles_sin_cos"]
   A__ =       template_feats["template_alt_torsion_angles_sin_cos"]
   A__ =       template_feats["template_torsion_angles_mask"]
   A__ =       torch.cat(
       [
           nn.functional.one_hot(lowercase_    ,				22		),
           torsion_angles_sin_cos.reshape(*torsion_angles_sin_cos.shape[:-2]    ,				14		),
           alt_torsion_angles_sin_cos.reshape(*alt_torsion_angles_sin_cos.shape[:-2]    ,				14		),
           torsion_angles_mask,
       ]    ,				dim=-1    ,				)
  
   return template_angle_feat
  
  
  
  
  
  
  
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				lowercase_    ,				lowercase_    ,				lowercase_    ,				lowercase_ = False    ,				lowercase_ = 1E-20    ,				lowercase_ = 1E8    ,				)		->	torch.Tensor:
   A__ =       batch["template_pseudo_beta_mask"]
   A__ =       template_mask[..., None] * template_mask[..., None, :]
  
   # Compute distogram (this seems to differ slightly from Alg. 5)
   A__ =       batch["template_pseudo_beta"]
   A__ =       torch.sum((tpb[..., None, :] - tpb[..., None, :, :]) ** 2    ,				dim=-1    ,				keepdim=lowercase_		)
   A__ =       torch.linspace(lowercase_    ,				lowercase_    ,				lowercase_    ,				device=tpb.device		) ** 2
   A__ =       torch.cat([lower[1:], lower.new_tensor([inf]		)]    ,				dim=-1		)
   A__ =       ((dgram > lower) * (dgram < upper)).type(dgram.dtype		)
  
   A__ =       [dgram, template_mask_ad[..., None]]
  
   A__ =       nn.functional.one_hot(
       batch["template_aatype"]    ,				rc.restype_num + 2    ,				)
  
   A__ =       batch["template_aatype"].shape[-1]
   to_concat.append(aatype_one_hot[..., None, :, :].expand(*aatype_one_hot.shape[:-2]    ,				lowercase_    ,				-1    ,				-1		)		)
   to_concat.append(aatype_one_hot[..., None, :].expand(*aatype_one_hot.shape[:-2]    ,				-1    ,				lowercase_    ,				-1		)		)
  
   A__,   A__,   A__ =       [rc.atom_order[a] for a in ["N", "CA", "C"]]
   A__ =       Rigid.make_transform_from_reference(
       n_xyz=batch["template_all_atom_positions"][..., n, :]    ,				ca_xyz=batch["template_all_atom_positions"][..., ca, :]    ,				c_xyz=batch["template_all_atom_positions"][..., c, :]    ,				eps=lowercase_    ,				)
   A__ =       rigids.get_trans()[..., None, :, :]
   A__ =       rigids[..., None].invert_apply(lowercase_		)
  
   A__ =       torch.rsqrt(eps + torch.sum(rigid_vec**2    ,				dim=-1		)		)
  
   A__ =       batch["template_all_atom_mask"]
   A__ =       t_aa_masks[..., n] * t_aa_masks[..., ca] * t_aa_masks[..., c]
   A__ =       template_mask[..., None] * template_mask[..., None, :]
  
   A__ =       inv_distance_scalar * template_mask_ad
   A__ =       rigid_vec * inv_distance_scalar[..., None]
  
   if not use_unit_vector:
    A__ =       unit_vector * 0.0
  
   to_concat.extend(torch.unbind(unit_vector[..., None, :]    ,				dim=-1		)		)
   to_concat.append(template_mask_ad[..., None]		)
  
   A__ =       torch.cat(lowercase_    ,				dim=-1		)
   A__ =       act * template_mask_ad[..., None]
  
   return act
  
  
  
  
  
  
  
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_		)		->	torch.Tensor:
   A__ =       nn.functional.one_hot(batch["extra_msa"]    ,				23		)
   A__ =       [
       msa_ahot,
       batch["extra_has_deletion"].unsqueeze(-1		),
       batch["extra_deletion_value"].unsqueeze(-1		),
   ]
   return torch.cat(lowercase_    ,				dim=-1		)
  
  
  
  
  
  
  
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				lowercase_    ,				lowercase_    ,				lowercase_    ,				)		->	Rigid:
   # [*, N, 8, 4, 4]
   A__ =       rrgdf[aatype, ...]
  
   # [*, N, 8] transformations, i.e.
   #   One [*, N, 8, 3, 3] rotation matrix and
   #   One [*, N, 8, 3]    translation matrix
   A__ =       r.from_tensor_axa(lowercase_		)
  
   A__ =       alpha.new_zeros((*((1,) * len(alpha.shape[:-1]		)), 2)		)
   A__ =       1
  
   # [*, N, 8, 2]
   A__ =       torch.cat([bb_rot.expand(*alpha.shape[:-2]    ,				-1    ,				-1		), alpha]    ,				dim=-2		)
  
   # [*, N, 8, 3, 3]
   # Produces rotation matrices of the form:
   # [
   #   [1, 0  , 0  ],
   #   [0, a_2,-a_1],
   #   [0, a_1, a_2]
   # ]
   # This follows the original code rather than the supplement, which uses
   # different indices.
  
   A__ =       alpha.new_zeros(default_r.get_rots().get_rot_mats().shape		)
   A__ =       1
   A__ =       alpha[..., 1]
   A__ =       -alpha[..., 0]
   A__ =       alpha
  
   A__ =       default_r.compose(Rigid(Rotation(rot_mats=lowercase_		)    ,				lowercase_		)		)
  
   A__ =       all_frames[..., 5]
   A__ =       all_frames[..., 6]
   A__ =       all_frames[..., 7]
  
   A__ =       all_frames[..., 4]
   A__ =       chia_frame_to_bb.compose(lowercase_		)
   A__ =       chia_frame_to_bb.compose(lowercase_		)
   A__ =       chia_frame_to_bb.compose(lowercase_		)
  
   A__ =       Rigid.cat(
       [
           all_frames[..., :5],
           chia_frame_to_bb.unsqueeze(-1		),
           chia_frame_to_bb.unsqueeze(-1		),
           chia_frame_to_bb.unsqueeze(-1		),
       ]    ,				dim=-1    ,				)
  
   A__ =       r[..., None].compose(lowercase_		)
  
   return all_frames_to_global
  
  
  
  
  
  
  
  def 						_SCREAMING_SNAKE_CASE     (							lowercase_    ,				lowercase_    ,				lowercase_    ,				lowercase_    ,				lowercase_    ,				lowercase_    ,				)		->	torch.Tensor:
   # [*, N, 14]
   A__ =       group_idx[aatype, ...]
  
   # [*, N, 14, 8]
   A__ =       nn.functional.one_hot(
       lowercase_    ,				num_classes=default_frames.shape[-3]    ,				)
  
   # [*, N, 14, 8]
   A__ =       r[..., None, :] * group_mask_one_hot
  
   # [*, N, 14]
   A__ =       t_atoms_to_global.map_tensor_fn(lambda lowercase_		: torch.sum(lowercase_    ,				dim=-1		)		)
  
   # [*, N, 14, 1]
   A__ =       atom_mask[aatype, ...].unsqueeze(-1		)
  
   # [*, N, 14, 3]
   A__ =       lit_positions[aatype, ...]
   A__ =       t_atoms_to_global.apply(lowercase_		)
   A__ =       pred_positions * atom_mask
  
   return pred_positions
  
  
  
  
  
  