


'''simple docstring'''

import math







class 			UpperCAmelCase			:

 def __init__(			self			:						List[Any],       a_			:						int,       a_			:						int,       a_			:						int,       a_			:						Tuple       ):





    """simple docstring"""



    UpperCamelCase__			    =    x
    UpperCamelCase__			    =    y
    UpperCamelCase__			    =    step_size
    UpperCamelCase__			    =    function_to_optimize

 def 		lowercase_    (			self			:						Dict       ):





    """simple docstring"""



    return self.function(self.x,       self.y       )

 def 		lowercase_    (			self			:						Union[str, Any]       ):





    """simple docstring"""



    UpperCamelCase__			    =    self.step_size
    return [
        SearchProblem(a_,       a_,       a_,       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]       ):





    """simple docstring"""



    return hash(str(self       )       )

 def __eq__(			self			:						int,       a_			:						Tuple       ):





    """simple docstring"""



    if isinstance(a_,       a_       ):
       return hash(str(self       )       ) == hash(str(a_       )       )
    return False

 def __str__(			self			:						List[str]       ):





    """simple docstring"""



    return f'x: {self.x} y: {self.y}'







def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					Tuple     ,		_UpperCamelCase   :					bool = True     ,		_UpperCamelCase   :					float = math.inf     ,		_UpperCamelCase   :					float = -math.inf     ,		_UpperCamelCase   :					float = math.inf     ,		_UpperCamelCase   :					float = -math.inf     ,		_UpperCamelCase   :					bool = False     ,		_UpperCamelCase   :					int = 1_00_00     ,		)		->       SearchProblem:





   '''simple docstring'''







   UpperCamelCase__			    =    search_prob
   UpperCamelCase__			    =    []  # list to store the current score at each iteration
   UpperCamelCase__			    =    0
   UpperCamelCase__			    =    False
   UpperCamelCase__			    =    set()
   while not solution_found and iterations < max_iter:
      visited.add(_UpperCamelCase )
      iterations += 1
      UpperCamelCase__			    =    current_state.score()
      scores.append(_UpperCamelCase )
      UpperCamelCase__			    =    current_state.get_neighbors()
      UpperCamelCase__			    =    -math.inf
      UpperCamelCase__			    =    math.inf
      UpperCamelCase__			    =    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
         UpperCamelCase__			    =    neighbor.score() - current_score
         if find_max:  # finding max
            # going to direction with greatest ascent
            if change > max_change and change > 0:
               UpperCamelCase__			    =    change
               UpperCamelCase__			    =    neighbor
         else:  # finding min
            # to direction with greatest descent
            if change < min_change and change < 0:
               UpperCamelCase__			    =    change
               UpperCamelCase__			    =    neighbor
      if next_state is not None:
         # we found at least one neighbor which improved the current state
         UpperCamelCase__			    =    next_state
      else:
         # since we have no neighbor that improves the solution we stop the search
         UpperCamelCase__			    =    True

   if visualization:
      from matplotlib import pyplot as plt

      plt.plot(range(_UpperCamelCase )     ,		_UpperCamelCase )
      plt.xlabel("Iterations" )
      plt.ylabel("Function values" )
      plt.show()

   return current_state


if __name__ == "__main__":
       import doctest

       doctest.testmod()



       def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					Tuple     ,		_UpperCamelCase   :					Any )		->       Any:





          '''simple docstring'''







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

       # starting the problem with initial coordinates (3, 4)
       __lowercase:		Tuple    						=  SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
       __lowercase:		Optional[Any]    						=  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)
       __lowercase:		List[str]    						=  SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
       __lowercase:		str    						=  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__(		_UpperCamelCase   :					int     ,		_UpperCamelCase   :					Union[str, Any] )		->       Any:





          '''simple docstring'''







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

       __lowercase:		Dict    						=  SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
       __lowercase:		Union[str, Any]    						=  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()}"""
       )



'''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__(		_UpperCamelCase   :					torch.Tensor     ,		_UpperCamelCase   :					torch.Tensor     ,		_UpperCamelCase   :					None )		->       torch.Tensor:





   '''simple docstring'''







   ...



@overload
def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					torch.Tensor     ,		_UpperCamelCase   :					torch.Tensor     ,		_UpperCamelCase   :					torch.Tensor )		->       Tuple[torch.Tensor, torch.Tensor]:





   '''simple docstring'''







   ...



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					int     ,		_UpperCamelCase   :					Dict     ,		_UpperCamelCase   :					str )		->       int:





   '''simple docstring'''







   UpperCamelCase__			    =    aatype == rc.restype_order["G"]
   UpperCamelCase__			    =    rc.atom_order["CA"]
   UpperCamelCase__			    =    rc.atom_order["CB"]
   UpperCamelCase__			    =    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:
      UpperCamelCase__			    =    torch.where(
          _UpperCamelCase     ,		all_atom_masks[..., ca_idx]     ,		all_atom_masks[..., cb_idx]     ,		)
      return pseudo_beta, pseudo_beta_mask
   else:
      return pseudo_beta



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					torch.Tensor     ,		_UpperCamelCase   :					Dict[str, torch.Tensor] )		->       torch.Tensor:





   '''simple docstring'''







   UpperCamelCase__			    =    batched_gather(
       _UpperCamelCase     ,		batch["residx_atom37_to_atom14"]     ,		dim=-2     ,		no_batch_dims=len(atomaa.shape[:-2] )     ,		)

   UpperCamelCase__			    =    atomaa_data * batch["atom37_atom_exists"][..., None]

   return atomaa_data



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					Dict[str, torch.Tensor] )		->       torch.Tensor:





   '''simple docstring'''







   UpperCamelCase__			    =    template_feats["template_aatype"]
   UpperCamelCase__			    =    template_feats["template_torsion_angles_sin_cos"]
   UpperCamelCase__			    =    template_feats["template_alt_torsion_angles_sin_cos"]
   UpperCamelCase__			    =    template_feats["template_torsion_angles_mask"]
   UpperCamelCase__			    =    torch.cat(
       [
           nn.functional.one_hot(_UpperCamelCase     ,		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__(		_UpperCamelCase   :					Dict[str, torch.Tensor]     ,		_UpperCamelCase   :					torch.types.Number     ,		_UpperCamelCase   :					torch.types.Number     ,		_UpperCamelCase   :					int     ,		_UpperCamelCase   :					bool = False     ,		_UpperCamelCase   :					float = 1e-20     ,		_UpperCamelCase   :					float = 1e8     ,		)		->       torch.Tensor:





   '''simple docstring'''







   UpperCamelCase__			    =    batch["template_pseudo_beta_mask"]
   UpperCamelCase__			    =    template_mask[..., None] * template_mask[..., None, :]

   # Compute distogram (this seems to differ slightly from Alg. 5)
   UpperCamelCase__			    =    batch["template_pseudo_beta"]
   UpperCamelCase__			    =    torch.sum((tpb[..., None, :] - tpb[..., None, :, :]) ** 2     ,		dim=-1     ,		keepdim=_UpperCamelCase )
   UpperCamelCase__			    =    torch.linspace(_UpperCamelCase     ,		_UpperCamelCase     ,		_UpperCamelCase     ,		device=tpb.device ) ** 2
   UpperCamelCase__			    =    torch.cat([lower[1:], lower.new_tensor([inf] )]     ,		dim=-1 )
   UpperCamelCase__			    =    ((dgram > lower) * (dgram < upper)).type(dgram.dtype )

   UpperCamelCase__			    =    [dgram, template_mask_ad[..., None]]

   UpperCamelCase__			    =    nn.functional.one_hot(
       batch["template_aatype"]     ,		rc.restype_num + 2     ,		)

   UpperCamelCase__			    =    batch["template_aatype"].shape[-1]
   to_concat.append(aatype_one_hot[..., None, :, :].expand(*aatype_one_hot.shape[:-2]     ,		_UpperCamelCase     ,		-1     ,		-1 ) )
   to_concat.append(aatype_one_hot[..., None, :].expand(*aatype_one_hot.shape[:-2]     ,		-1     ,		_UpperCamelCase     ,		-1 ) )

   UpperCamelCase__    ,		UpperCamelCase__    ,		UpperCamelCase__			    =    [rc.atom_order[a] for a in ["N", "CA", "C"]]
   UpperCamelCase__			    =    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=_UpperCamelCase     ,		)
   UpperCamelCase__			    =    rigids.get_trans()[..., None, :, :]
   UpperCamelCase__			    =    rigids[..., None].invert_apply(_UpperCamelCase )

   UpperCamelCase__			    =    torch.rsqrt(eps + torch.sum(rigid_vec**2     ,		dim=-1 ) )

   UpperCamelCase__			    =    batch["template_all_atom_mask"]
   UpperCamelCase__			    =    t_aa_masks[..., n] * t_aa_masks[..., ca] * t_aa_masks[..., c]
   UpperCamelCase__			    =    template_mask[..., None] * template_mask[..., None, :]

   UpperCamelCase__			    =    inv_distance_scalar * template_mask_ad
   UpperCamelCase__			    =    rigid_vec * inv_distance_scalar[..., None]

   if not use_unit_vector:
      UpperCamelCase__			    =    unit_vector * 0.0

   to_concat.extend(torch.unbind(unit_vector[..., None, :]     ,		dim=-1 ) )
   to_concat.append(template_mask_ad[..., None] )

   UpperCamelCase__			    =    torch.cat(_UpperCamelCase     ,		dim=-1 )
   UpperCamelCase__			    =    act * template_mask_ad[..., None]

   return act



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					Dict[str, torch.Tensor] )		->       torch.Tensor:





   '''simple docstring'''







   UpperCamelCase__			    =    nn.functional.one_hot(batch["extra_msa"]     ,		23 )
   UpperCamelCase__			    =    [
       msa_ahot,
       batch["extra_has_deletion"].unsqueeze(-1 ),
       batch["extra_deletion_value"].unsqueeze(-1 ),
   ]
   return torch.cat(_UpperCamelCase     ,		dim=-1 )



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					Rigid     ,		_UpperCamelCase   :					torch.Tensor     ,		_UpperCamelCase   :					torch.Tensor     ,		_UpperCamelCase   :					torch.Tensor     ,		)		->       Rigid:





   '''simple docstring'''







   UpperCamelCase__			    =    rrgdf[aatype, ...]

   # [*, N, 8] transformations, i.e.
   #   One [*, N, 8, 3, 3] rotation matrix and
   #   One [*, N, 8, 3]    translation matrix
   UpperCamelCase__			    =    r.from_tensor_axa(_UpperCamelCase )

   UpperCamelCase__			    =    alpha.new_zeros((*((1,) * len(alpha.shape[:-1] )), 2) )
   UpperCamelCase__			    =    1

   # [*, N, 8, 2]
   UpperCamelCase__			    =    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.

   UpperCamelCase__			    =    alpha.new_zeros(default_r.get_rots().get_rot_mats().shape )
   UpperCamelCase__			    =    1
   UpperCamelCase__			    =    alpha[..., 1]
   UpperCamelCase__			    =    -alpha[..., 0]
   UpperCamelCase__			    =    alpha

   UpperCamelCase__			    =    default_r.compose(Rigid(Rotation(rot_mats=_UpperCamelCase )     ,		_UpperCamelCase ) )

   UpperCamelCase__			    =    all_frames[..., 5]
   UpperCamelCase__			    =    all_frames[..., 6]
   UpperCamelCase__			    =    all_frames[..., 7]

   UpperCamelCase__			    =    all_frames[..., 4]
   UpperCamelCase__			    =    chia_frame_to_bb.compose(_UpperCamelCase )
   UpperCamelCase__			    =    chia_frame_to_bb.compose(_UpperCamelCase )
   UpperCamelCase__			    =    chia_frame_to_bb.compose(_UpperCamelCase )

   UpperCamelCase__			    =    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     ,		)

   UpperCamelCase__			    =    r[..., None].compose(_UpperCamelCase )

   return all_frames_to_global






def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					Rigid     ,		_UpperCamelCase   :					torch.Tensor     ,		_UpperCamelCase   :					torch.Tensor     ,		_UpperCamelCase   :					torch.Tensor     ,		_UpperCamelCase   :					torch.Tensor     ,		_UpperCamelCase   :					torch.Tensor     ,		)		->       torch.Tensor:





   '''simple docstring'''







   UpperCamelCase__			    =    group_idx[aatype, ...]

   # [*, N, 14, 8]
   UpperCamelCase__			    =    nn.functional.one_hot(
       _UpperCamelCase     ,		num_classes=default_frames.shape[-3]     ,		)

   # [*, N, 14, 8]
   UpperCamelCase__			    =    r[..., None, :] * group_mask_one_hot

   # [*, N, 14]
   UpperCamelCase__			    =    t_atoms_to_global.map_tensor_fn(lambda _UpperCamelCase : torch.sum(_UpperCamelCase     ,		dim=-1 ) )

   # [*, N, 14, 1]
   UpperCamelCase__			    =    atom_mask[aatype, ...].unsqueeze(-1 )

   # [*, N, 14, 3]
   UpperCamelCase__			    =    lit_positions[aatype, ...]
   UpperCamelCase__			    =    t_atoms_to_global.apply(_UpperCamelCase )
   UpperCamelCase__			    =    pred_positions * atom_mask

   return pred_positions