



'''simple docstring'''







import math




class 				__lowerCAmelCase:






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




					"""simple docstring"""







					SCREAMING_SNAKE_CASE_						:List[str]										=      x
					SCREAMING_SNAKE_CASE_						:Union[str, Any]										=      y
					SCREAMING_SNAKE_CASE_						:List[str]										=      step_size
					SCREAMING_SNAKE_CASE_						:Optional[int]										=      function_to_optimize






			def 				_lowercase	(   self  :							Dict	):




					"""simple docstring"""







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






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




					"""simple docstring"""







					SCREAMING_SNAKE_CASE_						:Any										=      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      ,       SCREAMING_SNAKE_CASE  :							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__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE = True ,		SCREAMING_SNAKE_CASE = math.inf ,		SCREAMING_SNAKE_CASE = -math.inf ,		SCREAMING_SNAKE_CASE = math.inf ,		SCREAMING_SNAKE_CASE = -math.inf ,		SCREAMING_SNAKE_CASE = False ,		SCREAMING_SNAKE_CASE = 1_0000 ,		):
		SCREAMING_SNAKE_CASE_						:Tuple										=      search_prob
		SCREAMING_SNAKE_CASE_						:str										=      []  # list to store the current score at each iteration
		SCREAMING_SNAKE_CASE_						:Optional[Any]										=      0
		SCREAMING_SNAKE_CASE_						:Union[str, Any]										=      False
		SCREAMING_SNAKE_CASE_						:Union[str, Any]										=      set()
		while not solution_found and iterations < max_iter:
				visited.add(_UpperCamelCase     )
				iterations += 1
				SCREAMING_SNAKE_CASE_						:int										=      current_state.score()
				scores.append(_UpperCamelCase     )
				SCREAMING_SNAKE_CASE_						:List[str]										=      current_state.get_neighbors()
				SCREAMING_SNAKE_CASE_						:Any										=      -math.inf
				SCREAMING_SNAKE_CASE_						:Tuple										=      math.inf
				SCREAMING_SNAKE_CASE_						:Tuple										=      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
						SCREAMING_SNAKE_CASE_						:Optional[int]										=      neighbor.score() - current_score
						if find_max:  # finding max
								# going to direction with greatest ascent
								if change > max_change and change > 0:
										SCREAMING_SNAKE_CASE_						:Optional[int]										=      change
										SCREAMING_SNAKE_CASE_						:Optional[int]										=      neighbor
						else:  # finding min
								# to direction with greatest descent
								if change < min_change and change < 0:
										SCREAMING_SNAKE_CASE_						:Union[str, Any]										=      change
										SCREAMING_SNAKE_CASE_						:Union[str, Any]										=      neighbor
				if next_state is not None:
						# we found at least one neighbor which improved the current state
						SCREAMING_SNAKE_CASE_						:Tuple										=      next_state
				else:
						# since we have no neighbor that improves the solution we stop the search
						SCREAMING_SNAKE_CASE_						:List[Any]										=      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__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
									return (x**2) + (y**2)

							# starting the problem with initial coordinates (3, 4)
							SCREAMING_SNAKE_CASE__     : Tuple				=   SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
							SCREAMING_SNAKE_CASE__     : 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)
							SCREAMING_SNAKE_CASE__     : List[str]				=   SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
							SCREAMING_SNAKE_CASE__     : str				=   hill_climbing(
							    prob, find_max=False, max_x=1_00, 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__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
									return (3 * x**2) - (6 * y)

							SCREAMING_SNAKE_CASE__     : Dict				=   SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
							SCREAMING_SNAKE_CASE__     : 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