
import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput




def 						A_			(				snake_case				: Optional[int]			,   snake_case				: Optional[Any]=0.999			,   snake_case				: List[str]="cosine"			,   )   ->     Optional[int]:



						'''simple docstring'''

						if alpha_transform_type == "cosine":

												def alpha_bar_fn(snake_case				: Tuple			):
																		return math.cos((t + 0.008) / 1.008 * math.pi / 2			) ** 2

						elif alpha_transform_type == "exp":

												def alpha_bar_fn(snake_case				: Dict			):
																		return math.exp(t * -12.0			)

						else:
												raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}"			)

						__UpperCamelCase  	=      []
						for i in range(snake_case			):
												__UpperCamelCase  	=      i / num_diffusion_timesteps
												__UpperCamelCase  	=      (i + 1) / num_diffusion_timesteps
												betas.append(min(1 - alpha_bar_fn(snake_case			) / alpha_bar_fn(snake_case			)			,   snake_case			)			)
						return torch.tensor(snake_case			,   dtype=torch.floataa			)






class 							SCREAMING_SNAKE_CASE__     (				SCREAMING_SNAKE_CASE_ ,		SCREAMING_SNAKE_CASE_     ):

							"""simple docstring"""






							_snake_case  		=	[e.name for e in KarrasDiffusionSchedulers]
							_snake_case  		=	2



							@register_to_config
							def __init__(	self  ,						SCREAMING_SNAKE_CASE_ = 1000  ,						SCREAMING_SNAKE_CASE_ = 0.0_0_0_8_5  ,						SCREAMING_SNAKE_CASE_ = 0.0_1_2  ,						SCREAMING_SNAKE_CASE_ = "linear"  ,						SCREAMING_SNAKE_CASE_ = None  ,						SCREAMING_SNAKE_CASE_ = "epsilon"  ,						SCREAMING_SNAKE_CASE_ = "linspace"  ,						SCREAMING_SNAKE_CASE_ = 0  ,						)-> List[Any]:





													'''simple docstring'''






													if trained_betas is not None:
																			__UpperCamelCase  	=      torch.tensor(SCREAMING_SNAKE_CASE_  ,						dtype=torch.floataa      )
													elif beta_schedule == "linear":
																			__UpperCamelCase  	=      torch.linspace(SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						dtype=torch.floataa      )
													elif beta_schedule == "scaled_linear":
																			# this schedule is very specific to the latent diffusion model.
																			__UpperCamelCase  	=      (
																			    torch.linspace(beta_start**0.5  ,						beta_end**0.5  ,						SCREAMING_SNAKE_CASE_  ,						dtype=torch.floataa      ) ** 2
																			)
													elif beta_schedule == "squaredcos_cap_v2":
																			# Glide cosine schedule
																			__UpperCamelCase  	=      betas_for_alpha_bar(SCREAMING_SNAKE_CASE_      )
													else:
																			raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}"      )

													__UpperCamelCase  	=      1.0 - self.betas
													__UpperCamelCase  	=      torch.cumprod(self.alphas  ,						dim=0      )

													#  set all values
													self.set_timesteps(SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_      )



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_=None      )-> List[str]:





													'''simple docstring'''






													if schedule_timesteps is None:
																			__UpperCamelCase  	=      self.timesteps

													__UpperCamelCase  	=      (schedule_timesteps == timestep).nonzero()

													# The sigma index that is taken for the **very** first `step`
													# is always the second index (or the last index if there is only 1)
													# This way we can ensure we don't accidentally skip a sigma in
													# case we start in the middle of the denoising schedule (e.g. for image-to-image)
													if len(self._index_counter      ) == 0:
																			__UpperCamelCase  	=      1 if len(SCREAMING_SNAKE_CASE_      ) > 1 else 0
													else:
																			__UpperCamelCase  	=      timestep.cpu().item() if torch.is_tensor(SCREAMING_SNAKE_CASE_      ) else timestep
																			__UpperCamelCase  	=      self._index_counter[timestep_int]

													return indices[pos].item()



							@property
							def      A__		(	self      )-> List[str]:





													'''simple docstring'''






													if self.config.timestep_spacing in ["linspace", "trailing"]:
																			return self.sigmas.max()

													return (self.sigmas.max() ** 2 + 1) ** 0.5



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						)-> torch.FloatTensor:





													'''simple docstring'''






													__UpperCamelCase  	=      self.index_for_timestep(SCREAMING_SNAKE_CASE_      )

													if self.state_in_first_order:
																			__UpperCamelCase  	=      self.sigmas[step_index]
													else:
																			__UpperCamelCase  	=      self.sigmas_interpol[step_index - 1]

													__UpperCamelCase  	=      sample / ((sigma**2 + 1) ** 0.5)
													return sample



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_ = None  ,						SCREAMING_SNAKE_CASE_ = None  ,						)-> List[Any]:





													'''simple docstring'''






													__UpperCamelCase  	=      num_inference_steps

													__UpperCamelCase  	=      num_train_timesteps or self.config.num_train_timesteps

													# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
													if self.config.timestep_spacing == "linspace":
																			__UpperCamelCase  	=      np.linspace(0  ,						num_train_timesteps - 1  ,						SCREAMING_SNAKE_CASE_  ,						dtype=SCREAMING_SNAKE_CASE_      )[::-1].copy()
													elif self.config.timestep_spacing == "leading":
																			__UpperCamelCase  	=      num_train_timesteps // self.num_inference_steps
																			# creates integer timesteps by multiplying by ratio
																			# casting to int to avoid issues when num_inference_step is power of 3
																			__UpperCamelCase  	=      (np.arange(0  ,						SCREAMING_SNAKE_CASE_      ) * step_ratio).round()[::-1].copy().astype(SCREAMING_SNAKE_CASE_      )
																			timesteps += self.config.steps_offset
													elif self.config.timestep_spacing == "trailing":
																			__UpperCamelCase  	=      num_train_timesteps / self.num_inference_steps
																			# creates integer timesteps by multiplying by ratio
																			# casting to int to avoid issues when num_inference_step is power of 3
																			__UpperCamelCase  	=      (np.arange(SCREAMING_SNAKE_CASE_  ,						0  ,						-step_ratio      )).round().copy().astype(SCREAMING_SNAKE_CASE_      )
																			timesteps -= 1
													else:
																			raise ValueError(
																			    F"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."      )

													__UpperCamelCase  	=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5      )
													__UpperCamelCase  	=      torch.from_numpy(np.log(SCREAMING_SNAKE_CASE_      )      ).to(SCREAMING_SNAKE_CASE_      )

													__UpperCamelCase  	=      np.interp(SCREAMING_SNAKE_CASE_  ,						np.arange(0  ,						len(SCREAMING_SNAKE_CASE_      )      )  ,						SCREAMING_SNAKE_CASE_      )
													__UpperCamelCase  	=      np.concatenate([sigmas, [0.0]]      ).astype(np.floataa      )
													__UpperCamelCase  	=      torch.from_numpy(SCREAMING_SNAKE_CASE_      ).to(device=SCREAMING_SNAKE_CASE_      )

													# compute up and down sigmas
													__UpperCamelCase  	=      sigmas.roll(-1      )
													__UpperCamelCase  	=      0.0
													__UpperCamelCase  	=      (sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
													__UpperCamelCase  	=      (sigmas_next**2 - sigmas_up**2) ** 0.5
													__UpperCamelCase  	=      0.0

													# compute interpolated sigmas
													__UpperCamelCase  	=      sigmas.log().lerp(sigmas_down.log()  ,						0.5      ).exp()
													__UpperCamelCase  	=      0.0

													# set sigmas
													__UpperCamelCase  	=      torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2      ), sigmas[-1:]]      )
													__UpperCamelCase  	=      torch.cat(
													    [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2      ), sigmas_interpol[-1:]]      )
													__UpperCamelCase  	=      torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2      ), sigmas_up[-1:]]      )
													__UpperCamelCase  	=      torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2      ), sigmas_down[-1:]]      )

													if str(SCREAMING_SNAKE_CASE_      ).startswith('''mps'''      ):
																			# mps does not support float64
																			__UpperCamelCase  	=      torch.from_numpy(SCREAMING_SNAKE_CASE_      ).to(SCREAMING_SNAKE_CASE_  ,						dtype=torch.floataa      )
													else:
																			__UpperCamelCase  	=      torch.from_numpy(SCREAMING_SNAKE_CASE_      ).to(SCREAMING_SNAKE_CASE_      )

													__UpperCamelCase  	=      self.sigma_to_t(SCREAMING_SNAKE_CASE_      ).to(SCREAMING_SNAKE_CASE_  ,						dtype=timesteps.dtype      )
													__UpperCamelCase  	=      torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])  ,						dim=-1      ).flatten()

													__UpperCamelCase  	=      torch.cat([timesteps[:1], interleaved_timesteps]      )

													__UpperCamelCase  	=      None

													# for exp beta schedules, such as the one for `pipeline_shap_e.py`
													# we need an index counter
													__UpperCamelCase  	=      defaultdict(SCREAMING_SNAKE_CASE_      )



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_      )-> List[Any]:





													'''simple docstring'''






													__UpperCamelCase  	=      sigma.log()

													# get distribution
													__UpperCamelCase  	=      log_sigma - self.log_sigmas[:, None]

													# get sigmas range
													__UpperCamelCase  	=      dists.ge(0      ).cumsum(dim=0      ).argmax(dim=0      ).clamp(max=self.log_sigmas.shape[0] - 2      )
													__UpperCamelCase  	=      low_idx + 1

													__UpperCamelCase  	=      self.log_sigmas[low_idx]
													__UpperCamelCase  	=      self.log_sigmas[high_idx]

													# interpolate sigmas
													__UpperCamelCase  	=      (low - log_sigma) / (low - high)
													__UpperCamelCase  	=      w.clamp(0  ,						1      )

													# transform interpolation to time range
													__UpperCamelCase  	=      (1 - w) * low_idx + w * high_idx
													__UpperCamelCase  	=      t.view(sigma.shape      )
													return t



							@property
							def      A__		(	self      )-> List[Any]:





													'''simple docstring'''






													return self.sample is None



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_ = None  ,						SCREAMING_SNAKE_CASE_ = True  ,						)-> Union[SchedulerOutput, Tuple]:





													'''simple docstring'''






													__UpperCamelCase  	=      self.index_for_timestep(SCREAMING_SNAKE_CASE_      )

													# advance index counter by 1
													__UpperCamelCase  	=      timestep.cpu().item() if torch.is_tensor(SCREAMING_SNAKE_CASE_      ) else timestep
													self._index_counter[timestep_int] += 1

													if self.state_in_first_order:
																			__UpperCamelCase  	=      self.sigmas[step_index]
																			__UpperCamelCase  	=      self.sigmas_interpol[step_index]
																			__UpperCamelCase  	=      self.sigmas_up[step_index]
																			__UpperCamelCase  	=      self.sigmas_down[step_index - 1]
													else:
																			# 2nd order / KPDM2's method
																			__UpperCamelCase  	=      self.sigmas[step_index - 1]
																			__UpperCamelCase  	=      self.sigmas_interpol[step_index - 1]
																			__UpperCamelCase  	=      self.sigmas_up[step_index - 1]
																			__UpperCamelCase  	=      self.sigmas_down[step_index - 1]

													# currently only gamma=0 is supported. This usually works best anyways.
													# We can support gamma in the future but then need to scale the timestep before
													# passing it to the model which requires a change in API
													__UpperCamelCase  	=      0
													__UpperCamelCase  	=      sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

													__UpperCamelCase  	=      model_output.device
													__UpperCamelCase  	=      randn_tensor(model_output.shape  ,						dtype=model_output.dtype  ,						device=SCREAMING_SNAKE_CASE_  ,						generator=SCREAMING_SNAKE_CASE_      )

													# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
													if self.config.prediction_type == "epsilon":
																			__UpperCamelCase  	=      sigma_hat if self.state_in_first_order else sigma_interpol
																			__UpperCamelCase  	=      sample - sigma_input * model_output
													elif self.config.prediction_type == "v_prediction":
																			__UpperCamelCase  	=      sigma_hat if self.state_in_first_order else sigma_interpol
																			__UpperCamelCase  	=      model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
																			    sample / (sigma_input**2 + 1)
																			)
													elif self.config.prediction_type == "sample":
																			raise NotImplementedError('''prediction_type not implemented yet: sample'''      )
													else:
																			raise ValueError(
																			    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"      )

													if self.state_in_first_order:
																			# 2. Convert to an ODE derivative for 1st order
																			__UpperCamelCase  	=      (sample - pred_original_sample) / sigma_hat
																			# 3. delta timestep
																			__UpperCamelCase  	=      sigma_interpol - sigma_hat

																			# store for 2nd order step
																			__UpperCamelCase  	=      sample
																			__UpperCamelCase  	=      dt
																			__UpperCamelCase  	=      sample + derivative * dt
													else:
																			# DPM-Solver-2
																			# 2. Convert to an ODE derivative for 2nd order
																			__UpperCamelCase  	=      (sample - pred_original_sample) / sigma_interpol
																			# 3. delta timestep
																			__UpperCamelCase  	=      sigma_down - sigma_hat

																			__UpperCamelCase  	=      self.sample
																			__UpperCamelCase  	=      None

																			__UpperCamelCase  	=      sample + derivative * dt
																			__UpperCamelCase  	=      prev_sample + noise * sigma_up

													if not return_dict:
																			return (prev_sample,)

													return SchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_      )



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						)-> torch.FloatTensor:





													'''simple docstring'''






													__UpperCamelCase  	=      self.sigmas.to(device=original_samples.device  ,						dtype=original_samples.dtype      )
													if original_samples.device.type == "mps" and torch.is_floating_point(SCREAMING_SNAKE_CASE_      ):
																			# mps does not support float64
																			__UpperCamelCase  	=      self.timesteps.to(original_samples.device  ,						dtype=torch.floataa      )
																			__UpperCamelCase  	=      timesteps.to(original_samples.device  ,						dtype=torch.floataa      )
													else:
																			__UpperCamelCase  	=      self.timesteps.to(original_samples.device      )
																			__UpperCamelCase  	=      timesteps.to(original_samples.device      )

													__UpperCamelCase  	=      [self.index_for_timestep(SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_      ) for t in timesteps]

													__UpperCamelCase  	=      sigmas[step_indices].flatten()
													while len(sigma.shape      ) < len(original_samples.shape      ):
																			__UpperCamelCase  	=      sigma.unsqueeze(-1      )

													__UpperCamelCase  	=      original_samples + noise * sigma
													return noisy_samples



							def __len__(	self      )-> Optional[int]:





													'''simple docstring'''






													return self.config.num_train_timesteps








'''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