

'''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 ,UpperCamelCase ,UpperCamelCase	)     ->     torch.Tensor:
	...







@overload
def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase	)     ->     Tuple[torch.Tensor, torch.Tensor]:
	...







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase	)     ->     str:
	UpperCAmelCase_		:   Union[str, Any]													=       aatype == rc.restype_order['G']
	UpperCAmelCase_		:   str													=       rc.atom_order['CA']
	UpperCAmelCase_		:   Tuple													=       rc.atom_order['CB']
	UpperCAmelCase_		:   int													=       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_		:   List[str]													=       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 ,UpperCamelCase	)     ->     torch.Tensor:
	UpperCAmelCase_		:   Tuple													=       batched_gather(
	    UpperCamelCase ,batch['residx_atom37_to_atom14'] ,dim=-2 ,no_batch_dims=len(atomaa.shape[:-2]	) ,)

	UpperCAmelCase_		:   List[str]													=       atomaa_data * batch['atom37_atom_exists'][..., None]

	return atomaa_data







def     SCREAMING_SNAKE_CASE(	UpperCamelCase	)     ->     torch.Tensor:
	UpperCAmelCase_		:   int													=       template_feats['template_aatype']
	UpperCAmelCase_		:   Optional[int]													=       template_feats['template_torsion_angles_sin_cos']
	UpperCAmelCase_		:   Any													=       template_feats['template_alt_torsion_angles_sin_cos']
	UpperCAmelCase_		:   Dict													=       template_feats['template_torsion_angles_mask']
	UpperCAmelCase_		:   Any													=       torch.cat(
	    [
	        nn.functional.one_hot(UpperCamelCase ,2_2	),
	        torsion_angles_sin_cos.reshape(*torsion_angles_sin_cos.shape[:-2] ,1_4	),
	        alt_torsion_angles_sin_cos.reshape(*alt_torsion_angles_sin_cos.shape[:-2] ,1_4	),
	        torsion_angles_mask,
	    ] ,dim=-1 ,)

	return template_angle_feat







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase = False ,UpperCamelCase = 1e-20 ,UpperCamelCase = 1e8 ,)     ->     torch.Tensor:
	UpperCAmelCase_		:   Any													=       batch['template_pseudo_beta_mask']
	UpperCAmelCase_		:   List[Any]													=       template_mask[..., None] * template_mask[..., None, :]

	# Compute distogram (this seems to differ slightly from Alg. 5)
	UpperCAmelCase_		:   Union[str, Any]													=       batch['template_pseudo_beta']
	UpperCAmelCase_		:   Optional[int]													=       torch.sum((tpb[..., None, :] - tpb[..., None, :, :]) ** 2 ,dim=-1 ,keepdim=UpperCamelCase	)
	UpperCAmelCase_		:   Optional[Any]													=       torch.linspace(UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,device=tpb.device	) ** 2
	UpperCAmelCase_		:   List[str]													=       torch.cat([lower[1:], lower.new_tensor([inf]	)] ,dim=-1	)
	UpperCAmelCase_		:   List[str]													=       ((dgram > lower) * (dgram < upper)).type(dgram.dtype	)

	UpperCAmelCase_		:   Union[str, Any]													=       [dgram, template_mask_ad[..., None]]

	UpperCAmelCase_		:   torch.LongTensor													=       nn.functional.one_hot(
	    batch['template_aatype'] ,rc.restype_num + 2 ,)

	UpperCAmelCase_		:   Tuple													=       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_		:   Optional[int]													=       [rc.atom_order[a] for a in ['N', 'CA', 'C']]
	UpperCAmelCase_		:   int													=       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_		:   str													=       rigids.get_trans()[..., None, :, :]
	UpperCAmelCase_		:   Tuple													=       rigids[..., None].invert_apply(UpperCamelCase	)

	UpperCAmelCase_		:   Optional[int]													=       torch.rsqrt(eps + torch.sum(rigid_vec**2 ,dim=-1	)	)

	UpperCAmelCase_		:   int													=       batch['template_all_atom_mask']
	UpperCAmelCase_		:   List[Any]													=       t_aa_masks[..., n] * t_aa_masks[..., ca] * t_aa_masks[..., c]
	UpperCAmelCase_		:   Union[str, Any]													=       template_mask[..., None] * template_mask[..., None, :]

	UpperCAmelCase_		:   Optional[int]													=       inv_distance_scalar * template_mask_ad
	UpperCAmelCase_		:   Dict													=       rigid_vec * inv_distance_scalar[..., None]

	if not use_unit_vector:
		UpperCAmelCase_		:   str													=       unit_vector * 0.0

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

	UpperCAmelCase_		:   Dict													=       torch.cat(UpperCamelCase ,dim=-1	)
	UpperCAmelCase_		:   Optional[int]													=       act * template_mask_ad[..., None]

	return act







def     SCREAMING_SNAKE_CASE(	UpperCamelCase	)     ->     torch.Tensor:
	UpperCAmelCase_		:   torch.LongTensor													=       nn.functional.one_hot(batch['extra_msa'] ,2_3	)
	UpperCAmelCase_		:   Dict													=       [
	    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 ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,)     ->     Rigid:
	# [*, N, 8, 4, 4]
	UpperCAmelCase_		:   Any													=       rrgdf[aatype, ...]

	# [*, N, 8] transformations, i.e.
	#   One [*, N, 8, 3, 3] rotation matrix and
	#   One [*, N, 8, 3]    translation matrix
	UpperCAmelCase_		:   str													=       r.from_tensor_axa(UpperCamelCase	)

	UpperCAmelCase_		:   List[str]													=       alpha.new_zeros((*((1,) * len(alpha.shape[:-1]	)), 2)	)
	UpperCAmelCase_		:   Dict													=       1

	# [*, N, 8, 2]
	UpperCAmelCase_		:   List[str]													=       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_		:   Optional[int]													=       alpha.new_zeros(default_r.get_rots().get_rot_mats().shape	)
	UpperCAmelCase_		:   Dict													=       1
	UpperCAmelCase_		:   Optional[Any]													=       alpha[..., 1]
	UpperCAmelCase_		:   Dict													=       -alpha[..., 0]
	UpperCAmelCase_		:   int													=       alpha

	UpperCAmelCase_		:   List[str]													=       default_r.compose(Rigid(Rotation(rot_mats=UpperCamelCase	) ,UpperCamelCase	)	)

	UpperCAmelCase_		:   Union[str, Any]													=       all_frames[..., 5]
	UpperCAmelCase_		:   Dict													=       all_frames[..., 6]
	UpperCAmelCase_		:   Any													=       all_frames[..., 7]

	UpperCAmelCase_		:   List[str]													=       all_frames[..., 4]
	UpperCAmelCase_		:   Union[str, Any]													=       chia_frame_to_bb.compose(UpperCamelCase	)
	UpperCAmelCase_		:   Optional[int]													=       chia_frame_to_bb.compose(UpperCamelCase	)
	UpperCAmelCase_		:   List[str]													=       chia_frame_to_bb.compose(UpperCamelCase	)

	UpperCAmelCase_		:   Any													=       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_		:   Union[str, Any]													=       r[..., None].compose(UpperCamelCase	)

	return all_frames_to_global







def     SCREAMING_SNAKE_CASE(	UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,UpperCamelCase ,)     ->     torch.Tensor:
	# [*, N, 14]
	UpperCAmelCase_		:   Dict													=       group_idx[aatype, ...]

	# [*, N, 14, 8]
	UpperCAmelCase_		:   torch.LongTensor													=       nn.functional.one_hot(
	    UpperCamelCase ,num_classes=default_frames.shape[-3] ,)

	# [*, N, 14, 8]
	UpperCAmelCase_		:   List[Any]													=       r[..., None, :] * group_mask_one_hot

	# [*, N, 14]
	UpperCAmelCase_		:   List[Any]													=       t_atoms_to_global.map_tensor_fn(lambda UpperCamelCase	: torch.sum(UpperCamelCase ,dim=-1	)	)

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

	# [*, N, 14, 3]
	UpperCAmelCase_		:   Any													=       lit_positions[aatype, ...]
	UpperCAmelCase_		:   Any													=       t_atoms_to_global.apply(UpperCamelCase	)
	UpperCAmelCase_		:   Any													=       pred_positions * atom_mask

	return pred_positions









'''simple docstring'''


def     SCREAMING_SNAKE_CASE(	UpperCamelCase	)     ->     int:
	if not isinstance(UpperCamelCase ,UpperCamelCase	):
		raise TypeError('recursive_lucas_number accepts only integer arguments.'	)
	if n_th_number == 0:
		return 2
	if n_th_number == 1:
		return 1

	return recursive_lucas_number(n_th_number - 1	) + recursive_lucas_number(
	    n_th_number - 2	)







def     SCREAMING_SNAKE_CASE(	UpperCamelCase	)     ->     int:
	if not isinstance(UpperCamelCase ,UpperCamelCase	):
		raise TypeError('dynamic_lucas_number accepts only integer arguments.'	)
	UpperCAmelCase_						,     UpperCAmelCase_		:   List[str]													=       2, 1
	for _ in range(UpperCamelCase	):
		UpperCAmelCase_						,     UpperCAmelCase_		:   Dict													=       b, a + b
	return a


if __name__ == "__main__":
						from doctest import testmod

						testmod()
						lowerCAmelCase__      				=			int(input("Enter the number of terms in lucas series:\n").strip())
						print("Using recursive function to calculate lucas series:")
						print(" ".join(str(recursive_lucas_number(i)) for i in range(n)))
						print("\nUsing dynamic function to calculate lucas series:")
						print(" ".join(str(dynamic_lucas_number(i)) for i in range(n)))






