


from collections.abc import Callable



def     lowerCAmelCase_					( __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase     ):
							__snake_case		:      float										=       a
							__snake_case		:      float										=       b
							if function(__lowerCamelCase     ) == 0:  # one of the a or b is a root for the function
														return a
							elif function(__lowerCamelCase     ) == 0:
														return b
							elif (
							    function(__lowerCamelCase     ) * function(__lowerCamelCase     ) > 0
							):  # if none of these are root and they are both positive or negative,
														# then this algorithm can't find the root
														raise ValueError("could not find root in given interval."     )
							else:
														__snake_case		:      float										=       start + (end - start) / 2.0
														while abs(start - mid     ) > 1_0**-7:  # until precisely equals to 10^-7
																					if function(__lowerCamelCase     ) == 0:
																												return mid
																					elif function(__lowerCamelCase     ) * function(__lowerCamelCase     ) < 0:
																												__snake_case		:      List[Any]										=       mid
																					else:
																												__snake_case		:      Optional[Any]										=       mid
																					__snake_case		:      Tuple										=       start + (end - start) / 2.0
														return mid



def     lowerCAmelCase_					( __lowerCamelCase     ):
							return x**3 - 2 * x - 5


if __name__ == "__main__":
			print(bisection(f, 1, 1_000))

			import doctest

			doctest.testmod()





from typing import Dict

import numpy as np
import torch

from . import residue_constants as rc
from .tensor_utils import tensor_tree_map, tree_map







def     lowerCAmelCase_					( __lowerCamelCase     ):
							__snake_case		:      Any										=       []
							__snake_case		:      Optional[Any]										=       []
							__snake_case		:      List[Any]										=       []

							for rt in rc.restypes:
														__snake_case		:      Any										=       rc.restype_name_to_atomaa_names[rc.restype_atoa[rt]]
														restype_atomaa_to_atomaa_list.append([(rc.atom_order[name] if name else 0) for name in atom_names]     )
														__snake_case		:      Tuple										=       {name: i for i, name in enumerate(__lowerCamelCase     )}
														restype_atomaa_to_atomaa_list.append(
														    [(atom_name_to_idxaa[name] if name in atom_name_to_idxaa else 0) for name in rc.atom_types]     )

														restype_atomaa_mask_list.append([(1.0 if name else 0.0) for name in atom_names]     )

							# Add dummy mapping for restype 'UNK'
							restype_atomaa_to_atomaa_list.append([0] * 1_4     )
							restype_atomaa_to_atomaa_list.append([0] * 3_7     )
							restype_atomaa_mask_list.append([0.0] * 1_4     )

							__snake_case		:      int										=       torch.tensor(
							    __lowerCamelCase							,     dtype=torch.intaa							,     device=protein["aatype"].device							,     )
							__snake_case		:      List[str]										=       torch.tensor(
							    __lowerCamelCase							,     dtype=torch.intaa							,     device=protein["aatype"].device							,     )
							__snake_case		:      Optional[Any]										=       torch.tensor(
							    __lowerCamelCase							,     dtype=torch.floataa							,     device=protein["aatype"].device							,     )
							__snake_case		:      Optional[int]										=       protein["aatype"].to(torch.long     )

							# create the mapping for (residx, atom14) --> atom37, i.e. an array
							# with shape (num_res, 14) containing the atom37 indices for this protein
							__snake_case		:      Optional[Any]										=       restype_atomaa_to_atomaa[protein_aatype]
							__snake_case		:      Tuple										=       restype_atomaa_mask[protein_aatype]

							__snake_case		:      Optional[Any]										=       residx_atomaa_mask
							__snake_case		:      Union[str, Any]										=       residx_atomaa_to_atomaa.long()

							# create the gather indices for mapping back
							__snake_case		:      Dict										=       restype_atomaa_to_atomaa[protein_aatype]
							__snake_case		:      Dict										=       residx_atomaa_to_atomaa.long()

							# create the corresponding mask
							__snake_case		:      List[str]										=       torch.zeros([2_1, 3_7]							,     dtype=torch.floataa							,     device=protein["aatype"].device     )
							for restype, restype_letter in enumerate(rc.restypes     ):
														__snake_case		:      List[str]										=       rc.restype_atoa[restype_letter]
														__snake_case		:      List[Any]										=       rc.residue_atoms[restype_name]
														for atom_name in atom_names:
																					__snake_case		:      Union[str, Any]										=       rc.atom_order[atom_name]
																					__snake_case		:      str										=       1

							__snake_case		:      List[str]										=       restype_atomaa_mask[protein_aatype]
							__snake_case		:      List[str]										=       residx_atomaa_mask

							return protein







def     lowerCAmelCase_					( __lowerCamelCase     ):
							__snake_case		:      str										=       tree_map(lambda __lowerCamelCase     : torch.tensor(__lowerCamelCase							,     device=batch["aatype"].device     )							,     __lowerCamelCase							,     np.ndarray     )
							__snake_case		:      str										=       tensor_tree_map(lambda __lowerCamelCase     : np.array(__lowerCamelCase     )							,     make_atomaa_masks(__lowerCamelCase     )     )
							return out

