

from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff







def 		_lowercase (     lowercase__   ,	lowercase__   ,	lowercase__ = 1_0**-1_0						):
      __lowerCAmelCase					:						List[str]					=					a
      while True:
            __lowerCAmelCase					:						Any					=					Decimal(lowercase__						) - (
                Decimal(eval(lowercase__						)						) / Decimal(eval(str(diff(lowercase__						)						)						)						)  # noqa: S307
            )
            # This number dictates the accuracy of the answer
            if abs(eval(lowercase__						)						) < precision:  # noqa: S307
                  return float(lowercase__						)


# Let's Execute
if __name__ == "__main__":
 # Find root of trigonometric function
 # Find value of pi
 print(F"The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}")
 # Find root of polynomial
 print(F"The root of x**2 - 5*x + 2 = 0 is {newton_raphson('x**2 - 5*x + 2', 0.4)}")
 # Find Square Root of 5
 print(F"The root of log(x) - 1 = 0 is {newton_raphson('log(x) - 1', 2)}")
 # Exponential Roots
 print(F"The root of exp(x) - 1 = 0 is {newton_raphson('exp(x) - 1', 0)}")





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 		_lowercase (     lowercase__						):
      __lowerCAmelCase					:						str					=					[]
      __lowerCAmelCase					:						List[Any]					=					[]
      __lowerCAmelCase					:						str					=					[]

      for rt in rc.restypes:
            __lowerCAmelCase					:						List[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]						)
            __lowerCAmelCase					:						List[str]					=					{name: i for i, name in enumerate(lowercase__						)}
            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						)

      __lowerCAmelCase					:						List[Any]					=					torch.tensor(
          lowercase__   ,	dtype=torch.intaa   ,	device=protein['''aatype'''].device   ,	)
      __lowerCAmelCase					:						Optional[Any]					=					torch.tensor(
          lowercase__   ,	dtype=torch.intaa   ,	device=protein['''aatype'''].device   ,	)
      __lowerCAmelCase					:						Tuple					=					torch.tensor(
          lowercase__   ,	dtype=torch.floataa   ,	device=protein['''aatype'''].device   ,	)
      __lowerCAmelCase					:						List[Any]					=					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
      __lowerCAmelCase					:						Any					=					restype_atomaa_to_atomaa[protein_aatype]
      __lowerCAmelCase					:						Union[str, Any]					=					restype_atomaa_mask[protein_aatype]

      __lowerCAmelCase					:						int					=					residx_atomaa_mask
      __lowerCAmelCase					:						List[str]					=					residx_atomaa_to_atomaa.long()

      # create the gather indices for mapping back
      __lowerCAmelCase					:						int					=					restype_atomaa_to_atomaa[protein_aatype]
      __lowerCAmelCase					:						Union[str, Any]					=					residx_atomaa_to_atomaa.long()

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

      __lowerCAmelCase					:						Union[str, Any]					=					restype_atomaa_mask[protein_aatype]
      __lowerCAmelCase					:						Any					=					residx_atomaa_mask

      return protein







def 		_lowercase (     lowercase__						):
      __lowerCAmelCase					:						Dict					=					tree_map(lambda lowercase__						: torch.tensor(lowercase__   ,	device=batch['''aatype'''].device						)   ,	lowercase__   ,	np.ndarray						)
      __lowerCAmelCase					:						Tuple					=					tensor_tree_map(lambda lowercase__						: np.array(lowercase__						)   ,	make_atomaa_masks(lowercase__						)						)
      return out


