






'''simple docstring'''







def 			__UpperCamelCase				(			lowercase_					:     Optional[int]      ,					lowercase_					:     List[str]      ):
       """simple docstring"""




       a_	    = (boundary[1] - boundary[0]) / steps
       a_	    = boundary[0]
       a_	    = boundary[1]
       a_	    = make_points(lowercase_      ,					lowercase_      ,					lowercase_      )
       a_	    = 0.0
       y += (h / 3.0) * f(lowercase_      )
       a_	    = 2
       for i in x_i:
              y += (h / 3) * (4 - 2 * (cnt % 2)) * f(lowercase_      )
              cnt += 1
       y += (h / 3.0) * f(lowercase_      )
       return y


def 			__UpperCamelCase				(			lowercase_					:     Optional[int]      ,					lowercase_					:     Optional[Any]      ,					lowercase_					:     List[str]      ):
       """simple docstring"""




       a_	    = a + h
       while x < (b - h):
              yield x
              a_	    = x + h


def 			__UpperCamelCase				(			lowercase_					:     str      ):  # enter your function here
       """simple docstring"""




       a_	    = (x - 0) * (x - 0)
       return y


def 			__UpperCamelCase				(			):
       """simple docstring"""




       a_	    = 0.0  # Lower bound of integration
       a_	    = 1.0  # Upper bound of integration
       a_	    = 10.0  # define number of steps or resolution
       a_	    = [a, b]  # define boundary of integration
       a_	    = method_a(lowercase_      ,					lowercase_      )
       print(F'y = {y}'      )


if __name__ == "__main__":
  main()












'''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 			__UpperCamelCase				(			lowercase_					:     torch.Tensor      ,					lowercase_					:     torch.Tensor      ,					lowercase_					:     None      ):
       """simple docstring"""




       ...


@overload
def 			__UpperCamelCase				(			lowercase_					:     torch.Tensor      ,					lowercase_					:     torch.Tensor      ,					lowercase_					:     torch.Tensor      ):
       """simple docstring"""




       ...


def 			__UpperCamelCase				(			lowercase_					:     Tuple      ,					lowercase_					:     Tuple      ,					lowercase_					:     List[Any]      ):
       """simple docstring"""




       a_	    = aatype == rc.restype_order['G']
       a_	    = rc.atom_order['CA']
       a_	    = rc.atom_order['CB']
       a_	    = 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:
              a_	    = torch.where(
                  lowercase_      ,					all_atom_masks[..., ca_idx]      ,					all_atom_masks[..., cb_idx]      ,					)
              return pseudo_beta, pseudo_beta_mask
       else:
              return pseudo_beta


def 			__UpperCamelCase				(			lowercase_					:     torch.Tensor      ,					lowercase_					:     Dict[str, torch.Tensor]      ):
       """simple docstring"""




       a_	    = batched_gather(
           lowercase_      ,					batch['residx_atom37_to_atom14']      ,					dim=-2      ,					no_batch_dims=len(atomaa.shape[:-2]      )      ,					)

       a_	    = atomaa_data * batch['atom37_atom_exists'][..., None]

       return atomaa_data


def 			__UpperCamelCase				(			lowercase_					:     Dict[str, torch.Tensor]      ):
       """simple docstring"""




       a_	    = template_feats['template_aatype']
       a_	    = template_feats['template_torsion_angles_sin_cos']
       a_	    = template_feats['template_alt_torsion_angles_sin_cos']
       a_	    = template_feats['template_torsion_angles_mask']
       a_	    = torch.cat(
           [
               nn.functional.one_hot(lowercase_      ,					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 			__UpperCamelCase				(			lowercase_					:     Dict[str, torch.Tensor]      ,					lowercase_					:     torch.types.Number      ,					lowercase_					:     torch.types.Number      ,					lowercase_					:     int      ,					lowercase_					:     bool = False      ,					lowercase_					:     float = 1E-20      ,					lowercase_					:     float = 1E8      ,					):
       """simple docstring"""




       a_	    = batch['template_pseudo_beta_mask']
       a_	    = template_mask[..., None] * template_mask[..., None, :]

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

       a_	    = [dgram, template_mask_ad[..., None]]

       a_	    = nn.functional.one_hot(
           batch['template_aatype']      ,					rc.restype_num + 2      ,					)

       a_	    = batch['template_aatype'].shape[-1]
       to_concat.append(aatype_one_hot[..., None, :, :].expand(*aatype_one_hot.shape[:-2]      ,					lowercase_      ,					-1      ,					-1      )      )
       to_concat.append(aatype_one_hot[..., None, :].expand(*aatype_one_hot.shape[:-2]      ,					-1      ,					lowercase_      ,					-1      )      )

       a_    ,  a_    ,  a_	    = [rc.atom_order[a] for a in ['N', 'CA', 'C']]
       a_	    = 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=lowercase_      ,					)
       a_	    = rigids.get_trans()[..., None, :, :]
       a_	    = rigids[..., None].invert_apply(lowercase_      )

       a_	    = torch.rsqrt(eps + torch.sum(rigid_vec**2      ,					dim=-1      )      )

       a_	    = batch['template_all_atom_mask']
       a_	    = t_aa_masks[..., n] * t_aa_masks[..., ca] * t_aa_masks[..., c]
       a_	    = template_mask[..., None] * template_mask[..., None, :]

       a_	    = inv_distance_scalar * template_mask_ad
       a_	    = rigid_vec * inv_distance_scalar[..., None]

       if not use_unit_vector:
              a_	    = unit_vector * 0.0

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

       a_	    = torch.cat(lowercase_      ,					dim=-1      )
       a_	    = act * template_mask_ad[..., None]

       return act


def 			__UpperCamelCase				(			lowercase_					:     Dict[str, torch.Tensor]      ):
       """simple docstring"""




       a_	    = nn.functional.one_hot(batch['extra_msa']      ,					23      )
       a_	    = [
           msa_ahot,
           batch['extra_has_deletion'].unsqueeze(-1      ),
           batch['extra_deletion_value'].unsqueeze(-1      ),
       ]
       return torch.cat(lowercase_      ,					dim=-1      )


def 			__UpperCamelCase				(			lowercase_					:     Rigid      ,					lowercase_					:     torch.Tensor      ,					lowercase_					:     torch.Tensor      ,					lowercase_					:     torch.Tensor      ,					):
       """simple docstring"""




       a_	    = rrgdf[aatype, ...]

       # [*, N, 8] transformations, i.e.
       #   One [*, N, 8, 3, 3] rotation matrix and
       #   One [*, N, 8, 3]    translation matrix
       a_	    = r.from_tensor_axa(lowercase_      )

       a_	    = alpha.new_zeros((*((1,) * len(alpha.shape[:-1]      )), 2)      )
       a_	    = 1

       # [*, N, 8, 2]
       a_	    = 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.

       a_	    = alpha.new_zeros(default_r.get_rots().get_rot_mats().shape      )
       a_	    = 1
       a_	    = alpha[..., 1]
       a_	    = -alpha[..., 0]
       a_	    = alpha

       a_	    = default_r.compose(Rigid(Rotation(rot_mats=lowercase_      )      ,					lowercase_      )      )

       a_	    = all_frames[..., 5]
       a_	    = all_frames[..., 6]
       a_	    = all_frames[..., 7]

       a_	    = all_frames[..., 4]
       a_	    = chia_frame_to_bb.compose(lowercase_      )
       a_	    = chia_frame_to_bb.compose(lowercase_      )
       a_	    = chia_frame_to_bb.compose(lowercase_      )

       a_	    = 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      ,					)

       a_	    = r[..., None].compose(lowercase_      )

       return all_frames_to_global


def 			__UpperCamelCase				(			lowercase_					:     Rigid      ,					lowercase_					:     torch.Tensor      ,					lowercase_					:     torch.Tensor      ,					lowercase_					:     torch.Tensor      ,					lowercase_					:     torch.Tensor      ,					lowercase_					:     torch.Tensor      ,					):
       """simple docstring"""




       a_	    = group_idx[aatype, ...]

       # [*, N, 14, 8]
       a_	    = nn.functional.one_hot(
           lowercase_      ,					num_classes=default_frames.shape[-3]      ,					)

       # [*, N, 14, 8]
       a_	    = r[..., None, :] * group_mask_one_hot

       # [*, N, 14]
       a_	    = t_atoms_to_global.map_tensor_fn(lambda lowercase_      : torch.sum(lowercase_      ,					dim=-1      )      )

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

       # [*, N, 14, 3]
       a_	    = lit_positions[aatype, ...]
       a_	    = t_atoms_to_global.apply(lowercase_      )
       a_	    = pred_positions * atom_mask

       return pred_positions




