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    lowerCamelCase_   (  _lowercase ,     _lowercase ,     _lowercase    )							->	torch.Tensor:
		...



@overload
def    lowerCamelCase_   (  _lowercase ,     _lowercase ,     _lowercase    )							->	Tuple[torch.Tensor, torch.Tensor]:
		...



def    lowerCamelCase_   (  _lowercase ,     _lowercase ,     _lowercase    )							->	Dict:
		__A							:   Optional[Any]	  =				aatype == rc.restype_order["G"]
		__A							:   List[str]	  =				rc.atom_order["CA"]
		__A							:   int	  =				rc.atom_order["CB"]
		__A							:   Any	  =				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							:   Tuple	  =				torch.where(
				    _lowercase ,     all_atom_masks[..., ca_idx] ,     all_atom_masks[..., cb_idx] ,     )
				return pseudo_beta, pseudo_beta_mask
		else:
				return pseudo_beta



def    lowerCamelCase_   (  _lowercase ,     _lowercase    )							->	torch.Tensor:
		__A							:   str	  =				batched_gather(
		    _lowercase ,     batch["residx_atom37_to_atom14"] ,     dim=-2 ,     no_batch_dims=len(atomaa.shape[:-2]    ) ,     )

		__A							:   List[str]	  =				atomaa_data * batch["atom37_atom_exists"][..., None]

		return atomaa_data



def    lowerCamelCase_   (  _lowercase    )							->	torch.Tensor:
		__A							:   Any	  =				template_feats["template_aatype"]
		__A							:   int	  =				template_feats["template_torsion_angles_sin_cos"]
		__A							:   Tuple	  =				template_feats["template_alt_torsion_angles_sin_cos"]
		__A							:   str	  =				template_feats["template_torsion_angles_mask"]
		__A							:   Optional[Any]	  =				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    lowerCamelCase_   (  _lowercase ,     _lowercase ,     _lowercase ,     _lowercase ,     _lowercase = False ,     _lowercase = 1E-20 ,     _lowercase = 1E8 ,     )							->	torch.Tensor:
		__A							:   Optional[Any]	  =				batch["template_pseudo_beta_mask"]
		__A							:   Optional[Any]	  =				template_mask[..., None] * template_mask[..., None, :]

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

		__A							:   Tuple	  =				[dgram, template_mask_ad[..., None]]

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

		__A							:   Optional[int]	  =				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							:   Tuple	  =				[rc.atom_order[a] for a in ["N", "CA", "C"]]
		__A							:   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=_lowercase ,     )
		__A							:   List[Any]	  =				rigids.get_trans()[..., None, :, :]
		__A							:   Dict	  =				rigids[..., None].invert_apply(_lowercase    )

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

		__A							:   int	  =				batch["template_all_atom_mask"]
		__A							:   List[Any]	  =				t_aa_masks[..., n] * t_aa_masks[..., ca] * t_aa_masks[..., c]
		__A							:   Optional[int]	  =				template_mask[..., None] * template_mask[..., None, :]

		__A							:   Optional[Any]	  =				inv_distance_scalar * template_mask_ad
		__A							:   int	  =				rigid_vec * inv_distance_scalar[..., None]

		if not use_unit_vector:
				__A							:   Tuple	  =				unit_vector * 0.0

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

		__A							:   Tuple	  =				torch.cat(_lowercase ,     dim=-1    )
		__A							:   Tuple	  =				act * template_mask_ad[..., None]

		return act



def    lowerCamelCase_   (  _lowercase    )							->	torch.Tensor:
		__A							:   torch.LongTensor	  =				nn.functional.one_hot(batch["extra_msa"] ,     23    )
		__A							:   Union[str, Any]	  =				[
		    msa_ahot,
		    batch["extra_has_deletion"].unsqueeze(-1    ),
		    batch["extra_deletion_value"].unsqueeze(-1    ),
		]
		return torch.cat(_lowercase ,     dim=-1    )



def    lowerCamelCase_   (  _lowercase ,     _lowercase ,     _lowercase ,     _lowercase ,     )							->	Rigid:
		# [*, N, 8, 4, 4]
		__A							:   Optional[int]	  =				rrgdf[aatype, ...]

		# [*, N, 8] transformations, i.e.
		#   One [*, N, 8, 3, 3] rotation matrix and
		#   One [*, N, 8, 3]    translation matrix
		__A							:   Dict	  =				r.from_tensor_axa(_lowercase    )

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

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

		__A							:   Any	  =				default_r.compose(Rigid(Rotation(rot_mats=_lowercase    ) ,     _lowercase    )    )

		__A							:   Optional[Any]	  =				all_frames[..., 5]
		__A							:   Optional[Any]	  =				all_frames[..., 6]
		__A							:   List[Any]	  =				all_frames[..., 7]

		__A							:   Optional[Any]	  =				all_frames[..., 4]
		__A							:   int	  =				chia_frame_to_bb.compose(_lowercase    )
		__A							:   Optional[Any]	  =				chia_frame_to_bb.compose(_lowercase    )
		__A							:   int	  =				chia_frame_to_bb.compose(_lowercase    )

		__A							:   List[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 ,     )

		__A							:   int	  =				r[..., None].compose(_lowercase    )

		return all_frames_to_global





def    lowerCamelCase_   (  _lowercase ,     _lowercase ,     _lowercase ,     _lowercase ,     _lowercase ,     _lowercase ,     )							->	torch.Tensor:
		# [*, N, 14]
		__A							:   str	  =				group_idx[aatype, ...]

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

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

		# [*, N, 14]
		__A							:   Union[str, Any]	  =				t_atoms_to_global.map_tensor_fn(lambda _lowercase    : torch.sum(_lowercase ,     dim=-1    )    )

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

		# [*, N, 14, 3]
		__A							:   Optional[Any]	  =				lit_positions[aatype, ...]
		__A							:   Union[str, Any]	  =				t_atoms_to_global.apply(_lowercase    )
		__A							:   Union[str, Any]	  =				pred_positions * atom_mask

		return pred_positions






from typing import Any

import numpy as np


class _a       :

	'''simple docstring'''



	def __init__(       self							,			__UpperCAmelCase							,			__UpperCAmelCase   ):
			# Check if RHS is negative
			if np.any(tableau[:, -1]							,			where=tableau[:, -1] < 0   ):
					raise ValueError("RHS must be > 0"   )

			__A							:   Any	  =				tableau
			__A  ,       __A							:   Dict	  =				tableau.shape

			# Number of decision variables x1, x2, x3...
			__A							:   Any	  =				n_vars

			# Number of artificial variables to be minimised
			__A							:   Optional[int]	  =				len(np.where(tableau[self.n_vars : -1] == -1   )[0]   )

			# 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
			__A							:   List[Any]	  =				(self.n_art_vars > 0) + 1

			# Number of slack variables added to make inequalities into equalities
			__A							:   Dict	  =				self.n_rows - self.n_stages

			# Objectives for each stage
			__A							:   List[Any]	  =				["max"]

			# In two stage simplex, first minimise then maximise
			if self.n_art_vars:
					self.objectives.append("min"   )

			__A							:   Tuple	  =				[""]

			# Index of current pivot row and column
			__A							:   Tuple	  =				None
			__A							:   List[str]	  =				None

			# Does objective row only contain (non)-negative values?
			__A							:   Optional[int]	  =				False

	@staticmethod
	def 					__UpperCAmelCase(       *__UpperCAmelCase   ):
			if len(__UpperCAmelCase   ) != 3:
					raise ValueError("Must provide n_vars, n_slack, and n_art_vars"   )

			if not all(x >= 0 and isinstance(__UpperCAmelCase							,			__UpperCAmelCase   ) for x in args   ):
					raise ValueError("All arguments must be non-negative integers"   )

			# decision | slack | artificial
			__A							:   List[Any]	  =				["x", "s", "a"]
			__A							:   List[str]	  =				[]
			for i in range(3   ):
					for j in range(args[i]   ):
							titles.append(string_starts[i] + str(j + 1   )   )
			titles.append("RHS"   )
			return titles

	def 					__UpperCAmelCase(       self							,			__UpperCAmelCase   ):
			__A							:   Optional[Any]	  =				self.objectives[-1]

			# Find entries of highest magnitude in objective rows
			__A							:   Optional[int]	  =				(objective == "min") - (objective == "max")
			__A							:   Any	  =				np.argmax(sign * tableau[0, : self.n_vars]   )

			# Choice is only valid if below 0 for maximise, and above for minimise
			if sign * self.tableau[0, col_idx] <= 0:
					__A							:   Any	  =				True
					return 0, 0

			# Pivot row is chosen as having the lowest quotient when elements of
			# the pivot column divide the right-hand side

			# Slice excluding the objective rows
			__A							:   Optional[int]	  =				slice(self.n_stages							,			self.n_rows   )

			# RHS
			__A							:   Optional[Any]	  =				tableau[s, -1]

			# Elements of pivot column within slice
			__A							:   List[Any]	  =				tableau[s, col_idx]

			# Array filled with nans
			__A							:   Union[str, Any]	  =				np.full(self.n_rows - self.n_stages							,			np.nan   )

			# If element in pivot column is greater than zeron_stages, return
			# quotient or nan otherwise
			__A							:   int	  =				np.divide(__UpperCAmelCase							,			__UpperCAmelCase							,			out=__UpperCAmelCase							,			where=divisor > 0   )

			# Arg of minimum quotient excluding the nan values. n_stages is added
			# to compensate for earlier exclusion of objective columns
			__A							:   Optional[Any]	  =				np.nanargmin(__UpperCAmelCase   ) + self.n_stages
			return row_idx, col_idx

	def 					__UpperCAmelCase(       self							,			__UpperCAmelCase							,			__UpperCAmelCase							,			__UpperCAmelCase   ):
			__A							:   List[Any]	  =				tableau[row_idx].copy()

			__A							:   Tuple	  =				piv_row[col_idx]

			# Entry becomes 1
			piv_row *= 1 / piv_val

			# Variable in pivot column becomes basic, ie the only non-zero entry
			for idx, coeff in enumerate(tableau[:, col_idx]   ):
					tableau[idx] += -coeff * piv_row
			__A							:   str	  =				piv_row
			return tableau

	def 					__UpperCAmelCase(       self							,			__UpperCAmelCase   ):
			self.objectives.pop()

			if not self.objectives:
					return tableau

			# Slice containing ids for artificial columns
			__A							:   List[Any]	  =				slice(-self.n_art_vars - 1							,			-1   )

			# Delete the artificial variable columns
			__A							:   Tuple	  =				np.delete(__UpperCAmelCase							,			__UpperCAmelCase							,			axis=1   )

			# Delete the objective row of the first stage
			__A							:   List[str]	  =				np.delete(__UpperCAmelCase							,			0							,			axis=0   )

			__A							:   Union[str, Any]	  =				1
			self.n_rows -= 1
			__A							:   str	  =				0
			__A							:   str	  =				False
			return tableau

	def 					__UpperCAmelCase(       self   ):
			# Stop simplex algorithm from cycling.
			for _ in range(100   ):
					# Completion of each stage removes an objective. If both stages
					# are complete, then no objectives are left
					if not self.objectives:
							__A							:   Optional[Any]	  =				self.generate_col_titles(
							    self.n_vars							,			self.n_slack							,			self.n_art_vars   )

							# Find the values of each variable at optimal solution
							return self.interpret_tableau(self.tableau							,			self.col_titles   )

					__A  ,       __A							:   Dict	  =				self.find_pivot(self.tableau   )

					# If there are no more negative values in objective row
					if self.stop_iter:
							# Delete artificial variable columns and rows. Update attributes
							__A							:   int	  =				self.change_stage(self.tableau   )
					else:
							__A							:   Dict	  =				self.pivot(self.tableau							,			__UpperCAmelCase							,			__UpperCAmelCase   )
			return {}







	def 					__UpperCAmelCase(       self							,			__UpperCAmelCase							,			__UpperCAmelCase   ):
			__A							:   Union[str, Any]	  =				{"P": abs(tableau[0, -1]   )}

			for i in range(self.n_vars   ):
					# Gives ids of nonzero entries in the ith column
					__A							:   str	  =				np.nonzero(tableau[:, i]   )
					__A							:   List[Any]	  =				len(nonzero[0]   )

					# First entry in the nonzero ids
					__A							:   List[Any]	  =				nonzero[0][0]
					__A							:   Tuple	  =				tableau[nonzero_rowidx, i]

					# If there is only one nonzero value in column, which is one
					if n_nonzero == nonzero_val == 1:
							__A							:   Union[str, Any]	  =				tableau[nonzero_rowidx, -1]
							__A							:   Optional[int]	  =				rhs_val

        # Check for basic variables
			for title in col_titles:
					# Don't add RHS or slack variables to output dict
					if title[0] not in "R-s-a":
							output_dict.setdefault(__UpperCAmelCase							,			0   )
			return output_dict


if __name__ == "__main__":
					import doctest

					doctest.testmod()





