
'''simple docstring'''

from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import SchedulerMixin


A_        =   logging.get_logger(__name__)  # pylint: disable=invalid-name




@dataclass
class 		SCREAMING_SNAKE_CASE_				(lowercase__			):



			"""simple docstring"""






			__magic_name__   :							torch.FloatTensor







class 		SCREAMING_SNAKE_CASE_				(lowercase__       ,							lowercase__			):



			"""simple docstring"""






			__magic_name__   :							Tuple             =					1



			@register_to_config
			def __init__(       self							, snake_case_ = 40							, snake_case_ = 0.002							, snake_case_ = 80.0							, snake_case_ = 0.5							, snake_case_ = 1.0							, snake_case_ = 7.0							, snake_case_ = True							, ):
									# standard deviation of the initial noise distribution
									snake_case   :					Union[str, Any]							=						sigma_max

									snake_case   :					Any							=						np.linspace(0							, 1							, _A				)
									snake_case   :					Dict							=						self._convert_to_karras(_A				)
									snake_case   :					Tuple							=						self.sigma_to_t(_A				)

									# setable values
									snake_case   :					List[str]							=						None
									snake_case   :					Tuple							=						torch.from_numpy(_A				)
									snake_case   :					Any							=						torch.from_numpy(_A				)
									snake_case   :					Dict							=						False
									snake_case   :					Any							=						False



			def      lowerCamelCase   (       self							, snake_case_							, snake_case_=None				):
									if schedule_timesteps is None:
															snake_case   :					Tuple							=						self.timesteps

									snake_case   :					Tuple							=						(schedule_timesteps == timestep).nonzero()
									return indices.item()



			def      lowerCamelCase   (       self							, snake_case_							, snake_case_				):
									# Get sigma corresponding to timestep
									if isinstance(_A							, torch.Tensor				):
															snake_case   :					Any							=						timestep.to(self.timesteps.device				)
									snake_case   :					Dict							=						self.index_for_timestep(_A				)
									snake_case   :					List[str]							=						self.sigmas[step_idx]

									snake_case   :					Any							=						sample / ((sigma**2 + self.config.sigma_data**2) ** 0.5)

									snake_case   :					Union[str, Any]							=						True
									return sample



			def      lowerCamelCase   (       self							, snake_case_				):
									if not isinstance(_A							, np.ndarray				):
															snake_case   :					List[str]							=						np.array(_A							, dtype=np.floataa				)

									snake_case   :					Dict							=						1_000 * 0.25 * np.log(sigmas + 1e-44				)

									return timesteps



			def      lowerCamelCase   (       self							, snake_case_ = None							, snake_case_ = None							, snake_case_ = None							, ):
									if num_inference_steps is None and timesteps is None:
															raise ValueError("Exactly one of `num_inference_steps` or `timesteps` must be supplied."				)

									if num_inference_steps is not None and timesteps is not None:
															raise ValueError("Can only pass one of `num_inference_steps` or `timesteps`."				)

									# Follow DDPMScheduler custom timesteps logic
									if timesteps is not None:
															for i in range(1							, len(_A				)				):
																					if timesteps[i] >= timesteps[i - 1]:
																											raise ValueError("`timesteps` must be in descending order."				)

															if timesteps[0] >= self.config.num_train_timesteps:
																					raise ValueError(
																					    F"""`timesteps` must start before `self.config.train_timesteps`:"""
																					    F""" {self.config.num_train_timesteps}."""				)

															snake_case   :					Optional[Any]							=						np.array(_A							, dtype=np.intaa				)
															snake_case   :					Tuple							=						True
									else:
															if num_inference_steps > self.config.num_train_timesteps:
																					raise ValueError(
																					    F"""`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"""
																					    F""" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"""
																					    F""" maximal {self.config.num_train_timesteps} timesteps."""				)

															snake_case   :					str							=						num_inference_steps

															snake_case   :					Union[str, Any]							=						self.config.num_train_timesteps // self.num_inference_steps
															snake_case   :					Optional[int]							=						(np.arange(0							, _A				) * step_ratio).round()[::-1].copy().astype(np.intaa				)
															snake_case   :					Tuple							=						False

									# Map timesteps to Karras sigmas directly for multistep sampling
									# See https://github.com/openai/consistency_models/blob/main/cm/karras_diffusion.py#L675
									snake_case   :					Union[str, Any]							=						self.config.num_train_timesteps
									snake_case   :					Optional[int]							=						timesteps[::-1].copy()
									snake_case   :					Optional[int]							=						ramp / (num_train_timesteps - 1)
									snake_case   :					Union[str, Any]							=						self._convert_to_karras(_A				)
									snake_case   :					str							=						self.sigma_to_t(_A				)

									snake_case   :					List[str]							=						np.concatenate([sigmas, [self.sigma_min]]				).astype(np.floataa				)
									snake_case   :					List[Any]							=						torch.from_numpy(_A				).to(device=_A				)

									if str(_A				).startswith("mps"				):
															# mps does not support float64
															snake_case   :					str							=						torch.from_numpy(_A				).to(_A							, dtype=torch.floataa				)
									else:
															snake_case   :					Any							=						torch.from_numpy(_A				).to(device=_A				)



			def      lowerCamelCase   (       self							, snake_case_				):
									snake_case   :					float							=						self.config.sigma_min
									snake_case   :					float							=						self.config.sigma_max

									snake_case   :					Tuple							=						self.config.rho
									snake_case   :					List[str]							=						sigma_min ** (1 / rho)
									snake_case   :					int							=						sigma_max ** (1 / rho)
									snake_case   :					Union[str, Any]							=						(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
									return sigmas



			def      lowerCamelCase   (       self							, snake_case_				):
									snake_case   :					str							=						self.config.sigma_data

									snake_case   :					Any							=						sigma_data**2 / (sigma**2 + sigma_data**2)
									snake_case   :					Optional[int]							=						sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
									return c_skip, c_out



			def      lowerCamelCase   (       self							, snake_case_				):
									snake_case   :					Dict							=						self.config.sigma_min
									snake_case   :					List[Any]							=						self.config.sigma_data

									snake_case   :					Optional[int]							=						sigma_data**2 / ((sigma - sigma_min) ** 2 + sigma_data**2)
									snake_case   :					Dict							=						(sigma - sigma_min) * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
									return c_skip, c_out



			def      lowerCamelCase   (       self							, snake_case_							, snake_case_							, snake_case_							, snake_case_ = None							, snake_case_ = True							, ):

									if (
									    isinstance(_A							, _A				)
									    or isinstance(_A							, torch.IntTensor				)
									    or isinstance(_A							, torch.LongTensor				)
									):
															raise ValueError(
															    (
															        "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
															        F""" `{self.__class__}.step()` is not supported. Make sure to pass"""
															        " one of the `scheduler.timesteps` as a timestep."
															    )							, )

									if not self.is_scale_input_called:
															logger.warning(
															    "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
															    "See `StableDiffusionPipeline` for a usage example."				)

									if isinstance(_A							, torch.Tensor				):
															snake_case   :					List[str]							=						timestep.to(self.timesteps.device				)

									snake_case   :					Optional[Any]							=						self.config.sigma_min
									snake_case   :					Any							=						self.config.sigma_max

									snake_case   :					Any							=						self.index_for_timestep(_A				)

									# sigma_next corresponds to next_t in original implementation
									snake_case   :					Tuple							=						self.sigmas[step_index]
									if step_index + 1 < self.config.num_train_timesteps:
															snake_case   :					Tuple							=						self.sigmas[step_index + 1]
									else:
															# Set sigma_next to sigma_min
															snake_case   :					int							=						self.sigmas[-1]

									# Get scalings for boundary conditions
									snake_case   :					Optional[Any]							=						self.get_scalings_for_boundary_condition(_A				)

									# 1. Denoise model output using boundary conditions
									snake_case   :					Dict							=						c_out * model_output + c_skip * sample
									if self.config.clip_denoised:
															snake_case   :					Tuple							=						denoised.clamp(-1							, 1				)

									# 2. Sample z ~ N(0, s_noise^2 * I)
									# Noise is not used for onestep sampling.
									if len(self.timesteps				) > 1:
															snake_case   :					Any							=						randn_tensor(
															    model_output.shape							, dtype=model_output.dtype							, device=model_output.device							, generator=_A				)
									else:
															snake_case   :					List[Any]							=						torch.zeros_like(_A				)
									snake_case   :					Tuple							=						noise * self.config.s_noise

									snake_case   :					Union[str, Any]							=						sigma_next.clamp(min=_A							, max=_A				)

									# 3. Return noisy sample
									# tau = sigma_hat, eps = sigma_min
									snake_case   :					Any							=						denoised + z * (sigma_hat**2 - sigma_min**2) ** 0.5

									if not return_dict:
															return (prev_sample,)

									return CMStochasticIterativeSchedulerOutput(prev_sample=_A				)



			def      lowerCamelCase   (       self							, snake_case_							, snake_case_							, snake_case_							, ):
									# Make sure sigmas and timesteps have the same device and dtype as original_samples
									snake_case   :					Tuple							=						self.sigmas.to(device=original_samples.device							, dtype=original_samples.dtype				)
									if original_samples.device.type == "mps" and torch.is_floating_point(_A				):
															# mps does not support float64
															snake_case   :					Optional[int]							=						self.timesteps.to(original_samples.device							, dtype=torch.floataa				)
															snake_case   :					Optional[Any]							=						timesteps.to(original_samples.device							, dtype=torch.floataa				)
									else:
															snake_case   :					Dict							=						self.timesteps.to(original_samples.device				)
															snake_case   :					List[str]							=						timesteps.to(original_samples.device				)

									snake_case   :					Union[str, Any]							=						[(schedule_timesteps == t).nonzero().item() for t in timesteps]

									snake_case   :					int							=						sigmas[step_indices].flatten()
									while len(sigma.shape				) < len(original_samples.shape				):
															snake_case   :					List[Any]							=						sigma.unsqueeze(-1				)

									snake_case   :					Any							=						original_samples + noise * sigma
									return noisy_samples






			def __len__(       self				):
									return self.config.num_train_timesteps






'''simple docstring'''

from __future__ import annotations

import random
from collections.abc import Iterable




class 		SCREAMING_SNAKE_CASE_				:



			"""simple docstring"""






			def __init__(       self							, snake_case_				):
									snake_case   :					dict[str, bool | None]							=						{literal: None for literal in literals}



			def __str__(       self				):
									return "{" + " , ".join(self.literals				) + "}"



			def __len__(       self				):
									return len(self.literals				)



			def      lowerCamelCase   (       self							, snake_case_				):
									for literal in self.literals:
															snake_case   :					Union[str, Any]							=						literal[:2]
															if symbol in model:
																					snake_case   :					str							=						model[symbol]
															else:
																					continue
															if value is not None:
																					# Complement assignment if literal is in complemented form
																					if literal.endswith("'"				):
																											snake_case   :					Dict							=						not value
															snake_case   :					str							=						value






			def      lowerCamelCase   (       self							, snake_case_				):
									for literal in self.literals:
															snake_case   :					int							=						literal.rstrip("'"				) if literal.endswith("'"				) else literal + "'"
															if symbol in self.literals:
																					return True

									self.assign(snake_case_				)
									for value in self.literals.values():
															if value in (True, None):
																					return value
									return any(self.literals.values()				)







class 		SCREAMING_SNAKE_CASE_				:



			"""simple docstring"""






			def __init__(       self							, snake_case_				):
									snake_case   :					Tuple							=						list(snake_case_				)






			def __str__(       self				):
									return "{" + " , ".join(str(snake_case_				) for clause in self.clauses				) + "}"







def 					UpperCAmelCase__      (							)						->		Clause:



						"""simple docstring"""

						snake_case   :					Optional[Any]							=						[]
						snake_case   :					Optional[Any]							=						random.randint(1,			5)
						snake_case   :					Tuple							=						"A"
						snake_case   :					Optional[Any]							=						0
						while i < no_of_literals:
												snake_case   :					Union[str, Any]							=						random.randint(1,			5)
												snake_case   :					List[Any]							=						base_var + str(_lowerCAmelCase)
												snake_case   :					Union[str, Any]							=						random.randint(0,			1)
												if var_complement == 1:
																		var_name += "'"
												if var_name in literals:
																		i -= 1
												else:
																		literals.append(_lowerCAmelCase)
												i += 1
						return Clause(_lowerCAmelCase)


def 					UpperCAmelCase__      (							)						->		Formula:



						"""simple docstring"""

						snake_case   :					set[Clause]							=						set()
						snake_case   :					Union[str, Any]							=						random.randint(1,			10)
						while len(_lowerCAmelCase) < no_of_clauses:
												clauses.add(generate_clause())
						return Formula(_lowerCAmelCase)


def 					UpperCAmelCase__      (							_lowerCAmelCase						: Formula)						->		tuple[list[Clause], list[str]]:



						"""simple docstring"""

						snake_case   :					Dict							=						formula.clauses
						snake_case   :					List[Any]							=						[]
						for clause in formula.clauses:
												for literal in clause.literals:
																		snake_case   :					Any							=						literal[:2]
																		if symbol not in symbols_set:
																								symbols_set.append(_lowerCAmelCase)
						return clauses, symbols_set


def 					UpperCAmelCase__      (							_lowerCAmelCase						: list[Clause],			_lowerCAmelCase						: list[str],			_lowerCAmelCase						: dict[str, bool | None])						->		tuple[list[str], dict[str, bool | None]]:



						"""simple docstring"""

						snake_case   :					Optional[int]							=						[]
						snake_case   :					dict[str, bool | None]							=						{}
						snake_case   :					Dict							=						[]

						for clause in clauses:
												if clause.evaluate(_lowerCAmelCase):
																		continue
												for literal in clause.literals:
																		literals.append(_lowerCAmelCase)

						for s in symbols:
												snake_case   :					Dict							=						s + "'"
												if (s in literals and sym not in literals) or (
												    s not in literals and sym in literals
												):
																		pure_symbols.append(_lowerCAmelCase)
						for p in pure_symbols:
												snake_case   :					List[Any]							=						None
						for s in pure_symbols:
												snake_case   :					Optional[Any]							=						s + "'"
												if s in literals:
																		snake_case   :					Dict							=						True
												elif sym in literals:
																		snake_case   :					Tuple							=						False
						return pure_symbols, assignment


def 					UpperCAmelCase__      (							_lowerCAmelCase						: list[Clause],			_lowerCAmelCase						: dict[str, bool | None])						->		tuple[list[str], dict[str, bool | None]]:



						"""simple docstring"""

						snake_case   :					Any							=						[]
						for clause in clauses:
												if len(_lowerCAmelCase) == 1:
																		unit_symbols.append(list(clause.literals.keys())[0])
												else:
																		snake_case							,				snake_case   :					Union[str, Any]							=						0, 0
																		for literal, value in clause.literals.items():
																								if value is False:
																														f_count += 1
																								elif value is None:
																														snake_case   :					str							=						literal
																														n_count += 1
																		if f_count == len(_lowerCAmelCase) - 1 and n_count == 1:
																								unit_symbols.append(_lowerCAmelCase)
						snake_case   :					dict[str, bool | None]							=						{}
						for i in unit_symbols:
												snake_case   :					str							=						i[:2]
												snake_case   :					Any							=						len(_lowerCAmelCase) == 2
						snake_case   :					int							=						[i[:2] for i in unit_symbols]

						return unit_symbols, assignment


def 					UpperCAmelCase__      (							_lowerCAmelCase						: list[Clause],			_lowerCAmelCase						: list[str],			_lowerCAmelCase						: dict[str, bool | None])						->		tuple[bool | None, dict[str, bool | None] | None]:



						"""simple docstring"""

						snake_case   :					Optional[int]							=						True
						for clause in clauses:
												snake_case   :					List[Any]							=						clause.evaluate(_lowerCAmelCase)
												if clause_check is False:
																		return False, None
												elif clause_check is None:
																		snake_case   :					Union[str, Any]							=						False
																		continue

						if check_clause_all_true:
												return True, model

						try:
												snake_case							,				snake_case   :					Union[str, Any]							=						find_pure_symbols(_lowerCAmelCase,			_lowerCAmelCase,			_lowerCAmelCase)
						except RecursionError:
												print("raises a RecursionError and is")
												return None, {}
						snake_case   :					Optional[int]							=						None
						if len(_lowerCAmelCase) > 0:
												snake_case							,				snake_case   :					List[Any]							=						pure_symbols[0], assignment[pure_symbols[0]]

						if p:
												snake_case   :					str							=						model
												snake_case   :					Union[str, Any]							=						value
												snake_case   :					Optional[Any]							=						list(_lowerCAmelCase)
												if p in tmp_symbols:
																		tmp_symbols.remove(_lowerCAmelCase)
												return dpll_algorithm(_lowerCAmelCase,			_lowerCAmelCase,			_lowerCAmelCase)

						snake_case							,				snake_case   :					Any							=						find_unit_clauses(_lowerCAmelCase,			_lowerCAmelCase)
						snake_case   :					Dict							=						None
						if len(_lowerCAmelCase) > 0:
												snake_case							,				snake_case   :					List[str]							=						unit_symbols[0], assignment[unit_symbols[0]]
						if p:
												snake_case   :					Any							=						model
												snake_case   :					Union[str, Any]							=						value
												snake_case   :					Optional[int]							=						list(_lowerCAmelCase)
												if p in tmp_symbols:
																		tmp_symbols.remove(_lowerCAmelCase)
												return dpll_algorithm(_lowerCAmelCase,			_lowerCAmelCase,			_lowerCAmelCase)
						snake_case   :					int							=						symbols[0]
						snake_case   :					str							=						symbols[1:]
						snake_case							,				snake_case   :					Union[str, Any]							=						model, model
						snake_case							,				snake_case   :					Optional[Any]							=						True, False

						return dpll_algorithm(_lowerCAmelCase,			_lowerCAmelCase,			_lowerCAmelCase) or dpll_algorithm(_lowerCAmelCase,			_lowerCAmelCase,			_lowerCAmelCase)


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						A_        =   generate_formula()
						print(f"The formula {formula} is", end=" ")

						A_      ,   A_        =   generate_parameters(formula)
						A_      ,   A_        =   dpll_algorithm(clauses, symbols, {})

						if solution:
												print(f"satisfiable with the assignment {model}.")
						else:
												print("not satisfiable.")





