





"""simple docstring"""


from __future__ import annotations

import random
from collections.abc import Iterable



class        lowercase_			:

       def __init__(     self				,   __SCREAMING_SNAKE_CASE       ):






        '''simple docstring'''

        snake_case__      							=			{literal: None for literal in literals}

       def __str__(     self       ):






        '''simple docstring'''

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

       def __len__(     self       ):






        '''simple docstring'''

        return len(self.literals       )

       def 						_SCREAMING_SNAKE_CASE(     self				,   __SCREAMING_SNAKE_CASE       ):






        '''simple docstring'''

        for literal in self.literals:
         snake_case__      							=			literal[:2]
         if symbol in model:
          snake_case__      							=			model[symbol]
         else:
          continue
         if value is not None:
          # Complement assignment if literal is in complemented form
          if literal.endswith("'"       ):
           snake_case__      							=			not value
         snake_case__      							=			value

       def 						_SCREAMING_SNAKE_CASE(     self				,   __SCREAMING_SNAKE_CASE       ):






        '''simple docstring'''

        for literal in self.literals:
         snake_case__      							=			literal.rstrip("'"       ) if literal.endswith("'"       ) else literal + "'"
         if symbol in self.literals:
          return True

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



class        lowercase_			:

       def __init__(     self				,   __SCREAMING_SNAKE_CASE       ):






        '''simple docstring'''

        snake_case__      							=			list(__SCREAMING_SNAKE_CASE       )

       def __str__(     self       ):






        '''simple docstring'''

        return "{" + " , ".join(str(__SCREAMING_SNAKE_CASE       ) for clause in self.clauses       ) + "}"





def 							a__     (					)      ->					Clause:

 '''simple docstring'''






 snake_case__      							=			[]
 snake_case__      							=			random.randint(1		,       5		)
 snake_case__      							=			"A"
 snake_case__      							=			0
 while i < no_of_literals:
  snake_case__      							=			random.randint(1		,       5		)
  snake_case__      							=			base_var + str(_UpperCAmelCase		)
  snake_case__      							=			random.randint(0		,       1		)
  if var_complement == 1:
   var_name += "'"
  if var_name in literals:
   i -= 1
  else:
   literals.append(_UpperCAmelCase		)
  i += 1
 return Clause(_UpperCAmelCase		)





def 							a__     (					)      ->					Formula:

 '''simple docstring'''






 snake_case__      							=			set()
 snake_case__      							=			random.randint(1		,       1_0		)
 while len(_UpperCAmelCase		) < no_of_clauses:
  clauses.add(generate_clause()		)
 return Formula(_UpperCAmelCase		)





def 							a__     (					_UpperCAmelCase		)      ->					tuple[list[Clause], list[str]]:

 '''simple docstring'''






 snake_case__      							=			formula.clauses
 snake_case__      							=			[]
 for clause in formula.clauses:
  for literal in clause.literals:
   snake_case__      							=			literal[:2]
   if symbol not in symbols_set:
    symbols_set.append(_UpperCAmelCase		)
 return clauses, symbols_set





def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)      ->					tuple[list[str], dict[str, bool | None]]:

 '''simple docstring'''






 snake_case__      							=			[]
 snake_case__      							=			{}
 snake_case__      							=			[]

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

 for s in symbols:
  snake_case__      							=			s + "'"
  if (s in literals and sym not in literals) or (
      s not in literals and sym in literals
  ):
   pure_symbols.append(_UpperCAmelCase		)
 for p in pure_symbols:
  snake_case__      							=			None
 for s in pure_symbols:
  snake_case__      							=			s + "'"
  if s in literals:
   snake_case__      							=			True
  elif sym in literals:
   snake_case__      							=			False
 return pure_symbols, assignment





def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		)      ->					tuple[list[str], dict[str, bool | None]]:

 '''simple docstring'''






 snake_case__      							=			[]
 for clause in clauses:
  if len(_UpperCAmelCase		) == 1:
   unit_symbols.append(list(clause.literals.keys()		)[0]		)
  else:
   snake_case__							,				snake_case__      							=			0, 0
   for literal, value in clause.literals.items():
    if value is False:
     f_count += 1
    elif value is None:
     snake_case__      							=			literal
     n_count += 1
   if f_count == len(_UpperCAmelCase		) - 1 and n_count == 1:
    unit_symbols.append(_UpperCAmelCase		)
 snake_case__      							=			{}
 for i in unit_symbols:
  snake_case__      							=			i[:2]
  snake_case__      							=			len(_UpperCAmelCase		) == 2
 snake_case__      							=			[i[:2] for i in unit_symbols]

 return unit_symbols, assignment





def 							a__     (					_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)      ->					tuple[bool | None, dict[str, bool | None] | None]:

 '''simple docstring'''






 snake_case__      							=			True
 for clause in clauses:
  snake_case__      							=			clause.evaluate(_UpperCAmelCase		)
  if clause_check is False:
   return False, None
  elif clause_check is None:
   snake_case__      							=			False
   continue

 if check_clause_all_true:
  return True, model

 try:
  snake_case__							,				snake_case__      							=			find_pure_symbols(_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)
 except RecursionError:
  print("raises a RecursionError and is"		)
  return None, {}
 snake_case__      							=			None
 if len(_UpperCAmelCase		) > 0:
  snake_case__							,				snake_case__      							=			pure_symbols[0], assignment[pure_symbols[0]]

 if p:
  snake_case__      							=			model
  snake_case__      							=			value
  snake_case__      							=			list(_UpperCAmelCase		)
  if p in tmp_symbols:
   tmp_symbols.remove(_UpperCAmelCase		)
  return dpll_algorithm(_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)

 snake_case__							,				snake_case__      							=			find_unit_clauses(_UpperCAmelCase		,       _UpperCAmelCase		)
 snake_case__      							=			None
 if len(_UpperCAmelCase		) > 0:
  snake_case__							,				snake_case__      							=			unit_symbols[0], assignment[unit_symbols[0]]
 if p:
  snake_case__      							=			model
  snake_case__      							=			value
  snake_case__      							=			list(_UpperCAmelCase		)
  if p in tmp_symbols:
   tmp_symbols.remove(_UpperCAmelCase		)
  return dpll_algorithm(_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)
 snake_case__      							=			symbols[0]
 snake_case__      							=			symbols[1:]
 snake_case__							,				snake_case__      							=			model, model
 snake_case__							,				snake_case__      							=			True, False

 return dpll_algorithm(_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		) or dpll_algorithm(_UpperCAmelCase		,       _UpperCAmelCase		,       _UpperCAmelCase		)


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   a__   :       int   						=			generate_formula()
   print(f'''The formula {formula} is''', end=""" """)

   a__						,	a__   :       Optional[Any]   						=			generate_parameters(formula)
   a__						,	a__   :       Optional[int]   						=			dpll_algorithm(clauses, symbols, {})

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








"""simple docstring"""


import torch

from diffusers import LMSDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest



class        lowercase_			(       __lowerCAmelCase							):
       snake_case__			:							Optional[int]										=       (LMSDiscreteScheduler,)
       snake_case__			:							int										=       10

       def 						_SCREAMING_SNAKE_CASE(     self				,   **__SCREAMING_SNAKE_CASE       ):






        '''simple docstring'''

        snake_case__      							=			{
            "num_train_timesteps": 1100,
            "beta_start": 0.0001,
            "beta_end": 0.02,
            "beta_schedule": "linear",
        }

        config.update(**__SCREAMING_SNAKE_CASE       )
        return config

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        for timesteps in [10, 50, 100, 1000]:
         self.check_over_configs(num_train_timesteps=__SCREAMING_SNAKE_CASE       )

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        for beta_start, beta_end in zip([0.00001, 0.0001, 0.001]				,   [0.0002, 0.002, 0.02]       ):
         self.check_over_configs(beta_start=__SCREAMING_SNAKE_CASE				,   beta_end=__SCREAMING_SNAKE_CASE       )

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        for schedule in ["linear", "scaled_linear"]:
         self.check_over_configs(beta_schedule=__SCREAMING_SNAKE_CASE       )

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        for prediction_type in ["epsilon", "v_prediction"]:
         self.check_over_configs(prediction_type=__SCREAMING_SNAKE_CASE       )

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        for t in [0, 500, 800]:
         self.check_over_forward(time_step=__SCREAMING_SNAKE_CASE       )

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        snake_case__      							=			self.scheduler_classes[0]
        snake_case__      							=			self.get_scheduler_config()
        snake_case__      							=			scheduler_class(**__SCREAMING_SNAKE_CASE       )

        scheduler.set_timesteps(self.num_inference_steps       )

        snake_case__      							=			self.dummy_model()
        snake_case__      							=			self.dummy_sample_deter * scheduler.init_noise_sigma

        for i, t in enumerate(scheduler.timesteps       ):
         snake_case__      							=			scheduler.scale_model_input(__SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE       )

         snake_case__      							=			model(__SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE       )

         snake_case__      							=			scheduler.step(__SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE       )
         snake_case__      							=			output.prev_sample

        snake_case__      							=			torch.sum(torch.abs(__SCREAMING_SNAKE_CASE       )       )
        snake_case__      							=			torch.mean(torch.abs(__SCREAMING_SNAKE_CASE       )       )

        assert abs(result_sum.item() - 1006.388       ) < 1e-2
        assert abs(result_mean.item() - 1.31       ) < 1e-3

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        snake_case__      							=			self.scheduler_classes[0]
        snake_case__      							=			self.get_scheduler_config(prediction_type="v_prediction"       )
        snake_case__      							=			scheduler_class(**__SCREAMING_SNAKE_CASE       )

        scheduler.set_timesteps(self.num_inference_steps       )

        snake_case__      							=			self.dummy_model()
        snake_case__      							=			self.dummy_sample_deter * scheduler.init_noise_sigma

        for i, t in enumerate(scheduler.timesteps       ):
         snake_case__      							=			scheduler.scale_model_input(__SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE       )

         snake_case__      							=			model(__SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE       )

         snake_case__      							=			scheduler.step(__SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE       )
         snake_case__      							=			output.prev_sample

        snake_case__      							=			torch.sum(torch.abs(__SCREAMING_SNAKE_CASE       )       )
        snake_case__      							=			torch.mean(torch.abs(__SCREAMING_SNAKE_CASE       )       )

        assert abs(result_sum.item() - 0.0017       ) < 1e-2
        assert abs(result_mean.item() - 2.2676e-06       ) < 1e-3

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        snake_case__      							=			self.scheduler_classes[0]
        snake_case__      							=			self.get_scheduler_config()
        snake_case__      							=			scheduler_class(**__SCREAMING_SNAKE_CASE       )

        scheduler.set_timesteps(self.num_inference_steps				,   device=__SCREAMING_SNAKE_CASE       )

        snake_case__      							=			self.dummy_model()
        snake_case__      							=			self.dummy_sample_deter * scheduler.init_noise_sigma.cpu()
        snake_case__      							=			sample.to(__SCREAMING_SNAKE_CASE       )

        for i, t in enumerate(scheduler.timesteps       ):
         snake_case__      							=			scheduler.scale_model_input(__SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE       )

         snake_case__      							=			model(__SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE       )

         snake_case__      							=			scheduler.step(__SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE       )
         snake_case__      							=			output.prev_sample

        snake_case__      							=			torch.sum(torch.abs(__SCREAMING_SNAKE_CASE       )       )
        snake_case__      							=			torch.mean(torch.abs(__SCREAMING_SNAKE_CASE       )       )

        assert abs(result_sum.item() - 1006.388       ) < 1e-2
        assert abs(result_mean.item() - 1.31       ) < 1e-3

       def 						_SCREAMING_SNAKE_CASE(     self       ):






        '''simple docstring'''

        snake_case__      							=			self.scheduler_classes[0]
        snake_case__      							=			self.get_scheduler_config()
        snake_case__      							=			scheduler_class(**__SCREAMING_SNAKE_CASE				,   use_karras_sigmas=__SCREAMING_SNAKE_CASE       )

        scheduler.set_timesteps(self.num_inference_steps				,   device=__SCREAMING_SNAKE_CASE       )

        snake_case__      							=			self.dummy_model()
        snake_case__      							=			self.dummy_sample_deter.to(__SCREAMING_SNAKE_CASE       ) * scheduler.init_noise_sigma
        snake_case__      							=			sample.to(__SCREAMING_SNAKE_CASE       )

        for t in scheduler.timesteps:
         snake_case__      							=			scheduler.scale_model_input(__SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE       )

         snake_case__      							=			model(__SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE       )

         snake_case__      							=			scheduler.step(__SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE				,   __SCREAMING_SNAKE_CASE       )
         snake_case__      							=			output.prev_sample

        snake_case__      							=			torch.sum(torch.abs(__SCREAMING_SNAKE_CASE       )       )
        snake_case__      							=			torch.mean(torch.abs(__SCREAMING_SNAKE_CASE       )       )

        assert abs(result_sum.item() - 3812.9927       ) < 2e-2
        assert abs(result_mean.item() - 4.9648       ) < 1e-3

