'''simple docstring'''

import torch

from diffusers import DDPMScheduler

from .test_schedulers import SchedulerCommonTest







class 				_lowercase     (				UpperCAmelCase__			):


 '''simple docstring'''






 _SCREAMING_SNAKE_CASE     :       Optional[int]      	=					(DDPMScheduler,)
 def a					(      self   :	List[Any]      ,       **SCREAMING_SNAKE_CASE__   :	Any							)  ->    List[Any]:
  __lowerCAmelCase											=						{
      """num_train_timesteps""": 10_00,
      """beta_start""": 0.0_0_0_1,
      """beta_end""": 0.0_2,
      """beta_schedule""": """linear""",
      """variance_type""": """fixed_small""",
      """clip_sample""": True,
  }

  config.update(**SCREAMING_SNAKE_CASE__							)
  return config
 def a					(      self   :	int							)  ->    List[str]:
  for timesteps in [1, 5, 1_00, 10_00]:
   self.check_over_configs(num_train_timesteps=SCREAMING_SNAKE_CASE__							)
 def a					(      self   :	List[str]							)  ->    Optional[int]:
  for beta_start, beta_end in zip([0.0_0_0_1, 0.0_0_1, 0.0_1, 0.1]      ,       [0.0_0_2, 0.0_2, 0.2, 2]							):
   self.check_over_configs(beta_start=SCREAMING_SNAKE_CASE__      ,       beta_end=SCREAMING_SNAKE_CASE__							)
 def a					(      self   :	Tuple							)  ->    Optional[int]:
  for schedule in ["linear", "squaredcos_cap_v2"]:
   self.check_over_configs(beta_schedule=SCREAMING_SNAKE_CASE__							)
 def a					(      self   :	str							)  ->    int:
  for variance in ["fixed_small", "fixed_large", "other"]:
   self.check_over_configs(variance_type=SCREAMING_SNAKE_CASE__							)
 def a					(      self   :	Dict							)  ->    Optional[int]:
  for clip_sample in [True, False]:
   self.check_over_configs(clip_sample=SCREAMING_SNAKE_CASE__							)
 def a					(      self   :	str							)  ->    List[Any]:
  self.check_over_configs(thresholding=SCREAMING_SNAKE_CASE__							)
  for threshold in [0.5, 1.0, 2.0]:
   for prediction_type in ["epsilon", "sample", "v_prediction"]:
    self.check_over_configs(
        thresholding=SCREAMING_SNAKE_CASE__      ,       prediction_type=SCREAMING_SNAKE_CASE__      ,       sample_max_value=SCREAMING_SNAKE_CASE__      ,       )
 def a					(      self   :	int							)  ->    int:
  for prediction_type in ["epsilon", "sample", "v_prediction"]:
   self.check_over_configs(prediction_type=SCREAMING_SNAKE_CASE__							)
 def a					(      self   :	str							)  ->    str:
  for t in [0, 5_00, 9_99]:
   self.check_over_forward(time_step=SCREAMING_SNAKE_CASE__							)
 def a					(      self   :	Dict							)  ->    int:
  __lowerCAmelCase											=						self.scheduler_classes[0]
  __lowerCAmelCase											=						self.get_scheduler_config()
  __lowerCAmelCase											=						scheduler_class(**SCREAMING_SNAKE_CASE__							)

  assert torch.sum(torch.abs(scheduler._get_variance(0							) - 0.0							)							) < 1e-5
  assert torch.sum(torch.abs(scheduler._get_variance(4_87							) - 0.0_0_9_7_9							)							) < 1e-5
  assert torch.sum(torch.abs(scheduler._get_variance(9_99							) - 0.0_2							)							) < 1e-5
 def a					(      self   :	List[str]							)  ->    str:
  __lowerCAmelCase											=						self.scheduler_classes[0]
  __lowerCAmelCase											=						self.get_scheduler_config()
  __lowerCAmelCase											=						scheduler_class(**SCREAMING_SNAKE_CASE__							)

  __lowerCAmelCase											=						len(SCREAMING_SNAKE_CASE__							)

  __lowerCAmelCase											=						self.dummy_model()
  __lowerCAmelCase											=						self.dummy_sample_deter
  __lowerCAmelCase											=						torch.manual_seed(0							)

  for t in reversed(range(SCREAMING_SNAKE_CASE__							)							):
   # 1. predict noise residual
   __lowerCAmelCase											=						model(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							)

   # 2. predict previous mean of sample x_t-1
   __lowerCAmelCase											=						scheduler.step(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__      ,       generator=SCREAMING_SNAKE_CASE__							).prev_sample

   # if t > 0:
   #     noise = self.dummy_sample_deter
   #     variance = scheduler.get_variance(t) ** (0.5) * noise
   #
   # sample = pred_prev_sample + variance
   __lowerCAmelCase											=						pred_prev_sample

  __lowerCAmelCase											=						torch.sum(torch.abs(SCREAMING_SNAKE_CASE__							)							)
  __lowerCAmelCase											=						torch.mean(torch.abs(SCREAMING_SNAKE_CASE__							)							)

  assert abs(result_sum.item() - 2_5_8.9_6_0_6							) < 1e-2
  assert abs(result_mean.item() - 0.3_3_7_2							) < 1e-3
 def a					(      self   :	Any							)  ->    Tuple:
  __lowerCAmelCase											=						self.scheduler_classes[0]
  __lowerCAmelCase											=						self.get_scheduler_config(prediction_type="""v_prediction"""							)
  __lowerCAmelCase											=						scheduler_class(**SCREAMING_SNAKE_CASE__							)

  __lowerCAmelCase											=						len(SCREAMING_SNAKE_CASE__							)

  __lowerCAmelCase											=						self.dummy_model()
  __lowerCAmelCase											=						self.dummy_sample_deter
  __lowerCAmelCase											=						torch.manual_seed(0							)

  for t in reversed(range(SCREAMING_SNAKE_CASE__							)							):
   # 1. predict noise residual
   __lowerCAmelCase											=						model(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							)

   # 2. predict previous mean of sample x_t-1
   __lowerCAmelCase											=						scheduler.step(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__      ,       generator=SCREAMING_SNAKE_CASE__							).prev_sample

   # if t > 0:
   #     noise = self.dummy_sample_deter
   #     variance = scheduler.get_variance(t) ** (0.5) * noise
   #
   # sample = pred_prev_sample + variance
   __lowerCAmelCase											=						pred_prev_sample

  __lowerCAmelCase											=						torch.sum(torch.abs(SCREAMING_SNAKE_CASE__							)							)
  __lowerCAmelCase											=						torch.mean(torch.abs(SCREAMING_SNAKE_CASE__							)							)

  assert abs(result_sum.item() - 2_0_2.0_2_9_6							) < 1e-2
  assert abs(result_mean.item() - 0.2_6_3_1							) < 1e-3
 def a					(      self   :	Any							)  ->    Tuple:
  __lowerCAmelCase											=						self.scheduler_classes[0]
  __lowerCAmelCase											=						self.get_scheduler_config()
  __lowerCAmelCase											=						scheduler_class(**SCREAMING_SNAKE_CASE__							)

  __lowerCAmelCase											=						[1_00, 87, 50, 1, 0]

  scheduler.set_timesteps(timesteps=SCREAMING_SNAKE_CASE__							)

  __lowerCAmelCase											=						scheduler.timesteps

  for i, timestep in enumerate(SCREAMING_SNAKE_CASE__							):
   if i == len(SCREAMING_SNAKE_CASE__							) - 1:
    __lowerCAmelCase											=						-1
   else:
    __lowerCAmelCase											=						timesteps[i + 1]

   __lowerCAmelCase											=						scheduler.previous_timestep(SCREAMING_SNAKE_CASE__							)
   __lowerCAmelCase											=						prev_t.item()

   self.assertEqual(SCREAMING_SNAKE_CASE__      ,       SCREAMING_SNAKE_CASE__							)
 def a					(      self   :	int							)  ->    Union[str, Any]:
  __lowerCAmelCase											=						self.scheduler_classes[0]
  __lowerCAmelCase											=						self.get_scheduler_config()
  __lowerCAmelCase											=						scheduler_class(**SCREAMING_SNAKE_CASE__							)

  __lowerCAmelCase											=						[1_00, 87, 50, 51, 0]

  with self.assertRaises(SCREAMING_SNAKE_CASE__      ,       msg="""`custom_timesteps` must be in descending order."""							):
   scheduler.set_timesteps(timesteps=SCREAMING_SNAKE_CASE__							)
 def a					(      self   :	int							)  ->    Dict:
  __lowerCAmelCase											=						self.scheduler_classes[0]
  __lowerCAmelCase											=						self.get_scheduler_config()
  __lowerCAmelCase											=						scheduler_class(**SCREAMING_SNAKE_CASE__							)

  __lowerCAmelCase											=						[1_00, 87, 50, 1, 0]
  __lowerCAmelCase											=						len(SCREAMING_SNAKE_CASE__							)

  with self.assertRaises(SCREAMING_SNAKE_CASE__      ,       msg="""Can only pass one of `num_inference_steps` or `custom_timesteps`."""							):
   scheduler.set_timesteps(num_inference_steps=SCREAMING_SNAKE_CASE__      ,       timesteps=SCREAMING_SNAKE_CASE__							)





 def a					(      self   :	List[Any]							)  ->    Optional[Any]:
  __lowerCAmelCase											=						self.scheduler_classes[0]
  __lowerCAmelCase											=						self.get_scheduler_config()
  __lowerCAmelCase											=						scheduler_class(**SCREAMING_SNAKE_CASE__							)

  __lowerCAmelCase											=						[scheduler.config.num_train_timesteps]

  with self.assertRaises(
      SCREAMING_SNAKE_CASE__      ,       msg="""`timesteps` must start before `self.config.train_timesteps`: {scheduler.config.num_train_timesteps}}"""      ,       ):
   scheduler.set_timesteps(timesteps=SCREAMING_SNAKE_CASE__							)







'''simple docstring'''

def      UpperCamelCase_						(					snake_case_       :       Union[str, Any]=2_81_23      )					->     str:






 '''simple docstring'''

 __lowerCAmelCase											=						[1] * (limit + 1)

 for i in range(2						,		int(limit**0.5      ) + 1      ):
  sum_divs[i * i] += i
  for k in range(i + 1						,		limit // i + 1      ):
   sum_divs[k * i] += k + i

 __lowerCAmelCase											=						set()
 __lowerCAmelCase											=						0

 for n in range(1						,		limit + 1      ):
  if sum_divs[n] > n:
   abundants.add(snake_case_      )

  if not any((n - a in abundants) for a in abundants      ):
   res += n

 return res


if __name__ == "__main__":
 print(solution())






