






"""simple docstring"""





import tempfile

import torch

from diffusers import PNDMScheduler

from .test_schedulers import SchedulerCommonTest
class    __lowerCamelCase    (  _a  ):
   a      :				Optional[Any] 						=(PNDMScheduler,)
   a      :				Optional[int] 						=(("""num_inference_steps""", 5_0),)

   def 						SCREAMING_SNAKE_CASE__ (					self ,				**snake_case_      )		->       Optional[int]:
       UpperCamelCase__         =    {
           'num_train_timesteps': 1000,
           'beta_start': 0.0_001,
           'beta_end': 0.02,
           'beta_schedule': 'linear',
       }

       config.update(**snake_case_      )
       return config

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_=0 ,				**snake_case_      )		->       int:
       UpperCamelCase__         =    dict(self.forward_default_kwargs      )
       UpperCamelCase__         =    kwargs.pop('num_inference_steps' ,				snake_case_      )
       UpperCamelCase__         =    self.dummy_sample
       UpperCamelCase__         =    0.1 * sample
       UpperCamelCase__         =    [residual + 0.2, residual + 0.15, residual + 0.1, residual + 0.05]

       for scheduler_class in self.scheduler_classes:
           UpperCamelCase__         =    self.get_scheduler_config(**snake_case_      )
           UpperCamelCase__         =    scheduler_class(**snake_case_      )
           scheduler.set_timesteps(snake_case_      )
           # copy over dummy past residuals
           UpperCamelCase__         =    dummy_past_residuals[:]

           with tempfile.TemporaryDirectory() as tmpdirname:
               scheduler.save_config(snake_case_      )
               UpperCamelCase__         =    scheduler_class.from_pretrained(snake_case_      )
               new_scheduler.set_timesteps(snake_case_      )
               # copy over dummy past residuals
               UpperCamelCase__         =    dummy_past_residuals[:]

           UpperCamelCase__         =    scheduler.step_prk(snake_case_ ,				snake_case_ ,				snake_case_ ,				**snake_case_      ).prev_sample
           UpperCamelCase__         =    new_scheduler.step_prk(snake_case_ ,				snake_case_ ,				snake_case_ ,				**snake_case_      ).prev_sample

           assert torch.sum(torch.abs(output - new_output      )      ) < 1E-5, "Scheduler outputs are not identical"

           UpperCamelCase__         =    scheduler.step_plms(snake_case_ ,				snake_case_ ,				snake_case_ ,				**snake_case_      ).prev_sample
           UpperCamelCase__         =    new_scheduler.step_plms(snake_case_ ,				snake_case_ ,				snake_case_ ,				**snake_case_      ).prev_sample

           assert torch.sum(torch.abs(output - new_output      )      ) < 1E-5, "Scheduler outputs are not identical"

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Optional[Any]:
       pass

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_=0 ,				**snake_case_      )		->       List[str]:
       UpperCamelCase__         =    dict(self.forward_default_kwargs      )
       UpperCamelCase__         =    kwargs.pop('num_inference_steps' ,				snake_case_      )
       UpperCamelCase__         =    self.dummy_sample
       UpperCamelCase__         =    0.1 * sample
       UpperCamelCase__         =    [residual + 0.2, residual + 0.15, residual + 0.1, residual + 0.05]

       for scheduler_class in self.scheduler_classes:
           UpperCamelCase__         =    self.get_scheduler_config()
           UpperCamelCase__         =    scheduler_class(**snake_case_      )
           scheduler.set_timesteps(snake_case_      )

           # copy over dummy past residuals (must be after setting timesteps)
           UpperCamelCase__         =    dummy_past_residuals[:]

           with tempfile.TemporaryDirectory() as tmpdirname:
               scheduler.save_config(snake_case_      )
               UpperCamelCase__         =    scheduler_class.from_pretrained(snake_case_      )
               # copy over dummy past residuals
               new_scheduler.set_timesteps(snake_case_      )

               # copy over dummy past residual (must be after setting timesteps)
               UpperCamelCase__         =    dummy_past_residuals[:]

           UpperCamelCase__         =    scheduler.step_prk(snake_case_ ,				snake_case_ ,				snake_case_ ,				**snake_case_      ).prev_sample
           UpperCamelCase__         =    new_scheduler.step_prk(snake_case_ ,				snake_case_ ,				snake_case_ ,				**snake_case_      ).prev_sample

           assert torch.sum(torch.abs(output - new_output      )      ) < 1E-5, "Scheduler outputs are not identical"

           UpperCamelCase__         =    scheduler.step_plms(snake_case_ ,				snake_case_ ,				snake_case_ ,				**snake_case_      ).prev_sample
           UpperCamelCase__         =    new_scheduler.step_plms(snake_case_ ,				snake_case_ ,				snake_case_ ,				**snake_case_      ).prev_sample

           assert torch.sum(torch.abs(output - new_output      )      ) < 1E-5, "Scheduler outputs are not identical"

   def 						SCREAMING_SNAKE_CASE__ (					self ,				**snake_case_      )		->       Union[str, Any]:
       UpperCamelCase__         =    self.scheduler_classes[0]
       UpperCamelCase__         =    self.get_scheduler_config(**snake_case_      )
       UpperCamelCase__         =    scheduler_class(**snake_case_      )

       UpperCamelCase__         =    10
       UpperCamelCase__         =    self.dummy_model()
       UpperCamelCase__         =    self.dummy_sample_deter
       scheduler.set_timesteps(snake_case_      )

       for i, t in enumerate(scheduler.prk_timesteps      ):
           UpperCamelCase__         =    model(snake_case_ ,				snake_case_      )
           UpperCamelCase__         =    scheduler.step_prk(snake_case_ ,				snake_case_ ,				snake_case_      ).prev_sample

       for i, t in enumerate(scheduler.plms_timesteps      ):
           UpperCamelCase__         =    model(snake_case_ ,				snake_case_      )
           UpperCamelCase__         =    scheduler.step_plms(snake_case_ ,				snake_case_ ,				snake_case_      ).prev_sample

       return sample

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Union[str, Any]:
       UpperCamelCase__         =    dict(self.forward_default_kwargs      )

       UpperCamelCase__         =    kwargs.pop('num_inference_steps' ,				snake_case_      )

       for scheduler_class in self.scheduler_classes:
           UpperCamelCase__         =    self.get_scheduler_config()
           UpperCamelCase__         =    scheduler_class(**snake_case_      )

           UpperCamelCase__         =    self.dummy_sample
           UpperCamelCase__         =    0.1 * sample

           if num_inference_steps is not None and hasattr(snake_case_ ,				'set_timesteps'      ):
               scheduler.set_timesteps(snake_case_      )
           elif num_inference_steps is not None and not hasattr(snake_case_ ,				'set_timesteps'      ):
               UpperCamelCase__         =    num_inference_steps

           # copy over dummy past residuals (must be done after set_timesteps)
           UpperCamelCase__         =    [residual + 0.2, residual + 0.15, residual + 0.1, residual + 0.05]
           UpperCamelCase__         =    dummy_past_residuals[:]

           UpperCamelCase__         =    scheduler.step_prk(snake_case_ ,				0 ,				snake_case_ ,				**snake_case_      ).prev_sample
           UpperCamelCase__         =    scheduler.step_prk(snake_case_ ,				1 ,				snake_case_ ,				**snake_case_      ).prev_sample

           self.assertEqual(output_a.shape ,				sample.shape      )
           self.assertEqual(output_a.shape ,				output_a.shape      )

           UpperCamelCase__         =    scheduler.step_plms(snake_case_ ,				0 ,				snake_case_ ,				**snake_case_      ).prev_sample
           UpperCamelCase__         =    scheduler.step_plms(snake_case_ ,				1 ,				snake_case_ ,				**snake_case_      ).prev_sample

           self.assertEqual(output_a.shape ,				sample.shape      )
           self.assertEqual(output_a.shape ,				output_a.shape      )

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Dict:
       for timesteps in [100, 1000]:
           self.check_over_configs(num_train_timesteps=snake_case_      )

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Any:
       for steps_offset in [0, 1]:
           self.check_over_configs(steps_offset=snake_case_      )

       UpperCamelCase__         =    self.scheduler_classes[0]
       UpperCamelCase__         =    self.get_scheduler_config(steps_offset=1      )
       UpperCamelCase__         =    scheduler_class(**snake_case_      )
       scheduler.set_timesteps(10      )
       assert torch.equal(
           scheduler.timesteps ,				torch.LongTensor(
               [901, 851, 851, 801, 801, 751, 751, 701, 701, 651, 651, 601, 601, 501, 401, 301, 201, 101, 1]      ) ,				)

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Optional[Any]:
       for beta_start, beta_end in zip([0.0_001, 0.001] ,				[0.002, 0.02]      ):
           self.check_over_configs(beta_start=snake_case_ ,				beta_end=snake_case_      )

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       str:
       for schedule in ["linear", "squaredcos_cap_v2"]:
           self.check_over_configs(beta_schedule=snake_case_      )

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Any:
       for prediction_type in ["epsilon", "v_prediction"]:
           self.check_over_configs(prediction_type=snake_case_      )

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Union[str, Any]:
       for t in [1, 5, 10]:
           self.check_over_forward(time_step=snake_case_      )

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Union[str, Any]:
       for t, num_inference_steps in zip([1, 5, 10] ,				[10, 50, 100]      ):
           self.check_over_forward(num_inference_steps=snake_case_      )

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Optional[int]:
       # earlier version of set_timesteps() caused an error indexing alpha's with inference steps as power of 3
       UpperCamelCase__         =    27

       for scheduler_class in self.scheduler_classes:
           UpperCamelCase__         =    self.dummy_sample
           UpperCamelCase__         =    0.1 * sample

           UpperCamelCase__         =    self.get_scheduler_config()
           UpperCamelCase__         =    scheduler_class(**snake_case_      )

           scheduler.set_timesteps(snake_case_      )

           # before power of 3 fix, would error on first step, so we only need to do two
           for i, t in enumerate(scheduler.prk_timesteps[:2]      ):
               UpperCamelCase__         =    scheduler.step_prk(snake_case_ ,				snake_case_ ,				snake_case_      ).prev_sample

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       List[str]:
       with self.assertRaises(snake_case_      ):
           UpperCamelCase__         =    self.scheduler_classes[0]
           UpperCamelCase__         =    self.get_scheduler_config()
           UpperCamelCase__         =    scheduler_class(**snake_case_      )

           scheduler.step_plms(self.dummy_sample ,				1 ,				self.dummy_sample      ).prev_sample

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Dict:
       UpperCamelCase__         =    self.full_loop()
       UpperCamelCase__         =    torch.sum(torch.abs(snake_case_      )      )
       UpperCamelCase__         =    torch.mean(torch.abs(snake_case_      )      )

       assert abs(result_sum.item() - 198.1_318      ) < 1E-2
       assert abs(result_mean.item() - 0.2_580      ) < 1E-3

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Optional[Any]:
       UpperCamelCase__         =    self.full_loop(prediction_type='v_prediction'      )
       UpperCamelCase__         =    torch.sum(torch.abs(snake_case_      )      )
       UpperCamelCase__         =    torch.mean(torch.abs(snake_case_      )      )

       assert abs(result_sum.item() - 67.3_986      ) < 1E-2
       assert abs(result_mean.item() - 0.0_878      ) < 1E-3

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       List[str]:
       # We specify different beta, so that the first alpha is 0.99
       UpperCamelCase__         =    self.full_loop(set_alpha_to_one=snake_case_ ,				beta_start=0.01      )
       UpperCamelCase__         =    torch.sum(torch.abs(snake_case_      )      )
       UpperCamelCase__         =    torch.mean(torch.abs(snake_case_      )      )

       assert abs(result_sum.item() - 230.0_399      ) < 1E-2
       assert abs(result_mean.item() - 0.2_995      ) < 1E-3







   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Union[str, Any]:
       # We specify different beta, so that the first alpha is 0.99
       UpperCamelCase__         =    self.full_loop(set_alpha_to_one=snake_case_ ,				beta_start=0.01      )
       UpperCamelCase__         =    torch.sum(torch.abs(snake_case_      )      )
       UpperCamelCase__         =    torch.mean(torch.abs(snake_case_      )      )

       assert abs(result_sum.item() - 186.9_482      ) < 1E-2
       assert abs(result_mean.item() - 0.2_434      ) < 1E-3












"""simple docstring"""





def   lowerCAmelCase_( SCREAMING_SNAKE_CASE					)					->	bool:
    """simple docstring"""

    UpperCamelCase__         =    (1 + 24 * n) ** 0.5
    return ((1 + root) / 6) % 1 == 0







def   lowerCAmelCase_( SCREAMING_SNAKE_CASE = 50_00					)					->	int:
    """simple docstring"""

    UpperCamelCase__         =    [(i * (3 * i - 1)) // 2 for i in range(1 ,	SCREAMING_SNAKE_CASE					)]
    for i, pentagonal_i in enumerate(SCREAMING_SNAKE_CASE					):
        for j in range(SCREAMING_SNAKE_CASE ,	len(SCREAMING_SNAKE_CASE					)					):
            UpperCamelCase__         =    pentagonal_nums[j]
            UpperCamelCase__         =    pentagonal_i + pentagonal_j
            UpperCamelCase__         =    pentagonal_j - pentagonal_i
            if is_pentagonal(SCREAMING_SNAKE_CASE					) and is_pentagonal(SCREAMING_SNAKE_CASE					):
                return b

    return -1


if __name__ == "__main__":
  print(F"""{solution() = }""")




