
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int				)			->						int:
       assert isinstance(UpperCAmelCase_			,							UpperCAmelCase_				), f'The input value of [n={number}] is not an integer'

       if number == 1:
              return 2
       elif number < 1:
              SCREAMING_SNAKE_CASE_							:				Optional[Any]		=f'The input value of [n={number}] has to be > 0'
              raise ValueError(UpperCAmelCase_				)
       else:
              SCREAMING_SNAKE_CASE_							:				List[Any]		=sylvester(number - 1				)
              SCREAMING_SNAKE_CASE_							:				str		=num - 1
              SCREAMING_SNAKE_CASE_							:				List[str]		=num
              return lower * upper + 1


if __name__ == "__main__":
 print(F"The 8th number in Sylvester's sequence: {sylvester(8)}")


import torch

from diffusers import DDIMParallelScheduler

from .test_schedulers import SchedulerCommonTest


class 			lowercase_		(      A       ):
       __lowerCamelCase				       =						(DDIMParallelScheduler,)
       __lowerCamelCase				       =						(("eta", 0.0), ("num_inference_steps", 5_0))


       def 	_snake_case				(    self						,       **__A				)						->    List[str]:
              SCREAMING_SNAKE_CASE_							:				Optional[Any]		={
                  '''num_train_timesteps''': 1_000,
                  '''beta_start''': 0.0_001,
                  '''beta_end''': 0.02,
                  '''beta_schedule''': '''linear''',
                  '''clip_sample''': True,
              }

              config.update(**__A				)
              return config


       def 	_snake_case				(    self						,       **__A				)						->    List[Any]:
              SCREAMING_SNAKE_CASE_							:				int		=self.scheduler_classes[0]
              SCREAMING_SNAKE_CASE_							:				str		=self.get_scheduler_config(**__A				)
              SCREAMING_SNAKE_CASE_							:				List[Any]		=scheduler_class(**__A				)

              SCREAMING_SNAKE_CASE_	,     SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=10, 0.0

              SCREAMING_SNAKE_CASE_							:				List[str]		=self.dummy_model()
              SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=self.dummy_sample_deter

              scheduler.set_timesteps(__A				)

              for t in scheduler.timesteps:
                     SCREAMING_SNAKE_CASE_							:				Optional[int]		=model(__A						,       __A				)
                     SCREAMING_SNAKE_CASE_							:				List[Any]		=scheduler.step(__A						,       __A						,       __A						,       __A				).prev_sample

              return sample


       def 	_snake_case				(    self				)						->    Optional[Any]:
              for timesteps in [100, 500, 1_000]:
                     self.check_over_configs(num_train_timesteps=__A				)


       def 	_snake_case				(    self				)						->    Optional[int]:
              for steps_offset in [0, 1]:
                     self.check_over_configs(steps_offset=__A				)

              SCREAMING_SNAKE_CASE_							:				Dict		=self.scheduler_classes[0]
              SCREAMING_SNAKE_CASE_							:				Optional[Any]		=self.get_scheduler_config(steps_offset=1				)
              SCREAMING_SNAKE_CASE_							:				Dict		=scheduler_class(**__A				)
              scheduler.set_timesteps(5				)
              assert torch.equal(scheduler.timesteps						,       torch.LongTensor([801, 601, 401, 201, 1]				)				)


       def 	_snake_case				(    self				)						->    Dict:
              for beta_start, beta_end in zip([0.0_001, 0.001, 0.01, 0.1]						,       [0.002, 0.02, 0.2, 2]				):
                     self.check_over_configs(beta_start=__A						,       beta_end=__A				)


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


       def 	_snake_case				(    self				)						->    List[str]:
              for prediction_type in ["epsilon", "v_prediction"]:
                     self.check_over_configs(prediction_type=__A				)


       def 	_snake_case				(    self				)						->    List[Any]:
              for clip_sample in [True, False]:
                     self.check_over_configs(clip_sample=__A				)


       def 	_snake_case				(    self				)						->    int:
              for timestep_spacing in ["trailing", "leading"]:
                     self.check_over_configs(timestep_spacing=__A				)


       def 	_snake_case				(    self				)						->    Tuple:
              for rescale_betas_zero_snr in [True, False]:
                     self.check_over_configs(rescale_betas_zero_snr=__A				)


       def 	_snake_case				(    self				)						->    List[Any]:
              self.check_over_configs(thresholding=__A				)
              for threshold in [0.5, 1.0, 2.0]:
                     for prediction_type in ["epsilon", "v_prediction"]:
                            self.check_over_configs(
                                thresholding=__A						,       prediction_type=__A						,       sample_max_value=__A						,       )


       def 	_snake_case				(    self				)						->    Dict:
              for t in [1, 10, 49]:
                     self.check_over_forward(time_step=__A				)


       def 	_snake_case				(    self				)						->    Dict:
              for t, num_inference_steps in zip([1, 10, 50]						,       [10, 50, 500]				):
                     self.check_over_forward(time_step=__A						,       num_inference_steps=__A				)


       def 	_snake_case				(    self				)						->    int:
              for t, eta in zip([1, 10, 49]						,       [0.0, 0.5, 1.0]				):
                     self.check_over_forward(time_step=__A						,       eta=__A				)


       def 	_snake_case				(    self				)						->    Optional[int]:
              SCREAMING_SNAKE_CASE_							:				List[Any]		=self.scheduler_classes[0]
              SCREAMING_SNAKE_CASE_							:				List[str]		=self.get_scheduler_config()
              SCREAMING_SNAKE_CASE_							:				List[str]		=scheduler_class(**__A				)

              assert torch.sum(torch.abs(scheduler._get_variance(0						,       0				) - 0.0				)				) < 1e-5
              assert torch.sum(torch.abs(scheduler._get_variance(420						,       400				) - 0.14_771				)				) < 1e-5
              assert torch.sum(torch.abs(scheduler._get_variance(980						,       960				) - 0.32_460				)				) < 1e-5
              assert torch.sum(torch.abs(scheduler._get_variance(0						,       0				) - 0.0				)				) < 1e-5
              assert torch.sum(torch.abs(scheduler._get_variance(487						,       486				) - 0.00_979				)				) < 1e-5
              assert torch.sum(torch.abs(scheduler._get_variance(999						,       998				) - 0.02				)				) < 1e-5


       def 	_snake_case				(    self				)						->    Union[str, Any]:
              SCREAMING_SNAKE_CASE_							:				List[str]		=self.scheduler_classes[0]
              SCREAMING_SNAKE_CASE_							:				List[str]		=self.get_scheduler_config()
              SCREAMING_SNAKE_CASE_							:				str		=scheduler_class(**__A				)

              SCREAMING_SNAKE_CASE_	,     SCREAMING_SNAKE_CASE_							:				List[str]		=10, 0.0
              scheduler.set_timesteps(__A				)

              SCREAMING_SNAKE_CASE_							:				List[str]		=self.dummy_model()
              SCREAMING_SNAKE_CASE_							:				str		=self.dummy_sample_deter
              SCREAMING_SNAKE_CASE_							:				int		=self.dummy_sample_deter + 0.1
              SCREAMING_SNAKE_CASE_							:				Tuple		=self.dummy_sample_deter - 0.1

              SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=samplea.shape[0]
              SCREAMING_SNAKE_CASE_							:				List[str]		=torch.stack([samplea, samplea, samplea]						,       dim=0				)
              SCREAMING_SNAKE_CASE_							:				Any		=torch.arange(__A				)[0:3, None].repeat(1						,       __A				)

              SCREAMING_SNAKE_CASE_							:				Dict		=model(samples.flatten(0						,       1				)						,       timesteps.flatten(0						,       1				)				)
              SCREAMING_SNAKE_CASE_							:				Optional[int]		=scheduler.batch_step_no_noise(__A						,       timesteps.flatten(0						,       1				)						,       samples.flatten(0						,       1				)						,       __A				)

              SCREAMING_SNAKE_CASE_							:				str		=torch.sum(torch.abs(__A				)				)
              SCREAMING_SNAKE_CASE_							:				int		=torch.mean(torch.abs(__A				)				)

              assert abs(result_sum.item() - 1_147.7_904				) < 1e-2
              assert abs(result_mean.item() - 0.4_982				) < 1e-3


       def 	_snake_case				(    self				)						->    Any:
              SCREAMING_SNAKE_CASE_							:				List[str]		=self.full_loop()

              SCREAMING_SNAKE_CASE_							:				List[Any]		=torch.sum(torch.abs(__A				)				)
              SCREAMING_SNAKE_CASE_							:				Optional[Any]		=torch.mean(torch.abs(__A				)				)

              assert abs(result_sum.item() - 172.0_067				) < 1e-2
              assert abs(result_mean.item() - 0.223_967				) < 1e-3


       def 	_snake_case				(    self				)						->    Optional[Any]:
              SCREAMING_SNAKE_CASE_							:				str		=self.full_loop(prediction_type='''v_prediction'''				)

              SCREAMING_SNAKE_CASE_							:				List[Any]		=torch.sum(torch.abs(__A				)				)
              SCREAMING_SNAKE_CASE_							:				str		=torch.mean(torch.abs(__A				)				)

              assert abs(result_sum.item() - 52.5_302				) < 1e-2
              assert abs(result_mean.item() - 0.0_684				) < 1e-3


       def 	_snake_case				(    self				)						->    Dict:
              # We specify different beta, so that the first alpha is 0.99
              SCREAMING_SNAKE_CASE_							:				Tuple		=self.full_loop(set_alpha_to_one=__A						,       beta_start=0.01				)
              SCREAMING_SNAKE_CASE_							:				Tuple		=torch.sum(torch.abs(__A				)				)
              SCREAMING_SNAKE_CASE_							:				int		=torch.mean(torch.abs(__A				)				)

              assert abs(result_sum.item() - 149.8_295				) < 1e-2
              assert abs(result_mean.item() - 0.1_951				) < 1e-3





       def 	_snake_case				(    self				)						->    Optional[Any]:
              # We specify different beta, so that the first alpha is 0.99
              SCREAMING_SNAKE_CASE_							:				List[str]		=self.full_loop(set_alpha_to_one=__A						,       beta_start=0.01				)
              SCREAMING_SNAKE_CASE_							:				Optional[int]		=torch.sum(torch.abs(__A				)				)
              SCREAMING_SNAKE_CASE_							:				Tuple		=torch.mean(torch.abs(__A				)				)

              assert abs(result_sum.item() - 149.0_784				) < 1e-2
              assert abs(result_mean.item() - 0.1_941				) < 1e-3
