





"""simple docstring"""


import torch

from diffusers import DDIMParallelScheduler

from .test_schedulers import SchedulerCommonTest






class 							lowercase__			(   __SCREAMING_SNAKE_CASE	):

			"""simple docstring"""
			__lowerCAmelCase     :				List[Any]										=  (DDIMParallelScheduler,)
			__lowerCAmelCase     :				Optional[Any]										=  (("""eta""", 0.0), ("""num_inference_steps""", 50))







			def   _a      (      self						,   **_A    ):






									'''simple docstring'''







									UpperCamelCase				:		List[str]				   =			{
									    """num_train_timesteps""": 1_0_0_0,
									    """beta_start""": 0.00_01,
									    """beta_end""": 0.02,
									    """beta_schedule""": """linear""",
									    """clip_sample""": True,
									}

									config.update(**_A    )
									return config







			def   _a      (      self						,   **_A    ):






									'''simple docstring'''







									UpperCamelCase				:		Tuple				   =			self.scheduler_classes[0]
									UpperCamelCase				:		Optional[Any]				   =			self.get_scheduler_config(**_A    )
									UpperCamelCase				:		str				   =			scheduler_class(**_A    )

									UpperCamelCase   ,						UpperCamelCase				:		List[Any]				   =			1_0, 0.0

									UpperCamelCase				:		List[Any]				   =			self.dummy_model()
									UpperCamelCase				:		Optional[Any]				   =			self.dummy_sample_deter

									scheduler.set_timesteps(_A    )

									for t in scheduler.timesteps:
															UpperCamelCase				:		List[str]				   =			model(_A						,   _A    )
															UpperCamelCase				:		int				   =			scheduler.step(_A						,   _A						,   _A						,   _A    ).prev_sample

									return sample







			def   _a      (      self    ):






									'''simple docstring'''







									for timesteps in [1_0_0, 5_0_0, 1_0_0_0]:
															self.check_over_configs(num_train_timesteps=_A    )







			def   _a      (      self    ):






									'''simple docstring'''







									for steps_offset in [0, 1]:
															self.check_over_configs(steps_offset=_A    )

									UpperCamelCase				:		Dict				   =			self.scheduler_classes[0]
									UpperCamelCase				:		str				   =			self.get_scheduler_config(steps_offset=1    )
									UpperCamelCase				:		str				   =			scheduler_class(**_A    )
									scheduler.set_timesteps(5    )
									assert torch.equal(scheduler.timesteps						,   torch.LongTensor([8_0_1, 6_0_1, 4_0_1, 2_0_1, 1]    )    )







			def   _a      (      self    ):






									'''simple docstring'''







									for beta_start, beta_end in zip([0.00_01, 0.0_01, 0.01, 0.1]						,   [0.0_02, 0.02, 0.2, 2]    ):
															self.check_over_configs(beta_start=_A						,   beta_end=_A    )







			def   _a      (      self    ):






									'''simple docstring'''







									for schedule in ["linear", "squaredcos_cap_v2"]:
															self.check_over_configs(beta_schedule=_A    )







			def   _a      (      self    ):






									'''simple docstring'''







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







			def   _a      (      self    ):






									'''simple docstring'''







									for clip_sample in [True, False]:
															self.check_over_configs(clip_sample=_A    )







			def   _a      (      self    ):






									'''simple docstring'''







									for timestep_spacing in ["trailing", "leading"]:
															self.check_over_configs(timestep_spacing=_A    )







			def   _a      (      self    ):






									'''simple docstring'''







									for rescale_betas_zero_snr in [True, False]:
															self.check_over_configs(rescale_betas_zero_snr=_A    )







			def   _a      (      self    ):






									'''simple docstring'''







									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   _a      (      self    ):






									'''simple docstring'''







									for t in [1, 1_0, 4_9]:
															self.check_over_forward(time_step=_A    )







			def   _a      (      self    ):






									'''simple docstring'''







									for t, num_inference_steps in zip([1, 1_0, 5_0]						,   [1_0, 5_0, 5_0_0]    ):
															self.check_over_forward(time_step=_A						,   num_inference_steps=_A    )







			def   _a      (      self    ):






									'''simple docstring'''







									for t, eta in zip([1, 1_0, 4_9]						,   [0.0, 0.5, 1.0]    ):
															self.check_over_forward(time_step=_A						,   eta=_A    )







			def   _a      (      self    ):






									'''simple docstring'''







									UpperCamelCase				:		Tuple				   =			self.scheduler_classes[0]
									UpperCamelCase				:		Any				   =			self.get_scheduler_config()
									UpperCamelCase				:		List[Any]				   =			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(4_2_0						,   4_0_0    ) - 0.1_47_71    )    ) < 1e-5
									assert torch.sum(torch.abs(scheduler._get_variance(9_8_0						,   9_6_0    ) - 0.3_24_60    )    ) < 1e-5
									assert torch.sum(torch.abs(scheduler._get_variance(0						,   0    ) - 0.0    )    ) < 1e-5
									assert torch.sum(torch.abs(scheduler._get_variance(4_8_7						,   4_8_6    ) - 0.0_09_79    )    ) < 1e-5
									assert torch.sum(torch.abs(scheduler._get_variance(9_9_9						,   9_9_8    ) - 0.02    )    ) < 1e-5







			def   _a      (      self    ):






									'''simple docstring'''







									UpperCamelCase				:		Dict				   =			self.scheduler_classes[0]
									UpperCamelCase				:		str				   =			self.get_scheduler_config()
									UpperCamelCase				:		List[str]				   =			scheduler_class(**_A    )

									UpperCamelCase   ,						UpperCamelCase				:		List[Any]				   =			1_0, 0.0
									scheduler.set_timesteps(_A    )

									UpperCamelCase				:		Optional[Any]				   =			self.dummy_model()
									UpperCamelCase				:		Union[str, Any]				   =			self.dummy_sample_deter
									UpperCamelCase				:		List[str]				   =			self.dummy_sample_deter + 0.1
									UpperCamelCase				:		List[str]				   =			self.dummy_sample_deter - 0.1

									UpperCamelCase				:		Optional[int]				   =			samplea.shape[0]
									UpperCamelCase				:		Union[str, Any]				   =			torch.stack([samplea, samplea, samplea]						,   dim=0    )
									UpperCamelCase				:		List[Any]				   =			torch.arange(_A    )[0:3, None].repeat(1						,   _A    )

									UpperCamelCase				:		str				   =			model(samples.flatten(0						,   1    )						,   timesteps.flatten(0						,   1    )    )
									UpperCamelCase				:		Optional[Any]				   =			scheduler.batch_step_no_noise(_A						,   timesteps.flatten(0						,   1    )						,   samples.flatten(0						,   1    )						,   _A    )

									UpperCamelCase				:		int				   =			torch.sum(torch.abs(_A    )    )
									UpperCamelCase				:		str				   =			torch.mean(torch.abs(_A    )    )

									assert abs(result_sum.item() - 11_47.79_04    ) < 1e-2
									assert abs(result_mean.item() - 0.49_82    ) < 1e-3







			def   _a      (      self    ):






									'''simple docstring'''







									UpperCamelCase				:		Any				   =			self.full_loop()

									UpperCamelCase				:		str				   =			torch.sum(torch.abs(_A    )    )
									UpperCamelCase				:		List[Any]				   =			torch.mean(torch.abs(_A    )    )

									assert abs(result_sum.item() - 1_72.00_67    ) < 1e-2
									assert abs(result_mean.item() - 0.22_39_67    ) < 1e-3







			def   _a      (      self    ):






									'''simple docstring'''







									UpperCamelCase				:		int				   =			self.full_loop(prediction_type="""v_prediction"""    )

									UpperCamelCase				:		str				   =			torch.sum(torch.abs(_A    )    )
									UpperCamelCase				:		Optional[int]				   =			torch.mean(torch.abs(_A    )    )

									assert abs(result_sum.item() - 52.53_02    ) < 1e-2
									assert abs(result_mean.item() - 0.06_84    ) < 1e-3







			def   _a      (      self    ):






									'''simple docstring'''







									UpperCamelCase				:		str				   =			self.full_loop(set_alpha_to_one=_A						,   beta_start=0.01    )
									UpperCamelCase				:		List[str]				   =			torch.sum(torch.abs(_A    )    )
									UpperCamelCase				:		Optional[Any]				   =			torch.mean(torch.abs(_A    )    )

									assert abs(result_sum.item() - 1_49.82_95    ) < 1e-2
									assert abs(result_mean.item() - 0.19_51    ) < 1e-3







			def   _a      (      self    ):






									'''simple docstring'''







									UpperCamelCase				:		Optional[Any]				   =			self.full_loop(set_alpha_to_one=_A						,   beta_start=0.01    )
									UpperCamelCase				:		Dict				   =			torch.sum(torch.abs(_A    )    )
									UpperCamelCase				:		str				   =			torch.mean(torch.abs(_A    )    )

									assert abs(result_sum.item() - 1_49.07_84    ) < 1e-2
									assert abs(result_mean.item() - 0.19_41    ) < 1e-3










"""simple docstring"""


from math import ceil, sqrt

def      UpperCamelCase							(SCREAMING_SNAKE_CASE = 100_0000     ):
						UpperCamelCase				:		int				   =			0

						for outer_width in range(3							,     (limit // 4) + 2     ):
												if outer_width**2 > limit:
																		UpperCamelCase				:		Optional[Any]				   =			max(ceil(sqrt(outer_width**2 - limit     )     )							,     1     )
												else:
																		UpperCamelCase				:		str				   =			1
												if (outer_width - hole_width_lower_bound) % 2:
																		hole_width_lower_bound += 1

												answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

						return answer


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



