




'''simple docstring'''




import torch

from diffusers import DDIMScheduler

from .test_schedulers import SchedulerCommonTest






class      UpperCamelCase_  (_UpperCamelCase  ):







						"""simple docstring"""


						_lowerCAmelCase         =       (DDIMScheduler,)
						_lowerCAmelCase         =       (('eta', 0.0), ('num_inference_steps', 5_0))







						def    _a     (  self   :							Dict				,			**_lowerCamelCase   :							List[Any]     ):





											"""simple docstring"""







											A_			:  Any			=				{
											    '''num_train_timesteps''': 1000,
											    '''beta_start''': 0.00_01,
											    '''beta_end''': 0.02,
											    '''beta_schedule''': '''linear''',
											    '''clip_sample''': True,
											}

											config.update(**_SCREAMING_SNAKE_CASE     )
											return config







						def    _a     (  self   :							List[str]				,			**_lowerCamelCase   :							Tuple     ):





											"""simple docstring"""







											A_			:  int			=				self.scheduler_classes[0]
											A_			:  Optional[Any]			=				self.get_scheduler_config(**_SCREAMING_SNAKE_CASE     )
											A_			:  List[Any]			=				scheduler_class(**_SCREAMING_SNAKE_CASE     )

											A_			,A_			:  int			=				10, 0.0

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

											scheduler.set_timesteps(_SCREAMING_SNAKE_CASE     )

											for t in scheduler.timesteps:
																A_			:  Union[str, Any]			=				model(_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE     )
																A_			:  Dict			=				scheduler.step(_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE				,			_SCREAMING_SNAKE_CASE     ).prev_sample

											return sample







						def    _a     (  self   :							int     ):





											"""simple docstring"""







											for timesteps in [100, 500, 1000]:
																self.check_over_configs(num_train_timesteps=_SCREAMING_SNAKE_CASE     )







						def    _a     (  self   :							List[Any]     ):





											"""simple docstring"""







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

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







						def    _a     (  self   :							Union[str, Any]     ):





											"""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=_SCREAMING_SNAKE_CASE				,			beta_end=_SCREAMING_SNAKE_CASE     )







						def    _a     (  self   :							str     ):





											"""simple docstring"""







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







						def    _a     (  self   :							str     ):





											"""simple docstring"""







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







						def    _a     (  self   :							Tuple     ):





											"""simple docstring"""







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







						def    _a     (  self   :							Dict     ):





											"""simple docstring"""







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







						def    _a     (  self   :							Union[str, Any]     ):





											"""simple docstring"""







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







						def    _a     (  self   :							Optional[int]     ):





											"""simple docstring"""







											self.check_over_configs(thresholding=_SCREAMING_SNAKE_CASE     )
											for threshold in [0.5, 1.0, 2.0]:
																for prediction_type in ["epsilon", "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     ):





											"""simple docstring"""







											for t in [1, 10, 49]:
																self.check_over_forward(time_step=_SCREAMING_SNAKE_CASE     )







						def    _a     (  self   :							int     ):





											"""simple docstring"""







											for t, num_inference_steps in zip([1, 10, 50]				,			[10, 50, 500]     ):
																self.check_over_forward(time_step=_SCREAMING_SNAKE_CASE				,			num_inference_steps=_SCREAMING_SNAKE_CASE     )







						def    _a     (  self   :							Dict     ):





											"""simple docstring"""







											for t, eta in zip([1, 10, 49]				,			[0.0, 0.5, 1.0]     ):
																self.check_over_forward(time_step=_SCREAMING_SNAKE_CASE				,			eta=_SCREAMING_SNAKE_CASE     )







						def    _a     (  self   :							Any     ):





											"""simple docstring"""







											A_			:  List[Any]			=				self.scheduler_classes[0]
											A_			:  Union[str, Any]			=				self.get_scheduler_config()
											A_			:  str			=				scheduler_class(**_SCREAMING_SNAKE_CASE     )

											assert torch.sum(torch.abs(scheduler._get_variance(0				,			0     ) - 0.0     )     ) < 1E-5
											assert torch.sum(torch.abs(scheduler._get_variance(420				,			400     ) - 0.1_47_71     )     ) < 1E-5
											assert torch.sum(torch.abs(scheduler._get_variance(980				,			960     ) - 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(487				,			486     ) - 0.0_09_79     )     ) < 1E-5
											assert torch.sum(torch.abs(scheduler._get_variance(999				,			998     ) - 0.02     )     ) < 1E-5







						def    _a     (  self   :							str     ):





											"""simple docstring"""







											A_			:  str			=				self.full_loop()

											A_			:  str			=				torch.sum(torch.abs(_SCREAMING_SNAKE_CASE     )     )
											A_			:  Tuple			=				torch.mean(torch.abs(_SCREAMING_SNAKE_CASE     )     )

											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   :							Any     ):





											"""simple docstring"""







											A_			:  Optional[int]			=				self.full_loop(prediction_type='''v_prediction'''     )

											A_			:  str			=				torch.sum(torch.abs(_SCREAMING_SNAKE_CASE     )     )
											A_			:  Tuple			=				torch.mean(torch.abs(_SCREAMING_SNAKE_CASE     )     )

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







						def    _a     (  self   :							Any     ):





											"""simple docstring"""







											A_			:  List[str]			=				self.full_loop(set_alpha_to_one=_SCREAMING_SNAKE_CASE				,			beta_start=0.01     )
											A_			:  List[str]			=				torch.sum(torch.abs(_SCREAMING_SNAKE_CASE     )     )
											A_			:  Union[str, Any]			=				torch.mean(torch.abs(_SCREAMING_SNAKE_CASE     )     )

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







						def    _a     (  self   :							List[str]     ):





											"""simple docstring"""







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

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




'''simple docstring'''




import itertools





def 	_UpperCAmelCase       (				_UpperCamelCase       :      int = 1_00_00_00  )      -> int:
    A_      =  [1]

    for i in itertools.count(len(_UpperCamelCase  )  ):
        A_      =  0
        for j in itertools.count(1  ):
            A_      =  -1 if j % 2 == 0 else +1
            A_      =  (j * j * 3 - j) // 2
            if index > i:
                break
            item += partitions[i - index] * sign
            item %= number
            index += j
            if index > i:
                break
            item += partitions[i - index] * sign
            item %= number

        if item == 0:
            return i
        partitions.append(_UpperCamelCase  )

    return 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  print(F"""{solution() = }""")






