code: 
  
  
  '''simple docstring'''
  
  
  
  from __future__ import annotations
  
  
  
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     int		,   _SCREAMING_SNAKE_CASE   :     int		,   _SCREAMING_SNAKE_CASE   :     int     ):
  					assert n > 1 and a > 0 and greatest_common_divisor(_SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE     ) == 1
  					(__a)    : List[Any]      					=						extended_gcd(_SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE     )  # Implemented below
  					__a    : Dict      					=						(b * s) % n
  					return x
  
  
  
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     int		,   _SCREAMING_SNAKE_CASE   :     int     ):
  					(__a)    : int      					=						extended_euclid(_SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE     )  # Implemented below
  					if b < 0:
  										__a    : Dict      					=						(b % n + n) % n
  					return b
  
  
  
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     int		,   _SCREAMING_SNAKE_CASE   :     int		,   _SCREAMING_SNAKE_CASE   :     int     ):
  					__a    : Dict      					=						invert_modulo(_SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE     )
  					__a    : str      					=						(b * s) % n
  					return x
  
  
  
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     int		,   _SCREAMING_SNAKE_CASE   :     int     ):
  					assert a >= 0 and b >= 0
  
  					if b == 0:
  										__a    : Optional[int]      					=						a, 1, 0
  					else:
  										(__a)    : str      					=						extended_gcd(_SCREAMING_SNAKE_CASE		,   a % b     )
  										__a    : List[Any]      					=						q
  										__a    : List[str]      					=						p - q * (a // b)
  
  					assert a % d == 0 and b % d == 0
  					assert d == a * x + b * y
  
  					return (d, x, y)
  
  
  
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     int		,   _SCREAMING_SNAKE_CASE   :     int     ):
  
  
  
  					if b == 0:
  										return (1, 0)
  					(__a)    : str      					=						extended_euclid(_SCREAMING_SNAKE_CASE		,   a % b     )
  					__a    : Union[str, Any]      					=						a // b
  					return (y, x - k * y)
  
  
  
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     int		,   _SCREAMING_SNAKE_CASE   :     int     ):
  
  
  
  					if a < b:
  										__a    : Any      					=						b, a
  
  					while a % b != 0:
  										__a    : List[str]      					=						b, a % b
  
  					return b
  
  
  if __name__ == "__main__":
  	from doctest import testmod
  
  	testmod(name='modular_division', verbose=True)
  	testmod(name='modular_division2', verbose=True)
  	testmod(name='invert_modulo', verbose=True)
  	testmod(name='extended_gcd', verbose=True)
  	testmod(name='extended_euclid', verbose=True)
  	testmod(name='greatest_common_divisor', verbose=True)
  
  
  
  
style_context: 
  
  
  '''simple docstring'''
  
  
  
  import torch
  
  from diffusers import KDPMaAncestralDiscreteScheduler
  from diffusers.utils import torch_device
  
  from .test_schedulers import SchedulerCommonTest
  
  
  
  
  
  class 							__UpperCamelCase       (	lowerCAmelCase_      ):
  	A_			    =					(KDPMaAncestralDiscreteScheduler,)
  	A_			    =					10
  
  
  
  
  	def    __UpperCAmelCase							(     self		,       **__a							):
  
  						'''simple docstring'''
  
  
  
  
  
  						__a    : Dict      					=						{
  						    'num_train_timesteps': 1100,
  						    'beta_start': 0.0001,
  						    'beta_end': 0.02,
  						    'beta_schedule': 'linear',
  						}
  
  						config.update(**__a							)
  						return config
  
  
  
  
  	def    __UpperCAmelCase							(     self							):
  
  						'''simple docstring'''
  
  
  
  
  
  						for timesteps in [10, 50, 100, 1000]:
  											self.check_over_configs(num_train_timesteps=__a							)
  
  
  
  
  	def    __UpperCAmelCase							(     self							):
  
  						'''simple docstring'''
  
  
  
  
  
  						for beta_start, beta_end in zip([0.00001, 0.0001, 0.001]		,       [0.0002, 0.002, 0.02]							):
  											self.check_over_configs(beta_start=__a		,       beta_end=__a							)
  
  
  
  
  	def    __UpperCAmelCase							(     self							):
  
  						'''simple docstring'''
  
  
  
  
  
  						for schedule in ["linear", "scaled_linear"]:
  											self.check_over_configs(beta_schedule=__a							)
  
  
  
  
  	def    __UpperCAmelCase							(     self							):
  
  						'''simple docstring'''
  
  
  
  
  
  						if torch_device == "mps":
  											return
  						__a    : Dict      					=						self.scheduler_classes[0]
  						__a    : Tuple      					=						self.get_scheduler_config()
  						__a    : Optional[int]      					=						scheduler_class(**__a							)
  
  						scheduler.set_timesteps(self.num_inference_steps							)
  
  						__a    : int      					=						torch.manual_seed(0							)
  
  						__a    : Dict      					=						self.dummy_model()
  						__a    : List[Any]      					=						self.dummy_sample_deter * scheduler.init_noise_sigma
  						__a    : int      					=						sample.to(__a							)
  
  						for i, t in enumerate(scheduler.timesteps							):
  											__a    : Any      					=						scheduler.scale_model_input(__a		,       __a							)
  
  											__a    : int      					=						model(__a		,       __a							)
  
  											__a    : Dict      					=						scheduler.step(__a		,       __a		,       __a		,       generator=__a							)
  											__a    : int      					=						output.prev_sample
  
  						__a    : Tuple      					=						torch.sum(torch.abs(__a							)							)
  						__a    : List[str]      					=						torch.mean(torch.abs(__a							)							)
  
  						assert abs(result_sum.item() - 13849.3877							) < 1E-2
  						assert abs(result_mean.item() - 18.0331							) < 5E-3
  
  
  
  
  	def    __UpperCAmelCase							(     self							):
  
  						'''simple docstring'''
  
  
  
  
  
  						for prediction_type in ["epsilon", "v_prediction"]:
  											self.check_over_configs(prediction_type=__a							)
  
  
  
  
  	def    __UpperCAmelCase							(     self							):
  
  						'''simple docstring'''
  
  
  
  
  
  						if torch_device == "mps":
  											return
  						__a    : Dict      					=						self.scheduler_classes[0]
  						__a    : Dict      					=						self.get_scheduler_config(prediction_type='v_prediction'							)
  						__a    : List[str]      					=						scheduler_class(**__a							)
  
  						scheduler.set_timesteps(self.num_inference_steps							)
  
  						__a    : Dict      					=						self.dummy_model()
  						__a    : List[str]      					=						self.dummy_sample_deter * scheduler.init_noise_sigma
  						__a    : List[str]      					=						sample.to(__a							)
  
  						__a    : Tuple      					=						torch.manual_seed(0							)
  
  						for i, t in enumerate(scheduler.timesteps							):
  											__a    : List[Any]      					=						scheduler.scale_model_input(__a		,       __a							)
  
  											__a    : Optional[int]      					=						model(__a		,       __a							)
  
  											__a    : Union[str, Any]      					=						scheduler.step(__a		,       __a		,       __a		,       generator=__a							)
  											__a    : Union[str, Any]      					=						output.prev_sample
  
  						__a    : Any      					=						torch.sum(torch.abs(__a							)							)
  						__a    : Optional[int]      					=						torch.mean(torch.abs(__a							)							)
  
  						assert abs(result_sum.item() - 328.9970							) < 1E-2
  						assert abs(result_mean.item() - 0.4284							) < 1E-3
  
  
  
  
  
  	def    __UpperCAmelCase							(     self							):
  
  						'''simple docstring'''
  
  
  
  
  
  						if torch_device == "mps":
  											return
  						__a    : List[str]      					=						self.scheduler_classes[0]
  						__a    : Union[str, Any]      					=						self.get_scheduler_config()
  						__a    : List[Any]      					=						scheduler_class(**__a							)
  
  						scheduler.set_timesteps(self.num_inference_steps		,       device=__a							)
  						__a    : Union[str, Any]      					=						torch.manual_seed(0							)
  
  						__a    : List[str]      					=						self.dummy_model()
  						__a    : Any      					=						self.dummy_sample_deter.to(__a							) * scheduler.init_noise_sigma
  
  						for t in scheduler.timesteps:
  											__a    : List[Any]      					=						scheduler.scale_model_input(__a		,       __a							)
  
  											__a    : str      					=						model(__a		,       __a							)
  
  											__a    : str      					=						scheduler.step(__a		,       __a		,       __a		,       generator=__a							)
  											__a    : Any      					=						output.prev_sample
  
  						__a    : Union[str, Any]      					=						torch.sum(torch.abs(__a							)							)
  						__a    : str      					=						torch.mean(torch.abs(__a							)							)
  
  						assert abs(result_sum.item() - 13849.3818							) < 1E-1
  						assert abs(result_mean.item() - 18.0331							) < 1E-3
  
  
  
  