
'''simple docstring'''







import torch

from diffusers import DPMSolverSDEScheduler
from diffusers.utils import torch_device
from diffusers.utils.testing_utils import require_torchsde

from .test_schedulers import SchedulerCommonTest






@require_torchsde
class  lowerCAmelCase__   (  _UpperCAmelCase     ):
					lowerCAmelCase_        =     (DPMSolverSDEScheduler,)
					lowerCAmelCase_        =     1_0






					def 	_snake_case    (   self				,							**__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											lowercase_	:     List[Any]													=       {
											    'num_train_timesteps': 11_00,
											    'beta_start': 0.0_001,
											    'beta_end': 0.02,
											    'beta_schedule': 'linear',
											    'noise_sampler_seed': 0,
											}

											config.update(**SCREAMING_SNAKE_CASE_		)
											return config






					def 	_snake_case    (   self		):


											"""simple docstring"""





											for timesteps in [10, 50, 1_00, 10_00]:
																	self.check_over_configs(num_train_timesteps=SCREAMING_SNAKE_CASE_		)






					def 	_snake_case    (   self		):


											"""simple docstring"""





											for beta_start, beta_end in zip([0.00_001, 0.0_001, 0.001]				,							[0.0_002, 0.002, 0.02]		):
																	self.check_over_configs(beta_start=SCREAMING_SNAKE_CASE_				,							beta_end=SCREAMING_SNAKE_CASE_		)






					def 	_snake_case    (   self		):


											"""simple docstring"""





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






					def 	_snake_case    (   self		):


											"""simple docstring"""





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






					def 	_snake_case    (   self		):


											"""simple docstring"""





											lowercase_	:     str													=       self.scheduler_classes[0]
											lowercase_	:     List[Any]													=       self.get_scheduler_config()
											lowercase_	:     int													=       scheduler_class(**SCREAMING_SNAKE_CASE_		)

											scheduler.set_timesteps(self.num_inference_steps		)

											lowercase_	:     Optional[int]													=       self.dummy_model()
											lowercase_	:     Any													=       self.dummy_sample_deter * scheduler.init_noise_sigma
											lowercase_	:     List[str]													=       sample.to(SCREAMING_SNAKE_CASE_		)

											for i, t in enumerate(scheduler.timesteps		):
																	lowercase_	:     List[str]													=       scheduler.scale_model_input(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		)

																	lowercase_	:     int													=       model(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		)

																	lowercase_	:     Optional[int]													=       scheduler.step(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		)
																	lowercase_	:     Optional[int]													=       output.prev_sample

											lowercase_	:     Tuple													=       torch.sum(torch.abs(SCREAMING_SNAKE_CASE_		)		)
											lowercase_	:     List[Any]													=       torch.mean(torch.abs(SCREAMING_SNAKE_CASE_		)		)

											if torch_device in ["mps"]:
																	assert abs(result_sum.item() - 1_67.47_82_10_44_92_18_75		) < 1E-2
																	assert abs(result_mean.item() - 0.2_178_705_964_565_277		) < 1E-3
											elif torch_device in ["cuda"]:
																	assert abs(result_sum.item() - 1_71.59_35_21_11_81_64_06		) < 1E-2
																	assert abs(result_mean.item() - 0.22_342_906_892_299_652		) < 1E-3
											else:
																	assert abs(result_sum.item() - 1_62.52_38_34_22_85_15_62		) < 1E-2
																	assert abs(result_mean.item() - 0.211_619_570_851_326		) < 1E-3






					def 	_snake_case    (   self		):


											"""simple docstring"""





											lowercase_	:     Any													=       self.scheduler_classes[0]
											lowercase_	:     Optional[int]													=       self.get_scheduler_config(prediction_type='''v_prediction'''		)
											lowercase_	:     Dict													=       scheduler_class(**SCREAMING_SNAKE_CASE_		)

											scheduler.set_timesteps(self.num_inference_steps		)

											lowercase_	:     Tuple													=       self.dummy_model()
											lowercase_	:     Optional[int]													=       self.dummy_sample_deter * scheduler.init_noise_sigma
											lowercase_	:     Tuple													=       sample.to(SCREAMING_SNAKE_CASE_		)

											for i, t in enumerate(scheduler.timesteps		):
																	lowercase_	:     Any													=       scheduler.scale_model_input(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		)

																	lowercase_	:     Optional[Any]													=       model(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		)

																	lowercase_	:     List[str]													=       scheduler.step(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		)
																	lowercase_	:     Optional[Any]													=       output.prev_sample

											lowercase_	:     Union[str, Any]													=       torch.sum(torch.abs(SCREAMING_SNAKE_CASE_		)		)
											lowercase_	:     List[str]													=       torch.mean(torch.abs(SCREAMING_SNAKE_CASE_		)		)

											if torch_device in ["mps"]:
																	assert abs(result_sum.item() - 1_24.77_14_92_00_43_94_53		) < 1E-2
																	assert abs(result_mean.item() - 0.16_226_289_014_816_284		) < 1E-3
											elif torch_device in ["cuda"]:
																	assert abs(result_sum.item() - 1_28.1_66_33_60_59_57_03		) < 1E-2
																	assert abs(result_mean.item() - 0.16_688_326_001_167_297		) < 1E-3
											else:
																	assert abs(result_sum.item() - 1_19.8_48_75_48_82_81_25		) < 1E-2
																	assert abs(result_mean.item() - 0.1_560_530_662_536_621		) < 1E-3






					def 	_snake_case    (   self		):


											"""simple docstring"""





											lowercase_	:     Tuple													=       self.scheduler_classes[0]
											lowercase_	:     Any													=       self.get_scheduler_config()
											lowercase_	:     Union[str, Any]													=       scheduler_class(**SCREAMING_SNAKE_CASE_		)

											scheduler.set_timesteps(self.num_inference_steps				,							device=SCREAMING_SNAKE_CASE_		)

											lowercase_	:     Any													=       self.dummy_model()
											lowercase_	:     Optional[Any]													=       self.dummy_sample_deter.to(SCREAMING_SNAKE_CASE_		) * scheduler.init_noise_sigma

											for t in scheduler.timesteps:
																	lowercase_	:     List[str]													=       scheduler.scale_model_input(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		)

																	lowercase_	:     Any													=       model(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		)

																	lowercase_	:     Optional[Any]													=       scheduler.step(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		)
																	lowercase_	:     Dict													=       output.prev_sample

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

											if torch_device in ["mps"]:
																	assert abs(result_sum.item() - 1_67.46_95_73_97_46_09_38		) < 1E-2
																	assert abs(result_mean.item() - 0.21_805_934_607_982_635		) < 1E-3
											elif torch_device in ["cuda"]:
																	assert abs(result_sum.item() - 1_71.59_35_36_37_69_53_12		) < 1E-2
																	assert abs(result_mean.item() - 0.22_342_908_382_415_771		) < 1E-3
											else:
																	assert abs(result_sum.item() - 1_62.52_38_34_22_85_15_62		) < 1E-2
																	assert abs(result_mean.item() - 0.211_619_570_851_326		) < 1E-3






					def 	_snake_case    (   self		):


											"""simple docstring"""





											lowercase_	:     int													=       self.scheduler_classes[0]
											lowercase_	:     Union[str, Any]													=       self.get_scheduler_config()
											lowercase_	:     Tuple													=       scheduler_class(**SCREAMING_SNAKE_CASE_				,							use_karras_sigmas=SCREAMING_SNAKE_CASE_		)

											scheduler.set_timesteps(self.num_inference_steps				,							device=SCREAMING_SNAKE_CASE_		)

											lowercase_	:     Optional[int]													=       self.dummy_model()
											lowercase_	:     int													=       self.dummy_sample_deter.to(SCREAMING_SNAKE_CASE_		) * scheduler.init_noise_sigma
											lowercase_	:     Union[str, Any]													=       sample.to(SCREAMING_SNAKE_CASE_		)

											for t in scheduler.timesteps:
																	lowercase_	:     Dict													=       scheduler.scale_model_input(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		)

																	lowercase_	:     Dict													=       model(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		)

																	lowercase_	:     str													=       scheduler.step(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		)
																	lowercase_	:     int													=       output.prev_sample

											lowercase_	:     Union[str, Any]													=       torch.sum(torch.abs(SCREAMING_SNAKE_CASE_		)		)
											lowercase_	:     Optional[int]													=       torch.mean(torch.abs(SCREAMING_SNAKE_CASE_		)		)

											if torch_device in ["mps"]:
																	assert abs(result_sum.item() - 1_76.66_97_41_35_74_21_88		) < 1E-2
																	assert abs(result_mean.item() - 0.23_003_872_730_981_811		) < 1E-2
											elif torch_device in ["cuda"]:
																	assert abs(result_sum.item() - 1_77.63_65_35_64_45_31_25		) < 1E-2
																	assert abs(result_mean.item() - 0.23_003_872_730_981_811		) < 1E-2
											else:
																	assert abs(result_sum.item() - 1_70.3_13_52_23_38_86_72		) < 1E-2
																	assert abs(result_mean.item() - 0.23_003_872_730_981_811		) < 1E-2







'''simple docstring'''



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				List[Any]							)     ->		str:
     __lowerCamelCase   :	Tuple								=		0
     __lowerCamelCase   :	Optional[int]								=		len(UpperCAmelCase_							)

     for i in range(n - 1							):
          for j in range(i + 1      ,    UpperCAmelCase_							):
               if arr[i] > arr[j]:
                    num_inversions += 1

     return num_inversions



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				str							)     ->		Optional[int]:
     if len(UpperCAmelCase_							) <= 1:
          return arr, 0
     __lowerCamelCase   :	str								=		len(UpperCAmelCase_							) // 2
     __lowerCamelCase   :	List[Any]								=		arr[0:mid]
     __lowerCamelCase   :	List[str]								=		arr[mid:]

     __lowerCamelCase				,       __lowerCamelCase   :	int								=		count_inversions_recursive(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Optional[Any]								=		count_inversions_recursive(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Any								=		_count_cross_inversions(UpperCAmelCase_      ,    UpperCAmelCase_							)

     __lowerCamelCase   :	Optional[int]								=		inversion_p + inversions_q + cross_inversions
     return c, num_inversions



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				List[Any]      ,    UpperCAmelCase_    :				List[str]							)     ->		Optional[Any]:
     __lowerCamelCase   :	List[str]								=		[]
     __lowerCamelCase   :	Optional[int]								=		0
     while i < len(UpperCAmelCase_							) and j < len(UpperCAmelCase_							):
          if p[i] > q[j]:
               # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
               # These are all inversions. The claim emerges from the
               # property that P is sorted.
               num_inversion += len(UpperCAmelCase_							) - i
               r.append(q[j]							)
               j += 1
          else:
               r.append(p[i]							)
               i += 1

     if i < len(UpperCAmelCase_							):
          r.extend(p[i:]							)
     else:
          r.extend(q[j:]							)

     return r, num_inversion



def 			UpperCAmelCase__					(	)     ->		List[str]:
     __lowerCamelCase   :	Any								=		[10, 2, 1, 5, 5, 2, 11]

     # this arr has 8 inversions:
     # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Dict								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 8

     print('number of inversions = '      ,    UpperCAmelCase_							)

     # testing an array with zero inversion (a sorted arr_1)

     arr_a.sort()
     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	int								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '      ,    UpperCAmelCase_							)

     # an empty list should also have zero inversions
     __lowerCamelCase   :	Dict								=		[]
     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Union[str, Any]								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '      ,    UpperCAmelCase_							)


if __name__ == "__main__":
      main()






