





import torch

from diffusers import KDPMaDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest

class 	A_       (a_			):
	UpperCAmelCase__					=			(KDPMaDiscreteScheduler,)
	UpperCAmelCase__					=			1_0
	def      _lowercase				(    self							,					**_A		):






				'''simple docstring'''







				UpperCAmelCase   		=				{
				    '''num_train_timesteps''': 1_1_0_0,
				    '''beta_start''': 0.00_01,
				    '''beta_end''': 0.02,
				    '''beta_schedule''': '''linear''',
				}

				config.update(**_A		)
				return config
	def      _lowercase				(    self		):






				'''simple docstring'''







				for timesteps in [1_0, 5_0, 1_0_0, 1_0_0_0]:
							self.check_over_configs(num_train_timesteps=_A		)
	def      _lowercase				(    self		):






				'''simple docstring'''







				for beta_start, beta_end in zip([0.0_00_01, 0.00_01, 0.0_01]							,					[0.00_02, 0.0_02, 0.02]		):
							self.check_over_configs(beta_start=_A							,					beta_end=_A		)
	def      _lowercase				(    self		):






				'''simple docstring'''







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






				'''simple docstring'''







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






				'''simple docstring'''







				UpperCAmelCase   		=				self.scheduler_classes[0]
				UpperCAmelCase   		=				self.get_scheduler_config(prediction_type='''v_prediction'''		)
				UpperCAmelCase   		=				scheduler_class(**_A		)

				scheduler.set_timesteps(self.num_inference_steps		)

				UpperCAmelCase   		=				self.dummy_model()
				UpperCAmelCase   		=				self.dummy_sample_deter * scheduler.init_noise_sigma
				UpperCAmelCase   		=				sample.to(_A		)

				for i, t in enumerate(scheduler.timesteps		):
							UpperCAmelCase   		=				scheduler.scale_model_input(_A							,					_A		)

							UpperCAmelCase   		=				model(_A							,					_A		)

							UpperCAmelCase   		=				scheduler.step(_A							,					_A							,					_A		)
							UpperCAmelCase   		=				output.prev_sample

				UpperCAmelCase   		=				torch.sum(torch.abs(_A		)		)
				UpperCAmelCase   		=				torch.mean(torch.abs(_A		)		)

				if torch_device in ["cpu", "mps"]:
							assert abs(result_sum.item() - 4.6934E-07		) < 1E-2
							assert abs(result_mean.item() - 6.1112E-10		) < 1E-3
				else:
							# CUDA
							assert abs(result_sum.item() - 4.693_4286_5017_0972E-07		) < 1E-2
							assert abs(result_mean.item() - 0.00_02		) < 1E-3
	def      _lowercase				(    self		):






				'''simple docstring'''







				if torch_device == "mps":
							return
				UpperCAmelCase   		=				self.scheduler_classes[0]
				UpperCAmelCase   		=				self.get_scheduler_config()
				UpperCAmelCase   		=				scheduler_class(**_A		)

				scheduler.set_timesteps(self.num_inference_steps		)

				UpperCAmelCase   		=				self.dummy_model()
				UpperCAmelCase   		=				self.dummy_sample_deter * scheduler.init_noise_sigma
				UpperCAmelCase   		=				sample.to(_A		)

				for i, t in enumerate(scheduler.timesteps		):
							UpperCAmelCase   		=				scheduler.scale_model_input(_A							,					_A		)

							UpperCAmelCase   		=				model(_A							,					_A		)

							UpperCAmelCase   		=				scheduler.step(_A							,					_A							,					_A		)
							UpperCAmelCase   		=				output.prev_sample

				UpperCAmelCase   		=				torch.sum(torch.abs(_A		)		)
				UpperCAmelCase   		=				torch.mean(torch.abs(_A		)		)

				if torch_device in ["cpu", "mps"]:
							assert abs(result_sum.item() - 20.41_25		) < 1E-2
							assert abs(result_mean.item() - 0.02_66		) < 1E-3
				else:
							# CUDA
							assert abs(result_sum.item() - 20.41_25		) < 1E-2
							assert abs(result_mean.item() - 0.02_66		) < 1E-3







	def      _lowercase				(    self		):






				'''simple docstring'''







				if torch_device == "mps":
							return
				UpperCAmelCase   		=				self.scheduler_classes[0]
				UpperCAmelCase   		=				self.get_scheduler_config()
				UpperCAmelCase   		=				scheduler_class(**_A		)

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

				UpperCAmelCase   		=				self.dummy_model()
				UpperCAmelCase   		=				self.dummy_sample_deter.to(_A		) * scheduler.init_noise_sigma

				for t in scheduler.timesteps:
							UpperCAmelCase   		=				scheduler.scale_model_input(_A							,					_A		)

							UpperCAmelCase   		=				model(_A							,					_A		)

							UpperCAmelCase   		=				scheduler.step(_A							,					_A							,					_A		)
							UpperCAmelCase   		=				output.prev_sample

				UpperCAmelCase   		=				torch.sum(torch.abs(_A		)		)
				UpperCAmelCase   		=				torch.mean(torch.abs(_A		)		)

				if str(_A		).startswith('''cpu'''		):
							# The following sum varies between 148 and 156 on mps. Why?
							assert abs(result_sum.item() - 20.41_25		) < 1E-2
							assert abs(result_mean.item() - 0.02_66		) < 1E-3
				else:
							# CUDA
							assert abs(result_sum.item() - 20.41_25		) < 1E-2
							assert abs(result_mean.item() - 0.02_66		) < 1E-3







'''simple docstring'''

import math





def __snake_case					(      UpperCAmelCase_						:						int		):
 lowerCamelCase_      =  math.loga(math.sqrt(4 * positive_integer + 1		) / 2 + 1 / 2		)

 return exponent == int(UpperCAmelCase_		)





def __snake_case					(      UpperCAmelCase_						:						float = 1 / 12345		):
 lowerCamelCase_      =  0
 lowerCamelCase_      =  0

 lowerCamelCase_      =  3
 while True:
  lowerCamelCase_      =  (integer**2 - 1) / 4
  # if candidate is an integer, then there is a partition for k
  if partition_candidate == int(UpperCAmelCase_		):
   lowerCamelCase_      =  int(UpperCAmelCase_		)
   total_partitions += 1
   if check_partition_perfect(UpperCAmelCase_		):
    perfect_partitions += 1
  if perfect_partitions > 0:
   if perfect_partitions / total_partitions < max_proportion:
    return int(UpperCAmelCase_		)
  integer += 1


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



