'''simple docstring'''


import tempfile

import torch

from diffusers import (
    DEISMultistepScheduler,
    DPMSolverMultistepScheduler,
    DPMSolverSinglestepScheduler,
    UniPCMultistepScheduler,
)

from .test_schedulers import SchedulerCommonTest






class 						A   (   UpperCAmelCase   ):
							a_        =      (DEISMultistepScheduler,)
							a_        =      (('''num_inference_steps''', 2_5),)





							def       snake_case__						(      self				:							int     ,		**__a				:							Union[str, Any]	)							->	int:
								__UpperCAmelCase							=			{
								    '''num_train_timesteps''': 1_0_0_0,
								    '''beta_start''': 0.0_0_0_1,
								    '''beta_end''': 0.0_2,
								    '''beta_schedule''': '''linear''',
								    '''solver_order''': 2,
								}

								config.update(**__a	)
								return config





							def       snake_case__						(      self				:							Optional[Any]     ,		__a				:							Dict=0     ,		**__a				:							int	)							->	List[Any]:
								__UpperCAmelCase							=			dict(self.forward_default_kwargs	)
								__UpperCAmelCase							=			kwargs.pop('''num_inference_steps'''     ,		__a	)
								__UpperCAmelCase							=			self.dummy_sample
								__UpperCAmelCase							=			0.1 * sample
								__UpperCAmelCase							=			[residual + 0.2, residual + 0.1_5, residual + 0.1_0]

								for scheduler_class in self.scheduler_classes:
									__UpperCAmelCase							=			self.get_scheduler_config(**__a	)
									__UpperCAmelCase							=			scheduler_class(**__a	)
									scheduler.set_timesteps(__a	)
									# copy over dummy past residuals
									__UpperCAmelCase							=			dummy_past_residuals[: scheduler.config.solver_order]

									with tempfile.TemporaryDirectory() as tmpdirname:
										scheduler.save_config(__a	)
										__UpperCAmelCase							=			scheduler_class.from_pretrained(__a	)
										new_scheduler.set_timesteps(__a	)
										# copy over dummy past residuals
										__UpperCAmelCase							=			dummy_past_residuals[: new_scheduler.config.solver_order]

									__UpperCAmelCase				,			__UpperCAmelCase							=			sample, sample
									for t in range(__a     ,		time_step + scheduler.config.solver_order + 1	):
										__UpperCAmelCase							=			scheduler.step(__a     ,		__a     ,		__a     ,		**__a	).prev_sample
										__UpperCAmelCase							=			new_scheduler.step(__a     ,		__a     ,		__a     ,		**__a	).prev_sample

										assert torch.sum(torch.abs(output - new_output	)	) < 1e-5, "Scheduler outputs are not identical"





							def       snake_case__						(      self				:							Union[str, Any]	)							->	Dict:
								pass





							def       snake_case__						(      self				:							str     ,		__a				:							Dict=0     ,		**__a				:							List[Any]	)							->	str:
								__UpperCAmelCase							=			dict(self.forward_default_kwargs	)
								__UpperCAmelCase							=			kwargs.pop('''num_inference_steps'''     ,		__a	)
								__UpperCAmelCase							=			self.dummy_sample
								__UpperCAmelCase							=			0.1 * sample
								__UpperCAmelCase							=			[residual + 0.2, residual + 0.1_5, residual + 0.1_0]

								for scheduler_class in self.scheduler_classes:
									__UpperCAmelCase							=			self.get_scheduler_config()
									__UpperCAmelCase							=			scheduler_class(**__a	)
									scheduler.set_timesteps(__a	)

									# copy over dummy past residuals (must be after setting timesteps)
									__UpperCAmelCase							=			dummy_past_residuals[: scheduler.config.solver_order]

									with tempfile.TemporaryDirectory() as tmpdirname:
										scheduler.save_config(__a	)
										__UpperCAmelCase							=			scheduler_class.from_pretrained(__a	)
										# copy over dummy past residuals
										new_scheduler.set_timesteps(__a	)

										# copy over dummy past residual (must be after setting timesteps)
										__UpperCAmelCase							=			dummy_past_residuals[: new_scheduler.config.solver_order]

									__UpperCAmelCase							=			scheduler.step(__a     ,		__a     ,		__a     ,		**__a	).prev_sample
									__UpperCAmelCase							=			new_scheduler.step(__a     ,		__a     ,		__a     ,		**__a	).prev_sample

									assert torch.sum(torch.abs(output - new_output	)	) < 1e-5, "Scheduler outputs are not identical"





							def       snake_case__						(      self				:							List[Any]     ,		__a				:							List[str]=None     ,		**__a				:							List[str]	)							->	Optional[int]:
								if scheduler is None:
									__UpperCAmelCase							=			self.scheduler_classes[0]
									__UpperCAmelCase							=			self.get_scheduler_config(**__a	)
									__UpperCAmelCase							=			scheduler_class(**__a	)

								__UpperCAmelCase							=			self.scheduler_classes[0]
								__UpperCAmelCase							=			self.get_scheduler_config(**__a	)
								__UpperCAmelCase							=			scheduler_class(**__a	)

								__UpperCAmelCase							=			1_0
								__UpperCAmelCase							=			self.dummy_model()
								__UpperCAmelCase							=			self.dummy_sample_deter
								scheduler.set_timesteps(__a	)

								for i, t in enumerate(scheduler.timesteps	):
									__UpperCAmelCase							=			model(__a     ,		__a	)
									__UpperCAmelCase							=			scheduler.step(__a     ,		__a     ,		__a	).prev_sample

								return sample





							def       snake_case__						(      self				:							Dict	)							->	Optional[Any]:
								__UpperCAmelCase							=			dict(self.forward_default_kwargs	)

								__UpperCAmelCase							=			kwargs.pop('''num_inference_steps'''     ,		__a	)

								for scheduler_class in self.scheduler_classes:
									__UpperCAmelCase							=			self.get_scheduler_config()
									__UpperCAmelCase							=			scheduler_class(**__a	)

									__UpperCAmelCase							=			self.dummy_sample
									__UpperCAmelCase							=			0.1 * sample

									if num_inference_steps is not None and hasattr(__a     ,		'''set_timesteps'''	):
										scheduler.set_timesteps(__a	)
									elif num_inference_steps is not None and not hasattr(__a     ,		'''set_timesteps'''	):
										__UpperCAmelCase							=			num_inference_steps

									# copy over dummy past residuals (must be done after set_timesteps)
									__UpperCAmelCase							=			[residual + 0.2, residual + 0.1_5, residual + 0.1_0]
									__UpperCAmelCase							=			dummy_past_residuals[: scheduler.config.solver_order]

									__UpperCAmelCase							=			scheduler.timesteps[5]
									__UpperCAmelCase							=			scheduler.timesteps[6]

									__UpperCAmelCase							=			scheduler.step(__a     ,		__a     ,		__a     ,		**__a	).prev_sample
									__UpperCAmelCase							=			scheduler.step(__a     ,		__a     ,		__a     ,		**__a	).prev_sample

									self.assertEqual(output_a.shape     ,		sample.shape	)
									self.assertEqual(output_a.shape     ,		output_a.shape	)





							def       snake_case__						(      self				:							Union[str, Any]	)							->	str:
								# make sure that iterating over schedulers with same config names gives same results
								# for defaults
								__UpperCAmelCase							=			DEISMultistepScheduler(**self.get_scheduler_config()	)
								__UpperCAmelCase							=			self.full_loop(scheduler=__a	)
								__UpperCAmelCase							=			torch.mean(torch.abs(__a	)	)

								assert abs(result_mean.item() - 0.2_3_9_1_6	) < 1e-3

								__UpperCAmelCase							=			DPMSolverSinglestepScheduler.from_config(scheduler.config	)
								__UpperCAmelCase							=			DPMSolverMultistepScheduler.from_config(scheduler.config	)
								__UpperCAmelCase							=			UniPCMultistepScheduler.from_config(scheduler.config	)
								__UpperCAmelCase							=			DEISMultistepScheduler.from_config(scheduler.config	)

								__UpperCAmelCase							=			self.full_loop(scheduler=__a	)
								__UpperCAmelCase							=			torch.mean(torch.abs(__a	)	)

								assert abs(result_mean.item() - 0.2_3_9_1_6	) < 1e-3





							def       snake_case__						(      self				:							List[Any]	)							->	Optional[int]:
								for timesteps in [2_5, 5_0, 1_0_0, 9_9_9, 1_0_0_0]:
									self.check_over_configs(num_train_timesteps=__a	)





							def       snake_case__						(      self				:							Dict	)							->	List[str]:
								self.check_over_configs(thresholding=__a	)
								for order in [1, 2, 3]:
									for solver_type in ["logrho"]:
										for threshold in [0.5, 1.0, 2.0]:
											for prediction_type in ["epsilon", "sample"]:
												self.check_over_configs(
												    thresholding=__a     ,		prediction_type=__a     ,		sample_max_value=__a     ,		algorithm_type='''deis'''     ,		solver_order=__a     ,		solver_type=__a     ,		)





							def       snake_case__						(      self				:							List[str]	)							->	int:
								for prediction_type in ["epsilon", "v_prediction"]:
									self.check_over_configs(prediction_type=__a	)





							def       snake_case__						(      self				:							Optional[Any]	)							->	int:
								for algorithm_type in ["deis"]:
									for solver_type in ["logrho"]:
										for order in [1, 2, 3]:
											for prediction_type in ["epsilon", "sample"]:
												self.check_over_configs(
												    solver_order=__a     ,		solver_type=__a     ,		prediction_type=__a     ,		algorithm_type=__a     ,		)
												__UpperCAmelCase							=			self.full_loop(
												    solver_order=__a     ,		solver_type=__a     ,		prediction_type=__a     ,		algorithm_type=__a     ,		)
												assert not torch.isnan(__a	).any(), "Samples have nan numbers"





							def       snake_case__						(      self				:							List[str]	)							->	Dict:
								self.check_over_configs(lower_order_final=__a	)
								self.check_over_configs(lower_order_final=__a	)





							def       snake_case__						(      self				:							str	)							->	Tuple:
								for num_inference_steps in [1, 2, 3, 5, 1_0, 5_0, 1_0_0, 9_9_9, 1_0_0_0]:
									self.check_over_forward(num_inference_steps=__a     ,		time_step=0	)





							def       snake_case__						(      self				:							int	)							->	List[Any]:
								__UpperCAmelCase							=			self.full_loop()
								__UpperCAmelCase							=			torch.mean(torch.abs(__a	)	)

								assert abs(result_mean.item() - 0.2_3_9_1_6	) < 1e-3





							def       snake_case__						(      self				:							Tuple	)							->	int:
								__UpperCAmelCase							=			self.full_loop(prediction_type='''v_prediction'''	)
								__UpperCAmelCase							=			torch.mean(torch.abs(__a	)	)

								assert abs(result_mean.item() - 0.0_9_1	) < 1e-3






							def       snake_case__						(      self				:							int	)							->	List[Any]:
								__UpperCAmelCase							=			self.scheduler_classes[0]
								__UpperCAmelCase							=			self.get_scheduler_config(thresholding=__a     ,		dynamic_thresholding_ratio=0	)
								__UpperCAmelCase							=			scheduler_class(**__a	)

								__UpperCAmelCase							=			1_0
								__UpperCAmelCase							=			self.dummy_model()
								__UpperCAmelCase							=			self.dummy_sample_deter.half()
								scheduler.set_timesteps(__a	)

								for i, t in enumerate(scheduler.timesteps	):
									__UpperCAmelCase							=			model(__a     ,		__a	)
									__UpperCAmelCase							=			scheduler.step(__a     ,		__a     ,		__a	).prev_sample

								assert sample.dtype == torch.floataa



'''simple docstring'''


from __future__ import annotations

import math





def       lowerCAmelCase					(		UpperCamelCase__				:   float    ,					UpperCamelCase__				:   int       ):


	"""simple docstring"""
	__UpperCAmelCase							=			u
	for i in range(1    ,					UpperCamelCase__       ):
		__UpperCAmelCase							=			temp * (u - i)
	return temp





def       lowerCAmelCase					(		):


	"""simple docstring"""
	__UpperCAmelCase							=			int(input('''enter the numbers of values: '''       )       )
	__UpperCAmelCase							=			[]
	for _ in range(UpperCamelCase__       ):
		y.append([]       )
	for i in range(UpperCamelCase__       ):
		for j in range(UpperCamelCase__       ):
			y[i].append(UpperCamelCase__       )
			__UpperCAmelCase							=			0

	print('''enter the values of parameters in a list: '''       )
	__UpperCAmelCase							=			list(map(UpperCamelCase__    ,					input().split()       )       )

	print('''enter the values of corresponding parameters: '''       )
	for i in range(UpperCamelCase__       ):
		__UpperCAmelCase							=			float(input()       )

	__UpperCAmelCase							=			int(input('''enter the value to interpolate: '''       )       )
	__UpperCAmelCase							=			(value - x[0]) / (x[1] - x[0])

	# for calculating forward difference table

	for i in range(1    ,					UpperCamelCase__       ):
		for j in range(n - i       ):
			__UpperCAmelCase							=			y[j + 1][i - 1] - y[j][i - 1]

	__UpperCAmelCase							=			y[0][0]
	for i in range(1    ,					UpperCamelCase__       ):
		summ += (ucal(UpperCamelCase__    ,					UpperCamelCase__       ) * y[0][i]) / math.factorial(UpperCamelCase__       )

	print(f"""the value at {value} is {summ}"""       )


if __name__ == "__main__":
					main()
