



'''simple docstring'''




import torch

from diffusers import UnCLIPScheduler

from .test_schedulers import SchedulerCommonTest







class      _lowerCAmelCase							(      _a			):
	__SCREAMING_SNAKE_CASE       :		List[str]		      = (UnCLIPScheduler,)


	def    _a     (self	,				**lowercase							):
				A_     :						List[Any]     =					{
				    """num_train_timesteps""": 1000,
				    """variance_type""": """fixed_small_log""",
				    """clip_sample""": True,
				    """clip_sample_range""": 1.0,
				    """prediction_type""": """epsilon""",
				}

				config.update(**__lowerCAmelCase							)
				return config


	def    _a     (self							):
				for timesteps in [1, 5, 100, 1000]:
							self.check_over_configs(num_train_timesteps=__lowerCAmelCase							)


	def    _a     (self							):
				for variance in ["fixed_small_log", "learned_range"]:
							self.check_over_configs(variance_type=__lowerCAmelCase							)


	def    _a     (self							):
				for clip_sample in [True, False]:
							self.check_over_configs(clip_sample=__lowerCAmelCase							)


	def    _a     (self							):
				for clip_sample_range in [1, 5, 10, 20]:
							self.check_over_configs(clip_sample_range=__lowerCAmelCase							)


	def    _a     (self							):
				for prediction_type in ["epsilon", "sample"]:
							self.check_over_configs(prediction_type=__lowerCAmelCase							)


	def    _a     (self							):
				for time_step in [0, 500, 999]:
							for prev_timestep in [None, 5, 100, 250, 500, 750]:
										if prev_timestep is not None and prev_timestep >= time_step:
													continue

										self.check_over_forward(time_step=__lowerCAmelCase	,				prev_timestep=__lowerCAmelCase							)


	def    _a     (self							):
				A_     :						Tuple     =					self.scheduler_classes[0]
				A_     :						Optional[Any]     =					self.get_scheduler_config(variance_type="""fixed_small_log"""							)
				A_     :						Optional[Any]     =					scheduler_class(**__lowerCAmelCase							)

				assert torch.sum(torch.abs(scheduler._get_variance(0							) - 1.0_000E-10							)							) < 1E-5
				assert torch.sum(torch.abs(scheduler._get_variance(487							) - 0.0_54_96_25							)							) < 1E-5
				assert torch.sum(torch.abs(scheduler._get_variance(999							) - 0.9_99_49_87							)							) < 1E-5


	def    _a     (self							):
				A_     :						Optional[int]     =					self.scheduler_classes[0]
				A_     :						Dict     =					self.get_scheduler_config(variance_type="""learned_range"""							)
				A_     :						int     =					scheduler_class(**__lowerCAmelCase							)

				A_     :						Optional[Any]     =					0.5

				assert scheduler._get_variance(1	,				predicted_variance=__lowerCAmelCase							) - -10.1_71_27_90 < 1E-5
				assert scheduler._get_variance(487	,				predicted_variance=__lowerCAmelCase							) - -5.7_99_80_52 < 1E-5
				assert scheduler._get_variance(999	,				predicted_variance=__lowerCAmelCase							) - -0.0_01_00_11 < 1E-5


	def    _a     (self							):
				A_     :						Any     =					self.scheduler_classes[0]
				A_     :						str     =					self.get_scheduler_config()
				A_     :						Optional[int]     =					scheduler_class(**__lowerCAmelCase							)

				A_     :						Any     =					scheduler.timesteps

				A_     :						Optional[Any]     =					self.dummy_model()
				A_     :						List[str]     =					self.dummy_sample_deter
				A_     :						int     =					torch.manual_seed(0							)

				for i, t in enumerate(__lowerCAmelCase							):
							# 1. predict noise residual
							A_     :						Union[str, Any]     =					model(__lowerCAmelCase	,				__lowerCAmelCase							)

							# 2. predict previous mean of sample x_t-1
							A_     :						int     =					scheduler.step(__lowerCAmelCase	,				__lowerCAmelCase	,				__lowerCAmelCase	,				generator=__lowerCAmelCase							).prev_sample

							A_     :						Any     =					pred_prev_sample

				A_     :						str     =					torch.sum(torch.abs(__lowerCAmelCase							)							)
				A_     :						Union[str, Any]     =					torch.mean(torch.abs(__lowerCAmelCase							)							)

				assert abs(result_sum.item() - 2_52.2_68_24_95							) < 1E-2
				assert abs(result_mean.item() - 0.3_28_47_43							) < 1E-3


	def    _a     (self							):
				A_     :						Any     =					self.scheduler_classes[0]
				A_     :						List[str]     =					self.get_scheduler_config()
				A_     :						Dict     =					scheduler_class(**__lowerCAmelCase							)

				scheduler.set_timesteps(25							)

				A_     :						int     =					scheduler.timesteps

				A_     :						Dict     =					self.dummy_model()
				A_     :						List[Any]     =					self.dummy_sample_deter
				A_     :						Optional[int]     =					torch.manual_seed(0							)

				for i, t in enumerate(__lowerCAmelCase							):
							# 1. predict noise residual
							A_     :						Optional[Any]     =					model(__lowerCAmelCase	,				__lowerCAmelCase							)

							if i + 1 == timesteps.shape[0]:
										A_     :						Any     =					None
							else:
										A_     :						Any     =					timesteps[i + 1]

							# 2. predict previous mean of sample x_t-1
							A_     :						str     =					scheduler.step(
							    __lowerCAmelCase	,				__lowerCAmelCase	,				__lowerCAmelCase	,				prev_timestep=__lowerCAmelCase	,				generator=__lowerCAmelCase							).prev_sample

							A_     :						List[str]     =					pred_prev_sample

				A_     :						int     =					torch.sum(torch.abs(__lowerCAmelCase							)							)
				A_     :						int     =					torch.mean(torch.abs(__lowerCAmelCase							)							)

				assert abs(result_sum.item() - 2_58.2_04_49_83							) < 1E-2
				assert abs(result_mean.item() - 0.3_36_20_38							) < 1E-3


	def    _a     (self							):
				pass


	def    _a     (self							):
				pass








'''simple docstring'''




from __future__ import annotations

from collections.abc import Callable

lowerCamelCase							:List[Any]       = list[list[float | int]]



def      a      (			lowerCamelCase__						,				lowerCamelCase__   ):
			'''simple docstring'''





			A_     :						int     =					len(lowerCamelCase__   )
			A_     :						Matrix     =					[[0 for _ in range(size + 1   )] for _ in range(lowerCamelCase__   )]
			A_     :						int
			A_     :						int
			A_     :						int
			A_     :						int
			A_     :						int
			A_     :						float

			for row in range(lowerCamelCase__   ):
						for col in range(lowerCamelCase__   ):
									A_     :						List[str]     =					matrix[row][col]

						A_     :						Optional[int]     =					vector[row][0]

			A_     :						Tuple     =					0
			A_     :						Tuple     =					0
			while row < size and col < size:
						# pivoting
						A_     :						Dict     =					max((abs(augmented[rowa][col]   ), rowa) for rowa in range(lowerCamelCase__						,				lowerCamelCase__   )   )[
						    1
						]
						if augmented[pivot_row][col] == 0:
									col += 1
									continue
						else:
									A_,   A_     :						Optional[Any]     =					augmented[pivot_row], augmented[row]

						for rowa in range(row + 1						,				lowerCamelCase__   ):
									A_     :						int     =					augmented[rowa][col] / augmented[row][col]
									A_     :						Union[str, Any]     =					0
									for cola in range(col + 1						,				size + 1   ):
												augmented[rowa][cola] -= augmented[row][cola] * ratio

						row += 1
						col += 1

			# back substitution
			for col in range(1						,				lowerCamelCase__   ):
						for row in range(lowerCamelCase__   ):
									A_     :						Tuple     =					augmented[row][col] / augmented[col][col]
									for cola in range(lowerCamelCase__						,				size + 1   ):
												augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
			return [
			    [round(augmented[row][size] / augmented[row][row]						,				10   )] for row in range(lowerCamelCase__   )
			]



def      a      (			lowerCamelCase__   ):
			'''simple docstring'''





			A_     :						int     =					len(lowerCamelCase__   )
			A_     :						Matrix     =					[[0 for _ in range(lowerCamelCase__   )] for _ in range(lowerCamelCase__   )]
			A_     :						Matrix     =					[[0] for _ in range(lowerCamelCase__   )]
			A_     :						Matrix
			A_     :						int
			A_     :						int
			A_     :						int

			for x_val, y_val in enumerate(lowerCamelCase__   ):
						for col in range(lowerCamelCase__   ):
									A_     :						Dict     =					(x_val + 1) ** (size - col - 1)
						A_     :						Any     =					y_val

			A_     :						Dict     =					solve(lowerCamelCase__						,				lowerCamelCase__   )

			def interpolated_func(lowerCamelCase__   ) -> int:
						return sum(
						    round(coeffs[x_val][0]   ) * (var ** (size - x_val - 1))
						    for x_val in range(lowerCamelCase__   )   )

			return interpolated_func



def      a      (			lowerCamelCase__   ):
			'''simple docstring'''





			return (
			    1
			    - variable
			    + variable**2
			    - variable**3
			    + variable**4
			    - variable**5
			    + variable**6
			    - variable**7
			    + variable**8
			    - variable**9
			    + variable**10
			)



def      a      (			lowerCamelCase__ = question_function						,				lowerCamelCase__ = 10   ):
			'''simple docstring'''





			A_     :						list[int]     =					[func(lowerCamelCase__   ) for x_val in range(1						,				order + 1   )]

			A_     :						list[Callable[[int], int]]     =					[
			    interpolate(data_points[:max_coeff]   ) for max_coeff in range(1						,				order + 1   )
			]

			A_     :						int     =					0
			A_     :						Callable[[int], int]
			A_     :						int

			for poly in polynomials:
						A_     :						int     =					1
						while func(lowerCamelCase__   ) == poly(lowerCamelCase__   ):
									x_val += 1

						ret += poly(lowerCamelCase__   )

			return ret


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