

'''simple docstring'''





from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin


@dataclass
class  UpperCAmelCase (							UpperCAmelCase__    ):

		'''simple docstring'''






		SCREAMING_SNAKE_CASE_           =					42
		SCREAMING_SNAKE_CASE_           =					42
		SCREAMING_SNAKE_CASE_           =					None


class  UpperCAmelCase (							UpperCAmelCase__  , UpperCAmelCase__    ):

		'''simple docstring'''






		SCREAMING_SNAKE_CASE_           =					2
		@register_to_config
		def __init__(					self   ,			SCREAMING_SNAKE_CASE_ = 0.02   ,			SCREAMING_SNAKE_CASE_ = 100   ,			SCREAMING_SNAKE_CASE_ = 1.007   ,			SCREAMING_SNAKE_CASE_ = 80   ,			SCREAMING_SNAKE_CASE_ = 0.05   ,			SCREAMING_SNAKE_CASE_ = 50   ,			)  ->     List[Any]:






							'''simple docstring'''



							lowerCamelCase_  				=      sigma_max

							# setable values
							lowerCamelCase_  				=      None
							lowerCamelCase_  				=      None
							lowerCamelCase_  				=      None  # sigma(t_i)
		def 			UpperCamelCase(					self   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_ = None		)  ->     torch.FloatTensor:






							'''simple docstring'''



							return sample
		def 			UpperCamelCase(					self   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_ = None		)  ->     Dict:






							'''simple docstring'''



							lowerCamelCase_  				=      num_inference_steps
							lowerCamelCase_  				=      np.arange(0   ,			self.num_inference_steps		)[::-1].copy()
							lowerCamelCase_  				=      torch.from_numpy(SCREAMING_SNAKE_CASE_		).to(SCREAMING_SNAKE_CASE_		)
							lowerCamelCase_  				=      [
							    (
							        self.config.sigma_max**2
							        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
							    )
							    for i in self.timesteps
							]
							lowerCamelCase_  				=      torch.tensor(SCREAMING_SNAKE_CASE_   ,			dtype=torch.floataa   ,			device=SCREAMING_SNAKE_CASE_		)
		def 			UpperCamelCase(					self   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_ = None		)  ->     Tuple[torch.FloatTensor, float]:






							'''simple docstring'''



							if self.config.s_min <= sigma <= self.config.s_max:
												lowerCamelCase_  				=      min(self.config.s_churn / self.num_inference_steps   ,			2**0.5 - 1		)
							else:
												lowerCamelCase_  				=      0

							# sample eps ~ N(0, S_noise^2 * I)
							lowerCamelCase_  				=      self.config.s_noise * randn_tensor(sample.shape   ,			generator=SCREAMING_SNAKE_CASE_		).to(sample.device		)
							lowerCamelCase_  				=      sigma + gamma * sigma
							lowerCamelCase_  				=      sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

							return sample_hat, sigma_hat
		def 			UpperCamelCase(					self   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_ = True   ,			)  ->     Union[KarrasVeOutput, Tuple]:






							'''simple docstring'''



							lowerCamelCase_  				=      sample_hat + sigma_hat * model_output
							lowerCamelCase_  				=      (sample_hat - pred_original_sample) / sigma_hat
							lowerCamelCase_  				=      sample_hat + (sigma_prev - sigma_hat) * derivative

							if not return_dict:
												return (sample_prev, derivative)

							return KarrasVeOutput(
							    prev_sample=SCREAMING_SNAKE_CASE_   ,			derivative=SCREAMING_SNAKE_CASE_   ,			pred_original_sample=SCREAMING_SNAKE_CASE_		)
		def 			UpperCamelCase(					self   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_ = True   ,			)  ->     Union[KarrasVeOutput, Tuple]:






							'''simple docstring'''



							lowerCamelCase_  				=      sample_prev + sigma_prev * model_output
							lowerCamelCase_  				=      (sample_prev - pred_original_sample) / sigma_prev
							lowerCamelCase_  				=      sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

							if not return_dict:
												return (sample_prev, derivative)

							return KarrasVeOutput(
							    prev_sample=SCREAMING_SNAKE_CASE_   ,			derivative=SCREAMING_SNAKE_CASE_   ,			pred_original_sample=SCREAMING_SNAKE_CASE_		)






		def 			UpperCamelCase(					self   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_   ,			SCREAMING_SNAKE_CASE_		)  ->     Any:






							'''simple docstring'''



							raise NotImplementedError()








'''simple docstring'''

def a_     (    __UpperCAmelCase				,							__UpperCAmelCase				,							__UpperCAmelCase					)				->					list:





			"""simple docstring"""







			snake_case:    Optional[int]      							=len(__UpperCAmelCase					)
			snake_case:    Optional[int]      							=[[0] * n for i in range(__UpperCAmelCase					)]
			for i in range(__UpperCAmelCase					):
						snake_case:    Optional[int]      							=y_points[i]

			for i in range(2				,							__UpperCAmelCase					):
						for j in range(__UpperCAmelCase				,							__UpperCAmelCase					):
									snake_case:    List[str]      							=(
									    (xa - x_points[j - i + 1]) * q[j][i - 1]
									    - (xa - x_points[j]) * q[j - 1][i - 1]
									) / (x_points[j] - x_points[j - i + 1])

			return [q[n - 1][n - 1], q]


if __name__ == "__main__":
	import doctest

	doctest.testmod()




