






# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

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

class 				lowerCAmelCase_	(		__snake_case   ,		__snake_case			):
				_UpperCamelCase					:       Any							       = 1


				@register_to_config
				def __init__(					self ,						_lowerCAmelCase=2_0_0_0 ,						_lowerCAmelCase=0.1 ,						_lowerCAmelCase=2_0 ,						_lowerCAmelCase=1E-3      ):
											_lowercase							:   Union[str, Any] 							=   None
											_lowercase							:   Dict 							=   None
											_lowercase							:   Optional[int] 							=   None


				def 						__a					(					self ,						_lowerCAmelCase ,						_lowerCAmelCase = None      ):
											_lowercase							:   Any 							=   torch.linspace(1 ,						self.config.sampling_eps ,						_lowerCAmelCase ,						device=_lowerCAmelCase      )


				def 						__a					(					self ,						_lowerCAmelCase ,						_lowerCAmelCase ,						_lowerCAmelCase ,						_lowerCAmelCase=None      ):
											if self.timesteps is None:
																		raise ValueError(
																		    '`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'      )

											# TODO(Patrick) better comments + non-PyTorch
											# postprocess model score
											_lowercase							:   List[Any] 							=   (
											    -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
											)
											_lowercase							:   Tuple 							=   torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff      )      )
											_lowercase							:   List[Any] 							=   std.flatten()
											while len(std.shape      ) < len(score.shape      ):
																		_lowercase							:   Union[str, Any] 							=   std.unsqueeze(-1      )
											_lowercase							:   Dict 							=   -score / std

											# compute
											_lowercase							:   Union[str, Any] 							=   -1.0 / len(self.timesteps      )

											_lowercase							:   Optional[int] 							=   self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
											_lowercase							:   Tuple 							=   beta_t.flatten()
											while len(beta_t.shape      ) < len(x.shape      ):
																		_lowercase							:   Dict 							=   beta_t.unsqueeze(-1      )
											_lowercase							:   Dict 							=   -0.5 * beta_t * x

											_lowercase							:   Tuple 							=   torch.sqrt(_lowerCAmelCase      )
											_lowercase							:   Dict 							=   drift - diffusion**2 * score
											_lowercase							:   Tuple 							=   x + drift * dt

											# add noise
											_lowercase							:   Any 							=   randn_tensor(x.shape ,						layout=x.layout ,						generator=_lowerCAmelCase ,						device=x.device ,						dtype=x.dtype      )
											_lowercase							:   List[str] 							=   x_mean + diffusion * math.sqrt(-dt      ) * noise

											return x, x_mean


				def __len__(					self      ):
											return self.config.num_train_timesteps








from __future__ import annotations

import math


def     lowercase	(    a     , a ):



		'''simple docstring'''




		SCREAMING_SNAKE_CASE_				:List[Any]				     =						u
		for i in range(1     , a ):
				SCREAMING_SNAKE_CASE_				:Union[str, Any]				     =						temp * (u - i)
		return temp


def     lowercase	(    ):



		'''simple docstring'''




		SCREAMING_SNAKE_CASE_				:int				     =						int(input("enter the numbers of values: " ) )
		SCREAMING_SNAKE_CASE_				:list[list[float]]				     =						[]
		for _ in range(a ):
				y.append([] )
		for i in range(a ):
				for j in range(a ):
						y[i].append(a )
						SCREAMING_SNAKE_CASE_				:Any				     =						0

		print("enter the values of parameters in a list: " )
		SCREAMING_SNAKE_CASE_				:Dict				     =						list(map(a     , input().split() ) )

		print("enter the values of corresponding parameters: " )
		for i in range(a ):
				SCREAMING_SNAKE_CASE_				:List[Any]				     =						float(input() )

		SCREAMING_SNAKE_CASE_				:Optional[Any]				     =						int(input("enter the value to interpolate: " ) )
		SCREAMING_SNAKE_CASE_				:str				     =						(value - x[0]) / (x[1] - x[0])

		# for calculating forward difference table

		for i in range(1     , a ):
				for j in range(n - i ):
						SCREAMING_SNAKE_CASE_				:List[str]				     =						y[j + 1][i - 1] - y[j][i - 1]

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

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


if __name__ == "__main__":
		main()






