


'''simple docstring'''
from __future__ import annotations

from collections.abc import MutableSequence
class      lowercase			:

		"""simple docstring"""

		def __init__(	self					,     UpperCamelCase_					,     UpperCamelCase_							):

							'''simple docstring'''


							if len(UpperCamelCase_							) != degree + 1:
												raise ValueError(
												    '''The number of coefficients should be equal to the degree + 1.'''							)

							UpperCamelCase__     :list[float]							      =				list(UpperCamelCase_							)
							UpperCamelCase__     :str							      =				degree




		def __add__(	self					,     UpperCamelCase_							):

							'''simple docstring'''


							if self.degree > polynomial_a.degree:
												UpperCamelCase__     :Any							      =				self.coefficients[:]
												for i in range(polynomial_a.degree + 1							):
																	coefficients[i] += polynomial_a.coefficients[i]
												return Polynomial(self.degree					,     UpperCamelCase_							)
							else:
												UpperCamelCase__     :Tuple							      =				polynomial_a.coefficients[:]
												for i in range(self.degree + 1							):
																	coefficients[i] += self.coefficients[i]
												return Polynomial(polynomial_a.degree					,     UpperCamelCase_							)




		def __sub__(	self					,     UpperCamelCase_							):

							'''simple docstring'''


							return self + polynomial_a * Polynomial(0					,     [-1]							)




		def __neg__(	self							):

							'''simple docstring'''


							return Polynomial(self.degree					,     [-c for c in self.coefficients]							)




		def __mul__(	self					,     UpperCamelCase_							):

							'''simple docstring'''


							UpperCamelCase__     :list[float]							      =				[0] * (self.degree + polynomial_a.degree + 1)
							for i in range(self.degree + 1							):
												for j in range(polynomial_a.degree + 1							):
																	coefficients[i + j] += (
																	    self.coefficients[i] * polynomial_a.coefficients[j]
																	)

							return Polynomial(self.degree + polynomial_a.degree					,     UpperCamelCase_							)




		def 					lowerCAmelCase__       (	self					,     UpperCamelCase_							):

							'''simple docstring'''


							UpperCamelCase__     :int | float							      =				0
							for i in range(self.degree + 1							):
												result += self.coefficients[i] * (substitution**i)
							return result




		def __str__(	self							):

							'''simple docstring'''


							UpperCamelCase__     :Optional[int]							      =				''''''
							for i in range(self.degree					,     -1					,     -1							):
												if self.coefficients[i] == 0:
																	continue
												elif self.coefficients[i] > 0:
																	if polynomial:
																						polynomial += " + "
												else:
																	polynomial += " - "

												if i == 0:
																	polynomial += str(abs(self.coefficients[i]							)							)
												elif i == 1:
																	polynomial += str(abs(self.coefficients[i]							)							) + "x"
												else:
																	polynomial += str(abs(self.coefficients[i]							)							) + "x^" + str(UpperCamelCase_							)

							return polynomial




		def __repr__(	self							):

							'''simple docstring'''


							return self.__str__()




		def 					lowerCAmelCase__       (	self							):

							'''simple docstring'''


							UpperCamelCase__     :list[float]							      =				[0] * self.degree
							for i in range(self.degree							):
												UpperCamelCase__     :int							      =				self.coefficients[i + 1] * (i + 1)
							return Polynomial(self.degree - 1					,     UpperCamelCase_							)




		def 					lowerCAmelCase__       (	self					,     UpperCamelCase_ = 0							):

							'''simple docstring'''


							UpperCamelCase__     :list[float]							      =				[0] * (self.degree + 2)
							UpperCamelCase__     :int							      =				constant
							for i in range(self.degree + 1							):
												UpperCamelCase__     :str							      =				self.coefficients[i] / (i + 1)
							return Polynomial(self.degree + 1					,     UpperCamelCase_							)




		def __eq__(	self					,     UpperCamelCase_							):

							'''simple docstring'''


							if not isinstance(UpperCamelCase_					,     UpperCamelCase_							):
												return False

							if self.degree != polynomial_a.degree:
												return False

							for i in range(self.degree + 1							):
												if self.coefficients[i] != polynomial_a.coefficients[i]:
																	return False

							return True




		def __ne__(	self					,     UpperCamelCase_							):

							'''simple docstring'''


							return not self.__eq__(UpperCamelCase_							)



'''simple docstring'''
# 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      lowercase			(							A__			,	A__      ):

		"""simple docstring"""

		_a									=       1




		@register_to_config
		def __init__(	self					,     UpperCamelCase_=2000					,     UpperCamelCase_=0.1					,     UpperCamelCase_=20					,     UpperCamelCase_=1e-3							):

							'''simple docstring'''


							UpperCamelCase__     :Dict							      =				None
							UpperCamelCase__     :Any							      =				None
							UpperCamelCase__     :List[str]							      =				None




		def 					lowerCAmelCase__       (	self					,     UpperCamelCase_					,     UpperCamelCase_ = None							):

							'''simple docstring'''


							UpperCamelCase__     :Union[str, Any]							      =				torch.linspace(1					,     self.config.sampling_eps					,     UpperCamelCase_					,     device=UpperCamelCase_							)




		def 					lowerCAmelCase__       (	self					,     UpperCamelCase_					,     UpperCamelCase_					,     UpperCamelCase_					,     UpperCamelCase_=None							):

							'''simple docstring'''


							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
							UpperCamelCase__     :Optional[int]							      =				(
							    -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
							)
							UpperCamelCase__     :Tuple							      =				torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff							)							)
							UpperCamelCase__     :Tuple							      =				std.flatten()
							while len(std.shape							) < len(score.shape							):
												UpperCamelCase__     :int							      =				std.unsqueeze(-1							)
							UpperCamelCase__     :List[Any]							      =				-score / std

							# compute
							UpperCamelCase__     :List[str]							      =				-1.0 / len(self.timesteps							)

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

							UpperCamelCase__     :int							      =				torch.sqrt(UpperCamelCase_							)
							UpperCamelCase__     :List[str]							      =				drift - diffusion**2 * score
							UpperCamelCase__     :Dict							      =				x + drift * dt

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

							return x, x_mean




		def __len__(	self							):

							'''simple docstring'''


							return self.config.num_train_timesteps