from __future__ import annotations

from collections.abc import MutableSequence






class      __lowercase					:

						def __init__(	self				:      Optional[Any]							,							__lowerCamelCase				:      int							,							__lowerCamelCase				:      MutableSequence[float]   )							->		None:


									'''simple docstring'''

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

									lowercase							=		list(__lowerCamelCase   )
									lowercase							=		degree

						def __add__(	self				:      Any							,							__lowerCamelCase				:      Polynomial   )							->		Polynomial:


									'''simple docstring'''

									if self.degree > polynomial_a.degree:
												lowercase							=		self.coefficients[:]
												for i in range(polynomial_a.degree + 1   ):
															coefficients[i] += polynomial_a.coefficients[i]
												return Polynomial(self.degree							,							__lowerCamelCase   )
									else:
												lowercase							=		polynomial_a.coefficients[:]
												for i in range(self.degree + 1   ):
															coefficients[i] += self.coefficients[i]
												return Polynomial(polynomial_a.degree							,							__lowerCamelCase   )

						def __sub__(	self				:      str							,							__lowerCamelCase				:      Polynomial   )							->		Polynomial:


									'''simple docstring'''

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

						def __neg__(	self				:      str   )							->		Polynomial:


									'''simple docstring'''

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

						def __mul__(	self				:      List[str]							,							__lowerCamelCase				:      Polynomial   )							->		Polynomial:


									'''simple docstring'''

									lowercase							=		[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							,							__lowerCamelCase   )

						def        __a		(	self				:      List[str]							,							__lowerCamelCase				:      int | float   )							->		int | float:


									'''simple docstring'''

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

						def __str__(	self				:      str   )							->		str:


									'''simple docstring'''

									lowercase							=		''''''
									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(__lowerCamelCase   )

									return polynomial

						def __repr__(	self				:      Tuple   )							->		str:


									'''simple docstring'''

									return self.__str__()

						def        __a		(	self				:      Union[str, Any]   )							->		Polynomial:


									'''simple docstring'''

									lowercase							=		[0] * self.degree
									for i in range(self.degree   ):
												lowercase							=		self.coefficients[i + 1] * (i + 1)
									return Polynomial(self.degree - 1							,							__lowerCamelCase   )

						def        __a		(	self				:      Union[str, Any]							,							__lowerCamelCase				:      int | float = 0   )							->		Polynomial:


									'''simple docstring'''

									lowercase							=		[0] * (self.degree + 2)
									lowercase							=		constant
									for i in range(self.degree + 1   ):
												lowercase							=		self.coefficients[i] / (i + 1)
									return Polynomial(self.degree + 1							,							__lowerCamelCase   )

						def __eq__(	self				:      Tuple							,							__lowerCamelCase				:      object   )							->		bool:


									'''simple docstring'''

									if not isinstance(__lowerCamelCase							,							__lowerCamelCase   ):
												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				:      Tuple							,							__lowerCamelCase				:      object   )							->		bool:


									'''simple docstring'''

									return not self.__eq__(__lowerCamelCase   )






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

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils_flax import FlaxSchedulerMixin






@flax.struct.dataclass
class      __lowercase					:
						# setable values
						lowercase					 =     None
						lowercase					 =     None
						lowercase					 =     None  # sigma(t_i)

						@classmethod
						def        __a		(	cls				:      List[str]   )							->		Dict:


									'''simple docstring'''

									return cls()






@dataclass
class      __lowercase					(    _A    ):
						lowercase					 =     42
						lowercase					 =     42
						lowercase					 =     42






class      __lowercase					(    _A       ,     _A    ):

						@property
						def        __a		(	self				:      Union[str, Any]   )							->		Optional[Any]:


									'''simple docstring'''

									return True

						@register_to_config
						def __init__(	self				:      int							,							__lowerCamelCase				:      float = 0.02							,							__lowerCamelCase				:      float = 1_00							,							__lowerCamelCase				:      float = 1.007							,							__lowerCamelCase				:      float = 80							,							__lowerCamelCase				:      float = 0.05							,							__lowerCamelCase				:      float = 50							,							)							->		List[Any]:


									'''simple docstring'''

									pass

						def        __a		(	self				:      Dict   )							->		Optional[int]:


									'''simple docstring'''

									return KarrasVeSchedulerState.create()

						def        __a		(	self				:      str							,							__lowerCamelCase				:      KarrasVeSchedulerState							,							__lowerCamelCase				:      int							,							__lowerCamelCase				:      Tuple = ()   )							->		KarrasVeSchedulerState:


									'''simple docstring'''

									lowercase							=		jnp.arange(0							,							__lowerCamelCase   )[::-1].copy()
									lowercase							=		[
									    (
									        self.config.sigma_max**2
									        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
									    )
									    for i in timesteps
									]

									return state.replace(
									    num_inference_steps=__lowerCamelCase							,							schedule=jnp.array(__lowerCamelCase							,							dtype=jnp.floataa   )							,							timesteps=__lowerCamelCase							,							)

						def        __a		(	self				:      Optional[Any]							,							__lowerCamelCase				:      KarrasVeSchedulerState							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      float							,							__lowerCamelCase				:      random.KeyArray							,							)							->		Tuple[jnp.ndarray, float]:


									'''simple docstring'''

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

									# sample eps ~ N(0, S_noise^2 * I)
									lowercase							=		random.split(__lowerCamelCase							,							num=1   )
									lowercase							=		self.config.s_noise * random.normal(key=__lowerCamelCase							,							shape=sample.shape   )
									lowercase							=		sigma + gamma * sigma
									lowercase							=		sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

									return sample_hat, sigma_hat

						def        __a		(	self				:      str							,							__lowerCamelCase				:      KarrasVeSchedulerState							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      float							,							__lowerCamelCase				:      float							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      bool = True							,							)							->		Union[FlaxKarrasVeOutput, Tuple]:


									'''simple docstring'''

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

									if not return_dict:
												return (sample_prev, derivative, state)

									return FlaxKarrasVeOutput(prev_sample=__lowerCamelCase							,							derivative=__lowerCamelCase							,							state=__lowerCamelCase   )

						def        __a		(	self				:      str							,							__lowerCamelCase				:      KarrasVeSchedulerState							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      float							,							__lowerCamelCase				:      float							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      bool = True							,							)							->		Union[FlaxKarrasVeOutput, Tuple]:


									'''simple docstring'''

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

									if not return_dict:
												return (sample_prev, derivative, state)

									return FlaxKarrasVeOutput(prev_sample=__lowerCamelCase							,							derivative=__lowerCamelCase							,							state=__lowerCamelCase   )



						def        __a		(	self				:      int							,							__lowerCamelCase				:      KarrasVeSchedulerState							,							__lowerCamelCase				:      str							,							__lowerCamelCase				:      str							,							__lowerCamelCase				:      Dict   )							->		Tuple:


									'''simple docstring'''

									raise NotImplementedError()





