


def     lowerCAmelCase_					( __lowerCamelCase     ):
							if not head:
														return True
							# split the list to two parts
							__snake_case			,      __snake_case		:      List[Any]										=       head.next, head
							while fast and fast.next:
														__snake_case		:      List[str]										=       fast.next.next
														__snake_case		:      List[Any]										=       slow.next
							__snake_case		:      Tuple										=       slow.next
							__snake_case		:      Any										=       None  # Don't forget here! But forget still works!
							# reverse the second part
							__snake_case		:      Tuple										=       None
							while second:
														__snake_case		:      List[Any]										=       second.next
														__snake_case		:      List[Any]										=       node
														__snake_case		:      str										=       second
														__snake_case		:      Union[str, Any]										=       nxt
							# compare two parts
							# second part has the same or one less node
							while node:
														if node.val != head.val:
																					return False
														__snake_case		:      Union[str, Any]										=       node.next
														__snake_case		:      Optional[int]										=       head.next
							return True







def     lowerCAmelCase_					( __lowerCamelCase     ):
							if not head or not head.next:
														return True

							# 1. Get the midpoint (slow)
							__snake_case		:      Union[str, Any]										=       head
							while fast and fast.next:
														__snake_case			,      __snake_case		:      List[Any]										=       fast.next.next, slow.next

							# 2. Push the second half into the stack
							__snake_case		:      Union[str, Any]										=       [slow.val]
							while slow.next:
														__snake_case		:      Any										=       slow.next
														stack.append(slow.val     )

							# 3. Comparison
							while stack:
														if stack.pop() != cur.val:
																					return False
														__snake_case		:      int										=       cur.next

							return True







def     lowerCAmelCase_					( __lowerCamelCase     ):
							if not head or not head.next:
														return True
							__snake_case		:      List[Any]										=       {}
							__snake_case		:      List[str]										=       0
							while head:
														if head.val in d:
																					d[head.val].append(__lowerCamelCase     )
														else:
																					__snake_case		:      List[str]										=       [pos]
														__snake_case		:      Dict										=       head.next
														pos += 1
							__snake_case		:      List[Any]										=       pos - 1
							__snake_case		:      Any										=       0
							for v in d.values():
														if len(__lowerCamelCase     ) % 2 != 0:
																					middle += 1
														else:
																					__snake_case		:      Union[str, Any]										=       0
																					for i in range(0							,     len(__lowerCamelCase     )     ):
																												if v[i] + v[len(__lowerCamelCase     ) - 1 - step] != checksum:
																																			return False
																												step += 1
														if middle > 1:
																					return False
							return True





import importlib
import math
import os
from dataclasses import dataclass
from enum import Enum
from typing import Any, Dict, Optional, Tuple, Union

import flax
import jax.numpy as jnp

from ..utils import BaseOutput


_snake_case					:		int      =    "scheduler_config.json"

class     a		(_lowerCAmelCase				):




							"""simple docstring"""


							__UpperCAmelCase   :							Tuple					  =  1
							__UpperCAmelCase   :							Tuple					  =  2
							__UpperCAmelCase   :							Union[str, Any]					  =  3
							__UpperCAmelCase   :							List[Any]					  =  4
							__UpperCAmelCase   :							Tuple					  =  5

@dataclass
class     a		(_lowerCAmelCase				):




							"""simple docstring"""


							__UpperCAmelCase   :							jnp.ndarray

class     a		:




							"""simple docstring"""


							__UpperCAmelCase   :							Dict					  =  SCHEDULER_CONFIG_NAME
							__UpperCAmelCase   :							Union[str, Any]					  =  ["dtype"]
							__UpperCAmelCase   :							Tuple					  =  []
							__UpperCAmelCase   :							int					  =  True

							@classmethod
							def    __snake_case (							cls	:  List[str]   ,     lowerCamelCase	:  Dict[str, Any] = None   ,     lowerCamelCase	:  Optional[str] = None   ,     lowerCamelCase	:  List[str]=False   ,     **lowerCamelCase	:  Union[str, Any]   ,     )     ->   List[str]:
														__snake_case			,      __snake_case		:      List[str]										=       cls.load_config(
														    pretrained_model_name_or_path=lowerCamelCase   ,     subfolder=lowerCamelCase   ,     return_unused_kwargs=lowerCamelCase   ,     **lowerCamelCase   ,     )
														__snake_case			,      __snake_case		:      Dict										=       cls.from_config(lowerCamelCase   ,     return_unused_kwargs=lowerCamelCase   ,     **lowerCamelCase    )

														if hasattr(lowerCamelCase   ,     "create_state"    ) and getattr(lowerCamelCase   ,     "has_state"   ,     lowerCamelCase    ):
																					__snake_case		:      Tuple										=       scheduler.create_state()

														if return_unused_kwargs:
																					return scheduler, state, unused_kwargs

														return scheduler, state

							def    __snake_case (							self	:  Any   ,     lowerCamelCase	:  Union[str, os.PathLike]   ,     lowerCamelCase	:  bool = False   ,     **lowerCamelCase	:  List[Any]    )     ->   int:
														self.save_config(save_directory=lowerCamelCase   ,     push_to_hub=lowerCamelCase   ,     **lowerCamelCase    )

							@property
							def    __snake_case (							self	:  Tuple    )     ->   List[Any]:
														return self._get_compatibles()






							@classmethod
							def    __snake_case (							cls	:  int    )     ->   Dict:
														__snake_case		:      Tuple										=       list(set([cls.__name__] + cls._compatibles    )    )
														__snake_case		:      int										=       importlib.import_module(__name__.split("."    )[0]    )
														__snake_case		:      Tuple										=       [
														    getattr(lowerCamelCase   ,     lowerCamelCase    ) for c in compatible_classes_str if hasattr(lowerCamelCase   ,     lowerCamelCase    )
														]
														return compatible_classes







def     lowerCAmelCase_					( __lowerCamelCase							,     __lowerCamelCase     ):
							assert len(__lowerCamelCase     ) >= x.ndim
							return jnp.broadcast_to(x.reshape(x.shape + (1,) * (len(__lowerCamelCase     ) - x.ndim)     )							,     __lowerCamelCase     )







def     lowerCAmelCase_					( __lowerCamelCase							,     __lowerCamelCase=0.9_9_9							,     __lowerCamelCase=jnp.floataa     ):

							def alpha_bar(__lowerCamelCase     ):
														return math.cos((time_step + 0.0_0_8) / 1.0_0_8 * math.pi / 2     ) ** 2

							__snake_case		:      List[Any]										=       []
							for i in range(__lowerCamelCase     ):
														__snake_case		:      Dict										=       i / num_diffusion_timesteps
														__snake_case		:      str										=       (i + 1) / num_diffusion_timesteps
														betas.append(min(1 - alpha_bar(__lowerCamelCase     ) / alpha_bar(__lowerCamelCase     )							,     __lowerCamelCase     )     )
							return jnp.array(__lowerCamelCase							,     dtype=__lowerCamelCase     )

@flax.struct.dataclass
class     a		:




							"""simple docstring"""


							__UpperCAmelCase   :							jnp.ndarray
							__UpperCAmelCase   :							jnp.ndarray
							__UpperCAmelCase   :							jnp.ndarray

							@classmethod
							def    __snake_case (							cls	:  Union[str, Any]   ,     lowerCamelCase	:  int    )     ->   List[Any]:
														__snake_case		:      Dict										=       scheduler.config

														if config.trained_betas is not None:
																					__snake_case		:      Dict										=       jnp.asarray(config.trained_betas   ,     dtype=scheduler.dtype    )
														elif config.beta_schedule == "linear":
																					__snake_case		:      Optional[int]										=       jnp.linspace(config.beta_start   ,     config.beta_end   ,     config.num_train_timesteps   ,     dtype=scheduler.dtype    )
														elif config.beta_schedule == "scaled_linear":
																					# this schedule is very specific to the latent diffusion model.
																					__snake_case		:      str										=       (
																					    jnp.linspace(
																					        config.beta_start**0.5   ,     config.beta_end**0.5   ,     config.num_train_timesteps   ,     dtype=scheduler.dtype    )
																					    ** 2
																					)
														elif config.beta_schedule == "squaredcos_cap_v2":
																					# Glide cosine schedule
																					__snake_case		:      Optional[Any]										=       betas_for_alpha_bar(config.num_train_timesteps   ,     dtype=scheduler.dtype    )
														else:
																					raise NotImplementedError(
																					    F'beta_schedule {config.beta_schedule} is not implemented for scheduler {scheduler.__class__.__name__}'    )

														__snake_case		:      Any										=       1.0 - betas

														__snake_case		:      int										=       jnp.cumprod(lowerCamelCase   ,     axis=0    )

														return cls(
														    alphas=lowerCamelCase   ,     betas=lowerCamelCase   ,     alphas_cumprod=lowerCamelCase   ,     )







def     lowerCAmelCase_					( __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase     ):
							__snake_case		:      List[Any]										=       state.alphas_cumprod

							__snake_case		:      str										=       alphas_cumprod[timesteps] ** 0.5
							__snake_case		:      Dict										=       sqrt_alpha_prod.flatten()
							__snake_case		:      str										=       broadcast_to_shape_from_left(__lowerCamelCase							,     original_samples.shape     )

							__snake_case		:      Tuple										=       (1 - alphas_cumprod[timesteps]) ** 0.5
							__snake_case		:      str										=       sqrt_one_minus_alpha_prod.flatten()
							__snake_case		:      Tuple										=       broadcast_to_shape_from_left(__lowerCamelCase							,     original_samples.shape     )

							return sqrt_alpha_prod, sqrt_one_minus_alpha_prod







def     lowerCAmelCase_					( __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase     ):
							__snake_case			,      __snake_case		:      Union[str, Any]										=       get_sqrt_alpha_prod(__lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase     )
							__snake_case		:      List[str]										=       sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
							return noisy_samples







def     lowerCAmelCase_					( __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase     ):
							__snake_case			,      __snake_case		:      Dict										=       get_sqrt_alpha_prod(__lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase     )
							__snake_case		:      Optional[int]										=       sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
							return velocity

