
"""simple docstring"""






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

import flax
import jax.numpy as jnp
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    broadcast_to_shape_from_left,
)

@flax.struct.dataclass
class 				__a    :



							'''simple docstring'''







							_lowerCamelCase				: CommonSchedulerState

							# setable values
							_lowerCamelCase				: jnp.ndarray
							_lowerCamelCase				: jnp.ndarray
							_lowerCamelCase				: jnp.ndarray
							_lowerCamelCase				: Optional[int]					      =      None

							# running values
							_lowerCamelCase				: Optional[jnp.ndarray]					      =      None
							@classmethod
							def      SCREAMING_SNAKE_CASE	(    cls     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase					) ->       Tuple:




										'''simple docstring'''
										return cls(common=_lowerCamelCase     ,						init_noise_sigma=_lowerCamelCase     ,						timesteps=_lowerCamelCase     ,						sigmas=_lowerCamelCase					)





@dataclass
class 				__a    (   __a					):



							'''simple docstring'''







							_lowerCamelCase				: LMSDiscreteSchedulerState





class 				__a    (   __a				,      __a					):



							'''simple docstring'''







							_lowerCamelCase				: List[Any]					      =      [e.name for e in FlaxKarrasDiffusionSchedulers]

							_lowerCamelCase				: jnp.dtype
							@property
							def      SCREAMING_SNAKE_CASE	(    self					) ->       List[str]:




										'''simple docstring'''
										return True
							@register_to_config
							def __init__(    self     ,						_lowerCamelCase = 1_000     ,						_lowerCamelCase = 0.0001     ,						_lowerCamelCase = 0.02     ,						_lowerCamelCase = "linear"     ,						_lowerCamelCase = None     ,						_lowerCamelCase = "epsilon"     ,						_lowerCamelCase = jnp.floataa     ,						) ->       Optional[int]:




										'''simple docstring'''
										__lowercase						      =					dtype
							def      SCREAMING_SNAKE_CASE	(    self     ,						_lowerCamelCase = None					) ->       LMSDiscreteSchedulerState:




										'''simple docstring'''
										if common is None:
													__lowercase						      =					CommonSchedulerState.create(self					)

										__lowercase						      =					jnp.arange(0     ,						self.config.num_train_timesteps					).round()[::-1]
										__lowercase						      =					((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

										# standard deviation of the initial noise distribution
										__lowercase						      =					sigmas.max()

										return LMSDiscreteSchedulerState.create(
										    common=_lowerCamelCase     ,						init_noise_sigma=_lowerCamelCase     ,						timesteps=_lowerCamelCase     ,						sigmas=_lowerCamelCase     ,						)
							def      SCREAMING_SNAKE_CASE	(    self     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase					) ->       jnp.ndarray:




										'''simple docstring'''
										((__lowercase)      ,				)						      =					jnp.where(state.timesteps == timestep     ,						size=1					)
										__lowercase						      =					step_index[0]

										__lowercase						      =					state.sigmas[step_index]
										__lowercase						      =					sample / ((sigma**2 + 1) ** 0.5)
										return sample
							def      SCREAMING_SNAKE_CASE	(    self     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase					) ->       Dict:




										'''simple docstring'''

										def lms_derivative(_lowerCamelCase					):
													__lowercase						      =					1.0
													for k in range(_lowerCamelCase					):
																if current_order == k:
																			continue
																prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
													return prod

										__lowercase						      =					integrate.quad(_lowerCamelCase     ,						state.sigmas[t]     ,						state.sigmas[t + 1]     ,						epsrel=1e-4					)[0]

										return integrated_coeff
							def      SCREAMING_SNAKE_CASE	(    self     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase = ()					) ->       LMSDiscreteSchedulerState:




										'''simple docstring'''
										__lowercase						      =					jnp.linspace(self.config.num_train_timesteps - 1     ,						0     ,						_lowerCamelCase     ,						dtype=self.dtype					)

										__lowercase						      =					jnp.floor(_lowerCamelCase					).astype(jnp.intaa					)
										__lowercase						      =					jnp.ceil(_lowerCamelCase					).astype(jnp.intaa					)

										__lowercase						      =					jnp.mod(_lowerCamelCase     ,						1.0					)

										__lowercase						      =					((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
										__lowercase						      =					(1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
										__lowercase						      =					jnp.concatenate([sigmas, jnp.array([0.0]     ,						dtype=self.dtype					)]					)

										__lowercase						      =					timesteps.astype(jnp.intaa					)

										# initial running values
										__lowercase						      =					jnp.zeros((0,) + shape     ,						dtype=self.dtype					)

										return state.replace(
										    timesteps=_lowerCamelCase     ,						sigmas=_lowerCamelCase     ,						num_inference_steps=_lowerCamelCase     ,						derivatives=_lowerCamelCase     ,						)
							def      SCREAMING_SNAKE_CASE	(    self     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase = 4     ,						_lowerCamelCase = True     ,						) ->       Union[FlaxLMSSchedulerOutput, Tuple]:




										'''simple docstring'''
										if state.num_inference_steps is None:
													raise ValueError(
													    "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"					)

										__lowercase						      =					state.sigmas[timestep]

										# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
										if self.config.prediction_type == "epsilon":
													__lowercase						      =					sample - sigma * model_output
										elif self.config.prediction_type == "v_prediction":
													# * c_out + input * c_skip
													__lowercase						      =					model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
										else:
													raise ValueError(
													    f'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''					)

										# 2. Convert to an ODE derivative
										__lowercase						      =					(sample - pred_original_sample) / sigma
										__lowercase						      =					state.replace(derivatives=jnp.append(state.derivatives     ,						_lowerCamelCase					)					)
										if len(state.derivatives					) > order:
													__lowercase						      =					state.replace(derivatives=jnp.delete(state.derivatives     ,						0					)					)

										# 3. Compute linear multistep coefficients
										__lowercase						      =					min(timestep + 1     ,						_lowerCamelCase					)
										__lowercase						      =					[self.get_lms_coefficient(_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase					) for curr_order in range(_lowerCamelCase					)]

										# 4. Compute previous sample based on the derivatives path
										__lowercase						      =					sample + sum(
										    coeff * derivative for coeff, derivative in zip(_lowerCamelCase     ,						reversed(state.derivatives					)					)					)

										if not return_dict:
													return (prev_sample, state)

										return FlaxLMSSchedulerOutput(prev_sample=_lowerCamelCase     ,						state=_lowerCamelCase					)
							def      SCREAMING_SNAKE_CASE	(    self     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						_lowerCamelCase     ,						) ->       jnp.ndarray:




										'''simple docstring'''
										__lowercase						      =					state.sigmas[timesteps].flatten()
										__lowercase						      =					broadcast_to_shape_from_left(_lowerCamelCase     ,						noise.shape					)

										__lowercase						      =					original_samples + noise * sigma

										return noisy_samples





							def __len__(    self					) ->       Tuple:




										'''simple docstring'''
										return self.config.num_train_timesteps







"""simple docstring"""






class 				__a    :



							'''simple docstring'''







							def __init__(    self     ,						_lowerCamelCase					) ->       Optional[Any]:




										'''simple docstring'''
										__lowercase						      =					data
										__lowercase						      =					None
										__lowercase						      =					None





							def __str__(    self					) ->       str:




										'''simple docstring'''
										return f'''{self.data}'''





class 				__a    :



							'''simple docstring'''







							def __init__(    self					) ->       List[str]:




										'''simple docstring'''
										__lowercase						      =					None
										__lowercase						      =					None
							def __iter__(    self					) ->       int:




										'''simple docstring'''
										__lowercase						      =					self.head
										while node:
													yield node.data
													__lowercase						      =					node.next
							def __str__(    self					) ->       Union[str, Any]:




										'''simple docstring'''
										return "->".join([str(_lowerCamelCase					) for item in self]					)
							def __len__(    self					) ->       Dict:




										'''simple docstring'''
										return sum(1 for _ in self					)
							def      SCREAMING_SNAKE_CASE	(    self     ,						_lowerCamelCase					) ->       Union[str, Any]:




										'''simple docstring'''
										self.insert_at_nth(0     ,						_lowerCamelCase					)
							def      SCREAMING_SNAKE_CASE	(    self     ,						_lowerCamelCase					) ->       List[str]:




										'''simple docstring'''
										self.insert_at_nth(len(self					)     ,						_lowerCamelCase					)
							def      SCREAMING_SNAKE_CASE	(    self     ,						_lowerCamelCase     ,						_lowerCamelCase					) ->       List[Any]:




										'''simple docstring'''
										__lowercase						      =					len(self					)

										if not 0 <= index <= length:
													raise IndexError("list index out of range"					)
										__lowercase						      =					Node(_lowerCamelCase					)
										if self.head is None:
													__lowercase						      =					__lowercase						      =					new_node
										elif index == 0:
													__lowercase						      =					new_node
													__lowercase						      =					self.head
													__lowercase						      =					new_node
										elif index == length:
													__lowercase						      =					new_node
													__lowercase						      =					self.tail
													__lowercase						      =					new_node
										else:
													__lowercase						      =					self.head
													for _ in range(0     ,						_lowerCamelCase					):
																__lowercase						      =					temp.next
													__lowercase						      =					new_node
													__lowercase						      =					temp.previous
													__lowercase						      =					temp
													__lowercase						      =					new_node
							def      SCREAMING_SNAKE_CASE	(    self					) ->       Any:




										'''simple docstring'''
										return self.delete_at_nth(0					)
							def      SCREAMING_SNAKE_CASE	(    self					) ->       str:




										'''simple docstring'''
										return self.delete_at_nth(len(self					) - 1					)
							def      SCREAMING_SNAKE_CASE	(    self     ,						_lowerCamelCase					) ->       str:




										'''simple docstring'''
										__lowercase						      =					len(self					)

										if not 0 <= index <= length - 1:
													raise IndexError("list index out of range"					)
										__lowercase						      =					self.head  # default first node
										if length == 1:
													__lowercase						      =					__lowercase						      =					None
										elif index == 0:
													__lowercase						      =					self.head.next
													__lowercase						      =					None
										elif index == length - 1:
													__lowercase						      =					self.tail
													__lowercase						      =					self.tail.previous
													__lowercase						      =					None
										else:
													__lowercase						      =					self.head
													for _ in range(0     ,						_lowerCamelCase					):
																__lowercase						      =					temp.next
													__lowercase						      =					temp
													__lowercase						      =					temp.previous
													__lowercase						      =					temp.next
										return delete_node.data
							def      SCREAMING_SNAKE_CASE	(    self     ,						_lowerCamelCase					) ->       str:




										'''simple docstring'''
										__lowercase						      =					self.head

										while current.data != data:  # Find the position to delete
													if current.next:
																__lowercase						      =					current.next
													else:  # We have reached the end an no value matches
																raise ValueError("No data matching given value"					)

										if current == self.head:
													self.delete_head()

										elif current == self.tail:
													self.delete_tail()

										else:  # Before: 1 <--> 2(current) <--> 3
													__lowercase						      =					current.next  # 1 --> 3
													__lowercase						      =					current.previous  # 1 <--> 3
										return data





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




										'''simple docstring'''
										return len(self					) == 0





def     lowerCAmelCase__ (		)	->None:
			__lowercase						      =					DoublyLinkedList()
			assert linked_list.is_empty() is True
			assert str(__magic_name__			) == ""

			try:
						linked_list.delete_head()
						raise AssertionError  # This should not happen.
			except IndexError:
						assert True  # This should happen.

			try:
						linked_list.delete_tail()
						raise AssertionError  # This should not happen.
			except IndexError:
						assert True  # This should happen.

			for i in range(1_0			):
						assert len(__magic_name__			) == i
						linked_list.insert_at_nth(__magic_name__ ,      i + 1			)
			assert str(__magic_name__			) == "->".join(str(__magic_name__			) for i in range(1 ,      1_1			)			)

			linked_list.insert_at_head(0			)
			linked_list.insert_at_tail(1_1			)
			assert str(__magic_name__			) == "->".join(str(__magic_name__			) for i in range(0 ,      1_2			)			)

			assert linked_list.delete_head() == 0
			assert linked_list.delete_at_nth(9			) == 1_0
			assert linked_list.delete_tail() == 1_1
			assert len(__magic_name__			) == 9
			assert str(__magic_name__			) == "->".join(str(__magic_name__			) for i in range(1 ,      1_0			)			)


if __name__ == "__main__":
					from doctest import testmod

					testmod()





