"""simple docstring"""




def 	UpperCAmelCase       (						UpperCamelCase__					):






							"""simple docstring"""





							if not isinstance(UpperCamelCase__							,     UpperCamelCase__					):
														raise ValueError('double_factorial() only accepts integral values'					)
							if n < 0:
														raise ValueError('double_factorial() not defined for negative values'					)
							return 1 if n <= 1 else n * double_factorial(n - 2					)


if __name__ == "__main__":
				import doctest

				doctest.testmod()






"""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      UpperCamelCase__:
						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 					snake_case__						(							cls		,__UpperCAmelCase		,__UpperCAmelCase		,__UpperCAmelCase		,__UpperCAmelCase  )       ->					Optional[Any]:
													return cls(common=__UpperCAmelCase		,init_noise_sigma=__UpperCAmelCase		,timesteps=__UpperCAmelCase		,sigmas=__UpperCAmelCase  )






@dataclass
class      UpperCamelCase__(      __A			):
						lowerCAmelCase__	:    LMSDiscreteSchedulerState






class      UpperCamelCase__(      __A		,    __A			):
						lowerCAmelCase__	:    List[str]    				=		[e.name for e in FlaxKarrasDiffusionSchedulers]

						lowerCAmelCase__	:    jnp.dtype





						@property
						def 					snake_case__						(							self  )       ->					Union[str, Any]:
													return True





						@register_to_config
						def __init__(							self		,__UpperCAmelCase = 10_00		,__UpperCAmelCase = 0.0_0_0_1		,__UpperCAmelCase = 0.0_2		,__UpperCAmelCase = "linear"		,__UpperCAmelCase = None		,__UpperCAmelCase = "epsilon"		,__UpperCAmelCase = jnp.floataa		,)       ->					str:
													A__						  =				dtype





						def 					snake_case__						(							self		,__UpperCAmelCase = None  )       ->					LMSDiscreteSchedulerState:
													if common is None:
																				A__						  =				CommonSchedulerState.create(self  )

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

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

													return LMSDiscreteSchedulerState.create(
													    common=__UpperCAmelCase		,init_noise_sigma=__UpperCAmelCase		,timesteps=__UpperCAmelCase		,sigmas=__UpperCAmelCase		,)





						def 					snake_case__						(							self		,__UpperCAmelCase		,__UpperCAmelCase		,__UpperCAmelCase  )       ->					jnp.ndarray:
													((A__)  ,	)						  =				jnp.where(state.timesteps == timestep		,size=1  )
													A__						  =				step_index[0]

													A__						  =				state.sigmas[step_index]
													A__						  =				sample / ((sigma**2 + 1) ** 0.5)
													return sample





						def 					snake_case__						(							self		,__UpperCAmelCase		,__UpperCAmelCase		,__UpperCAmelCase		,__UpperCAmelCase  )       ->					Optional[int]:

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

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

													return integrated_coeff





						def 					snake_case__						(							self		,__UpperCAmelCase		,__UpperCAmelCase		,__UpperCAmelCase = ()  )       ->					LMSDiscreteSchedulerState:
													A__						  =				jnp.linspace(self.config.num_train_timesteps - 1		,0		,__UpperCAmelCase		,dtype=self.dtype  )

													A__						  =				jnp.floor(__UpperCAmelCase  ).astype(jnp.intaa  )
													A__						  =				jnp.ceil(__UpperCAmelCase  ).astype(jnp.intaa  )

													A__						  =				jnp.mod(__UpperCAmelCase		,1.0  )

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

													A__						  =				timesteps.astype(jnp.intaa  )

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

													return state.replace(
													    timesteps=__UpperCAmelCase		,sigmas=__UpperCAmelCase		,num_inference_steps=__UpperCAmelCase		,derivatives=__UpperCAmelCase		,)





						def 					snake_case__						(							self		,__UpperCAmelCase		,__UpperCAmelCase		,__UpperCAmelCase		,__UpperCAmelCase		,__UpperCAmelCase = 4		,__UpperCAmelCase = True		,)       ->					Union[FlaxLMSSchedulerOutput, Tuple]:
													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'  )

													A__						  =				state.sigmas[timestep]

													# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
													if self.config.prediction_type == "epsilon":
																				A__						  =				sample - sigma * model_output
													elif self.config.prediction_type == "v_prediction":
																				# * c_out + input * c_skip
																				A__						  =				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
													A__						  =				(sample - pred_original_sample) / sigma
													A__						  =				state.replace(derivatives=jnp.append(state.derivatives		,__UpperCAmelCase  )  )
													if len(state.derivatives  ) > order:
																				A__						  =				state.replace(derivatives=jnp.delete(state.derivatives		,0  )  )

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

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

													if not return_dict:
																				return (prev_sample, state)

													return FlaxLMSSchedulerOutput(prev_sample=__UpperCAmelCase		,state=__UpperCAmelCase  )





						def 					snake_case__						(							self		,__UpperCAmelCase		,__UpperCAmelCase		,__UpperCAmelCase		,__UpperCAmelCase		,)       ->					jnp.ndarray:
													A__						  =				state.sigmas[timesteps].flatten()
													A__						  =				broadcast_to_shape_from_left(__UpperCAmelCase		,noise.shape  )

													A__						  =				original_samples + noise * sigma

													return noisy_samples





						def __len__(							self  )       ->					Optional[Any]:
													return self.config.num_train_timesteps





