
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 							lowercase						:
							lowercase_			:			CommonSchedulerState

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

							# running values
							lowercase_			:			Optional[jnp.ndarray]			   =None




							@classmethod
							def 					A__ (							cls  ,A__  ,A__  ,A__  ,A__):
												return cls(common=A__  ,init_noise_sigma=A__  ,timesteps=A__  ,sigmas=A__)







@dataclass
class 							lowercase						(   SCREAMING_SNAKE_CASE__						):
							lowercase_			:			LMSDiscreteSchedulerState







class 							lowercase						(   SCREAMING_SNAKE_CASE__			,    SCREAMING_SNAKE_CASE__						):
							lowercase_			:			str			   =[e.name for e in FlaxKarrasDiffusionSchedulers]

							lowercase_			:			jnp.dtype




							@property
							def 					A__ (							self):
												return True




							@register_to_config
							def __init__(							self  ,A__ = 1_0_0_0  ,A__ = 0.0001  ,A__ = 0.02  ,A__ = "linear"  ,A__ = None  ,A__ = "epsilon"  ,A__ = jnp.floataa  ,):
												lowercase		      =		dtype




							def 					A__ (							self  ,A__ = None):
												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=A__  ,init_noise_sigma=A__  ,timesteps=A__  ,sigmas=A__  ,)




							def 					A__ (							self  ,A__  ,A__  ,A__):
												((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 					A__ (							self  ,A__  ,A__  ,A__  ,A__):

												def lms_derivative(A__):
																	lowercase		      =		1.0
																	for k in range(A__):
																						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(A__  ,state.sigmas[t]  ,state.sigmas[t + 1]  ,epsrel=1E-4)[0]

												return integrated_coeff




							def 					A__ (							self  ,A__  ,A__  ,A__ = ()):
												lowercase		      =		jnp.linspace(self.config.num_train_timesteps - 1  ,0  ,A__  ,dtype=self.dtype)

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

												lowercase		      =		jnp.mod(A__  ,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=A__  ,sigmas=A__  ,num_inference_steps=A__  ,derivatives=A__  ,)




							def 					A__ (							self  ,A__  ,A__  ,A__  ,A__  ,A__ = 4  ,A__ = True  ,):
												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  ,A__))
												if len(state.derivatives) > order:
																	lowercase		      =		state.replace(derivatives=jnp.delete(state.derivatives  ,0))

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

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

												if not return_dict:
																	return (prev_sample, state)

												return FlaxLMSSchedulerOutput(prev_sample=A__  ,state=A__)




							def 					A__ (							self  ,A__  ,A__  ,A__  ,A__  ,):
												lowercase		      =		state.sigmas[timesteps].flatten()
												lowercase		      =		broadcast_to_shape_from_left(A__  ,noise.shape)

												lowercase		      =		original_samples + noise * sigma

												return noisy_samples





							def __len__(							self):
												return self.config.num_train_timesteps






def 			UpperCamelCase       (				lowerCAmelCase__ = 30						):
					'''simple docstring'''
					lowercase		      =		exponent + 2
					lowercase		      =		(1 + 5**0.5) / 2
					lowercase		      =		(phi**fibonacci_index - (phi - 1) ** fibonacci_index) / 5**0.5

					return int(lowerCAmelCase__						)


if __name__ == "__main__":
							print(F'{solution() = }')




