






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 __lowerCamelCase				:





	"""simple docstring"""






	UpperCamelCase__			=   42

	# setable values
	UpperCamelCase__			=   42
	UpperCamelCase__			=   42
	UpperCamelCase__			=   42
	UpperCamelCase__			=   None

	# running values
	UpperCamelCase__			=   None

	@classmethod
	def  UpperCamelCase					(							cls ,					UpperCAmelCase ,					UpperCAmelCase ,					UpperCAmelCase ,					UpperCAmelCase					):
							"""simple docstring"""







							return cls(common=UpperCAmelCase ,					init_noise_sigma=UpperCAmelCase ,					timesteps=UpperCAmelCase ,					sigmas=UpperCAmelCase					)





@dataclass
class __lowerCamelCase				(   snake_case__):





	"""simple docstring"""






	UpperCamelCase__			=   42





class __lowerCamelCase				(   snake_case__  , snake_case__):





	"""simple docstring"""






	UpperCamelCase__			=   [e.name for e in FlaxKarrasDiffusionSchedulers]

	UpperCamelCase__			=   42

	@property
	def  UpperCamelCase					(							self					):
							"""simple docstring"""







							return True

	@register_to_config
	def __init__(							self ,					UpperCAmelCase = 1000 ,					UpperCAmelCase = 0.00_01 ,					UpperCAmelCase = 0.02 ,					UpperCAmelCase = "linear" ,					UpperCAmelCase = None ,					UpperCAmelCase = "epsilon" ,					UpperCAmelCase = jnp.floataa ,					):
							"""simple docstring"""







							_UpperCAmelCase             =    dtype

	def  UpperCamelCase					(							self ,					UpperCAmelCase = None					):
							"""simple docstring"""







							if common is None:
													_UpperCAmelCase             =    CommonSchedulerState.create(self					)

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

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

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

	def  UpperCamelCase					(							self ,					UpperCAmelCase ,					UpperCAmelCase ,					UpperCAmelCase					):
							"""simple docstring"""







							((_UpperCAmelCase)      ,				)             =    jnp.where(state.timesteps == timestep ,					size=1					)
							_UpperCAmelCase             =    step_index[0]

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

	def  UpperCamelCase					(							self ,					UpperCAmelCase ,					UpperCAmelCase ,					UpperCAmelCase ,					UpperCAmelCase					):
							"""simple docstring"""







							def lms_derivative(UpperCAmelCase					):
													_UpperCAmelCase             =    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

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

							return integrated_coeff

	def  UpperCamelCase					(							self ,					UpperCAmelCase ,					UpperCAmelCase ,					UpperCAmelCase = ()					):
							"""simple docstring"""







							_UpperCAmelCase             =    jnp.linspace(self.config.num_train_timesteps - 1 ,					0 ,					UpperCAmelCase ,					dtype=self.dtype					)

							_UpperCAmelCase             =    jnp.floor(UpperCAmelCase					).astype(jnp.intaa					)
							_UpperCAmelCase             =    jnp.ceil(UpperCAmelCase					).astype(jnp.intaa					)

							_UpperCAmelCase             =    jnp.mod(UpperCAmelCase ,					1.0					)

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

							_UpperCAmelCase             =    timesteps.astype(jnp.intaa					)

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

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

	def  UpperCamelCase					(							self ,					UpperCAmelCase ,					UpperCAmelCase ,					UpperCAmelCase ,					UpperCAmelCase ,					UpperCAmelCase = 4 ,					UpperCAmelCase = True ,					):
							"""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'					)

							_UpperCAmelCase             =    state.sigmas[timestep]

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

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

							# 4. Compute previous sample based on the derivatives path
							_UpperCAmelCase             =    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  UpperCamelCase					(							self ,					UpperCAmelCase ,					UpperCAmelCase ,					UpperCAmelCase ,					UpperCAmelCase ,					):
							"""simple docstring"""







							_UpperCAmelCase             =    state.sigmas[timesteps].flatten()
							_UpperCAmelCase             =    broadcast_to_shape_from_left(UpperCAmelCase ,					noise.shape					)

							_UpperCAmelCase             =    original_samples + noise * sigma

							return noisy_samples

	def __len__(							self					):
							"""simple docstring"""







							return self.config.num_train_timesteps








from itertools import combinations_with_replacement


def __A					(   __lowerCAmelCase = 100			)->						int:





						"""simple docstring"""



						_UpperCAmelCase             =    [*list(range(1				,	21			)			), 25]
						_UpperCAmelCase             =    [2 * x for x in range(1				,	21			)] + [50]
						_UpperCAmelCase             =    [3 * x for x in range(1				,	21			)]
						_UpperCAmelCase             =    singles + doubles + triples + [0]

						_UpperCAmelCase             =    0
						_UpperCAmelCase             =    42
						_UpperCAmelCase             =    42
						_UpperCAmelCase             =    42
						_UpperCAmelCase             =    42

						for double in doubles:
												for throwa, throwa in combinations_with_replacement(__lowerCAmelCase				,	2			):
																		_UpperCAmelCase             =    double + throwa + throwa
																		if checkout_total < limit:
																								num_checkouts += 1

						return num_checkouts


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