




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       SCREAMING_SNAKE_CASE_							:



	"""simple docstring"""


	__magic_name__      :					CommonSchedulerState

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

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






	@classmethod
	def 				lowerCamelCase__    (				cls		:	Dict				,    lowerCAmelCase		:	CommonSchedulerState				,    lowerCAmelCase		:	jnp.ndarray				,    lowerCAmelCase		:	jnp.ndarray				,    lowerCAmelCase		:	jnp.ndarray  )  ->					List[Any]:







						"""simple docstring"""







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






@dataclass
class       SCREAMING_SNAKE_CASE_							(					_UpperCamelCase      ):



	"""simple docstring"""


	__magic_name__      :					LMSDiscreteSchedulerState






class       SCREAMING_SNAKE_CASE_							(					_UpperCamelCase  ,     _UpperCamelCase      ):



	"""simple docstring"""


	__magic_name__      :					Dict			  =		[e.name for e in FlaxKarrasDiffusionSchedulers]

	__magic_name__      :					jnp.dtype






	@property
	def 				lowerCamelCase__    (				self		:	Union[str, Any]  )  ->					List[str]:







						"""simple docstring"""







						return True






	@register_to_config
	def __init__(				self		:	List[Any]				,    lowerCAmelCase		:	int = 1000				,    lowerCAmelCase		:	float = 0.00_01				,    lowerCAmelCase		:	float = 0.02				,    lowerCAmelCase		:	str = "linear"				,    lowerCAmelCase		:	Optional[jnp.ndarray] = None				,    lowerCAmelCase		:	str = "epsilon"				,    lowerCAmelCase		:	jnp.dtype = jnp.floataa				,    )  ->					int:







						"""simple docstring"""







						__UpperCamelCase				:  str								=			dtype






	def 				lowerCamelCase__    (				self		:	Union[str, Any]				,    lowerCAmelCase		:	Optional[CommonSchedulerState] = None  )  ->					LMSDiscreteSchedulerState:







						"""simple docstring"""







						if common is None:
											__UpperCamelCase				:  Optional[Any]								=			CommonSchedulerState.create(self  )

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

						# standard deviation of the initial noise distribution
						__UpperCamelCase				:  List[str]								=			sigmas.max()

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






	def 				lowerCamelCase__    (				self		:	Any				,    lowerCAmelCase		:	LMSDiscreteSchedulerState				,    lowerCAmelCase		:	jnp.ndarray				,    lowerCAmelCase		:	int  )  ->					jnp.ndarray:







						"""simple docstring"""







						((__UpperCamelCase)			, )				:  Dict								=			jnp.where(state.timesteps == timestep				,    size=1  )
						__UpperCamelCase				:  Tuple								=			step_index[0]

						__UpperCamelCase				:  Dict								=			state.sigmas[step_index]
						__UpperCamelCase				:  Optional[int]								=			sample / ((sigma**2 + 1) ** 0.5)
						return sample






	def 				lowerCamelCase__    (				self		:	Any				,    lowerCAmelCase		:	LMSDiscreteSchedulerState				,    lowerCAmelCase		:	Union[str, Any]				,    lowerCAmelCase		:	str				,    lowerCAmelCase		:	Optional[int]  )  ->					Union[str, Any]:







						"""simple docstring"""







						def lms_derivative(lowerCAmelCase		:	Tuple  ):
											__UpperCamelCase				:  Dict								=			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

						__UpperCamelCase				:  Any								=			integrate.quad(lowerCAmelCase				,    state.sigmas[t]				,    state.sigmas[t + 1]				,    epsrel=1E-4  )[0]

						return integrated_coeff






	def 				lowerCamelCase__    (				self		:	str				,    lowerCAmelCase		:	LMSDiscreteSchedulerState				,    lowerCAmelCase		:	int				,    lowerCAmelCase		:	Tuple = ()  )  ->					LMSDiscreteSchedulerState:







						"""simple docstring"""







						__UpperCamelCase				:  str								=			jnp.linspace(self.config.num_train_timesteps - 1				,    0				,    lowerCAmelCase				,    dtype=self.dtype  )

						__UpperCamelCase				:  str								=			jnp.floor(lowerCAmelCase  ).astype(jnp.intaa  )
						__UpperCamelCase				:  Tuple								=			jnp.ceil(lowerCAmelCase  ).astype(jnp.intaa  )

						__UpperCamelCase				:  Optional[Any]								=			jnp.mod(lowerCAmelCase				,    1.0  )

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

						__UpperCamelCase				:  Optional[int]								=			timesteps.astype(jnp.intaa  )

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

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






	def 				lowerCamelCase__    (				self		:	Union[str, Any]				,    lowerCAmelCase		:	LMSDiscreteSchedulerState				,    lowerCAmelCase		:	jnp.ndarray				,    lowerCAmelCase		:	int				,    lowerCAmelCase		:	jnp.ndarray				,    lowerCAmelCase		:	int = 4				,    lowerCAmelCase		:	bool = 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"""  )

						__UpperCamelCase				:  Any								=			state.sigmas[timestep]

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

						# 3. Compute linear multistep coefficients
						__UpperCamelCase				:  Tuple								=			min(timestep + 1				,    lowerCAmelCase  )
						__UpperCamelCase				:  Tuple								=			[self.get_lms_coefficient(lowerCAmelCase				,    lowerCAmelCase				,    lowerCAmelCase				,    lowerCAmelCase  ) for curr_order in range(lowerCAmelCase  )]

						# 4. Compute previous sample based on the derivatives path
						__UpperCamelCase				:  Union[str, Any]								=			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 				lowerCamelCase__    (				self		:	int				,    lowerCAmelCase		:	LMSDiscreteSchedulerState				,    lowerCAmelCase		:	jnp.ndarray				,    lowerCAmelCase		:	jnp.ndarray				,    lowerCAmelCase		:	jnp.ndarray				,    )  ->					jnp.ndarray:







						"""simple docstring"""







						__UpperCamelCase				:  int								=			state.sigmas[timesteps].flatten()
						__UpperCamelCase				:  Any								=			broadcast_to_shape_from_left(lowerCAmelCase				,    noise.shape  )

						__UpperCamelCase				:  int								=			original_samples + noise * sigma

						return noisy_samples






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







						"""simple docstring"""







						return self.config.num_train_timesteps












import os





def 							A__   ()    ->	int:
					__UpperCamelCase				:  int								=			os.path.dirname(os.path.realpath(snake_case							)							)
					__UpperCamelCase				:  List[str]								=			os.path.join(snake_case		,  """triangle.txt"""							)

					with open(snake_case							) as in_file:
										__UpperCamelCase				:  Optional[Any]								=			[[int(snake_case							) for i in line.split()] for line in in_file]

					while len(snake_case							) != 1:
										__UpperCamelCase				:  Union[str, Any]								=			triangle.pop()
										__UpperCamelCase				:  List[str]								=			triangle[-1]
										for j in range(len(snake_case							) - 1							):
															curr_row[j] += max(last_row[j]		,  last_row[j + 1]							)
					return triangle[0][0]


if __name__ == "__main__":
	print(solution())






