

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_					:
     _lowercase     :	List[Any]        =      4_2

     # setable values
     _lowercase     :	Tuple        =      4_2
     _lowercase     :	int        =      4_2
     _lowercase     :	List[str]        =      4_2
     _lowercase     :	int        =      None

     # running values
     _lowercase     :	Optional[int]        =      None


     @classmethod
     def     UpperCAmelCase    (				cls     :						Union[str, Any]     ,    UpperCAmelCase     :						CommonSchedulerState     ,    UpperCAmelCase     :						jnp.ndarray     ,    UpperCAmelCase     :						jnp.ndarray     ,    UpperCAmelCase     :						jnp.ndarray   )				->      Dict:
      return cls(common=_SCREAMING_SNAKE_CASE     ,    init_noise_sigma=_SCREAMING_SNAKE_CASE     ,    timesteps=_SCREAMING_SNAKE_CASE     ,    sigmas=_SCREAMING_SNAKE_CASE   )







@dataclass
class 				A_					(						snake_case__   ):
     _lowercase     :	Union[str, Any]        =      4_2







class 				A_					(						snake_case__				,      snake_case__   ):
     _lowercase     :	Optional[Any]        =      [e.name for e in FlaxKarrasDiffusionSchedulers]

     _lowercase     :	List[str]        =      4_2


     @property
     def     UpperCAmelCase    (				self     :						List[str]   )				->      int:
      return True


     @register_to_config
     def __init__(				self     :						Any     ,    UpperCAmelCase     :						int = 1_0_0_0     ,    UpperCAmelCase     :						float = 0.0001     ,    UpperCAmelCase     :						float = 0.02     ,    UpperCAmelCase     :						str = "linear"     ,    UpperCAmelCase     :						Optional[jnp.ndarray] = None     ,    UpperCAmelCase     :						str = "epsilon"     ,    UpperCAmelCase     :						jnp.dtype = jnp.floataa     ,    )				->      str:
      __lowerCAmelCase:  List[str]        = dtype


     def     UpperCAmelCase    (				self     :						int     ,    UpperCAmelCase     :						Optional[CommonSchedulerState] = None   )				->      LMSDiscreteSchedulerState:
      if common is None:
       __lowerCAmelCase:  Dict        = CommonSchedulerState.create(self   )

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

      # standard deviation of the initial noise distribution
      __lowerCAmelCase:  int        = sigmas.max()

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


     def     UpperCAmelCase    (				self     :						int     ,    UpperCAmelCase     :						LMSDiscreteSchedulerState     ,    UpperCAmelCase     :						jnp.ndarray     ,    UpperCAmelCase     :						int   )				->      jnp.ndarray:
      ((__lowerCAmelCase		)      ,						):  int        = jnp.where(state.timesteps == timestep     ,    size=1   )
      __lowerCAmelCase:  List[str]        = step_index[0]

      __lowerCAmelCase:  str        = state.sigmas[step_index]
      __lowerCAmelCase:  List[str]        = sample / ((sigma**2 + 1) ** 0.5)
      return sample


     def     UpperCAmelCase    (				self     :						Any     ,    UpperCAmelCase     :						LMSDiscreteSchedulerState     ,    UpperCAmelCase     :						Any     ,    UpperCAmelCase     :						Any     ,    UpperCAmelCase     :						List[str]   )				->      Optional[int]:

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

      __lowerCAmelCase:  Dict        = integrate.quad(_SCREAMING_SNAKE_CASE     ,    state.sigmas[t]     ,    state.sigmas[t + 1]     ,    epsrel=1E-4   )[0]

      return integrated_coeff


     def     UpperCAmelCase    (				self     :						Optional[int]     ,    UpperCAmelCase     :						LMSDiscreteSchedulerState     ,    UpperCAmelCase     :						int     ,    UpperCAmelCase     :						Tuple = ()   )				->      LMSDiscreteSchedulerState:
      __lowerCAmelCase:  List[str]        = jnp.linspace(self.config.num_train_timesteps - 1     ,    0     ,    _SCREAMING_SNAKE_CASE     ,    dtype=self.dtype   )

      __lowerCAmelCase:  Optional[int]        = jnp.floor(_SCREAMING_SNAKE_CASE   ).astype(jnp.intaa   )
      __lowerCAmelCase:  Optional[Any]        = jnp.ceil(_SCREAMING_SNAKE_CASE   ).astype(jnp.intaa   )

      __lowerCAmelCase:  Dict        = jnp.mod(_SCREAMING_SNAKE_CASE     ,    1.0   )

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

      __lowerCAmelCase:  Union[str, Any]        = timesteps.astype(jnp.intaa   )

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

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


     def     UpperCAmelCase    (				self     :						Tuple     ,    UpperCAmelCase     :						LMSDiscreteSchedulerState     ,    UpperCAmelCase     :						jnp.ndarray     ,    UpperCAmelCase     :						int     ,    UpperCAmelCase     :						jnp.ndarray     ,    UpperCAmelCase     :						int = 4     ,    UpperCAmelCase     :						bool = 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'   )

      __lowerCAmelCase:  str        = state.sigmas[timestep]

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

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

      # 4. Compute previous sample based on the derivatives path
      __lowerCAmelCase:  Optional[int]        = sample + sum(
          coeff * derivative for coeff, derivative in zip(_SCREAMING_SNAKE_CASE     ,    reversed(state.derivatives   )   )   )

      if not return_dict:
       return (prev_sample, state)

      return FlaxLMSSchedulerOutput(prev_sample=_SCREAMING_SNAKE_CASE     ,    state=_SCREAMING_SNAKE_CASE   )


     def     UpperCAmelCase    (				self     :						str     ,    UpperCAmelCase     :						LMSDiscreteSchedulerState     ,    UpperCAmelCase     :						jnp.ndarray     ,    UpperCAmelCase     :						jnp.ndarray     ,    UpperCAmelCase     :						jnp.ndarray     ,    )				->      jnp.ndarray:
      __lowerCAmelCase:  Any        = state.sigmas[timesteps].flatten()
      __lowerCAmelCase:  int        = broadcast_to_shape_from_left(_SCREAMING_SNAKE_CASE     ,    noise.shape   )

      __lowerCAmelCase:  List[str]        = original_samples + noise * sigma

      return noisy_samples


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













def   snake_case		(				UpperCAmelCase						:							Optional[int],    UpperCAmelCase						:							str ):
				# "Simpson Rule"
				# int(f) = delta_x/2 * (b-a)/3*(f1 + 4f2 + 2f_3 + ... + fn)
				A									=   (boundary[1] - boundary[0]) / steps
				A									=   boundary[0]
				A									=   boundary[1]
				A									=   make_points(UpperCAmelCase,    UpperCAmelCase,    UpperCAmelCase )
				A									=   0.0
				y += (h / 3.0) * f(UpperCAmelCase )
				A									=   2
				for i in x_i:
								y += (h / 3) * (4 - 2 * (cnt % 2)) * f(UpperCAmelCase )
								cnt += 1
				y += (h / 3.0) * f(UpperCAmelCase )
				return y







def   snake_case		(				UpperCAmelCase						:							int,    UpperCAmelCase						:							int,    UpperCAmelCase						:							List[Any] ):
				A									=   a + h
				while x < (b - h):
								yield x
								A									=   x + h







def   snake_case		(				UpperCAmelCase						:							str ):  # enter your function here
				A									=   (x - 0) * (x - 0)
				return y







def   snake_case		(				):
				A									=   0.0  # Lower bound of integration
				A									=   1.0  # Upper bound of integration
				A									=   10.0  # define number of steps or resolution
				A									=   [a, b]  # define boundary of integration
				A									=   method_a(UpperCAmelCase,    UpperCAmelCase )
				print(f'y = {y}' )


if __name__ == "__main__":
					main()





