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"""







  A_						 =      42

  # setable values
  A_						 =      42
  A_						 =      42
  A_						 =      42
  A_						 =      None

  # running values
  A_						 =      None



  @classmethod
  def 				_a				(			cls    :				str  ,					__SCREAMING_SNAKE_CASE    :				Union[str, Any]  ,					__SCREAMING_SNAKE_CASE    :				Tuple  ,					__SCREAMING_SNAKE_CASE    :				Any  ,					__SCREAMING_SNAKE_CASE    :				Union[str, Any]   ):






     """simple docstring"""
     return cls(common=__UpperCamelCase  ,					init_noise_sigma=__UpperCamelCase  ,					timesteps=__UpperCamelCase  ,					sigmas=__UpperCamelCase   )

@dataclass
class 	_SCREAMING_SNAKE_CASE							(     UpperCAmelCase_							):






  """simple docstring"""







  A_						 =      42

class 	_SCREAMING_SNAKE_CASE							(     UpperCAmelCase_      ,     UpperCAmelCase_							):






  """simple docstring"""







  A_						 =      [e.name for e in FlaxKarrasDiffusionSchedulers]

  A_						 =      42



  @property
  def 				_a				(			self    :				Optional[Any]   ):






     """simple docstring"""
     return True



  @register_to_config
  def __init__(			self    :				Any  ,					__SCREAMING_SNAKE_CASE    :				Any = 1_000  ,					__SCREAMING_SNAKE_CASE    :				List[str] = 0.0_0_0_1  ,					__SCREAMING_SNAKE_CASE    :				Any = 0.0_2  ,					__SCREAMING_SNAKE_CASE    :				Tuple = "linear"  ,					__SCREAMING_SNAKE_CASE    :				List[str] = None  ,					__SCREAMING_SNAKE_CASE    :				str = "epsilon"  ,					__SCREAMING_SNAKE_CASE    :				int = jnp.floataa  ,					):






     """simple docstring"""
     _snake_case              =      dtype



  def 				_a				(			self    :				Union[str, Any]  ,					__SCREAMING_SNAKE_CASE    :				Optional[Any] = None   ):






     """simple docstring"""
     if common is None:
        _snake_case              =      CommonSchedulerState.create(self   )

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

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

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



  def 				_a				(			self    :				str  ,					__SCREAMING_SNAKE_CASE    :				Union[str, Any]  ,					__SCREAMING_SNAKE_CASE    :				Union[str, Any]  ,					__SCREAMING_SNAKE_CASE    :				Dict   ):






     """simple docstring"""
     ((_snake_case					)       , 					)              =      jnp.where(state.timesteps == timestep  ,					size=1   )
     _snake_case              =      step_index[0]

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



  def 				_a				(			self    :				str  ,					__SCREAMING_SNAKE_CASE    :				Optional[int]  ,					__SCREAMING_SNAKE_CASE    :				Optional[Any]  ,					__SCREAMING_SNAKE_CASE    :				Union[str, Any]  ,					__SCREAMING_SNAKE_CASE    :				List[str]   ):






     """simple docstring"""

     def lms_derivative(__SCREAMING_SNAKE_CASE    :				List[Any]   ):
        _snake_case              =      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

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

     return integrated_coeff



  def 				_a				(			self    :				str  ,					__SCREAMING_SNAKE_CASE    :				Optional[Any]  ,					__SCREAMING_SNAKE_CASE    :				Union[str, Any]  ,					__SCREAMING_SNAKE_CASE    :				Tuple = ()   ):






     """simple docstring"""
     _snake_case              =      jnp.linspace(self.config.num_train_timesteps - 1  ,					0  ,					__UpperCamelCase  ,					dtype=self.dtype   )

     _snake_case              =      jnp.floor(__UpperCamelCase   ).astype(jnp.intaa   )
     _snake_case              =      jnp.ceil(__UpperCamelCase   ).astype(jnp.intaa   )

     _snake_case              =      jnp.mod(__UpperCamelCase  ,					1.0   )

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

     _snake_case              =      timesteps.astype(jnp.intaa   )

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

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



  def 				_a				(			self    :				List[Any]  ,					__SCREAMING_SNAKE_CASE    :				Optional[int]  ,					__SCREAMING_SNAKE_CASE    :				Any  ,					__SCREAMING_SNAKE_CASE    :				Optional[Any]  ,					__SCREAMING_SNAKE_CASE    :				str  ,					__SCREAMING_SNAKE_CASE    :				List[Any] = 4  ,					__SCREAMING_SNAKE_CASE    :				str = 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"   )

     _snake_case              =      state.sigmas[timestep]

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

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

     # 4. Compute previous sample based on the derivatives path
     _snake_case              =      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 				_a				(			self    :				Dict  ,					__SCREAMING_SNAKE_CASE    :				Dict  ,					__SCREAMING_SNAKE_CASE    :				Optional[Any]  ,					__SCREAMING_SNAKE_CASE    :				Union[str, Any]  ,					__SCREAMING_SNAKE_CASE    :				Dict  ,					):






     """simple docstring"""
     _snake_case              =      state.sigmas[timesteps].flatten()
     _snake_case              =      broadcast_to_shape_from_left(__UpperCamelCase  ,					noise.shape   )

     _snake_case              =      original_samples + noise * sigma

     return noisy_samples







  def __len__(			self    :				Dict   ):






     """simple docstring"""
     return self.config.num_train_timesteps


from math import gcd






def    UpperCAmelCase__(						lowerCamelCase_ = 12000  ):



			"""simple docstring"""





			_snake_case              =      0
			for d in range(max_d + 1  ):
						for n in range(d // 3 + 1							,	(d + 1) // 2  ):
									if gcd(lowerCamelCase_							,	lowerCamelCase_  ) == 1:
												fractions_number += 1
			return fractions_number


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

