



"""simple docstring"""







from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax
import jax.numpy as jnp

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    add_noise_common,
    get_velocity_common,
)







@flax.struct.dataclass
class 				UpperCamelCase__       :




      """simple docstring"""




      _SCREAMING_SNAKE_CASE      =					42

      # setable values
      _SCREAMING_SNAKE_CASE      =					42
      _SCREAMING_SNAKE_CASE      =					42
      _SCREAMING_SNAKE_CASE      =					None



      @classmethod
      def 					SCREAMING_SNAKE_CASE__			(				cls    :				Dict   ,      SCREAMING_SNAKE_CASE_    :				Dict   ,      SCREAMING_SNAKE_CASE_    :				List[Any]   ,      SCREAMING_SNAKE_CASE_    :				Tuple	):
        return cls(common=lowerCamelCase_   ,      init_noise_sigma=lowerCamelCase_   ,      timesteps=lowerCamelCase_	)







@dataclass
class 				UpperCamelCase__       (     lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE      =					42







class 				UpperCamelCase__       (     lowercase_, lowercase_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE      =					[e.name for e in FlaxKarrasDiffusionSchedulers]

      _SCREAMING_SNAKE_CASE      =					42



      @property
      def 					SCREAMING_SNAKE_CASE__			(				self    :				str	):
        return True



      @register_to_config
      def __init__(				self    :				List[Any]   ,      SCREAMING_SNAKE_CASE_    :				Dict = 1_0_0_0   ,      SCREAMING_SNAKE_CASE_    :				Optional[int] = 0.00_01   ,      SCREAMING_SNAKE_CASE_    :				Dict = 0.02   ,      SCREAMING_SNAKE_CASE_    :				Union[str, Any] = "linear"   ,      SCREAMING_SNAKE_CASE_    :				Optional[int] = None   ,      SCREAMING_SNAKE_CASE_    :				Dict = "fixed_small"   ,      SCREAMING_SNAKE_CASE_    :				Tuple = True   ,      SCREAMING_SNAKE_CASE_    :				Dict = "epsilon"   ,      SCREAMING_SNAKE_CASE_    :				Optional[Any] = jnp.floataa   ,      ):
        lowerCAmelCase_       :    Any								=			dtype



      def 					SCREAMING_SNAKE_CASE__			(				self    :				List[str]   ,      SCREAMING_SNAKE_CASE_    :				List[Any] = None	):
        if common is None:
          lowerCAmelCase_       :    Optional[Any]								=			CommonSchedulerState.create(self	)

        # standard deviation of the initial noise distribution
        lowerCAmelCase_       :    Any								=			jnp.array(1.0   ,      dtype=self.dtype	)

        lowerCAmelCase_       :    Union[str, Any]								=			jnp.arange(0   ,      self.config.num_train_timesteps	).round()[::-1]

        return DDPMSchedulerState.create(
            common=lowerCamelCase_   ,      init_noise_sigma=lowerCamelCase_   ,      timesteps=lowerCamelCase_   ,      )



      def 					SCREAMING_SNAKE_CASE__			(				self    :				Tuple   ,      SCREAMING_SNAKE_CASE_    :				str   ,      SCREAMING_SNAKE_CASE_    :				List[Any]   ,      SCREAMING_SNAKE_CASE_    :				Dict = None	):
        return sample



      def 					SCREAMING_SNAKE_CASE__			(				self    :				Any   ,      SCREAMING_SNAKE_CASE_    :				Any   ,      SCREAMING_SNAKE_CASE_    :				Optional[Any]   ,      SCREAMING_SNAKE_CASE_    :				Dict = ()	):
        lowerCAmelCase_       :    Union[str, Any]								=			self.config.num_train_timesteps // num_inference_steps
        # creates integer timesteps by multiplying by ratio
        # rounding to avoid issues when num_inference_step is power of 3
        lowerCAmelCase_       :    Any								=			(jnp.arange(0   ,      lowerCamelCase_	) * step_ratio).round()[::-1]

        return state.replace(
            num_inference_steps=lowerCamelCase_   ,      timesteps=lowerCamelCase_   ,      )



      def 					SCREAMING_SNAKE_CASE__			(				self    :				List[Any]   ,      SCREAMING_SNAKE_CASE_    :				Tuple   ,      SCREAMING_SNAKE_CASE_    :				Dict   ,      SCREAMING_SNAKE_CASE_    :				List[Any]=None   ,      SCREAMING_SNAKE_CASE_    :				str=None	):
        lowerCAmelCase_       :    Any								=			state.common.alphas_cumprod[t]
        lowerCAmelCase_       :    Union[str, Any]								=			jnp.where(t > 0   ,      state.common.alphas_cumprod[t - 1]   ,      jnp.array(1.0   ,      dtype=self.dtype	)	)

        # For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
        # and sample from it to get previous sample
        # x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
        lowerCAmelCase_       :    Union[str, Any]								=			(1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

        if variance_type is None:
          lowerCAmelCase_       :    Optional[int]								=			self.config.variance_type

        # hacks - were probably added for training stability
        if variance_type == "fixed_small":
          lowerCAmelCase_       :    str								=			jnp.clip(lowerCamelCase_   ,      a_min=1E-20	)
        # for rl-diffuser https://arxiv.org/abs/2205.09991
        elif variance_type == "fixed_small_log":
          lowerCAmelCase_       :    Dict								=			jnp.log(jnp.clip(lowerCamelCase_   ,      a_min=1E-20	)	)
        elif variance_type == "fixed_large":
          lowerCAmelCase_       :    Optional[int]								=			state.common.betas[t]
        elif variance_type == "fixed_large_log":
          # Glide max_log
          lowerCAmelCase_       :    Optional[int]								=			jnp.log(state.common.betas[t]	)
        elif variance_type == "learned":
          return predicted_variance
        elif variance_type == "learned_range":
          lowerCAmelCase_       :    Union[str, Any]								=			variance
          lowerCAmelCase_       :    Dict								=			state.common.betas[t]
          lowerCAmelCase_       :    Tuple								=			(predicted_variance + 1) / 2
          lowerCAmelCase_       :    int								=			frac * max_log + (1 - frac) * min_log

        return variance



      def 					SCREAMING_SNAKE_CASE__			(				self    :				Any   ,      SCREAMING_SNAKE_CASE_    :				Optional[Any]   ,      SCREAMING_SNAKE_CASE_    :				Optional[int]   ,      SCREAMING_SNAKE_CASE_    :				Optional[int]   ,      SCREAMING_SNAKE_CASE_    :				Any   ,      SCREAMING_SNAKE_CASE_    :				Dict = None   ,      SCREAMING_SNAKE_CASE_    :				Union[str, Any] = True   ,      ):
        lowerCAmelCase_       :    Any								=			timestep

        if key is None:
          lowerCAmelCase_       :    Dict								=			jax.random.PRNGKey(0	)

        if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
          lowerCAmelCase_						,lowerCAmelCase_       :    str								=			jnp.split(lowerCamelCase_   ,      sample.shape[1]   ,      axis=1	)
        else:
          lowerCAmelCase_       :    str								=			None

        # 1. compute alphas, betas
        lowerCAmelCase_       :    List[Any]								=			state.common.alphas_cumprod[t]
        lowerCAmelCase_       :    Dict								=			jnp.where(t > 0   ,      state.common.alphas_cumprod[t - 1]   ,      jnp.array(1.0   ,      dtype=self.dtype	)	)
        lowerCAmelCase_       :    Optional[int]								=			1 - alpha_prod_t
        lowerCAmelCase_       :    int								=			1 - alpha_prod_t_prev

        # 2. compute predicted original sample from predicted noise also called
        # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
        if self.config.prediction_type == "epsilon":
          lowerCAmelCase_       :    int								=			(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
        elif self.config.prediction_type == "sample":
          lowerCAmelCase_       :    Optional[int]								=			model_output
        elif self.config.prediction_type == "v_prediction":
          lowerCAmelCase_       :    Dict								=			(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
        else:
          raise ValueError(
              F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` "
              ' for the FlaxDDPMScheduler.'	)

        # 3. Clip "predicted x_0"
        if self.config.clip_sample:
          lowerCAmelCase_       :    List[Any]								=			jnp.clip(lowerCamelCase_   ,      -1   ,      1	)

        # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
        # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
        lowerCAmelCase_       :    str								=			(alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
        lowerCAmelCase_       :    List[str]								=			state.common.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

        # 5. Compute predicted previous sample µ_t
        # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
        lowerCAmelCase_       :    str								=			pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

        # 6. Add noise
        def random_variance():
          lowerCAmelCase_       :    Union[str, Any]								=			jax.random.split(lowerCamelCase_   ,      num=1	)
          lowerCAmelCase_       :    Optional[Any]								=			jax.random.normal(lowerCamelCase_   ,      shape=model_output.shape   ,      dtype=self.dtype	)
          return (self._get_variance(lowerCamelCase_   ,      lowerCamelCase_   ,      predicted_variance=lowerCamelCase_	) ** 0.5) * noise

        lowerCAmelCase_       :    Optional[int]								=			jnp.where(t > 0   ,      random_variance()   ,      jnp.zeros(model_output.shape   ,      dtype=self.dtype	)	)

        lowerCAmelCase_       :    Tuple								=			pred_prev_sample + variance

        if not return_dict:
          return (pred_prev_sample, state)

        return FlaxDDPMSchedulerOutput(prev_sample=lowerCamelCase_   ,      state=lowerCamelCase_	)



      def 					SCREAMING_SNAKE_CASE__			(				self    :				Optional[int]   ,      SCREAMING_SNAKE_CASE_    :				Any   ,      SCREAMING_SNAKE_CASE_    :				str   ,      SCREAMING_SNAKE_CASE_    :				List[Any]   ,      SCREAMING_SNAKE_CASE_    :				Union[str, Any]   ,      ):
        return add_noise_common(state.common   ,      lowerCamelCase_   ,      lowerCamelCase_   ,      lowerCamelCase_	)



      def 					SCREAMING_SNAKE_CASE__			(				self    :				Any   ,      SCREAMING_SNAKE_CASE_    :				Optional[int]   ,      SCREAMING_SNAKE_CASE_    :				List[Any]   ,      SCREAMING_SNAKE_CASE_    :				List[Any]   ,      SCREAMING_SNAKE_CASE_    :				Optional[int]   ,      ):
        return get_velocity_common(state.common   ,      lowerCamelCase_   ,      lowerCamelCase_   ,      lowerCamelCase_	)





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










"""simple docstring"""







from __future__ import annotations

def     UpperCamelCase_   (   lowerCAmelCase__				:    int						)						->       list[int]:

  """simple docstring"""




  lowerCAmelCase_       :    Any								=			2
  lowerCAmelCase_       :    List[Any]								=			[]
  while i * i <= n:
    if n % i:
      i += 1
    else:
      n //= i
      factors.append(lowerCAmelCase__						)
  if n > 1:
    factors.append(lowerCAmelCase__						)
  return factors


if __name__ == "__main__":
     import doctest

     doctest.testmod()





