'''simple docstring'''





# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion

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

import flax
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 							_SCREAMING_SNAKE_CASE:
   UpperCamelCase_				:						CommonSchedulerState
   UpperCamelCase_				:						jnp.ndarray

   # setable values
   UpperCamelCase_				:						jnp.ndarray
   UpperCamelCase_				:						jnp.ndarray
   UpperCamelCase_				:						Optional[int] 			=   None
   @classmethod
   def _lowercase(    cls							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     )	->Any:
        return cls(
            common=lowerCAmelCase_							,     final_alpha_cumprod=lowerCAmelCase_							,     init_noise_sigma=lowerCAmelCase_							,     timesteps=lowerCAmelCase_							,     )






@dataclass
class 							_SCREAMING_SNAKE_CASE(   snake_case__	):
   UpperCamelCase_				:						DDIMSchedulerState






class 							_SCREAMING_SNAKE_CASE(   snake_case__       ,      snake_case__	):
   UpperCamelCase_				:						int 			=   [e.name for e in FlaxKarrasDiffusionSchedulers]

   UpperCamelCase_				:						jnp.dtype
   @property
   def _lowercase(    self    )	->List[Any]:
        return True
   @register_to_config
   def __init__(    self							,     lowerCAmelCase_ = 10_00							,     lowerCAmelCase_ = 0.00_01							,     lowerCAmelCase_ = 0.02							,     lowerCAmelCase_ = "linear"							,     lowerCAmelCase_ = None							,     lowerCAmelCase_ = True							,     lowerCAmelCase_ = 0							,     lowerCAmelCase_ = "epsilon"							,     lowerCAmelCase_ = jnp.floataa							,     )	->int:
        a  :    Tuple				=						dtype
   def _lowercase(    self							,     lowerCAmelCase_ = None    )	->DDIMSchedulerState:
        if common is None:
             a  :    List[Any]				=						CommonSchedulerState.create(self    )

        # At every step in ddim, we are looking into the previous alphas_cumprod
        # For the final step, there is no previous alphas_cumprod because we are already at 0
        # `set_alpha_to_one` decides whether we set this parameter simply to one or
        # whether we use the final alpha of the "non-previous" one.
        a  :    Optional[int]				=						(
            jnp.array(1.0							,     dtype=self.dtype    ) if self.config.set_alpha_to_one else common.alphas_cumprod[0]
        )

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

        a  :    List[str]				=						jnp.arange(0							,     self.config.num_train_timesteps    ).round()[::-1]

        return DDIMSchedulerState.create(
            common=lowerCAmelCase_							,     final_alpha_cumprod=lowerCAmelCase_							,     init_noise_sigma=lowerCAmelCase_							,     timesteps=lowerCAmelCase_							,     )
   def _lowercase(    self							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_ = None    )	->jnp.ndarray:
        return sample
   def _lowercase(    self							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_ = ()    )	->DDIMSchedulerState:
        a  :    Optional[int]				=						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
        a  :    Any				=						(jnp.arange(0							,     lowerCAmelCase_    ) * step_ratio).round()[::-1] + self.config.steps_offset

        return state.replace(
            num_inference_steps=lowerCAmelCase_							,     timesteps=lowerCAmelCase_							,     )
   def _lowercase(    self							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_    )	->str:
        a  :    Any				=						state.common.alphas_cumprod[timestep]
        a  :    int				=						jnp.where(
            prev_timestep >= 0							,     state.common.alphas_cumprod[prev_timestep]							,     state.final_alpha_cumprod    )
        a  :    str				=						1 - alpha_prod_t
        a  :    int				=						1 - alpha_prod_t_prev

        a  :    Tuple				=						(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

        return variance
   def _lowercase(    self							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_ = 0.0							,     lowerCAmelCase_ = True							,     )	->Union[FlaxDDIMSchedulerOutput, 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'''    )

        # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
        # Ideally, read DDIM paper in-detail understanding

        # Notation (<variable name> -> <name in paper>
        # - pred_noise_t -> e_theta(x_t, t)
        # - pred_original_sample -> f_theta(x_t, t) or x_0
        # - std_dev_t -> sigma_t
        # - eta -> η
        # - pred_sample_direction -> "direction pointing to x_t"
        # - pred_prev_sample -> "x_t-1"

        # 1. get previous step value (=t-1)
        a  :    List[Any]				=						timestep - self.config.num_train_timesteps // state.num_inference_steps

        a  :    Tuple				=						state.common.alphas_cumprod
        a  :    Optional[Any]				=						state.final_alpha_cumprod

        # 2. compute alphas, betas
        a  :    Dict				=						alphas_cumprod[timestep]
        a  :    Optional[Any]				=						jnp.where(prev_timestep >= 0							,     alphas_cumprod[prev_timestep]							,     lowerCAmelCase_    )

        a  :    Any				=						1 - alpha_prod_t

        # 3. compute predicted original sample from predicted noise also called
        # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        if self.config.prediction_type == "epsilon":
             a  :    List[Any]				=						(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
             a  :    Tuple				=						model_output
        elif self.config.prediction_type == "sample":
             a  :    Union[str, Any]				=						model_output
             a  :    int				=						(sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
        elif self.config.prediction_type == "v_prediction":
             a  :    Optional[int]				=						(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
             a  :    Optional[Any]				=						(alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
        else:
             raise ValueError(
                 F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"""
                 ''' `v_prediction`'''    )

        # 4. compute variance: "sigma_t(η)" -> see formula (16)
        # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
        a  :    Any				=						self._get_variance(lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_    )
        a  :    List[str]				=						eta * variance ** 0.5

        # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        a  :    Any				=						(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * pred_epsilon

        # 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        a  :    Any				=						alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

        if not return_dict:
             return (prev_sample, state)

        return FlaxDDIMSchedulerOutput(prev_sample=lowerCAmelCase_							,     state=lowerCAmelCase_    )
   def _lowercase(    self							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     )	->jnp.ndarray:
        return add_noise_common(state.common							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_    )
   def _lowercase(    self							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_							,     )	->jnp.ndarray:
        return get_velocity_common(state.common							,     lowerCAmelCase_							,     lowerCAmelCase_							,     lowerCAmelCase_    )


   def __len__(    self    )	->Optional[Any]:
        return self.config.num_train_timesteps
from __future__ import annotations

UpperCAmelCase							   =      [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]






class 							_SCREAMING_SNAKE_CASE:
   def __init__(    self							,     lowerCAmelCase_    )	->None:
        a  :    int				=						-1
        a  :    int				=						-1
        a  :    list[int]				=						[-1] * length
        a  :    Node | None				=						None
        a  :    Node | None				=						None


   def __repr__(    self    )	->str:
        return F"""Node(min_value={self.minn} max_value={self.maxx})"""







def 	UpperCAmelCase       (		lowerCAmelCase_       )	->	Node | None:
     a  :    Dict				=						Node(len(lowerCAmelCase_       )       )
     a			,							a  :    Tuple				=						min(lowerCAmelCase_       ), max(lowerCAmelCase_       )
     # Leaf node case where the node contains only one unique value
     if root.minn == root.maxx:
          return root
     a  :    Optional[Any]				=						(root.minn + root.maxx) // 2

     a  :    list[int]				=						[]
     a  :    list[int]				=						[]

     for index, num in enumerate(lowerCAmelCase_       ):
          if num <= pivot:
               left_arr.append(lowerCAmelCase_       )
          else:
               right_arr.append(lowerCAmelCase_       )
          a  :    int				=						len(lowerCAmelCase_       )
     a  :    List[str]				=						build_tree(lowerCAmelCase_       )
     a  :    List[str]				=						build_tree(lowerCAmelCase_       )
     return root







def 	UpperCAmelCase       (		lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_       )	->	int:
     if index < 0 or node is None:
          return 0
     # Leaf node cases
     if node.minn == node.maxx:
          return index + 1 if node.minn == num else 0
     a  :    List[Any]				=						(node.minn + node.maxx) // 2
     if num <= pivot:
          # go the left subtree and map index to the left subtree
          return rank_till_index(node.left						,      lowerCAmelCase_						,      node.map_left[index] - 1       )
     else:
          # go to the right subtree and map index to the right subtree
          return rank_till_index(node.right						,      lowerCAmelCase_						,      index - node.map_left[index]       )







def 	UpperCAmelCase       (		lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_       )	->	int:
     if start > end:
          return 0
     a  :    Optional[Any]				=						rank_till_index(lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_       )
     a  :    Any				=						rank_till_index(lowerCAmelCase_						,      lowerCAmelCase_						,      start - 1       )
     return rank_till_end - rank_before_start







def 	UpperCAmelCase       (		lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_       )	->	int:
     if index > (end - start) or start > end or node is None:
          return -1
     # Leaf node case
     if node.minn == node.maxx:
          return node.minn
     # Number of elements in the left subtree in interval [start, end]
     a  :    Optional[int]				=						node.map_left[end] - (
         node.map_left[start - 1] if start else 0
     )
     if num_elements_in_left_tree > index:
          return quantile(
              node.left						,      lowerCAmelCase_						,      (node.map_left[start - 1] if start else 0)						,      node.map_left[end] - 1						,      )
     else:
          return quantile(
              node.right						,      index - num_elements_in_left_tree						,      start - (node.map_left[start - 1] if start else 0)						,      end - node.map_left[end]						,      )







def 	UpperCAmelCase       (		lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_       )	->	int:
     if (
         start > end
         or node is None
         or start_num > end_num
         or node.minn > end_num
         or node.maxx < start_num
     ):
          return 0
     if start_num <= node.minn and node.maxx <= end_num:
          return end - start + 1
     a  :    Tuple				=						range_counting(
         node.left						,      (node.map_left[start - 1] if start else 0)						,      node.map_left[end] - 1						,      lowerCAmelCase_						,      lowerCAmelCase_						,      )
     a  :    int				=						range_counting(
         node.right						,      start - (node.map_left[start - 1] if start else 0)						,      end - node.map_left[end]						,      lowerCAmelCase_						,      lowerCAmelCase_						,      )
     return left + right


if __name__ == "__main__":
  import doctest

  doctest.testmod()