
# 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__     :

							"""simple docstring"""






							_snake_case  		=	42
							_snake_case  		=	42

							# setable values
							_snake_case  		=	42
							_snake_case  		=	42
							_snake_case  		=	None



							@classmethod
							def      A__		(	cls  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						)-> Union[str, Any]:





													'''simple docstring'''






													return cls(
													    common=SCREAMING_SNAKE_CASE_  ,						final_alpha_cumprod=SCREAMING_SNAKE_CASE_  ,						init_noise_sigma=SCREAMING_SNAKE_CASE_  ,						timesteps=SCREAMING_SNAKE_CASE_  ,						)






@dataclass
class 							SCREAMING_SNAKE_CASE__     (				SCREAMING_SNAKE_CASE_     ):

							"""simple docstring"""






							_snake_case  		=	42






class 							SCREAMING_SNAKE_CASE__     (				SCREAMING_SNAKE_CASE_ ,		SCREAMING_SNAKE_CASE_     ):

							"""simple docstring"""






							_snake_case  		=	[e.name for e in FlaxKarrasDiffusionSchedulers]

							_snake_case  		=	42



							@property
							def      A__		(	self      )-> List[Any]:





													'''simple docstring'''






													return True



							@register_to_config
							def __init__(	self  ,						SCREAMING_SNAKE_CASE_ = 1000  ,						SCREAMING_SNAKE_CASE_ = 0.0_0_0_1  ,						SCREAMING_SNAKE_CASE_ = 0.0_2  ,						SCREAMING_SNAKE_CASE_ = "linear"  ,						SCREAMING_SNAKE_CASE_ = None  ,						SCREAMING_SNAKE_CASE_ = True  ,						SCREAMING_SNAKE_CASE_ = 0  ,						SCREAMING_SNAKE_CASE_ = "epsilon"  ,						SCREAMING_SNAKE_CASE_ = jnp.floataa  ,						)-> str:





													'''simple docstring'''






													__UpperCamelCase  	=      dtype



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_ = None      )-> DDIMSchedulerState:





													'''simple docstring'''






													if common is None:
																			__UpperCamelCase  	=      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.
													__UpperCamelCase  	=      (
													    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
													__UpperCamelCase  	=      jnp.array(1.0  ,						dtype=self.dtype      )

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

													return DDIMSchedulerState.create(
													    common=SCREAMING_SNAKE_CASE_  ,						final_alpha_cumprod=SCREAMING_SNAKE_CASE_  ,						init_noise_sigma=SCREAMING_SNAKE_CASE_  ,						timesteps=SCREAMING_SNAKE_CASE_  ,						)



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_ = None      )-> jnp.ndarray:





													'''simple docstring'''






													return sample



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_ = ()      )-> DDIMSchedulerState:





													'''simple docstring'''






													__UpperCamelCase  	=      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
													__UpperCamelCase  	=      (jnp.arange(0  ,						SCREAMING_SNAKE_CASE_      ) * step_ratio).round()[::-1] + self.config.steps_offset

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



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_      )-> Optional[int]:





													'''simple docstring'''






													__UpperCamelCase  	=      state.common.alphas_cumprod[timestep]
													__UpperCamelCase  	=      jnp.where(
													    prev_timestep >= 0  ,						state.common.alphas_cumprod[prev_timestep]  ,						state.final_alpha_cumprod      )
													__UpperCamelCase  	=      1 - alpha_prod_t
													__UpperCamelCase  	=      1 - alpha_prod_t_prev

													__UpperCamelCase  	=      (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

													return variance



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_ = 0.0  ,						SCREAMING_SNAKE_CASE_ = True  ,						)-> Union[FlaxDDIMSchedulerOutput, 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'''      )

													# 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)
													__UpperCamelCase  	=      timestep - self.config.num_train_timesteps // state.num_inference_steps

													__UpperCamelCase  	=      state.common.alphas_cumprod
													__UpperCamelCase  	=      state.final_alpha_cumprod

													# 2. compute alphas, betas
													__UpperCamelCase  	=      alphas_cumprod[timestep]
													__UpperCamelCase  	=      jnp.where(prev_timestep >= 0  ,						alphas_cumprod[prev_timestep]  ,						SCREAMING_SNAKE_CASE_      )

													__UpperCamelCase  	=      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":
																			__UpperCamelCase  	=      (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
																			__UpperCamelCase  	=      model_output
													elif self.config.prediction_type == "sample":
																			__UpperCamelCase  	=      model_output
																			__UpperCamelCase  	=      (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
													elif self.config.prediction_type == "v_prediction":
																			__UpperCamelCase  	=      (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
																			__UpperCamelCase  	=      (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)
													__UpperCamelCase  	=      self._get_variance(SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_      )
													__UpperCamelCase  	=      eta * variance ** 0.5

													# 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
													__UpperCamelCase  	=      (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
													__UpperCamelCase  	=      alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

													if not return_dict:
																			return (prev_sample, state)

													return FlaxDDIMSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_  ,						state=SCREAMING_SNAKE_CASE_      )



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						)-> jnp.ndarray:





													'''simple docstring'''






													return add_noise_common(state.common  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_      )



							def      A__		(	self  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						)-> jnp.ndarray:





													'''simple docstring'''






													return get_velocity_common(state.common  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_  ,						SCREAMING_SNAKE_CASE_      )



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





													'''simple docstring'''






													return self.config.num_train_timesteps








from __future__ import annotations

__SCREAMING_SNAKE_CASE	:							Union[str, Any]           =  [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]


class        __lowerCamelCase      :


				"""simple docstring"""







				def __init__(				self     :    Dict	,							lowerCamelCase_     :    int					):
								_lowerCAmelCase  						=-1
								_lowerCAmelCase  						=-1
								_lowerCAmelCase  						=[-1] * length
								_lowerCAmelCase  						=None
								_lowerCAmelCase  						=None






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

def 		snake_case_   (				lowercase__     :    list[int]     ):






				'''simple docstring'''






				_lowerCAmelCase  						=Node(len(lowercase__     )     )
				_lowerCAmelCase						,							_lowerCAmelCase  						=min(lowercase__     ), max(lowercase__     )
				# Leaf node case where the node contains only one unique value
				if root.minn == root.maxx:
								return root
				_lowerCAmelCase  						=(root.minn + root.maxx) // 2

				_lowerCAmelCase  						=[]
				_lowerCAmelCase  						=[]

				for index, num in enumerate(lowercase__     ):
								if num <= pivot:
												left_arr.append(lowercase__     )
								else:
												right_arr.append(lowercase__     )
								_lowerCAmelCase  						=len(lowercase__     )
				_lowerCAmelCase  						=build_tree(lowercase__     )
				_lowerCAmelCase  						=build_tree(lowercase__     )
				return root

def 		snake_case_   (				lowercase__     :    Node | None       ,     lowercase__     :    int       ,     lowercase__     :    int     ):






				'''simple docstring'''






				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
				_lowerCAmelCase  						=(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       ,     lowercase__       ,     node.map_left[index] - 1     )
				else:
								# go to the right subtree and map index to the right subtree
								return rank_till_index(node.right       ,     lowercase__       ,     index - node.map_left[index]     )

def 		snake_case_   (				lowercase__     :    Node | None       ,     lowercase__     :    int       ,     lowercase__     :    int       ,     lowercase__     :    int     ):






				'''simple docstring'''






				if start > end:
								return 0
				_lowerCAmelCase  						=rank_till_index(lowercase__       ,     lowercase__       ,     lowercase__     )
				_lowerCAmelCase  						=rank_till_index(lowercase__       ,     lowercase__       ,     start - 1     )
				return rank_till_end - rank_before_start

def 		snake_case_   (				lowercase__     :    Node | None       ,     lowercase__     :    int       ,     lowercase__     :    int       ,     lowercase__     :    int     ):






				'''simple docstring'''






				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]
				_lowerCAmelCase  						=node.map_left[end] - (
				    node.map_left[start - 1] if start else 0
				)
				if num_elements_in_left_tree > index:
								return quantile(
								    node.left       ,     lowercase__       ,     (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 		snake_case_   (				lowercase__     :    Node | None       ,     lowercase__     :    int       ,     lowercase__     :    int       ,     lowercase__     :    int       ,     lowercase__     :    int     ):






				'''simple docstring'''






				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
				_lowerCAmelCase  						=range_counting(
				    node.left       ,     (node.map_left[start - 1] if start else 0)       ,     node.map_left[end] - 1       ,     lowercase__       ,     lowercase__       ,     )
				_lowerCAmelCase  						=range_counting(
				    node.right       ,     start - (node.map_left[start - 1] if start else 0)       ,     end - node.map_left[end]       ,     lowercase__       ,     lowercase__       ,     )
				return left + right


if __name__ == "__main__":
		import doctest

		doctest.testmod()

