






# 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       :
						_SCREAMING_SNAKE_CASE						:							CommonSchedulerState
						_SCREAMING_SNAKE_CASE						:							jnp.ndarray

						# setable values
						_SCREAMING_SNAKE_CASE						:							jnp.ndarray
						_SCREAMING_SNAKE_CASE						:							jnp.ndarray
						_SCREAMING_SNAKE_CASE						:							Optional[int]				=       None






						@classmethod
						def    UpperCamelCase__   (						cls  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    ):






												"""simple docstring"""
												return cls(
												    common=_UpperCamelCase  ,    final_alpha_cumprod=_UpperCamelCase  ,    init_noise_sigma=_UpperCamelCase  ,    timesteps=_UpperCamelCase  ,    )




@dataclass
class      __SCREAMING_SNAKE_CASE       ( __lowercase):
						_SCREAMING_SNAKE_CASE						:							DDIMSchedulerState




class      __SCREAMING_SNAKE_CASE       ( __lowercase		,       __lowercase):
						_SCREAMING_SNAKE_CASE						:							List[str]				=       [e.name for e in FlaxKarrasDiffusionSchedulers]

						_SCREAMING_SNAKE_CASE						:							jnp.dtype






						@property
						def    UpperCamelCase__   (						self ):






												"""simple docstring"""
												return True






						@register_to_config
						def __init__(						self  ,    _UpperCamelCase = 10_00  ,    _UpperCamelCase = 0.00_01  ,    _UpperCamelCase = 0.02  ,    _UpperCamelCase = "linear"  ,    _UpperCamelCase = None  ,    _UpperCamelCase = True  ,    _UpperCamelCase = 0  ,    _UpperCamelCase = "epsilon"  ,    _UpperCamelCase = jnp.floataa  ,    ):






												"""simple docstring"""
												lowerCAmelCase__         =    dtype






						def    UpperCamelCase__   (						self  ,    _UpperCamelCase = None ):






												"""simple docstring"""
												if common is None:
																		lowerCAmelCase__         =    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.
												lowerCAmelCase__         =    (
												    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
												lowerCAmelCase__         =    jnp.array(1.0  ,    dtype=self.dtype )

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

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






						def    UpperCamelCase__   (						self  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase = None ):






												"""simple docstring"""
												return sample






						def    UpperCamelCase__   (						self  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase = () ):






												"""simple docstring"""
												lowerCAmelCase__         =    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__         =    (jnp.arange(0  ,    _UpperCamelCase ) * step_ratio).round()[::-1] + self.config.steps_offset

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






						def    UpperCamelCase__   (						self  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase ):






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

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

												return variance






						def    UpperCamelCase__   (						self  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase = 0.0  ,    _UpperCamelCase = 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' )

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

												lowerCAmelCase__         =    state.common.alphas_cumprod
												lowerCAmelCase__         =    state.final_alpha_cumprod

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

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

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

												if not return_dict:
																		return (prev_sample, state)

												return FlaxDDIMSchedulerOutput(prev_sample=_UpperCamelCase  ,    state=_UpperCamelCase )






						def    UpperCamelCase__   (						self  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    ):






												"""simple docstring"""
												return add_noise_common(state.common  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase )






						def    UpperCamelCase__   (						self  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    ):






												"""simple docstring"""
												return get_velocity_common(state.common  ,    _UpperCamelCase  ,    _UpperCamelCase  ,    _UpperCamelCase )







						def __len__(						self ):






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













from __future__ import annotations







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

						"""simple docstring"""



						if not list_of_ints:
												return []

						if min(UpperCamelCase_		) < 0:
												raise ValueError('All numbers must be positive'		)

						lowerCAmelCase__         =    max(len(bin(UpperCamelCase_		)[2:]		) for x in list_of_ints		)
						return _msd_radix_sort(UpperCamelCase_     ,							UpperCamelCase_		)







def 						_UpperCamelCase (     UpperCamelCase_							:       list[int]     ,							UpperCamelCase_							:       int		)	-> list[int]:

						"""simple docstring"""



						if bit_position == 0 or len(UpperCamelCase_		) in [0, 1]:
												return list_of_ints

						lowerCAmelCase__         =    []
						lowerCAmelCase__         =    []
						# Split numbers based on bit at bit_position from the right
						for number in list_of_ints:
												if (number >> (bit_position - 1)) & 1:
																		# number has a one at bit bit_position
																		ones.append(UpperCamelCase_		)
												else:
																		# number has a zero at bit bit_position
																		zeros.append(UpperCamelCase_		)

    # recursively split both lists further
						lowerCAmelCase__         =    _msd_radix_sort(UpperCamelCase_     ,							bit_position - 1		)
						lowerCAmelCase__         =    _msd_radix_sort(UpperCamelCase_     ,							bit_position - 1		)

						# recombine lists
						lowerCAmelCase__         =    zeros
						res.extend(UpperCamelCase_		)

						return res







def 						_UpperCamelCase (     UpperCamelCase_							:       list[int]		)	-> Any:

						"""simple docstring"""



						lowerCAmelCase__         =    len(UpperCamelCase_		)
						if not list_of_ints or length == 1:
												return

						if min(UpperCamelCase_		) < 0:
												raise ValueError('All numbers must be positive'		)

						lowerCAmelCase__         =    max(len(bin(UpperCamelCase_		)[2:]		) for x in list_of_ints		)
						_msd_radix_sort_inplace(UpperCamelCase_     ,							UpperCamelCase_     ,							0     ,							UpperCamelCase_		)







def 						_UpperCamelCase (     UpperCamelCase_							:       list[int]     ,							UpperCamelCase_							:       int     ,							UpperCamelCase_							:       int     ,							UpperCamelCase_							:       int		)	-> int:

						"""simple docstring"""



						if bit_position == 0 or end_index - begin_index <= 1:
												return

						bit_position -= 1

						lowerCAmelCase__         =    begin_index
						lowerCAmelCase__         =    end_index - 1
						while i <= j:
												lowerCAmelCase__         =    False
												if not (list_of_ints[i] >> bit_position) & 1:
																		# found zero at the beginning
																		i += 1
																		lowerCAmelCase__         =    True
												if (list_of_ints[j] >> bit_position) & 1:
																		# found one at the end
																		j -= 1
																		lowerCAmelCase__         =    True

												if changed:
																		continue

												lowerCAmelCase__    ,							lowerCAmelCase__         =    list_of_ints[j], list_of_ints[i]
												j -= 1
												if j != i:
																		i += 1

						_msd_radix_sort_inplace(UpperCamelCase_     ,							UpperCamelCase_     ,							UpperCamelCase_     ,							UpperCamelCase_		)
						_msd_radix_sort_inplace(UpperCamelCase_     ,							UpperCamelCase_     ,							UpperCamelCase_     ,							UpperCamelCase_		)


if __name__ == "__main__":
					import doctest

					doctest.testmod()





