






'''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 					lowercase							:


    '''simple docstring'''

    lowerCAmelCase__   					=				42
    lowerCAmelCase__   					=				42

    # setable values
    lowerCAmelCase__   					=				42
    lowerCAmelCase__   					=				42
    lowerCAmelCase__   					=				None

    @classmethod
    def  a__					(       cls  :  Dict					,  __lowerCamelCase  :  CommonSchedulerState					,  __lowerCamelCase  :  jnp.ndarray					,  __lowerCamelCase  :  jnp.ndarray					,  __lowerCamelCase  :  jnp.ndarray					,  )				->				List[str]:

     '''simple docstring'''




     return cls(
         common=__lowerCamelCase					,  final_alpha_cumprod=__lowerCamelCase					,  init_noise_sigma=__lowerCamelCase					,  timesteps=__lowerCamelCase					,  )
@dataclass
class 					lowercase							(				_lowerCamelCase   ):


    '''simple docstring'''

    lowerCAmelCase__   					=				42
class 					lowercase							(				_lowerCamelCase			,							_lowerCamelCase   ):


    '''simple docstring'''

    lowerCAmelCase__   					=				[e.name for e in FlaxKarrasDiffusionSchedulers]

    lowerCAmelCase__   					=				42

    @property
    def  a__					(       self  :  Tuple  )				->				Any:

     '''simple docstring'''




     return True

    @register_to_config
    def __init__(       self  :  Union[str, Any]					,  __lowerCamelCase  :  int = 1000					,  __lowerCamelCase  :  float = 0.0_0_0_1					,  __lowerCamelCase  :  float = 0.0_2					,  __lowerCamelCase  :  str = "linear"					,  __lowerCamelCase  :  Optional[jnp.ndarray] = None					,  __lowerCamelCase  :  bool = True					,  __lowerCamelCase  :  int = 0					,  __lowerCamelCase  :  str = "epsilon"					,  __lowerCamelCase  :  jnp.dtype = jnp.floataa					,  )				->				Optional[Any]:

     '''simple docstring'''




     lowerCamelCase__	=  dtype

    def  a__					(       self  :  int					,  __lowerCamelCase  :  Optional[CommonSchedulerState] = None  )				->				DDIMSchedulerState:

     '''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=__lowerCamelCase					,  final_alpha_cumprod=__lowerCamelCase					,  init_noise_sigma=__lowerCamelCase					,  timesteps=__lowerCamelCase					,  )

    def  a__					(       self  :  List[Any]					,  __lowerCamelCase  :  DDIMSchedulerState					,  __lowerCamelCase  :  jnp.ndarray					,  __lowerCamelCase  :  Optional[int] = None  )				->				jnp.ndarray:

     '''simple docstring'''




     return sample

    def  a__					(       self  :  Any					,  __lowerCamelCase  :  DDIMSchedulerState					,  __lowerCamelCase  :  int					,  __lowerCamelCase  :  Tuple = ()  )				->				DDIMSchedulerState:

     '''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					,  __lowerCamelCase  ) * step_ratio).round()[::-1] + self.config.steps_offset

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

    def  a__					(       self  :  Tuple					,  __lowerCamelCase  :  DDIMSchedulerState					,  __lowerCamelCase  :  Optional[int]					,  __lowerCamelCase  :  Optional[int]  )				->				List[str]:

     '''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  a__					(       self  :  Optional[int]					,  __lowerCamelCase  :  DDIMSchedulerState					,  __lowerCamelCase  :  jnp.ndarray					,  __lowerCamelCase  :  int					,  __lowerCamelCase  :  jnp.ndarray					,  __lowerCamelCase  :  float = 0.0					,  __lowerCamelCase  :  bool = 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)
     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]					,  __lowerCamelCase  )

     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(__lowerCamelCase					,  __lowerCamelCase					,  __lowerCamelCase  )
     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=__lowerCamelCase					,  state=__lowerCamelCase  )

    def  a__					(       self  :  List[Any]					,  __lowerCamelCase  :  DDIMSchedulerState					,  __lowerCamelCase  :  jnp.ndarray					,  __lowerCamelCase  :  jnp.ndarray					,  __lowerCamelCase  :  jnp.ndarray					,  )				->				jnp.ndarray:

     '''simple docstring'''




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

    def  a__					(       self  :  Tuple					,  __lowerCamelCase  :  DDIMSchedulerState					,  __lowerCamelCase  :  jnp.ndarray					,  __lowerCamelCase  :  jnp.ndarray					,  __lowerCamelCase  :  jnp.ndarray					,  )				->				jnp.ndarray:

     '''simple docstring'''




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




    def __len__(       self  :  Optional[int]  )				->				Optional[int]:

     '''simple docstring'''




     return self.config.num_train_timesteps









'''simple docstring'''





from math import cos, sin






def  lowerCamelCase_  (     lowercase__):
 lowerCamelCase__	=  float(lowercase__)
 return [[scaling_factor * int(x == y) for x in range(2)] for y in range(2)]






def  lowerCamelCase_  (     lowercase__):
 lowerCamelCase__	,						lowerCamelCase__	=  cos(lowercase__), sin(lowercase__)
 return [[c, -s], [s, c]]






def  lowerCamelCase_  (     lowercase__):
 lowerCamelCase__	,						lowerCamelCase__	=  cos(lowercase__), sin(lowercase__)
 lowerCamelCase__	=  c * s
 return [[c * c, cs], [cs, s * s]]






def  lowerCamelCase_  (     lowercase__):
 lowerCamelCase__	,						lowerCamelCase__	=  cos(lowercase__), sin(lowercase__)
 lowerCamelCase__	=  c * s
 return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(F"""    {scaling(5) = }""")
print(F"""  {rotation(45) = }""")
print(F"""{projection(45) = }""")
print(F"""{reflection(45) = }""")

