





"""simple docstring"""





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

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate




@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class 							snake_case							(			__UpperCAmelCase ):

      '''simple docstring'''



      _A     :       torch.FloatTensor
      _A     :       Optional[torch.FloatTensor]         =       None


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_=0.999  ,			UpperCAmelCase_="cosine"  ,			)						->Any:





       """simple docstring"""


       if alpha_transform_type == "cosine":

              def alpha_bar_fn(UpperCAmelCase_  ):
                     return math.cos((t + 0.008) / 1.008 * math.pi / 2  ) ** 2

       elif alpha_transform_type == "exp":

              def alpha_bar_fn(UpperCAmelCase_  ):
                     return math.exp(t * -12.0  )

       else:
              raise ValueError(f'''Unsupported alpha_tranform_type: {alpha_transform_type}'''  )

       __UpperCAmelCase    :						int       =						[]
       for i in range(UpperCAmelCase_  ):
              __UpperCAmelCase    :						List[Any]       =						i / num_diffusion_timesteps
              __UpperCAmelCase    :						Optional[Any]       =						(i + 1) / num_diffusion_timesteps
              betas.append(min(1 - alpha_bar_fn(UpperCAmelCase_  ) / alpha_bar_fn(UpperCAmelCase_  )  ,			UpperCAmelCase_  )  )
       return torch.tensor(UpperCAmelCase_  ,			dtype=torch.floataa  )







class 							snake_case							(			__UpperCAmelCase      ,  __UpperCAmelCase ):

      '''simple docstring'''



      _A     :       int         =       1

      @register_to_config
      def __init__(							self       :      Tuple						,				__lowercase       :      int = 1_000						,				__lowercase       :      float = 0.0_0_0_1						,				__lowercase       :      float = 0.0_2						,				__lowercase       :      str = "linear"						,				__lowercase       :      Optional[Union[np.ndarray, List[float]]] = None						,				__lowercase       :      bool = True						,				__lowercase       :      bool = True						,				__lowercase       :      int = 0						,				__lowercase       :      str = "epsilon"						,				__lowercase       :      float = 1.0						,				**__lowercase       :      List[Any]						,				):


             '''simple docstring'''




             if kwargs.get('''set_alpha_to_one'''						,				__lowercase ) is not None:
                    __UpperCAmelCase    :						Dict       =						(
                        '''The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead.'''
                    )
                    deprecate('''set_alpha_to_one'''						,				'''1.0.0'''						,				__lowercase						,				standard_warn=__lowercase )
                    __UpperCAmelCase    :						Optional[Any]       =						kwargs['''set_alpha_to_one''']
             if trained_betas is not None:
                    __UpperCAmelCase    :						Tuple       =						torch.tensor(__lowercase						,				dtype=torch.floataa )
             elif beta_schedule == "linear":
                    __UpperCAmelCase    :						Any       =						torch.linspace(__lowercase						,				__lowercase						,				__lowercase						,				dtype=torch.floataa )
             elif beta_schedule == "scaled_linear":
                    # this schedule is very specific to the latent diffusion model.
                    __UpperCAmelCase    :						Tuple       =						(
                        torch.linspace(beta_start**0.5						,				beta_end**0.5						,				__lowercase						,				dtype=torch.floataa ) ** 2
                    )
             elif beta_schedule == "squaredcos_cap_v2":
                    # Glide cosine schedule
                    __UpperCAmelCase    :						int       =						betas_for_alpha_bar(__lowercase )
             else:
                    raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}''' )

             __UpperCAmelCase    :						Union[str, Any]       =						1.0 - self.betas
             __UpperCAmelCase    :						Optional[Any]       =						torch.cumprod(self.alphas						,				dim=0 )

             # At every step in inverted ddim, we are looking into the next alphas_cumprod
             # For the final step, there is no next alphas_cumprod, and the index is out of bounds
             # `set_alpha_to_zero` decides whether we set this parameter simply to zero
             # in this case, self.step() just output the predicted noise
             # or whether we use the final alpha of the "non-previous" one.
             __UpperCAmelCase    :						Optional[Any]       =						torch.tensor(0.0 ) if set_alpha_to_zero else self.alphas_cumprod[-1]

             # standard deviation of the initial noise distribution
             __UpperCAmelCase    :						Any       =						1.0

             # setable values
             __UpperCAmelCase    :						Tuple       =						None
             __UpperCAmelCase    :						Tuple       =						torch.from_numpy(np.arange(0						,				__lowercase ).copy().astype(np.intaa ) )

      def       A_					(							self       :      Optional[int]						,				__lowercase       :      torch.FloatTensor						,				__lowercase       :      Optional[int] = None ):


             '''simple docstring'''




             return sample

      def       A_					(							self       :      Tuple						,				__lowercase       :      int						,				__lowercase       :      Union[str, torch.device] = None ):


             '''simple docstring'''




             if num_inference_steps > self.config.num_train_timesteps:
                    raise ValueError(
                        f'''`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:'''
                        f''' {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle'''
                        f''' maximal {self.config.num_train_timesteps} timesteps.''' )

             __UpperCAmelCase    :						Dict       =						num_inference_steps
             __UpperCAmelCase    :						List[Any]       =						self.config.num_train_timesteps // self.num_inference_steps
             # creates integer timesteps by multiplying by ratio
             # casting to int to avoid issues when num_inference_step is power of 3
             __UpperCAmelCase    :						Optional[Any]       =						(np.arange(0						,				__lowercase ) * step_ratio).round().copy().astype(np.intaa )
             __UpperCAmelCase    :						Tuple       =						torch.from_numpy(__lowercase ).to(__lowercase )
             self.timesteps += self.config.steps_offset

      def       A_					(							self       :      List[str]						,				__lowercase       :      torch.FloatTensor						,				__lowercase       :      int						,				__lowercase       :      torch.FloatTensor						,				__lowercase       :      float = 0.0						,				__lowercase       :      bool = False						,				__lowercase       :      Optional[torch.FloatTensor] = None						,				__lowercase       :      bool = True						,				):


             '''simple docstring'''




             __UpperCAmelCase    :						int       =						timestep + self.config.num_train_timesteps // self.num_inference_steps

             # 2. compute alphas, betas
             # change original implementation to exactly match noise levels for analogous forward process
             __UpperCAmelCase    :						int       =						self.alphas_cumprod[timestep]
             __UpperCAmelCase    :						Optional[Any]       =						(
                 self.alphas_cumprod[prev_timestep]
                 if prev_timestep < self.config.num_train_timesteps
                 else self.final_alpha_cumprod
             )

             __UpperCAmelCase    :						Dict       =						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    :						Tuple       =						(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
                    __UpperCAmelCase    :						Dict       =						model_output
             elif self.config.prediction_type == "sample":
                    __UpperCAmelCase    :						int       =						model_output
                    __UpperCAmelCase    :						Optional[Any]       =						(sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
             elif self.config.prediction_type == "v_prediction":
                    __UpperCAmelCase    :						Optional[int]       =						(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
                    __UpperCAmelCase    :						Tuple       =						(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. Clip or threshold "predicted x_0"
             if self.config.clip_sample:
                    __UpperCAmelCase    :						List[Any]       =						pred_original_sample.clamp(
                        -self.config.clip_sample_range						,				self.config.clip_sample_range )

             # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
             __UpperCAmelCase    :						Union[str, Any]       =						(1 - alpha_prod_t_prev) ** 0.5 * pred_epsilon

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

             if not return_dict:
                    return (prev_sample, pred_original_sample)
             return DDIMSchedulerOutput(prev_sample=__lowercase						,				pred_original_sample=__lowercase )







      def __len__(							self       :      str ):


             '''simple docstring'''




             return self.config.num_train_timesteps






"""simple docstring"""





def       lowerCamelCase_       (   UpperCAmelCase_  )						->float:





  """simple docstring"""


  return 10 - x * x


def       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  )						->float:





  """simple docstring"""


  if equation(UpperCAmelCase_  ) * equation(UpperCAmelCase_  ) >= 0:
    raise ValueError('''Wrong space!'''  )

  __UpperCAmelCase    :						Tuple       =						a
  while (b - a) >= 0.01:
    # Find middle point
    __UpperCAmelCase    :						List[str]       =						(a + b) / 2
    # Check if middle point is root
    if equation(UpperCAmelCase_  ) == 0.0:
      break
    # Decide the side to repeat the steps
    if equation(UpperCAmelCase_  ) * equation(UpperCAmelCase_  ) < 0:
      __UpperCAmelCase    :						Union[str, Any]       =						c
    else:
      __UpperCAmelCase    :						str       =						c
  return c


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  print(bisection(-2, 5))
  print(bisection(0, 6))