






"""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      a						(					_UpperCAmelCase		):
    SCREAMING_SNAKE_CASE						:     torch.FloatTensor
    SCREAMING_SNAKE_CASE						:     Optional[torch.FloatTensor]						= None







def      lowerCamelCase__       (							_lowerCamelCase       :		List[str]		,				_lowerCamelCase       :		List[str]=0.9_99		,				_lowerCamelCase       :		Union[str, Any]="cosine"		,				)      ->				Any:
  if alpha_transform_type == "cosine":

    def alpha_bar_fn(_lowerCamelCase       :		List[Any] ):
      return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2 ) ** 2

  elif alpha_transform_type == "exp":

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

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

  lowerCamelCase_         =						[]
  for i in range(__UpperCAmelCase ):
    lowerCamelCase_         =						i / num_diffusion_timesteps
    lowerCamelCase_         =						(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      a						(					_UpperCAmelCase  ,      _UpperCAmelCase		):
    SCREAMING_SNAKE_CASE						:     Tuple						= 1






    @register_to_config
    def __init__(       self     :							List[str]       ,						__SCREAMING_SNAKE_CASE     :							Optional[Any] = 1000       ,						__SCREAMING_SNAKE_CASE     :							Union[str, Any] = 0.0_001       ,						__SCREAMING_SNAKE_CASE     :							List[str] = 0.02       ,						__SCREAMING_SNAKE_CASE     :							int = "linear"       ,						__SCREAMING_SNAKE_CASE     :							List[Any] = None       ,						__SCREAMING_SNAKE_CASE     :							Optional[int] = True       ,						__SCREAMING_SNAKE_CASE     :							int = True       ,						__SCREAMING_SNAKE_CASE     :							Any = 0       ,						__SCREAMING_SNAKE_CASE     :							Optional[int] = "epsilon"       ,						__SCREAMING_SNAKE_CASE     :							Dict = 1.0       ,						**__SCREAMING_SNAKE_CASE     :							Any       ,						)     ->		List[Any]:
      if kwargs.get('set_alpha_to_one'       ,						_UpperCAmelCase					) is not None:
        lowerCamelCase_         =						(
            '''The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead.'''
        )
        deprecate('set_alpha_to_one'       ,						'1.0.0'       ,						_UpperCAmelCase       ,						standard_warn=_UpperCAmelCase					)
        lowerCamelCase_         =						kwargs['''set_alpha_to_one''']
      if trained_betas is not None:
        lowerCamelCase_         =						torch.tensor(_UpperCAmelCase       ,						dtype=torch.floataa					)
      elif beta_schedule == "linear":
        lowerCamelCase_         =						torch.linspace(_UpperCAmelCase       ,						_UpperCAmelCase       ,						_UpperCAmelCase       ,						dtype=torch.floataa					)
      elif beta_schedule == "scaled_linear":
        # this schedule is very specific to the latent diffusion model.
        lowerCamelCase_         =						(
            torch.linspace(beta_start**0.5       ,						beta_end**0.5       ,						_UpperCAmelCase       ,						dtype=torch.floataa					) ** 2
        )
      elif beta_schedule == "squaredcos_cap_v2":
        # Glide cosine schedule
        lowerCamelCase_         =						betas_for_alpha_bar(_UpperCAmelCase					)
      else:
        raise NotImplementedError(F'''{beta_schedule} does is not implemented for {self.__class__}'''					)

      lowerCamelCase_         =						1.0 - self.betas
      lowerCamelCase_         =						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.
      lowerCamelCase_         =						torch.tensor(0.0					) if set_alpha_to_zero else self.alphas_cumprod[-1]

      # standard deviation of the initial noise distribution
      lowerCamelCase_         =						1.0

      # setable values
      lowerCamelCase_         =						None
      lowerCamelCase_         =						torch.from_numpy(np.arange(0       ,						_UpperCAmelCase					).copy().astype(np.intaa					)					)






    def    UpperCamelCase       (       self     :							Dict       ,						__SCREAMING_SNAKE_CASE     :							Union[str, Any]       ,						__SCREAMING_SNAKE_CASE     :							Optional[int] = None					)     ->		List[Any]:
      return sample






    def    UpperCamelCase       (       self     :							str       ,						__SCREAMING_SNAKE_CASE     :							Dict       ,						__SCREAMING_SNAKE_CASE     :							List[Any] = None					)     ->		Optional[int]:

      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.'''					)

      lowerCamelCase_         =						num_inference_steps
      lowerCamelCase_         =						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
      lowerCamelCase_         =						(np.arange(0       ,						_UpperCAmelCase					) * step_ratio).round().copy().astype(np.intaa					)
      lowerCamelCase_         =						torch.from_numpy(_UpperCAmelCase					).to(_UpperCAmelCase					)
      self.timesteps += self.config.steps_offset






    def    UpperCamelCase       (       self     :							str       ,						__SCREAMING_SNAKE_CASE     :							str       ,						__SCREAMING_SNAKE_CASE     :							Any       ,						__SCREAMING_SNAKE_CASE     :							Union[str, Any]       ,						__SCREAMING_SNAKE_CASE     :							List[Any] = 0.0       ,						__SCREAMING_SNAKE_CASE     :							int = False       ,						__SCREAMING_SNAKE_CASE     :							Union[str, Any] = None       ,						__SCREAMING_SNAKE_CASE     :							List[Any] = True       ,						)     ->		str:
      # 1. get previous step value (=t+1)
      lowerCamelCase_         =						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
      lowerCamelCase_         =						self.alphas_cumprod[timestep]
      lowerCamelCase_         =						(
          self.alphas_cumprod[prev_timestep]
          if prev_timestep < self.config.num_train_timesteps
          else self.final_alpha_cumprod
      )

      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. Clip or threshold "predicted x_0"
      if self.config.clip_sample:
        lowerCamelCase_         =						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
      lowerCamelCase_         =						(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
      lowerCamelCase_         =						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=_UpperCAmelCase       ,						pred_original_sample=_UpperCAmelCase					)






    def __len__(       self     :							Optional[Any]					)     ->		str:
      return self.config.num_train_timesteps





"""simple docstring"""






def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase )  ->  List[str]:
   lowercase__:   Optional[Any]					=      0
   lowercase__:   List[Any]					=      len(__UpperCAmelCase ) - 1

   while left <= right:
      # avoid divided by 0 during interpolation
      if sorted_collection[left] == sorted_collection[right]:
         if sorted_collection[left] == item:
            return left
         else:
            return None

      lowercase__:   Tuple					=      left + ((item - sorted_collection[left]) * (right - left)) // (
          sorted_collection[right] - sorted_collection[left]
      )

      # out of range check
      if point < 0 or point >= len(__UpperCAmelCase ):
         return None

      lowercase__:   Optional[int]					=      sorted_collection[point]
      if current_item == item:
         return point
      else:
         if point < left:
            lowercase__:   List[Any]					=      left
            lowercase__:   int					=      point
         elif point > right:
            lowercase__:   Dict					=      right
            lowercase__:   List[str]					=      point
         else:
            if item < current_item:
               lowercase__:   int					=      point - 1
            else:
               lowercase__:   int					=      point + 1
   return None



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )  ->  List[str]:

   # avoid divided by 0 during interpolation
   if sorted_collection[left] == sorted_collection[right]:
      if sorted_collection[left] == item:
         return left
      else:
         return None

   lowercase__:   Optional[int]					=      left + ((item - sorted_collection[left]) * (right - left)) // (
       sorted_collection[right] - sorted_collection[left]
   )

   # out of range check
   if point < 0 or point >= len(__UpperCAmelCase ):
      return None

   if sorted_collection[point] == item:
      return point
   elif point < left:
      return interpolation_search_by_recursion(__UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )
   elif point > right:
      return interpolation_search_by_recursion(__UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase )
   else:
      if sorted_collection[point] > item:
         return interpolation_search_by_recursion(
             __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    point - 1 )
      else:
         return interpolation_search_by_recursion(
             __UpperCAmelCase       ,    __UpperCAmelCase       ,    point + 1       ,    __UpperCAmelCase )



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase )  ->  List[Any]:
   if collection != sorted(__UpperCAmelCase ):
      raise ValueError('''Collection must be ascending sorted''' )
   return True


if __name__ == "__main__":
       import sys
       __A			   = 0
       if debug == 1:
              __A			   = [1_0, 3_0, 4_0, 4_5, 5_0, 6_6, 7_7, 9_3]
              try:
                     __assert_sorted(collection)
              except ValueError:
                     sys.exit("Sequence must be ascending sorted to apply interpolation search")
              __A			   = 6_7

       __A			   = interpolation_search(collection, target)
       if result is not None:
              print(f'''{target} found at positions: {result}''')
       else:
              print("Not found")
