

'''simple docstring'''
import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput




def 	UpperCamelCase   (       lowercase_						:    List[str]     ,					lowercase_						:    str=0.9_9_9     ,					lowercase_						:    str="cosine"     ,					)		->	List[str]:




  '''simple docstring'''



  if alpha_transform_type == "cosine":

    def alpha_bar_fn(lowercase_						:    List[Any]	):
      return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2	) ** 2

  elif alpha_transform_type == "exp":

    def alpha_bar_fn(lowercase_						:    List[str]	):
      return math.exp(t * -1_2.0	)

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

  lowercase									=[]
  for i in range(lowerCAmelCase_	):
    lowercase									=i / num_diffusion_timesteps
    lowercase									=(i + 1) / num_diffusion_timesteps
    betas.append(min(1 - alpha_bar_fn(lowerCAmelCase_	) / alpha_bar_fn(lowerCAmelCase_	)     ,					lowerCAmelCase_	)	)
  return torch.tensor(lowerCAmelCase_     ,					dtype=torch.floataa	)




class 						__magic_name__   (							__snake_case ,				__snake_case ):
 UpperCamelCase__     =       [e.name for e in KarrasDiffusionSchedulers]
 UpperCamelCase__     =       2







 @register_to_config
 def __init__(       self  , snake_case_ = 10_00  , snake_case_ = 0.0_00_85  , snake_case_ = 0.0_12  , snake_case_ = "linear"  , snake_case_ = None  , snake_case_ = "epsilon"  , snake_case_ = False  , snake_case_ = False  , snake_case_ = 1.0  , snake_case_ = "linspace"  , snake_case_ = 0  , ):







   if trained_betas is not None:
     lowercase									=torch.tensor(__lowerCamelCase  , dtype=torch.floataa   )
   elif beta_schedule == "linear":
     lowercase									=torch.linspace(__lowerCamelCase  , __lowerCamelCase  , __lowerCamelCase  , dtype=torch.floataa   )
   elif beta_schedule == "scaled_linear":
     # this schedule is very specific to the latent diffusion model.
     lowercase									=(
         torch.linspace(beta_start**0.5  , beta_end**0.5  , __lowerCamelCase  , dtype=torch.floataa   ) ** 2
     )
   elif beta_schedule == "squaredcos_cap_v2":
     # Glide cosine schedule
     lowercase									=betas_for_alpha_bar(__lowerCamelCase  , alpha_transform_type='''cosine'''   )
   elif beta_schedule == "exp":
     lowercase									=betas_for_alpha_bar(__lowerCamelCase  , alpha_transform_type='''exp'''   )
   else:
     raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'   )

   lowercase									=1.0 - self.betas
   lowercase									=torch.cumprod(self.alphas  , dim=0   )

   #  set all values
   self.set_timesteps(__lowerCamelCase  , __lowerCamelCase  , __lowerCamelCase   )
   lowercase									=use_karras_sigmas







 def 						_A(       self  , snake_case_  , snake_case_=None   ):







   if schedule_timesteps is None:
     lowercase									=self.timesteps

   lowercase									=(schedule_timesteps == timestep).nonzero()

   # The sigma index that is taken for the **very** first `step`
   # is always the second index (or the last index if there is only 1)
   # This way we can ensure we don't accidentally skip a sigma in
   # case we start in the middle of the denoising schedule (e.g. for image-to-image)
   if len(self._index_counter   ) == 0:
     lowercase									=1 if len(__lowerCamelCase   ) > 1 else 0
   else:
     lowercase									=timestep.cpu().item() if torch.is_tensor(__lowerCamelCase   ) else timestep
     lowercase									=self._index_counter[timestep_int]

   return indices[pos].item()







 @property
 def 						_A(       self   ):







   if self.config.timestep_spacing in ["linspace", "trailing"]:
     return self.sigmas.max()

   return (self.sigmas.max() ** 2 + 1) ** 0.5







 def 						_A(       self  , snake_case_  , snake_case_  , ):
   lowercase									=self.index_for_timestep(__lowerCamelCase   )

   lowercase									=self.sigmas[step_index]
   lowercase									=sample / ((sigma**2 + 1) ** 0.5)
   return sample







 def 						_A(       self  , snake_case_  , snake_case_ = None  , snake_case_ = None  , ):
   lowercase									=num_inference_steps

   lowercase									=num_train_timesteps or self.config.num_train_timesteps

   # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
   if self.config.timestep_spacing == "linspace":
     lowercase									=np.linspace(0  , num_train_timesteps - 1  , __lowerCamelCase  , dtype=__lowerCamelCase   )[::-1].copy()
   elif self.config.timestep_spacing == "leading":
     lowercase									=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
     lowercase									=(np.arange(0  , __lowerCamelCase   ) * step_ratio).round()[::-1].copy().astype(__lowerCamelCase   )
     timesteps += self.config.steps_offset
   elif self.config.timestep_spacing == "trailing":
     lowercase									=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
     lowercase									=(np.arange(__lowerCamelCase  , 0  , -step_ratio   )).round().copy().astype(__lowerCamelCase   )
     timesteps -= 1
   else:
     raise ValueError(
         f'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'   )

   lowercase									=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
   lowercase									=np.log(__lowerCamelCase   )
   lowercase									=np.interp(__lowerCamelCase  , np.arange(0  , len(__lowerCamelCase   )   )  , __lowerCamelCase   )

   if self.config.use_karras_sigmas:
     lowercase									=self._convert_to_karras(in_sigmas=__lowerCamelCase  , num_inference_steps=self.num_inference_steps   )
     lowercase									=np.array([self._sigma_to_t(__lowerCamelCase  , __lowerCamelCase   ) for sigma in sigmas]   )

   lowercase									=np.concatenate([sigmas, [0.0]]   ).astype(np.floataa   )
   lowercase									=torch.from_numpy(__lowerCamelCase   ).to(device=__lowerCamelCase   )
   lowercase									=torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2   ), sigmas[-1:]]   )

   lowercase									=torch.from_numpy(__lowerCamelCase   )
   lowercase									=torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2   )]   )

   if str(__lowerCamelCase   ).startswith('''mps'''   ):
     # mps does not support float64
     lowercase									=timesteps.to(__lowerCamelCase  , dtype=torch.floataa   )
   else:
     lowercase									=timesteps.to(device=__lowerCamelCase   )

   # empty dt and derivative
   lowercase									=None
   lowercase									=None

   # for exp beta schedules, such as the one for `pipeline_shap_e.py`
   # we need an index counter
   lowercase									=defaultdict(__lowerCamelCase   )







 def 						_A(       self  , snake_case_  , snake_case_   ):
   lowercase									=np.log(__lowerCamelCase   )

   # get distribution
   lowercase									=log_sigma - log_sigmas[:, np.newaxis]

   # get sigmas range
   lowercase									=np.cumsum((dists >= 0)  , axis=0   ).argmax(axis=0   ).clip(max=log_sigmas.shape[0] - 2   )
   lowercase									=low_idx + 1

   lowercase									=log_sigmas[low_idx]
   lowercase									=log_sigmas[high_idx]

   # interpolate sigmas
   lowercase									=(low - log_sigma) / (low - high)
   lowercase									=np.clip(__lowerCamelCase  , 0  , 1   )

   # transform interpolation to time range
   lowercase									=(1 - w) * low_idx + w * high_idx
   lowercase									=t.reshape(sigma.shape   )
   return t







 def 						_A(       self  , snake_case_  , snake_case_   ):
   lowercase									=in_sigmas[-1].item()
   lowercase									=in_sigmas[0].item()

   lowercase									=7.0  # 7.0 is the value used in the paper
   lowercase									=np.linspace(0  , 1  , __lowerCamelCase   )
   lowercase									=sigma_min ** (1 / rho)
   lowercase									=sigma_max ** (1 / rho)
   lowercase									=(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
   return sigmas







 @property
 def 						_A(       self   ):
   return self.dt is None







 def 						_A(       self  , snake_case_  , snake_case_  , snake_case_  , snake_case_ = True  , ):
   lowercase									=self.index_for_timestep(__lowerCamelCase   )

   # advance index counter by 1
   lowercase									=timestep.cpu().item() if torch.is_tensor(__lowerCamelCase   ) else timestep
   self._index_counter[timestep_int] += 1

   if self.state_in_first_order:
     lowercase									=self.sigmas[step_index]
     lowercase									=self.sigmas[step_index + 1]
   else:
     # 2nd order / Heun's method
     lowercase									=self.sigmas[step_index - 1]
     lowercase									=self.sigmas[step_index]

   # currently only gamma=0 is supported. This usually works best anyways.
   # We can support gamma in the future but then need to scale the timestep before
   # passing it to the model which requires a change in API
   lowercase									=0
   lowercase									=sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

   # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
   if self.config.prediction_type == "epsilon":
     lowercase									=sigma_hat if self.state_in_first_order else sigma_next
     lowercase									=sample - sigma_input * model_output
   elif self.config.prediction_type == "v_prediction":
     lowercase									=sigma_hat if self.state_in_first_order else sigma_next
     lowercase									=model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
         sample / (sigma_input**2 + 1)
     )
   elif self.config.prediction_type == "sample":
     lowercase									=model_output
   else:
     raise ValueError(
         f'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'   )

   if self.config.clip_sample:
     lowercase									=pred_original_sample.clamp(
         -self.config.clip_sample_range  , self.config.clip_sample_range   )

   if self.state_in_first_order:
     # 2. Convert to an ODE derivative for 1st order
     lowercase									=(sample - pred_original_sample) / sigma_hat
     # 3. delta timestep
     lowercase									=sigma_next - sigma_hat

     # store for 2nd order step
     lowercase									=derivative
     lowercase									=dt
     lowercase									=sample
   else:
     # 2. 2nd order / Heun's method
     lowercase									=(sample - pred_original_sample) / sigma_next
     lowercase									=(self.prev_derivative + derivative) / 2

     # 3. take prev timestep & sample
     lowercase									=self.dt
     lowercase									=self.sample

     # free dt and derivative
     # Note, this puts the scheduler in "first order mode"
     lowercase									=None
     lowercase									=None
     lowercase									=None

   lowercase									=sample + derivative * dt

   if not return_dict:
     return (prev_sample,)

   return SchedulerOutput(prev_sample=__lowerCamelCase   )







 def 						_A(       self  , snake_case_  , snake_case_  , snake_case_  , ):
   lowercase									=self.sigmas.to(device=original_samples.device  , dtype=original_samples.dtype   )
   if original_samples.device.type == "mps" and torch.is_floating_point(__lowerCamelCase   ):
     # mps does not support float64
     lowercase									=self.timesteps.to(original_samples.device  , dtype=torch.floataa   )
     lowercase									=timesteps.to(original_samples.device  , dtype=torch.floataa   )
   else:
     lowercase									=self.timesteps.to(original_samples.device   )
     lowercase									=timesteps.to(original_samples.device   )

   lowercase									=[self.index_for_timestep(__lowerCamelCase  , __lowerCamelCase   ) for t in timesteps]

   lowercase									=sigmas[step_indices].flatten()
   while len(sigma.shape   ) < len(original_samples.shape   ):
     lowercase									=sigma.unsqueeze(-1   )

   lowercase									=original_samples + noise * sigma
   return noisy_samples







 def __len__(       self   ):
   return self.config.num_train_timesteps




from __future__ import annotations
def 	_UpperCamelCase					(    lowerCAmelCase_	,    lowerCAmelCase_ )    ->Optional[int]:
   # Checks if the entire collection has been sorted
   if len(lowerCAmelCase_ ) <= 1 or n <= 1:
      return

   insert_next(lowerCAmelCase_	,    n - 1 )
   rec_insertion_sort(lowerCAmelCase_	,    n - 1 )
def 	_UpperCamelCase					(    lowerCAmelCase_	,    lowerCAmelCase_ )    ->Dict:
   # Checks order between adjacent elements
   if index >= len(lowerCAmelCase_ ) or collection[index - 1] <= collection[index]:
      return

   # Swaps adjacent elements since they are not in ascending order
   UpperCAmelCase					,	UpperCAmelCase      					=  (
       collection[index],
       collection[index - 1],
   )

   insert_next(lowerCAmelCase_	,    index + 1 )


if __name__ == "__main__":
 __a	 =      input("""Enter integers separated by spaces: """)
 __a	 =      [int(num) for num in numbers.split()]
 rec_insertion_sort(number_list, len(number_list))
 print(number_list)



