





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

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin





@dataclass
class A_   (     _lowerCamelCase  ):
   lowerCAmelCase__  	=					42
   lowerCAmelCase__  	=					42





def _a							(      lowerCamelCase:  Any   ,							lowerCamelCase:  int=0.999   ,							lowerCamelCase:  Optional[Any]="cosine"   ,							)      ->		List[Any]:







      '''simple docstring'''






      if alpha_transform_type == "cosine":

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

      elif alpha_transform_type == "exp":

            def alpha_bar_fn(lowerCamelCase:  Optional[Any]					):
                  return math.exp(t * -12.0					)

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

      __A			  =							[]
      for i in range(lowerCamelCase					):
            __A			  =							i / num_diffusion_timesteps
            __A			  =							(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 A_   (     _lowerCamelCase					, _lowerCamelCase  ):
   lowerCAmelCase__  	=					1




   @register_to_config
   def __init__(self      :Any       ,  _UpperCamelCase      :int = 1000       ,  _UpperCamelCase      :float = 0.0_0_0_1       ,  _UpperCamelCase      :float = 0.0_2       ,  _UpperCamelCase      :str = "linear"       ,  _UpperCamelCase      :float = 0.0       ,  _UpperCamelCase      :Optional[np.ndarray] = None       ,  _UpperCamelCase      :bool = True       ,  )->   Union[str, Any]:
         if trained_betas is not None:
               __A			  =							torch.from_numpy(_UpperCamelCase					)
         elif beta_schedule == "linear":
               __A			  =							torch.linspace(_UpperCamelCase       ,  _UpperCamelCase       ,  _UpperCamelCase       ,  dtype=torch.floataa					)
         elif beta_schedule == "scaled_linear":
               # this schedule is very specific to the latent diffusion model.
               __A			  =							(
                   torch.linspace(beta_start**0.5       ,  beta_end**0.5       ,  _UpperCamelCase       ,  dtype=torch.floataa					) ** 2
               )
         elif beta_schedule == "squaredcos_cap_v2":
               # Glide cosine schedule
               __A			  =							betas_for_alpha_bar(_UpperCamelCase					)
         elif beta_schedule == "sigmoid":
               # GeoDiff sigmoid schedule
               __A			  =							torch.linspace(-6       ,  6       ,  _UpperCamelCase					)
               __A			  =							torch.sigmoid(_UpperCamelCase					) * (beta_end - beta_start) + beta_start
         else:
               raise NotImplementedError(f"""{beta_schedule} does is not implemented for {self.__class__}"""					)

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

         __A			  =							torch.tensor(1.0					)

         # standard deviation of the initial noise distribution
         __A			  =							1.0

         # setable values
         __A			  =							None
         __A			  =							torch.from_numpy(np.arange(0       ,  _UpperCamelCase					)[::-1].copy()					)

         __A			  =							eta




   def _lowerCAmelCase (self      :int       ,  _UpperCamelCase      :torch.FloatTensor       ,  _UpperCamelCase      :Optional[int] = None					)->   torch.FloatTensor:
         return sample




   def _lowerCAmelCase (self      :str       ,  _UpperCamelCase      :int       ,  _UpperCamelCase      :int = 10       ,  _UpperCamelCase      :int = 10       ,  _UpperCamelCase      :Union[str, torch.device] = None       ,  )->   Any:
         __A			  =							min(self.config.num_train_timesteps       ,  _UpperCamelCase					)
         __A			  =							num_inference_steps

         __A			  =							[]

         __A			  =							{}
         for j in range(0       ,  num_inference_steps - jump_length       ,  _UpperCamelCase					):
               __A			  =							jump_n_sample - 1

         __A			  =							num_inference_steps
         while t >= 1:
               __A			  =							t - 1
               timesteps.append(_UpperCamelCase					)

               if jumps.get(_UpperCamelCase       ,  0					) > 0:
                     __A			  =							jumps[t] - 1
                     for _ in range(_UpperCamelCase					):
                           __A			  =							t + 1
                           timesteps.append(_UpperCamelCase					)

         __A			  =							np.array(_UpperCamelCase					) * (self.config.num_train_timesteps // self.num_inference_steps)
         __A			  =							torch.from_numpy(_UpperCamelCase					).to(_UpperCamelCase					)




   def _lowerCAmelCase (self      :Tuple       ,  _UpperCamelCase      :int					)->   Dict:
         __A			  =							t - self.config.num_train_timesteps // self.num_inference_steps

         __A			  =							self.alphas_cumprod[t]
         __A			  =							self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
         __A			  =							1 - alpha_prod_t
         __A			  =							1 - alpha_prod_t_prev

         # For t > 0, compute predicted variance βt (see formula (6) and (7) from
         # https://arxiv.org/pdf/2006.11239.pdf) and sample from it to get
         # previous sample x_{t-1} ~ N(pred_prev_sample, variance) == add
         # variance to pred_sample
         # Is equivalent to formula (16) in https://arxiv.org/pdf/2010.02502.pdf
         # without eta.
         # variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]
         __A			  =							(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

         return variance




   def _lowerCAmelCase (self      :Any       ,  _UpperCamelCase      :torch.FloatTensor       ,  _UpperCamelCase      :int       ,  _UpperCamelCase      :torch.FloatTensor       ,  _UpperCamelCase      :torch.FloatTensor       ,  _UpperCamelCase      :torch.FloatTensor       ,  _UpperCamelCase      :Optional[torch.Generator] = None       ,  _UpperCamelCase      :bool = True       ,  )->   Union[RePaintSchedulerOutput, Tuple]:
         __A			  =							timestep
         __A			  =							timestep - self.config.num_train_timesteps // self.num_inference_steps

         # 1. compute alphas, betas
         __A			  =							self.alphas_cumprod[t]
         __A			  =							self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
         __A			  =							1 - alpha_prod_t

         # 2. compute predicted original sample from predicted noise also called
         # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
         __A			  =							(sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

         # 3. Clip "predicted x_0"
         if self.config.clip_sample:
               __A			  =							torch.clamp(_UpperCamelCase       ,  -1       ,  1					)

         # We choose to follow RePaint Algorithm 1 to get x_{t-1}, however we
         # substitute formula (7) in the algorithm coming from DDPM paper
         # (formula (4) Algorithm 2 - Sampling) with formula (12) from DDIM paper.
         # DDIM schedule gives the same results as DDPM with eta = 1.0
         # Noise is being reused in 7. and 8., but no impact on quality has
         # been observed.

         # 5. Add noise
         __A			  =							model_output.device
         __A			  =							randn_tensor(model_output.shape       ,  generator=_UpperCamelCase       ,  device=_UpperCamelCase       ,  dtype=model_output.dtype					)
         __A			  =							self.eta * self._get_variance(_UpperCamelCase					) ** 0.5

         __A			  =							0
         if t > 0 and self.eta > 0:
               __A			  =							std_dev_t * noise

         # 6. compute "direction pointing to x_t" of formula (12)
         # from https://arxiv.org/pdf/2010.02502.pdf
         __A			  =							(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

         # 7. compute x_{t-1} of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
         __A			  =							alpha_prod_t_prev**0.5 * pred_original_sample + pred_sample_direction + variance

         # 8. Algorithm 1 Line 5 https://arxiv.org/pdf/2201.09865.pdf
         __A			  =							(alpha_prod_t_prev**0.5) * original_image + ((1 - alpha_prod_t_prev) ** 0.5) * noise

         # 9. Algorithm 1 Line 8 https://arxiv.org/pdf/2201.09865.pdf
         __A			  =							mask * prev_known_part + (1.0 - mask) * prev_unknown_part

         if not return_dict:
               return (
                   pred_prev_sample,
                   pred_original_sample,
               )

         return RePaintSchedulerOutput(prev_sample=_UpperCamelCase       ,  pred_original_sample=_UpperCamelCase					)




   def _lowerCAmelCase (self      :Optional[Any]       ,  _UpperCamelCase      :Optional[Any]       ,  _UpperCamelCase      :str       ,  _UpperCamelCase      :str=None					)->   List[Any]:
         __A			  =							self.config.num_train_timesteps // self.num_inference_steps

         for i in range(_UpperCamelCase					):
               __A			  =							self.betas[timestep + i]
               if sample.device.type == "mps":
                     # randn does not work reproducibly on mps
                     __A			  =							randn_tensor(sample.shape       ,  dtype=sample.dtype       ,  generator=_UpperCamelCase					)
                     __A			  =							noise.to(sample.device					)
               else:
                     __A			  =							randn_tensor(sample.shape       ,  generator=_UpperCamelCase       ,  device=sample.device       ,  dtype=sample.dtype					)

               # 10. Algorithm 1 Line 10 https://arxiv.org/pdf/2201.09865.pdf
               __A			  =							(1 - beta) ** 0.5 * sample + beta**0.5 * noise

         return sample




   def _lowerCAmelCase (self      :Any       ,  _UpperCamelCase      :torch.FloatTensor       ,  _UpperCamelCase      :torch.FloatTensor       ,  _UpperCamelCase      :torch.IntTensor       ,  )->   torch.FloatTensor:
         raise NotImplementedError('''Use `DDPMScheduler.add_noise()` to train for sampling with RePaint.'''					)






   def __len__(self      :Tuple					)->   Optional[int]:
         return self.config.num_train_timesteps












def _a							(      lowerCamelCase:  List[Any]					)      ->		Optional[Any]:







      '''simple docstring'''






      __A			  =							[7_01, 3_01, 1_32, 57, 23, 10, 4, 1]
      for gap in gaps:
            for i in range(lowerCamelCase   ,							len(lowerCamelCase					)					):
                  __A			  =							collection[i]
                  __A			  =							i
                  while j >= gap and collection[j - gap] > insert_value:
                        __A			  =							collection[j - gap]
                        j -= gap
                  if j != i:
                        __A			  =							insert_value
      return collection


if __name__ == "__main__":
       from doctest import testmod

       testmod()
       snake_case__   :				Optional[int]						=	input('Enter numbers separated by a comma:\n').strip()
       snake_case__   :				int						=	[int(item) for item in user_input.split(',')]
       print(shell_sort(unsorted))





