





'''simple docstring'''
import math
def 				lowercase__   (   __lowercase						:  int     ) ->      int:



       """simple docstring"""






       if not isinstance(__lowercase				,  __lowercase     ):
              __UpperCamelCase       =  F'''Input value of [number={number}] must be an integer'''
              raise TypeError(__lowercase     )

       if number < 1:
              __UpperCamelCase       =  F'''Input value of [number={number}] must be > 0'''
              raise ValueError(__lowercase     )
       elif number == 1:
              return 3
       elif number == 2:
              return 5
       else:
              __UpperCamelCase       =  int(math.log(number // 3				,  2     )     ) + 2

              __UpperCamelCase       =  [3, 5]
              __UpperCamelCase       =  2
              __UpperCamelCase       =  3
              for block in range(1				,  __lowercase     ):
                     for _ in range(__lowercase     ):
                            proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1]     )
                            proth_index += 1
                     increment *= 2

       return proth_list[number - 1]


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    for number in range(11):
        a__							:							str =0
        try:
            a__							:							Dict =proth(number)
        except ValueError:
            print(f'ValueError: there is no {number}th Proth number')
            continue

        print(f'The {number}th Proth number: {value}')







'''simple docstring'''




import inspect
from typing import List, Optional, Tuple, Union

import numpy as np
import PIL
import torch
import torch.utils.checkpoint

from ...models import UNetaDModel, VQModel
from ...schedulers import (
    DDIMScheduler,
    DPMSolverMultistepScheduler,
    EulerAncestralDiscreteScheduler,
    EulerDiscreteScheduler,
    LMSDiscreteScheduler,
    PNDMScheduler,
)
from ...utils import PIL_INTERPOLATION, randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput
def 	UpperCAmelCase_							(					__lowercase							:      str       )		->       List[str]:


     '''simple docstring'''



     _UpperCAmelCase							,  _UpperCAmelCase     							=   image.size
     _UpperCAmelCase							,  _UpperCAmelCase     							=   (x - x % 32 for x in (w, h))  # resize to integer multiple of 32
     _UpperCAmelCase     							=   image.resize((w, h)			,     resample=PIL_INTERPOLATION["lanczos"]       )
     _UpperCAmelCase     							=   np.array(__lowercase       ).astype(np.floataa       ) / 255.0
     _UpperCAmelCase     							=   image[None].transpose(0			,     3			,     1			,     2       )
     _UpperCAmelCase     							=   torch.from_numpy(__lowercase       )
     return 2.0 * image - 1.0







class   A_	(  lowerCAmelCase_			):




 def __init__(					self       :    Optional[Any]	,			snake_case_       :    VQModel	,			snake_case_       :    UNetaDModel	,			snake_case_       :    Union[
         DDIMScheduler,
         PNDMScheduler,
         LMSDiscreteScheduler,
         EulerDiscreteScheduler,
         EulerAncestralDiscreteScheduler,
         DPMSolverMultistepScheduler,
     ]	,			):
      super().__init__()
      self.register_modules(vqvae=snake_case_	,			unet=snake_case_	,			scheduler=snake_case_    )




 @torch.no_grad()
 def __call__(					self       :    Any	,			snake_case_       :    Union[torch.Tensor, PIL.Image.Image] = None	,			snake_case_       :    Optional[int] = 1	,			snake_case_       :    Optional[int] = 1_0_0	,			snake_case_       :    Optional[float] = 0.0	,			snake_case_       :    Optional[Union[torch.Generator, List[torch.Generator]]] = None	,			snake_case_       :    Optional[str] = "pil"	,			snake_case_       :    bool = True	,			):
      if isinstance(snake_case_	,			PIL.Image.Image    ):
           _UpperCAmelCase     							=   1
      elif isinstance(snake_case_	,			torch.Tensor    ):
           _UpperCAmelCase     							=   image.shape[0]
      else:
           raise ValueError(f'`image` has to be of type `PIL.Image.Image` or `torch.Tensor` but is {type(snake_case_    )}'    )

      if isinstance(snake_case_	,			PIL.Image.Image    ):
           _UpperCAmelCase     							=   preprocess(snake_case_    )

      _UpperCAmelCase							,  _UpperCAmelCase     							=   image.shape[-2:]

      # in_channels should be 6: 3 for latents, 3 for low resolution image
      _UpperCAmelCase     							=   (batch_size, self.unet.config.in_channels // 2, height, width)
      _UpperCAmelCase     							=   next(self.unet.parameters()    ).dtype

      _UpperCAmelCase     							=   randn_tensor(snake_case_	,			generator=snake_case_	,			device=self.device	,			dtype=snake_case_    )

      _UpperCAmelCase     							=   image.to(device=self.device	,			dtype=snake_case_    )

      # set timesteps and move to the correct device
      self.scheduler.set_timesteps(snake_case_	,			device=self.device    )
      _UpperCAmelCase     							=   self.scheduler.timesteps

      # scale the initial noise by the standard deviation required by the scheduler
      _UpperCAmelCase     							=   latents * self.scheduler.init_noise_sigma

      # prepare extra kwargs for the scheduler step, since not all schedulers have the same signature.
      # eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
      # eta corresponds to η in DDIM paper: https://arxiv.org/abs/2010.02502
      # and should be between [0, 1]
      _UpperCAmelCase     							=   "eta" in set(inspect.signature(self.scheduler.step    ).parameters.keys()    )
      _UpperCAmelCase     							=   {}
      if accepts_eta:
           _UpperCAmelCase     							=   eta

      for t in self.progress_bar(snake_case_    ):
           # concat latents and low resolution image in the channel dimension.
           _UpperCAmelCase     							=   torch.cat([latents, image]	,			dim=1    )
           _UpperCAmelCase     							=   self.scheduler.scale_model_input(snake_case_	,			snake_case_    )
           # predict the noise residual
           _UpperCAmelCase     							=   self.unet(snake_case_	,			snake_case_    ).sample
           # compute the previous noisy sample x_t -> x_t-1
           _UpperCAmelCase     							=   self.scheduler.step(snake_case_	,			snake_case_	,			snake_case_	,			**snake_case_    ).prev_sample

      # decode the image latents with the VQVAE
      _UpperCAmelCase     							=   self.vqvae.decode(snake_case_    ).sample
      _UpperCAmelCase     							=   torch.clamp(snake_case_	,			-1.0	,			1.0    )
      _UpperCAmelCase     							=   image / 2 + 0.5
      _UpperCAmelCase     							=   image.cpu().permute(0	,			2	,			3	,			1    ).numpy()

      if output_type == "pil":
           _UpperCAmelCase     							=   self.numpy_to_pil(snake_case_    )

      if not return_dict:
           return (image,)

      return ImagePipelineOutput(images=snake_case_    )




