

'''simple docstring'''






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

import torch

from ...models import UNetaDModel, VQModel
from ...schedulers import DDIMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput






class 			lowercase_	(lowerCamelCase__      ):




  """simple docstring"""




  def __init__(      self   :     Tuple					,lowercase__   :     VQModel					,lowercase__   :     UNetaDModel					,lowercase__   :     DDIMScheduler			):
   super().__init__()
   self.register_modules(vqvae=lowercase__					,unet=lowercase__					,scheduler=lowercase__			)






  @torch.no_grad()
  def __call__(      self   :     Tuple					,lowercase__   :     int = 1					,lowercase__   :     Optional[Union[torch.Generator, List[torch.Generator]]] = None					,lowercase__   :     float = 0.0					,lowercase__   :     int = 5_0					,lowercase__   :     Optional[str] = "pil"					,lowercase__   :     bool = True					,**lowercase__   :     List[str]					,):
   __lowercase							  = randn_tensor(
       (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)					,generator=lowercase__					,)
   __lowercase							  = latents.to(self.device			)

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

   self.scheduler.set_timesteps(lowercase__			)

   # prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
   __lowercase							  = '''eta''' in set(inspect.signature(self.scheduler.step			).parameters.keys()			)

   __lowercase							  = {}
   if accepts_eta:
    __lowercase							  = eta

   for t in self.progress_bar(self.scheduler.timesteps			):
    __lowercase							  = self.scheduler.scale_model_input(lowercase__					,lowercase__			)
    # predict the noise residual
    __lowercase							  = self.unet(lowercase__					,lowercase__			).sample
    # compute the previous noisy sample x_t -> x_t-1
    __lowercase							  = self.scheduler.step(lowercase__					,lowercase__					,lowercase__					,**lowercase__			).prev_sample

   # decode the image latents with the VAE
   __lowercase							  = self.vqvae.decode(lowercase__			).sample

   __lowercase							  = (image / 2 + 0.5).clamp(0					,1			)
   __lowercase							  = image.cpu().permute(0					,2					,3					,1			).numpy()
   if output_type == "pil":
    __lowercase							  = self.numpy_to_pil(lowercase__			)

   if not return_dict:
    return (image,)

   return ImagePipelineOutput(images=lowercase__			)





from __future__ import annotations

from math import ceil, floor, sqrt



def 				UpperCamelCase_(      lowerCamelCase_ = 200_0000 )    ->						int:
    _lowercase       :							list[int]      		=		[0]
    _lowercase       :							int

    for idx in range(1							, ceil(sqrt(target * 2 ) * 1.1 ) ):
        triangle_numbers.append(triangle_numbers[-1] + idx )

    # we want this to be as close as possible to target
    _lowercase       :							int      		=		0
    # the area corresponding to the grid that gives the product closest to target
    _lowercase       :							int      		=		0
    # an estimate of b, using the quadratic formula
    _lowercase       :							float
    # the largest integer less than b_estimate
    _lowercase       :							int
    # the largest integer less than b_estimate
    _lowercase       :							int
    # the triangle number corresponding to b_floor
    _lowercase       :							int
    # the triangle number corresponding to b_ceil
    _lowercase       :							int

    for idx_a, triangle_a in enumerate(triangle_numbers[1:]							, 1 ):
        _lowercase       :							Optional[int]      		=		(-1 + sqrt(1 + 8 * target / triangle_a )) / 2
        _lowercase       :							List[str]      		=		floor(lowerCamelCase_ )
        _lowercase       :							Dict      		=		ceil(lowerCamelCase_ )
        _lowercase       :							List[str]      		=		triangle_numbers[b_floor]
        _lowercase       :							List[str]      		=		triangle_numbers[b_ceil]

        if abs(target - triangle_b_first_guess * triangle_a ) < abs(
            target - best_product ):
            _lowercase       :							Union[str, Any]      		=		triangle_b_first_guess * triangle_a
            _lowercase       :							Union[str, Any]      		=		idx_a * b_floor

        if abs(target - triangle_b_second_guess * triangle_a ) < abs(
            target - best_product ):
            _lowercase       :							Any      		=		triangle_b_second_guess * triangle_a
            _lowercase       :							Optional[Any]      		=		idx_a * b_ceil

    return area


if __name__ == "__main__":
 print(F"{solution() = }")


