





"""simple docstring"""




from typing import Optional, Tuple, Union

import torch

from diffusers.pipeline_utils import DiffusionPipeline, ImagePipelineOutput

class 			_UpperCAmelCase  (       UpperCAmelCase__		):



      '''simple docstring'''

      def __init__(					self ,				snake_case_ ,				snake_case_  ):

        """simple docstring"""

        super().__init__()
        self.register_modules(unet=snake_case_ ,				scheduler=snake_case_  )

      @torch.no_grad()
      def __call__(					self ,				snake_case_ = 1 ,				snake_case_ = None ,				snake_case_ = 5_0 ,				snake_case_ = "pil" ,				snake_case_ = True ,				**snake_case_ ,				):

        """simple docstring"""

        A_  :	Dict    						=  torch.randn(
            (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size) ,				generator=snake_case_ ,				)
        A_  :	Union[str, Any]    						=  image.to(self.device  )

        # set step values
        self.scheduler.set_timesteps(snake_case_  )

        for t in self.progress_bar(self.scheduler.timesteps  ):
          # 1. predict noise model_output
          A_  :	Any    						=  self.unet(snake_case_ ,				snake_case_  ).sample

          # 2. predict previous mean of image x_t-1 and add variance depending on eta
          # eta corresponds to η in paper and should be between [0, 1]
          # do x_t -> x_t-1
          A_  :	Optional[Any]    						=  self.scheduler.step(snake_case_ ,				snake_case_ ,				snake_case_  ).prev_sample

        A_  :	Dict    						=  (image / 2 + 0.5).clamp(0 ,				1  )
        A_  :	Optional[Any]    						=  image.cpu().permute(0 ,				2 ,				3 ,				1  ).numpy()
        if output_type == "pil":
          A_  :	Tuple    						=  self.numpy_to_pil(snake_case_  )

        if not return_dict:
          return (image,), "This is a local test"

        return ImagePipelineOutput(images=snake_case_  ), "This is a local test"






"""simple docstring"""




import math as m





def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase			, _UpperCAmelCase=0.001 ):






  """simple docstring"""





  return (f(a + h ) - f(a - h )) / (2 * h)





def 						UpperCAmelCase__		(					_UpperCAmelCase			, _UpperCAmelCase=0			, _UpperCAmelCase=100			, _UpperCAmelCase=0.0_001			, _UpperCAmelCase=1E-6			, _UpperCAmelCase=False ):






  """simple docstring"""





  A_  :	Optional[int]    						=  xa  # set the initial guess
  A_  :	Any    						=  [a]
  A_  :	str    						=  abs(f(_UpperCAmelCase ) )
  A_  :	str    						=  lambda _UpperCAmelCase : calc_derivative(_UpperCAmelCase			, _UpperCAmelCase			, h=_UpperCAmelCase )  # noqa: E731  Derivative of f(x)
  for _ in range(_UpperCAmelCase ):
    if fa(_UpperCAmelCase ) == 0:
      raise ValueError('No converging solution found' )
    A_  :	Union[str, Any]    						=  a - f(_UpperCAmelCase ) / fa(_UpperCAmelCase )  # Calculate the next estimate
    if logsteps:
      steps.append(_UpperCAmelCase )
    if error < maxerror:
      break
  else:
    raise ValueError('Iteration limit reached, no converging solution found' )
  if logsteps:
    # If logstep is true, then log intermediate steps
    return a, error, steps
  return a, error


if __name__ == "__main__":
   from matplotlib import pyplot as plt

   lowerCamelCase_					:						str      = lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
   lowerCamelCase_ , lowerCamelCase_ , lowerCamelCase_					:						int      = newton_raphson(
       f, xa=10, maxiter=10_00, step=1E-6, logsteps=True
   )
   plt.plot([abs(f(x)) for x in steps])
   plt.xlabel('step')
   plt.ylabel('error')
   plt.show()
   print(F"solution = {{{solution:f}}}, error = {{{error:f}}}")