code: 
  
  
  from typing import List, Optional, Tuple, Union
  
  import torch
  
  from ...utils import randn_tensor
  from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput
  
  
  
  
  
  class    A					(     A_				):
  
  
         def __init__(self   ,       lowerCAmelCase   ,       lowerCAmelCase      ):
           super().__init__()
           self.register_modules(unet=lowerCAmelCase   ,       scheduler=lowerCAmelCase      )
  
  
  
  
  
  
  
         @torch.no_grad()
         def __call__(self   ,       lowerCAmelCase = 1   ,       lowerCAmelCase = None   ,       lowerCAmelCase = 1_0_0_0   ,       lowerCAmelCase = "pil"   ,       lowerCAmelCase = True   ,       ):
  
  
  
           if isinstance(self.unet.config.sample_size   ,       lowerCAmelCase      ):
             __lowercase=    (
                 batch_size,
                 self.unet.config.in_channels,
                 self.unet.config.sample_size,
                 self.unet.config.sample_size,
             )
           else:
             __lowercase=    (batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)
  
           if self.device.type == "mps":
             # randn does not work reproducibly on mps
             __lowercase=    randn_tensor(lowerCAmelCase   ,       generator=lowerCAmelCase      )
             __lowercase=    image.to(self.device      )
           else:
             __lowercase=    randn_tensor(lowerCAmelCase   ,       generator=lowerCAmelCase   ,       device=self.device      )
  
           # set step values
           self.scheduler.set_timesteps(lowerCAmelCase      )
  
           for t in self.progress_bar(self.scheduler.timesteps      ):
             # 1. predict noise model_output
             __lowercase=    self.unet(lowerCAmelCase   ,       lowerCAmelCase      ).sample
  
             # 2. compute previous image: x_t -> x_t-1
             __lowercase=    self.scheduler.step(lowerCAmelCase   ,       lowerCAmelCase   ,       lowerCAmelCase   ,       generator=lowerCAmelCase      ).prev_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(lowerCAmelCase      )
  
           if not return_dict:
             return (image,)
  
           return ImagePipelineOutput(images=lowerCAmelCase      )
  
  
  
  
  
  
  
style_context: 
  
  
  def  _lowerCamelCase(			lowercase__			)		->			str:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		if len(lowercase__			) == 0 or not all(len(lowercase__			) == 2 for pair in coordinates			):
  				raise ValueError('The program cannot work out a fitting polynomial.'			)
  
  		if len({tuple(lowercase__			) for pair in coordinates}			) != len(lowercase__			):
  				raise ValueError('The program cannot work out a fitting polynomial.'			)
  
  		__lowercase=    {x for x, _ in coordinates}
  		if len(lowercase__			) == 1:
  				return F'x={coordinates[0][0]}'
  
  		if len(lowercase__			) != len(lowercase__			):
  				raise ValueError('The program cannot work out a fitting polynomial.'			)
  
  		__lowercase=    len(lowercase__			)
  
  		__lowercase=    0
  		__lowercase=    []
  		# put the x and x to the power values in a matrix
  		while count_of_line < x:
  				__lowercase=    0
  				__lowercase=    coordinates[count_of_line][0]
  				__lowercase=    []
  				while count_in_line < x:
  						count_line.append(a ** (x - (count_in_line + 1))			)
  						count_in_line += 1
  				matrix.append(lowercase__			)
  				count_of_line += 1
  
  		__lowercase=    0
  		# put the y values into a vector
  		__lowercase=    []
  		while count_of_line < x:
  				vector.append(coordinates[count_of_line][1]			)
  				count_of_line += 1
  
  		__lowercase=    0
  
  		while count < x:
  				__lowercase=    0
  				while zahlen < x:
  						if count == zahlen:
  								zahlen += 1
  						if zahlen == x:
  								break
  						__lowercase=    matrix[zahlen][count] / matrix[count][count]
  						for counting_columns, item in enumerate(matrix[count]			):
  								# manipulating all the values in the matrix
  								matrix[zahlen][counting_columns] -= item * bruch
  						# manipulating the values in the vector
  						vector[zahlen] -= vector[count] * bruch
  						zahlen += 1
  				count += 1
  
  		__lowercase=    0
  		# make solutions
  		__lowercase=    []
  		while count < x:
  				solution.append(str(vector[count] / matrix[count][count]			)			)
  				count += 1
  
  		__lowercase=    0
  		__lowercase=    'f(x)='
  
  		while count < x:
  				__lowercase=    solution[count].split('E'			)
  				if len(lowercase__			) > 1:
  						__lowercase=    F'{remove_e[0]}*10^{remove_e[1]}'
  				solved += F'x^{x - (count + 1)}*{solution[count]}'
  				if count + 1 != x:
  						solved += "+"
  				count += 1
  
  		return solved
  
  
  if __name__ == "__main__":
  	print(points_to_polynomial([]))
  	print(points_to_polynomial([[]]))
  	print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
  	print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
  	print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
  	print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
  	print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
  	print(points_to_polynomial([[1, 3], [2, 6], [3, 1_1]]))
  	print(points_to_polynomial([[1, -3], [2, -6], [3, -1_1]]))
  	print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
  
  
  
  
  
  
  