


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      )










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]]))






