def      lowerCAmelCase_				(  __A							)  ->       List[Any]:







      '''simple docstring'''


      if len(__A							) == 0 or not all(len(__A							) == 2 for pair in coordinates							):
            raise ValueError("The program cannot work out a fitting polynomial."							)

      if len({tuple(__A							) for pair in coordinates}							) != len(__A							):
            raise ValueError("The program cannot work out a fitting polynomial."							)

      UpperCAmelCase__			=						{x for x, _ in coordinates}
      if len(__A							) == 1:
            return f"""x={coordinates[0][0]}"""

      if len(__A							) != len(__A							):
            raise ValueError("The program cannot work out a fitting polynomial."							)

      UpperCAmelCase__			=						len(__A							)

      UpperCAmelCase__			=						0
      UpperCAmelCase__			=						[]
      # put the x and x to the power values in a matrix
      while count_of_line < x:
            UpperCAmelCase__			=						0
            UpperCAmelCase__			=						coordinates[count_of_line][0]
            UpperCAmelCase__			=						[]
            while count_in_line < x:
                  count_line.append(a ** (x - (count_in_line + 1))							)
                  count_in_line += 1
            matrix.append(__A							)
            count_of_line += 1

      UpperCAmelCase__			=						0
      # put the y values into a vector
      UpperCAmelCase__			=						[]
      while count_of_line < x:
            vector.append(coordinates[count_of_line][1]							)
            count_of_line += 1

      UpperCAmelCase__			=						0

      while count < x:
            UpperCAmelCase__			=						0
            while zahlen < x:
                  if count == zahlen:
                        zahlen += 1
                  if zahlen == x:
                        break
                  UpperCAmelCase__			=						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

      UpperCAmelCase__			=						0
      # make solutions
      UpperCAmelCase__			=						[]
      while count < x:
            solution.append(str(vector[count] / matrix[count][count]							)							)
            count += 1

      UpperCAmelCase__			=						0
      UpperCAmelCase__			=						'f(x)='

      while count < x:
            UpperCAmelCase__			=						solution[count].split("E"							)
            if len(__A							) > 1:
                  UpperCAmelCase__			=						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]]))




import unittest

import numpy as np

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
      import torch

if is_vision_available():
      from PIL import Image

      from transformers import EfficientNetImageProcessor





class   A							(       unittest.TestCase  ):


   def __init__(self  :		Optional[int] ,						__UpperCAmelCase  :		Dict ,						__UpperCAmelCase  :		List[Any]=1_3 ,						__UpperCAmelCase  :		int=3 ,						__UpperCAmelCase  :		int=1_8 ,						__UpperCAmelCase  :		Tuple=3_0 ,						__UpperCAmelCase  :		List[Any]=4_0_0 ,						__UpperCAmelCase  :		Any=True ,						__UpperCAmelCase  :		Dict=None ,						__UpperCAmelCase  :		Optional[Any]=True ,						__UpperCAmelCase  :		Tuple=[0.5, 0.5, 0.5] ,						__UpperCAmelCase  :		Optional[Any]=[0.5, 0.5, 0.5] ,						)		->       Any:
         """simple docstring"""



         UpperCAmelCase__			=						size if size is not None else {"height": 1_8, "width": 1_8}
         UpperCAmelCase__			=						parent
         UpperCAmelCase__			=						batch_size
         UpperCAmelCase__			=						num_channels
         UpperCAmelCase__			=						image_size
         UpperCAmelCase__			=						min_resolution
         UpperCAmelCase__			=						max_resolution
         UpperCAmelCase__			=						do_resize
         UpperCAmelCase__			=						size
         UpperCAmelCase__			=						do_normalize
         UpperCAmelCase__			=						image_mean
         UpperCAmelCase__			=						image_std





   def     lowercase_   (self  :		Optional[int]	)		->       Optional[Any]:
         """simple docstring"""



         return {
             "image_mean": self.image_mean,
             "image_std": self.image_std,
             "do_normalize": self.do_normalize,
             "do_resize": self.do_resize,
             "size": self.size,
         }





@require_torch
@require_vision
class   A							(       UpperCAmelCase_	,       unittest.TestCase  ):
   __UpperCAmelCase				:				Dict          =    EfficientNetImageProcessor if is_vision_available() else None


   def     lowercase_   (self  :		str	)		->       int:
         """simple docstring"""



         UpperCAmelCase__			=						EfficientNetImageProcessorTester(self	)


   @property
   def     lowercase_   (self  :		Tuple	)		->       Optional[Any]:
         """simple docstring"""



         return self.image_processor_tester.prepare_image_processor_dict()


   def     lowercase_   (self  :		Tuple	)		->       List[Any]:
         """simple docstring"""



         UpperCAmelCase__			=						self.image_processing_class(**self.image_processor_dict	)
         self.assertTrue(hasattr(__UpperCAmelCase ,						"image_mean"	)	)
         self.assertTrue(hasattr(__UpperCAmelCase ,						"image_std"	)	)
         self.assertTrue(hasattr(__UpperCAmelCase ,						"do_normalize"	)	)
         self.assertTrue(hasattr(__UpperCAmelCase ,						"do_resize"	)	)
         self.assertTrue(hasattr(__UpperCAmelCase ,						"size"	)	)


   def     lowercase_   (self  :		Tuple	)		->       str:
         """simple docstring"""



         UpperCAmelCase__			=						self.image_processing_class.from_dict(self.image_processor_dict	)
         self.assertEqual(image_processor.size ,						{"height": 1_8, "width": 1_8}	)

         UpperCAmelCase__			=						self.image_processing_class.from_dict(self.image_processor_dict ,						size=4_2	)
         self.assertEqual(image_processor.size ,						{"height": 4_2, "width": 4_2}	)


   def     lowercase_   (self  :		List[Any]	)		->       Optional[int]:
         """simple docstring"""



         UpperCAmelCase__			=						self.image_processing_class(**self.image_processor_dict	)
         # create random PIL images
         UpperCAmelCase__			=						prepare_image_inputs(self.image_processor_tester ,						equal_resolution=__UpperCAmelCase	)
         for image in image_inputs:
               self.assertIsInstance(__UpperCAmelCase ,						Image.Image	)

         # Test not batched input
         UpperCAmelCase__			=						image_processing(image_inputs[0] ,						return_tensors="pt"	).pixel_values
         self.assertEqual(
             encoded_images.shape ,						(
                 1,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.size["height"],
                 self.image_processor_tester.size["width"],
             ) ,						)

         # Test batched
         UpperCAmelCase__			=						image_processing(__UpperCAmelCase ,						return_tensors="pt"	).pixel_values
         self.assertEqual(
             encoded_images.shape ,						(
                 self.image_processor_tester.batch_size,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.size["height"],
                 self.image_processor_tester.size["width"],
             ) ,						)


   def     lowercase_   (self  :		Tuple	)		->       Optional[Any]:
         """simple docstring"""



         UpperCAmelCase__			=						self.image_processing_class(**self.image_processor_dict	)
         # create random numpy tensors
         UpperCAmelCase__			=						prepare_image_inputs(self.image_processor_tester ,						equal_resolution=__UpperCAmelCase ,						numpify=__UpperCAmelCase	)
         for image in image_inputs:
               self.assertIsInstance(__UpperCAmelCase ,						np.ndarray	)

         # Test not batched input
         UpperCAmelCase__			=						image_processing(image_inputs[0] ,						return_tensors="pt"	).pixel_values
         self.assertEqual(
             encoded_images.shape ,						(
                 1,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.size["height"],
                 self.image_processor_tester.size["width"],
             ) ,						)

         # Test batched
         UpperCAmelCase__			=						image_processing(__UpperCAmelCase ,						return_tensors="pt"	).pixel_values
         self.assertEqual(
             encoded_images.shape ,						(
                 self.image_processor_tester.batch_size,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.size["height"],
                 self.image_processor_tester.size["width"],
             ) ,						)





   def     lowercase_   (self  :		Optional[int]	)		->       str:
         """simple docstring"""



         UpperCAmelCase__			=						self.image_processing_class(**self.image_processor_dict	)
         # create random PyTorch tensors
         UpperCAmelCase__			=						prepare_image_inputs(self.image_processor_tester ,						equal_resolution=__UpperCAmelCase ,						torchify=__UpperCAmelCase	)
         for image in image_inputs:
               self.assertIsInstance(__UpperCAmelCase ,						torch.Tensor	)

         # Test not batched input
         UpperCAmelCase__			=						image_processing(image_inputs[0] ,						return_tensors="pt"	).pixel_values
         self.assertEqual(
             encoded_images.shape ,						(
                 1,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.size["height"],
                 self.image_processor_tester.size["width"],
             ) ,						)

         # Test batched
         UpperCAmelCase__			=						image_processing(__UpperCAmelCase ,						return_tensors="pt"	).pixel_values
         self.assertEqual(
             encoded_images.shape ,						(
                 self.image_processor_tester.batch_size,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.size["height"],
                 self.image_processor_tester.size["width"],
             ) ,						)



