






def  UpperCAmelCase__						(    lowerCamelCase	:			list[list[int]]    ):
   if len(lowerCamelCase    ) == 0 or not all(len(lowerCamelCase    ) == 2 for pair in coordinates    ):
      raise ValueError("""The program cannot work out a fitting polynomial."""    )

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

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

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

   lowerCamelCase									=len(lowerCamelCase    )

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

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

   lowerCamelCase									=0

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

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

   lowerCamelCase									=0
   lowerCamelCase									="""f(x)="""

   while count < x:
      lowerCamelCase									=solution[count].split("""E"""    )
      if len(lowerCamelCase    ) > 1:
         lowerCamelCase									=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, 11]]))
   print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
   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


if is_torch_available():
   import torch

if is_vision_available():
   from PIL import Image

   from transformers import BlipImageProcessor


class 		lowerCAmelCase_				(  unittest.TestCase ):





     def __init__(	self							, _UpperCAmelCase							, _UpperCAmelCase=7							, _UpperCAmelCase=3							, _UpperCAmelCase=18							, _UpperCAmelCase=30							, _UpperCAmelCase=400							, _UpperCAmelCase=True							, _UpperCAmelCase=None							, _UpperCAmelCase=True							, _UpperCAmelCase=False							, _UpperCAmelCase=[0.48145466, 0.4578275, 0.40821073]							, _UpperCAmelCase=[0.26862954, 0.26130258, 0.27577711]							, _UpperCAmelCase=True							, )		->				List[str]:
        lowerCamelCase									=size if size is not None else {"""height""": 20, """width""": 20}
        lowerCamelCase									=parent
        lowerCamelCase									=batch_size
        lowerCamelCase									=num_channels
        lowerCamelCase									=image_size
        lowerCamelCase									=min_resolution
        lowerCamelCase									=max_resolution
        lowerCamelCase									=do_resize
        lowerCamelCase									=size
        lowerCamelCase									=do_normalize
        lowerCamelCase									=image_mean
        lowerCamelCase									=image_std
        lowerCamelCase									=do_pad
        lowerCamelCase									=do_convert_rgb





     def 						lowerCamelCase							(	self  )		->				str:
        return {
            "do_resize": self.do_resize,
            "size": self.size,
            "do_normalize": self.do_normalize,
            "image_mean": self.image_mean,
            "image_std": self.image_std,
            "do_convert_rgb": self.do_convert_rgb,
            "do_pad": self.do_pad,
        }





     def 						lowerCamelCase							(	self							, _UpperCAmelCase=False							, _UpperCAmelCase=False							, _UpperCAmelCase=False  )		->				Optional[int]:
        assert not (numpify and torchify), "You cannot specify both numpy and PyTorch tensors at the same time"

        if equal_resolution:
           lowerCamelCase									=[]
           for i in range(self.batch_size  ):
              image_inputs.append(
                  np.random.randint(
                      255							, size=(self.num_channels, self.max_resolution, self.max_resolution)							, dtype=np.uinta  )  )
        else:
           lowerCamelCase									=[]
           for i in range(self.batch_size  ):
              lowerCamelCase				,       lowerCamelCase									=np.random.choice(np.arange(self.min_resolution							, self.max_resolution  )							, 2  )
              image_inputs.append(np.random.randint(255							, size=(self.num_channels, width, height)							, dtype=np.uinta  )  )

        if not numpify and not torchify:
           # PIL expects the channel dimension as last dimension
           lowerCamelCase									=[Image.fromarray(np.moveaxis(_UpperCAmelCase							, 0							, -1  )  ) for x in image_inputs]

        if torchify:
           lowerCamelCase									=[torch.from_numpy(_UpperCAmelCase  ) for x in image_inputs]

        return image_inputs




@require_torch
@require_vision
class 		lowerCAmelCase_				(  UpperCamelCase				,     unittest.TestCase ):
     __lowerCamelCase       :    str 	=     BlipImageProcessor if is_vision_available() else None





     def 						lowerCamelCase							(	self  )		->				Dict:
        lowerCamelCase									=BlipImageProcessingTester(self  )





     @property
     def 						lowerCamelCase							(	self  )		->				Optional[int]:
        return self.image_processor_tester.prepare_image_processor_dict()





     def 						lowerCamelCase							(	self  )		->				Union[str, Any]:
        lowerCamelCase									=self.image_processing_class(**self.image_processor_dict  )
        self.assertTrue(hasattr(_UpperCAmelCase							, """do_resize"""  )  )
        self.assertTrue(hasattr(_UpperCAmelCase							, """size"""  )  )
        self.assertTrue(hasattr(_UpperCAmelCase							, """do_normalize"""  )  )
        self.assertTrue(hasattr(_UpperCAmelCase							, """image_mean"""  )  )
        self.assertTrue(hasattr(_UpperCAmelCase							, """image_std"""  )  )
        self.assertTrue(hasattr(_UpperCAmelCase							, """do_convert_rgb"""  )  )





     def 						lowerCamelCase							(	self  )		->				Union[str, Any]:
        pass





     def 						lowerCamelCase							(	self  )		->				int:
        # Initialize image_processor
        lowerCamelCase									=self.image_processing_class(**self.image_processor_dict  )
        # create random PIL images
        lowerCamelCase									=self.image_processor_tester.prepare_inputs(equal_resolution=_UpperCAmelCase  )
        for image in image_inputs:
           self.assertIsInstance(_UpperCAmelCase							, Image.Image  )

        # Test not batched input
        lowerCamelCase									=image_processor(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
        lowerCamelCase									=image_processor(_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 						lowerCamelCase							(	self  )		->				Union[str, Any]:
        # Initialize image_processor
        lowerCamelCase									=self.image_processing_class(**self.image_processor_dict  )
        # create random numpy tensors
        lowerCamelCase									=self.image_processor_tester.prepare_inputs(equal_resolution=_UpperCAmelCase							, numpify=_UpperCAmelCase  )
        for image in image_inputs:
           self.assertIsInstance(_UpperCAmelCase							, np.ndarray  )

        # Test not batched input
        lowerCamelCase									=image_processor(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
        lowerCamelCase									=image_processor(_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 						lowerCamelCase							(	self  )		->				Optional[Any]:
        # Initialize image_processor
        lowerCamelCase									=self.image_processing_class(**self.image_processor_dict  )
        # create random PyTorch tensors
        lowerCamelCase									=self.image_processor_tester.prepare_inputs(equal_resolution=_UpperCAmelCase							, torchify=_UpperCAmelCase  )
        for image in image_inputs:
           self.assertIsInstance(_UpperCAmelCase							, torch.Tensor  )

        # Test not batched input
        lowerCamelCase									=image_processor(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
        lowerCamelCase									=image_processor(_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"""],
            )							, )




@require_torch
@require_vision
class 		lowerCAmelCase_				(  UpperCamelCase				,     unittest.TestCase ):
     __lowerCamelCase       :    Any 	=     BlipImageProcessor if is_vision_available() else None





     def 						lowerCamelCase							(	self  )		->				Optional[int]:
        lowerCamelCase									=BlipImageProcessingTester(self							, num_channels=4  )
        lowerCamelCase									=3





     @property
     def 						lowerCamelCase							(	self  )		->				Any:
        return self.image_processor_tester.prepare_image_processor_dict()





     def 						lowerCamelCase							(	self  )		->				List[str]:
        lowerCamelCase									=self.image_processing_class(**self.image_processor_dict  )
        self.assertTrue(hasattr(_UpperCAmelCase							, """do_resize"""  )  )
        self.assertTrue(hasattr(_UpperCAmelCase							, """size"""  )  )
        self.assertTrue(hasattr(_UpperCAmelCase							, """do_normalize"""  )  )
        self.assertTrue(hasattr(_UpperCAmelCase							, """image_mean"""  )  )
        self.assertTrue(hasattr(_UpperCAmelCase							, """image_std"""  )  )
        self.assertTrue(hasattr(_UpperCAmelCase							, """do_convert_rgb"""  )  )





     def 						lowerCamelCase							(	self  )		->				Optional[int]:
        pass





     def 						lowerCamelCase							(	self  )		->				List[Any]:
        # Initialize image_processor
        lowerCamelCase									=self.image_processing_class(**self.image_processor_dict  )
        # create random PIL images
        lowerCamelCase									=self.image_processor_tester.prepare_inputs(equal_resolution=_UpperCAmelCase  )
        for image in image_inputs:
           self.assertIsInstance(_UpperCAmelCase							, Image.Image  )

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

        # Test batched
        lowerCamelCase									=image_processor(_UpperCAmelCase							, return_tensors="""pt"""  ).pixel_values
        self.assertEqual(
            encoded_images.shape							, (
                self.image_processor_tester.batch_size,
                self.expected_encoded_image_num_channels,
                self.image_processor_tester.size["""height"""],
                self.image_processor_tester.size["""width"""],
            )							, )