code: 
  
  
  
  
  """simple docstring"""
  
  
  
  
  from typing import SupportsIndex
  
  import numpy as np
  from scipy.ndimage import convolve
  def 					A_			(		snake_case_     :       np.ndarray						,snake_case_     :       np.ndarray						,snake_case_     :       np.ndarray    ):
  
  
  
  
  
  
  
      '''simple docstring'''
      UpperCamelCase				:   List[Any]          =							np.stack((horizontal_flow, vertical_flow)						,2    )
  
      # Create a grid of all pixel coordinates and subtract the flow to get the
      # target pixels coordinates
      UpperCamelCase				:   Dict          =							np.stack(
          np.meshgrid(np.arange(0						,image.shape[1]    )						,np.arange(0						,image.shape[0]    )    )						,2    )
      UpperCamelCase				:   Union[str, Any]          =							np.round(grid - flow    ).astype(np.intaa    )
  
      # Find the locations outside of the original image
      UpperCamelCase				:   Tuple          =							(grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]]    ))
      UpperCamelCase				:   Tuple          =							0
  
      UpperCamelCase				:   Dict          =							image[grid[:, :, 1], grid[:, :, 0]]
  
      # Set pixels at invalid locations to 0
      UpperCamelCase				:   Union[str, Any]          =							0
  
      return warped
  def 					A_			(		snake_case_     :       np.ndarray						,snake_case_     :       np.ndarray						,snake_case_     :       SupportsIndex						,snake_case_     :       float | None = None						,):
  
  
  
  
  
  
  
      '''simple docstring'''
      if alpha is None:
          UpperCamelCase				:   str          =							0.1
  
      # Initialize flow
      UpperCamelCase				:   Optional[int]          =							np.zeros_like(snake_case_    )
      UpperCamelCase				:   Optional[int]          =							np.zeros_like(snake_case_    )
  
      # Prepare kernels for the calculation of the derivatives and the average velocity
      UpperCamelCase				:   Union[str, Any]          =							np.array([[-1, 1], [-1, 1]]    ) * 0.25
      UpperCamelCase				:   Optional[Any]          =							np.array([[-1, -1], [1, 1]]    ) * 0.25
      UpperCamelCase				:   Optional[int]          =							np.array([[1, 1], [1, 1]]    ) * 0.25
      UpperCamelCase				:   int          =							np.array(
          [[1 / 1_2, 1 / 6, 1 / 1_2], [1 / 6, 0, 1 / 6], [1 / 1_2, 1 / 6, 1 / 1_2]]    )
  
      # Iteratively refine the flow
      for _ in range(snake_case_    ):
          UpperCamelCase				:   int          =							warp(snake_case_						,snake_case_						,snake_case_    )
          UpperCamelCase				:   Tuple          =							convolve(snake_case_						,snake_case_    ) + convolve(snake_case_						,snake_case_    )
          UpperCamelCase				:   Optional[Any]          =							convolve(snake_case_						,snake_case_    ) + convolve(snake_case_						,snake_case_    )
          UpperCamelCase				:   Optional[Any]          =							convolve(snake_case_						,snake_case_    ) + convolve(snake_case_						,-kernel_t    )
  
          UpperCamelCase				:   Dict          =							convolve(snake_case_						,snake_case_    )
          UpperCamelCase				:   Tuple          =							convolve(snake_case_						,snake_case_    )
  
          # This updates the flow as proposed in the paper (Step 12)
          UpperCamelCase				:   Any          =							(
              derivative_x * avg_horizontal_velocity
              + derivative_y * avg_vertical_velocity
              + derivative_t
          )
          UpperCamelCase				:   Optional[int]          =							update / (alpha**2 + derivative_x**2 + derivative_y**2)
  
          UpperCamelCase				:   List[str]          =							avg_horizontal_velocity - derivative_x * update
          UpperCamelCase				:   List[str]          =							avg_vertical_velocity - derivative_y * update
  
      return horizontal_flow, vertical_flow
  
  
  if __name__ == "__main__":
    import doctest
  
    doctest.testmod()
  
  
  
  
  
style_context: 
  
  
  
  
  """simple docstring"""
  
  
  
  
  class 							lowerCamelCase		:
  
  
  
  
  
  
  
     def __init__(							self    ,      SCREAMING_SNAKE_CASE_=None ):
         UpperCamelCase				:   Optional[Any]          =							data
         UpperCamelCase				:   str          =							None
  
  
  
  
  
  
  
     def __repr__(							self ):
         UpperCamelCase				:   str          =							""""""
         UpperCamelCase				:   Any          =							self
         while temp:
             string_rep += f'<{temp.data}> ---> '
             UpperCamelCase				:   Optional[int]          =							temp.next
         string_rep += "<END>"
         return string_rep
  
  
  
  
  
  
  
  def 					A_			(		snake_case_     :       Tuple    ):
  
  
  
  
  
  
  
      '''simple docstring'''
  
      # if elements_list is empty
      if not elements_list:
          raise Exception("""The Elements List is empty"""    )
  
      # Set first element as Head
      UpperCamelCase				:   List[Any]          =							Node(elements_list[0]    )
      UpperCamelCase				:   str          =							head
      # Loop through elements from position 1
      for data in elements_list[1:]:
          UpperCamelCase				:   Optional[int]          =							Node(snake_case_    )
          UpperCamelCase				:   Optional[Any]          =							current.next
      return head
  
  
  __A :		List[Any]      							=    [1, 3, 5, 32, 44, 12, 43]
  print(F'''List: {list_data}''')
  print('''Creating Linked List from List.''')
  __A :		int      							=    make_linked_list(list_data)
  print('''Linked List:''')
  
  
  print(linked_list)
  
  
  
  
  