
"""simple docstring"""

from __future__ import annotations

from collections.abc import Iterable
from dataclasses import dataclass
from typing import Any
class    _UpperCAmelCase							:
      __SCREAMING_SNAKE_CASE      :							Any												=		("_front", "_back", "_len")
      @dataclass
      class    _UpperCAmelCase							:
            __SCREAMING_SNAKE_CASE      :							Any												=		None
            __SCREAMING_SNAKE_CASE      :							Deque._Node | None												=		None
            __SCREAMING_SNAKE_CASE      :							Deque._Node | None												=		None

      class    _UpperCAmelCase							:
            __SCREAMING_SNAKE_CASE      :							Tuple												=		("_cur",)




            def __init__(							self      ,				lowercase_							)  ->    None:
                UpperCAmelCase  	=    cur




            def __iter__(							self							)  ->    Deque._Iterator:
                return self




            def 			a_					(							self							)  ->    Any:
                if self._cur is None:
                    # finished iterating
                    raise StopIteration
                UpperCAmelCase  	=    self._cur.val
                UpperCAmelCase  	=    self._cur.next_node

                return val




      def __init__(							self      ,				lowercase_ = None							)  ->    None:
          UpperCAmelCase  	=    None
          UpperCAmelCase  	=    None
          UpperCAmelCase  	=    0

          if iterable is not None:
              # append every value to the deque
              for val in iterable:
                  self.append(lowercase_							)




      def 			a_					(							self      ,				lowercase_							)  ->    None:
          UpperCAmelCase  	=    self._Node(lowercase_      ,				lowercase_      ,				lowercase_							)
          if self.is_empty():
              # front = back
              UpperCAmelCase  	=    UpperCAmelCase  	=    node
              UpperCAmelCase  	=    1
          else:
              # connect nodes
              UpperCAmelCase  	=    node
              UpperCAmelCase  	=    self._back
              UpperCAmelCase  	=    node  # assign new back to the new node

              self._len += 1

              # make sure there were no errors
              assert not self.is_empty(), "Error on appending value."




      def 			a_					(							self      ,				lowercase_							)  ->    None:
          UpperCAmelCase  	=    self._Node(lowercase_      ,				lowercase_      ,				lowercase_							)
          if self.is_empty():
              # front = back
              UpperCAmelCase  	=    UpperCAmelCase  	=    node
              UpperCAmelCase  	=    1
          else:
              # connect nodes
              UpperCAmelCase  	=    self._front
              UpperCAmelCase  	=    node
              UpperCAmelCase  	=    node  # assign new front to the new node

              self._len += 1

              # make sure there were no errors
              assert not self.is_empty(), "Error on appending value."




      def 			a_					(							self      ,				lowercase_							)  ->    None:
          for val in iterable:
              self.append(lowercase_							)




      def 			a_					(							self      ,				lowercase_							)  ->    None:
          for val in iterable:
              self.appendleft(lowercase_							)




      def 			a_					(							self							)  ->    Any:
          assert not self.is_empty(), "Deque is empty."

          UpperCAmelCase  	=    self._back
          UpperCAmelCase  	=    self._back.prev_node  # set new back
          # drop the last node - python will deallocate memory automatically
          UpperCAmelCase  	=    None

          self._len -= 1

          return topop.val




      def 			a_					(							self							)  ->    Any:
          assert not self.is_empty(), "Deque is empty."

          UpperCAmelCase  	=    self._front
          UpperCAmelCase  	=    self._front.next_node  # set new front and drop the first node
          UpperCAmelCase  	=    None

          self._len -= 1

          return topop.val




      def 			a_					(							self							)  ->    bool:
          return self._front is None




      def __len__(							self							)  ->    int:
          return self._len




      def __eq__(							self      ,				lowercase_							)  ->    bool:

          if not isinstance(lowercase_      ,				lowercase_							):
              return NotImplemented

          UpperCAmelCase  	=    self._front
          UpperCAmelCase  	=    other._front

          # if the length of the dequeues are not the same, they are not equal
          if len(self							) != len(lowercase_							):
              return False

          while me is not None and oth is not None:
              # compare every value
              if me.val != oth.val:
                  return False
              UpperCAmelCase  	=    me.next_node
              UpperCAmelCase  	=    oth.next_node

          return True




      def __iter__(							self							)  ->    Deque._Iterator:
          return Deque._Iterator(self._front							)




      def __repr__(							self							)  ->    str:
          UpperCAmelCase  	=    []
          UpperCAmelCase  	=    self._front
          while aux is not None:
              # append the values in a list to display
              values_list.append(aux.val							)
              UpperCAmelCase  	=    aux.next_node

          return F"[{', '.join(repr(lowercase_							) for val in values_list							)}]"


if __name__ == "__main__":
   import doctest

   doctest.testmod()





"""simple docstring"""

from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve




def 			lowercase__  (    lowerCAmelCase :    np.ndarray       , lowerCAmelCase :    np.ndarray       , lowerCAmelCase :    np.ndarray       )       ->					np.ndarray:






    """simple docstring"""




    UpperCAmelCase  	=    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  	=    np.stack(
        np.meshgrid(np.arange(0       , image.shape[1]       )       , np.arange(0       , image.shape[0]       )       )       , 2       )
    UpperCAmelCase  	=    np.round(grid - flow       ).astype(np.intaa       )

    # Find the locations outside of the original image
    UpperCAmelCase  	=    (grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]]       ))
    UpperCAmelCase  	=    0

    UpperCAmelCase  	=    image[grid[:, :, 1], grid[:, :, 0]]

    # Set pixels at invalid locations to 0
    UpperCAmelCase  	=    0

    return warped




def 			lowercase__  (    lowerCAmelCase :    np.ndarray       , lowerCAmelCase :    np.ndarray       , lowerCAmelCase :    SupportsIndex       , lowerCAmelCase :    float | None = None       , )       ->					tuple[np.ndarray, np.ndarray]:






    """simple docstring"""




    if alpha is None:
        UpperCAmelCase  	=    0.1

    # Initialize flow
    UpperCAmelCase  	=    np.zeros_like(lowerCAmelCase       )
    UpperCAmelCase  	=    np.zeros_like(lowerCAmelCase       )

    # Prepare kernels for the calculation of the derivatives and the average velocity
    UpperCAmelCase  	=    np.array([[-1, 1], [-1, 1]]       ) * 0.25
    UpperCAmelCase  	=    np.array([[-1, -1], [1, 1]]       ) * 0.25
    UpperCAmelCase  	=    np.array([[1, 1], [1, 1]]       ) * 0.25
    UpperCAmelCase  	=    np.array(
        [[1 / 12, 1 / 6, 1 / 12], [1 / 6, 0, 1 / 6], [1 / 12, 1 / 6, 1 / 12]]       )

    # Iteratively refine the flow
    for _ in range(lowerCAmelCase       ):
        UpperCAmelCase  	=    warp(lowerCAmelCase       , lowerCAmelCase       , lowerCAmelCase       )
        UpperCAmelCase  	=    convolve(lowerCAmelCase       , lowerCAmelCase       ) + convolve(lowerCAmelCase       , lowerCAmelCase       )
        UpperCAmelCase  	=    convolve(lowerCAmelCase       , lowerCAmelCase       ) + convolve(lowerCAmelCase       , lowerCAmelCase       )
        UpperCAmelCase  	=    convolve(lowerCAmelCase       , lowerCAmelCase       ) + convolve(lowerCAmelCase       , -kernel_t       )

        UpperCAmelCase  	=    convolve(lowerCAmelCase       , lowerCAmelCase       )
        UpperCAmelCase  	=    convolve(lowerCAmelCase       , lowerCAmelCase       )

        # This updates the flow as proposed in the paper (Step 12)
        UpperCAmelCase  	=    (
            derivative_x * avg_horizontal_velocity
            + derivative_y * avg_vertical_velocity
            + derivative_t
        )
        UpperCAmelCase  	=    update / (alpha**2 + derivative_x**2 + derivative_y**2)

        UpperCAmelCase  	=    avg_horizontal_velocity - derivative_x * update
        UpperCAmelCase  	=    avg_vertical_velocity - derivative_y * update

    return horizontal_flow, vertical_flow


if __name__ == "__main__":
   import doctest

   doctest.testmod()



