"""simple docstring"""


from __future__ import annotations

from typing import Any






class    __UpperCAmelCase						:

				def __init__(      self	, _lowerCamelCase	, _lowerCamelCase      ):  # noqa: A002
										lowerCamelCase__					=item
										lowerCamelCase__					=next






class    __UpperCAmelCase						:

				def __init__(      self      ):
										lowerCamelCase__					=None
										lowerCamelCase__					=0

				def 		_a	(      self	, _lowerCamelCase      ):
										lowerCamelCase__					=Node(_lowerCamelCase	, self.head      )
										self.size += 1

				def 		_a	(      self      ):
										# Switched 'self.is_empty()' to 'self.head is None'
										# because mypy was considering the possibility that 'self.head'
										# can be None in below else part and giving error
										if self.head is None:
																return None
										else:
																lowerCamelCase__					=self.head.item
																lowerCamelCase__					=self.head.next
																self.size -= 1
																return item

				def 		_a	(      self      ):
										return self.head is None

				def __str__(      self      ):
										if self.is_empty():
																return ""
										else:
																lowerCamelCase__					=self.head
																lowerCamelCase__					=""
																lowerCamelCase__					=[]
																while iterate:
																						item_list.append(str(iterate.item      )      )
																						lowerCamelCase__					=iterate.next

																lowerCamelCase__					=" --> ".join(_lowerCamelCase      )

																return item_str






				def __len__(      self      ):
										return self.size




"""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()



