



from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve
def 						snake_case__							(       __lowercase				,  __lowercase				,  __lowercase							)		->		np.ndarray:







						"""simple docstring"""

						A__						:				Union[str, 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
						A__						:				Union[str, Any]         =			np.stack(
						    np.meshgrid(np.arange(0				,  image.shape[1]							)				,  np.arange(0				,  image.shape[0]							)							)				,  2							)
						A__						:				List[Any]         =			np.round(grid - flow							).astype(np.intaa							)

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

						A__						:				str         =			image[grid[:, :, 1], grid[:, :, 0]]

						# Set pixels at invalid locations to 0
						A__						:				Any         =			0

						return warped
def 						snake_case__							(       __lowercase				,  __lowercase				,  __lowercase				,  __lowercase = None				,  )		->		tuple[np.ndarray, np.ndarray]:







						"""simple docstring"""

						if alpha is None:
												A__						:				Tuple         =			0.1

						# Initialize flow
						A__						:				Any         =			np.zeros_like(__lowercase							)
						A__						:				List[Any]         =			np.zeros_like(__lowercase							)

						# Prepare kernels for the calculation of the derivatives and the average velocity
						A__						:				Dict         =			np.array([[-1, 1], [-1, 1]]							) * 0.25
						A__						:				int         =			np.array([[-1, -1], [1, 1]]							) * 0.25
						A__						:				Optional[int]         =			np.array([[1, 1], [1, 1]]							) * 0.25
						A__						:				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(__lowercase							):
												A__						:				Dict         =			warp(__lowercase				,  __lowercase				,  __lowercase							)
												A__						:				Dict         =			convolve(__lowercase				,  __lowercase							) + convolve(__lowercase				,  __lowercase							)
												A__						:				Dict         =			convolve(__lowercase				,  __lowercase							) + convolve(__lowercase				,  __lowercase							)
												A__						:				Any         =			convolve(__lowercase				,  __lowercase							) + convolve(__lowercase				,  -kernel_t							)

												A__						:				str         =			convolve(__lowercase				,  __lowercase							)
												A__						:				Dict         =			convolve(__lowercase				,  __lowercase							)

												# This updates the flow as proposed in the paper (Step 12)
												A__						:				Tuple         =			(
												    derivative_x * avg_horizontal_velocity
												    + derivative_y * avg_vertical_velocity
												    + derivative_t
												)
												A__						:				Union[str, Any]         =			update / (alpha**2 + derivative_x**2 + derivative_y**2)

												A__						:				Dict         =			avg_horizontal_velocity - derivative_x * update
												A__						:				Dict         =			avg_vertical_velocity - derivative_y * update

						return horizontal_flow, vertical_flow


if __name__ == "__main__":
		import doctest

		doctest.testmod()


'''simple docstring'''

def      __magic_name__							(			A				)      ->		tuple[int, int]:
	# base case
	if len(A				) == 1:
		return a[0], a[0]
	else:
		# split A into half.
		snake_case							=					a[: len(A				) // 2]
		snake_case							=					a[len(A				) // 2 :]

		# 2 sub problems, 1/2 of original size.
		snake_case			,			snake_case							=					max_difference(A				)
		snake_case			,			snake_case							=					max_difference(A				)

		# get min of first and max of second
		# linear time
		snake_case							=					min(A				)
		snake_case							=					max(A				)

		# 3 cases, either (small1, big1),
		# (min_first, max_second), (small2, big2)
		# constant comparisons
		if biga - smalla > max_second - min_first and biga - smalla > biga - smalla:
			return smalla, biga
		elif biga - smalla > max_second - min_first:
			return smalla, biga
		else:
			return min_first, max_second


if __name__ == "__main__":
						import doctest

						doctest.testmod()





