

'''simple docstring'''

from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve

def     __magic_name__       ( A					,   A					,   A							)			->		np.ndarray:
	snake_case							 =				np.stack((horizontal_flow, vertical_flow)					,   2							)

	# Create a grid of all pixel coordinates and subtract the flow to get the
	# target pixels coordinates
	snake_case							 =				np.stack(
	    np.meshgrid(np.arange(0					,   image.shape[1]							)					,   np.arange(0					,   image.shape[0]							)							)					,   2							)
	snake_case							 =				np.round(grid - flow							).astype(np.intaa							)

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

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

	# Set pixels at invalid locations to 0
	snake_case							 =				0

	return warped

def     __magic_name__       ( A					,   A					,   A					,   A = None					,   )			->		tuple[np.ndarray, np.ndarray]:
	if alpha is None:
		snake_case							 =				0.1

	# Initialize flow
	snake_case							 =				np.zeros_like(A							)
	snake_case							 =				np.zeros_like(A							)

	# Prepare kernels for the calculation of the derivatives and the average velocity
	snake_case							 =				np.array([[-1, 1], [-1, 1]]							) * 0.25
	snake_case							 =				np.array([[-1, -1], [1, 1]]							) * 0.25
	snake_case							 =				np.array([[1, 1], [1, 1]]							) * 0.25
	snake_case							 =				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(A							):
		snake_case							 =				warp(A					,   A					,   A							)
		snake_case							 =				convolve(A					,   A							) + convolve(A					,   A							)
		snake_case							 =				convolve(A					,   A							) + convolve(A					,   A							)
		snake_case							 =				convolve(A					,   A							) + convolve(A					,   -kernel_t							)

		snake_case							 =				convolve(A					,   A							)
		snake_case							 =				convolve(A					,   A							)

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

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

	return horizontal_flow, vertical_flow


if __name__ == "__main__":
						import doctest

						doctest.testmod()








'''simple docstring'''

lowerCAmelCase_						   =			{0: [1, 2], 1: [0, 3], 2: [0], 3: [1], 4: [5, 6], 5: [4, 6], 6: [4, 5]}

lowerCAmelCase_						   =			{0: [1, 2, 3], 1: [0, 3], 2: [0], 3: [0, 1], 4: [], 5: []}

def     __magic_name__       ( A					,   A					,   A							)			->		list:
	snake_case							 =				True
	snake_case							 =				[]

	for neighbour in graph[vert]:
		if not visited[neighbour]:
			connected_verts += dfs(A					,   A					,   A							)

	return [vert, *connected_verts]

def     __magic_name__       ( A							)			->		list:
	snake_case							 =				len(A							)
	snake_case							 =				graph_size * [False]
	snake_case							 =				[]

	for i in range(A							):
		if not visited[i]:
			snake_case							 =				dfs(A					,   A					,   A							)
			components_list.append(A							)

	return components_list


if __name__ == "__main__":
						import doctest

						doctest.testmod()





