

'''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'''

from .balanced_parentheses import balanced_parentheses
from .stack import Stack

def      __magic_name__							(			A				)      ->		int:
	return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(A       , -1				)

def      __magic_name__							(			A				)      ->		str:
	if not balanced_parentheses(A				):
		raise ValueError('Mismatched parentheses'				)
	snake_case							=					Stack()
	snake_case							=					[]
	for char in expression_str:
		if char.isalpha() or char.isdigit():
			postfix.append(A				)
		elif char == "(":
			stack.push(A				)
		elif char == ")":
			while not stack.is_empty() and stack.peek() != "(":
				postfix.append(stack.pop()				)
			stack.pop()
		else:
			while not stack.is_empty() and precedence(A				) <= precedence(stack.peek()				):
				postfix.append(stack.pop()				)
			stack.push(A				)
	while not stack.is_empty():
		postfix.append(stack.pop()				)
	return " ".join(A				)


if __name__ == "__main__":
						from doctest import testmod

						testmod()
						lowerCAmelCase_     =      "a+b*(c^d-e)^(f+g*h)-i"

						print("Infix to Postfix Notation demonstration:\n")
						print("Infix notation: " + expression)
						print("Postfix notation: " + infix_to_postfix(expression))





