
'''simple docstring'''





from __future__ import annotations
def 	snake_case_							(				_a  :				str			,       _a  :				dict[str, str]      ):
      snake_case_							,						snake_case_							,						snake_case_    							=				"", "", ""
      snake_case_    							=				[]

      for character in message_part:
            tmp.append(character_to_number[character]      )

      for each in tmp:
            one += each[0]
            two += each[1]
            three += each[2]

      return one + two + three
def 	snake_case_							(				_a  :				str			,       _a  :				dict[str, str]      ):
      snake_case_							,						snake_case_    							=				"", ""
      snake_case_    							=				[]

      for character in message_part:
            this_part += character_to_number[character]

      for digit in this_part:
            tmp += digit
            if len(_a      ) == len(_a      ):
                  result.append(_a      )
                  snake_case_    							=				""

      return result[0], result[1], result[2]
def 	snake_case_							(				_a  :				str			,       _a  :				str      ):
      # Validate message and alphabet, set to upper and remove spaces
      snake_case_    							=				alphabet.replace(" "			,       ""      ).upper()
      snake_case_    							=				message.replace(" "			,       ""      ).upper()

      # Check length and characters
      if len(_a      ) != 27:
            raise KeyError("Length of alphabet has to be 27."      )
      for each in message:
            if each not in alphabet:
                  raise ValueError("Each message character has to be included in alphabet!"      )

    # Generate dictionares
      snake_case_    							=				(
          "111",
          "112",
          "113",
          "121",
          "122",
          "123",
          "131",
          "132",
          "133",
          "211",
          "212",
          "213",
          "221",
          "222",
          "223",
          "231",
          "232",
          "233",
          "311",
          "312",
          "313",
          "321",
          "322",
          "323",
          "331",
          "332",
          "333",
      )
      snake_case_    							=				{}
      snake_case_    							=				{}
      for letter, number in zip(_a			,       _a      ):
            snake_case_    							=				number
            snake_case_    							=				letter

      return message, alphabet, character_to_number, number_to_character
def 	snake_case_							(				_a  :				str			,       _a  :				str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."			,       _a  :				int = 5      ):
      snake_case_							,						snake_case_							,						snake_case_							,						snake_case_    							=				__prepare(
          _a			,       _a      )
      snake_case_							,						snake_case_    							=				"", ""

      for i in range(0			,       len(_a      ) + 1			,       _a      ):
            encrypted_numeric += __encrypt_part(
                message[i : i + period]			,       _a      )

      for i in range(0			,       len(_a      )			,       3      ):
            encrypted += number_to_character[encrypted_numeric[i : i + 3]]

      return encrypted
def 	snake_case_							(				_a  :				str			,       _a  :				str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."			,       _a  :				int = 5      ):
      snake_case_							,						snake_case_							,						snake_case_							,						snake_case_    							=				__prepare(
          _a			,       _a      )
      snake_case_    							=				[]
      snake_case_    							=				""

      for i in range(0			,       len(_a      ) + 1			,       _a      ):
            snake_case_							,						snake_case_							,						snake_case_    							=				__decrypt_part(message[i : i + period]			,       _a      )

            for j in range(0			,       len(_a      )      ):
                  decrypted_numeric.append(a[j] + b[j] + c[j]      )

      for each in decrypted_numeric:
            decrypted += number_to_character[each]

      return decrypted


if __name__ == "__main__":
     A							     = "DEFEND THE EAST WALL OF THE CASTLE."
     A							     = encrypt_message(msg, "EPSDUCVWYM.ZLKXNBTFGORIJHAQ")
     A							     = decrypt_message(encrypted, "EPSDUCVWYM.ZLKXNBTFGORIJHAQ")
     print(F"""Encrypted: {encrypted}\nDecrypted: {decrypted}""")









from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve



def        _lowerCamelCase(      lowerCAmelCase__					:		np.ndarray     ,     lowerCAmelCase__					:		np.ndarray     ,     lowerCAmelCase__					:		np.ndarray   ):





				'''simple docstring'''







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

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

				SCREAMING_SNAKE_CASE_ :						Optional[Any]    				= image[grid[:, :, 1], grid[:, :, 0]]

				# Set pixels at invalid locations to 0
				SCREAMING_SNAKE_CASE_ :						Optional[int]    				= 0

				return warped



def        _lowerCamelCase(      lowerCAmelCase__					:		np.ndarray     ,     lowerCAmelCase__					:		np.ndarray     ,     lowerCAmelCase__					:		SupportsIndex     ,     lowerCAmelCase__					:		float | None = None     ,     ):





				'''simple docstring'''







				if alpha is None:
								SCREAMING_SNAKE_CASE_ :						Any    				= 0.1

				# Initialize flow
				SCREAMING_SNAKE_CASE_ :						List[Any]    				= np.zeros_like(lowerCAmelCase__   )
				SCREAMING_SNAKE_CASE_ :						Any    				= np.zeros_like(lowerCAmelCase__   )

				# Prepare kernels for the calculation of the derivatives and the average velocity
				SCREAMING_SNAKE_CASE_ :						Optional[int]    				= np.array([[-1, 1], [-1, 1]]   ) * 0.25
				SCREAMING_SNAKE_CASE_ :						Tuple    				= np.array([[-1, -1], [1, 1]]   ) * 0.25
				SCREAMING_SNAKE_CASE_ :						Optional[int]    				= np.array([[1, 1], [1, 1]]   ) * 0.25
				SCREAMING_SNAKE_CASE_ :						Tuple    				= 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__   ):
								SCREAMING_SNAKE_CASE_ :						Union[str, Any]    				= warp(lowerCAmelCase__     ,     lowerCAmelCase__     ,     lowerCAmelCase__   )
								SCREAMING_SNAKE_CASE_ :						Any    				= convolve(lowerCAmelCase__     ,     lowerCAmelCase__   ) + convolve(lowerCAmelCase__     ,     lowerCAmelCase__   )
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= convolve(lowerCAmelCase__     ,     lowerCAmelCase__   ) + convolve(lowerCAmelCase__     ,     lowerCAmelCase__   )
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= convolve(lowerCAmelCase__     ,     lowerCAmelCase__   ) + convolve(lowerCAmelCase__     ,     -kernel_t   )

								SCREAMING_SNAKE_CASE_ :						List[str]    				= convolve(lowerCAmelCase__     ,     lowerCAmelCase__   )
								SCREAMING_SNAKE_CASE_ :						Optional[Any]    				= convolve(lowerCAmelCase__     ,     lowerCAmelCase__   )

								# This updates the flow as proposed in the paper (Step 12)
								SCREAMING_SNAKE_CASE_ :						Tuple    				= (
								    derivative_x * avg_horizontal_velocity
								    + derivative_y * avg_vertical_velocity
								    + derivative_t
								)
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= update / (alpha**2 + derivative_x**2 + derivative_y**2)

								SCREAMING_SNAKE_CASE_ :						List[str]    				= avg_horizontal_velocity - derivative_x * update
								SCREAMING_SNAKE_CASE_ :						Optional[int]    				= avg_vertical_velocity - derivative_y * update

				return horizontal_flow, vertical_flow


if __name__ == "__main__":
				import doctest

				doctest.testmod()