

'''simple docstring'''






snake_case_       =       [0.3_3, 0.4_4, 0.5_5, 0.4_4, 0.3_3]
snake_case_       =       3
snake_case_       =       5

# Buffer Space (with Parameters Space)
snake_case_       =       []
snake_case_       =       []

# Machine Time
snake_case_       =       0


def 					__lowerCamelCase			(      SCREAMING_SNAKE_CASE_     :	Any    )							->   Optional[int]:
      """simple docstring"""

      global buffer_space, params_space, machine_time, K, m, t

      # Choosing Dynamical Systems (All)
      for key, value in enumerate(SCREAMING_SNAKE_CASE_    ):
            # Evolution Parameter
            SCREAMING_SNAKE_CASE_      :			int     =       float(seed / value    )

            # Control Theory: Orbit Change
            SCREAMING_SNAKE_CASE_      :			Dict     =       (buffer_space[(key + 1) % m] + e) % 1

            # Control Theory: Trajectory Change
            SCREAMING_SNAKE_CASE_      :			Union[str, Any]     =       (params_space[key] + e) % 1 + 3

            # Modification (Transition Function) - Jumps
            SCREAMING_SNAKE_CASE_      :			Optional[Any]     =       round(float(r * value * (1 - value)    )  ,  1_0    )
            SCREAMING_SNAKE_CASE_      :			Any     =       r  # Saving to Parameters Space

      # Logistic Map
      assert max(SCREAMING_SNAKE_CASE_    ) < 1
      assert max(SCREAMING_SNAKE_CASE_    ) < 4

      # Machine Time
      machine_time += 1


def 					__lowerCamelCase			(      )							->   Union[str, Any]:
      """simple docstring"""

      global buffer_space, params_space, machine_time, K, m, t

      # PRNG (Xorshift by George Marsaglia)
      def xorshift(SCREAMING_SNAKE_CASE_     :	Any  ,  SCREAMING_SNAKE_CASE_     :	Union[str, Any]    ):
            x ^= y >> 1_3
            y ^= x << 1_7
            x ^= y >> 5
            return x

      # Choosing Dynamical Systems (Increment)
      SCREAMING_SNAKE_CASE_      :			int     =       machine_time % m

      # Evolution (Time Length)
      for _ in range(0  ,  SCREAMING_SNAKE_CASE_    ):
            # Variables (Position + Parameters)
            SCREAMING_SNAKE_CASE_      :			Union[str, Any]     =       params_space[key]
            SCREAMING_SNAKE_CASE_      :			List[str]     =       buffer_space[key]

            # Modification (Transition Function) - Flow
            SCREAMING_SNAKE_CASE_      :			Union[str, Any]     =       round(float(r * value * (1 - value)    )  ,  1_0    )
            SCREAMING_SNAKE_CASE_      :			Dict     =       (machine_time * 0.01 + r * 1.01) % 1 + 3

      # Choosing Chaotic Data
      SCREAMING_SNAKE_CASE_      :			Any     =       int(buffer_space[(key + 2) % m] * (1_0**1_0)    )
      SCREAMING_SNAKE_CASE_      :			List[Any]     =       int(buffer_space[(key - 2) % m] * (1_0**1_0)    )

      # Machine Time
      machine_time += 1

      return xorshift(SCREAMING_SNAKE_CASE_  ,  SCREAMING_SNAKE_CASE_    ) % 0xFF_FF_FF_FF


def 					__lowerCamelCase			(      )							->   Optional[int]:
      """simple docstring"""

      global buffer_space, params_space, machine_time, K, m, t

      SCREAMING_SNAKE_CASE_      :			List[str]     =       K
      SCREAMING_SNAKE_CASE_      :			Dict     =       [0] * m
      SCREAMING_SNAKE_CASE_      :			List[Any]     =       0


if __name__ == "__main__":
      # Initialization
      reset()

      # Pushing Data (Input)
      import random

      snake_case_       =       random.sample(range(0XFFFF_FFFF), 1_0_0)
      for chunk in message:
            push(chunk)

      # for controlling
      snake_case_       =       ''

      # Pulling Data (Output)
      while inp in ("e", "E"):
            print(F'''{format(pull(), "#04x")}''')
            print(buffer_space)
            print(params_space)
            snake_case_       =       input('(e)exit? ').strip()



"""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()



