

from .number_theory.prime_numbers import next_prime






class 				A_					:


     def __init__(				self     :						Dict     ,    UpperCAmelCase     :						int     ,    UpperCAmelCase     :						int | None = None     ,    UpperCAmelCase     :						float | None = None     ,    )				->      None:
      __lowerCAmelCase:  int        = size_table
      __lowerCAmelCase:  Tuple        = [None] * self.size_table
      __lowerCAmelCase:  Tuple        = 0.75 if lim_charge is None else lim_charge
      __lowerCAmelCase:  List[str]        = 1 if charge_factor is None else charge_factor
      __lowerCAmelCase:  list        = []
      __lowerCAmelCase:  dict        = {}


     def     UpperCAmelCase    (				self     :						List[str]   )				->      Any:
      return self._keys


     def     UpperCAmelCase    (				self     :						Union[str, Any]   )				->      str:
      return sum(1 for slot in self.values if slot is not None   ) / (
          self.size_table * self.charge_factor
      )


     def     UpperCAmelCase    (				self     :						List[Any]     ,    UpperCAmelCase     :						Dict   )				->      Union[str, Any]:
      return key % self.size_table


     def     UpperCAmelCase    (				self     :						Tuple     ,    UpperCAmelCase     :						Any   )				->      int:
      print(F'''step {step_ord}'''   )
      print(list(range(len(self.values   )   )   )   )
      print(self.values   )


     def     UpperCAmelCase    (				self     :						int     ,    UpperCAmelCase     :						Optional[int]   )				->      List[Any]:
      __lowerCAmelCase:  Tuple        = 1
      __lowerCAmelCase:  int        = values
      for value in values:
       self.insert_data(UpperCAmelCase   )
       self._step_by_step(UpperCAmelCase   )
       i += 1


     def     UpperCAmelCase    (				self     :						Tuple     ,    UpperCAmelCase     :						Optional[Any]     ,    UpperCAmelCase     :						int   )				->      List[Any]:
      __lowerCAmelCase:  Any        = data
      __lowerCAmelCase:  str        = data


     def     UpperCAmelCase    (				self     :						List[Any]     ,    UpperCAmelCase     :						Optional[Any]     ,    UpperCAmelCase     :						Tuple=None   )				->      Any:
      __lowerCAmelCase:  Dict        = self.hash_function(key + 1   )

      while self.values[new_key] is not None and self.values[new_key] != key:
       if self.values.count(UpperCAmelCase   ) > 0:
        __lowerCAmelCase:  Any        = self.hash_function(new_key + 1   )
       else:
        __lowerCAmelCase:  Optional[Any]        = None
        break

      return new_key


     def     UpperCAmelCase    (				self     :						Optional[int]   )				->      Tuple:
      __lowerCAmelCase:  List[str]        = [value for value in self.values if value is not None]
      __lowerCAmelCase:  str        = next_prime(self.size_table     ,    factor=2   )
      self._keys.clear()
      __lowerCAmelCase:  List[str]        = [None] * self.size_table  # hell's pointers D: don't DRY ;/
      for value in survivor_values:
       self.insert_data(UpperCAmelCase   )


     def     UpperCAmelCase    (				self     :						List[Any]     ,    UpperCAmelCase     :						List[str]   )				->      Optional[Any]:
      __lowerCAmelCase:  int        = self.hash_function(UpperCAmelCase   )

      if self.values[key] is None:
       self._set_value(UpperCAmelCase     ,    UpperCAmelCase   )

      elif self.values[key] == data:
       pass

      else:
       __lowerCAmelCase:  Optional[Any]        = self._collision_resolution(UpperCAmelCase     ,    UpperCAmelCase   )
       if collision_resolution is not None:
        self._set_value(UpperCAmelCase     ,    UpperCAmelCase   )
       else:
        self.rehashing()
        self.insert_data(UpperCAmelCase   )








from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve







def _a					(			SCREAMING_SNAKE_CASE						:     np.ndarray       ,   SCREAMING_SNAKE_CASE						:     np.ndarray       ,   SCREAMING_SNAKE_CASE						:     np.ndarray						)       ->       np.ndarray:

 """simple docstring"""






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

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

 __lowerCAmelCase:  List[str]        = image[grid[:, :, 1], grid[:, :, 0]]

 # Set pixels at invalid locations to 0
 __lowerCAmelCase:  List[str]        = 0

 return warped







def _a					(			SCREAMING_SNAKE_CASE						:     np.ndarray       ,   SCREAMING_SNAKE_CASE						:     np.ndarray       ,   SCREAMING_SNAKE_CASE						:     SupportsIndex       ,   SCREAMING_SNAKE_CASE						:     float | None = None       ,   )       ->       tuple[np.ndarray, np.ndarray]:

 """simple docstring"""






 if alpha is None:
  __lowerCAmelCase:  Tuple        = 0.1

 # Initialize flow
 __lowerCAmelCase:  Optional[int]        = np.zeros_like(SCREAMING_SNAKE_CASE						)
 __lowerCAmelCase:  Dict        = np.zeros_like(SCREAMING_SNAKE_CASE						)

 # Prepare kernels for the calculation of the derivatives and the average velocity
 __lowerCAmelCase:  List[Any]        = np.array([[-1, 1], [-1, 1]]						) * 0.2_5
 __lowerCAmelCase:  int        = np.array([[-1, -1], [1, 1]]						) * 0.2_5
 __lowerCAmelCase:  Tuple        = np.array([[1, 1], [1, 1]]						) * 0.2_5
 __lowerCAmelCase:  Dict        = 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(SCREAMING_SNAKE_CASE						):
  __lowerCAmelCase:  Optional[int]        = warp(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						)
  __lowerCAmelCase:  List[str]        = convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						) + convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						)
  __lowerCAmelCase:  int        = convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						) + convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						)
  __lowerCAmelCase:  List[Any]        = convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						) + convolve(SCREAMING_SNAKE_CASE       ,   -kernel_t						)

  __lowerCAmelCase:  Any        = convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						)
  __lowerCAmelCase:  Dict        = convolve(SCREAMING_SNAKE_CASE       ,   SCREAMING_SNAKE_CASE						)

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

  __lowerCAmelCase:  List[Any]        = avg_horizontal_velocity - derivative_x * update
  __lowerCAmelCase:  Union[str, Any]        = avg_vertical_velocity - derivative_y * update

 return horizontal_flow, vertical_flow


if __name__ == "__main__":
  import doctest

  doctest.testmod()





