


import numpy as np
from cva import destroyAllWindows, imread, imshow, waitKey


class       __lowerCAmelCase       :






  """simple docstring"""





  def __init__(       self    :    Optional[Any]      ,			_lowerCAmelCase    :    Union[str, Any]      ,			_lowerCAmelCase    :    int					)				->	Tuple:




     """simple docstring"""
     snake_case_         =   0
     # max greyscale value for #FFFFFF
     snake_case_         =   int(self.get_greyscale(2_5_5      ,			2_5_5      ,			2_5_5					)					)

     if not self.min_threshold < threshold < self.max_threshold:
        snake_case_         =   F'''Factor value should be from 0 to {self.max_threshold}'''
        raise ValueError(_lowerCAmelCase					)

     snake_case_         =   input_img
     snake_case_         =   threshold
     snake_case_      ,      snake_case_         =   self.input_img.shape[1], self.input_img.shape[0]

     # error table size (+4 columns and +1 row) greater than input image because of
     # lack of if statements
     snake_case_         =   [
         [0 for _ in range(self.height + 4					)] for __ in range(self.width + 1					)
     ]
     snake_case_         =   np.ones((self.width, self.height, 3)      ,			np.uinta					) * 2_5_5



  @classmethod
  def    lowerCAmelCase__					(       cls    :    Optional[Any]      ,			_lowerCAmelCase    :    int      ,			_lowerCAmelCase    :    int      ,			_lowerCAmelCase    :    int					)				->	float:




     """simple docstring"""
     return 0.114 * blue + 0.587 * green + 0.2_126 * red



  def    lowerCAmelCase__					(       self    :    Union[str, Any]					)				->	None:




     """simple docstring"""
     for y in range(self.height					):
        for x in range(self.width					):
           snake_case_         =   int(self.get_greyscale(*self.input_img[y][x]					)					)
           if self.threshold > greyscale + self.error_table[y][x]:
              snake_case_         =   (0, 0, 0)
              snake_case_         =   greyscale + self.error_table[x][y]
           else:
              snake_case_         =   (2_5_5, 2_5_5, 2_5_5)
              snake_case_         =   greyscale + self.error_table[x][y] - 2_5_5
           self.error_table[y][x + 1] += int(8 / 3_2 * current_error					)
           self.error_table[y][x + 2] += int(4 / 3_2 * current_error					)
           self.error_table[y + 1][x] += int(8 / 3_2 * current_error					)
           self.error_table[y + 1][x + 1] += int(4 / 3_2 * current_error					)
           self.error_table[y + 1][x + 2] += int(2 / 3_2 * current_error					)
           self.error_table[y + 1][x - 1] += int(4 / 3_2 * current_error					)
           self.error_table[y + 1][x - 2] += int(2 / 3_2 * current_error					)


if __name__ == "__main__":
   # create Burke's instances with original images in greyscale
   SCREAMING_SNAKE_CASE		:Dict											=       [
       Burkes(imread('''image_data/lena.jpg''', 1), threshold)
       for threshold in (1, 1_26, 1_30, 1_40)
   ]

   for burkes in burkes_instances:
      burkes.process()

   for burkes in burkes_instances:
      imshow(
          F'''Original image with dithering threshold: {burkes.threshold}''',
          burkes.output_img,
      )

   waitKey(0)
   destroyAllWindows()








from typing import Any

import numpy as np



def      _lowerCAmelCase  (							lowerCAmelCase_							:np.ndarray							)->bool:
   '''simple docstring'''






   assert np.shape(lowerCAmelCase_							)[0] == np.shape(lowerCAmelCase_							)[1]

   # If matrix not symmetric, exit right away.
   if np.allclose(lowerCAmelCase_						,  matrix.T							) is False:
      return False

   # Get eigenvalues and eignevectors for a symmetric matrix.
   snake_case_      ,      snake_case_         =   np.linalg.eigh(lowerCAmelCase_							)

   # Check sign of all eigenvalues.
   # np.all returns a value of type np.bool_
   return bool(np.all(eigen_values > 0							)							)



def      _lowerCAmelCase  (							lowerCAmelCase_							:int							)->Any:
   '''simple docstring'''






   snake_case_         =   np.random.randn(lowerCAmelCase_						,  lowerCAmelCase_							)
   snake_case_         =   np.dot(lowerCAmelCase_						,  random_matrix.T							)
   assert _is_matrix_spd(lowerCAmelCase_							)
   return spd_matrix



def      _lowerCAmelCase  (							lowerCAmelCase_							:np.ndarray						,  lowerCAmelCase_							:np.ndarray						,  lowerCAmelCase_							:int = 1_000						,  lowerCAmelCase_							:float = 1e-8						,  )->Any:
   '''simple docstring'''






   assert np.shape(lowerCAmelCase_							)[0] == np.shape(lowerCAmelCase_							)[1]
   assert np.shape(lowerCAmelCase_							)[0] == np.shape(lowerCAmelCase_							)[0]
   assert _is_matrix_spd(lowerCAmelCase_							)

   # Initialize solution guess, residual, search direction.
   snake_case_         =   np.zeros((np.shape(lowerCAmelCase_							)[0], 1)							)
   snake_case_         =   np.copy(lowerCAmelCase_							)
   snake_case_         =   np.copy(lowerCAmelCase_							)

   # Set initial errors in solution guess and residual.
   snake_case_         =   1e9
   snake_case_         =   1e9
   snake_case_         =   1e9

   # Set iteration counter to threshold number of iterations.
   snake_case_         =   0

   while error > tol:
      # Save this value so we only calculate the matrix-vector product once.
      snake_case_         =   np.dot(lowerCAmelCase_						,  lowerCAmelCase_							)

      # The main algorithm.

      # Update search direction magnitude.
      snake_case_         =   np.dot(ra.T						,  lowerCAmelCase_							) / np.dot(pa.T						,  lowerCAmelCase_							)
      # Update solution guess.
      snake_case_         =   xa + alpha * pa
      # Calculate new residual.
      snake_case_         =   ra - alpha * w
      # Calculate new Krylov subspace scale.
      snake_case_         =   np.dot(r.T						,  lowerCAmelCase_							) / np.dot(ra.T						,  lowerCAmelCase_							)
      # Calculate new A conjuage search direction.
      snake_case_         =   r + beta * pa

      # Calculate errors.
      snake_case_         =   np.linalg.norm(r - ra							)
      snake_case_         =   np.linalg.norm(x - xa							)
      snake_case_         =   np.maximum(lowerCAmelCase_						,  lowerCAmelCase_							)

      # Update variables.
      snake_case_         =   np.copy(lowerCAmelCase_							)
      snake_case_         =   np.copy(lowerCAmelCase_							)
      snake_case_         =   np.copy(lowerCAmelCase_							)

      # Update number of iterations.
      iterations += 1
      if iterations > max_iterations:
         break

   return x



def      _lowerCAmelCase  (							)->None:
   '''simple docstring'''






   snake_case_         =   3
   snake_case_         =   _create_spd_matrix(lowerCAmelCase_							)
   snake_case_         =   np.random.randn(lowerCAmelCase_						,  1							)
   snake_case_         =   np.dot(lowerCAmelCase_						,  lowerCAmelCase_							)

   # Numpy solution.
   snake_case_         =   np.linalg.solve(lowerCAmelCase_						,  lowerCAmelCase_							)

   # Our implementation.
   snake_case_         =   conjugate_gradient(lowerCAmelCase_						,  lowerCAmelCase_							)

   # Ensure both solutions are close to x_true (and therefore one another).
   assert np.linalg.norm(x_numpy - x_true							) <= 1e-6
   assert np.linalg.norm(x_conjugate_gradient - x_true							) <= 1e-6


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   test_conjugate_gradient()




