
import unittest

import numpy as np






def 						__magic_name__ (    __a			:       np.ndarray       ,		__a			:       np.ndarray       ,		__a			:       np.ndarray       ,		__a			:       np.ndarray | None = None       ,		):



     '''simple docstring'''




     UpperCamelCase__				=				np.shape(__snake_case						)
     UpperCamelCase__				=				np.shape(__snake_case						)
     UpperCamelCase__				=				np.shape(__snake_case						)

     if shape_a[0] != shape_b[0]:
          UpperCamelCase__				=				(
              'Expected the same number of rows for A and B. '
              f"Instead found A of size {shape_a} and B of size {shape_b}"
          )
          raise ValueError(__snake_case						)

     if shape_b[1] != shape_c[1]:
          UpperCamelCase__				=				(
              'Expected the same number of columns for B and C. '
              f"Instead found B of size {shape_b} and C of size {shape_c}"
          )
          raise ValueError(__snake_case						)

     UpperCamelCase__				=				pseudo_inv
     if a_inv is None:
          try:
               UpperCamelCase__				=				np.linalg.inv(__snake_case						)
          except np.linalg.LinAlgError:
               raise ValueError(
                   """Input matrix A is not invertible. Cannot compute Schur complement."""						)

     return mat_c - mat_b.T @ a_inv @ mat_b




class 	__A(				unittest.TestCase ):

  """simple docstring"""







  def        UpperCAmelCase_					(self						):
       UpperCamelCase__				=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]						)
       UpperCamelCase__				=				np.array([[0, 3], [3, 0], [2, 3]]						)
       UpperCamelCase__				=				np.array([[2, 1], [6, 3]]						)

       UpperCamelCase__				=				schur_complement(_UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase						)

       UpperCamelCase__				=				np.block([[a, b], [b.T, c]]						)

       UpperCamelCase__				=				np.linalg.det(_UpperCAmelCase						)
       UpperCamelCase__				=				np.linalg.det(_UpperCAmelCase						)
       UpperCamelCase__				=				np.linalg.det(_UpperCAmelCase						)

       self.assertAlmostEqual(_UpperCAmelCase       ,			det_a * det_s						)







  def        UpperCAmelCase_					(self						):
       UpperCamelCase__				=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]						)
       UpperCamelCase__				=				np.array([[0, 3], [3, 0], [2, 3]]						)
       UpperCamelCase__				=				np.array([[2, 1], [6, 3]]						)

       with self.assertRaises(_UpperCAmelCase						):
            schur_complement(_UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase						)







  def        UpperCAmelCase_					(self						):
       UpperCamelCase__				=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]						)
       UpperCamelCase__				=				np.array([[0, 3], [3, 0], [2, 3]]						)
       UpperCamelCase__				=				np.array([[2, 1, 3], [6, 3, 5]]						)

       with self.assertRaises(_UpperCAmelCase						):
            schur_complement(_UpperCAmelCase       ,			_UpperCAmelCase       ,			_UpperCAmelCase						)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    unittest.main()












'''simple docstring'''




from itertools import product

from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import dot, exp, mgrid, pi, ravel, square, uinta, zeros






def        _lowerCAmelCase			(  __snake_case  : Optional[Any] ,							__snake_case  : Optional[int]			)     ->     List[str]:
     __A						: List[str]      =       k_size // 2
     __A ,__A						: List[Any]      =       mgrid[0 - center : k_size - center, 0 - center : k_size - center]
     __A						: List[Any]      =       1 / (2 * pi * sigma) * exp(-(square(__snake_case			) + square(__snake_case			)) / (2 * square(__snake_case			))			)
     return g






def        _lowerCAmelCase			(  __snake_case  : List[str] ,							__snake_case  : List[str] ,							__snake_case  : int			)     ->     Union[str, Any]:
     __A ,__A						: Tuple      =       image.shape[0], image.shape[1]
     # dst image height and width
     __A						: Tuple      =       height - k_size + 1
     __A						: Optional[Any]      =       width - k_size + 1

     # im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
     __A						: str      =       zeros((dst_height * dst_width, k_size * k_size)			)
     __A						: Optional[Any]      =       0
     for i, j in product(range(__snake_case			) ,							range(__snake_case			)			):
          __A						: int      =       ravel(image[i : i + k_size, j : j + k_size]			)
          __A						: List[str]      =       window
          row += 1

     #  turn the kernel into shape(k*k, 1)
     __A						: List[Any]      =       gen_gaussian_kernel(__snake_case ,							__snake_case			)
     __A						: Any      =       ravel(__snake_case			)

     # reshape and get the dst image
     __A						: Dict      =       dot(__snake_case ,							__snake_case			).reshape(__snake_case ,							__snake_case			).astype(__snake_case			)

     return dst


if __name__ == "__main__":
  # read original image
  lowercase__    :      List[Any]						=    imread(r'''../image_data/lena.jpg''')
  # turn image in gray scale value
  lowercase__    :      Dict						=    cvtColor(img, COLOR_BGR2GRAY)

  # get values with two different mask size
  lowercase__    :      Any						=    gaussian_filter(gray, 3, sigma=1)
  lowercase__    :      str						=    gaussian_filter(gray, 5, sigma=0.8)

  # show result images
  imshow('''gaussian filter with 3x3 mask''', gaussianaxa)
  imshow('''gaussian filter with 5x5 mask''', gaussianaxa)
  waitKey()