




import cva
import numpy as np

def 					A				(				_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE   )     ->			int:

       try:
              return int(image[x_coordinate][y_coordinate] >= center   )
       except (IndexError, TypeError):
              return 0

def 					A				(				_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE   )     ->			int:
       lowerCamelCase       :				str      			= image[x_coordinate][y_coordinate]
       lowerCamelCase       :				Dict      			= [1, 2, 4, 8, 16, 32, 64, 128]

       # skip get_neighbors_pixel if center is null
       if center is None:
              return 0

       # Starting from the top right, assigning value to pixels clockwise
       lowerCamelCase       :				Optional[int]      			= [
           get_neighbors_pixel(_SCREAMING_SNAKE_CASE			,x_coordinate - 1			,y_coordinate + 1			,_SCREAMING_SNAKE_CASE   ),
           get_neighbors_pixel(_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE			,y_coordinate + 1			,_SCREAMING_SNAKE_CASE   ),
           get_neighbors_pixel(_SCREAMING_SNAKE_CASE			,x_coordinate - 1			,_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE   ),
           get_neighbors_pixel(_SCREAMING_SNAKE_CASE			,x_coordinate + 1			,y_coordinate + 1			,_SCREAMING_SNAKE_CASE   ),
           get_neighbors_pixel(_SCREAMING_SNAKE_CASE			,x_coordinate + 1			,_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE   ),
           get_neighbors_pixel(_SCREAMING_SNAKE_CASE			,x_coordinate + 1			,y_coordinate - 1			,_SCREAMING_SNAKE_CASE   ),
           get_neighbors_pixel(_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE			,y_coordinate - 1			,_SCREAMING_SNAKE_CASE   ),
           get_neighbors_pixel(_SCREAMING_SNAKE_CASE			,x_coordinate - 1			,y_coordinate - 1			,_SCREAMING_SNAKE_CASE   ),
       ]

       # Converting the binary value to decimal.
       return sum(
           binary_value * power for binary_value, power in zip(_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE   )   )


if __name__ == "__main__":
       # Reading the image and converting it to grayscale.
       SCREAMING_SNAKE_CASE__	:				Tuple  =       cva.imread(
           'digital_image_processing/image_data/lena.jpg', cva.IMREAD_GRAYSCALE
       )

       # Create a numpy array as the same height and width of read image
       SCREAMING_SNAKE_CASE__	:				List[str]  =       np.zeros((image.shape[0], image.shape[1]))

       # Iterating through the image and calculating the
       # local binary pattern value for each pixel.
       for i in range(0, image.shape[0]):
              for j in range(0, image.shape[1]):
                     SCREAMING_SNAKE_CASE__	:				Tuple  =       local_binary_value(image, i, j)

       cva.imshow('local binary pattern', lbp_image)
       cva.waitKey(0)
       cva.destroyAllWindows()












import numpy as np

def 					A				(				_SCREAMING_SNAKE_CASE   )     ->			str:
       lowerCamelCase			,				lowerCamelCase       :				Dict      			= a.shape
       lowerCamelCase       :				Union[str, Any]      			= min(_SCREAMING_SNAKE_CASE			,_SCREAMING_SNAKE_CASE   )
       lowerCamelCase       :				Union[str, Any]      			= np.eye(_SCREAMING_SNAKE_CASE   )
       lowerCamelCase       :				List[Any]      			= a.copy()

       for k in range(t - 1   ):
              # select a column of modified matrix A':
              lowerCamelCase       :				Optional[Any]      			= r[k:, [k]]
              # construct first basis vector
              lowerCamelCase       :				Union[str, Any]      			= np.zeros_like(_SCREAMING_SNAKE_CASE   )
              lowerCamelCase       :				int      			= 1.0
              # determine scaling factor
              lowerCamelCase       :				Any      			= np.linalg.norm(_SCREAMING_SNAKE_CASE   )
              # construct vector v for Householder reflection
              lowerCamelCase       :				List[str]      			= x + np.sign(x[0]   ) * alpha * ea
              v /= np.linalg.norm(_SCREAMING_SNAKE_CASE   )

              # construct the Householder matrix
              lowerCamelCase       :				List[Any]      			= np.eye(m - k   ) - 2.0 * v @ v.T
              # pad with ones and zeros as necessary
              lowerCamelCase       :				Union[str, Any]      			= np.block([[np.eye(_SCREAMING_SNAKE_CASE   ), np.zeros((k, m - k)   )], [np.zeros((m - k, k)   ), q_k]]   )

              lowerCamelCase       :				Any      			= q @ q_k.T
              lowerCamelCase       :				List[Any]      			= q_k @ r

       return q, r


if __name__ == "__main__":
       import doctest

       doctest.testmod()






