

import numpy as np
from numpy import floataa
from numpy.typing import NDArray







def       snake_case__    (       lowerCAmelCase_,   lowerCAmelCase_      ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE						,  SCREAMING_SNAKE_CASE										=np.shape(lowerCAmelCase_      )

     SCREAMING_SNAKE_CASE										=np.zeros((rows, 1),   dtype=lowerCAmelCase_      )
     for row in reversed(range(lowerCAmelCase_      )      ):
          SCREAMING_SNAKE_CASE										=0
          for col in range(row + 1,   lowerCAmelCase_      ):
               total += coefficients[row, col] * x[col]

          SCREAMING_SNAKE_CASE										=(vector[row] - total) / coefficients[row, row]

     return x







def       snake_case__    (       lowerCAmelCase_,   lowerCAmelCase_      ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE						,  SCREAMING_SNAKE_CASE										=np.shape(lowerCAmelCase_      )
     if rows != columns:
          return np.array((),   dtype=lowerCAmelCase_      )

     # augmented matrix
     SCREAMING_SNAKE_CASE										=np.concatenate((coefficients, vector),   axis=1      )
     SCREAMING_SNAKE_CASE										=augmented_mat.astype('float64'      )

     # scale the matrix leaving it triangular
     for row in range(rows - 1      ):
          SCREAMING_SNAKE_CASE										=augmented_mat[row, row]
          for col in range(row + 1,   lowerCAmelCase_      ):
               SCREAMING_SNAKE_CASE										=augmented_mat[col, row] / pivot
               augmented_mat[col, :] -= factor * augmented_mat[row, :]

     SCREAMING_SNAKE_CASE										=retroactive_resolution(
         augmented_mat[:, 0:columns],   augmented_mat[:, columns : columns + 1]      )

     return x


if __name__ == "__main__":
 import doctest

 doctest.testmod()




import numpy as np
from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey

from digital_image_processing.filters.convolve import img_convolve







def       snake_case__    (       lowerCAmelCase_      ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE										=np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]]      )
     SCREAMING_SNAKE_CASE										=np.array([[1, 2, 1], [0, 0, 0], [-1, -2, -1]]      )

     SCREAMING_SNAKE_CASE										=np.abs(img_convolve(lowerCAmelCase_,   lowerCAmelCase_      )      )
     SCREAMING_SNAKE_CASE										=np.abs(img_convolve(lowerCAmelCase_,   lowerCAmelCase_      )      )
     # modify the pix within [0, 255]
     SCREAMING_SNAKE_CASE										=dst_x * 255 / np.max(lowerCAmelCase_      )
     SCREAMING_SNAKE_CASE										=dst_y * 255 / np.max(lowerCAmelCase_      )

     SCREAMING_SNAKE_CASE										=np.sqrt((np.square(lowerCAmelCase_      )) + (np.square(lowerCAmelCase_      ))      )
     SCREAMING_SNAKE_CASE										=dst_xy * 255 / np.max(lowerCAmelCase_      )
     SCREAMING_SNAKE_CASE										=dst_xy.astype(np.uinta      )

     SCREAMING_SNAKE_CASE										=np.arctana(lowerCAmelCase_,   lowerCAmelCase_      )
     return dst, theta


if __name__ == "__main__":
 # read original image
 _lowerCamelCase								=imread("../image_data/lena.jpg")
 # turn image in gray scale value
 _lowerCamelCase								=cvtColor(img, COLOR_BGR2GRAY)

 _lowerCamelCase	,			_lowerCamelCase								=sobel_filter(gray)

 # show result images
 imshow("sobel filter", sobel_grad)
 imshow("sobel theta", sobel_theta)
 waitKey(0)

