






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

def        _lowerCamelCase		(  __A      :							Optional[Any]						,						__A      :							Union[str, Any]	) ->   Optional[Any]:
    _UpperCAmelCase					,	_UpperCAmelCase			: Optional[Any]     					=			np.shape(_lowerCAmelCase	)

    _UpperCAmelCase			: Dict     					=			np.zeros((rows, 1)						,						dtype=_lowerCAmelCase	)
    for row in reversed(range(_lowerCAmelCase	)	):
        _UpperCAmelCase			: List[Any]     					=			0
        for col in range(row + 1						,						_lowerCAmelCase	):
            total += coefficients[row, col] * x[col]

        _UpperCAmelCase			: Optional[Any]     					=			(vector[row] - total) / coefficients[row, row]

    return x

def        _lowerCamelCase		(  __A      :							int						,						__A      :							int	) ->   List[str]:
    _UpperCAmelCase					,	_UpperCAmelCase			: Union[str, Any]     					=			np.shape(_lowerCAmelCase	)
    if rows != columns:
        return np.array(()						,						dtype=_lowerCAmelCase	)

    # augmented matrix
    _UpperCAmelCase			: Union[str, Any]     					=			np.concatenate((coefficients, vector)						,						axis=1	)
    _UpperCAmelCase			: Optional[Any]     					=			augmented_mat.astype('''float64'''	)

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

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

    return x


if __name__ == "__main__":
  import doctest

  doctest.testmod()












from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import divide, inta, multiply, ravel, sort, zeros_like

def        _lowerCamelCase		(  __A      :							str						,						__A      :							List[str]=3	) ->   List[Any]:
    _UpperCAmelCase			: Tuple     					=			int(mask / 2	)
    # copy image size
    _UpperCAmelCase			: Any     					=			zeros_like(__A	)
    for i in range(__A						,						gray_img.shape[0] - bd	):
        for j in range(__A						,						gray_img.shape[1] - bd	):
            # get mask according with mask
            _UpperCAmelCase			: Any     					=			ravel(gray_img[i - bd : i + bd + 1, j - bd : j + bd + 1]	)
            # calculate mask median
            _UpperCAmelCase			: List[str]     					=			sort(__A	)[inta(divide((multiply(__A						,						__A	))						,						2	) + 1	)]
            _UpperCAmelCase			: int     					=			median
    return median_img


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

  # get values with two different mask size
  SCREAMING_SNAKE_CASE								=  median_filter(gray, 3)
  SCREAMING_SNAKE_CASE								=  median_filter(gray, 5)

  # show result images
  imshow('median filter with 3x3 mask', medianaxa)
  imshow('median filter with 5x5 mask', medianaxa)
  waitKey(0)




