

'''simple docstring'''


import math
import sys

import cva
import numpy as np




def 	_a       (				__lowerCAmelCase		:      np.ndarray   ,							__lowerCAmelCase		:      float     ):

		"""simple docstring"""

		snake_case__						:       Optional[int]       						=  math.sqrt(__lowerCAmelCase     )
		snake_case__						:       Union[str, Any]       						=  1 / (sigma * math.sqrt(2 * math.pi     ))
		return cons * np.exp(-((img / sigma) ** 2) * 0.5     )




def 	_a       (				__lowerCAmelCase		:      np.ndarray   ,							__lowerCAmelCase		:      int   ,							__lowerCAmelCase		:      int   ,							__lowerCAmelCase		:      int     ):

		"""simple docstring"""

		snake_case__						:       List[Any]       						=  kernel_size // 2
		return img[x - half : x + half + 1, y - half : y + half + 1]




def 	_a       (				__lowerCAmelCase		:      int   ,							__lowerCAmelCase		:      float     ):

		"""simple docstring"""

		snake_case__						:       Any       						=  np.zeros((kernel_size, kernel_size)     )
		for i in range(0   ,							__lowerCAmelCase     ):
				for j in range(0   ,							__lowerCAmelCase     ):
						snake_case__						:       Any       						=  math.sqrt(
						    abs(i - kernel_size // 2     ) ** 2 + abs(j - kernel_size // 2     ) ** 2     )
		return vec_gaussian(__lowerCAmelCase   ,							__lowerCAmelCase     )




def 	_a       (				__lowerCAmelCase		:      np.ndarray   ,							__lowerCAmelCase		:      float   ,							__lowerCAmelCase		:      float   ,							__lowerCAmelCase		:      int   ,							):

		"""simple docstring"""

		snake_case__						:       Optional[int]       						=  np.zeros(img.shape     )
		snake_case__						:       Optional[Any]       						=  get_gauss_kernel(__lowerCAmelCase   ,							__lowerCAmelCase     )
		snake_case__						,       snake_case__						:       Optional[Any]       						=  img.shape
		for i in range(kernel_size // 2   ,							size_x - kernel_size // 2     ):
				for j in range(kernel_size // 2   ,							size_y - kernel_size // 2     ):
						snake_case__						:       Tuple       						=  get_slice(__lowerCAmelCase   ,							__lowerCAmelCase   ,							__lowerCAmelCase   ,							__lowerCAmelCase     )
						snake_case__						:       str       						=  img_s - img_s[kernel_size // 2, kernel_size // 2]
						snake_case__						:       List[Any]       						=  vec_gaussian(__lowerCAmelCase   ,							__lowerCAmelCase     )
						snake_case__						:       Any       						=  np.multiply(__lowerCAmelCase   ,							__lowerCAmelCase     )
						snake_case__						:       List[Any]       						=  np.multiply(__lowerCAmelCase   ,							__lowerCAmelCase     )
						snake_case__						:       Dict       						=  np.sum(__lowerCAmelCase     ) / np.sum(__lowerCAmelCase     )
						snake_case__						:       Any       						=  val
		return imga




def 	_a       (				__lowerCAmelCase		:      list     ):

		"""simple docstring"""

		snake_case__						:       Optional[int]       						=  args[1] if args[1:] else '''../image_data/lena.jpg'''
		snake_case__						:       List[str]       						=  float(args[2]     ) if args[2:] else 1.0
		snake_case__						:       Dict       						=  float(args[3]     ) if args[3:] else 1.0
		if args[4:]:
				snake_case__						:       Union[str, Any]       						=  int(args[4]     )
				snake_case__						:       Any       						=  kernel_size + abs(kernel_size % 2 - 1     )
		else:
				snake_case__						:       Any       						=  5
		return filename, spatial_variance, intensity_variance, kernel_size


if __name__ == "__main__":
					lowerCAmelCase__						,			lowerCAmelCase__						,			lowerCAmelCase__						,			lowerCAmelCase__						:       Any										=						parse_args(sys.argv)
					lowerCAmelCase__						:       str										=						cva.imread(filename, 0)
					cva.imshow("""input image""", img)

					lowerCAmelCase__						:       int										=						img / 255
					lowerCAmelCase__						:       Dict										=						out.astype("""float32""")
					lowerCAmelCase__						:       Any										=						bilateral_filter(out, spatial_variance, intensity_variance, kernel_size)
					lowerCAmelCase__						:       str										=						out * 255
					lowerCAmelCase__						:       str										=						np.uinta(out)
					cva.imshow("""output image""", out)
					cva.waitKey(0)
					cva.destroyAllWindows()






'''simple docstring'''


def 	_a       (				__lowerCAmelCase		:      int     ):

		"""simple docstring"""

		if p < 2:
				raise ValueError('''p should not be less than 2!'''     )
		elif p == 2:
				return True

		snake_case__						:       Any       						=  4
		snake_case__						:       int       						=  (1 << p) - 1
		for _ in range(p - 2     ):
				snake_case__						:       Tuple       						=  ((s * s) - 2) % m
		return s == 0


if __name__ == "__main__":
					print(lucas_lehmer_test(7))
					print(lucas_lehmer_test(11))



