



from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
_lowerCAmelCase	:   List[Any]    =   2_9_9_7_9_2_4_5_8

# Symbols
_lowerCAmelCase,		_lowerCAmelCase,		_lowerCAmelCase,		_lowerCAmelCase	:   Optional[Any]    =   symbols("ct x y z")







def     UpperCAmelCase_		(					snake_case__					)	->     float:



				"""simple docstring"""





				if velocity > c:
								raise ValueError('Speed must not exceed light speed 299,792,458 [m/s]!'					)
				elif velocity < 1:
								# Usually the speed should be much higher than 1 (c order of magnitude)
								raise ValueError('Speed must be greater than or equal to 1!'					)

				return velocity / c







def     UpperCAmelCase_		(					snake_case__					)	->     float:



				"""simple docstring"""





				return 1 / sqrt(1 - beta(snake_case__					) ** 2					)







def     UpperCAmelCase_		(					snake_case__					)	->     np.ndarray:



				"""simple docstring"""





				return np.array(
				    [
				        [gamma(snake_case__					), -gamma(snake_case__					) * beta(snake_case__					), 0, 0],
				        [-gamma(snake_case__					) * beta(snake_case__					), gamma(snake_case__					), 0, 0],
				        [0, 0, 1, 0],
				        [0, 0, 0, 1],
				    ]					)







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__ = None					)	->     np.ndarray:



				"""simple docstring"""





				if event is None:
								lowerCAmelCase__		  =  np.array([ct, x, y, z]					)  # Symbolic four vector
				else:
								event[0] *= c  # x0 is ct (speed of light * time)

				return transformation_matrix(snake_case__					) @ event


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	# Example of symbolic vector:
	_lowerCAmelCase	:   List[str]    =   transform(2_9_9_7_9_2_4_5)
	print("Example of four vector: ")
	print(f"""ct' = {four_vector[0]}""")
	print(f"""x' = {four_vector[1]}""")
	print(f"""y' = {four_vector[2]}""")
	print(f"""z' = {four_vector[3]}""")

	# Substitute symbols with numerical values
	_lowerCAmelCase	:   Optional[int]    =   {ct: c, x: 1, y: 1, z: 1}
	_lowerCAmelCase	:   Tuple    =   [four_vector[i].subs(sub_dict) for i in range(4)]

	print(f"""\n{numerical_vector}""")





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     UpperCAmelCase_		(					snake_case__    ,			snake_case__					)	->     Dict:



				"""simple docstring"""





				lowerCAmelCase__		  =  k_size // 2
				lowerCAmelCase__  ,   lowerCAmelCase__		  =  mgrid[0 - center : k_size - center, 0 - center : k_size - center]
				lowerCAmelCase__		  =  1 / (2 * pi * sigma) * exp(-(square(snake_case__					) + square(snake_case__					)) / (2 * square(snake_case__					))					)
				return g







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__    ,			snake_case__					)	->     str:



				"""simple docstring"""





				lowerCAmelCase__  ,   lowerCAmelCase__		  =  image.shape[0], image.shape[1]
				# dst image height and width
				lowerCAmelCase__		  =  height - k_size + 1
				lowerCAmelCase__		  =  width - k_size + 1

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

				#  turn the kernel into shape(k*k, 1)
				lowerCAmelCase__		  =  gen_gaussian_kernel(snake_case__    ,			snake_case__					)
				lowerCAmelCase__		  =  ravel(snake_case__					)

				# reshape and get the dst image
				lowerCAmelCase__		  =  dot(snake_case__    ,			snake_case__					).reshape(snake_case__    ,			snake_case__					).astype(snake_case__					)

				return dst


if __name__ == "__main__":
	# read original image
	_lowerCAmelCase	:   List[str]    =   imread(R"../image_data/lena.jpg")
	# turn image in gray scale value
	_lowerCAmelCase	:   Optional[Any]    =   cvtColor(img, COLOR_BGR2GRAY)

	# get values with two different mask size
	_lowerCAmelCase	:   Optional[int]    =   gaussian_filter(gray, 3, sigma=1)
	_lowerCAmelCase	:   Tuple    =   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()
