





from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
A       :   int					= 2_9_9_7_9_2_4_5_8

# Symbols
A,      A,      A,      A       :   Union[str, Any]					= symbols('''ct x y z''')







def   __lowerCamelCase   (				__a  :float       )						->							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   __lowerCamelCase   (				__a  :float       )						->							float:






		"""simple docstring"""

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







def   __lowerCamelCase   (				__a  :float       )						->							np.ndarray:






		"""simple docstring"""

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







def   __lowerCamelCase   (				__a  :float       ,	__a  :np.ndarray | None = None       )						->							np.ndarray:






		"""simple docstring"""

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

		return transformation_matrix(__a       ) @ event


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					# Example of symbolic vector:
					A       :   Dict					= 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
					A       :   List[str]					= {ct: c, x: 1, y: 1, z: 1}
					A       :   Any					= [four_vector[i].subs(sub_dict) for i in range(4)]

					print(F'''\n{numerical_vector}''')










import numpy as np







def   __lowerCamelCase   (				__a  :np.array       )						->							np.array:






		"""simple docstring"""

		return 1 / (1 + np.exp(-vector       ))







def   __lowerCamelCase   (				__a  :np.array       )						->							np.array:






		"""simple docstring"""

		return vector * sigmoid(1.702 * vector       )


if __name__ == "__main__":
					import doctest

					doctest.testmod()



