Python:实现lorenz transformation 洛伦兹变换算法(附完整源码)

51CTO 2022-08-06 10:22:51 阅读数:316

Python实现transformationlorenz洛伦兹变换


Python:实现lorenz transformation 洛伦兹变换算法

from __future__ import annotations

from math import sqrt

import numpy as np # type: ignore
from sympy import symbols # type: ignore

# Coefficient
# Speed of light (m/s)
c = 299792458

# Symbols
ct, x, y, z = symbols( "ct x y z")
ct_p, x_p, y_p, z_p = symbols( "ct' x' y' z'")


# Vehicle's speed divided by speed of light (no units)
def beta( velocity: float) - > float:
"""
>>> beta(c)
1.0

>>> beta(199792458)
0.666435904801848

>>> beta(1e5)
0.00033356409519815205

>>> beta(0.2)
Traceback (most recent call last):
...
ValueError: Speed must be greater than 1!
"""
if velocity > c:
raise ValueError( "Speed must not exceed Light Speed 299,792,458 [m/s]!")

# Usually the speed u should be much higher than 1 (c order of magnitude)
elif velocity < 1:
raise ValueError( "Speed must be greater than 1!")
return velocity / c


def gamma( velocity: float) - > float:

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


def transformation_matrix( velocity: float) - > np. array:

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


def transform(
velocity: float, event: np. array = np. zeros( 4), symbolic: bool = True
) - > np. array:

# Ensure event is not a vector of zeros
if not symbolic:

# x0 is ct (speed of ligt * time)
event[ 0] = event[ 0] * c
else:

# Symbolic four vector
event = np. array([ ct, x, y, z])

return transformation_matrix( velocity). dot( event)


if __name__ == "__main__":
import doctest

doctest. testmod()

# Example of symbolic vector:
four_vector = transform( 29979245)
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:
values = np. array([ 1, 1, 1, 1])
sub_dict = { ct: c * values[ 0], x: values[ 1], y: values[ 2], z: values[ 3]}
numerical_vector = [ four_vector[ i]. subs( sub_dict) for i in range( 0, 4)]

print( f"\n{ numerical_vector} ")
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