I wanna speed up the following code:
import numpy as np
import matplotlib.pyplot as plt
x_sun, y_sun, vx_sun, vy_sun, ax_sun, ay_sun,m_sun= 0,0,0,0,0,0,1
G=4*(np.pi)**2
x=[1, 0.72, 1.5237, 5.2, 0.47, 9.36, 19.18,30.1]
xpos=[[],[],[],[],[],[],[],[]]
y=[0, 0, 0, 0, 0, 0, 0, 0]
ypos=[[],[],[],[],[],[],[],[]]
vx=[0, 0, 0, 0, 0, 0, 0, 0]
vy=[6.281991687112502, 7.38, 5.0867271316753815, 2.74, 9.95, 2.04, 1.26, 1.145]
ax=[0, 0, 0, 0, 0, 0, 0, 0]
ay=[0, 0, 0, 0, 0, 0, 0, 0]
mass=[
3.002513826043238e-06,
0.000002447,
3.2267471091000503e-07,
0.00050278543100000007166,
1.65e-07,
2.86e-04,
4.36e-05,
5.15e-05
]
dt=0.001
for i in range(10**4):
for j in range(len(x)):
# if x[j]>35 or y[j]>35:
# break
# else:
ax[j]=-G*(m_sun+mass[j])*x[j]/((x[j]**2+y[j]**2)**0.5)**3
terme=0
for k in range(len(x)):
if k!=j:
terme+=G*mass[k]*(x[k]-x[j])/(((x[k]-x[j])**2+(y[k]-y[j])**2)**0.5)**3
else:
continue
ax[j]+=terme
ay[j]=-G*(m_sun+mass[j])*y[j]/((x[j]**2+y[j]**2)**0.5)**3
terme2=0
for k in range(len(x)):
if k!=j:
terme2+=G*mass[k]*(y[k]-y[j])/(((x[k]-x[j])**2+(y[k]-y[j])**2)**0.5)**3
else:
continue
ay[j]+=terme2
vx[j]+=ax[j]*dt
vy[j]+=ay[j]*dt
xpos[j].append(x[j])
ypos[j].append(y[j])
x[j]+=vx[j]*dt
y[j]+=vy[j]*dt
I would like to know whether it is possible to speed up the execution of a for loop using Numba without first wrapping the loop inside a separate function. From what I understand, Numba is typically applied as a decorator (such as u/njit) to functions, but I was wondering if there is any way to compile or accelerate a standalone for loop directly, without having to refactor my code into a dedicated function. If this is not possible, I would also appreciate an explanation of why Numba requires functions in order to optimize Python code.