我正在尝试使用射击方法找到一个周期轨道

如何解决我正在尝试使用射击方法找到一个周期轨道

def integrate_ode(ode,u0,T):
    sol=solve_ivp(ode,T,u0)
    return sol.y[:,-1]

def phase(ode,u0):
    return ode(0,u0)[0] #dx/dt(0)

def shooting(ode,U):
    print(len(U))
    u0=U[0:-1]
    #print(u0)
    T=U[-1]
    #print(T)
    G=np.concatenate((integrate_ode(ode,T)-u0,phase(ode,u0)))
    return G

要获得我正在使用的解决方案：

fsolve(lambda U:shooting(ode1,U),...(initial conditions))

我收到此错误：

IndexError: invalid index to scalar variable.

这是我的完整追溯：

Traceback (most recent call last):
  "...Python\workweek16.py",line 62,in <module>
    G=fsolve(lambda U:shooting(ode1,(0,0))
  File "C:\Users\tmara\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.9_qbz5n2kfra8p0\LocalCache\local-packages\python39\site-packages\scipy\optimize\minpack.py",line 160,in fsolve
    res = _root_hybr(func,x0,args,jac=fprime,**options)
  File "C:\Users\tmara\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.9_qbz5n2kfra8p0\LocalCache\local-packages\python39\site-packages\scipy\optimize\minpack.py",line 226,in _root_hybr
    shape,dtype = _check_func('fsolve','func',func,n,(n,))
  File "C:\Users\tmara\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.9_qbz5n2kfra8p0\LocalCache\local-packages\python39\site-packages\scipy\optimize\minpack.py",line 24,in _check_func
    res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
  File "...Python\workweek16.py",in <lambda>
    G=fsolve(lambda U:shooting(ode1,0))
  File "...Python\workweek16.py",line 51,in shooting
    G=np.concatenate((integrate_ode(ode,u0)))
  File "...Python\workweek16.py",line 40,in integrate_ode
    sol=solve_ivp(ode,u0)
  File "C:\Users\tmara\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.9_qbz5n2kfra8p0\LocalCache\local-packages\python39\site-packages\scipy\integrate\_ivp\ivp.py",line 508,in solve_ivp
    t0,tf = float(t_span[0]),float(t_span[1])
IndexError: invalid index to scalar variable.

有人知道该怎么做吗？

解决方法

t_span 的 solve_ivp 参数实际上需要是一个时间跨度。因此，将 T 替换为 [0,T]。