如何将参数传递给`scipy.integrate.solve_ivp`中的事件函数？

Question

Scipy 正在从 odeint 转向 solve_ivp，它不再支持为动态函数传递额外的参数。相反，lambdas are recommended。但是，当我对事件尝试相同的操作时，它们无法正常工作。有什么想法吗？

MWE（修改自doc page）：

import numpy as np
from scipy.integrate import solve_ivp
import matplotlib.pyplot as plt

# dynamics of a simple mass with ballistic flight and a bit of drag
def cannon(t, y, p): 
    return [y[2],y[3], -p['friction']*y[2], p['gravity']-p['friction']*y[3]]

# termination condition: cannonball hits the ground
# this event does not require parameters, but more complex events might
def hit_ground1(t, y, p): 
    return y[1]
hit_ground1.terminal = True
hit_ground1.direction = -1

def hit_ground2(t,y):
    return y[1]
hit_ground2.terminal = True
hit_ground2.direction = -1

p = {'gravity':-1,'friction':0} # paramters as a dict
y0 = [0, 0, 0, 10] # initial conditions
t_span = [0, 22] # integration time a bit over what is necessary

# we can handle dynamics with parameters by using lambdas
# but somehow the same doesn't seem to work with events
sol1 = solve_ivp(fun=lambda t,x:cannon(t,x,p), t_span=t_span, 
    y0=y0, events=hit_ground2, max_step=0.01)    
sol2 = solve_ivp(fun=lambda t,x:cannon(t,x,p), t_span=t_span, 
    y0=y0, events=lambda t,x:hit_ground1(t,x,p), max_step=0.01)

print(sol1.t[-1]) # terminates correctly
print(sol2.t[-1]) # continues integrating
plt.plot(sol1.t,sol1.y[1], linewidth=3)
plt.plot(sol2.t,sol2.y[1],'--',linewidth=3)
plt.show()

Answer 1

事件的属性 terminal 和 direction 不会转移到您的 lambda 表达式中。您需要将 lambda 保存到一个变量中，并在其中添加属性，而不是在 hit_ground1 函数上。

def hit_ground1(t, y, p):
    return y[1]

ground_event = lambda t,x:hit_ground1(t,x,p)
ground_event.terminal = True
ground_event.direction = -1

使用此事件，它应该会按预期工作。

 sol2 = solve_ivp(fun=lambda t,x:cannon(t,x,p), t_span=t_span,
    y0=y0, events=ground_event, max_step=0.01)