如何使odeint成功？

Question

我是一个python初学者，目前使用scipy的odeint来计算耦合的ODE系统，但是，当我运行时，python shell总是告诉我

>>> 
Excess work done on this call (perhaps wrong Dfun type).
Run with full_output = 1 to get quantitative information.
>>> 

所以，我必须改变我的时间步和最后时间，以使其可积。要做到这一点，我需要尝试不同的组合，这是相当痛苦的。有谁能告诉我怎样才能让odeint自动改变时间步骤和最终时间来成功地集成这个ode系统吗？

下面是代码的一部分，它调用了odeint：

def main(t, init_pop_a, init_pop_b, *args, **kwargs):
    """
    solve the obe for a given set of parameters
    """
    # construct initial condition
    # initially, rho_ee = 0
    rho_init = zeros((16,16))*1j ########
    rho_init[1,1] = init_pop_a
    rho_init[2,2] = init_pop_b
    rho_init[0,0] = 1 - (init_pop_a + init_pop_b)########
    rho_init_ravel, params = to_1d(rho_init)
    # perform the integration
    result = odeint(wrapped_bloch3, rho_init_ravel, t, args=args)
                        # BUG: need to pass kwargs
    # rewrap the result
    return from_1d(result, params, prepend=(len(t),))

things = [2*pi, 20*pi, 0,0, 0,0, 0.1,100]
Omega_a, Omega_b, Delta_a, Delta_b, \
init_pop_a, init_pop_b, tstep, tfinal = things
args = ( Delta_a, Delta_b, Omega_a, Omega_b )
t = arange(0, tfinal + tstep, tstep)
data = main(t, init_pop_a, init_pop_b, *args)

plt.plot(t,abs(data[:,4,4]))

其中wrapped_bloch3是compute dy/dt函数。

Answer 1

编辑：我注意到您已经在这里得到了答案：complex ODE systems in scipy

odeint不适用于复数方程。我明白了

from scipy.integrate import odeint
import numpy as np
def func(t, y):
    return 1 + 1j
t = np.linspace(0, 1, 200)
y = odeint(func, 0, t)
# -> This outputs:
#
# TypeError: can't convert complex to float
# odepack.error: Result from function call is not a proper array of floats.

您可以通过另一个ode解算器来解方程：

from scipy.integrate import ode
import numpy as np

def myodeint(func, y0, t):
    y0 = np.array(y0, complex)
    func2 = lambda t, y: func(y, t)   # odeint has these the other way :/
    sol = ode(func2).set_integrator('zvode').set_initial_value(y0, t=t[0])
    y = [sol.integrate(tp) for tp in t[1:]]
    y.insert(0, y0)
    return np.array(y)

def func(y, t, alpha):
    return 1j*alpha*y

alpha = 3.3
t = np.linspace(0, 1, 200)
y = myodeint(lambda y, t: func(y, t, alpha), [1, 0, 0], t)