Ode integrator Python TypeError 'float' object is not subscriptable

Question

I am desperately trying to use the scipy ODE integrator, but I keep getting the following error :

Y[0] = (1/I3) * T_z(INP[0], INP[1], INP[2], INP[3], INP[4])
TypeError: 'float' object is not subscriptable

My code is the following :

import scipy.integrate as spi
import numpy as np

import pylab as pl
from time import time

#Constants

I3 = 0.00396
lamb = 1
L = 5*10**-1
mu = 1
m = 0.1
Cz = 0.5
rho = 1.2
S = 0.03*0.4
K_z = 1/2*rho*S*Cz
g = 9.81

#Initial conditions

omega0 = 10*2*np.pi
V0 = 25
theta0 =np.pi/2
phi0 = 0
psi0 = -np.pi/9
X0 = 0
Y0 = 0
Z0 = 1.8

#for integration

t_start = 0.0
t_end = 5
t_step = 0.1
t_range = np.arange(t_start, t_end+t_step, t_step)

INPUT = omega0, V0, theta0, phi0, psi0, X0, Y0, Z0 #initial conditions 

def diff_eqs(INP,t):  

    def M(v_G, w_z):
        return L*K_z*(v_G**2 + v_G*L*w_z*np.sin(w_z*t_step)+(L*w_z)**2)


    def F_x(w_z, v_G, theta, phi, psi):
        return K_z*(v_G**2+(L*w_z)**2)*np.sin(theta)*np.sin(phi) + lamb*v_G*(np.cos(psi)*np.cos(phi) - np.cos(theta)*np.sin(phi)*np.sin(psi))

    def F_y(w_z, v_G, theta, phi, psi):
        return -K_z*(v_G**2+(L*w_z)**2)*np.sin(theta)*np.cos(phi) + lamb*v_G*(np.cos(psi)*np.sin(phi) + np.cos(theta)*np.cos(phi)*np.sin(psi))

    def F_z(w_z, v_G, theta, phi, psi):
        return -K_z*(v_G**2+(L*w_z)**2)*np.cos(theta) + lamb*v_G*np.sin(theta)*np.sin(psi) - m*g


    def T_x(w_z, v_G, theta, phi, psi):
        return M(v_G, w_z)*(-np.sin(w_z*t_step)*(np.cos(psi)*np.cos(phi) - np.cos(theta)*np.sin(phi)*np.sin(psi)) \
        + np.cos(w_z*t_step)*(-np.sin(psi)*np.cos(phi) - np.cos(theta)*np.sin(phi)*np.cos(psi))) \
        - mu * w_z * (np.sin(theta)*np.sin(phi))

    def T_y(w_z, v_G, theta, phi, psi):
        return M(v_G, w_z)*(-np.sin(w_z*t_step)*(np.cos(psi)*np.sin(phi) + np.cos(theta)*np.cos(phi)*np.sin(psi)) \
        + np.cos(w_z*t_step)*(-np.sin(psi)*np.sin(phi) - np.cos(theta)*np.cos(phi)*np.cos(psi)))
        - mu * w_z * (np.sin(theta)*np.cos(phi))

    def T_z(w_z, v_G, theta, phi, psi):
        return M(v_G, w_z)*(-np.sin(w_z*t_step)*np.sin(theta)*np.sin(psi) + np.cos(w_z*t_step)*np.sin(theta)*np.cos(psi)) \
        - mu * w_z * np.cos(theta)

    Y = np.zeros(8)

    Y[0] = (1/I3) * T_z(INP[0], INP[1], INP[2], INP[3], INP[4])
    Y[1] = -(lamb/m)*F_x(INP[0], INP[1], INP[2], INP[3], INP[4])
    Y[2] = (1/(I3*INP[0]))*(-T_y(INP[0], INP[1], INP[2], INP[3], INP[4])*np.cos(INP[4]) - T_x(INP[0], INP[1], INP[2], INP[3], INP[4])*np.sin(INP[4]))
    Y[3] = (1/(I3*INP[0]*np.cos(INP[3]))) * (-T_y(INP[0], INP[1], INP[2], INP[3], INP[4])*np.sin(INP[4]) + T_x(INP[0], INP[1], INP[2], INP[3], INP[4])*np.cos(INP[4]))
    Y[4] = -(1/(m*INP[1]))*F_y(INP[0], INP[1], INP[2], INP[3], INP[4])
    Y[5] = INP[1]*(-np.cos(INP[4])*np.cos(INP[3]) + np.sin(INP[4])*np.sin(INP[3])*np.cos(INP[2]))
    Y[6] = INP[1]*(-np.cos(INP[4])*np.sin(INP[3]) - np.sin(INP[4])*np.cos(INP[3])*np.cos(INP[2]))
    Y[7] = INP[1]*(-np.sin(INP[4])*np.sin(INP[2]))


    return Y

ode =  spi.ode(diff_eqs)

# BDF method suited to stiff systems of ODEs
ode.set_integrator('vode',nsteps=500,method='bdf')
ode.set_initial_value(INPUT,t_start)

ts = []
ys = []

while ode.successful() and ode.t < t_end:
    ode.integrate(ode.t + t_step)
    ts.append(ode.t)
    ys.append(ode.y)

t = np.vstack(ts)

I have a set of 8 differentials equations I want to numerically solve. Therefore I have 8 initial values stored in "INPUT". But when I use this variable in ode.set_initial_value(INPUT,t_start), it keeps repeating that the variable is a float ! It has been bugging me for hours and the answer is maybe obvious but I can't see where I made a mistake. And I don't think the equations themselves, even though they are pretty messy, are involved here.

Thanks in advance for your help.

Answer 1

Your argument order is the one required in the ODE function for odeint. For ode you need the order (t, INP).

Try to use the more recent solve_ivp interface, it has about the same functionality of the ode class and about the same compact call structure as odeint.