Python Solving a Set of Equations with Python Odeint | Code and Example

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The discussion revolves around solving a set of equations using Python's odeint function, with the user encountering incorrect output. The provided code includes a complex function definition that applies mathematical operations involving multiple variables and parameters. Users express frustration over the lengthy code and seek clarification on specific equations rather than the entire codebase. The conversation highlights the challenges of debugging intricate mathematical models in Python, particularly when using numerical integration methods. Overall, the thread emphasizes the need for clearer explanations and potential simplifications in the code to aid understanding.
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I want to solve a set of equations using Python odeint, but output shows me it is wrong.

Can you help me? Thanks.

Code:


# -*- coding: utf-8 -*-
from scipy.integrate import odeint
import numpy as np
from pylab import *
import math


def func(y, t, k, c, Zr):

#px, py, pz, x, y, z = y & px=y[0]; py=y[1]; pz=y[2]; x=y[3]; y=y[4]; z=y[5]
# apply func formula

return (

-k/((1+y[5]**2/Zr**2)**(1.0/2))*exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))
-((-1.0/2*(1+y[5]**2/Zr**2)**(-3.0/2)*2*y[5]/Zr**2*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+(1+y[5]**2/Zr**2)**(-1.0/2)*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(1+y[5]**2/Zr**2)**(-2.0))*2*y[5]/Zr**2*(y[3]**2+y[4]**2)/(2*Zr/k)*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*(k+(y[3]**2+y[4]**2)*(Zr**2-y[5]**2)/(2.0/k*(Zr**2+y[5]**2))-1.0/(1+y[5]**2/Zr**2)))-1.0/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+
y[3]*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[3])/(2*Zr/k*(1+y[5]**2/Zr**2))*
(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*2*y[3]*y[5]/(2/k*(Zr**2+y[5]**2))+y[5]/Zr*2*y[3]*y[4]/(2.0/k*(Zr**2+y[5]**2))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))))))*y[2]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),

0+(y[3]/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[4]/(2*Zr/k*(1+y[5]**2/Zr**2))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+2*y[4]*y[5]/(2/k*(Zr**2+y[5]**2))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+y[5]/Zr*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))))*y[2]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),

(y[3]/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(k*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+k*y[5]/Zr*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))))
+(y[0]*((-1.0/2*(1+y[5]**2/Zr**2)**(-3.0/2)*2*y[5]/Zr**2*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+(1+y[5]**2/Zr**2)**(-1.0/2)*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(1+y[5]**2/Zr**2)**(-2.0))*2*y[5]/Zr**2*(y[3]**2+y[4]**2)/(2*Zr/k)*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*(k+(y[3]**2+y[4]**2)*(Zr**2-y[5]**2)/(2.0/k*(Zr**2+y[5]**2))-1.0/(1+y[5]**2/Zr**2)))-1.0/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+
y[3]*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[3])/(2*Zr/k*(1+y[5]**2/Zr**2))*
(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*2*y[3]*y[5]/(2/k*(Zr**2+y[5]**2))+y[5]/Zr*2*y[3]*y[4]/(2.0/k*(Zr**2+y[5]**2))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))))))-
y[1]*((y[3]/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[4]/(2*Zr/k*(1+y[5]**2/Zr**2))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+2*y[4]*y[5]/(2/k*(Zr**2+y[5]**2))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+y[5]/Zr*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))))))/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),

y[0]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),
y[1]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),
y[2]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2))

y0=[0.0, 0.0, 1.0, 0.0, 0.0, 0.0]
k=30.0
Zr=120.0
c=3e8
t = np.arange(0.0, 1000.0, 0.05) # create time point

# use odeint to solve func
track= odeint(func, y0, t, args=(k, c, Zr))


# plot
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

fig = plt.figure()
ax = Axes3D(fig)
ax.plot(track[:,3], track[:,4], track[:,5])

plt.show()
 
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goldin2008 said:
I want to solve a set of equations using Python odeint, but output shows me it is wrong.

Can you help me? Thanks.

Code:


# -*- coding: utf-8 -*-
from scipy.integrate import odeint
import numpy as np
from pylab import *
import math


def func(y, t, k, c, Zr):

#px, py, pz, x, y, z = y & px=y[0]; py=y[1]; pz=y[2]; x=y[3]; y=y[4]; z=y[5]
# apply func formula

return (

-k/((1+y[5]**2/Zr**2)**(1.0/2))*exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))
-((-1.0/2*(1+y[5]**2/Zr**2)**(-3.0/2)*2*y[5]/Zr**2*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+(1+y[5]**2/Zr**2)**(-1.0/2)*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(1+y[5]**2/Zr**2)**(-2.0))*2*y[5]/Zr**2*(y[3]**2+y[4]**2)/(2*Zr/k)*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*(k+(y[3]**2+y[4]**2)*(Zr**2-y[5]**2)/(2.0/k*(Zr**2+y[5]**2))-1.0/(1+y[5]**2/Zr**2)))-1.0/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+
y[3]*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[3])/(2*Zr/k*(1+y[5]**2/Zr**2))*
(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*2*y[3]*y[5]/(2/k*(Zr**2+y[5]**2))+y[5]/Zr*2*y[3]*y[4]/(2.0/k*(Zr**2+y[5]**2))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))))))*y[2]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),

0+(y[3]/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[4]/(2*Zr/k*(1+y[5]**2/Zr**2))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+2*y[4]*y[5]/(2/k*(Zr**2+y[5]**2))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+y[5]/Zr*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))))*y[2]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),

(y[3]/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(k*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+k*y[5]/Zr*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))))
+(y[0]*((-1.0/2*(1+y[5]**2/Zr**2)**(-3.0/2)*2*y[5]/Zr**2*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+(1+y[5]**2/Zr**2)**(-1.0/2)*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(1+y[5]**2/Zr**2)**(-2.0))*2*y[5]/Zr**2*(y[3]**2+y[4]**2)/(2*Zr/k)*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*(k+(y[3]**2+y[4]**2)*(Zr**2-y[5]**2)/(2.0/k*(Zr**2+y[5]**2))-1.0/(1+y[5]**2/Zr**2)))-1.0/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+
y[3]*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[3])/(2*Zr/k*(1+y[5]**2/Zr**2))*
(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*2*y[3]*y[5]/(2/k*(Zr**2+y[5]**2))+y[5]/Zr*2*y[3]*y[4]/(2.0/k*(Zr**2+y[5]**2))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))))))-
y[1]*((y[3]/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[4]/(2*Zr/k*(1+y[5]**2/Zr**2))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+2*y[4]*y[5]/(2/k*(Zr**2+y[5]**2))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+y[5]/Zr*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))))))/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),

y[0]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),
y[1]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),
y[2]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2))

y0=[0.0, 0.0, 1.0, 0.0, 0.0, 0.0]
k=30.0
Zr=120.0
c=3e8
t = np.arange(0.0, 1000.0, 0.05) # create time point

# use odeint to solve func
track= odeint(func, y0, t, args=(k, c, Zr))


# plot
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

fig = plt.figure()
ax = Axes3D(fig)
ax.plot(track[:,3], track[:,4], track[:,5])

plt.show()

You're kidding, right? You don't really expect that we're going to look at that huge wad of code, do you?
 
Mark44 said:
You're kidding, right? You don't really expect that we're going to look at that enormous lump of goop, do you?

Sorry. Actually, just the equations are a little long.

The idea is simple.

# -*- coding: utf-8 -*-
from scipy.integrate import odeint
import numpy as np
from pylab import *
import math


def func(y, t, k, c, Zr):

#px, py, pz, x, y, z = y & px=y[0]; py=y[1]; pz=y[2]; x=y[3]; y=y[4]; z=y[5]
# apply func formula

return (

-k/((1+y[5]**2/Zr**2)**(1.0/2))*exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))
-((-1.0/2*(1+y[5]**2/Zr**2)**(-3.0/2)*2*y[5]/Zr**2*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+(1+y[5]**2/Zr**2)**(-1.0/2)*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(1+y[5]**2/Zr**2)**(-2.0))*2*y[5]/Zr**2*(y[3]**2+y[4]**2)/(2*Zr/k)*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*(k+(y[3]**2+y[4]**2)*(Zr**2-y[5]**2)/(2.0/k*(Zr**2+y[5]**2))-1.0/(1+y[5]**2/Zr**2)))-1.0/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+
y[3]*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[3])/(2*Zr/k*(1+y[5]**2/Zr**2))*
(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*2*y[3]*y[5]/(2/k*(Zr**2+y[5]**2))+y[5]/Zr*2*y[3]*y[4]/(2.0/k*(Zr**2+y[5]**2))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))))))*y[2]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),

0+(y[3]/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[4]/(2*Zr/k*(1+y[5]**2/Zr**2))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+2*y[4]*y[5]/(2/k*(Zr**2+y[5]**2))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+y[5]/Zr*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))))*y[2]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),

(y[3]/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(k*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+k*y[5]/Zr*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))))
+(y[0]*((-1.0/2*(1+y[5]**2/Zr**2)**(-3.0/2)*2*y[5]/Zr**2*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+(1+y[5]**2/Zr**2)**(-1.0/2)*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(1+y[5]**2/Zr**2)**(-2.0))*2*y[5]/Zr**2*(y[3]**2+y[4]**2)/(2*Zr/k)*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*(k+(y[3]**2+y[4]**2)*(Zr**2-y[5]**2)/(2.0/k*(Zr**2+y[5]**2))-1.0/(1+y[5]**2/Zr**2)))-1.0/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+
y[3]*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[3])/(2*Zr/k*(1+y[5]**2/Zr**2))*
(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*2*y[3]*y[5]/(2/k*(Zr**2+y[5]**2))+y[5]/Zr*2*y[3]*y[4]/(2.0/k*(Zr**2+y[5]**2))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))))))-
y[1]*((y[3]/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[4]/(2*Zr/k*(1+y[5]**2/Zr**2))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+2*y[4]*y[5]/(2/k*(Zr**2+y[5]**2))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+y[5]/Zr*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))))))/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),

y[0]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),
y[1]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),
y[2]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2))

y0=[0.0, 0.0, 1.0, 0.0, 0.0, 0.0]
k=30.0
Zr=120.0
c=3e8
t = np.arange(0.0, 1000.0, 0.05) # create time point

# use odeint to solve func
track= odeint(func, y0, t, args=(k, c, Zr))


# plot
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

fig = plt.figure()
ax = Axes3D(fig)
ax.plot(track[:,3], track[:,4], track[:,5])

plt.show()
 
different colors mean 6 equations for y[0], y[1], y[2], y[3], y[4], y[5]
I just want to integrate them and get px, py, pz, x, y, and z. And then use x, y, and z to
draw trajectory of the particle.

# -*- coding: utf-8 -*-
from scipy.integrate import odeint
import numpy as np
from pylab import *
import mathdef func(y, t, k, c, Zr):

#px, py, pz, x, y, z = y & 的d(px)/dt=y[0]; d(py)/dt=y[1]; d(pz)/dt=y[2]; d(x)/dt=y[3]; d(y)/dt=y[4]; d(z)/dt=y[5]
# apply func formula

return (

d(px)/dt,

d(py)/dt,

d(pz)/dt,

d(x)/dt,
d(y)/dt,
d(z)/dt)

y0=[0.0, 0.0, 1.0, 0.0, 0.0, 0.0]
k=30.0
Zr=120.0
c=3e8
t = np.arange(0.0, 1000.0, 0.05) # create time point

# use odeint to solve func
track= odeint(func, y0, t, args=(k, c, Zr))# plot
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

fig = plt.figure()
ax = Axes3D(fig)
ax.plot(track[:,3], track[:,4], track[:,5])

plt.show()
 
Last edited:
And the error message?
 
Pythagorean said:
And the error message?

I want to print track[:,3] (which is x coordinate)
but the output is

lsoda-- at current t (=r1), mxstep (=i1) steps
taken on this call before reaching tout
In above message, I1 = 500
In above message, R1 = 0.4578094279642E-05
Excess work done on this call (perhaps wrong Dfun type).
Run with full_output = 1 to get quantitative information.
[ 0.00000000e+00 -9.26095625e-12 0.00000000e+00 ..., 0.00000000e+00
0.00000000e+00 0.00000000e+00]

And the 3D trajectory is obviously wrong, which should not be a straight line.
 
no idea, but here's how I've successfully called the ode integrator in one of my python programs:

Code: 
result,info = odeint(func,y0, arange(0,tf,dt), args = (I,D),full_output=1)

compared to your:

Code: 
track= odeint(func, y0, t, args=(k, c, Zr))

the only difference I see is full_output argument and I called the second output argument.
 
goldin2008 said:
I want to solve a set of equations using Python odeint, but output shows me it is wrong.

Can you help me? Thanks.

Code:


# -*- coding: utf-8 -*-
from scipy.integrate import odeint
import numpy as np
from pylab import *
import math


def func(y, t, k, c, Zr):

#px, py, pz, x, y, z = y & px=y[0]; py=y[1]; pz=y[2]; x=y[3]; y=y[4]; z=y[5]
# apply func formula

return (

-k/((1+y[5]**2/Zr**2)**(1.0/2))*exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))
-((-1.0/2*(1+y[5]**2/Zr**2)**(-3.0/2)*2*y[5]/Zr**2*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+(1+y[5]**2/Zr**2)**(-1.0/2)*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(1+y[5]**2/Zr**2)**(-2.0))*2*y[5]/Zr**2*(y[3]**2+y[4]**2)/(2*Zr/k)*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*(k+(y[3]**2+y[4]**2)*(Zr**2-y[5]**2)/(2.0/k*(Zr**2+y[5]**2))-1.0/(1+y[5]**2/Zr**2)))-1.0/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+
y[3]*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[3])/(2*Zr/k*(1+y[5]**2/Zr**2))*
(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*2*y[3]*y[5]/(2/k*(Zr**2+y[5]**2))+y[5]/Zr*2*y[3]*y[4]/(2.0/k*(Zr**2+y[5]**2))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))))))*y[2]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),

0+(y[3]/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[4]/(2*Zr/k*(1+y[5]**2/Zr**2))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+2*y[4]*y[5]/(2/k*(Zr**2+y[5]**2))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+y[5]/Zr*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))))*y[2]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),

(y[3]/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(k*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+k*y[5]/Zr*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))))
+(y[0]*((-1.0/2*(1+y[5]**2/Zr**2)**(-3.0/2)*2*y[5]/Zr**2*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+(1+y[5]**2/Zr**2)**(-1.0/2)*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(1+y[5]**2/Zr**2)**(-2.0))*2*y[5]/Zr**2*(y[3]**2+y[4]**2)/(2*Zr/k)*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*(k+(y[3]**2+y[4]**2)*(Zr**2-y[5]**2)/(2.0/k*(Zr**2+y[5]**2))-1.0/(1+y[5]**2/Zr**2)))-1.0/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+
y[3]*(math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[3])/(2*Zr/k*(1+y[5]**2/Zr**2))*
(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))*2*y[3]*y[5]/(2/k*(Zr**2+y[5]**2))+y[5]/Zr*2*y[3]*y[4]/(2.0/k*(Zr**2+y[5]**2))*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))))))-
y[1]*((y[3]/(Zr*(1+y[5]**2/Zr**2)**(3.0/2))*math.exp(-(y[3]**2+y[4]**2)/(2*Zr/k*(1+y[5]**2/Zr**2)))*(-2*y[4]/(2*Zr/k*(1+y[5]**2/Zr**2))*(math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))-y[5]/Zr*math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))+2*y[4]*y[5]/(2/k*(Zr**2+y[5]**2))*(math.cos(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr))+y[5]/Zr*math.sin(k*(y[5]-c*t)+y[5]*(y[3]**2+y[4]**2)/(2/k*(Zr**2+y[5]**2))-math.atan(y[5]/Zr)))))))/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),

y[0]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),
y[1]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2),
y[2]/(1+y[0]**2+y[1]**2+y[2]**2)**(1.0/2))

y0=[0.0, 0.0, 1.0, 0.0, 0.0, 0.0]
k=30.0
Zr=120.0
c=3e8
t = np.arange(0.0, 1000.0, 0.05) # create time point

# use odeint to solve func
track= odeint(func, y0, t, args=(k, c, Zr))


# plot
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

fig = plt.figure()
ax = Axes3D(fig)
ax.plot(track[:,3], track[:,4], track[:,5])

plt.show()

Even assembler code is easier to read than this!
 
chiro said:
Even assembler code is easier to read than this!

I think this should be easier to read.

# -*- coding: utf-8 -*-
from scipy.integrate import odeint
import numpy as np
from pylab import *
import math


def func(y, t, k, c, Zr):

#px, py, pz, x, y, z = y & 的d(px)/dt=y[0]; d(py)/dt=y[1]; d(pz)/dt=y[2]; d(x)/dt=y[3]; d(y)/dt=y[4]; d(z)/dt=y[5]
# apply func formula

return (

d(px)/dt,

d(py)/dt,

d(pz)/dt,

d(x)/dt,
d(y)/dt,
d(z)/dt)

y0=[0.0, 0.0, 1.0, 0.0, 0.0, 0.0]
k=30.0
Zr=120.0
c=3e8
t = np.arange(0.0, 1000.0, 0.05) # create time point

# use odeint to solve func
track= odeint(func, y0, t, args=(k, c, Zr))


# plot
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

fig = plt.figure()
ax = Axes3D(fig)
ax.plot(track[:,3], track[:,4], track[:,5])

plt.show()
 
  • #10
Pythagorean said:
no idea, but here's how I've successfully called the ode integrator in one of my python programs:

Code: 
result,info = odeint(func,y0, arange(0,tf,dt), args = (I,D),full_output=1)

compared to your:

Code: 
track= odeint(func, y0, t, args=(k, c, Zr))

the only difference I see is full_output argument and I called the second output argument.

thanks for reply.

what does "info" means? and what is usefulness of "full_output=1"?
 

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