I would like to solve a system of 7 ordinary differential equations (ODEs) with 15 time dependent coefficients using scipy's odeint function.
I store my coefficients in a dictionary so that I can access them by Key names within the function (func) that I defined to be used with odeint(). The coefficients depend on time, so within the dictionary for each coefficient I call the function time_dep(t). However, since my dictionary is stored outside of the function used by odeint(), I initialized a time variable t = 0 in the beginning. Now I fear that the coefficients are kept constant (at t = 0) when they are accessed by the odeint() analysis.
Any help would be very appreciated!
This is an attempt of a minimal working example it is not perfect but I print out the coefficient value and it doesnt change which is what I do not want :) :
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
t = 0
def time_dep(t):
return (10 * np.exp(-t))
coefficients = {'coeff1' : 1 + time_dep(t)}
def func(state, t, coefficients):
mrna = state[0]
protein = state[1]
dt_mrna = coefficients['coeff1'] * mrna * protein
dt_protein = coefficients['coeff1'] * protein
print(coefficients['coeff1'])
return[dt_mrna,dt_protein]
state0 = [1,1]
t = np.arange(0,100,0.1)
solve = odeint(func,state0,t,args=(coefficients,))
plt.plot(t,solve)
plt.show()
The dictionary should contain functions and not the evaluated value (as right now):
coefficients = {'coeff1' : lambda x: 1+time_dep(x)}
And then later on get the function and call with the correct time:
dt_mrna = coefficients['coeff1'](t) * mrna * protein
You have stored the single number 1 + time_dep(0)
as the value of coefficients['coeff1']
. Instead of doing that, store the function itself in the dictionary, and call the function in func()
. Something like this:
coefficients = {'coeff1' : time_dep}
def func(state, t, coefficients):
mrna = state[0]
protein = state[1]
c1 = 1 + coefficients['coeff1'](t)
dt_mrna = c1 * mrna * protein
dt_protein = c1 * protein
return [dt_mrna, dt_protein]
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