Consider this simple first-order differential equation:
Where k is a constant with value 0.5 andis a variable that changes with time.
I used the following code to input the values of y_bar at different times which works perfectly.
import numpy as np
from scipy.integrate import odeint
from matplotlib import pyplot as plt
def get_y_bar(t):
if t>=0 and t<=1:
return 0.0
elif t<=2:
return 1.0
elif t<=3:
return 2.0
elif t<=4:
return 3.0
elif t<=5:
return 4.0
else:
return 5.0
def ode(y,t):
k=0.5
y_bar=get_y_bar(t)
dy=k*(y_bar-y)
return dy
y0=0.0
t0=np.linspace(0,10,100)
sol=odeint(ode,y0,t0)
plt.plot(t0,sol)
plt.show()
But, this method is feasible only when I have a small data and can enter it using if.. elif..else loop manually. What can I do if I have large values of y_bar in smaller time steps (eg, t= 0.01, 0.025, 0.03,..., 5.0)??
I have the data in CSV format and tried looping through the data but got stuck?? Is there any simple way to do this??
def get_y_bar(t):
data=np.genfromtxt('data.csv',delimiter=',')
time=data[:,0]
y_bar=data[:,1]
for i in range(len(time)):
if t>=time[i] and t<=time[i=1]:
return y_bar[i]
else:
I am not sure if I understood your question completely. But if you want to replace the numerous elif
loops in get_y_bar
, try this:
import math
def get_y_bar(t):
return math.floor(t)
That is, math.floor(4.2)
will return 4
, which is the largest integer smaller than 4.2
With that approach you would load your file every time odeint
does a call to your ode
function, which will be highly inefficient.
A more convenient way to solve your problem is to replace your get_y_bar
function by using scipy.interpolate.interp1d
instead, with kind = zero
, ie constant interpolation . You should do this interpolation outside of your ode
function, so you only do it once.
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