How to get data points after plot it? (Python)

Question

I just used scipy.odeint to solve a diff_equation system, and use matplotlib to plot it. I got the graphs. My question is can I get some specific data points, like when t = 1, what is x1, x2, x3. I need when t = 1,2,3,4..., what value of concentration is. Thank you.

import matplotlib.pyplot as plt
from scipy.integrate import odeint
Dose = 100
V = 43.8
k12 = 1.2 # rate of central -> peripheral
k21 = 1.4 # rate of peripheral -> central
kel = 0.20 # rate of excrete from plasma
def diff(d_list, t):
    x1, x2, x3, = d_list
    # X1(t), X2(t), X3(t)
    return np.array([(-k12*x1-kel*x1+k21*x2),
                     (k12*x1-k21*x2),
                     (kel*x1)])
t = np.linspace(0, 24, 960)
result = odeint(diff, [(Dose/V), 0, 0], t)
plt.plot(t, result[:, 0], label='x1: central')
plt.plot(t, result[:, 1], label='x2: tissue')
plt.plot(t, result[:, 2], label='x3: excreted')
plt.legend()
plt.xlabel('t (hr)')
plt.ylabel('Concentration (mg/L)')
plt.show()

Answer 1

This is not related to matplotlib or scipy. You can either interpolate or get the closest data point.

Interpolated value

If you need to get the x1 , x2 and x3 for values of t which do not correspond to a data point (you mentioned 1,2,3,4 which are not in your t array), you will need to interpolate. To get x1 , x2 and x3 at t=1 , you can do (at the end of your script):

valuesAt1 = [np.interp(1, t, result[:,col]) for col in range(result.shape[1])]

The output of print(valuesAt1) is then:

[1.1059703843218311, 0.8813129004034452, 0.2958217381057726]

If you only need x1 , just do

valuesAt1 = np.interp(1, t, result[:,0])

then, the output of print(valuesAt1) is:

1.1059703843218311

Closest data point

If you do not want to do interpolation but want the value of x1 , x2 and x3 for the value of the t array element which is the closest from 1, do:

valuesAtClosestPointFrom1 = result[ np.argmin(np.abs(t-1))]

The output from print(valuesAtClosestPointFrom1) is:

[1.10563546 0.88141641 0.29605315]

Answer 2

This can be done by interpolation and using scipy.interpolate.InterpolatedUnivariateSpline as follows:

from scipy.interpolate import InterpolatedUnivariateSpline

splx1 = InterpolatedUnivariateSpline(t, result[:,0])
splx2 = InterpolatedUnivariateSpline(t, result[:,1])
splx3 = InterpolatedUnivariateSpline(t, result[:,2])

Firstly, you need to pass the x and y data that you want to interpolate. Secondly, create a list for x for which you want the desired values of y.

import numpy as np

desired_time = np.arange(1,25)

x1 = splx1(desired_time)
x2 = splx2(desired_time)
x3 = splx3(desired_time)

Lastly, pass it to the respective spline object to get the desired values. For example, a desired_time array from 1 to 24 using np.arange is created and passed to the spline objects in the example above.