Drawing directions fields

Question

Is there a way to draw direction fields in python?

My attempt is to modify http://www.compdigitec.com/labs/files/slopefields.py giving

#!/usr/bin/python
         


        

Answer 1

You can use this matplotlib code as a base. Modify it for your needs. I have updated the code to show same length arrows. The important option is to set the angles option of the quiver function, so that the arrows are correctly printed from (x,y) to (x+u,y+v) (instead of the default, which just takes into account of (u,v) when computing the angles).

It is also possible to change the axis form "boxes" to "arrows". Let me know if you need that change and I could add it.

import matplotlib.pyplot as plt
from scipy.integrate import odeint
import numpy as np

fig = plt.figure()

def vf(x, t):
    dx = np.zeros(2)
    dx[0] = 1.0
    dx[1] = x[0] ** 2 - x[0] - 2.0
    return dx


# Solution curves
t0 = 0.0
tEnd = 10.0

# Vector field
X, Y = np.meshgrid(np.linspace(-5, 5, 20), np.linspace(-10, 10, 20))
U = 1.0
V = X ** 2 - X - 2
# Normalize arrows
N = np.sqrt(U ** 2 + V ** 2)
U = U / N
V = V / N
plt.quiver(X, Y, U, V, angles="xy")

t = np.linspace(t0, tEnd, 100)
for y0 in np.linspace(-5.0, 0.0, 10):
    y_initial = [y0, -10.0]
    y = odeint(vf, y_initial, t)
    plt.plot(y[:, 0], y[:, 1], "-")

plt.xlim([-5, 5])
plt.ylim([-10, 10])
plt.xlabel(r"$x$")
plt.ylabel(r"$y$")