python - Plot equation showing a circle

Question

The following formula is used to classify points from a 2-dimensional space:

f(x1,x2) = np.sign(x1^2+x2^2-.6)

All points are in space X = [-1,1] x [-1,1] with a uniform probability of picking each x.

Now I would like to visualize the circle that equals:

0 = x1^2+x2^2-.6

The values of x1 should be on the x-axis and values of x2 on the y-axis.

It must be possible but I have difficulty transforming the equation to a plot.

Answer 1

You can use a contour plot, as follows (based on the examples at http://matplotlib.org/examples/pylab_examples/contour_demo.html):

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(-1.0, 1.0, 100)
y = np.linspace(-1.0, 1.0, 100)
X, Y = np.meshgrid(x,y)
F = X**2 + Y**2 - 0.6
plt.contour(X,Y,F,[0])
plt.show()

This yields the following graph

Lastly, some general statements:

1. x^2 does not mean what you think it does in python, you have to use x**2.
2. x1 and x2 are terribly misleading (to me), especially if you state that x2 has to be on the y-axis.
3. (Thanks to Dux) You can add plt.gca().set_aspect('equal') to make the figure actually look circular, by making the axis equal.