Question

I have a simple problem in python and matplotlib.
I have 3 lists : x, y and rho with rho[i] a density at the point x[i], y[i].
All values of x and y are between -1. and 1. but they are not in a specific order.

How to make a contour plot (like with imshow) of the density rho (interpolated at the points x, y).

Thank you very much.

EDIT : I work with large arrays : x, y and rho have between 10,000 and 1,000,000 elements

Answer 1

You need to interpolate your rho values. There’s no one way to do this, and the “best” method depends entirely on the a-priori information you should be incorporating into the interpolation.

Before I go into a rant on “black-box” interpolation methods, though, a radial basis function (e.g. a “thin-plate-spline” is a particular type of radial basis function) is often a good choice. If you have millions of points, this implementation will be inefficient, but as a starting point:

import numpy as np
import matplotlib.pyplot as plt
import scipy.interpolate

# Generate data:
x, y, z = 10 * np.random.random((3,10))

# Set up a regular grid of interpolation points
xi, yi = np.linspace(x.min(), x.max(), 100), np.linspace(y.min(), y.max(), 100)
xi, yi = np.meshgrid(xi, yi)

# Interpolate
rbf = scipy.interpolate.Rbf(x, y, z, function='linear')
zi = rbf(xi, yi)

plt.imshow(zi, vmin=z.min(), vmax=z.max(), origin='lower',
           extent=[x.min(), x.max(), y.min(), y.max()])
plt.scatter(x, y, c=z)
plt.colorbar()
plt.show()