# Python : 2d contour plot from 3 lists : x, y and rho?

## 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

## Answers:

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()
```

You can use scipy’s `griddata`

(requires Scipy >= 0.10), it’s a triangulation-based method.

```
import numpy as np
import matplotlib.pyplot as plt
import scipy.interpolate
# Generate data: for N=1e6, the triangulation hogs 1 GB of memory
N = 1000000
x, y = 10 * np.random.random((2, N))
rho = np.sin(3*x) + np.cos(7*y)**3
# Set up a regular grid of interpolation points
xi, yi = np.linspace(x.min(), x.max(), 300), np.linspace(y.min(), y.max(), 300)
xi, yi = np.meshgrid(xi, yi)
# Interpolate; there's also method='cubic' for 2-D data such as here
zi = scipy.interpolate.griddata((x, y), rho, (xi, yi), method='linear')
plt.imshow(zi, vmin=rho.min(), vmax=rho.max(), origin='lower',
extent=[x.min(), x.max(), y.min(), y.max()])
plt.colorbar()
plt.show()
```

There’s also inverse distance weighed interpolation — similar to RBF, but should work better for large # of points: Inverse Distance Weighted (IDW) Interpolation with Python