connecting all numpy array plot points to each other using plt.plot() from matplotlib

Question

I have a numpy array with xy co-ordinates for points. I have plotted each of these points and want a line connecting each point to every other point (a complete graph). The array is a 2x50 structure so I have transposed it and used a view to let me iterate through the rows. However, I am getting an 'index out of bounds' error with the following:

     plt.plot(*zip(*v.T)) #to plot all the points
     viewVX = (v[0]).T
     viewVY = (v[1]).T
     for i in range(0, 49):
        xPoints = viewVX[i], viewVX[i+1]
        print("xPoints is", xPoints)
        yPoints = viewVY[i+2], viewVY[i+3]
        print("yPoints is", yPoints)
        xy = xPoints, yPoints
        plt.plot(*zip(*xy), ls ='-')

I was hoping that the indexing would 'wrap-around' so that for the ypoints, it'd start with y0, y1 etc. Is there an easier way to accomplish what I'm trying to achieve?

Answer 1

import matplotlib.pyplot as plt
import numpy as np
import itertools

v=np.random.random((2,50))
plt.plot(
    *zip(*itertools.chain.from_iterable(itertools.combinations(v.T,2))),
    marker='o', markerfacecolor='red')
plt.show()

The advantage of doing it this way is that there are fewer calls to plt.plot. This should be significantly faster than methods that make O(N**2) calls to plt.plot.

Note also that you do not need to plot the points separately. Instead, you can use the marker='o' parameter.

---

Explanation: I think the easiest way to understand this code is to see how it operates on a simple v:

In [4]: import numpy as np
In [5]: import itertools
In [7]: v=np.arange(8).reshape(2,4)
In [8]: v
Out[8]: 
array([[0, 1, 2, 3],
       [4, 5, 6, 7]])

itertools.combinations(...,2) generates all possible pairs of points:

In [10]: list(itertools.combinations(v.T,2))
Out[10]: 
[(array([0, 4]), array([1, 5])),
 (array([0, 4]), array([2, 6])),
 (array([0, 4]), array([3, 7])),
 (array([1, 5]), array([2, 6])),
 (array([1, 5]), array([3, 7])),
 (array([2, 6]), array([3, 7]))]

Now we use itertools.chain.from_iterable to convert this list of pairs of points into a (flattened) list of points:

In [11]: list(itertools.chain.from_iterable(itertools.combinations(v.T,2)))
Out[11]: 
[array([0, 4]),
 array([1, 5]),
 array([0, 4]),
 array([2, 6]),
 array([0, 4]),
 array([3, 7]),
 array([1, 5]),
 array([2, 6]),
 array([1, 5]),
 array([3, 7]),
 array([2, 6]),
 array([3, 7])]

If we plot these points one after another, connected by lines, we get our complete graph. The only problem is that plt.plot(x,y) expects x to be a sequence of x-values, and y to be a sequence of y-values.

We can use zip to convert the list of points into a list of x-values and y-values:

In [12]: zip(*itertools.chain.from_iterable(itertools.combinations(v.T,2)))
Out[12]: [(0, 1, 0, 2, 0, 3, 1, 2, 1, 3, 2, 3), (4, 5, 4, 6, 4, 7, 5, 6, 5, 7, 6, 7)]

The use of the splat operator (*) in zip and plt.plot is explained here.

Thus we've managed to massage the data into the right form to be fed to plt.plot.

Answer 2

With a 2 by 50 array,

 for i in range(0, 49):
    xPoints = viewVX[i], viewVX[i+1]
    print("xPoints is", xPoints)
    yPoints = viewVY[i+2], viewVY[i+3]

would get out of bounds for i = 47 and i = 48 since you use i+2 and i+3 as indices into viewVY.