demoGershgorin(A) plots the Gershgorin discs that bound the eigenvalues of a matrix A, and also the actual eigenvalues.

Gerschgorin.py

import numpy as np
import matplotlib
from matplotlib.patches import Circle
from matplotlib.collections import PatchCollection
import matplotlib.pyplot as plt
from numpy import linalg as LA

def demoGerschgorin(A):

    n = len(A)
    eval, evec = LA.eig(A)

    patches = []
    
    # draw discs
    
    for i in range(n):
        xi = np.real(A[i,i])
        yi = np.imag(A[i,i])
        ri = np.sum(np.abs(A[i,:])) - np.abs(A[i,i]) 
        
        circle = Circle((xi, yi), ri)
        patches.append(circle)

    fig, ax = plt.subplots()

    p = PatchCollection(patches, cmap=matplotlib.cm.jet, alpha=0.1)
    ax.add_collection(p)
    plt.axis('equal')
    
    for xi, yi in zip(np.real(eval), np.imag(eval)):
        plt.plot(xi, yi,'o')
    
    plt.show()