import numpy as np
import matplotlib.pyplot as plt

# Graph setup
yellow = "#e9eabb"
blue = "#122a8c"
gray = '#757575'
plt.rcParams["text.color"] = gray
plt.rcParams["font.size"] = 12
plt.rcParams["xtick.color"] = gray
plt.rcParams["ytick.color"] = gray
plt.rcParams["axes.labelcolor"] = gray
plt.rcParams["axes.edgecolor"] = gray
plt.rcParams["axes.spines.right"] = False
plt.rcParams["axes.spines.top"] = False


A = np.array([
  [10, -1, 0, 1],
  [0.2, 8, 0.2, 0.2],
  [1, 1, 2, 1],
  [-1, -1, -1, -11]])
vals = np.linalg.eigvals(A)
fig = plt.figure(figsize=(6, 4))
for cont, val in enumerate(vals):
    real = np.real(val)
    imag = np.imag(val)
    center = A[cont, cont]
    radius = sum(np.abs(A[cont, k]) for k in range(4) if k != cont)
    circle = plt.Circle((center, 0), radius, color=yellow)
    plt.plot(real, imag, color=blue, marker="x", linewidth=0)
    plt.gca().add_artist(circle)

plt.legend(["Eigenvalues"], frameon=False)
plt.xlabel("Real axis")
plt.ylabel("Imaginary axis")
plt.yticks([-10, -5, 0, 5, 10])
plt.axis("image")
plt.xlim(-15, 15)
plt.ylim(-10, 10)
plt.savefig("Gershgorin Disk Theorem Example.svg", bbox_inches="tight")
plt.show()