import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
plot_args = {'rstride': 1, 'cstride': 1, 'cmap':"viridis",
             'linewidth': 0.4, 'antialiased': True,
             'vmin': -2, 'vmax': 2}


x, y = np.mgrid[-1:1:31j, -1:1:31j]
z = x**3 - 3*x*y**2

ax.plot_surface(x, y, z, **plot_args)
ax.view_init(azim=-60, elev=20)
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.set_zlim(-2, 2)
plt.xticks([-1, -0.5, 0, 0.5, 1],
           [r"$-1$", r"$-1/2$", r"$0$", r"$1/2$", r"$1$"])
plt.yticks([-1, -0.5, 0, 0.5, 1],
           [r"$-1$", r"$-1/2$", r"$0$", r"$1/2$", r"$1$"])
ax.set_zticks([-2, -1, 0, 1, 2])
ax.set_zticklabels([r"$-2$", r"$-1$", r"$0$", r"$1$", r"$2$"])
ax.w_xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) 
ax.w_yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) 
ax.w_zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.set_xlabel(r"$x$", fontsize=18)
ax.set_ylabel(r"$y$", fontsize=18)
ax.set_zlabel(r"$x^3 - 3xy^2$", fontsize=18)
plt.savefig("monkey_saddle.svg", bbox_inches="tight", transparent=True)
plt.show()