鞍點

當函數為多次方程式時，就會有鞍點的產生，如下是四次方程式$(f(x)=x^{4}-60x^{3}-x+1)$ 的圖形

import numpy as np
import pylab as plt
shrink_y=1e6
ax=plt.subplot()
x=np.linspace(-30,60,100)
y=(np.power(x,4)-60*pow(x,3)-x+1)/shrink_y
ax.set_xlim(-45, 70)
ax.set_ylim(-2, 3)
plt.plot(x, y)
plt.savefig("saddle_1.jpg")
plt.show()

3D鞍點

網路上有一個很酷的3D鞍點製作程式，如下代碼所示

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x, y = np.mgrid[-1:1:40j, -1:1:40j]
print(x)
print(y)
z = x**2 - y**2
#plot_args不用設定也沒關係，只是設定後圖形比較漂亮
plot_args = dict(
    cmap = "Blues_r",
    linewidth= 0.4,
    alpha =1,
    vmin = -1,
    vmax = 1)
ax.plot([0], [0], [0], 'ro', markersize= 10)
ax.plot_surface(x, y, z, **plot_args)
ax.view_init(azim=-60, elev=10)
plt.show()