等高线优化问题的解空间

在说明优化问题的解空间时，等高线绘图特别有用。不仅可以用 axes.Axes.contour 来表示目标函数的地形，还可以用来生成约束函数的边界曲线。约束线可以使用 TickedStroke 绘制，以区分约束边界的有效和无效侧。

axes.Axes.contour 生成具有更大值的曲线位于等高线的左侧。角度参数以正前方为 0 度，向左增加值。因此，在使用 TickedStroke 来说明典型优化问题中的约束时，角度应设置为 0 度到 180 度之间。

import matplotlib.pyplot as plt
import numpy as np

from matplotlib import patheffects

fig, ax = plt.subplots(figsize=(6, 6))

nx = 101
ny = 105

# Set up survey vectors
xvec = np.linspace(0.001, 4.0, nx)
yvec = np.linspace(0.001, 4.0, ny)

# Set up survey matrices.  Design disk loading and gear ratio.
x1, x2 = np.meshgrid(xvec, yvec)

# Evaluate some stuff to plot
obj = x1**2 + x2**2 - 2*x1 - 2*x2 + 2
g1 = -(3*x1 + x2 - 5.5)
g2 = -(x1 + 2*x2 - 4.5)
g3 = 0.8 + x1**-3 - x2

cntr = ax.contour(x1, x2, obj, [0.01, 0.1, 0.5, 1, 2, 4, 8, 16],
                  colors='black')
ax.clabel(cntr, fmt="%2.1f", use_clabeltext=True)

cg1 = ax.contour(x1, x2, g1, [0], colors='sandybrown')
cg1.set(path_effects=[patheffects.withTickedStroke(angle=135)])

cg2 = ax.contour(x1, x2, g2, [0], colors='orangered')
cg2.set(path_effects=[patheffects.withTickedStroke(angle=60, length=2)])

cg3 = ax.contour(x1, x2, g3, [0], colors='mediumblue')
cg3.set(path_effects=[patheffects.withTickedStroke(spacing=7)])

ax.set_xlim(0, 4)
ax.set_ylim(0, 4)

plt.show()