1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
|
"""
==============================================
Contouring the solution space of optimizations
==============================================
Contour plotting is particularly handy when illustrating the solution
space of optimization problems. Not only can `.axes.Axes.contour` be
used to represent the topography of the objective function, it can be
used to generate boundary curves of the constraint functions. The
constraint lines can be drawn with
`~matplotlib.patheffects.TickedStroke` to distinguish the valid and
invalid sides of the constraint boundaries.
`.axes.Axes.contour` generates curves with larger values to the left
of the contour. The angle parameter is measured zero ahead with
increasing values to the left. Consequently, when using
`~matplotlib.patheffects.TickedStroke` to illustrate a constraint in
a typical optimization problem, the angle should be set between
zero and 180 degrees.
"""
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()
|
