具有4个方程的图由f（x，y，xy）组成

Question

I'd like to plot a graph which contains 4 functions as shown below:

 xy1: - 12.8 x - 0.108 y + xy >= -1.3824
 xy2: - 40 x - 5 y + xy >= -200
 xy3: - 40 x - 0.108 y + xy <= -4.32
 xy4: - 12.8 x - 5 y + xy <= -64

I started off by generating data for x and y

 import numpy as np
 x = np.linspace(0, 5, 100)
 y = np.linspace(0, 40, 100)

But then when I tried to plot the graph, I started to confuse about how should I reformulate the equations so that it is appropriate value for x, y, xy?

 import matplotlib.pyplot as plt
 plt.plot((-1.3824 + (12.8 * x) + (0.108 * y)), y)   <--- this doesn't seems to be right
 plt.show()

Answer 1

You can use contour for implicit function plotting. By the way I don't think you can plot multiple functions with inequality on the same graph because you have to show the ranges in the 2D plane, and they overlap each other.

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 5, 100)
y = np.linspace(0, 40, 100)

X, Y = np.meshgrid(x, y)

XY1 = (-12.8*X - 0.108*Y + X*Y) >= -1.3824
XY2 = - 40*X - 5*Y + X*Y >= -200
XY3 = - 40*X - 0.108*y + X*Y <= -4.32
XY4 = - 12.8*X - 5*Y + X*Y <= -64

plt.contour(X,Y, XY1)
plt.contour(X,Y, XY2)
plt.contour(X,Y, XY3)
plt.contour(X,Y, XY4)
plt.show()

================================================================

UPDATE:

Seems like sympy 's plot_implicit works so much better. You may need to install it.

from sympy import plot_implicit, symbols, And
x, y = symbols('x y') 

p1 = plot_implicit(And(-12.8*x - 0.108*y + x*y >= -1.3824), (x,0,5), (y,0,40))
p2 = plot_implicit(And(-40*x - 5*y + x*y >= -200), (x,0,5), (y,0,40))
p3 = plot_implicit(And(-40*x - 0.108*y + x*y <= -4.32), (x,0,5), (y,0,40))
p4 = plot_implicit(And(-12.8*x - 5*y + x*y <= -64), (x,0,5), (y,0,40))

Results:

Answer 2

you can use contourf :

import pylab as pl
import numpy as np

x, y = np.mgrid[-10:10:100j, -10:50:100j]
z1 = - 12.8 * x - 0.108 * y + x * y + 1.3824
z2 = - 40 * x - 5 * y + x * y + 200
z3 = - 40 * x - 0.108 * y + x * y + 4.32
z4 = - 12.8 * x - 5 * y + x * y + 64

fig, axes = pl.subplots(2, 2, figsize=(12, 8))
axes = axes.ravel()
axes[0].contourf(x, y, z1, levels=[0, 1e10], alpha=0.2, colors=["blue"])
axes[1].contourf(x, y, z2, levels=[0, 1e10], alpha=0.2, colors=["green"])
axes[2].contourf(x, y, z3, levels=[-1e10, 0], alpha=0.2, colors=["red"])
axes[3].contourf(x, y, z4, levels=[-1e10, 0], alpha=0.2, colors=["yellow"])

Here is the output: