在 Python 中绘制多项式
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Plotting a polynomial in Python
提问by Ally
I am new to Python plotting apart from some basic knowledge of matplotlib.pyplot. My question is how to plot some higher degree polynomials? One method I saw was expressing y in terms of x and then plotting the values. But I have 2 difficulties:
除了一些基本的matplotlib.pyplot. 我的问题是如何绘制一些更高次的多项式？我看到的一种方法是用 x 表示 y，然后绘制这些值。但我有两个困难：
- y and x cannot be separated.
- I am expecting a closed curve(actually a complicated curve)
- y 和 x 不能分开。
- 我期待一条闭合曲线（实际上是一条复杂的曲线）
The polynomial I am trying to plot is:
我试图绘制的多项式是：
c0 + c1*x + c2*y +c3*x*x + c4*x*y + c5*y*y + c6*x**3 + c7*x**2*y + ..... c26*x*y**5 + c27*y**6
All coefficients c0to c27are known.
How do I plot this curve?
所有系数c0toc27都是已知的。我如何绘制这条曲线？
Also could you please suggest me resources from where I can learn plotting and visualization in Python?
另外，您能否向我推荐可以在 Python 中学习绘图和可视化的资源？
Clarification:Sorry everyone for not making it clear enough. It is not an equation of a surface (which involves 3 variables: x, y and z). I should have put a zero at the end: c0 + c1*x + c2*y +c3*x*x + c4*x*y + c5*y*y + c6*x**3 + c7*x**2*y + ..... c26*x*y**5 + c27*y**6 =0
澄清：对不起，大家没有说得足够清楚。它不是一个表面方程（它涉及 3 个变量：x、y 和 z）。我应该在最后放一个零：c0 + c1*x + c2*y +c3*x*x + c4*x*y + c5*y*y + c6*x**3 + c7*x** 2*y + ..... c26*x*y**5 + c27*y**6 =0
回答by Viktor Kerkez
I'm not sure I fully understood your question, but I think you want a surface plot
我不确定我是否完全理解你的问题，但我认为你想要一个表面图
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
x = np.arange(-5, 5, 0.25)
y = np.arange(-5, 5, 0.25)
X, Y = np.meshgrid(x, y)
F = 3 + 2*X + 4*X*Y + 5*X*X
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, F)
plt.show()
And for the resources: official documentationand pyvideos
回答by Saullo G. P. Castro
Your equation represents a 3D surface, which you can plot creating first a mesh grid of xand yvalues, easily achieved using numpy:
你的方程代表一个 3D 表面，你可以绘制首先创建一个网格网格x和y值，使用 numpy 很容易实现：
X,Y = np.meshgrid( np.linspace( xmin, xmax, 100), np.linspace( ymin, ymax, 200) )
Xand Yare both 2D arrays containing the X and Y coordinates, respectively.
X和Y都是分别包含 X 和 Y 坐标的二维数组。
Then you can calculate zvalues for each point in this mesh, using the known coefficients:
然后，您可以z使用已知系数计算此网格中每个点的值：
Z = c0 + c1*X + c2*Y +c3*X*X + c4*X*Y + c5*Y*Y + c6*X**3 + c7*X**2*Y + ..... c26*X*Y**5 + c27*Y**6
After that you can plot it using matplotlib:
之后，您可以使用matplotlib以下方法绘制它：
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
ax = plt.subplot(111, projection='3d')
ax.plot_surface( X, Y, Z )
plt.show()
