Python3：用matplotlib绘制f(x,y)

Question

有没有办法，最好是用matplotlib这个库，在Python中绘制一个有两个变量的函数f(x,y)？提前谢谢你。

Answer 1

如果你有Z的表达式

如果你有一个关于Z的表达式，你就可以生成网格，并调用surface_plot来绘制图形：

#!/usr/bin/python3

import sys

import matplotlib
import matplotlib.pyplot as plt
from matplotlib.ticker import MaxNLocator
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D

import numpy
from numpy.random import randn, shuffle
from scipy import linspace, meshgrid, arange, empty, concatenate, newaxis, shape


# =========================
## generating ordered data:

N = 32
x = sorted(randn(N))
y = sorted(randn(N))

X, Y = meshgrid(x, y)
Z = X**2 + Y**2


# ======================================
## reference picture (X, Y and Z in 2D):

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.jet, linewidth=0)
fig.colorbar(surf)

title = ax.set_title("plot_surface: given X, Y and Z as 2D:")
title.set_y(1.01)

ax.xaxis.set_major_locator(MaxNLocator(5))
ax.yaxis.set_major_locator(MaxNLocator(6))
ax.zaxis.set_major_locator(MaxNLocator(5))

fig.tight_layout()
fig.savefig('3D-constructing-{}.png'.format(N))

结果：

如果你没有Z的表达式

上面提到的surface_plot函数只接受X、Y和Z作为二维数组。如果你没有Z的表达式，而只是把数据存储在一个列表的列表中，比如[[x1, y1, z1],[x2,y2,z2],...]，那么就不能直接使用这个函数。在这种情况下，你可以使用plot_trisurf。

在下面的代码中，我构建了X、Y和Z的二维数据，然后把这些数据重新整理成一维的X、Y和Z，打乱顺序，最后用plot_trisurf来绘制相同的数据：

#!/usr/bin/python3

import sys

import matplotlib
import matplotlib.pyplot as plt
from matplotlib.ticker import MaxNLocator
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D

import numpy
from numpy.random import randn, shuffle
from scipy import linspace, meshgrid, arange, empty, concatenate, newaxis, shape


# =========================
## generating ordered data:

N = 128
x = sorted(randn(N))
y = sorted(randn(N))

X, Y = meshgrid(x, y)
Z = X**2 + Y**2


# =======================
## re-shaping data in 1D:

# flat and prepare for concat:
X_flat = X.flatten()[:, newaxis]
Y_flat = Y.flatten()[:, newaxis]
Z_flat = Z.flatten()[:, newaxis]

DATA = concatenate((X_flat, Y_flat, Z_flat), axis=1)

shuffle(DATA)

Xs = DATA[:,0]
Ys = DATA[:,1]
Zs = DATA[:,2]


# ====================================================
## plotting surface using X, Y and Z given as 1D data:

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

surf = ax.plot_trisurf(Xs, Ys, Zs, cmap=cm.jet, linewidth=0)
fig.colorbar(surf)

title = ax.set_title("plot_trisurf: takes X, Y and Z as 1D")
title.set_y(1.01)

ax.xaxis.set_major_locator(MaxNLocator(5))
ax.yaxis.set_major_locator(MaxNLocator(6))
ax.zaxis.set_major_locator(MaxNLocator(5))

fig.tight_layout()
fig.savefig('3D-reconstructing-{}.png'.format(N))

结果：