使用Python的Matplotlib创建3D表面图

Question

我正在尝试绘制一个三维曲面，但是因为matplotlib的文档似乎不太充分，并且缺乏示例，所以遇到了一些问题。无论如何，我编写的程序旨在通过有限差分法数值求解热传导方程。以下是我的代码：

    ## This program is to implement a Finite Difference method approximation
## to solve the Heat Equation, u_t = k * u_xx,
## in 1D w/out sources & on a finite interval 0 < x < L. The PDE
## is subject to B.C: u(0,t) = u(L,t) = 0,
## and the I.C: u(x,0) = f(x).
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D

# Parameters    
L = 1 # length of the rod
T = 10 # terminal time
N = 40 # spatial values
M = 1600 # time values/hops; (M ~ N^2)
s = 0.25 # s := k * ( (dt) / (dx)^2 )

# uniform mesh
x_init = 0
x_end = L
dx = float(x_end - x_init) / N

x = np.arange(x_init, x_end, dx)
x[0] = x_init

# time discretization
t_init = 0
t_end = T
dt = float(t_end - t_init) / M

t = np.arange(t_init, t_end, dt)
t[0] = t_init

# time-vector
for m in xrange(0, M):
    t[m] = m * dt

# spatial-vector
for j in xrange(0, N):
    x[j] = j * dx

# definition of the solution u(x,t) to u_t = k * u_xx
u = np.zeros((N, M+1)) # array to store values of the solution

# Finite Difference Scheme:

u[:,0] = x * (x - 1) #initial condition

for m in xrange(0, M):
    for j in xrange(1, N-1):
        if j == 1:
            u[j-1,m] = 0 # Boundary condition
        elif j == N-1:
            u[j+1,m] = 0 # Boundary Condition
        else:
            u[j,m+1] = u[j,m] + s * ( u[j+1,m] - 
            2 * u[j,m] + u[j-1,m] )

这是我写的尝试绘制3D曲面图的内容：

    # for 3D graph
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
surf = ax.plot_surface(x, t, u, rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=0, antialiased=False)
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()

我在运行绘制图表的代码时遇到了这个错误："ValueError: shape mismatch: two or more arrays have incompatible dimensions on axis 1."，请帮忙解决。我认为出现这个错误是因为我把定义为Nx(M+1)矩阵，但这是必须的使原始程序正常运行。我不确定如何更正以便正确绘制图表。谢谢！

- Javier

Answer 1

请使用以下代码（请查看注释）：

# plot 3d surface
# create a meshgrid of (x,t) points
# T and X are 2-d arrays
T, X = np.meshgrid(t,x)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
# Use X and T arrays to plot u 
# shape of X, T and u must to be the same
# but shape of u is [40,1601] and I will skip last row while plotting
surf = ax.plot_surface(X, T, u[:,:1600], rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=0, antialiased=False)
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()

结果：

结果：

由于matplotlib的文档似乎不够详细，缺乏示例

http://matplotlib.org/examples/mplot3d/index.html

- Serenity

Answer 2

打印变量 x、t 和 u 的形状是有帮助的：

x.shape == (40,)
t.shape == (1600,)
u.shape == (40, 1601)

所以这里有两个问题。 首先，x和t是一维的，但需要是二维的。 其次，u在第二维比t多一个元素。 你可以通过运行以下代码来解决这两个问题。

t, x = np.meshgrid(t, x)
u = u[:,:-1]

在创建3D图之前。

- ibab