Creating a 3D surface plot with matplotlib in python

Question

I am trying to plot a 3D surface but I am having some trouble because the documentation for matplotlib does not appear to be very thorough and is lacking in examples. Anyways the program I have written is to solve the Heat Equation Numerically via Method of Finite Differences. Here is my code:

    ## 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] )

This is what I have written to try and plot a 3D surface graph:

    # 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()

I am getting this error when I run the code to plot the graph: "ValueError: shape mismatch: two or more arrays have incompatible dimensions on axis 1."

Please, any and all help is very greatly appreicated. I think the error comes up because I defined u to be a Nx(M+1) matrix but it is necessary to make the original program run. I am unsure of how to correct this so the graph plots properly. Thanks!

Serenity · Accepted Answer · 2016-07-12 22:05:38Z

3

Use this code (look at the comments):

# 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()

Result:

because the documentation for matplotlib does not appear to be very thorough and is lacking in examples

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

answered Jul 12, 2016 at 22:05

Serenity

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Comments

ibab · Accepted Answer · 2016-07-12 22:07:33Z

2

It's helpful to print out the shapes of the variables x, t, and u:

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

So there are two problems here. The first one is that x and t are 1-dimensional, even though they need to be 2-dimensional. And the second one is that u has one more element than t in the second dimension. You can fix both by running

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

before creating the 3d plot.

answered Jul 12, 2016 at 22:07

ibab

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