Plot 3d in Python

Question

I wish to know how to plot a surface of type $(t,x,u=u(t,x))$ in Python. More precisely, $t,x$ are vectors and $u$ is a matrix that are initialized as np.zeros(), while the function plot does not draw the surface as I desire. Could someone help? The code is as follow:

 eps=0.1
m=2000
n=100
dt=1.0/m
dx=1.0/(n*n)
time=np.zeros(m+1)
for i in range(m+1):
  time[i]=i*dt
space=np.zeros(2*n+1)
for j in range(2*n+1):
  space[j]=(j-n)*dx*n
sol=np.zeros((m+1,2*n+1))
for i in range(m):
  index_i=m-1-i
  for j in range(1,2*n):
    sol[index_i, j] =sol[index_i+1, j]-0.5*dt*math.log(eps+abs(sol[index_i+1, j+1]+sol[index_i+1, j-1]-2*sol[index_i+1, j])/dx)
t_mesh, x_mesh = np.meshgrid(time, space)
fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
surf = ax.plot_surface(t_mesh, x_mesh, sol, cmap=cm.coolwarm,
                           linewidth=0, antialiased=False)

Which format should be used such that plt.plot(time,space,sol) works?

PS : I do research in maths and I code rarely. Sorry if my statement is not clear.

I don't follow the mathematics of this question. You want to plot the function u(t, x), where t and x are both vectors, which means that the plot is at least 4D? (2 or more dimensions for first vector, and 2 or more for second vector.) How does the plot look? — Nick ODell
– Nick ODell, Commented Jul 16, 2022 at 15:50
@NickODell Indeed, time=(i/m: 0<=i<=m), space=(j/n: -n<=j<=n) and sol=(u_i,j: 0<=i<=m, -n<=j<=n). I wish to plot sol as a function of time/space — Philo18
– Philo18, Commented Jul 16, 2022 at 16:00
So say that time is X coordinate, space is Y coordinate, and sol is Z coordinate. sol is a 2D array, right? So it can't be used directly. How should that be turned into a 1D array? — Nick ODell
– Nick ODell, Commented Jul 16, 2022 at 16:03
@NickODell My function u is not explicite, while I have its values at the chosen grid — Philo18
– Philo18, Commented Jul 16, 2022 at 16:44

Nick ODell · Accepted Answer · 2022-07-16 18:18:50Z

2

You can plot that function like so:

import numpy as np
import math
import matplotlib.pyplot as plt
from matplotlib import cm

# ... your original code here ...

def plot_surface_from_arrays(X, Y, Z, rotate=0):
    assert Y.shape + X.shape == Z.shape, "X and Y shapes don't match Z"
    X_mesh, Y_mesh = np.meshgrid(X, Y)
    fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
    ax.view_init(elev=30, azim=-60 + rotate)
    surf = ax.plot_surface(X_mesh, Y_mesh, Z, cmap=cm.coolwarm,
                           linewidth=0, antialiased=False)
plot_surface_from_arrays(space, time, sol, rotate=90)

Result:

Code adapted from this documentation example.

edited Jul 16, 2022 at 18:18

answered Jul 16, 2022 at 17:02

Nick ODell

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11 Comments

Philo18 Over a year ago

It is still not working. Indeed, even my matrix sol is created as np.zeros(m+1,2*n+1). The system still treats it as an one-dimensional array/vector, instead of a matrix or 2d array

Nick ODell Over a year ago

Can you clarify? On my system, sol is created as a 2D array, eg. sol.shape shows (2001, 201).

Philo18 Over a year ago

The same for me. I've uploaded the code which yields an error

Nick ODell Over a year ago

You swapped the order of time and space. If you want to do that you have to swap the order of axes for sol too, using e.g. np.swapaxes().

Philo18 Over a year ago

I don't undestand... Do you mean ax.plot_surface(x_mesh, t_mesh, sol) instead of ax.plot_surface(t_mesh, x_mesh, sol)?

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