IndexError: index out of bounds When tryin to plot in Matplotlib

Question

I am trying to convert the following code from Trefethen's Spectral Methods in MATLAB to Python. But run into the following error regarding an index out of bounds. I am a bit confused as to what index is out of bounds and how to fix it. Any help would be appreciated.

Error

Traceback (most recent call last):
  File "C:\Documents and Settings\My Documents\Computational Physics\Wave-eqn.py", line 56, in <module>
ax.plot_wireframe(x,tdata,data,rstride=10, cstride=10)
  File "C:\Python32\lib\site-packages\mpl_toolkits\mplot3d\axes3d.py", line 906, in  plot_wireframe
    tylines = [tY[i] for i in cii]
  File "C:\Python32\lib\site-packages\mpl_toolkits\mplot3d\axes3d.py", line 906, in  <listcomp>
    tylines = [tY[i] for i in cii]
IndexError: index out of bounds

Trefethen's Code

% p6.m - variable coefficient wave equation using differentiation matrices

% Grid, variable coefficient, and initial data:
N = 512; h = 2*pi/N; x = h*(1:N); t = 0; dt = h/4;
a = .1;
c = a + sin (x-1).^2;
v = exp(-100*(x-1).^2); vold = exp(-100*(x-a*dt-1).^2);

column = [0 .5*(-1).^(1:N-1).*cot((1:N-1)*h/2)];
D = toeplitz(column,-column);

% Time-stepping by leap frog formula:
tmax = 15; tplot = .15; clf, drawnow, set(gcf,'renderer','zbuffer')
plotgap = round(tplot/dt); dt = tplot/plotgap;
nplots = round(tmax/tplot);
data = [v; zeros(nplots,N)]; tdata = t;
for i = 1:nplots
 for n = 1:plotgap
        t = t+dt;
        %       v_hat = fft(v);
        %       w_hat = 1i*[0:N/2-1 0 -N/2+1:-1] .* v_hat;
        %       w = real(ifft(w_hat));
        w = (D*v')';
        vnew = vold - 2*dt*c.*w; vold = v; v = vnew;
    end
    data(i+1,:) = v; tdata = [tdata; t];
end
waterfall(x,tdata,data), view(10,70), colormap(1e-6*[1 1 1]);
axis([0 2*pi 0 tmax 0 3]), ylabel t, zlabel u, grid off

My Code

import numpy as np
from numpy import *
from math import  pi
from scipy.linalg import toeplitz
from scipy.special import cotdg
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt


N = 512
h = (2*np.pi)/N
x = h*(np.arange(N)+1)
t = 0
dt = h/4.
a = .1
c = a + np.sin(x - 1)**2
v = np.exp(-100 * (x - 1)**2)
vold = np.exp(-100 * (x - a*dt - 1)**2)

column = ((0.5*(-1)**arange(N))*cotdg(arange(N))*(h/2));
D = toeplitz(column,-column);
#print(D.shape);


tmax = 15   
tplot = .15
plotgap = int(around(tplot/dt));print(plotgap)
dt = tplot/plotgap
nplots = int(round((tmax/tplot)));print(nplots)
k = np.zeros(((nplots,N))) 
data = np.concatenate((v.reshape((512,1)).transpose(), k))
tdata = t

for i in range(nplots):
    for n in range(plotgap):
        t = t+dt
        w = (D*v)
        vnew = vold-2*dt*c*w
        vold = v
        v = vnew
    data[i,:] = v[0,:]
    tdata = vstack([tdata, t])
print('shape data =',data.shape)
print('shape v =',v.shape)
print('shape tdata =',tdata.shape)
print('shape x =',x.shape)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(x,tdata,data,rstride=10, cstride=10)
plt.show()

Shapes of arrays done by python

 shape data = (101, 512)
 shape tdata = (101, 1)
 shape x = (512,)

I had a friend run the size() command in MatLab for this code and he came up with these shapes for the arrays

data =  101 512
tdata = 101 1
x =     1   512

I'm not really familiar with the details of matplotlib,scipy or numpy, but I'm guessing that you introduced some off-by-1 errors when porting from Matlab, since Matlab arrays are index from 1 to n, whereas python arrays are from 0 to n-1. I hope this comment is actually useful! — Gordon Bailey
– Gordon Bailey, Commented Aug 1, 2012 at 20:35
That's a good point, but it only applies to indexing, not the total number of elements -- shape in numpy and size in Matlab should return the same numbers. — Steve Tjoa
– Steve Tjoa, Commented Aug 1, 2012 at 20:46
I took that in to account by having the (1:N-1) lines in the Matlab code be arange(N)) in the Python code. — Stripers247
– Stripers247, Commented Aug 1, 2012 at 20:49
@SteveTjoa is there a way to change shape =(512,) to (1,512) like the Matlab output? — Stripers247
– Stripers247, Commented Aug 1, 2012 at 20:54

Steve Tjoa · Accepted Answer · 2012-08-01 20:50:00Z

1

The first two arguments of plot_wireframe need to be 2D arrays. Documentation.

I don't know exactly how to customize your code (because there is a lot of it), but I hope that helps.

EDIT: Try axes3d.get_test_data to see an example of what valid inputs are supposed to look like.

edited Aug 1, 2012 at 20:50

answered Aug 1, 2012 at 20:39

Steve Tjoa

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2 Comments

Stripers247 Over a year ago

so I need to some how make x a 2D array?

Stripers247 Over a year ago

so I did X,Y,Z=axes3d.get_test_data(0.05) print(X.shape) print(Y.shape) print(Z.shape) and got (120, 120) (120, 120) (120, 120) so does this mean that the length of each dimension of the arrays must be the same?

Stripers247 · Accepted Answer · 2012-08-03 04:35:29Z

0

With the help of the folks over at [email protected] I figured it out. The arrays

x and tdata

Need to be broadcast so I did

X,Y = np.broadcast_arrays(x,tdata)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(X,Y,data,rstride=5, cstride=5)
plt.show()

answered Aug 3, 2012 at 4:35

Stripers247

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