Strange set of errors

[Stephen Webb]

Greetings all,

I've recently begun using Python to do scientific computation, and I wrote
the following script to find approximate eigenvalues for a semi-infinite
matrix:


from pylab import *
from numpy import *
from scipy import *

def bandstructure(N,s):

    b = s/4.0

    jmax = 10 + N**2

    spectrum1 = [0]*2*N
    spectrum2 = [0]*2*N
    spectrum3 = [0]*2*N


    for k in arange(1, 2*N+1, 1):

        A = zeros( (jmax,jmax) )

        i = 0
        while i <= jmax-1:
            if i <= jmax-2:
                A[i,i+1] = b
                A[i+1,i] = b
                A[i,i] = ((k + 2.0*i*N)/N)**2
                i = i+1
            else:
                A[i,i] = ((k + 2.0*i*N)/N)**2
                i = i+1

        #This portion of the code builds a matrix twice as large to check
against

        B = zeros( (2*jmax,2*jmax) )

        i = 0
        while i <= 2*jmax-1:
            if i <= 2*jmax-2:
                B[i,i+1] = b
                B[i+1,i] = b
                B[i,i] = ((k + 2.0*i*N)/N)**2
                i = i+1
            else:
                B[i,i] = ((k + 2.0*i*N)/N)**2
                i = i+1

        x = linalg.eigvals(A)
        y = linalg.eigvals(B)

        j = 1
        while j<=3:
            if abs(y[j]-x[j]) <= 10.0**(-5):
                j = j + 1
            else:
                print 'jmax not large enough to obtain accurate results'

        spectrum1[k-1] = x[0] + 0.5*s
        spectrum2[k-1] = x[1] + 0.5*s
        spectrum3[k-1] = x[2] + 0.5*s

    plot (k, spectrum1, k, spectrum2, k, spectrum3)

    xlabel('k (energy level)')
    ylabel('E/E_r')
    title('Finite Size Band Structure, N = %d, s = %f' % (N, s))
    grid(true)


When I run this script, I get the following message, which I can't figure
out:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "bandstruc.py", line 61, in bandstructure
    plot (k, spectrum1, k, spectrum2, k, spectrum3)
  File
"/Library/Frameworks/Python.framework/Versions/2.5/lib/python2.5/site-packages/matplotlib/pylab.py",
line 2028, in plot
    ret =  gca().plot(*args, **kwargs)
  File
"/Library/Frameworks/Python.framework/Versions/2.5/lib/python2.5/site-packages/matplotlib/axes.py",
line 2535, in plot
    for line in self._get_lines(*args, **kwargs):
  File
"/Library/Frameworks/Python.framework/Versions/2.5/lib/python2.5/site-packages/matplotlib/axes.py",
line 437, in _grab_next_args
    for seg in self._plot_2_args(remaining[:2], **kwargs):
  File
"/Library/Frameworks/Python.framework/Versions/2.5/lib/python2.5/site-packages/matplotlib/axes.py",
line 337, in _plot_2_args
    x, y, multicol = self._xy_from_xy(x, y)
  File
"/Library/Frameworks/Python.framework/Versions/2.5/lib/python2.5/site-packages/matplotlib/axes.py",
line 266, in _xy_from_xy
    nrx, ncx = x.shape
ValueError: need more than 0 values to unpack

Also, I've been having trouble with the plot function in matplotlib. For
example, I enter the following in the terminal:

>>> from pylab import *
>>> plot([1,2,3])
[<matplotlib.lines.Line2D instance at 0x16adda30>]

I'm reasonably sure that the issue in the first big error message is just an
indexing error on my part, but I have no idea what the second thing means.
Every time I run the plot([1,2,3]) I get a different ending number that
seems to vary randomly.

Could anybody please help me out with these problems?

Thanks,

Stephen
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