Question

I have a Numpy matrix, for example, numpy.matrix([[-1, 2],[1, -2]], dtype='int'). I want to get its integer-valued eigenvectors, if any; for example, numpy.array([[-1], [1]]) for the above matrix. What Numpy returns are eigenvectors in floating numbers, scaled to have unit length.

One can do this in Sage, where one can specify the field (i.e., data type) of the matrix and operations done on the matrix will respect the field one specifies.

Any idea of how to do this nicely in Python? Many thanks in advance.

Answer 1

I am personally content with the following solution: I called sage in Python and let sage compute what I want. sage, being math-oriented, is rather versatile in computations involving fields other than reals.

Below is my script compute_intarrs.py and it requires sage be installed. Be aware it is a little slow.

import subprocess
import re
import numpy as np

# construct a numpy matrix
mat = np.matrix([[1,-1],[-1,1]])
# convert the matrix into a string recognizable by sage
matstr = re.sub('\s|[a-z]|\(|\)', '', mat.__repr__())

# write a (sage) python script "mat.py";
# for more info of the sage commands: 
# www.sagemath.org/doc/faq/faq-usage.html#how-do-i-import-sage-into-a-python-script
# www.sagemath.org/doc/tutorial/tour_linalg.html
f = open('mat.py', 'w')
f.write('from sage.all import *\n\n')
f.write('A = matrix(ZZ, %s)\n\n' % matstr)
f.write('print A.kernel()')  # this returns the left nullspace vectors
f.close()

# call sage and run mat.py
p = subprocess.Popen(['sage', '-python', 'mat.py'], stdout=subprocess.PIPE)

# process the output from sage
arrstrs = p.communicate()[0].split('\n')[2:-1]
arrs = [np.array(eval(re.sub('(?<=\d)\s*(?=\d|-)', ',', arrstr))) 
        for arrstr in arrstrs]
print arrs

Result:

In [1]: %run compute_intarrs.py

[array([1, 1])]