calculate kl divergence between two documents

gistfile1.py

# refer to http://staff.science.uva.nl/~tsagias/?p=185
import re, math, collections
 
def tokenize(_str):
    stopwords = ['and', 'for', 'if', 'the', 'then', 'be', 'is', 'are', 'will', 'in', 'it', 'to', 'that']
    tokens = collections.defaultdict(lambda: 0.)
    for m in re.finditer(r"(\w+)", _str, re.UNICODE):
        m = m.group(1).lower()
        if len(m) < 2: continue
        if m in stopwords: continue
        tokens[m] += 1
 
    return tokens
#end of tokenize
 
def kldiv(_s, _t):
    if (len(_s) == 0):
        return 1e33
 
    if (len(_t) == 0):
        return 1e33
 
    ssum = 0. + sum(_s.values())
    slen = len(_s)
 
    tsum = 0. + sum(_t.values())
    tlen = len(_t)
 
    vocabdiff = set(_s.keys()).difference(set(_t.keys()))
    lenvocabdiff = len(vocabdiff)
 
    """ epsilon """
    epsilon = min(min(_s.values())/ssum, min(_t.values())/tsum) * 0.001
 
    """ gamma """
    gamma = 1 - lenvocabdiff * epsilon
 
    # print "_s: %s" % _s
    # print "_t: %s" % _t
 
    """ Check if distribution probabilities sum to 1"""
    sc = sum([v/ssum for v in _s.itervalues()])
    st = sum([v/tsum for v in _t.itervalues()])
 
    if sc < 9e-6:
        print "Sum P: %e, Sum Q: %e" % (sc, st)
        print "*** ERROR: sc does not sum up to 1. Bailing out .."
        sys.exit(2)
    if st < 9e-6:
        print "Sum P: %e, Sum Q: %e" % (sc, st)
        print "*** ERROR: st does not sum up to 1. Bailing out .."
        sys.exit(2)
 
    div = 0.
    for t, v in _s.iteritems():
        pts = v / ssum
 
        ptt = epsilon
        if t in _t:
            ptt = gamma * (_t[t] / tsum)
 
        ckl = (pts - ptt) * math.log(pts / ptt)
 
        div +=  ckl
 
    return div
#end of kldiv
 
d1 = """Many research publications want you to use BibTeX, which better
organizes the whole process. Suppose for concreteness your source
file is x.tex. Basically, you create a file x.bib containing the
bibliography, and run bibtex on that file."""
d2 = """In this case you must supply both a \left and a \right because the
delimiter height are made to match whatever is contained between the
two commands. But, the \left doesn't have to be an actual 'left
delimiter', that is you can use '\left)' if there were some reason
to do it."""
 
print "KL-divergence between d1 and d2:", kldiv(tokenize(d1), tokenize(d2))
print "KL-divergence between d2 and d1:", kldiv(tokenize(d2), tokenize(d1))

" sc = sum([v/ssum for v in _s.itervalues()])"
AttributeError: 'collections.defaultdict' object has no attribute 'itervalues'

Shouldn't KL divergence be a number between 0 and 1?