import sys
import math
import numpy as np

def fast_logdet(A):
    """
    Compute log(det(A)) for A symmetric
    Equivalent to : np.log(nl.det(A))
    but more robust
    It returns -Inf if det(A) is non positive or is not defined.
    """
    ld = np.sum(np.log(np.diag(A)))
    a = np.exp(ld/A.shape[0])
    d = np.linalg.det(A/a)
    ld += np.log(d)
    if not np.isfinite(ld):
        return -np.inf
    return ld

if sys.version_info[1] < 6:
    # math.factorial is only available in 2.6
    def factorial(x) :
        # simple recursive implementation
        if x == 0: return 1
        return x * factorial(x-1)
else:
    factorial = math.factorial


if sys.version_info[1] < 6:
    def combinations(seq, r=None):
        """Generator returning combinations of items from sequence <seq>
        taken <r> at a time. Order is not significant. If <r> is not given,
        the entire sequence is returned.
        """
        if r == None:
            r = len(seq)
        if r <= 0:
            yield []
        else:
            for i in xrange(len(seq)):
                for cc in combinations(seq[i+1:], r-1):
                    yield [seq[i]]+cc

else:
    import itertools
    combinations = itertools.combinations



def density(w, **kwargs):
    """Compute density of a sparse vector
        Return a value between 0 and 1
    """
    d = 0 if w is None else float((w != 0).sum()) / w.size
    return d