import numpy as np
import operator as op

def sigmoid(x):
    return 1.0/(1 + np.exp(-x))

def choose(n, r):
    if n < r: return 0
    if r == 0: return 1
    denom = reduce(op.mul, xrange(1, r+1), 1)
    numer = reduce(op.mul, xrange(n, n-r, -1), 1)
    return numer//denom

# Just to have a less heavyweight name for this extremely common operation
#
# We may wish to have more fine-grained control over division by zero behavior
# in the future (separate specifiable values for 0/0 and x/0 with x != 0),
# but for now, we just allow the option to handle indeterminate 0/0.
def fdiv(a, b, zero_over_zero_value = None):
    if zero_over_zero_value != None:
        out = np.full_like(a, zero_over_zero_value)
        where = np.logical_or (a != 0, b != 0)
    else:
        out = None
        where = True

    return np.true_divide(a, b, out = out, where = where)