def print_cumulative_prob(n=1, m=1, digits=4):
"""Given a number of top results n and a number of nodes m print odds.
Inputs
:n: total number (e.g., total number of highest scoring results)
:m: number of non-negative integers to sum to n (e.g., # of workers)
:digits: number of digits after decimal to print
Output
print the probability of a result being omitted from returned set
Exceptions
raises ValueError if inputs are not non-negative integers
"""
for param in (n, m, digits):
if not is_nonneg_int(param):
raise ValueError
print_template = ('Probability of %(count_str)s or more of top %(n)d' +
' from one of %(m)d sets is %(p_str)s.')
formats = {'count': '%%%dd' % len(str(n)), 'p': '%%0.%se' % str(digits)}
for stats in compute_all_probabilities(n, m):
stats['count_str'] = formats['count'] % stats['count']
stats['p_str'] = formats['p'] % stats['p']
print print_template % stats
def compute_probabilities(n, m, t=()):
"""Compute probability that a result is missed.
Inputs
:n: total number (e.g., total number of highest scoring results)
:m: number of non-negative integers to sum to n (e.g., number of
workers, each returning an integer number of results)
:t: optional threshold to short-circuit computation
* integer t is the maximum number of results to return per worker
Output
:stats: dict containing fields:
* count is the the number of results returned per worker
* n is the total number of highest scoring results
* m is the number of workers
* p is the cumulative probability that a result is missed
"""
if not is_nonneg_int(t):
t = ()
numerator = m ** n
denominator = float(numerator)
stats = {'n': n, 'm': m, 'count': 0, 'p': 0}
mset = Multiset(n)
for (cnt, ways) in mset.num_ways(n, m):
stats['count'] = cnt
stats['p'] = numerator / denominator
if cnt < t:
yield stats.copy()
elif cnt == t:
yield stats.copy()
raise StopIteration
else:
raise StopIteration
numerator -= ways
def test_is_nonneg_int_on_several_inputs(self):
"""Test is_nonneg_int on several inputs."""
pairs = ((None, False), (-1, False), (0, True), (1, True), (5.0, True))
for (value, expected) in pairs:
self.assertEqual(is_nonneg_int(value), expected)
def test_is_nonneg_int_on_several_inputs(self):
"""Test is_nonneg_int on several inputs."""
pairs = ((None, False), (-1, False),
(0, True), (1, True), (5.0, True))
for (value, expected) in pairs:
self.assertEqual(is_nonneg_int(value), expected)
