def test_fresh_reservoir(self):
res = ensemble.FreshReservoir(10000, 80.0)
for i in range(1, 1000000 + 1):
res.append_maybe(lambda: i) # pylint: disable=cell-var-from-loop
items = np.array([item for item in res]).astype(np.float64)
desired_mean = 0.5 * (200000.0 + 1000000.0)
computed_mean = np.mean(items)
logging.info("Fresh reservoir, true mean %.2f, computed mean %.2f",
desired_mean, computed_mean)
self.assertAlmostEqual(desired_mean,
computed_mean,
delta=1000.0,
msg="Fresh reservoir item freshness is off.")
def test_fresh_reservoir_distribution(self, freshness, n, capacity):
res = ensemble.FreshReservoir(capacity, freshness=freshness)
for item in range(1, n + 1):
res.append_maybe(lambda: item) # pylint: disable=cell-var-from-loop
items = np.asarray(list(res))
# Variance of the uniform discrete distr. on {(freshness/100)*n,...,n},
# from https://en.wikipedia.org/wiki/Discrete_uniform_distribution
var_true = ((n -
((100.0 - freshness) / 100.0) * n + 1)**2.0 - 1.0) / 12.0
# The number of fresh items, len(items), varies stochastically in fresh
# reservoir sampling.
sample_mean_stddev = math.sqrt(var_true) / math.sqrt(len(items))
# Check mean is in +/- 4 sampling stddev
mean_true = 0.5 * (((100.0 - freshness) / 100.0) * n + n)
mean_estimate = np.mean(items)
logging.info(
"Reservoir(n=%d, cap=%d, freshness=%.1f) has "
"sample mean %.1f, true mean %.1f, sample stddev %.2f", n,
capacity, freshness, mean_estimate, mean_true, sample_mean_stddev)
self.assertAlmostEqual(
mean_true,
mean_estimate,
delta=4.0 * sample_mean_stddev,
msg="Mean %.1f deviates from true mean %.1f by "
"more than allowed 4 sigma tolerance (%.2f)" %
(mean_estimate, mean_true, 4.0 * sample_mean_stddev))
# Check sample variance agrees with true variance
var_var_est = 2.0 * (var_true**2.0) / (len(items) - 1
) # var of the sample var
sample_var_stddev = math.sqrt(var_var_est)
var_estimate = np.var(items)
logging.info(
"Reservoir(n=%d, cap=%d, freshness=%.1f) has "
"sample var %.1f, true var %.1f, sample var stddev %.2f", n,
capacity, freshness, var_estimate, var_true, sample_var_stddev)
self.assertAlmostEqual(
var_true,
var_estimate,
delta=4.0 * sample_var_stddev,
msg="Sample variance %.1f deviates from true "
"variance %.1f by more than allowed 4 sigma "
"tolerance (%.2f)" %
(var_estimate, var_true, 4.0 * sample_var_stddev))