import __builtin__
import math
import random
+import time
def median(x, use_float=True):
# there exist better algorithms...
res[k] = res.get(k, 0) + v
return dict((k, v) for k, v in res.iteritems() if v)
+mult_dict = lambda c, x: dict((k, c*v) for k, v in x.iteritems())
+
def format(x):
prefixes = 'kMGTPEZY'
count = 0
s = '' if count == 0 else prefixes[count - 1]
return '%i' % (x,) + s
+def format_dt(dt):
+ for value, name in [(60*60*24, 'days'), (60*60, 'hours'), (60, 'minutes'), (1, 'seconds')]:
+ if dt > value:
+ break
+ return '%.01f %s' % (dt/value, name)
+
perfect_round = lambda x: int(x + random.random())
def erf(x):
try:
from scipy import special
except ImportError:
- print 'Install SciPy for more accurate confidence intervals!'
def binomial_conf_interval(x, n, conf=0.95):
assert 0 <= x <= n and 0 <= conf < 1
if n == 0:
left = random.random()*(1 - conf)
+ return left, left + conf
# approximate - Wilson score interval
z = math.sqrt(2)*ierf(conf)
p = x/n
if n == 0:
left = random.random()*(1 - conf)
return left, left + conf
- b = special.beta(x+1, n-x+1)
+ bl = float(special.betaln(x+1, n-x+1))
def f(left_a):
- left, right = max(1e-8, special.betaincinv(x+1, n-x+1, left_a)), min(1-1e-8, special.betaincinv(x+1, n-x+1, left_a + conf))
- top = right**(x+1) * (1-right)**(n-x+1) * left*(1-left) - left**(x+1) * (1-left)**(n-x+1) * right * (1-right)
+ left, right = max(1e-8, float(special.betaincinv(x+1, n-x+1, left_a))), min(1-1e-8, float(special.betaincinv(x+1, n-x+1, left_a + conf)))
+ top = math.exp(math.log(right)*(x+1) + math.log(1-right)*(n-x+1) + math.log(left) + math.log(1-left) - bl) - math.exp(math.log(left)*(x+1) + math.log(1-left)*(n-x+1) + math.log(right) + math.log(1-right) - bl)
bottom = (x - n*right)*left*(1-left) - (x - n*left)*right*(1-right)
- return top/bottom/b
+ return top/bottom
left_a = find_root(f, (1-conf)/2, bounds=(0, 1-conf))
- return special.betaincinv(x+1, n-x+1, left_a), special.betaincinv(x+1, n-x+1, left_a + conf)
-
-def binomial_conf_center_radius(x, n, conf=0.95):
- assert 0 <= x <= n and 0 <= conf < 1
- left, right = binomial_conf_interval(x, n, conf)
- if n == 0:
- return (left+right)/2, (right-left)/2
- p = x/n
- return p, max(p - left, right - p)
+ return float(special.betaincinv(x+1, n-x+1, left_a)), float(special.betaincinv(x+1, n-x+1, left_a + conf))
minmax = lambda x: (min(x), max(x))
if n == 0:
return '???'
left, right = minmax(map(f, binomial_conf_interval(x, n, conf)))
- return '~%.1f%% (%i-%i%%)' % (f(x/n), int(100*left), 100-int(100-100*right))
+ return '~%.1f%% (%.f-%.f%%)' % (100*f(x/n), math.floor(100*left), math.ceil(100*right))
def reversed(x):
try:
assert not s.startswith(alphabet[0])
return sum(alphabet.index(char) * len(alphabet)**i for i, char in enumerate(reversed(s)))
+class RateMonitor(object):
+ def __init__(self, max_lookback_time):
+ self.max_lookback_time = max_lookback_time
+
+ self.datums = []
+ self.first_timestamp = None
+
+ def _prune(self):
+ start_time = time.time() - self.max_lookback_time
+ for i, (ts, datum) in enumerate(self.datums):
+ if ts > start_time:
+ self.datums[:] = self.datums[i:]
+ return
+
+ def get_datums_in_last(self, dt=None):
+ if dt is None:
+ dt = self.max_lookback_time
+ assert dt <= self.max_lookback_time
+ self._prune()
+ now = time.time()
+ return [datum for ts, datum in self.datums if ts > now - dt], min(dt, now - self.first_timestamp) if self.first_timestamp is not None else 0
+
+ def add_datum(self, datum):
+ self._prune()
+ t = time.time()
+ self.datums.append((t, datum))
+ if self.first_timestamp is None:
+ self.first_timestamp = t
+
if __name__ == '__main__':
import random
a = 1