1 from __future__ import absolute_import, division
8 def median(x, use_float=True):
9 # there exist better algorithms...
12 raise ValueError('empty sequence!')
13 left = (len(y) - 1)//2
15 sum = y[left] + y[right]
40 def clip(x, (low, high)):
48 add_to_range = lambda x, (low, high): (min(low, x), max(high, x))
58 raise ValueError('p must be in the interval (0.0, 1.0]')
61 return int(math.log1p(-random.random()) / math.log1p(-p)) + 1
63 def add_dicts_ext(add_func=lambda a, b: a+b, zero=0):
64 def add_dicts(*dicts):
67 for k, v in d.iteritems():
68 res[k] = add_func(res.get(k, zero), v)
69 return dict((k, v) for k, v in res.iteritems() if v != zero)
71 add_dicts = add_dicts_ext()
73 mult_dict = lambda c, x: dict((k, c*v) for k, v in x.iteritems())
78 while x >= 100000 and count < len(prefixes) - 2:
81 s = '' if count == 0 else prefixes[count - 1]
82 return '%i' % (x,) + s
85 for value, name in [(365.2425*60*60*24, 'years'), (60*60*24, 'days'), (60*60, 'hours'), (60, 'minutes'), (1, 'seconds')]:
88 return '%.01f %s' % (dt/value, name)
90 perfect_round = lambda x: int(x + random.random())
109 y = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*math.exp(-x*x)
110 return sign*y # erf(-x) = -erf(x)
112 def find_root(y_over_dy, start, steps=10, bounds=(None, None)):
114 for i in xrange(steps):
115 prev, guess = guess, guess - y_over_dy(guess)
116 if bounds[0] is not None and guess < bounds[0]: guess = bounds[0]
117 if bounds[1] is not None and guess > bounds[1]: guess = bounds[1]
123 return find_root(lambda x: (erf(x) - z)/(2*math.e**(-x**2)/math.sqrt(math.pi)), 0)
125 def binomial_conf_interval(x, n, conf=0.95):
126 assert 0 <= x <= n and 0 <= conf < 1
128 left = random.random()*(1 - conf)
129 return left, left + conf
130 # approximate - Wilson score interval
131 z = math.sqrt(2)*ierf(conf)
134 topb = z * math.sqrt(p*(1-p)/n + z**2/4/n**2)
136 return [clip(x, (0, 1)) for x in add_to_range(x/n, [(topa - topb)/bottom, (topa + topb)/bottom])]
138 minmax = lambda x: (min(x), max(x))
140 def format_binomial_conf(x, n, conf=0.95, f=lambda x: x):
143 left, right = minmax(map(f, binomial_conf_interval(x, n, conf)))
144 return '~%.1f%% (%.f-%.f%%)' % (100*f(x/n), math.floor(100*left), math.ceil(100*right))
148 return __builtin__.reversed(x)
150 return reversed(list(x))
152 class Object(object):
153 def __init__(self, **kwargs):
154 for k, v in kwargs.iteritems():
157 def add_tuples(res, *tuples):
159 if len(t) != len(res):
160 raise ValueError('tuples must all be the same length')
161 res = tuple(a + b for a, b in zip(res, t))
164 def flatten_linked_list(x):
169 def weighted_choice(choices):
170 choices = list((item, weight) for item, weight in choices)
171 target = random.randrange(sum(weight for item, weight in choices))
172 for item, weight in choices:
176 raise AssertionError()
178 def natural_to_string(n, alphabet=None):
180 raise TypeError('n must be a natural')
182 s = ('%x' % (n,)).lstrip('0')
185 return s.decode('hex')
187 assert len(set(alphabet)) == len(alphabet)
190 n, x = divmod(n, len(alphabet))
191 res.append(alphabet[x])
195 def string_to_natural(s, alphabet=None):
197 assert not s.startswith('\x00')
198 return int(s.encode('hex'), 16) if s else 0
200 assert len(set(alphabet)) == len(alphabet)
201 assert not s.startswith(alphabet[0])
202 return sum(alphabet.index(char) * len(alphabet)**i for i, char in enumerate(reversed(s)))
204 class RateMonitor(object):
205 def __init__(self, max_lookback_time):
206 self.max_lookback_time = max_lookback_time
209 self.first_timestamp = None
212 start_time = time.time() - self.max_lookback_time
213 for i, (ts, datum) in enumerate(self.datums):
215 self.datums[:] = self.datums[i:]
218 def get_datums_in_last(self, dt=None):
220 dt = self.max_lookback_time
221 assert dt <= self.max_lookback_time
224 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
226 def add_datum(self, datum):
229 if self.first_timestamp is None:
230 self.first_timestamp = t
232 self.datums.append((t, datum))
234 def merge_dicts(*dicts):
236 for d in dicts: res.update(d)