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)):
56 raise ValueError('p must be in the interval (0.0, 1.0]')
59 return int(math.log1p(-random.random()) / math.log1p(-p)) + 1
61 def add_dicts(*dicts):
64 for k, v in d.iteritems():
65 res[k] = res.get(k, 0) + v
66 return dict((k, v) for k, v in res.iteritems() if v)
68 mult_dict = lambda c, x: dict((k, c*v) for k, v in x.iteritems())
73 while x >= 100000 and count < len(prefixes) - 2:
76 s = '' if count == 0 else prefixes[count - 1]
77 return '%i' % (x,) + s
80 for value, name in [(60*60*24, 'days'), (60*60, 'hours'), (60, 'minutes'), (1, 'seconds')]:
83 return '%.01f %s' % (dt/value, name)
85 perfect_round = lambda x: int(x + random.random())
104 y = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*math.exp(-x*x)
105 return sign*y # erf(-x) = -erf(x)
107 def find_root(y_over_dy, start, steps=10, bounds=(None, None)):
109 for i in xrange(steps):
110 prev, guess = guess, guess - y_over_dy(guess)
111 if bounds[0] is not None and guess < bounds[0]: guess = bounds[0]
112 if bounds[1] is not None and guess > bounds[1]: guess = bounds[1]
118 return find_root(lambda x: (erf(x) - z)/(2*math.e**(-x**2)/math.sqrt(math.pi)), 0)
121 from scipy import special
123 def binomial_conf_interval(x, n, conf=0.95):
124 assert 0 <= x <= n and 0 <= conf < 1
126 left = random.random()*(1 - conf)
127 return left, left + conf
128 # approximate - Wilson score interval
129 z = math.sqrt(2)*ierf(conf)
132 topb = z * math.sqrt(p*(1-p)/n + z**2/4/n**2)
134 return (topa - topb)/bottom, (topa + topb)/bottom
136 def binomial_conf_interval(x, n, conf=0.95):
137 assert 0 <= x <= n and 0 <= conf < 1
139 left = random.random()*(1 - conf)
140 return left, left + conf
141 bl = float(special.betaln(x+1, n-x+1))
143 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)))
144 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)
145 bottom = (x - n*right)*left*(1-left) - (x - n*left)*right*(1-right)
147 left_a = find_root(f, (1-conf)/2, bounds=(0, 1-conf))
148 return float(special.betaincinv(x+1, n-x+1, left_a)), float(special.betaincinv(x+1, n-x+1, left_a + conf))
150 minmax = lambda x: (min(x), max(x))
152 def format_binomial_conf(x, n, conf=0.95, f=lambda x: x):
155 left, right = minmax(map(f, binomial_conf_interval(x, n, conf)))
156 return '~%.1f%% (%.f-%.f%%)' % (100*f(x/n), math.floor(100*left), math.ceil(100*right))
160 return __builtin__.reversed(x)
162 return reversed(list(x))
164 class Object(object):
165 def __init__(self, **kwargs):
166 for k, v in kwargs.iteritems():
169 def add_tuples(res, *tuples):
171 if len(t) != len(res):
172 raise ValueError('tuples must all be the same length')
173 res = tuple(a + b for a, b in zip(res, t))
176 def flatten_linked_list(x):
181 def weighted_choice(choices):
182 choices = list((item, weight) for item, weight in choices)
183 target = random.randrange(sum(weight for item, weight in choices))
184 for item, weight in choices:
188 raise AssertionError()
190 def natural_to_string(n, alphabet=None):
192 raise TypeError('n must be a natural')
197 return s.decode('hex')
199 assert len(set(alphabet)) == len(alphabet)
202 n, x = divmod(n, len(alphabet))
203 res.append(alphabet[x])
207 def string_to_natural(s, alphabet=None):
209 assert not s.startswith('\x00')
210 return int(s.encode('hex'), 16) if s else 0
212 assert len(set(alphabet)) == len(alphabet)
213 assert not s.startswith(alphabet[0])
214 return sum(alphabet.index(char) * len(alphabet)**i for i, char in enumerate(reversed(s)))
216 class RateMonitor(object):
217 def __init__(self, max_lookback_time):
218 self.max_lookback_time = max_lookback_time
221 self.first_timestamp = None
224 start_time = time.time() - self.max_lookback_time
225 for i, (ts, datum) in enumerate(self.datums):
227 self.datums[:] = self.datums[i:]
230 def get_datums_in_last(self, dt=None):
232 dt = self.max_lookback_time
233 assert dt <= self.max_lookback_time
236 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
238 def add_datum(self, datum):
241 self.datums.append((t, datum))
242 if self.first_timestamp is None:
243 self.first_timestamp = t
245 if __name__ == '__main__':
249 print a, format(a) + 'H/s'
250 a = a * random.randrange(2, 5)