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 [(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)
126 from scipy import special
128 def binomial_conf_interval(x, n, conf=0.95):
129 assert 0 <= x <= n and 0 <= conf < 1
131 left = random.random()*(1 - conf)
132 return left, left + conf
133 # approximate - Wilson score interval
134 z = math.sqrt(2)*ierf(conf)
137 topb = z * math.sqrt(p*(1-p)/n + z**2/4/n**2)
139 return [clip(x, (0, 1)) for x in add_to_range(x/n, [(topa - topb)/bottom, (topa + topb)/bottom])]
141 def binomial_conf_interval(x, n, conf=0.95):
142 assert 0 <= x <= n and 0 <= conf < 1
144 left = random.random()*(1 - conf)
145 return left, left + conf
146 bl = float(special.betaln(x+1, n-x+1))
148 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)))
149 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)
150 bottom = (x - n*right)*left*(1-left) - (x - n*left)*right*(1-right)
152 left_a = find_root(f, (1-conf)/2, bounds=(0, 1-conf))
153 return float(special.betaincinv(x+1, n-x+1, left_a)), float(special.betaincinv(x+1, n-x+1, left_a + conf))
155 minmax = lambda x: (min(x), max(x))
157 def format_binomial_conf(x, n, conf=0.95, f=lambda x: x):
160 left, right = minmax(map(f, binomial_conf_interval(x, n, conf)))
161 return '~%.1f%% (%.f-%.f%%)' % (100*f(x/n), math.floor(100*left), math.ceil(100*right))
165 return __builtin__.reversed(x)
167 return reversed(list(x))
169 class Object(object):
170 def __init__(self, **kwargs):
171 for k, v in kwargs.iteritems():
174 def add_tuples(res, *tuples):
176 if len(t) != len(res):
177 raise ValueError('tuples must all be the same length')
178 res = tuple(a + b for a, b in zip(res, t))
181 def flatten_linked_list(x):
186 def weighted_choice(choices):
187 choices = list((item, weight) for item, weight in choices)
188 target = random.randrange(sum(weight for item, weight in choices))
189 for item, weight in choices:
193 raise AssertionError()
195 def natural_to_string(n, alphabet=None):
197 raise TypeError('n must be a natural')
202 return s.decode('hex')
204 assert len(set(alphabet)) == len(alphabet)
207 n, x = divmod(n, len(alphabet))
208 res.append(alphabet[x])
212 def string_to_natural(s, alphabet=None):
214 assert not s.startswith('\x00')
215 return int(s.encode('hex'), 16) if s else 0
217 assert len(set(alphabet)) == len(alphabet)
218 assert not s.startswith(alphabet[0])
219 return sum(alphabet.index(char) * len(alphabet)**i for i, char in enumerate(reversed(s)))
221 class RateMonitor(object):
222 def __init__(self, max_lookback_time):
223 self.max_lookback_time = max_lookback_time
226 self.first_timestamp = None
229 start_time = time.time() - self.max_lookback_time
230 for i, (ts, datum) in enumerate(self.datums):
232 self.datums[:] = self.datums[i:]
235 def get_datums_in_last(self, dt=None):
237 dt = self.max_lookback_time
238 assert dt <= self.max_lookback_time
241 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
243 def add_datum(self, datum):
246 self.datums.append((t, datum))
247 if self.first_timestamp is None:
248 self.first_timestamp = t
250 if __name__ == '__main__':
254 print a, format(a) + 'H/s'
255 a = a * random.randrange(2, 5)