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(*dicts):
66 for k, v in d.iteritems():
67 res[k] = res.get(k, 0) + v
68 return dict((k, v) for k, v in res.iteritems() if v)
70 mult_dict = lambda c, x: dict((k, c*v) for k, v in x.iteritems())
75 while x >= 100000 and count < len(prefixes) - 2:
78 s = '' if count == 0 else prefixes[count - 1]
79 return '%i' % (x,) + s
82 for value, name in [(60*60*24, 'days'), (60*60, 'hours'), (60, 'minutes'), (1, 'seconds')]:
85 return '%.01f %s' % (dt/value, name)
87 perfect_round = lambda x: int(x + random.random())
106 y = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*math.exp(-x*x)
107 return sign*y # erf(-x) = -erf(x)
109 def find_root(y_over_dy, start, steps=10, bounds=(None, None)):
111 for i in xrange(steps):
112 prev, guess = guess, guess - y_over_dy(guess)
113 if bounds[0] is not None and guess < bounds[0]: guess = bounds[0]
114 if bounds[1] is not None and guess > bounds[1]: guess = bounds[1]
120 return find_root(lambda x: (erf(x) - z)/(2*math.e**(-x**2)/math.sqrt(math.pi)), 0)
123 from scipy import special
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 def binomial_conf_interval(x, n, conf=0.95):
139 assert 0 <= x <= n and 0 <= conf < 1
141 left = random.random()*(1 - conf)
142 return left, left + conf
143 bl = float(special.betaln(x+1, n-x+1))
145 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)))
146 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)
147 bottom = (x - n*right)*left*(1-left) - (x - n*left)*right*(1-right)
149 left_a = find_root(f, (1-conf)/2, bounds=(0, 1-conf))
150 return float(special.betaincinv(x+1, n-x+1, left_a)), float(special.betaincinv(x+1, n-x+1, left_a + conf))
152 minmax = lambda x: (min(x), max(x))
154 def format_binomial_conf(x, n, conf=0.95, f=lambda x: x):
157 left, right = minmax(map(f, binomial_conf_interval(x, n, conf)))
158 return '~%.1f%% (%.f-%.f%%)' % (100*f(x/n), math.floor(100*left), math.ceil(100*right))
162 return __builtin__.reversed(x)
164 return reversed(list(x))
166 class Object(object):
167 def __init__(self, **kwargs):
168 for k, v in kwargs.iteritems():
171 def add_tuples(res, *tuples):
173 if len(t) != len(res):
174 raise ValueError('tuples must all be the same length')
175 res = tuple(a + b for a, b in zip(res, t))
178 def flatten_linked_list(x):
183 def weighted_choice(choices):
184 choices = list((item, weight) for item, weight in choices)
185 target = random.randrange(sum(weight for item, weight in choices))
186 for item, weight in choices:
190 raise AssertionError()
192 def natural_to_string(n, alphabet=None):
194 raise TypeError('n must be a natural')
199 return s.decode('hex')
201 assert len(set(alphabet)) == len(alphabet)
204 n, x = divmod(n, len(alphabet))
205 res.append(alphabet[x])
209 def string_to_natural(s, alphabet=None):
211 assert not s.startswith('\x00')
212 return int(s.encode('hex'), 16) if s else 0
214 assert len(set(alphabet)) == len(alphabet)
215 assert not s.startswith(alphabet[0])
216 return sum(alphabet.index(char) * len(alphabet)**i for i, char in enumerate(reversed(s)))
218 class RateMonitor(object):
219 def __init__(self, max_lookback_time):
220 self.max_lookback_time = max_lookback_time
223 self.first_timestamp = None
226 start_time = time.time() - self.max_lookback_time
227 for i, (ts, datum) in enumerate(self.datums):
229 self.datums[:] = self.datums[i:]
232 def get_datums_in_last(self, dt=None):
234 dt = self.max_lookback_time
235 assert dt <= self.max_lookback_time
238 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
240 def add_datum(self, datum):
243 self.datums.append((t, datum))
244 if self.first_timestamp is None:
245 self.first_timestamp = t
247 if __name__ == '__main__':
251 print a, format(a) + 'H/s'
252 a = a * random.randrange(2, 5)