1 from __future__ import absolute_import, division
7 def median(x, use_float=True):
8 # there exist better algorithms...
11 raise ValueError('empty sequence!')
12 left = (len(y) - 1)//2
14 sum = y[left] + y[right]
39 def clip(x, (low, high)):
55 raise ValueError('p must be in the interval (0.0, 1.0]')
58 return int(math.log1p(-random.random()) / math.log1p(-p)) + 1
60 def add_dicts(*dicts):
63 for k, v in d.iteritems():
64 res[k] = res.get(k, 0) + v
65 return dict((k, v) for k, v in res.iteritems() if v)
70 while x >= 100000 and count < len(prefixes) - 2:
73 s = '' if count == 0 else prefixes[count - 1]
74 return '%i' % (x,) + s
76 perfect_round = lambda x: int(x + random.random())
95 y = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*math.exp(-x*x)
96 return sign*y # erf(-x) = -erf(x)
98 def find_root(f, fp, start, steps=10):
100 for i in xrange(steps):
102 guess = guess - f(guess)/d
106 return find_root(lambda x: erf(x) - z, lambda guess: 2*math.e**(-guess**2)/math.sqrt(math.pi), 0)
109 from scipy import special
111 print 'Install SciPy for more accurate confidence intervals!'
112 def binomial_conf_interval(x, n, conf=0.95):
114 return (1-conf)/2, 1-(1-conf)/2
115 # approximate - Wilson score interval
116 z = math.sqrt(2)*ierf(conf)
119 topb = z * math.sqrt(p*(1-p)/n + z**2/4/n**2)
121 return (topa - topb)/bottom, (topa + topb)/bottom
123 def binomial_conf_interval(x, n, conf=0.95):
124 return special.betaincinv(x+1, n-x+1, (1-conf)/2), special.betaincinv(x+1, n-x+1, 1-(1-conf)/2)
126 def binomial_conf_center_radius(x, n, conf=0.95):
127 left, right = binomial_conf_interval(x, n, conf)
129 return (left+right)/2, (right-left)/2
131 return p, max(p - left, right - p)
135 return __builtin__.reversed(x)
137 return reversed(list(x))
139 class Object(object):
140 def __init__(self, **kwargs):
141 for k, v in kwargs.iteritems():
144 def add_tuples(res, *tuples):
146 if len(t) != len(res):
147 raise ValueError('tuples must all be the same length')
148 res = tuple(a + b for a, b in zip(res, t))
151 def flatten_linked_list(x):
156 def weighted_choice(choices):
157 choices = list((item, weight) for item, weight in choices)
158 target = random.randrange(sum(weight for item, weight in choices))
159 for item, weight in choices:
163 raise AssertionError()
165 if __name__ == '__main__':
169 print a, format(a) + 'H/s'
170 a = a * random.randrange(2, 5)