3 """Mathematical helpers."""
8 from heapq import heappop, heappush
9 from typing import Dict, List, Optional, Tuple
14 class NumericPopulation(object):
15 """A numeric population with some statistics such as median, mean, pN,
18 >>> pop = NumericPopulation()
20 >>> pop.add_number(10)
30 >>> round(pop.get_stdev(), 2)
32 >>> pop.get_percentile(20)
34 >>> pop.get_percentile(60)
40 self.lowers, self.highers = [], []
42 self.sorted_copy: Optional[List[float]] = None
44 def add_number(self, number: float):
47 if not self.highers or number > self.highers[0]:
48 heappush(self.highers, number)
50 heappush(self.lowers, -number) # for lowers we need a max heap
51 self.aggregate += number
55 if len(self.lowers) - len(self.highers) > 1:
56 heappush(self.highers, -heappop(self.lowers))
57 elif len(self.highers) - len(self.lowers) > 1:
58 heappush(self.lowers, -heappop(self.highers))
60 def get_median(self) -> float:
61 """Returns the approximate median (p50) so far in O(1) time."""
63 if len(self.lowers) == len(self.highers):
64 return -self.lowers[0]
65 elif len(self.lowers) > len(self.highers):
66 return -self.lowers[0]
68 return self.highers[0]
70 def get_mean(self) -> float:
71 """Returns the mean (arithmetic mean) so far in O(1) time."""
73 count = len(self.lowers) + len(self.highers)
74 return self.aggregate / count
76 def get_mode(self) -> Tuple[float, int]:
77 """Returns the mode (most common member)."""
79 count: Dict[float, int] = collections.defaultdict(int)
82 for n in self.highers:
84 return dict_utils.item_with_max_value(count)
86 def get_stdev(self) -> float:
87 """Returns the stdev so far in O(n) time."""
89 mean = self.get_mean()
93 variance += (n - mean) ** 2
94 for n in self.highers:
95 variance += (n - mean) ** 2
96 count = len(self.lowers) + len(self.highers) - 1
97 return math.sqrt(variance) / count
99 def get_percentile(self, n: float) -> float:
100 """Returns the number at approximately pn% (i.e. the nth percentile)
101 of the distribution in O(n log n) time (expensive, requires a
102 complete sort). Not thread safe. Caching does across
103 multiple calls without an invocation to add_number.
107 return self.get_median()
108 count = len(self.lowers) + len(self.highers)
109 if self.sorted_copy is not None:
110 if count == len(self.sorted_copy):
111 index = round(count * (n / 100.0))
112 assert 0 <= index < count
113 return self.sorted_copy[index]
114 self.sorted_copy = [-x for x in self.lowers]
115 for x in self.highers:
116 self.sorted_copy.append(x)
117 self.sorted_copy = sorted(self.sorted_copy)
118 index = round(count * (n / 100.0))
119 assert 0 <= index < count
120 return self.sorted_copy[index]
123 def gcd_floats(a: float, b: float) -> float:
125 return gcd_floats(b, a)
130 return gcd_floats(b, a - math.floor(a / b) * b)
133 def gcd_float_sequence(lst: List[float]) -> float:
135 raise ValueError("Need at least one number")
139 gcd = gcd_floats(lst[0], lst[1])
140 for i in range(2, len(lst)):
141 gcd = gcd_floats(gcd, lst[i])
145 def truncate_float(n: float, decimals: int = 2):
147 Truncate a float to a particular number of decimals.
149 >>> truncate_float(3.1415927, 3)
153 assert 0 < decimals < 10
154 multiplier = 10**decimals
155 return int(n * multiplier) / multiplier
158 def percentage_to_multiplier(percent: float) -> float:
159 """Given a percentage (e.g. 155%), return a factor needed to scale a
160 number by that percentage.
162 >>> percentage_to_multiplier(155)
164 >>> percentage_to_multiplier(45)
166 >>> percentage_to_multiplier(-25)
170 multiplier = percent / 100
175 def multiplier_to_percent(multiplier: float) -> float:
176 """Convert a multiplicative factor into a percent change.
178 >>> multiplier_to_percent(0.75)
180 >>> multiplier_to_percent(1.0)
182 >>> multiplier_to_percent(1.99)
190 percent = 1.0 - percent
195 @functools.lru_cache(maxsize=1024, typed=True)
196 def is_prime(n: int) -> bool:
198 Returns True if n is prime and False otherwise. Obviously(?) very slow for
199 very large input numbers.
205 >>> is_prime(51602981)
209 if not isinstance(n, int):
210 raise TypeError("argument passed to is_prime is not of 'int' type")
218 # This is checked so that we can skip middle five numbers in below
220 if n % 2 == 0 or n % 3 == 0:
225 if n % i == 0 or n % (i + 2) == 0:
231 if __name__ == '__main__':