3 # © Copyright 2021-2022, Scott Gasch
5 """Mathematical helpers."""
10 from heapq import heappop, heappush
11 from typing import Dict, List, Optional, Tuple
13 from pyutils import dict_utils
16 class NumericPopulation(object):
17 """A numeric population with some statistics such as median, mean, pN,
20 >>> pop = NumericPopulation()
22 >>> pop.add_number(10)
32 >>> round(pop.get_stdev(), 1)
34 >>> pop.get_percentile(20)
36 >>> pop.get_percentile(60)
41 self.lowers, self.highers = [], []
43 self.sorted_copy: Optional[List[float]] = None
47 def add_number(self, number: float):
48 """Adds a number to the population. Runtime complexity of this
49 operation is :math:`O(2 log_2 n)`"""
51 if not self.highers or number > self.highers[0]:
52 heappush(self.highers, number)
54 heappush(self.lowers, -number) # for lowers we need a max heap
55 self.aggregate += number
57 if not self.maximum or number > self.maximum:
59 if not self.minimum or number < self.minimum:
63 if len(self.lowers) - len(self.highers) > 1:
64 heappush(self.highers, -heappop(self.lowers))
65 elif len(self.highers) - len(self.lowers) > 1:
66 heappush(self.lowers, -heappop(self.highers))
68 def get_median(self) -> float:
69 """Returns the approximate median (p50) so far in O(1) time."""
71 if len(self.lowers) == len(self.highers):
72 return -self.lowers[0]
73 elif len(self.lowers) > len(self.highers):
74 return -self.lowers[0]
76 return self.highers[0]
78 def get_mean(self) -> float:
79 """Returns the mean (arithmetic mean) so far in O(1) time."""
81 count = len(self.lowers) + len(self.highers)
82 return self.aggregate / count
84 def get_mode(self) -> Tuple[float, int]:
85 """Returns the mode (most common member in the population)
88 count: Dict[float, int] = collections.defaultdict(int)
91 for n in self.highers:
93 return dict_utils.item_with_max_value(count)
95 def get_stdev(self) -> float:
96 """Returns the stdev so far in O(n) time."""
98 mean = self.get_mean()
100 for n in self.lowers:
102 variance += (n - mean) ** 2
103 for n in self.highers:
104 variance += (n - mean) ** 2
105 count = len(self.lowers) + len(self.highers)
106 return math.sqrt(variance) / count
108 def _create_sorted_copy_if_needed(self, count: int):
109 if not self.sorted_copy or count != len(self.sorted_copy):
110 self.sorted_copy = []
111 for x in self.lowers:
112 self.sorted_copy.append(-x)
113 for x in self.highers:
114 self.sorted_copy.append(x)
115 self.sorted_copy = sorted(self.sorted_copy)
117 def get_percentile(self, n: float) -> float:
118 """Returns the number at approximately pn% (i.e. the nth percentile)
119 of the distribution in O(n log n) time. Not thread-safe;
120 does caching across multiple calls without an invocation to
121 add_number for perf reasons.
124 return self.get_median()
125 count = len(self.lowers) + len(self.highers)
126 self._create_sorted_copy_if_needed(count)
127 assert self.sorted_copy
128 index = round(count * (n / 100.0))
129 index = max(0, index)
130 index = min(count - 1, index)
131 return self.sorted_copy[index]
134 def gcd_floats(a: float, b: float) -> float:
135 """Returns the greatest common divisor of a and b."""
137 return gcd_floats(b, a)
142 return gcd_floats(b, a - math.floor(a / b) * b)
145 def gcd_float_sequence(lst: List[float]) -> float:
146 """Returns the greatest common divisor of a list of floats."""
148 raise ValueError("Need at least one number")
152 gcd = gcd_floats(lst[0], lst[1])
153 for i in range(2, len(lst)):
154 gcd = gcd_floats(gcd, lst[i])
158 def truncate_float(n: float, decimals: int = 2):
159 """Truncate a float to a particular number of decimals.
161 >>> truncate_float(3.1415927, 3)
165 assert 0 < decimals < 10
166 multiplier = 10**decimals
167 return int(n * multiplier) / multiplier
170 def percentage_to_multiplier(percent: float) -> float:
171 """Given a percentage (e.g. 155%), return a factor needed to scale a
172 number by that percentage.
174 >>> percentage_to_multiplier(155)
176 >>> percentage_to_multiplier(45)
178 >>> percentage_to_multiplier(-25)
181 multiplier = percent / 100
186 def multiplier_to_percent(multiplier: float) -> float:
187 """Convert a multiplicative factor into a percent change.
189 >>> multiplier_to_percent(0.75)
191 >>> multiplier_to_percent(1.0)
193 >>> multiplier_to_percent(1.99)
200 percent = 1.0 - percent
205 @functools.lru_cache(maxsize=1024, typed=True)
206 def is_prime(n: int) -> bool:
208 Returns True if n is prime and False otherwise. Obviously(?) very slow for
209 very large input numbers.
215 >>> is_prime(51602981)
218 if not isinstance(n, int):
219 raise TypeError("argument passed to is_prime is not of 'int' type")
227 # This is checked so that we can skip middle five numbers in below
229 if n % 2 == 0 or n % 3 == 0:
234 if n % i == 0 or n % (i + 2) == 0:
240 if __name__ == '__main__':