#!/usr/bin/env python3
-import math
-from typing import List
-from heapq import heappush, heappop
+# © Copyright 2021-2022, Scott Gasch
+
+"""Mathematical helpers."""
+import collections
+import functools
+import math
+from heapq import heappop, heappush
+from typing import Dict, List, Optional, Tuple
+
+import dict_utils
+
+
+class NumericPopulation(object):
+ """A numeric population with some statistics such as median, mean, pN,
+ stdev, etc...
+
+ >>> pop = NumericPopulation()
+ >>> pop.add_number(1)
+ >>> pop.add_number(10)
+ >>> pop.add_number(3)
+ >>> pop.get_median()
+ 3
+ >>> pop.add_number(7)
+ >>> pop.add_number(5)
+ >>> pop.get_median()
+ 5
+ >>> pop.get_mean()
+ 5.2
+ >>> round(pop.get_stdev(), 2)
+ 1.75
+ >>> pop.get_percentile(20)
+ 3
+ >>> pop.get_percentile(60)
+ 7
+ """
-class RunningMedian:
def __init__(self):
self.lowers, self.highers = [], []
+ self.aggregate = 0.0
+ self.sorted_copy: Optional[List[float]] = None
+ self.maximum = None
+ self.minimum = None
+
+ def add_number(self, number: float):
+ """Adds a number to the population. Runtime complexity of this
+ operation is :math:`O(2 log_2 n)`"""
- def add_number(self, number):
if not self.highers or number > self.highers[0]:
heappush(self.highers, number)
else:
heappush(self.lowers, -number) # for lowers we need a max heap
- self.rebalance()
-
- def rebalance(self):
+ self.aggregate += number
+ self._rebalance()
+ if not self.maximum or number > self.maximum:
+ self.maximum = number
+ if not self.minimum or number < self.minimum:
+ self.minimum = number
+
+ def _rebalance(self):
if len(self.lowers) - len(self.highers) > 1:
heappush(self.highers, -heappop(self.lowers))
elif len(self.highers) - len(self.lowers) > 1:
heappush(self.lowers, -heappop(self.highers))
- def get_median(self):
+ def get_median(self) -> float:
+ """Returns the approximate median (p50) so far in O(1) time."""
+
if len(self.lowers) == len(self.highers):
- return (-self.lowers[0] + self.highers[0])/2
+ return -self.lowers[0]
elif len(self.lowers) > len(self.highers):
return -self.lowers[0]
else:
return self.highers[0]
+ def get_mean(self) -> float:
+ """Returns the mean (arithmetic mean) so far in O(1) time."""
+
+ count = len(self.lowers) + len(self.highers)
+ return self.aggregate / count
+
+ def get_mode(self) -> Tuple[float, int]:
+ """Returns the mode (most common member in the population)
+ in O(n) time."""
+
+ count: Dict[float, int] = collections.defaultdict(int)
+ for n in self.lowers:
+ count[-n] += 1
+ for n in self.highers:
+ count[n] += 1
+ return dict_utils.item_with_max_value(count)
+
+ def get_stdev(self) -> float:
+ """Returns the stdev so far in O(n) time."""
+
+ mean = self.get_mean()
+ variance = 0.0
+ for n in self.lowers:
+ n = -n
+ variance += (n - mean) ** 2
+ for n in self.highers:
+ variance += (n - mean) ** 2
+ count = len(self.lowers) + len(self.highers)
+ return math.sqrt(variance) / count
+
+ def _create_sorted_copy_if_needed(self, count: int):
+ if not self.sorted_copy or count != len(self.sorted_copy):
+ self.sorted_copy = []
+ for x in self.lowers:
+ self.sorted_copy.append(-x)
+ for x in self.highers:
+ self.sorted_copy.append(x)
+ self.sorted_copy = sorted(self.sorted_copy)
+
+ def get_percentile(self, n: float) -> float:
+ """Returns the number at approximately pn% (i.e. the nth percentile)
+ of the distribution in O(n log n) time. Not thread-safe;
+ does caching across multiple calls without an invocation to
+ add_number for perf reasons.
+ """
+ if n == 50:
+ return self.get_median()
+ count = len(self.lowers) + len(self.highers)
+ self._create_sorted_copy_if_needed(count)
+ assert self.sorted_copy
+ index = round(count * (n / 100.0))
+ index = max(0, index)
+ index = min(count - 1, index)
+ return self.sorted_copy[index]
+
def gcd_floats(a: float, b: float) -> float:
+ """Returns the greatest common divisor of a and b."""
if a < b:
return gcd_floats(b, a)
def gcd_float_sequence(lst: List[float]) -> float:
+ """Returns the greatest common divisor of a list of floats."""
if len(lst) <= 0:
raise ValueError("Need at least one number")
elif len(lst) == 1:
def truncate_float(n: float, decimals: int = 2):
- """Truncate a float to a particular number of decimals."""
- assert decimals > 0 and decimals < 10
- multiplier = 10 ** decimals
+ """Truncate a float to a particular number of decimals.
+
+ >>> truncate_float(3.1415927, 3)
+ 3.141
+
+ """
+ assert 0 < decimals < 10
+ multiplier = 10**decimals
return int(n * multiplier) / multiplier
+def percentage_to_multiplier(percent: float) -> float:
+ """Given a percentage (e.g. 155%), return a factor needed to scale a
+ number by that percentage.
+
+ >>> percentage_to_multiplier(155)
+ 2.55
+ >>> percentage_to_multiplier(45)
+ 1.45
+ >>> percentage_to_multiplier(-25)
+ 0.75
+ """
+ multiplier = percent / 100
+ multiplier += 1.0
+ return multiplier
+
+
+def multiplier_to_percent(multiplier: float) -> float:
+ """Convert a multiplicative factor into a percent change.
+
+ >>> multiplier_to_percent(0.75)
+ -25.0
+ >>> multiplier_to_percent(1.0)
+ 0.0
+ >>> multiplier_to_percent(1.99)
+ 99.0
+ """
+ percent = multiplier
+ if percent > 0.0:
+ percent -= 1.0
+ else:
+ percent = 1.0 - percent
+ percent *= 100.0
+ return percent
+
+
def is_prime(n: int) -> bool:
- """Returns True if n is prime and False otherwise"""
+ """
+ Returns True if n is prime and False otherwise. Obviously(?) very slow for
+ very large input numbers.
+
+ >>> is_prime(13)
+ True
+ >>> is_prime(22)
+ False
+ >>> is_prime(51602981)
+ True
+ """
if not isinstance(n, int):
raise TypeError("argument passed to is_prime is not of 'int' type")
# This is checked so that we can skip middle five numbers in below
# loop
- if (n % 2 == 0 or n % 3 == 0):
+ if n % 2 == 0 or n % 3 == 0:
return False
i = 5
while i * i <= n:
- if (n % i == 0 or n % (i + 2) == 0):
+ if n % i == 0 or n % (i + 2) == 0:
return False
i = i + 6
return True
+
+
+if __name__ == '__main__':
+ import doctest
+
+ doctest.testmod()
projects / python_utils.git / blobdiff