X-Git-Url: https://wannabe.guru.org/gitweb/?a=blobdiff_plain;f=math_utils.py;h=31610ba5fd2a0726b5b1f151dc87cc362b7389d4;hb=f2600f30801c849fc1d139386e3ddc3c9eb43e30;hp=e0e3f6c10732b9a3ab20a251a225a0e963c362e9;hpb=eb9e6df32ed696158bf34dba6464277b648f5c74;p=python_utils.git

diff --git a/math_utils.py b/math_utils.py
index e0e3f6c..31610ba 100644
--- a/math_utils.py
+++ b/math_utils.py
@@ -1,50 +1,110 @@
 #!/usr/bin/env python3
 
+"""Mathematical helpers."""
+
 import functools
 import math
-from typing import List
-from heapq import heappush, heappop
+from heapq import heappop, heappush
+from typing import List, Optional
 
 
-class RunningMedian(object):
-    """A running median computer.
+class NumericPopulation(object):
+    """A numeric population with some statistics such as median, mean, pN,
+    stdev, etc...
 
-    >>> median = RunningMedian()
-    >>> median.add_number(1)
-    >>> median.add_number(10)
-    >>> median.add_number(3)
-    >>> median.get_median()
+    >>> pop = NumericPopulation()
+    >>> pop.add_number(1)
+    >>> pop.add_number(10)
+    >>> pop.add_number(3)
+    >>> pop.get_median()
     3
-    >>> median.add_number(7)
-    >>> median.add_number(5)
-    >>> median.get_median()
+    >>> pop.add_number(7)
+    >>> pop.add_number(5)
+    >>> pop.get_median()
     5
+    >>> pop.get_mean()
+    5.2
+    >>> round(pop.get_stdev(), 2)
+    6.99
+    >>> pop.get_percentile(20)
+    3
+    >>> pop.get_percentile(60)
+    7
+
     """
 
     def __init__(self):
         self.lowers, self.highers = [], []
+        self.aggregate = 0.0
+        self.sorted_copy: Optional[List[float]] = None
+
+    def add_number(self, number: float):
+        """O(2 log2 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()
+        self.aggregate += number
+        self._rebalance()
 
-    def rebalance(self):
+    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_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
+        return math.sqrt(variance)
+
+    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 (expensive, requires a
+        complete sort).  Not thread safe.  Caching does across
+        multiple calls without an invocation to add_number.
+
+        """
+        if n == 50:
+            return self.get_median()
+        count = len(self.lowers) + len(self.highers)
+        if self.sorted_copy is not None:
+            if count == len(self.sorted_copy):
+                index = round(count * (n / 100.0))
+                assert 0 <= index < count
+                return self.sorted_copy[index]
+        self.sorted_copy = [-x for x in self.lowers]
+        for x in self.highers:
+            self.sorted_copy.append(x)
+        self.sorted_copy = sorted(self.sorted_copy)
+        index = round(count * (n / 100.0))
+        assert 0 <= index < count
+        return self.sorted_copy[index]
+
 
 def gcd_floats(a: float, b: float) -> float:
     if a < b:
@@ -76,8 +136,8 @@ def truncate_float(n: float, decimals: int = 2):
     3.141
 
     """
-    assert decimals > 0 and decimals < 10
-    multiplier = 10 ** decimals
+    assert 0 < decimals < 10
+    multiplier = 10**decimals
     return int(n * multiplier) / multiplier
 
 
@@ -143,12 +203,12 @@ def is_prime(n: int) -> bool:
 
     # 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
@@ -156,4 +216,5 @@ def is_prime(n: int) -> bool:
 
 if __name__ == '__main__':
     import doctest
+
     doctest.testmod()