bpo-38308: Add optional weighting to statistics.harmonic_mean() (GH-23914)

Doc/library/statistics.rst

@@ -156,10 +156,11 @@ However, for reading convenience, most of the examples show sorted sequences.
    .. versionadded:: 3.8
 
 
-.. function:: harmonic_mean(data)
+.. function:: harmonic_mean(data, weights=None)
 
    Return the harmonic mean of *data*, a sequence or iterable of
-   real-valued numbers.
+   real-valued numbers.  If *weights* is omitted or *None*, then
+   equal weighting is assumed.
 
    The harmonic mean, sometimes called the subcontrary mean, is the
    reciprocal of the arithmetic :func:`mean` of the reciprocals of the
@@ -179,17 +180,17 @@ However, for reading convenience, most of the examples show sorted sequences.
       >>> harmonic_mean([40, 60])
       48.0
 
-   Suppose an investor purchases an equal value of shares in each of
+   Suppose a car travels 40 km/hr for 5 km, and when traffic clears,
-   three companies, with P/E (price/earning) ratios of 2.5, 3 and 10.
+   speeds-up to 60 km/hr for the remaining 30 km of the journey. What
-   What is the average P/E ratio for the investor's portfolio?
+   is the average speed?
 
    .. doctest::
 
-      >>> harmonic_mean([2.5, 3, 10])  # For an equal investment portfolio.
+      >>> harmonic_mean([40, 60], weights=[5, 30])
-      3.6
+      56.0
 
-   :exc:`StatisticsError` is raised if *data* is empty, or any element
+   :exc:`StatisticsError` is raised if *data* is empty, any element
-   is less than zero.
+   is less than zero, or if the weighted sum isn't positive.
 
    The current algorithm has an early-out when it encounters a zero
    in the input.  This means that the subsequent inputs are not tested
@@ -197,6 +198,8 @@ However, for reading convenience, most of the examples show sorted sequences.
 
    .. versionadded:: 3.6
 
+   .. versionchanged:: 3.8
+      Added support for *weights*.
 
 .. function:: median(data)
 

Lib/statistics.py

@@ -106,7 +106,7 @@ import random
 
 from fractions import Fraction
 from decimal import Decimal
-from itertools import groupby
+from itertools import groupby, repeat
 from bisect import bisect_left, bisect_right
 from math import hypot, sqrt, fabs, exp, erf, tau, log, fsum
 from operator import itemgetter
@@ -364,37 +364,37 @@ def geometric_mean(data):
                               ' containing positive numbers') from None
 
 
-def harmonic_mean(data):
+def harmonic_mean(data, weights=None):
     """Return the harmonic mean of data.
 
     The harmonic mean, sometimes called the subcontrary mean, is the
     reciprocal of the arithmetic mean of the reciprocals of the data,
     and is often appropriate when averaging quantities which are rates
-    or ratios, for example speeds. Example:
+    or ratios, for example speeds.
 
-    Suppose an investor purchases an equal value of shares in each of
+    Suppose a car travels 40 km/hr for 5 km and then speeds-up to
-    three companies, with P/E (price/earning) ratios of 2.5, 3 and 10.
+    60 km/hr for another 5 km. What is the average speed?
-    What is the average P/E ratio for the investor's portfolio?
 
-    >>> harmonic_mean([2.5, 3, 10])  # For an equal investment portfolio.
+        >>> harmonic_mean([40, 60])
-    3.6
+        48.0
 
-    Using the arithmetic mean would give an average of about 5.167, which
+    Suppose a car travels 40 km/hr for 5 km, and when traffic clears,
-    is too high.
+    speeds-up to 60 km/hr for the remaining 30 km of the journey. What
+    is the average speed?
+
+        >>> harmonic_mean([40, 60], weights=[5, 30])
+        56.0
 
     If ``data`` is empty, or any element is less than zero,
     ``harmonic_mean`` will raise ``StatisticsError``.
     """
-    # For a justification for using harmonic mean for P/E ratios, see
-    # http://fixthepitch.pellucid.com/comps-analysis-the-missing-harmony-of-summary-statistics/
-    # http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2621087
     if iter(data) is data:
         data = list(data)
     errmsg = 'harmonic mean does not support negative values'
     n = len(data)
     if n < 1:
         raise StatisticsError('harmonic_mean requires at least one data point')
-    elif n == 1:
+    elif n == 1 and weights is None:
         x = data[0]
         if isinstance(x, (numbers.Real, Decimal)):
             if x < 0:
@@ -402,13 +402,23 @@ def harmonic_mean(data):
             return x
         else:
             raise TypeError('unsupported type')
+    if weights is None:
+        weights = repeat(1, n)
+        sum_weights = n
+    else:
+        if iter(weights) is weights:
+            weights = list(weights)
+        if len(weights) != n:
+            raise StatisticsError('Number of weights does not match data size')
+        _, sum_weights, _ = _sum(w for w in _fail_neg(weights, errmsg))
     try:
-        T, total, count = _sum(1 / x for x in _fail_neg(data, errmsg))
+        data = _fail_neg(data, errmsg)
+        T, total, count = _sum(w / x if w else 0 for w, x in zip(weights, data))
     except ZeroDivisionError:
         return 0
-    assert count == n
+    if total <= 0:
-    return _convert(n / total, T)
+        raise StatisticsError('Weighted sum must be positive')
-
+    return _convert(sum_weights / total, T)
 
 # FIXME: investigate ways to calculate medians without sorting? Quickselect?
 def median(data):

Lib/test/test_statistics.py

@@ -1599,6 +1599,27 @@ class TestHarmonicMean(NumericTestCase, AverageMixin, UnivariateTypeMixin):
         actual = self.func(data*2)
         self.assertApproxEqual(actual, expected)
 
+    def test_with_weights(self):
+        self.assertEqual(self.func([40, 60], [5, 30]), 56.0)  # common case
+        self.assertEqual(self.func([40, 60],
+                                   weights=[5, 30]), 56.0)    # keyword argument
+        self.assertEqual(self.func(iter([40, 60]),
+                                   iter([5, 30])), 56.0)      # iterator inputs
+        self.assertEqual(
+            self.func([Fraction(10, 3), Fraction(23, 5), Fraction(7, 2)], [5, 2, 10]),
+            self.func([Fraction(10, 3)] * 5 +
+                      [Fraction(23, 5)] * 2 +
+                      [Fraction(7, 2)] * 10))
+        self.assertEqual(self.func([10], [7]), 10)            # n=1 fast path
+        with self.assertRaises(TypeError):
+            self.func([1, 2, 3], [1, (), 3])                  # non-numeric weight
+        with self.assertRaises(statistics.StatisticsError):
+            self.func([1, 2, 3], [1, 2])                      # wrong number of weights
+        with self.assertRaises(statistics.StatisticsError):
+            self.func([10], [0])                              # no non-zero weights
+        with self.assertRaises(statistics.StatisticsError):
+            self.func([10, 20], [0, 0])                       # no non-zero weights
+
 
 class TestMedian(NumericTestCase, AverageMixin):
     # Common tests for median and all median.* functions.

Misc/NEWS.d/next/Library/2020-12-23-15-16-12.bpo-38308.lB4Sv0.rst

@@ -0,0 +1 @@
+Add optional *weights* to *statistics.harmonic_mean()*.