bpo-36546: Add statistics.quantiles() (#12710)

1 files changed, 142 insertions, 0 deletions

diff --git a/Lib/test/test_statistics.py b/Lib/test/test_statistics.py
index 4d397eb..c988d7f 100644
--- a/Lib/test/test_statistics.py
+++ b/Lib/test/test_statistics.py
@@ -3,6 +3,7 @@ approx_equal function.
 
 """
 
+import bisect
 import collections
 import collections.abc
 import copy
@@ -2038,6 +2039,7 @@ class TestStdev(VarianceStdevMixin, NumericTestCase):
         expected = math.sqrt(statistics.variance(data))
         self.assertEqual(self.func(data), expected)
 
+
 class TestGeometricMean(unittest.TestCase):
 
     def test_basics(self):
@@ -2126,6 +2128,146 @@ class TestGeometricMean(unittest.TestCase):
         with self.assertRaises(ValueError):
             geometric_mean([Inf, -Inf])
 
+
+class TestQuantiles(unittest.TestCase):
+
+    def test_specific_cases(self):
+        # Match results computed by hand and cross-checked
+        # against the PERCENTILE.EXC function in MS Excel.
+        quantiles = statistics.quantiles
+        data = [120, 200, 250, 320, 350]
+        random.shuffle(data)
+        for n, expected in [
+            (1, []),
+            (2, [250.0]),
+            (3, [200.0, 320.0]),
+            (4, [160.0, 250.0, 335.0]),
+            (5, [136.0, 220.0, 292.0, 344.0]),
+            (6, [120.0, 200.0, 250.0, 320.0, 350.0]),
+            (8, [100.0, 160.0, 212.5, 250.0, 302.5, 335.0, 357.5]),
+            (10, [88.0, 136.0, 184.0, 220.0, 250.0, 292.0, 326.0, 344.0, 362.0]),
+            (12, [80.0, 120.0, 160.0, 200.0, 225.0, 250.0, 285.0, 320.0, 335.0,
+                  350.0, 365.0]),
+            (15, [72.0, 104.0, 136.0, 168.0, 200.0, 220.0, 240.0, 264.0, 292.0,
+                  320.0, 332.0, 344.0, 356.0, 368.0]),
+                ]:
+            self.assertEqual(expected, quantiles(data, n=n))
+            self.assertEqual(len(quantiles(data, n=n)), n - 1)
+            self.assertEqual(list(map(float, expected)),
+                             quantiles(map(Decimal, data), n=n))
+            self.assertEqual(list(map(Decimal, expected)),
+                             quantiles(map(Decimal, data), n=n))
+            self.assertEqual(list(map(Fraction, expected)),
+                             quantiles(map(Fraction, data), n=n))
+            # Invariant under tranlation and scaling
+            def f(x):
+                return 3.5 * x - 1234.675
+            exp = list(map(f, expected))
+            act = quantiles(map(f, data), n=n)
+            self.assertTrue(all(math.isclose(e, a) for e, a in zip(exp, act)))
+        # Quartiles of a standard normal distribution
+        for n, expected in [
+            (1, []),
+            (2, [0.0]),
+            (3, [-0.4307, 0.4307]),
+            (4 ,[-0.6745, 0.0, 0.6745]),
+                ]:
+            actual = quantiles(statistics.NormalDist(), n=n)
+            self.assertTrue(all(math.isclose(e, a, abs_tol=0.0001)
+                            for e, a in zip(expected, actual)))
+
+    def test_specific_cases_inclusive(self):
+        # Match results computed by hand and cross-checked
+        # against the PERCENTILE.INC function in MS Excel
+        # and against the quaatile() function in SciPy.
+        quantiles = statistics.quantiles
+        data = [100, 200, 400, 800]
+        random.shuffle(data)
+        for n, expected in [
+            (1, []),
+            (2, [300.0]),
+            (3, [200.0, 400.0]),
+            (4, [175.0, 300.0, 500.0]),
+            (5, [160.0, 240.0, 360.0, 560.0]),
+            (6, [150.0, 200.0, 300.0, 400.0, 600.0]),
+            (8, [137.5, 175, 225.0, 300.0, 375.0, 500.0,650.0]),
+            (10, [130.0, 160.0, 190.0, 240.0, 300.0, 360.0, 440.0, 560.0, 680.0]),
+            (12, [125.0, 150.0, 175.0, 200.0, 250.0, 300.0, 350.0, 400.0,
+                  500.0, 600.0, 700.0]),
+            (15, [120.0, 140.0, 160.0, 180.0, 200.0, 240.0, 280.0, 320.0, 360.0,
+                  400.0, 480.0, 560.0, 640.0, 720.0]),
+                ]:
+            self.assertEqual(expected, quantiles(data, n=n, method="inclusive"))
+            self.assertEqual(len(quantiles(data, n=n, method="inclusive")), n - 1)
+            self.assertEqual(list(map(float, expected)),
+                             quantiles(map(Decimal, data), n=n, method="inclusive"))
+            self.assertEqual(list(map(Decimal, expected)),
+                             quantiles(map(Decimal, data), n=n, method="inclusive"))
+            self.assertEqual(list(map(Fraction, expected)),
+                             quantiles(map(Fraction, data), n=n, method="inclusive"))
+            # Invariant under tranlation and scaling
+            def f(x):
+                return 3.5 * x - 1234.675
+            exp = list(map(f, expected))
+            act = quantiles(map(f, data), n=n, method="inclusive")
+            self.assertTrue(all(math.isclose(e, a) for e, a in zip(exp, act)))
+        # Quartiles of a standard normal distribution
+        for n, expected in [
+            (1, []),
+            (2, [0.0]),
+            (3, [-0.4307, 0.4307]),
+            (4 ,[-0.6745, 0.0, 0.6745]),
+                ]:
+            actual = quantiles(statistics.NormalDist(), n=n, method="inclusive")
+            self.assertTrue(all(math.isclose(e, a, abs_tol=0.0001)
+                            for e, a in zip(expected, actual)))
+
+    def test_equal_sized_groups(self):
+        quantiles = statistics.quantiles
+        total = 10_000
+        data = [random.expovariate(0.2) for i in range(total)]
+        while len(set(data)) != total:
+            data.append(random.expovariate(0.2))
+        data.sort()
+
+        # Cases where the group size exactly divides the total
+        for n in (1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000):
+            group_size = total // n
+            self.assertEqual(
+                [bisect.bisect(data, q) for q in quantiles(data, n=n)],
+                list(range(group_size, total, group_size)))
+
+        # When the group sizes can't be exactly equal, they should
+        # differ by no more than one
+        for n in (13, 19, 59, 109, 211, 571, 1019, 1907, 5261, 9769):
+            group_sizes = {total // n, total // n + 1}
+            pos = [bisect.bisect(data, q) for q in quantiles(data, n=n)]
+            sizes = {q - p for p, q in zip(pos, pos[1:])}
+            self.assertTrue(sizes <= group_sizes)
+
+    def test_error_cases(self):
+        quantiles = statistics.quantiles
+        StatisticsError = statistics.StatisticsError
+        with self.assertRaises(TypeError):
+            quantiles()                         # Missing arguments
+        with self.assertRaises(TypeError):
+            quantiles([10, 20, 30], 13, n=4)    # Too many arguments
+        with self.assertRaises(TypeError):
+            quantiles([10, 20, 30], 4)          # n is a positional argument
+        with self.assertRaises(StatisticsError):
+            quantiles([10, 20, 30], n=0)        # n is zero
+        with self.assertRaises(StatisticsError):
+            quantiles([10, 20, 30], n=-1)       # n is negative
+        with self.assertRaises(TypeError):
+            quantiles([10, 20, 30], n=1.5)      # n is not an integer
+        with self.assertRaises(ValueError):
+            quantiles([10, 20, 30], method='X') # method is unknown
+        with self.assertRaises(StatisticsError):
+            quantiles([10], n=4)                # not enough data points
+        with self.assertRaises(TypeError):
+            quantiles([10, None, 30], n=4)      # data is non-numeric
+
+
 class TestNormalDist(unittest.TestCase):
 
     # General note on precision: The pdf(), cdf(), and overlap() methods