diff options
| -rw-r--r-- | Lib/statistics.py | 78 | ||||
| -rw-r--r-- | Lib/test/test_statistics.py | 28 | ||||
| -rw-r--r-- | Misc/NEWS.d/next/Library/2021-09-08-01-19-31.bpo-20499.tSxx8Y.rst | 1 |
3 files changed, 51 insertions, 56 deletions
diff --git a/Lib/statistics.py b/Lib/statistics.py index a14c48e..13e5fe7 100644 --- a/Lib/statistics.py +++ b/Lib/statistics.py @@ -147,21 +147,17 @@ class StatisticsError(ValueError): # === Private utilities === -def _sum(data, start=0): - """_sum(data [, start]) -> (type, sum, count) +def _sum(data): + """_sum(data) -> (type, sum, count) Return a high-precision sum of the given numeric data as a fraction, together with the type to be converted to and the count of items. - If optional argument ``start`` is given, it is added to the total. - If ``data`` is empty, ``start`` (defaulting to 0) is returned. - - Examples -------- - >>> _sum([3, 2.25, 4.5, -0.5, 1.0], 0.75) - (<class 'float'>, Fraction(11, 1), 5) + >>> _sum([3, 2.25, 4.5, -0.5, 0.25]) + (<class 'float'>, Fraction(19, 2), 5) Some sources of round-off error will be avoided: @@ -184,10 +180,9 @@ def _sum(data, start=0): allowed. """ count = 0 - n, d = _exact_ratio(start) - partials = {d: n} + partials = {} partials_get = partials.get - T = _coerce(int, type(start)) + T = int for typ, values in groupby(data, type): T = _coerce(T, typ) # or raise TypeError for n, d in map(_exact_ratio, values): @@ -200,8 +195,7 @@ def _sum(data, start=0): assert not _isfinite(total) else: # Sum all the partial sums using builtin sum. - # FIXME is this faster if we sum them in order of the denominator? - total = sum(Fraction(n, d) for d, n in sorted(partials.items())) + total = sum(Fraction(n, d) for d, n in partials.items()) return (T, total, count) @@ -252,27 +246,19 @@ def _exact_ratio(x): x is expected to be an int, Fraction, Decimal or float. """ try: - # Optimise the common case of floats. We expect that the most often - # used numeric type will be builtin floats, so try to make this as - # fast as possible. - if type(x) is float or type(x) is Decimal: - return x.as_integer_ratio() - try: - # x may be an int, Fraction, or Integral ABC. - return (x.numerator, x.denominator) - except AttributeError: - try: - # x may be a float or Decimal subclass. - return x.as_integer_ratio() - except AttributeError: - # Just give up? - pass + return x.as_integer_ratio() + except AttributeError: + pass except (OverflowError, ValueError): # float NAN or INF. assert not _isfinite(x) return (x, None) - msg = "can't convert type '{}' to numerator/denominator" - raise TypeError(msg.format(type(x).__name__)) + try: + # x may be an Integral ABC. + return (x.numerator, x.denominator) + except AttributeError: + msg = f"can't convert type '{type(x).__name__}' to numerator/denominator" + raise TypeError(msg) def _convert(value, T): @@ -730,18 +716,20 @@ def _ss(data, c=None): if c is not None: T, total, count = _sum((d := x - c) * d for x in data) return (T, total) - # Compute the mean accurate to within 1/2 ulp - c = mean(data) - # Initial computation for the sum of square deviations - T, total, count = _sum((d := x - c) * d for x in data) - # Correct any remaining inaccuracy in the mean c. - # The following sum should mathematically equal zero, - # but due to the final rounding of the mean, it may not. - U, error, count2 = _sum((x - c) for x in data) - assert count == count2 - correction = error * error / len(data) - total -= correction - assert not total < 0, 'negative sum of square deviations: %f' % total + T, total, count = _sum(data) + mean_n, mean_d = (total / count).as_integer_ratio() + partials = Counter() + for n, d in map(_exact_ratio, data): + diff_n = n * mean_d - d * mean_n + diff_d = d * mean_d + partials[diff_d * diff_d] += diff_n * diff_n + if None in partials: + # The sum will be a NAN or INF. We can ignore all the finite + # partials, and just look at this special one. + total = partials[None] + assert not _isfinite(total) + else: + total = sum(Fraction(n, d) for d, n in partials.items()) return (T, total) @@ -845,6 +833,9 @@ def stdev(data, xbar=None): 1.0810874155219827 """ + # Fixme: Despite the exact sum of squared deviations, some inaccuracy + # remain because there are two rounding steps. The first occurs in + # the _convert() step for variance(), the second occurs in math.sqrt(). var = variance(data, xbar) try: return var.sqrt() @@ -861,6 +852,9 @@ def pstdev(data, mu=None): 0.986893273527251 """ + # Fixme: Despite the exact sum of squared deviations, some inaccuracy + # remain because there are two rounding steps. The first occurs in + # the _convert() step for pvariance(), the second occurs in math.sqrt(). var = pvariance(data, mu) try: return var.sqrt() diff --git a/Lib/test/test_statistics.py b/Lib/test/test_statistics.py index 64ebd0e..5cb055c 100644 --- a/Lib/test/test_statistics.py +++ b/Lib/test/test_statistics.py @@ -1250,20 +1250,14 @@ class TestSum(NumericTestCase): # Override test for empty data. for data in ([], (), iter([])): self.assertEqual(self.func(data), (int, Fraction(0), 0)) - self.assertEqual(self.func(data, 23), (int, Fraction(23), 0)) - self.assertEqual(self.func(data, 2.3), (float, Fraction(2.3), 0)) def test_ints(self): self.assertEqual(self.func([1, 5, 3, -4, -8, 20, 42, 1]), (int, Fraction(60), 8)) - self.assertEqual(self.func([4, 2, 3, -8, 7], 1000), - (int, Fraction(1008), 5)) def test_floats(self): self.assertEqual(self.func([0.25]*20), (float, Fraction(5.0), 20)) - self.assertEqual(self.func([0.125, 0.25, 0.5, 0.75], 1.5), - (float, Fraction(3.125), 4)) def test_fractions(self): self.assertEqual(self.func([Fraction(1, 1000)]*500), @@ -1284,14 +1278,6 @@ class TestSum(NumericTestCase): data = [random.uniform(-100, 1000) for _ in range(1000)] self.assertApproxEqual(float(self.func(data)[1]), math.fsum(data), rel=2e-16) - def test_start_argument(self): - # Test that the optional start argument works correctly. - data = [random.uniform(1, 1000) for _ in range(100)] - t = self.func(data)[1] - self.assertEqual(t+42, self.func(data, 42)[1]) - self.assertEqual(t-23, self.func(data, -23)[1]) - self.assertEqual(t+Fraction(1e20), self.func(data, 1e20)[1]) - def test_strings_fail(self): # Sum of strings should fail. self.assertRaises(TypeError, self.func, [1, 2, 3], '999') @@ -2101,6 +2087,13 @@ class TestPVariance(VarianceStdevMixin, NumericTestCase, UnivariateTypeMixin): self.assertEqual(result, exact) self.assertIsInstance(result, Decimal) + def test_accuracy_bug_20499(self): + data = [0, 0, 1] + exact = 2 / 9 + result = self.func(data) + self.assertEqual(result, exact) + self.assertIsInstance(result, float) + class TestVariance(VarianceStdevMixin, NumericTestCase, UnivariateTypeMixin): # Tests for sample variance. @@ -2141,6 +2134,13 @@ class TestVariance(VarianceStdevMixin, NumericTestCase, UnivariateTypeMixin): self.assertEqual(self.func(data), 0.5) self.assertEqual(self.func(data, xbar=2.0), 1.0) + def test_accuracy_bug_20499(self): + data = [0, 0, 2] + exact = 4 / 3 + result = self.func(data) + self.assertEqual(result, exact) + self.assertIsInstance(result, float) + class TestPStdev(VarianceStdevMixin, NumericTestCase): # Tests for population standard deviation. def setUp(self): diff --git a/Misc/NEWS.d/next/Library/2021-09-08-01-19-31.bpo-20499.tSxx8Y.rst b/Misc/NEWS.d/next/Library/2021-09-08-01-19-31.bpo-20499.tSxx8Y.rst new file mode 100644 index 0000000..cbbe61a --- /dev/null +++ b/Misc/NEWS.d/next/Library/2021-09-08-01-19-31.bpo-20499.tSxx8Y.rst @@ -0,0 +1 @@ +Improve the speed and accuracy of statistics.pvariance(). |