| """Test suite for statistics module, including helper NumericTestCase and | |
| approx_equal function. | |
| """ | |
| import collections | |
| import collections.abc | |
| import decimal | |
| import doctest | |
| import math | |
| import random | |
| import sys | |
| import unittest | |
| from decimal import Decimal | |
| from fractions import Fraction | |
| # Module to be tested. | |
| import statistics | |
| # === Helper functions and class === | |
| def sign(x): | |
| """Return -1.0 for negatives, including -0.0, otherwise +1.0.""" | |
| return math.copysign(1, x) | |
| def _nan_equal(a, b): | |
| """Return True if a and b are both the same kind of NAN. | |
| >>> _nan_equal(Decimal('NAN'), Decimal('NAN')) | |
| True | |
| >>> _nan_equal(Decimal('sNAN'), Decimal('sNAN')) | |
| True | |
| >>> _nan_equal(Decimal('NAN'), Decimal('sNAN')) | |
| False | |
| >>> _nan_equal(Decimal(42), Decimal('NAN')) | |
| False | |
| >>> _nan_equal(float('NAN'), float('NAN')) | |
| True | |
| >>> _nan_equal(float('NAN'), 0.5) | |
| False | |
| >>> _nan_equal(float('NAN'), Decimal('NAN')) | |
| False | |
| NAN payloads are not compared. | |
| """ | |
| if type(a) is not type(b): | |
| return False | |
| if isinstance(a, float): | |
| return math.isnan(a) and math.isnan(b) | |
| aexp = a.as_tuple()[2] | |
| bexp = b.as_tuple()[2] | |
| return (aexp == bexp) and (aexp in ('n', 'N')) # Both NAN or both sNAN. | |
| def _calc_errors(actual, expected): | |
| """Return the absolute and relative errors between two numbers. | |
| >>> _calc_errors(100, 75) | |
| (25, 0.25) | |
| >>> _calc_errors(100, 100) | |
| (0, 0.0) | |
| Returns the (absolute error, relative error) between the two arguments. | |
| """ | |
| base = max(abs(actual), abs(expected)) | |
| abs_err = abs(actual - expected) | |
| rel_err = abs_err/base if base else float('inf') | |
| return (abs_err, rel_err) | |
| def approx_equal(x, y, tol=1e-12, rel=1e-7): | |
| """approx_equal(x, y [, tol [, rel]]) => True|False | |
| Return True if numbers x and y are approximately equal, to within some | |
| margin of error, otherwise return False. Numbers which compare equal | |
| will also compare approximately equal. | |
| x is approximately equal to y if the difference between them is less than | |
| an absolute error tol or a relative error rel, whichever is bigger. | |
| If given, both tol and rel must be finite, non-negative numbers. If not | |
| given, default values are tol=1e-12 and rel=1e-7. | |
| >>> approx_equal(1.2589, 1.2587, tol=0.0003, rel=0) | |
| True | |
| >>> approx_equal(1.2589, 1.2587, tol=0.0001, rel=0) | |
| False | |
| Absolute error is defined as abs(x-y); if that is less than or equal to | |
| tol, x and y are considered approximately equal. | |
| Relative error is defined as abs((x-y)/x) or abs((x-y)/y), whichever is | |
| smaller, provided x or y are not zero. If that figure is less than or | |
| equal to rel, x and y are considered approximately equal. | |
| Complex numbers are not directly supported. If you wish to compare to | |
| complex numbers, extract their real and imaginary parts and compare them | |
| individually. | |
| NANs always compare unequal, even with themselves. Infinities compare | |
| approximately equal if they have the same sign (both positive or both | |
| negative). Infinities with different signs compare unequal; so do | |
| comparisons of infinities with finite numbers. | |
| """ | |
| if tol < 0 or rel < 0: | |
| raise ValueError('error tolerances must be non-negative') | |
| # NANs are never equal to anything, approximately or otherwise. | |
| if math.isnan(x) or math.isnan(y): | |
| return False | |
| # Numbers which compare equal also compare approximately equal. | |
| if x == y: | |
| # This includes the case of two infinities with the same sign. | |
| return True | |
| if math.isinf(x) or math.isinf(y): | |
| # This includes the case of two infinities of opposite sign, or | |
| # one infinity and one finite number. | |
| return False | |
| # Two finite numbers. | |
| actual_error = abs(x - y) | |
| allowed_error = max(tol, rel*max(abs(x), abs(y))) | |
| return actual_error <= allowed_error | |
| # This class exists only as somewhere to stick a docstring containing | |
| # doctests. The following docstring and tests were originally in a separate | |
| # module. Now that it has been merged in here, I need somewhere to hang the. | |
| # docstring. Ultimately, this class will die, and the information below will | |
| # either become redundant, or be moved into more appropriate places. | |
| class _DoNothing: | |
| """ | |
| When doing numeric work, especially with floats, exact equality is often | |
| not what you want. Due to round-off error, it is often a bad idea to try | |
| to compare floats with equality. Instead the usual procedure is to test | |
| them with some (hopefully small!) allowance for error. | |
| The ``approx_equal`` function allows you to specify either an absolute | |
| error tolerance, or a relative error, or both. | |
| Absolute error tolerances are simple, but you need to know the magnitude | |
| of the quantities being compared: | |
| >>> approx_equal(12.345, 12.346, tol=1e-3) | |
| True | |
| >>> approx_equal(12.345e6, 12.346e6, tol=1e-3) # tol is too small. | |
| False | |
| Relative errors are more suitable when the values you are comparing can | |
| vary in magnitude: | |
| >>> approx_equal(12.345, 12.346, rel=1e-4) | |
| True | |
| >>> approx_equal(12.345e6, 12.346e6, rel=1e-4) | |
| True | |
| but a naive implementation of relative error testing can run into trouble | |
| around zero. | |
| If you supply both an absolute tolerance and a relative error, the | |
| comparison succeeds if either individual test succeeds: | |
| >>> approx_equal(12.345e6, 12.346e6, tol=1e-3, rel=1e-4) | |
| True | |
| """ | |
| pass | |
| # We prefer this for testing numeric values that may not be exactly equal, | |
| # and avoid using TestCase.assertAlmostEqual, because it sucks :-) | |
| class NumericTestCase(unittest.TestCase): | |
| """Unit test class for numeric work. | |
| This subclasses TestCase. In addition to the standard method | |
| ``TestCase.assertAlmostEqual``, ``assertApproxEqual`` is provided. | |
| """ | |
| # By default, we expect exact equality, unless overridden. | |
| tol = rel = 0 | |
| def assertApproxEqual( | |
| self, first, second, tol=None, rel=None, msg=None | |
| ): | |
| """Test passes if ``first`` and ``second`` are approximately equal. | |
| This test passes if ``first`` and ``second`` are equal to | |
| within ``tol``, an absolute error, or ``rel``, a relative error. | |
| If either ``tol`` or ``rel`` are None or not given, they default to | |
| test attributes of the same name (by default, 0). | |
| The objects may be either numbers, or sequences of numbers. Sequences | |
| are tested element-by-element. | |
| >>> class MyTest(NumericTestCase): | |
| ... def test_number(self): | |
| ... x = 1.0/6 | |
| ... y = sum([x]*6) | |
| ... self.assertApproxEqual(y, 1.0, tol=1e-15) | |
| ... def test_sequence(self): | |
| ... a = [1.001, 1.001e-10, 1.001e10] | |
| ... b = [1.0, 1e-10, 1e10] | |
| ... self.assertApproxEqual(a, b, rel=1e-3) | |
| ... | |
| >>> import unittest | |
| >>> from io import StringIO # Suppress test runner output. | |
| >>> suite = unittest.TestLoader().loadTestsFromTestCase(MyTest) | |
| >>> unittest.TextTestRunner(stream=StringIO()).run(suite) | |
| <unittest.runner.TextTestResult run=2 errors=0 failures=0> | |
| """ | |
| if tol is None: | |
| tol = self.tol | |
| if rel is None: | |
| rel = self.rel | |
| if ( | |
| isinstance(first, collections.abc.Sequence) and | |
| isinstance(second, collections.abc.Sequence) | |
| ): | |
| check = self._check_approx_seq | |
| else: | |
| check = self._check_approx_num | |
| check(first, second, tol, rel, msg) | |
| def _check_approx_seq(self, first, second, tol, rel, msg): | |
| if len(first) != len(second): | |
| standardMsg = ( | |
| "sequences differ in length: %d items != %d items" | |
| % (len(first), len(second)) | |
| ) | |
| msg = self._formatMessage(msg, standardMsg) | |
| raise self.failureException(msg) | |
| for i, (a,e) in enumerate(zip(first, second)): | |
| self._check_approx_num(a, e, tol, rel, msg, i) | |
| def _check_approx_num(self, first, second, tol, rel, msg, idx=None): | |
| if approx_equal(first, second, tol, rel): | |
| # Test passes. Return early, we are done. | |
| return None | |
| # Otherwise we failed. | |
| standardMsg = self._make_std_err_msg(first, second, tol, rel, idx) | |
| msg = self._formatMessage(msg, standardMsg) | |
| raise self.failureException(msg) | |
| @staticmethod | |
| def _make_std_err_msg(first, second, tol, rel, idx): | |
| # Create the standard error message for approx_equal failures. | |
| assert first != second | |
| template = ( | |
| ' %r != %r\n' | |
| ' values differ by more than tol=%r and rel=%r\n' | |
| ' -> absolute error = %r\n' | |
| ' -> relative error = %r' | |
| ) | |
| if idx is not None: | |
| header = 'numeric sequences first differ at index %d.\n' % idx | |
| template = header + template | |
| # Calculate actual errors: | |
| abs_err, rel_err = _calc_errors(first, second) | |
| return template % (first, second, tol, rel, abs_err, rel_err) | |
| # ======================== | |
| # === Test the helpers === | |
| # ======================== | |
| class TestSign(unittest.TestCase): | |
| """Test that the helper function sign() works correctly.""" | |
| def testZeroes(self): | |
| # Test that signed zeroes report their sign correctly. | |
| self.assertEqual(sign(0.0), +1) | |
| self.assertEqual(sign(-0.0), -1) | |
| # --- Tests for approx_equal --- | |
| class ApproxEqualSymmetryTest(unittest.TestCase): | |
| # Test symmetry of approx_equal. | |
| def test_relative_symmetry(self): | |
| # Check that approx_equal treats relative error symmetrically. | |
| # (a-b)/a is usually not equal to (a-b)/b. Ensure that this | |
| # doesn't matter. | |
| # | |
| # Note: the reason for this test is that an early version | |
| # of approx_equal was not symmetric. A relative error test | |
| # would pass, or fail, depending on which value was passed | |
| # as the first argument. | |
| # | |
| args1 = [2456, 37.8, -12.45, Decimal('2.54'), Fraction(17, 54)] | |
| args2 = [2459, 37.2, -12.41, Decimal('2.59'), Fraction(15, 54)] | |
| assert len(args1) == len(args2) | |
| for a, b in zip(args1, args2): | |
| self.do_relative_symmetry(a, b) | |
| def do_relative_symmetry(self, a, b): | |
| a, b = min(a, b), max(a, b) | |
| assert a < b | |
| delta = b - a # The absolute difference between the values. | |
| rel_err1, rel_err2 = abs(delta/a), abs(delta/b) | |
| # Choose an error margin halfway between the two. | |
| rel = (rel_err1 + rel_err2)/2 | |
| # Now see that values a and b compare approx equal regardless of | |
| # which is given first. | |
| self.assertTrue(approx_equal(a, b, tol=0, rel=rel)) | |
| self.assertTrue(approx_equal(b, a, tol=0, rel=rel)) | |
| def test_symmetry(self): | |
| # Test that approx_equal(a, b) == approx_equal(b, a) | |
| args = [-23, -2, 5, 107, 93568] | |
| delta = 2 | |
| for a in args: | |
| for type_ in (int, float, Decimal, Fraction): | |
| x = type_(a)*100 | |
| y = x + delta | |
| r = abs(delta/max(x, y)) | |
| # There are five cases to check: | |
| # 1) actual error <= tol, <= rel | |
| self.do_symmetry_test(x, y, tol=delta, rel=r) | |
| self.do_symmetry_test(x, y, tol=delta+1, rel=2*r) | |
| # 2) actual error > tol, > rel | |
| self.do_symmetry_test(x, y, tol=delta-1, rel=r/2) | |
| # 3) actual error <= tol, > rel | |
| self.do_symmetry_test(x, y, tol=delta, rel=r/2) | |
| # 4) actual error > tol, <= rel | |
| self.do_symmetry_test(x, y, tol=delta-1, rel=r) | |
| self.do_symmetry_test(x, y, tol=delta-1, rel=2*r) | |
| # 5) exact equality test | |
| self.do_symmetry_test(x, x, tol=0, rel=0) | |
| self.do_symmetry_test(x, y, tol=0, rel=0) | |
| def do_symmetry_test(self, a, b, tol, rel): | |
| template = "approx_equal comparisons don't match for %r" | |
| flag1 = approx_equal(a, b, tol, rel) | |
| flag2 = approx_equal(b, a, tol, rel) | |
| self.assertEqual(flag1, flag2, template.format((a, b, tol, rel))) | |
| class ApproxEqualExactTest(unittest.TestCase): | |
| # Test the approx_equal function with exactly equal values. | |
| # Equal values should compare as approximately equal. | |
| # Test cases for exactly equal values, which should compare approx | |
| # equal regardless of the error tolerances given. | |
| def do_exactly_equal_test(self, x, tol, rel): | |
| result = approx_equal(x, x, tol=tol, rel=rel) | |
| self.assertTrue(result, 'equality failure for x=%r' % x) | |
| result = approx_equal(-x, -x, tol=tol, rel=rel) | |
| self.assertTrue(result, 'equality failure for x=%r' % -x) | |
| def test_exactly_equal_ints(self): | |
| # Test that equal int values are exactly equal. | |
| for n in [42, 19740, 14974, 230, 1795, 700245, 36587]: | |
| self.do_exactly_equal_test(n, 0, 0) | |
| def test_exactly_equal_floats(self): | |
| # Test that equal float values are exactly equal. | |
| for x in [0.42, 1.9740, 1497.4, 23.0, 179.5, 70.0245, 36.587]: | |
| self.do_exactly_equal_test(x, 0, 0) | |
| def test_exactly_equal_fractions(self): | |
| # Test that equal Fraction values are exactly equal. | |
| F = Fraction | |
| for f in [F(1, 2), F(0), F(5, 3), F(9, 7), F(35, 36), F(3, 7)]: | |
| self.do_exactly_equal_test(f, 0, 0) | |
| def test_exactly_equal_decimals(self): | |
| # Test that equal Decimal values are exactly equal. | |
| D = Decimal | |
| for d in map(D, "8.2 31.274 912.04 16.745 1.2047".split()): | |
| self.do_exactly_equal_test(d, 0, 0) | |
| def test_exactly_equal_absolute(self): | |
| # Test that equal values are exactly equal with an absolute error. | |
| for n in [16, 1013, 1372, 1198, 971, 4]: | |
| # Test as ints. | |
| self.do_exactly_equal_test(n, 0.01, 0) | |
| # Test as floats. | |
| self.do_exactly_equal_test(n/10, 0.01, 0) | |
| # Test as Fractions. | |
| f = Fraction(n, 1234) | |
| self.do_exactly_equal_test(f, 0.01, 0) | |
| def test_exactly_equal_absolute_decimals(self): | |
| # Test equal Decimal values are exactly equal with an absolute error. | |
| self.do_exactly_equal_test(Decimal("3.571"), Decimal("0.01"), 0) | |
| self.do_exactly_equal_test(-Decimal("81.3971"), Decimal("0.01"), 0) | |
| def test_exactly_equal_relative(self): | |
| # Test that equal values are exactly equal with a relative error. | |
| for x in [8347, 101.3, -7910.28, Fraction(5, 21)]: | |
| self.do_exactly_equal_test(x, 0, 0.01) | |
| self.do_exactly_equal_test(Decimal("11.68"), 0, Decimal("0.01")) | |
| def test_exactly_equal_both(self): | |
| # Test that equal values are equal when both tol and rel are given. | |
| for x in [41017, 16.742, -813.02, Fraction(3, 8)]: | |
| self.do_exactly_equal_test(x, 0.1, 0.01) | |
| D = Decimal | |
| self.do_exactly_equal_test(D("7.2"), D("0.1"), D("0.01")) | |
| class ApproxEqualUnequalTest(unittest.TestCase): | |
| # Unequal values should compare unequal with zero error tolerances. | |
| # Test cases for unequal values, with exact equality test. | |
| def do_exactly_unequal_test(self, x): | |
| for a in (x, -x): | |
| result = approx_equal(a, a+1, tol=0, rel=0) | |
| self.assertFalse(result, 'inequality failure for x=%r' % a) | |
| def test_exactly_unequal_ints(self): | |
| # Test unequal int values are unequal with zero error tolerance. | |
| for n in [951, 572305, 478, 917, 17240]: | |
| self.do_exactly_unequal_test(n) | |
| def test_exactly_unequal_floats(self): | |
| # Test unequal float values are unequal with zero error tolerance. | |
| for x in [9.51, 5723.05, 47.8, 9.17, 17.24]: | |
| self.do_exactly_unequal_test(x) | |
| def test_exactly_unequal_fractions(self): | |
| # Test that unequal Fractions are unequal with zero error tolerance. | |
| F = Fraction | |
| for f in [F(1, 5), F(7, 9), F(12, 11), F(101, 99023)]: | |
| self.do_exactly_unequal_test(f) | |
| def test_exactly_unequal_decimals(self): | |
| # Test that unequal Decimals are unequal with zero error tolerance. | |
| for d in map(Decimal, "3.1415 298.12 3.47 18.996 0.00245".split()): | |
| self.do_exactly_unequal_test(d) | |
| class ApproxEqualInexactTest(unittest.TestCase): | |
| # Inexact test cases for approx_error. | |
| # Test cases when comparing two values that are not exactly equal. | |
| # === Absolute error tests === | |
| def do_approx_equal_abs_test(self, x, delta): | |
| template = "Test failure for x={!r}, y={!r}" | |
| for y in (x + delta, x - delta): | |
| msg = template.format(x, y) | |
| self.assertTrue(approx_equal(x, y, tol=2*delta, rel=0), msg) | |
| self.assertFalse(approx_equal(x, y, tol=delta/2, rel=0), msg) | |
| def test_approx_equal_absolute_ints(self): | |
| # Test approximate equality of ints with an absolute error. | |
| for n in [-10737, -1975, -7, -2, 0, 1, 9, 37, 423, 9874, 23789110]: | |
| self.do_approx_equal_abs_test(n, 10) | |
| self.do_approx_equal_abs_test(n, 2) | |
| def test_approx_equal_absolute_floats(self): | |
| # Test approximate equality of floats with an absolute error. | |
| for x in [-284.126, -97.1, -3.4, -2.15, 0.5, 1.0, 7.8, 4.23, 3817.4]: | |
| self.do_approx_equal_abs_test(x, 1.5) | |
| self.do_approx_equal_abs_test(x, 0.01) | |
| self.do_approx_equal_abs_test(x, 0.0001) | |
| def test_approx_equal_absolute_fractions(self): | |
| # Test approximate equality of Fractions with an absolute error. | |
| delta = Fraction(1, 29) | |
| numerators = [-84, -15, -2, -1, 0, 1, 5, 17, 23, 34, 71] | |
| for f in (Fraction(n, 29) for n in numerators): | |
| self.do_approx_equal_abs_test(f, delta) | |
| self.do_approx_equal_abs_test(f, float(delta)) | |
| def test_approx_equal_absolute_decimals(self): | |
| # Test approximate equality of Decimals with an absolute error. | |
| delta = Decimal("0.01") | |
| for d in map(Decimal, "1.0 3.5 36.08 61.79 7912.3648".split()): | |
| self.do_approx_equal_abs_test(d, delta) | |
| self.do_approx_equal_abs_test(-d, delta) | |
| def test_cross_zero(self): | |
| # Test for the case of the two values having opposite signs. | |
| self.assertTrue(approx_equal(1e-5, -1e-5, tol=1e-4, rel=0)) | |
| # === Relative error tests === | |
| def do_approx_equal_rel_test(self, x, delta): | |
| template = "Test failure for x={!r}, y={!r}" | |
| for y in (x*(1+delta), x*(1-delta)): | |
| msg = template.format(x, y) | |
| self.assertTrue(approx_equal(x, y, tol=0, rel=2*delta), msg) | |
| self.assertFalse(approx_equal(x, y, tol=0, rel=delta/2), msg) | |
| def test_approx_equal_relative_ints(self): | |
| # Test approximate equality of ints with a relative error. | |
| self.assertTrue(approx_equal(64, 47, tol=0, rel=0.36)) | |
| self.assertTrue(approx_equal(64, 47, tol=0, rel=0.37)) | |
| # --- | |
| self.assertTrue(approx_equal(449, 512, tol=0, rel=0.125)) | |
| self.assertTrue(approx_equal(448, 512, tol=0, rel=0.125)) | |
| self.assertFalse(approx_equal(447, 512, tol=0, rel=0.125)) | |
| def test_approx_equal_relative_floats(self): | |
| # Test approximate equality of floats with a relative error. | |
| for x in [-178.34, -0.1, 0.1, 1.0, 36.97, 2847.136, 9145.074]: | |
| self.do_approx_equal_rel_test(x, 0.02) | |
| self.do_approx_equal_rel_test(x, 0.0001) | |
| def test_approx_equal_relative_fractions(self): | |
| # Test approximate equality of Fractions with a relative error. | |
| F = Fraction | |
| delta = Fraction(3, 8) | |
| for f in [F(3, 84), F(17, 30), F(49, 50), F(92, 85)]: | |
| for d in (delta, float(delta)): | |
| self.do_approx_equal_rel_test(f, d) | |
| self.do_approx_equal_rel_test(-f, d) | |
| def test_approx_equal_relative_decimals(self): | |
| # Test approximate equality of Decimals with a relative error. | |
| for d in map(Decimal, "0.02 1.0 5.7 13.67 94.138 91027.9321".split()): | |
| self.do_approx_equal_rel_test(d, Decimal("0.001")) | |
| self.do_approx_equal_rel_test(-d, Decimal("0.05")) | |
| # === Both absolute and relative error tests === | |
| # There are four cases to consider: | |
| # 1) actual error <= both absolute and relative error | |
| # 2) actual error <= absolute error but > relative error | |
| # 3) actual error <= relative error but > absolute error | |
| # 4) actual error > both absolute and relative error | |
| def do_check_both(self, a, b, tol, rel, tol_flag, rel_flag): | |
| check = self.assertTrue if tol_flag else self.assertFalse | |
| check(approx_equal(a, b, tol=tol, rel=0)) | |
| check = self.assertTrue if rel_flag else self.assertFalse | |
| check(approx_equal(a, b, tol=0, rel=rel)) | |
| check = self.assertTrue if (tol_flag or rel_flag) else self.assertFalse | |
| check(approx_equal(a, b, tol=tol, rel=rel)) | |
| def test_approx_equal_both1(self): | |
| # Test actual error <= both absolute and relative error. | |
| self.do_check_both(7.955, 7.952, 0.004, 3.8e-4, True, True) | |
| self.do_check_both(-7.387, -7.386, 0.002, 0.0002, True, True) | |
| def test_approx_equal_both2(self): | |
| # Test actual error <= absolute error but > relative error. | |
| self.do_check_both(7.955, 7.952, 0.004, 3.7e-4, True, False) | |
| def test_approx_equal_both3(self): | |
| # Test actual error <= relative error but > absolute error. | |
| self.do_check_both(7.955, 7.952, 0.001, 3.8e-4, False, True) | |
| def test_approx_equal_both4(self): | |
| # Test actual error > both absolute and relative error. | |
| self.do_check_both(2.78, 2.75, 0.01, 0.001, False, False) | |
| self.do_check_both(971.44, 971.47, 0.02, 3e-5, False, False) | |
| class ApproxEqualSpecialsTest(unittest.TestCase): | |
| # Test approx_equal with NANs and INFs and zeroes. | |
| def test_inf(self): | |
| for type_ in (float, Decimal): | |
| inf = type_('inf') | |
| self.assertTrue(approx_equal(inf, inf)) | |
| self.assertTrue(approx_equal(inf, inf, 0, 0)) | |
| self.assertTrue(approx_equal(inf, inf, 1, 0.01)) | |
| self.assertTrue(approx_equal(-inf, -inf)) | |
| self.assertFalse(approx_equal(inf, -inf)) | |
| self.assertFalse(approx_equal(inf, 1000)) | |
| def test_nan(self): | |
| for type_ in (float, Decimal): | |
| nan = type_('nan') | |
| for other in (nan, type_('inf'), 1000): | |
| self.assertFalse(approx_equal(nan, other)) | |
| def test_float_zeroes(self): | |
| nzero = math.copysign(0.0, -1) | |
| self.assertTrue(approx_equal(nzero, 0.0, tol=0.1, rel=0.1)) | |
| def test_decimal_zeroes(self): | |
| nzero = Decimal("-0.0") | |
| self.assertTrue(approx_equal(nzero, Decimal(0), tol=0.1, rel=0.1)) | |
| class TestApproxEqualErrors(unittest.TestCase): | |
| # Test error conditions of approx_equal. | |
| def test_bad_tol(self): | |
| # Test negative tol raises. | |
| self.assertRaises(ValueError, approx_equal, 100, 100, -1, 0.1) | |
| def test_bad_rel(self): | |
| # Test negative rel raises. | |
| self.assertRaises(ValueError, approx_equal, 100, 100, 1, -0.1) | |
| # --- Tests for NumericTestCase --- | |
| # The formatting routine that generates the error messages is complex enough | |
| # that it too needs testing. | |
| class TestNumericTestCase(unittest.TestCase): | |
| # The exact wording of NumericTestCase error messages is *not* guaranteed, | |
| # but we need to give them some sort of test to ensure that they are | |
| # generated correctly. As a compromise, we look for specific substrings | |
| # that are expected to be found even if the overall error message changes. | |
| def do_test(self, args): | |
| actual_msg = NumericTestCase._make_std_err_msg(*args) | |
| expected = self.generate_substrings(*args) | |
| for substring in expected: | |
| self.assertIn(substring, actual_msg) | |
| def test_numerictestcase_is_testcase(self): | |
| # Ensure that NumericTestCase actually is a TestCase. | |
| self.assertTrue(issubclass(NumericTestCase, unittest.TestCase)) | |
| def test_error_msg_numeric(self): | |
| # Test the error message generated for numeric comparisons. | |
| args = (2.5, 4.0, 0.5, 0.25, None) | |
| self.do_test(args) | |
| def test_error_msg_sequence(self): | |
| # Test the error message generated for sequence comparisons. | |
| args = (3.75, 8.25, 1.25, 0.5, 7) | |
| self.do_test(args) | |
| def generate_substrings(self, first, second, tol, rel, idx): | |
| """Return substrings we expect to see in error messages.""" | |
| abs_err, rel_err = _calc_errors(first, second) | |
| substrings = [ | |
| 'tol=%r' % tol, | |
| 'rel=%r' % rel, | |
| 'absolute error = %r' % abs_err, | |
| 'relative error = %r' % rel_err, | |
| ] | |
| if idx is not None: | |
| substrings.append('differ at index %d' % idx) | |
| return substrings | |
| # ======================================= | |
| # === Tests for the statistics module === | |
| # ======================================= | |
| class GlobalsTest(unittest.TestCase): | |
| module = statistics | |
| expected_metadata = ["__doc__", "__all__"] | |
| def test_meta(self): | |
| # Test for the existence of metadata. | |
| for meta in self.expected_metadata: | |
| self.assertTrue(hasattr(self.module, meta), | |
| "%s not present" % meta) | |
| def test_check_all(self): | |
| # Check everything in __all__ exists and is public. | |
| module = self.module | |
| for name in module.__all__: | |
| # No private names in __all__: | |
| self.assertFalse(name.startswith("_"), | |
| 'private name "%s" in __all__' % name) | |
| # And anything in __all__ must exist: | |
| self.assertTrue(hasattr(module, name), | |
| 'missing name "%s" in __all__' % name) | |
| class DocTests(unittest.TestCase): | |
| @unittest.skipIf(sys.flags.optimize >= 2, | |
| "Docstrings are omitted with -OO and above") | |
| def test_doc_tests(self): | |
| failed, tried = doctest.testmod(statistics, optionflags=doctest.ELLIPSIS) | |
| self.assertGreater(tried, 0) | |
| self.assertEqual(failed, 0) | |
| class StatisticsErrorTest(unittest.TestCase): | |
| def test_has_exception(self): | |
| errmsg = ( | |
| "Expected StatisticsError to be a ValueError, but got a" | |
| " subclass of %r instead." | |
| ) | |
| self.assertTrue(hasattr(statistics, 'StatisticsError')) | |
| self.assertTrue( | |
| issubclass(statistics.StatisticsError, ValueError), | |
| errmsg % statistics.StatisticsError.__base__ | |
| ) | |
| # === Tests for private utility functions === | |
| class ExactRatioTest(unittest.TestCase): | |
| # Test _exact_ratio utility. | |
| def test_int(self): | |
| for i in (-20, -3, 0, 5, 99, 10**20): | |
| self.assertEqual(statistics._exact_ratio(i), (i, 1)) | |
| def test_fraction(self): | |
| numerators = (-5, 1, 12, 38) | |
| for n in numerators: | |
| f = Fraction(n, 37) | |
| self.assertEqual(statistics._exact_ratio(f), (n, 37)) | |
| def test_float(self): | |
| self.assertEqual(statistics._exact_ratio(0.125), (1, 8)) | |
| self.assertEqual(statistics._exact_ratio(1.125), (9, 8)) | |
| data = [random.uniform(-100, 100) for _ in range(100)] | |
| for x in data: | |
| num, den = statistics._exact_ratio(x) | |
| self.assertEqual(x, num/den) | |
| def test_decimal(self): | |
| D = Decimal | |
| _exact_ratio = statistics._exact_ratio | |
| self.assertEqual(_exact_ratio(D("0.125")), (1, 8)) | |
| self.assertEqual(_exact_ratio(D("12.345")), (2469, 200)) | |
| self.assertEqual(_exact_ratio(D("-1.98")), (-99, 50)) | |
| def test_inf(self): | |
| INF = float("INF") | |
| class MyFloat(float): | |
| pass | |
| class MyDecimal(Decimal): | |
| pass | |
| for inf in (INF, -INF): | |
| for type_ in (float, MyFloat, Decimal, MyDecimal): | |
| x = type_(inf) | |
| ratio = statistics._exact_ratio(x) | |
| self.assertEqual(ratio, (x, None)) | |
| self.assertEqual(type(ratio[0]), type_) | |
| self.assertTrue(math.isinf(ratio[0])) | |
| def test_float_nan(self): | |
| NAN = float("NAN") | |
| class MyFloat(float): | |
| pass | |
| for nan in (NAN, MyFloat(NAN)): | |
| ratio = statistics._exact_ratio(nan) | |
| self.assertTrue(math.isnan(ratio[0])) | |
| self.assertIs(ratio[1], None) | |
| self.assertEqual(type(ratio[0]), type(nan)) | |
| def test_decimal_nan(self): | |
| NAN = Decimal("NAN") | |
| sNAN = Decimal("sNAN") | |
| class MyDecimal(Decimal): | |
| pass | |
| for nan in (NAN, MyDecimal(NAN), sNAN, MyDecimal(sNAN)): | |
| ratio = statistics._exact_ratio(nan) | |
| self.assertTrue(_nan_equal(ratio[0], nan)) | |
| self.assertIs(ratio[1], None) | |
| self.assertEqual(type(ratio[0]), type(nan)) | |
| class DecimalToRatioTest(unittest.TestCase): | |
| # Test _exact_ratio private function. | |
| def test_infinity(self): | |
| # Test that INFs are handled correctly. | |
| inf = Decimal('INF') | |
| self.assertEqual(statistics._exact_ratio(inf), (inf, None)) | |
| self.assertEqual(statistics._exact_ratio(-inf), (-inf, None)) | |
| def test_nan(self): | |
| # Test that NANs are handled correctly. | |
| for nan in (Decimal('NAN'), Decimal('sNAN')): | |
| num, den = statistics._exact_ratio(nan) | |
| # Because NANs always compare non-equal, we cannot use assertEqual. | |
| # Nor can we use an identity test, as we don't guarantee anything | |
| # about the object identity. | |
| self.assertTrue(_nan_equal(num, nan)) | |
| self.assertIs(den, None) | |
| def test_sign(self): | |
| # Test sign is calculated correctly. | |
| numbers = [Decimal("9.8765e12"), Decimal("9.8765e-12")] | |
| for d in numbers: | |
| # First test positive decimals. | |
| assert d > 0 | |
| num, den = statistics._exact_ratio(d) | |
| self.assertGreaterEqual(num, 0) | |
| self.assertGreater(den, 0) | |
| # Then test negative decimals. | |
| num, den = statistics._exact_ratio(-d) | |
| self.assertLessEqual(num, 0) | |
| self.assertGreater(den, 0) | |
| def test_negative_exponent(self): | |
| # Test result when the exponent is negative. | |
| t = statistics._exact_ratio(Decimal("0.1234")) | |
| self.assertEqual(t, (617, 5000)) | |
| def test_positive_exponent(self): | |
| # Test results when the exponent is positive. | |
| t = statistics._exact_ratio(Decimal("1.234e7")) | |
| self.assertEqual(t, (12340000, 1)) | |
| def test_regression_20536(self): | |
| # Regression test for issue 20536. | |
| # See http://bugs.python.org/issue20536 | |
| t = statistics._exact_ratio(Decimal("1e2")) | |
| self.assertEqual(t, (100, 1)) | |
| t = statistics._exact_ratio(Decimal("1.47e5")) | |
| self.assertEqual(t, (147000, 1)) | |
| class IsFiniteTest(unittest.TestCase): | |
| # Test _isfinite private function. | |
| def test_finite(self): | |
| # Test that finite numbers are recognised as finite. | |
| for x in (5, Fraction(1, 3), 2.5, Decimal("5.5")): | |
| self.assertTrue(statistics._isfinite(x)) | |
| def test_infinity(self): | |
| # Test that INFs are not recognised as finite. | |
| for x in (float("inf"), Decimal("inf")): | |
| self.assertFalse(statistics._isfinite(x)) | |
| def test_nan(self): | |
| # Test that NANs are not recognised as finite. | |
| for x in (float("nan"), Decimal("NAN"), Decimal("sNAN")): | |
| self.assertFalse(statistics._isfinite(x)) | |
| class CoerceTest(unittest.TestCase): | |
| # Test that private function _coerce correctly deals with types. | |
| # The coercion rules are currently an implementation detail, although at | |
| # some point that should change. The tests and comments here define the | |
| # correct implementation. | |
| # Pre-conditions of _coerce: | |
| # | |
| # - The first time _sum calls _coerce, the | |
| # - coerce(T, S) will never be called with bool as the first argument; | |
| # this is a pre-condition, guarded with an assertion. | |
| # | |
| # - coerce(T, T) will always return T; we assume T is a valid numeric | |
| # type. Violate this assumption at your own risk. | |
| # | |
| # - Apart from as above, bool is treated as if it were actually int. | |
| # | |
| # - coerce(int, X) and coerce(X, int) return X. | |
| # - | |
| def test_bool(self): | |
| # bool is somewhat special, due to the pre-condition that it is | |
| # never given as the first argument to _coerce, and that it cannot | |
| # be subclassed. So we test it specially. | |
| for T in (int, float, Fraction, Decimal): | |
| self.assertIs(statistics._coerce(T, bool), T) | |
| class MyClass(T): pass | |
| self.assertIs(statistics._coerce(MyClass, bool), MyClass) | |
| def assertCoerceTo(self, A, B): | |
| """Assert that type A coerces to B.""" | |
| self.assertIs(statistics._coerce(A, B), B) | |
| self.assertIs(statistics._coerce(B, A), B) | |
| def check_coerce_to(self, A, B): | |
| """Checks that type A coerces to B, including subclasses.""" | |
| # Assert that type A is coerced to B. | |
| self.assertCoerceTo(A, B) | |
| # Subclasses of A are also coerced to B. | |
| class SubclassOfA(A): pass | |
| self.assertCoerceTo(SubclassOfA, B) | |
| # A, and subclasses of A, are coerced to subclasses of B. | |
| class SubclassOfB(B): pass | |
| self.assertCoerceTo(A, SubclassOfB) | |
| self.assertCoerceTo(SubclassOfA, SubclassOfB) | |
| def assertCoerceRaises(self, A, B): | |
| """Assert that coercing A to B, or vice versa, raises TypeError.""" | |
| self.assertRaises(TypeError, statistics._coerce, (A, B)) | |
| self.assertRaises(TypeError, statistics._coerce, (B, A)) | |
| def check_type_coercions(self, T): | |
| """Check that type T coerces correctly with subclasses of itself.""" | |
| assert T is not bool | |
| # Coercing a type with itself returns the same type. | |
| self.assertIs(statistics._coerce(T, T), T) | |
| # Coercing a type with a subclass of itself returns the subclass. | |
| class U(T): pass | |
| class V(T): pass | |
| class W(U): pass | |
| for typ in (U, V, W): | |
| self.assertCoerceTo(T, typ) | |
| self.assertCoerceTo(U, W) | |
| # Coercing two subclasses that aren't parent/child is an error. | |
| self.assertCoerceRaises(U, V) | |
| self.assertCoerceRaises(V, W) | |
| def test_int(self): | |
| # Check that int coerces correctly. | |
| self.check_type_coercions(int) | |
| for typ in (float, Fraction, Decimal): | |
| self.check_coerce_to(int, typ) | |
| def test_fraction(self): | |
| # Check that Fraction coerces correctly. | |
| self.check_type_coercions(Fraction) | |
| self.check_coerce_to(Fraction, float) | |
| def test_decimal(self): | |
| # Check that Decimal coerces correctly. | |
| self.check_type_coercions(Decimal) | |
| def test_float(self): | |
| # Check that float coerces correctly. | |
| self.check_type_coercions(float) | |
| def test_non_numeric_types(self): | |
| for bad_type in (str, list, type(None), tuple, dict): | |
| for good_type in (int, float, Fraction, Decimal): | |
| self.assertCoerceRaises(good_type, bad_type) | |
| def test_incompatible_types(self): | |
| # Test that incompatible types raise. | |
| for T in (float, Fraction): | |
| class MySubclass(T): pass | |
| self.assertCoerceRaises(T, Decimal) | |
| self.assertCoerceRaises(MySubclass, Decimal) | |
| class ConvertTest(unittest.TestCase): | |
| # Test private _convert function. | |
| def check_exact_equal(self, x, y): | |
| """Check that x equals y, and has the same type as well.""" | |
| self.assertEqual(x, y) | |
| self.assertIs(type(x), type(y)) | |
| def test_int(self): | |
| # Test conversions to int. | |
| x = statistics._convert(Fraction(71), int) | |
| self.check_exact_equal(x, 71) | |
| class MyInt(int): pass | |
| x = statistics._convert(Fraction(17), MyInt) | |
| self.check_exact_equal(x, MyInt(17)) | |
| def test_fraction(self): | |
| # Test conversions to Fraction. | |
| x = statistics._convert(Fraction(95, 99), Fraction) | |
| self.check_exact_equal(x, Fraction(95, 99)) | |
| class MyFraction(Fraction): | |
| def __truediv__(self, other): | |
| return self.__class__(super().__truediv__(other)) | |
| x = statistics._convert(Fraction(71, 13), MyFraction) | |
| self.check_exact_equal(x, MyFraction(71, 13)) | |
| def test_float(self): | |
| # Test conversions to float. | |
| x = statistics._convert(Fraction(-1, 2), float) | |
| self.check_exact_equal(x, -0.5) | |
| class MyFloat(float): | |
| def __truediv__(self, other): | |
| return self.__class__(super().__truediv__(other)) | |
| x = statistics._convert(Fraction(9, 8), MyFloat) | |
| self.check_exact_equal(x, MyFloat(1.125)) | |
| def test_decimal(self): | |
| # Test conversions to Decimal. | |
| x = statistics._convert(Fraction(1, 40), Decimal) | |
| self.check_exact_equal(x, Decimal("0.025")) | |
| class MyDecimal(Decimal): | |
| def __truediv__(self, other): | |
| return self.__class__(super().__truediv__(other)) | |
| x = statistics._convert(Fraction(-15, 16), MyDecimal) | |
| self.check_exact_equal(x, MyDecimal("-0.9375")) | |
| def test_inf(self): | |
| for INF in (float('inf'), Decimal('inf')): | |
| for inf in (INF, -INF): | |
| x = statistics._convert(inf, type(inf)) | |
| self.check_exact_equal(x, inf) | |
| def test_nan(self): | |
| for nan in (float('nan'), Decimal('NAN'), Decimal('sNAN')): | |
| x = statistics._convert(nan, type(nan)) | |
| self.assertTrue(_nan_equal(x, nan)) | |
| class FailNegTest(unittest.TestCase): | |
| """Test _fail_neg private function.""" | |
| def test_pass_through(self): | |
| # Test that values are passed through unchanged. | |
| values = [1, 2.0, Fraction(3), Decimal(4)] | |
| new = list(statistics._fail_neg(values)) | |
| self.assertEqual(values, new) | |
| def test_negatives_raise(self): | |
| # Test that negatives raise an exception. | |
| for x in [1, 2.0, Fraction(3), Decimal(4)]: | |
| seq = [-x] | |
| it = statistics._fail_neg(seq) | |
| self.assertRaises(statistics.StatisticsError, next, it) | |
| def test_error_msg(self): | |
| # Test that a given error message is used. | |
| msg = "badness #%d" % random.randint(10000, 99999) | |
| try: | |
| next(statistics._fail_neg([-1], msg)) | |
| except statistics.StatisticsError as e: | |
| errmsg = e.args[0] | |
| else: | |
| self.fail("expected exception, but it didn't happen") | |
| self.assertEqual(errmsg, msg) | |
| # === Tests for public functions === | |
| class UnivariateCommonMixin: | |
| # Common tests for most univariate functions that take a data argument. | |
| def test_no_args(self): | |
| # Fail if given no arguments. | |
| self.assertRaises(TypeError, self.func) | |
| def test_empty_data(self): | |
| # Fail when the data argument (first argument) is empty. | |
| for empty in ([], (), iter([])): | |
| self.assertRaises(statistics.StatisticsError, self.func, empty) | |
| def prepare_data(self): | |
| """Return int data for various tests.""" | |
| data = list(range(10)) | |
| while data == sorted(data): | |
| random.shuffle(data) | |
| return data | |
| def test_no_inplace_modifications(self): | |
| # Test that the function does not modify its input data. | |
| data = self.prepare_data() | |
| assert len(data) != 1 # Necessary to avoid infinite loop. | |
| assert data != sorted(data) | |
| saved = data[:] | |
| assert data is not saved | |
| _ = self.func(data) | |
| self.assertListEqual(data, saved, "data has been modified") | |
| def test_order_doesnt_matter(self): | |
| # Test that the order of data points doesn't change the result. | |
| # CAUTION: due to floating point rounding errors, the result actually | |
| # may depend on the order. Consider this test representing an ideal. | |
| # To avoid this test failing, only test with exact values such as ints | |
| # or Fractions. | |
| data = [1, 2, 3, 3, 3, 4, 5, 6]*100 | |
| expected = self.func(data) | |
| random.shuffle(data) | |
| actual = self.func(data) | |
| self.assertEqual(expected, actual) | |
| def test_type_of_data_collection(self): | |
| # Test that the type of iterable data doesn't effect the result. | |
| class MyList(list): | |
| pass | |
| class MyTuple(tuple): | |
| pass | |
| def generator(data): | |
| return (obj for obj in data) | |
| data = self.prepare_data() | |
| expected = self.func(data) | |
| for kind in (list, tuple, iter, MyList, MyTuple, generator): | |
| result = self.func(kind(data)) | |
| self.assertEqual(result, expected) | |
| def test_range_data(self): | |
| # Test that functions work with range objects. | |
| data = range(20, 50, 3) | |
| expected = self.func(list(data)) | |
| self.assertEqual(self.func(data), expected) | |
| def test_bad_arg_types(self): | |
| # Test that function raises when given data of the wrong type. | |
| # Don't roll the following into a loop like this: | |
| # for bad in list_of_bad: | |
| # self.check_for_type_error(bad) | |
| # | |
| # Since assertRaises doesn't show the arguments that caused the test | |
| # failure, it is very difficult to debug these test failures when the | |
| # following are in a loop. | |
| self.check_for_type_error(None) | |
| self.check_for_type_error(23) | |
| self.check_for_type_error(42.0) | |
| self.check_for_type_error(object()) | |
| def check_for_type_error(self, *args): | |
| self.assertRaises(TypeError, self.func, *args) | |
| def test_type_of_data_element(self): | |
| # Check the type of data elements doesn't affect the numeric result. | |
| # This is a weaker test than UnivariateTypeMixin.testTypesConserved, | |
| # because it checks the numeric result by equality, but not by type. | |
| class MyFloat(float): | |
| def __truediv__(self, other): | |
| return type(self)(super().__truediv__(other)) | |
| def __add__(self, other): | |
| return type(self)(super().__add__(other)) | |
| __radd__ = __add__ | |
| raw = self.prepare_data() | |
| expected = self.func(raw) | |
| for kind in (float, MyFloat, Decimal, Fraction): | |
| data = [kind(x) for x in raw] | |
| result = type(expected)(self.func(data)) | |
| self.assertEqual(result, expected) | |
| class UnivariateTypeMixin: | |
| """Mixin class for type-conserving functions. | |
| This mixin class holds test(s) for functions which conserve the type of | |
| individual data points. E.g. the mean of a list of Fractions should itself | |
| be a Fraction. | |
| Not all tests to do with types need go in this class. Only those that | |
| rely on the function returning the same type as its input data. | |
| """ | |
| def prepare_types_for_conservation_test(self): | |
| """Return the types which are expected to be conserved.""" | |
| class MyFloat(float): | |
| def __truediv__(self, other): | |
| return type(self)(super().__truediv__(other)) | |
| def __rtruediv__(self, other): | |
| return type(self)(super().__rtruediv__(other)) | |
| def __sub__(self, other): | |
| return type(self)(super().__sub__(other)) | |
| def __rsub__(self, other): | |
| return type(self)(super().__rsub__(other)) | |
| def __pow__(self, other): | |
| return type(self)(super().__pow__(other)) | |
| def __add__(self, other): | |
| return type(self)(super().__add__(other)) | |
| __radd__ = __add__ | |
| return (float, Decimal, Fraction, MyFloat) | |
| def test_types_conserved(self): | |
| # Test that functions keeps the same type as their data points. | |
| # (Excludes mixed data types.) This only tests the type of the return | |
| # result, not the value. | |
| data = self.prepare_data() | |
| for kind in self.prepare_types_for_conservation_test(): | |
| d = [kind(x) for x in data] | |
| result = self.func(d) | |
| self.assertIs(type(result), kind) | |
| class TestSumCommon(UnivariateCommonMixin, UnivariateTypeMixin): | |
| # Common test cases for statistics._sum() function. | |
| # This test suite looks only at the numeric value returned by _sum, | |
| # after conversion to the appropriate type. | |
| def setUp(self): | |
| def simplified_sum(*args): | |
| T, value, n = statistics._sum(*args) | |
| return statistics._coerce(value, T) | |
| self.func = simplified_sum | |
| class TestSum(NumericTestCase): | |
| # Test cases for statistics._sum() function. | |
| # These tests look at the entire three value tuple returned by _sum. | |
| def setUp(self): | |
| self.func = statistics._sum | |
| def test_empty_data(self): | |
| # 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), | |
| (Fraction, Fraction(1, 2), 500)) | |
| def test_decimals(self): | |
| D = Decimal | |
| data = [D("0.001"), D("5.246"), D("1.702"), D("-0.025"), | |
| D("3.974"), D("2.328"), D("4.617"), D("2.843"), | |
| ] | |
| self.assertEqual(self.func(data), | |
| (Decimal, Decimal("20.686"), 8)) | |
| def test_compare_with_math_fsum(self): | |
| # Compare with the math.fsum function. | |
| # Ideally we ought to get the exact same result, but sometimes | |
| # we differ by a very slight amount :-( | |
| 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') | |
| self.assertRaises(TypeError, self.func, [1, 2, 3, '999']) | |
| def test_bytes_fail(self): | |
| # Sum of bytes should fail. | |
| self.assertRaises(TypeError, self.func, [1, 2, 3], b'999') | |
| self.assertRaises(TypeError, self.func, [1, 2, 3, b'999']) | |
| def test_mixed_sum(self): | |
| # Mixed input types are not (currently) allowed. | |
| # Check that mixed data types fail. | |
| self.assertRaises(TypeError, self.func, [1, 2.0, Decimal(1)]) | |
| # And so does mixed start argument. | |
| self.assertRaises(TypeError, self.func, [1, 2.0], Decimal(1)) | |
| class SumTortureTest(NumericTestCase): | |
| def test_torture(self): | |
| # Tim Peters' torture test for sum, and variants of same. | |
| self.assertEqual(statistics._sum([1, 1e100, 1, -1e100]*10000), | |
| (float, Fraction(20000.0), 40000)) | |
| self.assertEqual(statistics._sum([1e100, 1, 1, -1e100]*10000), | |
| (float, Fraction(20000.0), 40000)) | |
| T, num, count = statistics._sum([1e-100, 1, 1e-100, -1]*10000) | |
| self.assertIs(T, float) | |
| self.assertEqual(count, 40000) | |
| self.assertApproxEqual(float(num), 2.0e-96, rel=5e-16) | |
| class SumSpecialValues(NumericTestCase): | |
| # Test that sum works correctly with IEEE-754 special values. | |
| def test_nan(self): | |
| for type_ in (float, Decimal): | |
| nan = type_('nan') | |
| result = statistics._sum([1, nan, 2])[1] | |
| self.assertIs(type(result), type_) | |
| self.assertTrue(math.isnan(result)) | |
| def check_infinity(self, x, inf): | |
| """Check x is an infinity of the same type and sign as inf.""" | |
| self.assertTrue(math.isinf(x)) | |
| self.assertIs(type(x), type(inf)) | |
| self.assertEqual(x > 0, inf > 0) | |
| assert x == inf | |
| def do_test_inf(self, inf): | |
| # Adding a single infinity gives infinity. | |
| result = statistics._sum([1, 2, inf, 3])[1] | |
| self.check_infinity(result, inf) | |
| # Adding two infinities of the same sign also gives infinity. | |
| result = statistics._sum([1, 2, inf, 3, inf, 4])[1] | |
| self.check_infinity(result, inf) | |
| def test_float_inf(self): | |
| inf = float('inf') | |
| for sign in (+1, -1): | |
| self.do_test_inf(sign*inf) | |
| def test_decimal_inf(self): | |
| inf = Decimal('inf') | |
| for sign in (+1, -1): | |
| self.do_test_inf(sign*inf) | |
| def test_float_mismatched_infs(self): | |
| # Test that adding two infinities of opposite sign gives a NAN. | |
| inf = float('inf') | |
| result = statistics._sum([1, 2, inf, 3, -inf, 4])[1] | |
| self.assertTrue(math.isnan(result)) | |
| def test_decimal_extendedcontext_mismatched_infs_to_nan(self): | |
| # Test adding Decimal INFs with opposite sign returns NAN. | |
| inf = Decimal('inf') | |
| data = [1, 2, inf, 3, -inf, 4] | |
| with decimal.localcontext(decimal.ExtendedContext): | |
| self.assertTrue(math.isnan(statistics._sum(data)[1])) | |
| def test_decimal_basiccontext_mismatched_infs_to_nan(self): | |
| # Test adding Decimal INFs with opposite sign raises InvalidOperation. | |
| inf = Decimal('inf') | |
| data = [1, 2, inf, 3, -inf, 4] | |
| with decimal.localcontext(decimal.BasicContext): | |
| self.assertRaises(decimal.InvalidOperation, statistics._sum, data) | |
| def test_decimal_snan_raises(self): | |
| # Adding sNAN should raise InvalidOperation. | |
| sNAN = Decimal('sNAN') | |
| data = [1, sNAN, 2] | |
| self.assertRaises(decimal.InvalidOperation, statistics._sum, data) | |
| # === Tests for averages === | |
| class AverageMixin(UnivariateCommonMixin): | |
| # Mixin class holding common tests for averages. | |
| def test_single_value(self): | |
| # Average of a single value is the value itself. | |
| for x in (23, 42.5, 1.3e15, Fraction(15, 19), Decimal('0.28')): | |
| self.assertEqual(self.func([x]), x) | |
| def prepare_values_for_repeated_single_test(self): | |
| return (3.5, 17, 2.5e15, Fraction(61, 67), Decimal('4.9712')) | |
| def test_repeated_single_value(self): | |
| # The average of a single repeated value is the value itself. | |
| for x in self.prepare_values_for_repeated_single_test(): | |
| for count in (2, 5, 10, 20): | |
| with self.subTest(x=x, count=count): | |
| data = [x]*count | |
| self.assertEqual(self.func(data), x) | |
| class TestMean(NumericTestCase, AverageMixin, UnivariateTypeMixin): | |
| def setUp(self): | |
| self.func = statistics.mean | |
| def test_torture_pep(self): | |
| # "Torture Test" from PEP-450. | |
| self.assertEqual(self.func([1e100, 1, 3, -1e100]), 1) | |
| def test_ints(self): | |
| # Test mean with ints. | |
| data = [0, 1, 2, 3, 3, 3, 4, 5, 5, 6, 7, 7, 7, 7, 8, 9] | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), 4.8125) | |
| def test_floats(self): | |
| # Test mean with floats. | |
| data = [17.25, 19.75, 20.0, 21.5, 21.75, 23.25, 25.125, 27.5] | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), 22.015625) | |
| def test_decimals(self): | |
| # Test mean with Decimals. | |
| D = Decimal | |
| data = [D("1.634"), D("2.517"), D("3.912"), D("4.072"), D("5.813")] | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), D("3.5896")) | |
| def test_fractions(self): | |
| # Test mean with Fractions. | |
| F = Fraction | |
| data = [F(1, 2), F(2, 3), F(3, 4), F(4, 5), F(5, 6), F(6, 7), F(7, 8)] | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), F(1479, 1960)) | |
| def test_inf(self): | |
| # Test mean with infinities. | |
| raw = [1, 3, 5, 7, 9] # Use only ints, to avoid TypeError later. | |
| for kind in (float, Decimal): | |
| for sign in (1, -1): | |
| inf = kind("inf")*sign | |
| data = raw + [inf] | |
| result = self.func(data) | |
| self.assertTrue(math.isinf(result)) | |
| self.assertEqual(result, inf) | |
| def test_mismatched_infs(self): | |
| # Test mean with infinities of opposite sign. | |
| data = [2, 4, 6, float('inf'), 1, 3, 5, float('-inf')] | |
| result = self.func(data) | |
| self.assertTrue(math.isnan(result)) | |
| def test_nan(self): | |
| # Test mean with NANs. | |
| raw = [1, 3, 5, 7, 9] # Use only ints, to avoid TypeError later. | |
| for kind in (float, Decimal): | |
| inf = kind("nan") | |
| data = raw + [inf] | |
| result = self.func(data) | |
| self.assertTrue(math.isnan(result)) | |
| def test_big_data(self): | |
| # Test adding a large constant to every data point. | |
| c = 1e9 | |
| data = [3.4, 4.5, 4.9, 6.7, 6.8, 7.2, 8.0, 8.1, 9.4] | |
| expected = self.func(data) + c | |
| assert expected != c | |
| result = self.func([x+c for x in data]) | |
| self.assertEqual(result, expected) | |
| def test_doubled_data(self): | |
| # Mean of [a,b,c...z] should be same as for [a,a,b,b,c,c...z,z]. | |
| data = [random.uniform(-3, 5) for _ in range(1000)] | |
| expected = self.func(data) | |
| actual = self.func(data*2) | |
| self.assertApproxEqual(actual, expected) | |
| def test_regression_20561(self): | |
| # Regression test for issue 20561. | |
| # See http://bugs.python.org/issue20561 | |
| d = Decimal('1e4') | |
| self.assertEqual(statistics.mean([d]), d) | |
| def test_regression_25177(self): | |
| # Regression test for issue 25177. | |
| # Ensure very big and very small floats don't overflow. | |
| # See http://bugs.python.org/issue25177. | |
| self.assertEqual(statistics.mean( | |
| [8.988465674311579e+307, 8.98846567431158e+307]), | |
| 8.98846567431158e+307) | |
| big = 8.98846567431158e+307 | |
| tiny = 5e-324 | |
| for n in (2, 3, 5, 200): | |
| self.assertEqual(statistics.mean([big]*n), big) | |
| self.assertEqual(statistics.mean([tiny]*n), tiny) | |
| class TestHarmonicMean(NumericTestCase, AverageMixin, UnivariateTypeMixin): | |
| def setUp(self): | |
| self.func = statistics.harmonic_mean | |
| def prepare_data(self): | |
| # Override mixin method. | |
| values = super().prepare_data() | |
| values.remove(0) | |
| return values | |
| def prepare_values_for_repeated_single_test(self): | |
| # Override mixin method. | |
| return (3.5, 17, 2.5e15, Fraction(61, 67), Decimal('4.125')) | |
| def test_zero(self): | |
| # Test that harmonic mean returns zero when given zero. | |
| values = [1, 0, 2] | |
| self.assertEqual(self.func(values), 0) | |
| def test_negative_error(self): | |
| # Test that harmonic mean raises when given a negative value. | |
| exc = statistics.StatisticsError | |
| for values in ([-1], [1, -2, 3]): | |
| with self.subTest(values=values): | |
| self.assertRaises(exc, self.func, values) | |
| def test_ints(self): | |
| # Test harmonic mean with ints. | |
| data = [2, 4, 4, 8, 16, 16] | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), 6*4/5) | |
| def test_floats_exact(self): | |
| # Test harmonic mean with some carefully chosen floats. | |
| data = [1/8, 1/4, 1/4, 1/2, 1/2] | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), 1/4) | |
| self.assertEqual(self.func([0.25, 0.5, 1.0, 1.0]), 0.5) | |
| def test_singleton_lists(self): | |
| # Test that harmonic mean([x]) returns (approximately) x. | |
| for x in range(1, 101): | |
| self.assertEqual(self.func([x]), x) | |
| def test_decimals_exact(self): | |
| # Test harmonic mean with some carefully chosen Decimals. | |
| D = Decimal | |
| self.assertEqual(self.func([D(15), D(30), D(60), D(60)]), D(30)) | |
| data = [D("0.05"), D("0.10"), D("0.20"), D("0.20")] | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), D("0.10")) | |
| data = [D("1.68"), D("0.32"), D("5.94"), D("2.75")] | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), D(66528)/70723) | |
| def test_fractions(self): | |
| # Test harmonic mean with Fractions. | |
| F = Fraction | |
| data = [F(1, 2), F(2, 3), F(3, 4), F(4, 5), F(5, 6), F(6, 7), F(7, 8)] | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), F(7*420, 4029)) | |
| def test_inf(self): | |
| # Test harmonic mean with infinity. | |
| values = [2.0, float('inf'), 1.0] | |
| self.assertEqual(self.func(values), 2.0) | |
| def test_nan(self): | |
| # Test harmonic mean with NANs. | |
| values = [2.0, float('nan'), 1.0] | |
| self.assertTrue(math.isnan(self.func(values))) | |
| def test_multiply_data_points(self): | |
| # Test multiplying every data point by a constant. | |
| c = 111 | |
| data = [3.4, 4.5, 4.9, 6.7, 6.8, 7.2, 8.0, 8.1, 9.4] | |
| expected = self.func(data)*c | |
| result = self.func([x*c for x in data]) | |
| self.assertEqual(result, expected) | |
| def test_doubled_data(self): | |
| # Harmonic mean of [a,b...z] should be same as for [a,a,b,b...z,z]. | |
| data = [random.uniform(1, 5) for _ in range(1000)] | |
| expected = self.func(data) | |
| actual = self.func(data*2) | |
| self.assertApproxEqual(actual, expected) | |
| class TestMedian(NumericTestCase, AverageMixin): | |
| # Common tests for median and all median.* functions. | |
| def setUp(self): | |
| self.func = statistics.median | |
| def prepare_data(self): | |
| """Overload method from UnivariateCommonMixin.""" | |
| data = super().prepare_data() | |
| if len(data)%2 != 1: | |
| data.append(2) | |
| return data | |
| def test_even_ints(self): | |
| # Test median with an even number of int data points. | |
| data = [1, 2, 3, 4, 5, 6] | |
| assert len(data)%2 == 0 | |
| self.assertEqual(self.func(data), 3.5) | |
| def test_odd_ints(self): | |
| # Test median with an odd number of int data points. | |
| data = [1, 2, 3, 4, 5, 6, 9] | |
| assert len(data)%2 == 1 | |
| self.assertEqual(self.func(data), 4) | |
| def test_odd_fractions(self): | |
| # Test median works with an odd number of Fractions. | |
| F = Fraction | |
| data = [F(1, 7), F(2, 7), F(3, 7), F(4, 7), F(5, 7)] | |
| assert len(data)%2 == 1 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), F(3, 7)) | |
| def test_even_fractions(self): | |
| # Test median works with an even number of Fractions. | |
| F = Fraction | |
| data = [F(1, 7), F(2, 7), F(3, 7), F(4, 7), F(5, 7), F(6, 7)] | |
| assert len(data)%2 == 0 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), F(1, 2)) | |
| def test_odd_decimals(self): | |
| # Test median works with an odd number of Decimals. | |
| D = Decimal | |
| data = [D('2.5'), D('3.1'), D('4.2'), D('5.7'), D('5.8')] | |
| assert len(data)%2 == 1 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), D('4.2')) | |
| def test_even_decimals(self): | |
| # Test median works with an even number of Decimals. | |
| D = Decimal | |
| data = [D('1.2'), D('2.5'), D('3.1'), D('4.2'), D('5.7'), D('5.8')] | |
| assert len(data)%2 == 0 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), D('3.65')) | |
| class TestMedianDataType(NumericTestCase, UnivariateTypeMixin): | |
| # Test conservation of data element type for median. | |
| def setUp(self): | |
| self.func = statistics.median | |
| def prepare_data(self): | |
| data = list(range(15)) | |
| assert len(data)%2 == 1 | |
| while data == sorted(data): | |
| random.shuffle(data) | |
| return data | |
| class TestMedianLow(TestMedian, UnivariateTypeMixin): | |
| def setUp(self): | |
| self.func = statistics.median_low | |
| def test_even_ints(self): | |
| # Test median_low with an even number of ints. | |
| data = [1, 2, 3, 4, 5, 6] | |
| assert len(data)%2 == 0 | |
| self.assertEqual(self.func(data), 3) | |
| def test_even_fractions(self): | |
| # Test median_low works with an even number of Fractions. | |
| F = Fraction | |
| data = [F(1, 7), F(2, 7), F(3, 7), F(4, 7), F(5, 7), F(6, 7)] | |
| assert len(data)%2 == 0 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), F(3, 7)) | |
| def test_even_decimals(self): | |
| # Test median_low works with an even number of Decimals. | |
| D = Decimal | |
| data = [D('1.1'), D('2.2'), D('3.3'), D('4.4'), D('5.5'), D('6.6')] | |
| assert len(data)%2 == 0 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), D('3.3')) | |
| class TestMedianHigh(TestMedian, UnivariateTypeMixin): | |
| def setUp(self): | |
| self.func = statistics.median_high | |
| def test_even_ints(self): | |
| # Test median_high with an even number of ints. | |
| data = [1, 2, 3, 4, 5, 6] | |
| assert len(data)%2 == 0 | |
| self.assertEqual(self.func(data), 4) | |
| def test_even_fractions(self): | |
| # Test median_high works with an even number of Fractions. | |
| F = Fraction | |
| data = [F(1, 7), F(2, 7), F(3, 7), F(4, 7), F(5, 7), F(6, 7)] | |
| assert len(data)%2 == 0 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), F(4, 7)) | |
| def test_even_decimals(self): | |
| # Test median_high works with an even number of Decimals. | |
| D = Decimal | |
| data = [D('1.1'), D('2.2'), D('3.3'), D('4.4'), D('5.5'), D('6.6')] | |
| assert len(data)%2 == 0 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), D('4.4')) | |
| class TestMedianGrouped(TestMedian): | |
| # Test median_grouped. | |
| # Doesn't conserve data element types, so don't use TestMedianType. | |
| def setUp(self): | |
| self.func = statistics.median_grouped | |
| def test_odd_number_repeated(self): | |
| # Test median.grouped with repeated median values. | |
| data = [12, 13, 14, 14, 14, 15, 15] | |
| assert len(data)%2 == 1 | |
| self.assertEqual(self.func(data), 14) | |
| #--- | |
| data = [12, 13, 14, 14, 14, 14, 15] | |
| assert len(data)%2 == 1 | |
| self.assertEqual(self.func(data), 13.875) | |
| #--- | |
| data = [5, 10, 10, 15, 20, 20, 20, 20, 25, 25, 30] | |
| assert len(data)%2 == 1 | |
| self.assertEqual(self.func(data, 5), 19.375) | |
| #--- | |
| data = [16, 18, 18, 18, 18, 20, 20, 20, 22, 22, 22, 24, 24, 26, 28] | |
| assert len(data)%2 == 1 | |
| self.assertApproxEqual(self.func(data, 2), 20.66666667, tol=1e-8) | |
| def test_even_number_repeated(self): | |
| # Test median.grouped with repeated median values. | |
| data = [5, 10, 10, 15, 20, 20, 20, 25, 25, 30] | |
| assert len(data)%2 == 0 | |
| self.assertApproxEqual(self.func(data, 5), 19.16666667, tol=1e-8) | |
| #--- | |
| data = [2, 3, 4, 4, 4, 5] | |
| assert len(data)%2 == 0 | |
| self.assertApproxEqual(self.func(data), 3.83333333, tol=1e-8) | |
| #--- | |
| data = [2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6] | |
| assert len(data)%2 == 0 | |
| self.assertEqual(self.func(data), 4.5) | |
| #--- | |
| data = [3, 4, 4, 4, 5, 5, 5, 5, 6, 6] | |
| assert len(data)%2 == 0 | |
| self.assertEqual(self.func(data), 4.75) | |
| def test_repeated_single_value(self): | |
| # Override method from AverageMixin. | |
| # Yet again, failure of median_grouped to conserve the data type | |
| # causes me headaches :-( | |
| for x in (5.3, 68, 4.3e17, Fraction(29, 101), Decimal('32.9714')): | |
| for count in (2, 5, 10, 20): | |
| data = [x]*count | |
| self.assertEqual(self.func(data), float(x)) | |
| def test_odd_fractions(self): | |
| # Test median_grouped works with an odd number of Fractions. | |
| F = Fraction | |
| data = [F(5, 4), F(9, 4), F(13, 4), F(13, 4), F(17, 4)] | |
| assert len(data)%2 == 1 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), 3.0) | |
| def test_even_fractions(self): | |
| # Test median_grouped works with an even number of Fractions. | |
| F = Fraction | |
| data = [F(5, 4), F(9, 4), F(13, 4), F(13, 4), F(17, 4), F(17, 4)] | |
| assert len(data)%2 == 0 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), 3.25) | |
| def test_odd_decimals(self): | |
| # Test median_grouped works with an odd number of Decimals. | |
| D = Decimal | |
| data = [D('5.5'), D('6.5'), D('6.5'), D('7.5'), D('8.5')] | |
| assert len(data)%2 == 1 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), 6.75) | |
| def test_even_decimals(self): | |
| # Test median_grouped works with an even number of Decimals. | |
| D = Decimal | |
| data = [D('5.5'), D('5.5'), D('6.5'), D('6.5'), D('7.5'), D('8.5')] | |
| assert len(data)%2 == 0 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), 6.5) | |
| #--- | |
| data = [D('5.5'), D('5.5'), D('6.5'), D('7.5'), D('7.5'), D('8.5')] | |
| assert len(data)%2 == 0 | |
| random.shuffle(data) | |
| self.assertEqual(self.func(data), 7.0) | |
| def test_interval(self): | |
| # Test median_grouped with interval argument. | |
| data = [2.25, 2.5, 2.5, 2.75, 2.75, 3.0, 3.0, 3.25, 3.5, 3.75] | |
| self.assertEqual(self.func(data, 0.25), 2.875) | |
| data = [2.25, 2.5, 2.5, 2.75, 2.75, 2.75, 3.0, 3.0, 3.25, 3.5, 3.75] | |
| self.assertApproxEqual(self.func(data, 0.25), 2.83333333, tol=1e-8) | |
| data = [220, 220, 240, 260, 260, 260, 260, 280, 280, 300, 320, 340] | |
| self.assertEqual(self.func(data, 20), 265.0) | |
| def test_data_type_error(self): | |
| # Test median_grouped with str, bytes data types for data and interval | |
| data = ["", "", ""] | |
| self.assertRaises(TypeError, self.func, data) | |
| #--- | |
| data = [b"", b"", b""] | |
| self.assertRaises(TypeError, self.func, data) | |
| #--- | |
| data = [1, 2, 3] | |
| interval = "" | |
| self.assertRaises(TypeError, self.func, data, interval) | |
| #--- | |
| data = [1, 2, 3] | |
| interval = b"" | |
| self.assertRaises(TypeError, self.func, data, interval) | |
| class TestMode(NumericTestCase, AverageMixin, UnivariateTypeMixin): | |
| # Test cases for the discrete version of mode. | |
| def setUp(self): | |
| self.func = statistics.mode | |
| def prepare_data(self): | |
| """Overload method from UnivariateCommonMixin.""" | |
| # Make sure test data has exactly one mode. | |
| return [1, 1, 1, 1, 3, 4, 7, 9, 0, 8, 2] | |
| def test_range_data(self): | |
| # Override test from UnivariateCommonMixin. | |
| data = range(20, 50, 3) | |
| self.assertRaises(statistics.StatisticsError, self.func, data) | |
| def test_nominal_data(self): | |
| # Test mode with nominal data. | |
| data = 'abcbdb' | |
| self.assertEqual(self.func(data), 'b') | |
| data = 'fe fi fo fum fi fi'.split() | |
| self.assertEqual(self.func(data), 'fi') | |
| def test_discrete_data(self): | |
| # Test mode with discrete numeric data. | |
| data = list(range(10)) | |
| for i in range(10): | |
| d = data + [i] | |
| random.shuffle(d) | |
| self.assertEqual(self.func(d), i) | |
| def test_bimodal_data(self): | |
| # Test mode with bimodal data. | |
| data = [1, 1, 2, 2, 2, 2, 3, 4, 5, 6, 6, 6, 6, 7, 8, 9, 9] | |
| assert data.count(2) == data.count(6) == 4 | |
| # Check for an exception. | |
| self.assertRaises(statistics.StatisticsError, self.func, data) | |
| def test_unique_data_failure(self): | |
| # Test mode exception when data points are all unique. | |
| data = list(range(10)) | |
| self.assertRaises(statistics.StatisticsError, self.func, data) | |
| def test_none_data(self): | |
| # Test that mode raises TypeError if given None as data. | |
| # This test is necessary because the implementation of mode uses | |
| # collections.Counter, which accepts None and returns an empty dict. | |
| self.assertRaises(TypeError, self.func, None) | |
| def test_counter_data(self): | |
| # Test that a Counter is treated like any other iterable. | |
| data = collections.Counter([1, 1, 1, 2]) | |
| # Since the keys of the counter are treated as data points, not the | |
| # counts, this should raise. | |
| self.assertRaises(statistics.StatisticsError, self.func, data) | |
| # === Tests for variances and standard deviations === | |
| class VarianceStdevMixin(UnivariateCommonMixin): | |
| # Mixin class holding common tests for variance and std dev. | |
| # Subclasses should inherit from this before NumericTestClass, in order | |
| # to see the rel attribute below. See testShiftData for an explanation. | |
| rel = 1e-12 | |
| def test_single_value(self): | |
| # Deviation of a single value is zero. | |
| for x in (11, 19.8, 4.6e14, Fraction(21, 34), Decimal('8.392')): | |
| self.assertEqual(self.func([x]), 0) | |
| def test_repeated_single_value(self): | |
| # The deviation of a single repeated value is zero. | |
| for x in (7.2, 49, 8.1e15, Fraction(3, 7), Decimal('62.4802')): | |
| for count in (2, 3, 5, 15): | |
| data = [x]*count | |
| self.assertEqual(self.func(data), 0) | |
| def test_domain_error_regression(self): | |
| # Regression test for a domain error exception. | |
| # (Thanks to Geremy Condra.) | |
| data = [0.123456789012345]*10000 | |
| # All the items are identical, so variance should be exactly zero. | |
| # We allow some small round-off error, but not much. | |
| result = self.func(data) | |
| self.assertApproxEqual(result, 0.0, tol=5e-17) | |
| self.assertGreaterEqual(result, 0) # A negative result must fail. | |
| def test_shift_data(self): | |
| # Test that shifting the data by a constant amount does not affect | |
| # the variance or stdev. Or at least not much. | |
| # Due to rounding, this test should be considered an ideal. We allow | |
| # some tolerance away from "no change at all" by setting tol and/or rel | |
| # attributes. Subclasses may set tighter or looser error tolerances. | |
| raw = [1.03, 1.27, 1.94, 2.04, 2.58, 3.14, 4.75, 4.98, 5.42, 6.78] | |
| expected = self.func(raw) | |
| # Don't set shift too high, the bigger it is, the more rounding error. | |
| shift = 1e5 | |
| data = [x + shift for x in raw] | |
| self.assertApproxEqual(self.func(data), expected) | |
| def test_shift_data_exact(self): | |
| # Like test_shift_data, but result is always exact. | |
| raw = [1, 3, 3, 4, 5, 7, 9, 10, 11, 16] | |
| assert all(x==int(x) for x in raw) | |
| expected = self.func(raw) | |
| shift = 10**9 | |
| data = [x + shift for x in raw] | |
| self.assertEqual(self.func(data), expected) | |
| def test_iter_list_same(self): | |
| # Test that iter data and list data give the same result. | |
| # This is an explicit test that iterators and lists are treated the | |
| # same; justification for this test over and above the similar test | |
| # in UnivariateCommonMixin is that an earlier design had variance and | |
| # friends swap between one- and two-pass algorithms, which would | |
| # sometimes give different results. | |
| data = [random.uniform(-3, 8) for _ in range(1000)] | |
| expected = self.func(data) | |
| self.assertEqual(self.func(iter(data)), expected) | |
| class TestPVariance(VarianceStdevMixin, NumericTestCase, UnivariateTypeMixin): | |
| # Tests for population variance. | |
| def setUp(self): | |
| self.func = statistics.pvariance | |
| def test_exact_uniform(self): | |
| # Test the variance against an exact result for uniform data. | |
| data = list(range(10000)) | |
| random.shuffle(data) | |
| expected = (10000**2 - 1)/12 # Exact value. | |
| self.assertEqual(self.func(data), expected) | |
| def test_ints(self): | |
| # Test population variance with int data. | |
| data = [4, 7, 13, 16] | |
| exact = 22.5 | |
| self.assertEqual(self.func(data), exact) | |
| def test_fractions(self): | |
| # Test population variance with Fraction data. | |
| F = Fraction | |
| data = [F(1, 4), F(1, 4), F(3, 4), F(7, 4)] | |
| exact = F(3, 8) | |
| result = self.func(data) | |
| self.assertEqual(result, exact) | |
| self.assertIsInstance(result, Fraction) | |
| def test_decimals(self): | |
| # Test population variance with Decimal data. | |
| D = Decimal | |
| data = [D("12.1"), D("12.2"), D("12.5"), D("12.9")] | |
| exact = D('0.096875') | |
| result = self.func(data) | |
| self.assertEqual(result, exact) | |
| self.assertIsInstance(result, Decimal) | |
| class TestVariance(VarianceStdevMixin, NumericTestCase, UnivariateTypeMixin): | |
| # Tests for sample variance. | |
| def setUp(self): | |
| self.func = statistics.variance | |
| def test_single_value(self): | |
| # Override method from VarianceStdevMixin. | |
| for x in (35, 24.7, 8.2e15, Fraction(19, 30), Decimal('4.2084')): | |
| self.assertRaises(statistics.StatisticsError, self.func, [x]) | |
| def test_ints(self): | |
| # Test sample variance with int data. | |
| data = [4, 7, 13, 16] | |
| exact = 30 | |
| self.assertEqual(self.func(data), exact) | |
| def test_fractions(self): | |
| # Test sample variance with Fraction data. | |
| F = Fraction | |
| data = [F(1, 4), F(1, 4), F(3, 4), F(7, 4)] | |
| exact = F(1, 2) | |
| result = self.func(data) | |
| self.assertEqual(result, exact) | |
| self.assertIsInstance(result, Fraction) | |
| def test_decimals(self): | |
| # Test sample variance with Decimal data. | |
| D = Decimal | |
| data = [D(2), D(2), D(7), D(9)] | |
| exact = 4*D('9.5')/D(3) | |
| result = self.func(data) | |
| self.assertEqual(result, exact) | |
| self.assertIsInstance(result, Decimal) | |
| class TestPStdev(VarianceStdevMixin, NumericTestCase): | |
| # Tests for population standard deviation. | |
| def setUp(self): | |
| self.func = statistics.pstdev | |
| def test_compare_to_variance(self): | |
| # Test that stdev is, in fact, the square root of variance. | |
| data = [random.uniform(-17, 24) for _ in range(1000)] | |
| expected = math.sqrt(statistics.pvariance(data)) | |
| self.assertEqual(self.func(data), expected) | |
| class TestStdev(VarianceStdevMixin, NumericTestCase): | |
| # Tests for sample standard deviation. | |
| def setUp(self): | |
| self.func = statistics.stdev | |
| def test_single_value(self): | |
| # Override method from VarianceStdevMixin. | |
| for x in (81, 203.74, 3.9e14, Fraction(5, 21), Decimal('35.719')): | |
| self.assertRaises(statistics.StatisticsError, self.func, [x]) | |
| def test_compare_to_variance(self): | |
| # Test that stdev is, in fact, the square root of variance. | |
| data = [random.uniform(-2, 9) for _ in range(1000)] | |
| expected = math.sqrt(statistics.variance(data)) | |
| self.assertEqual(self.func(data), expected) | |
| # === Run tests === | |
| def load_tests(loader, tests, ignore): | |
| """Used for doctest/unittest integration.""" | |
| tests.addTests(doctest.DocTestSuite()) | |
| return tests | |
| if __name__ == "__main__": | |
| unittest.main() |