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3061 lines
120 KiB
Python
3061 lines
120 KiB
Python
"""Test suite for statistics module, including helper NumericTestCase and
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approx_equal function.
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"""
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import bisect
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import collections
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import collections.abc
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import copy
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import decimal
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import doctest
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import itertools
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import math
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import pickle
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import random
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import sys
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import unittest
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from test import support
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from test.support import import_helper, requires_IEEE_754
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from decimal import Decimal
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from fractions import Fraction
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# Module to be tested.
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import statistics
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# === Helper functions and class ===
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def sign(x):
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"""Return -1.0 for negatives, including -0.0, otherwise +1.0."""
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return math.copysign(1, x)
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def _nan_equal(a, b):
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"""Return True if a and b are both the same kind of NAN.
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>>> _nan_equal(Decimal('NAN'), Decimal('NAN'))
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True
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>>> _nan_equal(Decimal('sNAN'), Decimal('sNAN'))
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True
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>>> _nan_equal(Decimal('NAN'), Decimal('sNAN'))
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False
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>>> _nan_equal(Decimal(42), Decimal('NAN'))
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False
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>>> _nan_equal(float('NAN'), float('NAN'))
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True
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>>> _nan_equal(float('NAN'), 0.5)
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False
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>>> _nan_equal(float('NAN'), Decimal('NAN'))
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False
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NAN payloads are not compared.
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"""
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if type(a) is not type(b):
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return False
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if isinstance(a, float):
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return math.isnan(a) and math.isnan(b)
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aexp = a.as_tuple()[2]
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bexp = b.as_tuple()[2]
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return (aexp == bexp) and (aexp in ('n', 'N')) # Both NAN or both sNAN.
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def _calc_errors(actual, expected):
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"""Return the absolute and relative errors between two numbers.
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>>> _calc_errors(100, 75)
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(25, 0.25)
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>>> _calc_errors(100, 100)
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(0, 0.0)
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Returns the (absolute error, relative error) between the two arguments.
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"""
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base = max(abs(actual), abs(expected))
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abs_err = abs(actual - expected)
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rel_err = abs_err/base if base else float('inf')
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return (abs_err, rel_err)
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def approx_equal(x, y, tol=1e-12, rel=1e-7):
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"""approx_equal(x, y [, tol [, rel]]) => True|False
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Return True if numbers x and y are approximately equal, to within some
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margin of error, otherwise return False. Numbers which compare equal
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will also compare approximately equal.
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x is approximately equal to y if the difference between them is less than
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an absolute error tol or a relative error rel, whichever is bigger.
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If given, both tol and rel must be finite, non-negative numbers. If not
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given, default values are tol=1e-12 and rel=1e-7.
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>>> approx_equal(1.2589, 1.2587, tol=0.0003, rel=0)
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True
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>>> approx_equal(1.2589, 1.2587, tol=0.0001, rel=0)
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False
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Absolute error is defined as abs(x-y); if that is less than or equal to
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tol, x and y are considered approximately equal.
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Relative error is defined as abs((x-y)/x) or abs((x-y)/y), whichever is
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smaller, provided x or y are not zero. If that figure is less than or
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equal to rel, x and y are considered approximately equal.
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Complex numbers are not directly supported. If you wish to compare to
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complex numbers, extract their real and imaginary parts and compare them
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individually.
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NANs always compare unequal, even with themselves. Infinities compare
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approximately equal if they have the same sign (both positive or both
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negative). Infinities with different signs compare unequal; so do
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comparisons of infinities with finite numbers.
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"""
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if tol < 0 or rel < 0:
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raise ValueError('error tolerances must be non-negative')
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# NANs are never equal to anything, approximately or otherwise.
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if math.isnan(x) or math.isnan(y):
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return False
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# Numbers which compare equal also compare approximately equal.
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if x == y:
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# This includes the case of two infinities with the same sign.
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return True
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if math.isinf(x) or math.isinf(y):
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# This includes the case of two infinities of opposite sign, or
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# one infinity and one finite number.
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return False
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# Two finite numbers.
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actual_error = abs(x - y)
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allowed_error = max(tol, rel*max(abs(x), abs(y)))
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return actual_error <= allowed_error
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# This class exists only as somewhere to stick a docstring containing
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# doctests. The following docstring and tests were originally in a separate
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# module. Now that it has been merged in here, I need somewhere to hang the.
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# docstring. Ultimately, this class will die, and the information below will
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# either become redundant, or be moved into more appropriate places.
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class _DoNothing:
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"""
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When doing numeric work, especially with floats, exact equality is often
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not what you want. Due to round-off error, it is often a bad idea to try
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to compare floats with equality. Instead the usual procedure is to test
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them with some (hopefully small!) allowance for error.
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The ``approx_equal`` function allows you to specify either an absolute
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error tolerance, or a relative error, or both.
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Absolute error tolerances are simple, but you need to know the magnitude
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of the quantities being compared:
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>>> approx_equal(12.345, 12.346, tol=1e-3)
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True
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>>> approx_equal(12.345e6, 12.346e6, tol=1e-3) # tol is too small.
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False
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Relative errors are more suitable when the values you are comparing can
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vary in magnitude:
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>>> approx_equal(12.345, 12.346, rel=1e-4)
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True
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>>> approx_equal(12.345e6, 12.346e6, rel=1e-4)
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True
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but a naive implementation of relative error testing can run into trouble
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around zero.
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If you supply both an absolute tolerance and a relative error, the
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comparison succeeds if either individual test succeeds:
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>>> approx_equal(12.345e6, 12.346e6, tol=1e-3, rel=1e-4)
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True
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"""
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pass
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# We prefer this for testing numeric values that may not be exactly equal,
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# and avoid using TestCase.assertAlmostEqual, because it sucks :-)
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py_statistics = import_helper.import_fresh_module('statistics',
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blocked=['_statistics'])
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c_statistics = import_helper.import_fresh_module('statistics',
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fresh=['_statistics'])
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class TestModules(unittest.TestCase):
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func_names = ['_normal_dist_inv_cdf']
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def test_py_functions(self):
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for fname in self.func_names:
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self.assertEqual(getattr(py_statistics, fname).__module__, 'statistics')
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@unittest.skipUnless(c_statistics, 'requires _statistics')
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def test_c_functions(self):
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for fname in self.func_names:
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self.assertEqual(getattr(c_statistics, fname).__module__, '_statistics')
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class NumericTestCase(unittest.TestCase):
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"""Unit test class for numeric work.
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This subclasses TestCase. In addition to the standard method
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``TestCase.assertAlmostEqual``, ``assertApproxEqual`` is provided.
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"""
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# By default, we expect exact equality, unless overridden.
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tol = rel = 0
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def assertApproxEqual(
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self, first, second, tol=None, rel=None, msg=None
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):
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"""Test passes if ``first`` and ``second`` are approximately equal.
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This test passes if ``first`` and ``second`` are equal to
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within ``tol``, an absolute error, or ``rel``, a relative error.
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If either ``tol`` or ``rel`` are None or not given, they default to
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test attributes of the same name (by default, 0).
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The objects may be either numbers, or sequences of numbers. Sequences
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are tested element-by-element.
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>>> class MyTest(NumericTestCase):
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... def test_number(self):
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... x = 1.0/6
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... y = sum([x]*6)
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... self.assertApproxEqual(y, 1.0, tol=1e-15)
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... def test_sequence(self):
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... a = [1.001, 1.001e-10, 1.001e10]
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... b = [1.0, 1e-10, 1e10]
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... self.assertApproxEqual(a, b, rel=1e-3)
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...
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>>> import unittest
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>>> from io import StringIO # Suppress test runner output.
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>>> suite = unittest.TestLoader().loadTestsFromTestCase(MyTest)
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>>> unittest.TextTestRunner(stream=StringIO()).run(suite)
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<unittest.runner.TextTestResult run=2 errors=0 failures=0>
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"""
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if tol is None:
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tol = self.tol
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if rel is None:
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rel = self.rel
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if (
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isinstance(first, collections.abc.Sequence) and
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isinstance(second, collections.abc.Sequence)
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):
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check = self._check_approx_seq
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else:
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check = self._check_approx_num
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check(first, second, tol, rel, msg)
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def _check_approx_seq(self, first, second, tol, rel, msg):
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if len(first) != len(second):
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standardMsg = (
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"sequences differ in length: %d items != %d items"
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% (len(first), len(second))
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)
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msg = self._formatMessage(msg, standardMsg)
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raise self.failureException(msg)
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for i, (a,e) in enumerate(zip(first, second)):
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self._check_approx_num(a, e, tol, rel, msg, i)
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def _check_approx_num(self, first, second, tol, rel, msg, idx=None):
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if approx_equal(first, second, tol, rel):
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# Test passes. Return early, we are done.
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return None
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# Otherwise we failed.
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standardMsg = self._make_std_err_msg(first, second, tol, rel, idx)
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msg = self._formatMessage(msg, standardMsg)
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raise self.failureException(msg)
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@staticmethod
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def _make_std_err_msg(first, second, tol, rel, idx):
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# Create the standard error message for approx_equal failures.
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assert first != second
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template = (
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' %r != %r\n'
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' values differ by more than tol=%r and rel=%r\n'
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' -> absolute error = %r\n'
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' -> relative error = %r'
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)
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if idx is not None:
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header = 'numeric sequences first differ at index %d.\n' % idx
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template = header + template
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# Calculate actual errors:
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abs_err, rel_err = _calc_errors(first, second)
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return template % (first, second, tol, rel, abs_err, rel_err)
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# ========================
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# === Test the helpers ===
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# ========================
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class TestSign(unittest.TestCase):
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"""Test that the helper function sign() works correctly."""
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def testZeroes(self):
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# Test that signed zeroes report their sign correctly.
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self.assertEqual(sign(0.0), +1)
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self.assertEqual(sign(-0.0), -1)
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# --- Tests for approx_equal ---
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class ApproxEqualSymmetryTest(unittest.TestCase):
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# Test symmetry of approx_equal.
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def test_relative_symmetry(self):
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# Check that approx_equal treats relative error symmetrically.
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# (a-b)/a is usually not equal to (a-b)/b. Ensure that this
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# doesn't matter.
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#
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# Note: the reason for this test is that an early version
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# of approx_equal was not symmetric. A relative error test
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# would pass, or fail, depending on which value was passed
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# as the first argument.
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#
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args1 = [2456, 37.8, -12.45, Decimal('2.54'), Fraction(17, 54)]
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args2 = [2459, 37.2, -12.41, Decimal('2.59'), Fraction(15, 54)]
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assert len(args1) == len(args2)
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for a, b in zip(args1, args2):
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self.do_relative_symmetry(a, b)
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def do_relative_symmetry(self, a, b):
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a, b = min(a, b), max(a, b)
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assert a < b
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delta = b - a # The absolute difference between the values.
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rel_err1, rel_err2 = abs(delta/a), abs(delta/b)
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# Choose an error margin halfway between the two.
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rel = (rel_err1 + rel_err2)/2
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# Now see that values a and b compare approx equal regardless of
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# which is given first.
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self.assertTrue(approx_equal(a, b, tol=0, rel=rel))
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self.assertTrue(approx_equal(b, a, tol=0, rel=rel))
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def test_symmetry(self):
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# Test that approx_equal(a, b) == approx_equal(b, a)
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args = [-23, -2, 5, 107, 93568]
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delta = 2
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for a in args:
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for type_ in (int, float, Decimal, Fraction):
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x = type_(a)*100
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y = x + delta
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r = abs(delta/max(x, y))
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# There are five cases to check:
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# 1) actual error <= tol, <= rel
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self.do_symmetry_test(x, y, tol=delta, rel=r)
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self.do_symmetry_test(x, y, tol=delta+1, rel=2*r)
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# 2) actual error > tol, > rel
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self.do_symmetry_test(x, y, tol=delta-1, rel=r/2)
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# 3) actual error <= tol, > rel
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self.do_symmetry_test(x, y, tol=delta, rel=r/2)
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# 4) actual error > tol, <= rel
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self.do_symmetry_test(x, y, tol=delta-1, rel=r)
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self.do_symmetry_test(x, y, tol=delta-1, rel=2*r)
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# 5) exact equality test
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self.do_symmetry_test(x, x, tol=0, rel=0)
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self.do_symmetry_test(x, y, tol=0, rel=0)
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def do_symmetry_test(self, a, b, tol, rel):
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template = "approx_equal comparisons don't match for %r"
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flag1 = approx_equal(a, b, tol, rel)
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flag2 = approx_equal(b, a, tol, rel)
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self.assertEqual(flag1, flag2, template.format((a, b, tol, rel)))
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class ApproxEqualExactTest(unittest.TestCase):
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# Test the approx_equal function with exactly equal values.
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# Equal values should compare as approximately equal.
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# Test cases for exactly equal values, which should compare approx
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# equal regardless of the error tolerances given.
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def do_exactly_equal_test(self, x, tol, rel):
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result = approx_equal(x, x, tol=tol, rel=rel)
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self.assertTrue(result, 'equality failure for x=%r' % x)
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result = approx_equal(-x, -x, tol=tol, rel=rel)
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self.assertTrue(result, 'equality failure for x=%r' % -x)
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def test_exactly_equal_ints(self):
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# Test that equal int values are exactly equal.
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for n in [42, 19740, 14974, 230, 1795, 700245, 36587]:
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self.do_exactly_equal_test(n, 0, 0)
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def test_exactly_equal_floats(self):
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# Test that equal float values are exactly equal.
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for x in [0.42, 1.9740, 1497.4, 23.0, 179.5, 70.0245, 36.587]:
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self.do_exactly_equal_test(x, 0, 0)
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def test_exactly_equal_fractions(self):
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# Test that equal Fraction values are exactly equal.
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F = Fraction
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for f in [F(1, 2), F(0), F(5, 3), F(9, 7), F(35, 36), F(3, 7)]:
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self.do_exactly_equal_test(f, 0, 0)
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def test_exactly_equal_decimals(self):
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# Test that equal Decimal values are exactly equal.
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D = Decimal
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for d in map(D, "8.2 31.274 912.04 16.745 1.2047".split()):
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self.do_exactly_equal_test(d, 0, 0)
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def test_exactly_equal_absolute(self):
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# Test that equal values are exactly equal with an absolute error.
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for n in [16, 1013, 1372, 1198, 971, 4]:
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# Test as ints.
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self.do_exactly_equal_test(n, 0.01, 0)
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# Test as floats.
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self.do_exactly_equal_test(n/10, 0.01, 0)
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# Test as Fractions.
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f = Fraction(n, 1234)
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self.do_exactly_equal_test(f, 0.01, 0)
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def test_exactly_equal_absolute_decimals(self):
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# Test equal Decimal values are exactly equal with an absolute error.
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self.do_exactly_equal_test(Decimal("3.571"), Decimal("0.01"), 0)
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self.do_exactly_equal_test(-Decimal("81.3971"), Decimal("0.01"), 0)
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def test_exactly_equal_relative(self):
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# Test that equal values are exactly equal with a relative error.
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for x in [8347, 101.3, -7910.28, Fraction(5, 21)]:
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self.do_exactly_equal_test(x, 0, 0.01)
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self.do_exactly_equal_test(Decimal("11.68"), 0, Decimal("0.01"))
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def test_exactly_equal_both(self):
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# Test that equal values are equal when both tol and rel are given.
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for x in [41017, 16.742, -813.02, Fraction(3, 8)]:
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self.do_exactly_equal_test(x, 0.1, 0.01)
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D = Decimal
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self.do_exactly_equal_test(D("7.2"), D("0.1"), D("0.01"))
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class ApproxEqualUnequalTest(unittest.TestCase):
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# Unequal values should compare unequal with zero error tolerances.
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# Test cases for unequal values, with exact equality test.
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def do_exactly_unequal_test(self, x):
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for a in (x, -x):
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result = approx_equal(a, a+1, tol=0, rel=0)
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self.assertFalse(result, 'inequality failure for x=%r' % a)
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def test_exactly_unequal_ints(self):
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# Test unequal int values are unequal with zero error tolerance.
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for n in [951, 572305, 478, 917, 17240]:
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self.do_exactly_unequal_test(n)
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def test_exactly_unequal_floats(self):
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# Test unequal float values are unequal with zero error tolerance.
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for x in [9.51, 5723.05, 47.8, 9.17, 17.24]:
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self.do_exactly_unequal_test(x)
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def test_exactly_unequal_fractions(self):
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# Test that unequal Fractions are unequal with zero error tolerance.
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F = Fraction
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for f in [F(1, 5), F(7, 9), F(12, 11), F(101, 99023)]:
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self.do_exactly_unequal_test(f)
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def test_exactly_unequal_decimals(self):
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# Test that unequal Decimals are unequal with zero error tolerance.
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for d in map(Decimal, "3.1415 298.12 3.47 18.996 0.00245".split()):
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self.do_exactly_unequal_test(d)
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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))
|
|
|
|
def test_invalid_input_type(self):
|
|
with self.assertRaises(TypeError):
|
|
statistics._convert(None, float)
|
|
|
|
|
|
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__
|
|
def __mul__(self, other):
|
|
return type(self)(super().__mul__(other))
|
|
__rmul__ = __mul__
|
|
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))
|
|
|
|
def test_ints(self):
|
|
self.assertEqual(self.func([1, 5, 3, -4, -8, 20, 42, 1]),
|
|
(int, Fraction(60), 8))
|
|
|
|
def test_floats(self):
|
|
self.assertEqual(self.func([0.25]*20),
|
|
(float, Fraction(5.0), 20))
|
|
|
|
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_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_invalid_type_error(self):
|
|
# Test error is raised when input contains invalid type(s)
|
|
for data in [
|
|
['3.14'], # single string
|
|
['1', '2', '3'], # multiple strings
|
|
[1, '2', 3, '4', 5], # mixed strings and valid integers
|
|
[2.3, 3.4, 4.5, '5.6'] # only one string and valid floats
|
|
]:
|
|
with self.subTest(data=data):
|
|
with self.assertRaises(TypeError):
|
|
self.func(data)
|
|
|
|
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)
|
|
|
|
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.
|
|
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_single_value(self):
|
|
# Override method from AverageMixin.
|
|
# Average of a single value is the value as a float.
|
|
for x in (23, 42.5, 1.3e15, Fraction(15, 19), Decimal('0.28')):
|
|
self.assertEqual(self.func([x]), 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.assertEqual(self.func(data), 20)
|
|
|
|
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
|
|
# mode() should return 2, the first encountered mode
|
|
self.assertEqual(self.func(data), 2)
|
|
|
|
def test_unique_data(self):
|
|
# Test mode when data points are all unique.
|
|
data = list(range(10))
|
|
# mode() should return 0, the first encountered mode
|
|
self.assertEqual(self.func(data), 0)
|
|
|
|
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.
|
|
# We're making sure mode() first calls iter() on its input.
|
|
# The concern is that a Counter of a Counter returns the original
|
|
# unchanged rather than counting its keys.
|
|
c = collections.Counter(a=1, b=2)
|
|
# If iter() is called, mode(c) loops over the keys, ['a', 'b'],
|
|
# all the counts will be 1, and the first encountered mode is 'a'.
|
|
self.assertEqual(self.func(c), 'a')
|
|
|
|
|
|
class TestMultiMode(unittest.TestCase):
|
|
|
|
def test_basics(self):
|
|
multimode = statistics.multimode
|
|
self.assertEqual(multimode('aabbbbbbbbcc'), ['b'])
|
|
self.assertEqual(multimode('aabbbbccddddeeffffgg'), ['b', 'd', 'f'])
|
|
self.assertEqual(multimode(''), [])
|
|
|
|
|
|
class TestFMean(unittest.TestCase):
|
|
|
|
def test_basics(self):
|
|
fmean = statistics.fmean
|
|
D = Decimal
|
|
F = Fraction
|
|
for data, expected_mean, kind in [
|
|
([3.5, 4.0, 5.25], 4.25, 'floats'),
|
|
([D('3.5'), D('4.0'), D('5.25')], 4.25, 'decimals'),
|
|
([F(7, 2), F(4, 1), F(21, 4)], 4.25, 'fractions'),
|
|
([True, False, True, True, False], 0.60, 'booleans'),
|
|
([3.5, 4, F(21, 4)], 4.25, 'mixed types'),
|
|
((3.5, 4.0, 5.25), 4.25, 'tuple'),
|
|
(iter([3.5, 4.0, 5.25]), 4.25, 'iterator'),
|
|
]:
|
|
actual_mean = fmean(data)
|
|
self.assertIs(type(actual_mean), float, kind)
|
|
self.assertEqual(actual_mean, expected_mean, kind)
|
|
|
|
def test_error_cases(self):
|
|
fmean = statistics.fmean
|
|
StatisticsError = statistics.StatisticsError
|
|
with self.assertRaises(StatisticsError):
|
|
fmean([]) # empty input
|
|
with self.assertRaises(StatisticsError):
|
|
fmean(iter([])) # empty iterator
|
|
with self.assertRaises(TypeError):
|
|
fmean(None) # non-iterable input
|
|
with self.assertRaises(TypeError):
|
|
fmean([10, None, 20]) # non-numeric input
|
|
with self.assertRaises(TypeError):
|
|
fmean() # missing data argument
|
|
with self.assertRaises(TypeError):
|
|
fmean([10, 20, 60], 70) # too many arguments
|
|
|
|
def test_special_values(self):
|
|
# Rules for special values are inherited from math.fsum()
|
|
fmean = statistics.fmean
|
|
NaN = float('Nan')
|
|
Inf = float('Inf')
|
|
self.assertTrue(math.isnan(fmean([10, NaN])), 'nan')
|
|
self.assertTrue(math.isnan(fmean([NaN, Inf])), 'nan and infinity')
|
|
self.assertTrue(math.isinf(fmean([10, Inf])), 'infinity')
|
|
with self.assertRaises(ValueError):
|
|
fmean([Inf, -Inf])
|
|
|
|
def test_weights(self):
|
|
fmean = statistics.fmean
|
|
StatisticsError = statistics.StatisticsError
|
|
self.assertEqual(
|
|
fmean([10, 10, 10, 50], [0.25] * 4),
|
|
fmean([10, 10, 10, 50]))
|
|
self.assertEqual(
|
|
fmean([10, 10, 20], [0.25, 0.25, 0.50]),
|
|
fmean([10, 10, 20, 20]))
|
|
self.assertEqual( # inputs are iterators
|
|
fmean(iter([10, 10, 20]), iter([0.25, 0.25, 0.50])),
|
|
fmean([10, 10, 20, 20]))
|
|
with self.assertRaises(StatisticsError):
|
|
fmean([10, 20, 30], [1, 2]) # unequal lengths
|
|
with self.assertRaises(StatisticsError):
|
|
fmean(iter([10, 20, 30]), iter([1, 2])) # unequal lengths
|
|
with self.assertRaises(StatisticsError):
|
|
fmean([10, 20], [-1, 1]) # sum of weights is zero
|
|
with self.assertRaises(StatisticsError):
|
|
fmean(iter([10, 20]), iter([-1, 1])) # sum of weights is zero
|
|
|
|
|
|
# === 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)
|
|
|
|
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.
|
|
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)
|
|
|
|
def test_center_not_at_mean(self):
|
|
data = (1.0, 2.0)
|
|
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):
|
|
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)
|
|
|
|
def test_center_not_at_mean(self):
|
|
# See issue: 40855
|
|
data = (3, 6, 7, 10)
|
|
self.assertEqual(self.func(data), 2.5)
|
|
self.assertEqual(self.func(data, mu=0.5), 6.5)
|
|
|
|
class TestSqrtHelpers(unittest.TestCase):
|
|
|
|
def test_integer_sqrt_of_frac_rto(self):
|
|
for n, m in itertools.product(range(100), range(1, 1000)):
|
|
r = statistics._integer_sqrt_of_frac_rto(n, m)
|
|
self.assertIsInstance(r, int)
|
|
if r*r*m == n:
|
|
# Root is exact
|
|
continue
|
|
# Inexact, so the root should be odd
|
|
self.assertEqual(r&1, 1)
|
|
# Verify correct rounding
|
|
self.assertTrue(m * (r - 1)**2 < n < m * (r + 1)**2)
|
|
|
|
@requires_IEEE_754
|
|
def test_float_sqrt_of_frac(self):
|
|
|
|
def is_root_correctly_rounded(x: Fraction, root: float) -> bool:
|
|
if not x:
|
|
return root == 0.0
|
|
|
|
# Extract adjacent representable floats
|
|
r_up: float = math.nextafter(root, math.inf)
|
|
r_down: float = math.nextafter(root, -math.inf)
|
|
assert r_down < root < r_up
|
|
|
|
# Convert to fractions for exact arithmetic
|
|
frac_root: Fraction = Fraction(root)
|
|
half_way_up: Fraction = (frac_root + Fraction(r_up)) / 2
|
|
half_way_down: Fraction = (frac_root + Fraction(r_down)) / 2
|
|
|
|
# Check a closed interval.
|
|
# Does not test for a midpoint rounding rule.
|
|
return half_way_down ** 2 <= x <= half_way_up ** 2
|
|
|
|
randrange = random.randrange
|
|
|
|
for i in range(60_000):
|
|
numerator: int = randrange(10 ** randrange(50))
|
|
denonimator: int = randrange(10 ** randrange(50)) + 1
|
|
with self.subTest(numerator=numerator, denonimator=denonimator):
|
|
x: Fraction = Fraction(numerator, denonimator)
|
|
root: float = statistics._float_sqrt_of_frac(numerator, denonimator)
|
|
self.assertTrue(is_root_correctly_rounded(x, root))
|
|
|
|
# Verify that corner cases and error handling match math.sqrt()
|
|
self.assertEqual(statistics._float_sqrt_of_frac(0, 1), 0.0)
|
|
with self.assertRaises(ValueError):
|
|
statistics._float_sqrt_of_frac(-1, 1)
|
|
with self.assertRaises(ValueError):
|
|
statistics._float_sqrt_of_frac(1, -1)
|
|
|
|
# Error handling for zero denominator matches that for Fraction(1, 0)
|
|
with self.assertRaises(ZeroDivisionError):
|
|
statistics._float_sqrt_of_frac(1, 0)
|
|
|
|
# The result is well defined if both inputs are negative
|
|
self.assertEqual(statistics._float_sqrt_of_frac(-2, -1), statistics._float_sqrt_of_frac(2, 1))
|
|
|
|
def test_decimal_sqrt_of_frac(self):
|
|
root: Decimal
|
|
numerator: int
|
|
denominator: int
|
|
|
|
for root, numerator, denominator in [
|
|
(Decimal('0.4481904599041192673635338663'), 200874688349065940678243576378, 1000000000000000000000000000000), # No adj
|
|
(Decimal('0.7924949131383786609961759598'), 628048187350206338833590574929, 1000000000000000000000000000000), # Adj up
|
|
(Decimal('0.8500554152289934068192208727'), 722594208960136395984391238251, 1000000000000000000000000000000), # Adj down
|
|
]:
|
|
with decimal.localcontext(decimal.DefaultContext):
|
|
self.assertEqual(statistics._decimal_sqrt_of_frac(numerator, denominator), root)
|
|
|
|
# Confirm expected root with a quad precision decimal computation
|
|
with decimal.localcontext(decimal.DefaultContext) as ctx:
|
|
ctx.prec *= 4
|
|
high_prec_ratio = Decimal(numerator) / Decimal(denominator)
|
|
ctx.rounding = decimal.ROUND_05UP
|
|
high_prec_root = high_prec_ratio.sqrt()
|
|
with decimal.localcontext(decimal.DefaultContext):
|
|
target_root = +high_prec_root
|
|
self.assertEqual(root, target_root)
|
|
|
|
# Verify that corner cases and error handling match Decimal.sqrt()
|
|
self.assertEqual(statistics._decimal_sqrt_of_frac(0, 1), 0.0)
|
|
with self.assertRaises(decimal.InvalidOperation):
|
|
statistics._decimal_sqrt_of_frac(-1, 1)
|
|
with self.assertRaises(decimal.InvalidOperation):
|
|
statistics._decimal_sqrt_of_frac(1, -1)
|
|
|
|
# Error handling for zero denominator matches that for Fraction(1, 0)
|
|
with self.assertRaises(ZeroDivisionError):
|
|
statistics._decimal_sqrt_of_frac(1, 0)
|
|
|
|
# The result is well defined if both inputs are negative
|
|
self.assertEqual(statistics._decimal_sqrt_of_frac(-2, -1), statistics._decimal_sqrt_of_frac(2, 1))
|
|
|
|
|
|
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.assertAlmostEqual(self.func(data), expected)
|
|
|
|
def test_center_not_at_mean(self):
|
|
data = (1.0, 2.0)
|
|
self.assertEqual(self.func(data, xbar=2.0), 1.0)
|
|
|
|
class TestGeometricMean(unittest.TestCase):
|
|
|
|
def test_basics(self):
|
|
geometric_mean = statistics.geometric_mean
|
|
self.assertAlmostEqual(geometric_mean([54, 24, 36]), 36.0)
|
|
self.assertAlmostEqual(geometric_mean([4.0, 9.0]), 6.0)
|
|
self.assertAlmostEqual(geometric_mean([17.625]), 17.625)
|
|
|
|
random.seed(86753095551212)
|
|
for rng in [
|
|
range(1, 100),
|
|
range(1, 1_000),
|
|
range(1, 10_000),
|
|
range(500, 10_000, 3),
|
|
range(10_000, 500, -3),
|
|
[12, 17, 13, 5, 120, 7],
|
|
[random.expovariate(50.0) for i in range(1_000)],
|
|
[random.lognormvariate(20.0, 3.0) for i in range(2_000)],
|
|
[random.triangular(2000, 3000, 2200) for i in range(3_000)],
|
|
]:
|
|
gm_decimal = math.prod(map(Decimal, rng)) ** (Decimal(1) / len(rng))
|
|
gm_float = geometric_mean(rng)
|
|
self.assertTrue(math.isclose(gm_float, float(gm_decimal)))
|
|
|
|
def test_various_input_types(self):
|
|
geometric_mean = statistics.geometric_mean
|
|
D = Decimal
|
|
F = Fraction
|
|
# https://www.wolframalpha.com/input/?i=geometric+mean+3.5,+4.0,+5.25
|
|
expected_mean = 4.18886
|
|
for data, kind in [
|
|
([3.5, 4.0, 5.25], 'floats'),
|
|
([D('3.5'), D('4.0'), D('5.25')], 'decimals'),
|
|
([F(7, 2), F(4, 1), F(21, 4)], 'fractions'),
|
|
([3.5, 4, F(21, 4)], 'mixed types'),
|
|
((3.5, 4.0, 5.25), 'tuple'),
|
|
(iter([3.5, 4.0, 5.25]), 'iterator'),
|
|
]:
|
|
actual_mean = geometric_mean(data)
|
|
self.assertIs(type(actual_mean), float, kind)
|
|
self.assertAlmostEqual(actual_mean, expected_mean, places=5)
|
|
|
|
def test_big_and_small(self):
|
|
geometric_mean = statistics.geometric_mean
|
|
|
|
# Avoid overflow to infinity
|
|
large = 2.0 ** 1000
|
|
big_gm = geometric_mean([54.0 * large, 24.0 * large, 36.0 * large])
|
|
self.assertTrue(math.isclose(big_gm, 36.0 * large))
|
|
self.assertFalse(math.isinf(big_gm))
|
|
|
|
# Avoid underflow to zero
|
|
small = 2.0 ** -1000
|
|
small_gm = geometric_mean([54.0 * small, 24.0 * small, 36.0 * small])
|
|
self.assertTrue(math.isclose(small_gm, 36.0 * small))
|
|
self.assertNotEqual(small_gm, 0.0)
|
|
|
|
def test_error_cases(self):
|
|
geometric_mean = statistics.geometric_mean
|
|
StatisticsError = statistics.StatisticsError
|
|
with self.assertRaises(StatisticsError):
|
|
geometric_mean([]) # empty input
|
|
with self.assertRaises(StatisticsError):
|
|
geometric_mean([3.5, 0.0, 5.25]) # zero input
|
|
with self.assertRaises(StatisticsError):
|
|
geometric_mean([3.5, -4.0, 5.25]) # negative input
|
|
with self.assertRaises(StatisticsError):
|
|
geometric_mean(iter([])) # empty iterator
|
|
with self.assertRaises(TypeError):
|
|
geometric_mean(None) # non-iterable input
|
|
with self.assertRaises(TypeError):
|
|
geometric_mean([10, None, 20]) # non-numeric input
|
|
with self.assertRaises(TypeError):
|
|
geometric_mean() # missing data argument
|
|
with self.assertRaises(TypeError):
|
|
geometric_mean([10, 20, 60], 70) # too many arguments
|
|
|
|
def test_special_values(self):
|
|
# Rules for special values are inherited from math.fsum()
|
|
geometric_mean = statistics.geometric_mean
|
|
NaN = float('Nan')
|
|
Inf = float('Inf')
|
|
self.assertTrue(math.isnan(geometric_mean([10, NaN])), 'nan')
|
|
self.assertTrue(math.isnan(geometric_mean([NaN, Inf])), 'nan and infinity')
|
|
self.assertTrue(math.isinf(geometric_mean([10, Inf])), 'infinity')
|
|
with self.assertRaises(ValueError):
|
|
geometric_mean([Inf, -Inf])
|
|
|
|
def test_mixed_int_and_float(self):
|
|
# Regression test for b.p.o. issue #28327
|
|
geometric_mean = statistics.geometric_mean
|
|
expected_mean = 3.80675409583932
|
|
values = [
|
|
[2, 3, 5, 7],
|
|
[2, 3, 5, 7.0],
|
|
[2, 3, 5.0, 7.0],
|
|
[2, 3.0, 5.0, 7.0],
|
|
[2.0, 3.0, 5.0, 7.0],
|
|
]
|
|
for v in values:
|
|
with self.subTest(v=v):
|
|
actual_mean = geometric_mean(v)
|
|
self.assertAlmostEqual(actual_mean, expected_mean, places=5)
|
|
|
|
|
|
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)
|
|
# Preserve datatype when possible
|
|
for datatype in (float, Decimal, Fraction):
|
|
result = quantiles(map(datatype, data), n=n)
|
|
self.assertTrue(all(type(x) == datatype) for x in result)
|
|
self.assertEqual(result, list(map(datatype, expected)))
|
|
# Quantiles should be idempotent
|
|
if len(expected) >= 2:
|
|
self.assertEqual(quantiles(expected, n=n), expected)
|
|
# Cross-check against method='inclusive' which should give
|
|
# the same result after adding in minimum and maximum values
|
|
# extrapolated from the two lowest and two highest points.
|
|
sdata = sorted(data)
|
|
lo = 2 * sdata[0] - sdata[1]
|
|
hi = 2 * sdata[-1] - sdata[-2]
|
|
padded_data = data + [lo, hi]
|
|
self.assertEqual(
|
|
quantiles(data, n=n),
|
|
quantiles(padded_data, n=n, method='inclusive'),
|
|
(n, data),
|
|
)
|
|
# Invariant under translation 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)))
|
|
# Q2 agrees with median()
|
|
for k in range(2, 60):
|
|
data = random.choices(range(100), k=k)
|
|
q1, q2, q3 = quantiles(data)
|
|
self.assertEqual(q2, statistics.median(data))
|
|
|
|
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 quantile() 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)
|
|
# Preserve datatype when possible
|
|
for datatype in (float, Decimal, Fraction):
|
|
result = quantiles(map(datatype, data), n=n, method="inclusive")
|
|
self.assertTrue(all(type(x) == datatype) for x in result)
|
|
self.assertEqual(result, list(map(datatype, expected)))
|
|
# Invariant under translation 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)))
|
|
# Natural deciles
|
|
self.assertEqual(quantiles([0, 100], n=10, method='inclusive'),
|
|
[10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 90.0])
|
|
self.assertEqual(quantiles(range(0, 101), n=10, method='inclusive'),
|
|
[10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 90.0])
|
|
# Whenever n is smaller than the number of data points, running
|
|
# method='inclusive' should give the same result as method='exclusive'
|
|
# after the two included extreme points are removed.
|
|
data = [random.randrange(10_000) for i in range(501)]
|
|
actual = quantiles(data, n=32, method='inclusive')
|
|
data.remove(min(data))
|
|
data.remove(max(data))
|
|
expected = quantiles(data, n=32)
|
|
self.assertEqual(expected, actual)
|
|
# Q2 agrees with median()
|
|
for k in range(2, 60):
|
|
data = random.choices(range(100), k=k)
|
|
q1, q2, q3 = quantiles(data, method='inclusive')
|
|
self.assertEqual(q2, statistics.median(data))
|
|
|
|
def test_equal_inputs(self):
|
|
quantiles = statistics.quantiles
|
|
for n in range(2, 10):
|
|
data = [10.0] * n
|
|
self.assertEqual(quantiles(data), [10.0, 10.0, 10.0])
|
|
self.assertEqual(quantiles(data, method='inclusive'),
|
|
[10.0, 10.0, 10.0])
|
|
|
|
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 TestBivariateStatistics(unittest.TestCase):
|
|
|
|
def test_unequal_size_error(self):
|
|
for x, y in [
|
|
([1, 2, 3], [1, 2]),
|
|
([1, 2], [1, 2, 3]),
|
|
]:
|
|
with self.assertRaises(statistics.StatisticsError):
|
|
statistics.covariance(x, y)
|
|
with self.assertRaises(statistics.StatisticsError):
|
|
statistics.correlation(x, y)
|
|
with self.assertRaises(statistics.StatisticsError):
|
|
statistics.linear_regression(x, y)
|
|
|
|
def test_small_sample_error(self):
|
|
for x, y in [
|
|
([], []),
|
|
([], [1, 2,]),
|
|
([1, 2,], []),
|
|
([1,], [1,]),
|
|
([1,], [1, 2,]),
|
|
([1, 2,], [1,]),
|
|
]:
|
|
with self.assertRaises(statistics.StatisticsError):
|
|
statistics.covariance(x, y)
|
|
with self.assertRaises(statistics.StatisticsError):
|
|
statistics.correlation(x, y)
|
|
with self.assertRaises(statistics.StatisticsError):
|
|
statistics.linear_regression(x, y)
|
|
|
|
|
|
class TestCorrelationAndCovariance(unittest.TestCase):
|
|
|
|
def test_results(self):
|
|
for x, y, result in [
|
|
([1, 2, 3], [1, 2, 3], 1),
|
|
([1, 2, 3], [-1, -2, -3], -1),
|
|
([1, 2, 3], [3, 2, 1], -1),
|
|
([1, 2, 3], [1, 2, 1], 0),
|
|
([1, 2, 3], [1, 3, 2], 0.5),
|
|
]:
|
|
self.assertAlmostEqual(statistics.correlation(x, y), result)
|
|
self.assertAlmostEqual(statistics.covariance(x, y), result)
|
|
|
|
def test_different_scales(self):
|
|
x = [1, 2, 3]
|
|
y = [10, 30, 20]
|
|
self.assertAlmostEqual(statistics.correlation(x, y), 0.5)
|
|
self.assertAlmostEqual(statistics.covariance(x, y), 5)
|
|
|
|
y = [.1, .2, .3]
|
|
self.assertAlmostEqual(statistics.correlation(x, y), 1)
|
|
self.assertAlmostEqual(statistics.covariance(x, y), 0.1)
|
|
|
|
|
|
def test_correlation_spearman(self):
|
|
# https://statistics.laerd.com/statistical-guides/spearmans-rank-order-correlation-statistical-guide-2.php
|
|
# Compare with:
|
|
# >>> import scipy.stats.mstats
|
|
# >>> scipy.stats.mstats.spearmanr(reading, mathematics)
|
|
# SpearmanrResult(correlation=0.6686960980480712, pvalue=0.03450954165178532)
|
|
# And Wolfram Alpha gives: 0.668696
|
|
# https://www.wolframalpha.com/input?i=SpearmanRho%5B%7B56%2C+75%2C+45%2C+71%2C+61%2C+64%2C+58%2C+80%2C+76%2C+61%7D%2C+%7B66%2C+70%2C+40%2C+60%2C+65%2C+56%2C+59%2C+77%2C+67%2C+63%7D%5D
|
|
reading = [56, 75, 45, 71, 61, 64, 58, 80, 76, 61]
|
|
mathematics = [66, 70, 40, 60, 65, 56, 59, 77, 67, 63]
|
|
self.assertAlmostEqual(statistics.correlation(reading, mathematics, method='ranked'),
|
|
0.6686960980480712)
|
|
|
|
with self.assertRaises(ValueError):
|
|
statistics.correlation(reading, mathematics, method='bad_method')
|
|
|
|
class TestLinearRegression(unittest.TestCase):
|
|
|
|
def test_constant_input_error(self):
|
|
x = [1, 1, 1,]
|
|
y = [1, 2, 3,]
|
|
with self.assertRaises(statistics.StatisticsError):
|
|
statistics.linear_regression(x, y)
|
|
|
|
def test_results(self):
|
|
for x, y, true_intercept, true_slope in [
|
|
([1, 2, 3], [0, 0, 0], 0, 0),
|
|
([1, 2, 3], [1, 2, 3], 0, 1),
|
|
([1, 2, 3], [100, 100, 100], 100, 0),
|
|
([1, 2, 3], [12, 14, 16], 10, 2),
|
|
([1, 2, 3], [-1, -2, -3], 0, -1),
|
|
([1, 2, 3], [21, 22, 23], 20, 1),
|
|
([1, 2, 3], [5.1, 5.2, 5.3], 5, 0.1),
|
|
]:
|
|
slope, intercept = statistics.linear_regression(x, y)
|
|
self.assertAlmostEqual(intercept, true_intercept)
|
|
self.assertAlmostEqual(slope, true_slope)
|
|
|
|
def test_proportional(self):
|
|
x = [10, 20, 30, 40]
|
|
y = [180, 398, 610, 799]
|
|
slope, intercept = statistics.linear_regression(x, y, proportional=True)
|
|
self.assertAlmostEqual(slope, 20 + 1/150)
|
|
self.assertEqual(intercept, 0.0)
|
|
|
|
class TestNormalDist:
|
|
|
|
# General note on precision: The pdf(), cdf(), and overlap() methods
|
|
# depend on functions in the math libraries that do not make
|
|
# explicit accuracy guarantees. Accordingly, some of the accuracy
|
|
# tests below may fail if the underlying math functions are
|
|
# inaccurate. There isn't much we can do about this short of
|
|
# implementing our own implementations from scratch.
|
|
|
|
def test_slots(self):
|
|
nd = self.module.NormalDist(300, 23)
|
|
with self.assertRaises(TypeError):
|
|
vars(nd)
|
|
self.assertEqual(tuple(nd.__slots__), ('_mu', '_sigma'))
|
|
|
|
def test_instantiation_and_attributes(self):
|
|
nd = self.module.NormalDist(500, 17)
|
|
self.assertEqual(nd.mean, 500)
|
|
self.assertEqual(nd.stdev, 17)
|
|
self.assertEqual(nd.variance, 17**2)
|
|
|
|
# default arguments
|
|
nd = self.module.NormalDist()
|
|
self.assertEqual(nd.mean, 0)
|
|
self.assertEqual(nd.stdev, 1)
|
|
self.assertEqual(nd.variance, 1**2)
|
|
|
|
# error case: negative sigma
|
|
with self.assertRaises(self.module.StatisticsError):
|
|
self.module.NormalDist(500, -10)
|
|
|
|
# verify that subclass type is honored
|
|
class NewNormalDist(self.module.NormalDist):
|
|
pass
|
|
nnd = NewNormalDist(200, 5)
|
|
self.assertEqual(type(nnd), NewNormalDist)
|
|
|
|
def test_alternative_constructor(self):
|
|
NormalDist = self.module.NormalDist
|
|
data = [96, 107, 90, 92, 110]
|
|
# list input
|
|
self.assertEqual(NormalDist.from_samples(data), NormalDist(99, 9))
|
|
# tuple input
|
|
self.assertEqual(NormalDist.from_samples(tuple(data)), NormalDist(99, 9))
|
|
# iterator input
|
|
self.assertEqual(NormalDist.from_samples(iter(data)), NormalDist(99, 9))
|
|
# error cases
|
|
with self.assertRaises(self.module.StatisticsError):
|
|
NormalDist.from_samples([]) # empty input
|
|
with self.assertRaises(self.module.StatisticsError):
|
|
NormalDist.from_samples([10]) # only one input
|
|
|
|
# verify that subclass type is honored
|
|
class NewNormalDist(NormalDist):
|
|
pass
|
|
nnd = NewNormalDist.from_samples(data)
|
|
self.assertEqual(type(nnd), NewNormalDist)
|
|
|
|
def test_sample_generation(self):
|
|
NormalDist = self.module.NormalDist
|
|
mu, sigma = 10_000, 3.0
|
|
X = NormalDist(mu, sigma)
|
|
n = 1_000
|
|
data = X.samples(n)
|
|
self.assertEqual(len(data), n)
|
|
self.assertEqual(set(map(type, data)), {float})
|
|
# mean(data) expected to fall within 8 standard deviations
|
|
xbar = self.module.mean(data)
|
|
self.assertTrue(mu - sigma*8 <= xbar <= mu + sigma*8)
|
|
|
|
# verify that seeding makes reproducible sequences
|
|
n = 100
|
|
data1 = X.samples(n, seed='happiness and joy')
|
|
data2 = X.samples(n, seed='trouble and despair')
|
|
data3 = X.samples(n, seed='happiness and joy')
|
|
data4 = X.samples(n, seed='trouble and despair')
|
|
self.assertEqual(data1, data3)
|
|
self.assertEqual(data2, data4)
|
|
self.assertNotEqual(data1, data2)
|
|
|
|
def test_pdf(self):
|
|
NormalDist = self.module.NormalDist
|
|
X = NormalDist(100, 15)
|
|
# Verify peak around center
|
|
self.assertLess(X.pdf(99), X.pdf(100))
|
|
self.assertLess(X.pdf(101), X.pdf(100))
|
|
# Test symmetry
|
|
for i in range(50):
|
|
self.assertAlmostEqual(X.pdf(100 - i), X.pdf(100 + i))
|
|
# Test vs CDF
|
|
dx = 2.0 ** -10
|
|
for x in range(90, 111):
|
|
est_pdf = (X.cdf(x + dx) - X.cdf(x)) / dx
|
|
self.assertAlmostEqual(X.pdf(x), est_pdf, places=4)
|
|
# Test vs table of known values -- CRC 26th Edition
|
|
Z = NormalDist()
|
|
for x, px in enumerate([
|
|
0.3989, 0.3989, 0.3989, 0.3988, 0.3986,
|
|
0.3984, 0.3982, 0.3980, 0.3977, 0.3973,
|
|
0.3970, 0.3965, 0.3961, 0.3956, 0.3951,
|
|
0.3945, 0.3939, 0.3932, 0.3925, 0.3918,
|
|
0.3910, 0.3902, 0.3894, 0.3885, 0.3876,
|
|
0.3867, 0.3857, 0.3847, 0.3836, 0.3825,
|
|
0.3814, 0.3802, 0.3790, 0.3778, 0.3765,
|
|
0.3752, 0.3739, 0.3725, 0.3712, 0.3697,
|
|
0.3683, 0.3668, 0.3653, 0.3637, 0.3621,
|
|
0.3605, 0.3589, 0.3572, 0.3555, 0.3538,
|
|
]):
|
|
self.assertAlmostEqual(Z.pdf(x / 100.0), px, places=4)
|
|
self.assertAlmostEqual(Z.pdf(-x / 100.0), px, places=4)
|
|
# Error case: variance is zero
|
|
Y = NormalDist(100, 0)
|
|
with self.assertRaises(self.module.StatisticsError):
|
|
Y.pdf(90)
|
|
# Special values
|
|
self.assertEqual(X.pdf(float('-Inf')), 0.0)
|
|
self.assertEqual(X.pdf(float('Inf')), 0.0)
|
|
self.assertTrue(math.isnan(X.pdf(float('NaN'))))
|
|
|
|
def test_cdf(self):
|
|
NormalDist = self.module.NormalDist
|
|
X = NormalDist(100, 15)
|
|
cdfs = [X.cdf(x) for x in range(1, 200)]
|
|
self.assertEqual(set(map(type, cdfs)), {float})
|
|
# Verify montonic
|
|
self.assertEqual(cdfs, sorted(cdfs))
|
|
# Verify center (should be exact)
|
|
self.assertEqual(X.cdf(100), 0.50)
|
|
# Check against a table of known values
|
|
# https://en.wikipedia.org/wiki/Standard_normal_table#Cumulative
|
|
Z = NormalDist()
|
|
for z, cum_prob in [
|
|
(0.00, 0.50000), (0.01, 0.50399), (0.02, 0.50798),
|
|
(0.14, 0.55567), (0.29, 0.61409), (0.33, 0.62930),
|
|
(0.54, 0.70540), (0.60, 0.72575), (1.17, 0.87900),
|
|
(1.60, 0.94520), (2.05, 0.97982), (2.89, 0.99807),
|
|
(3.52, 0.99978), (3.98, 0.99997), (4.07, 0.99998),
|
|
]:
|
|
self.assertAlmostEqual(Z.cdf(z), cum_prob, places=5)
|
|
self.assertAlmostEqual(Z.cdf(-z), 1.0 - cum_prob, places=5)
|
|
# Error case: variance is zero
|
|
Y = NormalDist(100, 0)
|
|
with self.assertRaises(self.module.StatisticsError):
|
|
Y.cdf(90)
|
|
# Special values
|
|
self.assertEqual(X.cdf(float('-Inf')), 0.0)
|
|
self.assertEqual(X.cdf(float('Inf')), 1.0)
|
|
self.assertTrue(math.isnan(X.cdf(float('NaN'))))
|
|
|
|
@support.skip_if_pgo_task
|
|
def test_inv_cdf(self):
|
|
NormalDist = self.module.NormalDist
|
|
|
|
# Center case should be exact.
|
|
iq = NormalDist(100, 15)
|
|
self.assertEqual(iq.inv_cdf(0.50), iq.mean)
|
|
|
|
# Test versus a published table of known percentage points.
|
|
# See the second table at the bottom of the page here:
|
|
# http://people.bath.ac.uk/masss/tables/normaltable.pdf
|
|
Z = NormalDist()
|
|
pp = {5.0: (0.000, 1.645, 2.576, 3.291, 3.891,
|
|
4.417, 4.892, 5.327, 5.731, 6.109),
|
|
2.5: (0.674, 1.960, 2.807, 3.481, 4.056,
|
|
4.565, 5.026, 5.451, 5.847, 6.219),
|
|
1.0: (1.282, 2.326, 3.090, 3.719, 4.265,
|
|
4.753, 5.199, 5.612, 5.998, 6.361)}
|
|
for base, row in pp.items():
|
|
for exp, x in enumerate(row, start=1):
|
|
p = base * 10.0 ** (-exp)
|
|
self.assertAlmostEqual(-Z.inv_cdf(p), x, places=3)
|
|
p = 1.0 - p
|
|
self.assertAlmostEqual(Z.inv_cdf(p), x, places=3)
|
|
|
|
# Match published example for MS Excel
|
|
# https://support.office.com/en-us/article/norm-inv-function-54b30935-fee7-493c-bedb-2278a9db7e13
|
|
self.assertAlmostEqual(NormalDist(40, 1.5).inv_cdf(0.908789), 42.000002)
|
|
|
|
# One million equally spaced probabilities
|
|
n = 2**20
|
|
for p in range(1, n):
|
|
p /= n
|
|
self.assertAlmostEqual(iq.cdf(iq.inv_cdf(p)), p)
|
|
|
|
# One hundred ever smaller probabilities to test tails out to
|
|
# extreme probabilities: 1 / 2**50 and (2**50-1) / 2 ** 50
|
|
for e in range(1, 51):
|
|
p = 2.0 ** (-e)
|
|
self.assertAlmostEqual(iq.cdf(iq.inv_cdf(p)), p)
|
|
p = 1.0 - p
|
|
self.assertAlmostEqual(iq.cdf(iq.inv_cdf(p)), p)
|
|
|
|
# Now apply cdf() first. Near the tails, the round-trip loses
|
|
# precision and is ill-conditioned (small changes in the inputs
|
|
# give large changes in the output), so only check to 5 places.
|
|
for x in range(200):
|
|
self.assertAlmostEqual(iq.inv_cdf(iq.cdf(x)), x, places=5)
|
|
|
|
# Error cases:
|
|
with self.assertRaises(self.module.StatisticsError):
|
|
iq.inv_cdf(0.0) # p is zero
|
|
with self.assertRaises(self.module.StatisticsError):
|
|
iq.inv_cdf(-0.1) # p under zero
|
|
with self.assertRaises(self.module.StatisticsError):
|
|
iq.inv_cdf(1.0) # p is one
|
|
with self.assertRaises(self.module.StatisticsError):
|
|
iq.inv_cdf(1.1) # p over one
|
|
|
|
# Supported case:
|
|
iq = NormalDist(100, 0) # sigma is zero
|
|
self.assertEqual(iq.inv_cdf(0.5), 100)
|
|
|
|
# Special values
|
|
self.assertTrue(math.isnan(Z.inv_cdf(float('NaN'))))
|
|
|
|
def test_quantiles(self):
|
|
# Quartiles of a standard normal distribution
|
|
Z = self.module.NormalDist()
|
|
for n, expected in [
|
|
(1, []),
|
|
(2, [0.0]),
|
|
(3, [-0.4307, 0.4307]),
|
|
(4 ,[-0.6745, 0.0, 0.6745]),
|
|
]:
|
|
actual = Z.quantiles(n=n)
|
|
self.assertTrue(all(math.isclose(e, a, abs_tol=0.0001)
|
|
for e, a in zip(expected, actual)))
|
|
|
|
def test_overlap(self):
|
|
NormalDist = self.module.NormalDist
|
|
|
|
# Match examples from Imman and Bradley
|
|
for X1, X2, published_result in [
|
|
(NormalDist(0.0, 2.0), NormalDist(1.0, 2.0), 0.80258),
|
|
(NormalDist(0.0, 1.0), NormalDist(1.0, 2.0), 0.60993),
|
|
]:
|
|
self.assertAlmostEqual(X1.overlap(X2), published_result, places=4)
|
|
self.assertAlmostEqual(X2.overlap(X1), published_result, places=4)
|
|
|
|
# Check against integration of the PDF
|
|
def overlap_numeric(X, Y, *, steps=8_192, z=5):
|
|
'Numerical integration cross-check for overlap() '
|
|
fsum = math.fsum
|
|
center = (X.mean + Y.mean) / 2.0
|
|
width = z * max(X.stdev, Y.stdev)
|
|
start = center - width
|
|
dx = 2.0 * width / steps
|
|
x_arr = [start + i*dx for i in range(steps)]
|
|
xp = list(map(X.pdf, x_arr))
|
|
yp = list(map(Y.pdf, x_arr))
|
|
total = max(fsum(xp), fsum(yp))
|
|
return fsum(map(min, xp, yp)) / total
|
|
|
|
for X1, X2 in [
|
|
# Examples from Imman and Bradley
|
|
(NormalDist(0.0, 2.0), NormalDist(1.0, 2.0)),
|
|
(NormalDist(0.0, 1.0), NormalDist(1.0, 2.0)),
|
|
# Example from https://www.rasch.org/rmt/rmt101r.htm
|
|
(NormalDist(0.0, 1.0), NormalDist(1.0, 2.0)),
|
|
# Gender heights from http://www.usablestats.com/lessons/normal
|
|
(NormalDist(70, 4), NormalDist(65, 3.5)),
|
|
# Misc cases with equal standard deviations
|
|
(NormalDist(100, 15), NormalDist(110, 15)),
|
|
(NormalDist(-100, 15), NormalDist(110, 15)),
|
|
(NormalDist(-100, 15), NormalDist(-110, 15)),
|
|
# Misc cases with unequal standard deviations
|
|
(NormalDist(100, 12), NormalDist(100, 15)),
|
|
(NormalDist(100, 12), NormalDist(110, 15)),
|
|
(NormalDist(100, 12), NormalDist(150, 15)),
|
|
(NormalDist(100, 12), NormalDist(150, 35)),
|
|
# Misc cases with small values
|
|
(NormalDist(1.000, 0.002), NormalDist(1.001, 0.003)),
|
|
(NormalDist(1.000, 0.002), NormalDist(1.006, 0.0003)),
|
|
(NormalDist(1.000, 0.002), NormalDist(1.001, 0.099)),
|
|
]:
|
|
self.assertAlmostEqual(X1.overlap(X2), overlap_numeric(X1, X2), places=5)
|
|
self.assertAlmostEqual(X2.overlap(X1), overlap_numeric(X1, X2), places=5)
|
|
|
|
# Error cases
|
|
X = NormalDist()
|
|
with self.assertRaises(TypeError):
|
|
X.overlap() # too few arguments
|
|
with self.assertRaises(TypeError):
|
|
X.overlap(X, X) # too may arguments
|
|
with self.assertRaises(TypeError):
|
|
X.overlap(None) # right operand not a NormalDist
|
|
with self.assertRaises(self.module.StatisticsError):
|
|
X.overlap(NormalDist(1, 0)) # right operand sigma is zero
|
|
with self.assertRaises(self.module.StatisticsError):
|
|
NormalDist(1, 0).overlap(X) # left operand sigma is zero
|
|
|
|
def test_zscore(self):
|
|
NormalDist = self.module.NormalDist
|
|
X = NormalDist(100, 15)
|
|
self.assertEqual(X.zscore(142), 2.8)
|
|
self.assertEqual(X.zscore(58), -2.8)
|
|
self.assertEqual(X.zscore(100), 0.0)
|
|
with self.assertRaises(TypeError):
|
|
X.zscore() # too few arguments
|
|
with self.assertRaises(TypeError):
|
|
X.zscore(1, 1) # too may arguments
|
|
with self.assertRaises(TypeError):
|
|
X.zscore(None) # non-numeric type
|
|
with self.assertRaises(self.module.StatisticsError):
|
|
NormalDist(1, 0).zscore(100) # sigma is zero
|
|
|
|
def test_properties(self):
|
|
X = self.module.NormalDist(100, 15)
|
|
self.assertEqual(X.mean, 100)
|
|
self.assertEqual(X.median, 100)
|
|
self.assertEqual(X.mode, 100)
|
|
self.assertEqual(X.stdev, 15)
|
|
self.assertEqual(X.variance, 225)
|
|
|
|
def test_same_type_addition_and_subtraction(self):
|
|
NormalDist = self.module.NormalDist
|
|
X = NormalDist(100, 12)
|
|
Y = NormalDist(40, 5)
|
|
self.assertEqual(X + Y, NormalDist(140, 13)) # __add__
|
|
self.assertEqual(X - Y, NormalDist(60, 13)) # __sub__
|
|
|
|
def test_translation_and_scaling(self):
|
|
NormalDist = self.module.NormalDist
|
|
X = NormalDist(100, 15)
|
|
y = 10
|
|
self.assertEqual(+X, NormalDist(100, 15)) # __pos__
|
|
self.assertEqual(-X, NormalDist(-100, 15)) # __neg__
|
|
self.assertEqual(X + y, NormalDist(110, 15)) # __add__
|
|
self.assertEqual(y + X, NormalDist(110, 15)) # __radd__
|
|
self.assertEqual(X - y, NormalDist(90, 15)) # __sub__
|
|
self.assertEqual(y - X, NormalDist(-90, 15)) # __rsub__
|
|
self.assertEqual(X * y, NormalDist(1000, 150)) # __mul__
|
|
self.assertEqual(y * X, NormalDist(1000, 150)) # __rmul__
|
|
self.assertEqual(X / y, NormalDist(10, 1.5)) # __truediv__
|
|
with self.assertRaises(TypeError): # __rtruediv__
|
|
y / X
|
|
|
|
def test_unary_operations(self):
|
|
NormalDist = self.module.NormalDist
|
|
X = NormalDist(100, 12)
|
|
Y = +X
|
|
self.assertIsNot(X, Y)
|
|
self.assertEqual(X.mean, Y.mean)
|
|
self.assertEqual(X.stdev, Y.stdev)
|
|
Y = -X
|
|
self.assertIsNot(X, Y)
|
|
self.assertEqual(X.mean, -Y.mean)
|
|
self.assertEqual(X.stdev, Y.stdev)
|
|
|
|
def test_equality(self):
|
|
NormalDist = self.module.NormalDist
|
|
nd1 = NormalDist()
|
|
nd2 = NormalDist(2, 4)
|
|
nd3 = NormalDist()
|
|
nd4 = NormalDist(2, 4)
|
|
nd5 = NormalDist(2, 8)
|
|
nd6 = NormalDist(8, 4)
|
|
self.assertNotEqual(nd1, nd2)
|
|
self.assertEqual(nd1, nd3)
|
|
self.assertEqual(nd2, nd4)
|
|
self.assertNotEqual(nd2, nd5)
|
|
self.assertNotEqual(nd2, nd6)
|
|
|
|
# Test NotImplemented when types are different
|
|
class A:
|
|
def __eq__(self, other):
|
|
return 10
|
|
a = A()
|
|
self.assertEqual(nd1.__eq__(a), NotImplemented)
|
|
self.assertEqual(nd1 == a, 10)
|
|
self.assertEqual(a == nd1, 10)
|
|
|
|
# All subclasses to compare equal giving the same behavior
|
|
# as list, tuple, int, float, complex, str, dict, set, etc.
|
|
class SizedNormalDist(NormalDist):
|
|
def __init__(self, mu, sigma, n):
|
|
super().__init__(mu, sigma)
|
|
self.n = n
|
|
s = SizedNormalDist(100, 15, 57)
|
|
nd4 = NormalDist(100, 15)
|
|
self.assertEqual(s, nd4)
|
|
|
|
# Don't allow duck type equality because we wouldn't
|
|
# want a lognormal distribution to compare equal
|
|
# to a normal distribution with the same parameters
|
|
class LognormalDist:
|
|
def __init__(self, mu, sigma):
|
|
self.mu = mu
|
|
self.sigma = sigma
|
|
lnd = LognormalDist(100, 15)
|
|
nd = NormalDist(100, 15)
|
|
self.assertNotEqual(nd, lnd)
|
|
|
|
def test_copy(self):
|
|
nd = self.module.NormalDist(37.5, 5.625)
|
|
nd1 = copy.copy(nd)
|
|
self.assertEqual(nd, nd1)
|
|
nd2 = copy.deepcopy(nd)
|
|
self.assertEqual(nd, nd2)
|
|
|
|
def test_pickle(self):
|
|
nd = self.module.NormalDist(37.5, 5.625)
|
|
for proto in range(pickle.HIGHEST_PROTOCOL + 1):
|
|
with self.subTest(proto=proto):
|
|
pickled = pickle.loads(pickle.dumps(nd, protocol=proto))
|
|
self.assertEqual(nd, pickled)
|
|
|
|
def test_hashability(self):
|
|
ND = self.module.NormalDist
|
|
s = {ND(100, 15), ND(100.0, 15.0), ND(100, 10), ND(95, 15), ND(100, 15)}
|
|
self.assertEqual(len(s), 3)
|
|
|
|
def test_repr(self):
|
|
nd = self.module.NormalDist(37.5, 5.625)
|
|
self.assertEqual(repr(nd), 'NormalDist(mu=37.5, sigma=5.625)')
|
|
|
|
# Swapping the sys.modules['statistics'] is to solving the
|
|
# _pickle.PicklingError:
|
|
# Can't pickle <class 'statistics.NormalDist'>:
|
|
# it's not the same object as statistics.NormalDist
|
|
class TestNormalDistPython(unittest.TestCase, TestNormalDist):
|
|
module = py_statistics
|
|
def setUp(self):
|
|
sys.modules['statistics'] = self.module
|
|
|
|
def tearDown(self):
|
|
sys.modules['statistics'] = statistics
|
|
|
|
|
|
@unittest.skipUnless(c_statistics, 'requires _statistics')
|
|
class TestNormalDistC(unittest.TestCase, TestNormalDist):
|
|
module = c_statistics
|
|
def setUp(self):
|
|
sys.modules['statistics'] = self.module
|
|
|
|
def tearDown(self):
|
|
sys.modules['statistics'] = statistics
|
|
|
|
|
|
# === Run tests ===
|
|
|
|
def load_tests(loader, tests, ignore):
|
|
"""Used for doctest/unittest integration."""
|
|
tests.addTests(doctest.DocTestSuite())
|
|
return tests
|
|
|
|
|
|
if __name__ == "__main__":
|
|
unittest.main()
|