Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1 | """Test suite for statistics module, including helper NumericTestCase and |
| 2 | approx_equal function. |
| 3 | |
| 4 | """ |
| 5 | |
Raymond Hettinger | 9013ccf | 2019-04-23 00:06:35 -0700 | [diff] [blame] | 6 | import bisect |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 7 | import collections |
Serhiy Storchaka | 2e576f5 | 2017-04-24 09:05:00 +0300 | [diff] [blame] | 8 | import collections.abc |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 9 | import copy |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 10 | import decimal |
| 11 | import doctest |
| 12 | import math |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 13 | import pickle |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 14 | import random |
Serhiy Storchaka | b12cb6a | 2013-12-08 18:16:18 +0200 | [diff] [blame] | 15 | import sys |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 16 | import unittest |
Miss Islington (bot) | 382cb85 | 2019-07-30 11:34:33 -0700 | [diff] [blame] | 17 | from test import support |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 18 | |
| 19 | from decimal import Decimal |
| 20 | from fractions import Fraction |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 21 | from test import support |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 22 | |
| 23 | |
| 24 | # Module to be tested. |
| 25 | import statistics |
| 26 | |
| 27 | |
| 28 | # === Helper functions and class === |
| 29 | |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 30 | def sign(x): |
| 31 | """Return -1.0 for negatives, including -0.0, otherwise +1.0.""" |
| 32 | return math.copysign(1, x) |
| 33 | |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 34 | def _nan_equal(a, b): |
| 35 | """Return True if a and b are both the same kind of NAN. |
| 36 | |
| 37 | >>> _nan_equal(Decimal('NAN'), Decimal('NAN')) |
| 38 | True |
| 39 | >>> _nan_equal(Decimal('sNAN'), Decimal('sNAN')) |
| 40 | True |
| 41 | >>> _nan_equal(Decimal('NAN'), Decimal('sNAN')) |
| 42 | False |
| 43 | >>> _nan_equal(Decimal(42), Decimal('NAN')) |
| 44 | False |
| 45 | |
| 46 | >>> _nan_equal(float('NAN'), float('NAN')) |
| 47 | True |
| 48 | >>> _nan_equal(float('NAN'), 0.5) |
| 49 | False |
| 50 | |
| 51 | >>> _nan_equal(float('NAN'), Decimal('NAN')) |
| 52 | False |
| 53 | |
| 54 | NAN payloads are not compared. |
| 55 | """ |
| 56 | if type(a) is not type(b): |
| 57 | return False |
| 58 | if isinstance(a, float): |
| 59 | return math.isnan(a) and math.isnan(b) |
| 60 | aexp = a.as_tuple()[2] |
| 61 | bexp = b.as_tuple()[2] |
| 62 | return (aexp == bexp) and (aexp in ('n', 'N')) # Both NAN or both sNAN. |
| 63 | |
| 64 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 65 | def _calc_errors(actual, expected): |
| 66 | """Return the absolute and relative errors between two numbers. |
| 67 | |
| 68 | >>> _calc_errors(100, 75) |
| 69 | (25, 0.25) |
| 70 | >>> _calc_errors(100, 100) |
| 71 | (0, 0.0) |
| 72 | |
| 73 | Returns the (absolute error, relative error) between the two arguments. |
| 74 | """ |
| 75 | base = max(abs(actual), abs(expected)) |
| 76 | abs_err = abs(actual - expected) |
| 77 | rel_err = abs_err/base if base else float('inf') |
| 78 | return (abs_err, rel_err) |
| 79 | |
| 80 | |
| 81 | def approx_equal(x, y, tol=1e-12, rel=1e-7): |
| 82 | """approx_equal(x, y [, tol [, rel]]) => True|False |
| 83 | |
| 84 | Return True if numbers x and y are approximately equal, to within some |
| 85 | margin of error, otherwise return False. Numbers which compare equal |
| 86 | will also compare approximately equal. |
| 87 | |
| 88 | x is approximately equal to y if the difference between them is less than |
| 89 | an absolute error tol or a relative error rel, whichever is bigger. |
| 90 | |
| 91 | If given, both tol and rel must be finite, non-negative numbers. If not |
| 92 | given, default values are tol=1e-12 and rel=1e-7. |
| 93 | |
| 94 | >>> approx_equal(1.2589, 1.2587, tol=0.0003, rel=0) |
| 95 | True |
| 96 | >>> approx_equal(1.2589, 1.2587, tol=0.0001, rel=0) |
| 97 | False |
| 98 | |
| 99 | Absolute error is defined as abs(x-y); if that is less than or equal to |
| 100 | tol, x and y are considered approximately equal. |
| 101 | |
| 102 | Relative error is defined as abs((x-y)/x) or abs((x-y)/y), whichever is |
| 103 | smaller, provided x or y are not zero. If that figure is less than or |
| 104 | equal to rel, x and y are considered approximately equal. |
| 105 | |
| 106 | Complex numbers are not directly supported. If you wish to compare to |
| 107 | complex numbers, extract their real and imaginary parts and compare them |
| 108 | individually. |
| 109 | |
| 110 | NANs always compare unequal, even with themselves. Infinities compare |
| 111 | approximately equal if they have the same sign (both positive or both |
| 112 | negative). Infinities with different signs compare unequal; so do |
| 113 | comparisons of infinities with finite numbers. |
| 114 | """ |
| 115 | if tol < 0 or rel < 0: |
| 116 | raise ValueError('error tolerances must be non-negative') |
| 117 | # NANs are never equal to anything, approximately or otherwise. |
| 118 | if math.isnan(x) or math.isnan(y): |
| 119 | return False |
| 120 | # Numbers which compare equal also compare approximately equal. |
| 121 | if x == y: |
| 122 | # This includes the case of two infinities with the same sign. |
| 123 | return True |
| 124 | if math.isinf(x) or math.isinf(y): |
| 125 | # This includes the case of two infinities of opposite sign, or |
| 126 | # one infinity and one finite number. |
| 127 | return False |
| 128 | # Two finite numbers. |
| 129 | actual_error = abs(x - y) |
| 130 | allowed_error = max(tol, rel*max(abs(x), abs(y))) |
| 131 | return actual_error <= allowed_error |
| 132 | |
| 133 | |
| 134 | # This class exists only as somewhere to stick a docstring containing |
| 135 | # doctests. The following docstring and tests were originally in a separate |
| 136 | # module. Now that it has been merged in here, I need somewhere to hang the. |
| 137 | # docstring. Ultimately, this class will die, and the information below will |
| 138 | # either become redundant, or be moved into more appropriate places. |
| 139 | class _DoNothing: |
| 140 | """ |
| 141 | When doing numeric work, especially with floats, exact equality is often |
| 142 | not what you want. Due to round-off error, it is often a bad idea to try |
| 143 | to compare floats with equality. Instead the usual procedure is to test |
| 144 | them with some (hopefully small!) allowance for error. |
| 145 | |
| 146 | The ``approx_equal`` function allows you to specify either an absolute |
| 147 | error tolerance, or a relative error, or both. |
| 148 | |
| 149 | Absolute error tolerances are simple, but you need to know the magnitude |
| 150 | of the quantities being compared: |
| 151 | |
| 152 | >>> approx_equal(12.345, 12.346, tol=1e-3) |
| 153 | True |
| 154 | >>> approx_equal(12.345e6, 12.346e6, tol=1e-3) # tol is too small. |
| 155 | False |
| 156 | |
| 157 | Relative errors are more suitable when the values you are comparing can |
| 158 | vary in magnitude: |
| 159 | |
| 160 | >>> approx_equal(12.345, 12.346, rel=1e-4) |
| 161 | True |
| 162 | >>> approx_equal(12.345e6, 12.346e6, rel=1e-4) |
| 163 | True |
| 164 | |
| 165 | but a naive implementation of relative error testing can run into trouble |
| 166 | around zero. |
| 167 | |
| 168 | If you supply both an absolute tolerance and a relative error, the |
| 169 | comparison succeeds if either individual test succeeds: |
| 170 | |
| 171 | >>> approx_equal(12.345e6, 12.346e6, tol=1e-3, rel=1e-4) |
| 172 | True |
| 173 | |
| 174 | """ |
| 175 | pass |
| 176 | |
| 177 | |
| 178 | |
| 179 | # We prefer this for testing numeric values that may not be exactly equal, |
| 180 | # and avoid using TestCase.assertAlmostEqual, because it sucks :-) |
| 181 | |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 182 | py_statistics = support.import_fresh_module('statistics', blocked=['_statistics']) |
| 183 | c_statistics = support.import_fresh_module('statistics', fresh=['_statistics']) |
| 184 | |
| 185 | |
| 186 | class TestModules(unittest.TestCase): |
| 187 | func_names = ['_normal_dist_inv_cdf'] |
| 188 | |
| 189 | def test_py_functions(self): |
| 190 | for fname in self.func_names: |
| 191 | self.assertEqual(getattr(py_statistics, fname).__module__, 'statistics') |
| 192 | |
| 193 | @unittest.skipUnless(c_statistics, 'requires _statistics') |
| 194 | def test_c_functions(self): |
| 195 | for fname in self.func_names: |
| 196 | self.assertEqual(getattr(c_statistics, fname).__module__, '_statistics') |
| 197 | |
| 198 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 199 | class NumericTestCase(unittest.TestCase): |
| 200 | """Unit test class for numeric work. |
| 201 | |
| 202 | This subclasses TestCase. In addition to the standard method |
| 203 | ``TestCase.assertAlmostEqual``, ``assertApproxEqual`` is provided. |
| 204 | """ |
| 205 | # By default, we expect exact equality, unless overridden. |
| 206 | tol = rel = 0 |
| 207 | |
| 208 | def assertApproxEqual( |
| 209 | self, first, second, tol=None, rel=None, msg=None |
| 210 | ): |
| 211 | """Test passes if ``first`` and ``second`` are approximately equal. |
| 212 | |
| 213 | This test passes if ``first`` and ``second`` are equal to |
| 214 | within ``tol``, an absolute error, or ``rel``, a relative error. |
| 215 | |
| 216 | If either ``tol`` or ``rel`` are None or not given, they default to |
| 217 | test attributes of the same name (by default, 0). |
| 218 | |
| 219 | The objects may be either numbers, or sequences of numbers. Sequences |
| 220 | are tested element-by-element. |
| 221 | |
| 222 | >>> class MyTest(NumericTestCase): |
| 223 | ... def test_number(self): |
| 224 | ... x = 1.0/6 |
| 225 | ... y = sum([x]*6) |
| 226 | ... self.assertApproxEqual(y, 1.0, tol=1e-15) |
| 227 | ... def test_sequence(self): |
| 228 | ... a = [1.001, 1.001e-10, 1.001e10] |
| 229 | ... b = [1.0, 1e-10, 1e10] |
| 230 | ... self.assertApproxEqual(a, b, rel=1e-3) |
| 231 | ... |
| 232 | >>> import unittest |
| 233 | >>> from io import StringIO # Suppress test runner output. |
| 234 | >>> suite = unittest.TestLoader().loadTestsFromTestCase(MyTest) |
| 235 | >>> unittest.TextTestRunner(stream=StringIO()).run(suite) |
| 236 | <unittest.runner.TextTestResult run=2 errors=0 failures=0> |
| 237 | |
| 238 | """ |
| 239 | if tol is None: |
| 240 | tol = self.tol |
| 241 | if rel is None: |
| 242 | rel = self.rel |
| 243 | if ( |
Serhiy Storchaka | 2e576f5 | 2017-04-24 09:05:00 +0300 | [diff] [blame] | 244 | isinstance(first, collections.abc.Sequence) and |
| 245 | isinstance(second, collections.abc.Sequence) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 246 | ): |
| 247 | check = self._check_approx_seq |
| 248 | else: |
| 249 | check = self._check_approx_num |
| 250 | check(first, second, tol, rel, msg) |
| 251 | |
| 252 | def _check_approx_seq(self, first, second, tol, rel, msg): |
| 253 | if len(first) != len(second): |
| 254 | standardMsg = ( |
| 255 | "sequences differ in length: %d items != %d items" |
| 256 | % (len(first), len(second)) |
| 257 | ) |
| 258 | msg = self._formatMessage(msg, standardMsg) |
| 259 | raise self.failureException(msg) |
| 260 | for i, (a,e) in enumerate(zip(first, second)): |
| 261 | self._check_approx_num(a, e, tol, rel, msg, i) |
| 262 | |
| 263 | def _check_approx_num(self, first, second, tol, rel, msg, idx=None): |
| 264 | if approx_equal(first, second, tol, rel): |
| 265 | # Test passes. Return early, we are done. |
| 266 | return None |
| 267 | # Otherwise we failed. |
| 268 | standardMsg = self._make_std_err_msg(first, second, tol, rel, idx) |
| 269 | msg = self._formatMessage(msg, standardMsg) |
| 270 | raise self.failureException(msg) |
| 271 | |
| 272 | @staticmethod |
| 273 | def _make_std_err_msg(first, second, tol, rel, idx): |
| 274 | # Create the standard error message for approx_equal failures. |
| 275 | assert first != second |
| 276 | template = ( |
| 277 | ' %r != %r\n' |
| 278 | ' values differ by more than tol=%r and rel=%r\n' |
| 279 | ' -> absolute error = %r\n' |
| 280 | ' -> relative error = %r' |
| 281 | ) |
| 282 | if idx is not None: |
| 283 | header = 'numeric sequences first differ at index %d.\n' % idx |
| 284 | template = header + template |
| 285 | # Calculate actual errors: |
| 286 | abs_err, rel_err = _calc_errors(first, second) |
| 287 | return template % (first, second, tol, rel, abs_err, rel_err) |
| 288 | |
| 289 | |
| 290 | # ======================== |
| 291 | # === Test the helpers === |
| 292 | # ======================== |
| 293 | |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 294 | class TestSign(unittest.TestCase): |
| 295 | """Test that the helper function sign() works correctly.""" |
| 296 | def testZeroes(self): |
| 297 | # Test that signed zeroes report their sign correctly. |
| 298 | self.assertEqual(sign(0.0), +1) |
| 299 | self.assertEqual(sign(-0.0), -1) |
| 300 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 301 | |
| 302 | # --- Tests for approx_equal --- |
| 303 | |
| 304 | class ApproxEqualSymmetryTest(unittest.TestCase): |
| 305 | # Test symmetry of approx_equal. |
| 306 | |
| 307 | def test_relative_symmetry(self): |
| 308 | # Check that approx_equal treats relative error symmetrically. |
| 309 | # (a-b)/a is usually not equal to (a-b)/b. Ensure that this |
| 310 | # doesn't matter. |
| 311 | # |
| 312 | # Note: the reason for this test is that an early version |
| 313 | # of approx_equal was not symmetric. A relative error test |
| 314 | # would pass, or fail, depending on which value was passed |
| 315 | # as the first argument. |
| 316 | # |
| 317 | args1 = [2456, 37.8, -12.45, Decimal('2.54'), Fraction(17, 54)] |
| 318 | args2 = [2459, 37.2, -12.41, Decimal('2.59'), Fraction(15, 54)] |
| 319 | assert len(args1) == len(args2) |
| 320 | for a, b in zip(args1, args2): |
| 321 | self.do_relative_symmetry(a, b) |
| 322 | |
| 323 | def do_relative_symmetry(self, a, b): |
| 324 | a, b = min(a, b), max(a, b) |
| 325 | assert a < b |
| 326 | delta = b - a # The absolute difference between the values. |
| 327 | rel_err1, rel_err2 = abs(delta/a), abs(delta/b) |
| 328 | # Choose an error margin halfway between the two. |
| 329 | rel = (rel_err1 + rel_err2)/2 |
| 330 | # Now see that values a and b compare approx equal regardless of |
| 331 | # which is given first. |
| 332 | self.assertTrue(approx_equal(a, b, tol=0, rel=rel)) |
| 333 | self.assertTrue(approx_equal(b, a, tol=0, rel=rel)) |
| 334 | |
| 335 | def test_symmetry(self): |
| 336 | # Test that approx_equal(a, b) == approx_equal(b, a) |
| 337 | args = [-23, -2, 5, 107, 93568] |
| 338 | delta = 2 |
Christian Heimes | ad39360 | 2013-11-26 01:32:15 +0100 | [diff] [blame] | 339 | for a in args: |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 340 | for type_ in (int, float, Decimal, Fraction): |
Christian Heimes | ad39360 | 2013-11-26 01:32:15 +0100 | [diff] [blame] | 341 | x = type_(a)*100 |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 342 | y = x + delta |
| 343 | r = abs(delta/max(x, y)) |
| 344 | # There are five cases to check: |
| 345 | # 1) actual error <= tol, <= rel |
| 346 | self.do_symmetry_test(x, y, tol=delta, rel=r) |
| 347 | self.do_symmetry_test(x, y, tol=delta+1, rel=2*r) |
| 348 | # 2) actual error > tol, > rel |
| 349 | self.do_symmetry_test(x, y, tol=delta-1, rel=r/2) |
| 350 | # 3) actual error <= tol, > rel |
| 351 | self.do_symmetry_test(x, y, tol=delta, rel=r/2) |
| 352 | # 4) actual error > tol, <= rel |
| 353 | self.do_symmetry_test(x, y, tol=delta-1, rel=r) |
| 354 | self.do_symmetry_test(x, y, tol=delta-1, rel=2*r) |
| 355 | # 5) exact equality test |
| 356 | self.do_symmetry_test(x, x, tol=0, rel=0) |
| 357 | self.do_symmetry_test(x, y, tol=0, rel=0) |
| 358 | |
| 359 | def do_symmetry_test(self, a, b, tol, rel): |
| 360 | template = "approx_equal comparisons don't match for %r" |
| 361 | flag1 = approx_equal(a, b, tol, rel) |
| 362 | flag2 = approx_equal(b, a, tol, rel) |
| 363 | self.assertEqual(flag1, flag2, template.format((a, b, tol, rel))) |
| 364 | |
| 365 | |
| 366 | class ApproxEqualExactTest(unittest.TestCase): |
| 367 | # Test the approx_equal function with exactly equal values. |
| 368 | # Equal values should compare as approximately equal. |
| 369 | # Test cases for exactly equal values, which should compare approx |
| 370 | # equal regardless of the error tolerances given. |
| 371 | |
| 372 | def do_exactly_equal_test(self, x, tol, rel): |
| 373 | result = approx_equal(x, x, tol=tol, rel=rel) |
| 374 | self.assertTrue(result, 'equality failure for x=%r' % x) |
| 375 | result = approx_equal(-x, -x, tol=tol, rel=rel) |
| 376 | self.assertTrue(result, 'equality failure for x=%r' % -x) |
| 377 | |
| 378 | def test_exactly_equal_ints(self): |
| 379 | # Test that equal int values are exactly equal. |
| 380 | for n in [42, 19740, 14974, 230, 1795, 700245, 36587]: |
| 381 | self.do_exactly_equal_test(n, 0, 0) |
| 382 | |
| 383 | def test_exactly_equal_floats(self): |
| 384 | # Test that equal float values are exactly equal. |
| 385 | for x in [0.42, 1.9740, 1497.4, 23.0, 179.5, 70.0245, 36.587]: |
| 386 | self.do_exactly_equal_test(x, 0, 0) |
| 387 | |
| 388 | def test_exactly_equal_fractions(self): |
| 389 | # Test that equal Fraction values are exactly equal. |
| 390 | F = Fraction |
| 391 | for f in [F(1, 2), F(0), F(5, 3), F(9, 7), F(35, 36), F(3, 7)]: |
| 392 | self.do_exactly_equal_test(f, 0, 0) |
| 393 | |
| 394 | def test_exactly_equal_decimals(self): |
| 395 | # Test that equal Decimal values are exactly equal. |
| 396 | D = Decimal |
| 397 | for d in map(D, "8.2 31.274 912.04 16.745 1.2047".split()): |
| 398 | self.do_exactly_equal_test(d, 0, 0) |
| 399 | |
| 400 | def test_exactly_equal_absolute(self): |
| 401 | # Test that equal values are exactly equal with an absolute error. |
| 402 | for n in [16, 1013, 1372, 1198, 971, 4]: |
| 403 | # Test as ints. |
| 404 | self.do_exactly_equal_test(n, 0.01, 0) |
| 405 | # Test as floats. |
| 406 | self.do_exactly_equal_test(n/10, 0.01, 0) |
| 407 | # Test as Fractions. |
| 408 | f = Fraction(n, 1234) |
| 409 | self.do_exactly_equal_test(f, 0.01, 0) |
| 410 | |
| 411 | def test_exactly_equal_absolute_decimals(self): |
| 412 | # Test equal Decimal values are exactly equal with an absolute error. |
| 413 | self.do_exactly_equal_test(Decimal("3.571"), Decimal("0.01"), 0) |
| 414 | self.do_exactly_equal_test(-Decimal("81.3971"), Decimal("0.01"), 0) |
| 415 | |
| 416 | def test_exactly_equal_relative(self): |
| 417 | # Test that equal values are exactly equal with a relative error. |
| 418 | for x in [8347, 101.3, -7910.28, Fraction(5, 21)]: |
| 419 | self.do_exactly_equal_test(x, 0, 0.01) |
| 420 | self.do_exactly_equal_test(Decimal("11.68"), 0, Decimal("0.01")) |
| 421 | |
| 422 | def test_exactly_equal_both(self): |
| 423 | # Test that equal values are equal when both tol and rel are given. |
| 424 | for x in [41017, 16.742, -813.02, Fraction(3, 8)]: |
| 425 | self.do_exactly_equal_test(x, 0.1, 0.01) |
| 426 | D = Decimal |
| 427 | self.do_exactly_equal_test(D("7.2"), D("0.1"), D("0.01")) |
| 428 | |
| 429 | |
| 430 | class ApproxEqualUnequalTest(unittest.TestCase): |
| 431 | # Unequal values should compare unequal with zero error tolerances. |
| 432 | # Test cases for unequal values, with exact equality test. |
| 433 | |
| 434 | def do_exactly_unequal_test(self, x): |
| 435 | for a in (x, -x): |
| 436 | result = approx_equal(a, a+1, tol=0, rel=0) |
| 437 | self.assertFalse(result, 'inequality failure for x=%r' % a) |
| 438 | |
| 439 | def test_exactly_unequal_ints(self): |
| 440 | # Test unequal int values are unequal with zero error tolerance. |
| 441 | for n in [951, 572305, 478, 917, 17240]: |
| 442 | self.do_exactly_unequal_test(n) |
| 443 | |
| 444 | def test_exactly_unequal_floats(self): |
| 445 | # Test unequal float values are unequal with zero error tolerance. |
| 446 | for x in [9.51, 5723.05, 47.8, 9.17, 17.24]: |
| 447 | self.do_exactly_unequal_test(x) |
| 448 | |
| 449 | def test_exactly_unequal_fractions(self): |
| 450 | # Test that unequal Fractions are unequal with zero error tolerance. |
| 451 | F = Fraction |
| 452 | for f in [F(1, 5), F(7, 9), F(12, 11), F(101, 99023)]: |
| 453 | self.do_exactly_unequal_test(f) |
| 454 | |
| 455 | def test_exactly_unequal_decimals(self): |
| 456 | # Test that unequal Decimals are unequal with zero error tolerance. |
| 457 | for d in map(Decimal, "3.1415 298.12 3.47 18.996 0.00245".split()): |
| 458 | self.do_exactly_unequal_test(d) |
| 459 | |
| 460 | |
| 461 | class ApproxEqualInexactTest(unittest.TestCase): |
| 462 | # Inexact test cases for approx_error. |
| 463 | # Test cases when comparing two values that are not exactly equal. |
| 464 | |
| 465 | # === Absolute error tests === |
| 466 | |
| 467 | def do_approx_equal_abs_test(self, x, delta): |
| 468 | template = "Test failure for x={!r}, y={!r}" |
| 469 | for y in (x + delta, x - delta): |
| 470 | msg = template.format(x, y) |
| 471 | self.assertTrue(approx_equal(x, y, tol=2*delta, rel=0), msg) |
| 472 | self.assertFalse(approx_equal(x, y, tol=delta/2, rel=0), msg) |
| 473 | |
| 474 | def test_approx_equal_absolute_ints(self): |
| 475 | # Test approximate equality of ints with an absolute error. |
| 476 | for n in [-10737, -1975, -7, -2, 0, 1, 9, 37, 423, 9874, 23789110]: |
| 477 | self.do_approx_equal_abs_test(n, 10) |
| 478 | self.do_approx_equal_abs_test(n, 2) |
| 479 | |
| 480 | def test_approx_equal_absolute_floats(self): |
| 481 | # Test approximate equality of floats with an absolute error. |
| 482 | for x in [-284.126, -97.1, -3.4, -2.15, 0.5, 1.0, 7.8, 4.23, 3817.4]: |
| 483 | self.do_approx_equal_abs_test(x, 1.5) |
| 484 | self.do_approx_equal_abs_test(x, 0.01) |
| 485 | self.do_approx_equal_abs_test(x, 0.0001) |
| 486 | |
| 487 | def test_approx_equal_absolute_fractions(self): |
| 488 | # Test approximate equality of Fractions with an absolute error. |
| 489 | delta = Fraction(1, 29) |
| 490 | numerators = [-84, -15, -2, -1, 0, 1, 5, 17, 23, 34, 71] |
| 491 | for f in (Fraction(n, 29) for n in numerators): |
| 492 | self.do_approx_equal_abs_test(f, delta) |
| 493 | self.do_approx_equal_abs_test(f, float(delta)) |
| 494 | |
| 495 | def test_approx_equal_absolute_decimals(self): |
| 496 | # Test approximate equality of Decimals with an absolute error. |
| 497 | delta = Decimal("0.01") |
| 498 | for d in map(Decimal, "1.0 3.5 36.08 61.79 7912.3648".split()): |
| 499 | self.do_approx_equal_abs_test(d, delta) |
| 500 | self.do_approx_equal_abs_test(-d, delta) |
| 501 | |
| 502 | def test_cross_zero(self): |
| 503 | # Test for the case of the two values having opposite signs. |
| 504 | self.assertTrue(approx_equal(1e-5, -1e-5, tol=1e-4, rel=0)) |
| 505 | |
| 506 | # === Relative error tests === |
| 507 | |
| 508 | def do_approx_equal_rel_test(self, x, delta): |
| 509 | template = "Test failure for x={!r}, y={!r}" |
| 510 | for y in (x*(1+delta), x*(1-delta)): |
| 511 | msg = template.format(x, y) |
| 512 | self.assertTrue(approx_equal(x, y, tol=0, rel=2*delta), msg) |
| 513 | self.assertFalse(approx_equal(x, y, tol=0, rel=delta/2), msg) |
| 514 | |
| 515 | def test_approx_equal_relative_ints(self): |
| 516 | # Test approximate equality of ints with a relative error. |
| 517 | self.assertTrue(approx_equal(64, 47, tol=0, rel=0.36)) |
| 518 | self.assertTrue(approx_equal(64, 47, tol=0, rel=0.37)) |
| 519 | # --- |
| 520 | self.assertTrue(approx_equal(449, 512, tol=0, rel=0.125)) |
| 521 | self.assertTrue(approx_equal(448, 512, tol=0, rel=0.125)) |
| 522 | self.assertFalse(approx_equal(447, 512, tol=0, rel=0.125)) |
| 523 | |
| 524 | def test_approx_equal_relative_floats(self): |
| 525 | # Test approximate equality of floats with a relative error. |
| 526 | for x in [-178.34, -0.1, 0.1, 1.0, 36.97, 2847.136, 9145.074]: |
| 527 | self.do_approx_equal_rel_test(x, 0.02) |
| 528 | self.do_approx_equal_rel_test(x, 0.0001) |
| 529 | |
| 530 | def test_approx_equal_relative_fractions(self): |
| 531 | # Test approximate equality of Fractions with a relative error. |
| 532 | F = Fraction |
| 533 | delta = Fraction(3, 8) |
| 534 | for f in [F(3, 84), F(17, 30), F(49, 50), F(92, 85)]: |
| 535 | for d in (delta, float(delta)): |
| 536 | self.do_approx_equal_rel_test(f, d) |
| 537 | self.do_approx_equal_rel_test(-f, d) |
| 538 | |
| 539 | def test_approx_equal_relative_decimals(self): |
| 540 | # Test approximate equality of Decimals with a relative error. |
| 541 | for d in map(Decimal, "0.02 1.0 5.7 13.67 94.138 91027.9321".split()): |
| 542 | self.do_approx_equal_rel_test(d, Decimal("0.001")) |
| 543 | self.do_approx_equal_rel_test(-d, Decimal("0.05")) |
| 544 | |
| 545 | # === Both absolute and relative error tests === |
| 546 | |
| 547 | # There are four cases to consider: |
| 548 | # 1) actual error <= both absolute and relative error |
| 549 | # 2) actual error <= absolute error but > relative error |
| 550 | # 3) actual error <= relative error but > absolute error |
| 551 | # 4) actual error > both absolute and relative error |
| 552 | |
| 553 | def do_check_both(self, a, b, tol, rel, tol_flag, rel_flag): |
| 554 | check = self.assertTrue if tol_flag else self.assertFalse |
| 555 | check(approx_equal(a, b, tol=tol, rel=0)) |
| 556 | check = self.assertTrue if rel_flag else self.assertFalse |
| 557 | check(approx_equal(a, b, tol=0, rel=rel)) |
| 558 | check = self.assertTrue if (tol_flag or rel_flag) else self.assertFalse |
| 559 | check(approx_equal(a, b, tol=tol, rel=rel)) |
| 560 | |
| 561 | def test_approx_equal_both1(self): |
| 562 | # Test actual error <= both absolute and relative error. |
| 563 | self.do_check_both(7.955, 7.952, 0.004, 3.8e-4, True, True) |
| 564 | self.do_check_both(-7.387, -7.386, 0.002, 0.0002, True, True) |
| 565 | |
| 566 | def test_approx_equal_both2(self): |
| 567 | # Test actual error <= absolute error but > relative error. |
| 568 | self.do_check_both(7.955, 7.952, 0.004, 3.7e-4, True, False) |
| 569 | |
| 570 | def test_approx_equal_both3(self): |
| 571 | # Test actual error <= relative error but > absolute error. |
| 572 | self.do_check_both(7.955, 7.952, 0.001, 3.8e-4, False, True) |
| 573 | |
| 574 | def test_approx_equal_both4(self): |
| 575 | # Test actual error > both absolute and relative error. |
| 576 | self.do_check_both(2.78, 2.75, 0.01, 0.001, False, False) |
| 577 | self.do_check_both(971.44, 971.47, 0.02, 3e-5, False, False) |
| 578 | |
| 579 | |
| 580 | class ApproxEqualSpecialsTest(unittest.TestCase): |
| 581 | # Test approx_equal with NANs and INFs and zeroes. |
| 582 | |
| 583 | def test_inf(self): |
| 584 | for type_ in (float, Decimal): |
| 585 | inf = type_('inf') |
| 586 | self.assertTrue(approx_equal(inf, inf)) |
| 587 | self.assertTrue(approx_equal(inf, inf, 0, 0)) |
| 588 | self.assertTrue(approx_equal(inf, inf, 1, 0.01)) |
| 589 | self.assertTrue(approx_equal(-inf, -inf)) |
| 590 | self.assertFalse(approx_equal(inf, -inf)) |
| 591 | self.assertFalse(approx_equal(inf, 1000)) |
| 592 | |
| 593 | def test_nan(self): |
| 594 | for type_ in (float, Decimal): |
| 595 | nan = type_('nan') |
| 596 | for other in (nan, type_('inf'), 1000): |
| 597 | self.assertFalse(approx_equal(nan, other)) |
| 598 | |
| 599 | def test_float_zeroes(self): |
| 600 | nzero = math.copysign(0.0, -1) |
| 601 | self.assertTrue(approx_equal(nzero, 0.0, tol=0.1, rel=0.1)) |
| 602 | |
| 603 | def test_decimal_zeroes(self): |
| 604 | nzero = Decimal("-0.0") |
| 605 | self.assertTrue(approx_equal(nzero, Decimal(0), tol=0.1, rel=0.1)) |
| 606 | |
| 607 | |
| 608 | class TestApproxEqualErrors(unittest.TestCase): |
| 609 | # Test error conditions of approx_equal. |
| 610 | |
| 611 | def test_bad_tol(self): |
| 612 | # Test negative tol raises. |
| 613 | self.assertRaises(ValueError, approx_equal, 100, 100, -1, 0.1) |
| 614 | |
| 615 | def test_bad_rel(self): |
| 616 | # Test negative rel raises. |
| 617 | self.assertRaises(ValueError, approx_equal, 100, 100, 1, -0.1) |
| 618 | |
| 619 | |
| 620 | # --- Tests for NumericTestCase --- |
| 621 | |
| 622 | # The formatting routine that generates the error messages is complex enough |
| 623 | # that it too needs testing. |
| 624 | |
| 625 | class TestNumericTestCase(unittest.TestCase): |
| 626 | # The exact wording of NumericTestCase error messages is *not* guaranteed, |
| 627 | # but we need to give them some sort of test to ensure that they are |
| 628 | # generated correctly. As a compromise, we look for specific substrings |
| 629 | # that are expected to be found even if the overall error message changes. |
| 630 | |
| 631 | def do_test(self, args): |
| 632 | actual_msg = NumericTestCase._make_std_err_msg(*args) |
| 633 | expected = self.generate_substrings(*args) |
| 634 | for substring in expected: |
| 635 | self.assertIn(substring, actual_msg) |
| 636 | |
| 637 | def test_numerictestcase_is_testcase(self): |
| 638 | # Ensure that NumericTestCase actually is a TestCase. |
| 639 | self.assertTrue(issubclass(NumericTestCase, unittest.TestCase)) |
| 640 | |
| 641 | def test_error_msg_numeric(self): |
| 642 | # Test the error message generated for numeric comparisons. |
| 643 | args = (2.5, 4.0, 0.5, 0.25, None) |
| 644 | self.do_test(args) |
| 645 | |
| 646 | def test_error_msg_sequence(self): |
| 647 | # Test the error message generated for sequence comparisons. |
| 648 | args = (3.75, 8.25, 1.25, 0.5, 7) |
| 649 | self.do_test(args) |
| 650 | |
| 651 | def generate_substrings(self, first, second, tol, rel, idx): |
| 652 | """Return substrings we expect to see in error messages.""" |
| 653 | abs_err, rel_err = _calc_errors(first, second) |
| 654 | substrings = [ |
| 655 | 'tol=%r' % tol, |
| 656 | 'rel=%r' % rel, |
| 657 | 'absolute error = %r' % abs_err, |
| 658 | 'relative error = %r' % rel_err, |
| 659 | ] |
| 660 | if idx is not None: |
| 661 | substrings.append('differ at index %d' % idx) |
| 662 | return substrings |
| 663 | |
| 664 | |
| 665 | # ======================================= |
| 666 | # === Tests for the statistics module === |
| 667 | # ======================================= |
| 668 | |
| 669 | |
| 670 | class GlobalsTest(unittest.TestCase): |
| 671 | module = statistics |
| 672 | expected_metadata = ["__doc__", "__all__"] |
| 673 | |
| 674 | def test_meta(self): |
| 675 | # Test for the existence of metadata. |
| 676 | for meta in self.expected_metadata: |
| 677 | self.assertTrue(hasattr(self.module, meta), |
| 678 | "%s not present" % meta) |
| 679 | |
| 680 | def test_check_all(self): |
| 681 | # Check everything in __all__ exists and is public. |
| 682 | module = self.module |
| 683 | for name in module.__all__: |
| 684 | # No private names in __all__: |
| 685 | self.assertFalse(name.startswith("_"), |
| 686 | 'private name "%s" in __all__' % name) |
| 687 | # And anything in __all__ must exist: |
| 688 | self.assertTrue(hasattr(module, name), |
| 689 | 'missing name "%s" in __all__' % name) |
| 690 | |
| 691 | |
| 692 | class DocTests(unittest.TestCase): |
Serhiy Storchaka | b12cb6a | 2013-12-08 18:16:18 +0200 | [diff] [blame] | 693 | @unittest.skipIf(sys.flags.optimize >= 2, |
| 694 | "Docstrings are omitted with -OO and above") |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 695 | def test_doc_tests(self): |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 696 | failed, tried = doctest.testmod(statistics, optionflags=doctest.ELLIPSIS) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 697 | self.assertGreater(tried, 0) |
| 698 | self.assertEqual(failed, 0) |
| 699 | |
| 700 | class StatisticsErrorTest(unittest.TestCase): |
| 701 | def test_has_exception(self): |
| 702 | errmsg = ( |
| 703 | "Expected StatisticsError to be a ValueError, but got a" |
| 704 | " subclass of %r instead." |
| 705 | ) |
| 706 | self.assertTrue(hasattr(statistics, 'StatisticsError')) |
| 707 | self.assertTrue( |
| 708 | issubclass(statistics.StatisticsError, ValueError), |
| 709 | errmsg % statistics.StatisticsError.__base__ |
| 710 | ) |
| 711 | |
| 712 | |
| 713 | # === Tests for private utility functions === |
| 714 | |
| 715 | class ExactRatioTest(unittest.TestCase): |
| 716 | # Test _exact_ratio utility. |
| 717 | |
| 718 | def test_int(self): |
| 719 | for i in (-20, -3, 0, 5, 99, 10**20): |
| 720 | self.assertEqual(statistics._exact_ratio(i), (i, 1)) |
| 721 | |
| 722 | def test_fraction(self): |
| 723 | numerators = (-5, 1, 12, 38) |
| 724 | for n in numerators: |
| 725 | f = Fraction(n, 37) |
| 726 | self.assertEqual(statistics._exact_ratio(f), (n, 37)) |
| 727 | |
| 728 | def test_float(self): |
| 729 | self.assertEqual(statistics._exact_ratio(0.125), (1, 8)) |
| 730 | self.assertEqual(statistics._exact_ratio(1.125), (9, 8)) |
| 731 | data = [random.uniform(-100, 100) for _ in range(100)] |
| 732 | for x in data: |
| 733 | num, den = statistics._exact_ratio(x) |
| 734 | self.assertEqual(x, num/den) |
| 735 | |
| 736 | def test_decimal(self): |
| 737 | D = Decimal |
| 738 | _exact_ratio = statistics._exact_ratio |
Steven D'Aprano | 3b06e24 | 2016-05-05 03:54:29 +1000 | [diff] [blame] | 739 | self.assertEqual(_exact_ratio(D("0.125")), (1, 8)) |
| 740 | self.assertEqual(_exact_ratio(D("12.345")), (2469, 200)) |
| 741 | self.assertEqual(_exact_ratio(D("-1.98")), (-99, 50)) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 742 | |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 743 | def test_inf(self): |
| 744 | INF = float("INF") |
| 745 | class MyFloat(float): |
| 746 | pass |
| 747 | class MyDecimal(Decimal): |
| 748 | pass |
| 749 | for inf in (INF, -INF): |
| 750 | for type_ in (float, MyFloat, Decimal, MyDecimal): |
| 751 | x = type_(inf) |
| 752 | ratio = statistics._exact_ratio(x) |
| 753 | self.assertEqual(ratio, (x, None)) |
| 754 | self.assertEqual(type(ratio[0]), type_) |
| 755 | self.assertTrue(math.isinf(ratio[0])) |
| 756 | |
| 757 | def test_float_nan(self): |
| 758 | NAN = float("NAN") |
| 759 | class MyFloat(float): |
| 760 | pass |
| 761 | for nan in (NAN, MyFloat(NAN)): |
| 762 | ratio = statistics._exact_ratio(nan) |
| 763 | self.assertTrue(math.isnan(ratio[0])) |
| 764 | self.assertIs(ratio[1], None) |
| 765 | self.assertEqual(type(ratio[0]), type(nan)) |
| 766 | |
| 767 | def test_decimal_nan(self): |
| 768 | NAN = Decimal("NAN") |
| 769 | sNAN = Decimal("sNAN") |
| 770 | class MyDecimal(Decimal): |
| 771 | pass |
| 772 | for nan in (NAN, MyDecimal(NAN), sNAN, MyDecimal(sNAN)): |
| 773 | ratio = statistics._exact_ratio(nan) |
| 774 | self.assertTrue(_nan_equal(ratio[0], nan)) |
| 775 | self.assertIs(ratio[1], None) |
| 776 | self.assertEqual(type(ratio[0]), type(nan)) |
| 777 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 778 | |
| 779 | class DecimalToRatioTest(unittest.TestCase): |
Steven D'Aprano | 3b06e24 | 2016-05-05 03:54:29 +1000 | [diff] [blame] | 780 | # Test _exact_ratio private function. |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 781 | |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 782 | def test_infinity(self): |
| 783 | # Test that INFs are handled correctly. |
| 784 | inf = Decimal('INF') |
Steven D'Aprano | 3b06e24 | 2016-05-05 03:54:29 +1000 | [diff] [blame] | 785 | self.assertEqual(statistics._exact_ratio(inf), (inf, None)) |
| 786 | self.assertEqual(statistics._exact_ratio(-inf), (-inf, None)) |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 787 | |
| 788 | def test_nan(self): |
| 789 | # Test that NANs are handled correctly. |
| 790 | for nan in (Decimal('NAN'), Decimal('sNAN')): |
Steven D'Aprano | 3b06e24 | 2016-05-05 03:54:29 +1000 | [diff] [blame] | 791 | num, den = statistics._exact_ratio(nan) |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 792 | # Because NANs always compare non-equal, we cannot use assertEqual. |
| 793 | # Nor can we use an identity test, as we don't guarantee anything |
| 794 | # about the object identity. |
| 795 | self.assertTrue(_nan_equal(num, nan)) |
| 796 | self.assertIs(den, None) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 797 | |
Nick Coghlan | 4a7668a | 2014-02-08 23:55:14 +1000 | [diff] [blame] | 798 | def test_sign(self): |
| 799 | # Test sign is calculated correctly. |
| 800 | numbers = [Decimal("9.8765e12"), Decimal("9.8765e-12")] |
| 801 | for d in numbers: |
| 802 | # First test positive decimals. |
| 803 | assert d > 0 |
Steven D'Aprano | 3b06e24 | 2016-05-05 03:54:29 +1000 | [diff] [blame] | 804 | num, den = statistics._exact_ratio(d) |
Nick Coghlan | 4a7668a | 2014-02-08 23:55:14 +1000 | [diff] [blame] | 805 | self.assertGreaterEqual(num, 0) |
| 806 | self.assertGreater(den, 0) |
| 807 | # Then test negative decimals. |
Steven D'Aprano | 3b06e24 | 2016-05-05 03:54:29 +1000 | [diff] [blame] | 808 | num, den = statistics._exact_ratio(-d) |
Nick Coghlan | 4a7668a | 2014-02-08 23:55:14 +1000 | [diff] [blame] | 809 | self.assertLessEqual(num, 0) |
| 810 | self.assertGreater(den, 0) |
| 811 | |
| 812 | def test_negative_exponent(self): |
| 813 | # Test result when the exponent is negative. |
Steven D'Aprano | 3b06e24 | 2016-05-05 03:54:29 +1000 | [diff] [blame] | 814 | t = statistics._exact_ratio(Decimal("0.1234")) |
| 815 | self.assertEqual(t, (617, 5000)) |
Nick Coghlan | 4a7668a | 2014-02-08 23:55:14 +1000 | [diff] [blame] | 816 | |
| 817 | def test_positive_exponent(self): |
| 818 | # Test results when the exponent is positive. |
Steven D'Aprano | 3b06e24 | 2016-05-05 03:54:29 +1000 | [diff] [blame] | 819 | t = statistics._exact_ratio(Decimal("1.234e7")) |
Nick Coghlan | 4a7668a | 2014-02-08 23:55:14 +1000 | [diff] [blame] | 820 | self.assertEqual(t, (12340000, 1)) |
| 821 | |
| 822 | def test_regression_20536(self): |
| 823 | # Regression test for issue 20536. |
| 824 | # See http://bugs.python.org/issue20536 |
Steven D'Aprano | 3b06e24 | 2016-05-05 03:54:29 +1000 | [diff] [blame] | 825 | t = statistics._exact_ratio(Decimal("1e2")) |
Nick Coghlan | 4a7668a | 2014-02-08 23:55:14 +1000 | [diff] [blame] | 826 | self.assertEqual(t, (100, 1)) |
Steven D'Aprano | 3b06e24 | 2016-05-05 03:54:29 +1000 | [diff] [blame] | 827 | t = statistics._exact_ratio(Decimal("1.47e5")) |
Nick Coghlan | 4a7668a | 2014-02-08 23:55:14 +1000 | [diff] [blame] | 828 | self.assertEqual(t, (147000, 1)) |
| 829 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 830 | |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 831 | class IsFiniteTest(unittest.TestCase): |
| 832 | # Test _isfinite private function. |
Nick Coghlan | 73afe2a | 2014-02-08 19:58:04 +1000 | [diff] [blame] | 833 | |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 834 | def test_finite(self): |
| 835 | # Test that finite numbers are recognised as finite. |
| 836 | for x in (5, Fraction(1, 3), 2.5, Decimal("5.5")): |
| 837 | self.assertTrue(statistics._isfinite(x)) |
Nick Coghlan | 73afe2a | 2014-02-08 19:58:04 +1000 | [diff] [blame] | 838 | |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 839 | def test_infinity(self): |
| 840 | # Test that INFs are not recognised as finite. |
| 841 | for x in (float("inf"), Decimal("inf")): |
| 842 | self.assertFalse(statistics._isfinite(x)) |
Nick Coghlan | 73afe2a | 2014-02-08 19:58:04 +1000 | [diff] [blame] | 843 | |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 844 | def test_nan(self): |
| 845 | # Test that NANs are not recognised as finite. |
| 846 | for x in (float("nan"), Decimal("NAN"), Decimal("sNAN")): |
| 847 | self.assertFalse(statistics._isfinite(x)) |
| 848 | |
| 849 | |
| 850 | class CoerceTest(unittest.TestCase): |
| 851 | # Test that private function _coerce correctly deals with types. |
| 852 | |
| 853 | # The coercion rules are currently an implementation detail, although at |
| 854 | # some point that should change. The tests and comments here define the |
| 855 | # correct implementation. |
| 856 | |
| 857 | # Pre-conditions of _coerce: |
| 858 | # |
| 859 | # - The first time _sum calls _coerce, the |
| 860 | # - coerce(T, S) will never be called with bool as the first argument; |
| 861 | # this is a pre-condition, guarded with an assertion. |
| 862 | |
| 863 | # |
| 864 | # - coerce(T, T) will always return T; we assume T is a valid numeric |
| 865 | # type. Violate this assumption at your own risk. |
| 866 | # |
| 867 | # - Apart from as above, bool is treated as if it were actually int. |
| 868 | # |
| 869 | # - coerce(int, X) and coerce(X, int) return X. |
| 870 | # - |
| 871 | def test_bool(self): |
| 872 | # bool is somewhat special, due to the pre-condition that it is |
| 873 | # never given as the first argument to _coerce, and that it cannot |
| 874 | # be subclassed. So we test it specially. |
| 875 | for T in (int, float, Fraction, Decimal): |
| 876 | self.assertIs(statistics._coerce(T, bool), T) |
| 877 | class MyClass(T): pass |
| 878 | self.assertIs(statistics._coerce(MyClass, bool), MyClass) |
| 879 | |
| 880 | def assertCoerceTo(self, A, B): |
| 881 | """Assert that type A coerces to B.""" |
| 882 | self.assertIs(statistics._coerce(A, B), B) |
| 883 | self.assertIs(statistics._coerce(B, A), B) |
| 884 | |
| 885 | def check_coerce_to(self, A, B): |
| 886 | """Checks that type A coerces to B, including subclasses.""" |
| 887 | # Assert that type A is coerced to B. |
| 888 | self.assertCoerceTo(A, B) |
| 889 | # Subclasses of A are also coerced to B. |
| 890 | class SubclassOfA(A): pass |
| 891 | self.assertCoerceTo(SubclassOfA, B) |
| 892 | # A, and subclasses of A, are coerced to subclasses of B. |
| 893 | class SubclassOfB(B): pass |
| 894 | self.assertCoerceTo(A, SubclassOfB) |
| 895 | self.assertCoerceTo(SubclassOfA, SubclassOfB) |
| 896 | |
| 897 | def assertCoerceRaises(self, A, B): |
| 898 | """Assert that coercing A to B, or vice versa, raises TypeError.""" |
| 899 | self.assertRaises(TypeError, statistics._coerce, (A, B)) |
| 900 | self.assertRaises(TypeError, statistics._coerce, (B, A)) |
| 901 | |
| 902 | def check_type_coercions(self, T): |
| 903 | """Check that type T coerces correctly with subclasses of itself.""" |
| 904 | assert T is not bool |
| 905 | # Coercing a type with itself returns the same type. |
| 906 | self.assertIs(statistics._coerce(T, T), T) |
| 907 | # Coercing a type with a subclass of itself returns the subclass. |
| 908 | class U(T): pass |
| 909 | class V(T): pass |
| 910 | class W(U): pass |
| 911 | for typ in (U, V, W): |
| 912 | self.assertCoerceTo(T, typ) |
| 913 | self.assertCoerceTo(U, W) |
| 914 | # Coercing two subclasses that aren't parent/child is an error. |
| 915 | self.assertCoerceRaises(U, V) |
| 916 | self.assertCoerceRaises(V, W) |
| 917 | |
| 918 | def test_int(self): |
| 919 | # Check that int coerces correctly. |
| 920 | self.check_type_coercions(int) |
| 921 | for typ in (float, Fraction, Decimal): |
| 922 | self.check_coerce_to(int, typ) |
| 923 | |
| 924 | def test_fraction(self): |
| 925 | # Check that Fraction coerces correctly. |
| 926 | self.check_type_coercions(Fraction) |
| 927 | self.check_coerce_to(Fraction, float) |
| 928 | |
| 929 | def test_decimal(self): |
| 930 | # Check that Decimal coerces correctly. |
| 931 | self.check_type_coercions(Decimal) |
| 932 | |
| 933 | def test_float(self): |
| 934 | # Check that float coerces correctly. |
| 935 | self.check_type_coercions(float) |
| 936 | |
| 937 | def test_non_numeric_types(self): |
| 938 | for bad_type in (str, list, type(None), tuple, dict): |
| 939 | for good_type in (int, float, Fraction, Decimal): |
| 940 | self.assertCoerceRaises(good_type, bad_type) |
| 941 | |
| 942 | def test_incompatible_types(self): |
| 943 | # Test that incompatible types raise. |
| 944 | for T in (float, Fraction): |
| 945 | class MySubclass(T): pass |
| 946 | self.assertCoerceRaises(T, Decimal) |
| 947 | self.assertCoerceRaises(MySubclass, Decimal) |
| 948 | |
| 949 | |
| 950 | class ConvertTest(unittest.TestCase): |
| 951 | # Test private _convert function. |
| 952 | |
| 953 | def check_exact_equal(self, x, y): |
| 954 | """Check that x equals y, and has the same type as well.""" |
| 955 | self.assertEqual(x, y) |
| 956 | self.assertIs(type(x), type(y)) |
| 957 | |
| 958 | def test_int(self): |
| 959 | # Test conversions to int. |
| 960 | x = statistics._convert(Fraction(71), int) |
| 961 | self.check_exact_equal(x, 71) |
| 962 | class MyInt(int): pass |
| 963 | x = statistics._convert(Fraction(17), MyInt) |
| 964 | self.check_exact_equal(x, MyInt(17)) |
| 965 | |
| 966 | def test_fraction(self): |
| 967 | # Test conversions to Fraction. |
| 968 | x = statistics._convert(Fraction(95, 99), Fraction) |
| 969 | self.check_exact_equal(x, Fraction(95, 99)) |
| 970 | class MyFraction(Fraction): |
| 971 | def __truediv__(self, other): |
| 972 | return self.__class__(super().__truediv__(other)) |
| 973 | x = statistics._convert(Fraction(71, 13), MyFraction) |
| 974 | self.check_exact_equal(x, MyFraction(71, 13)) |
| 975 | |
| 976 | def test_float(self): |
| 977 | # Test conversions to float. |
| 978 | x = statistics._convert(Fraction(-1, 2), float) |
| 979 | self.check_exact_equal(x, -0.5) |
| 980 | class MyFloat(float): |
| 981 | def __truediv__(self, other): |
| 982 | return self.__class__(super().__truediv__(other)) |
| 983 | x = statistics._convert(Fraction(9, 8), MyFloat) |
| 984 | self.check_exact_equal(x, MyFloat(1.125)) |
| 985 | |
| 986 | def test_decimal(self): |
| 987 | # Test conversions to Decimal. |
| 988 | x = statistics._convert(Fraction(1, 40), Decimal) |
| 989 | self.check_exact_equal(x, Decimal("0.025")) |
| 990 | class MyDecimal(Decimal): |
| 991 | def __truediv__(self, other): |
| 992 | return self.__class__(super().__truediv__(other)) |
| 993 | x = statistics._convert(Fraction(-15, 16), MyDecimal) |
| 994 | self.check_exact_equal(x, MyDecimal("-0.9375")) |
| 995 | |
| 996 | def test_inf(self): |
| 997 | for INF in (float('inf'), Decimal('inf')): |
| 998 | for inf in (INF, -INF): |
| 999 | x = statistics._convert(inf, type(inf)) |
| 1000 | self.check_exact_equal(x, inf) |
| 1001 | |
| 1002 | def test_nan(self): |
| 1003 | for nan in (float('nan'), Decimal('NAN'), Decimal('sNAN')): |
| 1004 | x = statistics._convert(nan, type(nan)) |
| 1005 | self.assertTrue(_nan_equal(x, nan)) |
Nick Coghlan | 73afe2a | 2014-02-08 19:58:04 +1000 | [diff] [blame] | 1006 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1007 | |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 1008 | class FailNegTest(unittest.TestCase): |
| 1009 | """Test _fail_neg private function.""" |
| 1010 | |
| 1011 | def test_pass_through(self): |
| 1012 | # Test that values are passed through unchanged. |
| 1013 | values = [1, 2.0, Fraction(3), Decimal(4)] |
| 1014 | new = list(statistics._fail_neg(values)) |
| 1015 | self.assertEqual(values, new) |
| 1016 | |
| 1017 | def test_negatives_raise(self): |
| 1018 | # Test that negatives raise an exception. |
| 1019 | for x in [1, 2.0, Fraction(3), Decimal(4)]: |
| 1020 | seq = [-x] |
| 1021 | it = statistics._fail_neg(seq) |
| 1022 | self.assertRaises(statistics.StatisticsError, next, it) |
| 1023 | |
| 1024 | def test_error_msg(self): |
| 1025 | # Test that a given error message is used. |
| 1026 | msg = "badness #%d" % random.randint(10000, 99999) |
| 1027 | try: |
| 1028 | next(statistics._fail_neg([-1], msg)) |
| 1029 | except statistics.StatisticsError as e: |
| 1030 | errmsg = e.args[0] |
| 1031 | else: |
| 1032 | self.fail("expected exception, but it didn't happen") |
| 1033 | self.assertEqual(errmsg, msg) |
| 1034 | |
| 1035 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1036 | # === Tests for public functions === |
| 1037 | |
| 1038 | class UnivariateCommonMixin: |
| 1039 | # Common tests for most univariate functions that take a data argument. |
| 1040 | |
| 1041 | def test_no_args(self): |
| 1042 | # Fail if given no arguments. |
| 1043 | self.assertRaises(TypeError, self.func) |
| 1044 | |
| 1045 | def test_empty_data(self): |
| 1046 | # Fail when the data argument (first argument) is empty. |
| 1047 | for empty in ([], (), iter([])): |
| 1048 | self.assertRaises(statistics.StatisticsError, self.func, empty) |
| 1049 | |
| 1050 | def prepare_data(self): |
| 1051 | """Return int data for various tests.""" |
| 1052 | data = list(range(10)) |
| 1053 | while data == sorted(data): |
| 1054 | random.shuffle(data) |
| 1055 | return data |
| 1056 | |
| 1057 | def test_no_inplace_modifications(self): |
| 1058 | # Test that the function does not modify its input data. |
| 1059 | data = self.prepare_data() |
| 1060 | assert len(data) != 1 # Necessary to avoid infinite loop. |
| 1061 | assert data != sorted(data) |
| 1062 | saved = data[:] |
| 1063 | assert data is not saved |
| 1064 | _ = self.func(data) |
| 1065 | self.assertListEqual(data, saved, "data has been modified") |
| 1066 | |
| 1067 | def test_order_doesnt_matter(self): |
| 1068 | # Test that the order of data points doesn't change the result. |
| 1069 | |
| 1070 | # CAUTION: due to floating point rounding errors, the result actually |
| 1071 | # may depend on the order. Consider this test representing an ideal. |
| 1072 | # To avoid this test failing, only test with exact values such as ints |
| 1073 | # or Fractions. |
| 1074 | data = [1, 2, 3, 3, 3, 4, 5, 6]*100 |
| 1075 | expected = self.func(data) |
| 1076 | random.shuffle(data) |
| 1077 | actual = self.func(data) |
| 1078 | self.assertEqual(expected, actual) |
| 1079 | |
| 1080 | def test_type_of_data_collection(self): |
| 1081 | # Test that the type of iterable data doesn't effect the result. |
| 1082 | class MyList(list): |
| 1083 | pass |
| 1084 | class MyTuple(tuple): |
| 1085 | pass |
| 1086 | def generator(data): |
| 1087 | return (obj for obj in data) |
| 1088 | data = self.prepare_data() |
| 1089 | expected = self.func(data) |
| 1090 | for kind in (list, tuple, iter, MyList, MyTuple, generator): |
| 1091 | result = self.func(kind(data)) |
| 1092 | self.assertEqual(result, expected) |
| 1093 | |
| 1094 | def test_range_data(self): |
| 1095 | # Test that functions work with range objects. |
| 1096 | data = range(20, 50, 3) |
| 1097 | expected = self.func(list(data)) |
| 1098 | self.assertEqual(self.func(data), expected) |
| 1099 | |
| 1100 | def test_bad_arg_types(self): |
| 1101 | # Test that function raises when given data of the wrong type. |
| 1102 | |
| 1103 | # Don't roll the following into a loop like this: |
| 1104 | # for bad in list_of_bad: |
| 1105 | # self.check_for_type_error(bad) |
| 1106 | # |
| 1107 | # Since assertRaises doesn't show the arguments that caused the test |
| 1108 | # failure, it is very difficult to debug these test failures when the |
| 1109 | # following are in a loop. |
| 1110 | self.check_for_type_error(None) |
| 1111 | self.check_for_type_error(23) |
| 1112 | self.check_for_type_error(42.0) |
| 1113 | self.check_for_type_error(object()) |
| 1114 | |
| 1115 | def check_for_type_error(self, *args): |
| 1116 | self.assertRaises(TypeError, self.func, *args) |
| 1117 | |
| 1118 | def test_type_of_data_element(self): |
| 1119 | # Check the type of data elements doesn't affect the numeric result. |
| 1120 | # This is a weaker test than UnivariateTypeMixin.testTypesConserved, |
| 1121 | # because it checks the numeric result by equality, but not by type. |
| 1122 | class MyFloat(float): |
| 1123 | def __truediv__(self, other): |
| 1124 | return type(self)(super().__truediv__(other)) |
| 1125 | def __add__(self, other): |
| 1126 | return type(self)(super().__add__(other)) |
| 1127 | __radd__ = __add__ |
| 1128 | |
| 1129 | raw = self.prepare_data() |
| 1130 | expected = self.func(raw) |
| 1131 | for kind in (float, MyFloat, Decimal, Fraction): |
| 1132 | data = [kind(x) for x in raw] |
| 1133 | result = type(expected)(self.func(data)) |
| 1134 | self.assertEqual(result, expected) |
| 1135 | |
| 1136 | |
| 1137 | class UnivariateTypeMixin: |
| 1138 | """Mixin class for type-conserving functions. |
| 1139 | |
| 1140 | This mixin class holds test(s) for functions which conserve the type of |
| 1141 | individual data points. E.g. the mean of a list of Fractions should itself |
| 1142 | be a Fraction. |
| 1143 | |
| 1144 | Not all tests to do with types need go in this class. Only those that |
| 1145 | rely on the function returning the same type as its input data. |
| 1146 | """ |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 1147 | def prepare_types_for_conservation_test(self): |
| 1148 | """Return the types which are expected to be conserved.""" |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1149 | class MyFloat(float): |
| 1150 | def __truediv__(self, other): |
| 1151 | return type(self)(super().__truediv__(other)) |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 1152 | def __rtruediv__(self, other): |
| 1153 | return type(self)(super().__rtruediv__(other)) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1154 | def __sub__(self, other): |
| 1155 | return type(self)(super().__sub__(other)) |
| 1156 | def __rsub__(self, other): |
| 1157 | return type(self)(super().__rsub__(other)) |
| 1158 | def __pow__(self, other): |
| 1159 | return type(self)(super().__pow__(other)) |
| 1160 | def __add__(self, other): |
| 1161 | return type(self)(super().__add__(other)) |
| 1162 | __radd__ = __add__ |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 1163 | return (float, Decimal, Fraction, MyFloat) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1164 | |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 1165 | def test_types_conserved(self): |
| 1166 | # Test that functions keeps the same type as their data points. |
| 1167 | # (Excludes mixed data types.) This only tests the type of the return |
| 1168 | # result, not the value. |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1169 | data = self.prepare_data() |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 1170 | for kind in self.prepare_types_for_conservation_test(): |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1171 | d = [kind(x) for x in data] |
| 1172 | result = self.func(d) |
| 1173 | self.assertIs(type(result), kind) |
| 1174 | |
| 1175 | |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1176 | class TestSumCommon(UnivariateCommonMixin, UnivariateTypeMixin): |
| 1177 | # Common test cases for statistics._sum() function. |
| 1178 | |
| 1179 | # This test suite looks only at the numeric value returned by _sum, |
| 1180 | # after conversion to the appropriate type. |
| 1181 | def setUp(self): |
| 1182 | def simplified_sum(*args): |
| 1183 | T, value, n = statistics._sum(*args) |
| 1184 | return statistics._coerce(value, T) |
| 1185 | self.func = simplified_sum |
| 1186 | |
| 1187 | |
| 1188 | class TestSum(NumericTestCase): |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1189 | # Test cases for statistics._sum() function. |
| 1190 | |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1191 | # These tests look at the entire three value tuple returned by _sum. |
| 1192 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1193 | def setUp(self): |
| 1194 | self.func = statistics._sum |
| 1195 | |
| 1196 | def test_empty_data(self): |
| 1197 | # Override test for empty data. |
| 1198 | for data in ([], (), iter([])): |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1199 | self.assertEqual(self.func(data), (int, Fraction(0), 0)) |
| 1200 | self.assertEqual(self.func(data, 23), (int, Fraction(23), 0)) |
| 1201 | self.assertEqual(self.func(data, 2.3), (float, Fraction(2.3), 0)) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1202 | |
| 1203 | def test_ints(self): |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1204 | self.assertEqual(self.func([1, 5, 3, -4, -8, 20, 42, 1]), |
| 1205 | (int, Fraction(60), 8)) |
| 1206 | self.assertEqual(self.func([4, 2, 3, -8, 7], 1000), |
| 1207 | (int, Fraction(1008), 5)) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1208 | |
| 1209 | def test_floats(self): |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1210 | self.assertEqual(self.func([0.25]*20), |
| 1211 | (float, Fraction(5.0), 20)) |
| 1212 | self.assertEqual(self.func([0.125, 0.25, 0.5, 0.75], 1.5), |
| 1213 | (float, Fraction(3.125), 4)) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1214 | |
| 1215 | def test_fractions(self): |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1216 | self.assertEqual(self.func([Fraction(1, 1000)]*500), |
| 1217 | (Fraction, Fraction(1, 2), 500)) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1218 | |
| 1219 | def test_decimals(self): |
| 1220 | D = Decimal |
| 1221 | data = [D("0.001"), D("5.246"), D("1.702"), D("-0.025"), |
| 1222 | D("3.974"), D("2.328"), D("4.617"), D("2.843"), |
| 1223 | ] |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1224 | self.assertEqual(self.func(data), |
| 1225 | (Decimal, Decimal("20.686"), 8)) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1226 | |
| 1227 | def test_compare_with_math_fsum(self): |
| 1228 | # Compare with the math.fsum function. |
| 1229 | # Ideally we ought to get the exact same result, but sometimes |
| 1230 | # we differ by a very slight amount :-( |
| 1231 | data = [random.uniform(-100, 1000) for _ in range(1000)] |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1232 | self.assertApproxEqual(float(self.func(data)[1]), math.fsum(data), rel=2e-16) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1233 | |
| 1234 | def test_start_argument(self): |
| 1235 | # Test that the optional start argument works correctly. |
| 1236 | data = [random.uniform(1, 1000) for _ in range(100)] |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1237 | t = self.func(data)[1] |
| 1238 | self.assertEqual(t+42, self.func(data, 42)[1]) |
| 1239 | self.assertEqual(t-23, self.func(data, -23)[1]) |
| 1240 | self.assertEqual(t+Fraction(1e20), self.func(data, 1e20)[1]) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1241 | |
| 1242 | def test_strings_fail(self): |
| 1243 | # Sum of strings should fail. |
| 1244 | self.assertRaises(TypeError, self.func, [1, 2, 3], '999') |
| 1245 | self.assertRaises(TypeError, self.func, [1, 2, 3, '999']) |
| 1246 | |
| 1247 | def test_bytes_fail(self): |
| 1248 | # Sum of bytes should fail. |
| 1249 | self.assertRaises(TypeError, self.func, [1, 2, 3], b'999') |
| 1250 | self.assertRaises(TypeError, self.func, [1, 2, 3, b'999']) |
| 1251 | |
| 1252 | def test_mixed_sum(self): |
Nick Coghlan | 73afe2a | 2014-02-08 19:58:04 +1000 | [diff] [blame] | 1253 | # Mixed input types are not (currently) allowed. |
| 1254 | # Check that mixed data types fail. |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1255 | self.assertRaises(TypeError, self.func, [1, 2.0, Decimal(1)]) |
Nick Coghlan | 73afe2a | 2014-02-08 19:58:04 +1000 | [diff] [blame] | 1256 | # And so does mixed start argument. |
| 1257 | self.assertRaises(TypeError, self.func, [1, 2.0], Decimal(1)) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1258 | |
| 1259 | |
| 1260 | class SumTortureTest(NumericTestCase): |
| 1261 | def test_torture(self): |
| 1262 | # Tim Peters' torture test for sum, and variants of same. |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1263 | self.assertEqual(statistics._sum([1, 1e100, 1, -1e100]*10000), |
| 1264 | (float, Fraction(20000.0), 40000)) |
| 1265 | self.assertEqual(statistics._sum([1e100, 1, 1, -1e100]*10000), |
| 1266 | (float, Fraction(20000.0), 40000)) |
| 1267 | T, num, count = statistics._sum([1e-100, 1, 1e-100, -1]*10000) |
| 1268 | self.assertIs(T, float) |
| 1269 | self.assertEqual(count, 40000) |
| 1270 | self.assertApproxEqual(float(num), 2.0e-96, rel=5e-16) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1271 | |
| 1272 | |
| 1273 | class SumSpecialValues(NumericTestCase): |
| 1274 | # Test that sum works correctly with IEEE-754 special values. |
| 1275 | |
| 1276 | def test_nan(self): |
| 1277 | for type_ in (float, Decimal): |
| 1278 | nan = type_('nan') |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1279 | result = statistics._sum([1, nan, 2])[1] |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1280 | self.assertIs(type(result), type_) |
| 1281 | self.assertTrue(math.isnan(result)) |
| 1282 | |
| 1283 | def check_infinity(self, x, inf): |
| 1284 | """Check x is an infinity of the same type and sign as inf.""" |
| 1285 | self.assertTrue(math.isinf(x)) |
| 1286 | self.assertIs(type(x), type(inf)) |
| 1287 | self.assertEqual(x > 0, inf > 0) |
| 1288 | assert x == inf |
| 1289 | |
| 1290 | def do_test_inf(self, inf): |
| 1291 | # Adding a single infinity gives infinity. |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1292 | result = statistics._sum([1, 2, inf, 3])[1] |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1293 | self.check_infinity(result, inf) |
| 1294 | # Adding two infinities of the same sign also gives infinity. |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1295 | result = statistics._sum([1, 2, inf, 3, inf, 4])[1] |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1296 | self.check_infinity(result, inf) |
| 1297 | |
| 1298 | def test_float_inf(self): |
| 1299 | inf = float('inf') |
| 1300 | for sign in (+1, -1): |
| 1301 | self.do_test_inf(sign*inf) |
| 1302 | |
| 1303 | def test_decimal_inf(self): |
| 1304 | inf = Decimal('inf') |
| 1305 | for sign in (+1, -1): |
| 1306 | self.do_test_inf(sign*inf) |
| 1307 | |
| 1308 | def test_float_mismatched_infs(self): |
| 1309 | # Test that adding two infinities of opposite sign gives a NAN. |
| 1310 | inf = float('inf') |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1311 | result = statistics._sum([1, 2, inf, 3, -inf, 4])[1] |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1312 | self.assertTrue(math.isnan(result)) |
| 1313 | |
Berker Peksag | f8c111d | 2014-09-24 15:03:25 +0300 | [diff] [blame] | 1314 | def test_decimal_extendedcontext_mismatched_infs_to_nan(self): |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1315 | # Test adding Decimal INFs with opposite sign returns NAN. |
| 1316 | inf = Decimal('inf') |
| 1317 | data = [1, 2, inf, 3, -inf, 4] |
| 1318 | with decimal.localcontext(decimal.ExtendedContext): |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1319 | self.assertTrue(math.isnan(statistics._sum(data)[1])) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1320 | |
Berker Peksag | f8c111d | 2014-09-24 15:03:25 +0300 | [diff] [blame] | 1321 | def test_decimal_basiccontext_mismatched_infs_to_nan(self): |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1322 | # Test adding Decimal INFs with opposite sign raises InvalidOperation. |
| 1323 | inf = Decimal('inf') |
| 1324 | data = [1, 2, inf, 3, -inf, 4] |
| 1325 | with decimal.localcontext(decimal.BasicContext): |
| 1326 | self.assertRaises(decimal.InvalidOperation, statistics._sum, data) |
| 1327 | |
| 1328 | def test_decimal_snan_raises(self): |
| 1329 | # Adding sNAN should raise InvalidOperation. |
| 1330 | sNAN = Decimal('sNAN') |
| 1331 | data = [1, sNAN, 2] |
| 1332 | self.assertRaises(decimal.InvalidOperation, statistics._sum, data) |
| 1333 | |
| 1334 | |
| 1335 | # === Tests for averages === |
| 1336 | |
| 1337 | class AverageMixin(UnivariateCommonMixin): |
| 1338 | # Mixin class holding common tests for averages. |
| 1339 | |
| 1340 | def test_single_value(self): |
| 1341 | # Average of a single value is the value itself. |
| 1342 | for x in (23, 42.5, 1.3e15, Fraction(15, 19), Decimal('0.28')): |
| 1343 | self.assertEqual(self.func([x]), x) |
| 1344 | |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 1345 | def prepare_values_for_repeated_single_test(self): |
| 1346 | return (3.5, 17, 2.5e15, Fraction(61, 67), Decimal('4.9712')) |
| 1347 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1348 | def test_repeated_single_value(self): |
| 1349 | # The average of a single repeated value is the value itself. |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 1350 | for x in self.prepare_values_for_repeated_single_test(): |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1351 | for count in (2, 5, 10, 20): |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 1352 | with self.subTest(x=x, count=count): |
| 1353 | data = [x]*count |
| 1354 | self.assertEqual(self.func(data), x) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1355 | |
| 1356 | |
| 1357 | class TestMean(NumericTestCase, AverageMixin, UnivariateTypeMixin): |
| 1358 | def setUp(self): |
| 1359 | self.func = statistics.mean |
| 1360 | |
| 1361 | def test_torture_pep(self): |
| 1362 | # "Torture Test" from PEP-450. |
| 1363 | self.assertEqual(self.func([1e100, 1, 3, -1e100]), 1) |
| 1364 | |
| 1365 | def test_ints(self): |
| 1366 | # Test mean with ints. |
| 1367 | data = [0, 1, 2, 3, 3, 3, 4, 5, 5, 6, 7, 7, 7, 7, 8, 9] |
| 1368 | random.shuffle(data) |
| 1369 | self.assertEqual(self.func(data), 4.8125) |
| 1370 | |
| 1371 | def test_floats(self): |
| 1372 | # Test mean with floats. |
| 1373 | data = [17.25, 19.75, 20.0, 21.5, 21.75, 23.25, 25.125, 27.5] |
| 1374 | random.shuffle(data) |
| 1375 | self.assertEqual(self.func(data), 22.015625) |
| 1376 | |
| 1377 | def test_decimals(self): |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 1378 | # Test mean with Decimals. |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1379 | D = Decimal |
| 1380 | data = [D("1.634"), D("2.517"), D("3.912"), D("4.072"), D("5.813")] |
| 1381 | random.shuffle(data) |
| 1382 | self.assertEqual(self.func(data), D("3.5896")) |
| 1383 | |
| 1384 | def test_fractions(self): |
| 1385 | # Test mean with Fractions. |
| 1386 | F = Fraction |
| 1387 | data = [F(1, 2), F(2, 3), F(3, 4), F(4, 5), F(5, 6), F(6, 7), F(7, 8)] |
| 1388 | random.shuffle(data) |
| 1389 | self.assertEqual(self.func(data), F(1479, 1960)) |
| 1390 | |
| 1391 | def test_inf(self): |
| 1392 | # Test mean with infinities. |
| 1393 | raw = [1, 3, 5, 7, 9] # Use only ints, to avoid TypeError later. |
| 1394 | for kind in (float, Decimal): |
| 1395 | for sign in (1, -1): |
| 1396 | inf = kind("inf")*sign |
| 1397 | data = raw + [inf] |
| 1398 | result = self.func(data) |
| 1399 | self.assertTrue(math.isinf(result)) |
| 1400 | self.assertEqual(result, inf) |
| 1401 | |
| 1402 | def test_mismatched_infs(self): |
| 1403 | # Test mean with infinities of opposite sign. |
| 1404 | data = [2, 4, 6, float('inf'), 1, 3, 5, float('-inf')] |
| 1405 | result = self.func(data) |
| 1406 | self.assertTrue(math.isnan(result)) |
| 1407 | |
| 1408 | def test_nan(self): |
| 1409 | # Test mean with NANs. |
| 1410 | raw = [1, 3, 5, 7, 9] # Use only ints, to avoid TypeError later. |
| 1411 | for kind in (float, Decimal): |
| 1412 | inf = kind("nan") |
| 1413 | data = raw + [inf] |
| 1414 | result = self.func(data) |
| 1415 | self.assertTrue(math.isnan(result)) |
| 1416 | |
| 1417 | def test_big_data(self): |
| 1418 | # Test adding a large constant to every data point. |
| 1419 | c = 1e9 |
| 1420 | data = [3.4, 4.5, 4.9, 6.7, 6.8, 7.2, 8.0, 8.1, 9.4] |
| 1421 | expected = self.func(data) + c |
| 1422 | assert expected != c |
| 1423 | result = self.func([x+c for x in data]) |
| 1424 | self.assertEqual(result, expected) |
| 1425 | |
| 1426 | def test_doubled_data(self): |
| 1427 | # Mean of [a,b,c...z] should be same as for [a,a,b,b,c,c...z,z]. |
| 1428 | data = [random.uniform(-3, 5) for _ in range(1000)] |
| 1429 | expected = self.func(data) |
| 1430 | actual = self.func(data*2) |
| 1431 | self.assertApproxEqual(actual, expected) |
| 1432 | |
Nick Coghlan | 4a7668a | 2014-02-08 23:55:14 +1000 | [diff] [blame] | 1433 | def test_regression_20561(self): |
| 1434 | # Regression test for issue 20561. |
| 1435 | # See http://bugs.python.org/issue20561 |
| 1436 | d = Decimal('1e4') |
| 1437 | self.assertEqual(statistics.mean([d]), d) |
| 1438 | |
Steven D'Aprano | b28c327 | 2015-12-01 19:59:53 +1100 | [diff] [blame] | 1439 | def test_regression_25177(self): |
| 1440 | # Regression test for issue 25177. |
| 1441 | # Ensure very big and very small floats don't overflow. |
| 1442 | # See http://bugs.python.org/issue25177. |
| 1443 | self.assertEqual(statistics.mean( |
| 1444 | [8.988465674311579e+307, 8.98846567431158e+307]), |
| 1445 | 8.98846567431158e+307) |
| 1446 | big = 8.98846567431158e+307 |
| 1447 | tiny = 5e-324 |
| 1448 | for n in (2, 3, 5, 200): |
| 1449 | self.assertEqual(statistics.mean([big]*n), big) |
| 1450 | self.assertEqual(statistics.mean([tiny]*n), tiny) |
| 1451 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1452 | |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 1453 | class TestHarmonicMean(NumericTestCase, AverageMixin, UnivariateTypeMixin): |
| 1454 | def setUp(self): |
| 1455 | self.func = statistics.harmonic_mean |
| 1456 | |
| 1457 | def prepare_data(self): |
| 1458 | # Override mixin method. |
| 1459 | values = super().prepare_data() |
| 1460 | values.remove(0) |
| 1461 | return values |
| 1462 | |
| 1463 | def prepare_values_for_repeated_single_test(self): |
| 1464 | # Override mixin method. |
| 1465 | return (3.5, 17, 2.5e15, Fraction(61, 67), Decimal('4.125')) |
| 1466 | |
| 1467 | def test_zero(self): |
| 1468 | # Test that harmonic mean returns zero when given zero. |
| 1469 | values = [1, 0, 2] |
| 1470 | self.assertEqual(self.func(values), 0) |
| 1471 | |
| 1472 | def test_negative_error(self): |
| 1473 | # Test that harmonic mean raises when given a negative value. |
| 1474 | exc = statistics.StatisticsError |
| 1475 | for values in ([-1], [1, -2, 3]): |
| 1476 | with self.subTest(values=values): |
| 1477 | self.assertRaises(exc, self.func, values) |
| 1478 | |
| 1479 | def test_ints(self): |
| 1480 | # Test harmonic mean with ints. |
| 1481 | data = [2, 4, 4, 8, 16, 16] |
| 1482 | random.shuffle(data) |
| 1483 | self.assertEqual(self.func(data), 6*4/5) |
| 1484 | |
| 1485 | def test_floats_exact(self): |
| 1486 | # Test harmonic mean with some carefully chosen floats. |
| 1487 | data = [1/8, 1/4, 1/4, 1/2, 1/2] |
| 1488 | random.shuffle(data) |
| 1489 | self.assertEqual(self.func(data), 1/4) |
| 1490 | self.assertEqual(self.func([0.25, 0.5, 1.0, 1.0]), 0.5) |
| 1491 | |
| 1492 | def test_singleton_lists(self): |
| 1493 | # Test that harmonic mean([x]) returns (approximately) x. |
| 1494 | for x in range(1, 101): |
Steven D'Aprano | e7fef52 | 2016-08-09 13:19:48 +1000 | [diff] [blame] | 1495 | self.assertEqual(self.func([x]), x) |
Steven D'Aprano | a474afd | 2016-08-09 12:49:01 +1000 | [diff] [blame] | 1496 | |
| 1497 | def test_decimals_exact(self): |
| 1498 | # Test harmonic mean with some carefully chosen Decimals. |
| 1499 | D = Decimal |
| 1500 | self.assertEqual(self.func([D(15), D(30), D(60), D(60)]), D(30)) |
| 1501 | data = [D("0.05"), D("0.10"), D("0.20"), D("0.20")] |
| 1502 | random.shuffle(data) |
| 1503 | self.assertEqual(self.func(data), D("0.10")) |
| 1504 | data = [D("1.68"), D("0.32"), D("5.94"), D("2.75")] |
| 1505 | random.shuffle(data) |
| 1506 | self.assertEqual(self.func(data), D(66528)/70723) |
| 1507 | |
| 1508 | def test_fractions(self): |
| 1509 | # Test harmonic mean with Fractions. |
| 1510 | F = Fraction |
| 1511 | data = [F(1, 2), F(2, 3), F(3, 4), F(4, 5), F(5, 6), F(6, 7), F(7, 8)] |
| 1512 | random.shuffle(data) |
| 1513 | self.assertEqual(self.func(data), F(7*420, 4029)) |
| 1514 | |
| 1515 | def test_inf(self): |
| 1516 | # Test harmonic mean with infinity. |
| 1517 | values = [2.0, float('inf'), 1.0] |
| 1518 | self.assertEqual(self.func(values), 2.0) |
| 1519 | |
| 1520 | def test_nan(self): |
| 1521 | # Test harmonic mean with NANs. |
| 1522 | values = [2.0, float('nan'), 1.0] |
| 1523 | self.assertTrue(math.isnan(self.func(values))) |
| 1524 | |
| 1525 | def test_multiply_data_points(self): |
| 1526 | # Test multiplying every data point by a constant. |
| 1527 | c = 111 |
| 1528 | data = [3.4, 4.5, 4.9, 6.7, 6.8, 7.2, 8.0, 8.1, 9.4] |
| 1529 | expected = self.func(data)*c |
| 1530 | result = self.func([x*c for x in data]) |
| 1531 | self.assertEqual(result, expected) |
| 1532 | |
| 1533 | def test_doubled_data(self): |
| 1534 | # Harmonic mean of [a,b...z] should be same as for [a,a,b,b...z,z]. |
| 1535 | data = [random.uniform(1, 5) for _ in range(1000)] |
| 1536 | expected = self.func(data) |
| 1537 | actual = self.func(data*2) |
| 1538 | self.assertApproxEqual(actual, expected) |
| 1539 | |
| 1540 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1541 | class TestMedian(NumericTestCase, AverageMixin): |
| 1542 | # Common tests for median and all median.* functions. |
| 1543 | def setUp(self): |
| 1544 | self.func = statistics.median |
| 1545 | |
| 1546 | def prepare_data(self): |
| 1547 | """Overload method from UnivariateCommonMixin.""" |
| 1548 | data = super().prepare_data() |
| 1549 | if len(data)%2 != 1: |
| 1550 | data.append(2) |
| 1551 | return data |
| 1552 | |
| 1553 | def test_even_ints(self): |
| 1554 | # Test median with an even number of int data points. |
| 1555 | data = [1, 2, 3, 4, 5, 6] |
| 1556 | assert len(data)%2 == 0 |
| 1557 | self.assertEqual(self.func(data), 3.5) |
| 1558 | |
| 1559 | def test_odd_ints(self): |
| 1560 | # Test median with an odd number of int data points. |
| 1561 | data = [1, 2, 3, 4, 5, 6, 9] |
| 1562 | assert len(data)%2 == 1 |
| 1563 | self.assertEqual(self.func(data), 4) |
| 1564 | |
| 1565 | def test_odd_fractions(self): |
| 1566 | # Test median works with an odd number of Fractions. |
| 1567 | F = Fraction |
| 1568 | data = [F(1, 7), F(2, 7), F(3, 7), F(4, 7), F(5, 7)] |
| 1569 | assert len(data)%2 == 1 |
| 1570 | random.shuffle(data) |
| 1571 | self.assertEqual(self.func(data), F(3, 7)) |
| 1572 | |
| 1573 | def test_even_fractions(self): |
| 1574 | # Test median works with an even number of Fractions. |
| 1575 | F = Fraction |
| 1576 | data = [F(1, 7), F(2, 7), F(3, 7), F(4, 7), F(5, 7), F(6, 7)] |
| 1577 | assert len(data)%2 == 0 |
| 1578 | random.shuffle(data) |
| 1579 | self.assertEqual(self.func(data), F(1, 2)) |
| 1580 | |
| 1581 | def test_odd_decimals(self): |
| 1582 | # Test median works with an odd number of Decimals. |
| 1583 | D = Decimal |
| 1584 | data = [D('2.5'), D('3.1'), D('4.2'), D('5.7'), D('5.8')] |
| 1585 | assert len(data)%2 == 1 |
| 1586 | random.shuffle(data) |
| 1587 | self.assertEqual(self.func(data), D('4.2')) |
| 1588 | |
| 1589 | def test_even_decimals(self): |
| 1590 | # Test median works with an even number of Decimals. |
| 1591 | D = Decimal |
| 1592 | data = [D('1.2'), D('2.5'), D('3.1'), D('4.2'), D('5.7'), D('5.8')] |
| 1593 | assert len(data)%2 == 0 |
| 1594 | random.shuffle(data) |
| 1595 | self.assertEqual(self.func(data), D('3.65')) |
| 1596 | |
| 1597 | |
| 1598 | class TestMedianDataType(NumericTestCase, UnivariateTypeMixin): |
| 1599 | # Test conservation of data element type for median. |
| 1600 | def setUp(self): |
| 1601 | self.func = statistics.median |
| 1602 | |
| 1603 | def prepare_data(self): |
| 1604 | data = list(range(15)) |
| 1605 | assert len(data)%2 == 1 |
| 1606 | while data == sorted(data): |
| 1607 | random.shuffle(data) |
| 1608 | return data |
| 1609 | |
| 1610 | |
| 1611 | class TestMedianLow(TestMedian, UnivariateTypeMixin): |
| 1612 | def setUp(self): |
| 1613 | self.func = statistics.median_low |
| 1614 | |
| 1615 | def test_even_ints(self): |
| 1616 | # Test median_low with an even number of ints. |
| 1617 | data = [1, 2, 3, 4, 5, 6] |
| 1618 | assert len(data)%2 == 0 |
| 1619 | self.assertEqual(self.func(data), 3) |
| 1620 | |
| 1621 | def test_even_fractions(self): |
| 1622 | # Test median_low works with an even number of Fractions. |
| 1623 | F = Fraction |
| 1624 | data = [F(1, 7), F(2, 7), F(3, 7), F(4, 7), F(5, 7), F(6, 7)] |
| 1625 | assert len(data)%2 == 0 |
| 1626 | random.shuffle(data) |
| 1627 | self.assertEqual(self.func(data), F(3, 7)) |
| 1628 | |
| 1629 | def test_even_decimals(self): |
| 1630 | # Test median_low works with an even number of Decimals. |
| 1631 | D = Decimal |
| 1632 | data = [D('1.1'), D('2.2'), D('3.3'), D('4.4'), D('5.5'), D('6.6')] |
| 1633 | assert len(data)%2 == 0 |
| 1634 | random.shuffle(data) |
| 1635 | self.assertEqual(self.func(data), D('3.3')) |
| 1636 | |
| 1637 | |
| 1638 | class TestMedianHigh(TestMedian, UnivariateTypeMixin): |
| 1639 | def setUp(self): |
| 1640 | self.func = statistics.median_high |
| 1641 | |
| 1642 | def test_even_ints(self): |
| 1643 | # Test median_high with an even number of ints. |
| 1644 | data = [1, 2, 3, 4, 5, 6] |
| 1645 | assert len(data)%2 == 0 |
| 1646 | self.assertEqual(self.func(data), 4) |
| 1647 | |
| 1648 | def test_even_fractions(self): |
| 1649 | # Test median_high works with an even number of Fractions. |
| 1650 | F = Fraction |
| 1651 | data = [F(1, 7), F(2, 7), F(3, 7), F(4, 7), F(5, 7), F(6, 7)] |
| 1652 | assert len(data)%2 == 0 |
| 1653 | random.shuffle(data) |
| 1654 | self.assertEqual(self.func(data), F(4, 7)) |
| 1655 | |
| 1656 | def test_even_decimals(self): |
| 1657 | # Test median_high works with an even number of Decimals. |
| 1658 | D = Decimal |
| 1659 | data = [D('1.1'), D('2.2'), D('3.3'), D('4.4'), D('5.5'), D('6.6')] |
| 1660 | assert len(data)%2 == 0 |
| 1661 | random.shuffle(data) |
| 1662 | self.assertEqual(self.func(data), D('4.4')) |
| 1663 | |
| 1664 | |
| 1665 | class TestMedianGrouped(TestMedian): |
| 1666 | # Test median_grouped. |
| 1667 | # Doesn't conserve data element types, so don't use TestMedianType. |
| 1668 | def setUp(self): |
| 1669 | self.func = statistics.median_grouped |
| 1670 | |
| 1671 | def test_odd_number_repeated(self): |
| 1672 | # Test median.grouped with repeated median values. |
| 1673 | data = [12, 13, 14, 14, 14, 15, 15] |
| 1674 | assert len(data)%2 == 1 |
| 1675 | self.assertEqual(self.func(data), 14) |
| 1676 | #--- |
| 1677 | data = [12, 13, 14, 14, 14, 14, 15] |
| 1678 | assert len(data)%2 == 1 |
| 1679 | self.assertEqual(self.func(data), 13.875) |
| 1680 | #--- |
| 1681 | data = [5, 10, 10, 15, 20, 20, 20, 20, 25, 25, 30] |
| 1682 | assert len(data)%2 == 1 |
| 1683 | self.assertEqual(self.func(data, 5), 19.375) |
| 1684 | #--- |
| 1685 | data = [16, 18, 18, 18, 18, 20, 20, 20, 22, 22, 22, 24, 24, 26, 28] |
| 1686 | assert len(data)%2 == 1 |
| 1687 | self.assertApproxEqual(self.func(data, 2), 20.66666667, tol=1e-8) |
| 1688 | |
| 1689 | def test_even_number_repeated(self): |
| 1690 | # Test median.grouped with repeated median values. |
| 1691 | data = [5, 10, 10, 15, 20, 20, 20, 25, 25, 30] |
| 1692 | assert len(data)%2 == 0 |
| 1693 | self.assertApproxEqual(self.func(data, 5), 19.16666667, tol=1e-8) |
| 1694 | #--- |
| 1695 | data = [2, 3, 4, 4, 4, 5] |
| 1696 | assert len(data)%2 == 0 |
| 1697 | self.assertApproxEqual(self.func(data), 3.83333333, tol=1e-8) |
| 1698 | #--- |
| 1699 | data = [2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6] |
| 1700 | assert len(data)%2 == 0 |
| 1701 | self.assertEqual(self.func(data), 4.5) |
| 1702 | #--- |
| 1703 | data = [3, 4, 4, 4, 5, 5, 5, 5, 6, 6] |
| 1704 | assert len(data)%2 == 0 |
| 1705 | self.assertEqual(self.func(data), 4.75) |
| 1706 | |
| 1707 | def test_repeated_single_value(self): |
| 1708 | # Override method from AverageMixin. |
| 1709 | # Yet again, failure of median_grouped to conserve the data type |
| 1710 | # causes me headaches :-( |
| 1711 | for x in (5.3, 68, 4.3e17, Fraction(29, 101), Decimal('32.9714')): |
| 1712 | for count in (2, 5, 10, 20): |
| 1713 | data = [x]*count |
| 1714 | self.assertEqual(self.func(data), float(x)) |
| 1715 | |
| 1716 | def test_odd_fractions(self): |
| 1717 | # Test median_grouped works with an odd number of Fractions. |
| 1718 | F = Fraction |
| 1719 | data = [F(5, 4), F(9, 4), F(13, 4), F(13, 4), F(17, 4)] |
| 1720 | assert len(data)%2 == 1 |
| 1721 | random.shuffle(data) |
| 1722 | self.assertEqual(self.func(data), 3.0) |
| 1723 | |
| 1724 | def test_even_fractions(self): |
| 1725 | # Test median_grouped works with an even number of Fractions. |
| 1726 | F = Fraction |
| 1727 | data = [F(5, 4), F(9, 4), F(13, 4), F(13, 4), F(17, 4), F(17, 4)] |
| 1728 | assert len(data)%2 == 0 |
| 1729 | random.shuffle(data) |
| 1730 | self.assertEqual(self.func(data), 3.25) |
| 1731 | |
| 1732 | def test_odd_decimals(self): |
| 1733 | # Test median_grouped works with an odd number of Decimals. |
| 1734 | D = Decimal |
| 1735 | data = [D('5.5'), D('6.5'), D('6.5'), D('7.5'), D('8.5')] |
| 1736 | assert len(data)%2 == 1 |
| 1737 | random.shuffle(data) |
| 1738 | self.assertEqual(self.func(data), 6.75) |
| 1739 | |
| 1740 | def test_even_decimals(self): |
| 1741 | # Test median_grouped works with an even number of Decimals. |
| 1742 | D = Decimal |
| 1743 | data = [D('5.5'), D('5.5'), D('6.5'), D('6.5'), D('7.5'), D('8.5')] |
| 1744 | assert len(data)%2 == 0 |
| 1745 | random.shuffle(data) |
| 1746 | self.assertEqual(self.func(data), 6.5) |
| 1747 | #--- |
| 1748 | data = [D('5.5'), D('5.5'), D('6.5'), D('7.5'), D('7.5'), D('8.5')] |
| 1749 | assert len(data)%2 == 0 |
| 1750 | random.shuffle(data) |
| 1751 | self.assertEqual(self.func(data), 7.0) |
| 1752 | |
| 1753 | def test_interval(self): |
| 1754 | # Test median_grouped with interval argument. |
| 1755 | data = [2.25, 2.5, 2.5, 2.75, 2.75, 3.0, 3.0, 3.25, 3.5, 3.75] |
| 1756 | self.assertEqual(self.func(data, 0.25), 2.875) |
| 1757 | data = [2.25, 2.5, 2.5, 2.75, 2.75, 2.75, 3.0, 3.0, 3.25, 3.5, 3.75] |
| 1758 | self.assertApproxEqual(self.func(data, 0.25), 2.83333333, tol=1e-8) |
| 1759 | data = [220, 220, 240, 260, 260, 260, 260, 280, 280, 300, 320, 340] |
| 1760 | self.assertEqual(self.func(data, 20), 265.0) |
| 1761 | |
Steven D'Aprano | 8c115a4 | 2016-07-08 02:38:45 +1000 | [diff] [blame] | 1762 | def test_data_type_error(self): |
| 1763 | # Test median_grouped with str, bytes data types for data and interval |
| 1764 | data = ["", "", ""] |
| 1765 | self.assertRaises(TypeError, self.func, data) |
| 1766 | #--- |
| 1767 | data = [b"", b"", b""] |
| 1768 | self.assertRaises(TypeError, self.func, data) |
| 1769 | #--- |
| 1770 | data = [1, 2, 3] |
| 1771 | interval = "" |
| 1772 | self.assertRaises(TypeError, self.func, data, interval) |
| 1773 | #--- |
| 1774 | data = [1, 2, 3] |
| 1775 | interval = b"" |
| 1776 | self.assertRaises(TypeError, self.func, data, interval) |
| 1777 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1778 | |
| 1779 | class TestMode(NumericTestCase, AverageMixin, UnivariateTypeMixin): |
| 1780 | # Test cases for the discrete version of mode. |
| 1781 | def setUp(self): |
| 1782 | self.func = statistics.mode |
| 1783 | |
| 1784 | def prepare_data(self): |
| 1785 | """Overload method from UnivariateCommonMixin.""" |
| 1786 | # Make sure test data has exactly one mode. |
| 1787 | return [1, 1, 1, 1, 3, 4, 7, 9, 0, 8, 2] |
| 1788 | |
| 1789 | def test_range_data(self): |
| 1790 | # Override test from UnivariateCommonMixin. |
| 1791 | data = range(20, 50, 3) |
Raymond Hettinger | fc06a19 | 2019-03-12 00:43:27 -0700 | [diff] [blame] | 1792 | self.assertEqual(self.func(data), 20) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1793 | |
| 1794 | def test_nominal_data(self): |
| 1795 | # Test mode with nominal data. |
| 1796 | data = 'abcbdb' |
| 1797 | self.assertEqual(self.func(data), 'b') |
| 1798 | data = 'fe fi fo fum fi fi'.split() |
| 1799 | self.assertEqual(self.func(data), 'fi') |
| 1800 | |
| 1801 | def test_discrete_data(self): |
| 1802 | # Test mode with discrete numeric data. |
| 1803 | data = list(range(10)) |
| 1804 | for i in range(10): |
| 1805 | d = data + [i] |
| 1806 | random.shuffle(d) |
| 1807 | self.assertEqual(self.func(d), i) |
| 1808 | |
| 1809 | def test_bimodal_data(self): |
| 1810 | # Test mode with bimodal data. |
| 1811 | data = [1, 1, 2, 2, 2, 2, 3, 4, 5, 6, 6, 6, 6, 7, 8, 9, 9] |
| 1812 | assert data.count(2) == data.count(6) == 4 |
Miss Islington (bot) | 4bd1d05 | 2019-08-30 13:42:54 -0700 | [diff] [blame] | 1813 | # mode() should return 2, the first encountered mode |
Raymond Hettinger | fc06a19 | 2019-03-12 00:43:27 -0700 | [diff] [blame] | 1814 | self.assertEqual(self.func(data), 2) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1815 | |
Raymond Hettinger | fc06a19 | 2019-03-12 00:43:27 -0700 | [diff] [blame] | 1816 | def test_unique_data(self): |
| 1817 | # Test mode when data points are all unique. |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1818 | data = list(range(10)) |
Miss Islington (bot) | 4bd1d05 | 2019-08-30 13:42:54 -0700 | [diff] [blame] | 1819 | # mode() should return 0, the first encountered mode |
Raymond Hettinger | fc06a19 | 2019-03-12 00:43:27 -0700 | [diff] [blame] | 1820 | self.assertEqual(self.func(data), 0) |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1821 | |
| 1822 | def test_none_data(self): |
| 1823 | # Test that mode raises TypeError if given None as data. |
| 1824 | |
| 1825 | # This test is necessary because the implementation of mode uses |
| 1826 | # collections.Counter, which accepts None and returns an empty dict. |
| 1827 | self.assertRaises(TypeError, self.func, None) |
| 1828 | |
Nick Coghlan | bfd68bf | 2014-02-08 19:44:16 +1000 | [diff] [blame] | 1829 | def test_counter_data(self): |
| 1830 | # Test that a Counter is treated like any other iterable. |
| 1831 | data = collections.Counter([1, 1, 1, 2]) |
| 1832 | # Since the keys of the counter are treated as data points, not the |
Raymond Hettinger | fc06a19 | 2019-03-12 00:43:27 -0700 | [diff] [blame] | 1833 | # counts, this should return the first mode encountered, 1 |
| 1834 | self.assertEqual(self.func(data), 1) |
| 1835 | |
| 1836 | |
| 1837 | class TestMultiMode(unittest.TestCase): |
| 1838 | |
| 1839 | def test_basics(self): |
| 1840 | multimode = statistics.multimode |
| 1841 | self.assertEqual(multimode('aabbbbbbbbcc'), ['b']) |
| 1842 | self.assertEqual(multimode('aabbbbccddddeeffffgg'), ['b', 'd', 'f']) |
| 1843 | self.assertEqual(multimode(''), []) |
| 1844 | |
Nick Coghlan | bfd68bf | 2014-02-08 19:44:16 +1000 | [diff] [blame] | 1845 | |
Raymond Hettinger | 47d9987 | 2019-02-21 15:06:29 -0800 | [diff] [blame] | 1846 | class TestFMean(unittest.TestCase): |
| 1847 | |
| 1848 | def test_basics(self): |
| 1849 | fmean = statistics.fmean |
| 1850 | D = Decimal |
| 1851 | F = Fraction |
| 1852 | for data, expected_mean, kind in [ |
| 1853 | ([3.5, 4.0, 5.25], 4.25, 'floats'), |
| 1854 | ([D('3.5'), D('4.0'), D('5.25')], 4.25, 'decimals'), |
| 1855 | ([F(7, 2), F(4, 1), F(21, 4)], 4.25, 'fractions'), |
| 1856 | ([True, False, True, True, False], 0.60, 'booleans'), |
| 1857 | ([3.5, 4, F(21, 4)], 4.25, 'mixed types'), |
| 1858 | ((3.5, 4.0, 5.25), 4.25, 'tuple'), |
| 1859 | (iter([3.5, 4.0, 5.25]), 4.25, 'iterator'), |
| 1860 | ]: |
| 1861 | actual_mean = fmean(data) |
| 1862 | self.assertIs(type(actual_mean), float, kind) |
| 1863 | self.assertEqual(actual_mean, expected_mean, kind) |
| 1864 | |
| 1865 | def test_error_cases(self): |
| 1866 | fmean = statistics.fmean |
| 1867 | StatisticsError = statistics.StatisticsError |
| 1868 | with self.assertRaises(StatisticsError): |
| 1869 | fmean([]) # empty input |
| 1870 | with self.assertRaises(StatisticsError): |
| 1871 | fmean(iter([])) # empty iterator |
| 1872 | with self.assertRaises(TypeError): |
| 1873 | fmean(None) # non-iterable input |
| 1874 | with self.assertRaises(TypeError): |
| 1875 | fmean([10, None, 20]) # non-numeric input |
| 1876 | with self.assertRaises(TypeError): |
| 1877 | fmean() # missing data argument |
| 1878 | with self.assertRaises(TypeError): |
| 1879 | fmean([10, 20, 60], 70) # too many arguments |
| 1880 | |
| 1881 | def test_special_values(self): |
| 1882 | # Rules for special values are inherited from math.fsum() |
| 1883 | fmean = statistics.fmean |
| 1884 | NaN = float('Nan') |
| 1885 | Inf = float('Inf') |
| 1886 | self.assertTrue(math.isnan(fmean([10, NaN])), 'nan') |
| 1887 | self.assertTrue(math.isnan(fmean([NaN, Inf])), 'nan and infinity') |
| 1888 | self.assertTrue(math.isinf(fmean([10, Inf])), 'infinity') |
| 1889 | with self.assertRaises(ValueError): |
| 1890 | fmean([Inf, -Inf]) |
Nick Coghlan | bfd68bf | 2014-02-08 19:44:16 +1000 | [diff] [blame] | 1891 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 1892 | |
| 1893 | # === Tests for variances and standard deviations === |
| 1894 | |
| 1895 | class VarianceStdevMixin(UnivariateCommonMixin): |
| 1896 | # Mixin class holding common tests for variance and std dev. |
| 1897 | |
| 1898 | # Subclasses should inherit from this before NumericTestClass, in order |
| 1899 | # to see the rel attribute below. See testShiftData for an explanation. |
| 1900 | |
| 1901 | rel = 1e-12 |
| 1902 | |
| 1903 | def test_single_value(self): |
| 1904 | # Deviation of a single value is zero. |
| 1905 | for x in (11, 19.8, 4.6e14, Fraction(21, 34), Decimal('8.392')): |
| 1906 | self.assertEqual(self.func([x]), 0) |
| 1907 | |
| 1908 | def test_repeated_single_value(self): |
| 1909 | # The deviation of a single repeated value is zero. |
| 1910 | for x in (7.2, 49, 8.1e15, Fraction(3, 7), Decimal('62.4802')): |
| 1911 | for count in (2, 3, 5, 15): |
| 1912 | data = [x]*count |
| 1913 | self.assertEqual(self.func(data), 0) |
| 1914 | |
| 1915 | def test_domain_error_regression(self): |
| 1916 | # Regression test for a domain error exception. |
| 1917 | # (Thanks to Geremy Condra.) |
| 1918 | data = [0.123456789012345]*10000 |
| 1919 | # All the items are identical, so variance should be exactly zero. |
| 1920 | # We allow some small round-off error, but not much. |
| 1921 | result = self.func(data) |
| 1922 | self.assertApproxEqual(result, 0.0, tol=5e-17) |
| 1923 | self.assertGreaterEqual(result, 0) # A negative result must fail. |
| 1924 | |
| 1925 | def test_shift_data(self): |
| 1926 | # Test that shifting the data by a constant amount does not affect |
| 1927 | # the variance or stdev. Or at least not much. |
| 1928 | |
| 1929 | # Due to rounding, this test should be considered an ideal. We allow |
| 1930 | # some tolerance away from "no change at all" by setting tol and/or rel |
| 1931 | # attributes. Subclasses may set tighter or looser error tolerances. |
| 1932 | raw = [1.03, 1.27, 1.94, 2.04, 2.58, 3.14, 4.75, 4.98, 5.42, 6.78] |
| 1933 | expected = self.func(raw) |
| 1934 | # Don't set shift too high, the bigger it is, the more rounding error. |
| 1935 | shift = 1e5 |
| 1936 | data = [x + shift for x in raw] |
| 1937 | self.assertApproxEqual(self.func(data), expected) |
| 1938 | |
| 1939 | def test_shift_data_exact(self): |
| 1940 | # Like test_shift_data, but result is always exact. |
| 1941 | raw = [1, 3, 3, 4, 5, 7, 9, 10, 11, 16] |
| 1942 | assert all(x==int(x) for x in raw) |
| 1943 | expected = self.func(raw) |
| 1944 | shift = 10**9 |
| 1945 | data = [x + shift for x in raw] |
| 1946 | self.assertEqual(self.func(data), expected) |
| 1947 | |
| 1948 | def test_iter_list_same(self): |
| 1949 | # Test that iter data and list data give the same result. |
| 1950 | |
| 1951 | # This is an explicit test that iterators and lists are treated the |
| 1952 | # same; justification for this test over and above the similar test |
| 1953 | # in UnivariateCommonMixin is that an earlier design had variance and |
| 1954 | # friends swap between one- and two-pass algorithms, which would |
| 1955 | # sometimes give different results. |
| 1956 | data = [random.uniform(-3, 8) for _ in range(1000)] |
| 1957 | expected = self.func(data) |
| 1958 | self.assertEqual(self.func(iter(data)), expected) |
| 1959 | |
| 1960 | |
| 1961 | class TestPVariance(VarianceStdevMixin, NumericTestCase, UnivariateTypeMixin): |
| 1962 | # Tests for population variance. |
| 1963 | def setUp(self): |
| 1964 | self.func = statistics.pvariance |
| 1965 | |
| 1966 | def test_exact_uniform(self): |
| 1967 | # Test the variance against an exact result for uniform data. |
| 1968 | data = list(range(10000)) |
| 1969 | random.shuffle(data) |
| 1970 | expected = (10000**2 - 1)/12 # Exact value. |
| 1971 | self.assertEqual(self.func(data), expected) |
| 1972 | |
| 1973 | def test_ints(self): |
| 1974 | # Test population variance with int data. |
| 1975 | data = [4, 7, 13, 16] |
| 1976 | exact = 22.5 |
| 1977 | self.assertEqual(self.func(data), exact) |
| 1978 | |
| 1979 | def test_fractions(self): |
| 1980 | # Test population variance with Fraction data. |
| 1981 | F = Fraction |
| 1982 | data = [F(1, 4), F(1, 4), F(3, 4), F(7, 4)] |
| 1983 | exact = F(3, 8) |
| 1984 | result = self.func(data) |
| 1985 | self.assertEqual(result, exact) |
| 1986 | self.assertIsInstance(result, Fraction) |
| 1987 | |
| 1988 | def test_decimals(self): |
| 1989 | # Test population variance with Decimal data. |
| 1990 | D = Decimal |
| 1991 | data = [D("12.1"), D("12.2"), D("12.5"), D("12.9")] |
| 1992 | exact = D('0.096875') |
| 1993 | result = self.func(data) |
| 1994 | self.assertEqual(result, exact) |
| 1995 | self.assertIsInstance(result, Decimal) |
| 1996 | |
| 1997 | |
| 1998 | class TestVariance(VarianceStdevMixin, NumericTestCase, UnivariateTypeMixin): |
| 1999 | # Tests for sample variance. |
| 2000 | def setUp(self): |
| 2001 | self.func = statistics.variance |
| 2002 | |
| 2003 | def test_single_value(self): |
| 2004 | # Override method from VarianceStdevMixin. |
| 2005 | for x in (35, 24.7, 8.2e15, Fraction(19, 30), Decimal('4.2084')): |
| 2006 | self.assertRaises(statistics.StatisticsError, self.func, [x]) |
| 2007 | |
| 2008 | def test_ints(self): |
| 2009 | # Test sample variance with int data. |
| 2010 | data = [4, 7, 13, 16] |
| 2011 | exact = 30 |
| 2012 | self.assertEqual(self.func(data), exact) |
| 2013 | |
| 2014 | def test_fractions(self): |
| 2015 | # Test sample variance with Fraction data. |
| 2016 | F = Fraction |
| 2017 | data = [F(1, 4), F(1, 4), F(3, 4), F(7, 4)] |
| 2018 | exact = F(1, 2) |
| 2019 | result = self.func(data) |
| 2020 | self.assertEqual(result, exact) |
| 2021 | self.assertIsInstance(result, Fraction) |
| 2022 | |
| 2023 | def test_decimals(self): |
| 2024 | # Test sample variance with Decimal data. |
| 2025 | D = Decimal |
| 2026 | data = [D(2), D(2), D(7), D(9)] |
| 2027 | exact = 4*D('9.5')/D(3) |
| 2028 | result = self.func(data) |
| 2029 | self.assertEqual(result, exact) |
| 2030 | self.assertIsInstance(result, Decimal) |
| 2031 | |
| 2032 | |
| 2033 | class TestPStdev(VarianceStdevMixin, NumericTestCase): |
| 2034 | # Tests for population standard deviation. |
| 2035 | def setUp(self): |
| 2036 | self.func = statistics.pstdev |
| 2037 | |
| 2038 | def test_compare_to_variance(self): |
| 2039 | # Test that stdev is, in fact, the square root of variance. |
| 2040 | data = [random.uniform(-17, 24) for _ in range(1000)] |
| 2041 | expected = math.sqrt(statistics.pvariance(data)) |
| 2042 | self.assertEqual(self.func(data), expected) |
| 2043 | |
| 2044 | |
| 2045 | class TestStdev(VarianceStdevMixin, NumericTestCase): |
| 2046 | # Tests for sample standard deviation. |
| 2047 | def setUp(self): |
| 2048 | self.func = statistics.stdev |
| 2049 | |
| 2050 | def test_single_value(self): |
| 2051 | # Override method from VarianceStdevMixin. |
| 2052 | for x in (81, 203.74, 3.9e14, Fraction(5, 21), Decimal('35.719')): |
| 2053 | self.assertRaises(statistics.StatisticsError, self.func, [x]) |
| 2054 | |
| 2055 | def test_compare_to_variance(self): |
| 2056 | # Test that stdev is, in fact, the square root of variance. |
| 2057 | data = [random.uniform(-2, 9) for _ in range(1000)] |
| 2058 | expected = math.sqrt(statistics.variance(data)) |
| 2059 | self.assertEqual(self.func(data), expected) |
| 2060 | |
Raymond Hettinger | 9013ccf | 2019-04-23 00:06:35 -0700 | [diff] [blame] | 2061 | |
Raymond Hettinger | 6463ba3 | 2019-04-07 09:20:03 -0700 | [diff] [blame] | 2062 | class TestGeometricMean(unittest.TestCase): |
| 2063 | |
| 2064 | def test_basics(self): |
| 2065 | geometric_mean = statistics.geometric_mean |
| 2066 | self.assertAlmostEqual(geometric_mean([54, 24, 36]), 36.0) |
| 2067 | self.assertAlmostEqual(geometric_mean([4.0, 9.0]), 6.0) |
| 2068 | self.assertAlmostEqual(geometric_mean([17.625]), 17.625) |
| 2069 | |
| 2070 | random.seed(86753095551212) |
| 2071 | for rng in [ |
| 2072 | range(1, 100), |
| 2073 | range(1, 1_000), |
| 2074 | range(1, 10_000), |
| 2075 | range(500, 10_000, 3), |
| 2076 | range(10_000, 500, -3), |
| 2077 | [12, 17, 13, 5, 120, 7], |
| 2078 | [random.expovariate(50.0) for i in range(1_000)], |
| 2079 | [random.lognormvariate(20.0, 3.0) for i in range(2_000)], |
| 2080 | [random.triangular(2000, 3000, 2200) for i in range(3_000)], |
| 2081 | ]: |
| 2082 | gm_decimal = math.prod(map(Decimal, rng)) ** (Decimal(1) / len(rng)) |
| 2083 | gm_float = geometric_mean(rng) |
| 2084 | self.assertTrue(math.isclose(gm_float, float(gm_decimal))) |
| 2085 | |
| 2086 | def test_various_input_types(self): |
| 2087 | geometric_mean = statistics.geometric_mean |
| 2088 | D = Decimal |
| 2089 | F = Fraction |
| 2090 | # https://www.wolframalpha.com/input/?i=geometric+mean+3.5,+4.0,+5.25 |
| 2091 | expected_mean = 4.18886 |
| 2092 | for data, kind in [ |
| 2093 | ([3.5, 4.0, 5.25], 'floats'), |
| 2094 | ([D('3.5'), D('4.0'), D('5.25')], 'decimals'), |
| 2095 | ([F(7, 2), F(4, 1), F(21, 4)], 'fractions'), |
| 2096 | ([3.5, 4, F(21, 4)], 'mixed types'), |
| 2097 | ((3.5, 4.0, 5.25), 'tuple'), |
| 2098 | (iter([3.5, 4.0, 5.25]), 'iterator'), |
| 2099 | ]: |
| 2100 | actual_mean = geometric_mean(data) |
| 2101 | self.assertIs(type(actual_mean), float, kind) |
| 2102 | self.assertAlmostEqual(actual_mean, expected_mean, places=5) |
| 2103 | |
| 2104 | def test_big_and_small(self): |
| 2105 | geometric_mean = statistics.geometric_mean |
| 2106 | |
| 2107 | # Avoid overflow to infinity |
| 2108 | large = 2.0 ** 1000 |
| 2109 | big_gm = geometric_mean([54.0 * large, 24.0 * large, 36.0 * large]) |
| 2110 | self.assertTrue(math.isclose(big_gm, 36.0 * large)) |
| 2111 | self.assertFalse(math.isinf(big_gm)) |
| 2112 | |
| 2113 | # Avoid underflow to zero |
| 2114 | small = 2.0 ** -1000 |
| 2115 | small_gm = geometric_mean([54.0 * small, 24.0 * small, 36.0 * small]) |
| 2116 | self.assertTrue(math.isclose(small_gm, 36.0 * small)) |
| 2117 | self.assertNotEqual(small_gm, 0.0) |
| 2118 | |
| 2119 | def test_error_cases(self): |
| 2120 | geometric_mean = statistics.geometric_mean |
| 2121 | StatisticsError = statistics.StatisticsError |
| 2122 | with self.assertRaises(StatisticsError): |
| 2123 | geometric_mean([]) # empty input |
| 2124 | with self.assertRaises(StatisticsError): |
| 2125 | geometric_mean([3.5, 0.0, 5.25]) # zero input |
| 2126 | with self.assertRaises(StatisticsError): |
| 2127 | geometric_mean([3.5, -4.0, 5.25]) # negative input |
| 2128 | with self.assertRaises(StatisticsError): |
| 2129 | geometric_mean(iter([])) # empty iterator |
| 2130 | with self.assertRaises(TypeError): |
| 2131 | geometric_mean(None) # non-iterable input |
| 2132 | with self.assertRaises(TypeError): |
| 2133 | geometric_mean([10, None, 20]) # non-numeric input |
| 2134 | with self.assertRaises(TypeError): |
| 2135 | geometric_mean() # missing data argument |
| 2136 | with self.assertRaises(TypeError): |
| 2137 | geometric_mean([10, 20, 60], 70) # too many arguments |
| 2138 | |
| 2139 | def test_special_values(self): |
| 2140 | # Rules for special values are inherited from math.fsum() |
| 2141 | geometric_mean = statistics.geometric_mean |
| 2142 | NaN = float('Nan') |
| 2143 | Inf = float('Inf') |
| 2144 | self.assertTrue(math.isnan(geometric_mean([10, NaN])), 'nan') |
| 2145 | self.assertTrue(math.isnan(geometric_mean([NaN, Inf])), 'nan and infinity') |
| 2146 | self.assertTrue(math.isinf(geometric_mean([10, Inf])), 'infinity') |
| 2147 | with self.assertRaises(ValueError): |
| 2148 | geometric_mean([Inf, -Inf]) |
| 2149 | |
Raymond Hettinger | 9013ccf | 2019-04-23 00:06:35 -0700 | [diff] [blame] | 2150 | |
| 2151 | class TestQuantiles(unittest.TestCase): |
| 2152 | |
| 2153 | def test_specific_cases(self): |
| 2154 | # Match results computed by hand and cross-checked |
| 2155 | # against the PERCENTILE.EXC function in MS Excel. |
| 2156 | quantiles = statistics.quantiles |
| 2157 | data = [120, 200, 250, 320, 350] |
| 2158 | random.shuffle(data) |
| 2159 | for n, expected in [ |
| 2160 | (1, []), |
| 2161 | (2, [250.0]), |
| 2162 | (3, [200.0, 320.0]), |
| 2163 | (4, [160.0, 250.0, 335.0]), |
| 2164 | (5, [136.0, 220.0, 292.0, 344.0]), |
| 2165 | (6, [120.0, 200.0, 250.0, 320.0, 350.0]), |
| 2166 | (8, [100.0, 160.0, 212.5, 250.0, 302.5, 335.0, 357.5]), |
| 2167 | (10, [88.0, 136.0, 184.0, 220.0, 250.0, 292.0, 326.0, 344.0, 362.0]), |
| 2168 | (12, [80.0, 120.0, 160.0, 200.0, 225.0, 250.0, 285.0, 320.0, 335.0, |
| 2169 | 350.0, 365.0]), |
| 2170 | (15, [72.0, 104.0, 136.0, 168.0, 200.0, 220.0, 240.0, 264.0, 292.0, |
| 2171 | 320.0, 332.0, 344.0, 356.0, 368.0]), |
| 2172 | ]: |
| 2173 | self.assertEqual(expected, quantiles(data, n=n)) |
| 2174 | self.assertEqual(len(quantiles(data, n=n)), n - 1) |
Raymond Hettinger | db81ba1 | 2019-04-28 21:31:55 -0700 | [diff] [blame] | 2175 | # Preserve datatype when possible |
| 2176 | for datatype in (float, Decimal, Fraction): |
| 2177 | result = quantiles(map(datatype, data), n=n) |
| 2178 | self.assertTrue(all(type(x) == datatype) for x in result) |
| 2179 | self.assertEqual(result, list(map(datatype, expected))) |
Raymond Hettinger | b0a2c0f | 2019-04-29 23:47:33 -0700 | [diff] [blame] | 2180 | # Quantiles should be idempotent |
| 2181 | if len(expected) >= 2: |
| 2182 | self.assertEqual(quantiles(expected, n=n), expected) |
Raymond Hettinger | e917f2e | 2019-05-18 10:18:29 -0700 | [diff] [blame] | 2183 | # Cross-check against method='inclusive' which should give |
| 2184 | # the same result after adding in minimum and maximum values |
| 2185 | # extrapolated from the two lowest and two highest points. |
| 2186 | sdata = sorted(data) |
| 2187 | lo = 2 * sdata[0] - sdata[1] |
| 2188 | hi = 2 * sdata[-1] - sdata[-2] |
| 2189 | padded_data = data + [lo, hi] |
| 2190 | self.assertEqual( |
| 2191 | quantiles(data, n=n), |
| 2192 | quantiles(padded_data, n=n, method='inclusive'), |
| 2193 | (n, data), |
| 2194 | ) |
Raymond Hettinger | 9013ccf | 2019-04-23 00:06:35 -0700 | [diff] [blame] | 2195 | # Invariant under tranlation and scaling |
| 2196 | def f(x): |
| 2197 | return 3.5 * x - 1234.675 |
| 2198 | exp = list(map(f, expected)) |
| 2199 | act = quantiles(map(f, data), n=n) |
| 2200 | self.assertTrue(all(math.isclose(e, a) for e, a in zip(exp, act))) |
Raymond Hettinger | e917f2e | 2019-05-18 10:18:29 -0700 | [diff] [blame] | 2201 | # Q2 agrees with median() |
| 2202 | for k in range(2, 60): |
| 2203 | data = random.choices(range(100), k=k) |
| 2204 | q1, q2, q3 = quantiles(data) |
| 2205 | self.assertEqual(q2, statistics.median(data)) |
Raymond Hettinger | 9013ccf | 2019-04-23 00:06:35 -0700 | [diff] [blame] | 2206 | |
| 2207 | def test_specific_cases_inclusive(self): |
| 2208 | # Match results computed by hand and cross-checked |
| 2209 | # against the PERCENTILE.INC function in MS Excel |
Xtreak | 874ad1b | 2019-05-02 23:50:59 +0530 | [diff] [blame] | 2210 | # and against the quantile() function in SciPy. |
Raymond Hettinger | 9013ccf | 2019-04-23 00:06:35 -0700 | [diff] [blame] | 2211 | quantiles = statistics.quantiles |
| 2212 | data = [100, 200, 400, 800] |
| 2213 | random.shuffle(data) |
| 2214 | for n, expected in [ |
| 2215 | (1, []), |
| 2216 | (2, [300.0]), |
| 2217 | (3, [200.0, 400.0]), |
| 2218 | (4, [175.0, 300.0, 500.0]), |
| 2219 | (5, [160.0, 240.0, 360.0, 560.0]), |
| 2220 | (6, [150.0, 200.0, 300.0, 400.0, 600.0]), |
| 2221 | (8, [137.5, 175, 225.0, 300.0, 375.0, 500.0,650.0]), |
| 2222 | (10, [130.0, 160.0, 190.0, 240.0, 300.0, 360.0, 440.0, 560.0, 680.0]), |
| 2223 | (12, [125.0, 150.0, 175.0, 200.0, 250.0, 300.0, 350.0, 400.0, |
| 2224 | 500.0, 600.0, 700.0]), |
| 2225 | (15, [120.0, 140.0, 160.0, 180.0, 200.0, 240.0, 280.0, 320.0, 360.0, |
| 2226 | 400.0, 480.0, 560.0, 640.0, 720.0]), |
| 2227 | ]: |
| 2228 | self.assertEqual(expected, quantiles(data, n=n, method="inclusive")) |
| 2229 | self.assertEqual(len(quantiles(data, n=n, method="inclusive")), n - 1) |
Raymond Hettinger | db81ba1 | 2019-04-28 21:31:55 -0700 | [diff] [blame] | 2230 | # Preserve datatype when possible |
| 2231 | for datatype in (float, Decimal, Fraction): |
| 2232 | result = quantiles(map(datatype, data), n=n, method="inclusive") |
| 2233 | self.assertTrue(all(type(x) == datatype) for x in result) |
| 2234 | self.assertEqual(result, list(map(datatype, expected))) |
Raymond Hettinger | 9013ccf | 2019-04-23 00:06:35 -0700 | [diff] [blame] | 2235 | # Invariant under tranlation and scaling |
| 2236 | def f(x): |
| 2237 | return 3.5 * x - 1234.675 |
| 2238 | exp = list(map(f, expected)) |
| 2239 | act = quantiles(map(f, data), n=n, method="inclusive") |
| 2240 | self.assertTrue(all(math.isclose(e, a) for e, a in zip(exp, act))) |
Raymond Hettinger | e917f2e | 2019-05-18 10:18:29 -0700 | [diff] [blame] | 2241 | # Natural deciles |
| 2242 | self.assertEqual(quantiles([0, 100], n=10, method='inclusive'), |
| 2243 | [10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 90.0]) |
| 2244 | self.assertEqual(quantiles(range(0, 101), n=10, method='inclusive'), |
| 2245 | [10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 90.0]) |
Raymond Hettinger | b0a2c0f | 2019-04-29 23:47:33 -0700 | [diff] [blame] | 2246 | # Whenever n is smaller than the number of data points, running |
| 2247 | # method='inclusive' should give the same result as method='exclusive' |
| 2248 | # after the two included extreme points are removed. |
| 2249 | data = [random.randrange(10_000) for i in range(501)] |
| 2250 | actual = quantiles(data, n=32, method='inclusive') |
| 2251 | data.remove(min(data)) |
| 2252 | data.remove(max(data)) |
| 2253 | expected = quantiles(data, n=32) |
| 2254 | self.assertEqual(expected, actual) |
Raymond Hettinger | e917f2e | 2019-05-18 10:18:29 -0700 | [diff] [blame] | 2255 | # Q2 agrees with median() |
| 2256 | for k in range(2, 60): |
| 2257 | data = random.choices(range(100), k=k) |
| 2258 | q1, q2, q3 = quantiles(data, method='inclusive') |
| 2259 | self.assertEqual(q2, statistics.median(data)) |
Raymond Hettinger | 9013ccf | 2019-04-23 00:06:35 -0700 | [diff] [blame] | 2260 | |
Raymond Hettinger | db81ba1 | 2019-04-28 21:31:55 -0700 | [diff] [blame] | 2261 | def test_equal_inputs(self): |
| 2262 | quantiles = statistics.quantiles |
| 2263 | for n in range(2, 10): |
| 2264 | data = [10.0] * n |
| 2265 | self.assertEqual(quantiles(data), [10.0, 10.0, 10.0]) |
| 2266 | self.assertEqual(quantiles(data, method='inclusive'), |
| 2267 | [10.0, 10.0, 10.0]) |
| 2268 | |
Raymond Hettinger | 9013ccf | 2019-04-23 00:06:35 -0700 | [diff] [blame] | 2269 | def test_equal_sized_groups(self): |
| 2270 | quantiles = statistics.quantiles |
| 2271 | total = 10_000 |
| 2272 | data = [random.expovariate(0.2) for i in range(total)] |
| 2273 | while len(set(data)) != total: |
| 2274 | data.append(random.expovariate(0.2)) |
| 2275 | data.sort() |
| 2276 | |
| 2277 | # Cases where the group size exactly divides the total |
| 2278 | for n in (1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000): |
| 2279 | group_size = total // n |
| 2280 | self.assertEqual( |
| 2281 | [bisect.bisect(data, q) for q in quantiles(data, n=n)], |
| 2282 | list(range(group_size, total, group_size))) |
| 2283 | |
| 2284 | # When the group sizes can't be exactly equal, they should |
| 2285 | # differ by no more than one |
| 2286 | for n in (13, 19, 59, 109, 211, 571, 1019, 1907, 5261, 9769): |
| 2287 | group_sizes = {total // n, total // n + 1} |
| 2288 | pos = [bisect.bisect(data, q) for q in quantiles(data, n=n)] |
| 2289 | sizes = {q - p for p, q in zip(pos, pos[1:])} |
| 2290 | self.assertTrue(sizes <= group_sizes) |
| 2291 | |
| 2292 | def test_error_cases(self): |
| 2293 | quantiles = statistics.quantiles |
| 2294 | StatisticsError = statistics.StatisticsError |
| 2295 | with self.assertRaises(TypeError): |
| 2296 | quantiles() # Missing arguments |
| 2297 | with self.assertRaises(TypeError): |
| 2298 | quantiles([10, 20, 30], 13, n=4) # Too many arguments |
| 2299 | with self.assertRaises(TypeError): |
| 2300 | quantiles([10, 20, 30], 4) # n is a positional argument |
| 2301 | with self.assertRaises(StatisticsError): |
| 2302 | quantiles([10, 20, 30], n=0) # n is zero |
| 2303 | with self.assertRaises(StatisticsError): |
| 2304 | quantiles([10, 20, 30], n=-1) # n is negative |
| 2305 | with self.assertRaises(TypeError): |
| 2306 | quantiles([10, 20, 30], n=1.5) # n is not an integer |
| 2307 | with self.assertRaises(ValueError): |
| 2308 | quantiles([10, 20, 30], method='X') # method is unknown |
| 2309 | with self.assertRaises(StatisticsError): |
| 2310 | quantiles([10], n=4) # not enough data points |
| 2311 | with self.assertRaises(TypeError): |
| 2312 | quantiles([10, None, 30], n=4) # data is non-numeric |
| 2313 | |
| 2314 | |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2315 | class TestNormalDist: |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2316 | |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2317 | # General note on precision: The pdf(), cdf(), and overlap() methods |
| 2318 | # depend on functions in the math libraries that do not make |
| 2319 | # explicit accuracy guarantees. Accordingly, some of the accuracy |
| 2320 | # tests below may fail if the underlying math functions are |
| 2321 | # inaccurate. There isn't much we can do about this short of |
| 2322 | # implementing our own implementations from scratch. |
| 2323 | |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2324 | def test_slots(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2325 | nd = self.module.NormalDist(300, 23) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2326 | with self.assertRaises(TypeError): |
| 2327 | vars(nd) |
Miss Islington (bot) | c613c33 | 2019-07-21 00:55:13 -0700 | [diff] [blame] | 2328 | self.assertEqual(tuple(nd.__slots__), ('_mu', '_sigma')) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2329 | |
| 2330 | def test_instantiation_and_attributes(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2331 | nd = self.module.NormalDist(500, 17) |
Miss Islington (bot) | c613c33 | 2019-07-21 00:55:13 -0700 | [diff] [blame] | 2332 | self.assertEqual(nd.mean, 500) |
| 2333 | self.assertEqual(nd.stdev, 17) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2334 | self.assertEqual(nd.variance, 17**2) |
| 2335 | |
| 2336 | # default arguments |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2337 | nd = self.module.NormalDist() |
Miss Islington (bot) | c613c33 | 2019-07-21 00:55:13 -0700 | [diff] [blame] | 2338 | self.assertEqual(nd.mean, 0) |
| 2339 | self.assertEqual(nd.stdev, 1) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2340 | self.assertEqual(nd.variance, 1**2) |
| 2341 | |
| 2342 | # error case: negative sigma |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2343 | with self.assertRaises(self.module.StatisticsError): |
| 2344 | self.module.NormalDist(500, -10) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2345 | |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2346 | # verify that subclass type is honored |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2347 | class NewNormalDist(self.module.NormalDist): |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2348 | pass |
| 2349 | nnd = NewNormalDist(200, 5) |
| 2350 | self.assertEqual(type(nnd), NewNormalDist) |
| 2351 | |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2352 | def test_alternative_constructor(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2353 | NormalDist = self.module.NormalDist |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2354 | data = [96, 107, 90, 92, 110] |
| 2355 | # list input |
| 2356 | self.assertEqual(NormalDist.from_samples(data), NormalDist(99, 9)) |
| 2357 | # tuple input |
| 2358 | self.assertEqual(NormalDist.from_samples(tuple(data)), NormalDist(99, 9)) |
| 2359 | # iterator input |
| 2360 | self.assertEqual(NormalDist.from_samples(iter(data)), NormalDist(99, 9)) |
| 2361 | # error cases |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2362 | with self.assertRaises(self.module.StatisticsError): |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2363 | NormalDist.from_samples([]) # empty input |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2364 | with self.assertRaises(self.module.StatisticsError): |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2365 | NormalDist.from_samples([10]) # only one input |
| 2366 | |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2367 | # verify that subclass type is honored |
| 2368 | class NewNormalDist(NormalDist): |
| 2369 | pass |
| 2370 | nnd = NewNormalDist.from_samples(data) |
| 2371 | self.assertEqual(type(nnd), NewNormalDist) |
| 2372 | |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2373 | def test_sample_generation(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2374 | NormalDist = self.module.NormalDist |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2375 | mu, sigma = 10_000, 3.0 |
| 2376 | X = NormalDist(mu, sigma) |
| 2377 | n = 1_000 |
| 2378 | data = X.samples(n) |
| 2379 | self.assertEqual(len(data), n) |
| 2380 | self.assertEqual(set(map(type, data)), {float}) |
| 2381 | # mean(data) expected to fall within 8 standard deviations |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2382 | xbar = self.module.mean(data) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2383 | self.assertTrue(mu - sigma*8 <= xbar <= mu + sigma*8) |
| 2384 | |
| 2385 | # verify that seeding makes reproducible sequences |
| 2386 | n = 100 |
| 2387 | data1 = X.samples(n, seed='happiness and joy') |
| 2388 | data2 = X.samples(n, seed='trouble and despair') |
| 2389 | data3 = X.samples(n, seed='happiness and joy') |
| 2390 | data4 = X.samples(n, seed='trouble and despair') |
| 2391 | self.assertEqual(data1, data3) |
| 2392 | self.assertEqual(data2, data4) |
| 2393 | self.assertNotEqual(data1, data2) |
| 2394 | |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2395 | def test_pdf(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2396 | NormalDist = self.module.NormalDist |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2397 | X = NormalDist(100, 15) |
| 2398 | # Verify peak around center |
| 2399 | self.assertLess(X.pdf(99), X.pdf(100)) |
| 2400 | self.assertLess(X.pdf(101), X.pdf(100)) |
| 2401 | # Test symmetry |
Raymond Hettinger | 18ee50d | 2019-03-06 02:31:14 -0800 | [diff] [blame] | 2402 | for i in range(50): |
| 2403 | self.assertAlmostEqual(X.pdf(100 - i), X.pdf(100 + i)) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2404 | # Test vs CDF |
| 2405 | dx = 2.0 ** -10 |
| 2406 | for x in range(90, 111): |
| 2407 | est_pdf = (X.cdf(x + dx) - X.cdf(x)) / dx |
| 2408 | self.assertAlmostEqual(X.pdf(x), est_pdf, places=4) |
Raymond Hettinger | 18ee50d | 2019-03-06 02:31:14 -0800 | [diff] [blame] | 2409 | # Test vs table of known values -- CRC 26th Edition |
| 2410 | Z = NormalDist() |
| 2411 | for x, px in enumerate([ |
| 2412 | 0.3989, 0.3989, 0.3989, 0.3988, 0.3986, |
| 2413 | 0.3984, 0.3982, 0.3980, 0.3977, 0.3973, |
| 2414 | 0.3970, 0.3965, 0.3961, 0.3956, 0.3951, |
| 2415 | 0.3945, 0.3939, 0.3932, 0.3925, 0.3918, |
| 2416 | 0.3910, 0.3902, 0.3894, 0.3885, 0.3876, |
| 2417 | 0.3867, 0.3857, 0.3847, 0.3836, 0.3825, |
| 2418 | 0.3814, 0.3802, 0.3790, 0.3778, 0.3765, |
| 2419 | 0.3752, 0.3739, 0.3725, 0.3712, 0.3697, |
| 2420 | 0.3683, 0.3668, 0.3653, 0.3637, 0.3621, |
| 2421 | 0.3605, 0.3589, 0.3572, 0.3555, 0.3538, |
| 2422 | ]): |
| 2423 | self.assertAlmostEqual(Z.pdf(x / 100.0), px, places=4) |
Raymond Hettinger | 1f58f4f | 2019-03-06 23:23:55 -0800 | [diff] [blame] | 2424 | self.assertAlmostEqual(Z.pdf(-x / 100.0), px, places=4) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2425 | # Error case: variance is zero |
| 2426 | Y = NormalDist(100, 0) |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2427 | with self.assertRaises(self.module.StatisticsError): |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2428 | Y.pdf(90) |
Raymond Hettinger | ef17fdb | 2019-02-28 09:16:25 -0800 | [diff] [blame] | 2429 | # Special values |
| 2430 | self.assertEqual(X.pdf(float('-Inf')), 0.0) |
| 2431 | self.assertEqual(X.pdf(float('Inf')), 0.0) |
| 2432 | self.assertTrue(math.isnan(X.pdf(float('NaN')))) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2433 | |
| 2434 | def test_cdf(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2435 | NormalDist = self.module.NormalDist |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2436 | X = NormalDist(100, 15) |
| 2437 | cdfs = [X.cdf(x) for x in range(1, 200)] |
| 2438 | self.assertEqual(set(map(type, cdfs)), {float}) |
| 2439 | # Verify montonic |
| 2440 | self.assertEqual(cdfs, sorted(cdfs)) |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2441 | # Verify center (should be exact) |
| 2442 | self.assertEqual(X.cdf(100), 0.50) |
Raymond Hettinger | 18ee50d | 2019-03-06 02:31:14 -0800 | [diff] [blame] | 2443 | # Check against a table of known values |
| 2444 | # https://en.wikipedia.org/wiki/Standard_normal_table#Cumulative |
| 2445 | Z = NormalDist() |
| 2446 | for z, cum_prob in [ |
| 2447 | (0.00, 0.50000), (0.01, 0.50399), (0.02, 0.50798), |
| 2448 | (0.14, 0.55567), (0.29, 0.61409), (0.33, 0.62930), |
| 2449 | (0.54, 0.70540), (0.60, 0.72575), (1.17, 0.87900), |
| 2450 | (1.60, 0.94520), (2.05, 0.97982), (2.89, 0.99807), |
| 2451 | (3.52, 0.99978), (3.98, 0.99997), (4.07, 0.99998), |
| 2452 | ]: |
| 2453 | self.assertAlmostEqual(Z.cdf(z), cum_prob, places=5) |
| 2454 | self.assertAlmostEqual(Z.cdf(-z), 1.0 - cum_prob, places=5) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2455 | # Error case: variance is zero |
| 2456 | Y = NormalDist(100, 0) |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2457 | with self.assertRaises(self.module.StatisticsError): |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2458 | Y.cdf(90) |
Raymond Hettinger | ef17fdb | 2019-02-28 09:16:25 -0800 | [diff] [blame] | 2459 | # Special values |
| 2460 | self.assertEqual(X.cdf(float('-Inf')), 0.0) |
| 2461 | self.assertEqual(X.cdf(float('Inf')), 1.0) |
| 2462 | self.assertTrue(math.isnan(X.cdf(float('NaN')))) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2463 | |
Miss Islington (bot) | 382cb85 | 2019-07-30 11:34:33 -0700 | [diff] [blame] | 2464 | @support.skip_if_pgo_task |
Raymond Hettinger | 714c60d | 2019-03-18 20:17:14 -0700 | [diff] [blame] | 2465 | def test_inv_cdf(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2466 | NormalDist = self.module.NormalDist |
Raymond Hettinger | 714c60d | 2019-03-18 20:17:14 -0700 | [diff] [blame] | 2467 | |
| 2468 | # Center case should be exact. |
| 2469 | iq = NormalDist(100, 15) |
| 2470 | self.assertEqual(iq.inv_cdf(0.50), iq.mean) |
| 2471 | |
| 2472 | # Test versus a published table of known percentage points. |
| 2473 | # See the second table at the bottom of the page here: |
| 2474 | # http://people.bath.ac.uk/masss/tables/normaltable.pdf |
| 2475 | Z = NormalDist() |
| 2476 | pp = {5.0: (0.000, 1.645, 2.576, 3.291, 3.891, |
| 2477 | 4.417, 4.892, 5.327, 5.731, 6.109), |
| 2478 | 2.5: (0.674, 1.960, 2.807, 3.481, 4.056, |
| 2479 | 4.565, 5.026, 5.451, 5.847, 6.219), |
| 2480 | 1.0: (1.282, 2.326, 3.090, 3.719, 4.265, |
| 2481 | 4.753, 5.199, 5.612, 5.998, 6.361)} |
| 2482 | for base, row in pp.items(): |
| 2483 | for exp, x in enumerate(row, start=1): |
| 2484 | p = base * 10.0 ** (-exp) |
| 2485 | self.assertAlmostEqual(-Z.inv_cdf(p), x, places=3) |
| 2486 | p = 1.0 - p |
| 2487 | self.assertAlmostEqual(Z.inv_cdf(p), x, places=3) |
| 2488 | |
| 2489 | # Match published example for MS Excel |
| 2490 | # https://support.office.com/en-us/article/norm-inv-function-54b30935-fee7-493c-bedb-2278a9db7e13 |
| 2491 | self.assertAlmostEqual(NormalDist(40, 1.5).inv_cdf(0.908789), 42.000002) |
| 2492 | |
| 2493 | # One million equally spaced probabilities |
| 2494 | n = 2**20 |
| 2495 | for p in range(1, n): |
| 2496 | p /= n |
| 2497 | self.assertAlmostEqual(iq.cdf(iq.inv_cdf(p)), p) |
| 2498 | |
| 2499 | # One hundred ever smaller probabilities to test tails out to |
| 2500 | # extreme probabilities: 1 / 2**50 and (2**50-1) / 2 ** 50 |
| 2501 | for e in range(1, 51): |
| 2502 | p = 2.0 ** (-e) |
| 2503 | self.assertAlmostEqual(iq.cdf(iq.inv_cdf(p)), p) |
| 2504 | p = 1.0 - p |
| 2505 | self.assertAlmostEqual(iq.cdf(iq.inv_cdf(p)), p) |
| 2506 | |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2507 | # Now apply cdf() first. Near the tails, the round-trip loses |
| 2508 | # precision and is ill-conditioned (small changes in the inputs |
| 2509 | # give large changes in the output), so only check to 5 places. |
| 2510 | for x in range(200): |
| 2511 | self.assertAlmostEqual(iq.inv_cdf(iq.cdf(x)), x, places=5) |
Raymond Hettinger | 714c60d | 2019-03-18 20:17:14 -0700 | [diff] [blame] | 2512 | |
| 2513 | # Error cases: |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2514 | with self.assertRaises(self.module.StatisticsError): |
Raymond Hettinger | 714c60d | 2019-03-18 20:17:14 -0700 | [diff] [blame] | 2515 | iq.inv_cdf(0.0) # p is zero |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2516 | with self.assertRaises(self.module.StatisticsError): |
Raymond Hettinger | 714c60d | 2019-03-18 20:17:14 -0700 | [diff] [blame] | 2517 | iq.inv_cdf(-0.1) # p under zero |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2518 | with self.assertRaises(self.module.StatisticsError): |
Raymond Hettinger | 714c60d | 2019-03-18 20:17:14 -0700 | [diff] [blame] | 2519 | iq.inv_cdf(1.0) # p is one |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2520 | with self.assertRaises(self.module.StatisticsError): |
Raymond Hettinger | 714c60d | 2019-03-18 20:17:14 -0700 | [diff] [blame] | 2521 | iq.inv_cdf(1.1) # p over one |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2522 | with self.assertRaises(self.module.StatisticsError): |
Miss Islington (bot) | c613c33 | 2019-07-21 00:55:13 -0700 | [diff] [blame] | 2523 | iq = NormalDist(100, 0) # sigma is zero |
Raymond Hettinger | 714c60d | 2019-03-18 20:17:14 -0700 | [diff] [blame] | 2524 | iq.inv_cdf(0.5) |
| 2525 | |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2526 | # Special values |
| 2527 | self.assertTrue(math.isnan(Z.inv_cdf(float('NaN')))) |
| 2528 | |
Raymond Hettinger | cc1bdf9 | 2019-09-08 18:40:06 -0700 | [diff] [blame] | 2529 | def test_quantiles(self): |
| 2530 | # Quartiles of a standard normal distribution |
| 2531 | Z = self.module.NormalDist() |
| 2532 | for n, expected in [ |
| 2533 | (1, []), |
| 2534 | (2, [0.0]), |
| 2535 | (3, [-0.4307, 0.4307]), |
| 2536 | (4 ,[-0.6745, 0.0, 0.6745]), |
| 2537 | ]: |
| 2538 | actual = Z.quantiles(n=n) |
| 2539 | self.assertTrue(all(math.isclose(e, a, abs_tol=0.0001) |
| 2540 | for e, a in zip(expected, actual))) |
| 2541 | |
Raymond Hettinger | 318d537 | 2019-03-06 22:59:40 -0800 | [diff] [blame] | 2542 | def test_overlap(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2543 | NormalDist = self.module.NormalDist |
Raymond Hettinger | 318d537 | 2019-03-06 22:59:40 -0800 | [diff] [blame] | 2544 | |
| 2545 | # Match examples from Imman and Bradley |
| 2546 | for X1, X2, published_result in [ |
| 2547 | (NormalDist(0.0, 2.0), NormalDist(1.0, 2.0), 0.80258), |
| 2548 | (NormalDist(0.0, 1.0), NormalDist(1.0, 2.0), 0.60993), |
| 2549 | ]: |
| 2550 | self.assertAlmostEqual(X1.overlap(X2), published_result, places=4) |
| 2551 | self.assertAlmostEqual(X2.overlap(X1), published_result, places=4) |
| 2552 | |
| 2553 | # Check against integration of the PDF |
| 2554 | def overlap_numeric(X, Y, *, steps=8_192, z=5): |
| 2555 | 'Numerical integration cross-check for overlap() ' |
| 2556 | fsum = math.fsum |
Miss Islington (bot) | c613c33 | 2019-07-21 00:55:13 -0700 | [diff] [blame] | 2557 | center = (X.mean + Y.mean) / 2.0 |
| 2558 | width = z * max(X.stdev, Y.stdev) |
Raymond Hettinger | 318d537 | 2019-03-06 22:59:40 -0800 | [diff] [blame] | 2559 | start = center - width |
| 2560 | dx = 2.0 * width / steps |
| 2561 | x_arr = [start + i*dx for i in range(steps)] |
| 2562 | xp = list(map(X.pdf, x_arr)) |
| 2563 | yp = list(map(Y.pdf, x_arr)) |
| 2564 | total = max(fsum(xp), fsum(yp)) |
| 2565 | return fsum(map(min, xp, yp)) / total |
| 2566 | |
| 2567 | for X1, X2 in [ |
| 2568 | # Examples from Imman and Bradley |
| 2569 | (NormalDist(0.0, 2.0), NormalDist(1.0, 2.0)), |
| 2570 | (NormalDist(0.0, 1.0), NormalDist(1.0, 2.0)), |
| 2571 | # Example from https://www.rasch.org/rmt/rmt101r.htm |
| 2572 | (NormalDist(0.0, 1.0), NormalDist(1.0, 2.0)), |
| 2573 | # Gender heights from http://www.usablestats.com/lessons/normal |
| 2574 | (NormalDist(70, 4), NormalDist(65, 3.5)), |
| 2575 | # Misc cases with equal standard deviations |
| 2576 | (NormalDist(100, 15), NormalDist(110, 15)), |
| 2577 | (NormalDist(-100, 15), NormalDist(110, 15)), |
| 2578 | (NormalDist(-100, 15), NormalDist(-110, 15)), |
| 2579 | # Misc cases with unequal standard deviations |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2580 | (NormalDist(100, 12), NormalDist(100, 15)), |
Raymond Hettinger | 318d537 | 2019-03-06 22:59:40 -0800 | [diff] [blame] | 2581 | (NormalDist(100, 12), NormalDist(110, 15)), |
| 2582 | (NormalDist(100, 12), NormalDist(150, 15)), |
| 2583 | (NormalDist(100, 12), NormalDist(150, 35)), |
| 2584 | # Misc cases with small values |
| 2585 | (NormalDist(1.000, 0.002), NormalDist(1.001, 0.003)), |
| 2586 | (NormalDist(1.000, 0.002), NormalDist(1.006, 0.0003)), |
| 2587 | (NormalDist(1.000, 0.002), NormalDist(1.001, 0.099)), |
| 2588 | ]: |
| 2589 | self.assertAlmostEqual(X1.overlap(X2), overlap_numeric(X1, X2), places=5) |
| 2590 | self.assertAlmostEqual(X2.overlap(X1), overlap_numeric(X1, X2), places=5) |
| 2591 | |
| 2592 | # Error cases |
| 2593 | X = NormalDist() |
| 2594 | with self.assertRaises(TypeError): |
| 2595 | X.overlap() # too few arguments |
| 2596 | with self.assertRaises(TypeError): |
| 2597 | X.overlap(X, X) # too may arguments |
| 2598 | with self.assertRaises(TypeError): |
| 2599 | X.overlap(None) # right operand not a NormalDist |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2600 | with self.assertRaises(self.module.StatisticsError): |
Raymond Hettinger | 318d537 | 2019-03-06 22:59:40 -0800 | [diff] [blame] | 2601 | X.overlap(NormalDist(1, 0)) # right operand sigma is zero |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2602 | with self.assertRaises(self.module.StatisticsError): |
Raymond Hettinger | 318d537 | 2019-03-06 22:59:40 -0800 | [diff] [blame] | 2603 | NormalDist(1, 0).overlap(X) # left operand sigma is zero |
| 2604 | |
Raymond Hettinger | 9e456bc | 2019-02-24 11:44:55 -0800 | [diff] [blame] | 2605 | def test_properties(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2606 | X = self.module.NormalDist(100, 15) |
Raymond Hettinger | 9e456bc | 2019-02-24 11:44:55 -0800 | [diff] [blame] | 2607 | self.assertEqual(X.mean, 100) |
Raymond Hettinger | cc1bdf9 | 2019-09-08 18:40:06 -0700 | [diff] [blame] | 2608 | self.assertEqual(X.median, 100) |
| 2609 | self.assertEqual(X.mode, 100) |
Raymond Hettinger | 9e456bc | 2019-02-24 11:44:55 -0800 | [diff] [blame] | 2610 | self.assertEqual(X.stdev, 15) |
| 2611 | self.assertEqual(X.variance, 225) |
| 2612 | |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2613 | def test_same_type_addition_and_subtraction(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2614 | NormalDist = self.module.NormalDist |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2615 | X = NormalDist(100, 12) |
| 2616 | Y = NormalDist(40, 5) |
| 2617 | self.assertEqual(X + Y, NormalDist(140, 13)) # __add__ |
| 2618 | self.assertEqual(X - Y, NormalDist(60, 13)) # __sub__ |
| 2619 | |
| 2620 | def test_translation_and_scaling(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2621 | NormalDist = self.module.NormalDist |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2622 | X = NormalDist(100, 15) |
| 2623 | y = 10 |
| 2624 | self.assertEqual(+X, NormalDist(100, 15)) # __pos__ |
| 2625 | self.assertEqual(-X, NormalDist(-100, 15)) # __neg__ |
| 2626 | self.assertEqual(X + y, NormalDist(110, 15)) # __add__ |
| 2627 | self.assertEqual(y + X, NormalDist(110, 15)) # __radd__ |
| 2628 | self.assertEqual(X - y, NormalDist(90, 15)) # __sub__ |
| 2629 | self.assertEqual(y - X, NormalDist(-90, 15)) # __rsub__ |
| 2630 | self.assertEqual(X * y, NormalDist(1000, 150)) # __mul__ |
| 2631 | self.assertEqual(y * X, NormalDist(1000, 150)) # __rmul__ |
| 2632 | self.assertEqual(X / y, NormalDist(10, 1.5)) # __truediv__ |
Raymond Hettinger | 1f58f4f | 2019-03-06 23:23:55 -0800 | [diff] [blame] | 2633 | with self.assertRaises(TypeError): # __rtruediv__ |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2634 | y / X |
| 2635 | |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2636 | def test_unary_operations(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2637 | NormalDist = self.module.NormalDist |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2638 | X = NormalDist(100, 12) |
| 2639 | Y = +X |
| 2640 | self.assertIsNot(X, Y) |
Miss Islington (bot) | c613c33 | 2019-07-21 00:55:13 -0700 | [diff] [blame] | 2641 | self.assertEqual(X.mean, Y.mean) |
| 2642 | self.assertEqual(X.stdev, Y.stdev) |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2643 | Y = -X |
| 2644 | self.assertIsNot(X, Y) |
Miss Islington (bot) | c613c33 | 2019-07-21 00:55:13 -0700 | [diff] [blame] | 2645 | self.assertEqual(X.mean, -Y.mean) |
| 2646 | self.assertEqual(X.stdev, Y.stdev) |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2647 | |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2648 | def test_equality(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2649 | NormalDist = self.module.NormalDist |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2650 | nd1 = NormalDist() |
| 2651 | nd2 = NormalDist(2, 4) |
| 2652 | nd3 = NormalDist() |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2653 | nd4 = NormalDist(2, 4) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2654 | self.assertNotEqual(nd1, nd2) |
| 2655 | self.assertEqual(nd1, nd3) |
Raymond Hettinger | 2afb598 | 2019-03-20 13:28:59 -0700 | [diff] [blame] | 2656 | self.assertEqual(nd2, nd4) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2657 | |
| 2658 | # Test NotImplemented when types are different |
| 2659 | class A: |
| 2660 | def __eq__(self, other): |
| 2661 | return 10 |
| 2662 | a = A() |
| 2663 | self.assertEqual(nd1.__eq__(a), NotImplemented) |
| 2664 | self.assertEqual(nd1 == a, 10) |
| 2665 | self.assertEqual(a == nd1, 10) |
| 2666 | |
| 2667 | # All subclasses to compare equal giving the same behavior |
| 2668 | # as list, tuple, int, float, complex, str, dict, set, etc. |
| 2669 | class SizedNormalDist(NormalDist): |
| 2670 | def __init__(self, mu, sigma, n): |
| 2671 | super().__init__(mu, sigma) |
| 2672 | self.n = n |
| 2673 | s = SizedNormalDist(100, 15, 57) |
| 2674 | nd4 = NormalDist(100, 15) |
| 2675 | self.assertEqual(s, nd4) |
| 2676 | |
| 2677 | # Don't allow duck type equality because we wouldn't |
| 2678 | # want a lognormal distribution to compare equal |
| 2679 | # to a normal distribution with the same parameters |
| 2680 | class LognormalDist: |
| 2681 | def __init__(self, mu, sigma): |
| 2682 | self.mu = mu |
| 2683 | self.sigma = sigma |
| 2684 | lnd = LognormalDist(100, 15) |
| 2685 | nd = NormalDist(100, 15) |
| 2686 | self.assertNotEqual(nd, lnd) |
| 2687 | |
| 2688 | def test_pickle_and_copy(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2689 | nd = self.module.NormalDist(37.5, 5.625) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2690 | nd1 = copy.copy(nd) |
| 2691 | self.assertEqual(nd, nd1) |
| 2692 | nd2 = copy.deepcopy(nd) |
| 2693 | self.assertEqual(nd, nd2) |
| 2694 | nd3 = pickle.loads(pickle.dumps(nd)) |
| 2695 | self.assertEqual(nd, nd3) |
| 2696 | |
Miss Islington (bot) | c613c33 | 2019-07-21 00:55:13 -0700 | [diff] [blame] | 2697 | def test_hashability(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2698 | ND = self.module.NormalDist |
Miss Islington (bot) | c613c33 | 2019-07-21 00:55:13 -0700 | [diff] [blame] | 2699 | s = {ND(100, 15), ND(100.0, 15.0), ND(100, 10), ND(95, 15), ND(100, 15)} |
| 2700 | self.assertEqual(len(s), 3) |
| 2701 | |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2702 | def test_repr(self): |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2703 | nd = self.module.NormalDist(37.5, 5.625) |
Raymond Hettinger | 11c7953 | 2019-02-23 14:44:07 -0800 | [diff] [blame] | 2704 | self.assertEqual(repr(nd), 'NormalDist(mu=37.5, sigma=5.625)') |
| 2705 | |
Miss Islington (bot) | d5a66bc | 2019-08-24 11:14:20 -0700 | [diff] [blame] | 2706 | # Swapping the sys.modules['statistics'] is to solving the |
| 2707 | # _pickle.PicklingError: |
| 2708 | # Can't pickle <class 'statistics.NormalDist'>: |
| 2709 | # it's not the same object as statistics.NormalDist |
| 2710 | class TestNormalDistPython(unittest.TestCase, TestNormalDist): |
| 2711 | module = py_statistics |
| 2712 | def setUp(self): |
| 2713 | sys.modules['statistics'] = self.module |
| 2714 | |
| 2715 | def tearDown(self): |
| 2716 | sys.modules['statistics'] = statistics |
| 2717 | |
| 2718 | |
| 2719 | @unittest.skipUnless(c_statistics, 'requires _statistics') |
| 2720 | class TestNormalDistC(unittest.TestCase, TestNormalDist): |
| 2721 | module = c_statistics |
| 2722 | def setUp(self): |
| 2723 | sys.modules['statistics'] = self.module |
| 2724 | |
| 2725 | def tearDown(self): |
| 2726 | sys.modules['statistics'] = statistics |
| 2727 | |
Larry Hastings | f5e987b | 2013-10-19 11:50:09 -0700 | [diff] [blame] | 2728 | |
| 2729 | # === Run tests === |
| 2730 | |
| 2731 | def load_tests(loader, tests, ignore): |
| 2732 | """Used for doctest/unittest integration.""" |
| 2733 | tests.addTests(doctest.DocTestSuite()) |
| 2734 | return tests |
| 2735 | |
| 2736 | |
| 2737 | if __name__ == "__main__": |
| 2738 | unittest.main() |