ENH: Make assert_almost_equal & assert_array_almost_equal consistent.

This changes the check for scalars in assert_almost_equal so that

    abs(actual - desired) < 1.5 * 10**(-decimal)

Note that the previous documentation claimed that the functions were
equivalent to

    abs(actual - desired) < .5 * 10**(-decimal)

but that was not how they behaved in practice.

Due to the change in implementation, some very delicate tests may fail
that did not fail before. No extra failures were noted in scipy.

Closes #5200.

1 files changed, 35 insertions, 1 deletions

diff --git a/numpy/testing/tests/test_utils.py b/numpy/testing/tests/test_utils.py
index fe1f411c4..842d55b37 100644
--- a/numpy/testing/tests/test_utils.py
+++ b/numpy/testing/tests/test_utils.py
@@ -11,7 +11,7 @@ from numpy.testing import (
     assert_warns, assert_no_warnings, assert_allclose, assert_approx_equal,
     assert_array_almost_equal_nulp, assert_array_max_ulp,
     clear_and_catch_warnings, run_module_suite,
-    assert_string_equal, assert_, tempdir, temppath, 
+    assert_string_equal, assert_, tempdir, temppath,
     )
 import unittest
 
@@ -246,6 +246,23 @@ class TestArrayAlmostEqual(_GenericTest, unittest.TestCase):
     def setUp(self):
         self._assert_func = assert_array_almost_equal
 
+    def test_closeness(self):
+        # Note that in the course of time we ended up with
+        #     `abs(x - y) < 1.5 * 10**(-decimal)`
+        # instead of the previously documented
+        #     `abs(x - y) < 0.5 * 10**(-decimal)`
+        # so this check serves to preserve the wrongness.
+
+        # test scalars
+        self._assert_func(1.499999, 0.0, decimal=0)
+        self.assertRaises(AssertionError,
+                          lambda: self._assert_func(1.5, 0.0, decimal=0))
+
+        # test arrays
+        self._assert_func([1.499999], [0.0], decimal=0)
+        self.assertRaises(AssertionError,
+                          lambda: self._assert_func([1.5], [0.0], decimal=0))
+
     def test_simple(self):
         x = np.array([1234.2222])
         y = np.array([1234.2223])
@@ -288,6 +305,23 @@ class TestAlmostEqual(_GenericTest, unittest.TestCase):
     def setUp(self):
         self._assert_func = assert_almost_equal
 
+    def test_closeness(self):
+        # Note that in the course of time we ended up with
+        #     `abs(x - y) < 1.5 * 10**(-decimal)`
+        # instead of the previously documented
+        #     `abs(x - y) < 0.5 * 10**(-decimal)`
+        # so this check serves to preserve the wrongness.
+
+        # test scalars
+        self._assert_func(1.499999, 0.0, decimal=0)
+        self.assertRaises(AssertionError,
+                          lambda: self._assert_func(1.5, 0.0, decimal=0))
+
+        # test arrays
+        self._assert_func([1.499999], [0.0], decimal=0)
+        self.assertRaises(AssertionError,
+                          lambda: self._assert_func([1.5], [0.0], decimal=0))
+
     def test_nan_item(self):
         self._assert_func(np.nan, np.nan)
         self.assertRaises(AssertionError,