Add support for numpy arrays (and dicts) to approx.

This fixes #1994.  It turned out to require a lot of refactoring because
subclassing numpy.ndarray was necessary to coerce python into calling
the right `__eq__` operator.

_pytest/python.py

@@ -1117,7 +1117,6 @@ def raises(expected_exception, *args, **kwargs):
           ...
         Failed: Expecting ZeroDivisionError
 
-
     .. note::
 
        When using ``pytest.raises`` as a context manager, it's worthwhile to
@@ -1150,7 +1149,6 @@ def raises(expected_exception, *args, **kwargs):
         >>> with raises(ValueError, match=r'must be \d+$'):
         ...     raise ValueError("value must be 42")
 
-
     Or you can specify a callable by passing a to-be-called lambda::
 
         >>> raises(ZeroDivisionError, lambda: 1/0)
@@ -1230,10 +1228,8 @@ def raises(expected_exception, *args, **kwargs):
             return _pytest._code.ExceptionInfo()
     fail(message)
 
-
 raises.Exception = fail.Exception
 
-
 class RaisesContext(object):
     def __init__(self, expected_exception, message, match_expr):
         self.expected_exception = expected_exception
@@ -1265,9 +1261,271 @@ class RaisesContext(object):
         return suppress_exception
 
 
+
 # builtin pytest.approx helper
 
-class approx(object):
+class ApproxBase(object):
+    """
+    Provide shared utilities for making approximate comparisons between numbers 
+    or sequences of numbers.
+    """
+
+    def __init__(self, expected, rel=None, abs=None):
+        self.expected = expected
+        self.abs = abs
+        self.rel = rel
+
+    def __repr__(self):
+        return ', '.join(
+                repr(self._approx_scalar(x))
+                for x in self._yield_expected())
+
+    def __eq__(self, actual):
+        return all(
+                a == self._approx_scalar(x)
+                for a, x in self._yield_comparisons(actual))
+
+    __hash__ = None
+
+    def __ne__(self, actual):
+        return not (actual == self)
+
+    def _approx_scalar(self, x):
+        return ApproxScalar(x, rel=self.rel, abs=self.abs)
+
+    def _yield_expected(self, actual):
+        """
+        Yield all the expected values associated with this object.  This is 
+        used to implement the `__repr__` method.
+        """
+        raise NotImplementedError
+
+    def _yield_comparisons(self, actual):
+        """
+        Yield all the pairs of numbers to be compared.  This is used to 
+        implement the `__eq__` method.
+        """
+        raise NotImplementedError
+
+
+
+try:
+    import numpy as np
+
+    class ApproxNumpy(ApproxBase, np.ndarray):
+        """
+        Perform approximate comparisons for numpy arrays.
+
+        This class must inherit from numpy.ndarray in order to allow the approx 
+        to be on either side of the `==` operator.  The reason for this has to 
+        do with how python decides whether to call `a.__eq__()` or `b.__eq__()` 
+        when it encounters `a == b`.  
+        
+        If `a` and `b` are not related by inheritance, `a` gets priority.  So 
+        as long as `a.__eq__` is defined, it will be called.  Because most 
+        implementations of `a.__eq__` end up calling `b.__eq__`, this detail 
+        usually doesn't matter.  However, `numpy.ndarray.__eq__` raises an 
+        error complaining that "the truth value of an array with more than 
+        one element is ambiguous. Use a.any() or a.all()" when compared with a 
+        custom class, so `b.__eq__` never gets called.
+
+        The trick is that the priority rules change if `a` and `b` are related 
+        by inheritance.  Specifically, `b.__eq__` gets priority if `b` is a 
+        subclass of `a`.  So we can guarantee that `ApproxNumpy.__eq__` gets 
+        called by inheriting from `numpy.ndarray`.
+        """
+
+        def __new__(cls, expected, rel=None, abs=None):
+            """
+            Numpy uses __new__ (rather than __init__) to initialize objects. 
+            
+            The `expected` argument must be a numpy array.  This should be 
+            ensured by the approx() delegator function.
+            """
+            assert isinstance(expected, np.ndarray)
+            obj = super(ApproxNumpy, cls).__new__(cls, expected.shape)
+            obj.__init__(expected, rel, abs)
+            return obj
+
+        def __repr__(self):
+            # It might be nice to rewrite this function to account for the 
+            # shape of the array...
+            return '[' + ApproxBase.__repr__(self) + ']'
+
+        def __eq__(self, actual):
+            try:
+                actual = np.array(actual)
+            except:
+                raise ValueError("cannot cast '{0}' to numpy.ndarray".format(actual))
+
+            if actual.shape != self.expected.shape:
+                return False
+
+            return ApproxBase.__eq__(self, actual)
+
+        def _yield_expected(self):
+            for x in self.expected:
+                yield x
+
+        def _yield_comparisons(self, actual):
+            # We can be sure that `actual` is a numpy array, because it's 
+            # casted in `__eq__` before being passed to `ApproxBase.__eq__`, 
+            # which is the only method that calls this one.
+            for i in np.ndindex(self.expected.shape):
+                yield actual[i], self.expected[i]
+
+
+except ImportError:
+    np = None
+
+class ApproxMapping(ApproxBase):
+    """
+    Perform approximate comparisons for mappings where the values are numbers 
+    (the keys can be anything).
+    """
+
+    def __repr__(self):
+        item = lambda k, v: "'{0}': {1}".format(k, self._approx_scalar(v))
+        return '{' + ', '.join(item(k,v) for k,v in self.expected.items()) + '}'
+
+    def __eq__(self, actual):
+        if actual.keys() != self.expected.keys():
+            return False
+
+        return ApproxBase.__eq__(self, actual)
+        
+    def _yield_comparisons(self, actual):
+        for k in self.expected.keys():
+            yield actual[k], self.expected[k]
+
+
+class ApproxSequence(ApproxBase):
+    """
+    Perform approximate comparisons for sequences of numbers.
+    """
+
+    def __repr__(self):
+        open, close = '()' if isinstance(self.expected, tuple) else '[]'
+        return open + ApproxBase.__repr__(self) + close
+
+    def __eq__(self, actual):
+        if len(actual) != len(self.expected):
+            return False
+        return ApproxBase.__eq__(self, actual)
+        
+    def _yield_expected(self):
+        return iter(self.expected)
+
+    def _yield_comparisons(self, actual):
+        return zip(actual, self.expected)
+
+
+class ApproxScalar(ApproxBase):
+    """
+    Perform approximate comparisons for single numbers only.
+    """
+
+    def __repr__(self):
+        """
+        Return a string communicating both the expected value and the tolerance 
+        for the comparison being made, e.g. '1.0 +- 1e-6'.  Use the unicode 
+        plus/minus symbol if this is python3 (it's too hard to get right for 
+        python2).
+        """
+        if isinstance(self.expected, complex):
+            return str(self.expected)
+
+        # Infinities aren't compared using tolerances, so don't show a
+        # tolerance.
+        if math.isinf(self.expected):
+            return str(self.expected)
+
+        # If a sensible tolerance can't be calculated, self.tolerance will
+        # raise a ValueError.  In this case, display '???'.
+        try:
+            vetted_tolerance = '{:.1e}'.format(self.tolerance)
+        except ValueError:
+            vetted_tolerance = '???'
+
+        if sys.version_info[0] == 2:
+            return '{0} +- {1}'.format(self.expected, vetted_tolerance)
+        else:
+            return u'{0} \u00b1 {1}'.format(self.expected, vetted_tolerance)
+
+    def __eq__(self, actual):
+        """
+        Return true if the given value is equal to the expected value within 
+        the pre-specified tolerance.
+        """
+        from numbers import Number
+
+        # Give a good error message we get values to compare that aren't 
+        # numbers, rather than choking on them later on.
+        if not isinstance(actual, Number):
+            raise ValueError("approx can only compare numbers, not '{0}'".format(actual))
+        if not isinstance(self.expected, Number):
+            raise ValueError("approx can only compare numbers, not '{0}'".format(self.expected))
+
+        # Short-circuit exact equality.
+        if actual == self.expected:
+            return True
+
+        # Infinity shouldn't be approximately equal to anything but itself, but
+        # if there's a relative tolerance, it will be infinite and infinity
+        # will seem approximately equal to everything.  The equal-to-itself
+        # case would have been short circuited above, so here we can just
+        # return false if the expected value is infinite.  The abs() call is
+        # for compatibility with complex numbers.
+        if math.isinf(abs(self.expected)):
+            return False
+
+        # Return true if the two numbers are within the tolerance.
+        return abs(self.expected - actual) <= self.tolerance
+
+    __hash__ = None
+
+    @property
+    def tolerance(self):
+        """
+        Return the tolerance for the comparison.  This could be either an 
+        absolute tolerance or a relative tolerance, depending on what the user 
+        specified or which would be larger.
+        """
+        set_default = lambda x, default: x if x is not None else default
+
+        # Figure out what the absolute tolerance should be.  ``self.abs`` is
+        # either None or a value specified by the user.
+        absolute_tolerance = set_default(self.abs, 1e-12)
+
+        if absolute_tolerance < 0:
+            raise ValueError("absolute tolerance can't be negative: {}".format(absolute_tolerance))
+        if math.isnan(absolute_tolerance):
+            raise ValueError("absolute tolerance can't be NaN.")
+
+        # If the user specified an absolute tolerance but not a relative one,
+        # just return the absolute tolerance.
+        if self.rel is None:
+            if self.abs is not None:
+                return absolute_tolerance
+
+        # Figure out what the relative tolerance should be.  ``self.rel`` is
+        # either None or a value specified by the user.  This is done after
+        # we've made sure the user didn't ask for an absolute tolerance only,
+        # because we don't want to raise errors about the relative tolerance if
+        # we aren't even going to use it.
+        relative_tolerance = set_default(self.rel, 1e-6) * abs(self.expected)
+
+        if relative_tolerance < 0:
+            raise ValueError("relative tolerance can't be negative: {}".format(absolute_tolerance))
+        if math.isnan(relative_tolerance):
+            raise ValueError("relative tolerance can't be NaN.")
+
+        # Return the larger of the relative and absolute tolerances.
+        return max(relative_tolerance, absolute_tolerance)
+
+
+
+def approx(expected, rel=None, abs=None):
     """
     Assert that two numbers (or two sets of numbers) are equal to each other
     within some tolerance.
@@ -1307,6 +1565,8 @@ class approx(object):
 
         >>> (0.1 + 0.2, 0.2 + 0.4) == approx((0.3, 0.6))
         True
+        >>> {'a': 0.1 + 0.2, 'b': 0.2 + 0.4} == approx({'a': 0.3, 'b': 0.6})
+        True
 
     By default, ``approx`` considers numbers within a relative tolerance of
     ``1e-6`` (i.e. one part in a million) of its expected value to be equal.
@@ -1381,138 +1641,36 @@ class approx(object):
       relative tolerance, only the absolute tolerance is considered.
     """
     
-    def __init__(self, expected, rel=None, abs=None):
+    from collections import Mapping, Sequence
-        self.expected = expected
-        self.abs = abs
-        self.rel = rel
-
-    def __repr__(self):
-        return ', '.join(repr(x) for x in self.expected)
-
-    def __eq__(self, actual):
-        from collections import Iterable
-        if not isinstance(actual, Iterable):
-            actual = [actual]
-        if len(actual) != len(self.expected):
-            return False
-        return all(a == x for a, x in zip(actual, self.expected))
-
-    __hash__ = None
-
-    def __ne__(self, actual):
-        return not (actual == self)
-
-    @property
-    def expected(self):
-        # Regardless of whether the user-specified expected value is a number
-        # or a sequence of numbers, return a list of ApproxNotIterable objects
-        # that can be compared against.
-        from collections import Iterable
-        approx_non_iter = lambda x: ApproxNonIterable(x, self.rel, self.abs)
-        if isinstance(self._expected, Iterable):
-            return [approx_non_iter(x) for x in self._expected]
-        else:
-            return [approx_non_iter(self._expected)]
-
-    @expected.setter
-    def expected(self, expected):
-        self._expected = expected
-
-
-class ApproxNonIterable(object):
-    """
-    Perform approximate comparisons for single numbers only.
-
-    In other words, the ``expected`` attribute for objects of this class must
-    be some sort of number.  This is in contrast to the ``approx`` class, where
-    the ``expected`` attribute can either be a number of a sequence of numbers.
-    This class is responsible for making comparisons, while ``approx`` is
-    responsible for abstracting the difference between numbers and sequences of
-    numbers.  Although this class can stand on its own, it's only meant to be
-    used within ``approx``.
-    """
-
-    def __init__(self, expected, rel=None, abs=None):
-        self.expected = expected
-        self.abs = abs
-        self.rel = rel
-
-    def __repr__(self):
-        if isinstance(self.expected, complex):
-            return str(self.expected)
-
-        # Infinities aren't compared using tolerances, so don't show a
-        # tolerance.
-        if math.isinf(self.expected):
-            return str(self.expected)
-
-        # If a sensible tolerance can't be calculated, self.tolerance will
-        # raise a ValueError.  In this case, display '???'.
     try:
-            vetted_tolerance = '{:.1e}'.format(self.tolerance)
+        String = basestring  # python2
-        except ValueError:
+    except NameError:
-            vetted_tolerance = '???'
+        String = str, bytes  # python3
 
-        if sys.version_info[0] == 2:
+    # Delegate the comparison to a class that knows how to deal with the type 
-            return '{0} +- {1}'.format(self.expected, vetted_tolerance)
+    # of the expected value (e.g. int, float, list, dict, numpy.array, etc).  
+    #
+    # This architecture is really driven by the need to support numpy arrays.  
+    # The only way to override `==` for arrays without requiring that approx be 
+    # the left operand is to inherit the approx object from `numpy.ndarray`.  
+    # But that can't be a general solution, because it requires (1) numpy to be 
+    # installed and (2) the expected value to be a numpy array.  So the general 
+    # solution is to delegate each type of expected value to a different class.
+    #
+    # This has the advantage that it made it easy to support mapping types 
+    # (i.e. dict).  The old code accepted mapping types, but would only compare 
+    # their keys, which is probably not what most people would expect.
+
+    if np and isinstance(expected, np.ndarray):
+        cls = ApproxNumpy
+    elif isinstance(expected, Mapping):
+        cls = ApproxMapping
+    elif isinstance(expected, Sequence) and not isinstance(expected, String):
+        cls = ApproxSequence
     else:
-            return u'{0} \u00b1 {1}'.format(self.expected, vetted_tolerance)
+        cls = ApproxScalar
 
-    def __eq__(self, actual):
+    return cls(expected, rel, abs)
-        # Short-circuit exact equality.
-        if actual == self.expected:
-            return True
-
-        # Infinity shouldn't be approximately equal to anything but itself, but
-        # if there's a relative tolerance, it will be infinite and infinity
-        # will seem approximately equal to everything.  The equal-to-itself
-        # case would have been short circuited above, so here we can just
-        # return false if the expected value is infinite.  The abs() call is
-        # for compatibility with complex numbers.
-        if math.isinf(abs(self.expected)):
-            return False
-
-        # Return true if the two numbers are within the tolerance.
-        return abs(self.expected - actual) <= self.tolerance
-
-    __hash__ = None
-
-    def __ne__(self, actual):
-        return not (actual == self)
-
-    @property
-    def tolerance(self):
-        set_default = lambda x, default: x if x is not None else default
-
-        # Figure out what the absolute tolerance should be.  ``self.abs`` is
-        # either None or a value specified by the user.
-        absolute_tolerance = set_default(self.abs, 1e-12)
-
-        if absolute_tolerance < 0:
-            raise ValueError("absolute tolerance can't be negative: {}".format(absolute_tolerance))
-        if math.isnan(absolute_tolerance):
-            raise ValueError("absolute tolerance can't be NaN.")
-
-        # If the user specified an absolute tolerance but not a relative one,
-        # just return the absolute tolerance.
-        if self.rel is None:
-            if self.abs is not None:
-                return absolute_tolerance
-
-        # Figure out what the relative tolerance should be.  ``self.rel`` is
-        # either None or a value specified by the user.  This is done after
-        # we've made sure the user didn't ask for an absolute tolerance only,
-        # because we don't want to raise errors about the relative tolerance if
-        # we aren't even going to use it.
-        relative_tolerance = set_default(self.rel, 1e-6) * abs(self.expected)
-
-        if relative_tolerance < 0:
-            raise ValueError("relative tolerance can't be negative: {}".format(absolute_tolerance))
-        if math.isnan(relative_tolerance):
-            raise ValueError("relative tolerance can't be NaN.")
-
-        # Return the larger of the relative and absolute tolerances.
-        return max(relative_tolerance, absolute_tolerance)
 
 
 #

testing/python/approx.py

@@ -9,7 +9,6 @@ from decimal import Decimal
 from fractions import Fraction
 inf, nan = float('inf'), float('nan')
 
-
 class MyDocTestRunner(doctest.DocTestRunner):
 
     def __init__(self):
@@ -29,12 +28,19 @@ class TestApprox(object):
         if sys.version_info[:2] == (2, 6):
             tol1, tol2, infr = '???', '???', '???'
         assert repr(approx(1.0)) == '1.0 {pm} {tol1}'.format(pm=plus_minus, tol1=tol1)
-        assert repr(approx([1.0, 2.0])) == '1.0 {pm} {tol1}, 2.0 {pm} {tol2}'.format(pm=plus_minus, tol1=tol1, tol2=tol2)
+        assert repr(approx([1.0, 2.0])) == '[1.0 {pm} {tol1}, 2.0 {pm} {tol2}]'.format(pm=plus_minus, tol1=tol1, tol2=tol2)
+        assert repr(approx((1.0, 2.0))) == '(1.0 {pm} {tol1}, 2.0 {pm} {tol2})'.format(pm=plus_minus, tol1=tol1, tol2=tol2)
         assert repr(approx(inf)) == 'inf'
         assert repr(approx(1.0, rel=nan)) == '1.0 {pm} ???'.format(pm=plus_minus)
         assert repr(approx(1.0, rel=inf)) == '1.0 {pm} {infr}'.format(pm=plus_minus, infr=infr)
         assert repr(approx(1.0j, rel=inf)) == '1j'
 
+        # Dictionaries aren't ordered, so we need to check both orders.
+        assert repr(approx({'a': 1.0, 'b': 2.0})) in (
+                "{{'a': 1.0 {pm} {tol1}, 'b': 2.0 {pm} {tol2}}}".format(pm=plus_minus, tol1=tol1, tol2=tol2),
+                "{{'b': 2.0 {pm} {tol2}, 'a': 1.0 {pm} {tol1}}}".format(pm=plus_minus, tol1=tol1, tol2=tol2),
+        )
+
     def test_operator_overloading(self):
         assert 1 == approx(1, rel=1e-6, abs=1e-12)
         assert not (1 != approx(1, rel=1e-6, abs=1e-12))
@@ -228,18 +234,38 @@ class TestApprox(object):
             # tolerance, so only an absolute tolerance is calculated.
             assert a != approx(x, abs=inf)
 
-    def test_expecting_sequence(self):
+    def test_int(self):
-        within_1e8 = [
+        within_1e6 = [
-                (1e8 + 1e0, 1e8),
+                (1000001, 1000000),
-                (1e0 + 1e-8, 1e0),
+                (-1000001, -1000000),
-                (1e-8 + 1e-16, 1e-8),
         ]
-        actual, expected = zip(*within_1e8)
+        for a, x in within_1e6:
-        assert actual == approx(expected, rel=5e-8, abs=0.0)
+            assert a == approx(x, rel=5e-6, abs=0)
+            assert a != approx(x, rel=5e-7, abs=0)
+            assert approx(x, rel=5e-6, abs=0) == a
+            assert approx(x, rel=5e-7, abs=0) != a
 
-    def test_expecting_sequence_wrong_len(self):
+    def test_decimal(self):
-        assert [1, 2] != approx([1])
+        within_1e6 = [
-        assert [1, 2] != approx([1,2,3])
+                (Decimal('1.000001'), Decimal('1.0')),
+                (Decimal('-1.000001'), Decimal('-1.0')),
+        ]
+        for a, x in within_1e6:
+            assert a == approx(x, rel=Decimal('5e-6'), abs=0)
+            assert a != approx(x, rel=Decimal('5e-7'), abs=0)
+            assert approx(x, rel=Decimal('5e-6'), abs=0) == a
+            assert approx(x, rel=Decimal('5e-7'), abs=0) != a
+
+    def test_fraction(self):
+        within_1e6 = [
+                (1 + Fraction(1, 1000000), Fraction(1)),
+                (-1 - Fraction(-1, 1000000), Fraction(-1)),
+        ]
+        for a, x in within_1e6:
+            assert a == approx(x, rel=5e-6, abs=0)
+            assert a != approx(x, rel=5e-7, abs=0)
+            assert approx(x, rel=5e-6, abs=0) == a
+            assert approx(x, rel=5e-7, abs=0) != a
 
     def test_complex(self):
         within_1e6 = [
@@ -251,33 +277,86 @@ class TestApprox(object):
         for a, x in within_1e6:
             assert a == approx(x, rel=5e-6, abs=0)
             assert a != approx(x, rel=5e-7, abs=0)
+            assert approx(x, rel=5e-6, abs=0) == a
+            assert approx(x, rel=5e-7, abs=0) != a
 
-    def test_int(self):
+    def test_list(self):
-        within_1e6 = [
+        actual = [1 + 1e-7, 2 + 1e-8]
-                (1000001, 1000000),
+        expected = [1, 2]
-                (-1000001, -1000000),
-        ]
-        for a, x in within_1e6:
-            assert a == approx(x, rel=5e-6, abs=0)
-            assert a != approx(x, rel=5e-7, abs=0)
 
-    def test_decimal(self):
+        # Return false if any element is outside the tolerance.
-        within_1e6 = [
+        assert actual == approx(expected, rel=5e-7, abs=0)
-                (Decimal('1.000001'), Decimal('1.0')),
+        assert actual != approx(expected, rel=5e-8, abs=0)
-                (Decimal('-1.000001'), Decimal('-1.0')),
+        assert approx(expected, rel=5e-7, abs=0) == actual
-        ]
+        assert approx(expected, rel=5e-8, abs=0) != actual
-        for a, x in within_1e6:
-            assert a == approx(x, rel=Decimal('5e-6'), abs=0)
-            assert a != approx(x, rel=Decimal('5e-7'), abs=0)
 
-    def test_fraction(self):
+    def test_list_wrong_len(self):
-        within_1e6 = [
+        assert [1, 2] != approx([1])
-                (1 + Fraction(1, 1000000), Fraction(1)),
+        assert [1, 2] != approx([1,2,3])
-                (-1 - Fraction(-1, 1000000), Fraction(-1)),
+
-        ]
+    def test_tuple(self):
-        for a, x in within_1e6:
+        actual = (1 + 1e-7, 2 + 1e-8)
-            assert a == approx(x, rel=5e-6, abs=0)
+        expected = (1, 2)
-            assert a != approx(x, rel=5e-7, abs=0)
+
+        # Return false if any element is outside the tolerance.
+        assert actual == approx(expected, rel=5e-7, abs=0)
+        assert actual != approx(expected, rel=5e-8, abs=0)
+        assert approx(expected, rel=5e-7, abs=0) == actual
+        assert approx(expected, rel=5e-8, abs=0) != actual
+
+    def test_tuple_wrong_len(self):
+        assert (1, 2) != approx((1,))
+        assert (1, 2) != approx((1,2,3))
+
+    def test_dict(self):
+        actual = {'a': 1 + 1e-7, 'b': 2 + 1e-8}
+        expected = {'b': 2, 'a': 1} # Dictionaries became ordered in python3.6,
+                                    # so make sure the order doesn't matter
+
+        # Return false if any element is outside the tolerance.
+        assert actual == approx(expected, rel=5e-7, abs=0)
+        assert actual != approx(expected, rel=5e-8, abs=0)
+        assert approx(expected, rel=5e-7, abs=0) == actual
+        assert approx(expected, rel=5e-8, abs=0) != actual
+
+    def test_dict_wrong_len(self):
+        assert {'a': 1, 'b': 2} != approx({'a': 1})
+        assert {'a': 1, 'b': 2} != approx({'a': 1, 'c': 2})
+        assert {'a': 1, 'b': 2} != approx({'a': 1, 'b': 2, 'c': 3})
+
+    def test_numpy_array(self):
+        try:
+            import numpy as np
+        except ImportError:
+            pytest.skip("numpy not installed")
+
+        actual = np.array([1 + 1e-7, 2 + 1e-8])
+        expected = np.array([1, 2])
+
+        # Return false if any element is outside the tolerance.
+        assert actual == approx(expected, rel=5e-7, abs=0)
+        assert actual != approx(expected, rel=5e-8, abs=0)
+        assert approx(expected, rel=5e-7, abs=0) == expected
+        assert approx(expected, rel=5e-8, abs=0) != actual
+
+    def test_numpy_array_wrong_shape(self):
+        try:
+            import numpy as np
+        except ImportError:
+            pytest.skip("numpy not installed")
+
+        import numpy as np
+        a12 = np.array([[1, 2]])
+        a21 = np.array([[1],[2]])
+
+        assert a12 != approx(a21)
+        assert a21 != approx(a12)
+
+    def test_non_number(self):
+        with pytest.raises(ValueError):
+            1 == approx("1")
+        with pytest.raises(ValueError):
+            "1" == approx(1)
 
     def test_doctests(self):
         parser = doctest.DocTestParser()