assertAlmostEqual in Python unit-test for collections of floats

The assertAlmostEqual(x, y) method in Python's unit testing framework tests whether x and y are approximately equal assuming they are floats.

The problem with assertAlmostEqual() is that it only works on floats. I'm looking for a method like assertAlmostEqual() which works on lists of floats, sets of floats, dictionaries of floats, tuples of floats, lists of tuples of floats, sets of lists of floats, etc.

For instance, let x = 0.1234567890, y = 0.1234567891. x and y are almost equal because they agree on each and every digit except for the last one. Therefore self.assertAlmostEqual(x, y) is True because assertAlmostEqual() works for floats.

I'm looking for a more generic assertAlmostEquals() which also evaluates the following calls to True:

• self.assertAlmostEqual_generic([x, x, x], [y, y, y]).
• self.assertAlmostEqual_generic({1: x, 2: x, 3: x}, {1: y, 2: y, 3: y}).
• self.assertAlmostEqual_generic([(x,x)], [(y,y)]).

Is there such a method or do I have to implement it myself?

Clarifications:

• assertAlmostEquals() has an optional parameter named places and the numbers are compared by computing the difference rounded to number of decimal places. By default places=7, hence self.assertAlmostEqual(0.5, 0.4) is False while self.assertAlmostEqual(0.12345678, 0.12345679) is True. My speculative assertAlmostEqual_generic() should have the same functionality.

• Two lists are considered almost equal if they have almost equal numbers in exactly the same order. formally, for i in range(n): self.assertAlmostEqual(list1[i], list2[i]).

• Similarly, two sets are considered almost equal if they can be converted to almost equal lists (by assigning an order to each set).

• Similarly, two dictionaries are considered almost equal if the key set of each dictionary is almost equal to the key set of the other dictionary, and for each such almost equal key pair there's a corresponding almost equal value.

• In general: I consider two collections almost equal if they're equal except for some corresponding floats which are just almost equal to each other. In other words, I would like to really compare objects but with a low (customized) precision when comparing floats along the way.

if you don't mind using NumPy (which comes with your Python(x,y)), you may want to look at the np.testing module which defines, among others, a assert_almost_equal function.

The signature is np.testing.assert_almost_equal(actual, desired, decimal=7, err_msg='', verbose=True)

>>> x = 1.000001
>>> y = 1.000002
>>> np.testing.assert_almost_equal(x, y)
AssertionError: 
Arrays are not almost equal to 7 decimals
ACTUAL: 1.000001
DESIRED: 1.000002
>>> np.testing.assert_almost_equal(x, y, 5)
>>> np.testing.assert_almost_equal([x, x, x], [y, y, y], 5)
>>> np.testing.assert_almost_equal((x, x, x), (y, y, y), 5)

As of python 3.5 you may compare using

math.isclose(a, b, rel_tol=1e-9, abs_tol=0.0)

As described in pep-0485. The implementation should be equivalent to

abs(a-b) <= max( rel_tol * max(abs(a), abs(b)), abs_tol )

Here's how I've implemented a generic is_almost_equal(first, second) function:

First, duplicate the objects you need to compare (first and second), but don't make an exact copy: cut the insignificant decimal digits of any float you encounter inside the object.

Now that you have copies of first and second for which the insignificant decimal digits are gone, just compare first and second using the == operator.

Let's assume we have a cut_insignificant_digits_recursively(obj, places) function which duplicates obj but leaves only the places most significant decimal digits of each float in the original obj. Here's a working implementation of is_almost_equals(first, second, places):

from insignificant_digit_cutter import cut_insignificant_digits_recursively

def is_almost_equal(first, second, places):
    '''returns True if first and second equal. 
    returns true if first and second aren't equal but have exactly the same
    structure and values except for a bunch of floats which are just almost
    equal (floats are almost equal if they're equal when we consider only the
    [places] most significant digits of each).'''
    if first == second: return True
    cut_first = cut_insignificant_digits_recursively(first, places)
    cut_second = cut_insignificant_digits_recursively(second, places)
    return cut_first == cut_second

And here's a working implementation of cut_insignificant_digits_recursively(obj, places):

def cut_insignificant_digits(number, places):
    '''cut the least significant decimal digits of a number, 
    leave only [places] decimal digits'''
    if  type(number) != float: return number
    number_as_str = str(number)
    end_of_number = number_as_str.find('.')+places+1
    if end_of_number > len(number_as_str): return number
    return float(number_as_str[:end_of_number])

def cut_insignificant_digits_lazy(iterable, places):
    for obj in iterable:
        yield cut_insignificant_digits_recursively(obj, places)

def cut_insignificant_digits_recursively(obj, places):
    '''return a copy of obj except that every float loses its least significant 
    decimal digits remaining only [places] decimal digits'''
    t = type(obj)
    if t == float: return cut_insignificant_digits(obj, places)
    if t in (list, tuple, set):
        return t(cut_insignificant_digits_lazy(obj, places))
    if t == dict:
        return {cut_insignificant_digits_recursively(key, places):
                cut_insignificant_digits_recursively(val, places)
                for key,val in obj.items()}
    return obj

The code and its unit tests are available here: https://github.com/snakile/approximate_comparator. I welcome any improvement and bug fix.