What are the rules for comparing numpy arrays using ==?

Question

For example, trying to make sense of these results:

>>> x
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> (x == np.array([[1],[2]])).astype(np.float32)
array([[ 0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]], dtype=float32)
>>> (x == np.array([1,2]))
   False
>>> (x == np.array([[1]])).astype(np.float32)
array([[ 0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]], dtype=float32)
>>> (x == np.array([1])).astype(np.float32)
array([ 0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.], dtype=float32)

>>> (x == np.array([[1,3],[2]]))
False
>>> 

What's going on here? In the case of [1], it's comparing 1 to each element of x and aggregating the result in an array. In the case of [[1]], same thing. It's easy to figure out what's going to occur for specific array shapes by just experimenting on the repl. But what are the underlying rules where both sides can have arbitrary shapes?

Answer 1

NumPy tries to broadcast the two arrays to compatible shapes before comparison. If the broadcasting fails, False is currently returned. In the future,

The equality operator == will in the future raise errors like np.equal if broadcasting or element comparisons, etc. fails.

Otherwise, a boolean array resulting from the element-by-element comparison is returned. For example, since x and np.array([1]) are broadcastable, an array of shape (10,) is returned:

In [49]: np.broadcast(x, np.array([1])).shape
Out[49]: (10,)

Since x and np.array([[1,3],[2]]) are not broadcastable, False is returned by x == np.array([[1,3],[2]]).

In [50]: np.broadcast(x, np.array([[1,3],[2]])).shape
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-50-56e4868cd7f7> in <module>()
----> 1 np.broadcast(x, np.array([[1,3],[2]])).shape

ValueError: shape mismatch: objects cannot be broadcast to a single shape

Answer 2

It's possible that what's confusing you is that:

1. some broadcasting is going on.

2. you appear to have an older version of numpy.

---

x == np.array([[1],[2]])

is broadcasting. It compares x to each of the first and second arrays; as they are scalars, broadcasting implies that it compares each element of x to each of the scalars.

---

However, each of

x == np.array([1,2])

and

x == np.array([[1,3],[2]])

can't be broadcast. By me, with numpy 1.10.4, this gives

/usr/local/bin/ipython:1: DeprecationWarning: elementwise == comparison failed; this will raise an error in the future.
#!/usr/bin/python
False