Numpy: Why doesn't 'a += a.T' work?

Question

As stated in scipy lecture notes, this will not work as expected:

a = np.random.randint(0, 10, (1000, 1000))
a += a.T
assert np.allclose(a, a.T)

But why? How does being a view affect this behavior?

Answer 1

a += a.T

does in-place summing up (it's using view a.T while processing), so you end up with a non-symmetric matrix you can easily check this, i.e. I got:

In [3]: a
Out[3]: 
array([[ 6, 15,  7, ...,  8,  9,  2],
       [15,  6,  9, ..., 14,  9,  7],
       [ 7,  9,  0, ...,  9,  5,  8],
       ..., 
       [ 8, 23, 15, ...,  6,  4, 10],
       [18, 13,  8, ...,  4,  2,  6],
       [ 3,  9,  9, ..., 16,  8,  4]])

You can see it's not symmetric, right? (compare right-top and left-bottom items)

if you do a real copy:

a += np.array(a.T)

it works fine, i.e.:

In [6]: a
Out[6]: 
array([[ 2, 11,  8, ...,  9, 15,  5],
       [11,  4, 14, ..., 10,  3, 13],
       [ 8, 14, 14, ..., 10,  9,  3],
       ..., 
       [ 9, 10, 10, ..., 16,  7,  6],
       [15,  3,  9, ...,  7, 14,  1],
       [ 5, 13,  3, ...,  6,  1,  2]])

To better understand why it does so, you can imagine you wrote the loop yourself as following:

In [8]: for i in xrange(1000):
            for j in xrange(1000):
                a[j,i] += a[i,j]
   ....:         

In [9]: a
Out[9]: 
array([[ 4,  5, 14, ..., 12, 16, 13],
       [ 3,  2, 16, ..., 16,  8,  8],
       [ 9, 12, 10, ...,  7,  7, 23],
       ..., 
       [ 8, 10,  6, ..., 14, 13, 23],
       [10,  4,  6, ...,  9, 16, 21],
       [11,  8, 14, ..., 16, 12, 12]])

It adds a[999,0] to calculate a[0,999] but a[999,0] already has sum of a[999,0] + a[0,999] -- so below the main diagonal you add the values twice.