python - Unexpected result with += on NumPy arrays

Question

I am creating symmetric matrices/arrays in Python with NumPy, using a standard method:

x = rand(500,500)
x = (x+x.T)
all(x==x.T)
> True

Now let's be clever:

x = rand(500,500)
x += x.T
all(x==x.T)
> False

Wait, what?

x==x.T
> array([[ True,  True,  True, ..., False, False, False],
       [ True,  True,  True, ..., False, False, False],
       [ True,  True,  True, ..., False, False, False],
       ..., 
       [False, False, False, ...,  True,  True,  True],
       [False, False, False, ...,  True,  True,  True],
       [False, False, False, ...,  True,  True,  True]], dtype=bool)

The upper left and lower right segments are symmetrical. What if I chose a smaller array?

x = rand(50,50)
x += x.T
all(x==x.T)
> True

OK....

x = rand(90,90)
x += x.T
all(x==x.T)
> True

x = rand(91,91)
x += x.T
all(x==x.T)
> False

And just to be sure...

x = rand(91,91)
x = (x+x.T)
all(x==x.T)
> True

Is this a bug, or am I about to learn something crazy about += and NumPy arrays?

Answer 1

The transpose operation returns a view of the array, which means that no new array is allocated. Which, in turn, means that you are reading and modifying the array at the same time. It's hard to tell why some sizes or some areas of the result work, but most likely it has to do with how numpy deals with array addition (maybe it makes copies of submatrices) and/or array views (maybe for small sizes it does create a new array).

The x = x + x.T operation works because there you are creating a new array and then assigning to x, of course.