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.

Answer 2

其他人提到的实现细节称为缓冲.您可以在有关数组迭代的文档中阅读有关它的更多信息.

如果你更详细地看一下你失败的例子:

>>> a = np.random.rand(91, 91)
>>> a += a.T
>>> a[:5, -1]
array([ 0.83818399,  1.06489316,  1.23675312,  0.00379798,  1.08967428])
>>> a[-1, :5]
array([ 0.83818399,  1.06489316,  1.75091827,  0.00416305,  1.76315071])

所以第一个错误的价值就是90*91 + 2 = 8192,我们得到的结果不出所料:

>>> np.getbufsize()
8192

我们也可以将它设置得更高,然后:

>>> np.setbufsize(16384)  # Must be a multiple of 16
8192  # returns the previous buffer size
>>> a = np.random.rand(91, 91)
>>> a += a.T
>>> np.all(a == a.T)
True

虽然现在:

>>> a = np.random.rand(129, 129)
>>> a += a.T
>>> np.all(a == a.T)
False

当然,依靠正确性这是一件危险的事情,因为它确实是一个可以改变的实现细节.