numpy.array（[]）和numpy.array（[[]]）有什么区别？

Question

Why can't I get the transpose when of alpha but I can get it for beta? What do the additional [] do?

alpha = np.array([1,2,3,4])
alpha.shape
alpha.T.shape

beta = np.array([[1,2,3,4]])
beta.shape
beta.T.shape

Answer 1

From the documention ( link ):

Transposing a 1-D array returns an unchanged view of the original array.

The array [1,2,3,4] is 1-D while the array [[1,2,3,4]] is a 1x4 2-D array.

Answer 2

The second pair of bracket indicates that it is a 2D array, so with such and array the transposed array is different from the first array (since the transpose switches the 2 dimensions). However if the array is only 1D the transpose doesn't change anything and the resulting array is equal to the starting one.

Answer 3

alpha is a 1D array, the transpose is itself.

beta is a 2D array, so you can transform (1,n) to (n,1) .

To do the same with alpha , you need to add a dimension, you don't need to transpose it:

alpha[:, None]

Answer 4

alpha is a 1D array with shape (4,). The transpose is just alpha again, ie alpha == alpha.T .

beta is a 2D array with shape (1,4). It's a single row, but it has two dimensions. Its transpose looks like a single column with shape (4,1).

Answer 5

When I arrived at the programming language world, having come from the "math side of the business" this also seemed strange to me. After giving some thought to it I realized that from a programming perspective they are different. Have a look at the following list:

a = [1,2,3,4,5]

This is a 1D structure. This is so, because to get back the values 1,2,3,4 and 5 you just need to assign one address value. 3 would be returned if you issued the command a[2] for instance.

Now take a look at this list:

b = [[ 1,  2,  3,  4,  5],
     [11, 22, 33, 44, 55]]

To get back the 11 for instance you would need two positional numbers, 1 because 11 is located in the 2nd list and 0 because in the second list it is located in the first position. In other words b[1,0] gives back to you 11.

Now comes the trick part. Look at this third list:

c = [ [ 100, 200, 300, 400, 500] ]

If you look carefully each number requires 2 positional numbers to be taken back from the list. 300 for instance requires 0 because it is located in the first (and only) list and 2 because it is the third element of the first list. c[0,2] gets you back 300.

This list can be transposed because it has two dimensions and the transposition operation is something that switches the positional arguments. So cT would give you back a list whose shape would be [5,1], since c has a [1,5] shape.

Get back to list a. There you have a list with only one positional number. That list has a shape of [5] only, so there´s no second positional argument to the transposition operation to work with. Therefore it remains [5] and if you try aT you get back a.

Got it?

Best regards,

Gustavo,