sum numpy ndarray with 3d array along a given axis 1

Question

I have an numpy ndarray with shape (2,3,3),for example:

array([[[ 1,  2,  3],
    [ 4,  5,  6],
    [12, 34, 90]],

   [[ 4,  5,  6],
    [ 2,  5,  6],
    [ 7,  3,  4]]])

I am getting lost in np.sum(above ndarray ,axis=1), why that answer is:

array([[17, 41, 99],
   [13, 13, 16]])

Thanks

Answer 1

Axes are defined for arrays with more than one dimension. A 2-dimensional array has two corresponding axes: the first running vertically downwards across rows (axis 0), and the second running horizontally across columns (axis 1).

Let A be the array, then in your example when axis is 1, [i,:,k] are added. Likewise, for axis 0, [:,j,k] are added and when axis is 2, [i,j,:] are added.

 A = np.array([[[ 1,  2,  3],[ 4,  5,  6],
    [12, 34, 90]],
    [[ 4,  5,  6],[ 2,  5,  6],
    [ 7,  3,  4]]])


np.sum(A,axis = 0)
    array([[ 5,  7,  9],
           [ 6, 10, 12],
           [19, 37, 94]])
np.sum(A,axis = 1)
    array([[17, 41, 99],
                   [13, 13, 16]])
np.sum(A,axis = 2)
    array([[  6,  15, 136],
           [ 15,  13,  14]])

Answer 2

Let's call the inout array A and the output array B = np.sum(A, axis=1) . It has elements B[i, j] which are calculated as

B[i, j] = np.sum(A[i, :, j])

Eg the first element B[0,0] = 17 is the sum of the elements in

A[0, :, 0] = array([ 1,  4, 12])

Answer 3

np.sum（）是垂直添加值，添加第一个列表中每个子列表的第一个元素：1 + 4 + 12 = 17，然后是第二个2 + 5 + 34 = 41等。

Answer 4

The array has shape (2,3,3) ; axis 1 is the middle one, of size 3. Eliminate that by sum and you are left with (2,3) , the shape of your result.

Interpreting 3d is a little tricky. I tend to think of this array as having 2 planes, each plane has 3 rows, and 3 columns. The sum on axis 1 is over the rows of each plane.

1 + 4 + 12 == 17

In effect you are reducing each 2d plane to a 1d row.