how is axis indexed in numpy's array?

Question

From Numpy\'s tutorial, axis can be indexed with integers, like 0 is for column, 1 is for row, but I don\'t grasp why they are indexed this way? An

Answer 1

In general, axis = 0, means all cells with first dimension varying with each value of 2nd dimension and 3rd dimension and so on

For example , 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)

For 3D, it becomes complex, so, use multiple for loops

>>> x = np.array([[[ 0,  1,  2],
    [ 3,  4,  5],
    [ 6,  7,  8]],
   [[ 9, 10, 11],
    [12, 13, 14],
    [15, 16, 17]],
   [[18, 19, 20],
    [21, 22, 23],
    [24, 25, 26]]])

>>> x.shape #(3, 3, 3)

#axis = 0 
>>> for j in range(0, x.shape[1]):
      for k in range(0, x.shape[2]):
        print( "element = ", (j,k), " ", [ x[i,j,k] for i in range(0, x.shape[0]) ])
...
element =  (0, 0)   [0, 9, 18]             #sum is 27
element =  (0, 1)   [1, 10, 19]            #sum is 30
element =  (0, 2)   [2, 11, 20]
element =  (1, 0)   [3, 12, 21]
element =  (1, 1)   [4, 13, 22]
element =  (1, 2)   [5, 14, 23]
element =  (2, 0)   [6, 15, 24]
element =  (2, 1)   [7, 16, 25]
element =  (2, 2)   [8, 17, 26]

>>> x.sum(axis=0)            
array([[27, 30, 33],
       [36, 39, 42],
       [45, 48, 51]])

#axis = 1    
for i in range(0, x.shape[0]):
    for k in range(0, x.shape[2]):
        print( "element = ", (i,k), " ", [ x[i,j,k] for j in range(0, x.shape[1]) ])

element =  (0, 0)   [0, 3, 6]      #sum is 9 
element =  (0, 1)   [1, 4, 7]
element =  (0, 2)   [2, 5, 8]
element =  (1, 0)   [9, 12, 15]
element =  (1, 1)   [10, 13, 16]
element =  (1, 2)   [11, 14, 17]
element =  (2, 0)   [18, 21, 24]
element =  (2, 1)   [19, 22, 25]
element =  (2, 2)   [20, 23, 26]

# for sum, axis is the first keyword, so we may omit it,

>>> x.sum(0), x.sum(1), x.sum(2)
(array([[27, 30, 33],
        [36, 39, 42],
        [45, 48, 51]]),
 array([[ 9, 12, 15],
        [36, 39, 42],
        [63, 66, 69]]),
 array([[ 3, 12, 21],
        [30, 39, 48],
        [57, 66, 75]]))