We can sum across different axes of a NumPy array by specifying the axis parameter of the sum function.
Y = np.arange(24).reshape(2,3,4)
print(Y)
Output will be
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] ] ] )
axis=0
axis = 0 means first dimension.
The first dimension in array Y (i.e. the outermost bracket '[') has two matrices i.e.
[ [ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11] ]
and
[ [ 12, 13, 14 15],
[ 16, 17, 18, 19],
[ 20, 21, 22, 23] ]
Hence, sum across the first dimension (axis=0) means the sum of these two matrices (element-wise) which will give us a single matrix in the final matrix, as shown below.
Y.sum(axis=0)
The output will be
array( [ [ 12, 14, 16, 18 ],
[ 20, 22, 24, 26 ],
[ 28, 30, 32, 34 ] ] )
This is calculated as
[ [ 12+0, 13+1, 14+2, 15+3 ],
[ 16+4, 17+5, 18+6, 19+7 ],
[ 20+8, 21+9, 22+10, 23+11 ] ]
axis=1
axis = 1 means the second dimension.
The second dimension in array Y (i.e. the second bracket '[' from the outer side) is the rows. The rows are
row 0:
[ 0, 1, 2, 3]
[ 4, 5, 6, 7]
[ 8, 9, 10, 11]
row 1:
[ 12, 13, 14, 15]
[ 16, 17, 18, 19]
[ 20, 21, 22, 23]
Hence, sum across the second dimension (axis=1) means the sum of the (along the) rows of the two matrices (element-wise) which will give us a single matrix in the final matrix, as shown below.
Y.sum(axis=1)
The output will be
array( [ [12, 15, 18, 21],
[48, 51, 54, 57] ] )
This is calculated as
array( [ [0+4+8, 1+5+9, 2+6+10, 3+7+11],
[12+16+20, 13+17+21, 14+18+22, 15+19+23] ] )
axis=2
axis = 2 means the third dimension.
The third dimension in array Y (i.e. the third bracket '[' from the outer side) is the columns.
print(Y)
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] ] ] )
The columns are
[ 0,
4,
8 ]
[ 1,
5,
9 ]
[ 2,
6,
10 ]
[ 3,
7,
11 ]
[ 12,
16,
20 ]
[ 13,
17,
21 ]
[ 14,
18,
22 ]
[ 15,
19,
23 ]
Hence, sum across third dimension (axis=2) means the sum of the (along with the) columns of the two matrices (element-wise) which will give us a single matrix in the final matrix, as shown below.
Y.sum(axis=2)
The output will be
array( [ [ 6, 22, 38],
[54, 70, 86] ] )
This is calculated as
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] ] )
Please follow the following steps:
(1) Please import the required libraries
import numpy as np
(2) Please create a NumPy array called Z, with a total of 18 elements, and shape as (2, 3, 3)
<<your code comes here>> = np.arange(<<your code comes here>>).reshape(<<your code comes here>>)
(3) Print the above array Z using the print() function to see its values.
print(Z)
(4) Please find the sum across axis=2 for the array Z, and print the result using the print() function
print( Z.sum(<<your code comes here>>))
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