Broadcasting operations¶

General principle¶

If you have an $(m, n)$ matrix $A$ and apply operations like sub(-), add(+), mul(*) or div(/) by a vector $v$ the shape of $v$ will be grow vertically or horizontally like:

$(1,n)$ -> $(m,n)$

$(m,1)$ -> $(m,n)$

Examples¶

First

$v = [1,2,3,4], x = 100$

$v + x =$ vector + escalar

Python turns the 100 into a vector with the same shape of $v$ , like:

$v = [1,2,3,4] + [100, 100, 100, 100]$

$v = [101, 102, 103, 104]$

Second

$v_1 = [[1,2,3],[4,5,6]]$ + $v_2 = [100, 200, 300]$

$v_2$ will become like: $[[100, 200, 300], [100, 200, 300]]$

Third

$v_1 = [[1,2,3],[4,5,6]]$ + $v2 = [[100],[200]]$

$v_2$ will become like: $[[100, 100, 100], [200, 200, 200]]$

In practice¶

In [2]:

import numpy as np;

In [43]:

A = np.array(
    [[56.0, 0.0, 4.4, 68.0],
    [1.2, 104.0, 52.0, 8.0],
    [1.8, 135.0, 99.0, 0.9]]
)
print(A)

[[ 56.    0.    4.4  68. ]
 [  1.2 104.   52.    8. ]
 [  1.8 135.   99.    0.9]]

In [45]:

sum = A.sum(axis = 0)
sum

Out[45]:

array([ 59. , 239. , 155.4,  76.9])

In [47]:

A/sum

Out[47]:

array([[0.94915254, 0.        , 0.02831403, 0.88426528],
       [0.02033898, 0.43514644, 0.33462033, 0.10403121],
       [0.03050847, 0.56485356, 0.63706564, 0.01170351]])