NumPy broadcasting

1. Add 1 to every element of the array by broadcasting. Note that changes to the array are not saved:

array_1 + 1
array([[ 1,  2],
       [ 3,  4],
       [ 5,  6],
       [ 7,  8],
       [ 9, 10]])

The term broadcasting refers to the smaller array being stretched or broadcast across the larger array. In the first example, the scalar 1 was stretched to a 5 x 2 shape and then added to array_1.

1. Create a new array_2 array. Observe what occurs when you multiply the array by itself (this is not matrix multiplication; it is element-wise multiplication of arrays):

array_2 = np.arange(10)
array_2 * array_2
array([ 0,  1,  4,  9, 16, 25, 36, 49, 64, 81])

1. Every element has been squared. Here, element-wise multiplication has occurred. Here is a more complicated example:

array_2 = array_2 ** 2  #Note that this is equivalent to array_2 * array_2
array_2 = array_2.reshape((5,2))
array_2
array([[ 0,  1],
       [ 4,  9],
       [16, 25],
       [36, 49],
       [64, 81]])

1. Change array_1 as well:

array_1 = array_1 + 1
array_1
array([[ 1,  2],
       [ 3,  4],
       [ 5,  6],
       [ 7,  8],
       [ 9, 10]])

1. Now add array_1 and array_2 element-wise by simply placing a plus sign between the arrays:

array_1 + array_2
array([[ 1,  3],
       [ 7, 13],
       [21, 31],
       [43, 57],
       [73, 91]])

1. The formal broadcasting rules require that whenever you are comparing the shapes of both arrays from right to left, all the numbers have to either match or be one. The shapes 5 X 2 and 5 X 2 match for both entries from right to left. However, the shape 5 X 2 X 1 does not match 5 X 2, as the second values from the right, 2 and 5 respectively, are mismatched: