Calculating the norm

We can review the basic concepts illustrated in this section by calculating the norm of a set of coordinates. For a two-dimensional vector, the norm is defined as follows:

    norm = sqrt(x**2 + y**2) 

Given an array of 10 coordinates (x, y), we want to find the norm of each coordinate. We can calculate the norm by taking these steps:

1. Square the coordinates, obtaining an array that contains (x**2, y**2) elements.
2. Sum those with numpy.sum over the last axis.
3. Take the square root, element-wise, with numpy.sqrt.

The final expression can be compressed in a single line:

    r_i = np.random.rand(10, 2) 
    norm = np.sqrt((r_i ** 2).sum(axis=1)) 
    print(norm)
    # Output:
    # [ 0.7314  0.9050  0.5063  0.2553  0.0778   0.9143   1.3245  
    0.9486  1.010   1.0212]