Feature Engineering - How to transform a dataset

Question

I have a dataset that contains an array of points with coordinates X,Y. I'd like to transform the dataset to another containing the following:

• Radius: From the point to the center of a circle. Circle with coordinates (0,0)
• Angle: Compute the angle of the point relative to the vector (1,0)

I have tried to apply the polar transformations but I'm struggling to get the results when coding. Please, see below the dataset and what it contains:

Dataset

data_circles = ('circles', *datasets.make_circles(n_samples=1000, factor=.5, noise=.05))

When accessing to the array of points we can see the following

 data_circles[1]

List of points

array([[-0.1824838 , -0.90538815],
       [-0.50596281, -0.29994453],
       [-0.40857322, -0.29386417],
       ...,
       [ 0.98727003, -0.4073737 ],
       [-0.74624763, -0.653247  ],
       [ 0.31444572,  0.3814041 ]])

I´ve achieved to compute the radius and angle but I´m struggling to apply it for the whole dataset. Please, see below:

import math
v = np.array(data_circles[1])
x = v[0][0]
y = v[0][1]
#Radius
r = math.sqrt(x ** 2 + y ** 2)
#Angle
phi = np.arctan(y/x)