Question

I’m working on Polynomial Transform for a homework assignment. I’m using a document from vanderbilt.edu as my starting point. Polynomial Transform

I have a set of points:

square_points = (
    # x, y
    (37, 44 ),  # x1,y1
    (67, 74 ),  # x2,y2
    (97,104 ),  # x3,y3
    (247,194),  # x4,y4
    (157, 97),  # x5,y5
)

that I’d like to turn into a Numpy array, rows as the polynomials:

[[1, x1, y1, x1*y1],
 [1, x2, y2, x2*y2],
 [1, x3, y3, x3*y3],
 [1, x4, y4, x4*y4],
 [1, x5, y5, x5*y5]]

I’m still learning Numpy. I’d like to learn a clean way to build such an array from my list of points. (As opposed to building the array from hardcoded square_points[0][1], etc.)

So far I have:

P = np.ones((5,5))
P[:,1] = [ n[0] for n in square_points ]
P[:,2] = [ n[1] for n in square_points ]
P[:,3] = [ n[0]*n[1] for n in square_points ]

which seems a bit cumbersome. Is there a cleaner, more Numpy-y way to create such an array?

Answer 1

Sure! Just do what you’re already doing, but leave out the list comprehension…

E.g.

import numpy as np
square_points = np.array([
    [37,  44],  # x1,y1
    [67,  74],  # x2,y2
    [97,  104], # x3,y3
    [247, 194], # x4,y4
    [157, 97],  # x5,y5
    ])
x, y = square_points.T

P = np.ones((5,4))
P[:,1] = x
P[:,2] = y
P[:,3] = x * y

Or if you’d prefer, you can even do it in one line:

P[:,1:] = np.array([x, y, x*y]).T