Python equivalent to R poly() function?

Question

I\'m trying to understand how to replicate the poly() function in R using scikit-learn (or other module).

For example, let\'s say I have a vector in R:

a         


        

Answer 1

It turns out that you can replicate the result of R's poly(x,p) function by performing a QR decomposition of a matrix whose columns are the powers of the input vector x from the 0th power (all ones) up to the pth power. The Q matrix, minus the first constant column, gives you the result you want.

So, the following should work:

import numpy as np

def poly(x, p):
    x = np.array(x)
    X = np.transpose(np.vstack((x**k for k in range(p+1))))
    return np.linalg.qr(X)[0][:,1:]

In particular:

In [29]: poly([1,2,3,4,5,6,7,8,9,10], 3)
Out[29]: 
array([[-0.49543369,  0.52223297,  0.45342519],
       [-0.38533732,  0.17407766, -0.15114173],
       [-0.27524094, -0.08703883, -0.37785433],
       [-0.16514456, -0.26111648, -0.33467098],
       [-0.05504819, -0.34815531, -0.12955006],
       [ 0.05504819, -0.34815531,  0.12955006],
       [ 0.16514456, -0.26111648,  0.33467098],
       [ 0.27524094, -0.08703883,  0.37785433],
       [ 0.38533732,  0.17407766,  0.15114173],
       [ 0.49543369,  0.52223297, -0.45342519]])

In [30]: 

Answer 2

The answer by K. A. Buhr is full and complete.

The R poly function also calculates interactions of different degrees of the members. That's why I was looking for the R poly equivalent.
sklearn.preprocessing.PolynomialFeatures Seems to provide such, you can do the np.linalg.qr(X)[0][:,1:] step after to get the orthogonal matrix.

Something like this:

import numpy as np
import pprint
import sklearn.preprocessing
PP = pprint.PrettyPrinter(indent=4)

MATRIX = np.array([[ 4,  2],[ 2,  3],[ 7,  4]])
poly = sklearn.preprocessing.PolynomialFeatures(2)
PP.pprint(MATRIX)
X = poly.fit_transform(MATRIX)
PP.pprint(X)

Results in:

array([[4, 2],
       [2, 3],
       [7, 4]])
array([[ 1.,  4.,  2., 16.,  8.,  4.],
       [ 1.,  2.,  3.,  4.,  6.,  9.],
       [ 1.,  7.,  4., 49., 28., 16.]])