How to create a 2D Numpy array using a function on a 1D array?

Question

I'm trying to write a function in Python using Numpy that would take as input a vector x = array([x_1, x_2, ..., x_n]) and a positive integer m and return an array of dimension n by m of the form (say n==3, m==4):

array([[ x_1,   x_1^2,   x_1^3,   x_1^4],
       [ x_2,   x_2^2,   x_2^3,   x_2^4],
       [ x_3,   x_3^2,   x_3^3,   x_3^4]])

So far I have

import numpy as np
def f(x, m):
    return x ** np.arange(1, m+1)

which works fine for n==1, but raises an exception for n > 1. I am trying to avoid using loops. Is there a nice way of making this in Numpy?
Thank you!

Paul Panzer · Accepted Answer · 2020-09-13 17:15:54Z

1

You can

Use np.vander

x = np.array([2.3,1.3,4.4])      
m = 4

np.vander(x,m+1,True)[:,1:]                                       
# array([[  2.3   ,   5.29  ,  12.167 ,  27.9841],
#        [  1.3   ,   1.69  ,   2.197 ,   2.8561],
#        [  4.4   ,  19.36  ,  85.184 , 374.8096]])

or

use np.power.outer

np.power.outer(x,np.arange(1,m+1))
#  same output

or

use np.logspace

np.logspace(1,m,m,True,x[:,None])
# same output

or

use np.multply.accumulate or cumprod

np.multiply.accumulate(np.broadcast_to(x,(m,np.size(x))),axis=0).T
# same output

np.broadcast_to(x,(m,np.size(x))).cumprod(axis=0).T
# same output

answered Sep 13, 2020 at 17:15

Paul Panzer

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Comments

Marcel · Accepted Answer · 2020-09-13 16:41:53Z

You can use broadcasting for this:

def f(x, m):
    return x[:, np.newaxis] ** np.arange(1, m + 1)[np.newaxis, :]

This sets x as a shape (n, 1) vector, the range as a (1, m) vector, and has them interact in the way that you want.

Here's what it looks like in my IPython REPL.

In [1]: import numpy as np

In [2]: def f(x, m):
   ...:     return x[:, np.newaxis] ** np.arange(1, m + 1)[np.newaxis, :]
   ...: 

In [3]: x = np.array([1,2,3,4,5])

In [4]: f(x, 6)
Out[4]: 
array([[    1,     1,     1,     1,     1,     1],
       [    2,     4,     8,    16,    32,    64],
       [    3,     9,    27,    81,   243,   729],
       [    4,    16,    64,   256,  1024,  4096],
       [    5,    25,   125,   625,  3125, 15625]])

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