How to raise every element of a vector to the power of every element of another vector?

Question

I would like to raise a vector by ascending powers form 0 to 5:

import numpy as np

a = np.array([1, 2, 3]) # list of 11 components
b = np.array([0, 1, 2, 3, 4]) # power
c = np.power(a,b)

desired results are:

c = [[1**0, 1**1, 1**2, 1**3, 1**4], [2**0, 2**1, ...], ...]

I keep getting this error:

ValueError: operands could not be broadcast together with shapes (3,) (5,)

Answer 1

One solution will be to add a new dimension to your array a

c = a[:,None]**b

# Using broadcasting : 
# (3,1)**(4,) --> (3,4)
#
#     [[1],
# c =  [2], ** [0,1,2,3,4]
#      [3]]

For more information check the numpy broadcasting documentation

Answer 2

Here's a solution:

num_of_powers = 5
num_of_components = 11

a = []
for i in range(1,num_of_components + 1):
    a.append(np.repeat(i,num_of_powers))
b = list(range(num_of_powers))
c = np.power(a,b)

The output c would look like:

array([[    1,     1,     1,     1,     1],
       [    1,     2,     4,     8,    16],
       [    1,     3,     9,    27,    81],
       [    1,     4,    16,    64,   256],
       [    1,     5,    25,   125,   625],
       [    1,     6,    36,   216,  1296],
       [    1,     7,    49,   343,  2401],
       [    1,     8,    64,   512,  4096],
       [    1,     9,    81,   729,  6561],
       [    1,    10,   100,  1000, 10000],
       [    1,    11,   121,  1331, 14641]], dtype=int32)

Your solution shows a broadcast error because as per the documentation:

If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output).

Answer 3

c = [[x**y for y in b] for x in a]