将 1 xn 数组提升到 mx 1 数组中的所有幂到 Python 中的 mxn 数组

Question

Given 2 1d arrays of any length I wish to raise each value in the 'base' array to each power in the 'exponent' array to produce a 2d array/matrix.

a = [a0, a1, a2, ... , an]
b = [b0, b1, b2, ... , bm]

desired output:

[a0^b0, a1^b0, ... , an^b0 ; 
 a0^b1, a1^b1, ... , an^b1 ;
 ...
 a0^bm, a1^bm, ... , an^bm ]

I am coming from a Matlab background where this can very easily be done for a column and row vector:

a.^b

as described here: https://www.mathworks.com/help/matlab/ref/power.html#mw_0a0fb331-989a-442b-ba2c-ede92a343828

However in Python with numpy or scipy etc I cant find any easy way to do this. I have to assume there is a fairly optimized way to do this simply (with no list comprehension), given how intuitive and easy it is in Matlab.

Answer 1

In Python the symbol used to indicate exponentiation is ** , and numpy supports vectorized exponentiation of equal-length arrays just fine:

>>> a = np.array([1, 2, 3, 4, 5])
>>> b = np.array([5, 4, 3, 2, 1])
>>> a**b
array([ 1, 16, 27, 16,  5])

If you want your desired result however you must exponentiate a row vector with a column vector:

>>> a = np.array([[1, 2, 3, 4, 5]]) # Notice now a 2D array, a horizontal vector.
>>> b = np.array([[5, 4, 3, 2, 1]])
>>> a
array([[1, 2, 3, 4, 5]])
>>> b.T
array([[5],
       [4],
       [3],
       [2],
       [1]])
>>> a**b.T
array([[   1,   32,  243, 1024, 3125],
       [   1,   16,   81,  256,  625],
       [   1,    8,   27,   64,  125],
       [   1,    4,    9,   16,   25],
       [   1,    2,    3,    4,    5]])