I have a vector and want to raise a number to the power of the vector's elements without using a loop. Is there an easy way to do that?
I tried a^b where a is a number and b is a vector but that doesn't seem to work for me.
The exponentiation operation must be carefully performed in R, since a negative base can give wrong results.
Wrong
power <- function(x, y) x^y
power(2, 3)
#[1] 8
power(2, -3)
#[1] 0.125
power(1, 1/3)
#[1] 1
power(-1, 1/3)
#[1] NaN
Right
power <- function(x, y) sign(x) * abs(x)^y
power(2, 3)
#[1] 8
power(2, -3)
#[1] 0.125
power(1, 1/3)
#[1] 1
power(-1, 1/3)
#[1] -1
Now see if this second power function is vectorized, like the question asks for.
power(2, c(1:4, pi, -pi, -1/3, 1/3))
#[1] 2.0000000 4.0000000 8.0000000 16.0000000 8.8249778 0.1133147
#[7] 0.7937005 1.2599210
outer(c(-2, 2), c(1:4, pi, -pi, -1/3, 1/3), power)
# [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#[1,] -2 -4 -8 -16 -8.824978 -0.1133147 -0.7937005 -1.259921
#[2,] 2 4 8 16 8.824978 0.1133147 0.7937005 1.259921