CODEWITHSUNDEEP
rggplot2graph
Blaszard
Blaszard

Reputation: 31985

Why is the power of a negative value omitted from my graph?

I would like to depict a graph that is the power of some values in a continuous way.

f <- function(x) {
  return (x^(1/3))
}  

ggplot(data.frame(x=seq(-5,5,length.out=10)), aes(x)) +
  stat_function(fun=f)

This only shows the values that are x > 0, though if I use online graph tool desmos it shows values of x < 0 too. In interactive sessions, -3^(1/3) returns -1.44225.

Why does R omit it and how can I depict the negative x values too?

enter image description here

Upvotes: 2

Views: 130

Answers (3)

Allan Cameron
Allan Cameron

Reputation: 174378

The fractional power of a negative number is a complex number. If you want to include these in your plot, you could show the imaginary and real components separately:

real_part <- function(x) {
  Re(complex(length(x), x, 0)^(1/3))
}

imaginary_part <- function(x) {
  Im(complex(length(x), x, 0)^(1/3))
}

We can plot with labels for clarity:

library(geomtextpath)
#> Loading required package: ggplot2

ggplot(data.frame(x = seq(-5, 5, length.out = 10)), aes(x)) +
  stat_function(fun = real_part, aes(label = "Real part"), geom = "textpath",
                hjust = 0.8, vjust = -0.2, size = 6) +
  stat_function(fun = imaginary_part, color = "red", linetype = 2, hjust = 0.2,
                aes(label = "Imaginary part"), geom = "textpath", vjust = -0.2,
                size = 6) +
  theme_minimal(base_size = 20)

enter image description here

Created on 2022-11-20 with reprex v2.0.2

Upvotes: 3

zephryl
zephryl

Reputation: 17204

As @JohnColeman explains, the results of your function are undefined for negative x. The reason -3^(1/3) seems to work in the console but not your functions is due to operator precedence. ^ has higher precedence in R than -, so your console input is evaluated as:

-(3^(1/3))
# -1.44225

But when you pass -3 to your function, it's evaluated as:

(-3)^(1/3)
# NaN

Upvotes: 3

John Coleman
John Coleman

Reputation: 52008

Exponential functions with a negative base are considered undefined over the set of real numbers. This is since e.g. (-2)^(m/n) is impossible if n is even and given any x there will be infinitely many fractions of that form which are arbitrarily close to x. If you want the cube root you can use

cuberoot <- function(x){sign(x)*abs(x)^(1/3)}

Upvotes: 3

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