I am doing some basic maths. I was to frustrate of Roger Bivand explaining stuff that I could not understand with my maths background (science background but loooong time ago!). I find a nice free book and practice with it. A lot can be done with pen + paper but sometimes you need to represent an equation in a Cartesian plane.
R is perfect for that (even if it is not a Computer algebra system) but I am always forgetting some specific ways to do it!
First we do a simple function:
\[y = \sqrt[3](1 - x^2)\]
simple_function <- function(x){
temp = (1 - x*x)
# R is using natural log so you need to adjust a bit, ie if you use negative
# value you will get NaN :
# kind of same idea of doing cube_root(-1) * cube_root(abs(x))
sign(temp)*abs(temp)**(1/3)
}
simple_function(-5:5) [1] -2.884499 -2.466212 -2.000000 -1.442250 0.000000 1.000000 0.000000
[8] -1.442250 -2.000000 -2.466212 -2.884499Then you have (as far as I know) 3 options!
Here this is simple we generate a sequence of values and apply our function on it.
x <- -5:5
y <- simple_function(x)
plot(x, y, type = "b", col = 2)
# if you prefer it can also go in data frame because both vectors have the same length
#df <- data.frame(x = x,
# y = simple_function(x))This is good but if you pay attention you can see that using type = "b" we are basically plotting the point and connecting them with a straight line. What happens if this is not a straight line:
x <- seq(from = -5, to = 5, by = .1)
y <- simple_function(x)
plot(x , y, type = "b", col = 2)
This is a bit better!
The base-R packagegraphics provide us with a lot of very cool functions and one of it is curve(). It can take a function or an expression.
curve(simple_function, from = -5, to = 5,
ylab = "y", col = 2) # some small tuning is still needed
Easy and simple.
Obviously, we can also do it with ggplot::stat_function():
library(ggplot2)
# I was lazy and just reused x
ggplot(data.frame(x), aes(x = x)) +
stat_function(fun = simple_function, colour = 2) +
theme_bw()