How does the curve function in R work? - Example of curve function

Question

How does the following code work? I got the example when I was reading the help line of R ?curve . But i have not understood this.

  for(ll in c("", "x", "y", "xy"))
     curve(log(1+x), 1, 100, log = ll,
        sub = paste("log= '", ll, "'", sep = ""))

Particularly , I am accustomed to numeric values as arguments inside the for-loop as,

  for(ll in 1:10)

But what is the following command saying:

  for(ll in c("","x","y","xy"))

c("","x","y","xy") looks like a string vector? How does c("","x","y","xy") work inside curve function as log(1+x) [what is x here? the string "x"? in c("","x","y","xy") ] and log=ll ?

Answer 1

Apparently, there are no answers on stack overflow about how the curve function in R works and especially about the log argument so this might be a good chance to delve into it a bit more (I liked the question btw):

First of all the easy part:

c("","x","y","xy") is a string vector or more formally a character vector.

for(ll in c("","x","y","xy")) will start a loop of 4 iterations and each time ll will be '','x','y','xy' respectively. Unfortunately, the way this example is built you will only see the last one plotted which is for ll = 'xy' .

Let's dive into the source code of the curve function to answer the rest:

• First of all the what does the x represent in log(1+x) ?

log(1+x) is a function. x represents a vector of numbers that gets created inside the curve function in the following part (from source code):

 x <- exp(seq.int(log(from), log(to), length.out = n)) #if the log argument is 'x' or
 x <- seq.int(from, to, length.out = n)               #if the log argument is not 'x' 
 #in  our case from and to are 1 and 100 respectively 

As long as the n argument is the default the x vector will contain 101 elements. Obviously the x in log(1+x) is totally different to the 'x' in the log argument.

as for y it is always created as (from source code):

 y <- eval(expr, envir = ll, enclos = parent.frame()) #where expr is in this case log(1+x), the others are not important to analyse now.
 #i.e. you get a y value for each x value on the x vector which was calculated just previously

• Second, what is the purpose of the log argument?

The log argument decides which of the x or y axis will be logged. The x-axis if 'x' is the log argument, y-axis if 'y' is the log argument, both axis if 'xy' is the log argument and no log-scale if the log argument is '' .

It needs to be mentioned here that the log of either x or y axis is being calculated in the plot function in the curve function, that is the curve function is only a wrapper for the plot function.

Having said the above this is why if the log argument is 'x' (see above) the exponential of the log values of the vector x are calculated so that they will return to the logged ones inside the plot function.

PS the source code for the curve function can be seen with typing graphics::curve on the console.

I hope this makes a bit of sense now!