How can you use ggplot to superimpose many plots of related functions in an automatic way? - r

Question

I have a family of functions that are all the same except for one adjustable parameter, and I want to plot all these functions on one set of axes all superimposed on one another. For instance, this could be sin(n*x), with various values of n, say 1:30, and I don't want to have to type out each command individually -- I figure there should be some way to do it programatically.
library(ggplot2)
define trig functions as a function of frequency: sin(x), sin(2x), sin(3x) etc.
trigf <- function(i)(function(x)(sin(i*x)))
Superimpose two function plots -- this works manually of course
ggplot(data.frame(x=c(0,pi)), aes(x)) + stat_function(fun=trigf(1)) + stat_function(fun=trigf(2))
now try to generalize -- my idea was to make a list of the stat_functions using lapply
plotTrigf <- lapply(1:5, function(i)(stat_function(fun=function(x)(sin(i*x))) ))
try using the elements of the list manually but it doesn't really work -- only the i=5 plot is shown and I'm not sure why when that's not what I referenced
ggplot(data.frame(x=c(0,pi)), aes(x)) +plotTrigf[[1]] + plotTrigf[[2]]
I Thought this Reduce might handle the 'generalized sum' to add to a ggplot() but it doesn't work -- it complains of a non-numeric argument to binary operator
Reduce("+", plotTrigf)
So I'm kind of stuck both in executing this strategy, or perhaps there's some other way to do this.

Answer 1

Are you using version R <3.2? The problem is that you actually need to evaluate your i parameter in your lapply call. Right now it's being left as a promise and not getting evaulated till you try to plot and at that point i has the last value it had in the lapply loop which is 5. Use:
plotTrigf <- lapply(1:5, function(i) {force(i);stat_function(fun=function(x)(sin(i*x))) })
You can't just add stat_function calls together, even without Reduce() you get the error
stat_function(fun=sin) + stat_function(fun=cos)
# Error in stat_function(fun = sin) + stat_function(fun = cos) :
# non-numeric argument to binary operator
You need to add them to a ggplot object. You can do this with Reduce() if you just specify the init= parameter
Reduce("+", plotTrigf, ggplot(data.frame(x=c(0,pi)), aes(x)))
And actually the special + operator for ggplot objects allows you to add a list of objects so you don't even need the Reduce at all (see code for ggplot2:::add_ggplot)
ggplot(data.frame(x=c(0,pi)), aes(x)) + plotTrigf
The final result is

Answer 2

You need to use force in order to make sure the parameter is being evaluated at the right time. It's a very useful technique and a common source of confusion in loops, you should read about it in Hadley's book http://adv-r.had.co.nz/Functions.html
To solve your question: you just need to add force(i) when defining all the plots, inside the lapply function, before making the call to stat_function. Then you can use Reduce or any other method to combine them. Here's a way to combine the plots using lapply (note that I'm using the <<- operator which is discouraged)
p <- ggplot(data.frame(x=c(0,pi)), aes(x))
lapply(plotTrigf, function(x) {
p <<- p + x
return()
})