Back solving a function or goal seek in R

Question

I'm trying to learn my way around R and I need a little help. Below is a little sample of the kind of problem I am working on.

myFunction <- function(price1) {
  prices <- c(1:50)
  prices[1] <- price1
  recursiveA <- vector(length = 51)
  recursiveA[1] <- 100
  for (i in 1:50) {
    recursiveA[i+1] <- 30*prices[i] + recursiveA[i]
  }
  target <- recursiveA[51]
  return(target)
}

What I want to do is create a new function that will find the price1 value needed to yield a target value. For example in this new function I would be able to set 47320 as a parameter and it would return 300. In the first function, myFunction, a value of 300 returns a value of 47320.

How can I write a function in R to do this? Is there an existing function in R? I see through my Googling and searching on this site, a lot of people recommend the uniroot() function or optimize(). I can't figure out how to use that for something other than algebraic quadratics.

If it helps, I know that in excel I can solve this easily by using the goal seek tool. You can set a desired output and it finds the needed input from the formula(s) you define.

Please let me know if anything's unclear and I will try my best to explain further.

Any help is much appreciated. Thank you.

Answer 1

You don't actually need a recursive function here.

Here's a vectorised approach:

f <- function(x) tail(cumsum(c(100, 30*c(x, 2:50))), 1)
f(123)
# 42010

And to reverse the operation:

anti_f <- function(x) (x - 30*50*51/2 + 30 - 100)/30
anti_f(42010)
# 123

Of course, this is less helpful when you actually do need to recurse. My point is just that you should look for opportunities to vectorise when possible.

---

If you want to do this with optimize, you can do:

f <- function(x) abs(myFunction(x) - 42010) 
optimize(f, lower=-1000, upper=1000)

# $minimum
# [1] 123
# 
# $objective
# [1] 2.512278e-05

R will search [-1000, 1000] in an attempt to find a value, x, that minimises the absolute value of myFunction(x) - 42010. In this case, it finds 123, for which myFunction(123) returns 42010 and so abs(myFunction(x) - 42010) returns 0.

If you want to wrap this in a function, you can do:

unfunction <- function(x, lower, upper) {
  optimize(function(y) abs(myFunction(y) - x), lower=lower, upper=upper)
}

unfunction(42010, -1000, 1000)

# $minimum
# [1] 123
# 
# $objective
# [1] 2.512278e-05

unfunction(47320, -1000, 1000)

# $minimum
# [1] 300
# 
# $objective
# [1] 0.0002383182

In our function unfunction, lower and upper specify the space to be searched.