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Construct an inverse regression via sapply and uniroot

I've a function as follows:

V <- seq(50, 350, by = 1)
> VK
    Voltage^0     Voltage^1     Voltage^2     Voltage^3 
-1.014021e+01  9.319875e-02 -2.738749e-04  2.923875e-07 
> plot(x = V, exp(exp(sapply(0:3, function(x) V^x) %*% VK)), type = "l"); grid()

Now I would like to do an inverse regression upon this certain function. I've seen Solving for the inverse of a function in R :

inverse = function (f, lower = -100, upper = 100) { function (y) uniroot((function (x) f(x) - y), lower = lower, upper = upper)1 }

square_inverse = inverse(function (x) x^2, 0.1, 100)

square_inverse(4)

and I'm trying to adjust it to my purposes as follows:

certain_function <- function(x=V) { exp(exp(sapply(0:3, function(x) V^x) %*% VK)) }

inverse = function (f, lower = 50, upper = 350) {
  function (y) uniroot((function (x) f(x) - y), lower = lower, upper = upper)[1]
}

inverse_regression = inverse(certain_function, 50, 350)

inverse_regression(2)

Unfortunately this yields: 

 Error in uniroot((function(x) f(x) - y), lower = lower, upper = upper) : 
  f() values at end points not of opposite sign In addition: Warning messages:
1: In if (is.na(f.lower)) stop("f.lower = f(lower) is NA") :
  the condition has length > 1 and only the first element will be used
2: In if (is.na(f.upper)) stop("f.upper = f(upper) is NA") :
  the condition has length > 1 and only the first element will be used

As far as I understood: The error means that there are more roots than only one (uniroot can only handle one root) but there shouldn't be more than one root since it's a strictly monotonically increasing function. The warnings I do not understand..

edit: I'm trying to get behind it.. I removed both exponentials which yields the following plot:

enter image description here

and this still generates the following error:

> inverse_regression(0.1)

 Error in uniroot((function(x) f(x) - y), lower = lower, upper = upper) : 
  f() values at end points not of opposite sign In addition: Warning messages:
1: In if (is.na(f.lower)) stop("f.lower = f(lower) is NA") :
  the condition has length > 1 and only the first element will be used
2: In if (is.na(f.upper)) stop("f.upper = f(upper) is NA") :
  the condition has length > 1 and only the first element will be used

Why is this? Obviously the curve has opposite signs at both end points.. I guess end points mean the points left and right to the root?

Solution

  • Probably the inverse regression did not work due to the definition of "certain_function". This is a matrix-vector product and the result is a vector again. Therefore I transformed this to a regular function function(x) exp(exp(sum(x^0*VK[1],x^1*VK[2],x^2*VK[3],x^3*VK[4])) and now it is working. Hence, one should be aware of the bounds each time in general.