error in integrate : 'upper' must be of length one

Question

fl=function(q,a=-23.0344,b=10.0249) (b/q)*dnorm((a+b*log(q)),0,1)

Fl=function(h) integrate(fl,lower=0,upper=h)$value

Fz=function(z){
  integrand=function(x){
    Fl((x-z)*10)*fl(10*x)
  }
  1-10*integrate(integrand,0,Inf)$value
}
library(GoFKernel)
inv=inverse(Fz,lower=-100000,upper=100000)

why do i get this error? "Error in integrate(fl, lower = 0, upper = h) : 'upper' must be of length one"

how can i solve it?

Answer 1

As suggested in the comments, when you run integrate(), it tries to evaluate the integrand for a vector of values.

> traceback()
9: stop(simpleError(msg, call = if (p <- sys.parent(1L)) sys.call(p)))
8: stopifnot(length(lower) == 1, length(upper) == 1)
7: integrate(fl, lower = 0, upper = h) at #1
6: Fl((x - z) * 10) at #3
5: f(x, ...)
4: (function (x) 
   f(x, ...))(c(1, 233.065168689948, 0.00429064542600244, 38.2988398013854, 
   0.0261104515224461, 13.7999516465199, 0.072464022020844, 6.73787740945863, 
   0.148414691931943, 3.83193602946711, 0.260964690514175, 2.36612585866545, 
   0.422631787036055, 1.52456705113438, 0.655923922306948))
3: integrate(integrand, 0, Inf) at #5
2: f(lower)
1: inverse(Fz, lower = -1e+05, upper = 1e+05)

I tried vectorizing the Fl function (there are a variety of ways of doing this: Vectorize, Map, purrr::map, vapply(), ... but I used a good old-fashioned for loop)

Fl <- function(h) {
   res <- numeric(length(h))
   for (i in seq_along(h)) {  
      res[i] <- integrate(fl,lower=0,upper=h[i])$value
   }
   res
}

Once this is fixed we hit.

Error in integrate(fl, lower = 0, upper = h[i]) : non-finite function value

We also get a warning that log(q) is being called for negative values of q, which will produce an NaN which will mess everything up downstream.

We can set options(error = browser), but I had trouble with that. Instead, I set up a checkpoint if negative values of q are used (which will inevitably lead to trouble):

fl=function(q,a=-23.0344,b=10.0249) {
   if (any(q <= 0)) browser()
   (b/q)*dnorm((a+b*log(q)),0,1)
}

When I get thrown in the browser I try:

print(q)
 [1] -499995.000  -13046.605 -986943.395  -67467.642 -932522.358 -160293.613
 [7] -839696.387 -283299.470 -716690.530 -425558.575 -574431.425   -2171.397
[13] -997818.603  -34920.905 -965069.095 -109590.041 -890399.959 -218619.246
[19] -781370.754 -352800.041 -647189.959

So you'll have to think about what you're doing (TBH I haven't tried to figure out the logic of your code) and whether you're inadvertently evaluating expressions over negative ranges when they're not allowed.