vectorized operation in r, evaluating an integral depending on two parameters

Question

evaluating an integral depending on two parameters

A <- 0.0004
B <- 0.0013
c <- 1.0780

f1 <- function(x) {
    f2 <- function(s) {
        A + B * c^(x+s)
    }

    return(f2)
}

tpx <- function(t,x) {
    exp(-integrate(f1(x), lower=0, upper=t)$value)
}

i get

> tpx(1,1)
[1] 0.9981463

for the ordered pair (1,1). when using the colon operator

> tpx(1,1:2)
[1] 0.9980945
Warning messages:
1: In x + s :
  longer object length is not a multiple of shorter object length
2: In x + s :
  longer object length is not a multiple of shorter object length
3: In x + s :

some error messages occur. is it possible to adjust the integration variable s? what causes the output right before the warning messages? it is neither

> tpx(1,1)
[1] 0.9981463

nor

> tpx(1,2)
[1] 0.998033

i suppose i get something wrong :S

Answer 1

You can use the following

sapply(1:2, tpx, t = 1)

Why?

The error is caused because: integrate expects f to be (quote from ?integrate)

an R function taking a numeric first argument and returning a numeric vector of the same length. Returning a non-finite element will generate an error.

But

> s = 1
> A + B * c^(1:2+s)
[1] 0.001910709 0.002028545

is of length 2 whereas s is of length 1.
sapply supplies one elements at a time the f1 and combines the result afterwards. That's why it works.

Comment:

You can also simplify your f1, f2 and tpx function as follows:

f1 <- function(s, x, A, B, c){
  A + B * c^(x+s)
}

tpx <- function(x,t){
  exp(-integrate(f1, lower=0, upper=t, x, A, B, c)$value)
}

Again quoting from ?integrate

... - additional arguments to be passed to f.

Meaning that the parameter x, A, B, c will be passed to f1 and only the first argument will be used by the integration.

Answer 2

Just do tpx = Vectorize(tpx) much easier than apply functions