Warning message reassigning values to integrals in R?

Question

I'm very new to R, but I'm just looking to do a simple conditional reassignment to elements in a vector Y. However, I keep getting warning messages when the reassignments are dealing with integrals. Here is the complete code:

> rm(list=ls())
> Y <- c()
> for (k in 1:20) {
+   Y[k] <- k
+ }
> for (k in 1:20) {
+   if (Y[k] < 12) {
+     Y[k] <- cos(3 * k)
+   } else {
+     Y[k] <- integrate(function(t) sqrt(t), lower = 0, upper = k)
+   }
+ }

One of the warning messages:

Warning messages:
1: In Y[k] <- integrate(function(t) sqrt(t), lower = 0, upper = k) :

number of items to replace is not a multiple of replacement length

And the returned Y: [[1]] [1] -0.9899925

[[2]]
[1] 0.9601703

[[3]]
[1] -0.9111303

[[4]]
[1] 0.843854

[[5]]
[1] -0.7596879

[[6]]
[1] 0.6603167

[[7]]
[1] -0.5477293

[[8]]
[1] 0.424179

[[9]]
[1] -0.2921388

[[10]]
[1] 0.1542514

[[11]]
[1] -0.01327675

[[12]]
[1] 27.71282

[[13]]
[1] 31.24811

[[14]]
[1] 34.92214

[[15]]
[1] 38.72984

[[16]]
[1] 42.66667

[[17]]
[1] 46.72854

[[18]]
[1] 50.91169

[[19]]
[1] 55.21273

[[20]]
[1] 59.62849

Additionally, I'm a bit curious about why the output is broken up with two numbers for each element as well. Normally I'm used to vector output looking like this:

 [1]  2  4  6  8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38
[20] 40

So any clarification about what I did wrong is highly appreciated.

Answer 1

Let me just show you how you can shorten your code:

Y <- numeric(20)
Y[1:12] <- cos(3 * (1:12))
Y[13:20] <- sapply(13:20, function (u) integrate(sqrt, lower = 0, upper = u)$value )

Answer 2

The result of:

integrate(function(t) sqrt(t), lower = 0, upper = k)

is a list.

you need to grab the first element of each list entry with [[1]] prior to inserting into the Y vector:

Y <- c()
#for (k in 1:20) { # This loop is unnecessary
#     Y[k] <- k    # as it will be overwritten
#}                 # with cos(3 * k) subsequently
for (k in 1:20) {
     if (Y[k] < 12) {
         Y[k] <- cos(3 * k)
     } else {
         Y[k] <- integrate(function(t) sqrt(t), lower = 0, upper = k)[[1]]
     }
}