[R] Integrate functions with loops

[Sundar Dorai-Raj]

A.Brennan wrote:
> Hi
> 
> i am having a problem with the 'integrate' function
> the function i want to integrate has the form
> sum(vector^x)
> 
> i have defined the function with a for loop first - 
> integrandtotest <- function(x)
>     {a<-rep(0,len=2)
>     for (i in 1:2)
>         {a[i]<-t[i]^x}
>         sum(a)
>         }
> 
> the results gives errors
> ###########
> Error in integrate(integrandtotest, lower = 0.1, upper = 2, 
> subdivisions = 10000) : 
>         evaluation of function gave a result of wrong length
> In addition: Warning messages:
> 1: number of items to replace is not a multiple of replacement 
> length 
> 2: number of items to replace is not a multiple of replacement 
> length 
> #######
> 
> I then tried a vector multiplication instead of the for loop
> 
> 
> integrandtotest3 <- function(x)
>     {b<-c(t[1],t[2])
>     a<-b^x
>     sum(a)
>         }
> 
> which gave errors
> ########
> Error in integrate(integrandtotest3, lower = 0.1, upper = 2, 
> subdivisions = 10000) : 
>         evaluation of function gave a result of wrong length
> In addition: Warning message:
> longer object length
>         is not a multiple of shorter object length in: b^x 
> ##########
> 
> but when i write the functio out long-hand as follows:
> 
> integrandtotest2 <- function(x)
>     {t[1]^x+t[2]^x}
> 
> the integrate function works perfectly.......
> ###
> 
>>integralresulttotest2<-integrate(integrandtotest2, lower=0.1, 
> 
> upper=2, subdivisions=10000)
> 
>>integralresulttotest2
> 
> 1.642369 with absolute error < 1.8e-14
> ###
> 
> Unfortunatley my real life example has the vector a with length at 
> least 100.
> 
> Is the any way round these errors?
> 
> Many thanks for answers to my first question to this list
> yours
> Alan
> 

Hi, Alan,

It might help if you print(x) in your integrate function.

integrandtotest <- function(x) {
   print(x)
   a <- rep(0, len=2)
   for(i in 1:2) {
     a[i] <- tt[i]^x
   }
   sum(a)
}

integrate(integrandtotest, lower = 0.1, upper = 2)

You will see that "x" is a vector and "tt[i]^x" returns a vector of the 
same length. You are trying to place this vector into "a[i]" which is 
length 1. Try the following *untested* code instead:

<untested>
integrandtotest <- function(x) {
   sum(sapply(x, function(xi) sum(tt^xi)))
}

integrate(integrandtotest, lower = 0.1, upper = 2)
</untested>

Also, I would avoid using "t" as a variable name. "t" is also a 
function. Most of the time R can tell the difference, but sometimes it 
cannot.

HTH,

--sundar