R: Error in Integration with Vector Function and Its Remedy

This post illustrates how to address an error arising from the integration of one of the results of a vector function in R. A straightforward remedy is to use Vectorize().

R Integration with a Single Element from a Vector Function

The Integration in R is simple and straightforward, as follows:

func1 <- function(x) {     return(x*x) }   integrate(func1,lower=5, upper=0)$value   # result ; works well > integrate(func1,lower=5, upper=0)$value [1] -41.66667   Colored by Color Scripter

cs

I used a vector function, which is also employed in another part of the code for computing function values. To eliminate redundancy, I employ this vector function even when integration is required.

However, I encountered an unexpected error when using a single entry of the vector function as an integrand, as shown below.

# vector function vec_func <- function(x) {     col1 <- x     col2 <- exp(-2*x)     ret <- cbind(col1, col2)     return(ret) }   wrapper_func <- function(x) {        # Reuse the vector function     B <- vec_func(x)          # the same result as the func1()     ret <- B[1]*B[1]     return(ret) }   integrate(wrapper_func,lower=5, upper=0)$value   > # does not work > integrate(wrapper_func,lower=5, upper=0)$value Error in integrate(wrapper_func, lower = 5, upper = 0) :  evaluation of function gave a result of wrong length   Colored by Color Scripter

cs

Google presented a solution to this error, suggesting the use of the Vectorize() function, as demonstrated below.

integrate(Vectorize(wrapper_func), lower=5, upper=0)$value   > # does work > integrate(Vectorize(wrapper_func), lower=5, upper=0)$value [1] -41.66667   Colored by Color Scripter

cs

I'm not entirely certain why this solution works. My suspicion is that vector operations affect the integration process. As long as the answer is correct exactly, I simply accept it as a rule within R since it is a technical issue.