## Vectorize!

**H**ere is an email sent by one of my students a few days ago:

Do you know how to integrate a function with an “if”?

For instance:

>X=rnorm(100)

>Femp=function(x){

+ return(sum(X<x))

+}

>integrate(Femp,0,1)$valuedoes not work.

My reply was that the fundamental reason it does not work is that integrate (or curve for instance) computes the function in several points of a grid by calling the function on a vector x and the comparison X<x does not make sense when both X and x are vectors. If one rewrites the code as

X=rnorm(100) Femp=function(x){ return((apply(as.matrix(outer(X,x,"-")<0),2,sum))}

the function can be integrated

> integrate(Femp,-2,2) 1.877735 with absolute error < 5.6e-05

However, this kind of syntactic gymnastic can be avoided by a simple call to Vectorize.

X=rnorm(100) Femp=function(x){ return(sum(X<x))} > integrate(Vectorize(Femp),-2,2) 1.877735 with absolute error < 5.6e-05

February 21, 2011 at 4:22 am

I used a lot apply, but I did not know that Vectorize function… It looks great ! thanks….

February 21, 2011 at 6:51 am

Obviously, it is time-consuming:

although a preliminary definition removes part of the time: