在r中的函数中遍历参数时使用Apply系列函数

Question

How can I loop over arguments in a functions using one of the apply type function to make code faster in R? For example, I have created a function to compute the joint mutual information of three random variables

### Function to loop over: Joint Mutual Information I({x_1,x_2};y)
library(infotheo)
JMI <-function(x1,x2,y){
      entropy(cbind(x1,x2),method="emp") + entropy(y, method="emp") - 
      entropy(cbind(x1,x2,y),method="emp")
   } 

Suppose I have two matricies (x1, x2) and one vector y like:

#### randomly generate binary variables from a bernoulli distribution
set.seed(12345)
f1 <- rbinom(n=300,size=1,prob=0.5)
f2 <- rbinom(n=300,size=1,prob=0.5)
f3 <- rbinom(n=300,size=1,prob=0.5)

## creat y using xor operation of the two feature: x1 XOR x2
#  this mean that y is 1 if f1[i]!=f2[i] and 0 otherwise
y <- ifelse(f1==f2,0,1)
x1 <-cbind(f1,f2)
x2 <- cbind(x1,f3)

Now, I want to loop over x1 and x2 in the JMI function. Using for-loops this looks like this:

# a length(x1) x length(x2)-Matrix with zeros
jmi <- matrix(rep(0,ncol(x2)*ncol(x1)),
          nrow=ncol(x1),ncol=ncol(x2))
#### For loops to be avoided
for(i in 1:ncol(x1)){
  for(j in 1:ncol(x2)){
    jmi[i,j] <- JMI(x1[,i],x2[,j],y)
  }#end out for(j)
}#end inner for(i)

Is there an easy way to avoid both for-loops?

Answer 1

This is a solution using apply:

g <- expand.grid(1:ncol(x1), 1:ncol(x2))
v <- apply(g, 1, function(i) JMI(x1[, i[1]], x2[, i[2]], y))
jmi <- matrix(v, nrow = ncol(x1))
jmi
##             [,1]        [,2]       [,3]
## [1,] 0.003809514 0.693147181 0.01082319
## [2,] 0.693147181 0.006485284 0.01152807

It proceeds in three steps:

• The indices for the columns of the matrices x1 and x2 are created using expand.grid . This creates a data frame g with two columns that contain all combinations of i and j that your for loop goes through.
• Then apply is used to go through all the rows of g and apply JMI to the corresponding columns of x1 and x2 . This results in a vector v .
• Finaly, v is converted to a matrix.