Write a function using a for loop to execute the targeted operation. Also, write another function without using a loop. Let's take a look at the following steps and see how we can do the preceding two tasks:

1. Execute the following code snippet that depicts a function using a loop:

        loopOperation <- function(mat){
          out<-matrix(NA, nrow = ncol(mat), ncol = ncol(mat))
          for(i in 1:ncol(mat)){
            for(j in 1:ncol(mat)){
              colI <- mat[,i]
              colJ <- mat[,j]
              out[i,j] <- t(colI) %*% colJ
            }
          }
         return(out)
        }

2. Execute another function without using the loop, but use only the matrix operation as shown in the following code snippet:

        vectorizedOp <- function(mat){
          return(t(mat) %*% mat)
        }

    library(microbenchmark) # To compare performance of the functions
    microbenchmark(loopOperation(mat = binMat), vectorizedOp(mat = binMat))
            Unit: milliseconds      
       expr                      min         lq         mean                       
       vectorized(mat=binMat)    7.009144    9.30052    10.67089        
       loopOperation(mat=binMat) 6826.260664 7476.98113 7766.50789 

   
        median        uq        max        neval cld
        9.89367       11.8099   21.3325    100    a
        7650.74206    8115.6440 9333.9608  100    b