Apply function in matrix in R

I have a matrix in R in the following form:

     x11 x12 x13 
     x21 x22 x23 
X =  x31 x32 x33 

which I generate in R as:

 set.seed(123)
 X <- matrix(sample(15,9,T),3)
 colnames(X) <- paste0("X",1:3)
> X
     X1 X2 X3
[1,] 15 14  2
[2,] 15  3  6
[3,]  3 10 11

and I want to generate a new matrix X_new using the following function:

xij = xij / ( w * sqrt(xii*xjj)), 

where w = 1 when xii=xjj and w=2 when xii≠xjj. For example (1,1)= 15 / (1*sqrt(15*15))=1 and (1,2)= 14/(2*sqrt(15*3))= 1,04

Basically the diagonal will be ones. How can I do this in R with an apply function?

The final result must be:

         1     1.04  0.07
X_new =  1.11     1  0.52
         0.11  0.87     1

>Solution :

Use outer as shown:

d <- diag(X)
w <- 2 - outer(d, d, `==`)
X / (w * sqrt(outer(d, d)))
##             X1        X2         X3
## [1,] 1.0000000 1.0434984 0.07784989
## [2,] 1.1180340 1.0000000 0.52223297
## [3,] 0.1167748 0.8703883 1.00000000

or to use sapply

sapply(1:3, 
  function(j) sapply(1:3, 
    function(i) X[i,j] / ((2 - (X[i, i] == X[j, j])) * sqrt(X[i,i] * X[j, j]))))
##           [,1]      [,2]       [,3]
## [1,] 1.0000000 1.0434984 0.07784989
## [2,] 1.1180340 1.0000000 0.52223297
## [3,] 0.1167748 0.8703883 1.00000000

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