How to replace an element of a symmetric matrix randomly? - r

Question

Suppose I have a matrix like so:
data=matrix(c(1,0,0,0,0,0,1,0,0.6583,0,0,0,1,0,0,0,0.6583,0,1,0,0,0,0,0,1),nrow=5,ncol=5)
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0.0000 0 0.0000 0
[2,] 0 1.0000 0 0.6583 0
[3,] 0 0.0000 1 0.0000 0
[4,] 0 0.6583 0 1.0000 0
[5,] 0 0.0000 0 0.0000 1
How do I create another matrix, say "data2", such that it has the same number of off-diagonal nonzero elements as "data" but in another location other than the one in data? The randomly simulated data will be uniform (so runif).

Answer 1

Here is a somewhat clumsy way to do this. It works well for small matrices but would be too slow if you're going to use this for some very high-dimensional problems.
# Current matrix:
data=matrix(c(1,0,0,0,0,0,1,0,0.6583,0,0,0,1,0,0,0,0.6583,0,1,0,0,0,0,0,1),nrow=5,ncol=5)
# Number of nonzero elements in upper triangle:
no.nonzero<-sum(upper.tri(data)*data>0)
# Generate same number of new nonzero correlations:
new.cor<-runif(no.nonzero,-1,1)
# Create new diagonal matrix:
p<-dim(data)[1]
data2<-diag(1,p,p)
### Insert nonzero correlations: ###
# Step 1. Identify the places where the nonzero elements can be placed:
pairs<-(p^2-p)/2 # Number of element in upper triangle
combinations<-matrix(NA,pairs,2) # Matrix containing indices for those elements (i.e. (1,2), (1,3), ... (2,3), ... and so on)
k<-0
for(i in 1:(p-1))
{
for(j in {i+1}:p)
{
k<-k+1
combinations[k,]<-c(i,j)
}
}
# Step 2. Randomly pick indices:
places<-sample(1:k,no.nonzero)
# Step 3. Insert nonzero correlations:
for(i in 1:no.nonzero)
{
data2[combinations[places[i],1],combinations[places[i],2]]<-data2[combinations[places[i],2],combinations[places[i],1]]<-new.cor[i]
}

Answer 2

Not really understood the question. There are two off-diagonal and non-zero elements (0.6583) in the example, right? Is matrix with two elements the result you want in this case?
data=matrix(c(1,0,0,0,0,0,1,0,0.6583,0,0,0,1,0,0,0,0.6583,0,1,0,0,0,0,0,1),nrow=5,ncol=5)
# Convert to vector
data2 <- as.numeric(data)
# Remove diagonal
data2 <- data2[as.logical(upper.tri(data) | lower.tri(data))]
# Remove 0 elements
data2 <- data2[data2 != 0]
data2