Parallel processing- Foraech and for loop in R - r

Question

I want to produce a matrix which I put produce process below. But it tooks so much time.
Is there any other way to get same result quicker with using foreach and parallel processing?
"""
library("foreach")
library("doParallel")
lambdas=seq(0.01,7, by = 0.01)
cl <- makeCluster(2) # create a cluster with 2 cores
registerDoParallel(cl) # register the cluster
nlambdas <-foreach(i = 1:1, .inorder=FALSE ,.combine = 'cbind', .multicombine=TRUE, .packages = "quantreg") %dopar% {
first<-rep()
second<-rep()
third<-rep()
fourth<-rep()
for (m in 1:700) {
for (j in 1:700) {
for (n in 1:700) {
for (k in 1:700) {
first<-rbind(first,lambdas[m])
second<-rbind(second,lambdas[j])
third<-rbind(third,lambdas[n])
fourth<-rbind(fourth,lambdas[k])
}
}
}
}
lambda_total<-cbind(first,second,third,fourth)
}
stopCluster(cl)
"""

Answer 1

You don't need parallel processing, you just need an algorithm with less than (O**4) complexity and a slow operation to compose this matrix.
The same matrix may easily be constructed by repeatedly sorting four vectors. In your case, however, with 700**4= 2.4e+11 elements, this might take some time.
I illustrate the algorithm with only 7 different values in the vector lambdas (and 2401 elements in total).
nsteps = 7
lambdas = seq(0.01,7,(7/nsteps))
h = rep(lambdas,nsteps**3)
i = rep(lambdas,nsteps**3)
j = rep(lambdas,nsteps**3)
k = rep(lambdas,nsteps**3)
ordering = order(k)
k = k[ordering]
k = k[ordering]
k = k[ordering]
k = k[ordering]
j = j[ordering]
j = j[ordering]
j = j[ordering]
i = i[ordering]
i = i[ordering]
h = h[ordering]
lambdas.total = cbind(first=h,second=i,third=j,fourth=k)
If your memory is large enough to cope with ordering a vector with length>10**10, you can do this with 700 steps for lambda in no time.
No need for any for loops.