Repeat chunks of a sequence arbitrary times with GNU R

Repeating arbitrary size chunks multiple times in a given sequence with preserving order of chunks would be needed in certain computations. For example in matrix multiplication that is reduced to a 1D problem. Mapping your sequence into a matrix and repeating certain column or generating another sequence in the appropriate loop are straight forward solutions indeed. However these approaches will suffer immensely in memory consumption with increasing sequence size and would generate the original problem it seek to solve. More efficient and the general way to achieve repeating chunks is solved with the following R code:

manyrep <-function(a,f,n) {
i <- as.integer(length(a)/f);
q <- f
for(j in 1:i) {
a<-append(a,a[(q-f+1):q],after=q);
q<-q+2*f
p <- 1;
while(p <= (n-1)) {
a<-append(a,a[(q-2*f+1):(q-f)],after=(q-f));
q<-q+f ;
p<-p+1
}
}
return(a)
}


For example if sequence a = {1,2,3,4}, frequency or chunk size f=2 and number of repetition n=1, hence manyrep(1:4,2,1) the output should look like {1,2,1,2,3,4,3,4}. If n was 2 output would be {1,2,1,2,1,2,3,4,3,4,3,4}.

Append to a vector in regular intervals efficiently in R

In many instances one may need to append a character or a value in a given sequence, usually represented as a vector or array. It is pretty easy to achieve this naively. However, the point is not to consume any more memory. This is one of the simple solutions I can propose in GNU R.

# This function appends a word into vector a in every f element
appendfreq<-function(a,f,word) { i <- as.integer(length(a)/f-1); q<-f; for(j in 1:i) { a<-append(a,word,after=q); q<-q+f+1; } ;return(a); }

GNU R Garbage Collection

On GNU R if you delete your objects by

rm(list=ls())

This action won't free any memory associated with those objects. For this reason, R provides a utility for garbage collection, simply apply

gc()

This will free not used allocations. If you like to apply this whenever R allocates memory, apply this:

gctorture(on = TRUE)

Consult with R Internals manual for further details.

Groebner Bases and Cryptography

You may have already heard the brilliant technique called Groebner bases to solve multivariate system of equations. But unfortunately it is pointed out that it isn't possible to use this in cryptography: [Why you cannot even hope to use Groebner Bases in Public Key Cryptography?].