my starting data:

ID  B4  B4  B3  B3
1   12  13  19  21
2   13  14  19  21
3   13  13  19  21
4   12  13  19  19
5   13  13  18  19
6   12  13  19  21

code:

data=read.csv("test.txt", stringsAsFactors = F, sep="")
row.names(data)=data[,1]
data=data[,c(-1)]
odd_columns=seq(1, ncol(data), by=2) 
odd=t(data[,odd_columns])
even_columns=seq(2, ncol(data), by=2) 
even=t(data[,even_columns])
oven=cbind(odd,even)
newoven=oven[,order(colnames(oven))]

results:

> newoven
    1  1  2  2  3  3  4  4  5  5  6  6
B4 12 13 13 14 13 13 12 13 13 13 12 13
B3 19 21 19 21 19 21 19 19 18 19 19 21

using R software mydata<-read.table("input",sep="\t") mydata_t<-t(mydata)

 m <- read.table(file=stdin(), header=T, sep="\t", row.names = 1, fill=F) ## adjust to your needs
 o <- matrix(ncol=nrow(m)*2,nrow=0)
 colindex <- seq(from=1, to=ncol(m)-1, by=2)
 for (i in colindex)  {  
  # this is difficult to do without for loop, because you want to 'zip' together one column with the next one
  tmprow <- as.numeric(unlist(apply(m[c(i,i+1)],1,list)))
  o <- rbind(o, tmprow)
 }
rownames(o) <- colnames(m)[colindex]
colnames(o) <- unlist(lapply(rownames(m), rep, 2))

o 
    1  1  2  2  3  3  4  4  5  5  6  6
B4 12 13 13 14 13 13 12 13 13 13 12 13
B3 19 21 19 21 19 21 19 19 18 19 19 21

This seems to work, including the column and row-names. If someone can write this without using a for loop, you will gain some extra points.

This should work as a quick hack, but there might be a better way to fix this without a loop.

Superfast script: I used it for 50,000 X 8,000

awk '
{ 
    for (i=1; i<=NF; i++)  {
        a[NR,i] = $i
    }
}
NF>p { p = NF }
END {    
    for(j=1; j<=p; j++) {
        str=a[1,j]
        for(i=2; i<=NR; i++){
            str=str"\t"a[i,j];
        }
        print str
    }
}' YOURFILE.TXT

GNU datamash:

cat data.tsv | datamash transpose  > data.t.tsv

csvtk (supporting Linux/Windows):

cat data.tsv | csvtk transpose -t  > data.t.tsv

awk 'FNR==1{id="ID";b4="B4";b3="B3"}FNR>1{id=id FS $1 FS $1;b4=b4 FS $2 FS $3;b3=b3 FS $4 FS $5}END{print id;print b4;print b3}' input.txt

So, here is a solution in R without for loops. The problem, using apply is that per default we do not know in which column we are at the moment of processing, and you cannot always rely on the assumption that the columns will be processed in sequence (e.g. using parapply etc.).

Solution:

split the matrix in two, one for the odd and one for the even columns. The add a row with the column number to the first matrix, so we know were we are again. Assuming, m is holding the input data, like before:

my.zipper <- function(x) {
    current.col = x['DELME'] # which column are we processing?
    x <- x[-length(x)] # remove the index from the processing
    as.numeric(unlist(apply(cbind(x,m2[,current.col]),1,list)))
}

m <- read.table(file=stdin(), header=T, sep="\t", row.names = 1, fill=F) ## adjust to your needs  
colindex <- seq(from=1, to=ncol(m)-1, by=2)
m1 <- m[,colindex] # even cols
m2 <- m[,colindex+1] # odd cols
m1 <- rbind(m1, DELME=1:ncol(m1)) # add the column number to the m1 matrix

o <-t(apply(m1, 2, my.zipper))
colnames(o) <- unlist(lapply(rownames(m), rep, 2)) # adjust column names, row.names are correct already.
o
 o

 1  1  2  2  3  3  4  4  5  5  6  6
B4 12 13 13 14 13 13 12 13 13 13 12 13
B3 19 21 19 21 19 21 19 19 18 19 19 21