On Apr 27, 2011, at 7:25 AM, Hans W Borchers wrote:
Jeroen Ooms <jeroenooms <at> gmail.com> writes:
Is there an easy way to turn a vector of length n into an n by n
matrix, in
which the diagonal equals the vector, the first off diagonal equals
the
first order differences, the second... etc. I.e. to do this more
efficiently:
diffmatrix <- function(x){
n <- length(x);
M <- diag(x);
for(i in 1:(n-1)){
differences <- diff(x, dif=i);
for(j in 1:length(differences)){
M[j,i+j] <- differences[j]
}
}
M[lower.tri(M)] <- t(M)[lower.tri(M)];
return(M);
}
x <- c(1,2,3,5,7,11,13,17,19);
diffmatrix(x);
I do not know whether you will call the appended version more elegant,
but at least it is much faster -- up to ten times for length(x) =
1000,
i.e. less than 2 secs for generating and filling a 1000-by-1000
matrix.
I also considered col(), row() indexing:
M[col(M) == row(M) + k] <- x
Surprisingly (for me), this makes it even slower than your version
with
a double 'for' loop.
Every call to row() or col() creates a matrix of the same size as M.
It might speed up if you created them outside the loop.
-- Hans Werner
# ----
diffmatrix <- function(x){
n <- length(x)
if (n == 1) return(x)
M <- diag(x)
for(i in 1:(n-1)){
x <- diff(x) # use 'diff' in a loop
for(j in 1:(n-i)){ # length is known
M[j, i+j] <- x[j] # and reuse x
}
}
M[lower.tri(M)] <- t(M)[lower.tri(M)]
return(M)
}
# ----
David Winsemius, MD
West Hartford, CT
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