Dear R users, Let f be a function over d variables x1,..,xd. I want to compute the k^th-order derivative with respect to x1,..,xk (k<=d). I have a by hand solution (see below) using an iterating code using D. However, I expect d to be high and f to be complicated. Then I want a vector x to be the input, instead of x1,..,xd. How to avoid the x1 <- x[1]; x2 <- x[2], etc steps in the code below? Moreover, D uses symbolic differentation and then eval evaluates the output to get a numerical result. But is there a way to compute the desired derivatives numerically directly (without using symbolic calculus at all)? Finally, what is the most efficient and fast way to get a numerical result for such derivatives?
Thank you very much in advance, Gildas ### Code ### ### dif takes a function f, an order k, and a vector x as input. f must be a function of x1,..,xd with d >= k. The correspondance is done between xi and x[i]. The expression for f must be at the last row of the body function. dif <- function(f,k,x){ o <- list() n <- length(body(f)) o[[1]] <- body(f)[[n]] for (i in 1:k){ xi <- paste("x",i,sep="") o[[i+1]] <- D(o[[i]],name=xi) } x1 <- x[1] x2 <- x[2] x3 <- x[3] eval(o[[k+1]]) } ### Examples ### ## function to differentiate f <- function(x){ x1 <- x[1] x2 <- x[2] x3 <- x[3] 0.5*x1*x2*x3^2 } ## derivative w.r.t. x1, x2 and x3 at the point (1,2,3). dif(f,3,c(1,2,3)) ### My Questions ### ## how to avoid to write by hand xi <- x[i] ?? ## is there a way in R to compute such derivatives without using symbolic calculation but numerical compuation instead. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.