Re: [R] NumDeriv - derivatives of covariance matrix

From: Paul Gilbert <pgilbert_at_bank-banque-canada.ca>
Date: Wed, 30 Apr 2008 10:27:43 -0400

Your calculation can be thought of as a function from R^m to R^(n*n), and functions in numDeriv can be used to calculate a numerical approximation to the derivative of the function. However, the functions in numDeriv try to calculate accurate approximations, as opposed to quick approximations like one might want in an optimization problem. Given that you already have an analytic solution, I doubt that even a quick approximation will be faster. You might better look at trying to convert parts of your double loop into vector or matrix calculations, or   focusing on the fact that the matrix is symmetric.

Paul Gilbert

Daomeng Gao wrote:
> Hello R-help,
>
> I need to compute matrices of first derivatives of a covariance matrix C
> with entries given by c_ij=theta*exp(-0.5* sum(eta*(x[i,]-x[j,])^2)), wrt to
> elements of eta, a m-dimensional vector of parameters, given a n*m data
> matrix x. So far, I have been computing matrices for each parameter (given
> by par[index]) analytically, using the following
>
> kmatder<- function(x, par, index) {
> ## x: n*m matrix
> ## par: vector of parameters, m=length(par)=ncol(x)
> ## compute matrix of partial derivatives wrt parameter par[index]: Cder
> = d C/d par[index]
> theta<-1
> eta<-par
> n<-nrow(x)
> Cder<-matrix(0,n,n)
> for (i in 1:n) {
> for (j in i:n) {
> Cder[i,j]<-(-0.5*((x[i,index]-x[j,index])^2))*theta*exp(-0.5*
> sum(eta*(x[i,]-x[j,])^2))
> }
> }
> Cder<-0.5*(Cder+t(Cder))
> Cder
> }
>
> I was wondering whether it might be possible to speed up things using
> numDeriv (jacobian). If so, what would be the right way to implement a
> suitable method ?
>
> Cheers,
> Gao Daomeng
>
> [[alternative HTML version deleted]]
>
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