# [R] NumDeriv - derivatives of covariance matrix

Date: Tue, 29 Apr 2008 14:39:30 +0200

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

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