[R] derivatives in R

[Lavan]

hi thanks,
pls see the code below. the elements of matrix Il should be the derivatives
in matrix h (in Boldface) plus some additional terms, here I did calculate
derivatoves in the matrix, but I want R to calculate it for me. 


pid<- function (tau1,tau2,sigma=10,n=100,x_bar=20) {

library(akima)
library(lattice)
library(rgl)

a1	<- 1.5
a2	<- 4

t1	<-seq(-1,1);
t2	<-seq(3,4);

l	<-length(t1);
m	<-length(t2);

N1	<- matrix(NA,l,m);
N2	<- matrix(NA,l,m);
wp	<- matrix(NA,l,m);
rr	<- matrix(NA,l,m);
N	<- matrix(NA,l,m);
mu	<- matrix(NA,l,m);
Il	<- matrix(NA,l,m);
iIl	<- matrix(NA,l,m);

theta 	<-expression(x+y);
dx	<-D(theta, "x");
dy	<-D(theta, "y"); 
	
d2x	<-D(dx, "x");
dxy	<-D(dx, "y"); 
dyx	<-D(dy, "x");
d2y	<-D(dy, "y");

h	<- matrix(c(d2x,dxy,dyx,d2y),nrow=2,ncol=2); 

for (i in 1:l)
	{
            for (j in 1:m)
	{
	wp[i,j]<-((t1[i]-a1)/tau1)^2+((t2[j]-a2)/tau2)^2
	mu[i,j] <-(t1[i] + t2[j]);
	Il[i,j]
<-matrix(c(n/(sigma^2)+1/(tau1^2),n/(sigma^2),n/(sigma^2),n/(sigma^2)+1/             
tau2^2)),2,2);
	iIl <-solve(Il);
            ul[i,j] <-
(c(n*(x_bar-mu[i,j])/(sigma^2)-(t1[i]-a1)/(tau1^2),n*(x_bar-mu[i,j])/			
(sigma^2)-(t2[j]-a2)/(tau2^2)));
	ul <-matrix(c(n*(x_bar-mu)/(sigma^2)-(theta1-a1)/(tau1^2),n*(x_bar-mu)/			
(sigma^2)-(theta2-a2)/(tau2^2)),2,1);
	ult <-t(ul);
	wl[i,j] <-t(ul)%*%solve(Il,ul);
	rr[i,j] <-(wp[i,j]/wl[i,j]);
	N[i,j]	<-(wl[i,j]-wp[i,j])/wl[i,j]
             }
  }

           list("Test Statistics Wp"= wp,"Stat Ratio"=rr, "N"=N,"N1"=N1,
"N2"=N2, "mean"=mu, "Il"=Il,
           "inverse of Il"=iIl)
}

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