R Under development (unstable) (2023-11-25 r85635 ucrt) -- "Unsuffered Consequences"
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> 
> library("nleqslv")
> 
> # Trigonometric function
> trig <- function(x) {
+ 	n <- length(x)
+ 	y <- cos(x)
+ 	s <- sum(y)
+ 	y <- n - s + c(1:n) * (1-y) - sin(x)
+ 
+ 	y
+ }
> 
> trigjac <- function(x) {
+ 	n <- length(x)
+ 	J <- matrix(numeric(n*n),n,n)
+ 
+ 	for (p in 1:n) {
+ 		J[,p]  <- sin(x[p])
+ 		J[p,p] <- (p+1) * sin(x[p]) - cos(x[p])
+ 	}
+ 
+ 	J
+ }
> 
> do.print.xf <- FALSE
> 
> print.result <- function(z) {
+     if( do.print.xf ) {
+         print(z$x)
+         print(z$fvec)
+     }
+     print(z$message)
+     print(all(abs(z$fvec)<=1e-8))
+ }
> 
> n <- 10
> xstart <- rep(1,n)/n
> fstart <- trig(xstart)
> 
> znlm <- nleqslv(xstart, trig, global="dbldog", control=list(trace=0))
> print.result(znlm)
[1] "Function criterion near zero"
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.14    0.03    0.17