R Under development (unstable) (2023-11-25 r85635 ucrt) -- "Unsuffered Consequences"
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> # Dennis & Schnabel,1996,"Numerical methods for unconstrained optimization and nonlinear equations", SIAM
> # example 6.5.1 page 149
> 
> library(nleqslv)
> 
> dslnex <- function(x) {
+     y <- numeric(2)
+     y[1] <- x[1]^2 + x[2]^2 - 2
+     y[2] <- exp(x[1]-1) + x[2]^3 - 2
+     y
+ }
> 
> jacdsln <- function(x) {
+     n <- length(x)
+     Df <- matrix(numeric(n*n),n,n)
+     Df[1,1] <- 2*x[1]
+     Df[1,2] <- 2*x[2]
+     Df[2,1] <- exp(x[1]-1)
+     Df[2,2] <- 3*x[2]^2
+ 
+     Df
+ }
> 
> do.print.xf <- FALSE
> do.trace <- 0
> 
> print.result <- function(z) {
+     if( do.print.xf ) {
+         print(z$x)
+         print(z$fvec)
+     }
+     print(z$message)
+     print(all(abs(z$fvec)<=1e-8))
+ }
> 
> xstart <- c(2,.5)
> 
> z <- nleqslv(xstart,dslnex, jacobian=TRUE, control=list(trace=do.trace))
> print.result(z)
[1] "Function criterion near zero"
[1] TRUE
> all.equal(z$jac,jacdsln(z$x), tolerance=0.05)
[1] TRUE
> 
> z <- nleqslv(xstart,dslnex,jacdsln, jacobian=TRUE, control=list(trace=do.trace))
> print.result(z)
[1] "Function criterion near zero"
[1] TRUE
> all.equal(z$jac,jacdsln(z$x), tolerance=0.05)
[1] TRUE
> 
> z <- nleqslv(xstart,dslnex, method="Newton", jacobian=TRUE, control=list(trace=do.trace))
> print.result(z)
[1] "Function criterion near zero"
[1] TRUE
> all.equal(z$jac,jacdsln(z$x), tolerance=10^3*.Machine$double.eps^0.5)
[1] TRUE
> 
> z <- nleqslv(xstart,dslnex, jacdsln, method="Newton", jacobian=TRUE, control=list(trace=do.trace))
> print.result(z)
[1] "Function criterion near zero"
[1] TRUE
> identical(z$jac,jacdsln(z$x))
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.15    0.06    0.20