R Under development (unstable) (2023-11-25 r85635 ucrt) -- "Unsuffered Consequences"
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> 
> library(nleqslv)
> 
> print.result <- function(z, do.print.xf=FALSE) {
+     if( do.print.xf ) {
+         print(z$x)
+         print(z$fvec)
+     }
+     print(z$message)
+     print(all(abs(z$fvec)<=1e-8))
+ }
> 
> # Powell cautionary example
> # M.J.D. Powell, "A Hybrid Method for Nonlinear Equations",
> # in Numerical methods for Nonlinear Algebraic Equations, ed. P. Rabinowitz, 1970.
> 
> 
> f <- function(x) {
+     y <- numeric(2)
+     y[1] <- x[1]
+     y[2] <- 10*x[1]/(x[1]+.1) + 2*x[2]^2
+ 
+     y
+ }
> 
> jac <- function(x) {
+     fjac <- matrix(0,nrow=2,ncol=2)
+ 
+     fjac[1, 1] <- 1
+     fjac[1, 2] <- 0
+     fjac[2, 1] <- 1/(x[1]+0.1)^2
+     fjac[2, 2] <- 4*x[2]
+ 
+     fjac
+ }
> 
> xstart <- c(3,1)
> z1 <- nleqslv(xstart,f, method="Newton",control=list(trace=0,allowSingular=TRUE))
> print.result(z1)
[1] "Function criterion near zero"
[1] TRUE
> xstart <- c(3,0) # singular start
> z2 <- nleqslv(xstart,f, method="Newton",control=list(trace=0,allowSingular=TRUE))
> print.result(z2)
[1] "Function criterion near zero"
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.14    0.04    0.17