R Under development (unstable) (2026-02-09 r89390 ucrt) -- "Unsuffered Consequences"
Copyright (C) 2026 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> 
>  objfun <- function(x) {
+      stopifnot(is.numeric(x))
+      stopifnot(length(x) == 2)
+      f <- expression(x1^2 - x2^2 + (1 / 100) * (x1^4 + x2^4))
+      g1 <- D(f, "x1")
+      g2 <- D(f, "x2")
+      h11 <- D(g1, "x1")
+      h12 <- D(g1, "x2")
+      h22 <- D(g2, "x2")
+      x1 <- x[1]
+      x2 <- x[2]
+      f <- eval(f)
+      g <- c(eval(g1), eval(g2))
+      B <- rbind(c(eval(h11), eval(h12)), c(eval(h12), eval(h22)))
+      list(value = f, gradient = g, hessian = B)
+  }
> 
>  library(trust)
> 
>  tout <- trust(objfun, c(0, 0), 1, 5, blather = TRUE)
> ## IGNORE_RDIFF_BEGIN
>  tout
$value
[1] -25

$gradient
[1]  0.000000e+00 -5.506706e-14

$hessian
     [,1] [,2]
[1,]    2    0
[2,]    0    4

$argument
[1]  0.000000 -7.071068

$converged
[1] TRUE

$iterations
[1] 6

$argpath
     [,1]      [,2]
[1,]    0  0.000000
[2,]    0 -1.000000
[3,]    0 -3.000000
[4,]    0 -7.000000
[5,]    0 -7.072165
[6,]    0 -7.071068

$argtry
     [,1]      [,2]
[1,]    0 -1.000000
[2,]    0 -3.000000
[3,]    0 -7.000000
[4,]    0 -7.072165
[5,]    0 -7.071068
[6,]    0 -7.071068

$steptype
[1] "hard-hard" "easy-easy" "easy-easy" "Newton"    "Newton"    "Newton"   

$accept
[1] TRUE TRUE TRUE TRUE TRUE TRUE

$r
[1] 1 2 4 4 4 4

$rho
[1] 0.9900000 0.9375000 0.6213018 0.9895576 1.0001551 0.9815034

$valpath
[1]   0.00  -0.99  -8.19 -24.99 -25.00 -25.00

$valtry
[1]  -0.99  -8.19 -24.99 -25.00 -25.00 -25.00

$preddiff
[1] -1.000000e+00 -7.680000e+00 -2.704000e+01 -1.010309e-02 -2.407417e-06
[6] -1.303079e-13

$stepnorm
[1] 1.000000e+00 2.000000e+00 4.000000e+00 7.216495e-02 1.096881e-03
[6] 2.552527e-07

> ## IGNORE_RDIFF_END
> 
>  (tout$stepnorm / tout$r)[tout$accept & tout$steptype != "Newton"]
[1] 1 1 1
> 
> proc.time()
   user  system elapsed 
   0.20    0.04    0.18