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((1 / 10) * x1 + 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] -25.0025

$gradient
[1] -3.803178e-18 -5.861978e-14

$hessian
       [,1] [,2]
[1,] 2.0003    0
[2,] 0.0000    4

$argument
[1] -0.0499975 -7.0710678

$converged
[1] TRUE

$iterations
[1] 6

$argpath
            [,1]       [,2]
[1,]  0.00000000  0.0000000
[2,] -0.02500000 -0.9996875
[3,] -0.03528824 -2.9996875
[4,] -0.04237731 -6.9996875
[5,] -0.04999766 -7.0721747
[6,] -0.04999750 -7.0710681

$argtry
            [,1]       [,2]
[1,] -0.02500000 -0.9996875
[2,] -0.03528824 -2.9996875
[3,] -0.04237731 -6.9996875
[4,] -0.04999766 -7.0721747
[5,] -0.04999750 -7.0710681
[6,] -0.04999750 -7.0710678

$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] 0.9900250 0.9375080 0.6213427 0.9895692 1.0001565 0.9998752

$valpath
[1]   0.0000000  -0.9912625  -8.1907459 -24.9923542 -25.0024975 -25.0024999

$valtry
[1]  -0.9912625  -8.1907459 -24.9923542 -25.0024975 -25.0024999 -25.0024999

$preddiff
[1] -1.001250e+00 -7.679383e+00 -2.704081e+01 -1.025025e-02 -2.450566e-06
[6] -1.350200e-13

$stepnorm
[1] 1.000000e+00 2.000026e+00 4.000006e+00 7.288674e-02 1.106665e-03
[6] 2.598268e-07

> ## IGNORE_RDIFF_END
> 
>  (tout$stepnorm / tout$r)[tout$accept & tout$steptype != "Newton"]
[1] 1.000000 1.000013 1.000002
> 
> 
> 
> proc.time()
   user  system elapsed 
   0.12    0.07    0.18