R Under development (unstable) (2026-02-18 r89435 ucrt) -- "Unsuffered Consequences"
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> if(!require("BB"))stop("this test requires package BB.")
Loading required package: BB
> if(!require("setRNG"))stop("this test requires setRNG.")
Loading required package: setRNG
> 
> # Use a preset seed so test values are reproducable. 
> test.rng <- list(kind="Mersenne-Twister", normal.kind="Inversion", seed=1236)
> old.seed <- setRNG(test.rng)
> #iseed <- 1236  # this seed was used for tests conducted on March 25, 2008.  
> #set.seed(iseed)
> 
> troesch <- function(x) {
+   n <- length(x)
+   tnm1 <- 2:(n-1)
+   F <- rep(NA, n)
+     h <- 1 / (n+1)
+     h2 <- 10 * h^2
+     F[1] <- 2 * x[1] + h2 * sinh(10 * x[1]) - x[2] 
+     F[tnm1] <- 2 * x[tnm1] + h2 * sinh(10 * x[tnm1]) - x[tnm1-1] - x[tnm1+1]    
+ 
+     F[n] <- 2 * x[n] + h2 * sinh(10* x[n]) - x[n-1] - 1
+   F
+   }
>   
> p0 <- sort(runif(100))
> ans1 <- dfsane(par=p0, fn=troesch, method=1)
Iteration:  0  ||F(x0)||:  2.112497 
iteration:  10  ||F(xn)|| =   0.1708528 
iteration:  20  ||F(xn)|| =   0.04376194 
iteration:  30  ||F(xn)|| =   0.03621161 
iteration:  40  ||F(xn)|| =   0.01936748 
iteration:  50  ||F(xn)|| =   0.01612449 
iteration:  60  ||F(xn)|| =   0.005286395 
iteration:  70  ||F(xn)|| =   0.004403901 
iteration:  80  ||F(xn)|| =   0.003846459 
iteration:  90  ||F(xn)|| =   0.003002941 
iteration:  100  ||F(xn)|| =   0.001871959 
iteration:  110  ||F(xn)|| =   9.861048e-05 
iteration:  120  ||F(xn)|| =   0.0004547003 
iteration:  130  ||F(xn)|| =   0.00238987 
iteration:  140  ||F(xn)|| =   0.001617593 
iteration:  150  ||F(xn)|| =   8.564658e-06 
iteration:  160  ||F(xn)|| =   8.383969e-06 
iteration:  170  ||F(xn)|| =   1.920274e-06 
> ans2 <- dfsane(par=p0, fn=troesch, method=2)
Iteration:  0  ||F(x0)||:  2.112497 
iteration:  10  ||F(xn)|| =   0.1697327 
iteration:  20  ||F(xn)|| =   0.04631053 
iteration:  30  ||F(xn)|| =   0.02047333 
iteration:  40  ||F(xn)|| =   0.0127475 
iteration:  50  ||F(xn)|| =   0.009584953 
iteration:  60  ||F(xn)|| =   0.005918844 
iteration:  70  ||F(xn)|| =   0.002319422 
iteration:  80  ||F(xn)|| =   0.001424931 
iteration:  90  ||F(xn)|| =   0.0008849832 
iteration:  100  ||F(xn)|| =   0.0004182595 
iteration:  110  ||F(xn)|| =   0.0003373133 
iteration:  120  ||F(xn)|| =   0.004946487 
iteration:  130  ||F(xn)|| =   7.547532e-05 
iteration:  140  ||F(xn)|| =   6.363869e-05 
iteration:  150  ||F(xn)|| =   3.572272e-05 
iteration:  160  ||F(xn)|| =   2.628939e-05 
iteration:  170  ||F(xn)|| =   0.00440232 
iteration:  180  ||F(xn)|| =   8.01035e-06 
iteration:  190  ||F(xn)|| =   7.29029e-06 
iteration:  200  ||F(xn)|| =   0.0002006002 
iteration:  210  ||F(xn)|| =   1.153591e-05 
iteration:  220  ||F(xn)|| =   0.001022267 
> ans3 <- sane(par=p0, fn=troesch, method=1)
Iteration:  0  ||F(x0)||:  2.112497 

 iteration:  10  ||F(xn)|| =   0.1708528 

 iteration:  20  ||F(xn)|| =   0.04376194 

 iteration:  30  ||F(xn)|| =   0.0369635 

 iteration:  40  ||F(xn)|| =   0.01911966 

 iteration:  50  ||F(xn)|| =   0.02283271 

 iteration:  60  ||F(xn)|| =   0.01258888 

 iteration:  70  ||F(xn)|| =   0.01702996 

 iteration:  80  ||F(xn)|| =   0.009203832 

 iteration:  90  ||F(xn)|| =   0.007663768 

 iteration:  100  ||F(xn)|| =   0.005572009 

 iteration:  110  ||F(xn)|| =   0.006098556 

 iteration:  120  ||F(xn)|| =   0.004225583 

 iteration:  130  ||F(xn)|| =   0.003419364 

 iteration:  140  ||F(xn)|| =   0.003384428 

 iteration:  150  ||F(xn)|| =   0.002462463 

 iteration:  160  ||F(xn)|| =   0.002223469 

 iteration:  170  ||F(xn)|| =   0.001894652 

 iteration:  180  ||F(xn)|| =   0.001593481 

 iteration:  190  ||F(xn)|| =   0.001544238 

 iteration:  200  ||F(xn)|| =   0.001371717 

 iteration:  210  ||F(xn)|| =   0.001380736 

 iteration:  220  ||F(xn)|| =   0.001050085 

 iteration:  230  ||F(xn)|| =   0.0008261566 

 iteration:  240  ||F(xn)|| =   0.0007552435 

 iteration:  250  ||F(xn)|| =   0.0007209885 

 iteration:  260  ||F(xn)|| =   0.000668964 

 iteration:  270  ||F(xn)|| =   0.0003739778 

 iteration:  280  ||F(xn)|| =   0.0002911901 

 iteration:  290  ||F(xn)|| =   0.0002275736 

 iteration:  300  ||F(xn)|| =   0.0003757738 

 iteration:  310  ||F(xn)|| =   0.0001164746 

 iteration:  320  ||F(xn)|| =   1.973216e-05 

 iteration:  330  ||F(xn)|| =   8.459368e-06 

 iteration:  340  ||F(xn)|| =   5.58544e-06 

 iteration:  350  ||F(xn)|| =   4.336389e-06 

 iteration:  360  ||F(xn)|| =   1.980692e-06 
> ans4 <- sane(par=p0, fn=troesch, method=2)
Iteration:  0  ||F(x0)||:  2.112497 

 iteration:  10  ||F(xn)|| =   0.1697327 

 iteration:  20  ||F(xn)|| =   0.04631053 

 iteration:  30  ||F(xn)|| =   0.02981959 

 iteration:  40  ||F(xn)|| =   0.0128087 

 iteration:  50  ||F(xn)|| =   0.007747446 

 iteration:  60  ||F(xn)|| =   0.00671027 

 iteration:  70  ||F(xn)|| =   0.003478671 

 iteration:  80  ||F(xn)|| =   0.002820685 

 iteration:  90  ||F(xn)|| =   0.0008380247 

 iteration:  100  ||F(xn)|| =   0.0004486009 

 iteration:  110  ||F(xn)|| =   0.0003331791 

 iteration:  120  ||F(xn)|| =   0.0002376972 

 iteration:  130  ||F(xn)|| =   0.0002024058 

 iteration:  140  ||F(xn)|| =   7.542183e-05 

 iteration:  150  ||F(xn)|| =   4.284926e-05 

 iteration:  160  ||F(xn)|| =   3.877718e-05 

 iteration:  170  ||F(xn)|| =   1.107082e-05 

 iteration:  180  ||F(xn)|| =   1.048127e-05 

 iteration:  190  ||F(xn)|| =   1.130515e-06 
> #ans <- nlsolve(par=p0, fn=troesch)
> 
> c(ans1$resid, ans2$resid,ans3$resid, ans4$resid) 
[1] 8.128599e-08 5.286920e-08 7.824700e-08 8.492120e-08
> c(ans1$feval, ans2$feval,ans3$feval,ans4$feval) 
[1]  240  266 1046  463
> 
> # switched BFGS=TRUE to BFGS=FALSE below for speed, and 500 to 100
> 
> nsim <- 50
> dfsane1.troesch <- dfsane2.troesch <- sane1.troesch <- sane2.troesch <- matrix(NA, nsim, 5)
> for (i in 1:nsim) {
+ cat("Simulation" , i, "\n")
+ p0 <- sort(runif(50))
+ t1 <- system.time(ans <- sane(par=p0, fn=troesch, method=1,
+                control=list(BFGS=FALSE, trace=F)))[1]
+ if (!is.null(ans))sane1.troesch[i, ] <- c(ans$resid, ans$feval, ans$iter, ans$conv, t1)
+ t2 <- system.time(ans <- sane(par=p0, fn=troesch, method=2,
+                 control=list(BFGS=FALSE, trace=F)))[1]
+ if (!is.null(ans))sane2.troesch[i, ] <- c(ans$resid, ans$feval, ans$iter, ans$conv, t2)
+ t3 <- system.time(ans <- dfsane(par=p0, fn=troesch, method=1,
+                 control=list(BFGS=FALSE, trace=F)))[1]
+ if (!is.null(ans))dfsane1.troesch[i, ] <- c(ans$resid, ans$feval, ans$iter, ans$conv, t3)
+ t4 <- system.time(ans <- dfsane(par=p0, fn=troesch, method=2,
+                 control=list(BFGS=FALSE, trace=F)))[1]
+ if (!is.null(ans)) dfsane2.troesch[i, ] <- c(ans$resid, ans$feval, ans$iter, ans$conv, t4)
+ }
Simulation 1 
Simulation 2 
Simulation 3 
Simulation 4 
Simulation 5 
Simulation 6 
Simulation 7 
Simulation 8 
Simulation 9 
Simulation 10 
Simulation 11 
Simulation 12 
Simulation 13 
Simulation 14 
Simulation 15 
Simulation 16 
Simulation 17 
Simulation 18 
Simulation 19 
Simulation 20 
Simulation 21 
Simulation 22 
Simulation 23 
Simulation 24 
Simulation 25 
Simulation 26 
Simulation 27 
Simulation 28 
Simulation 29 
Simulation 30 
Simulation 31 
Simulation 32 
Simulation 33 
Simulation 34 
Simulation 35 
Simulation 36 
Simulation 37 
Simulation 38 
Simulation 39 
Simulation 40 
Simulation 41 
Simulation 42 
Simulation 43 
Simulation 44 
Simulation 45 
Simulation 46 
Simulation 47 
Simulation 48 
Simulation 49 
Simulation 50 
> 
> z <- apply(sane1.troesch, 2, summary)
> print(z)
                [,1]   [,2]   [,3] [,4]  [,5]
Min.    2.236800e-09 209.00  97.00    0 0.000
1st Qu. 5.319011e-08 247.00 106.25    0 0.000
Median  7.169645e-08 264.00 115.00    0 0.000
Mean    6.502567e-08 270.94 117.04    0 0.007
3rd Qu. 8.580688e-08 292.50 123.75    0 0.010
Max.    9.876373e-08 407.00 162.00    0 0.020
> print(z[,1], digits=18)
                   Min.                 1st Qu.                  Median 
2.23679963633939700e-09 5.31901101511107478e-08 7.16964544866227192e-08 
                   Mean                 3rd Qu.                    Max. 
6.50256652046534884e-08 8.58068778276177998e-08 9.87637293450962375e-08 
> 
> z <- apply(sane2.troesch, 2, summary)
> print(z)
                [,1]   [,2]   [,3] [,4]   [,5]
Min.    3.353729e-09 191.00  87.00    0 0.0000
1st Qu. 5.126360e-08 214.00  97.25    0 0.0000
Median  7.571545e-08 223.00 102.50    0 0.0000
Mean    6.818466e-08 231.22 104.98    0 0.0056
3rd Qu. 8.745042e-08 242.00 108.75    0 0.0100
Max.    9.982193e-08 302.00 137.00    0 0.0200
> print(z[,1], digits=18)
                   Min.                 1st Qu.                  Median 
3.35372943154086864e-09 5.12636046020707421e-08 7.57154464742049401e-08 
                   Mean                 3rd Qu.                    Max. 
6.81846564602675467e-08 8.74504152835740862e-08 9.98219278065438380e-08 
> 
> z <- apply(dfsane1.troesch, 2, summary)
> print(z)
                [,1]   [,2]   [,3] [,4]   [,5]
Min.    1.892016e-08 104.00  97.00    0 0.0000
1st Qu. 6.561860e-08 131.25 116.75    0 0.0000
Median  8.047880e-08 144.50 128.00    0 0.0000
Mean    7.626571e-08 145.64 128.44    0 0.0058
3rd Qu. 9.052229e-08 159.50 139.75    0 0.0100
Max.    9.907555e-08 194.00 159.00    0 0.0200
> print(z[,1], digits=18)
                   Min.                 1st Qu.                  Median 
1.89201573236015297e-08 6.56185951863389370e-08 8.04788015884763866e-08 
                   Mean                 3rd Qu.                    Max. 
7.62657083386709856e-08 9.05222946544071492e-08 9.90755489236852945e-08 
> 
> z <- apply(dfsane2.troesch, 2, summary)
> print(z)
                [,1]   [,2]   [,3] [,4]  [,5]
Min.    2.149523e-08  95.00  91.00    0 0.000
1st Qu. 6.071587e-08 108.00 103.50    0 0.000
Median  7.347776e-08 117.00 112.50    0 0.000
Mean    7.236210e-08 116.34 112.42    0 0.003
3rd Qu. 8.656972e-08 124.00 120.75    0 0.000
Max.    9.990350e-08 140.00 136.00    0 0.020
> print(z[,1], digits=18)
                   Min.                 1st Qu.                  Median 
2.14952285301628333e-08 6.07158653622953798e-08 7.34777641955904645e-08 
                   Mean                 3rd Qu.                    Max. 
7.23620986210723977e-08 8.65697237671817762e-08 9.99035028380436505e-08 
> 
> 
> 
> proc.time()
   user  system elapsed 
   6.25    0.07    6.32