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)
> 
> trigexp <- function(x) {
+ n <- length(x)
+ F <- rep(NA, n)
+ F[1] <- 3*x[1]^2 + 2*x[2] - 5 + sin(x[1] - x[2]) * sin(x[1] + x[2])
+ tn1 <- 2:(n-1)
+ F[tn1] <- -x[tn1-1] * exp(x[tn1-1] - x[tn1]) + x[tn1] * ( 4 + 3*x[tn1]^2) +
+         2 * x[tn1 + 1] + sin(x[tn1] - x[tn1 + 1]) * sin(x[tn1] + x[tn1 + 1]) - 8 
+ F[n] <- -x[n-1] * exp(x[n-1] - x[n]) + 4*x[n] - 3
+ F
+ }
> 
> p0 <- rnorm(50, sd=2)
> ans1 <- dfsane(par=p0, fn=trigexp, method=1)
Iteration:  0  ||F(x0)||:  114.3739 
iteration:  10  ||F(xn)|| =   16.40765 
iteration:  20  ||F(xn)|| =   0.3262413 
iteration:  30  ||F(xn)|| =   6.407245e-05 
> ans2 <- dfsane(par=p0, fn=trigexp, method=2)
Iteration:  0  ||F(x0)||:  114.3739 
iteration:  10  ||F(xn)|| =   14.67524 
iteration:  20  ||F(xn)|| =   0.8598656 
iteration:  30  ||F(xn)|| =   0.08099395 
iteration:  40  ||F(xn)|| =   0.009453123 
iteration:  50  ||F(xn)|| =   0.0007637905 
iteration:  60  ||F(xn)|| =   5.64327e-06 
> ans3 <- sane(par=p0, fn=trigexp, method=2)
Iteration:  0  ||F(x0)||:  114.3739 

 iteration:  10  ||F(xn)|| =   17.26152 

 iteration:  20  ||F(xn)|| =   1.324045 

 iteration:  30  ||F(xn)|| =   0.1256207 

 iteration:  40  ||F(xn)|| =   0.02494378 

 iteration:  50  ||F(xn)|| =   0.007438894 

 iteration:  60  ||F(xn)|| =   0.00261932 

 iteration:  70  ||F(xn)|| =   0.001928832 

 iteration:  80  ||F(xn)|| =   0.0004144328 

 iteration:  90  ||F(xn)|| =   0.0001384958 

 iteration:  100  ||F(xn)|| =   1.460952e-05 

 iteration:  110  ||F(xn)|| =   2.329118e-06 

 iteration:  120  ||F(xn)|| =   1.100372e-06 
> ans4 <- sane(par=p0, fn=trigexp, method=3)
Iteration:  0  ||F(x0)||:  114.3739 

 iteration:  10  ||F(xn)|| =   3.847994 

 iteration:  20  ||F(xn)|| =   0.0005474832 
> 
> c(ans1$resid, ans2$resid,ans3$resid, ans4$resid) 
[1] 4.630919e-08 2.251931e-08 9.031200e-08 4.287158e-08
> c(ans1$feval, ans2$feval,ans3$feval,ans4$feval) 
[1]  41  63 249  59
> 
> 
> nsim <- 50
> dfsane1.trigexp <- dfsane2.trigexp <- sane1.trigexp <- sane2.trigexp <- matrix(NA, nsim, 5)
> for (i in 1:nsim) {
+ cat("Simulation" , i, "\n")
+ p0 <- rnorm(50)
+ t1 <- system.time(ans <- sane(par=p0, fn=trigexp, method=1, control=list(BFGS=TRUE, trace=F)))[1]
+ if (!is.null(ans))sane1.trigexp[i, ] <- c(ans$resid, ans$feval, ans$iter, ans$conv, t1)
+ t2 <- system.time(ans <- sane(par=p0, fn=trigexp, method=2, control=list(BFGS=TRUE, trace=F)))[1]
+ if (!is.null(ans))sane2.trigexp[i, ] <- c(ans$resid, ans$feval, ans$iter, ans$conv, t2)
+ t3 <- system.time(ans <- dfsane(par=p0, fn=trigexp, method=1, control=list(BFGS=TRUE, trace=F)))[1]
+ if (!is.null(ans))dfsane1.trigexp[i, ] <- c(ans$resid, ans$feval, ans$iter, ans$conv, t3)
+ t4 <- system.time(ans <- dfsane(par=p0, fn=trigexp, method=2, control=list(BFGS=TRUE, trace=F)))[1]
+ if (!is.null(ans)) dfsane2.trigexp[i, ] <- c(ans$resid, ans$feval, ans$iter, ans$conv, t4)
+ }
Simulation 1 
Simulation 2 
Simulation 3 
Simulation 4 
Simulation 5 
Simulation 6 
Calling `L-BFGS-B' in `optim' 
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 
Warning message:
In sane(par = p0, fn = trigexp, method = 1, control = list(BFGS = TRUE,  :
  Unsuccessful convergence.
> 
> z <- apply(sane1.trigexp, 2, summary)
> print(z)
                [,1]    [,2]  [,3] [,4]  [,5]
Min.    2.098074e-08   45.00  22.0  0.0 0.000
1st Qu. 4.222894e-08   51.00  25.0  0.0 0.000
Median  5.875738e-08   53.00  26.0  0.0 0.000
Mean    5.822881e-08   76.02  34.6  0.1 0.004
3rd Qu. 7.178740e-08   55.00  27.0  0.0 0.000
Max.    1.230045e-07 1210.00 463.0  5.0 0.060
> print(z[,1], digits=18)
                   Min.                 1st Qu.                  Median 
2.09807351835747434e-08 4.22289393998594829e-08 5.87573781140228863e-08 
                   Mean                 3rd Qu.                    Max. 
5.82288096561370791e-08 7.17873996527257309e-08 1.23004549521364436e-07 
> z <- apply(sane2.trigexp, 2, summary)
> print(z)
                [,1]   [,2]   [,3] [,4]  [,5]
Min.    1.373811e-08  45.00  22.00    0 0.000
1st Qu. 3.689446e-08  51.50  25.25    0 0.000
Median  5.171509e-08  53.00  26.00    0 0.000
Mean    5.759578e-08  91.06  45.02    0 0.002
3rd Qu. 8.456510e-08  55.00  27.00    0 0.000
Max.    9.950710e-08 301.00 150.00    0 0.020
> print(z[,1], digits=18)
                   Min.                 1st Qu.                  Median 
1.37381089904388297e-08 3.68944598635170985e-08 5.17150927531454527e-08 
                   Mean                 3rd Qu.                    Max. 
5.75957771721168104e-08 8.45650999387159440e-08 9.95070989222273082e-08 
> z <- apply(dfsane1.trigexp, 2, summary)
> print(z)
                [,1]  [,2]  [,3] [,4]   [,5]
Min.    2.092360e-08 23.00 22.00    0 0.0000
1st Qu. 4.109701e-08 26.00 25.00    0 0.0000
Median  5.578676e-08 27.00 26.00    0 0.0000
Mean    5.614983e-08 29.74 28.34    0 0.0014
3rd Qu. 7.048637e-08 28.00 27.00    0 0.0000
Max.    9.790307e-08 79.00 70.00    0 0.0200
> print(z[,1], digits=18)
                   Min.                 1st Qu.                  Median 
2.09235988020218251e-08 4.10970093776468935e-08 5.57867639448368199e-08 
                   Mean                 3rd Qu.                    Max. 
5.61498340169320198e-08 7.04863737048591054e-08 9.79030660995622125e-08 
> z <- apply(dfsane2.trigexp, 2, summary)
> print(z)
                [,1]  [,2]  [,3] [,4]  [,5]
Min.    1.373811e-08 23.00 22.00    0 0.000
1st Qu. 3.138502e-08 26.25 25.25    0 0.000
Median  4.781262e-08 27.00 26.00    0 0.000
Mean    5.216212e-08 32.98 31.98    0 0.002
3rd Qu. 6.690892e-08 28.00 27.00    0 0.000
Max.    9.950710e-08 70.00 69.00    0 0.020
> print(z[,1], digits=18)
                   Min.                 1st Qu.                  Median 
1.37381089105846531e-08 3.13850216815464159e-08 4.78126238374416507e-08 
                   Mean                 3rd Qu.                    Max. 
5.21621160656281439e-08 6.69089156895273988e-08 9.95070988312179856e-08 
> 
> 
> proc.time()
   user  system elapsed 
   4.84    0.15    4.95