R Under development (unstable) (2024-05-17 r86566 ucrt) -- "Unsuffered Consequences"
Copyright (C) 2024 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.

> library(minqa)
> # rm(list=ls())
> cyq.f <- function (x) {
+   rv<-cyq.res(x)
+   f<-sum(rv*rv)
+ }
> 
> cyq.res <- function (x) {
+ # Fletcher's chebyquad function m = n -- residuals 
+    n<-length(x)
+    res<-rep(0,n) # initialize
+    for (i in 1:n) { #loop over resids
+      rr<-0.0
+      for (k in 1:n) {
+ 	z7<-1.0
+ 	z2<-2.0*x[k]-1.0
+         z8<-z2
+         j<-1
+         while (j<i) {
+             z6<-z7
+             z7<-z8
+             z8<-2*z2*z7-z6 # recurrence to compute Chebyshev polynomial
+             j<-j+1
+         } # end recurrence loop
+         rr<-rr+z8
+       } # end loop on k
+       rr<-rr/n
+       if (2*trunc(i/2) == i) { rr <- rr + 1.0/(i*i - 1) }
+       res[i]<-rr
+     } # end loop on i
+     res
+ }
> 
> xstart<-rep(1,6)
> lower<-rep(-10,6)
> upper<-rep(10,6)
> tu6<-system.time(cu6<-uobyqa(xstart,cyq.f,control=list(iprint=2,maxfun=25000)))
npt = 8 , n =  6 
rhobeg =  0.2 , rhoend =  2e-07 
start par. =  1 1 1 1 1 1 fn =  6.973515 
rho:    0.020 eval:  29 fn:      3.14975 par:0.762144 0.762144 0.836126 0.836126 0.836126 0.836126 
rho:   0.0020 eval: 296 fn:  0.000120341 par:-0.139380 0.543844 -0.778352 0.950676 -0.338641 0.350418 
rho:  0.00020 eval: 340 fn:  2.69590e-07 par:0.361732 0.709121 0.0638755 0.931719 0.287934 0.632422 
rho:  2.0e-05 eval: 368 fn:  1.26011e-09 par:0.367062 0.711693 0.0669086 0.933197 0.288717 0.633350 
rho:  2.0e-06 eval: 393 fn:  1.97003e-12 par:0.366690 0.711278 0.0668671 0.933126 0.288713 0.633296 
rho:  2.0e-07 eval: 395 fn:  2.82847e-16 par:0.366682 0.711259 0.0668761 0.933123 0.288740 0.633317 
At return
eval: 401 fn:  2.8284722e-16 par: 0.366682 0.711259 0.0668766 0.933123 0.288741 0.633318
> str(cu6)
List of 5
 $ par  : num [1:6] 0.3667 0.7113 0.0669 0.9331 0.2887 ...
 $ fval : num 2.83e-16
 $ feval: int 401
 $ ierr : int 0
 $ msg  : chr "Normal exit from uobyqa"
 - attr(*, "class")= chr [1:2] "uobyqa" "minqa"
> tu6
   user  system elapsed 
   0.03    0.00    0.03 
> tn6<-system.time(cn6<-newuoa(xstart,cyq.f,control=list(iprint=2,maxfun=25000)))
npt = 8 , n =  6 
rhobeg =  0.2 , rhoend =  2e-07 
start par. =  1 1 1 1 1 1 fn =  6.973515 
rho:    0.020 eval:  11 fn:      1.60811 par: 1.04277 0.911033 0.911033 0.911033 0.911033 0.911033 
rho:   0.0020 eval:  21 fn:      1.58471 par: 1.04243 0.909386 0.908411 0.900540 0.921593 0.898046 
rho:  0.00020 eval: 139 fn:     0.695387 par:0.956398 0.723322 0.990382 0.602663 0.948355 0.836784 
rho:  2.0e-05 eval: 1208 fn:  0.000492565 par:0.724316 0.271811 0.936396 0.0631646 0.375099 0.624009 
rho:  2.0e-06 eval: 1510 fn:  3.95767e-07 par:0.710703 0.288792 0.932977 0.0668048 0.366144 0.633226 
rho:  2.0e-07 eval: 1825 fn:  1.05863e-10 par:0.711267 0.288746 0.933127 0.0668787 0.366688 0.633322 
At return
eval: 1875 fn:  5.7125222e-14 par: 0.711259 0.288741 0.933123 0.0668766 0.366682 0.633318
> str(cn6)
List of 5
 $ par  : num [1:6] 0.7113 0.2887 0.9331 0.0669 0.3667 ...
 $ fval : num 5.71e-14
 $ feval: int 1875
 $ ierr : int 0
 $ msg  : chr "Normal exit from newuoa"
 - attr(*, "class")= chr [1:2] "newuoa" "minqa"
> tn6
   user  system elapsed 
   0.05    0.00    0.04 
> tb6<-system.time(cb6<-bobyqa(xstart,cyq.f,lower=lower, upper=upper, control=list(iprint=2,maxfun=25000)))
ctrl$force.start =  FALSE 
npt = 8 , n =  6 
rhobeg =  0.2 , rhoend =  2e-07 
start par. =  1 1 1 1 1 1 fn =  6.973515 
rho:    0.020 eval:  11 fn:      1.70861 par:0.652960 0.953103 0.953103 0.953103 0.953103 0.953103 
rho:   0.0020 eval:  23 fn:      1.42929 par:0.741459  1.00427 0.960418 0.955000 0.946916 0.920746 
rho:  0.00020 eval:  99 fn:     0.201556 par:0.730681 0.950091 0.322996 0.744196 0.967810 0.463371 
rho:  2.0e-05 eval: 774 fn:  0.000129730 par:0.635509 0.934839 0.0661256 0.372517 0.712588 0.283395 
rho:  2.0e-06 eval: 948 fn:  1.38882e-06 par:0.633767 0.933306 0.0669111 0.367142 0.711068 0.288676 
rho:  2.0e-07 eval: 1065 fn:  2.73325e-08 par:0.633221 0.933149 0.0668557 0.366748 0.711363 0.288603 
At return
eval: 1304 fn:  1.1168924e-10 par: 0.633321 0.933125 0.0668785 0.366680 0.711262 0.288749
> str(cb6)
List of 5
 $ par  : num [1:6] 0.6333 0.9331 0.0669 0.3667 0.7113 ...
 $ fval : num 1.12e-10
 $ feval: int 1304
 $ ierr : int 0
 $ msg  : chr "Normal exit from bobyqa"
 - attr(*, "class")= chr [1:2] "bobyqa" "minqa"
> tb6
   user  system elapsed 
   0.03    0.00    0.03 
> 
> 
> proc.time()
   user  system elapsed 
   0.35    0.04    0.40