R Under development (unstable) (2023-11-25 r85635 ucrt) -- "Unsuffered Consequences"
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> # Broyden banded function
> 
> library("nleqslv")
> 
> brdban <- function(x) {
+ 	ml <- 5
+ 	mu <- 1
+ 	n <- length(x)
+     y <- numeric(n)
+ 
+ 	for( k in 1:n ) {
+ 
+ 		k1 <- max(1, k - ml)
+ 		k2 <- min(n, k + mu)
+ 
+ 		temp = 0.0
+ 		for(j in k1:k2) {
+ 			if ( j != k ) {
+ 				temp <- temp + x[j] * (1.0 + x[j])
+ 		    }
+ 		}
+ 
+ 		y[k] <- x[k] * (2.0 + 5.0 * x[k]**2) + 1.0 - temp
+ 
+ 	}
+ 	y
+ }
> 
> n <- 10
> xstart <- -rep(1,n)
> 
> xsol <- c( -0.42830,  -0.47660,  -0.51965,  -0.55810,  -0.59251,
+            -0.62450,  -0.62324,  -0.62139,  -0.62045,  -0.58647  )
> 
> fsol <- brdban(xsol)
> 
> znlq <- nleqslv(xstart, brdban, global="dbldog", method="Newton",
+                 control=list(trace=0,ftol=1e-8,xtol=1e-8,btol=1e-2,delta=-1.0))
> znlq$termcd                 # should be 2 for x values within tolerance
[1] 1
> all(abs(znlq$fvec)<=1e-7)   # may not have achieved ftol
[1] TRUE
> 
> xstart <- -2*rep(1,n)
> znlq <- nleqslv(xstart, brdban, global="dbldog", method="Newton",
+                 control=list(trace=0,ftol=1e-8,xtol=1e-8,btol=1e-2,delta=-1.0))
> znlq$termcd
[1] 1
> all(abs(znlq$fvec)<=1e-8)
[1] TRUE
> 
> znlq <- nleqslv(xstart, brdban, global="dbldog",
+                 control=list(trace=0,ftol=1e-8,xtol=1e-8,btol=1e-2,delta=-1.0))
> znlq$termcd                 # should be 2 for x values within tolerance
[1] 1
> all(abs(znlq$fvec)<=1e-7)   # may not have achieved ftol
[1] TRUE
> 
> xstart <- -2*rep(1,n)
> znlq <- nleqslv(xstart, brdban, global="dbldog",
+                 control=list(trace=0,ftol=1e-8,xtol=1e-8,btol=1e-2,delta=-1.0))
> znlq$termcd
[1] 1
> all(abs(znlq$fvec)<=1e-8)
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.14    0.04    0.18