R Under development (unstable) (2023-11-25 r85635 ucrt) -- "Unsuffered Consequences"
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> # Broyden banded function
> 
> library(nleqslv)
> 
> brdtri <- function(x) {
+ 	n <- length(x)
+     y <- numeric(n)
+ 
+     # y[1] <- (3-2*x[1])*x[1] - 2*x[2] + 1
+     # y[n] <- (3-2*x[n])*x[n] - x[n-1] + 1
+     #
+     # k <- 2:(n-1)
+     # y[k] <- (3-2*x[k])*x[k] - x[k-1] - 2 * x[k+1] + 1
+     #
+     y <- (3-2*x)*x - c(0,x[-n]) - 2*c(x[-1],0) + 1
+ 	y
+ }
> 
> brdtrijac <- function(x) {
+     n <- length(x)
+     J <- diag(3-4*x,n,n)
+     J[row(J)==col(J)+1] <- -1
+     J[row(J)==col(J)-1] <- -2
+     J
+ }
> 
> options(echo=TRUE)
> 
> n <- 10
> xstart <- -rep(1,n)
> fstart <- brdtri(xstart)
> 
> z0 <- nleqslv(xstart,brdtri, method="Newton", global="dbldog")
> z0$message
[1] "Function criterion near zero"
> 
> z1 <- nleqslv(xstart,brdtri, brdtrijac, method="Newton", global="dbldog",control=list(trace=0))
> z1$message
[1] "Function criterion near zero"
> all.equal(z1$x,z0$x)
[1] TRUE
> 
> z2 <- nleqslv(xstart,brdtri, brdtrijac, method="Newton", global="dbldog",control=list(trace=0,chkjac=TRUE))
> z2$message
[1] "Function criterion near zero"
> all.equal(z2$x,z0$x)
[1] TRUE
> 
> z3 <- nleqslv(xstart,brdtri, brdtrijac, method="Newton", global="dbldog",control=list(trace=0,dsub=1,dsuper=1))
> z3$message
[1] "Function criterion near zero"
> all.equal(z2$x,z0$x)
[1] TRUE
> 
> z4 <- nleqslv(xstart,brdtri, brdtrijac, method="Newton", global="dbldog",control=list(trace=0,dsub=1,dsuper=1,chkjac=TRUE))
> z4$message
[1] "Function criterion near zero"
> all.equal(z2$x,z0$x)
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.20    0.03    0.18