R Under development (unstable) (2023-11-25 r85635 ucrt) -- "Unsuffered Consequences"
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> # Broyden tridiagonal
> 
> 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
+ }
> 
> n <- 100
> xstart <- -rep(1,n)
> ztol <- 1000*.Machine$double.eps
> 
> z1 <- nleqslv(xstart,brdtri, method="Newton")
> z2 <- nleqslv(xstart,brdtri, method="Newton", control=list(dsub=1,dsuper=1))
> 
> cat("z1 termcd=",z1$termcd, "jcnt,fcnt=",z1$njcnt,z1$nfcnt,"\n")
z1 termcd= 1 jcnt,fcnt= 4 4 
> cat("z2 termcd=",z2$termcd, "jcnt,fcnt=",z2$njcnt,z2$nfcnt,"\n")
z2 termcd= 1 jcnt,fcnt= 4 4 
> z1$message
[1] "Function criterion near zero"
> z2$message
[1] "Function criterion near zero"
> all.equal(z2$x,z1$x)
[1] TRUE
> all.equal(z2$x,z1$x, tolerance=ztol)
[1] TRUE
> 
> z1 <- nleqslv(xstart,brdtri, method="Newton")
> z2 <- nleqslv(xstart,brdtri, method="Newton", control=list(dsub=1,dsuper=1))
> 
> cat("z1 termcd=",z1$termcd, "jcnt,fcnt=",z1$njcnt,z1$nfcnt,"\n")
z1 termcd= 1 jcnt,fcnt= 4 4 
> cat("z2 termcd=",z2$termcd, "jcnt,fcnt=",z2$njcnt,z2$nfcnt,"\n")
z2 termcd= 1 jcnt,fcnt= 4 4 
> z1$message
[1] "Function criterion near zero"
> z2$message
[1] "Function criterion near zero"
> all.equal(z2$x,z1$x, tolerance=ztol)
[1] TRUE
> 
> z3 <- nleqslv(xstart,brdtri, method="Broyden")
> z4 <- nleqslv(xstart,brdtri, method="Broyden", control=list(dsub=1,dsuper=1))
> 
> cat("z3 termcd=",z1$termcd, "jcnt,fcnt=",z3$njcnt,z3$nfcnt,"\n")
z3 termcd= 1 jcnt,fcnt= 1 10 
> cat("z4 termcd=",z2$termcd, "jcnt,fcnt=",z4$njcnt,z4$nfcnt,"\n")
z4 termcd= 1 jcnt,fcnt= 1 10 
> z3$message
[1] "x-values within tolerance 'xtol'"
> z4$message
[1] "x-values within tolerance 'xtol'"
> all.equal(z3$x,z1$x)
[1] TRUE
> all.equal(z4$x,z1$x)
[1] TRUE
> all.equal(z4$x,z3$x, tolerance=ztol)
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   0.15    0.04    0.20