R Under development (unstable) (2023-11-25 r85635 ucrt) -- "Unsuffered Consequences"
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> # Broyden banded
> 
> 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)
> ztol <- 1000*.Machine$double.eps
> 
> z1 <- nleqslv(xstart,brdban, method="Newton")
> z2 <- nleqslv(xstart,brdban, method="Newton", control=list(dsub=5,dsuper=1))
> 
> cat("z1 termcd=",z1$termcd, "jcnt,fcnt=",z1$njcnt,z1$nfcnt,"\n")
z1 termcd= 1 jcnt,fcnt= 5 5 
> cat("z2 termcd=",z2$termcd, "jcnt,fcnt=",z2$njcnt,z2$nfcnt,"\n")
z2 termcd= 1 jcnt,fcnt= 5 5 
> z1$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$x, tolerance=ztol)
[1] TRUE
> 
> z1 <- nleqslv(xstart,brdban, ml=2,mu=2, method="Newton")
> z2 <- nleqslv(xstart,brdban, ml=2,mu=2, method="Newton", control=list(dsub=2,dsuper=2))
> 
> cat("z1 termcd=",z1$termcd, "jcnt,fcnt=",z1$njcnt,z1$nfcnt,"\n")
z1 termcd= 1 jcnt,fcnt= 5 5 
> cat("z2 termcd=",z2$termcd, "jcnt,fcnt=",z2$njcnt,z2$nfcnt,"\n")
z2 termcd= 1 jcnt,fcnt= 5 5 
> z1$message
[1] "Function criterion near zero"
> z2$message
[1] "Function criterion near zero"
> all.equal(z2$x,z1$x, tolerance=ztol)
[1] TRUE
> 
> z3 <- nleqslv(xstart,brdban, ml=2,mu=2, method="Broyden")
> z4 <- nleqslv(xstart,brdban, ml=2,mu=2, method="Broyden", control=list(dsub=2,dsuper=2))
> 
> cat("z3 termcd=",z1$termcd, "jcnt,fcnt=",z3$njcnt,z3$nfcnt,"\n")
z3 termcd= 1 jcnt,fcnt= 1 20 
> cat("z4 termcd=",z2$termcd, "jcnt,fcnt=",z4$njcnt,z4$nfcnt,"\n")
z4 termcd= 1 jcnt,fcnt= 1 20 
> z3$message
[1] "Function criterion near zero"
> z4$message
[1] "Function criterion near zero"
> all.equal(z3$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 
   0.14    0.06    0.18