R Under development (unstable) (2023-11-25 r85635 ucrt) -- "Unsuffered Consequences"
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> # Dennis Schnabel example
> 
> library("nleqslv")
> 
> dslnex <- function(x) {
+     y <- numeric(2)
+     y[1] <- x[1]^2 + x[2]^2 - 2
+     y[2] <- exp(x[1]-1) + x[2]^3 - 2
+     y
+ }
> 
> jacdsln <- function(x) {
+     n <- length(x)
+     Df <- matrix(numeric(n*n),n,n)
+     Df[1,1] <- 2*x[1]
+     Df[1,2] <- 2*x[2]
+     Df[2,1] <- exp(x[1]-1)
+     Df[2,2] <- 3*x[2]^2
+ 
+     Df
+ }
> 
> xstart <- c(2,0.5)
> fstart <- dslnex(xstart)
> xstart
[1] 2.0 0.5
> fstart
[1] 2.2500000 0.8432818
> 
> # a solution is c(1,1)
> 
> do.print.xf <- FALSE
> 
> print.result <- function(z) {
+     if( do.print.xf ) {
+         print(z$x)
+         print(z$fvec)
+     }
+     print(z$message)
+     print(all(abs(z$fvec)<=1e-8))
+ }
> 
> # Use automatic scaling of x-values. Dosn't always work.
> 
> # Broyden numerical Jacobian
> for( z in c("qline", "gline") ) {  # quadratic, geometric linesearch
+     znlq <- nleqslv(xstart, dslnex, global=z,xscalm="auto",control=list(btol=.01))
+     print.result(znlq)
+ }
[1] "Function criterion near zero"
[1] TRUE
[1] "Function criterion near zero"
[1] TRUE
> 
> # Broyden numerical Jacobian
> for( z in c("dbldog","pwldog") ) {  # double dogleg, Powell (single) dogleg
+     for( delta in c(-1.0, -2.0) ) { # Cauchy step , Newton step
+         znlq <- nleqslv(xstart, dslnex, global=z,xscalm="auto", control=list(btol=.01,delta=delta))
+         print.result(znlq)
+     }
+ }
[1] "Function criterion near zero"
[1] TRUE
[1] "No better point found (algorithm has stalled)"
[1] FALSE
[1] "Function criterion near zero"
[1] TRUE
[1] "No better point found (algorithm has stalled)"
[1] FALSE
> 
> # Broyden analytical jacobian
> for( z in c("dbldog","pwldog") ) {  # double dogleg, Powell (single) dogleg
+     for( delta in c(-1.0, -2.0) ) { # Cauchy step , Newton step
+         znlq <- nleqslv(xstart, dslnex, jacdsln, global=z,xscalm="auto", control=list(btol=.01,delta=delta))
+         print.result(znlq)
+     }
+ }
[1] "Function criterion near zero"
[1] TRUE
[1] "No better point found (algorithm has stalled)"
[1] FALSE
[1] "Function criterion near zero"
[1] TRUE
[1] "No better point found (algorithm has stalled)"
[1] FALSE
> 
> # Newton analytical jacobian
> for( z in c("dbldog","pwldog") ) {  # double dogleg, Powell (single) dogleg
+     for( delta in c(-1.0, -2.0) ) { # Cauchy step , Newton step
+         znlq <- nleqslv(xstart, dslnex, jacdsln, method="Newton", global=z,xscalm="auto", control=list(btol=.01,delta=delta))
+         print.result(znlq)
+     }
+ }
[1] "No better point found (algorithm has stalled)"
[1] FALSE
[1] "No better point found (algorithm has stalled)"
[1] FALSE
[1] "No better point found (algorithm has stalled)"
[1] FALSE
[1] "No better point found (algorithm has stalled)"
[1] FALSE
> 
> proc.time()
   user  system elapsed 
   0.14    0.07    0.20