library("nleqslv")

# Dennis & Schnabel,1996,"Numerical methods for unconstrained optimization and nonlinear equations", SIAM
# example 6.5.1 page 149

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
fstart

# 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))
}

# Broyden numerical Jacobian
for( z in c("cline", "qline", "gline") ) {  # cubic, quadratic, geometric linesearch
    znlq <- nleqslv(xstart, dslnex, global=z,control=list(btol=.01))
    print.result(znlq)
}

# 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, control=list(btol=.01,delta=delta))
        print.result(znlq)
    }
}

# 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, control=list(btol=.01,delta=delta))
        print.result(znlq)
    }
}

# 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, control=list(btol=.01,delta=delta))
        print.result(znlq)
    }
}