/*
**  NL5.E
**
**  Extended Powell Singular Function
**
**  A test program for nonlinear equation solution.
**  (See Dennis and Schnabel, 1983 and More', Garbow
**  and Hillstrom);
**
**  The equations to be solved are:
**
**      For n = 1:
**
**      Eq 1:   x1 + 10*x2 = 0
**      Eq 2:   sqrt(5)*(x3 - x4) = 0
**      Eq 3:   (x2 - 2*x4)^2
**      Eq 2:   sqrt(10)*(x1 - x4)^2 = 0
**
**  Starting values:
**      x0 = 3,-1,0,1
**  Solution:
**      x* = 0,0,0,0
**
** References:
**      Dennis and Schnabel 1983,
**      Numerical Methods for Unconstrained Optimization and
**      Nonlinear Equations (New Jersey: Prentice-Hall)
**
*/

library nlsys;
nlset;

proc  F(x);
    local f1,f2,f3,f4;
    f1 =  x[1] + 10*x[2];
    f2 =  sqrt(5)*(x[3] - x[4]);
    f3 =  (x[2] - 2*x[4])^2;
    f4 =  sqrt(10)*(x[1] - x[4])^2;
    retp(f1|f2|f3|f4);
endp;

output file = nl5.out reset;

                    /* starting values */
let x0 = 3 -1 0 1;

_nlchpf = 0;
_nlalgr = 1;
_nlfvtol = 1e-8;
__title = "Extended Powell Singular Function";

{ x,fvp,jc,tcode }= nlprt(nlsys(&f,x0));

output off;