/*
**   nl8.e  - Helical Valley Function
**            More, Garbow and Hillstrom, 1981, "Testing Unconstrained
**                 Optimization Software", TOMS 7, 17-41.
*/

library nlsys;

proc F(x);
    local eqns;
    eqns = x;
    eqns[1] = 10*(x[3] - 10 * (atan(x[2]/x[1])/(2*pi) + (x[1] < 0)/2));
    eqns[2] = 10*(sqrt(x[1]*x[1] + x[2]*x[2]) - 1);
    retp(eqns);
endp;

output file = nl8.out reset;

nlset;

/* starting values */
x0 =  { -1, 0, 0 };

__title = "Helical Valley Function";
_nlchpf = 1;
_nlalgr = 2;

call nlprt(nlsys(&f,x0));

output off;