/*
** Lesson 6.2: Two-Variable Scalar-Valued Function
** g(x) = (x[1]^2+x[2]-11)^2 + (x[1]+x[2]^2-7)^2
*/
use gpe2;
output file=gpe\output6.2 reset;

fn g(data,x)=(x[1]^2+x[2]-11)^2+(x[1]+x[2]^2-7)^2;

call reset;
_nlopt=0;
_method=1;
_iter=100;
_step=1;
_conv=1;
_b={3,-2};

call estimate(&g,0);
/*
_deriv=&g1|&g2;
call estimate(&g,0);
*/

end;

proc g1(data,x); @ 1st derivative of g(x) @
    local f1,f2;
    f1=4*x[1]*(x[1]^2+x[2]-11)+2*(x[1]+x[2]^2-7);
    f2=2*(x[1]^2+x[2]-11)+4*x[2]*(x[1]+x[2]^2-7);
    retp (f1~f2);
endp;

proc g2(data,x); @ 2nd derivative of g(x) @
    local f11,f22,f12;
    f11=12*x[1]^2+4*x[2]-42;
    f22=4*x[1]+12*x[2]^2-26;
    f12=4*(x[1]+x[2]);
    retp ((f11~f12)|(f12~f22));
endp;