[ADMB Users] Using atan2 with df1b2variables

[dave fournier]

I figure the df1b2variable version of atan2 should be a lot like this.
the derivative code could stand some optimization.


df1b2variable atan2(const df1b2variable& y,const df1b2variable& x)
   {
     df1b2variable z;
     double xu=*x.get_u();
     double yu=*y.get_u();
     double r2=square(xu)+square(yu);
     double zu=::atan2(yu,xu);
     *z.get_u()=zu;

     double dfx=-yu/r2;
     double dfy=xu/r2;
     double dfxx=2.0*yu*xu/square(r2);
     double dfxy=-1.0/r2+2.0*square(yu)/square(r2);
     double dfyy=-2.0*xu*yu/square(r2);
     double dfxxx=2.0*yu/square(r2)-8.0*yu*square(xu)/cube(r2);
     double dfxxy=2.0*xu/square(r2)-8.0*square(yu)*xu/cube(r2);
     double dfxyy=-2.0*yu/square(r2)+8.0*square(xu)*yu/cube(r2);
     double dfyyy=-2.0*xu/square(r2)+8.0*xu*square(yu)/cube(r2);

     double * xd=x.get_u_dot();
     double * yd=y.get_u_dot();
     double * zd=z.get_u_dot();

     for (int i=0;i<df1b2variable::nvar;i++)
     {
       *zd++ = dfx * *xd++ + dfy * *yd++;
     }

     f1b2gradlist->write_pass1(&y,&x,&z,
       dfy,
       dfx,
       dfyy,dfxy,dfxx,
       dfyyy,dfxyy,dfxxy,dfxxx);
     return z;
   }
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