fnset_xyz.inc : intrinsics tests for f(x,y,z)

File : fnset_xyz.inc  used by :  fnncpf.gms [html]   fnncpf2.gms [htmlfnncpcm.gms [html]   fnncpcm2.gms [html]   fnncpvus.gms [html]   fnncpvup.gms [html]   fnncpvux.gms [html]

How is relative accuracy defined?  Given:
  1. a point x,
  2. the computed value f(x), and
  3. the known value fbar,

we can compute the relative accuracy of f vis-a-vis fbar in two ways:
  1. |f-fbar| <= reps * |fbar|
  2. |f-fbar| <= reps * max(1,|x|)

The first case is the most common, but for some functions
the second is more appropriate (e.g. sin(x)).

We can also pass a test if the absolute accuracy is within some
tolerance aeps:
  1. |f-fbar| <= aeps

Contributor: Steven Dirkse, October 2004

set V / x, y, z
        f,     f_,     f_a,     f_r
       fx,    fx_,    fx_a,    fx_r
       fy,    fy_,    fy_a,    fy_r
       fz,    fz_,    fz_a,    fz_r
      fxx,   fxx_,   fxx_a,   fxx_r
      fxy,   fxy_,   fxy_a,   fxy_r
      fxz,   fxz_,   fxz_a,   fxz_r
      fyx,   fyx_,   fyx_a,   fyx_r
      fyy,   fyy_,   fyy_a,   fyy_r
      fyz,   fyz_,   fyz_a,   fyz_r
      fzx,   fzx_,   fzx_a,   fzx_r
      fzy,   fzy_,   fzy_a,   fzy_r
      fzz,   fzz_,   fzz_a,   fzz_r
       rc,    rc_,    rc_e
       ec,    ec_,    ec_e

scalar aeps       'absolute error tolerance';
scalar aeps0      'absolute error tolerance, function';
scalar aeps1      'absolute error tolerance, first derivative';
scalar aeps2      'absolute error tolerance, second derivative';
scalar reps       'relative error tolerance';
scalar reps0      'relative error tolerance, function';
scalar reps1      'relative error tolerance, first derivative';
scalar reps2      'relative error tolerance, second derivative';
scalar relToInput 'reps is relative to input (not output) magnitude';
set T;
parameter data(T,V), tmp(T);