$title Test of correctness for levels & marginals of NLP (NLP01,SEQ=415)

$onText
Test of correctness of the levels and marginals returned.
Although this test should work for all NLP solvers,
it is designed specifically to test a MINOS-style link.
It includes most/all of the different sorts of variables and
constraints one finds in such links.

Contributor: Steve
$offText

$if not set MTYPE   $set MTYPE nlp
$if not set TESTTOL $set TESTTOL 1e-6
scalar mchecks / 0 /;
$if not %MCHECKS% == 0 mchecks = 1;

$escape =
$echo if{%=1, display '%=1 failed', '%=2'; failed=1}; > tmp.gms
$escape %

scalars
  cz / 1 /
  cb / 0 /;

variables
  t   'linear in obj, nonlinear in constraints'
  u   'nonlinear in obj and constraints'
  v   'nonlinear in obj, linear in constraints'
  w   'not in obj, nonlinear in constraints'
  x   'linear in obj and constraints'
  y   'not in obj, linear in constraints'
  z   'objective var'
  ;
equations
  obj
  e   'linear, equality'
  f   'nonlinear, less-than'
  g   'nonlinear, greater-than'
  h   'nonlinear, equality'
  L   'linear, less-than'
  ;

obj.. cz * z =E= cb + 2*t + sqr(u) + sin(v/10) + 5*x;
e..   w =E= 2*t;
L..   x + y =L= 7;
f..   u**1.5 + y =L= 3;
g..   1 =G= log(t) + v;
h..   w**1.1 =E= y;

model m / e, L, obj, f, g, h /;

t.lo = .1;    t.up = 2;
u.lo = 1e-3;  u.up = 3;
v.lo = 1e-3;  v.up = 4;
w.lo = 1e-3;  w.up = 1;
x.lo = 0;     x.up = 10;
y.lo = 0;     y.up = 10;

* solve m using nlp max z;
* $exit

scalars
  failed  /    0 /
  isMax   /    0 /
  tol     /    %TESTTOL% /
  obj_l   /    0.0 /
  obj_m   /    1.0 /
  objval  /   38.67540837055 /
  e_l     /    0 /
  e_m     /   -6.448473234922 /
  f_l     /    3 /
  f_m     /    1.8859080143051 /
  g_l     /   -1 /
  g_m     /   -0.094595854378246 /
  h_l     /    0 /
  h_m     /    6.8859080143051 /
  L_l     /    7 /
  L_m     /    5 /
  t_l     /    0.1 /
  t_m     /  -11.842905013627 /
  u_l     /    2.00061508410989 /
  u_m     /    0 /
  v_l     /    3.30258509299405 /
  v_m     /    0 /
  w_l     /    0.2 /
  w_m     /    0 /
  x_l     /    6.82973201549584 /
  x_m     /    0 /
  y_l     /    0.170267984504157 /
  y_m     /    0 /
  ;

set czvals 'obj multipliers' /
'cz=1',
'cz=0.5'
'cz=3'
'cz=-1'
'cz=-0.5'
'cz=-3'
/;
parameter czv(czvals) /
'cz=1'          1
'cz=0.5'        0.5
'cz=3'          3
'cz=-1'        -1
'cz=-0.5'      -0.5
'cz=-3'        -3
/;

set cbvals 'obj constants' /
'cb=0'
'cb=2'
'cb=-2'
/;
parameter cbv(cbvals) /
'cb=0'          0
'cb=2'          2
'cb=-2'        -2
/;

loop {czvals$[ord(czvals) <= INF],
 cz = czv(czvals);
 loop {cbvals$[ord(cbvals) <= INF],
  cb = cbv(cbvals);
  if {(cz > 0),
    isMax = 1;
    solve m using %MTYPE% max z;
  else
    isMax = -1;
    solve m using %MTYPE% min z;
  }

  if {(m.modelstat = %modelStat.noSolutionReturned%) and (m.solvestat = %solveStat.capabilityProblems%),
*   capability problems due to sin() or non-convex model
    abort.noerror 'Capability problems: further testing skipped: TEST PASSED';
  };
$ batInclude tmp "( m.solvestat <> %solveStat.normalCompletion% or (m.modelstat > %modelStat.locallyOptimal% and m.modelstat <> %modelStat.feasibleSolution%))" "wrong status codes"

$ batInclude tmp "(abs(cz*z.l-cb-objval) > tol)"          "bad z.l"

$ batInclude tmp "(abs(t.l-t_l) > tol)"                   "bad t.l"
$ batInclude tmp "(abs(u.l-u_l) > tol)"                   "bad u.l"
$ batInclude tmp "(abs(v.l-v_l) > tol)"                   "bad v.l"
$ batInclude tmp "(abs(w.l-w_l) > tol)"                   "bad w.l"
$ batInclude tmp "(abs(x.l-x_l) > tol)"                   "bad x.l"
$ batInclude tmp "(abs(y.l-y_l) > tol)"                   "bad y.l"

$ batInclude tmp "(abs(obj.l-cb) > tol)"                  "bad obj.l"
$ batInclude tmp "(abs(e.l-e_l) > tol)"                   "bad e.l"
$ batInclude tmp "(abs(f.l-f_l) > tol)"                   "bad f.l"
$ batInclude tmp "(abs(g.l-g_l) > tol)"                   "bad g.l"
$ batInclude tmp "(abs(h.l-h_l) > tol)"                   "bad h.l"
$ batInclude tmp "(abs(L.l-L_l) > tol)"                   "bad L.l"

  if {mchecks,
$   batInclude tmp "(abs(z.m) > tol)"                     "bad z.m"
$   batInclude tmp "(abs(cz*t.m -t_m) > tol)"             "bad t.m"
$   batInclude tmp "(abs(cz*u.m -u_m) > tol)"             "bad u.m"
$   batInclude tmp "(abs(cz*v.m -v_m) > tol)"             "bad v.m"
$   batInclude tmp "(abs(cz*w.m -w_m) > tol)"             "bad w.m"
$   batInclude tmp "(abs(cz*x.m -x_m) > tol)"             "bad x.m"
$   batInclude tmp "(abs(cz*y.m -y_m) > tol)"             "bad y.m"

$   batInclude tmp "(abs(cz*obj.m-obj_m) > tol)"          "bad obj.m"
$   batInclude tmp "(abs(cz*e.m -e_m) > tol)"             "bad e.m"
$   batInclude tmp "(abs(cz*f.m -f_m) > tol)"             "bad f.m"
$   batInclude tmp "(abs(cz*g.m -g_m) > tol)"             "bad g.m"
$   batInclude tmp "(abs(cz*h.m -h_m) > tol)"             "bad h.m"
$   batInclude tmp "(abs(cz*L.m -L_m) > tol)"             "bad L.m"
  };

$ifThen set doscalar
  if {failed,
    option %MTYPE%=convert;
    if {(cz > 0),
      solve m using %MTYPE% max z;
    else
      solve m using %MTYPE% min z;
    };
  };
$endIf
  abort$failed 'test failed', cz, cb;
 };
};