$title Test for interval evaluation (INTERVAL,SEQ=506)
$onText

Contributer: Arne Drud, December 2010

$offText

$onEchoV > decr.gms
$eolCom !
*
*  Monotonely decreasing function in various combinations
*

$if not set global $set global 0
Scalar Global        1 if solver is global and 0 otherwise           / %global% /
       LOpt_Stat     Model Status for locally optimal solutions      / 2 /
       LInfeas_Stat  Model Status for locally infeasible solutions   / 5 /
       GOpt_Stat     Model Status for globally optimal solutions     / 1 /
       GInfeas_Stat  Model Status for globally infeasible solutions  / 4 /
       Opt_Stat      Model Status for optimal solutions used here
       Infeas_Stat   Model Status for infeasible solutions used here ;

set case / high, mid, low /;
parameter RhsV(case)
scalar Rhs;
variable x;

$if not set case $abort Parameter case must define an existing include file
$include %case%

abort$(x.lo >= x.up) "lower and upper bounds are not consistent", x.lo, x.up;
*
*  Define Rhsv such that it is above function value at lower end of the
*  interval and belowe the function value at the upper end of the interval
*  and matches the function value in the middle for rhsv(mid):

Rhsv("high") = func(x.lo) + 1.0;
Rhsv("mid")  = func(((x.lo+x.up)/2));
Rhsv("low")  = func(x.up) - 1.0;

equation e_eq;
e_eq .. func(x) =E= Rhs;
model decr_eq / e_eq /;

equation e_gt;
e_gt .. func(x) =G= Rhs;
model decr_gt / e_gt /;

equation e_lt;
e_lt .. func(x) =L= Rhs;
model decr_lt / e_lt /;

*
*  Desired Model Status for local solver: 2 = Locally optimal, 5 = Locally infeasible
*
Parameter Mstat_eq(Case) / high 5
                           mid  2
                           low  5 /;
Parameter Mstat_gt(Case) / high 5
                           mid  2
                           low  2 /;
Parameter Mstat_lt(Case) / high 2
                           mid  2
                           low  5 /;
*
*  Translate into Global return codes if relevant
*
if ( Global,
  option nlp=conopt4;
  Opt_Stat = GOpt_Stat; Infeas_Stat = GInfeas_Stat;
  Mstat_eq(case)$(Mstat_eq(case) eq LOpt_Stat)    = Opt_Stat;
  Mstat_eq(case)$(Mstat_eq(case) eq LInfeas_Stat) = Infeas_Stat;
  Mstat_gt(case)$(Mstat_gt(case) eq LOpt_Stat)    = Opt_Stat;
  Mstat_gt(case)$(Mstat_gt(case) eq LInfeas_Stat) = Infeas_Stat;
  Mstat_lt(case)$(Mstat_lt(case) eq LOpt_Stat)    = Opt_Stat;
  Mstat_lt(case)$(Mstat_lt(case) eq LInfeas_Stat) = Infeas_Stat;
else
  option nlp=conopt3;
  Opt_Stat = LOpt_Stat; Infeas_Stat = LInfeas_Stat;
);
*
*  Characteristics for solution for optimal models:
*  1: Variable at upper bound
*  2: Variable determined by constraint as equality
*
Parameter Char_eq(case) / mid 2 /;
Parameter Char_gt(case) / mid 2, low 1 /;
Parameter Char_lt(case) / high 1, mid 1 /;

option limrow = 0, limcol = 0;
loop( case,
   Rhs = RhsV(case);

   if(not Global,x.l = (x.up+x.lo)/2;);
   solve decr_eq using nlp maximizing x;
   abort$(decr_eq.solvestat ne 1) "Solver Status is not 1";
   abort$(decr_eq.modelstat ne Mstat_eq(case)) "Model Status is not as expected";
   if ( decr_eq.modelstat eq Opt_Stat,
      if ( Char_eq(case) eq 1,
         abort$(abs(x.l-x.up) > 1.e-7) "Solution value is not as expected"; );
      if ( Char_eq(case) eq 2,
         abort$(abs(func(x.l)-RhsV(case)) > 1.e-7) "Solution value is not as expected"; );
   );

   if(not Global,x.l = (x.up+x.lo)/2;);
   solve decr_gt using nlp maximizing x;
   abort$(decr_gt.solvestat ne 1) "Solver Status is not 1";
   abort$(decr_gt.modelstat ne Mstat_gt(case)) "Model Status is not as expected";
   if ( decr_gt.modelstat eq Opt_Stat,
      if ( Char_gt(case) eq 1,
         abort$(abs(x.l-x.up) > 1.e-7) "Solution value is not as expected"; );
      if ( Char_gt(case) eq 2,
         abort$(abs(func(x.l)-RhsV(case)) > 1.e-7) "Solution value is not as expected"; );
   );

   if(not Global,x.l = (x.up+x.lo)/2;);
   solve decr_lt using nlp maximizing x;
   abort$(decr_lt.solvestat ne 1) "Solver Status is not 1";
   abort$(decr_lt.modelstat ne Mstat_lt(case)) "Model Status is not as expected";
   if ( decr_lt.modelstat eq Opt_Stat,
      if ( Char_lt(case) eq 1,
         abort$(abs(x.l-x.up) > 1.e-7) "Solution value is not as expected"; );
      if ( Char_lt(case) eq 2,
         abort$(abs(func(x.l)-RhsV(case)) > 1.e-7) "Solution value is not as expected"; );
   );

);
$offEcho

$onEcho > dcase1.gms
$macro func(x) -log(x)
x.lo = 0.1; x.up = 2;
$offEcho

$onEcho > dcase2.gms
$macro func(x) -power(x,3)-x
x.lo = 0.0; x.up = 1.0;
$offEcho

$onEcho > dcase3.gms
$macro func(x) -power(x,3)
x.lo = -1.0; x.up = -0.1;
$offEcho

$onEcho > dcase4.gms
$macro func(x) -power(x,3)
x.lo = -1.0; x.up = 0;
if(not Global,x.l = -1;);
$offEcho

$onEcho > dcase5.gms
$macro func(x) -exp(x)
x.lo = -1; x.up = 2;
$offEcho

$onEcho > dcase6.gms
$macro func(x) -exp(x)+exp(-x)
x.lo = -1; x.up = 2;
$offEcho

$onEcho > dcase7.gms
$macro func(x) 1-errorf(x)
x.lo = 0.1; x.up = 2;
$offEcho

$onEcho > dcase8.gms
$macro func(x) sqr(x)
x.lo = -2.0; x.up = -0.1;
$offEcho

$onEcho > dcase9.gms
$macro func(x) sqr(x)-power(x,3)
x.lo = -1.0; x.up = -0.1;
$offEcho

$onEcho > dcase10.gms
$macro func(x) -power(x,3)-x
x.lo = -1.0; x.up = 1.0;
$offEcho

$onEcho > dcase11.gms
$macro func(x) -power(x,3)
x.lo = -1.0; x.up = 1.2;
$offEcho

$onEcho > dcase12.gms
$macro func(x) -power(x,3)
x.lo = 0.0; x.up = 1.2;
$offEcho

$call gams decr --case=dcase1  --global=1 lo=2 o=dcase1.lst
$if errorlevel 1 $abort 'dcase1  --global=1 failed, see dcase1.lst'
$call gams decr --case=dcase2  --global=1 lo=2 o=dcase2.lst
$if errorlevel 1 $abort 'dcase2  --global=1 failed, see dcase2.lst'
$call gams decr --case=dcase3  --global=1 lo=2 o=dcase3.lst
$if errorlevel 1 $abort 'dcase3  --global=1 failed, see dcase3.lst'
$call gams decr --case=dcase4  --global=1 lo=2 o=dcase4.lst
$if errorlevel 1 $abort 'dcase4  --global=1 failed, see dcase4.lst'
$call gams decr --case=dcase5  --global=1 lo=2 o=dcase5.lst
$if errorlevel 1 $abort 'dcase5  --global=1 failed, see dcase5.lst'
$call gams decr --case=dcase6  --global=1 lo=2 o=dcase6.lst
$if errorlevel 1 $abort 'dcase6  --global=1 failed, see dcase6.lst'
$call gams decr --case=dcase7  --global=1 lo=2 o=dcase7.lst
$if errorlevel 1 $abort 'dcase7  --global=1 failed, see dcase7.lst'
$call gams decr --case=dcase8  --global=1 lo=2 o=dcase8.lst
$if errorlevel 1 $abort 'dcase8  --global=1 failed, see dcase8.lst'
$call gams decr --case=dcase9  --global=1 lo=2 o=dcase9.lst
$if errorlevel 1 $abort 'dcase9  --global=1 failed, see dcase9.lst'
$call gams decr --case=dcase10 --global=1 lo=2 o=dcase10.lst
$if errorlevel 1 $abort 'dcase10 --global=1 failed, see dcase10.lst'
$call gams decr --case=dcase11 --global=1 lo=2 o=dcase11.lst
$if errorlevel 1 $abort 'dcase11 --global=1 failed, see dcase11.lst'
$call gams decr --case=dcase12 --global=1 lo=2 o=dcase12.lst
$if errorlevel 1 $abort 'dcase12 --global=1 failed, see dcase12.lst'

$call gams decr --case=dcase1  --global=0 lo=2 o=dcase1.lst
$if errorlevel 1 $abort 'dcase1  --global=0 failed, see dcase1.lst'
$call gams decr --case=dcase2  --global=0 lo=2 o=dcase2.lst
$if errorlevel 1 $abort 'dcase2  --global=0 failed, see dcase2.lst'
$call gams decr --case=dcase3  --global=0 lo=2 o=dcase3.lst
$if errorlevel 1 $abort 'dcase3  --global=0 failed, see dcase3.lst'
$call gams decr --case=dcase4  --global=0 lo=2 o=dcase4.lst
$if errorlevel 1 $abort 'dcase4  --global=0 failed, see dcase4.lst'
$call gams decr --case=dcase5  --global=0 lo=2 o=dcase5.lst
$if errorlevel 1 $abort 'dcase5  --global=0 failed, see dcase5.lst'
$call gams decr --case=dcase6  --global=0 lo=2 o=dcase6.lst
$if errorlevel 1 $abort 'dcase6  --global=0 failed, see dcase6.lst'
$call gams decr --case=dcase7  --global=0 lo=2 o=dcase7.lst
$if errorlevel 1 $abort 'dcase7  --global=0 failed, see dcase7.lst'
$call gams decr --case=dcase8  --global=0 lo=2 o=dcase8.lst
$if errorlevel 1 $abort 'dcase8  --global=0 failed, see dcase8.lst'
$call gams decr --case=dcase9  --global=0 lo=2 o=dcase9.lst
$if errorlevel 1 $abort 'dcase9  --global=0 failed, see dcase9.lst'
$call gams decr --case=dcase10 --global=0 lo=2 o=dcase10.lst
$if errorlevel 1 $abort 'dcase10 --global=0 failed, see dcase10.lst'
$call gams decr --case=dcase11 --global=0 lo=2 o=dcase11.lst
$if errorlevel 1 $abort 'dcase11 --global=0 failed, see dcase11.lst'
$call gams decr --case=dcase12 --global=0 lo=2 o=dcase12.lst
$if errorlevel 1 $abort 'dcase12 --global=0 failed, see dcase12.lst'