$title Advanced test for limited domains for variables in model (limdom04,SEQ=815)

$onText
With GAMS 31 we introduced the capability to limit the domain of variables
in the model statement. This test uses a dummy model to verify that this new
feature leads to the same result as using explicit dollar conditions.
The focus of this test is on non-trivial cases for the index use, like
lag and lead operations, explicit labels or singleton sets.

Contributor: Lutz Westermann, March 2020
$offText

Set    i  / i1 * i20 /;
Alias (i,j,k,l);
Set    sub(i,j,k);
Singleton Set si(i) / i12 /;
Alias (si,sj,sk);

sub(i,j,k)$(uniform(0,1)<0.2) = yes;

Positive Variable x(i,j,k);
Variable          z;

Equation obj        Dummy objective function
         plainDLV   Plain indices with Domain Limited Variables
         plainDOL   Plain indices using explicit DOLlar condition
         lagLeadDLV Indices with lag and lead operators with Domain Limited Variables
         lagLeadDOL Indices with lag and lead operators using explicit DOLlar condition
         labelDLV   Indices with explicit labels with Domain Limited Variables
         labelDOL   Indices with explicit labels using explicit DOLlar condition
         singleDLV  Indices with singleton sets with Domain Limited Variables
         singleDOL  Indices with singleton sets using explicit DOLlar condition
         suffixDLV  Using suffixes on variables with Domain Limited Variables
         suffixDOL  Using suffixes on variables using explicit DOLlar condition
         ;

obj.. z =e= 1;

plainDLV.. sum((i,j,k), x(i,j,k))            =l= 42;
plainDOL.. sum((i,j,k), x(i,j,k)$sub(i,j,k)) =l= 42;

lagLeadDLV.. sum((i,j,k), x(i-1,j+[2+6/3-ord(j)+card(k)],k+[min(5,ceil(sum(l,sqr(0.2))))]))                                                                    =l= 42;
lagLeadDOL.. sum((i,j,k), x(i-1,j+[2+6/3-ord(j)+card(k)],k+[min(5,ceil(sum(l,sqr(0.2))))])$sub(i-1,j+[2+6/3-ord(j)+card(k)],k+[min(5,ceil(sum(l,sqr(0.2))))])) =l= 42;

labelDLV.. sum((j,k), x('i11',j,'i12'))                    =l= 42;
labelDOL.. sum((j,k), x('i11',j,'i12')$sub('i11',j,'i12')) =l= 42;

singleDLV.. sum((si,sj,sk(k)), x(si,sj,k))              =l= 42;
singleDOL.. sum((si,sj,sk(k)), x(si,sj,k)$sub(si,sj,k)) =l= 42;

Model mDLV / obj, plainDLV, lagLeadDLV, labelDLV, singleDLV, x(sub) /;
Model mDOL / obj, plainDOL, lagLeadDOL, labelDOL, singleDOL         /;

option limrow   = 0,
       limcol   = 0,
       solprint = off
       lp       = convert;

solve mDLV min z use lp;
execute.CheckErrorLevel 'grep -v "LP written by GAMS" gams.gms > mDLV.gms';
solve mDOL min z use lp;
execute.CheckErrorLevel 'grep -v "LP written by GAMS" gams.gms > mDOL.gms';

execute.CheckErrorLevel '=diff -b mDLV.gms mDOL.gms';

$onSuffixDLVars

suffixDLV.. sum((i,j,k), x('i11',j,'i12' )                   * x.l(i-1,j+[2+6/3-ord(j)+card(k)],k+[min(5,ceil(sum(l,sqr(0.2))))]))                                                                    =l= 42;
suffixDOL.. sum((i,j,k), x('i11',j,'i12')$sub('i11',j,'i12') * x.l(i-1,j+[2+6/3-ord(j)+card(k)],k+[min(5,ceil(sum(l,sqr(0.2))))])$sub(i-1,j+[2+6/3-ord(j)+card(k)],k+[min(5,ceil(sum(l,sqr(0.2))))])) =l= 42;

Model mDLVSuf / obj, suffixDLV, x(sub) /;
Model mDOLSuf / obj, suffixDOL         /;

option limrow   = 0,
       limcol   = 0,
       solprint = off
       lp       = convert;

solve mDLVSuf min z use lp;
execute.CheckErrorLevel 'grep -v "LP written by GAMS" gams.gms > mDLVSuf.gms';
solve mDOLSuf min z use lp;
execute.CheckErrorLevel 'grep -v "LP written by GAMS" gams.gms > mDOLSuf.gms';

execute.CheckErrorLevel '=diff -b mDLVSuf.gms mDOLSuf.gms';