emp21.gms : Test JAMS/EMP on implicit variable handling

Description

Test JAMS behavior on a small equilibrium model with implicit variables.

Contributors: Youngdae Kim & Steve Dirkse, Dec 2016


Small Model of Type : GAMS


Category : GAMS Test library


Main file : emp21.gms

$TITLE 'Test JAMS/EMP on implicit variable handling' (EMP21,SEQ=703)

$ontext
Test JAMS behavior on a small equilibrium model with implicit variables.

Contributors: Youngdae Kim & Steve Dirkse, Dec 2016
$offtext


$if not set TESTTOL $set TESTTOL 1e-3
scalars tol / %TESTTOL% /;
file opt  / 'jams.opt' /;
file info / '%emp.info%' /;

set i agents / 1*5 /;
alias(i,ii);

parameter q(i)    / 1 1.36, 2 1.5, 3 1.48, 4 1.5, 5 1.4 /;
parameter c(i)    / 1 10  , 2 8  , 3 6   , 4 4  , 5 2 /;
parameter K(i)    / 1 5   , 2 5  , 3 5   , 4 5  , 5 5 /;
parameter beta(i) / 1 1.2 , 2 1.1, 3 1.0 , 4 0.9, 5 0.8 /;
parameter e(i)    / 1 25  , 2 25 , 3 25  , 4 25 , 5 25 /;
parameter gamma   / 1.3 /;
parameter xi;

xi = sum(i, e(i));

* The scalar files generated depend on the variable declaration order,
* so do not change the declarations lightly

positive variable
    y(i)          production
    pi            price of the rare resource
    ;

variable
    x(i)          purchased rare resource
    obj(i)        objective variable of each agent
    zExp(i)       replication of z
    z             implicit variable
    ;

equation
    defobjExp(i)  objective function of each agent with replicated variables
    defobj(i)     objective function of each agent with implicit variable
    defcons(i)    constraint on production and trade
    defequil      Walas-equilibrium constraint
    defzExp(i)    replicated definition of z
    defz          definition of z
    ;

$macro cost(y,i) (c(i)*y(i) + \
    (beta(i)/(1+beta(i)))*(K(i)**(-1/beta(i)))*(y(i)**((1+beta(i))/beta(i))))

$macro tech(y,i) ((q(i)*y(i) + sqrt(y(i)+1) - 1)$sameas(i,'1') + \
                 (q(i)*y(i))$(not sameas(i,'1')))

* testing with explicit formulation

$macro priceExp     (5000**(1/gamma)*(zExp(i)**(-1/gamma)))

defobjExp(i)..
    obj(i) =E= cost(y,i) + pi*x(i) - priceExp*y(i);

defcons(i)..
    tech(y,i) =L= x(i) + e(i);

defequil..
    xi - sum(i, e(i) + x(i)) =G= 0;

defzExp(i)..
    zExp(i) =E= sum(ii, y(ii));

y.lo(i) = 0$(not sameas(i,'5')) + 1$sameas(i,'5');
y.up(i) = 30;
zExp.l(i) = 50;

model me 'explicit formulation' / defobjExp, defcons, defequil, defzExp /;

put info 'equilibrium';
loop(i,
    put / 'min', obj(i), y(i), x(i), zExp(i);
    put / defobjExp(i), defcons(i), defzExp(i);
);
put / 'vi', defequil, pi;
putclose;

putclose opt
  'Dict     explDict.txt' /
  'FileName expl.gms' ;

me.optfile = 1;
solve me using emp;

display obj.l, y.l, x.l, zExp.l, pi.l;

abort$[me.solvestat <> %solvestat.NormalCompletion%]
   'wrong me.solvestat', me.solvestat;
abort$[me.modelstat  > %modelstat.LocallyOptimal%]
   'wrong me.modelstat', me.modelstat;
abort$[ abs(obj.l('1')+176.647) > tol ]       'bad obj.l("1")', obj.l;
abort$[ abs(obj.l('2')+216.959) > tol ]       'bad obj.l("2")', obj.l;
abort$[ abs(obj.l('3')+264.905) > tol ]       'bad obj.l("3")', obj.l;
abort$[ abs(obj.l('4')+309.177) > tol ]       'bad obj.l("4")', obj.l;
abort$[ abs(obj.l('5')+372.600) > tol ]       'bad obj.l("5")', obj.l;
abort$[ abs(y.l('1')- 8.016) > tol ]          'bad y.l("1")', y.l;
abort$[ abs(y.l('2')-13.597) > tol ]          'bad y.l("2")', y.l;
abort$[ abs(y.l('3')-18.218) > tol ]          'bad y.l("3")', y.l;
abort$[ abs(y.l('4')-21.009) > tol ]          'bad y.l("4")', y.l;
abort$[ abs(y.l('5')-23.732) > tol ]          'bad y.l("5")', y.l;
abort$[ abs(x.l('1')+12.096) > tol ]          'bad x.l("1")', x.l;
abort$[ abs(x.l('2')+ 4.604) > tol ]          'bad x.l("2")', x.l;
abort$[ abs(x.l('3')- 1.962) > tol ]          'bad x.l("3")', x.l;
abort$[ abs(x.l('4')- 6.513) > tol ]          'bad x.l("4")', x.l;
abort$[ abs(x.l('5')- 8.224) > tol ]          'bad x.l("5")', x.l;
abort$[smax{i, abs(zExp.l(i)-84.571)} > tol ] 'bad zExp.l(i)', zExp.l;
abort$[ abs(pi.l- 6.484) > tol ]              'bad pi.l', pi.l;

obj.l(i) = 0;
y.l(i) = y.lo(i);
x.l(i) = 0;
z.l = 50;
pi.l = 0;
defobj.m(i) = 0;
defcons.m(i) = 0;
defequil.m = 0;
defz.m = 0;

$onecho > expl_gms
***********************************************
* written by GAMS/JAMS at 12/04/16 09:42:37
* for more information use JAMS option "Dict"
***********************************************

Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x17,x18,x19,x20,x21,u6,u7,u8,u9
          ,u10,u12,u13,u14,u15,u16;

Negative Variables  u6,u7,u8,u9,u10;

Positive Variables  x1,x2,x3,x4,x6;

Equations  e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,dL_dx1,dL_dx2,dL_dx3,dL_dx4
          ,dL_dx5,dL_dx7,dL_dx8,dL_dx9,dL_dx10,dL_dx11,dL_dx17,dL_dx18,dL_dx19
          ,dL_dx20,dL_dx21;


e6.. sqrt(1 + x1) + 1.36*x1 - x7 =L= 26;

e7..    1.5*x2 - x8 =L= 25;

e8..    1.48*x3 - x9 =L= 25;

e9..    1.5*x4 - x10 =L= 25;

e10..    1.4*x5 - x11 =L= 25;

e11..  - x7 - x8 - x9 - x10 - x11 =G= 0;

e12..  - x1 - x2 - x3 - x4 - x5 + x17 =E= 0;

e13..  - x1 - x2 - x3 - x4 - x5 + x18 =E= 0;

e14..  - x1 - x2 - x3 - x4 - x5 + x19 =E= 0;

e15..  - x1 - x2 - x3 - x4 - x5 + x20 =E= 0;

e16..  - x1 - x2 - x3 - x4 - x5 + x21 =E= 0;

dL_dx1.. (-(10 + 0.261532097202366*x1**0.833333333333333 - 700.424843564501*x17
         **(-0.769230769230769)))/(-1) - (1.36 + 0.5/sqrt(1 + x1))*u6 + u12
          =N= 0;

dL_dx2.. (-(8 + 0.231511582354131*x2**0.909090909090909 - 700.424843564501*x18
         **(-0.769230769230769)))/(-1) - 1.5*u7 + u13 =N= 0;

dL_dx3.. (-(6 + 0.2*x3**1 - 700.424843564501*x19**(-0.769230769230769)))/(-1)
          - 1.48*u8 + u14 =N= 0;

dL_dx4.. (-(4 + 0.167250206190075*x4**1.11111111111111 - 700.424843564501*x20**
         (-0.769230769230769)))/(-1) - 1.5*u9 + u15 =N= 0;

dL_dx5.. (-(2 + 0.133748060995284*x5**1.25 - 700.424843564501*x21**(-
         0.769230769230769)))/(-1) - 1.4*u10 + u16 =N= 0;

dL_dx7.. (-x6)/(-1) + u6 + eps*x7 =E= 0;

dL_dx8.. (-x6)/(-1) + u7 + eps*x8 =E= 0;

dL_dx9.. (-x6)/(-1) + u8 + eps*x9 =E= 0;

dL_dx10.. (-x6)/(-1) + u9 + eps*x10 =E= 0;

dL_dx11.. (-x6)/(-1) + u10 + eps*x11 =E= 0;

dL_dx17.. (-538.788341203462*x17**(-1.76923076923077)*x1)/(-1) - u12 =E= 0;

dL_dx18.. (-538.788341203462*x18**(-1.76923076923077)*x2)/(-1) - u13 =E= 0;

dL_dx19.. (-538.788341203462*x19**(-1.76923076923077)*x3)/(-1) - u14 =E= 0;

dL_dx20.. (-538.788341203462*x20**(-1.76923076923077)*x4)/(-1) - u15 =E= 0;

dL_dx21.. (-538.788341203462*x21**(-1.76923076923077)*x5)/(-1) - u16 =E= 0;

* set non-default bounds
x1.up = 30;
x2.up = 30;
x3.up = 30;
x4.up = 30;
x5.lo = 1; x5.up = 30;

* set non-default levels
x5.l = 1;
x17.l = 50;
x18.l = 50;
x19.l = 50;
x20.l = 50;
x21.l = 50;

Model m / e6.u6,e7.u7,e8.u8,e9.u9,e10.u10,e11.x6,e12.u12,e13.u13,e14.u14
         ,e15.u15,e16.u16,dL_dx1.x1,dL_dx2.x2,dL_dx3.x3,dL_dx4.x4,dL_dx5.x5
         ,dL_dx7.x7,dL_dx8.x8,dL_dx9.x9,dL_dx10.x10,dL_dx11.x11,dL_dx17.x17
         ,dL_dx18.x18,dL_dx19.x19,dL_dx20.x20,dL_dx21.x21 /;

m.limrow=0; m.limcol=0;

Solve m using MCP;
$offecho

execute 'grep -v " written by GAMS" expl_gms > expl.gms.want'
execute 'grep -v " written by GAMS" expl.gms > expl.gms.got'
execute '=diff -bw expl.gms.want expl.gms.got'
abort$errorlevel 'Files expl.gms.want and expl.gms.got differ';

$onecho > expl_dict
* written by GAMS/JAMS at 12/04/16 09:42:37

********************************************************************************
 Contents
 1 Content of EMP Information File
 2 Processed EMP Information
 3 Dictionary
  3.1 Constraints
  3.2 Variables
********************************************************************************


 1 Content of EMP Information File
 ---------------------------------

     1:equilibrium
     2:min obj('1') y('1') x('1') zExp('1')
     3:defobjExp('1') defcons('1') defzExp('1')
     4:min obj('2') y('2') x('2') zExp('2')
     5:defobjExp('2') defcons('2') defzExp('2')
     6:min obj('3') y('3') x('3') zExp('3')
     7:defobjExp('3') defcons('3') defzExp('3')
     8:min obj('4') y('4') x('4') zExp('4')
     9:defobjExp('4') defcons('4') defzExp('4')
    10:min obj('5') y('5') x('5') zExp('5')
    11:defobjExp('5') defcons('5') defzExp('5')
    12:vi defequil pi


 2 Processed EMP Information
 ---------------------------

   Number of VI functions specified = 1
   * e11 is VI Func and perpendicular to x6


 3 Dictionary
 ------------
  3.1 Constraints
  ---------------

      {reformulated}  defobjExp(1)
      {reformulated}  defobjExp(2)
      {reformulated}  defobjExp(3)
      {reformulated}  defobjExp(4)
      {reformulated}  defobjExp(5)
                  e6  defcons(1)
                  e7  defcons(2)
                  e8  defcons(3)
                  e9  defcons(4)
                 e10  defcons(5)
                 e11  defequil
                 e12  defzExp(1)
                 e13  defzExp(2)
                 e14  defzExp(3)
                 e15  defzExp(4)
                 e16  defzExp(5)
              dL_dx1  {new}
              dL_dx2  {new}
              dL_dx3  {new}
              dL_dx4  {new}
              dL_dx5  {new}
              dL_dx7  {new}
              dL_dx8  {new}
              dL_dx9  {new}
             dL_dx10  {new}
             dL_dx11  {new}
             dL_dx17  {new}
             dL_dx18  {new}
             dL_dx19  {new}
             dL_dx20  {new}
             dL_dx21  {new}


  3.2 Variables
 --------------

                  x1  y(1)
                  x2  y(2)
                  x3  y(3)
                  x4  y(4)
                  x5  y(5)
                  x6  pi
                  x7  x(1)
                  x8  x(2)
                  x9  x(3)
                 x10  x(4)
                 x11  x(5)
      {reformulated}  obj(1)
      {reformulated}  obj(2)
      {reformulated}  obj(3)
      {reformulated}  obj(4)
      {reformulated}  obj(5)
                 x17  zExp(1)
                 x18  zExp(2)
                 x19  zExp(3)
                 x20  zExp(4)
                 x21  zExp(5)
                  u6  {new}
                  u7  {new}
                  u8  {new}
                  u9  {new}
                 u10  {new}
                 u12  {new}
                 u13  {new}
                 u14  {new}
                 u15  {new}
                 u16  {new}
$offecho

execute 'grep -v " written by GAMS" expl_dict > expldict.txt.want'
execute 'grep -v " written by GAMS" explDict.txt > expldict.txt.got'
execute '=diff -bw expldict.txt.want expldict.txt.got'
abort$errorlevel 'Files expldict.txt.want and expldict.txt.got differ';

$macro price     (5000**(1/gamma)*(z**(-1/gamma)))

defobj(i)..
    obj(i) =E= cost(y,i) + pi*x(i) - price*y(i);

defz..
    z =E= sum(i, y(i));

model mi 'implicit formulation' / defobj, defcons, defequil, defz /;

put info 'equilibrium';
put / 'implicit z defz';
loop(i,
    put / 'min', obj(i), y(i), x(i), z;
    put / defobj(i), defcons(i);
);
put / 'vi', defequil, pi;
putclose;

* testing with implicit
putclose opt
  'Dict     implDict.txt' /
  'FileName impl.gms' ;

mi.optfile = 1;
solve mi using emp;
abort$[mi.solvestat <> %solvestat.NormalCompletion%]
   'wrong mi.solvestat', mi.solvestat;
abort$[mi.modelstat  > %modelstat.LocallyOptimal%]
   'wrong mi.modelstat', mi.modelstat;
abort$[ abs(obj.l('1')+176.647) > tol ]      'bad obj.l("1")', obj.l;
abort$[ abs(obj.l('2')+216.959) > tol ]      'bad obj.l("2")', obj.l;
abort$[ abs(obj.l('3')+264.905) > tol ]      'bad obj.l("3")', obj.l;
abort$[ abs(obj.l('4')+309.177) > tol ]      'bad obj.l("4")', obj.l;
abort$[ abs(obj.l('5')+372.600) > tol ]      'bad obj.l("5")', obj.l;
abort$[ abs(y.l('1')- 8.016) > tol ]         'bad y.l("1")', y.l;
abort$[ abs(y.l('2')-13.597) > tol ]         'bad y.l("2")', y.l;
abort$[ abs(y.l('3')-18.218) > tol ]         'bad y.l("3")', y.l;
abort$[ abs(y.l('4')-21.009) > tol ]         'bad y.l("4")', y.l;
abort$[ abs(y.l('5')-23.732) > tol ]         'bad y.l("5")', y.l;
abort$[ abs(x.l('1')+12.096) > tol ]         'bad x.l("1")', x.l;
abort$[ abs(x.l('2')+ 4.604) > tol ]         'bad x.l("2")', x.l;
abort$[ abs(x.l('3')- 1.962) > tol ]         'bad x.l("3")', x.l;
abort$[ abs(x.l('4')- 6.513) > tol ]         'bad x.l("4")', x.l;
abort$[ abs(x.l('5')- 8.224) > tol ]         'bad x.l("5")', x.l;
abort$[ abs(z.l-84.571) > tol ]              'bad z.l', z.l;
abort$[ abs(pi.l- 6.484) > tol ]             'bad pi.l', pi.l;

obj.l(i) = 0;
y.l(i) = y.lo(i);
x.l(i) = 0;
z.l = 50;
pi.l = 0;
defobj.m(i) = 0;
defcons.m(i) = 0;
defequil.m = 0;
defz.m = 0;

$onecho > impl_gms
***********************************************
* written by GAMS/JAMS at 12/04/16 09:51:34
* for more information use JAMS option "Dict"
***********************************************

Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x17,u6,u7,u8,u9,u10;

Negative Variables  u6,u7,u8,u9,u10;

Positive Variables  x1,x2,x3,x4,x6;

Equations  e6,e7,e8,e9,e10,e11,e12,dL_dx1,dL_dx2,dL_dx3,dL_dx4,dL_dx5,dL_dx7
          ,dL_dx8,dL_dx9,dL_dx10,dL_dx11;


e6.. sqrt(1 + x1) + 1.36*x1 - x7 =L= 26;

e7..    1.5*x2 - x8 =L= 25;

e8..    1.48*x3 - x9 =L= 25;

e9..    1.5*x4 - x10 =L= 25;

e10..    1.4*x5 - x11 =L= 25;

e11..  - x7 - x8 - x9 - x10 - x11 =G= 0;

e12..  - x1 - x2 - x3 - x4 - x5 + x17 =E= 0;

dL_dx1.. (-(10 + 0.261532097202366*x1**0.833333333333333 - 700.424843564501*x17
         **(-0.769230769230769)))/(-1) + ((-538.788341203462*x17**(-
         1.76923076923077)*x1)/(-1))*(1) - (1.36 + 0.5/sqrt(1 + x1))*u6 =N= 0;

dL_dx2.. (-(8 + 0.231511582354131*x2**0.909090909090909 - 700.424843564501*x17
         **(-0.769230769230769)))/(-1) + ((-538.788341203462*x17**(-
         1.76923076923077)*x2)/(-1))*(1) - 1.5*u7 =N= 0;

dL_dx3.. (-(6 + 0.2*x3**1 - 700.424843564501*x17**(-0.769230769230769)))/(-1)
          + ((-538.788341203462*x17**(-1.76923076923077)*x3)/(-1))*(1)
          - 1.48*u8 =N= 0;

dL_dx4.. (-(4 + 0.167250206190075*x4**1.11111111111111 - 700.424843564501*x17**
         (-0.769230769230769)))/(-1) + ((-538.788341203462*x17**(-
         1.76923076923077)*x4)/(-1))*(1) - 1.5*u9 =N= 0;

dL_dx5.. (-(2 + 0.133748060995284*x5**1.25 - 700.424843564501*x17**(-
         0.769230769230769)))/(-1) + ((-538.788341203462*x17**(-
         1.76923076923077)*x5)/(-1))*(1) - 1.4*u10 =N= 0;

dL_dx7.. (-x6)/(-1) + u6 + eps*x7 =E= 0;

dL_dx8.. (-x6)/(-1) + u7 + eps*x8 =E= 0;

dL_dx9.. (-x6)/(-1) + u8 + eps*x9 =E= 0;

dL_dx10.. (-x6)/(-1) + u9 + eps*x10 =E= 0;

dL_dx11.. (-x6)/(-1) + u10 + eps*x11 =E= 0;

* set non-default bounds
x1.up = 30;
x2.up = 30;
x3.up = 30;
x4.up = 30;
x5.lo = 1; x5.up = 30;

* set non-default levels
x5.l = 1;
x17.l = 50;

Model m / e6.u6,e7.u7,e8.u8,e9.u9,e10.u10,e11.x6,e12.x17,dL_dx1.x1,dL_dx2.x2
         ,dL_dx3.x3,dL_dx4.x4,dL_dx5.x5,dL_dx7.x7,dL_dx8.x8,dL_dx9.x9
         ,dL_dx10.x10,dL_dx11.x11 /;

m.limrow=0; m.limcol=0;

Solve m using MCP;
$offecho

execute 'grep -v " written by GAMS" impl_gms > impl.gms.want'
execute 'grep -v " written by GAMS" impl.gms > impl.gms.got'
execute '=diff -bw impl.gms.want impl.gms.got'
abort$errorlevel 'Files impl.gms.want and impl.gms.got differ';

$onecho > impl_dict
* written by GAMS/JAMS at 12/04/16 09:53:06

********************************************************************************
 Contents
 1 Content of EMP Information File
 2 Processed EMP Information
 3 Dictionary
  3.1 Constraints
  3.2 Variables
********************************************************************************


 1 Content of EMP Information File
 ---------------------------------

     1:equilibrium
     2:implicit z defz
     3:min obj('1') y('1') x('1') z
     4:defobj('1') defcons('1')
     5:min obj('2') y('2') x('2') z
     6:defobj('2') defcons('2')
     7:min obj('3') y('3') x('3') z
     8:defobj('3') defcons('3')
     9:min obj('4') y('4') x('4') z
    10:defobj('4') defcons('4')
    11:min obj('5') y('5') x('5') z
    12:defobj('5') defcons('5')
    13:vi defequil pi


 2 Processed EMP Information
 ---------------------------

   Number of VI functions specified = 1
   * e11 is VI Func and perpendicular to x6


 3 Dictionary
 ------------
  3.1 Constraints
  ---------------

      {reformulated}  defobj(1)
      {reformulated}  defobj(2)
      {reformulated}  defobj(3)
      {reformulated}  defobj(4)
      {reformulated}  defobj(5)
                  e6  defcons(1)
                  e7  defcons(2)
                  e8  defcons(3)
                  e9  defcons(4)
                 e10  defcons(5)
                 e11  defequil
                 e12  defz
              dL_dx1  {new}
              dL_dx2  {new}
              dL_dx3  {new}
              dL_dx4  {new}
              dL_dx5  {new}
              dL_dx7  {new}
              dL_dx8  {new}
              dL_dx9  {new}
             dL_dx10  {new}
             dL_dx11  {new}


  3.2 Variables
 --------------

                  x1  y(1)
                  x2  y(2)
                  x3  y(3)
                  x4  y(4)
                  x5  y(5)
                  x6  pi
                  x7  x(1)
                  x8  x(2)
                  x9  x(3)
                 x10  x(4)
                 x11  x(5)
      {reformulated}  obj(1)
      {reformulated}  obj(2)
      {reformulated}  obj(3)
      {reformulated}  obj(4)
      {reformulated}  obj(5)
                 x17  z
                  u6  {new}
                  u7  {new}
                  u8  {new}
                  u9  {new}
                 u10  {new}
$offecho

execute 'grep -v " written by GAMS" impl_dict > impldict.txt.want'
execute 'grep -v " written by GAMS" implDict.txt > impldict.txt.got'
execute '=diff -bw impldict.txt.want impldict.txt.got'
abort$errorlevel 'Files impldict.txt.want and impldict.txt.got differ';

* testing with adjoint

putclose opt
  'Dict     implAdjointDict.txt' /
  'FileName implAdjoint.gms' /
  'Adjoint' / ;

solve mi using emp;
abort$[mi.solvestat <> %solvestat.NormalCompletion%]
   'wrong mi.solvestat', mi.solvestat;
abort$[mi.modelstat  > %modelstat.LocallyOptimal%]
   'wrong mi.modelstat', mi.modelstat;
abort$[ abs(obj.l('1')+176.647) > tol ]      'bad obj.l("1")', obj.l;
abort$[ abs(obj.l('2')+216.959) > tol ]      'bad obj.l("2")', obj.l;
abort$[ abs(obj.l('3')+264.905) > tol ]      'bad obj.l("3")', obj.l;
abort$[ abs(obj.l('4')+309.177) > tol ]      'bad obj.l("4")', obj.l;
abort$[ abs(obj.l('5')+372.600) > tol ]      'bad obj.l("5")', obj.l;
abort$[ abs(y.l('1')- 8.016) > tol ]         'bad y.l("1")', y.l;
abort$[ abs(y.l('2')-13.597) > tol ]         'bad y.l("2")', y.l;
abort$[ abs(y.l('3')-18.218) > tol ]         'bad y.l("3")', y.l;
abort$[ abs(y.l('4')-21.009) > tol ]         'bad y.l("4")', y.l;
abort$[ abs(y.l('5')-23.732) > tol ]         'bad y.l("5")', y.l;
abort$[ abs(x.l('1')+12.096) > tol ]         'bad x.l("1")', x.l;
abort$[ abs(x.l('2')+ 4.604) > tol ]         'bad x.l("2")', x.l;
abort$[ abs(x.l('3')- 1.962) > tol ]         'bad x.l("3")', x.l;
abort$[ abs(x.l('4')- 6.513) > tol ]         'bad x.l("4")', x.l;
abort$[ abs(x.l('5')- 8.224) > tol ]         'bad x.l("5")', x.l;
abort$[ abs(z.l-84.571) > tol ]              'bad z.l', z.l;
abort$[ abs(pi.l- 6.484) > tol ]             'bad pi.l', pi.l;

obj.l(i) = 0;
y.l(i) = y.lo(i);
x.l(i) = 0;
z.l = 50;
pi.l = 0;
defobj.m(i) = 0;
defcons.m(i) = 0;
defequil.m = 0;
defz.m = 0;

$onecho > implAdjoint_gms
***********************************************
* written by GAMS/JAMS at 12/05/16 14:32:45
* for more information use JAMS option "Dict"
***********************************************

Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x17,u6,u7,u8,u9,u10,IMPL1_a4_x1
          ,IMPL1_a5_x1,IMPL1_a6_x1,IMPL1_a7_x1,IMPL1_a8_x1;

Negative Variables  u6,u7,u8,u9,u10;

Positive Variables  x1,x2,x3,x4,x6;

Equations  e6,e7,e8,e9,e10,e11,e12,IMPL1_a4_e1,IMPL1_a5_e1,IMPL1_a6_e1
          ,IMPL1_a7_e1,IMPL1_a8_e1,dL_dx1,dL_dx2,dL_dx3,dL_dx4,dL_dx5,dL_dx7
          ,dL_dx8,dL_dx9,dL_dx10,dL_dx11;


e6.. sqrt(1 + x1) + 1.36*x1 - x7 =L= 26;

e7..    1.5*x2 - x8 =L= 25;

e8..    1.48*x3 - x9 =L= 25;

e9..    1.5*x4 - x10 =L= 25;

e10..    1.4*x5 - x11 =L= 25;

e11..  - x7 - x8 - x9 - x10 - x11 =G= 0;

e12..  - x1 - x2 - x3 - x4 - x5 + x17 =E= 0;

IMPL1_a4_e1.. (1)*(IMPL1_a4_x1) + (-538.788341203462*x17**(-1.76923076923077)*
              x1)/(-1) =E= 0;

IMPL1_a5_e1.. (1)*(IMPL1_a5_x1) + (-538.788341203462*x17**(-1.76923076923077)*
              x2)/(-1) =E= 0;

IMPL1_a6_e1.. (1)*(IMPL1_a6_x1) + (-538.788341203462*x17**(-1.76923076923077)*
              x3)/(-1) =E= 0;

IMPL1_a7_e1.. (1)*(IMPL1_a7_x1) + (-538.788341203462*x17**(-1.76923076923077)*
              x4)/(-1) =E= 0;

IMPL1_a8_e1.. (1)*(IMPL1_a8_x1) + (-538.788341203462*x17**(-1.76923076923077)*
              x5)/(-1) =E= 0;

dL_dx1.. (-(10 + 0.261532097202366*x1**0.833333333333333 - 700.424843564501*x17
         **(-0.769230769230769)))/(-1) + (-1)*(IMPL1_a4_x1) - (1.36 + 0.5/sqrt(
         1 + x1))*u6 =N= 0;

dL_dx2.. (-(8 + 0.231511582354131*x2**0.909090909090909 - 700.424843564501*x17
         **(-0.769230769230769)))/(-1) + (-1)*(IMPL1_a5_x1) - 1.5*u7 =N= 0;

dL_dx3.. (-(6 + 0.2*x3**1 - 700.424843564501*x17**(-0.769230769230769)))/(-1)
          + (-1)*(IMPL1_a6_x1) - 1.48*u8 =N= 0;

dL_dx4.. (-(4 + 0.167250206190075*x4**1.11111111111111 - 700.424843564501*x17**
         (-0.769230769230769)))/(-1) + (-1)*(IMPL1_a7_x1) - 1.5*u9 =N= 0;

dL_dx5.. (-(2 + 0.133748060995284*x5**1.25 - 700.424843564501*x17**(-
         0.769230769230769)))/(-1) + (-1)*(IMPL1_a8_x1) - 1.4*u10 =N= 0;

dL_dx7.. (-x6)/(-1) + u6 + eps*x7 =E= 0;

dL_dx8.. (-x6)/(-1) + u7 + eps*x8 =E= 0;

dL_dx9.. (-x6)/(-1) + u8 + eps*x9 =E= 0;

dL_dx10.. (-x6)/(-1) + u9 + eps*x10 =E= 0;

dL_dx11.. (-x6)/(-1) + u10 + eps*x11 =E= 0;

* set non-default bounds
x1.up = 30;
x2.up = 30;
x3.up = 30;
x4.up = 30;
x5.lo = 1; x5.up = 30;

* set non-default levels
x5.l = 1;
x17.l = 50;

Model m / e6.u6,e7.u7,e8.u8,e9.u9,e10.u10,e11.x6,e12.x17
         ,IMPL1_a4_e1.IMPL1_a4_x1,IMPL1_a5_e1.IMPL1_a5_x1
         ,IMPL1_a6_e1.IMPL1_a6_x1,IMPL1_a7_e1.IMPL1_a7_x1
         ,IMPL1_a8_e1.IMPL1_a8_x1,dL_dx1.x1,dL_dx2.x2,dL_dx3.x3,dL_dx4.x4
         ,dL_dx5.x5,dL_dx7.x7,dL_dx8.x8,dL_dx9.x9,dL_dx10.x10,dL_dx11.x11 /;

m.limrow=0; m.limcol=0;

Solve m using MCP;
$offecho

execute 'grep -v " written by GAMS" implAdjoint_gms > implAdjoint.gms.want'
execute 'grep -v " written by GAMS" implAdjoint.gms > implAdjoint.gms.got'
execute '=diff -bw implAdjoint.gms.want implAdjoint.gms.got'
abort$errorlevel 'Files implAdjoint.gms.want and implAdjoint.gms.got differ';

$onecho > implAdjoint_dict
* written by GAMS/JAMS at 12/05/16 14:32:45

********************************************************************************
 Contents
 1 Content of EMP Information File
 2 Processed EMP Information
 3 Dictionary
  3.1 Constraints
  3.2 Variables
********************************************************************************


 1 Content of EMP Information File
 ---------------------------------

     1:equilibrium
     2:implicit z defz
     3:min obj('1') y('1') x('1') z
     4:defobj('1') defcons('1')
     5:min obj('2') y('2') x('2') z
     6:defobj('2') defcons('2')
     7:min obj('3') y('3') x('3') z
     8:defobj('3') defcons('3')
     9:min obj('4') y('4') x('4') z
    10:defobj('4') defcons('4')
    11:min obj('5') y('5') x('5') z
    12:defobj('5') defcons('5')
    13:vi defequil pi


 2 Processed EMP Information
 ---------------------------

   Number of VI functions specified = 1
   * e11 is VI Func and perpendicular to x6


 3 Dictionary
 ------------
  3.1 Constraints
  ---------------

      {reformulated}  defobj(1)
      {reformulated}  defobj(2)
      {reformulated}  defobj(3)
      {reformulated}  defobj(4)
      {reformulated}  defobj(5)
                  e6  defcons(1)
                  e7  defcons(2)
                  e8  defcons(3)
                  e9  defcons(4)
                 e10  defcons(5)
                 e11  defequil
                 e12  defz
         IMPL1_a4_e1  {new}
         IMPL1_a5_e1  {new}
         IMPL1_a6_e1  {new}
         IMPL1_a7_e1  {new}
         IMPL1_a8_e1  {new}
              dL_dx1  {new}
              dL_dx2  {new}
              dL_dx3  {new}
              dL_dx4  {new}
              dL_dx5  {new}
              dL_dx7  {new}
              dL_dx8  {new}
              dL_dx9  {new}
             dL_dx10  {new}
             dL_dx11  {new}


  3.2 Variables
 --------------

                  x1  y(1)
                  x2  y(2)
                  x3  y(3)
                  x4  y(4)
                  x5  y(5)
                  x6  pi
                  x7  x(1)
                  x8  x(2)
                  x9  x(3)
                 x10  x(4)
                 x11  x(5)
      {reformulated}  obj(1)
      {reformulated}  obj(2)
      {reformulated}  obj(3)
      {reformulated}  obj(4)
      {reformulated}  obj(5)
                 x17  z
                  u6  {new}
                  u7  {new}
                  u8  {new}
                  u9  {new}
                 u10  {new}
         IMPL1_a4_x1  {new}
         IMPL1_a5_x1  {new}
         IMPL1_a6_x1  {new}
         IMPL1_a7_x1  {new}
         IMPL1_a8_x1  {new}
$offecho

execute 'grep -v " written by GAMS" implAdjoint_dict > implAdjointDict.txt.want'
execute 'grep -v " written by GAMS" implAdjointDict.txt > implAdjointDict.txt.got'
execute '=diff -bw implAdjointDict.txt.want implAdjointDict.txt.got'
abort$errorlevel 'Files implAdjointDict.txt.want and implAdjointDict.txt.got differ';

* testing with replication
putclose opt
  'Dict     implRepDict.txt' /
  'FileName implRep.gms' /
  'CopyImplVar' ;

solve mi using emp;
abort$[mi.solvestat <> %solvestat.NormalCompletion%]
   'wrong mi.solvestat', mi.solvestat;
abort$[mi.modelstat  > %modelstat.LocallyOptimal%]
   'wrong mi.modelstat', mi.modelstat;
abort$[ abs(obj.l('1')+176.647) > tol ]      'bad obj.l("1")', obj.l;
abort$[ abs(obj.l('2')+216.959) > tol ]      'bad obj.l("2")', obj.l;
abort$[ abs(obj.l('3')+264.905) > tol ]      'bad obj.l("3")', obj.l;
abort$[ abs(obj.l('4')+309.177) > tol ]      'bad obj.l("4")', obj.l;
abort$[ abs(obj.l('5')+372.600) > tol ]      'bad obj.l("5")', obj.l;
abort$[ abs(y.l('1')- 8.016) > tol ]         'bad y.l("1")', y.l;
abort$[ abs(y.l('2')-13.597) > tol ]         'bad y.l("2")', y.l;
abort$[ abs(y.l('3')-18.218) > tol ]         'bad y.l("3")', y.l;
abort$[ abs(y.l('4')-21.009) > tol ]         'bad y.l("4")', y.l;
abort$[ abs(y.l('5')-23.732) > tol ]         'bad y.l("5")', y.l;
abort$[ abs(x.l('1')+12.096) > tol ]         'bad x.l("1")', x.l;
abort$[ abs(x.l('2')+ 4.604) > tol ]         'bad x.l("2")', x.l;
abort$[ abs(x.l('3')- 1.962) > tol ]         'bad x.l("3")', x.l;
abort$[ abs(x.l('4')- 6.513) > tol ]         'bad x.l("4")', x.l;
abort$[ abs(x.l('5')- 8.224) > tol ]         'bad x.l("5")', x.l;
abort$[ abs(z.l-84.571) > tol ]              'bad z.l', z.l;
abort$[ abs(pi.l- 6.484) > tol ]             'bad pi.l', pi.l;

obj.l(i) = 0;
y.l(i) = y.lo(i);
x.l(i) = 0;
z.l = 50;
pi.l = 0;
defobj.m(i) = 0;
defcons.m(i) = 0;
defequil.m = 0;
defz.m = 0;

$onechoV > implRep_gms
***********************************************
* written by GAMS/JAMS at 12/05/16 14:33:42
* for more information use JAMS option "Dict"
***********************************************

Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17_4,x17_5
          ,x17_6,x17_7,x17_8;

Negative Variables  u6,u7,u8,u9,u10;

Positive Variables  x1,x2,x3,x4,x6;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12_4,e12_5,e12_6,e12_7,e12_8;


e1.. -(0.142653871201291*x1**1.83333333333333 + 10*x1 + x6*x7 - 
     700.424843564501*x17_4**(-0.769230769230769)*x1) + x12 =E= 0;

e2.. -(0.121267971709307*x2**1.90909090909091 + 8*x2 + x6*x8 - 700.424843564501
     *x17_5**(-0.769230769230769)*x2) + x13 =E= 0;

e3.. -(0.1*x3**2 + 6*x3 + x6*x9 - 700.424843564501*x17_6**(-0.769230769230769)*
     x3) + x14 =E= 0;

e4.. -(0.0792237818795091*x4**2.11111111111111 + 4*x4 + x6*x10 - 
     700.424843564501*x17_7**(-0.769230769230769)*x4) + x15 =E= 0;

e5.. -(0.0594435826645709*x5**2.25 + 2*x5 + x6*x11 - 700.424843564501*x17_8**(-
     0.769230769230769)*x5) + x16 =E= 0;

e6.. sqrt(1 + x1) + 1.36*x1 - x7 =L= 26;

e7..    1.5*x2 - x8 =L= 25;

e8..    1.48*x3 - x9 =L= 25;

e9..    1.5*x4 - x10 =L= 25;

e10..    1.4*x5 - x11 =L= 25;

e11..  - x7 - x8 - x9 - x10 - x11 =G= 0;

e12_4..  - x1 - x2 - x3 - x4 - x5 + x17_4 =E= 0;

e12_5..  - x1 - x2 - x3 - x4 - x5 + x17_5 =E= 0;

e12_6..  - x1 - x2 - x3 - x4 - x5 + x17_6 =E= 0;

e12_7..  - x1 - x2 - x3 - x4 - x5 + x17_7 =E= 0;

e12_8..  - x1 - x2 - x3 - x4 - x5 + x17_8 =E= 0;

* set non-default bounds
x1.up = 30;
x2.up = 30;
x3.up = 30;
x4.up = 30;
x5.lo = 1; x5.up = 30;

* set non-default levels
x5.l = 1;
x17_4.l = 50;
x17_5.l = 50;
x17_6.l = 50;
x17_7.l = 50;
x17_8.l = 50;

Model m / e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12_4,e12_5,e12_6,e12_7,e12_8 /;

m.limrow=0; m.limcol=0;


File empinfo / '%emp.info%' /;

Put empinfo 'equilibrium' /;
Put 'min',x12,x1,x7,x17_4,e1,e6,e12_4 /;
Put 'min',x13,x2,x8,x17_5,e2,e7,e12_5 /;
Put 'min',x14,x3,x9,x17_6,e3,e8,e12_6 /;
Put 'min',x15,x4,x10,x17_7,e4,e9,e12_7 /;
Put 'min',x16,x5,x11,x17_8,e5,e10,e12_8 /;
Put 'vi',e11,x6 /;
Putclose empinfo;

m.optfile = 0;

Solve m using EMP;
$offecho

execute 'grep -v " written by GAMS" implRep_gms > implRep.gms.want'
execute 'grep -v " written by GAMS" implRep.gms > implRep.gms.got'
execute '=diff -bw implRep.gms.want implRep.gms.got'
abort$errorlevel 'Files implRep.gms.want and implRep.gms.got differ';

$onecho > implRep_dict
* written by GAMS/JAMS at 12/05/16 14:33:42

********************************************************************************
 Contents
 1 Content of EMP Information File
 2 Processed EMP Information
 3 Dictionary
  3.1 Constraints
  3.2 Variables
********************************************************************************


 1 Content of EMP Information File
 ---------------------------------

     1:equilibrium
     2:implicit z defz
     3:min obj('1') y('1') x('1') z
     4:defobj('1') defcons('1')
     5:min obj('2') y('2') x('2') z
     6:defobj('2') defcons('2')
     7:min obj('3') y('3') x('3') z
     8:defobj('3') defcons('3')
     9:min obj('4') y('4') x('4') z
    10:defobj('4') defcons('4')
    11:min obj('5') y('5') x('5') z
    12:defobj('5') defcons('5')
    13:vi defequil pi


 2 Processed EMP Information
 ---------------------------

   Number of VI functions specified = 1
   * e11 is VI Func and perpendicular to x6


 3 Dictionary
 ------------
  3.1 Constraints
  ---------------

                  e1  defobj(1)
                  e2  defobj(2)
                  e3  defobj(3)
                  e4  defobj(4)
                  e5  defobj(5)
                  e6  defcons(1)
                  e7  defcons(2)
                  e8  defcons(3)
                  e9  defcons(4)
                 e10  defcons(5)
                 e11  defequil
               e12_4  defz
               e12_5  defz
               e12_6  defz
               e12_7  defz
               e12_8  defz


  3.2 Variables
 --------------

                  x1  y(1)
                  x2  y(2)
                  x3  y(3)
                  x4  y(4)
                  x5  y(5)
                  x6  pi
                  x7  x(1)
                  x8  x(2)
                  x9  x(3)
                 x10  x(4)
                 x11  x(5)
                 x12  obj(1)
                 x13  obj(2)
                 x14  obj(3)
                 x15  obj(4)
                 x16  obj(5)
               x17_4  z
               x17_5  z
               x17_6  z
               x17_7  z
               x17_8  z
$offecho

execute 'grep -v " written by GAMS" implRep_dict > implRepDict.txt.want'
execute 'grep -v " written by GAMS" implRepDict.txt > implRepDict.txt.got'
execute '=diff -bw implRepDict.txt.want implRepDict.txt.got'
abort$errorlevel 'Files implRepDict.txt.want and implRepDict.txt.got differ';

* testing with replication and matching
putclose opt
  'Dict     implRepMMDict.txt' /
  'FileName implRepMM.gms' /
  'CopyImplVar' /
  'MixMatch' /
  ;

solve mi using emp;
abort$[mi.solvestat <> %solvestat.NormalCompletion%]
   'wrong mi.solvestat', mi.solvestat;
abort$[mi.modelstat  > %modelstat.LocallyOptimal%]
   'wrong mi.modelstat', mi.modelstat;
abort$[ abs(obj.l('1')+176.647) > tol ]      'bad obj.l("1")', obj.l;
abort$[ abs(obj.l('2')+216.959) > tol ]      'bad obj.l("2")', obj.l;
abort$[ abs(obj.l('3')+264.905) > tol ]      'bad obj.l("3")', obj.l;
abort$[ abs(obj.l('4')+309.177) > tol ]      'bad obj.l("4")', obj.l;
abort$[ abs(obj.l('5')+372.600) > tol ]      'bad obj.l("5")', obj.l;
abort$[ abs(y.l('1')- 8.016) > tol ]         'bad y.l("1")', y.l;
abort$[ abs(y.l('2')-13.597) > tol ]         'bad y.l("2")', y.l;
abort$[ abs(y.l('3')-18.218) > tol ]         'bad y.l("3")', y.l;
abort$[ abs(y.l('4')-21.009) > tol ]         'bad y.l("4")', y.l;
abort$[ abs(y.l('5')-23.732) > tol ]         'bad y.l("5")', y.l;
abort$[ abs(x.l('1')+12.096) > tol ]         'bad x.l("1")', x.l;
abort$[ abs(x.l('2')+ 4.604) > tol ]         'bad x.l("2")', x.l;
abort$[ abs(x.l('3')- 1.962) > tol ]         'bad x.l("3")', x.l;
abort$[ abs(x.l('4')- 6.513) > tol ]         'bad x.l("4")', x.l;
abort$[ abs(x.l('5')- 8.224) > tol ]         'bad x.l("5")', x.l;
abort$[ abs(z.l-84.571) > tol ]              'bad z.l', z.l;
abort$[ abs(pi.l- 6.484) > tol ]             'bad pi.l', pi.l;

obj.l(i) = 0;
y.l(i) = y.lo(i);
x.l(i) = 0;
z.l = 50;
pi.l = 0;
defobj.m(i) = 0;
defcons.m(i) = 0;
defequil.m = 0;
defz.m = 0;

$onechoV > implRepMM_gms
***********************************************
* written by GAMS/JAMS at 12/05/16 14:34:20
* for more information use JAMS option "Dict"
***********************************************

Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17_4,x17_5
          ,x17_6,x17_7,x17_8;

Negative Variables  u6,u7,u8,u9,u10;

Positive Variables  x1,x2,x3,x4,x6;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12_4,e12_5,e12_6,e12_7,e12_8;


e1.. -(0.142653871201291*x1**1.83333333333333 + 10*x1 + x6*x7 - 
     700.424843564501*x17_4**(-0.769230769230769)*x1) + x12 =E= 0;

e2.. -(0.121267971709307*x2**1.90909090909091 + 8*x2 + x6*x8 - 700.424843564501
     *x17_5**(-0.769230769230769)*x2) + x13 =E= 0;

e3.. -(0.1*x3**2 + 6*x3 + x6*x9 - 700.424843564501*x17_6**(-0.769230769230769)*
     x3) + x14 =E= 0;

e4.. -(0.0792237818795091*x4**2.11111111111111 + 4*x4 + x6*x10 - 
     700.424843564501*x17_7**(-0.769230769230769)*x4) + x15 =E= 0;

e5.. -(0.0594435826645709*x5**2.25 + 2*x5 + x6*x11 - 700.424843564501*x17_8**(-
     0.769230769230769)*x5) + x16 =E= 0;

e6.. sqrt(1 + x1) + 1.36*x1 - x7 =L= 26;

e7..    1.5*x2 - x8 =L= 25;

e8..    1.48*x3 - x9 =L= 25;

e9..    1.5*x4 - x10 =L= 25;

e10..    1.4*x5 - x11 =L= 25;

e11..  - x7 - x8 - x9 - x10 - x11 =G= 0;

e12_4..  - x1 - x2 - x3 - x4 - x5 + x17_4 =E= 0;

e12_5..  - x1 - x2 - x3 - x4 - x5 + x17_5 =E= 0;

e12_6..  - x1 - x2 - x3 - x4 - x5 + x17_6 =E= 0;

e12_7..  - x1 - x2 - x3 - x4 - x5 + x17_7 =E= 0;

e12_8..  - x1 - x2 - x3 - x4 - x5 + x17_8 =E= 0;

* set non-default bounds
x1.up = 30;
x2.up = 30;
x3.up = 30;
x4.up = 30;
x5.lo = 1; x5.up = 30;

* set non-default levels
x5.l = 1;
x17_4.l = 50;
x17_5.l = 50;
x17_6.l = 50;
x17_7.l = 50;
x17_8.l = 50;

Model m / e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12_4,e12_5,e12_6,e12_7,e12_8 /;

m.limrow=0; m.limcol=0;


File empinfo / '%emp.info%' /;

Put empinfo 'equilibrium' /;
Put 'min',x12,x1,x7,x17_4,e1,e6,e12_4 /;
Put 'min',x13,x2,x8,x17_5,e2,e7,e12_5 /;
Put 'min',x14,x3,x9,x17_6,e3,e8,e12_6 /;
Put 'min',x15,x4,x10,x17_7,e4,e9,e12_7 /;
Put 'min',x16,x5,x11,x17_8,e5,e10,e12_8 /;
Put 'vi',e11,x6 /;
Putclose empinfo;

m.optfile = 0;

Solve m using EMP;
$offecho

execute 'grep -v " written by GAMS" implRepMM_gms > implRepMM.gms.want'
execute 'grep -v " written by GAMS" implRepMM.gms > implRepMM.gms.got'
execute '=diff -bw implRepMM.gms.want implRepMM.gms.got'
abort$errorlevel 'Files implRepMM.gms.want and implRepMM.gms.got differ';

$onecho > implRepMM_dict
* written by GAMS/JAMS at 12/05/16 14:34:20

********************************************************************************
 Contents
 1 Content of EMP Information File
 2 Processed EMP Information
 3 Dictionary
  3.1 Constraints
  3.2 Variables
********************************************************************************


 1 Content of EMP Information File
 ---------------------------------

     1:equilibrium
     2:implicit z defz
     3:min obj('1') y('1') x('1') z
     4:defobj('1') defcons('1')
     5:min obj('2') y('2') x('2') z
     6:defobj('2') defcons('2')
     7:min obj('3') y('3') x('3') z
     8:defobj('3') defcons('3')
     9:min obj('4') y('4') x('4') z
    10:defobj('4') defcons('4')
    11:min obj('5') y('5') x('5') z
    12:defobj('5') defcons('5')
    13:vi defequil pi


 2 Processed EMP Information
 ---------------------------

   Number of VI functions specified = 1
   * e11 is VI Func and perpendicular to x6


 3 Dictionary
 ------------
  3.1 Constraints
  ---------------

                  e1  defobj(1)
                  e2  defobj(2)
                  e3  defobj(3)
                  e4  defobj(4)
                  e5  defobj(5)
                  e6  defcons(1)
                  e7  defcons(2)
                  e8  defcons(3)
                  e9  defcons(4)
                 e10  defcons(5)
                 e11  defequil
               e12_4  defz
               e12_5  defz
               e12_6  defz
               e12_7  defz
               e12_8  defz


  3.2 Variables
 --------------

                  x1  y(1)
                  x2  y(2)
                  x3  y(3)
                  x4  y(4)
                  x5  y(5)
                  x6  pi
                  x7  x(1)
                  x8  x(2)
                  x9  x(3)
                 x10  x(4)
                 x11  x(5)
                 x12  obj(1)
                 x13  obj(2)
                 x14  obj(3)
                 x15  obj(4)
                 x16  obj(5)
               x17_4  z
               x17_5  z
               x17_6  z
               x17_7  z
               x17_8  z
$offecho

execute 'grep -v " written by GAMS" implRepMM_dict > implRepMMDict.txt.want'
execute 'grep -v " written by GAMS" implRepMMDict.txt > implRepMMDict.txt.got'
execute '=diff -bw implRepMMDict.txt.want implRepMMDict.txt.got'
abort$errorlevel 'Files implRepMMDict.txt.want and implRepMMDict.txt.got differ';