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 : emp20.gms
$title 'Test JAMS/EMP on implicit variable handling' (EMP20,SEQ=702)
$onText
Test JAMS behavior on a small equilibrium model with implicit variables.
Contributors: Youngdae Kim & Steve Dirkse, Dec 2016
$offText
$if not set TESTTOL $set TESTTOL 1e-6
scalars tol / %TESTTOL% /;
file opt / 'jams.opt' /;
file info / '%emp.info%' /;
set j agents / 1*3 /
i(j) variables and optagents / 1*2 /
;
alias(i,ii);
* i has dual purposes: variable index and optimization agent index
* j indicates who owns the copy of the var or equation
* The scalar files generated depend on the variable declaration order,
* so do not change the declarations lightly
variables
obj(i)
zExp(i,j) 'copy of z_i owned by agent j'
z(i) 'z_i done with implicit variables'
x 'VI agent variable'
;
positive variables t(i);
equations
defFExp(i,j) 'copy of F_i for agent j'
defF(i) 'F_i done with implicit variables'
defobjExp(i)
defobj(i)
defviExp
defvi
;
defobjExp(i)..
obj(i) =E=
(sqr(zExp(i,i)) - 0.5*t(i) + 0.25)$sameas(i,'1') +
(sqr(zExp(i,i)) - 2*t(i) + 1)$sameas(i,'2');
defFExp(i,j)..
(2*zExp('1',j) + zExp('2',j) + t('1') - t('2'))$sameas(i,'1') +
(-2*zExp('1',j) + 3*zExp('2',j) - t('1') - 3*t('2'))$sameas(i,'2') =E= 0;
defviExp..
x =E= sum(i, zExp(i,'3'));
model me 'explicit formulation' / defobjExp, defFExp, defviExp /;
put info 'equilibrium';
loop(i,
put / 'min', obj(i), t(i);
loop(j$(i.val eq j.val), loop(ii, put zExp(ii,j);););
put / defobjExp(i);
loop(j$(i.val eq j.val), loop(ii, put defFExp(ii,j);););
);
put / 'vi', defviExp, x;
put / 'vi', loop(i, put defFexp(i,'3'), zExp(i,'3'););
putclose;
putclose opt
'Dict explDict.txt' /
'FileName expl.gms' ;
me.optfile = 1;
solve me using emp;
abort$[me.solvestat <> %solveStat.normalCompletion%]
'wrong me.solvestat', me.solvestat;
abort$[me.modelstat > %modelStat.locallyOptimal%]
'wrong me.modelstat', me.modelstat;
abort$[ abs(obj.l('1')-0) > tol ] 'bad obj.l("1")', obj.l;
abort$[ abs(obj.l('2')-0) > tol ] 'bad obj.l("2")', obj.l;
abort$[smax{j, abs(zExp.l('1',j)+.5)} > tol] 'bad zExp.l("1",j)', zExp.l;
abort$[smax{j, abs(zExp.l('2',j)-1)} > tol] 'bad zExp.l("2",j)', zExp.l;
abort$[ abs(t.l('1')-1) > tol ] 'bad t.l("1")', t.l;
abort$[ abs(t.l('2')-1) > tol ] 'bad t.l("2")', t.l;
abort$[ abs(x.l-.5) > tol ] 'bad x.l', x.l;
obj.l(i) = 0;
zExp.l(i,j) = 0;
t.l(i) = 0;
x.l = 0;
$onEcho > expl_gms
***********************************************
* written by GAMS/JAMS at 12/03/16 23:15:28
* for more information use JAMS option "Dict"
***********************************************
Variables x3,x4,x5,x6,x7,x8,x9,x10,x11,u3,u4,u6,u7;
Positive Variables x10,x11;
Equations e3,e4,e5,e6,e7,e8,e9,dL_dx3,dL_dx4,dL_dx6,dL_dx7,dL_dx10,dL_dx11;
e3.. 2*x3 + x6 + x10 - x11 =E= 0;
e4.. 2*x4 + x7 + x10 - x11 =E= 0;
e5.. 2*x5 + x8 + x10 - x11 =E= 0;
e6.. - 2*x3 + 3*x6 - x10 - 3*x11 =E= 0;
e7.. - 2*x4 + 3*x7 - x10 - 3*x11 =E= 0;
e8.. - 2*x5 + 3*x8 - x10 - 3*x11 =E= 0;
e9.. - x5 - x8 + x9 =E= 0;
dL_dx3.. (-2*x3)/(-1) - 2*u3 + 2*u6 =E= 0;
dL_dx4.. - 2*u4 + 2*u7 + eps*x4 =E= 0;
dL_dx6.. - u3 - 3*u6 + eps*x6 =E= 0;
dL_dx7.. (-2*x7)/(-1) - u4 - 3*u7 =E= 0;
dL_dx10.. -0.5 - u3 + u6 + eps*x10 =G= 0;
dL_dx11.. -2 + u4 + 3*u7 + eps*x11 =G= 0;
Model m / e3.u3,e4.u4,e5.x5,e6.u6,e7.u7,e8.x8,e9.x9,dL_dx3.x3,dL_dx4.x4
,dL_dx6.x6,dL_dx7.x7,dL_dx10.x10,dL_dx11.x11 /;
m.limrow=0; m.limcol=0;
Solve m using MCP;
$offEcho
execute 'grep -v " written by GAMS" expl_gms > expl.gms.want'
execute 'grep -v " written by GAMS" expl.gms > expl.gms.got'
execute '=diff -I reslim -bw expl.gms.want expl.gms.got'
abort$errorlevel 'Files expl.gms.want and expl.gms.got differ';
$onEcho > expl_dict
* written by GAMS/JAMS at 12/03/16 23:15:28
********************************************************************************
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') t('1') zExp('1','1') zExp('2','1')
3:defobjExp('1') defFExp('1','1') defFExp('2','1')
4:min obj('2') t('2') zExp('1','2') zExp('2','2')
5:defobjExp('2') defFExp('1','2') defFExp('2','2')
6:vi defviExp x
7:vi defFExp('1','3') zExp('1','3') defFExp('2','3') zExp('2','3')
2 Processed EMP Information
---------------------------
Number of VI functions specified = 3
* e5 is VI Func and perpendicular to x5
* e8 is VI Func and perpendicular to x8
* e9 is VI Func and perpendicular to x9
3 Dictionary
------------
3.1 Constraints
---------------
{reformulated} defobjExp(1)
{reformulated} defobjExp(2)
e3 defFExp(1,1)
e4 defFExp(1,2)
e5 defFExp(1,3)
e6 defFExp(2,1)
e7 defFExp(2,2)
e8 defFExp(2,3)
e9 defviExp
dL_dx3 {new}
dL_dx4 {new}
dL_dx6 {new}
dL_dx7 {new}
dL_dx10 {new}
dL_dx11 {new}
3.2 Variables
--------------
{reformulated} obj(1)
{reformulated} obj(2)
x3 zExp(1,1)
x4 zExp(1,2)
x5 zExp(1,3)
x6 zExp(2,1)
x7 zExp(2,2)
x8 zExp(2,3)
x9 x
x10 t(1)
x11 t(2)
u3 {new}
u4 {new}
u6 {new}
u7 {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';
defobj(i)..
obj(i) =E=
(sqr(z(i)) - 0.5*t(i) + 0.25)$sameas(i,'1') +
(sqr(z(i)) - 2*t(i) + 1)$sameas(i,'2');
defF(i)..
(2*z('1') + z('2') + t('1') - t('2'))$sameas(i,'1') +
(-2*z('1') + 3*z('2') - t('1') - 3*t('2'))$sameas(i,'2') =E= 0;
defvi..
x =E= sum(i, z(i));
model mi 'implicit formulation' / defobj, defF, defvi /;
put info 'equilibrium' /;
put 'implicit z defF' /;
loop(i,
put 'min', obj(i), t(i), 'z', defobj(i) /;
);
put 'vi', defvi, x;
putclose;
* testing with implicit
putclose opt
'Dict implDict.txt' /
'FileName impl.gms' /
'ImplVarModel substitution' ;
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$[ abs(obj.l('1')-0) > tol ] 'bad obj.l("1")', obj.l;
abort$[ abs(obj.l('2')-0) > tol ] 'bad obj.l("2")', obj.l;
abort$[ abs(z.l('1')+.5) > tol] 'bad z.l("1")', z.l;
abort$[ abs(z.l('2')-1) > tol] 'bad z.l("2")', z.l;
abort$[ abs(t.l('1')-1) > tol ] 'bad t.l("1")', t.l;
abort$[ abs(t.l('2')-1) > tol ] 'bad t.l("2")', t.l;
abort$[ abs(x.l-0.5) > tol ] 'bad x.l', x.l;
obj.l(i) = 0;
z.l(i) = 0;
t.l(i) = 0;
x.l = 0;
defobj.m(i) = 0;
defF.m(i) = 0;
defvi.m = 0;
$onEchoV > impl_gms
***********************************************
* written by GAMS/JAMS at 12/03/16 23:21:59
* for more information use JAMS option "Dict"
***********************************************
Variables x3,x4,x5,x6,x7,dx3_dx6,dx3_dx7,dx4_dx6,dx4_dx7;
Positive Variables x6,x7;
Equations e3,e4,e5,IMPL_de3_dx6,IMPL_de3_dx7,IMPL_de4_dx6,IMPL_de4_dx7,dL_dx6
,dL_dx7;
e3.. 2*x3 + x4 + x6 - x7 =E= 0;
e4.. - 2*x3 + 3*x4 - x6 - 3*x7 =E= 0;
e5.. - x3 - x4 + x5 =E= 0;
* equations below are for newly defined implicit variables
IMPL_de3_dx6.. (2)*(dx3_dx6) + (1)*(dx4_dx6) + (1) =E= 0;
IMPL_de3_dx7.. (2)*(dx3_dx7) + (1)*(dx4_dx7) + (-1) =E= 0;
IMPL_de4_dx6.. (-2)*(dx3_dx6) + (3)*(dx4_dx6) + (-1) =E= 0;
IMPL_de4_dx7.. (-2)*(dx3_dx7) + (3)*(dx4_dx7) + (-3) =E= 0;
dL_dx6.. -0.5 + ((-2*x3)/(-1))*(dx3_dx6) + eps*x6 =G= 0;
dL_dx7.. -2 + ((-2*x4)/(-1))*(dx4_dx7) + eps*x7 =G= 0;
Model m / e3.x3,e4.x4,e5.x5,IMPL_de3_dx6.dx3_dx6,IMPL_de3_dx7.dx3_dx7
,IMPL_de4_dx6.dx4_dx6,IMPL_de4_dx7.dx4_dx7,dL_dx6.x6,dL_dx7.x7 /;
File implvarfile / '%gams.scrdir%implvar.dat' /;
Put implvarfile;
$onPutV
x3
x4
dx3_dx6
dx3_dx7
dx4_dx6
dx4_dx7
$offPut
m.limrow=0; m.limcol=0;
Solve m using MCP;
$offEcho
execute 'grep -v " written by GAMS" impl_gms > impl.gms.want'
execute 'grep -v " written by GAMS" impl.gms > impl.gms.got'
execute '=diff -I reslim -bw impl.gms.want impl.gms.got'
abort$errorlevel 'Files impl.gms.want and impl.gms.got differ';
$onEcho > impl_dict
* written by GAMS/JAMS at 12/03/16 23:21:59
********************************************************************************
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 defF
3:min obj('1') t('1') z defobj('1')
4:min obj('2') t('2') z defobj('2')
5:vi defvi x
2 Processed EMP Information
---------------------------
Number of VI functions specified = 1
* e5 is VI Func and perpendicular to x5
3 Dictionary
------------
3.1 Constraints
---------------
{reformulated} defobj(1)
{reformulated} defobj(2)
e3 defF(1)
e4 defF(2)
e5 defvi
IMPL_de3_dx6 {new}
IMPL_de3_dx7 {new}
IMPL_de4_dx6 {new}
IMPL_de4_dx7 {new}
dL_dx6 {new}
dL_dx7 {new}
3.2 Variables
--------------
{reformulated} obj(1)
{reformulated} obj(2)
x3 z(1)
x4 z(2)
x5 x
x6 t(1)
x7 t(2)
dx3_dx6 {new}
dx3_dx7 {new}
dx4_dx6 {new}
dx4_dx7 {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 implSwitchingDict.txt' /
'FileName implSwitching.gms' /
'ImplVarModel switching' ;
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$[ abs(obj.l('1')-0) > tol ] 'bad obj.l("1")', obj.l;
abort$[ abs(obj.l('2')-0) > tol ] 'bad obj.l("2")', obj.l;
abort$[ abs(z.l('1')+.5) > tol] 'bad z.l("1")', z.l;
abort$[ abs(z.l('2')-1) > tol] 'bad z.l("2")', z.l;
abort$[ abs(t.l('1')-1) > tol ] 'bad t.l("1")', t.l;
abort$[ abs(t.l('2')-1) > tol ] 'bad t.l("2")', t.l;
abort$[ abs(x.l-.5) > tol ] 'bad x.l', x.l;
obj.l(i) = 0;
z.l(i) = 0;
t.l(i) = 0;
x.l = 0;
defobj.m(i) = 0;
defF.m(i) = 0;
defvi.m = 0;
$onEchoV > implSwitching_gms
***********************************************
* for more information use JAMS option "Dict"
***********************************************
Variables x3,x4,x5,x6,x7,u3_4,u4_4,u3_5,u4_5;
Positive Variables x6,x7;
Equations e3,e4,e5,dL_dx3_4,dL_dx4_4,dL_dx6,dL_dx7,dL_dx3_5,dL_dx4_5;
e3.. 2*x3 + x4 + x6 - x7 =E= 0;
e4.. - 2*x3 + 3*x4 - x6 - 3*x7 =E= 0;
e5.. - x3 - x4 + x5 =E= 0;
dL_dx3_4.. (-2*x3)/(-1) - 2*u3_4 + 2*u4_4 =E= 0;
dL_dx4_4.. - u3_4 - 3*u4_4 + eps*x4 =E= 0;
dL_dx6.. -0.5 - u3_4 + u4_4 + eps*x6 =G= 0;
dL_dx7.. -2 + u3_5 + 3*u4_5 + eps*x7 =G= 0;
dL_dx3_5.. - 2*u3_5 + 2*u4_5 + eps*x3 =E= 0;
dL_dx4_5.. (-2*x4)/(-1) - u3_5 - 3*u4_5 =E= 0;
Model m / e3.x3,e4.x4,e5.x5,dL_dx3_4.u3_4,dL_dx4_4.u4_4,dL_dx6.x6,dL_dx7.x7
,dL_dx3_5.u3_5,dL_dx4_5.u4_5 /;
File implvarfile / '%gams.scrdir%implvar.dat' /;
Put implvarfile;
$onPutV
x3
x4
u3_4
u3_5
u4_4
u4_5
$offPut
m.limrow=0; m.limcol=0;
Solve m using MCP;
$offEcho
execute 'grep -v " written by GAMS" implSwitching_gms > implSwitching.gms.want'
execute 'grep -v " written by GAMS" implSwitching.gms > implSwitching.gms.got'
execute '=diff -I reslim -bw implSwitching.gms.want implSwitching.gms.got'
abort$errorlevel 'Files implSwitching.gms.want and implSwitching.gms.got differ';
$onEcho > implSwitching_dict
********************************************************************************
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 defF
3:min obj('1') t('1') z defobj('1')
4:min obj('2') t('2') z defobj('2')
5:vi defvi x
2 Processed EMP Information
---------------------------
Number of VI functions specified = 1
* e5 is VI Func and perpendicular to x5
3 Dictionary
------------
3.1 Constraints
---------------
{reformulated} defobj(1)
{reformulated} defobj(2)
e3 defF(1)
e4 defF(2)
e5 defvi
dL_dx3_4 {new}
dL_dx4_4 {new}
dL_dx6 {new}
dL_dx7 {new}
dL_dx3_5 {new}
dL_dx4_5 {new}
3.2 Variables
--------------
{reformulated} obj(1)
{reformulated} obj(2)
x3 z(1)
x4 z(2)
x5 x
x6 t(1)
x7 t(2)
u3_4 {new}
u4_4 {new}
u3_5 {new}
u4_5 {new}
$offEcho
execute 'grep -v " written by GAMS" implSwitching_dict > implSwitchingDict.txt.want'
execute 'grep -v " written by GAMS" implSwitchingDict.txt > implSwitchingDict.txt.got'
execute '=diff -bw implSwitchingDict.txt.want implSwitchingDict.txt.got'
abort$errorlevel 'Files implSwitchingDict.txt.want and implSwitchingDict.txt.got differ';