$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';