Actual source code: ex20adj.c

      1: static char help[] = "Performs adjoint sensitivity analysis for the van der Pol equation.\n";

      3: /* ------------------------------------------------------------------------

      5:    This program solves the van der Pol DAE ODE equivalent
      6:       [ u_1' ] = [          u_2                ]  (2)
      7:       [ u_2' ]   [ \mu ((1 - u_1^2) u_2 - u_1) ]
      8:    on the domain 0 <= x <= 1, with the boundary conditions
      9:        u_1(0) = 2, u_2(0) = - 2/3 +10/(81*\mu) - 292/(2187*\mu^2),
     10:    and
     11:        \mu = 10^6 ( y'(0) ~ -0.6666665432100101).,
     12:    and computes the sensitivities of the final solution w.r.t. initial conditions and parameter \mu with the implicit theta method and its discrete adjoint.

     14:    Notes:
     15:    This code demonstrates the TSAdjoint interface to a DAE system.

     17:    The user provides the implicit right-hand-side function
     18:    [ F(u',u,t) ] = [u' - f(u,t)] = [ u_1'] - [        u_2             ]
     19:                                    [ u_2']   [ \mu ((1-u_1^2)u_2-u_1) ]

     21:    and the Jacobian of F (from the PETSc user manual)

     23:               dF   dF
     24:    J(F) = a * -- + --
     25:               du'  du

     27:    and the JacobianP of the explicit right-hand side of (2) f(u,t) ( which is equivalent to -F(0,u,t)).
     28:    df   [       0               ]
     29:    -- = [                       ]
     30:    dp   [ (1 - u_1^2) u_2 - u_1 ].

     32:    See ex20.c for more details on the Jacobian.

     34:   ------------------------------------------------------------------------- */
     35: #include <petscts.h>
     36: #include <petsctao.h>

     38: typedef struct _n_User *User;
     39: struct _n_User {
     40:   PetscReal mu;
     41:   PetscReal next_output;

     43:   /* Sensitivity analysis support */
     44:   PetscInt  steps;
     45:   PetscReal ftime;
     46:   Mat       A;                   /* Jacobian matrix */
     47:   Mat       Jacp;                /* JacobianP matrix */
     48:   Vec       U,lambda[2],mup[2];  /* adjoint variables */
     49: };

     51: /* ----------------------- Explicit form of the ODE  -------------------- */

     53: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,void *ctx)
     54: {
     55:   User              user = (User)ctx;
     56:   PetscScalar       *f;
     57:   const PetscScalar *u;

     60:   VecGetArrayRead(U,&u);
     61:   VecGetArray(F,&f);
     62:   f[0] = u[1];
     63:   f[1] = user->mu*((1.-u[0]*u[0])*u[1]-u[0]);
     64:   VecRestoreArrayRead(U,&u);
     65:   VecRestoreArray(F,&f);
     66:   return 0;
     67: }

     69: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,void *ctx)
     70: {
     71:   User              user = (User)ctx;
     72:   PetscReal         mu   = user->mu;
     73:   PetscInt          rowcol[] = {0,1};
     74:   PetscScalar       J[2][2];
     75:   const PetscScalar *u;

     78:   VecGetArrayRead(U,&u);
     79:   J[0][0] = 0;
     80:   J[1][0] = -mu*(2.0*u[1]*u[0]+1.);
     81:   J[0][1] = 1.0;
     82:   J[1][1] = mu*(1.0-u[0]*u[0]);
     83:   MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
     84:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     85:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     86:   if (A != B) {
     87:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     88:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
     89:   }
     90:   VecRestoreArrayRead(U,&u);
     91:   return 0;
     92: }

     94: /* ----------------------- Implicit form of the ODE  -------------------- */

     96: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
     97: {
     98:   User              user = (User)ctx;
     99:   const PetscScalar *u,*udot;
    100:   PetscScalar       *f;

    103:   VecGetArrayRead(U,&u);
    104:   VecGetArrayRead(Udot,&udot);
    105:   VecGetArray(F,&f);
    106:   f[0] = udot[0] - u[1];
    107:   f[1] = udot[1] - user->mu*((1.0-u[0]*u[0])*u[1] - u[0]);
    108:   VecRestoreArrayRead(U,&u);
    109:   VecRestoreArrayRead(Udot,&udot);
    110:   VecRestoreArray(F,&f);
    111:   return 0;
    112: }

    114: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,void *ctx)
    115: {
    116:   User              user     = (User)ctx;
    117:   PetscInt          rowcol[] = {0,1};
    118:   PetscScalar       J[2][2];
    119:   const PetscScalar *u;

    122:   VecGetArrayRead(U,&u);

    124:   J[0][0] = a;     J[0][1] =  -1.0;
    125:   J[1][0] = user->mu*(2.0*u[0]*u[1] + 1.0);   J[1][1] = a - user->mu*(1.0-u[0]*u[0]);

    127:   MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
    128:   VecRestoreArrayRead(U,&u);

    130:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    131:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    132:   if (B && A != B) {
    133:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    134:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    135:   }
    136:   return 0;
    137: }

    139: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec U,Mat A,void *ctx)
    140: {
    141:   PetscInt          row[] = {0,1},col[]={0};
    142:   PetscScalar       J[2][1];
    143:   const PetscScalar *u;

    146:   VecGetArrayRead(U,&u);
    147:   J[0][0] = 0;
    148:   J[1][0] = (1.-u[0]*u[0])*u[1]-u[0];
    149:   MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
    150:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    151:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    152:   VecRestoreArrayRead(U,&u);
    153:   return 0;
    154: }

    156: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
    157: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec U,void *ctx)
    158: {
    159:   const PetscScalar *u;
    160:   PetscReal         tfinal, dt;
    161:   User              user = (User)ctx;
    162:   Vec               interpolatedU;

    165:   TSGetTimeStep(ts,&dt);
    166:   TSGetMaxTime(ts,&tfinal);

    168:   while (user->next_output <= t && user->next_output <= tfinal) {
    169:     VecDuplicate(U,&interpolatedU);
    170:     TSInterpolate(ts,user->next_output,interpolatedU);
    171:     VecGetArrayRead(interpolatedU,&u);
    172:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"[%g] %D TS %g (dt = %g) X %g %g\n",
    173:                         (double)user->next_output,step,(double)t,(double)dt,(double)PetscRealPart(u[0]),
    174:                         (double)PetscRealPart(u[1])));
    175:     VecRestoreArrayRead(interpolatedU,&u);
    176:     VecDestroy(&interpolatedU);
    177:     user->next_output += 0.1;
    178:   }
    179:   return 0;
    180: }

    182: int main(int argc,char **argv)
    183: {
    184:   TS             ts;
    185:   PetscBool      monitor = PETSC_FALSE,implicitform = PETSC_TRUE;
    186:   PetscScalar    *x_ptr,*y_ptr,derp;
    187:   PetscMPIInt    size;
    188:   struct _n_User user;

    190:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    191:      Initialize program
    192:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    193:   PetscInitialize(&argc,&argv,NULL,help);
    194:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

    197:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    198:     Set runtime options
    199:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    200:   user.next_output = 0.0;
    201:   user.mu          = 1.0e3;
    202:   user.steps       = 0;
    203:   user.ftime       = 0.5;
    204:   PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
    205:   PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);
    206:   PetscOptionsGetBool(NULL,NULL,"-implicitform",&implicitform,NULL);

    208:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    209:     Create necessary matrix and vectors, solve same ODE on every process
    210:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    211:   MatCreate(PETSC_COMM_WORLD,&user.A);
    212:   MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
    213:   MatSetFromOptions(user.A);
    214:   MatSetUp(user.A);
    215:   MatCreateVecs(user.A,&user.U,NULL);

    217:   MatCreate(PETSC_COMM_WORLD,&user.Jacp);
    218:   MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
    219:   MatSetFromOptions(user.Jacp);
    220:   MatSetUp(user.Jacp);

    222:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    223:      Create timestepping solver context
    224:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    225:   TSCreate(PETSC_COMM_WORLD,&ts);
    226:   TSSetEquationType(ts,TS_EQ_ODE_EXPLICIT); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
    227:   if (implicitform) {
    228:     TSSetIFunction(ts,NULL,IFunction,&user);
    229:     TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);
    230:     TSSetType(ts,TSCN);
    231:   } else {
    232:     TSSetRHSFunction(ts,NULL,RHSFunction,&user);
    233:     TSSetRHSJacobian(ts,user.A,user.A,RHSJacobian,&user);
    234:     TSSetType(ts,TSRK);
    235:   }
    236:   TSSetRHSJacobianP(ts,user.Jacp,RHSJacobianP,&user);
    237:   TSSetMaxTime(ts,user.ftime);
    238:   TSSetTimeStep(ts,0.001);
    239:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
    240:   if (monitor) TSMonitorSet(ts,Monitor,&user,NULL);

    242:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    243:      Set initial conditions
    244:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    245:   VecGetArray(user.U,&x_ptr);
    246:   x_ptr[0] = 2.0;
    247:   x_ptr[1] = -2.0/3.0 + 10.0/(81.0*user.mu) - 292.0/(2187.0*user.mu*user.mu);
    248:   VecRestoreArray(user.U,&x_ptr);
    249:   TSSetTimeStep(ts,0.001);

    251:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    252:     Save trajectory of solution so that TSAdjointSolve() may be used
    253:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    254:   TSSetSaveTrajectory(ts);

    256:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    257:      Set runtime options
    258:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    259:   TSSetFromOptions(ts);

    261:   TSSolve(ts,user.U);
    262:   TSGetSolveTime(ts,&user.ftime);
    263:   TSGetStepNumber(ts,&user.steps);

    265:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    266:      Adjoint model starts here
    267:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    268:   MatCreateVecs(user.A,&user.lambda[0],NULL);
    269:   /* Set initial conditions for the adjoint integration */
    270:   VecGetArray(user.lambda[0],&y_ptr);
    271:   y_ptr[0] = 1.0; y_ptr[1] = 0.0;
    272:   VecRestoreArray(user.lambda[0],&y_ptr);
    273:   MatCreateVecs(user.A,&user.lambda[1],NULL);
    274:   VecGetArray(user.lambda[1],&y_ptr);
    275:   y_ptr[0] = 0.0; y_ptr[1] = 1.0;
    276:   VecRestoreArray(user.lambda[1],&y_ptr);

    278:   MatCreateVecs(user.Jacp,&user.mup[0],NULL);
    279:   VecGetArray(user.mup[0],&x_ptr);
    280:   x_ptr[0] = 0.0;
    281:   VecRestoreArray(user.mup[0],&x_ptr);
    282:   MatCreateVecs(user.Jacp,&user.mup[1],NULL);
    283:   VecGetArray(user.mup[1],&x_ptr);
    284:   x_ptr[0] = 0.0;
    285:   VecRestoreArray(user.mup[1],&x_ptr);

    287:   TSSetCostGradients(ts,2,user.lambda,user.mup);

    289:   TSAdjointSolve(ts);

    291:   PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[y(tf)]/d[y0]  d[y(tf)]/d[z0]\n");
    292:   VecView(user.lambda[0],PETSC_VIEWER_STDOUT_WORLD);
    293:   PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[z(tf)]/d[y0]  d[z(tf)]/d[z0]\n");
    294:   VecView(user.lambda[1],PETSC_VIEWER_STDOUT_WORLD);

    296:   VecGetArray(user.mup[0],&x_ptr);
    297:   VecGetArray(user.lambda[0],&y_ptr);
    298:   derp = y_ptr[1]*(-10.0/(81.0*user.mu*user.mu)+2.0*292.0/(2187.0*user.mu*user.mu*user.mu))+x_ptr[0];
    299:   VecRestoreArray(user.mup[0],&x_ptr);
    300:   VecRestoreArray(user.lambda[0],&y_ptr);
    301:   PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt parameters: d[y(tf)]/d[mu]\n%g\n",(double)PetscRealPart(derp));

    303:   VecGetArray(user.mup[1],&x_ptr);
    304:   VecGetArray(user.lambda[1],&y_ptr);
    305:   derp = y_ptr[1]*(-10.0/(81.0*user.mu*user.mu)+2.0*292.0/(2187.0*user.mu*user.mu*user.mu))+x_ptr[0];
    306:   VecRestoreArray(user.mup[1],&x_ptr);
    307:   VecRestoreArray(user.lambda[1],&y_ptr);
    308:   PetscPrintf(PETSC_COMM_WORLD,"\n sensivitity wrt parameters: d[z(tf)]/d[mu]\n%g\n",(double)PetscRealPart(derp));

    310:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    311:      Free work space.  All PETSc objects should be destroyed when they
    312:      are no longer needed.
    313:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    314:   MatDestroy(&user.A);
    315:   MatDestroy(&user.Jacp);
    316:   VecDestroy(&user.U);
    317:   VecDestroy(&user.lambda[0]);
    318:   VecDestroy(&user.lambda[1]);
    319:   VecDestroy(&user.mup[0]);
    320:   VecDestroy(&user.mup[1]);
    321:   TSDestroy(&ts);

    323:   PetscFinalize();
    324:   return 0;
    325: }

    327: /*TEST

    329:     test:
    330:       requires: revolve
    331:       args: -monitor 0 -ts_type theta -ts_theta_endpoint -ts_theta_theta 0.5 -viewer_binary_skip_info -ts_dt 0.001 -mu 100000

    333:     test:
    334:       suffix: 2
    335:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only

    337:     test:
    338:       suffix: 3
    339:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only 0
    340:       output_file: output/ex20adj_2.out

    342:     test:
    343:       suffix: 4
    344:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_stride 5 -ts_trajectory_solution_only -ts_trajectory_save_stack
    345:       output_file: output/ex20adj_2.out

    347:     test:
    348:       suffix: 5
    349:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack
    350:       output_file: output/ex20adj_2.out

    352:     test:
    353:       suffix: 6
    354:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_stride 5 -ts_trajectory_solution_only -ts_trajectory_save_stack 0
    355:       output_file: output/ex20adj_2.out

    357:     test:
    358:       suffix: 7
    359:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack 0
    360:       output_file: output/ex20adj_2.out

    362:     test:
    363:       suffix: 8
    364:       requires: revolve !cams
    365:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 5 -ts_trajectory_solution_only -ts_trajectory_monitor
    366:       output_file: output/ex20adj_3.out

    368:     test:
    369:       suffix: 9
    370:       requires: revolve !cams
    371:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 5 -ts_trajectory_solution_only 0 -ts_trajectory_monitor
    372:       output_file: output/ex20adj_4.out

    374:     test:
    375:       requires: revolve
    376:       suffix: 10
    377:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 5 -ts_trajectory_revolve_online -ts_trajectory_solution_only
    378:       output_file: output/ex20adj_2.out

    380:     test:
    381:       requires: revolve
    382:       suffix: 11
    383:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 5 -ts_trajectory_revolve_online -ts_trajectory_solution_only 0
    384:       output_file: output/ex20adj_2.out

    386:     test:
    387:       suffix: 12
    388:       requires: revolve
    389:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_max_cps_disk 8 -ts_trajectory_solution_only
    390:       output_file: output/ex20adj_2.out

    392:     test:
    393:       suffix: 13
    394:       requires: revolve
    395:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_max_cps_disk 8 -ts_trajectory_solution_only 0
    396:       output_file: output/ex20adj_2.out

    398:     test:
    399:       suffix: 14
    400:       requires: revolve
    401:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_stride 5 -ts_trajectory_solution_only -ts_trajectory_save_stack
    402:       output_file: output/ex20adj_2.out

    404:     test:
    405:       suffix: 15
    406:       requires: revolve
    407:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_stride 5 -ts_trajectory_solution_only -ts_trajectory_save_stack 0
    408:       output_file: output/ex20adj_2.out

    410:     test:
    411:       suffix: 16
    412:       requires: revolve
    413:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack
    414:       output_file: output/ex20adj_2.out

    416:     test:
    417:       suffix: 17
    418:       requires: revolve
    419:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack 0
    420:       output_file: output/ex20adj_2.out

    422:     test:
    423:       suffix: 18
    424:       requires: revolve
    425:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_max_cps_disk 8 -ts_trajectory_stride 5 -ts_trajectory_solution_only -ts_trajectory_save_stack
    426:       output_file: output/ex20adj_2.out

    428:     test:
    429:       suffix: 19
    430:       requires: revolve
    431:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_max_cps_disk 8 -ts_trajectory_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack
    432:       output_file: output/ex20adj_2.out

    434:     test:
    435:       suffix: 20
    436:       requires: revolve
    437:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_max_cps_disk 8 -ts_trajectory_solution_only 0
    438:       output_file: output/ex20adj_2.out

    440:     test:
    441:       suffix: 21
    442:       requires: revolve
    443:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_max_cps_disk 8 -ts_trajectory_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack 0
    444:       output_file: output/ex20adj_2.out

    446:     test:
    447:       suffix: 22
    448:       args: -ts_type beuler -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only
    449:       output_file: output/ex20adj_2.out

    451:     test:
    452:       suffix: 23
    453:       requires: cams
    454:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_units_ram 5 -ts_trajectory_solution_only -ts_trajectory_monitor -ts_trajectory_memory_type cams
    455:       output_file: output/ex20adj_5.out

    457:     test:
    458:       suffix: 24
    459:       requires: cams
    460:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_units_ram 5 -ts_trajectory_solution_only 0 -ts_trajectory_monitor -ts_trajectory_memory_type cams
    461:       output_file: output/ex20adj_6.out

    463: TEST*/