Date: 2022-03-31T04:48:46+00:00

Actual source code: ex20adj.c

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

      3: /*
      4:    Concepts: TS^time-dependent nonlinear problems
      5:    Concepts: TS^van der Pol equation DAE equivalent
      6:    Concepts: TS^adjoint sensitivity analysis
      7:    Processors: 1
      8: */
      9: /* ------------------------------------------------------------------------

     11:    This program solves the van der Pol DAE ODE equivalent
     12:       [ u_1' ] = [          u_2                ]  (2)
     13:       [ u_2' ]   [ \mu ((1 - u_1^2) u_2 - u_1) ]
     14:    on the domain 0 <= x <= 1, with the boundary conditions
     15:        u_1(0) = 2, u_2(0) = - 2/3 +10/(81*\mu) - 292/(2187*\mu^2),
     16:    and
     17:        \mu = 10^6 ( y'(0) ~ -0.6666665432100101).,
     18:    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.

     20:    Notes:
     21:    This code demonstrates the TSAdjoint interface to a DAE system.

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

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

     29:               dF   dF
     30:    J(F) = a * -- + --
     31:               du'  du

     33:    and the JacobianP of the explicit right-hand side of (2) f(u,t) ( which is equivalent to -F(0,u,t)).
     34:    df   [       0               ]
     35:    -- = [                       ]
     36:    dp   [ (1 - u_1^2) u_2 - u_1 ].

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

     40:   ------------------------------------------------------------------------- */
     41: #include <petscts.h>
     42: #include <petsctao.h>

     44: typedef struct _n_User *User;
     45: struct _n_User {
     46:   PetscReal mu;
     47:   PetscReal next_output;

     49:   /* Sensitivity analysis support */
     50:   PetscInt  steps;
     51:   PetscReal ftime;
     52:   Mat       A;                   /* Jacobian matrix */
     53:   Mat       Jacp;                /* JacobianP matrix */
     54:   Vec       U,lambda[2],mup[2];  /* adjoint variables */
     55: };

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

     59: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,void *ctx)
     60: {
     61:   User              user = (User)ctx;
     62:   PetscScalar       *f;
     63:   const PetscScalar *u;

     66:   VecGetArrayRead(U,&u);
     67:   VecGetArray(F,&f);
     68:   f[0] = u[1];
     69:   f[1] = user->mu*((1.-u[0]*u[0])*u[1]-u[0]);
     70:   VecRestoreArrayRead(U,&u);
     71:   VecRestoreArray(F,&f);
     72:   return 0;
     73: }

     75: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,void *ctx)
     76: {
     77:   User              user = (User)ctx;
     78:   PetscReal         mu   = user->mu;
     79:   PetscInt          rowcol[] = {0,1};
     80:   PetscScalar       J[2][2];
     81:   const PetscScalar *u;

     84:   VecGetArrayRead(U,&u);
     85:   J[0][0] = 0;
     86:   J[1][0] = -mu*(2.0*u[1]*u[0]+1.);
     87:   J[0][1] = 1.0;
     88:   J[1][1] = mu*(1.0-u[0]*u[0]);
     89:   MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
     90:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     91:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     92:   if (A != B) {
     93:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     94:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
     95:   }
     96:   VecRestoreArrayRead(U,&u);
     97:   return 0;
     98: }

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

    102: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
    103: {
    104:   User              user = (User)ctx;
    105:   const PetscScalar *u,*udot;
    106:   PetscScalar       *f;

    109:   VecGetArrayRead(U,&u);
    110:   VecGetArrayRead(Udot,&udot);
    111:   VecGetArray(F,&f);
    112:   f[0] = udot[0] - u[1];
    113:   f[1] = udot[1] - user->mu*((1.0-u[0]*u[0])*u[1] - u[0]);
    114:   VecRestoreArrayRead(U,&u);
    115:   VecRestoreArrayRead(Udot,&udot);
    116:   VecRestoreArray(F,&f);
    117:   return 0;
    118: }

    120: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,void *ctx)
    121: {
    122:   User              user     = (User)ctx;
    123:   PetscInt          rowcol[] = {0,1};
    124:   PetscScalar       J[2][2];
    125:   const PetscScalar *u;

    128:   VecGetArrayRead(U,&u);

    130:   J[0][0] = a;     J[0][1] =  -1.0;
    131:   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]);

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

    136:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    137:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    138:   if (B && A != B) {
    139:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    140:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    141:   }
    142:   return 0;
    143: }

    145: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec U,Mat A,void *ctx)
    146: {
    147:   PetscInt          row[] = {0,1},col[]={0};
    148:   PetscScalar       J[2][1];
    149:   const PetscScalar *u;

    152:   VecGetArrayRead(U,&u);
    153:   J[0][0] = 0;
    154:   J[1][0] = (1.-u[0]*u[0])*u[1]-u[0];
    155:   MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
    156:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    157:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    158:   VecRestoreArrayRead(U,&u);
    159:   return 0;
    160: }

    162: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
    163: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec U,void *ctx)
    164: {
    165:   const PetscScalar *u;
    166:   PetscReal         tfinal, dt;
    167:   User              user = (User)ctx;
    168:   Vec               interpolatedU;

    171:   TSGetTimeStep(ts,&dt);
    172:   TSGetMaxTime(ts,&tfinal);

    174:   while (user->next_output <= t && user->next_output <= tfinal) {
    175:     VecDuplicate(U,&interpolatedU);
    176:     TSInterpolate(ts,user->next_output,interpolatedU);
    177:     VecGetArrayRead(interpolatedU,&u);
    178:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"[%g] %D TS %g (dt = %g) X %g %g\n",
    179:                         (double)user->next_output,step,(double)t,(double)dt,(double)PetscRealPart(u[0]),
    180:                         (double)PetscRealPart(u[1])));
    181:     VecRestoreArrayRead(interpolatedU,&u);
    182:     VecDestroy(&interpolatedU);
    183:     user->next_output += 0.1;
    184:   }
    185:   return 0;
    186: }

    188: int main(int argc,char **argv)
    189: {
    190:   TS             ts;
    191:   PetscBool      monitor = PETSC_FALSE,implicitform = PETSC_TRUE;
    192:   PetscScalar    *x_ptr,*y_ptr,derp;
    193:   PetscMPIInt    size;
    194:   struct _n_User user;

    196:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    197:      Initialize program
    198:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    199:   PetscInitialize(&argc,&argv,NULL,help);
    200:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

    203:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    204:     Set runtime options
    205:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    206:   user.next_output = 0.0;
    207:   user.mu          = 1.0e3;
    208:   user.steps       = 0;
    209:   user.ftime       = 0.5;
    210:   PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
    211:   PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);
    212:   PetscOptionsGetBool(NULL,NULL,"-implicitform",&implicitform,NULL);

    214:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    215:     Create necessary matrix and vectors, solve same ODE on every process
    216:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    217:   MatCreate(PETSC_COMM_WORLD,&user.A);
    218:   MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
    219:   MatSetFromOptions(user.A);
    220:   MatSetUp(user.A);
    221:   MatCreateVecs(user.A,&user.U,NULL);

    223:   MatCreate(PETSC_COMM_WORLD,&user.Jacp);
    224:   MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
    225:   MatSetFromOptions(user.Jacp);
    226:   MatSetUp(user.Jacp);

    228:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    229:      Create timestepping solver context
    230:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    231:   TSCreate(PETSC_COMM_WORLD,&ts);
    232:   TSSetEquationType(ts,TS_EQ_ODE_EXPLICIT); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
    233:   if (implicitform) {
    234:     TSSetIFunction(ts,NULL,IFunction,&user);
    235:     TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);
    236:     TSSetType(ts,TSCN);
    237:   } else {
    238:     TSSetRHSFunction(ts,NULL,RHSFunction,&user);
    239:     TSSetRHSJacobian(ts,user.A,user.A,RHSJacobian,&user);
    240:     TSSetType(ts,TSRK);
    241:   }
    242:   TSSetRHSJacobianP(ts,user.Jacp,RHSJacobianP,&user);
    243:   TSSetMaxTime(ts,user.ftime);
    244:   TSSetTimeStep(ts,0.001);
    245:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
    246:   if (monitor) TSMonitorSet(ts,Monitor,&user,NULL);

    248:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    249:      Set initial conditions
    250:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    251:   VecGetArray(user.U,&x_ptr);
    252:   x_ptr[0] = 2.0;
    253:   x_ptr[1] = -2.0/3.0 + 10.0/(81.0*user.mu) - 292.0/(2187.0*user.mu*user.mu);
    254:   VecRestoreArray(user.U,&x_ptr);
    255:   TSSetTimeStep(ts,0.001);

    257:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    258:     Save trajectory of solution so that TSAdjointSolve() may be used
    259:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    260:   TSSetSaveTrajectory(ts);

    262:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    263:      Set runtime options
    264:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    265:   TSSetFromOptions(ts);

    267:   TSSolve(ts,user.U);
    268:   TSGetSolveTime(ts,&user.ftime);
    269:   TSGetStepNumber(ts,&user.steps);

    271:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    272:      Adjoint model starts here
    273:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    274:   MatCreateVecs(user.A,&user.lambda[0],NULL);
    275:   /* Set initial conditions for the adjoint integration */
    276:   VecGetArray(user.lambda[0],&y_ptr);
    277:   y_ptr[0] = 1.0; y_ptr[1] = 0.0;
    278:   VecRestoreArray(user.lambda[0],&y_ptr);
    279:   MatCreateVecs(user.A,&user.lambda[1],NULL);
    280:   VecGetArray(user.lambda[1],&y_ptr);
    281:   y_ptr[0] = 0.0; y_ptr[1] = 1.0;
    282:   VecRestoreArray(user.lambda[1],&y_ptr);

    284:   MatCreateVecs(user.Jacp,&user.mup[0],NULL);
    285:   VecGetArray(user.mup[0],&x_ptr);
    286:   x_ptr[0] = 0.0;
    287:   VecRestoreArray(user.mup[0],&x_ptr);
    288:   MatCreateVecs(user.Jacp,&user.mup[1],NULL);
    289:   VecGetArray(user.mup[1],&x_ptr);
    290:   x_ptr[0] = 0.0;
    291:   VecRestoreArray(user.mup[1],&x_ptr);

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

    295:   TSAdjointSolve(ts);

    297:   PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[y(tf)]/d[y0]  d[y(tf)]/d[z0]\n");
    298:   VecView(user.lambda[0],PETSC_VIEWER_STDOUT_WORLD);
    299:   PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[z(tf)]/d[y0]  d[z(tf)]/d[z0]\n");
    300:   VecView(user.lambda[1],PETSC_VIEWER_STDOUT_WORLD);

    302:   VecGetArray(user.mup[0],&x_ptr);
    303:   VecGetArray(user.lambda[0],&y_ptr);
    304:   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];
    305:   VecRestoreArray(user.mup[0],&x_ptr);
    306:   VecRestoreArray(user.lambda[0],&y_ptr);
    307:   PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt parameters: d[y(tf)]/d[mu]\n%g\n",(double)PetscRealPart(derp));

    309:   VecGetArray(user.mup[1],&x_ptr);
    310:   VecGetArray(user.lambda[1],&y_ptr);
    311:   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];
    312:   VecRestoreArray(user.mup[1],&x_ptr);
    313:   VecRestoreArray(user.lambda[1],&y_ptr);
    314:   PetscPrintf(PETSC_COMM_WORLD,"\n sensivitity wrt parameters: d[z(tf)]/d[mu]\n%g\n",(double)PetscRealPart(derp));

    316:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    317:      Free work space.  All PETSc objects should be destroyed when they
    318:      are no longer needed.
    319:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    320:   MatDestroy(&user.A);
    321:   MatDestroy(&user.Jacp);
    322:   VecDestroy(&user.U);
    323:   VecDestroy(&user.lambda[0]);
    324:   VecDestroy(&user.lambda[1]);
    325:   VecDestroy(&user.mup[0]);
    326:   VecDestroy(&user.mup[1]);
    327:   TSDestroy(&ts);

    329:   PetscFinalize();
    330:   return 0;
    331: }

    333: /*TEST

    335:     test:
    336:       requires: revolve
    337:       args: -monitor 0 -ts_type theta -ts_theta_endpoint -ts_theta_theta 0.5 -viewer_binary_skip_info -ts_dt 0.001 -mu 100000

    339:     test:
    340:       suffix: 2
    341:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only

    343:     test:
    344:       suffix: 3
    345:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only 0
    346:       output_file: output/ex20adj_2.out

    348:     test:
    349:       suffix: 4
    350:       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
    351:       output_file: output/ex20adj_2.out

    353:     test:
    354:       suffix: 5
    355:       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
    356:       output_file: output/ex20adj_2.out

    358:     test:
    359:       suffix: 6
    360:       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
    361:       output_file: output/ex20adj_2.out

    363:     test:
    364:       suffix: 7
    365:       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
    366:       output_file: output/ex20adj_2.out

    368:     test:
    369:       suffix: 8
    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 -ts_trajectory_monitor
    372:       output_file: output/ex20adj_3.out

    374:     test:
    375:       suffix: 9
    376:       requires: revolve !cams
    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_solution_only 0 -ts_trajectory_monitor
    378:       output_file: output/ex20adj_4.out

    380:     test:
    381:       requires: revolve
    382:       suffix: 10
    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
    384:       output_file: output/ex20adj_2.out

    386:     test:
    387:       requires: revolve
    388:       suffix: 11
    389:       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
    390:       output_file: output/ex20adj_2.out

    392:     test:
    393:       suffix: 12
    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
    396:       output_file: output/ex20adj_2.out

    398:     test:
    399:       suffix: 13
    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_max_cps_disk 8 -ts_trajectory_solution_only 0
    402:       output_file: output/ex20adj_2.out

    404:     test:
    405:       suffix: 14
    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
    408:       output_file: output/ex20adj_2.out

    410:     test:
    411:       suffix: 15
    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 -ts_trajectory_save_stack 0
    414:       output_file: output/ex20adj_2.out

    416:     test:
    417:       suffix: 16
    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
    420:       output_file: output/ex20adj_2.out

    422:     test:
    423:       suffix: 17
    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_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack 0
    426:       output_file: output/ex20adj_2.out

    428:     test:
    429:       suffix: 18
    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 -ts_trajectory_save_stack
    432:       output_file: output/ex20adj_2.out

    434:     test:
    435:       suffix: 19
    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_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack
    438:       output_file: output/ex20adj_2.out

    440:     test:
    441:       suffix: 20
    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_solution_only 0
    444:       output_file: output/ex20adj_2.out

    446:     test:
    447:       suffix: 21
    448:       requires: revolve
    449:       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
    450:       output_file: output/ex20adj_2.out

    452:     test:
    453:       suffix: 22
    454:       args: -ts_type beuler -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only
    455:       output_file: output/ex20adj_2.out

    457:     test:
    458:       suffix: 23
    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 -ts_trajectory_monitor -ts_trajectory_memory_type cams
    461:       output_file: output/ex20adj_5.out

    463:     test:
    464:       suffix: 24
    465:       requires: cams
    466:       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
    467:       output_file: output/ex20adj_6.out

    469: TEST*/