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:   PetscErrorCode    ierr;
     62:   User              user = (User)ctx;
     63:   PetscScalar       *f;
     64:   const PetscScalar *u;

     67:   VecGetArrayRead(U,&u);
     68:   VecGetArray(F,&f);
     69:   f[0] = u[1];
     70:   f[1] = user->mu*((1.-u[0]*u[0])*u[1]-u[0]);
     71:   VecRestoreArrayRead(U,&u);
     72:   VecRestoreArray(F,&f);
     73:   return(0);
     74: }

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

     86:   VecGetArrayRead(U,&u);
     87:   J[0][0] = 0;
     88:   J[1][0] = -mu*(2.0*u[1]*u[0]+1.);
     89:   J[0][1] = 1.0;
     90:   J[1][1] = mu*(1.0-u[0]*u[0]);
     91:   MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
     92:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     93:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     94:   if (A != B) {
     95:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     96:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
     97:   }
     98:   VecRestoreArrayRead(U,&u);
     99:   return(0);
    100: }

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

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

    112:   VecGetArrayRead(U,&u);
    113:   VecGetArrayRead(Udot,&udot);
    114:   VecGetArray(F,&f);
    115:   f[0] = udot[0] - u[1];
    116:   f[1] = udot[1] - user->mu*((1.0-u[0]*u[0])*u[1] - u[0]);
    117:   VecRestoreArrayRead(U,&u);
    118:   VecRestoreArrayRead(Udot,&udot);
    119:   VecRestoreArray(F,&f);
    120:   return(0);
    121: }

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

    132:   VecGetArrayRead(U,&u);

    134:   J[0][0] = a;     J[0][1] =  -1.0;
    135:   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]);

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

    140:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    141:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    142:   if (B && A != B) {
    143:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    144:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    145:   }
    146:   return(0);
    147: }

    149: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec U,Mat A,void *ctx)
    150: {
    151:   PetscErrorCode    ierr;
    152:   PetscInt          row[] = {0,1},col[]={0};
    153:   PetscScalar       J[2][1];
    154:   const PetscScalar *u;

    157:   VecGetArrayRead(U,&u);
    158:   J[0][0] = 0;
    159:   J[1][0] = (1.-u[0]*u[0])*u[1]-u[0];
    160:   MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
    161:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    162:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    163:   VecRestoreArrayRead(U,&u);
    164:   return(0);
    165: }

    167: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
    168: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec U,void *ctx)
    169: {
    170:   PetscErrorCode    ierr;
    171:   const PetscScalar *u;
    172:   PetscReal         tfinal, dt;
    173:   User              user = (User)ctx;
    174:   Vec               interpolatedU;

    177:   TSGetTimeStep(ts,&dt);
    178:   TSGetMaxTime(ts,&tfinal);

    180:   while (user->next_output <= t && user->next_output <= tfinal) {
    181:     VecDuplicate(U,&interpolatedU);
    182:     TSInterpolate(ts,user->next_output,interpolatedU);
    183:     VecGetArrayRead(interpolatedU,&u);
    184:     PetscPrintf(PETSC_COMM_WORLD,"[%g] %D TS %g (dt = %g) X %g %g\n",
    185:                        (double)user->next_output,step,(double)t,(double)dt,(double)PetscRealPart(u[0]),
    186:                        (double)PetscRealPart(u[1]));
    187:     VecRestoreArrayRead(interpolatedU,&u);
    188:     VecDestroy(&interpolatedU);
    189:     user->next_output += 0.1;
    190:   }
    191:   return(0);
    192: }

    194: int main(int argc,char **argv)
    195: {
    196:   TS             ts;
    197:   PetscBool      monitor = PETSC_FALSE,implicitform = PETSC_TRUE;
    198:   PetscScalar    *x_ptr,*y_ptr,derp;
    199:   PetscMPIInt    size;
    200:   struct _n_User user;

    203:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    204:      Initialize program
    205:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    206:   PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
    207:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
    208:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");

    210:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    211:     Set runtime options
    212:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    213:   user.next_output = 0.0;
    214:   user.mu          = 1.0e3;
    215:   user.steps       = 0;
    216:   user.ftime       = 0.5;
    217:   PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
    218:   PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);
    219:   PetscOptionsGetBool(NULL,NULL,"-implicitform",&implicitform,NULL);

    221:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    222:     Create necessary matrix and vectors, solve same ODE on every process
    223:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    224:   MatCreate(PETSC_COMM_WORLD,&user.A);
    225:   MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);
    226:   MatSetFromOptions(user.A);
    227:   MatSetUp(user.A);
    228:   MatCreateVecs(user.A,&user.U,NULL);

    230:   MatCreate(PETSC_COMM_WORLD,&user.Jacp);
    231:   MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
    232:   MatSetFromOptions(user.Jacp);
    233:   MatSetUp(user.Jacp);

    235:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    236:      Create timestepping solver context
    237:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    238:   TSCreate(PETSC_COMM_WORLD,&ts);
    239:   TSSetEquationType(ts,TS_EQ_ODE_EXPLICIT); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
    240:   if (implicitform) {
    241:     TSSetIFunction(ts,NULL,IFunction,&user);
    242:     TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);
    243:     TSSetType(ts,TSCN);
    244:   } else {
    245:     TSSetRHSFunction(ts,NULL,RHSFunction,&user);
    246:     TSSetRHSJacobian(ts,user.A,user.A,RHSJacobian,&user);
    247:     TSSetType(ts,TSRK);
    248:   }
    249:   TSSetRHSJacobianP(ts,user.Jacp,RHSJacobianP,&user);
    250:   TSSetMaxTime(ts,user.ftime);
    251:   TSSetTimeStep(ts,0.001);
    252:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
    253:   if (monitor) {
    254:     TSMonitorSet(ts,Monitor,&user,NULL);
    255:   }

    257:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    258:      Set initial conditions
    259:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    260:   VecGetArray(user.U,&x_ptr);
    261:   x_ptr[0] = 2.0;
    262:   x_ptr[1] = -2.0/3.0 + 10.0/(81.0*user.mu) - 292.0/(2187.0*user.mu*user.mu);
    263:   VecRestoreArray(user.U,&x_ptr);
    264:   TSSetTimeStep(ts,0.001);

    266:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    267:     Save trajectory of solution so that TSAdjointSolve() may be used
    268:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    269:   TSSetSaveTrajectory(ts);

    271:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    272:      Set runtime options
    273:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    274:   TSSetFromOptions(ts);

    276:   TSSolve(ts,user.U);
    277:   TSGetSolveTime(ts,&user.ftime);
    278:   TSGetStepNumber(ts,&user.steps);

    280:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    281:      Adjoint model starts here
    282:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    283:   MatCreateVecs(user.A,&user.lambda[0],NULL);
    284:   /* Set initial conditions for the adjoint integration */
    285:   VecGetArray(user.lambda[0],&y_ptr);
    286:   y_ptr[0] = 1.0; y_ptr[1] = 0.0;
    287:   VecRestoreArray(user.lambda[0],&y_ptr);
    288:   MatCreateVecs(user.A,&user.lambda[1],NULL);
    289:   VecGetArray(user.lambda[1],&y_ptr);
    290:   y_ptr[0] = 0.0; y_ptr[1] = 1.0;
    291:   VecRestoreArray(user.lambda[1],&y_ptr);

    293:   MatCreateVecs(user.Jacp,&user.mup[0],NULL);
    294:   VecGetArray(user.mup[0],&x_ptr);
    295:   x_ptr[0] = 0.0;
    296:   VecRestoreArray(user.mup[0],&x_ptr);
    297:   MatCreateVecs(user.Jacp,&user.mup[1],NULL);
    298:   VecGetArray(user.mup[1],&x_ptr);
    299:   x_ptr[0] = 0.0;
    300:   VecRestoreArray(user.mup[1],&x_ptr);

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

    304:   TSAdjointSolve(ts);

    306:   PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[y(tf)]/d[y0]  d[y(tf)]/d[z0]\n");
    307:   VecView(user.lambda[0],PETSC_VIEWER_STDOUT_WORLD);
    308:   PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[z(tf)]/d[y0]  d[z(tf)]/d[z0]\n");
    309:   VecView(user.lambda[1],PETSC_VIEWER_STDOUT_WORLD);

    311:   VecGetArray(user.mup[0],&x_ptr);
    312:   VecGetArray(user.lambda[0],&y_ptr);
    313:   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];
    314:   VecRestoreArray(user.mup[0],&x_ptr);
    315:   VecRestoreArray(user.lambda[0],&y_ptr);
    316:   PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt parameters: d[y(tf)]/d[mu]\n%g\n",(double)PetscRealPart(derp));

    318:   VecGetArray(user.mup[1],&x_ptr);
    319:   VecGetArray(user.lambda[1],&y_ptr);
    320:   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];
    321:   VecRestoreArray(user.mup[1],&x_ptr);
    322:   VecRestoreArray(user.lambda[1],&y_ptr);
    323:   PetscPrintf(PETSC_COMM_WORLD,"\n sensivitity wrt parameters: d[z(tf)]/d[mu]\n%g\n",(double)PetscRealPart(derp));

    325:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    326:      Free work space.  All PETSc objects should be destroyed when they
    327:      are no longer needed.
    328:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    329:   MatDestroy(&user.A);
    330:   MatDestroy(&user.Jacp);
    331:   VecDestroy(&user.U);
    332:   VecDestroy(&user.lambda[0]);
    333:   VecDestroy(&user.lambda[1]);
    334:   VecDestroy(&user.mup[0]);
    335:   VecDestroy(&user.mup[1]);
    336:   TSDestroy(&ts);

    338:   PetscFinalize();
    339:   return(ierr);
    340: }

    342: /*TEST

    344:     test:
    345:       requires: revolve
    346:       args: -monitor 0 -ts_type theta -ts_theta_endpoint -ts_theta_theta 0.5 -viewer_binary_skip_info -ts_dt 0.001 -mu 100000

    348:     test:
    349:       suffix: 2
    350:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only

    352:     test:
    353:       suffix: 3
    354:       args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only 0
    355:       output_file: output/ex20adj_2.out

    357:     test:
    358:       suffix: 4
    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 -ts_trajectory_save_stack
    360:       output_file: output/ex20adj_2.out

    362:     test:
    363:       suffix: 5
    364:       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
    365:       output_file: output/ex20adj_2.out

    367:     test:
    368:       suffix: 6
    369:       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
    370:       output_file: output/ex20adj_2.out

    372:     test:
    373:       suffix: 7
    374:       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
    375:       output_file: output/ex20adj_2.out

    377:     test:
    378:       suffix: 8
    379:       requires: revolve
    380:       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
    381:       output_file: output/ex20adj_3.out

    383:     test:
    384:       suffix: 9
    385:       requires: revolve
    386:       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
    387:       output_file: output/ex20adj_4.out

    389:     test:
    390:       requires: revolve
    391:       suffix: 10
    392:       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
    393:       output_file: output/ex20adj_2.out

    395:     test:
    396:       requires: revolve
    397:       suffix: 11
    398:       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
    399:       output_file: output/ex20adj_2.out

    401:     test:
    402:       suffix: 12
    403:       requires: revolve
    404:       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
    405:       output_file: output/ex20adj_2.out

    407:     test:
    408:       suffix: 13
    409:       requires: revolve
    410:       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
    411:       output_file: output/ex20adj_2.out

    413:     test:
    414:       suffix: 14
    415:       requires: revolve
    416:       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
    417:       output_file: output/ex20adj_2.out

    419:     test:
    420:       suffix: 15
    421:       requires: revolve
    422:       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
    423:       output_file: output/ex20adj_2.out

    425:     test:
    426:       suffix: 16
    427:       requires: revolve
    428:       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
    429:       output_file: output/ex20adj_2.out

    431:     test:
    432:       suffix: 17
    433:       requires: revolve
    434:       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
    435:       output_file: output/ex20adj_2.out

    437:     test:
    438:       suffix: 18
    439:       requires: revolve
    440:       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
    441:       output_file: output/ex20adj_2.out

    443:     test:
    444:       suffix: 19
    445:       requires: revolve
    446:       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
    447:       output_file: output/ex20adj_2.out

    449:     test:
    450:       suffix: 20
    451:       requires: revolve
    452:       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
    453:       output_file: output/ex20adj_2.out

    455:     test:
    456:       suffix: 21
    457:       requires: revolve
    458:       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
    459:       output_file: output/ex20adj_2.out

    461:     test:
    462:       suffix: 22
    463:       args: -ts_type beuler -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only
    464:       output_file: output/ex20adj_2.out
    465: TEST*/