xref: /petsc/src/ts/tutorials/ex20adj.c (revision 2a8381b23c702518c6b1ccbeafee50b9375df0e4)

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

/* ------------------------------------------------------------------------

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

   In an IMEX setting,  we can split (2) by component,

   [ u_1' ] = [ u_2 ] + [            0                ]
   [ u_2' ]   [  0  ]   [ \mu ((1 - u_1^2) u_2 - u_1) ]

   where

   [ G(u,t) ] = [ u_2 ]
                [  0  ]

   and

   [ F(u',u,t) ] = [ u_1' ] - [            0                ]
                   [ u_2' ]   [ \mu ((1 - u_1^2) u_2 - u_1) ]

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

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

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

              dF   dF
   J(F) = a * -- + --
              du'  du

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

   See ex20.c for more details on the Jacobian.

  ------------------------------------------------------------------------- */
#include <petscts.h>
#include <petsctao.h>

typedef struct _n_User *User;
struct _n_User {
  PetscReal mu;
  PetscReal next_output;
  PetscBool imex;
  /* Sensitivity analysis support */
  PetscInt  steps;
  PetscReal ftime;
  Mat       A;                    /* IJacobian matrix */
  Mat       B;                    /* RHSJacobian matrix */
  Mat       Jacp;                 /* IJacobianP matrix */
  Mat       Jacprhs;              /* RHSJacobianP matrix */
  Vec       U, lambda[2], mup[2]; /* adjoint variables */
};

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

static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec U, Vec F, PetscCtx ctx)
{
  User               user = (User)ctx;
  PetscScalar       *f;
  const PetscScalar *u;

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(U, &u));
  PetscCall(VecGetArray(F, &f));
  f[0] = u[1];
  if (user->imex) {
    f[1] = 0.0;
  } else {
    f[1] = user->mu * ((1. - u[0] * u[0]) * u[1] - u[0]);
  }
  PetscCall(VecRestoreArrayRead(U, &u));
  PetscCall(VecRestoreArray(F, &f));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat A, Mat B, PetscCtx ctx)
{
  User               user     = (User)ctx;
  PetscReal          mu       = user->mu;
  PetscInt           rowcol[] = {0, 1};
  PetscScalar        J[2][2];
  const PetscScalar *u;

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(U, &u));
  J[0][0] = 0;
  J[0][1] = 1.0;
  if (user->imex) {
    J[1][0] = 0.0;
    J[1][1] = 0.0;
  } else {
    J[1][0] = -mu * (2.0 * u[1] * u[0] + 1.);
    J[1][1] = mu * (1.0 - u[0] * u[0]);
  }
  PetscCall(MatSetValues(A, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  if (A != B) {
    PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  }
  PetscCall(VecRestoreArrayRead(U, &u));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, PetscCtx ctx)
{
  User               user = (User)ctx;
  const PetscScalar *u, *udot;
  PetscScalar       *f;

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(U, &u));
  PetscCall(VecGetArrayRead(Udot, &udot));
  PetscCall(VecGetArray(F, &f));
  if (user->imex) {
    f[0] = udot[0];
  } else {
    f[0] = udot[0] - u[1];
  }
  f[1] = udot[1] - user->mu * ((1.0 - u[0] * u[0]) * u[1] - u[0]);
  PetscCall(VecRestoreArrayRead(U, &u));
  PetscCall(VecRestoreArrayRead(Udot, &udot));
  PetscCall(VecRestoreArray(F, &f));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(U, &u));

  if (user->imex) {
    J[0][0] = a;
    J[0][1] = 0.0;
  } else {
    J[0][0] = a;
    J[0][1] = -1.0;
  }
  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]);

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

  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  if (B && A != B) {
    PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode IJacobianP(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, PetscCtx ctx)
{
  PetscInt           row[] = {0, 1}, col[] = {0};
  PetscScalar        J[2][1];
  const PetscScalar *u;

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(U, &u));
  J[0][0] = 0;
  J[1][0] = -((1.0 - u[0] * u[0]) * u[1] - u[0]);
  PetscCall(MatSetValues(A, 2, row, 1, col, &J[0][0], INSERT_VALUES));
  PetscCall(VecRestoreArrayRead(U, &u));
  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode RHSJacobianP(TS ts, PetscReal t, Vec U, Mat A, PetscCtx ctx)
{
  User user = (User)ctx;

  PetscFunctionBeginUser;
  if (!user->imex) {
    PetscInt           row[] = {0, 1}, col[] = {0};
    PetscScalar        J[2][1];
    const PetscScalar *u;
    PetscCall(VecGetArrayRead(U, &u));
    J[0][0] = 0;
    J[1][0] = (1. - u[0] * u[0]) * u[1] - u[0];
    PetscCall(MatSetValues(A, 2, row, 1, col, &J[0][0], INSERT_VALUES));
    PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
    PetscCall(VecRestoreArrayRead(U, &u));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
static PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal t, Vec U, PetscCtx ctx)
{
  const PetscScalar *u;
  PetscReal          tfinal, dt;
  User               user = (User)ctx;
  Vec                interpolatedU;

  PetscFunctionBeginUser;
  PetscCall(TSGetTimeStep(ts, &dt));
  PetscCall(TSGetMaxTime(ts, &tfinal));

  while (user->next_output <= t && user->next_output <= tfinal) {
    PetscCall(VecDuplicate(U, &interpolatedU));
    PetscCall(TSInterpolate(ts, user->next_output, interpolatedU));
    PetscCall(VecGetArrayRead(interpolatedU, &u));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "[%g] %" PetscInt_FMT " TS %g (dt = %g) X %g %g\n", (double)user->next_output, step, (double)t, (double)dt, (double)PetscRealPart(u[0]), (double)PetscRealPart(u[1])));
    PetscCall(VecRestoreArrayRead(interpolatedU, &u));
    PetscCall(VecDestroy(&interpolatedU));
    user->next_output += 0.1;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

int main(int argc, char **argv)
{
  TS             ts;
  PetscBool      monitor = PETSC_FALSE, implicitform = PETSC_TRUE;
  PetscScalar   *x_ptr, *y_ptr, derp;
  PetscMPIInt    size;
  struct _n_User user;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize program
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));
  PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
  PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Set runtime options
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  user.next_output = 0.0;
  user.mu          = 1.0e3;
  user.steps       = 0;
  user.ftime       = 0.5;
  user.imex        = PETSC_FALSE;
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-monitor", &monitor, NULL));
  PetscCall(PetscOptionsGetReal(NULL, NULL, "-mu", &user.mu, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-implicitform", &implicitform, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-imexform", &user.imex, NULL));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Create necessary matrix and vectors, solve same ODE on every process
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatCreate(PETSC_COMM_WORLD, &user.A));
  PetscCall(MatSetSizes(user.A, PETSC_DECIDE, PETSC_DECIDE, 2, 2));
  PetscCall(MatSetFromOptions(user.A));
  PetscCall(MatSetUp(user.A));
  PetscCall(MatCreateVecs(user.A, &user.U, NULL));
  PetscCall(MatDuplicate(user.A, MAT_DO_NOT_COPY_VALUES, &user.B));
  PetscCall(MatCreate(PETSC_COMM_WORLD, &user.Jacp));
  PetscCall(MatSetSizes(user.Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1));
  PetscCall(MatSetFromOptions(user.Jacp));
  PetscCall(MatSetUp(user.Jacp));
  PetscCall(MatDuplicate(user.Jacp, MAT_DO_NOT_COPY_VALUES, &user.Jacprhs));
  PetscCall(MatZeroEntries(user.Jacprhs));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
  PetscCall(TSSetEquationType(ts, TS_EQ_ODE_EXPLICIT)); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
  if (user.imex) {
    PetscCall(TSSetIFunction(ts, NULL, IFunction, &user));
    PetscCall(TSSetIJacobian(ts, user.A, user.A, IJacobian, &user));
    PetscCall(TSSetIJacobianP(ts, user.Jacp, IJacobianP, &user));
    PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, &user));
    PetscCall(TSSetRHSJacobian(ts, user.B, NULL, RHSJacobian, &user));
    PetscCall(TSSetRHSJacobianP(ts, user.Jacprhs, NULL, &user));
    PetscCall(TSSetType(ts, TSARKIMEX));
  } else {
    if (implicitform) {
      PetscCall(TSSetIFunction(ts, NULL, IFunction, &user));
      PetscCall(TSSetIJacobian(ts, user.A, user.A, IJacobian, &user));
      PetscCall(TSSetIJacobianP(ts, user.Jacp, IJacobianP, &user));
      PetscCall(TSSetType(ts, TSCN));
    } else {
      PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, &user));
      PetscCall(TSSetRHSJacobian(ts, user.A, user.A, RHSJacobian, &user));
      PetscCall(TSSetRHSJacobianP(ts, user.Jacp, RHSJacobianP, &user));
      PetscCall(TSSetType(ts, TSRK));
    }
  }
  PetscCall(TSSetMaxTime(ts, user.ftime));
  PetscCall(TSSetTimeStep(ts, 0.001));
  PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
  if (monitor) PetscCall(TSMonitorSet(ts, Monitor, &user, NULL));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(VecGetArray(user.U, &x_ptr));
  x_ptr[0] = 2.0;
  x_ptr[1] = -2.0 / 3.0 + 10.0 / (81.0 * user.mu) - 292.0 / (2187.0 * user.mu * user.mu);
  PetscCall(VecRestoreArray(user.U, &x_ptr));
  PetscCall(TSSetTimeStep(ts, 0.001));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Save trajectory of solution so that TSAdjointSolve() may be used
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetSaveTrajectory(ts));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set runtime options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetFromOptions(ts));

  PetscCall(TSSolve(ts, user.U));
  PetscCall(TSGetSolveTime(ts, &user.ftime));
  PetscCall(TSGetStepNumber(ts, &user.steps));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Adjoint model starts here
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatCreateVecs(user.A, &user.lambda[0], NULL));
  /* Set initial conditions for the adjoint integration */
  PetscCall(VecGetArray(user.lambda[0], &y_ptr));
  y_ptr[0] = 1.0;
  y_ptr[1] = 0.0;
  PetscCall(VecRestoreArray(user.lambda[0], &y_ptr));
  PetscCall(MatCreateVecs(user.A, &user.lambda[1], NULL));
  PetscCall(VecGetArray(user.lambda[1], &y_ptr));
  y_ptr[0] = 0.0;
  y_ptr[1] = 1.0;
  PetscCall(VecRestoreArray(user.lambda[1], &y_ptr));

  PetscCall(MatCreateVecs(user.Jacp, &user.mup[0], NULL));
  PetscCall(VecGetArray(user.mup[0], &x_ptr));
  x_ptr[0] = 0.0;
  PetscCall(VecRestoreArray(user.mup[0], &x_ptr));
  PetscCall(MatCreateVecs(user.Jacp, &user.mup[1], NULL));
  PetscCall(VecGetArray(user.mup[1], &x_ptr));
  x_ptr[0] = 0.0;
  PetscCall(VecRestoreArray(user.mup[1], &x_ptr));

  PetscCall(TSSetCostGradients(ts, 2, user.lambda, user.mup));

  PetscCall(TSAdjointSolve(ts));

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

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

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

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Free work space.  All PETSc objects should be destroyed when they
     are no longer needed.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatDestroy(&user.A));
  PetscCall(MatDestroy(&user.B));
  PetscCall(MatDestroy(&user.Jacp));
  PetscCall(MatDestroy(&user.Jacprhs));
  PetscCall(VecDestroy(&user.U));
  PetscCall(VecDestroy(&user.lambda[0]));
  PetscCall(VecDestroy(&user.lambda[1]));
  PetscCall(VecDestroy(&user.mup[0]));
  PetscCall(VecDestroy(&user.mup[1]));
  PetscCall(TSDestroy(&ts));

  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

    test:
      requires: revolve
      args: -monitor 0 -ts_type theta -ts_theta_endpoint -ts_theta_theta 0.5 -viewer_binary_skip_info -ts_time_step 0.001 -mu 100000

    test:
      suffix: 2
      args: -ts_type cn -ts_time_step 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only

    test:
      suffix: 3
      args: -ts_type cn -ts_time_step 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only 0
      output_file: output/ex20adj_2.out

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

    test:
      suffix: 5
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 6
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 7
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 8
      requires: revolve !cams
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_3.out

    test:
      suffix: 9
      requires: revolve !cams
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_4.out

    test:
      requires: revolve
      suffix: 10
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      requires: revolve
      suffix: 11
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 12
      requires: revolve
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 13
      requires: revolve
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 14
      requires: revolve
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 15
      requires: revolve
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 16
      requires: revolve
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 17
      requires: revolve
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 18
      requires: revolve
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 19
      requires: revolve
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 20
      requires: revolve
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 21
      requires: revolve
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_2.out

    test:
      suffix: 22
      args: -ts_type beuler -ts_time_step 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only
      output_file: output/ex20adj_2.out

    test:
      suffix: 23
      requires: cams
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_5.out

    test:
      suffix: 24
      requires: cams
      args: -ts_type cn -ts_time_step 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
      output_file: output/ex20adj_6.out

    test:
      suffix: 25
      args: -imexform -ts_max_steps 15 -ts_trajectory_type memory
      output_file: output/ex20adj_imex.out
TEST*/