Actual source code: ex9opt.c

      1: static char help[] = "Basic equation for generator stability analysis.\n";

      3: /*F

      5: \begin{eqnarray}
      6:                  \frac{d \theta}{dt} = \omega_b (\omega - \omega_s)
      7:                  \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\omega - \omega_s)\\
      8: \end{eqnarray}

     10:   Ensemble of initial conditions
     11:    ./ex2 -ensemble -ts_monitor_draw_solution_phase -1,-3,3,3      -ts_adapt_dt_max .01  -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly

     13:   Fault at .1 seconds
     14:    ./ex2           -ts_monitor_draw_solution_phase .42,.95,.6,1.05 -ts_adapt_dt_max .01  -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly

     16:   Initial conditions same as when fault is ended
     17:    ./ex2 -u 0.496792,1.00932 -ts_monitor_draw_solution_phase .42,.95,.6,1.05  -ts_adapt_dt_max .01  -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly

     19: F*/

     21: /*
     22:    Include "petscts.h" so that we can use TS solvers.  Note that this
     23:    file automatically includes:
     24:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     25:      petscmat.h - matrices
     26:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     27:      petscviewer.h - viewers               petscpc.h  - preconditioners
     28:      petscksp.h   - linear solvers
     29: */

     31: #include <petsctao.h>
     32: #include <petscts.h>

     34: typedef struct {
     35:   TS          ts;
     36:   PetscScalar H, D, omega_b, omega_s, Pmax, Pm, E, V, X, u_s, c;
     37:   PetscInt    beta;
     38:   PetscReal   tf, tcl, dt;
     39: } AppCtx;

     41: PetscErrorCode FormFunction(Tao, Vec, PetscReal *, void *);
     42: PetscErrorCode FormGradient(Tao, Vec, Vec, void *);

     44: /*
     45:      Defines the ODE passed to the ODE solver
     46: */
     47: static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec U, Vec F, AppCtx *ctx)
     48: {
     49:   PetscScalar       *f, Pmax;
     50:   const PetscScalar *u;

     52:   PetscFunctionBegin;
     53:   /*  The next three lines allow us to access the entries of the vectors directly */
     54:   PetscCall(VecGetArrayRead(U, &u));
     55:   PetscCall(VecGetArray(F, &f));
     56:   if ((t > ctx->tf) && (t < ctx->tcl)) Pmax = 0.0; /* A short-circuit on the generator terminal that drives the electrical power output (Pmax*sin(delta)) to 0 */
     57:   else Pmax = ctx->Pmax;

     59:   f[0] = ctx->omega_b * (u[1] - ctx->omega_s);
     60:   f[1] = (-Pmax * PetscSinScalar(u[0]) - ctx->D * (u[1] - ctx->omega_s) + ctx->Pm) * ctx->omega_s / (2.0 * ctx->H);

     62:   PetscCall(VecRestoreArrayRead(U, &u));
     63:   PetscCall(VecRestoreArray(F, &f));
     64:   PetscFunctionReturn(PETSC_SUCCESS);
     65: }

     67: /*
     68:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
     69: */
     70: static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat A, Mat B, AppCtx *ctx)
     71: {
     72:   PetscInt           rowcol[] = {0, 1};
     73:   PetscScalar        J[2][2], Pmax;
     74:   const PetscScalar *u;

     76:   PetscFunctionBegin;
     77:   PetscCall(VecGetArrayRead(U, &u));
     78:   if ((t > ctx->tf) && (t < ctx->tcl)) Pmax = 0.0; /* A short-circuit on the generator terminal that drives the electrical power output (Pmax*sin(delta)) to 0 */
     79:   else Pmax = ctx->Pmax;

     81:   J[0][0] = 0;
     82:   J[0][1] = ctx->omega_b;
     83:   J[1][1] = -ctx->D * ctx->omega_s / (2.0 * ctx->H);
     84:   J[1][0] = -Pmax * PetscCosScalar(u[0]) * ctx->omega_s / (2.0 * ctx->H);

     86:   PetscCall(MatSetValues(A, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
     87:   PetscCall(VecRestoreArrayRead(U, &u));

     89:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
     90:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
     91:   if (A != B) {
     92:     PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
     93:     PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
     94:   }
     95:   PetscFunctionReturn(PETSC_SUCCESS);
     96: }

     98: static PetscErrorCode RHSJacobianP(TS ts, PetscReal t, Vec X, Mat A, void *ctx0)
     99: {
    100:   PetscInt    row[] = {0, 1}, col[] = {0};
    101:   PetscScalar J[2][1];
    102:   AppCtx     *ctx = (AppCtx *)ctx0;

    104:   PetscFunctionBeginUser;
    105:   J[0][0] = 0;
    106:   J[1][0] = ctx->omega_s / (2.0 * ctx->H);
    107:   PetscCall(MatSetValues(A, 2, row, 1, col, &J[0][0], INSERT_VALUES));
    108:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
    109:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
    110:   PetscFunctionReturn(PETSC_SUCCESS);
    111: }

    113: static PetscErrorCode CostIntegrand(TS ts, PetscReal t, Vec U, Vec R, AppCtx *ctx)
    114: {
    115:   PetscScalar       *r;
    116:   const PetscScalar *u;

    118:   PetscFunctionBegin;
    119:   PetscCall(VecGetArrayRead(U, &u));
    120:   PetscCall(VecGetArray(R, &r));
    121:   r[0] = ctx->c * PetscPowScalarInt(PetscMax(0., u[0] - ctx->u_s), ctx->beta);
    122:   PetscCall(VecRestoreArray(R, &r));
    123:   PetscCall(VecRestoreArrayRead(U, &u));
    124:   PetscFunctionReturn(PETSC_SUCCESS);
    125: }

    127: static PetscErrorCode DRDUJacobianTranspose(TS ts, PetscReal t, Vec U, Mat DRDU, Mat B, AppCtx *ctx)
    128: {
    129:   PetscScalar        ru[1];
    130:   const PetscScalar *u;
    131:   PetscInt           row[] = {0}, col[] = {0};

    133:   PetscFunctionBegin;
    134:   PetscCall(VecGetArrayRead(U, &u));
    135:   ru[0] = ctx->c * ctx->beta * PetscPowScalarInt(PetscMax(0., u[0] - ctx->u_s), ctx->beta - 1);
    136:   PetscCall(VecRestoreArrayRead(U, &u));
    137:   PetscCall(MatSetValues(DRDU, 1, row, 1, col, ru, INSERT_VALUES));
    138:   PetscCall(MatAssemblyBegin(DRDU, MAT_FINAL_ASSEMBLY));
    139:   PetscCall(MatAssemblyEnd(DRDU, MAT_FINAL_ASSEMBLY));
    140:   PetscFunctionReturn(PETSC_SUCCESS);
    141: }

    143: static PetscErrorCode DRDPJacobianTranspose(TS ts, PetscReal t, Vec U, Mat DRDP, AppCtx *ctx)
    144: {
    145:   PetscFunctionBegin;
    146:   PetscCall(MatZeroEntries(DRDP));
    147:   PetscCall(MatAssemblyBegin(DRDP, MAT_FINAL_ASSEMBLY));
    148:   PetscCall(MatAssemblyEnd(DRDP, MAT_FINAL_ASSEMBLY));
    149:   PetscFunctionReturn(PETSC_SUCCESS);
    150: }

    152: PetscErrorCode ComputeSensiP(Vec lambda, Vec mu, AppCtx *ctx)
    153: {
    154:   PetscScalar       *y, sensip;
    155:   const PetscScalar *x;

    157:   PetscFunctionBegin;
    158:   PetscCall(VecGetArrayRead(lambda, &x));
    159:   PetscCall(VecGetArray(mu, &y));
    160:   sensip = 1. / PetscSqrtScalar(1. - (ctx->Pm / ctx->Pmax) * (ctx->Pm / ctx->Pmax)) / ctx->Pmax * x[0] + y[0];
    161:   y[0]   = sensip;
    162:   PetscCall(VecRestoreArray(mu, &y));
    163:   PetscCall(VecRestoreArrayRead(lambda, &x));
    164:   PetscFunctionReturn(PETSC_SUCCESS);
    165: }

    167: int main(int argc, char **argv)
    168: {
    169:   Vec          p;
    170:   PetscScalar *x_ptr;
    171:   PetscMPIInt  size;
    172:   AppCtx       ctx;
    173:   Vec          lowerb, upperb;
    174:   Tao          tao;
    175:   KSP          ksp;
    176:   PC           pc;
    177:   Vec          U, lambda[1], mu[1];
    178:   Mat          A;    /* Jacobian matrix */
    179:   Mat          Jacp; /* Jacobian matrix */
    180:   Mat          DRDU, DRDP;
    181:   PetscInt     n = 2;
    182:   TS           quadts;

    184:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    185:      Initialize program
    186:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    187:   PetscFunctionBeginUser;
    188:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
    189:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
    190:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");

    192:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    193:     Set runtime options
    194:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    195:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
    196:   {
    197:     ctx.beta    = 2;
    198:     ctx.c       = PetscRealConstant(10000.0);
    199:     ctx.u_s     = PetscRealConstant(1.0);
    200:     ctx.omega_s = PetscRealConstant(1.0);
    201:     ctx.omega_b = PetscRealConstant(120.0) * PETSC_PI;
    202:     ctx.H       = PetscRealConstant(5.0);
    203:     PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL));
    204:     ctx.D = PetscRealConstant(5.0);
    205:     PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL));
    206:     ctx.E    = PetscRealConstant(1.1378);
    207:     ctx.V    = PetscRealConstant(1.0);
    208:     ctx.X    = PetscRealConstant(0.545);
    209:     ctx.Pmax = ctx.E * ctx.V / ctx.X;
    210:     PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL));
    211:     ctx.Pm = PetscRealConstant(1.0194);
    212:     PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL));
    213:     ctx.tf  = PetscRealConstant(0.1);
    214:     ctx.tcl = PetscRealConstant(0.2);
    215:     PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL));
    216:     PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL));
    217:   }
    218:   PetscOptionsEnd();

    220:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    221:     Create necessary matrix and vectors
    222:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    223:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
    224:   PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
    225:   PetscCall(MatSetType(A, MATDENSE));
    226:   PetscCall(MatSetFromOptions(A));
    227:   PetscCall(MatSetUp(A));

    229:   PetscCall(MatCreateVecs(A, &U, NULL));

    231:   PetscCall(MatCreate(PETSC_COMM_WORLD, &Jacp));
    232:   PetscCall(MatSetSizes(Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1));
    233:   PetscCall(MatSetFromOptions(Jacp));
    234:   PetscCall(MatSetUp(Jacp));
    235:   PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &DRDP));
    236:   PetscCall(MatSetUp(DRDP));
    237:   PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 2, NULL, &DRDU));
    238:   PetscCall(MatSetUp(DRDU));

    240:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    241:      Create timestepping solver context
    242:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    243:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ctx.ts));
    244:   PetscCall(TSSetProblemType(ctx.ts, TS_NONLINEAR));
    245:   PetscCall(TSSetEquationType(ctx.ts, TS_EQ_ODE_EXPLICIT)); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
    246:   PetscCall(TSSetType(ctx.ts, TSRK));
    247:   PetscCall(TSSetRHSFunction(ctx.ts, NULL, (TSRHSFunctionFn *)RHSFunction, &ctx));
    248:   PetscCall(TSSetRHSJacobian(ctx.ts, A, A, (TSRHSJacobianFn *)RHSJacobian, &ctx));
    249:   PetscCall(TSSetExactFinalTime(ctx.ts, TS_EXACTFINALTIME_MATCHSTEP));

    251:   PetscCall(MatCreateVecs(A, &lambda[0], NULL));
    252:   PetscCall(MatCreateVecs(Jacp, &mu[0], NULL));
    253:   PetscCall(TSSetCostGradients(ctx.ts, 1, lambda, mu));
    254:   PetscCall(TSSetRHSJacobianP(ctx.ts, Jacp, RHSJacobianP, &ctx));

    256:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    257:      Set solver options
    258:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    259:   PetscCall(TSSetMaxTime(ctx.ts, PetscRealConstant(1.0)));
    260:   PetscCall(TSSetTimeStep(ctx.ts, PetscRealConstant(0.01)));
    261:   PetscCall(TSSetFromOptions(ctx.ts));

    263:   PetscCall(TSGetTimeStep(ctx.ts, &ctx.dt)); /* save the stepsize */

    265:   PetscCall(TSCreateQuadratureTS(ctx.ts, PETSC_TRUE, &quadts));
    266:   PetscCall(TSSetRHSFunction(quadts, NULL, (TSRHSFunctionFn *)CostIntegrand, &ctx));
    267:   PetscCall(TSSetRHSJacobian(quadts, DRDU, DRDU, (TSRHSJacobianFn *)DRDUJacobianTranspose, &ctx));
    268:   PetscCall(TSSetRHSJacobianP(quadts, DRDP, (TSRHSJacobianPFn *)DRDPJacobianTranspose, &ctx));
    269:   PetscCall(TSSetSolution(ctx.ts, U));

    271:   /* Create TAO solver and set desired solution method */
    272:   PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
    273:   PetscCall(TaoSetType(tao, TAOBLMVM));

    275:   /*
    276:      Optimization starts
    277:   */
    278:   /* Set initial solution guess */
    279:   PetscCall(VecCreateSeq(PETSC_COMM_WORLD, 1, &p));
    280:   PetscCall(VecGetArray(p, &x_ptr));
    281:   x_ptr[0] = ctx.Pm;
    282:   PetscCall(VecRestoreArray(p, &x_ptr));

    284:   PetscCall(TaoSetSolution(tao, p));
    285:   /* Set routine for function and gradient evaluation */
    286:   PetscCall(TaoSetObjective(tao, FormFunction, (void *)&ctx));
    287:   PetscCall(TaoSetGradient(tao, NULL, FormGradient, (void *)&ctx));

    289:   /* Set bounds for the optimization */
    290:   PetscCall(VecDuplicate(p, &lowerb));
    291:   PetscCall(VecDuplicate(p, &upperb));
    292:   PetscCall(VecGetArray(lowerb, &x_ptr));
    293:   x_ptr[0] = 0.;
    294:   PetscCall(VecRestoreArray(lowerb, &x_ptr));
    295:   PetscCall(VecGetArray(upperb, &x_ptr));
    296:   x_ptr[0] = PetscRealConstant(1.1);
    297:   PetscCall(VecRestoreArray(upperb, &x_ptr));
    298:   PetscCall(TaoSetVariableBounds(tao, lowerb, upperb));

    300:   /* Check for any TAO command line options */
    301:   PetscCall(TaoSetFromOptions(tao));
    302:   PetscCall(TaoGetKSP(tao, &ksp));
    303:   if (ksp) {
    304:     PetscCall(KSPGetPC(ksp, &pc));
    305:     PetscCall(PCSetType(pc, PCNONE));
    306:   }

    308:   /* SOLVE THE APPLICATION */
    309:   PetscCall(TaoSolve(tao));

    311:   PetscCall(VecView(p, PETSC_VIEWER_STDOUT_WORLD));
    312:   /* Free TAO data structures */
    313:   PetscCall(TaoDestroy(&tao));
    314:   PetscCall(VecDestroy(&p));
    315:   PetscCall(VecDestroy(&lowerb));
    316:   PetscCall(VecDestroy(&upperb));

    318:   PetscCall(TSDestroy(&ctx.ts));
    319:   PetscCall(VecDestroy(&U));
    320:   PetscCall(MatDestroy(&A));
    321:   PetscCall(MatDestroy(&Jacp));
    322:   PetscCall(MatDestroy(&DRDU));
    323:   PetscCall(MatDestroy(&DRDP));
    324:   PetscCall(VecDestroy(&lambda[0]));
    325:   PetscCall(VecDestroy(&mu[0]));
    326:   PetscCall(PetscFinalize());
    327:   return 0;
    328: }

    330: /* ------------------------------------------------------------------ */
    331: /*
    332:    FormFunction - Evaluates the function

    334:    Input Parameters:
    335:    tao - the Tao context
    336:    X   - the input vector
    337:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()

    339:    Output Parameters:
    340:    f   - the newly evaluated function
    341: */
    342: PetscErrorCode FormFunction(Tao tao, Vec P, PetscReal *f, void *ctx0)
    343: {
    344:   AppCtx      *ctx = (AppCtx *)ctx0;
    345:   TS           ts  = ctx->ts;
    346:   Vec          U; /* solution will be stored here */
    347:   PetscScalar *u;
    348:   PetscScalar *x_ptr;
    349:   Vec          q;

    351:   PetscFunctionBeginUser;
    352:   PetscCall(VecGetArrayRead(P, (const PetscScalar **)&x_ptr));
    353:   ctx->Pm = x_ptr[0];
    354:   PetscCall(VecRestoreArrayRead(P, (const PetscScalar **)&x_ptr));

    356:   /* reset time */
    357:   PetscCall(TSSetTime(ts, 0.0));
    358:   /* reset step counter, this is critical for adjoint solver */
    359:   PetscCall(TSSetStepNumber(ts, 0));
    360:   /* reset step size, the step size becomes negative after TSAdjointSolve */
    361:   PetscCall(TSSetTimeStep(ts, ctx->dt));
    362:   /* reinitialize the integral value */
    363:   PetscCall(TSGetCostIntegral(ts, &q));
    364:   PetscCall(VecSet(q, 0.0));

    366:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    367:      Set initial conditions
    368:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    369:   PetscCall(TSGetSolution(ts, &U));
    370:   PetscCall(VecGetArray(U, &u));
    371:   u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
    372:   u[1] = PetscRealConstant(1.0);
    373:   PetscCall(VecRestoreArray(U, &u));

    375:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    376:      Solve nonlinear system
    377:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    378:   PetscCall(TSSolve(ts, U));
    379:   PetscCall(TSGetCostIntegral(ts, &q));
    380:   PetscCall(VecGetArray(q, &x_ptr));
    381:   *f = -ctx->Pm + x_ptr[0];
    382:   PetscCall(VecRestoreArray(q, &x_ptr));
    383:   PetscFunctionReturn(PETSC_SUCCESS);
    384: }

    386: PetscErrorCode FormGradient(Tao tao, Vec P, Vec G, void *ctx0)
    387: {
    388:   AppCtx      *ctx = (AppCtx *)ctx0;
    389:   TS           ts  = ctx->ts;
    390:   Vec          U; /* solution will be stored here */
    391:   PetscReal    ftime;
    392:   PetscInt     steps;
    393:   PetscScalar *u;
    394:   PetscScalar *x_ptr, *y_ptr;
    395:   Vec         *lambda, q, *mu;

    397:   PetscFunctionBeginUser;
    398:   PetscCall(VecGetArrayRead(P, (const PetscScalar **)&x_ptr));
    399:   ctx->Pm = x_ptr[0];
    400:   PetscCall(VecRestoreArrayRead(P, (const PetscScalar **)&x_ptr));

    402:   /* reset time */
    403:   PetscCall(TSSetTime(ts, 0.0));
    404:   /* reset step counter, this is critical for adjoint solver */
    405:   PetscCall(TSSetStepNumber(ts, 0));
    406:   /* reset step size, the step size becomes negative after TSAdjointSolve */
    407:   PetscCall(TSSetTimeStep(ts, ctx->dt));
    408:   /* reinitialize the integral value */
    409:   PetscCall(TSGetCostIntegral(ts, &q));
    410:   PetscCall(VecSet(q, 0.0));

    412:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    413:      Set initial conditions
    414:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    415:   PetscCall(TSGetSolution(ts, &U));
    416:   PetscCall(VecGetArray(U, &u));
    417:   u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
    418:   u[1] = PetscRealConstant(1.0);
    419:   PetscCall(VecRestoreArray(U, &u));

    421:   /* Set up to save trajectory before TSSetFromOptions() so that TSTrajectory options can be captured */
    422:   PetscCall(TSSetSaveTrajectory(ts));
    423:   PetscCall(TSSetFromOptions(ts));

    425:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    426:      Solve nonlinear system
    427:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    428:   PetscCall(TSSolve(ts, U));

    430:   PetscCall(TSGetSolveTime(ts, &ftime));
    431:   PetscCall(TSGetStepNumber(ts, &steps));

    433:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    434:      Adjoint model starts here
    435:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    436:   PetscCall(TSGetCostGradients(ts, NULL, &lambda, &mu));
    437:   /*   Set initial conditions for the adjoint integration */
    438:   PetscCall(VecGetArray(lambda[0], &y_ptr));
    439:   y_ptr[0] = 0.0;
    440:   y_ptr[1] = 0.0;
    441:   PetscCall(VecRestoreArray(lambda[0], &y_ptr));
    442:   PetscCall(VecGetArray(mu[0], &x_ptr));
    443:   x_ptr[0] = PetscRealConstant(-1.0);
    444:   PetscCall(VecRestoreArray(mu[0], &x_ptr));

    446:   PetscCall(TSAdjointSolve(ts));
    447:   PetscCall(TSGetCostIntegral(ts, &q));
    448:   PetscCall(ComputeSensiP(lambda[0], mu[0], ctx));
    449:   PetscCall(VecCopy(mu[0], G));
    450:   PetscFunctionReturn(PETSC_SUCCESS);
    451: }

    453: /*TEST

    455:    build:
    456:       requires: !complex !single

    458:    test:
    459:       args: -viewer_binary_skip_info -ts_adapt_type none -tao_monitor -tao_gatol 0.0 -tao_grtol 1.e-3 -tao_converged_reason

    461:    test:
    462:       suffix: 2
    463:       args: -viewer_binary_skip_info -ts_adapt_type none -tao_monitor -tao_gatol 0.0 -tao_grtol 1.e-3 -tao_converged_reason -tao_test_gradient

    465: TEST*/