Actual source code: ex3opt.c

      1: static char help[] = "Finds optimal parameter P_m for the generator system while maintaining generator stability.\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: F*/

     12: /*
     13:   This code demonstrates how to solve a ODE-constrained optimization problem with TAO, TSEvent, TSAdjoint and TS.
     14:   The problem features discontinuities and a cost function in integral form.
     15:   The gradient is computed with the discrete adjoint of an implicit theta method, see ex3adj.c for details.
     16: */

     18: #include <petsctao.h>
     19: #include <petscts.h>
     20: #include "ex3.h"

     22: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal *, Vec, void *);

     24: PetscErrorCode monitor(Tao tao, AppCtx *ctx)
     25: {
     26:   FILE              *fp;
     27:   PetscInt           iterate;
     28:   PetscReal          f, gnorm, cnorm, xdiff;
     29:   TaoConvergedReason reason;

     31:   PetscFunctionBeginUser;
     32:   PetscCall(TaoGetSolutionStatus(tao, &iterate, &f, &gnorm, &cnorm, &xdiff, &reason));

     34:   fp = fopen("ex3opt_conv.out", "a");
     35:   PetscCall(PetscFPrintf(PETSC_COMM_WORLD, fp, "%" PetscInt_FMT " %g\n", iterate, (double)gnorm));
     36:   fclose(fp);
     37:   PetscFunctionReturn(PETSC_SUCCESS);
     38: }

     40: int main(int argc, char **argv)
     41: {
     42:   Vec          p;
     43:   PetscScalar *x_ptr;
     44:   PetscMPIInt  size;
     45:   AppCtx       ctx;
     46:   Tao          tao;
     47:   KSP          ksp;
     48:   PC           pc;
     49:   Vec          lambda[1], mu[1], lowerb, upperb;
     50:   PetscBool    printtofile;
     51:   PetscInt     direction[2];
     52:   PetscBool    terminate[2];
     53:   Mat          qgrad; /* Forward sesivitiy */
     54:   Mat          sp;    /* Forward sensitivity matrix */

     56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     57:      Initialize program
     58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     59:   PetscFunctionBeginUser;
     60:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
     61:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
     62:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");

     64:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     65:     Set runtime options
     66:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     67:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", "");
     68:   {
     69:     ctx.beta    = 2;
     70:     ctx.c       = 10000.0;
     71:     ctx.u_s     = 1.0;
     72:     ctx.omega_s = 1.0;
     73:     ctx.omega_b = 120.0 * PETSC_PI;
     74:     ctx.H       = 5.0;
     75:     PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL));
     76:     ctx.D = 5.0;
     77:     PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL));
     78:     ctx.E        = 1.1378;
     79:     ctx.V        = 1.0;
     80:     ctx.X        = 0.545;
     81:     ctx.Pmax     = ctx.E * ctx.V / ctx.X;
     82:     ctx.Pmax_ini = ctx.Pmax;
     83:     PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL));
     84:     ctx.Pm = 1.06;
     85:     PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL));
     86:     ctx.tf  = 0.1;
     87:     ctx.tcl = 0.2;
     88:     PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL));
     89:     PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL));
     90:     printtofile = PETSC_FALSE;
     91:     PetscCall(PetscOptionsBool("-printtofile", "Print convergence results to file", "", printtofile, &printtofile, NULL));
     92:     ctx.sa = SA_ADJ;
     93:     PetscCall(PetscOptionsEnum("-sa_method", "Sensitivity analysis method (adj or tlm)", "", SAMethods, (PetscEnum)ctx.sa, (PetscEnum *)&ctx.sa, NULL));
     94:   }
     95:   PetscOptionsEnd();

     97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     98:     Create necessary matrix and vectors
     99:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    100:   PetscCall(MatCreate(PETSC_COMM_WORLD, &ctx.Jac));
    101:   PetscCall(MatSetSizes(ctx.Jac, 2, 2, PETSC_DETERMINE, PETSC_DETERMINE));
    102:   PetscCall(MatSetType(ctx.Jac, MATDENSE));
    103:   PetscCall(MatSetFromOptions(ctx.Jac));
    104:   PetscCall(MatSetUp(ctx.Jac));
    105:   PetscCall(MatCreate(PETSC_COMM_WORLD, &ctx.Jacp));
    106:   PetscCall(MatSetSizes(ctx.Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1));
    107:   PetscCall(MatSetFromOptions(ctx.Jacp));
    108:   PetscCall(MatSetUp(ctx.Jacp));
    109:   PetscCall(MatCreateVecs(ctx.Jac, &ctx.U, NULL));
    110:   PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &ctx.DRDP));
    111:   PetscCall(MatSetUp(ctx.DRDP));
    112:   PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, &ctx.DRDU));
    113:   PetscCall(MatSetUp(ctx.DRDU));

    115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    116:      Create timestepping solver context
    117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    118:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ctx.ts));
    119:   PetscCall(TSSetProblemType(ctx.ts, TS_NONLINEAR));
    120:   PetscCall(TSSetType(ctx.ts, TSCN));
    121:   PetscCall(TSSetRHSFunction(ctx.ts, NULL, (TSRHSFunctionFn *)RHSFunction, &ctx));
    122:   PetscCall(TSSetRHSJacobian(ctx.ts, ctx.Jac, ctx.Jac, (TSRHSJacobianFn *)RHSJacobian, &ctx));
    123:   PetscCall(TSSetRHSJacobianP(ctx.ts, ctx.Jacp, RHSJacobianP, &ctx));

    125:   if (ctx.sa == SA_ADJ) {
    126:     PetscCall(MatCreateVecs(ctx.Jac, &lambda[0], NULL));
    127:     PetscCall(MatCreateVecs(ctx.Jacp, &mu[0], NULL));
    128:     PetscCall(TSSetSaveTrajectory(ctx.ts));
    129:     PetscCall(TSSetCostGradients(ctx.ts, 1, lambda, mu));
    130:     PetscCall(TSCreateQuadratureTS(ctx.ts, PETSC_FALSE, &ctx.quadts));
    131:     PetscCall(TSSetRHSFunction(ctx.quadts, NULL, (TSRHSFunctionFn *)CostIntegrand, &ctx));
    132:     PetscCall(TSSetRHSJacobian(ctx.quadts, ctx.DRDU, ctx.DRDU, (TSRHSJacobianFn *)DRDUJacobianTranspose, &ctx));
    133:     PetscCall(TSSetRHSJacobianP(ctx.quadts, ctx.DRDP, DRDPJacobianTranspose, &ctx));
    134:   }
    135:   if (ctx.sa == SA_TLM) {
    136:     PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &qgrad));
    137:     PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, &sp));
    138:     PetscCall(TSForwardSetSensitivities(ctx.ts, 1, sp));
    139:     PetscCall(TSCreateQuadratureTS(ctx.ts, PETSC_TRUE, &ctx.quadts));
    140:     PetscCall(TSForwardSetSensitivities(ctx.quadts, 1, qgrad));
    141:     PetscCall(TSSetRHSFunction(ctx.quadts, NULL, (TSRHSFunctionFn *)CostIntegrand, &ctx));
    142:     PetscCall(TSSetRHSJacobian(ctx.quadts, ctx.DRDU, ctx.DRDU, (TSRHSJacobianFn *)DRDUJacobianTranspose, &ctx));
    143:     PetscCall(TSSetRHSJacobianP(ctx.quadts, ctx.DRDP, DRDPJacobianTranspose, &ctx));
    144:   }

    146:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    147:      Set solver options
    148:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    149:   PetscCall(TSSetMaxTime(ctx.ts, 1.0));
    150:   PetscCall(TSSetExactFinalTime(ctx.ts, TS_EXACTFINALTIME_MATCHSTEP));
    151:   PetscCall(TSSetTimeStep(ctx.ts, 0.03125));
    152:   PetscCall(TSSetFromOptions(ctx.ts));

    154:   direction[0] = direction[1] = 1;
    155:   terminate[0] = terminate[1] = PETSC_FALSE;
    156:   PetscCall(TSSetEventHandler(ctx.ts, 2, direction, terminate, EventFunction, PostEventFunction, &ctx));

    158:   /* Create TAO solver and set desired solution method */
    159:   PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
    160:   PetscCall(TaoSetType(tao, TAOBLMVM));
    161:   if (printtofile) PetscCall(TaoMonitorSet(tao, (PetscErrorCode (*)(Tao, void *))monitor, (void *)&ctx, NULL));
    162:   /*
    163:      Optimization starts
    164:   */
    165:   /* Set initial solution guess */
    166:   PetscCall(VecCreateSeq(PETSC_COMM_WORLD, 1, &p));
    167:   PetscCall(VecGetArray(p, &x_ptr));
    168:   x_ptr[0] = ctx.Pm;
    169:   PetscCall(VecRestoreArray(p, &x_ptr));

    171:   PetscCall(TaoSetSolution(tao, p));
    172:   /* Set routine for function and gradient evaluation */
    173:   PetscCall(TaoSetObjectiveAndGradient(tao, NULL, FormFunctionGradient, (void *)&ctx));

    175:   /* Set bounds for the optimization */
    176:   PetscCall(VecDuplicate(p, &lowerb));
    177:   PetscCall(VecDuplicate(p, &upperb));
    178:   PetscCall(VecGetArray(lowerb, &x_ptr));
    179:   x_ptr[0] = 0.;
    180:   PetscCall(VecRestoreArray(lowerb, &x_ptr));
    181:   PetscCall(VecGetArray(upperb, &x_ptr));
    182:   x_ptr[0] = 1.1;
    183:   PetscCall(VecRestoreArray(upperb, &x_ptr));
    184:   PetscCall(TaoSetVariableBounds(tao, lowerb, upperb));

    186:   /* Check for any TAO command line options */
    187:   PetscCall(TaoSetFromOptions(tao));
    188:   PetscCall(TaoGetKSP(tao, &ksp));
    189:   if (ksp) {
    190:     PetscCall(KSPGetPC(ksp, &pc));
    191:     PetscCall(PCSetType(pc, PCNONE));
    192:   }

    194:   /* SOLVE THE APPLICATION */
    195:   PetscCall(TaoSolve(tao));

    197:   PetscCall(VecView(p, PETSC_VIEWER_STDOUT_WORLD));

    199:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    200:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    201:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    202:   PetscCall(MatDestroy(&ctx.Jac));
    203:   PetscCall(MatDestroy(&ctx.Jacp));
    204:   PetscCall(MatDestroy(&ctx.DRDU));
    205:   PetscCall(MatDestroy(&ctx.DRDP));
    206:   PetscCall(VecDestroy(&ctx.U));
    207:   if (ctx.sa == SA_ADJ) {
    208:     PetscCall(VecDestroy(&lambda[0]));
    209:     PetscCall(VecDestroy(&mu[0]));
    210:   }
    211:   if (ctx.sa == SA_TLM) {
    212:     PetscCall(MatDestroy(&qgrad));
    213:     PetscCall(MatDestroy(&sp));
    214:   }
    215:   PetscCall(TSDestroy(&ctx.ts));
    216:   PetscCall(VecDestroy(&p));
    217:   PetscCall(VecDestroy(&lowerb));
    218:   PetscCall(VecDestroy(&upperb));
    219:   PetscCall(TaoDestroy(&tao));
    220:   PetscCall(PetscFinalize());
    221:   return 0;
    222: }

    224: /* ------------------------------------------------------------------ */
    225: /*
    226:    FormFunctionGradient - Evaluates the function and corresponding gradient.

    228:    Input Parameters:
    229:    tao - the Tao context
    230:    X   - the input vector
    231:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()

    233:    Output Parameters:
    234:    f   - the newly evaluated function
    235:    G   - the newly evaluated gradient
    236: */
    237: PetscErrorCode FormFunctionGradient(Tao tao, Vec P, PetscReal *f, Vec G, PetscCtx ctx0)
    238: {
    239:   AppCtx      *ctx = (AppCtx *)ctx0;
    240:   PetscInt     nadj;
    241:   PetscReal    ftime;
    242:   PetscInt     steps;
    243:   PetscScalar *u;
    244:   PetscScalar *x_ptr, *y_ptr;
    245:   Vec          q;
    246:   Mat          qgrad;

    248:   PetscFunctionBeginUser;
    249:   PetscCall(VecGetArrayRead(P, (const PetscScalar **)&x_ptr));
    250:   ctx->Pm = x_ptr[0];
    251:   PetscCall(VecRestoreArrayRead(P, (const PetscScalar **)&x_ptr));

    253:   /* reinitialize the solution vector */
    254:   PetscCall(VecGetArray(ctx->U, &u));
    255:   u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
    256:   u[1] = 1.0;
    257:   PetscCall(VecRestoreArray(ctx->U, &u));
    258:   PetscCall(TSSetSolution(ctx->ts, ctx->U));

    260:   /* reset time */
    261:   PetscCall(TSSetTime(ctx->ts, 0.0));

    263:   /* reset step counter, this is critical for adjoint solver */
    264:   PetscCall(TSSetStepNumber(ctx->ts, 0));

    266:   /* reset step size, the step size becomes negative after TSAdjointSolve */
    267:   PetscCall(TSSetTimeStep(ctx->ts, 0.03125));

    269:   /* reinitialize the integral value */
    270:   PetscCall(TSGetQuadratureTS(ctx->ts, NULL, &ctx->quadts));
    271:   PetscCall(TSGetSolution(ctx->quadts, &q));
    272:   PetscCall(VecSet(q, 0.0));

    274:   if (ctx->sa == SA_TLM) { /* reset the forward sensitivities */
    275:     TS             quadts;
    276:     Mat            sp;
    277:     PetscScalar    val[2];
    278:     const PetscInt row[] = {0, 1}, col[] = {0};

    280:     PetscCall(TSGetQuadratureTS(ctx->ts, NULL, &quadts));
    281:     PetscCall(TSForwardGetSensitivities(quadts, NULL, &qgrad));
    282:     PetscCall(MatZeroEntries(qgrad));
    283:     PetscCall(TSForwardGetSensitivities(ctx->ts, NULL, &sp));
    284:     val[0] = 1. / PetscSqrtScalar(1. - (ctx->Pm / ctx->Pmax) * (ctx->Pm / ctx->Pmax)) / ctx->Pmax;
    285:     val[1] = 0.0;
    286:     PetscCall(MatSetValues(sp, 2, row, 1, col, val, INSERT_VALUES));
    287:     PetscCall(MatAssemblyBegin(sp, MAT_FINAL_ASSEMBLY));
    288:     PetscCall(MatAssemblyEnd(sp, MAT_FINAL_ASSEMBLY));
    289:   }

    291:   /* solve the ODE */
    292:   PetscCall(TSSolve(ctx->ts, ctx->U));
    293:   PetscCall(TSGetSolveTime(ctx->ts, &ftime));
    294:   PetscCall(TSGetStepNumber(ctx->ts, &steps));

    296:   if (ctx->sa == SA_ADJ) {
    297:     Vec *lambda, *mu;
    298:     /* reset the terminal condition for adjoint */
    299:     PetscCall(TSGetCostGradients(ctx->ts, &nadj, &lambda, &mu));
    300:     PetscCall(VecGetArray(lambda[0], &y_ptr));
    301:     y_ptr[0] = 0.0;
    302:     y_ptr[1] = 0.0;
    303:     PetscCall(VecRestoreArray(lambda[0], &y_ptr));
    304:     PetscCall(VecGetArray(mu[0], &x_ptr));
    305:     x_ptr[0] = -1.0;
    306:     PetscCall(VecRestoreArray(mu[0], &x_ptr));

    308:     /* solve the adjont */
    309:     PetscCall(TSAdjointSolve(ctx->ts));

    311:     PetscCall(ComputeSensiP(lambda[0], mu[0], ctx));
    312:     PetscCall(VecCopy(mu[0], G));
    313:   }

    315:   if (ctx->sa == SA_TLM) {
    316:     PetscCall(VecGetArray(G, &x_ptr));
    317:     PetscCall(MatDenseGetArray(qgrad, &y_ptr));
    318:     x_ptr[0] = y_ptr[0] - 1.;
    319:     PetscCall(MatDenseRestoreArray(qgrad, &y_ptr));
    320:     PetscCall(VecRestoreArray(G, &x_ptr));
    321:   }

    323:   PetscCall(TSGetSolution(ctx->quadts, &q));
    324:   PetscCall(VecGetArray(q, &x_ptr));
    325:   *f = -ctx->Pm + x_ptr[0];
    326:   PetscCall(VecRestoreArray(q, &x_ptr));
    327:   PetscFunctionReturn(PETSC_SUCCESS);
    328: }

    330: /*TEST

    332:    build:
    333:       requires: !complex !single

    335:    test:
    336:       args: -viewer_binary_skip_info -ts_type cn -pc_type lu -tao_monitor

    338:    test:
    339:       suffix: 2
    340:       output_file: output/ex3opt_1.out
    341:       args: -sa_method tlm -ts_type cn -pc_type lu -tao_monitor
    342: TEST*/