Actual source code: ex3opt.c

      2: static char help[] = "Finds optimal parameter P_m for the generator system while maintaining generator stability.\n";

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

     13: /*
     14:   This code demonstrates how to solve a ODE-constrained optimization problem with TAO, TSEvent, TSAdjoint and TS.
     15:   The problem features discontinuities and a cost function in integral form.
     16:   The gradient is computed with the discrete adjoint of an implicit theta method, see ex3adj.c for details.
     17: */

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

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

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

     33:   TaoGetSolutionStatus(tao,&iterate,&f,&gnorm,&cnorm,&xdiff,&reason);

     35:   fp = fopen("ex3opt_conv.out","a");
     36:   PetscFPrintf(PETSC_COMM_WORLD,fp,"%D %g\n",iterate,(double)gnorm);
     37:   fclose(fp);
     38:   return 0;
     39: }

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

     58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     59:      Initialize program
     60:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     61:   PetscInitialize(&argc,&argv,NULL,help);
     63:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

     66:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     67:     Set runtime options
     68:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     69:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
     70:   {
     71:     ctx.beta    = 2;
     72:     ctx.c       = 10000.0;
     73:     ctx.u_s     = 1.0;
     74:     ctx.omega_s = 1.0;
     75:     ctx.omega_b = 120.0*PETSC_PI;
     76:     ctx.H       = 5.0;
     77:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
     78:     ctx.D       = 5.0;
     79:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
     80:     ctx.E       = 1.1378;
     81:     ctx.V       = 1.0;
     82:     ctx.X       = 0.545;
     83:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
     84:     ctx.Pmax_ini = ctx.Pmax;
     85:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
     86:     ctx.Pm      = 1.06;
     87:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
     88:     ctx.tf      = 0.1;
     89:     ctx.tcl     = 0.2;
     90:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
     91:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
     92:     printtofile = PETSC_FALSE;
     93:     PetscOptionsBool("-printtofile","Print convergence results to file","",printtofile,&printtofile,NULL);
     94:     ctx.sa      = SA_ADJ;
     95:     PetscOptionsEnum("-sa_method","Sensitivity analysis method (adj or tlm)","",SAMethods,(PetscEnum)ctx.sa,(PetscEnum*)&ctx.sa,NULL);
     96:   }
     97:   PetscOptionsEnd();

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

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

    127:   if (ctx.sa == SA_ADJ) {
    128:     MatCreateVecs(ctx.Jac,&lambda[0],NULL);
    129:     MatCreateVecs(ctx.Jacp,&mu[0],NULL);
    130:     TSSetSaveTrajectory(ctx.ts);
    131:     TSSetCostGradients(ctx.ts,1,lambda,mu);
    132:     TSCreateQuadratureTS(ctx.ts,PETSC_FALSE,&ctx.quadts);
    133:     TSSetRHSFunction(ctx.quadts,NULL,(TSRHSFunction)CostIntegrand,&ctx);
    134:     TSSetRHSJacobian(ctx.quadts,ctx.DRDU,ctx.DRDU,(TSRHSJacobian)DRDUJacobianTranspose,&ctx);
    135:     TSSetRHSJacobianP(ctx.quadts,ctx.DRDP,DRDPJacobianTranspose,&ctx);
    136:   }
    137:   if (ctx.sa == SA_TLM) {
    138:     MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,&qgrad);
    139:     MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,2,1,NULL,&sp);
    140:     TSForwardSetSensitivities(ctx.ts,1,sp);
    141:     TSCreateQuadratureTS(ctx.ts,PETSC_TRUE,&ctx.quadts);
    142:     TSForwardSetSensitivities(ctx.quadts,1,qgrad);
    143:     TSSetRHSFunction(ctx.quadts,NULL,(TSRHSFunction)CostIntegrand,&ctx);
    144:     TSSetRHSJacobian(ctx.quadts,ctx.DRDU,ctx.DRDU,(TSRHSJacobian)DRDUJacobianTranspose,&ctx);
    145:     TSSetRHSJacobianP(ctx.quadts,ctx.DRDP,DRDPJacobianTranspose,&ctx);
    146:   }

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

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

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

    175:   TaoSetSolution(tao,p);
    176:   /* Set routine for function and gradient evaluation */
    177:   TaoSetObjectiveAndGradient(tao,NULL,FormFunctionGradient,(void *)&ctx);

    179:   /* Set bounds for the optimization */
    180:   VecDuplicate(p,&lowerb);
    181:   VecDuplicate(p,&upperb);
    182:   VecGetArray(lowerb,&x_ptr);
    183:   x_ptr[0] = 0.;
    184:   VecRestoreArray(lowerb,&x_ptr);
    185:   VecGetArray(upperb,&x_ptr);
    186:   x_ptr[0] = 1.1;
    187:   VecRestoreArray(upperb,&x_ptr);
    188:   TaoSetVariableBounds(tao,lowerb,upperb);

    190:   /* Check for any TAO command line options */
    191:   TaoSetFromOptions(tao);
    192:   TaoGetKSP(tao,&ksp);
    193:   if (ksp) {
    194:     KSPGetPC(ksp,&pc);
    195:     PCSetType(pc,PCNONE);
    196:   }

    198:   /* SOLVE THE APPLICATION */
    199:   TaoSolve(tao);

    201:   VecView(p,PETSC_VIEWER_STDOUT_WORLD);

    203:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    204:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    205:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    206:   MatDestroy(&ctx.Jac);
    207:   MatDestroy(&ctx.Jacp);
    208:   MatDestroy(&ctx.DRDU);
    209:   MatDestroy(&ctx.DRDP);
    210:   VecDestroy(&ctx.U);
    211:   if (ctx.sa == SA_ADJ) {
    212:     VecDestroy(&lambda[0]);
    213:     VecDestroy(&mu[0]);
    214:   }
    215:   if (ctx.sa == SA_TLM) {
    216:     MatDestroy(&qgrad);
    217:     MatDestroy(&sp);
    218:   }
    219:   TSDestroy(&ctx.ts);
    220:   VecDestroy(&p);
    221:   VecDestroy(&lowerb);
    222:   VecDestroy(&upperb);
    223:   TaoDestroy(&tao);
    224:   PetscFinalize();
    225:   return 0;
    226: }

    228: /* ------------------------------------------------------------------ */
    229: /*
    230:    FormFunctionGradient - Evaluates the function and corresponding gradient.

    232:    Input Parameters:
    233:    tao - the Tao context
    234:    X   - the input vector
    235:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()

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

    252:   VecGetArrayRead(P,(const PetscScalar**)&x_ptr);
    253:   ctx->Pm = x_ptr[0];
    254:   VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);

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

    263:   /* reset time */
    264:   TSSetTime(ctx->ts,0.0);

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

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

    272:   /* reinitialize the integral value */
    273:   TSGetQuadratureTS(ctx->ts,NULL,&ctx->quadts);
    274:   TSGetSolution(ctx->quadts,&q);
    275:   VecSet(q,0.0);

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

    283:     TSGetQuadratureTS(ctx->ts,NULL,&quadts);
    284:     TSForwardGetSensitivities(quadts,NULL,&qgrad);
    285:     MatZeroEntries(qgrad);
    286:     TSForwardGetSensitivities(ctx->ts,NULL,&sp);
    287:     val[0] = 1./PetscSqrtScalar(1.-(ctx->Pm/ctx->Pmax)*(ctx->Pm/ctx->Pmax))/ctx->Pmax;
    288:     val[1] = 0.0;
    289:     MatSetValues(sp,2,row,1,col,val,INSERT_VALUES);
    290:     MatAssemblyBegin(sp,MAT_FINAL_ASSEMBLY);
    291:     MatAssemblyEnd(sp,MAT_FINAL_ASSEMBLY);
    292:   }

    294:   /* solve the ODE */
    295:   TSSolve(ctx->ts,ctx->U);
    296:   TSGetSolveTime(ctx->ts,&ftime);
    297:   TSGetStepNumber(ctx->ts,&steps);

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

    310:     /* solve the adjont */
    311:     TSAdjointSolve(ctx->ts);

    313:     ComputeSensiP(lambda[0],mu[0],ctx);
    314:     VecCopy(mu[0],G);
    315:   }

    317:   if (ctx->sa == SA_TLM) {
    318:     VecGetArray(G,&x_ptr);
    319:     MatDenseGetArray(qgrad,&y_ptr);
    320:     x_ptr[0] = y_ptr[0]-1.;
    321:     MatDenseRestoreArray(qgrad,&y_ptr);
    322:     VecRestoreArray(G,&x_ptr);
    323:   }

    325:   TSGetSolution(ctx->quadts,&q);
    326:   VecGetArray(q,&x_ptr);
    327:   *f   = -ctx->Pm + x_ptr[0];
    328:   VecRestoreArray(q,&x_ptr);
    329:   return 0;
    330: }

    332: /*TEST

    334:    build:
    335:       requires: !complex !single

    337:    test:
    338:       args: -viewer_binary_skip_info -ts_type cn -pc_type lu -tao_monitor

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