Actual source code: ex9opt.c

petsc-3.7.1 2016-05-15
Report Typos and Errors
  2: static char help[] = "Basic equation for generator stability analysis.\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}



Ensemble of initial conditions
./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

Fault at .1 seconds
./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

Initial conditions same as when fault is ended
./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


 25: /*
 26:    Include "petscts.h" so that we can use TS solvers.  Note that this
 27:    file automatically includes:
 28:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 29:      petscmat.h - matrices
 30:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 31:      petscviewer.h - viewers               petscpc.h  - preconditioners
 32:      petscksp.h   - linear solvers
 33: */
 34: #include <petsctao.h>
 35: #include <petscts.h>

 37: typedef struct {
 38:   PetscScalar H,D,omega_b,omega_s,Pmax,Pm,E,V,X,u_s,c;
 39:   PetscInt    beta;
 40:   PetscReal   tf,tcl;
 41: } AppCtx;

 43: PetscErrorCode FormFunction(Tao,Vec,PetscReal*,void*);
 44: PetscErrorCode FormGradient(Tao,Vec,Vec,void*);

 48: /*
 49:      Defines the ODE passed to the ODE solver
 50: */
 51: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
 52: {
 53:   PetscErrorCode    ierr;
 54:   PetscScalar       *f,Pmax;
 55:   const PetscScalar *u;

 58:   /*  The next three lines allow us to access the entries of the vectors directly */
 59:   VecGetArrayRead(U,&u);
 60:   VecGetArray(F,&f);
 61:   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 */
 62:   else Pmax = ctx->Pmax;

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

 67:   VecRestoreArrayRead(U,&u);
 68:   VecRestoreArray(F,&f);
 69:   return(0);
 70: }

 74: /*
 75:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
 76: */
 77: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx *ctx)
 78: {
 79:   PetscErrorCode    ierr;
 80:   PetscInt          rowcol[] = {0,1};
 81:   PetscScalar       J[2][2],Pmax;
 82:   const PetscScalar *u;

 85:   VecGetArrayRead(U,&u);
 86:   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 */
 87:   else Pmax = ctx->Pmax;

 89:   J[0][0] = 0;                                  J[0][1] = ctx->omega_b;
 90:   J[1][1] = -ctx->D*ctx->omega_s/(2.0*ctx->H);  J[1][0] = -Pmax*PetscCosScalar(u[0])*ctx->omega_s/(2.0*ctx->H);

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

 95:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 96:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 97:   if (A != B) {
 98:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 99:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
100:   }
101:   return(0);
102: }

106: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx0)
107: {
109:   PetscInt       row[] = {0,1},col[]={0};
110:   PetscScalar    J[2][1];
111:   AppCtx         *ctx=(AppCtx*)ctx0;

114:   J[0][0] = 0;
115:   J[1][0] = ctx->omega_s/(2.0*ctx->H);
116:   MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
117:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
118:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
119:   return(0);
120: }

124: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,AppCtx *ctx)
125: {
126:   PetscErrorCode    ierr;
127:   PetscScalar       *r;
128:   const PetscScalar *u;

131:   VecGetArrayRead(U,&u);
132:   VecGetArray(R,&r);
133:   r[0] = ctx->c*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta);
134:   VecRestoreArray(R,&r);
135:   VecRestoreArrayRead(U,&u);
136:   return(0);
137: }

141: static PetscErrorCode DRDYFunction(TS ts,PetscReal t,Vec U,Vec *drdy,AppCtx *ctx)
142: {
143:   PetscErrorCode    ierr;
144:   PetscScalar       *ry;
145:   const PetscScalar *u;

148:   VecGetArrayRead(U,&u);
149:   VecGetArray(drdy[0],&ry);
150:   ry[0] = ctx->c*ctx->beta*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta-1);
151:   VecRestoreArray(drdy[0],&ry);
152:   VecRestoreArrayRead(U,&u);
153:   return(0);
154: }

158: static PetscErrorCode DRDPFunction(TS ts,PetscReal t,Vec U,Vec *drdp,AppCtx *ctx)
159: {
161:   PetscScalar    *rp;

164:   VecGetArray(drdp[0],&rp);
165:   rp[0] = 0.;
166:   VecRestoreArray(drdp[0],&rp);
167:   return(0);
168: }

172: PetscErrorCode ComputeSensiP(Vec lambda,Vec mu,AppCtx *ctx)
173: {
174:   PetscErrorCode    ierr;
175:   PetscScalar       *y,sensip;
176:   const PetscScalar *x;

179:   VecGetArrayRead(lambda,&x);
180:   VecGetArray(mu,&y);
181:   sensip = 1./PetscSqrtScalar(1.-(ctx->Pm/ctx->Pmax)*(ctx->Pm/ctx->Pmax))/ctx->Pmax*x[0]+y[0];
182:   /*PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt parameter pm: %g \n",(double)sensip);*/
183:   y[0] = sensip;
184:   VecRestoreArray(mu,&y);
185:   VecRestoreArrayRead(lambda,&x);
186:   return(0);
187: }

191: int main(int argc,char **argv)
192: {
193:   Vec                p;
194:   PetscScalar        *x_ptr;
195:   PetscErrorCode     ierr;
196:   PetscMPIInt        size;
197:   AppCtx             ctx;
198:   Vec                lowerb,upperb;
199:   Tao                tao;
200:   KSP                ksp;
201:   PC                 pc;

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

211:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
212:     Set runtime options
213:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
214:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
215:   {
216:     ctx.beta    = 2;
217:     ctx.c       = 10000.0;
218:     ctx.u_s     = 1.0;
219:     ctx.omega_s = 1.0;
220:     ctx.omega_b = 120.0*PETSC_PI;
221:     ctx.H       = 5.0;
222:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
223:     ctx.D       = 5.0;
224:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
225: #if defined(PETSC_USE_REAL___FLOAT128)
226:     ctx.E       = 1.1378q;
227: #else
228:     ctx.E       = 1.1378;
229: #endif
230:     ctx.V       = 1.0;
231: #if defined(PETSC_USE_REAL___FLOAT128)
232:     ctx.X       = 0.545q;
233: #else
234:     ctx.X       = 0.545;
235: #endif
236:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;;
237:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
238: #if defined(PETSC_USE_REAL___FLOAT128)
239:     ctx.Pm      = 1.0194q;
240: #else
241:     ctx.Pm      = 1.0194;
242: #endif
243:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
244: #if defined(PETSC_USE_REAL___FLOAT128)
245:     ctx.tf      = 0.1q;
246:     ctx.tcl     = 0.2q;
247: #else
248:     ctx.tf      = 0.1;
249:     ctx.tcl     = 0.2;
250: #endif
251:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
252:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);

254:   }
255:   PetscOptionsEnd();

257:   /* Create TAO solver and set desired solution method */
258:   TaoCreate(PETSC_COMM_WORLD,&tao);
259:   TaoSetType(tao,TAOBLMVM);

261:   /*
262:      Optimization starts
263:   */
264:   /* Set initial solution guess */
265:   VecCreateSeq(PETSC_COMM_WORLD,1,&p);
266:   VecGetArray(p,&x_ptr);
267:   x_ptr[0]   = ctx.Pm;
268:   VecRestoreArray(p,&x_ptr);

270:   TaoSetInitialVector(tao,p);
271:   /* Set routine for function and gradient evaluation */
272:   TaoSetObjectiveRoutine(tao,FormFunction,(void *)&ctx);
273:   TaoSetGradientRoutine(tao,FormGradient,(void *)&ctx);

275:   /* Set bounds for the optimization */
276:   VecDuplicate(p,&lowerb);
277:   VecDuplicate(p,&upperb);
278:   VecGetArray(lowerb,&x_ptr);
279:   x_ptr[0] = 0.;
280:   VecRestoreArray(lowerb,&x_ptr);
281:   VecGetArray(upperb,&x_ptr);
282: #if defined(PETSC_USE_REAL___FLOAT128)
283:   x_ptr[0] = 1.1q;
284: #else
285:   x_ptr[0] = 1.1;
286: #endif
287:   VecRestoreArray(upperb,&x_ptr);
288:   TaoSetVariableBounds(tao,lowerb,upperb);

290:   /* Check for any TAO command line options */
291:   TaoSetFromOptions(tao);
292:   TaoGetKSP(tao,&ksp);
293:   if (ksp) {
294:     KSPGetPC(ksp,&pc);
295:     PCSetType(pc,PCNONE);
296:   }

298:   /* SOLVE THE APPLICATION */
299:   TaoSolve(tao);

301:   VecView(p,PETSC_VIEWER_STDOUT_WORLD);
302:   /* Free TAO data structures */
303:   TaoDestroy(&tao);
304:   VecDestroy(&p);
305:   VecDestroy(&lowerb);
306:   VecDestroy(&upperb);
307:   PetscFinalize();
308:   return 0;
309: }

311: /* ------------------------------------------------------------------ */
314: /*
315:    FormFunction - Evaluates the function

317:    Input Parameters:
318:    tao - the Tao context
319:    X   - the input vector
320:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()

322:    Output Parameters:
323:    f   - the newly evaluated function
324: */
325: PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
326: {
327:   AppCtx         *ctx = (AppCtx*)ctx0;
328:   TS             ts;

330:   Vec            U;             /* solution will be stored here */
331:   Mat            A;             /* Jacobian matrix */
333:   PetscInt       n = 2;
334:   PetscScalar    *u;
335:   PetscScalar    *x_ptr;
336:   Vec            lambda[1],q,mu[1];

338:   VecGetArray(P,&x_ptr);
339:   ctx->Pm = x_ptr[0];
340:   VecRestoreArray(P,&x_ptr);
341:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
342:     Create necessary matrix and vectors
343:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
344:   MatCreate(PETSC_COMM_WORLD,&A);
345:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
346:   MatSetType(A,MATDENSE);
347:   MatSetFromOptions(A);
348:   MatSetUp(A);

350:   MatCreateVecs(A,&U,NULL);
351:   MatCreateVecs(A,&lambda[0],NULL);
352:   MatCreateVecs(A,&mu[0],NULL);

354:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
355:      Create timestepping solver context
356:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
357:   TSCreate(PETSC_COMM_WORLD,&ts);
358:   TSSetProblemType(ts,TS_NONLINEAR);
359:   TSSetType(ts,TSRK);
360:   TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,ctx);
361:   TSSetRHSJacobian(ts,A,A,(TSRHSJacobian)RHSJacobian,ctx);
362:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);

364:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
365:      Set initial conditions
366:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
367:   VecGetArray(U,&u);
368:   u[0] = PetscAsinScalar(ctx->Pm/ctx->Pmax);
369:   u[1] = 1.0;
370:   VecRestoreArray(U,&u);
371:   TSSetSolution(ts,U);

373:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
374:     Save trajectory of solution so that TSAdjointSolve() may be used
375:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
376:   TSSetSaveTrajectory(ts);

378:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
379:      Set solver options
380:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
381:   TSSetDuration(ts,PETSC_DEFAULT,1.0);
382: #if defined(PETSC_USE_REAL___FLOAT128)
383:   TSSetInitialTimeStep(ts,0.0,.01q);
384: #else
385:   TSSetInitialTimeStep(ts,0.0,.01);
386: #endif
387:   TSSetFromOptions(ts);

389:   TSSetCostGradients(ts,1,lambda,mu);
390:   TSSetCostIntegrand(ts,1,(PetscErrorCode (*)(TS,PetscReal,Vec,Vec,void*))CostIntegrand,
391:                                         (PetscErrorCode (*)(TS,PetscReal,Vec,Vec*,void*))DRDYFunction,
392:                                         (PetscErrorCode (*)(TS,PetscReal,Vec,Vec*,void*))DRDPFunction,PETSC_TRUE,ctx);

394:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
395:      Solve nonlinear system
396:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
397:   TSSolve(ts,U);
398:   TSGetCostIntegral(ts,&q);
399:   VecGetArray(q,&x_ptr);
400:   *f   = -ctx->Pm + x_ptr[0];
401:   VecRestoreArray(q,&x_ptr);

403:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
404:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
405:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
406:   MatDestroy(&A);
407:   VecDestroy(&U);
408:   VecDestroy(&lambda[0]);
409:   VecDestroy(&mu[0]);
410:   TSDestroy(&ts);

412:   return 0;
413: }


416: PetscErrorCode FormGradient(Tao tao,Vec P,Vec G,void *ctx0)
417: {
418:   AppCtx         *ctx = (AppCtx*)ctx0;
419:   TS             ts;

421:   Vec            U;             /* solution will be stored here */
422:   Mat            A;             /* Jacobian matrix */
423:   Mat            Jacp;          /* Jacobian matrix */
425:   PetscInt       n = 2;
426:   PetscReal      ftime;
427:   PetscInt       steps;
428:   PetscScalar    *u;
429:   PetscScalar    *x_ptr,*y_ptr;
430:   Vec            lambda[1],q,mu[1];

432:   VecGetArray(P,&x_ptr);
433:   ctx->Pm = x_ptr[0];
434:   VecRestoreArray(P,&x_ptr);

436:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
437:     Create necessary matrix and vectors
438:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
439:   MatCreate(PETSC_COMM_WORLD,&A);
440:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
441:   MatSetType(A,MATDENSE);
442:   MatSetFromOptions(A);
443:   MatSetUp(A);

445:   MatCreateVecs(A,&U,NULL);

447:   MatCreate(PETSC_COMM_WORLD,&Jacp);
448:   MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
449:   MatSetFromOptions(Jacp);
450:   MatSetUp(Jacp);

452:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
453:      Create timestepping solver context
454:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
455:   TSCreate(PETSC_COMM_WORLD,&ts);
456:   TSSetProblemType(ts,TS_NONLINEAR);
457:   TSSetType(ts,TSRK);
458:   TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,ctx);
459:   TSSetRHSJacobian(ts,A,A,(TSRHSJacobian)RHSJacobian,ctx);
460:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);

462:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
463:      Set initial conditions
464:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
465:   VecGetArray(U,&u);
466:   u[0] = PetscAsinScalar(ctx->Pm/ctx->Pmax);
467:   u[1] = 1.0;
468:   VecRestoreArray(U,&u);
469:   TSSetSolution(ts,U);

471:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
472:     Save trajectory of solution so that TSAdjointSolve() may be used
473:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
474:   TSSetSaveTrajectory(ts);

476:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
477:      Set solver options
478:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
479:   TSSetDuration(ts,PETSC_DEFAULT,1.0);
480: #if defined(PETSC_USE_REAL___FLOAT128)
481:   TSSetInitialTimeStep(ts,0.0,.01q);
482: #else
483:   TSSetInitialTimeStep(ts,0.0,.01);
484: #endif
485:   TSSetFromOptions(ts);

487:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
488:      Solve nonlinear system
489:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
490:   TSSolve(ts,U);

492:   TSGetSolveTime(ts,&ftime);
493:   TSGetTimeStepNumber(ts,&steps);

495:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
496:      Adjoint model starts here
497:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
498:   MatCreateVecs(A,&lambda[0],NULL);
499:   /*   Set initial conditions for the adjoint integration */
500:   VecGetArray(lambda[0],&y_ptr);
501:   y_ptr[0] = 0.0; y_ptr[1] = 0.0;
502:   VecRestoreArray(lambda[0],&y_ptr);

504:   MatCreateVecs(Jacp,&mu[0],NULL);
505:   VecGetArray(mu[0],&x_ptr);
506:   x_ptr[0] = -1.0;
507:   VecRestoreArray(mu[0],&x_ptr);
508:   TSSetCostGradients(ts,1,lambda,mu);

510:   TSAdjointSetRHSJacobian(ts,Jacp,RHSJacobianP,ctx);

512:   TSSetCostIntegrand(ts,1,(PetscErrorCode (*)(TS,PetscReal,Vec,Vec,void*))CostIntegrand,
513:                                         (PetscErrorCode (*)(TS,PetscReal,Vec,Vec*,void*))DRDYFunction,
514:                                         (PetscErrorCode (*)(TS,PetscReal,Vec,Vec*,void*))DRDPFunction,PETSC_FALSE,ctx);

516:   TSAdjointSolve(ts);
517:   TSGetCostIntegral(ts,&q);
518:   ComputeSensiP(lambda[0],mu[0],ctx);

520:   VecCopy(mu[0],G);

522:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
523:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
524:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
525:   MatDestroy(&A);
526:   MatDestroy(&Jacp);
527:   VecDestroy(&U);
528:   VecDestroy(&lambda[0]);
529:   VecDestroy(&mu[0]);
530:   TSDestroy(&ts);

532:   return 0;
533: }