Actual source code: ex3opt.c


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

  4: /*F

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

 11: F*/

 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;

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

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

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

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

 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:     PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL));
 78:     ctx.D = 5.0;
 79:     PetscCall(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:     PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL));
 86:     ctx.Pm = 1.06;
 87:     PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL));
 88:     ctx.tf  = 0.1;
 89:     ctx.tcl = 0.2;
 90:     PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL));
 91:     PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL));
 92:     printtofile = PETSC_FALSE;
 93:     PetscCall(PetscOptionsBool("-printtofile", "Print convergence results to file", "", printtofile, &printtofile, NULL));
 94:     ctx.sa = SA_ADJ;
 95:     PetscCall(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:   PetscCall(MatCreate(PETSC_COMM_WORLD, &ctx.Jac));
103:   PetscCall(MatSetSizes(ctx.Jac, 2, 2, PETSC_DETERMINE, PETSC_DETERMINE));
104:   PetscCall(MatSetType(ctx.Jac, MATDENSE));
105:   PetscCall(MatSetFromOptions(ctx.Jac));
106:   PetscCall(MatSetUp(ctx.Jac));
107:   PetscCall(MatCreate(PETSC_COMM_WORLD, &ctx.Jacp));
108:   PetscCall(MatSetSizes(ctx.Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1));
109:   PetscCall(MatSetFromOptions(ctx.Jacp));
110:   PetscCall(MatSetUp(ctx.Jacp));
111:   PetscCall(MatCreateVecs(ctx.Jac, &ctx.U, NULL));
112:   PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &ctx.DRDP));
113:   PetscCall(MatSetUp(ctx.DRDP));
114:   PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, &ctx.DRDU));
115:   PetscCall(MatSetUp(ctx.DRDU));

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

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

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

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

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

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

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

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

196:   /* SOLVE THE APPLICATION */
197:   PetscCall(TaoSolve(tao));

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

201:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
202:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
203:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
204:   PetscCall(MatDestroy(&ctx.Jac));
205:   PetscCall(MatDestroy(&ctx.Jacp));
206:   PetscCall(MatDestroy(&ctx.DRDU));
207:   PetscCall(MatDestroy(&ctx.DRDP));
208:   PetscCall(VecDestroy(&ctx.U));
209:   if (ctx.sa == SA_ADJ) {
210:     PetscCall(VecDestroy(&lambda[0]));
211:     PetscCall(VecDestroy(&mu[0]));
212:   }
213:   if (ctx.sa == SA_TLM) {
214:     PetscCall(MatDestroy(&qgrad));
215:     PetscCall(MatDestroy(&sp));
216:   }
217:   PetscCall(TSDestroy(&ctx.ts));
218:   PetscCall(VecDestroy(&p));
219:   PetscCall(VecDestroy(&lowerb));
220:   PetscCall(VecDestroy(&upperb));
221:   PetscCall(TaoDestroy(&tao));
222:   PetscCall(PetscFinalize());
223:   return 0;
224: }

226: /* ------------------------------------------------------------------ */
227: /*
228:    FormFunctionGradient - Evaluates the function and corresponding gradient.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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