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*/