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, void *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*/