Actual source code: ex3opt_fd.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: Solve the same optimization problem as in ex3opt.c.
15: Use finite difference to approximate the gradients.
16: */
17: #include <petsctao.h>
18: #include <petscts.h>
19: #include "ex3.h"
21: PetscErrorCode FormFunction(Tao, Vec, PetscReal *, void *);
23: PetscErrorCode monitor(Tao tao, AppCtx *ctx)
24: {
25: FILE *fp;
26: PetscInt iterate;
27: PetscReal f, gnorm, cnorm, xdiff;
28: Vec X, G;
29: const PetscScalar *x, *g;
30: TaoConvergedReason reason;
33: TaoGetSolutionStatus(tao, &iterate, &f, &gnorm, &cnorm, &xdiff, &reason);
34: TaoGetSolution(tao, &X);
35: TaoGetGradient(tao, &G, NULL, NULL);
36: VecGetArrayRead(X, &x);
37: VecGetArrayRead(G, &g);
38: fp = fopen("ex3opt_fd_conv.out", "a");
39: PetscFPrintf(PETSC_COMM_WORLD, fp, "%" PetscInt_FMT " %g %.12lf %.12lf\n", iterate, (double)gnorm, (double)PetscRealPart(x[0]), (double)PetscRealPart(g[0]));
40: VecRestoreArrayRead(X, &x);
41: VecRestoreArrayRead(G, &g);
42: fclose(fp);
43: return 0;
44: }
46: int main(int argc, char **argv)
47: {
48: Vec p;
49: PetscScalar *x_ptr;
50: PetscMPIInt size;
51: AppCtx ctx;
52: Vec lowerb, upperb;
53: Tao tao;
54: KSP ksp;
55: PC pc;
56: PetscBool printtofile;
57: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
58: Initialize program
59: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
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: }
95: PetscOptionsEnd();
97: /* Create TAO solver and set desired solution method */
98: TaoCreate(PETSC_COMM_WORLD, &tao);
99: TaoSetType(tao, TAOBLMVM);
100: if (printtofile) TaoSetMonitor(tao, (PetscErrorCode(*)(Tao, void *))monitor, (void *)&ctx, PETSC_NULL);
101: TaoSetMaximumIterations(tao, 30);
102: /*
103: Optimization starts
104: */
105: /* Set initial solution guess */
106: VecCreateSeq(PETSC_COMM_WORLD, 1, &p);
107: VecGetArray(p, &x_ptr);
108: x_ptr[0] = ctx.Pm;
109: VecRestoreArray(p, &x_ptr);
111: TaoSetSolution(tao, p);
112: /* Set routine for function and gradient evaluation */
113: TaoSetObjective(tao, FormFunction, (void *)&ctx);
114: TaoSetGradient(tao, NULL, TaoDefaultComputeGradient, (void *)&ctx);
116: /* Set bounds for the optimization */
117: VecDuplicate(p, &lowerb);
118: VecDuplicate(p, &upperb);
119: VecGetArray(lowerb, &x_ptr);
120: x_ptr[0] = 0.;
121: VecRestoreArray(lowerb, &x_ptr);
122: VecGetArray(upperb, &x_ptr);
123: x_ptr[0] = 1.1;
124: VecRestoreArray(upperb, &x_ptr);
125: TaoSetVariableBounds(tao, lowerb, upperb);
127: /* Check for any TAO command line options */
128: TaoSetFromOptions(tao);
129: TaoGetKSP(tao, &ksp);
130: if (ksp) {
131: KSPGetPC(ksp, &pc);
132: PCSetType(pc, PCNONE);
133: }
135: /* SOLVE THE APPLICATION */
136: TaoSolve(tao);
138: VecView(p, PETSC_VIEWER_STDOUT_WORLD);
140: /* Free TAO data structures */
141: TaoDestroy(&tao);
142: VecDestroy(&p);
143: VecDestroy(&lowerb);
144: VecDestroy(&upperb);
145: PetscFinalize();
146: return 0;
147: }
149: /* ------------------------------------------------------------------ */
150: /*
151: FormFunction - Evaluates the function and corresponding gradient.
153: Input Parameters:
154: tao - the Tao context
155: X - the input vector
156: ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()
158: Output Parameters:
159: f - the newly evaluated function
160: */
161: PetscErrorCode FormFunction(Tao tao, Vec P, PetscReal *f, void *ctx0)
162: {
163: AppCtx *ctx = (AppCtx *)ctx0;
164: TS ts, quadts;
165: Vec U; /* solution will be stored here */
166: Mat A; /* Jacobian matrix */
167: PetscInt n = 2;
168: PetscReal ftime;
169: PetscInt steps;
170: PetscScalar *u;
171: const PetscScalar *x_ptr, *qx_ptr;
172: Vec q;
173: PetscInt direction[2];
174: PetscBool terminate[2];
176: VecGetArrayRead(P, &x_ptr);
177: ctx->Pm = x_ptr[0];
178: VecRestoreArrayRead(P, &x_ptr);
179: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
180: Create necessary matrix and vectors
181: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
182: MatCreate(PETSC_COMM_WORLD, &A);
183: MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE);
184: MatSetType(A, MATDENSE);
185: MatSetFromOptions(A);
186: MatSetUp(A);
188: MatCreateVecs(A, &U, NULL);
190: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
191: Create timestepping solver context
192: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
193: TSCreate(PETSC_COMM_WORLD, &ts);
194: TSSetProblemType(ts, TS_NONLINEAR);
195: TSSetType(ts, TSCN);
196: TSSetIFunction(ts, NULL, (TSIFunction)IFunction, ctx);
197: TSSetIJacobian(ts, A, A, (TSIJacobian)IJacobian, ctx);
199: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
200: Set initial conditions
201: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
202: VecGetArray(U, &u);
203: u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
204: u[1] = 1.0;
205: VecRestoreArray(U, &u);
206: TSSetSolution(ts, U);
208: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209: Set solver options
210: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
211: TSSetMaxTime(ts, 1.0);
212: TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP);
213: TSSetTimeStep(ts, 0.03125);
214: TSCreateQuadratureTS(ts, PETSC_TRUE, &quadts);
215: TSGetSolution(quadts, &q);
216: VecSet(q, 0.0);
217: TSSetRHSFunction(quadts, NULL, (TSRHSFunction)CostIntegrand, ctx);
218: TSSetFromOptions(ts);
220: direction[0] = direction[1] = 1;
221: terminate[0] = terminate[1] = PETSC_FALSE;
223: TSSetEventHandler(ts, 2, direction, terminate, EventFunction, PostEventFunction, (void *)ctx);
225: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
226: Solve nonlinear system
227: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
228: TSSolve(ts, U);
230: TSGetSolveTime(ts, &ftime);
231: TSGetStepNumber(ts, &steps);
232: VecGetArrayRead(q, &qx_ptr);
233: *f = -ctx->Pm + qx_ptr[0];
234: VecRestoreArrayRead(q, &qx_ptr);
236: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
237: Free work space. All PETSc objects should be destroyed when they are no longer needed.
238: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
239: MatDestroy(&A);
240: VecDestroy(&U);
241: TSDestroy(&ts);
242: return 0;
243: }
245: /*TEST
247: build:
248: requires: !complex !single
250: test:
251: args: -ts_type cn -pc_type lu -tao_monitor -tao_gatol 1e-3
253: TEST*/