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;

 32:   PetscFunctionBeginUser;
 33:   PetscCall(TaoGetSolutionStatus(tao, &iterate, &f, &gnorm, &cnorm, &xdiff, &reason));
 34:   PetscCall(TaoGetSolution(tao, &X));
 35:   PetscCall(TaoGetGradient(tao, &G, NULL, NULL));
 36:   PetscCall(VecGetArrayRead(X, &x));
 37:   PetscCall(VecGetArrayRead(G, &g));
 38:   fp = fopen("ex3opt_fd_conv.out", "a");
 39:   PetscCall(PetscFPrintf(PETSC_COMM_WORLD, fp, "%" PetscInt_FMT " %g %.12lf %.12lf\n", iterate, (double)gnorm, (double)PetscRealPart(x[0]), (double)PetscRealPart(g[0])));
 40:   PetscCall(VecRestoreArrayRead(X, &x));
 41:   PetscCall(VecRestoreArrayRead(G, &g));
 42:   fclose(fp);
 43:   PetscFunctionReturn(PETSC_SUCCESS);
 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:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 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:   }
 95:   PetscOptionsEnd();

 97:   /* Create TAO solver and set desired solution method */
 98:   PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
 99:   PetscCall(TaoSetType(tao, TAOBLMVM));
100:   if (printtofile) PetscCall(TaoSetMonitor(tao, (PetscErrorCode(*)(Tao, void *))monitor, (void *)&ctx, NULL));
101:   PetscCall(TaoSetMaximumIterations(tao, 30));
102:   /*
103:      Optimization starts
104:   */
105:   /* Set initial solution guess */
106:   PetscCall(VecCreateSeq(PETSC_COMM_WORLD, 1, &p));
107:   PetscCall(VecGetArray(p, &x_ptr));
108:   x_ptr[0] = ctx.Pm;
109:   PetscCall(VecRestoreArray(p, &x_ptr));

111:   PetscCall(TaoSetSolution(tao, p));
112:   /* Set routine for function and gradient evaluation */
113:   PetscCall(TaoSetObjective(tao, FormFunction, (void *)&ctx));
114:   PetscCall(TaoSetGradient(tao, NULL, TaoDefaultComputeGradient, (void *)&ctx));

116:   /* Set bounds for the optimization */
117:   PetscCall(VecDuplicate(p, &lowerb));
118:   PetscCall(VecDuplicate(p, &upperb));
119:   PetscCall(VecGetArray(lowerb, &x_ptr));
120:   x_ptr[0] = 0.;
121:   PetscCall(VecRestoreArray(lowerb, &x_ptr));
122:   PetscCall(VecGetArray(upperb, &x_ptr));
123:   x_ptr[0] = 1.1;
124:   PetscCall(VecRestoreArray(upperb, &x_ptr));
125:   PetscCall(TaoSetVariableBounds(tao, lowerb, upperb));

127:   /* Check for any TAO command line options */
128:   PetscCall(TaoSetFromOptions(tao));
129:   PetscCall(TaoGetKSP(tao, &ksp));
130:   if (ksp) {
131:     PetscCall(KSPGetPC(ksp, &pc));
132:     PetscCall(PCSetType(pc, PCNONE));
133:   }

135:   /* SOLVE THE APPLICATION */
136:   PetscCall(TaoSolve(tao));

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

140:   /* Free TAO data structures */
141:   PetscCall(TaoDestroy(&tao));
142:   PetscCall(VecDestroy(&p));
143:   PetscCall(VecDestroy(&lowerb));
144:   PetscCall(VecDestroy(&upperb));
145:   PetscCall(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:   PetscFunctionBeginUser;
177:   PetscCall(VecGetArrayRead(P, &x_ptr));
178:   ctx->Pm = x_ptr[0];
179:   PetscCall(VecRestoreArrayRead(P, &x_ptr));
180:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181:     Create necessary matrix and vectors
182:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
184:   PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
185:   PetscCall(MatSetType(A, MATDENSE));
186:   PetscCall(MatSetFromOptions(A));
187:   PetscCall(MatSetUp(A));

189:   PetscCall(MatCreateVecs(A, &U, NULL));

191:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
192:      Create timestepping solver context
193:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
194:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
195:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
196:   PetscCall(TSSetType(ts, TSCN));
197:   PetscCall(TSSetIFunction(ts, NULL, (TSIFunction)IFunction, ctx));
198:   PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobian)IJacobian, ctx));

200:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
201:      Set initial conditions
202:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
203:   PetscCall(VecGetArray(U, &u));
204:   u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
205:   u[1] = 1.0;
206:   PetscCall(VecRestoreArray(U, &u));
207:   PetscCall(TSSetSolution(ts, U));

209:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
210:      Set solver options
211:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
212:   PetscCall(TSSetMaxTime(ts, 1.0));
213:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
214:   PetscCall(TSSetTimeStep(ts, 0.03125));
215:   PetscCall(TSCreateQuadratureTS(ts, PETSC_TRUE, &quadts));
216:   PetscCall(TSGetSolution(quadts, &q));
217:   PetscCall(VecSet(q, 0.0));
218:   PetscCall(TSSetRHSFunction(quadts, NULL, (TSRHSFunction)CostIntegrand, ctx));
219:   PetscCall(TSSetFromOptions(ts));

221:   direction[0] = direction[1] = 1;
222:   terminate[0] = terminate[1] = PETSC_FALSE;

224:   PetscCall(TSSetEventHandler(ts, 2, direction, terminate, EventFunction, PostEventFunction, (void *)ctx));

226:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
227:      Solve nonlinear system
228:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
229:   PetscCall(TSSolve(ts, U));

231:   PetscCall(TSGetSolveTime(ts, &ftime));
232:   PetscCall(TSGetStepNumber(ts, &steps));
233:   PetscCall(VecGetArrayRead(q, &qx_ptr));
234:   *f = -ctx->Pm + qx_ptr[0];
235:   PetscCall(VecRestoreArrayRead(q, &qx_ptr));

237:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
238:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
239:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
240:   PetscCall(MatDestroy(&A));
241:   PetscCall(VecDestroy(&U));
242:   PetscCall(TSDestroy(&ts));
243:   PetscFunctionReturn(PETSC_SUCCESS);
244: }

246: /*TEST

248:    build:
249:       requires: !complex !single

251:    test:
252:       args: -ts_type cn -pc_type lu -tao_monitor -tao_gatol 1e-3

254: TEST*/