Actual source code: ex3opt_fd.c


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


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

 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,"%d %g %.12lf %.12lf\n",iterate,gnorm,x[0],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:   PetscErrorCode     ierr;
 51:   PetscMPIInt        size;
 52:   AppCtx             ctx;
 53:   Vec                lowerb,upperb;
 54:   Tao                tao;
 55:   KSP                ksp;
 56:   PC                 pc;
 57:   PetscBool          printtofile;
 58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 59:      Initialize program
 60:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 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) {
101:     TaoSetMonitor(tao,(PetscErrorCode (*)(Tao, void*))monitor,(void *)&ctx,PETSC_NULL);
102:   }
103:   TaoSetMaximumIterations(tao,30);
104:   /*
105:      Optimization starts
106:   */
107:   /* Set initial solution guess */
108:   VecCreateSeq(PETSC_COMM_WORLD,1,&p);
109:   VecGetArray(p,&x_ptr);
110:   x_ptr[0]   = ctx.Pm;
111:   VecRestoreArray(p,&x_ptr);

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

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

129:   /* Check for any TAO command line options */
130:   TaoSetFromOptions(tao);
131:   TaoGetKSP(tao,&ksp);
132:   if (ksp) {
133:     KSPGetPC(ksp,&pc);
134:     PCSetType(pc,PCNONE);
135:   }

137:   /* SOLVE THE APPLICATION */
138:   TaoSolve(tao);

140:   VecView(p,PETSC_VIEWER_STDOUT_WORLD);

142:   /* Free TAO data structures */
143:   TaoDestroy(&tao);
144:   VecDestroy(&p);
145:   VecDestroy(&lowerb);
146:   VecDestroy(&upperb);
147:   PetscFinalize();
148:   return 0;
149: }

151: /* ------------------------------------------------------------------ */
152: /*
153:    FormFunction - Evaluates the function and corresponding gradient.

155:    Input Parameters:
156:    tao - the Tao context
157:    X   - the input vector
158:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()

160:    Output Parameters:
161:    f   - the newly evaluated function
162: */
163: PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
164: {
165:   AppCtx            *ctx = (AppCtx*)ctx0;
166:   TS                ts,quadts;
167:   Vec               U;             /* solution will be stored here */
168:   Mat               A;             /* Jacobian matrix */
169:   PetscInt          n = 2;
170:   PetscReal         ftime;
171:   PetscInt          steps;
172:   PetscScalar       *u;
173:   const PetscScalar *x_ptr,*qx_ptr;
174:   Vec               q;
175:   PetscInt          direction[2];
176:   PetscBool         terminate[2];

178:   VecGetArrayRead(P,&x_ptr);
179:   ctx->Pm = x_ptr[0];
180:   VecRestoreArrayRead(P,&x_ptr);
181:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
182:     Create necessary matrix and vectors
183:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
184:   MatCreate(PETSC_COMM_WORLD,&A);
185:   MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
186:   MatSetType(A,MATDENSE);
187:   MatSetFromOptions(A);
188:   MatSetUp(A);

190:   MatCreateVecs(A,&U,NULL);

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

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

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

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

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

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

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

238:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
239:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
240:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
241:   MatDestroy(&A);
242:   VecDestroy(&U);
243:   TSDestroy(&ts);
244:   return 0;
245: }

247: /*TEST

249:    build:
250:       requires: !complex !single

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

255: TEST*/