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;
     31:   PetscErrorCode     ierr;

     34:   TaoGetSolutionStatus(tao,&iterate,&f,&gnorm,&cnorm,&xdiff,&reason);
     35:   TaoGetSolutionVector(tao,&X);
     36:   TaoGetGradientVector(tao,&G);
     37:   VecGetArrayRead(X,&x);
     38:   VecGetArrayRead(G,&g);
     39:   fp = fopen("ex3opt_fd_conv.out","a");
     40:   PetscFPrintf(PETSC_COMM_WORLD,fp,"%d %g %.12lf %.12lf\n",iterate,gnorm,x[0],g[0]);
     41:   VecRestoreArrayRead(X,&x);
     42:   VecRestoreArrayRead(G,&g);
     43:   fclose(fp);
     44:   return(0);
     45: }

     47: int main(int argc,char **argv)
     48: {
     49:   Vec                p;
     50:   PetscScalar        *x_ptr;
     51:   PetscErrorCode     ierr;
     52:   PetscMPIInt        size;
     53:   AppCtx             ctx;
     54:   Vec                lowerb,upperb;
     55:   Tao                tao;
     56:   KSP                ksp;
     57:   PC                 pc;
     58:   PetscBool          printtofile;
     59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     60:      Initialize program
     61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     62:   PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
     64:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     65:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");

     67:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     68:     Set runtime options
     69:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     70:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
     71:   {
     72:     ctx.beta    = 2;
     73:     ctx.c       = 10000.0;
     74:     ctx.u_s     = 1.0;
     75:     ctx.omega_s = 1.0;
     76:     ctx.omega_b = 120.0*PETSC_PI;
     77:     ctx.H       = 5.0;
     78:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
     79:     ctx.D       = 5.0;
     80:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
     81:     ctx.E       = 1.1378;
     82:     ctx.V       = 1.0;
     83:     ctx.X       = 0.545;
     84:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
     85:     ctx.Pmax_ini = ctx.Pmax;
     86:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
     87:     ctx.Pm      = 1.06;
     88:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
     89:     ctx.tf      = 0.1;
     90:     ctx.tcl     = 0.2;
     91:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
     92:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
     93:     printtofile = PETSC_FALSE;
     94:     PetscOptionsBool("-printtofile","Print convergence results to file","",printtofile,&printtofile,NULL);
     95:   }
     96:   PetscOptionsEnd();

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

    114:   TaoSetInitialVector(tao,p);
    115:   /* Set routine for function and gradient evaluation */
    116:   TaoSetObjectiveRoutine(tao,FormFunction,(void *)&ctx);
    117:   TaoSetGradientRoutine(tao,TaoDefaultComputeGradient,(void *)&ctx);

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

    130:   /* Check for any TAO command line options */
    131:   TaoSetFromOptions(tao);
    132:   TaoGetKSP(tao,&ksp);
    133:   if (ksp) {
    134:     KSPGetPC(ksp,&pc);
    135:     PCSetType(pc,PCNONE);
    136:   }

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

    141:   VecView(p,PETSC_VIEWER_STDOUT_WORLD);

    143:   /* Free TAO data structures */
    144:   TaoDestroy(&tao);
    145:   VecDestroy(&p);
    146:   VecDestroy(&lowerb);
    147:   VecDestroy(&upperb);
    148:   PetscFinalize();
    149:   return ierr;
    150: }

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

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

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

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

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

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

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

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

    224:   direction[0] = direction[1] = 1;
    225:   terminate[0] = terminate[1] = PETSC_FALSE;

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

    229:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    230:      Solve nonlinear system
    231:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    232:   TSSolve(ts,U);

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

    240:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    241:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    242:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    243:   MatDestroy(&A);
    244:   VecDestroy(&U);
    245:   TSDestroy(&ts);
    246:   return 0;
    247: }

    249: /*TEST

    251:    build:
    252:       requires: !complex !single

    254:    test:
    255:       args: -ts_type cn -pc_type lu -tao_monitor -tao_gatol 1e-3

    257: TEST*/