Actual source code: ex3opt_fd.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:   Solve the same optimization problem as in ex3opt.c.
     14:   Use finite difference to approximate the gradients.
     15: */
     16: #include <petsctao.h>
     17: #include <petscts.h>
     18: #include "ex3.h"

     20: PetscErrorCode FormFunction(Tao, Vec, PetscReal *, void *);

     22: PetscErrorCode monitor(Tao tao, AppCtx *ctx)
     23: {
     24:   FILE              *fp;
     25:   PetscInt           iterate;
     26:   PetscReal          f, gnorm, cnorm, xdiff;
     27:   Vec                X, G;
     28:   const PetscScalar *x, *g;
     29:   TaoConvergedReason reason;

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

     45: int main(int argc, char **argv)
     46: {
     47:   Vec          p;
     48:   PetscScalar *x_ptr;
     49:   PetscMPIInt  size;
     50:   AppCtx       ctx;
     51:   Vec          lowerb, upperb;
     52:   Tao          tao;
     53:   KSP          ksp;
     54:   PC           pc;
     55:   PetscBool    printtofile;
     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:   }
     93:   PetscOptionsEnd();

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

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

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

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

    133:   /* SOLVE THE APPLICATION */
    134:   PetscCall(TaoSolve(tao));

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

    138:   /* Free TAO data structures */
    139:   PetscCall(TaoDestroy(&tao));
    140:   PetscCall(VecDestroy(&p));
    141:   PetscCall(VecDestroy(&lowerb));
    142:   PetscCall(VecDestroy(&upperb));
    143:   PetscCall(PetscFinalize());
    144:   return 0;
    145: }

    147: /* ------------------------------------------------------------------ */
    148: /*
    149:    FormFunction - Evaluates the function and corresponding gradient.

    151:    Input Parameters:
    152:    tao - the Tao context
    153:    X   - the input vector
    154:    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient()

    156:    Output Parameters:
    157:    f   - the newly evaluated function
    158: */
    159: PetscErrorCode FormFunction(Tao tao, Vec P, PetscReal *f, void *ctx0)
    160: {
    161:   AppCtx            *ctx = (AppCtx *)ctx0;
    162:   TS                 ts, quadts;
    163:   Vec                U; /* solution will be stored here */
    164:   Mat                A; /* Jacobian matrix */
    165:   PetscInt           n = 2;
    166:   PetscReal          ftime;
    167:   PetscInt           steps;
    168:   PetscScalar       *u;
    169:   const PetscScalar *x_ptr, *qx_ptr;
    170:   Vec                q;
    171:   PetscInt           direction[2];
    172:   PetscBool          terminate[2];

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

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

    189:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    190:      Create timestepping solver context
    191:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    192:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
    193:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
    194:   PetscCall(TSSetType(ts, TSCN));
    195:   PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, ctx));
    196:   PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, ctx));

    198:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    199:      Set initial conditions
    200:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    201:   PetscCall(VecGetArray(U, &u));
    202:   u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
    203:   u[1] = 1.0;
    204:   PetscCall(VecRestoreArray(U, &u));
    205:   PetscCall(TSSetSolution(ts, U));

    207:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    208:      Set solver options
    209:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    210:   PetscCall(TSSetMaxTime(ts, 1.0));
    211:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
    212:   PetscCall(TSSetTimeStep(ts, 0.03125));
    213:   PetscCall(TSCreateQuadratureTS(ts, PETSC_TRUE, &quadts));
    214:   PetscCall(TSGetSolution(quadts, &q));
    215:   PetscCall(VecSet(q, 0.0));
    216:   PetscCall(TSSetRHSFunction(quadts, NULL, (TSRHSFunctionFn *)CostIntegrand, ctx));
    217:   PetscCall(TSSetFromOptions(ts));

    219:   direction[0] = direction[1] = 1;
    220:   terminate[0] = terminate[1] = PETSC_FALSE;

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

    224:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    225:      Solve nonlinear system
    226:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    227:   PetscCall(TSSolve(ts, U));

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

    235:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    236:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    237:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    238:   PetscCall(MatDestroy(&A));
    239:   PetscCall(VecDestroy(&U));
    240:   PetscCall(TSDestroy(&ts));
    241:   PetscFunctionReturn(PETSC_SUCCESS);
    242: }

    244: /*TEST

    246:    build:
    247:       requires: !complex !single

    249:    test:
    250:       args: -ts_type cn -pc_type lu -tao_monitor -tao_gatol 1e-3

    252: TEST*/