static char help[] = "Finds optimal parameter P_m for the generator system while maintaining generator stability.\n"; /*F \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} F*/ /* Solve the same optimization problem as in ex3opt.c. Use finite difference to approximate the gradients. */ #include #include #include "ex3.h" PetscErrorCode FormFunction(Tao, Vec, PetscReal *, void *); PetscErrorCode monitor(Tao tao, AppCtx *ctx) { FILE *fp; PetscInt iterate; PetscReal f, gnorm, cnorm, xdiff; Vec X, G; const PetscScalar *x, *g; TaoConvergedReason reason; PetscFunctionBeginUser; PetscCall(TaoGetSolutionStatus(tao, &iterate, &f, &gnorm, &cnorm, &xdiff, &reason)); PetscCall(TaoGetSolution(tao, &X)); PetscCall(TaoGetGradient(tao, &G, NULL, NULL)); PetscCall(VecGetArrayRead(X, &x)); PetscCall(VecGetArrayRead(G, &g)); fp = fopen("ex3opt_fd_conv.out", "a"); PetscCall(PetscFPrintf(PETSC_COMM_WORLD, fp, "%" PetscInt_FMT " %g %.12lf %.12lf\n", iterate, (double)gnorm, (double)PetscRealPart(x[0]), (double)PetscRealPart(g[0]))); PetscCall(VecRestoreArrayRead(X, &x)); PetscCall(VecRestoreArrayRead(G, &g)); fclose(fp); PetscFunctionReturn(PETSC_SUCCESS); } int main(int argc, char **argv) { Vec p; PetscScalar *x_ptr; PetscMPIInt size; AppCtx ctx; Vec lowerb, upperb; Tao tao; KSP ksp; PC pc; PetscBool printtofile; /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Initialize program - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscFunctionBeginUser; PetscCall(PetscInitialize(&argc, &argv, NULL, help)); PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!"); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", ""); { ctx.beta = 2; ctx.c = 10000.0; ctx.u_s = 1.0; ctx.omega_s = 1.0; ctx.omega_b = 120.0 * PETSC_PI; ctx.H = 5.0; PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL)); ctx.D = 5.0; PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL)); ctx.E = 1.1378; ctx.V = 1.0; ctx.X = 0.545; ctx.Pmax = ctx.E * ctx.V / ctx.X; ctx.Pmax_ini = ctx.Pmax; PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL)); ctx.Pm = 1.06; PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL)); ctx.tf = 0.1; ctx.tcl = 0.2; PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL)); PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL)); printtofile = PETSC_FALSE; PetscCall(PetscOptionsBool("-printtofile", "Print convergence results to file", "", printtofile, &printtofile, NULL)); } PetscOptionsEnd(); /* Create TAO solver and set desired solution method */ PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao)); PetscCall(TaoSetType(tao, TAOBLMVM)); if (printtofile) PetscCall(TaoMonitorSet(tao, (PetscErrorCode (*)(Tao, void *))monitor, (void *)&ctx, NULL)); PetscCall(TaoSetMaximumIterations(tao, 30)); /* Optimization starts */ /* Set initial solution guess */ PetscCall(VecCreateSeq(PETSC_COMM_WORLD, 1, &p)); PetscCall(VecGetArray(p, &x_ptr)); x_ptr[0] = ctx.Pm; PetscCall(VecRestoreArray(p, &x_ptr)); PetscCall(TaoSetSolution(tao, p)); /* Set routine for function and gradient evaluation */ PetscCall(TaoSetObjective(tao, FormFunction, (void *)&ctx)); PetscCall(TaoSetGradient(tao, NULL, TaoDefaultComputeGradient, (void *)&ctx)); /* Set bounds for the optimization */ PetscCall(VecDuplicate(p, &lowerb)); PetscCall(VecDuplicate(p, &upperb)); PetscCall(VecGetArray(lowerb, &x_ptr)); x_ptr[0] = 0.; PetscCall(VecRestoreArray(lowerb, &x_ptr)); PetscCall(VecGetArray(upperb, &x_ptr)); x_ptr[0] = 1.1; PetscCall(VecRestoreArray(upperb, &x_ptr)); PetscCall(TaoSetVariableBounds(tao, lowerb, upperb)); /* Check for any TAO command line options */ PetscCall(TaoSetFromOptions(tao)); PetscCall(TaoGetKSP(tao, &ksp)); if (ksp) { PetscCall(KSPGetPC(ksp, &pc)); PetscCall(PCSetType(pc, PCNONE)); } /* SOLVE THE APPLICATION */ PetscCall(TaoSolve(tao)); PetscCall(VecView(p, PETSC_VIEWER_STDOUT_WORLD)); /* Free TAO data structures */ PetscCall(TaoDestroy(&tao)); PetscCall(VecDestroy(&p)); PetscCall(VecDestroy(&lowerb)); PetscCall(VecDestroy(&upperb)); PetscCall(PetscFinalize()); return 0; } /* ------------------------------------------------------------------ */ /* FormFunction - Evaluates the function and corresponding gradient. Input Parameters: tao - the Tao context X - the input vector ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient() Output Parameters: f - the newly evaluated function */ PetscErrorCode FormFunction(Tao tao, Vec P, PetscReal *f, void *ctx0) { AppCtx *ctx = (AppCtx *)ctx0; TS ts, quadts; Vec U; /* solution will be stored here */ Mat A; /* Jacobian matrix */ PetscInt n = 2; PetscReal ftime; PetscInt steps; PetscScalar *u; const PetscScalar *x_ptr, *qx_ptr; Vec q; PetscInt direction[2]; PetscBool terminate[2]; PetscFunctionBeginUser; PetscCall(VecGetArrayRead(P, &x_ptr)); ctx->Pm = x_ptr[0]; PetscCall(VecRestoreArrayRead(P, &x_ptr)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create necessary matrix and vectors - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); PetscCall(MatSetType(A, MATDENSE)); PetscCall(MatSetFromOptions(A)); PetscCall(MatSetUp(A)); PetscCall(MatCreateVecs(A, &U, NULL)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create timestepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); PetscCall(TSSetType(ts, TSCN)); PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, ctx)); PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, ctx)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(VecGetArray(U, &u)); u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax); u[1] = 1.0; PetscCall(VecRestoreArray(U, &u)); PetscCall(TSSetSolution(ts, U)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set solver options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSetMaxTime(ts, 1.0)); PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); PetscCall(TSSetTimeStep(ts, 0.03125)); PetscCall(TSCreateQuadratureTS(ts, PETSC_TRUE, &quadts)); PetscCall(TSGetSolution(quadts, &q)); PetscCall(VecSet(q, 0.0)); PetscCall(TSSetRHSFunction(quadts, NULL, (TSRHSFunctionFn *)CostIntegrand, ctx)); PetscCall(TSSetFromOptions(ts)); direction[0] = direction[1] = 1; terminate[0] = terminate[1] = PETSC_FALSE; PetscCall(TSSetEventHandler(ts, 2, direction, terminate, EventFunction, PostEventFunction, (void *)ctx)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Solve nonlinear system - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSolve(ts, U)); PetscCall(TSGetSolveTime(ts, &ftime)); PetscCall(TSGetStepNumber(ts, &steps)); PetscCall(VecGetArrayRead(q, &qx_ptr)); *f = -ctx->Pm + qx_ptr[0]; PetscCall(VecRestoreArrayRead(q, &qx_ptr)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. All PETSc objects should be destroyed when they are no longer needed. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(MatDestroy(&A)); PetscCall(VecDestroy(&U)); PetscCall(TSDestroy(&ts)); PetscFunctionReturn(PETSC_SUCCESS); } /*TEST build: requires: !complex !single test: args: -ts_type cn -pc_type lu -tao_monitor -tao_gatol 1e-3 TEST*/