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*/

/*
  This code demonstrates how to solve a ODE-constrained optimization problem with TAO, TSEvent, TSAdjoint and TS.
  The problem features discontinuities and a cost function in integral form.
  The gradient is computed with the discrete adjoint of an implicit theta method, see ex3adj.c for details.
*/

#include <petsctao.h>
#include <petscts.h>
#include "ex3.h"

PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal *, Vec, void *);

PetscErrorCode monitor(Tao tao, AppCtx *ctx)
{
  FILE              *fp;
  PetscInt           iterate;
  PetscReal          f, gnorm, cnorm, xdiff;
  TaoConvergedReason reason;

  PetscFunctionBeginUser;
  PetscCall(TaoGetSolutionStatus(tao, &iterate, &f, &gnorm, &cnorm, &xdiff, &reason));

  fp = fopen("ex3opt_conv.out", "a");
  PetscCall(PetscFPrintf(PETSC_COMM_WORLD, fp, "%" PetscInt_FMT " %g\n", iterate, (double)gnorm));
  fclose(fp);
  PetscFunctionReturn(PETSC_SUCCESS);
}

int main(int argc, char **argv)
{
  Vec          p;
  PetscScalar *x_ptr;
  PetscMPIInt  size;
  AppCtx       ctx;
  Tao          tao;
  KSP          ksp;
  PC           pc;
  Vec          lambda[1], mu[1], lowerb, upperb;
  PetscBool    printtofile;
  PetscInt     direction[2];
  PetscBool    terminate[2];
  Mat          qgrad; /* Forward sesivitiy */
  Mat          sp;    /* Forward sensitivity matrix */

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     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));
    ctx.sa = SA_ADJ;
    PetscCall(PetscOptionsEnum("-sa_method", "Sensitivity analysis method (adj or tlm)", "", SAMethods, (PetscEnum)ctx.sa, (PetscEnum *)&ctx.sa, NULL));
  }
  PetscOptionsEnd();

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Create necessary matrix and vectors
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatCreate(PETSC_COMM_WORLD, &ctx.Jac));
  PetscCall(MatSetSizes(ctx.Jac, 2, 2, PETSC_DETERMINE, PETSC_DETERMINE));
  PetscCall(MatSetType(ctx.Jac, MATDENSE));
  PetscCall(MatSetFromOptions(ctx.Jac));
  PetscCall(MatSetUp(ctx.Jac));
  PetscCall(MatCreate(PETSC_COMM_WORLD, &ctx.Jacp));
  PetscCall(MatSetSizes(ctx.Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1));
  PetscCall(MatSetFromOptions(ctx.Jacp));
  PetscCall(MatSetUp(ctx.Jacp));
  PetscCall(MatCreateVecs(ctx.Jac, &ctx.U, NULL));
  PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &ctx.DRDP));
  PetscCall(MatSetUp(ctx.DRDP));
  PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, &ctx.DRDU));
  PetscCall(MatSetUp(ctx.DRDU));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSCreate(PETSC_COMM_WORLD, &ctx.ts));
  PetscCall(TSSetProblemType(ctx.ts, TS_NONLINEAR));
  PetscCall(TSSetType(ctx.ts, TSCN));
  PetscCall(TSSetRHSFunction(ctx.ts, NULL, (TSRHSFunctionFn *)RHSFunction, &ctx));
  PetscCall(TSSetRHSJacobian(ctx.ts, ctx.Jac, ctx.Jac, (TSRHSJacobianFn *)RHSJacobian, &ctx));
  PetscCall(TSSetRHSJacobianP(ctx.ts, ctx.Jacp, RHSJacobianP, &ctx));

  if (ctx.sa == SA_ADJ) {
    PetscCall(MatCreateVecs(ctx.Jac, &lambda[0], NULL));
    PetscCall(MatCreateVecs(ctx.Jacp, &mu[0], NULL));
    PetscCall(TSSetSaveTrajectory(ctx.ts));
    PetscCall(TSSetCostGradients(ctx.ts, 1, lambda, mu));
    PetscCall(TSCreateQuadratureTS(ctx.ts, PETSC_FALSE, &ctx.quadts));
    PetscCall(TSSetRHSFunction(ctx.quadts, NULL, (TSRHSFunctionFn *)CostIntegrand, &ctx));
    PetscCall(TSSetRHSJacobian(ctx.quadts, ctx.DRDU, ctx.DRDU, (TSRHSJacobianFn *)DRDUJacobianTranspose, &ctx));
    PetscCall(TSSetRHSJacobianP(ctx.quadts, ctx.DRDP, DRDPJacobianTranspose, &ctx));
  }
  if (ctx.sa == SA_TLM) {
    PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &qgrad));
    PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, &sp));
    PetscCall(TSForwardSetSensitivities(ctx.ts, 1, sp));
    PetscCall(TSCreateQuadratureTS(ctx.ts, PETSC_TRUE, &ctx.quadts));
    PetscCall(TSForwardSetSensitivities(ctx.quadts, 1, qgrad));
    PetscCall(TSSetRHSFunction(ctx.quadts, NULL, (TSRHSFunctionFn *)CostIntegrand, &ctx));
    PetscCall(TSSetRHSJacobian(ctx.quadts, ctx.DRDU, ctx.DRDU, (TSRHSJacobianFn *)DRDUJacobianTranspose, &ctx));
    PetscCall(TSSetRHSJacobianP(ctx.quadts, ctx.DRDP, DRDPJacobianTranspose, &ctx));
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set solver options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetMaxTime(ctx.ts, 1.0));
  PetscCall(TSSetExactFinalTime(ctx.ts, TS_EXACTFINALTIME_MATCHSTEP));
  PetscCall(TSSetTimeStep(ctx.ts, 0.03125));
  PetscCall(TSSetFromOptions(ctx.ts));

  direction[0] = direction[1] = 1;
  terminate[0] = terminate[1] = PETSC_FALSE;
  PetscCall(TSSetEventHandler(ctx.ts, 2, direction, terminate, EventFunction, PostEventFunction, &ctx));

  /* 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));
  /*
     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(TaoSetObjectiveAndGradient(tao, NULL, FormFunctionGradient, (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 work space.  All PETSc objects should be destroyed when they are no longer needed.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatDestroy(&ctx.Jac));
  PetscCall(MatDestroy(&ctx.Jacp));
  PetscCall(MatDestroy(&ctx.DRDU));
  PetscCall(MatDestroy(&ctx.DRDP));
  PetscCall(VecDestroy(&ctx.U));
  if (ctx.sa == SA_ADJ) {
    PetscCall(VecDestroy(&lambda[0]));
    PetscCall(VecDestroy(&mu[0]));
  }
  if (ctx.sa == SA_TLM) {
    PetscCall(MatDestroy(&qgrad));
    PetscCall(MatDestroy(&sp));
  }
  PetscCall(TSDestroy(&ctx.ts));
  PetscCall(VecDestroy(&p));
  PetscCall(VecDestroy(&lowerb));
  PetscCall(VecDestroy(&upperb));
  PetscCall(TaoDestroy(&tao));
  PetscCall(PetscFinalize());
  return 0;
}

/* ------------------------------------------------------------------ */
/*
   FormFunctionGradient - 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
   G   - the newly evaluated gradient
*/
PetscErrorCode FormFunctionGradient(Tao tao, Vec P, PetscReal *f, Vec G, PetscCtx ctx0)
{
  AppCtx      *ctx = (AppCtx *)ctx0;
  PetscInt     nadj;
  PetscReal    ftime;
  PetscInt     steps;
  PetscScalar *u;
  PetscScalar *x_ptr, *y_ptr;
  Vec          q;
  Mat          qgrad;

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(P, (const PetscScalar **)&x_ptr));
  ctx->Pm = x_ptr[0];
  PetscCall(VecRestoreArrayRead(P, (const PetscScalar **)&x_ptr));

  /* reinitialize the solution vector */
  PetscCall(VecGetArray(ctx->U, &u));
  u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax);
  u[1] = 1.0;
  PetscCall(VecRestoreArray(ctx->U, &u));
  PetscCall(TSSetSolution(ctx->ts, ctx->U));

  /* reset time */
  PetscCall(TSSetTime(ctx->ts, 0.0));

  /* reset step counter, this is critical for adjoint solver */
  PetscCall(TSSetStepNumber(ctx->ts, 0));

  /* reset step size, the step size becomes negative after TSAdjointSolve */
  PetscCall(TSSetTimeStep(ctx->ts, 0.03125));

  /* reinitialize the integral value */
  PetscCall(TSGetQuadratureTS(ctx->ts, NULL, &ctx->quadts));
  PetscCall(TSGetSolution(ctx->quadts, &q));
  PetscCall(VecSet(q, 0.0));

  if (ctx->sa == SA_TLM) { /* reset the forward sensitivities */
    TS             quadts;
    Mat            sp;
    PetscScalar    val[2];
    const PetscInt row[] = {0, 1}, col[] = {0};

    PetscCall(TSGetQuadratureTS(ctx->ts, NULL, &quadts));
    PetscCall(TSForwardGetSensitivities(quadts, NULL, &qgrad));
    PetscCall(MatZeroEntries(qgrad));
    PetscCall(TSForwardGetSensitivities(ctx->ts, NULL, &sp));
    val[0] = 1. / PetscSqrtScalar(1. - (ctx->Pm / ctx->Pmax) * (ctx->Pm / ctx->Pmax)) / ctx->Pmax;
    val[1] = 0.0;
    PetscCall(MatSetValues(sp, 2, row, 1, col, val, INSERT_VALUES));
    PetscCall(MatAssemblyBegin(sp, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(sp, MAT_FINAL_ASSEMBLY));
  }

  /* solve the ODE */
  PetscCall(TSSolve(ctx->ts, ctx->U));
  PetscCall(TSGetSolveTime(ctx->ts, &ftime));
  PetscCall(TSGetStepNumber(ctx->ts, &steps));

  if (ctx->sa == SA_ADJ) {
    Vec *lambda, *mu;
    /* reset the terminal condition for adjoint */
    PetscCall(TSGetCostGradients(ctx->ts, &nadj, &lambda, &mu));
    PetscCall(VecGetArray(lambda[0], &y_ptr));
    y_ptr[0] = 0.0;
    y_ptr[1] = 0.0;
    PetscCall(VecRestoreArray(lambda[0], &y_ptr));
    PetscCall(VecGetArray(mu[0], &x_ptr));
    x_ptr[0] = -1.0;
    PetscCall(VecRestoreArray(mu[0], &x_ptr));

    /* solve the adjont */
    PetscCall(TSAdjointSolve(ctx->ts));

    PetscCall(ComputeSensiP(lambda[0], mu[0], ctx));
    PetscCall(VecCopy(mu[0], G));
  }

  if (ctx->sa == SA_TLM) {
    PetscCall(VecGetArray(G, &x_ptr));
    PetscCall(MatDenseGetArray(qgrad, &y_ptr));
    x_ptr[0] = y_ptr[0] - 1.;
    PetscCall(MatDenseRestoreArray(qgrad, &y_ptr));
    PetscCall(VecRestoreArray(G, &x_ptr));
  }

  PetscCall(TSGetSolution(ctx->quadts, &q));
  PetscCall(VecGetArray(q, &x_ptr));
  *f = -ctx->Pm + x_ptr[0];
  PetscCall(VecRestoreArray(q, &x_ptr));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*TEST

   build:
      requires: !complex !single

   test:
      args: -viewer_binary_skip_info -ts_type cn -pc_type lu -tao_monitor

   test:
      suffix: 2
      output_file: output/ex3opt_1.out
      args: -sa_method tlm -ts_type cn -pc_type lu -tao_monitor
TEST*/