static char help[] = "Parallel bouncing ball example formulated as a second-order system to test TS event feature.\n";

/*
  The dynamics of the bouncing ball with drag coefficient Cd is described by the ODE

      u_tt = -9.8 - 1/2 Cd (u_t)^2 sign(u_t)

  There is one event set in this example, which checks for the ball hitting the
  ground (u = 0). Every time the ball hits the ground, its velocity u_t is attenuated by
  a restitution coefficient Cr. On reaching the limit on the number of ball bounces,
  the TS run is requested to terminate from the PostEvent() callback.
*/

#include <petscts.h>

typedef struct {
  PetscReal Cd; /* drag coefficient */
  PetscReal Cr; /* restitution coefficient */
  PetscInt  bounces;
  PetscInt  maxbounces;
} AppCtx;

static PetscErrorCode Event(TS ts, PetscReal t, Vec U, PetscReal *fvalue, void *ctx)
{
  Vec                V;
  const PetscScalar *u;

  PetscFunctionBeginUser;
  /* Event for ball height */
  PetscCall(TS2GetSolution(ts, &U, &V));
  PetscCall(VecGetArrayRead(U, &u));
  fvalue[0] = PetscRealPart(u[0]);
  PetscCall(VecRestoreArrayRead(U, &u));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PostEvent(TS ts, PetscInt nevents, PetscInt event_list[], PetscReal t, Vec U, PetscBool forwardsolve, void *ctx)
{
  AppCtx      *app = (AppCtx *)ctx;
  Vec          V;
  PetscScalar *u, *v;
  PetscMPIInt  rank;
  PetscBool    inflag = PETSC_FALSE, outflag;

  PetscFunctionBeginUser;
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
  if (nevents > 0) {
    PetscCall(PetscPrintf(PETSC_COMM_SELF, "Processor [%d]: Ball hit the ground at t = %5.2f seconds\n", rank, (double)t));
    /* Set new initial conditions with attenuation Cr */
    PetscCall(TS2GetSolution(ts, &U, &V));
    PetscCall(VecGetArray(U, &u));
    PetscCall(VecGetArray(V, &v));
    u[0] = 0.0;
    v[0] = -app->Cr * v[0];
    PetscCall(VecRestoreArray(U, &u));
    PetscCall(VecRestoreArray(V, &v));
    app->bounces++;
  }
  if (app->bounces >= app->maxbounces) { // 'app->bounces' may be different on different processes
    PetscCall(PetscPrintf(PETSC_COMM_SELF, "Processor [%d]: Ball bounced %" PetscInt_FMT " times\n", rank, app->bounces));
    inflag = PETSC_TRUE; // current process requested to terminate
  }
  PetscCallMPI(MPIU_Allreduce(&inflag, &outflag, 1, MPIU_BOOL, MPI_LOR, PetscObjectComm((PetscObject)ts)));
  if (outflag) PetscCall(TSSetConvergedReason(ts, TS_CONVERGED_USER)); // request TS to terminate, sync on all ranks
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode I2Function(TS ts, PetscReal t, Vec U, Vec V, Vec A, Vec F, void *ctx)
{
  AppCtx            *app = (AppCtx *)ctx;
  const PetscScalar *u, *v, *a;
  PetscScalar        Res, *f;

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(U, &u));
  PetscCall(VecGetArrayRead(V, &v));
  PetscCall(VecGetArrayRead(A, &a));
  Res = a[0] + 9.8 + 0.5 * app->Cd * v[0] * v[0] * PetscSignReal(PetscRealPart(v[0]));
  PetscCall(VecRestoreArrayRead(U, &u));
  PetscCall(VecRestoreArrayRead(V, &v));
  PetscCall(VecRestoreArrayRead(A, &a));

  PetscCall(VecGetArray(F, &f));
  f[0] = Res;
  PetscCall(VecRestoreArray(F, &f));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode I2Jacobian(TS ts, PetscReal t, Vec U, Vec V, Vec A, PetscReal shiftV, PetscReal shiftA, Mat J, Mat P, void *ctx)
{
  AppCtx            *app = (AppCtx *)ctx;
  const PetscScalar *u, *v, *a;
  PetscInt           i;
  PetscScalar        Jac;

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(U, &u));
  PetscCall(VecGetArrayRead(V, &v));
  PetscCall(VecGetArrayRead(A, &a));
  Jac = shiftA + shiftV * app->Cd * v[0];
  PetscCall(VecRestoreArrayRead(U, &u));
  PetscCall(VecRestoreArrayRead(V, &v));
  PetscCall(VecRestoreArrayRead(A, &a));

  PetscCall(MatGetOwnershipRange(P, &i, NULL));
  PetscCall(MatSetValue(P, i, i, Jac, INSERT_VALUES));
  PetscCall(MatAssemblyBegin(P, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(P, MAT_FINAL_ASSEMBLY));
  if (J != P) {
    PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

int main(int argc, char **argv)
{
  TS           ts;   /* ODE integrator */
  Vec          U, V; /* solution will be stored here */
  Vec          F;    /* residual vector */
  Mat          J;    /* Jacobian matrix */
  PetscMPIInt  rank;
  PetscScalar *u, *v;
  AppCtx       app;
  PetscInt     direction[1];
  PetscBool    terminate[1];
  TSAdapt      adapt;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));

  app.Cd         = 0.0;
  app.Cr         = 0.9;
  app.bounces    = 0;
  app.maxbounces = 10;
  PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "ex44 options", "");
  PetscCall(PetscOptionsReal("-Cd", "Drag coefficient", "", app.Cd, &app.Cd, NULL));
  PetscCall(PetscOptionsReal("-Cr", "Restitution coefficient", "", app.Cr, &app.Cr, NULL));
  PetscCall(PetscOptionsInt("-maxbounces", "Maximum number of bounces", "", app.maxbounces, &app.maxbounces, NULL));
  PetscOptionsEnd();

  PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
  /*PetscCall(TSSetSaveTrajectory(ts));*/
  PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
  PetscCall(TSSetType(ts, TSALPHA2));

  PetscCall(TSSetMaxTime(ts, PETSC_INFINITY));
  PetscCall(TSSetTimeStep(ts, 0.1));
  PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
  PetscCall(TSGetAdapt(ts, &adapt));
  PetscCall(TSAdaptSetStepLimits(adapt, 0.0, 0.5));

  direction[0] = -1;
  terminate[0] = PETSC_FALSE;
  PetscCall(TSSetEventHandler(ts, 1, direction, terminate, Event, PostEvent, &app)); // each process has one event-function defined

  PetscCall(MatCreateAIJ(PETSC_COMM_WORLD, 1, 1, PETSC_DECIDE, PETSC_DECIDE, 1, NULL, 0, NULL, &J));
  PetscCall(MatSetFromOptions(J));
  PetscCall(MatSetUp(J));
  PetscCall(MatCreateVecs(J, NULL, &F));
  PetscCall(TSSetI2Function(ts, F, I2Function, &app));
  PetscCall(TSSetI2Jacobian(ts, J, J, I2Jacobian, &app));
  PetscCall(VecDestroy(&F));
  PetscCall(MatDestroy(&J));

  PetscCall(TSGetI2Jacobian(ts, &J, NULL, NULL, NULL));
  PetscCall(MatCreateVecs(J, &U, NULL));
  PetscCall(MatCreateVecs(J, &V, NULL));
  PetscCall(VecGetArray(U, &u));
  PetscCall(VecGetArray(V, &v));
  u[0] = 5.0 * rank;
  v[0] = 20.0;
  PetscCall(VecRestoreArray(U, &u));
  PetscCall(VecRestoreArray(V, &v));

  PetscCall(TS2SetSolution(ts, U, V));
  PetscCall(TSSetFromOptions(ts));
  PetscCall(TSSolve(ts, NULL));

  PetscCall(VecDestroy(&U));
  PetscCall(VecDestroy(&V));
  PetscCall(TSDestroy(&ts));

  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

    test:
      suffix: a
      args: -ts_alpha_radius {{1.0 0.5}} -ts_max_time 50
      output_file: output/ex44.out

    test:
      suffix: b
      args: -ts_rtol 0 -ts_atol 1e-1 -ts_adapt_type basic -ts_max_time 50
      output_file: output/ex44.out

    test:
      suffix: bmf
      args: -snes_mf_operator -ts_rtol 0 -ts_atol 1e-1 -ts_adapt_type basic -ts_max_time 50
      output_file: output/ex44.out

    test:
      suffix: 2
      nsize: 2
      args: -ts_rtol 0 -ts_atol 1e-1 -ts_adapt_type basic -ts_max_time 50
      output_file: output/ex44_2.out
      filter: sort -b
      filter_output: sort -b

    test:
      requires: !single
      args: -ts_dt 0.25 -ts_adapt_type basic -ts_adapt_wnormtype INFINITY -ts_adapt_monitor
      args: -ts_max_steps 1 -ts_max_reject {{0 1 2}separate_output} -ts_error_if_step_fails false

TEST*/