static char help[] = "Demonstrates automatic Jacobian generation using ADOL-C for an ODE-constrained optimization problem.\n\
Input parameters include:\n\
      -mu : stiffness parameter\n\n";

/*
   REQUIRES configuration of PETSc with option --download-adolc.

   For documentation on ADOL-C, see
     $PETSC_ARCH/externalpackages/ADOL-C-2.6.0/ADOL-C/doc/adolc-manual.pdf
*/
/* ------------------------------------------------------------------------
  See ex16opt_ic for a description of the problem being solved.
  ------------------------------------------------------------------------- */
#include <petsctao.h>
#include <petscts.h>
#include <petscmat.h>
#include "adolc-utils/drivers.cxx"
#include <adolc/adolc.h>

typedef struct _n_User *User;
struct _n_User {
  PetscReal mu;
  PetscReal next_output;
  PetscInt  steps;

  /* Sensitivity analysis support */
  PetscReal ftime, x_ob[2];
  Mat       A;            /* Jacobian matrix */
  Vec       x, lambda[2]; /* adjoint variables */

  /* Automatic differentiation support */
  AdolcCtx *adctx;
};

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

/*
  'Passive' RHS function, used in residual evaluations during the time integration.
*/
static PetscErrorCode RHSFunctionPassive(TS ts, PetscReal t, Vec X, Vec F, PetscCtx ctx)
{
  User               user = (User)ctx;
  PetscScalar       *f;
  const PetscScalar *x;

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(X, &x));
  PetscCall(VecGetArray(F, &f));
  f[0] = x[1];
  f[1] = user->mu * (1. - x[0] * x[0]) * x[1] - x[0];
  PetscCall(VecRestoreArrayRead(X, &x));
  PetscCall(VecRestoreArray(F, &f));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Trace RHS to mark on tape 1 the dependence of f upon x. This tape is used in generating the
  Jacobian transform.
*/
static PetscErrorCode RHSFunctionActive(TS ts, PetscReal t, Vec X, Vec F, PetscCtx ctx)
{
  User               user = (User)ctx;
  PetscReal          mu   = user->mu;
  PetscScalar       *f;
  const PetscScalar *x;

  adouble f_a[2]; /* adouble for dependent variables */
  adouble x_a[2]; /* adouble for independent variables */

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(X, &x));
  PetscCall(VecGetArray(F, &f));

  trace_on(1); /* Start of active section */
  x_a[0] <<= x[0];
  x_a[1] <<= x[1]; /* Mark as independent */
  f_a[0] = x_a[1];
  f_a[1] = mu * (1. - x_a[0] * x_a[0]) * x_a[1] - x_a[0];
  f_a[0] >>= f[0];
  f_a[1] >>= f[1]; /* Mark as dependent */
  trace_off(1);    /* End of active section */

  PetscCall(VecRestoreArrayRead(X, &x));
  PetscCall(VecRestoreArray(F, &f));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Compute the Jacobian w.r.t. x using PETSc-ADOL-C driver.
*/
static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec X, Mat A, Mat B, PetscCtx ctx)
{
  User               user = (User)ctx;
  const PetscScalar *x;

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(X, &x));
  PetscCall(PetscAdolcComputeRHSJacobian(1, A, x, user->adctx));
  PetscCall(VecRestoreArrayRead(X, &x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Monitor timesteps and use interpolation to output at integer multiples of 0.1
*/
static PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal t, Vec X, PetscCtx ctx)
{
  const PetscScalar *x;
  PetscReal          tfinal, dt, tprev;
  User               user = (User)ctx;

  PetscFunctionBeginUser;
  PetscCall(TSGetTimeStep(ts, &dt));
  PetscCall(TSGetMaxTime(ts, &tfinal));
  PetscCall(TSGetPrevTime(ts, &tprev));
  PetscCall(VecGetArrayRead(X, &x));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "[%.1f] %" PetscInt_FMT " TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n", (double)user->next_output, step, (double)t, (double)dt, (double)PetscRealPart(x[0]), (double)PetscRealPart(x[1])));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "t %.6f (tprev = %.6f) \n", (double)t, (double)tprev));
  PetscCall(VecGetArrayRead(X, &x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

int main(int argc, char **argv)
{
  TS             ts = NULL; /* nonlinear solver */
  Vec            ic, r;
  PetscBool      monitor = PETSC_FALSE;
  PetscScalar   *x_ptr;
  PetscMPIInt    size;
  struct _n_User user;
  AdolcCtx      *adctx;
  Tao            tao;
  KSP            ksp;
  PC             pc;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     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 and create AdolcCtx
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(PetscNew(&adctx));
  user.mu          = 1.0;
  user.next_output = 0.0;
  user.steps       = 0;
  user.ftime       = 0.5;
  adctx->m         = 2;
  adctx->n         = 2;
  adctx->p         = 2;
  user.adctx       = adctx;

  PetscCall(PetscOptionsGetReal(NULL, NULL, "-mu", &user.mu, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-monitor", &monitor, NULL));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Create necessary matrix and vectors, solve same ODE on every process
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatCreate(PETSC_COMM_WORLD, &user.A));
  PetscCall(MatSetSizes(user.A, PETSC_DECIDE, PETSC_DECIDE, 2, 2));
  PetscCall(MatSetFromOptions(user.A));
  PetscCall(MatSetUp(user.A));
  PetscCall(MatCreateVecs(user.A, &user.x, NULL));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(VecGetArray(user.x, &x_ptr));
  x_ptr[0] = 2.0;
  x_ptr[1] = 0.66666654321;
  PetscCall(VecRestoreArray(user.x, &x_ptr));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Trace just once on each tape and put zeros on Jacobian diagonal
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(VecDuplicate(user.x, &r));
  PetscCall(RHSFunctionActive(ts, 0., user.x, r, &user));
  PetscCall(VecSet(r, 0));
  PetscCall(MatDiagonalSet(user.A, r, INSERT_VALUES));
  PetscCall(VecDestroy(&r));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
  PetscCall(TSSetType(ts, TSRK));
  PetscCall(TSSetRHSFunction(ts, NULL, RHSFunctionPassive, &user));
  PetscCall(TSSetRHSJacobian(ts, user.A, user.A, RHSJacobian, &user));
  PetscCall(TSSetMaxTime(ts, user.ftime));
  PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
  if (monitor) PetscCall(TSMonitorSet(ts, Monitor, &user, NULL));

  PetscCall(TSSetTime(ts, 0.0));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "mu %g, steps %" PetscInt_FMT ", ftime %g\n", (double)user.mu, user.steps, (double)user.ftime));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Save trajectory of solution so that TSAdjointSolve() may be used
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetSaveTrajectory(ts));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set runtime options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetFromOptions(ts));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Solve nonlinear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSolve(ts, user.x));
  PetscCall(TSGetSolveTime(ts, &user.ftime));
  PetscCall(TSGetStepNumber(ts, &user.steps));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "mu %g, steps %" PetscInt_FMT ", ftime %g\n", (double)user.mu, user.steps, (double)user.ftime));

  PetscCall(VecGetArray(user.x, &x_ptr));
  user.x_ob[0] = x_ptr[0];
  user.x_ob[1] = x_ptr[1];
  PetscCall(VecRestoreArray(user.x, &x_ptr));

  PetscCall(MatCreateVecs(user.A, &user.lambda[0], NULL));

  /* Create TAO solver and set desired solution method */
  PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao));
  PetscCall(TaoSetType(tao, TAOCG));

  /* Set initial solution guess */
  PetscCall(MatCreateVecs(user.A, &ic, NULL));
  PetscCall(VecGetArray(ic, &x_ptr));
  x_ptr[0] = 2.1;
  x_ptr[1] = 0.7;
  PetscCall(VecRestoreArray(ic, &x_ptr));

  PetscCall(TaoSetSolution(tao, ic));

  /* Set routine for function and gradient evaluation */
  PetscCall(TaoSetObjectiveAndGradient(tao, NULL, FormFunctionGradient, (void *)&user));

  /* Check for any TAO command line options */
  PetscCall(TaoSetFromOptions(tao));
  PetscCall(TaoGetKSP(tao, &ksp));
  if (ksp) {
    PetscCall(KSPGetPC(ksp, &pc));
    PetscCall(PCSetType(pc, PCNONE));
  }

  PetscCall(TaoSetTolerances(tao, 1e-10, PETSC_CURRENT, PETSC_CURRENT));

  /* SOLVE THE APPLICATION */
  PetscCall(TaoSolve(tao));

  /* Free TAO data structures */
  PetscCall(TaoDestroy(&tao));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Free work space.  All PETSc objects should be destroyed when they
     are no longer needed.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatDestroy(&user.A));
  PetscCall(VecDestroy(&user.x));
  PetscCall(VecDestroy(&user.lambda[0]));
  PetscCall(TSDestroy(&ts));
  PetscCall(VecDestroy(&ic));
  PetscCall(PetscFree(adctx));
  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 IC, PetscReal *f, Vec G, PetscCtx ctx)
{
  User         user = (User)ctx;
  TS           ts;
  PetscScalar *x_ptr, *y_ptr;

  PetscFunctionBeginUser;
  PetscCall(VecCopy(IC, user->x));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
  PetscCall(TSSetType(ts, TSRK));
  PetscCall(TSSetRHSFunction(ts, NULL, RHSFunctionPassive, user));
  /*   Set RHS Jacobian  for the adjoint integration */
  PetscCall(TSSetRHSJacobian(ts, user->A, user->A, RHSJacobian, user));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set time
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetTime(ts, 0.0));
  PetscCall(TSSetTimeStep(ts, .001));
  PetscCall(TSSetMaxTime(ts, 0.5));
  PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));

  PetscCall(TSSetTolerances(ts, 1e-7, NULL, 1e-7, NULL));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Save trajectory of solution so that TSAdjointSolve() may be used
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetSaveTrajectory(ts));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set runtime options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetFromOptions(ts));

  PetscCall(TSSolve(ts, user->x));
  PetscCall(TSGetSolveTime(ts, &user->ftime));
  PetscCall(TSGetStepNumber(ts, &user->steps));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "mu %.6f, steps %" PetscInt_FMT ", ftime %g\n", (double)user->mu, user->steps, (double)user->ftime));

  PetscCall(VecGetArray(user->x, &x_ptr));
  *f = (x_ptr[0] - user->x_ob[0]) * (x_ptr[0] - user->x_ob[0]) + (x_ptr[1] - user->x_ob[1]) * (x_ptr[1] - user->x_ob[1]);
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Observed value y_ob=[%f; %f], ODE solution y=[%f;%f], Cost function f=%f\n", (double)user->x_ob[0], (double)user->x_ob[1], (double)x_ptr[0], (double)x_ptr[1], (double)(*f)));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Adjoint model starts here
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  /*   Redet initial conditions for the adjoint integration */
  PetscCall(VecGetArray(user->lambda[0], &y_ptr));
  y_ptr[0] = 2. * (x_ptr[0] - user->x_ob[0]);
  y_ptr[1] = 2. * (x_ptr[1] - user->x_ob[1]);
  PetscCall(VecRestoreArray(user->lambda[0], &y_ptr));
  PetscCall(VecRestoreArray(user->x, &x_ptr));
  PetscCall(TSSetCostGradients(ts, 1, user->lambda, NULL));

  PetscCall(TSAdjointSolve(ts));

  PetscCall(VecCopy(user->lambda[0], G));

  PetscCall(TSDestroy(&ts));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*TEST

  build:
    requires: double !complex adolc

  test:
    suffix: 1
    args: -ts_rhs_jacobian_test_mult_transpose FALSE -tao_max_it 2 -ts_rhs_jacobian_test_mult FALSE
    output_file: output/ex16opt_ic_1.out

TEST*/