static char help[] = "Demonstrates automatic Jacobian generation using ADOL-C for an adjoint sensitivity analysis of the van der Pol equation.\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 ex16adj for a description of the problem being solved.
  ------------------------------------------------------------------------- */

#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;
  PetscReal tprev;

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

/*
  '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;
  PetscScalar       *f;
  const PetscScalar *x;

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

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

  /* Start of active section */
  trace_on(1);
  x_a[0] <<= x[0];
  x_a[1] <<= x[1]; /* Mark independence */
  f_a[0] = x_a[1];
  f_a[1] = user->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 dependence */
  trace_off();
  /* End of active section */

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

/*
  Trace RHS again to mark on tape 2 the dependence of f upon the parameter mu. This tape is used in
  generating JacobianP.
*/
static PetscErrorCode RHSFunctionActiveP(TS ts, PetscReal t, Vec X, Vec F, PetscCtx ctx)
{
  User               user = (User)ctx;
  PetscScalar       *f;
  const PetscScalar *x;

  adouble f_a[2];       /* 'active' double for dependent variables */
  adouble x_a[2], mu_a; /* 'active' double for independent variables */

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

  /* Start of active section */
  trace_on(3);
  x_a[0] <<= x[0];
  x_a[1] <<= x[1];
  mu_a <<= user->mu; /* Mark independence */
  f_a[0] = x_a[1];
  f_a[1] = mu_a * (1. - x_a[0] * x_a[0]) * x_a[1] - x_a[0];
  f_a[0] >>= f[0];
  f_a[1] >>= f[1]; /* Mark dependence */
  trace_off();
  /* 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 for explicit TS.
*/
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);
}

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

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(X, &x));
  PetscCall(PetscAdolcComputeRHSJacobianP(3, A, x, &user->mu, 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(VecRestoreArrayRead(X, &x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

int main(int argc, char **argv)
{
  TS             ts;   /* nonlinear solver */
  Vec            x;    /* solution, residual vectors */
  Mat            A;    /* Jacobian matrix */
  Mat            Jacp; /* JacobianP matrix */
  PetscInt       steps;
  PetscReal      ftime   = 0.5;
  PetscBool      monitor = PETSC_FALSE;
  PetscScalar   *x_ptr;
  PetscMPIInt    size;
  struct _n_User user;
  AdolcCtx      *adctx;
  Vec            lambda[2], mu[2], r;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     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;
  user.next_output  = 0.0;
  adctx->m          = 2;
  adctx->n          = 2;
  adctx->p          = 2;
  adctx->num_params = 1;
  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, &A));
  PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, 2, 2));
  PetscCall(MatSetFromOptions(A));
  PetscCall(MatSetUp(A));
  PetscCall(MatCreateVecs(A, &x, NULL));

  PetscCall(MatCreate(PETSC_COMM_WORLD, &Jacp));
  PetscCall(MatSetSizes(Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1));
  PetscCall(MatSetFromOptions(Jacp));
  PetscCall(MatSetUp(Jacp));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
  PetscCall(TSSetType(ts, TSRK));
  PetscCall(TSSetRHSFunction(ts, NULL, RHSFunctionPassive, &user));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(VecGetArray(x, &x_ptr));
  x_ptr[0] = 2;
  x_ptr[1] = 0.66666654321;
  PetscCall(VecRestoreArray(x, &x_ptr));

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

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set RHS Jacobian for the adjoint integration
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetRHSJacobian(ts, A, A, RHSJacobian, &user));
  PetscCall(TSSetMaxTime(ts, ftime));
  PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
  if (monitor) PetscCall(TSMonitorSet(ts, Monitor, &user, NULL));
  PetscCall(TSSetTimeStep(ts, .001));

  /*
    Have the TS save its trajectory so that TSAdjointSolve() may be used
  */
  PetscCall(TSSetSaveTrajectory(ts));

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

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

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Start the Adjoint model
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatCreateVecs(A, &lambda[0], NULL));
  PetscCall(MatCreateVecs(A, &lambda[1], NULL));
  /*   Reset initial conditions for the adjoint integration */
  PetscCall(VecGetArray(lambda[0], &x_ptr));
  x_ptr[0] = 1.0;
  x_ptr[1] = 0.0;
  PetscCall(VecRestoreArray(lambda[0], &x_ptr));
  PetscCall(VecGetArray(lambda[1], &x_ptr));
  x_ptr[0] = 0.0;
  x_ptr[1] = 1.0;
  PetscCall(VecRestoreArray(lambda[1], &x_ptr));

  PetscCall(MatCreateVecs(Jacp, &mu[0], NULL));
  PetscCall(MatCreateVecs(Jacp, &mu[1], NULL));
  PetscCall(VecGetArray(mu[0], &x_ptr));
  x_ptr[0] = 0.0;
  PetscCall(VecRestoreArray(mu[0], &x_ptr));
  PetscCall(VecGetArray(mu[1], &x_ptr));
  x_ptr[0] = 0.0;
  PetscCall(VecRestoreArray(mu[1], &x_ptr));
  PetscCall(TSSetCostGradients(ts, 2, lambda, mu));

  /*   Set RHS JacobianP */
  PetscCall(TSSetRHSJacobianP(ts, Jacp, RHSJacobianP, &user));

  PetscCall(TSAdjointSolve(ts));

  PetscCall(VecView(lambda[0], PETSC_VIEWER_STDOUT_WORLD));
  PetscCall(VecView(lambda[1], PETSC_VIEWER_STDOUT_WORLD));
  PetscCall(VecView(mu[0], PETSC_VIEWER_STDOUT_WORLD));
  PetscCall(VecView(mu[1], PETSC_VIEWER_STDOUT_WORLD));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Free work space.  All PETSc objects should be destroyed when they
     are no longer needed.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatDestroy(&A));
  PetscCall(MatDestroy(&Jacp));
  PetscCall(VecDestroy(&x));
  PetscCall(VecDestroy(&lambda[0]));
  PetscCall(VecDestroy(&lambda[1]));
  PetscCall(VecDestroy(&mu[0]));
  PetscCall(VecDestroy(&mu[1]));
  PetscCall(TSDestroy(&ts));
  PetscCall(PetscFree(adctx));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

  build:
    requires: double !complex adolc

  test:
    suffix: 1
    args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor
    output_file: output/ex16adj_1.out

  test:
    suffix: 2
    args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor -mu 5
    output_file: output/ex16adj_2.out

  test:
    suffix: 3
    args: -ts_max_steps 10 -monitor
    output_file: output/ex16adj_3.out

  test:
    suffix: 4
    args: -ts_max_steps 10 -monitor -mu 5
    output_file: output/ex16adj_4.out

TEST*/