static char help[] = "Solves DAE with integrator only on non-algebraic terms \n";

#include <petscts.h>

/*
        \dot{U} = f(U,V)
        F(U,V)  = 0

    Same as ex6.c and ex7.c except calls the TSROSW integrator on the entire DAE
*/

/*
   f(U,V) = U + V

*/
PetscErrorCode f(PetscReal t, Vec UV, Vec F)
{
  const PetscScalar *u, *v;
  PetscScalar       *f;
  PetscInt           n, i;

  PetscFunctionBeginUser;
  PetscCall(VecGetLocalSize(UV, &n));
  n = n / 2;
  PetscCall(VecGetArrayRead(UV, &u));
  v = u + n;
  PetscCall(VecGetArrayWrite(F, &f));
  for (i = 0; i < n; i++) f[i] = u[i] + v[i];
  PetscCall(VecRestoreArrayRead(UV, &u));
  PetscCall(VecRestoreArrayWrite(F, &f));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
   F(U,V) = U - V

*/
PetscErrorCode F(PetscReal t, Vec UV, Vec F)
{
  const PetscScalar *u, *v;
  PetscScalar       *f;
  PetscInt           n, i;

  PetscFunctionBeginUser;
  PetscCall(VecGetLocalSize(UV, &n));
  n = n / 2;
  PetscCall(VecGetArrayRead(UV, &u));
  v = u + n;
  PetscCall(VecGetArrayWrite(F, &f));
  f = f + n;
  for (i = 0; i < n; i++) f[i] = u[i] - v[i];
  f = f - n;
  PetscCall(VecRestoreArrayRead(UV, &u));
  PetscCall(VecRestoreArrayWrite(F, &f));
  PetscFunctionReturn(PETSC_SUCCESS);
}

typedef struct {
  PetscErrorCode (*f)(PetscReal, Vec, Vec);
  PetscErrorCode (*F)(PetscReal, Vec, Vec);
} AppCtx;

extern PetscErrorCode TSFunctionRHS(TS, PetscReal, Vec, Vec, void *);
extern PetscErrorCode TSFunctionI(TS, PetscReal, Vec, Vec, Vec, void *);

int main(int argc, char **argv)
{
  AppCtx ctx;
  TS     ts;
  Vec    tsrhs, UV;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));
  PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
  PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
  PetscCall(TSSetType(ts, TSROSW));
  PetscCall(TSSetFromOptions(ts));
  PetscCall(VecCreateMPI(PETSC_COMM_WORLD, 2, PETSC_DETERMINE, &tsrhs));
  PetscCall(VecDuplicate(tsrhs, &UV));
  PetscCall(TSSetRHSFunction(ts, tsrhs, TSFunctionRHS, &ctx));
  PetscCall(TSSetIFunction(ts, NULL, TSFunctionI, &ctx));
  PetscCall(TSSetMaxTime(ts, 1.0));
  ctx.f = f;
  ctx.F = F;

  PetscCall(VecSet(UV, 1.0));
  PetscCall(TSSolve(ts, UV));
  PetscCall(VecDestroy(&tsrhs));
  PetscCall(VecDestroy(&UV));
  PetscCall(TSDestroy(&ts));
  PetscCall(PetscFinalize());
  return 0;
}

/*
   Defines the RHS function that is passed to the time-integrator.
*/
PetscErrorCode TSFunctionRHS(TS ts, PetscReal t, Vec UV, Vec F, void *actx)
{
  AppCtx *ctx = (AppCtx *)actx;

  PetscFunctionBeginUser;
  PetscCall(VecSet(F, 0.0));
  PetscCall((*ctx->f)(t, UV, F));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
   Defines the nonlinear function that is passed to the time-integrator
*/
PetscErrorCode TSFunctionI(TS ts, PetscReal t, Vec UV, Vec UVdot, Vec F, void *actx)
{
  AppCtx *ctx = (AppCtx *)actx;

  PetscFunctionBeginUser;
  PetscCall(VecCopy(UVdot, F));
  PetscCall((*ctx->F)(t, UV, F));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*TEST

    test:
      args: -ts_view

    test:
      suffix: 2
      args: -snes_lag_jacobian 2 -ts_view

TEST*/