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 except the user provided functions take input values as a single vector instead of two vectors
*/

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

typedef struct {
  PetscReal  t;
  SNES       snes;
  Vec        UV, V;
  VecScatter scatterU, scatterV;
  PetscErrorCode (*f)(PetscReal, Vec, Vec);
  PetscErrorCode (*F)(PetscReal, Vec, Vec);
} AppCtx;

extern PetscErrorCode TSFunction(TS, PetscReal, Vec, Vec, void *);
extern PetscErrorCode SNESFunction(SNES, Vec, Vec, void *);

int main(int argc, char **argv)
{
  AppCtx      ctx;
  TS          ts;
  Vec         tsrhs, U;
  IS          is;
  PetscInt    i;
  PetscMPIInt rank;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
  PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
  PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
  PetscCall(TSSetType(ts, TSEULER));
  PetscCall(TSSetFromOptions(ts));
  PetscCall(VecCreateMPI(PETSC_COMM_WORLD, 1, PETSC_DETERMINE, &tsrhs));
  PetscCall(VecDuplicate(tsrhs, &U));
  PetscCall(TSSetRHSFunction(ts, tsrhs, TSFunction, &ctx));
  PetscCall(TSSetMaxTime(ts, 1.0));
  ctx.f = f;

  PetscCall(SNESCreate(PETSC_COMM_WORLD, &ctx.snes));
  PetscCall(SNESSetFromOptions(ctx.snes));
  PetscCall(SNESSetFunction(ctx.snes, NULL, SNESFunction, &ctx));
  PetscCall(SNESSetJacobian(ctx.snes, NULL, NULL, SNESComputeJacobianDefault, &ctx));
  ctx.F = F;
  PetscCall(VecCreateMPI(PETSC_COMM_WORLD, 1, PETSC_DETERMINE, &ctx.V));

  /* Create scatters to move between separate U and V representation and UV representation of solution */
  PetscCall(VecCreateMPI(PETSC_COMM_WORLD, 2, PETSC_DETERMINE, &ctx.UV));
  i = 2 * rank;
  PetscCall(ISCreateGeneral(PETSC_COMM_WORLD, 1, &i, PETSC_COPY_VALUES, &is));
  PetscCall(VecScatterCreate(U, NULL, ctx.UV, is, &ctx.scatterU));
  PetscCall(ISDestroy(&is));
  i = 2 * rank + 1;
  PetscCall(ISCreateGeneral(PETSC_COMM_WORLD, 1, &i, PETSC_COPY_VALUES, &is));
  PetscCall(VecScatterCreate(ctx.V, NULL, ctx.UV, is, &ctx.scatterV));
  PetscCall(ISDestroy(&is));

  PetscCall(VecSet(U, 1.0));
  PetscCall(TSSolve(ts, U));

  PetscCall(VecDestroy(&ctx.V));
  PetscCall(VecDestroy(&ctx.UV));
  PetscCall(VecScatterDestroy(&ctx.scatterU));
  PetscCall(VecScatterDestroy(&ctx.scatterV));
  PetscCall(VecDestroy(&tsrhs));
  PetscCall(VecDestroy(&U));
  PetscCall(SNESDestroy(&ctx.snes));
  PetscCall(TSDestroy(&ts));
  PetscCall(PetscFinalize());
  return 0;
}

/*
   Defines the RHS function that is passed to the time-integrator.

   Solves F(U,V) for V and then computes f(U,V)
*/
PetscErrorCode TSFunction(TS ts, PetscReal t, Vec U, Vec F, void *actx)
{
  AppCtx *ctx = (AppCtx *)actx;

  PetscFunctionBeginUser;
  ctx->t = t;
  PetscCall(VecScatterBegin(ctx->scatterU, U, ctx->UV, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(ctx->scatterU, U, ctx->UV, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(SNESSolve(ctx->snes, NULL, ctx->V));
  PetscCall(VecScatterBegin(ctx->scatterV, ctx->V, ctx->UV, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(ctx->scatterV, ctx->V, ctx->UV, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall((*ctx->f)(t, ctx->UV, F));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
   Defines the nonlinear function that is passed to the nonlinear solver

*/
PetscErrorCode SNESFunction(SNES snes, Vec V, Vec F, void *actx)
{
  AppCtx *ctx = (AppCtx *)actx;

  PetscFunctionBeginUser;
  PetscCall(VecScatterBegin(ctx->scatterV, V, ctx->UV, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(ctx->scatterV, V, ctx->UV, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall((*ctx->F)(ctx->t, ctx->UV, F));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*TEST

    test:
      args: -ts_monitor -ts_view

TEST*/