static char help[] = "Test TSComputeIJacobian()\n\n";

#include <petscsys.h>
#include <petscdm.h>
#include <petscdmda.h>
#include <petscts.h>

typedef struct {
  PetscScalar u,v;
} Field;

typedef struct {
  PetscReal D1,D2,gamma,kappa;
} AppCtx;

PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat BB,void *ctx)
{
  AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */
  DM             da;
  PetscInt       i,j,Mx,My,xs,ys,xm,ym;
  PetscReal      hx,hy,sx,sy;
  PetscScalar    uc,vc;
  Field          **u;
  Vec            localU;
  MatStencil     stencil[6],rowstencil;
  PetscScalar    entries[6];

  PetscFunctionBegin;
  CHKERRQ(TSGetDM(ts,&da));
  CHKERRQ(DMGetLocalVector(da,&localU));
  CHKERRQ(DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE));

  hx = 2.50/(PetscReal)Mx; sx = 1.0/(hx*hx);
  hy = 2.50/(PetscReal)My; sy = 1.0/(hy*hy);

  /*
     Scatter ghost points to local vector,using the 2-step process
        DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
     By placing code between these two statements, computations can be
     done while messages are in transition.
  */
  CHKERRQ(DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU));
  CHKERRQ(DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU));

  /*
     Get pointers to vector data
  */
  CHKERRQ(DMDAVecGetArrayRead(da,localU,&u));

  /*
     Get local grid boundaries
  */
  CHKERRQ(DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL));

  stencil[0].k = 0;
  stencil[1].k = 0;
  stencil[2].k = 0;
  stencil[3].k = 0;
  stencil[4].k = 0;
  stencil[5].k = 0;
  rowstencil.k = 0;
  /*
     Compute function over the locally owned part of the grid
  */
  for (j=ys; j<ys+ym; j++) {

    stencil[0].j = j-1;
    stencil[1].j = j+1;
    stencil[2].j = j;
    stencil[3].j = j;
    stencil[4].j = j;
    stencil[5].j = j;
    rowstencil.k = 0; rowstencil.j = j;
    for (i=xs; i<xs+xm; i++) {
      uc = u[j][i].u;
      vc = u[j][i].v;

      /*      uxx       = (-2.0*uc + u[j][i-1].u + u[j][i+1].u)*sx;
      uyy       = (-2.0*uc + u[j-1][i].u + u[j+1][i].u)*sy;

      vxx       = (-2.0*vc + u[j][i-1].v + u[j][i+1].v)*sx;
      vyy       = (-2.0*vc + u[j-1][i].v + u[j+1][i].v)*sy;
       f[j][i].u = appctx->D1*(uxx + uyy) - uc*vc*vc + appctx->gamma*(1.0 - uc);*/

      stencil[0].i = i; stencil[0].c = 0; entries[0] = appctx->D1*sy;
      stencil[1].i = i; stencil[1].c = 0; entries[1] = appctx->D1*sy;
      stencil[2].i = i-1; stencil[2].c = 0; entries[2] = appctx->D1*sx;
      stencil[3].i = i+1; stencil[3].c = 0; entries[3] = appctx->D1*sx;
      stencil[4].i = i; stencil[4].c = 0; entries[4] = -2.0*appctx->D1*(sx + sy) - vc*vc - appctx->gamma;
      stencil[5].i = i; stencil[5].c = 1; entries[5] = -2.0*uc*vc;
      rowstencil.i = i; rowstencil.c = 0;

      CHKERRQ(MatSetValuesStencil(A,1,&rowstencil,6,stencil,entries,INSERT_VALUES));
      stencil[0].c = 1; entries[0] = appctx->D2*sy;
      stencil[1].c = 1; entries[1] = appctx->D2*sy;
      stencil[2].c = 1; entries[2] = appctx->D2*sx;
      stencil[3].c = 1; entries[3] = appctx->D2*sx;
      stencil[4].c = 1; entries[4] = -2.0*appctx->D2*(sx + sy) + 2.0*uc*vc - appctx->gamma - appctx->kappa;
      stencil[5].c = 0; entries[5] = vc*vc;
      rowstencil.c = 1;

      CHKERRQ(MatSetValuesStencil(A,1,&rowstencil,6,stencil,entries,INSERT_VALUES));
      /* f[j][i].v = appctx->D2*(vxx + vyy) + uc*vc*vc - (appctx->gamma + appctx->kappa)*vc; */
    }
  }

  /*
     Restore vectors
  */
  CHKERRQ(PetscLogFlops(19*xm*ym));
  CHKERRQ(DMDAVecRestoreArrayRead(da,localU,&u));
  CHKERRQ(DMRestoreLocalVector(da,&localU));
  CHKERRQ(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
  CHKERRQ(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
  CHKERRQ(MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE));
  PetscFunctionReturn(0);
}

PetscErrorCode InitialConditions(DM da,Vec U)
{
  PetscInt       i,j,xs,ys,xm,ym,Mx,My;
  Field          **u;
  PetscReal      hx,hy,x,y;

  PetscFunctionBegin;
  CHKERRQ(DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE));

  hx = 2.5/(PetscReal)Mx;
  hy = 2.5/(PetscReal)My;

  /*
     Get pointers to vector data
  */
  CHKERRQ(DMDAVecGetArray(da,U,&u));

  /*
     Get local grid boundaries
  */
  CHKERRQ(DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL));

  /*
     Compute function over the locally owned part of the grid
  */
  for (j=ys; j<ys+ym; j++) {
    y = j*hy;
    for (i=xs; i<xs+xm; i++) {
      x = i*hx;
      if ((1.0 <= x) && (x <= 1.5) && (1.0 <= y) && (y <= 1.5)) u[j][i].v = .25*PetscPowReal(PetscSinReal(4.0*PETSC_PI*x),2.0)*PetscPowReal(PetscSinReal(4.0*PETSC_PI*y),2.0);
      else u[j][i].v = 0.0;

      u[j][i].u = 1.0 - 2.0*u[j][i].v;
    }
  }

  /*
     Restore vectors
  */
  CHKERRQ(DMDAVecRestoreArray(da,U,&u));
  PetscFunctionReturn(0);
}

int main(int argc,char **argv)
{
  TS             ts;
  Vec            U,Udot;
  Mat            Jac,Jac2;
  DM             da;
  AppCtx         appctx;
  PetscReal      t = 0,shift,norm;
  PetscErrorCode ierr;

  ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

  appctx.D1    = 8.0e-5;
  appctx.D2    = 4.0e-5;
  appctx.gamma = .024;
  appctx.kappa = .06;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create distributed array (DMDA) to manage parallel grid and vectors
  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,DMDA_STENCIL_STAR,64,64,PETSC_DECIDE,PETSC_DECIDE,2,1,NULL,NULL,&da));
  CHKERRQ(DMSetFromOptions(da));
  CHKERRQ(DMSetUp(da));
  CHKERRQ(DMDASetFieldName(da,0,"u"));
  CHKERRQ(DMDASetFieldName(da,1,"v"));
  CHKERRQ(DMSetMatType(da,MATAIJ));
  CHKERRQ(DMCreateMatrix(da,&Jac));
  CHKERRQ(DMCreateMatrix(da,&Jac2));

  /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Extract global vectors from DMDA; then duplicate for remaining
     vectors that are the same types
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(DMCreateGlobalVector(da,&U));
  CHKERRQ(VecDuplicate(U,&Udot));
  CHKERRQ(VecSet(Udot,0.0));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(TSCreate(PETSC_COMM_WORLD,&ts));
  CHKERRQ(TSSetDM(ts,da));
  CHKERRQ(TSSetProblemType(ts,TS_NONLINEAR));
  CHKERRQ(TSSetRHSJacobian(ts,Jac,Jac,RHSJacobian,&appctx));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(InitialConditions(da,U));
  CHKERRQ(TSSetSolution(ts,U));
  CHKERRQ(TSSetFromOptions(ts));
  CHKERRQ(TSSetUp(ts));

  shift = 2.;
  CHKERRQ(TSComputeIJacobian(ts,t,U,Udot,shift,Jac2,Jac2,PETSC_FALSE));
  shift = 1.;
  CHKERRQ(TSComputeIJacobian(ts,t,U,Udot,shift,Jac,Jac,PETSC_FALSE));
  shift = 2.;
  CHKERRQ(TSComputeIJacobian(ts,t,U,Udot,shift,Jac,Jac,PETSC_FALSE));
  CHKERRQ(MatAXPY(Jac,-1,Jac2,SAME_NONZERO_PATTERN));
  CHKERRQ(MatNorm(Jac,NORM_INFINITY,&norm));
  if (norm > 100.0*PETSC_MACHINE_EPSILON) {
    CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"Error Norm %g \n Incorrect behaviour of TSComputeIJacobian(). The two matrices should have the same results.\n",norm));
  }
  CHKERRQ(MatDestroy(&Jac));
  CHKERRQ(MatDestroy(&Jac2));
  CHKERRQ(VecDestroy(&U));
  CHKERRQ(VecDestroy(&Udot));
  CHKERRQ(TSDestroy(&ts));
  CHKERRQ(DMDestroy(&da));
  ierr = PetscFinalize();
  return(ierr);
}

/*TEST
  test:

TEST*/