static char help[] = "Bratu nonlinear PDE in 2d.\n\
We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular\n\
domain, using distributed arrays (DAs) to partition the parallel grid.\n\
The command line options include:\n\
  -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
     problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)\n\n";

/*T
   Concepts: SNES^parallel Bratu example
   Concepts: DA^using distributed arrays;
   Concepts: IS coloirng types;
   Processors: n
T*/

/* ------------------------------------------------------------------------

    Solid Fuel Ignition (SFI) problem.  This problem is modeled by
    the partial differential equation
  
            -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
  
    with boundary conditions
   
             u = 0  for  x = 0, x = 1, y = 0, y = 1.
  
    A finite difference approximation with the usual 5-point stencil
    is used to discretize the boundary value problem to obtain a nonlinear 
    system of equations.

    Program usage:  mpiexec -np <procs> ex5 [-help] [all PETSc options] 
     e.g.,
      ./ex5 -fd_jacobian -mat_fd_coloring_view_draw -draw_pause -1
      mpiexec -np 2 ./ex5 -fd_jacobian_ghosted -log_summary

  ------------------------------------------------------------------------- */

/* 
   Include "petscda.h" so that we can use distributed arrays (DAs).
   Include "petscsnes.h" so that we can use SNES solvers.  Note that this
   file automatically includes:
     petsc.h       - base PETSc routines   petscvec.h - vectors
     petscsys.h    - system routines       petscmat.h - matrices
     petscis.h     - index sets            petscksp.h - Krylov subspace methods
     petscviewer.h - viewers               petscpc.h  - preconditioners
     petscksp.h   - linear solvers
*/
#include "petscda.h"
#include "petscsnes.h"

/* 
   User-defined application context - contains data needed by the 
   application-provided call-back routines, FormJacobianLocal() and
   FormFunctionLocal().
*/
typedef struct {
   DA          da;             /* distributed array data structure */
   PassiveReal param;          /* test problem parameter */
} AppCtx;

/* 
   User-defined routines
*/
extern PetscErrorCode FormInitialGuess(AppCtx*,Vec),FormFunctionMatlab(SNES,Vec,Vec,void*);
extern PetscErrorCode FormFunctionLocal(DALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*);
extern PetscErrorCode FormJacobianLocal(DALocalInfo*,PetscScalar**,Mat,AppCtx*);
extern PetscErrorCode MySNESDefaultComputeJacobianColor(SNES,Vec,Mat*,Mat*,MatStructure*,void*);

#undef __FUNCT__
#define __FUNCT__ "main"
int main(int argc,char **argv)
{
  SNES                   snes;                 /* nonlinear solver */
  Vec                    x,r;                  /* solution, residual vectors */
  Mat                    A,J;                    /* Jacobian matrix */
  AppCtx                 user;                 /* user-defined work context */
  PetscInt               its;                  /* iterations for convergence */
  PetscTruth             matlab_function = PETSC_FALSE;
  PetscTruth             fd_jacobian = PETSC_FALSE,adic_jacobian=PETSC_FALSE,fd_jacobian_ghosted=PETSC_FALSE;
  PetscTruth             adicmf_jacobian = PETSC_FALSE;
  PetscErrorCode         ierr;
  PetscReal              bratu_lambda_max = 6.81,bratu_lambda_min = 0.;
  MatFDColoring          matfdcoloring = 0;
  ISColoring             iscoloring;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize program
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  PetscInitialize(&argc,&argv,(char *)0,help);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize problem parameters
  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  user.param = 6.0;
  ierr = PetscOptionsGetReal(PETSC_NULL,"-par",&user.param,PETSC_NULL);CHKERRQ(ierr);
  if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) {
    SETERRQ(1,"Lambda is out of range");
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create nonlinear solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create distributed array (DA) to manage parallel grid and vectors
  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,-4,-4,PETSC_DECIDE,PETSC_DECIDE,
                    1,1,PETSC_NULL,PETSC_NULL,&user.da);CHKERRQ(ierr);

  /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Extract global vectors from DA; then duplicate for remaining
     vectors that are the same types
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = DACreateGlobalVector(user.da,&x);CHKERRQ(ierr);
  ierr = VecDuplicate(x,&r);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create matrix data structure; set Jacobian evaluation routine

     Set Jacobian matrix data structure and default Jacobian evaluation
     routine. User can override with:
     -snes_mf : matrix-free Newton-Krylov method with no preconditioning
                (unless user explicitly sets preconditioner) 
     -snes_mf_operator : form preconditioning matrix as set by the user,
                         but use matrix-free approx for Jacobian-vector
                         products within Newton-Krylov method

     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  /* J can be type of MATAIJ,MATBAIJ or MATSBAIJ */
  ierr = DAGetMatrix(user.da,MATAIJ,&J);CHKERRQ(ierr);
  
  A    = J;
  ierr = PetscOptionsGetTruth(PETSC_NULL,"-fd_jacobian",&fd_jacobian,0);CHKERRQ(ierr);
  ierr = PetscOptionsGetTruth(PETSC_NULL,"-fd_jacobian_ghosted",&fd_jacobian_ghosted,0);CHKERRQ(ierr);
  ierr = PetscOptionsGetTruth(PETSC_NULL,"-adic_jacobian",&adic_jacobian,0);CHKERRQ(ierr);
  ierr = PetscOptionsGetTruth(PETSC_NULL,"-adicmf_jacobian",&adicmf_jacobian,0);CHKERRQ(ierr);
#if defined(PETSC_HAVE_ADIC)
  if (adicmf_jacobian) {
    ierr = DASetLocalAdicMFFunction(user.da,admf_FormFunctionLocal);CHKERRQ(ierr);
    ierr = MatRegisterDAAD();CHKERRQ(ierr);
    ierr = MatCreateDAAD(user.da,&A);CHKERRQ(ierr);
    ierr = MatDAADSetSNES(A,snes);CHKERRQ(ierr);
    ierr = MatDAADSetCtx(A,&user);CHKERRQ(ierr);
  }    
#endif

  if (fd_jacobian) {
    ierr = DAGetColoring(user.da,IS_COLORING_GLOBAL,&iscoloring);CHKERRQ(ierr);
    ierr = MatFDColoringCreate(J,iscoloring,&matfdcoloring);CHKERRQ(ierr);
    ierr = ISColoringDestroy(iscoloring);CHKERRQ(ierr);
    ierr = MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESDAFormFunction,&user);CHKERRQ(ierr);
    ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);
    ierr = SNESSetJacobian(snes,A,J,SNESDefaultComputeJacobianColor,matfdcoloring);CHKERRQ(ierr);
  } else if (fd_jacobian_ghosted) {
    ierr = DAGetColoring(user.da,IS_COLORING_GHOSTED,&iscoloring);CHKERRQ(ierr);
    ierr = MatFDColoringCreate(J,iscoloring,&matfdcoloring);CHKERRQ(ierr);
    ierr = ISColoringDestroy(iscoloring);CHKERRQ(ierr);
    ierr = MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESDAFormFunction,&user);CHKERRQ(ierr);
    ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);
    /* now, call a customized SNESDefaultComputeJacobianColor() */
    ierr = SNESSetJacobian(snes,A,J,MySNESDefaultComputeJacobianColor,matfdcoloring);CHKERRQ(ierr);
#if defined(PETSC_HAVE_ADIC)
  } else if (adic_jacobian) {
    ierr = DAGetColoring(user.da,IS_COLORING_GHOSTED,&iscoloring);CHKERRQ(ierr);
    ierr = MatSetColoring(J,iscoloring);CHKERRQ(ierr);
    ierr = ISColoringDestroy(iscoloring);CHKERRQ(ierr);
    ierr = SNESSetJacobian(snes,A,J,SNESDAComputeJacobianWithAdic,&user);CHKERRQ(ierr);
#endif
  } else {
    ierr = SNESSetJacobian(snes,A,J,SNESDAComputeJacobian,&user);CHKERRQ(ierr);
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set local function evaluation routine
  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = DASetLocalFunction(user.da,(DALocalFunction1)FormFunctionLocal);CHKERRQ(ierr);
  ierr = DASetLocalJacobian(user.da,(DALocalFunction1)FormJacobianLocal);CHKERRQ(ierr); 
  ierr = DASetLocalAdicFunction(user.da,ad_FormFunctionLocal);CHKERRQ(ierr);

  /* Decide which FormFunction to use */
  ierr = PetscOptionsGetTruth(PETSC_NULL,"-matlab_function",&matlab_function,0);CHKERRQ(ierr);

  ierr = SNESSetFunction(snes,r,SNESDAFormFunction,&user);CHKERRQ(ierr);
#if defined(PETSC_HAVE_MATLAB_ENGINE)
  if (matlab_function) {
    ierr = SNESSetFunction(snes,r,FormFunctionMatlab,&user);CHKERRQ(ierr);
  }
#endif

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Customize nonlinear solver; set runtime options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Evaluate initial guess
     Note: The user should initialize the vector, x, with the initial guess
     for the nonlinear solver prior to calling SNESSolve().  In particular,
     to employ an initial guess of zero, the user should explicitly set
     this vector to zero by calling VecSet().
  */
  ierr = FormInitialGuess(&user,x);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Solve nonlinear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = SNESSolve(snes,PETSC_NULL,x);CHKERRQ(ierr); 
  ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = PetscPrintf(PETSC_COMM_WORLD,"Number of Newton iterations = %D\n",its);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Free work space.  All PETSc objects should be destroyed when they
     are no longer needed.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  if (A != J) {
    ierr = MatDestroy(A);CHKERRQ(ierr);
  }
  ierr = MatDestroy(J);CHKERRQ(ierr);
  if (matfdcoloring) {
    ierr = MatFDColoringDestroy(matfdcoloring);CHKERRQ(ierr);
  }
  ierr = VecDestroy(x);CHKERRQ(ierr);
  ierr = VecDestroy(r);CHKERRQ(ierr);      
  ierr = SNESDestroy(snes);CHKERRQ(ierr);
  ierr = DADestroy(user.da);CHKERRQ(ierr);
  ierr = PetscFinalize();CHKERRQ(ierr);

  PetscFunctionReturn(0);
}
/* ------------------------------------------------------------------- */
#undef __FUNCT__
#define __FUNCT__ "FormInitialGuess"
/* 
   FormInitialGuess - Forms initial approximation.

   Input Parameters:
   user - user-defined application context
   X - vector

   Output Parameter:
   X - vector
 */
PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
{
  PetscInt       i,j,Mx,My,xs,ys,xm,ym;
  PetscErrorCode ierr;
  PetscReal      lambda,temp1,temp,hx,hy;
  PetscScalar    **x;

  PetscFunctionBegin;
  ierr = DAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
                   PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

  lambda = user->param;
  hx     = 1.0/(PetscReal)(Mx-1);
  hy     = 1.0/(PetscReal)(My-1);
  temp1  = lambda/(lambda + 1.0);

  /*
     Get a pointer to vector data.
       - For default PETSc vectors, VecGetArray() returns a pointer to
         the data array.  Otherwise, the routine is implementation dependent.
       - You MUST call VecRestoreArray() when you no longer need access to
         the array.
  */
  ierr = DAVecGetArray(user->da,X,&x);CHKERRQ(ierr);

  /*
     Get local grid boundaries (for 2-dimensional DA):
       xs, ys   - starting grid indices (no ghost points)
       xm, ym   - widths of local grid (no ghost points)

  */
  ierr = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL);CHKERRQ(ierr);

  /*
     Compute initial guess over the locally owned part of the grid
  */
  for (j=ys; j<ys+ym; j++) {
    temp = (PetscReal)(PetscMin(j,My-j-1))*hy;
    for (i=xs; i<xs+xm; i++) {
      if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
        /* boundary conditions are all zero Dirichlet */
        x[j][i] = 0.0; 
      } else {
        x[j][i] = temp1*sqrt(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,temp)); 
      }
    }
  }

  /*
     Restore vector
  */
  ierr = DAVecRestoreArray(user->da,X,&x);CHKERRQ(ierr);

  PetscFunctionReturn(0);
} 
/* ------------------------------------------------------------------- */
#undef __FUNCT__
#define __FUNCT__ "FormFunctionLocal"
/* 
   FormFunctionLocal - Evaluates nonlinear function, F(x).

       Process adiC(36): FormFunctionLocal

 */
PetscErrorCode FormFunctionLocal(DALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
{
  PetscErrorCode ierr;
  PetscInt       i,j;
  PetscReal      lambda,hx,hy,hxdhy,hydhx,sc;
  PetscScalar    u,uxx,uyy;

  PetscFunctionBegin;

  lambda = user->param;
  hx     = 1.0/(PetscReal)(info->mx-1);
  hy     = 1.0/(PetscReal)(info->my-1);
  sc     = hx*hy*lambda;
  hxdhy  = hx/hy; 
  hydhx  = hy/hx;
  /*
     Compute function over the locally owned part of the grid
  */
  for (j=info->ys; j<info->ys+info->ym; j++) {
    for (i=info->xs; i<info->xs+info->xm; i++) {
      if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
        f[j][i] = x[j][i];
      } else {
        u       = x[j][i];
        uxx     = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx;
        uyy     = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy;
        f[j][i] = uxx + uyy - sc*PetscExpScalar(u);
      }
    }
  }

  ierr = PetscLogFlops(11*info->ym*info->xm);CHKERRQ(ierr);
  PetscFunctionReturn(0); 
} 

#undef __FUNCT__
#define __FUNCT__ "FormJacobianLocal"
/*
   FormJacobianLocal - Evaluates Jacobian matrix.
*/
PetscErrorCode FormJacobianLocal(DALocalInfo *info,PetscScalar **x,Mat jac,AppCtx *user)
{
  PetscErrorCode ierr;
  PetscInt       i,j;
  MatStencil     col[5],row;
  PetscScalar    lambda,v[5],hx,hy,hxdhy,hydhx,sc;

  PetscFunctionBegin;
  lambda = user->param;
  hx     = 1.0/(PetscReal)(info->mx-1);
  hy     = 1.0/(PetscReal)(info->my-1);
  sc     = hx*hy*lambda;
  hxdhy  = hx/hy; 
  hydhx  = hy/hx;


  /* 
     Compute entries for the locally owned part of the Jacobian.
      - Currently, all PETSc parallel matrix formats are partitioned by
        contiguous chunks of rows across the processors. 
      - Each processor needs to insert only elements that it owns
        locally (but any non-local elements will be sent to the
        appropriate processor during matrix assembly). 
      - Here, we set all entries for a particular row at once.
      - We can set matrix entries either using either
        MatSetValuesLocal() or MatSetValues(), as discussed above.
  */
  for (j=info->ys; j<info->ys+info->ym; j++) {
    for (i=info->xs; i<info->xs+info->xm; i++) {
      row.j = j; row.i = i;
      /* boundary points */
      if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
        v[0] = 1.0;
        ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
      } else {
      /* interior grid points */
        v[0] = -hxdhy;                                           col[0].j = j - 1; col[0].i = i;
        v[1] = -hydhx;                                           col[1].j = j;     col[1].i = i-1;
        v[2] = 2.0*(hydhx + hxdhy) - sc*PetscExpScalar(x[j][i]); col[2].j = row.j; col[2].i = row.i;
        v[3] = -hydhx;                                           col[3].j = j;     col[3].i = i+1;
        v[4] = -hxdhy;                                           col[4].j = j + 1; col[4].i = i;
        ierr = MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
      }
    }
  }

  /* 
     Assemble matrix, using the 2-step process:
       MatAssemblyBegin(), MatAssemblyEnd().
  */
  ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  /*
     Tell the matrix we will never add a new nonzero location to the
     matrix. If we do, it will generate an error.
  */
  ierr = MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*
      Variant of FormFunction() that computes the function in Matlab
*/
#if defined(PETSC_HAVE_MATLAB_ENGINE)
PetscErrorCode FormFunctionMatlab(SNES snes,Vec X,Vec F,void *ptr)
{
  AppCtx         *user = (AppCtx*)ptr;
  PetscErrorCode ierr;
  PetscInt       Mx,My;
  PetscReal      lambda,hx,hy;
  Vec            localX,localF;
  MPI_Comm       comm;

  PetscFunctionBegin;
  ierr = DAGetLocalVector(user->da,&localX);CHKERRQ(ierr);
  ierr = DAGetLocalVector(user->da,&localF);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)localX,"localX");CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)localF,"localF");CHKERRQ(ierr);
  ierr = DAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
                   PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

  lambda = user->param;
  hx     = 1.0/(PetscReal)(Mx-1);
  hy     = 1.0/(PetscReal)(My-1);

  ierr = PetscObjectGetComm((PetscObject)snes,&comm);CHKERRQ(ierr);
  /*
     Scatter ghost points to local vector,using the 2-step process
        DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
     By placing code between these two statements, computations can be
     done while messages are in transition.
  */
  ierr = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
  ierr = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
  ierr = PetscMatlabEnginePut(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localX);CHKERRQ(ierr);
  ierr = PetscMatlabEngineEvaluate(PETSC_MATLAB_ENGINE_(comm),"localF=ex5m(localX,%18.16e,%18.16e,%18.16e)",hx,hy,lambda);CHKERRQ(ierr);
  ierr = PetscMatlabEngineGet(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localF);CHKERRQ(ierr);

  /*
     Insert values into global vector
  */
  ierr = DALocalToGlobal(user->da,localF,INSERT_VALUES,F);CHKERRQ(ierr);
  ierr = DARestoreLocalVector(user->da,&localX);CHKERRQ(ierr);
  ierr = DARestoreLocalVector(user->da,&localF);CHKERRQ(ierr);
  PetscFunctionReturn(0); 
} 
#endif

#undef __FUNCT__
#define __FUNCT__ "MySNESDefaultComputeJacobianColor"
/*
  MySNESDefaultComputeJacobianColor - Computes the Jacobian using
    finite differences and coloring to exploit matrix sparsity. 
    It is customized from SNESDefaultComputeJacobianColor.
    The input global vector x1 is scattered to x1_local
    which then is passed into MatFDColoringApply() for reducing the
    VecScatterBingin/End.
*/
PetscErrorCode MySNESDefaultComputeJacobianColor(SNES snes,Vec x1,Mat *J,Mat *B,MatStructure *flag,void *ctx)
{
  MatFDColoring  color = (MatFDColoring) ctx;
  PetscErrorCode ierr;
  PetscInt       freq,it;
  Vec            f;
  PetscErrorCode (*ff)(void),(*fd)(void);
  void           *fctx;
  DA             da;
  Vec            x1_loc;

  PetscFunctionBegin;
  ierr = MatFDColoringGetFrequency(color,&freq);CHKERRQ(ierr);
  ierr = SNESGetIterationNumber(snes,&it);CHKERRQ(ierr);

  if ((freq > 1) && ((it % freq))) {
    ierr = PetscInfo2(color,"Skipping Jacobian recomputation, it %D, freq %D\n",it,freq);CHKERRQ(ierr);
    *flag = SAME_PRECONDITIONER;
  } else {
    ierr = PetscInfo2(color,"Computing Jacobian, it %D, freq %D\n",it,freq);CHKERRQ(ierr);
    *flag = SAME_NONZERO_PATTERN;
    ierr  = SNESGetFunction(snes,&f,(PetscErrorCode (**)(SNES,Vec,Vec,void*))&ff,0);CHKERRQ(ierr);
    ierr  = MatFDColoringGetFunction(color,&fd,&fctx);CHKERRQ(ierr);
    if (fd == ff) { /* reuse function value computed in SNES */
      ierr  = MatFDColoringSetF(color,f);CHKERRQ(ierr);
    }
    /* Now, get x1_loc and scatter global x1 onto x1_loc */ 
    da = *(DA*)fctx;
    ierr = DAGetLocalVector(da,&x1_loc);CHKERRQ(ierr); 
    ierr = DAGlobalToLocalBegin(da,x1,INSERT_VALUES,x1_loc);CHKERRQ(ierr); 
    ierr = DAGlobalToLocalEnd(da,x1,INSERT_VALUES,x1_loc);CHKERRQ(ierr);   
    ierr  = MatFDColoringApply(*B,color,x1_loc,flag,snes);CHKERRQ(ierr);   
    ierr = DARestoreLocalVector(da,&x1_loc);CHKERRQ(ierr);
  }
  if (*J != *B) {
    ierr = MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}