    /*$Id: eptorsion.c, v 1.1 2002/08/08 10:30 lopezca@mauddib.mcs.anl.gov $*/

    /* Program usage: mpirun -np <proc> eptorsion [-help] [all TAO options] */

    /*
      Include "tao.h" so we can use TAO solvers.
      petscda.h for distributed array
      ad_deriv.h for AD gradient
    */

    #include "petscda.h"
    #include "tao.h"
    #include "taodaapplication.h"

    static char help[] = "This example is based on the Elastic-Plastic Torsion (dept)\n\
    problem from the MINPACK-2 test suite.\n\
    The command line options are:\n\
      -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction\n\
      -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction\n\
      -nlevels <nlevels>, where <nlevels> = number of levels in multigrid\n\
      -byelement, if computation is made by functions on rectangular elements\n\
      -adic, if AD is used (AD is not used by default)\n\
      -u1 <u1>, where <u1> = upper limit in the 1st coordinate direction\n\
      -u2 <u2>, where <u2> = upper limit in the 2nd coordinate direction\n\
      -par <param>, where <param> = angle of twist per unit length\n\n";

    /*T
       Concepts: TAO - Solving a bounded minimization problem
       Routines: TaoInitialize(); TaoFinalize();
       Routines: TaoCreate(); TaoDestroy();
       Routines: DAApplicationCreate(); DAApplicationDestroy();
       Routines: DAAppSetVariableBoundsRoutine();
       Routines: DAAppSetElementObjectiveAndGradientRoutine();
       Routines: DAAppSetElementHessianRoutine();
       Routines: DAAppSetObjectiveAndGradientRoutine();
       Routines: DAAppSetADElementFunctionGradient();
       Routines: DAAppSetHessianRoutine();
       Routines: TaoSetOptions();
       Routines: TaoGetSolutionStatus(); TaoDAAppSolve();
       Routines: DAAppSetMonitor(); TaoView();
       Routines: DAAppGetSolution();
       Routines: DAAppGetInterpolationMatrix();
       Processors: n
    T*/

    /*
       User-defined application context - contains data needed by the
       application-provided call-back routines.
    */
    typedef struct {
      InactiveDouble      param;
      InactiveDouble      hx, hy;        /* increment size in both directions */
      InactiveDouble      area;          /* area of the triangles */
    } ADFGCtx;

    typedef struct {
      PetscReal      param;          /* 'c' parameter */
      PetscReal      u1, u2;         /* domain upper limits (lower limits = 0) */
      double      hx, hy;        /* increment size in both directions */
      double      area;          /* area of the triangles */
      ADFGCtx     fgctx;         /* Used only when an ADIC generated gradient is used */
    } AppCtx;
    int ad_EPTorsLocalFunction(int[2], DERIV_TYPE[4], DERIV_TYPE*, void*);

    /* User-defined routines found in this file */
    static int AppCtxInitialize(void *ptr);
    static int FormInitialGuess(DA, Vec);

    static int EPTorsLocalFunctionGradient(int[2], double x[4], double *f, double g[4], void *ptr);
    static int EPTorsLocalHessian(int[2], double x[4], double H[4][4], void *ptr);

    static int WholeEPTorsFunctionGradient(TAO_APPLICATION,DA,Vec,double *,Vec,void*);
    static int WholeEPTorsHessian(TAO_APPLICATION,DA,Vec,Mat,void*);

    static int DASetBounds(TAO_APPLICATION, DA, Vec, Vec, void*);

    static int MyGridMonitorBefore(TAO_APPLICATION, DA, int, void *);

    #undef __FUNCT__
    #define __FUNCT__ "main"

    int main( int argc, char **argv ) {

      int             info;                           /* used to check for functions returning nonzeros */
      int             mx,my,Nx,Ny;
      double          ff,gnorm;
      int             iter, nlevels;                                                /* multigrid levels */
      DA              DAarray[20];
      Vec             X;
      PetscTruth      flg, PreLoad = PETSC_TRUE;                                               /* flags */
      TaoMethod       method = "tao_gpcg";                                       /* minimization method */
      AppCtx          user;                                                /* user-defined work context */
      TAO_SOLVER      tao;                                                 /* TAO_SOLVER solver context */
      TAO_APPLICATION EPTorsApp;                                            /* The PETSc application */
      TaoTerminateReason reason;

      /* Initialize TAO */
      PetscInitialize(&argc, &argv, (char *)0, help);
      TaoInitialize(&argc, &argv, (char *)0, help);

      PreLoadBegin(PreLoad,"Solve");

      info = AppCtxInitialize((void*)&user); CHKERRQ(info);

      nlevels=5;
      info = PetscOptionsGetInt(PETSC_NULL,"-nlevels",&nlevels,&flg); CHKERRQ(info);
      mx = my = 11;                               /* these correspond to 10 segments on each dimension */
      info = PetscOptionsGetInt(TAO_NULL, "-mx", &mx, &flg); CHKERRQ(info);
      info = PetscOptionsGetInt(TAO_NULL, "-my", &my, &flg); CHKERRQ(info);
      if (PreLoadIt == 0) {
        nlevels = 1; mx = 11; my = 11; }

      PetscPrintf(MPI_COMM_WORLD,"\n---- Elastic-Plastic Torsion Problem -----\n\n");

      /* Let PETSc determine the vector distribution */
      Nx = PETSC_DECIDE; Ny = PETSC_DECIDE;

      /* Create distributed array (DA) to manage parallel grid and vectors  */
      info = DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX,mx,
                        my,Nx,Ny,1,1,PETSC_NULL,PETSC_NULL,&DAarray[0]); CHKERRQ(info);
      for (iter=1;iter<nlevels;iter++){
        info = DARefine(DAarray[iter-1],PETSC_COMM_WORLD,&DAarray[iter]); CHKERRQ(info);
      }

      /* Create TAO solver and set desired solution method */
      info = TaoCreate(MPI_COMM_WORLD,method,&tao); CHKERRQ(info);
      info = TaoApplicationCreate(PETSC_COMM_WORLD,&EPTorsApp); CHKERRQ(info);
      info = TaoAppSetDAApp(EPTorsApp, DAarray, nlevels ); CHKERRQ(info);
      /* Sets routines for function, gradient and bounds evaluation */
      info = DAAppSetVariableBoundsRoutine(EPTorsApp,DASetBounds,(void *)&user); CHKERRQ(info);

      info = PetscOptionsHasName(TAO_NULL, "-byelement", &flg); CHKERRQ(info);
      if (flg) {

        /* Sets routines for function and gradient evaluation, element by element */
        info = PetscOptionsHasName(TAO_NULL, "-adic", &flg); CHKERRQ(info);
        if (flg) {
          info = DAAppSetADElementFunctionGradient(EPTorsApp,ad_EPTorsLocalFunction,192,(void *)&user.fgctx); CHKERRQ(info);
        } else {
          info = DAAppSetElementObjectiveAndGradientRoutine(EPTorsApp,EPTorsLocalFunctionGradient,42,(void *)&user); CHKERRQ(info);
        }
        /* Sets routines for Hessian evaluation, element by element */
        info = DAAppSetElementHessianRoutine(EPTorsApp,EPTorsLocalHessian,6,(void*)&user); CHKERRQ(info);

      } else {

        /* Sets routines for function and gradient evaluation, all in one routine */
        info = DAAppSetObjectiveAndGradientRoutine(EPTorsApp,WholeEPTorsFunctionGradient,(void *)&user); CHKERRQ(info);

        /* Sets routines for Hessian evaluation, all in one routine */
        info = DAAppSetHessianRoutine(EPTorsApp,WholeEPTorsHessian,(void*)&user); CHKERRQ(info);

      }

      info = DAAppSetBeforeMonitor(EPTorsApp,MyGridMonitorBefore,(void*)&user); CHKERRQ(info);
      info = PetscOptionsHasName(TAO_NULL,"-tao_monitor", &flg); CHKERRQ(info);
      if (flg){
        info = DAAppPrintStageTimes(EPTorsApp); CHKERRQ(info);
        info = DAAppPrintInterpolationError(EPTorsApp); CHKERRQ(info);
      }
      info = TaoAppSetRelativeTolerance(EPTorsApp,1.0e-8); CHKERRQ(info);
      info = TaoSetTolerances(tao,0,0,0,0); CHKERRQ(info);
      info = TaoSetGradientTolerances(tao,0,0,0); CHKERRQ(info);

      /* Check for any tao command line options */
      info = TaoSetOptions(EPTorsApp, tao); CHKERRQ(info);

      info = DAAppGetSolution(EPTorsApp,0,&X); CHKERRQ(info);
      info = FormInitialGuess(DAarray[0],X); CHKERRQ(info);
      info = DAAppSetInitialSolution(EPTorsApp,X); CHKERRQ(info);

      /* SOLVE THE APPLICATION */
      info = TaoDAAppSolve(EPTorsApp, tao);  CHKERRQ(info);

      /* Get information on termination */
      info = TaoGetSolutionStatus(tao,&iter,&ff,&gnorm,0,0,&reason); CHKERRQ(info);
      if (reason <= 0 ){
        PetscPrintf(MPI_COMM_WORLD,"Try a different TAO method, adjust some parameters, or check the function evaluation routines\n");
        PetscPrintf(MPI_COMM_WORLD," Iterations: %d,  Function Value: %4.2e, Residual: %4.2e \n",iter,ff,gnorm);
      }

      info = PetscOptionsHasName(PETSC_NULL,"-view_sol",&flg); CHKERRQ(info);
      if (flg){
        info = DAAppGetSolution(EPTorsApp,nlevels-1,&X); CHKERRQ(info);
        info=VecView(X,PETSC_VIEWER_STDOUT_WORLD); CHKERRQ(info);
      }

      /*  To View TAO solver information */
      // info = TaoView(tao); CHKERRQ(info);

      /* Free TAO data structures */
      info = TaoDestroy(tao); CHKERRQ(info);
      info = TaoAppDestroy(EPTorsApp); CHKERRQ(info);

      /* Free PETSc data structures */
      for (iter=0;iter<nlevels;iter++){
        info = DADestroy(DAarray[iter]); CHKERRQ(info);
      }

      PreLoadEnd();

      /* Finalize TAO */
      TaoFinalize();
      PetscFinalize();

      return 0;
    } /* main */

    /*----- The following two routines
      MyGridMonitorBefore    MyGridMonitorAfter
      help diplay info of iterations at every grid level
    */
    #undef __FUNCT__
    #define __FUNCT__ "MyGridMonitorBefore"
    static int MyGridMonitorBefore(TAO_APPLICATION myapp, DA da, int level, void *ctx) {

      AppCtx *user = (AppCtx*)ctx;
      int info,mx,my;

      info = DAGetInfo(da,PETSC_NULL,&mx,&my,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL,
    		   PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(info);
      user->hx = user->u1 / (mx - 1);
      user->hy = user->u2 / (my - 1);
      user->area = 0.5 * user->hx * user->hy;
      user->fgctx.hx   = user->hx;
      user->fgctx.hy   = user->hy;
      user->fgctx.area = user->area;
      user->fgctx.param = user->param;

      PetscPrintf(MPI_COMM_WORLD,"Grid: %d,    mx: %d     my: %d   \n",level,mx,my);

      return 0;
    }

    /*------- USER-DEFINED: initialize the application context information -------*/
    #undef __FUNCT__
    #define __FUNCT__ "AppCtxInitialize"
    /*
      AppCtxInitialize - Sets initial values for the application context parameters

      Input:
        ptr - void user-defined application context

      Output:
        ptr - user-defined application context with the default or user-provided
                 parameters
    */
    static int AppCtxInitialize(void *ptr) {

      AppCtx *user = (AppCtx*)ptr;
      PetscTruth    flg;            /* flag for PETSc calls */
      int info;

      /* Specify default parameters */
      user->param = 25.0;
      user->u1 = user->u2 = 1.0;

      /* Check for command line arguments that override defaults */
      info = PetscOptionsGetReal(TAO_NULL, "-par", &user->param, &flg); CHKERRQ(info);
      info = PetscOptionsGetReal(TAO_NULL, "-u1", &user->u1, &flg); CHKERRQ(info);
      info = PetscOptionsGetReal(TAO_NULL, "-u2", &user->u2, &flg); CHKERRQ(info);

      return 0;
    } /* AppCtxInitialize */

    #undef __FUNCT__
    #define __FUNCT__ "FormInitialGuess"
    static int FormInitialGuess(DA da, Vec X)
    {
      int    info, i, j, mx, my;
      int    xs, ys, xm, ym, xe, ye;
      PetscReal hx, hy, temp, val;
      double **x;

      /* Get local mesh boundaries */
      info = DAGetInfo(da,PETSC_NULL,&mx,&my,PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL,
                       PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(info);
      hx = 1.0/(mx-1);  hy = 1.0/(my-1);

      info = DAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
      xe = xs+xm; ye = ys+ym;

      info = DAVecGetArray(da, X, (void**)&x); CHKERRQ(info);
      /* Compute initial guess over locally owned part of mesh */
      for (j=ys; j<ye; j++) {  /*  for (j=0; j<my; j++) */
        temp = PetscMin(j+1,my-j)*hy;
        for (i=xs; i<xe; i++) {  /*  for (i=0; i<mx; i++) */
          val = PetscMin((PetscMin(i+1,mx-i))*hx,temp);
          x[j][i] = val;
        }
      }
      info = DAVecRestoreArray(da, X, (void**)&x); CHKERRQ(info);

      return 0;
    }

    /*------- USER-DEFINED: set the upper and lower bounds for the variables  -------*/

    #undef __FUNCT__
    #define __FUNCT__ "DASetBounds"
    /*
      FormBounds - Forms bounds on the variables

      Input:
        user - user-defined application context

      Output:
        XL - vector of lower bounds
        XU - vector of upper bounds
    */
    static int DASetBounds(TAO_APPLICATION daapplication, DA da, Vec XL, Vec XU, void *ptr)
    {
      AppCtx *user = (AppCtx*)ptr;
      int i, j, info, xs, xm, ys, ym;
      double hx, hy, u1, u2, dist, d1, d2, hd, vd;
      double **xl, **xu;

      hx = user->hx;
      hy = user->hy;
      u1 = user->u1;
      u2 = user->u2;

      info = DAVecGetArray(da, XL, (void**)&xl); CHKERRQ(info);
      info = DAVecGetArray(da, XU, (void**)&xu); CHKERRQ(info);
      info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);

      for (j = ys; j < ys+ym; j++){
        for (i = xs; i < xs+xm; i++){
          d1 = i * hx; d2 = u1 - d1; hd = PetscMin(d1,d2);
          d1 = j * hy; d2 = u2 - d1; vd = PetscMin(d1,d2);
          dist = PetscMin(hd,vd);
          xl[j][i] = -dist;
          xu[j][i] = dist;
        }
      }

      info = DAVecRestoreArray(da, XL, (void**)&xl); CHKERRQ(info);
      info = DAVecRestoreArray(da, XU, (void**)&xu); CHKERRQ(info);

      info = PetscLogFlops(xm * ym * 4); CHKERRQ(info);
      return 0;

    } /* DASetBounds */

    #undef __FUNCT__
    #define __FUNCT__ "EPTorsLocalFunctionGradient"
    /*
      EPTorsLocalFunctionGradient - Evaluates function and gradient over the
          local rectangular element

      Input:
        coor - vector with the indices of the position of current element
                 in the first, second and third directions
        x - current point (values over the current rectangular element)
        df - degrees of freedom at each point
        ptr - user-defined application context

      Output:
        f - value of the objective funtion at the local rectangular element
        g - gradient of the local function
    */
    static int EPTorsLocalFunctionGradient(int coor[2], double x[4], double *f, double g[4], void *ptr) {

      AppCtx *user = (AppCtx*)ptr;

      double fquad, flin;
      double hx, hy, dvdx, dvdy, area;
      double cdiv3, cnt;

      cdiv3 = user->param / 3.0;
      hx = user->hx;
      hy = user->hy;
      area = user->area;
      cnt = area * cdiv3;

      /* lower triangle contribution */
      dvdx = (x[0] - x[1]) / hx;
      dvdy = (x[0] - x[2]) / hy;
      fquad = dvdx * dvdx + dvdy * dvdy;
      flin = x[0] + x[1] + x[2];

      dvdx = 0.5 * dvdx * hy;
      dvdy = 0.5 * dvdy * hx;
      g[0] = dvdx + dvdy - cnt;
      g[1] = -dvdx - 2.0 * cnt;
      g[2] = -dvdy - 2.0 * cnt;

      /* upper triangle contribution */
      dvdx = (x[3] - x[2]) / hx;
      dvdy = (x[3] - x[1]) / hy;
      fquad += dvdx * dvdx + dvdy * dvdy;
      flin += x[1] + x[2] + x[3];

      dvdx = 0.5 * dvdx * hy;
      dvdy = 0.5 * dvdy * hx;
      g[1] += -dvdy;
      g[2] += -dvdx;
      g[3] = dvdx + dvdy - cnt;

      *f = area * (0.5 * fquad - flin * cdiv3);

      return 0;
    } /* EPTorsLocalFunctionGradient */

    /*------- USER-DEFINED: routine to evaluate the Hessian
               at a local (rectangular element) level       -------*/
    #undef __FUNCT__
    #define __FUNCT__ "EPTorsLocalHessian"
    /*
      EPTorsLocalHessian - Computes the Hessian of the local (partial) function
             defined over the current rectangle

      Input:
        coor - vector with the indices of the position of current element
                 in the first, second and third directions
        x - current local solution (over the rectangle only)
        df - degrees of freedom at each point
        ptr - user-defined application context

      Output:
        H - Hessian matrix of the local function (wrt the four
               points of the rectangle only)
    */
    static int EPTorsLocalHessian(int coor[2], double x[4], double H[4][4], void *ptr) {

      AppCtx *user = (AppCtx*)ptr;
      double hx, hy, dxdy, dydx;
      double diagxy, bandxy, bandyx;

      hx = user->hx;
      hy = user->hy;
      dxdy = hx/hy;
      dydx = hy/hx;
      diagxy = 0.5 * (dxdy + dydx);
      bandxy = -0.5 * dxdy;
      bandyx = -0.5 * dydx;

              /* Hessian contribution at 0,0 */
      H[0][0] = diagxy;
      H[0][1] =  H[1][0] = bandyx;
      H[0][2] =  H[2][0] = bandxy;
      H[0][3] =  H[3][0] = 0.0;

              /* Hessian contribution at 1,0 */
      H[1][1] = diagxy;
      H[1][2] =  H[2][1] = 0.0;
      H[1][3] =  H[3][1] = bandxy;

              /* Hessian contribution at 0,1 */
      H[2][2] = diagxy;
      H[2][3] =  H[3][2] = bandyx;

              /* Hessian contribution at 1,1 */
      H[3][3] = diagxy;

      return 0;

    } /* EPTorsLocalHessian */

    /*------- USER-DEFINED: routine to evaluate the function
              and gradient at the whole grid             -------*/
    #undef __FUNCT__
    #define __FUNCT__ "WholeEPTorsFunctionGradient"
    /*
      WholeEPTorsFunctionGradient - Evaluates function and gradient over the
          whole grid

      Input:
        daapplication - TAO application object
        da  - distributed array
        X   - the current point, at which the function and gradient are evaluated
        ptr - user-defined application context

      Output:
        f - value of the objective funtion at X
        G - gradient at X
    */
    static int WholeEPTorsFunctionGradient(TAO_APPLICATION daapplication, DA da, Vec X, double *f, Vec G, void *ptr) {

      AppCtx *user = (AppCtx*)ptr;
      Vec localX, localG;
      int info, i, j;
      int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
      double **x, **g;
      double floc = 0.0;
      PetscScalar zero = 0.0;

      double fquad, flin;
      double hx, hy, dvdx, dvdy, area;
      double cdiv3, cnt;

      cdiv3 = user->param / 3.0;
      hx = user->hx;
      hy = user->hy;
      area = user->area;
      cnt = area * cdiv3;

      info = DAGetLocalVector(da, &localX); CHKERRQ(info);
      info = DAGetLocalVector(da, &localG); CHKERRQ(info);
      info = VecSet(G, zero); CHKERRQ(info);
      info = VecSet(localG, zero); CHKERRQ(info);

      info = DAGlobalToLocalBegin(da, X, INSERT_VALUES, localX); CHKERRQ(info);
      info = DAGlobalToLocalEnd(da, X, INSERT_VALUES, localX); CHKERRQ(info);

      info = DAVecGetArray(da, localX, (void**)&x); CHKERRQ(info);
      info = DAVecGetArray(da, localG, (void**)&g); CHKERRQ(info);

      info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);
      info = DAGetGhostCorners(da, &gxs, &gys, TAO_NULL, &gxm, &gym, TAO_NULL); CHKERRQ(info);

      xe = gxs + gxm - 1;
      ye = gys + gym - 1;
      for (j = ys; j < ye; j++) {
        for (i = xs; i < xe; i++) {

          /* lower triangle contribution */
          dvdx = (x[j][i] - x[j][i+1]) / hx;
          dvdy = (x[j][i] - x[j+1][i]) / hy;
          fquad = dvdx * dvdx + dvdy * dvdy;
          flin = x[j][i] + x[j][i+1] + x[j+1][i];

          dvdx = 0.5 * dvdx * hy;
          dvdy = 0.5 * dvdy * hx;
          g[j][i] += dvdx + dvdy - cnt;
          g[j][i+1] += -dvdx - 2.0 * cnt;
          g[j+1][i] += -dvdy - 2.0 * cnt;

          /* upper triangle contribution */
          dvdx = (x[j+1][i+1] - x[j+1][i]) / hx;
          dvdy = (x[j+1][i+1] - x[j][i+1]) / hy;
          fquad += dvdx * dvdx + dvdy * dvdy;
          flin += x[j][i+1] + x[j+1][i] + x[j+1][i+1];

          dvdx = 0.5 * dvdx * hy;
          dvdy = 0.5 * dvdy * hx;
          g[j][i+1] += -dvdy;
          g[j+1][i] += -dvdx;
          g[j+1][i+1] += dvdx + dvdy - cnt;

          floc += area * (0.5 * fquad - flin * cdiv3);

        }
      }

      info = MPI_Allreduce(&floc, f, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD); CHKERRQ(info);

      info = DAVecRestoreArray(da, localX, (void**)&x); CHKERRQ(info);
      info = DAVecRestoreArray(da, localG, (void**)&g); CHKERRQ(info);

      info = DALocalToGlobalBegin(da, localG, G); CHKERRQ(info);
      info = DALocalToGlobalEnd(da, localG, G); CHKERRQ(info);

      info = DARestoreLocalVector(da, &localX); CHKERRQ(info);
      info = DARestoreLocalVector(da, &localG); CHKERRQ(info);

      info = PetscLogFlops((xe-xs) * (ye-ys) * 47 + 2); CHKERRQ(info);
      return 0;
    } /* WholeEPTorsFunctionGradient */

    /*------- USER-DEFINED: routine to evaluate the Hessian
              at the whole grid             -------*/
    #undef __FUNCT__
    #define __FUNCT__ "WholeEPTorsHessian"
    /*
      WholeEPTorsHessian - Evaluates Hessian over the whole grid

      Input:
        daapplication - TAO application object
        da  - distributed array
        X   - the current point, at which the function and gradient are evaluated
        ptr - user-defined application context

      Output:
        H - Hessian at X
    */
    static int WholeEPTorsHessian(TAO_APPLICATION daapplication, DA da, Vec X, Mat H, void *ptr) {

      AppCtx *user = (AppCtx*)ptr;
      int info, i, j, ind[4];
      int xs, xm, gxs, gxm, xe, ys, ym, gys, gym, ye;
      double smallH[4][4];

      double hx, hy, dxdy, dydx;
      double diagxy, bandxy, bandyx;
      PetscTruth assembled;

      hx = user->hx;
      hy = user->hy;
      dxdy = hx/hy;
      dydx = hy/hx;
      diagxy = 0.5 * (dxdy + dydx);
      bandxy = -0.5 * dxdy;
      bandyx = -0.5 * dydx;

      info = MatAssembled(H,&assembled); CHKERRQ(info);
      if (assembled){info = MatZeroEntries(H);  CHKERRQ(info);}

      info = DAGetCorners(da, &xs, &ys, TAO_NULL, &xm, &ym, TAO_NULL); CHKERRQ(info);
      info = DAGetGhostCorners(da, &gxs, &gys, TAO_NULL, &gxm, &gym, TAO_NULL); CHKERRQ(info);

      xe = gxs + gxm - 1;
      ye = gys + gym - 1;
      for (j = ys; j < ye; j++) {
        for (i = xs; i < xe; i++) {

              /* Hessian contribution at 0,0 */
          smallH[0][0] = diagxy;
          smallH[0][1] = smallH[1][0] = bandyx;
          smallH[0][2] = smallH[2][0] = bandxy;
          smallH[0][3] = smallH[3][0] = 0.0;

              /* Hessian contribution at 1,0 */
          smallH[1][1] = diagxy;
          smallH[1][2] = smallH[2][1] = 0.0;
          smallH[1][3] = smallH[3][1] = bandxy;

              /* Hessian contribution at 0,1 */
          smallH[2][2] = diagxy;
          smallH[2][3] = smallH[3][2] = bandyx;

              /* Hessian contribution at 1,1 */
          smallH[3][3] = diagxy;

          ind[0] = (j-gys) * gxm + (i-gxs);
          ind[1] = ind[0] + 1;
          ind[2] = ind[0] + gxm;
          ind[3] = ind[2] + 1;
          info = MatSetValuesLocal(H,4,ind,4,ind,(PetscScalar*)smallH,ADD_VALUES); CHKERRQ(info);

        }
      }

      info = MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY); CHKERRQ(info);
      info = MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY); CHKERRQ(info);
      info = MatSetOption(H, MAT_SYMMETRIC); CHKERRQ(info);

      info = PetscLogFlops(6); CHKERRQ(info);
      return 0;

    } /* WholeEPTorsHessian */