    /*$Id: minsurf1.c 1.51 05/05/04 10:48:58-05:00 sarich@zorak.(none) $*/

    /* Program usage: mpirun -np 1 minsurf1 [-help] [all TAO options] */

    /*  Include "tao.h" so we can use TAO solvers.  */
    #include "tao.h"

    static char  help[] =
    "This example demonstrates use of the TAO package to \n\
    solve an unconstrained minimization problem.  This example is based on a \n\
    problem from the MINPACK-2 test suite.  Given a rectangular 2-D domain and \n\
    boundary values along the edges of the domain, the objective is to find the\n\
    surface with the minimal area that satisfies the boundary conditions.\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\
      -start <st>, where <st> =0 for zero vector, and an average of the boundary conditions otherwise \n\n";

    /*T
       Concepts: TAO - Solving an unconstrained minimization problem
       Routines: TaoInitialize(); TaoFinalize();
       Routines: TaoCreate(); TaoDestroy();
       Routines: TaoApplicationCreate(); TaoAppDestroy();
       Routines: TaoAppSetObjectiveAndGradientRoutine(); TaoAppSetInitialSolutionVec();
       Routines: TaoAppSetHessianMat(); TaoSetHessianRoutine();
       Routines: TaoSetFromOptions(); TaoGetKSP();
       Routines: TaoSolve(); TaoView();
       Processors: 1
    T*/

    /*
       User-defined application context - contains data needed by the
       application-provided call-back routines, FormFunctionGradient()
       and FormHessian().
    */
    typedef struct {
      int         mx, my;                 /* discretization in x, y directions */
      double      *bottom, *top, *left, *right;             /* boundary values */
      Mat         H;
    } AppCtx;

    /* -------- User-defined Routines --------- */

    static int MSA_BoundaryConditions(AppCtx*);
    static int MSA_InitialPoint(AppCtx*,Vec);
    int QuadraticH(AppCtx*,Vec,Mat);
    int FormFunctionGradient(TAO_APPLICATION,Vec,double*,Vec,void*);
    int FormHessian(TAO_APPLICATION,Vec,Mat*,Mat*,MatStructure *,void*);

    #undef __FUNCT__
    #define __FUNCT__ "main"
    int main( int argc, char **argv )
    {
      int             info;              /* used to check for functions returning nonzeros */
      int             N;                 /* Size of vector */
      int             size;              /* Number of processors */
      Vec             x;                 /* solution, gradient vectors */
      KSP             ksp;               /*  PETSc Krylov subspace method */
      PetscTruth      flg;               /* A return value when checking for user options */
      TaoMethod       method="tao_nls";  /* minimization method */
      TaoTerminateReason reason;
      TAO_SOLVER      tao;               /* TAO_SOLVER solver context */
      TAO_APPLICATION minsurfapp;        /* The PETSc application */
      AppCtx          user;              /* user-defined work context */

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

      MPI_Comm_size(MPI_COMM_WORLD,&size);
      if (size >1) {
        PetscPrintf(PETSC_COMM_SELF,"This example is intended for single processor use!\n");
        PetscPrintf(PETSC_COMM_SELF,"Try the example minsurf2!\n");
        SETERRQ(1,"Incorrect number of processors");
      }

      /* Specify default dimension of the problem */
      user.mx = 4; user.my = 4;

      /* Check for any command line arguments that override defaults */
      info = PetscOptionsGetInt(PETSC_NULL,"-mx",&user.mx,&flg); CHKERRQ(info);
      info = PetscOptionsGetInt(PETSC_NULL,"-my",&user.my,&flg); CHKERRQ(info);

      PetscPrintf(PETSC_COMM_SELF,"\n---- Minimum Surface Area Problem -----\n");
      PetscPrintf(PETSC_COMM_SELF,"mx: %d     my: %d   \n\n",user.mx,user.my);

      /* Calculate any derived values from parameters */
      N    = user.mx*user.my;

      /* Create TAO solver and set desired solution method  */
      info = TaoCreate(PETSC_COMM_SELF,method,&tao); CHKERRQ(info);
      info = TaoApplicationCreate(PETSC_COMM_SELF,&minsurfapp); CHKERRQ(info);

      /* Initialize minsurf application data structure for use in the function evaluations  */
      info = MSA_BoundaryConditions(&user); CHKERRQ(info);            /* Application specific routine */

      /*
         Create a vector to hold the variables.  Compute an initial solution.
         Set this vector, which will be used by TAO.
      */
      info = VecCreateSeq(PETSC_COMM_SELF,N,&x);                      /* PETSc routine                */
      info = MSA_InitialPoint(&user,x); CHKERRQ(info);                /* Application specific routine */
      info = TaoAppSetInitialSolutionVec(minsurfapp,x); CHKERRQ(info);   /* A TAO routine                */

      /* Provide TAO routines for function, gradient, and Hessian evaluation */
      info = TaoAppSetObjectiveAndGradientRoutine(minsurfapp,FormFunctionGradient,(void *)&user); CHKERRQ(info);
      info = TaoAppSetHessianRoutine(minsurfapp,FormHessian,(void *)&user); CHKERRQ(info);

      /* Create a matrix data structure to store the Hessian.  This structure will be used by TAO */
      info = MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,7,PETSC_NULL,&(user.H));        /* PETSc routine */
      info = MatSetOption(user.H,MAT_SYMMETRIC); CHKERRQ(info);                  /* PETSc flag    */
      info = TaoAppSetHessianMat(minsurfapp,user.H,user.H); CHKERRQ(info);          /* A TAO routine */

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

      /* Limit the number of iterations in the KSP linear solver */
      info = TaoGetKSP(tao,&ksp); CHKERRQ(info);
      if (ksp) {                                                  /* Modify PETSc KSP structure */
        info = KSPSetTolerances(ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,user.mx*user.my);
        CHKERRQ(info);
      }

      /* SOLVE THE APPLICATION */
      info = TaoSolveApplication(minsurfapp,tao); CHKERRQ(info);

      /* Get information on termination */
      info = TaoGetTerminationReason(tao,&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");

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

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

      /* Free PETSc data structures */
      info = VecDestroy(x); CHKERRQ(info);
      info = MatDestroy(user.H); CHKERRQ(info);
      PetscFree(user.bottom);
      PetscFree(user.top);
      PetscFree(user.left);
      PetscFree(user.right);

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

      return 0;
    }

    /* -------------------------------------------------------------------- */
    #undef __FUNCT__
    #define __FUNCT__ "FormFunctionGradient"

    /*  FormFunctionGradient - Evaluates function and corresponding gradient.

        Input Parameters:
    .   taoapp     - the TAO_APPLICATION context
    .   X       - input vector
    .   userCtx - optional user-defined context, as set by TaoSetFunctionGradient()

        Output Parameters:
    .   fcn     - the newly evaluated function
    .   G       - vector containing the newly evaluated gradient
    */
    int FormFunctionGradient(TAO_APPLICATION taoapp,Vec X,double *fcn,Vec G,void *userCtx) {

      AppCtx * user = (AppCtx *) userCtx;
      int    info,i,j,row;
      int    mx=user->mx, my=user->my;
      double rhx=mx+1, rhy=my+1;
      double hx=1.0/(mx+1),hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy, area=0.5*hx*hy, ft=0;
      double f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
      double df1dxc,df2dxc,df3dxc,df4dxc,df5dxc,df6dxc;
      PetscScalar zero=0.0;
      PetscScalar *g, *x;

      /* Initialize vector to zero */
      info = VecSet(G, zero); CHKERRQ(info);

      /* Get pointers to vector data */
      info = VecGetArray(X,&x); CHKERRQ(info);
      info = VecGetArray(G,&g); CHKERRQ(info);

      /* Compute function over the locally owned part of the mesh */
      for (j=0; j<my; j++){
        for (i=0; i< mx; i++){
          row=(j)*mx + (i);

          xc = x[row];
          xlt=xrb=xl=xr=xb=xt=xc;

          if (i==0){ /* left side */
            xl= user->left[j+1];
            xlt = user->left[j+2];
          } else {
            xl = x[row-1];
          }

          if (j==0){ /* bottom side */
            xb=user->bottom[i+1];
            xrb = user->bottom[i+2];
          } else {
            xb = x[row-mx];
          }

          if (i+1 == mx){ /* right side */
            xr=user->right[j+1];
            xrb = user->right[j];
          } else {
            xr = x[row+1];
          }

          if (j+1==0+my){ /* top side */
            xt=user->top[i+1];
            xlt = user->top[i];
          }else {
            xt = x[row+mx];
          }

          if (i>0 && j+1<my){
            xlt = x[row-1+mx];
          }
          if (j>0 && i+1<mx){
            xrb = x[row+1-mx];
          }

          d1 = (xc-xl);
          d2 = (xc-xr);
          d3 = (xc-xt);
          d4 = (xc-xb);
          d5 = (xr-xrb);
          d6 = (xrb-xb);
          d7 = (xlt-xl);
          d8 = (xt-xlt);

          df1dxc = d1*hydhx;
          df2dxc = ( d1*hydhx + d4*hxdhy );
          df3dxc = d3*hxdhy;
          df4dxc = ( d2*hydhx + d3*hxdhy );
          df5dxc = d2*hydhx;
          df6dxc = d4*hxdhy;

          d1 *= rhx;
          d2 *= rhx;
          d3 *= rhy;
          d4 *= rhy;
          d5 *= rhy;
          d6 *= rhx;
          d7 *= rhy;
          d8 *= rhx;

          f1 = sqrt( 1.0 + d1*d1 + d7*d7);
          f2 = sqrt( 1.0 + d1*d1 + d4*d4);
          f3 = sqrt( 1.0 + d3*d3 + d8*d8);
          f4 = sqrt( 1.0 + d3*d3 + d2*d2);
          f5 = sqrt( 1.0 + d2*d2 + d5*d5);
          f6 = sqrt( 1.0 + d4*d4 + d6*d6);

          ft = ft + (f2 + f4);

          df1dxc /= f1;
          df2dxc /= f2;
          df3dxc /= f3;
          df4dxc /= f4;
          df5dxc /= f5;
          df6dxc /= f6;

          g[row] = (df1dxc+df2dxc+df3dxc+df4dxc+df5dxc+df6dxc )/2.0;

        }
      }

      for (j=0; j<my; j++){   /* left side */
        d3=(user->left[j+1] - user->left[j+2])*rhy;
        d2=(user->left[j+1] - x[j*mx])*rhx;
        ft = ft+sqrt( 1.0 + d3*d3 + d2*d2);
      }

      for (i=0; i<mx; i++){ /* bottom */
        d2=(user->bottom[i+1]-user->bottom[i+2])*rhx;
        d3=(user->bottom[i+1]-x[i])*rhy;
        ft = ft+sqrt( 1.0 + d3*d3 + d2*d2);
      }

      for (j=0; j< my; j++){ /* right side */
        d1=(x[(j+1)*mx-1]-user->right[j+1])*rhx;
        d4=(user->right[j]-user->right[j+1])*rhy;
        ft = ft+sqrt( 1.0 + d1*d1 + d4*d4);
      }

      for (i=0; i<mx; i++){ /* top side */
        d1=(x[(my-1)*mx + i] - user->top[i+1])*rhy;
        d4=(user->top[i+1] - user->top[i])*rhx;
        ft = ft+sqrt( 1.0 + d1*d1 + d4*d4);
      }

      /* Bottom left corner */
      d1=(user->left[0]-user->left[1])*rhy;
      d2=(user->bottom[0]-user->bottom[1])*rhx;
      ft +=sqrt( 1.0 + d1*d1 + d2*d2);

      /* Top right corner */
      d1=(user->right[my+1] - user->right[my])*rhy;
      d2=(user->top[mx+1] - user->top[mx])*rhx;
      ft +=sqrt( 1.0 + d1*d1 + d2*d2);

      (*fcn)=ft*area;

      /* Restore vectors */
      info = VecRestoreArray(X,&x); CHKERRQ(info);
      info = VecRestoreArray(G,&g); CHKERRQ(info);

      PetscLogFlops(67*mx*my);

      return 0;
    }

    /* ------------------------------------------------------------------- */
    #undef __FUNCT__
    #define __FUNCT__ "FormHessian"
    /*
       FormHessian - Evaluates the Hessian matrix.

       Input Parameters:
    .  taoapp  - the TAO_APPLICATION context
    .  x    - input vector
    .  ptr  - optional user-defined context, as set by TaoSetHessian()

       Output Parameters:
    .  H    - Hessian matrix
    .  Hpre - optionally different preconditioning matrix
    .  flg  - flag indicating matrix structure

    */
    int FormHessian(TAO_APPLICATION taoapp,Vec X,Mat *H, Mat *Hpre, MatStructure *flg, void *ptr)
    {
      int    info;
      AppCtx *user = (AppCtx *) ptr;

      /* Evaluate the Hessian entries*/
      info = QuadraticH(user,X,*H); CHKERRQ(info);

      /* Indicate that this matrix has the same sparsity pattern during
         successive iterations; setting this flag can save significant work
         in computing the preconditioner for some methods. */
      *flg=SAME_NONZERO_PATTERN;

      return 0;
    }

    /* ------------------------------------------------------------------- */
    #undef __FUNCT__
    #define __FUNCT__ "QuadraticH"
    /*
       QuadraticH - Evaluates the Hessian matrix.

       Input Parameters:
    .  user - user-defined context, as set by TaoSetHessian()
    .  X    - input vector

       Output Parameter:
    .  H    - Hessian matrix
    */
    int QuadraticH(AppCtx *user, Vec X, Mat Hessian)
    {
      int    i,j,k,row,info;
      int    mx=user->mx, my=user->my;
      int    col[7];
      double hx=1.0/(mx+1), hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy;
      double rhx=mx+1, rhy=my+1;
      double f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
      double hl,hr,ht,hb,hc,htl,hbr;
      PetscScalar *x, v[7];

      /* Get pointers to vector data */
      info = VecGetArray(X,&x); CHKERRQ(info);

      /* Initialize matrix entries to zero */
      info = MatZeroEntries(Hessian);  CHKERRQ(info);

      /* Set various matrix options */
      info = MatSetOption(Hessian,MAT_IGNORE_OFF_PROC_ENTRIES); CHKERRQ(info);
      info = MatSetOption(Hessian,MAT_COLUMNS_SORTED); CHKERRQ(info);
      info = MatSetOption(Hessian,MAT_ROWS_SORTED); CHKERRQ(info);

      /* Compute Hessian over the locally owned part of the mesh */
      for (i=0; i< mx; i++){
        for (j=0; j<my; j++){

          row=(j)*mx + (i);

          xc = x[row];
          xlt=xrb=xl=xr=xb=xt=xc;

          /* Left side */
          if (i==0){
            xl= user->left[j+1];
            xlt = user->left[j+2];
          } else {
            xl = x[row-1];
          }

          if (j==0){
            xb=user->bottom[i+1];
            xrb = user->bottom[i+2];
          } else {
            xb = x[row-mx];
          }

          if (i+1 == mx){
            xr=user->right[j+1];
            xrb = user->right[j];
          } else {
            xr = x[row+1];
          }

          if (j+1==my){
            xt=user->top[i+1];
            xlt = user->top[i];
          }else {
            xt = x[row+mx];
          }

          if (i>0 && j+1<my){
            xlt = x[row-1+mx];
          }
          if (j>0 && i+1<mx){
            xrb = x[row+1-mx];
          }

          d1 = (xc-xl)*rhx;
          d2 = (xc-xr)*rhx;
          d3 = (xc-xt)*rhy;
          d4 = (xc-xb)*rhy;
          d5 = (xrb-xr)*rhy;
          d6 = (xrb-xb)*rhx;
          d7 = (xlt-xl)*rhy;
          d8 = (xlt-xt)*rhx;

          f1 = sqrt( 1.0 + d1*d1 + d7*d7);
          f2 = sqrt( 1.0 + d1*d1 + d4*d4);
          f3 = sqrt( 1.0 + d3*d3 + d8*d8);
          f4 = sqrt( 1.0 + d3*d3 + d2*d2);
          f5 = sqrt( 1.0 + d2*d2 + d5*d5);
          f6 = sqrt( 1.0 + d4*d4 + d6*d6);

          hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+
    	(-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2);
          hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+
    	(-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4);
          ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+
    	(-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4);
          hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+
    	(-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2);

          hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6);
          htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3);

          hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) +
    	hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) +
    	(hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2*d1*d4)/(f2*f2*f2) +
    	(hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4);

          hl*=0.5; hr*=0.5; ht*=0.5; hb*=0.5; hbr*=0.5; htl*=0.5;  hc*=0.5;

          k=0;
          if (j>0){
    	v[k]=hb; col[k]=row - mx; k++;
          }

          if (j>0 && i < mx -1){
    	v[k]=hbr; col[k]=row - mx+1; k++;
          }

          if (i>0){
    	v[k]= hl; col[k]=row - 1; k++;
          }

          v[k]= hc; col[k]=row; k++;

          if (i < mx-1 ){
    	v[k]= hr; col[k]=row+1; k++;
          }

          if (i>0 && j < my-1 ){
    	v[k]= htl; col[k] = row+mx-1; k++;
          }

          if (j < my-1 ){
    	v[k]= ht; col[k] = row+mx; k++;
          }

          /*
    	 Set matrix values using local numbering, which was defined
    	 earlier, in the main routine.
          */
          info = MatSetValues(Hessian,1,&row,k,col,v,INSERT_VALUES);
          CHKERRQ(info);

        }
      }

      /* Restore vectors */
      info = VecRestoreArray(X,&x); CHKERRQ(info);

      /* Assemble the matrix */
      info = MatAssemblyBegin(Hessian,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
      info = MatAssemblyEnd(Hessian,MAT_FINAL_ASSEMBLY); CHKERRQ(info);

      PetscLogFlops(199*mx*my);
      return 0;
    }

    /* ------------------------------------------------------------------- */
    #undef __FUNCT__
    #define __FUNCT__ "MSA_BoundaryConditions"
    /*
       MSA_BoundaryConditions -  Calculates the boundary conditions for
       the region.

       Input Parameter:
    .  user - user-defined application context

       Output Parameter:
    .  user - user-defined application context
    */
    static int MSA_BoundaryConditions(AppCtx * user)
    {
      int        i,j,k,limit=0,info,maxits=5;
      int        mx=user->mx,my=user->my;
      int        bsize=0, lsize=0, tsize=0, rsize=0;
      double     one=1.0, two=2.0, three=3.0, tol=1e-10;
      double     fnorm,det,hx,hy,xt=0,yt=0;
      double     u1,u2,nf1,nf2,njac11,njac12,njac21,njac22;
      double     b=-0.5, t=0.5, l=-0.5, r=0.5;
      double     *boundary;

      bsize=mx+2; lsize=my+2; rsize=my+2; tsize=mx+2;

      info = PetscMalloc(bsize*sizeof(double),&user->bottom); CHKERRQ(info);
      info = PetscMalloc(tsize*sizeof(double),&user->top); CHKERRQ(info);
      info = PetscMalloc(lsize*sizeof(double),&user->left); CHKERRQ(info);
      info = PetscMalloc(rsize*sizeof(double),&user->right); CHKERRQ(info);

      hx= (r-l)/(mx+1); hy=(t-b)/(my+1);

      for (j=0; j<4; j++){
        if (j==0){
          yt=b;
          xt=l;
          limit=bsize;
          boundary=user->bottom;
        } else if (j==1){
          yt=t;
          xt=l;
          limit=tsize;
          boundary=user->top;
        } else if (j==2){
          yt=b;
          xt=l;
          limit=lsize;
          boundary=user->left;
        } else {  // if (j==3)
          yt=b;
          xt=r;
          limit=rsize;
          boundary=user->right;
        }

        for (i=0; i<limit; i++){
          u1=xt;
          u2=-yt;
          for (k=0; k<maxits; k++){
    	nf1=u1 + u1*u2*u2 - u1*u1*u1/three-xt;
    	nf2=-u2 - u1*u1*u2 + u2*u2*u2/three-yt;
    	fnorm=sqrt(nf1*nf1+nf2*nf2);
    	if (fnorm <= tol) break;
    	njac11=one+u2*u2-u1*u1;
    	njac12=two*u1*u2;
    	njac21=-two*u1*u2;
    	njac22=-one - u1*u1 + u2*u2;
    	det = njac11*njac22-njac21*njac12;
    	u1 = u1-(njac22*nf1-njac12*nf2)/det;
    	u2 = u2-(njac11*nf2-njac21*nf1)/det;
          }

          boundary[i]=u1*u1-u2*u2;
          if (j==0 || j==1) {
    	xt=xt+hx;
          } else { // if (j==2 || j==3)
    	yt=yt+hy;
          }

        }

      }

      return 0;
    }

    /* ------------------------------------------------------------------- */
    #undef __FUNCT__
    #define __FUNCT__ "MSA_InitialPoint"
    /*
       MSA_InitialPoint - Calculates the initial guess in one of three ways.

       Input Parameters:
    .  user - user-defined application context
    .  X - vector for initial guess

       Output Parameters:
    .  X - newly computed initial guess
    */
    static int MSA_InitialPoint(AppCtx * user, Vec X)
    {
      int      start=-1,i,j,info;
      PetscScalar   zero=0.0;
      PetscTruth flg;

      info = VecSet(X, zero); CHKERRQ(info);
      info = PetscOptionsGetInt(PETSC_NULL,"-start",&start,&flg); CHKERRQ(info);

      if (flg && start==0){ /* The zero vector is reasonable */

        info = VecSet(X, zero); CHKERRQ(info);
        /* PetscLogInfo((user,"Min. Surface Area Problem: Start with 0 vector \n")); */

      } else { /* Take an average of the boundary conditions */

        int    row;
        int    mx=user->mx,my=user->my;
        PetscScalar *x;

        /* Get pointers to vector data */
        info = VecGetArray(X,&x); CHKERRQ(info);

        /* Perform local computations */
        for (j=0; j<my; j++){
          for (i=0; i< mx; i++){
    	row=(j)*mx + (i);
    	x[row] = ( ((j+1)*user->bottom[i+1]+(my-j+1)*user->top[i+1])/(my+2)+
    		   ((i+1)*user->left[j+1]+(mx-i+1)*user->right[j+1])/(mx+2))/2.0;
          }
        }

        /* Restore vectors */
        info = VecRestoreArray(X,&x); CHKERRQ(info);

      }
      return 0;
    }