mat/matfd/fdmatrix.c

#define PETSCMAT_DLL

/*
   This is where the abstract matrix operations are defined that are
  used for finite difference computations of Jacobians using coloring.
*/

#include "private/matimpl.h"        /*I "petscmat.h" I*/

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringSetF"
PetscErrorCode PETSCMAT_DLLEXPORT MatFDColoringSetF(MatFDColoring fd,Vec F)
{
  PetscFunctionBegin;
  fd->F = F;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringView_Draw_Zoom"
static PetscErrorCode MatFDColoringView_Draw_Zoom(PetscDraw draw,void *Aa)
{
  MatFDColoring  fd = (MatFDColoring)Aa;
  PetscErrorCode ierr;
  PetscInt       i,j;
  PetscReal      x,y;

  PetscFunctionBegin;

  /* loop over colors  */
  for (i=0; i<fd->ncolors; i++) {
    for (j=0; j<fd->nrows[i]; j++) {
      y = fd->M - fd->rows[i][j] - fd->rstart;
      x = fd->columnsforrow[i][j];
      ierr = PetscDrawRectangle(draw,x,y,x+1,y+1,i+1,i+1,i+1,i+1);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringView_Draw"
static PetscErrorCode MatFDColoringView_Draw(MatFDColoring fd,PetscViewer viewer)
{
  PetscErrorCode ierr;
  PetscTruth     isnull;
  PetscDraw      draw;
  PetscReal      xr,yr,xl,yl,h,w;

  PetscFunctionBegin;
  ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
  ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);

  ierr = PetscObjectCompose((PetscObject)fd,"Zoomviewer",(PetscObject)viewer);CHKERRQ(ierr);

  xr  = fd->N; yr = fd->M; h = yr/10.0; w = xr/10.0;
  xr += w;     yr += h;    xl = -w;     yl = -h;
  ierr = PetscDrawSetCoordinates(draw,xl,yl,xr,yr);CHKERRQ(ierr);
  ierr = PetscDrawZoom(draw,MatFDColoringView_Draw_Zoom,fd);CHKERRQ(ierr);
  ierr = PetscObjectCompose((PetscObject)fd,"Zoomviewer",PETSC_NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringView"
/*@C
   MatFDColoringView - Views a finite difference coloring context.

   Collective on MatFDColoring

   Input  Parameters:
+  c - the coloring context
-  viewer - visualization context

   Level: intermediate

   Notes:
   The available visualization contexts include
+     PETSC_VIEWER_STDOUT_SELF - standard output (default)
.     PETSC_VIEWER_STDOUT_WORLD - synchronized standard
        output where only the first processor opens
        the file.  All other processors send their
        data to the first processor to print.
-     PETSC_VIEWER_DRAW_WORLD - graphical display of nonzero structure

   Notes:
     Since PETSc uses only a small number of basic colors (currently 33), if the coloring
   involves more than 33 then some seemingly identical colors are displayed making it look
   like an illegal coloring. This is just a graphical artifact.

.seealso: MatFDColoringCreate()

.keywords: Mat, finite differences, coloring, view
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatFDColoringView(MatFDColoring c,PetscViewer viewer)
{
  PetscErrorCode    ierr;
  PetscInt          i,j;
  PetscTruth        isdraw,iascii;
  PetscViewerFormat format;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(c,MAT_FDCOLORING_COOKIE,1);
  if (!viewer) {
    ierr = PetscViewerASCIIGetStdout(((PetscObject)c)->comm,&viewer);CHKERRQ(ierr);
  }
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_COOKIE,2);
  PetscCheckSameComm(c,1,viewer,2);

  ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
  ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);CHKERRQ(ierr);
  if (isdraw) {
    ierr = MatFDColoringView_Draw(c,viewer);CHKERRQ(ierr);
  } else if (iascii) {
    ierr = PetscViewerASCIIPrintf(viewer,"MatFDColoring Object:\n");CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  Error tolerance=%G\n",c->error_rel);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  Umin=%G\n",c->umin);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  Number of colors=%D\n",c->ncolors);CHKERRQ(ierr);

    ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
    if (format != PETSC_VIEWER_ASCII_INFO) {
      for (i=0; i<c->ncolors; i++) {
        ierr = PetscViewerASCIIPrintf(viewer,"  Information for color %D\n",i);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(viewer,"    Number of columns %D\n",c->ncolumns[i]);CHKERRQ(ierr);
        for (j=0; j<c->ncolumns[i]; j++) {
          ierr = PetscViewerASCIIPrintf(viewer,"      %D\n",c->columns[i][j]);CHKERRQ(ierr);
        }
        ierr = PetscViewerASCIIPrintf(viewer,"    Number of rows %D\n",c->nrows[i]);CHKERRQ(ierr);
        for (j=0; j<c->nrows[i]; j++) {
          ierr = PetscViewerASCIIPrintf(viewer,"      %D %D \n",c->rows[i][j],c->columnsforrow[i][j]);CHKERRQ(ierr);
        }
      }
    }
    ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
  } else {
    SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for MatFDColoring",((PetscObject)viewer)->type_name);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringSetParameters"
/*@
   MatFDColoringSetParameters - Sets the parameters for the sparse approximation of
   a Jacobian matrix using finite differences.

   Collective on MatFDColoring

   The Jacobian is estimated with the differencing approximation
.vb
       F'(u)_{:,i} = [F(u+h*dx_{i}) - F(u)]/h where
       h = error_rel*u[i]                 if  abs(u[i]) > umin
         = +/- error_rel*umin             otherwise, with +/- determined by the sign of u[i]
       dx_{i} = (0, ... 1, .... 0)
.ve

   Input Parameters:
+  coloring - the coloring context
.  error_rel - relative error
-  umin - minimum allowable u-value magnitude

   Level: advanced

.keywords: Mat, finite differences, coloring, set, parameters

.seealso: MatFDColoringCreate()
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatFDColoringSetParameters(MatFDColoring matfd,PetscReal error,PetscReal umin)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(matfd,MAT_FDCOLORING_COOKIE,1);

  if (error != PETSC_DEFAULT) matfd->error_rel = error;
  if (umin != PETSC_DEFAULT)  matfd->umin      = umin;
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatFDColoringGetFunction"
/*@C
   MatFDColoringGetFunction - Gets the function to use for computing the Jacobian.

   Collective on MatFDColoring

   Input Parameters:
.  coloring - the coloring context

   Output Parameters:
+  f - the function
-  fctx - the optional user-defined function context

   Level: intermediate

.keywords: Mat, Jacobian, finite differences, set, function
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatFDColoringGetFunction(MatFDColoring matfd,PetscErrorCode (**f)(void),void **fctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(matfd,MAT_FDCOLORING_COOKIE,1);
  if (f) *f = matfd->f;
  if (fctx) *fctx = matfd->fctx;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringSetFunction"
/*@C
   MatFDColoringSetFunction - Sets the function to use for computing the Jacobian.

   Collective on MatFDColoring

   Input Parameters:
+  coloring - the coloring context
.  f - the function
-  fctx - the optional user-defined function context

   Calling sequence of (*f) function:
    For SNES:    PetscErrorCode (*f)(SNES,Vec,Vec,void*)
    For TS:      PetscErrorCode (*f)(TS,PetscReal,Vec,Vec,void*)
    If not using SNES or TS: PetscErrorCode (*f)(void *dummy,Vec,Vec,void*) and dummy is ignored

   Level: advanced

   Notes: This function is usually used automatically by SNES or TS (when one uses SNESSetJacobian() with the argument
     SNESDefaultComputeJacobianColor() or TSSetRHSJacobian() with the argument TSDefaultComputeJacobianColor()) and only needs to be used
     by someone computing a matrix via coloring directly by calling MatFDColoringApply()

   Fortran Notes:
    In Fortran you must call MatFDColoringSetFunction() for a coloring object to
  be used without SNES or TS or within the SNES solvers and MatFDColoringSetFunctionTS() if it is to be used
  within the TS solvers.

.keywords: Mat, Jacobian, finite differences, set, function
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatFDColoringSetFunction(MatFDColoring matfd,PetscErrorCode (*f)(void),void *fctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(matfd,MAT_FDCOLORING_COOKIE,1);
  matfd->f    = f;
  matfd->fctx = fctx;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringSetFromOptions"
/*@
   MatFDColoringSetFromOptions - Sets coloring finite difference parameters from
   the options database.

   Collective on MatFDColoring

   The Jacobian, F'(u), is estimated with the differencing approximation
.vb
       F'(u)_{:,i} = [F(u+h*dx_{i}) - F(u)]/h where
       h = error_rel*u[i]                 if  abs(u[i]) > umin
         = +/- error_rel*umin             otherwise, with +/- determined by the sign of u[i]
       dx_{i} = (0, ... 1, .... 0)
.ve

   Input Parameter:
.  coloring - the coloring context

   Options Database Keys:
+  -mat_fd_coloring_err <err> - Sets <err> (square root
           of relative error in the function)
.  -mat_fd_coloring_umin <umin> - Sets umin, the minimum allowable u-value magnitude
.  -mat_fd_type - "wp" or "ds" (see MATMFFD_WP or MATMFFD_DS)
.  -mat_fd_coloring_view - Activates basic viewing
.  -mat_fd_coloring_view_info - Activates viewing info
-  -mat_fd_coloring_view_draw - Activates drawing

    Level: intermediate

.keywords: Mat, finite differences, parameters

.seealso: MatFDColoringCreate(), MatFDColoringView(), MatFDColoringSetParameters()

@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatFDColoringSetFromOptions(MatFDColoring matfd)
{
  PetscErrorCode ierr;
  PetscTruth     flg;
  char           value[3];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(matfd,MAT_FDCOLORING_COOKIE,1);

  ierr = PetscOptionsBegin(((PetscObject)matfd)->comm,((PetscObject)matfd)->prefix,"Jacobian computation via finite differences option","MatFD");CHKERRQ(ierr);
    ierr = PetscOptionsReal("-mat_fd_coloring_err","Square root of relative error in function","MatFDColoringSetParameters",matfd->error_rel,&matfd->error_rel,0);CHKERRQ(ierr);
    ierr = PetscOptionsReal("-mat_fd_coloring_umin","Minimum allowable u magnitude","MatFDColoringSetParameters",matfd->umin,&matfd->umin,0);CHKERRQ(ierr);
    ierr = PetscOptionsString("-mat_fd_type","Algorithm to compute h, wp or ds","MatFDColoringCreate",matfd->htype,value,2,&flg);CHKERRQ(ierr);
    if (flg) {
      if (value[0] == 'w' && value[1] == 'p') matfd->htype = "wp";
      else if (value[0] == 'd' && value[1] == 's') matfd->htype = "ds";
      else SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"Unknown finite differencing type %s",value);
    }
    /* not used here; but so they are presented in the GUI */
    ierr = PetscOptionsName("-mat_fd_coloring_view","Print entire datastructure used for Jacobian","None",0);CHKERRQ(ierr);
    ierr = PetscOptionsName("-mat_fd_coloring_view_info","Print number of colors etc for Jacobian","None",0);CHKERRQ(ierr);
    ierr = PetscOptionsName("-mat_fd_coloring_view_draw","Plot nonzero structure ofJacobian","None",0);CHKERRQ(ierr);
  PetscOptionsEnd();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringView_Private"
PetscErrorCode MatFDColoringView_Private(MatFDColoring fd)
{
  PetscErrorCode ierr;
  PetscTruth     flg;
  PetscViewer    viewer;

  PetscFunctionBegin;
  ierr = PetscViewerASCIIGetStdout(((PetscObject)fd)->comm,&viewer);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(PETSC_NULL,"-mat_fd_coloring_view",&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = MatFDColoringView(fd,viewer);CHKERRQ(ierr);
  }
  ierr = PetscOptionsHasName(PETSC_NULL,"-mat_fd_coloring_view_info",&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO);CHKERRQ(ierr);
    ierr = MatFDColoringView(fd,viewer);CHKERRQ(ierr);
    ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
  }
  ierr = PetscOptionsHasName(PETSC_NULL,"-mat_fd_coloring_view_draw",&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = MatFDColoringView(fd,PETSC_VIEWER_DRAW_(((PetscObject)fd)->comm));CHKERRQ(ierr);
    ierr = PetscViewerFlush(PETSC_VIEWER_DRAW_(((PetscObject)fd)->comm));CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringCreate"
/*@
   MatFDColoringCreate - Creates a matrix coloring context for finite difference
   computation of Jacobians.

   Collective on Mat

   Input Parameters:
+  mat - the matrix containing the nonzero structure of the Jacobian
-  iscoloring - the coloring of the matrix

    Output Parameter:
.   color - the new coloring context

    Level: intermediate

.seealso: MatFDColoringDestroy(),SNESDefaultComputeJacobianColor(), ISColoringCreate(),
          MatFDColoringSetFunction(), MatFDColoringSetFromOptions(), MatFDColoringApply(),
          MatFDColoringView(), MatFDColoringSetParameters()
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatFDColoringCreate(Mat mat,ISColoring iscoloring,MatFDColoring *color)
{
  MatFDColoring  c;
  MPI_Comm       comm;
  PetscErrorCode ierr;
  PetscInt       M,N;
  PetscMPIInt    size;

  PetscFunctionBegin;
  ierr = PetscLogEventBegin(MAT_FDColoringCreate,mat,0,0,0);CHKERRQ(ierr);
  ierr = MatGetSize(mat,&M,&N);CHKERRQ(ierr);
  if (M != N) SETERRQ(PETSC_ERR_SUP,"Only for square matrices");

  ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
  ierr = PetscHeaderCreate(c,_p_MatFDColoring,int,MAT_FDCOLORING_COOKIE,0,"MatFDColoring",comm,MatFDColoringDestroy,MatFDColoringView);CHKERRQ(ierr);

  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
  c->ctype = iscoloring->ctype;

  if (mat->ops->fdcoloringcreate) {
    ierr = (*mat->ops->fdcoloringcreate)(mat,iscoloring,c);CHKERRQ(ierr);
  } else {
    SETERRQ(PETSC_ERR_SUP,"Code not yet written for this matrix type");
  }

  ierr = MatGetVecs(mat,PETSC_NULL,&c->w1);CHKERRQ(ierr);
  ierr = PetscLogObjectParent(c,c->w1);CHKERRQ(ierr);
  ierr = VecDuplicate(c->w1,&c->w2);CHKERRQ(ierr);
  ierr = PetscLogObjectParent(c,c->w2);CHKERRQ(ierr);

  c->error_rel         = PETSC_SQRT_MACHINE_EPSILON;
  c->umin              = 100.0*PETSC_SQRT_MACHINE_EPSILON;
  c->currentcolor      = -1;
  c->htype             = "wp";

  *color = c;
  ierr = PetscLogEventEnd(MAT_FDColoringCreate,mat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringDestroy"
/*@
    MatFDColoringDestroy - Destroys a matrix coloring context that was created
    via MatFDColoringCreate().

    Collective on MatFDColoring

    Input Parameter:
.   c - coloring context

    Level: intermediate

.seealso: MatFDColoringCreate()
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatFDColoringDestroy(MatFDColoring c)
{
  PetscErrorCode ierr;
  PetscInt       i;

  PetscFunctionBegin;
  if (--((PetscObject)c)->refct > 0) PetscFunctionReturn(0);

  for (i=0; i<c->ncolors; i++) {
    ierr = PetscFree(c->columns[i]);CHKERRQ(ierr);
    ierr = PetscFree(c->rows[i]);CHKERRQ(ierr);
    ierr = PetscFree(c->columnsforrow[i]);CHKERRQ(ierr);
    if (c->vscaleforrow) {ierr = PetscFree(c->vscaleforrow[i]);CHKERRQ(ierr);}
  }
  ierr = PetscFree(c->ncolumns);CHKERRQ(ierr);
  ierr = PetscFree(c->columns);CHKERRQ(ierr);
  ierr = PetscFree(c->nrows);CHKERRQ(ierr);
  ierr = PetscFree(c->rows);CHKERRQ(ierr);
  ierr = PetscFree(c->columnsforrow);CHKERRQ(ierr);
  ierr = PetscFree(c->vscaleforrow);CHKERRQ(ierr);
  if (c->vscale)       {ierr = VecDestroy(c->vscale);CHKERRQ(ierr);}
  if (c->w1) {
    ierr = VecDestroy(c->w1);CHKERRQ(ierr);
    ierr = VecDestroy(c->w2);CHKERRQ(ierr);
  }
  if (c->w3){
    ierr = VecDestroy(c->w3);CHKERRQ(ierr);
  }
  ierr = PetscHeaderDestroy(c);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringGetPerturbedColumns"
/*@C
    MatFDColoringGetPerturbedColumns - Returns the indices of the columns that
      that are currently being perturbed.

    Not Collective

    Input Parameters:
.   coloring - coloring context created with MatFDColoringCreate()

    Output Parameters:
+   n - the number of local columns being perturbed
-   cols - the column indices, in global numbering

   Level: intermediate

.seealso: MatFDColoringCreate(), MatFDColoringDestroy(), MatFDColoringView(), MatFDColoringApply()

.keywords: coloring, Jacobian, finite differences
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatFDColoringGetPerturbedColumns(MatFDColoring coloring,PetscInt *n,PetscInt *cols[])
{
  PetscFunctionBegin;
  if (coloring->currentcolor >= 0) {
    *n    = coloring->ncolumns[coloring->currentcolor];
    *cols = coloring->columns[coloring->currentcolor];
  } else {
    *n = 0;
  }
  PetscFunctionReturn(0);
}

#include "petscda.h"      /*I      "petscda.h"    I*/

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringApply"
/*@
    MatFDColoringApply - Given a matrix for which a MatFDColoring context
    has been created, computes the Jacobian for a function via finite differences.

    Collective on MatFDColoring

    Input Parameters:
+   mat - location to store Jacobian
.   coloring - coloring context created with MatFDColoringCreate()
.   x1 - location at which Jacobian is to be computed
-   sctx - context required by function, if this is being used with the SNES solver then it is SNES object, otherwise it is null

    Options Database Keys:
+    -mat_fd_type - "wp" or "ds"  (see MATMFFD_WP or MATMFFD_DS)
.    -mat_fd_coloring_view - Activates basic viewing or coloring
.    -mat_fd_coloring_view_draw - Activates drawing of coloring
-    -mat_fd_coloring_view_info - Activates viewing of coloring info

    Level: intermediate

.seealso: MatFDColoringCreate(), MatFDColoringDestroy(), MatFDColoringView(), MatFDColoringSetFunction()

.keywords: coloring, Jacobian, finite differences
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatFDColoringApply(Mat J,MatFDColoring coloring,Vec x1,MatStructure *flag,void *sctx)
{
  PetscErrorCode (*f)(void*,Vec,Vec,void*) = (PetscErrorCode (*)(void*,Vec,Vec,void *))coloring->f;
  PetscErrorCode ierr;
  PetscInt       k,start,end,l,row,col,srow,**vscaleforrow,m1,m2;
  PetscScalar    dx,*y,*xx,*w3_array;
  PetscScalar    *vscale_array;
  PetscReal      epsilon = coloring->error_rel,umin = coloring->umin,unorm;
  Vec            w1=coloring->w1,w2=coloring->w2,w3;
  void           *fctx = coloring->fctx;
  PetscTruth     flg;
  PetscInt       ctype=coloring->ctype,N,col_start=0,col_end=0;
  Vec            x1_tmp;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(J,MAT_COOKIE,1);
  PetscValidHeaderSpecific(coloring,MAT_FDCOLORING_COOKIE,2);
  PetscValidHeaderSpecific(x1,VEC_COOKIE,3);
  if (!f) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Must call MatFDColoringSetFunction()");

  ierr = PetscLogEventBegin(MAT_FDColoringApply,coloring,J,x1,0);CHKERRQ(ierr);
  ierr = MatSetUnfactored(J);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(PETSC_NULL,"-mat_fd_coloring_dont_rezero",&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscInfo(coloring,"Not calling MatZeroEntries()\n");CHKERRQ(ierr);
  } else {
    PetscTruth assembled;
    ierr = MatAssembled(J,&assembled);CHKERRQ(ierr);
    if (assembled) {
      ierr = MatZeroEntries(J);CHKERRQ(ierr);
    }
  }

  x1_tmp = x1;
  if (!coloring->vscale){
    ierr = VecDuplicate(x1_tmp,&coloring->vscale);CHKERRQ(ierr);
  }

  /*
    This is a horrible, horrible, hack. See DMMGComputeJacobian_Multigrid() it inproperly sets
    coloring->F for the coarser grids from the finest
  */
  if (coloring->F) {
    ierr = VecGetLocalSize(coloring->F,&m1);CHKERRQ(ierr);
    ierr = VecGetLocalSize(w1,&m2);CHKERRQ(ierr);
    if (m1 != m2) {
      coloring->F = 0;
      }
    }

  if (coloring->htype[0] == 'w') { /* tacky test; need to make systematic if we add other approaches to computing h*/
    ierr = VecNorm(x1_tmp,NORM_2,&unorm);CHKERRQ(ierr);
  }
  ierr = VecGetOwnershipRange(w1,&start,&end);CHKERRQ(ierr); /* OwnershipRange is used by ghosted x! */

  /* Set w1 = F(x1) */
  if (coloring->F) {
    w1          = coloring->F; /* use already computed value of function */
    coloring->F = 0;
  } else {
    ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
    ierr = (*f)(sctx,x1_tmp,w1,fctx);CHKERRQ(ierr);
    ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
  }

  if (!coloring->w3) {
    ierr = VecDuplicate(x1_tmp,&coloring->w3);CHKERRQ(ierr);
    ierr = PetscLogObjectParent(coloring,coloring->w3);CHKERRQ(ierr);
  }
  w3 = coloring->w3;

    /* Compute all the local scale factors, including ghost points */
  ierr = VecGetLocalSize(x1_tmp,&N);CHKERRQ(ierr);
  ierr = VecGetArray(x1_tmp,&xx);CHKERRQ(ierr);
  ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
  if (ctype == IS_COLORING_GHOSTED){
    col_start = 0; col_end = N;
  } else if (ctype == IS_COLORING_GLOBAL){
    xx = xx - start;
    vscale_array = vscale_array - start;
    col_start = start; col_end = N + start;
  }
  for (col=col_start; col<col_end; col++){
    /* Loop over each local column, vscale[col] = 1./(epsilon*dx[col]) */
    if (coloring->htype[0] == 'w') {
      dx = 1.0 + unorm;
    } else {
      dx  = xx[col];
    }
    if (dx == 0.0) dx = 1.0;
#if !defined(PETSC_USE_COMPLEX)
    if (dx < umin && dx >= 0.0)      dx = umin;
    else if (dx < 0.0 && dx > -umin) dx = -umin;
#else
    if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
    else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
#endif
    dx               *= epsilon;
    vscale_array[col] = 1.0/dx;
  }
  if (ctype == IS_COLORING_GLOBAL)  vscale_array = vscale_array + start;
  ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
  if (ctype == IS_COLORING_GLOBAL){
    ierr = VecGhostUpdateBegin(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecGhostUpdateEnd(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  }

  if (coloring->vscaleforrow) {
    vscaleforrow = coloring->vscaleforrow;
  } else {
    SETERRQ(PETSC_ERR_ARG_NULL,"Null Object: coloring->vscaleforrow");
  }

  /*
    Loop over each color
  */
  ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
  for (k=0; k<coloring->ncolors; k++) {
    coloring->currentcolor = k;
    ierr = VecCopy(x1_tmp,w3);CHKERRQ(ierr);
    ierr = VecGetArray(w3,&w3_array);CHKERRQ(ierr);
    if (ctype == IS_COLORING_GLOBAL) w3_array = w3_array - start;
    /*
      Loop over each column associated with color
      adding the perturbation to the vector w3.
    */
    for (l=0; l<coloring->ncolumns[k]; l++) {
      col = coloring->columns[k][l];    /* local column of the matrix we are probing for */
      if (coloring->htype[0] == 'w') {
        dx = 1.0 + unorm;
      } else {
        dx  = xx[col];
      }
      if (dx == 0.0) dx = 1.0;
#if !defined(PETSC_USE_COMPLEX)
      if (dx < umin && dx >= 0.0)      dx = umin;
      else if (dx < 0.0 && dx > -umin) dx = -umin;
#else
      if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
      else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
#endif
      dx            *= epsilon;
      if (!PetscAbsScalar(dx)) SETERRQ(PETSC_ERR_PLIB,"Computed 0 differencing parameter");
      w3_array[col] += dx;
    }
    if (ctype == IS_COLORING_GLOBAL) w3_array = w3_array + start;
    ierr = VecRestoreArray(w3,&w3_array);CHKERRQ(ierr);

    /*
      Evaluate function at w3 = x1 + dx (here dx is a vector of perturbations)
                           w2 = F(x1 + dx) - F(x1)
    */
    ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
    ierr = (*f)(sctx,w3,w2,fctx);CHKERRQ(ierr);
    ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
    ierr = VecAXPY(w2,-1.0,w1);CHKERRQ(ierr);

    /*
      Loop over rows of vector, putting results into Jacobian matrix
    */
    ierr = VecGetArray(w2,&y);CHKERRQ(ierr);
    for (l=0; l<coloring->nrows[k]; l++) {
      row    = coloring->rows[k][l];             /* local row index */
      col    = coloring->columnsforrow[k][l];    /* global column index */
      y[row] *= vscale_array[vscaleforrow[k][l]];
      srow   = row + start;
      ierr   = MatSetValues(J,1,&srow,1,&col,y+row,INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = VecRestoreArray(w2,&y);CHKERRQ(ierr);
  } /* endof for each color */
  if (ctype == IS_COLORING_GLOBAL) xx = xx + start;
  ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
  ierr = VecRestoreArray(x1_tmp,&xx);CHKERRQ(ierr);

  coloring->currentcolor = -1;
  ierr  = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr  = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_FDColoringApply,coloring,J,x1,0);CHKERRQ(ierr);

  ierr = PetscOptionsHasName(PETSC_NULL,"-mat_null_space_test",&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = MatNullSpaceTest(J->nullsp,J,PETSC_NULL);CHKERRQ(ierr);
  }
  ierr = MatFDColoringView_Private(coloring);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringApplyTS"
/*@
    MatFDColoringApplyTS - Given a matrix for which a MatFDColoring context
    has been created, computes the Jacobian for a function via finite differences.

   Collective on Mat, MatFDColoring, and Vec

    Input Parameters:
+   mat - location to store Jacobian
.   coloring - coloring context created with MatFDColoringCreate()
.   x1 - location at which Jacobian is to be computed
-   sctx - context required by function, if this is being used with the TS solver then it is TS object, otherwise it is null

   Level: intermediate

.seealso: MatFDColoringCreate(), MatFDColoringDestroy(), MatFDColoringView(), MatFDColoringSetFunction()

.keywords: coloring, Jacobian, finite differences
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatFDColoringApplyTS(Mat J,MatFDColoring coloring,PetscReal t,Vec x1,MatStructure *flag,void *sctx)
{
  PetscErrorCode (*f)(void*,PetscReal,Vec,Vec,void*)=(PetscErrorCode (*)(void*,PetscReal,Vec,Vec,void *))coloring->f;
  PetscErrorCode ierr;
  PetscInt       k,N,start,end,l,row,col,srow,**vscaleforrow;
  PetscScalar    dx,*y,*xx,*w3_array;
  PetscScalar    *vscale_array;
  PetscReal      epsilon = coloring->error_rel,umin = coloring->umin;
  Vec            w1=coloring->w1,w2=coloring->w2,w3;
  void           *fctx = coloring->fctx;
  PetscTruth     flg;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(J,MAT_COOKIE,1);
  PetscValidHeaderSpecific(coloring,MAT_FDCOLORING_COOKIE,2);
  PetscValidHeaderSpecific(x1,VEC_COOKIE,4);

  ierr = PetscLogEventBegin(MAT_FDColoringApply,coloring,J,x1,0);CHKERRQ(ierr);
  if (!coloring->w3) {
    ierr = VecDuplicate(x1,&coloring->w3);CHKERRQ(ierr);
    ierr = PetscLogObjectParent(coloring,coloring->w3);CHKERRQ(ierr);
  }
  w3 = coloring->w3;

  ierr = MatSetUnfactored(J);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(PETSC_NULL,"-mat_fd_coloring_dont_rezero",&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscInfo(coloring,"Not calling MatZeroEntries()\n");CHKERRQ(ierr);
  } else {
    PetscTruth assembled;
    ierr = MatAssembled(J,&assembled);CHKERRQ(ierr);
    if (assembled) {
      ierr = MatZeroEntries(J);CHKERRQ(ierr);
    }
  }

  ierr = VecGetOwnershipRange(x1,&start,&end);CHKERRQ(ierr);
  ierr = VecGetSize(x1,&N);CHKERRQ(ierr);
  ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
  ierr = (*f)(sctx,t,x1,w1,fctx);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);

  /*
      Compute all the scale factors and share with other processors
  */
  ierr = VecGetArray(x1,&xx);CHKERRQ(ierr);xx = xx - start;
  ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);vscale_array = vscale_array - start;
  for (k=0; k<coloring->ncolors; k++) {
    /*
       Loop over each column associated with color adding the
       perturbation to the vector w3.
    */
    for (l=0; l<coloring->ncolumns[k]; l++) {
      col = coloring->columns[k][l];    /* column of the matrix we are probing for */
      dx  = xx[col];
      if (dx == 0.0) dx = 1.0;
#if !defined(PETSC_USE_COMPLEX)
      if (dx < umin && dx >= 0.0)      dx = umin;
      else if (dx < 0.0 && dx > -umin) dx = -umin;
#else
      if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
      else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
#endif
      dx                *= epsilon;
      vscale_array[col] = 1.0/dx;
    }
  }
  vscale_array = vscale_array - start;ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
  ierr = VecGhostUpdateBegin(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = VecGhostUpdateEnd(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);

  if (coloring->vscaleforrow) vscaleforrow = coloring->vscaleforrow;
  else                        vscaleforrow = coloring->columnsforrow;

  ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
  /*
      Loop over each color
  */
  for (k=0; k<coloring->ncolors; k++) {
    ierr = VecCopy(x1,w3);CHKERRQ(ierr);
    ierr = VecGetArray(w3,&w3_array);CHKERRQ(ierr);w3_array = w3_array - start;
    /*
       Loop over each column associated with color adding the
       perturbation to the vector w3.
    */
    for (l=0; l<coloring->ncolumns[k]; l++) {
      col = coloring->columns[k][l];    /* column of the matrix we are probing for */
      dx  = xx[col];
      if (dx == 0.0) dx = 1.0;
#if !defined(PETSC_USE_COMPLEX)
      if (dx < umin && dx >= 0.0)      dx = umin;
      else if (dx < 0.0 && dx > -umin) dx = -umin;
#else
      if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
      else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
#endif
      dx            *= epsilon;
      w3_array[col] += dx;
    }
    w3_array = w3_array + start; ierr = VecRestoreArray(w3,&w3_array);CHKERRQ(ierr);

    /*
       Evaluate function at x1 + dx (here dx is a vector of perturbations)
    */
    ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
    ierr = (*f)(sctx,t,w3,w2,fctx);CHKERRQ(ierr);
    ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
    ierr = VecAXPY(w2,-1.0,w1);CHKERRQ(ierr);

    /*
       Loop over rows of vector, putting results into Jacobian matrix
    */
    ierr = VecGetArray(w2,&y);CHKERRQ(ierr);
    for (l=0; l<coloring->nrows[k]; l++) {
      row    = coloring->rows[k][l];
      col    = coloring->columnsforrow[k][l];
      y[row] *= vscale_array[vscaleforrow[k][l]];
      srow   = row + start;
      ierr   = MatSetValues(J,1,&srow,1,&col,y+row,INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = VecRestoreArray(w2,&y);CHKERRQ(ierr);
  }
  ierr  = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
  xx    = xx + start; ierr  = VecRestoreArray(x1,&xx);CHKERRQ(ierr);
  ierr  = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr  = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr  = PetscLogEventEnd(MAT_FDColoringApply,coloring,J,x1,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}