mat/matfd/fdmatrix.c

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

#include <petsc/private/matimpl.h> /*I "petscmat.h" I*/
#include <petsc/private/isimpl.h>

PetscErrorCode MatFDColoringSetF(MatFDColoring fd, Vec F)
{
  PetscFunctionBegin;
  if (F) {
    PetscCall(VecCopy(F, fd->w1));
    fd->fset = PETSC_TRUE;
  } else {
    fd->fset = PETSC_FALSE;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

#include <petscdraw.h>
static PetscErrorCode MatFDColoringView_Draw_Zoom(PetscDraw draw, void *Aa)
{
  MatFDColoring fd = (MatFDColoring)Aa;
  PetscMPIInt   i, j, nz;
  PetscInt      row;
  PetscReal     x, y;
  MatEntry     *Jentry = fd->matentry;

  PetscFunctionBegin;
  /* loop over colors  */
  nz = 0;
  for (i = 0; i < fd->ncolors; i++) {
    for (j = 0; j < fd->nrows[i]; j++) {
      row = Jentry[nz].row;
      y   = fd->M - row - fd->rstart;
      x   = (PetscReal)Jentry[nz++].col;
      PetscCall(PetscDrawRectangle(draw, x, y, x + 1, y + 1, i + 1, i + 1, i + 1, i + 1));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatFDColoringView_Draw(MatFDColoring fd, PetscViewer viewer)
{
  PetscBool isnull;
  PetscDraw draw;
  PetscReal xr, yr, xl, yl, h, w;

  PetscFunctionBegin;
  PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
  PetscCall(PetscDrawIsNull(draw, &isnull));
  if (isnull) PetscFunctionReturn(PETSC_SUCCESS);

  xr = fd->N;
  yr = fd->M;
  h  = yr / 10.0;
  w  = xr / 10.0;
  xr += w;
  yr += h;
  xl = -w;
  yl = -h;
  PetscCall(PetscDrawSetCoordinates(draw, xl, yl, xr, yr));
  PetscCall(PetscObjectCompose((PetscObject)fd, "Zoomviewer", (PetscObject)viewer));
  PetscCall(PetscDrawZoom(draw, MatFDColoringView_Draw_Zoom, fd));
  PetscCall(PetscObjectCompose((PetscObject)fd, "Zoomviewer", NULL));
  PetscCall(PetscDrawSave(draw));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatFDColoringView - Views a finite difference coloring context.

  Collective

  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

  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: `Mat`, `MatFDColoring`, `MatFDColoringCreate()`
@*/
PetscErrorCode MatFDColoringView(MatFDColoring c, PetscViewer viewer)
{
  PetscInt          i, j;
  PetscBool         isdraw, iascii;
  PetscViewerFormat format;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(c, MAT_FDCOLORING_CLASSID, 1);
  if (!viewer) PetscCall(PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)c), &viewer));
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  PetscCheckSameComm(c, 1, viewer, 2);

  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
  if (isdraw) {
    PetscCall(MatFDColoringView_Draw(c, viewer));
  } else if (iascii) {
    PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)c, viewer));
    PetscCall(PetscViewerASCIIPrintf(viewer, "  Error tolerance=%g\n", (double)c->error_rel));
    PetscCall(PetscViewerASCIIPrintf(viewer, "  Umin=%g\n", (double)c->umin));
    PetscCall(PetscViewerASCIIPrintf(viewer, "  Number of colors=%" PetscInt_FMT "\n", c->ncolors));

    PetscCall(PetscViewerGetFormat(viewer, &format));
    if (format != PETSC_VIEWER_ASCII_INFO) {
      PetscInt row, col, nz;
      nz = 0;
      for (i = 0; i < c->ncolors; i++) {
        PetscCall(PetscViewerASCIIPrintf(viewer, "  Information for color %" PetscInt_FMT "\n", i));
        PetscCall(PetscViewerASCIIPrintf(viewer, "    Number of columns %" PetscInt_FMT "\n", c->ncolumns[i]));
        for (j = 0; j < c->ncolumns[i]; j++) PetscCall(PetscViewerASCIIPrintf(viewer, "      %" PetscInt_FMT "\n", c->columns[i][j]));
        PetscCall(PetscViewerASCIIPrintf(viewer, "    Number of rows %" PetscInt_FMT "\n", c->nrows[i]));
        if (c->matentry) {
          for (j = 0; j < c->nrows[i]; j++) {
            row = c->matentry[nz].row;
            col = c->matentry[nz++].col;
            PetscCall(PetscViewerASCIIPrintf(viewer, "      %" PetscInt_FMT " %" PetscInt_FMT " \n", row, col));
          }
        }
      }
    }
    PetscCall(PetscViewerFlush(viewer));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatFDColoringSetParameters - Sets the parameters for the sparse approximation of
  a Jacobian matrix using finite differences.

  Logically Collective

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

  Level: advanced

  Note:
  The Jacobian is estimated with the differencing approximation
.vb
       F'(u)_{:,i} = [F(u+h*dx_{i}) - F(u)]/h where
       htype = 'ds':
         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)

       htype = 'wp':
         h = error_rel * sqrt(1 + ||u||)
.ve

.seealso: `Mat`, `MatFDColoring`, `MatFDColoringCreate()`, `MatFDColoringSetFromOptions()`
@*/
PetscErrorCode MatFDColoringSetParameters(MatFDColoring matfd, PetscReal error, PetscReal umin)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(matfd, MAT_FDCOLORING_CLASSID, 1);
  PetscValidLogicalCollectiveReal(matfd, error, 2);
  PetscValidLogicalCollectiveReal(matfd, umin, 3);
  if (error != (PetscReal)PETSC_DEFAULT) matfd->error_rel = error;
  if (umin != (PetscReal)PETSC_DEFAULT) matfd->umin = umin;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatFDColoringSetBlockSize - Sets block size for efficient inserting entries of Jacobian matrix.

  Logically Collective

  Input Parameters:
+ matfd - the coloring context
. brows - number of rows in the block
- bcols - number of columns in the block

  Level: intermediate

.seealso: `Mat`, `MatFDColoring`, `MatFDColoringCreate()`, `MatFDColoringSetFromOptions()`
@*/
PetscErrorCode MatFDColoringSetBlockSize(MatFDColoring matfd, PetscInt brows, PetscInt bcols)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(matfd, MAT_FDCOLORING_CLASSID, 1);
  PetscValidLogicalCollectiveInt(matfd, brows, 2);
  PetscValidLogicalCollectiveInt(matfd, bcols, 3);
  if (brows != PETSC_DEFAULT) matfd->brows = brows;
  if (bcols != PETSC_DEFAULT) matfd->bcols = bcols;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatFDColoringSetUp - Sets up the internal data structures of matrix coloring context for the later use.

  Collective

  Input Parameters:
+ mat        - the matrix containing the nonzero structure of the Jacobian
. iscoloring - the coloring of the matrix; usually obtained with `MatGetColoring()` or `DMCreateColoring()`
- color      - the matrix coloring context

  Level: beginner

  Notes:
  When the coloring type is `IS_COLORING_LOCAL` the coloring is in the local ordering of the unknowns.

.seealso: `Mat`, `MatFDColoring`, `MatFDColoringCreate()`, `MatFDColoringDestroy()`
@*/
PetscErrorCode MatFDColoringSetUp(Mat mat, ISColoring iscoloring, MatFDColoring color)
{
  PetscBool eq;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
  PetscValidHeaderSpecific(color, MAT_FDCOLORING_CLASSID, 3);
  if (color->setupcalled) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscObjectCompareId((PetscObject)mat, color->matid, &eq));
  PetscCheck(eq, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONG, "Matrix used with MatFDColoringSetUp() must be that used with MatFDColoringCreate()");

  PetscCall(PetscLogEventBegin(MAT_FDColoringSetUp, mat, 0, 0, 0));
  PetscUseTypeMethod(mat, fdcoloringsetup, iscoloring, color);

  color->setupcalled = PETSC_TRUE;
  PetscCall(PetscLogEventEnd(MAT_FDColoringSetUp, mat, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatFDColoringGetFunction - Gets the function to use for computing the Jacobian.

  Not Collective

  Input Parameter:
. matfd - the coloring context

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

  Level: intermediate

.seealso: `Mat`, `MatFDColoring`, `MatFDColoringCreate()`, `MatFDColoringSetFunction()`, `MatFDColoringSetFromOptions()`
@*/
PetscErrorCode MatFDColoringGetFunction(MatFDColoring matfd, PetscErrorCode (**f)(void), void **fctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(matfd, MAT_FDCOLORING_CLASSID, 1);
  if (f) *f = matfd->f;
  if (fctx) *fctx = matfd->fctx;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatFDColoringSetFunction - Sets the function to use for computing the Jacobian.

  Logically Collective

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

  Level: advanced

  Note:
  `f` has two possible calling configurations\:
$ PetscErrorCode f(SNES snes, Vec in, Vec out, void *fctx)
+ snes - the nonlinear solver `SNES` object
. in   - the location where the Jacobian is to be computed
. out  - the location to put the computed function value
- fctx - the function context

  and
$ PetscErrorCode f(void *dummy, Vec in, Vec out, void *fctx)
+ dummy - an unused parameter
. in    - the location where the Jacobian is to be computed
. out   - the location to put the computed function value
- fctx  - the function context

  This function is usually used automatically by `SNES` (when one uses `SNESSetJacobian()` with the argument
  `SNESComputeJacobianDefaultColor()`) 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 within the `SNES` solvers.

.seealso: `Mat`, `MatFDColoring`, `MatFDColoringCreate()`, `MatFDColoringGetFunction()`, `MatFDColoringSetFromOptions()`
@*/
PetscErrorCode MatFDColoringSetFunction(MatFDColoring matfd, PetscErrorCode (*f)(void), void *fctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(matfd, MAT_FDCOLORING_CLASSID, 1);
  matfd->f    = f;
  matfd->fctx = fctx;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatFDColoringSetFromOptions - Sets coloring finite difference parameters from
  the options database.

  Collective

  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:
. matfd - 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 ::ascii_info - Activates viewing info
- -mat_fd_coloring_view draw         - Activates drawing

  Level: intermediate

.seealso: `Mat`, `MatFDColoring`, `MatFDColoringCreate()`, `MatFDColoringView()`, `MatFDColoringSetParameters()`
@*/
PetscErrorCode MatFDColoringSetFromOptions(MatFDColoring matfd)
{
  PetscBool flg;
  char      value[3];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(matfd, MAT_FDCOLORING_CLASSID, 1);

  PetscObjectOptionsBegin((PetscObject)matfd);
  PetscCall(PetscOptionsReal("-mat_fd_coloring_err", "Square root of relative error in function", "MatFDColoringSetParameters", matfd->error_rel, &matfd->error_rel, NULL));
  PetscCall(PetscOptionsReal("-mat_fd_coloring_umin", "Minimum allowable u magnitude", "MatFDColoringSetParameters", matfd->umin, &matfd->umin, NULL));
  PetscCall(PetscOptionsString("-mat_fd_type", "Algorithm to compute h, wp or ds", "MatFDColoringCreate", matfd->htype, value, sizeof(value), &flg));
  if (flg) {
    if (value[0] == 'w' && value[1] == 'p') matfd->htype = "wp";
    else if (value[0] == 'd' && value[1] == 's') matfd->htype = "ds";
    else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Unknown finite differencing type %s", value);
  }
  PetscCall(PetscOptionsInt("-mat_fd_coloring_brows", "Number of block rows", "MatFDColoringSetBlockSize", matfd->brows, &matfd->brows, NULL));
  PetscCall(PetscOptionsInt("-mat_fd_coloring_bcols", "Number of block columns", "MatFDColoringSetBlockSize", matfd->bcols, &matfd->bcols, &flg));
  if (flg && matfd->bcols > matfd->ncolors) {
    /* input bcols cannot be > matfd->ncolors, thus set it as ncolors */
    matfd->bcols = matfd->ncolors;
  }

  /* process any options handlers added with PetscObjectAddOptionsHandler() */
  PetscCall(PetscObjectProcessOptionsHandlers((PetscObject)matfd, PetscOptionsObject));
  PetscOptionsEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatFDColoringSetType - Sets the approach for computing the finite difference parameter

  Collective

  Input Parameters:
+ matfd - the coloring context
- type  - either `MATMFFD_WP` or `MATMFFD_DS`

  Options Database Key:
. -mat_fd_type - "wp" or "ds"

  Level: intermediate

  Note:
  It is goofy that the argument type is `MatMFFDType` since the `MatFDColoring` actually computes the matrix entries
  but the process of computing the entries is the same as with the `MATMFFD` operation so we should reuse the names instead of
  introducing another one.

.seealso: `Mat`, `MatFDColoring`, `MatFDColoringCreate()`, `MatFDColoringView()`, `MatFDColoringSetParameters()`
@*/
PetscErrorCode MatFDColoringSetType(MatFDColoring matfd, MatMFFDType type)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(matfd, MAT_FDCOLORING_CLASSID, 1);
  /*
     It is goofy to handle the strings this way but currently there is no code to free a dynamically created matfd->htype
     and this function is being provided as patch for a release so it shouldn't change the implementation
  */
  if (type[0] == 'w' && type[1] == 'p') matfd->htype = "wp";
  else if (type[0] == 'd' && type[1] == 's') matfd->htype = "ds";
  else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Unknown finite differencing type %s", type);
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatFDColoringViewFromOptions(MatFDColoring fd, const char prefix[], const char optionname[])
{
  PetscBool         flg;
  PetscViewer       viewer;
  PetscViewerFormat format;

  PetscFunctionBegin;
  if (prefix) {
    PetscCall(PetscOptionsCreateViewer(PetscObjectComm((PetscObject)fd), ((PetscObject)fd)->options, prefix, optionname, &viewer, &format, &flg));
  } else {
    PetscCall(PetscOptionsCreateViewer(PetscObjectComm((PetscObject)fd), ((PetscObject)fd)->options, ((PetscObject)fd)->prefix, optionname, &viewer, &format, &flg));
  }
  if (flg) {
    PetscCall(PetscViewerPushFormat(viewer, format));
    PetscCall(MatFDColoringView(fd, viewer));
    PetscCall(PetscViewerPopFormat(viewer));
    PetscCall(PetscViewerDestroy(&viewer));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatFDColoringCreate - Creates a matrix coloring context for finite difference
  computation of Jacobians.

  Collective

  Input Parameters:
+ mat        - the matrix containing the nonzero structure of the Jacobian
- iscoloring - the coloring of the matrix; usually obtained with `MatColoringCreate()` or `DMCreateColoring()`

  Output Parameter:
. color - the new coloring context

  Level: intermediate

.seealso: `Mat`, `MatFDColoring`, `MatFDColoringDestroy()`, `SNESComputeJacobianDefaultColor()`, `ISColoringCreate()`,
          `MatFDColoringSetFunction()`, `MatFDColoringSetFromOptions()`, `MatFDColoringApply()`,
          `MatFDColoringView()`, `MatFDColoringSetParameters()`, `MatColoringCreate()`, `DMCreateColoring()`, `MatFDColoringSetValues()`
@*/
PetscErrorCode MatFDColoringCreate(Mat mat, ISColoring iscoloring, MatFDColoring *color)
{
  MatFDColoring c;
  MPI_Comm      comm;
  PetscInt      M, N;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
  PetscAssertPointer(color, 3);
  PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Matrix must be assembled by calls to MatAssemblyBegin/End();");
  PetscCall(PetscLogEventBegin(MAT_FDColoringCreate, mat, 0, 0, 0));
  PetscCall(MatGetSize(mat, &M, &N));
  PetscCheck(M == N, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Only for square matrices");
  PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
  PetscCall(PetscHeaderCreate(c, MAT_FDCOLORING_CLASSID, "MatFDColoring", "Jacobian computation via finite differences with coloring", "Mat", comm, MatFDColoringDestroy, MatFDColoringView));

  c->ctype = iscoloring->ctype;
  PetscCall(PetscObjectGetId((PetscObject)mat, &c->matid));

  PetscUseTypeMethod(mat, fdcoloringcreate, iscoloring, c);

  PetscCall(MatCreateVecs(mat, NULL, &c->w1));
  /* Vec is used intensively in particular piece of scalar CPU code; won't benefit from bouncing back and forth to the GPU */
  PetscCall(VecBindToCPU(c->w1, PETSC_TRUE));
  PetscCall(VecDuplicate(c->w1, &c->w2));
  /* Vec is used intensively in particular piece of scalar CPU code; won't benefit from bouncing back and forth to the GPU */
  PetscCall(VecBindToCPU(c->w2, PETSC_TRUE));

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

  *color = c;
  PetscCall(PetscObjectCompose((PetscObject)mat, "SNESMatFDColoring", (PetscObject)c));
  PetscCall(PetscLogEventEnd(MAT_FDColoringCreate, mat, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatFDColoringDestroy - Destroys a matrix coloring context that was created
  via `MatFDColoringCreate()`.

  Collective

  Input Parameter:
. c - coloring context

  Level: intermediate

.seealso: `Mat`, `MatFDColoring`, `MatFDColoringCreate()`
@*/
PetscErrorCode MatFDColoringDestroy(MatFDColoring *c)
{
  PetscInt      i;
  MatFDColoring color = *c;

  PetscFunctionBegin;
  if (!*c) PetscFunctionReturn(PETSC_SUCCESS);
  if (--((PetscObject)color)->refct > 0) {
    *c = NULL;
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  /* we do not free the column arrays since their entries are owned by the ISs in color->isa */
  for (i = 0; i < color->ncolors; i++) PetscCall(ISDestroy(&color->isa[i]));
  PetscCall(PetscFree(color->isa));
  PetscCall(PetscFree2(color->ncolumns, color->columns));
  PetscCall(PetscFree(color->nrows));
  if (color->htype[0] == 'w') {
    PetscCall(PetscFree(color->matentry2));
  } else {
    PetscCall(PetscFree(color->matentry));
  }
  PetscCall(PetscFree(color->dy));
  if (color->vscale) PetscCall(VecDestroy(&color->vscale));
  PetscCall(VecDestroy(&color->w1));
  PetscCall(VecDestroy(&color->w2));
  PetscCall(VecDestroy(&color->w3));
  PetscCall(PetscHeaderDestroy(c));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  MatFDColoringGetPerturbedColumns - Returns the indices of the columns that
  that are currently being perturbed.

  Not Collective

  Input Parameter:
. coloring - coloring context created with `MatFDColoringCreate()`

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

  Level: advanced

  Note:
  IF the matrix type is `MATBAIJ`, then the block column indices are returned

  Fortran Notes:
  This routine has a different interface for Fortran
.vb
     #include <petsc/finclude/petscmat.h>
          use petscmat
          PetscInt, pointer :: array(:)
          PetscErrorCode  ierr
          MatFDColoring   i
          call MatFDColoringGetPerturbedColumnsF90(i,array,ierr)
      use the entries of array ...
          call MatFDColoringRestorePerturbedColumnsF90(i,array,ierr)
.ve

.seealso: `Mat`, `MatFDColoring`, `MatFDColoringCreate()`, `MatFDColoringDestroy()`, `MatFDColoringView()`, `MatFDColoringApply()`
@*/
PetscErrorCode MatFDColoringGetPerturbedColumns(MatFDColoring coloring, PetscInt *n, const PetscInt *cols[])
{
  PetscFunctionBegin;
  if (coloring->currentcolor >= 0) {
    *n    = coloring->ncolumns[coloring->currentcolor];
    *cols = coloring->columns[coloring->currentcolor];
  } else {
    *n = 0;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  Collective

  Input Parameters:
+ J        - 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 ::ascii_info - Activates viewing of coloring info

  Level: intermediate

.seealso: `Mat`, `MatFDColoring`, `MatFDColoringCreate()`, `MatFDColoringDestroy()`, `MatFDColoringView()`, `MatFDColoringSetFunction()`, `MatFDColoringSetValues()`
@*/
PetscErrorCode MatFDColoringApply(Mat J, MatFDColoring coloring, Vec x1, void *sctx)
{
  PetscBool eq;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(J, MAT_CLASSID, 1);
  PetscValidHeaderSpecific(coloring, MAT_FDCOLORING_CLASSID, 2);
  PetscValidHeaderSpecific(x1, VEC_CLASSID, 3);
  PetscCall(PetscObjectCompareId((PetscObject)J, coloring->matid, &eq));
  PetscCheck(eq, PetscObjectComm((PetscObject)J), PETSC_ERR_ARG_WRONG, "Matrix used with MatFDColoringApply() must be that used with MatFDColoringCreate()");
  PetscCheck(coloring->f, PetscObjectComm((PetscObject)J), PETSC_ERR_ARG_WRONGSTATE, "Must call MatFDColoringSetFunction()");
  PetscCheck(coloring->setupcalled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Must call MatFDColoringSetUp()");

  PetscCall(MatSetUnfactored(J));
  PetscCall(PetscLogEventBegin(MAT_FDColoringApply, coloring, J, x1, 0));
  PetscUseTypeMethod(J, fdcoloringapply, coloring, x1, sctx);
  PetscCall(PetscLogEventEnd(MAT_FDColoringApply, coloring, J, x1, 0));
  if (!coloring->viewed) {
    PetscCall(MatFDColoringViewFromOptions(coloring, NULL, "-mat_fd_coloring_view"));
    coloring->viewed = PETSC_TRUE;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}