snes/tutorials/ex3.c

static char help[] = "Newton methods to solve u'' + u^{2} = f in parallel.\n\
This example employs a user-defined monitoring routine and optionally a user-defined\n\
routine to check candidate iterates produced by line search routines.\n\
The command line options include:\n\
  -pre_check_iterates : activate checking of iterates\n\
  -post_check_iterates : activate checking of iterates\n\
  -check_tol <tol>: set tolerance for iterate checking\n\
  -user_precond : activate a (trivial) user-defined preconditioner\n\n";

/*
   Include "petscdm.h" so that we can use data management objects (DMs)
   Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
   Include "petscsnes.h" so that we can use SNES solvers.  Note that this
   file automatically includes:
     petscsys.h    - base PETSc routines
     petscvec.h    - vectors
     petscmat.h    - matrices
     petscis.h     - index sets
     petscksp.h    - Krylov subspace methods
     petscviewer.h - viewers
     petscpc.h     - preconditioners
     petscksp.h    - linear solvers
*/

#include <petscdm.h>
#include <petscdmda.h>
#include <petscsnes.h>

/*
   User-defined routines.
*/
PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void *);
PetscErrorCode FormFunction(SNES, Vec, Vec, void *);
PetscErrorCode FormInitialGuess(Vec);
PetscErrorCode Monitor(SNES, PetscInt, PetscReal, void *);
PetscErrorCode PreCheck(SNESLineSearch, Vec, Vec, PetscBool *, void *);
PetscErrorCode PostCheck(SNESLineSearch, Vec, Vec, Vec, PetscBool *, PetscBool *, void *);
PetscErrorCode PostSetSubKSP(SNESLineSearch, Vec, Vec, Vec, PetscBool *, PetscBool *, void *);
PetscErrorCode MatrixFreePreconditioner(PC, Vec, Vec);

/*
   User-defined application context
*/
typedef struct
{
  DM          da;    /* distributed array */
  Vec         F;     /* right-hand-side of PDE */
  PetscMPIInt rank;  /* rank of processor */
  PetscMPIInt size;  /* size of communicator */
  PetscReal   h;     /* mesh spacing */
  PetscBool   sjerr; /* if or not to test jacobian domain error */
} ApplicationCtx;

/*
   User-defined context for monitoring
*/
typedef struct
{
  PetscViewer viewer;
} MonitorCtx;

/*
   User-defined context for checking candidate iterates that are
   determined by line search methods
*/
typedef struct
{
  Vec             last_step; /* previous iterate */
  PetscReal       tolerance; /* tolerance for changes between successive iterates */
  ApplicationCtx *user;
} StepCheckCtx;

typedef struct
{
  PetscInt its0; /* num of prevous outer KSP iterations */
} SetSubKSPCtx;

int main(int argc, char **argv)
{
  SNES           snes;       /* SNES context */
  SNESLineSearch linesearch; /* SNESLineSearch context */
  Mat            J;          /* Jacobian matrix */
  ApplicationCtx ctx;        /* user-defined context */
  Vec            x, r, U, F; /* vectors */
  MonitorCtx     monP;       /* monitoring context */
  StepCheckCtx   checkP;     /* step-checking context */
  SetSubKSPCtx   checkP1;
  PetscBool      pre_check, post_check, post_setsubksp; /* flag indicating whether we're checking candidate iterates */
  PetscScalar    xp, *FF, *UU, none = -1.0;
  PetscInt       its, N = 5, i, maxit, maxf, xs, xm;
  PetscReal      abstol, rtol, stol, norm;
  PetscBool      flg, viewinitial = PETSC_FALSE;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &ctx.rank));
  PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &ctx.size));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &N, NULL));
  ctx.h     = 1.0 / (N - 1);
  ctx.sjerr = PETSC_FALSE;
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_jacobian_domain_error", &ctx.sjerr, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_initial", &viewinitial, NULL));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create nonlinear solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create vector data structures; set function evaluation routine
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*
     Create distributed array (DMDA) to manage parallel grid and vectors
  */
  PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, N, 1, 1, NULL, &ctx.da));
  PetscCall(DMSetFromOptions(ctx.da));
  PetscCall(DMSetUp(ctx.da));

  /*
     Extract global and local vectors from DMDA; then duplicate for remaining
     vectors that are the same types
  */
  PetscCall(DMCreateGlobalVector(ctx.da, &x));
  PetscCall(VecDuplicate(x, &r));
  PetscCall(VecDuplicate(x, &F));
  ctx.F = F;
  PetscCall(VecDuplicate(x, &U));

  /*
     Set function evaluation routine and vector.  Whenever the nonlinear
     solver needs to compute the nonlinear function, it will call this
     routine.
      - Note that the final routine argument is the user-defined
        context that provides application-specific data for the
        function evaluation routine.
  */
  PetscCall(SNESSetFunction(snes, r, FormFunction, &ctx));

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

  PetscCall(MatCreate(PETSC_COMM_WORLD, &J));
  PetscCall(MatSetSizes(J, PETSC_DECIDE, PETSC_DECIDE, N, N));
  PetscCall(MatSetFromOptions(J));
  PetscCall(MatSeqAIJSetPreallocation(J, 3, NULL));
  PetscCall(MatMPIAIJSetPreallocation(J, 3, NULL, 3, NULL));

  /*
     Set Jacobian matrix data structure and default Jacobian evaluation
     routine.  Whenever the nonlinear solver needs to compute the
     Jacobian matrix, it will call this routine.
      - Note that the final routine argument is the user-defined
        context that provides application-specific data for the
        Jacobian evaluation routine.
  */
  PetscCall(SNESSetJacobian(snes, J, J, FormJacobian, &ctx));

  /*
     Optionally allow user-provided preconditioner
   */
  PetscCall(PetscOptionsHasName(NULL, NULL, "-user_precond", &flg));
  if (flg) {
    KSP ksp;
    PC  pc;
    PetscCall(SNESGetKSP(snes, &ksp));
    PetscCall(KSPGetPC(ksp, &pc));
    PetscCall(PCSetType(pc, PCSHELL));
    PetscCall(PCShellSetApply(pc, MatrixFreePreconditioner));
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Customize nonlinear solver; set runtime options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*
     Set an optional user-defined monitoring routine
  */
  PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD, 0, 0, 0, 0, 400, 400, &monP.viewer));
  PetscCall(SNESMonitorSet(snes, Monitor, &monP, 0));

  /*
     Set names for some vectors to facilitate monitoring (optional)
  */
  PetscCall(PetscObjectSetName((PetscObject)x, "Approximate Solution"));
  PetscCall(PetscObjectSetName((PetscObject)U, "Exact Solution"));

  /*
     Set SNES/KSP/KSP/PC runtime options, e.g.,
         -snes_view -snes_monitor -ksp_type <ksp> -pc_type <pc>
  */
  PetscCall(SNESSetFromOptions(snes));

  /*
     Set an optional user-defined routine to check the validity of candidate
     iterates that are determined by line search methods
  */
  PetscCall(SNESGetLineSearch(snes, &linesearch));
  PetscCall(PetscOptionsHasName(NULL, NULL, "-post_check_iterates", &post_check));

  if (post_check) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Activating post step checking routine\n"));
    PetscCall(SNESLineSearchSetPostCheck(linesearch, PostCheck, &checkP));
    PetscCall(VecDuplicate(x, &(checkP.last_step)));

    checkP.tolerance = 1.0;
    checkP.user      = &ctx;

    PetscCall(PetscOptionsGetReal(NULL, NULL, "-check_tol", &checkP.tolerance, NULL));
  }

  PetscCall(PetscOptionsHasName(NULL, NULL, "-post_setsubksp", &post_setsubksp));
  if (post_setsubksp) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Activating post setsubksp\n"));
    PetscCall(SNESLineSearchSetPostCheck(linesearch, PostSetSubKSP, &checkP1));
  }

  PetscCall(PetscOptionsHasName(NULL, NULL, "-pre_check_iterates", &pre_check));
  if (pre_check) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Activating pre step checking routine\n"));
    PetscCall(SNESLineSearchSetPreCheck(linesearch, PreCheck, &checkP));
  }

  /*
     Print parameters used for convergence testing (optional) ... just
     to demonstrate this routine; this information is also printed with
     the option -snes_view
  */
  PetscCall(SNESGetTolerances(snes, &abstol, &rtol, &stol, &maxit, &maxf));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "atol=%g, rtol=%g, stol=%g, maxit=%" PetscInt_FMT ", maxf=%" PetscInt_FMT "\n", (double)abstol, (double)rtol, (double)stol, maxit, maxf));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize application:
     Store right-hand-side of PDE and exact solution
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*
     Get local grid boundaries (for 1-dimensional DMDA):
       xs, xm - starting grid index, width of local grid (no ghost points)
  */
  PetscCall(DMDAGetCorners(ctx.da, &xs, NULL, NULL, &xm, NULL, NULL));

  /*
     Get pointers to vector data
  */
  PetscCall(DMDAVecGetArray(ctx.da, F, &FF));
  PetscCall(DMDAVecGetArray(ctx.da, U, &UU));

  /*
     Compute local vector entries
  */
  xp = ctx.h * xs;
  for (i = xs; i < xs + xm; i++) {
    FF[i] = 6.0 * xp + PetscPowScalar(xp + 1.e-12, 6.0); /* +1.e-12 is to prevent 0^6 */
    UU[i] = xp * xp * xp;
    xp += ctx.h;
  }

  /*
     Restore vectors
  */
  PetscCall(DMDAVecRestoreArray(ctx.da, F, &FF));
  PetscCall(DMDAVecRestoreArray(ctx.da, U, &UU));
  if (viewinitial) {
    PetscCall(VecView(U, 0));
    PetscCall(VecView(F, 0));
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Evaluate initial guess; then solve nonlinear system
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*
     Note: The user should initialize the vector, x, with the initial guess
     for the nonlinear solver prior to calling SNESSolve().  In particular,
     to employ an initial guess of zero, the user should explicitly set
     this vector to zero by calling VecSet().
  */
  PetscCall(FormInitialGuess(x));
  PetscCall(SNESSolve(snes, NULL, x));
  PetscCall(SNESGetIterationNumber(snes, &its));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Number of SNES iterations = %" PetscInt_FMT "\n", its));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Check solution and clean up
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*
     Check the error
  */
  PetscCall(VecAXPY(x, none, U));
  PetscCall(VecNorm(x, NORM_2, &norm));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g Iterations %" PetscInt_FMT "\n", (double)norm, its));
  if (ctx.sjerr) {
    SNESType snestype;
    PetscCall(SNESGetType(snes, &snestype));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "SNES Type %s\n", snestype));
  }

  /*
     Free work space.  All PETSc objects should be destroyed when they
     are no longer needed.
  */
  PetscCall(PetscViewerDestroy(&monP.viewer));
  if (post_check) PetscCall(VecDestroy(&checkP.last_step));
  PetscCall(VecDestroy(&x));
  PetscCall(VecDestroy(&r));
  PetscCall(VecDestroy(&U));
  PetscCall(VecDestroy(&F));
  PetscCall(MatDestroy(&J));
  PetscCall(SNESDestroy(&snes));
  PetscCall(DMDestroy(&ctx.da));
  PetscCall(PetscFinalize());
  return 0;
}

/* ------------------------------------------------------------------- */
/*
   FormInitialGuess - Computes initial guess.

   Input/Output Parameter:
.  x - the solution vector
*/
PetscErrorCode FormInitialGuess(Vec x)
{
  PetscScalar pfive = .50;

  PetscFunctionBeginUser;
  PetscCall(VecSet(x, pfive));
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------- */
/*
   FormFunction - Evaluates nonlinear function, F(x).

   Input Parameters:
.  snes - the SNES context
.  x - input vector
.  ctx - optional user-defined context, as set by SNESSetFunction()

   Output Parameter:
.  f - function vector

   Note:
   The user-defined context can contain any application-specific
   data needed for the function evaluation.
*/
PetscErrorCode FormFunction(SNES snes, Vec x, Vec f, void *ctx)
{
  ApplicationCtx    *user = (ApplicationCtx *)ctx;
  DM                 da   = user->da;
  PetscScalar       *ff, d;
  const PetscScalar *xx, *FF;
  PetscInt           i, M, xs, xm;
  Vec                xlocal;

  PetscFunctionBeginUser;
  PetscCall(DMGetLocalVector(da, &xlocal));
  /*
     Scatter ghost points to local vector, using the 2-step process
        DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
     By placing code between these two statements, computations can
     be done while messages are in transition.
  */
  PetscCall(DMGlobalToLocalBegin(da, x, INSERT_VALUES, xlocal));
  PetscCall(DMGlobalToLocalEnd(da, x, INSERT_VALUES, xlocal));

  /*
     Get pointers to vector data.
       - The vector xlocal includes ghost point; the vectors x and f do
         NOT include ghost points.
       - Using DMDAVecGetArray() allows accessing the values using global ordering
  */
  PetscCall(DMDAVecGetArrayRead(da, xlocal, (void *)&xx));
  PetscCall(DMDAVecGetArray(da, f, &ff));
  PetscCall(DMDAVecGetArrayRead(da, user->F, (void *)&FF));

  /*
     Get local grid boundaries (for 1-dimensional DMDA):
       xs, xm  - starting grid index, width of local grid (no ghost points)
  */
  PetscCall(DMDAGetCorners(da, &xs, NULL, NULL, &xm, NULL, NULL));
  PetscCall(DMDAGetInfo(da, NULL, &M, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));

  /*
     Set function values for boundary points; define local interior grid point range:
        xsi - starting interior grid index
        xei - ending interior grid index
  */
  if (xs == 0) { /* left boundary */
    ff[0] = xx[0];
    xs++;
    xm--;
  }
  if (xs + xm == M) { /* right boundary */
    ff[xs + xm - 1] = xx[xs + xm - 1] - 1.0;
    xm--;
  }

  /*
     Compute function over locally owned part of the grid (interior points only)
  */
  d = 1.0 / (user->h * user->h);
  for (i = xs; i < xs + xm; i++) ff[i] = d * (xx[i - 1] - 2.0 * xx[i] + xx[i + 1]) + xx[i] * xx[i] - FF[i];

  /*
     Restore vectors
  */
  PetscCall(DMDAVecRestoreArrayRead(da, xlocal, (void *)&xx));
  PetscCall(DMDAVecRestoreArray(da, f, &ff));
  PetscCall(DMDAVecRestoreArrayRead(da, user->F, (void *)&FF));
  PetscCall(DMRestoreLocalVector(da, &xlocal));
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------- */
/*
   FormJacobian - Evaluates Jacobian matrix.

   Input Parameters:
.  snes - the SNES context
.  x - input vector
.  dummy - optional user-defined context (not used here)

   Output Parameters:
.  jac - Jacobian matrix
.  B - optionally different preconditioning matrix
.  flag - flag indicating matrix structure
*/
PetscErrorCode FormJacobian(SNES snes, Vec x, Mat jac, Mat B, void *ctx)
{
  ApplicationCtx *user = (ApplicationCtx *)ctx;
  PetscScalar    *xx, d, A[3];
  PetscInt        i, j[3], M, xs, xm;
  DM              da = user->da;

  PetscFunctionBeginUser;
  if (user->sjerr) {
    PetscCall(SNESSetJacobianDomainError(snes));
    PetscFunctionReturn(0);
  }
  /*
     Get pointer to vector data
  */
  PetscCall(DMDAVecGetArrayRead(da, x, &xx));
  PetscCall(DMDAGetCorners(da, &xs, NULL, NULL, &xm, NULL, NULL));

  /*
    Get range of locally owned matrix
  */
  PetscCall(DMDAGetInfo(da, NULL, &M, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));

  /*
     Determine starting and ending local indices for interior grid points.
     Set Jacobian entries for boundary points.
  */

  if (xs == 0) { /* left boundary */
    i    = 0;
    A[0] = 1.0;

    PetscCall(MatSetValues(jac, 1, &i, 1, &i, A, INSERT_VALUES));
    xs++;
    xm--;
  }
  if (xs + xm == M) { /* right boundary */
    i    = M - 1;
    A[0] = 1.0;
    PetscCall(MatSetValues(jac, 1, &i, 1, &i, A, INSERT_VALUES));
    xm--;
  }

  /*
     Interior grid points
      - Note that in this case we set all elements for a particular
        row at once.
  */
  d = 1.0 / (user->h * user->h);
  for (i = xs; i < xs + xm; i++) {
    j[0] = i - 1;
    j[1] = i;
    j[2] = i + 1;
    A[0] = A[2] = d;
    A[1]        = -2.0 * d + 2.0 * xx[i];
    PetscCall(MatSetValues(jac, 1, &i, 3, j, A, INSERT_VALUES));
  }

  /*
     Assemble matrix, using the 2-step process:
       MatAssemblyBegin(), MatAssemblyEnd().
     By placing code between these two statements, computations can be
     done while messages are in transition.

     Also, restore vector.
  */

  PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY));
  PetscCall(DMDAVecRestoreArrayRead(da, x, &xx));
  PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY));

  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------- */
/*
   Monitor - Optional user-defined monitoring routine that views the
   current iterate with an x-window plot. Set by SNESMonitorSet().

   Input Parameters:
   snes - the SNES context
   its - iteration number
   norm - 2-norm function value (may be estimated)
   ctx - optional user-defined context for private data for the
         monitor routine, as set by SNESMonitorSet()

   Note:
   See the manpage for PetscViewerDrawOpen() for useful runtime options,
   such as -nox to deactivate all x-window output.
 */
PetscErrorCode Monitor(SNES snes, PetscInt its, PetscReal fnorm, void *ctx)
{
  MonitorCtx *monP = (MonitorCtx *)ctx;
  Vec         x;

  PetscFunctionBeginUser;
  PetscCall(PetscPrintf(PETSC_COMM_WORLD, "iter = %" PetscInt_FMT ",SNES Function norm %g\n", its, (double)fnorm));
  PetscCall(SNESGetSolution(snes, &x));
  PetscCall(VecView(x, monP->viewer));
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------- */
/*
   PreCheck - Optional user-defined routine that checks the validity of
   candidate steps of a line search method.  Set by SNESLineSearchSetPreCheck().

   Input Parameters:
   snes - the SNES context
   xcurrent - current solution
   y - search direction and length

   Output Parameters:
   y         - proposed step (search direction and length) (possibly changed)
   changed_y - tells if the step has changed or not
 */
PetscErrorCode PreCheck(SNESLineSearch linesearch, Vec xcurrent, Vec y, PetscBool *changed_y, void *ctx)
{
  PetscFunctionBeginUser;
  *changed_y = PETSC_FALSE;
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------- */
/*
   PostCheck - Optional user-defined routine that checks the validity of
   candidate steps of a line search method.  Set by SNESLineSearchSetPostCheck().

   Input Parameters:
   snes - the SNES context
   ctx  - optional user-defined context for private data for the
          monitor routine, as set by SNESLineSearchSetPostCheck()
   xcurrent - current solution
   y - search direction and length
   x    - the new candidate iterate

   Output Parameters:
   y    - proposed step (search direction and length) (possibly changed)
   x    - current iterate (possibly modified)

 */
PetscErrorCode PostCheck(SNESLineSearch linesearch, Vec xcurrent, Vec y, Vec x, PetscBool *changed_y, PetscBool *changed_x, void *ctx)
{
  PetscInt        i, iter, xs, xm;
  StepCheckCtx   *check;
  ApplicationCtx *user;
  PetscScalar    *xa, *xa_last, tmp;
  PetscReal       rdiff;
  DM              da;
  SNES            snes;

  PetscFunctionBeginUser;
  *changed_x = PETSC_FALSE;
  *changed_y = PETSC_FALSE;

  PetscCall(SNESLineSearchGetSNES(linesearch, &snes));
  check = (StepCheckCtx *)ctx;
  user  = check->user;
  PetscCall(SNESGetIterationNumber(snes, &iter));

  /* iteration 1 indicates we are working on the second iteration */
  if (iter > 0) {
    da = user->da;
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Checking candidate step at iteration %" PetscInt_FMT " with tolerance %g\n", iter, (double)check->tolerance));

    /* Access local array data */
    PetscCall(DMDAVecGetArray(da, check->last_step, &xa_last));
    PetscCall(DMDAVecGetArray(da, x, &xa));
    PetscCall(DMDAGetCorners(da, &xs, NULL, NULL, &xm, NULL, NULL));

    /*
       If we fail the user-defined check for validity of the candidate iterate,
       then modify the iterate as we like.  (Note that the particular modification
       below is intended simply to demonstrate how to manipulate this data, not
       as a meaningful or appropriate choice.)
    */
    for (i = xs; i < xs + xm; i++) {
      if (!PetscAbsScalar(xa[i])) rdiff = 2 * check->tolerance;
      else rdiff = PetscAbsScalar((xa[i] - xa_last[i]) / xa[i]);
      if (rdiff > check->tolerance) {
        tmp        = xa[i];
        xa[i]      = .5 * (xa[i] + xa_last[i]);
        *changed_x = PETSC_TRUE;
        PetscCall(PetscPrintf(PETSC_COMM_WORLD, "  Altering entry %" PetscInt_FMT ": x=%g, x_last=%g, diff=%g, x_new=%g\n", i, (double)PetscAbsScalar(tmp), (double)PetscAbsScalar(xa_last[i]), (double)rdiff, (double)PetscAbsScalar(xa[i])));
      }
    }
    PetscCall(DMDAVecRestoreArray(da, check->last_step, &xa_last));
    PetscCall(DMDAVecRestoreArray(da, x, &xa));
  }
  PetscCall(VecCopy(x, check->last_step));
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------- */
/*
   PostSetSubKSP - Optional user-defined routine that reset SubKSP options when hierarchical bjacobi PC is used
   e.g,
     mpiexec -n 8 ./ex3 -nox -n 10000 -ksp_type fgmres -pc_type bjacobi -pc_bjacobi_blocks 4 -sub_ksp_type gmres -sub_ksp_max_it 3 -post_setsubksp -sub_ksp_rtol 1.e-16
   Set by SNESLineSearchSetPostCheck().

   Input Parameters:
   linesearch - the LineSearch context
   xcurrent - current solution
   y - search direction and length
   x    - the new candidate iterate

   Output Parameters:
   y    - proposed step (search direction and length) (possibly changed)
   x    - current iterate (possibly modified)

 */
PetscErrorCode PostSetSubKSP(SNESLineSearch linesearch, Vec xcurrent, Vec y, Vec x, PetscBool *changed_y, PetscBool *changed_x, void *ctx)
{
  SetSubKSPCtx *check;
  PetscInt      iter, its, sub_its, maxit;
  KSP           ksp, sub_ksp, *sub_ksps;
  PC            pc;
  PetscReal     ksp_ratio;
  SNES          snes;

  PetscFunctionBeginUser;
  PetscCall(SNESLineSearchGetSNES(linesearch, &snes));
  check = (SetSubKSPCtx *)ctx;
  PetscCall(SNESGetIterationNumber(snes, &iter));
  PetscCall(SNESGetKSP(snes, &ksp));
  PetscCall(KSPGetPC(ksp, &pc));
  PetscCall(PCBJacobiGetSubKSP(pc, NULL, NULL, &sub_ksps));
  sub_ksp = sub_ksps[0];
  PetscCall(KSPGetIterationNumber(ksp, &its));         /* outer KSP iteration number */
  PetscCall(KSPGetIterationNumber(sub_ksp, &sub_its)); /* inner KSP iteration number */

  if (iter) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "    ...PostCheck snes iteration %" PetscInt_FMT ", ksp_it %" PetscInt_FMT " %" PetscInt_FMT ", subksp_it %" PetscInt_FMT "\n", iter, check->its0, its, sub_its));
    ksp_ratio = ((PetscReal)(its)) / check->its0;
    maxit     = (PetscInt)(ksp_ratio * sub_its + 0.5);
    if (maxit < 2) maxit = 2;
    PetscCall(KSPSetTolerances(sub_ksp, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT, maxit));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "    ...ksp_ratio %g, new maxit %" PetscInt_FMT "\n\n", (double)ksp_ratio, maxit));
  }
  check->its0 = its; /* save current outer KSP iteration number */
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------- */
/*
   MatrixFreePreconditioner - This routine demonstrates the use of a
   user-provided preconditioner.  This code implements just the null
   preconditioner, which of course is not recommended for general use.

   Input Parameters:
+  pc - preconditioner
-  x - input vector

   Output Parameter:
.  y - preconditioned vector
*/
PetscErrorCode MatrixFreePreconditioner(PC pc, Vec x, Vec y)
{
  PetscCall(VecCopy(x, y));
  return 0;
}

/*TEST

   test:
      args: -nox -snes_monitor_cancel -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

   test:
      suffix: 2
      nsize: 3
      args: -nox -pc_type asm -mat_type mpiaij -snes_monitor_cancel -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

   test:
      suffix: 3
      nsize: 2
      args: -nox -snes_monitor_cancel -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always

   test:
      suffix: 4
      args: -nox -pre_check_iterates -post_check_iterates

   test:
      suffix: 5
      requires: double !complex !single
      nsize: 2
      args: -nox -snes_test_jacobian  -snes_test_jacobian_view

   test:
      suffix: 6
      requires: double !complex !single
      nsize: 4
      args: -test_jacobian_domain_error -snes_converged_reason -snes_check_jacobian_domain_error 1

   test:
      suffix: 7
      requires: double !complex !single
      nsize: 4
      args: -test_jacobian_domain_error -snes_converged_reason -snes_type newtontr -snes_check_jacobian_domain_error 1

   test:
      suffix: 8
      requires: double !complex !single
      nsize: 4
      args: -test_jacobian_domain_error -snes_converged_reason -snes_type vinewtonrsls -snes_check_jacobian_domain_error 1

   test:
      suffix: 9
      requires: double !complex !single
      nsize: 4
      args: -test_jacobian_domain_error -snes_converged_reason -snes_type vinewtonssls -snes_check_jacobian_domain_error 1

   test:
      suffix: 10
      requires: double !complex !single
      nsize: 4
      args: -test_jacobian_domain_error -snes_converged_reason -snes_type qn -snes_qn_scale_type jacobian -snes_check_jacobian_domain_error 1

   test:
      suffix: 11
      requires: double !complex !single
      nsize: 4
      args: -test_jacobian_domain_error -snes_converged_reason -snes_type ms -snes_ms_type m62 -snes_ms_damping 0.9 -snes_check_jacobian_domain_error 1

   test:
      suffix: 12
      args: -view_initial
      filter: grep -v "type:"

   test:
      suffix: 13
      requires: double !complex !single
      nsize: 4
      args: -test_jacobian_domain_error -snes_converged_reason -snes_type newtontrdc -snes_check_jacobian_domain_error 1

TEST*/