pc/interface/precon.c

/*
    The PC (preconditioner) interface routines, callable by users.
*/
#include <petsc/private/pcimpl.h> /*I "petscksp.h" I*/
#include <petscdm.h>

/* Logging support */
PetscClassId  PC_CLASSID;
PetscLogEvent PC_SetUp, PC_SetUpOnBlocks, PC_Apply, PC_MatApply, PC_ApplyCoarse, PC_ApplyMultiple, PC_ApplySymmetricLeft;
PetscLogEvent PC_ApplySymmetricRight, PC_ModifySubMatrices, PC_ApplyOnBlocks, PC_ApplyTransposeOnBlocks;
PetscInt      PetscMGLevelId;
PetscLogStage PCMPIStage;

PetscErrorCode PCGetDefaultType_Private(PC pc, const char *type[])
{
  PetscMPIInt size;
  PetscBool   hasop, flg1, flg2, set, flg3, isnormal;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
  if (pc->pmat) {
    PetscCall(MatHasOperation(pc->pmat, MATOP_GET_DIAGONAL_BLOCK, &hasop));
    if (size == 1) {
      PetscCall(MatGetFactorAvailable(pc->pmat, "petsc", MAT_FACTOR_ICC, &flg1));
      PetscCall(MatGetFactorAvailable(pc->pmat, "petsc", MAT_FACTOR_ILU, &flg2));
      PetscCall(MatIsSymmetricKnown(pc->pmat, &set, &flg3));
      PetscCall(PetscObjectTypeCompareAny((PetscObject)pc->pmat, &isnormal, MATNORMAL, MATNORMALHERMITIAN, NULL));
      if (flg1 && (!flg2 || (set && flg3))) {
        *type = PCICC;
      } else if (flg2) {
        *type = PCILU;
      } else if (isnormal) {
        *type = PCNONE;
      } else if (hasop) { /* likely is a parallel matrix run on one processor */
        *type = PCBJACOBI;
      } else {
        *type = PCNONE;
      }
    } else {
      if (hasop) {
        *type = PCBJACOBI;
      } else {
        *type = PCNONE;
      }
    }
  } else {
    if (size == 1) {
      *type = PCILU;
    } else {
      *type = PCBJACOBI;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCReset - Resets a PC context to the pcsetupcalled = 0 state and removes any allocated `Vec`s and `Mat`s

   Collective

   Input Parameter:
.  pc - the preconditioner context

   Level: developer

   Note:
    This allows a `PC` to be reused for a different sized linear system but using the same options that have been previously set in the PC

.seealso: `PC`, `PCCreate()`, `PCSetUp()`
@*/
PetscErrorCode PCReset(PC pc)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscTryTypeMethod(pc, reset);
  PetscCall(VecDestroy(&pc->diagonalscaleright));
  PetscCall(VecDestroy(&pc->diagonalscaleleft));
  PetscCall(MatDestroy(&pc->pmat));
  PetscCall(MatDestroy(&pc->mat));

  pc->setupcalled = 0;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   PCDestroy - Destroys `PC` context that was created with `PCCreate()`.

   Collective

   Input Parameter:
.  pc - the preconditioner context

   Level: developer

.seealso: `PC`, `PCCreate()`, `PCSetUp()`
@*/
PetscErrorCode PCDestroy(PC *pc)
{
  PetscFunctionBegin;
  if (!*pc) PetscFunctionReturn(PETSC_SUCCESS);
  PetscValidHeaderSpecific((*pc), PC_CLASSID, 1);
  if (--((PetscObject)(*pc))->refct > 0) {
    *pc = NULL;
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  PetscCall(PCReset(*pc));

  /* if memory was published with SAWs then destroy it */
  PetscCall(PetscObjectSAWsViewOff((PetscObject)*pc));
  PetscTryTypeMethod((*pc), destroy);
  PetscCall(DMDestroy(&(*pc)->dm));
  PetscCall(PetscHeaderDestroy(pc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   PCGetDiagonalScale - Indicates if the preconditioner applies an additional left and right
      scaling as needed by certain time-stepping codes.

   Logically Collective

   Input Parameter:
.  pc - the preconditioner context

   Output Parameter:
.  flag - `PETSC_TRUE` if it applies the scaling

   Level: developer

   Note:
    If this returns `PETSC_TRUE` then the system solved via the Krylov method is
.vb
      D M A D^{-1} y = D M b  for left preconditioning or
      D A M D^{-1} z = D b for right preconditioning
.ve

.seealso: `PC`, `PCCreate()`, `PCSetUp()`, `PCDiagonalScaleLeft()`, `PCDiagonalScaleRight()`, `PCSetDiagonalScale()`
@*/
PetscErrorCode PCGetDiagonalScale(PC pc, PetscBool *flag)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidBoolPointer(flag, 2);
  *flag = pc->diagonalscale;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCSetDiagonalScale - Indicates the left scaling to use to apply an additional left and right
      scaling as needed by certain time-stepping codes.

   Logically Collective

   Input Parameters:
+  pc - the preconditioner context
-  s - scaling vector

   Level: intermediate

   Notes:
    The system solved via the Krylov method is
.vb
           D M A D^{-1} y = D M b  for left preconditioning or
           D A M D^{-1} z = D b for right preconditioning
.ve

   `PCDiagonalScaleLeft()` scales a vector by D. `PCDiagonalScaleRight()` scales a vector by D^{-1}.

.seealso: `PCCreate()`, `PCSetUp()`, `PCDiagonalScaleLeft()`, `PCDiagonalScaleRight()`, `PCGetDiagonalScale()`
@*/
PetscErrorCode PCSetDiagonalScale(PC pc, Vec s)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(s, VEC_CLASSID, 2);
  pc->diagonalscale = PETSC_TRUE;

  PetscCall(PetscObjectReference((PetscObject)s));
  PetscCall(VecDestroy(&pc->diagonalscaleleft));

  pc->diagonalscaleleft = s;

  PetscCall(VecDuplicate(s, &pc->diagonalscaleright));
  PetscCall(VecCopy(s, pc->diagonalscaleright));
  PetscCall(VecReciprocal(pc->diagonalscaleright));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCDiagonalScaleLeft - Scales a vector by the left scaling as needed by certain time-stepping codes.

   Logically Collective

   Input Parameters:
+  pc - the preconditioner context
.  in - input vector
-  out - scaled vector (maybe the same as in)

   Level: intermediate

   Notes:
    The system solved via the Krylov method is
.vb
        D M A D^{-1} y = D M b  for left preconditioning or
        D A M D^{-1} z = D b for right preconditioning
.ve

   `PCDiagonalScaleLeft()` scales a vector by D. `PCDiagonalScaleRight()` scales a vector by D^{-1}.

   If diagonal scaling is turned off and in is not out then in is copied to out

.seealso: `PCCreate()`, `PCSetUp()`, `PCDiagonalScaleSet()`, `PCDiagonalScaleRight()`, `PCDiagonalScale()`
@*/
PetscErrorCode PCDiagonalScaleLeft(PC pc, Vec in, Vec out)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(in, VEC_CLASSID, 2);
  PetscValidHeaderSpecific(out, VEC_CLASSID, 3);
  if (pc->diagonalscale) {
    PetscCall(VecPointwiseMult(out, pc->diagonalscaleleft, in));
  } else if (in != out) {
    PetscCall(VecCopy(in, out));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCDiagonalScaleRight - Scales a vector by the right scaling as needed by certain time-stepping codes.

   Logically Collective

   Input Parameters:
+  pc - the preconditioner context
.  in - input vector
-  out - scaled vector (maybe the same as in)

   Level: intermediate

   Notes:
    The system solved via the Krylov method is
.vb
        D M A D^{-1} y = D M b  for left preconditioning or
        D A M D^{-1} z = D b for right preconditioning
.ve

   `PCDiagonalScaleLeft()` scales a vector by D. `PCDiagonalScaleRight()` scales a vector by D^{-1}.

   If diagonal scaling is turned off and in is not out then in is copied to out

.seealso: `PCCreate()`, `PCSetUp()`, `PCDiagonalScaleLeft()`, `PCDiagonalScaleSet()`, `PCDiagonalScale()`
@*/
PetscErrorCode PCDiagonalScaleRight(PC pc, Vec in, Vec out)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(in, VEC_CLASSID, 2);
  PetscValidHeaderSpecific(out, VEC_CLASSID, 3);
  if (pc->diagonalscale) {
    PetscCall(VecPointwiseMult(out, pc->diagonalscaleright, in));
  } else if (in != out) {
    PetscCall(VecCopy(in, out));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCSetUseAmat - Sets a flag to indicate that when the preconditioner needs to apply (part of) the
   operator during the preconditioning process it applies the Amat provided to `TSSetRHSJacobian()`,
   `TSSetIJacobian()`, `SNESSetJacobian()`, `KSPSetOperators()` or `PCSetOperators()` not the Pmat.

   Logically Collective

   Input Parameters:
+  pc - the preconditioner context
-  flg - `PETSC_TRUE` to use the Amat, `PETSC_FALSE` to use the Pmat (default is false)

   Options Database Key:
.  -pc_use_amat <true,false> - use the amat to apply the operator

   Level: intermediate

   Note:
   For the common case in which the linear system matrix and the matrix used to construct the
   preconditioner are identical, this routine is does nothing.

.seealso: `PC`, `PCGetUseAmat()`, `PCBJACOBI`, `PGMG`, `PCFIELDSPLIT`, `PCCOMPOSITE`
@*/
PetscErrorCode PCSetUseAmat(PC pc, PetscBool flg)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  pc->useAmat = flg;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCSetErrorIfFailure - Causes `PC` to generate an error if a FPE, for example a zero pivot, is detected.

   Logically Collective

   Input Parameters:
+  pc - iterative context obtained from PCCreate()
-  flg - `PETSC_TRUE` indicates you want the error generated

   Level: advanced

   Notes:
    Normally PETSc continues if a linear solver fails due to a failed setup of a preconditioner, you can call `KSPGetConvergedReason()` after a `KSPSolve()`
    to determine if it has converged or failed. Or use -ksp_error_if_not_converged to cause the program to terminate as soon as lack of convergence is
    detected.

    This is propagated into KSPs used by this PC, which then propagate it into PCs used by those KSPs

.seealso: `PC`, `KSPSetErrorIfNotConverged()`, `PCGetInitialGuessNonzero()`, `PCSetInitialGuessKnoll()`, `PCGetInitialGuessKnoll()`
@*/
PetscErrorCode PCSetErrorIfFailure(PC pc, PetscBool flg)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidLogicalCollectiveBool(pc, flg, 2);
  pc->erroriffailure = flg;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCGetUseAmat - Gets a flag to indicate that when the preconditioner needs to apply (part of) the
   operator during the preconditioning process it applies the Amat provided to `TSSetRHSJacobian()`,
   `TSSetIJacobian()`, `SNESSetJacobian()`, `KSPSetOperators()` or `PCSetOperators()` not the Pmat.

   Logically Collective

   Input Parameter:
.  pc - the preconditioner context

   Output Parameter:
.  flg - `PETSC_TRUE` to use the Amat, `PETSC_FALSE` to use the Pmat (default is false)

   Level: intermediate

   Note:
   For the common case in which the linear system matrix and the matrix used to construct the
   preconditioner are identical, this routine is does nothing.

.seealso: `PC`, `PCSetUseAmat()`, `PCBJACOBI`, `PGMG`, `PCFIELDSPLIT`, `PCCOMPOSITE`
@*/
PetscErrorCode PCGetUseAmat(PC pc, PetscBool *flg)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  *flg = pc->useAmat;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCCreate - Creates a preconditioner context, `PC`

   Collective

   Input Parameter:
.  comm - MPI communicator

   Output Parameter:
.  pc - location to put the preconditioner context

   Level: developer

   Note:
   The default preconditioner for sparse matrices is `PCILU` or `PCICC` with 0 fill on one process and block Jacobi (`PCBJACOBI`) with `PCILU` or `PCICC`
   in parallel. For dense matrices it is always `PCNONE`.

.seealso: `PC`, `PCSetUp()`, `PCApply()`, `PCDestroy()`
@*/
PetscErrorCode PCCreate(MPI_Comm comm, PC *newpc)
{
  PC pc;

  PetscFunctionBegin;
  PetscValidPointer(newpc, 2);
  *newpc = NULL;
  PetscCall(PCInitializePackage());

  PetscCall(PetscHeaderCreate(pc, PC_CLASSID, "PC", "Preconditioner", "PC", comm, PCDestroy, PCView));

  pc->mat                  = NULL;
  pc->pmat                 = NULL;
  pc->setupcalled          = 0;
  pc->setfromoptionscalled = 0;
  pc->data                 = NULL;
  pc->diagonalscale        = PETSC_FALSE;
  pc->diagonalscaleleft    = NULL;
  pc->diagonalscaleright   = NULL;

  pc->modifysubmatrices  = NULL;
  pc->modifysubmatricesP = NULL;

  *newpc = pc;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCApply - Applies the preconditioner to a vector.

   Collective

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

   Output Parameter:
.  y - output vector

   Level: developer

.seealso: `PC`, `PCApplyTranspose()`, `PCApplyBAorAB()`
@*/
PetscErrorCode PCApply(PC pc, Vec x, Vec y)
{
  PetscInt m, n, mv, nv;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(x, VEC_CLASSID, 2);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 3);
  PetscCheck(x != y, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_IDN, "x and y must be different vectors");
  if (pc->erroriffailure) PetscCall(VecValidValues_Internal(x, 2, PETSC_TRUE));
  /* use pmat to check vector sizes since for KSPLSQR the pmat may be of a different size than mat */
  PetscCall(MatGetLocalSize(pc->pmat, &m, &n));
  PetscCall(VecGetLocalSize(x, &mv));
  PetscCall(VecGetLocalSize(y, &nv));
  /* check pmat * y = x is feasible */
  PetscCheck(mv == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Preconditioner number of local rows %" PetscInt_FMT " does not equal input vector size %" PetscInt_FMT, m, mv);
  PetscCheck(nv == n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Preconditioner number of local columns %" PetscInt_FMT " does not equal output vector size %" PetscInt_FMT, n, nv);
  PetscCall(VecSetErrorIfLocked(y, 3));

  PetscCall(PCSetUp(pc));
  PetscCall(VecLockReadPush(x));
  PetscCall(PetscLogEventBegin(PC_Apply, pc, x, y, 0));
  PetscUseTypeMethod(pc, apply, x, y);
  PetscCall(PetscLogEventEnd(PC_Apply, pc, x, y, 0));
  if (pc->erroriffailure) PetscCall(VecValidValues_Internal(y, 3, PETSC_FALSE));
  PetscCall(VecLockReadPop(x));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCMatApply - Applies the preconditioner to multiple vectors stored as a `MATDENSE`. Like `PCApply()`, Y and X must be different matrices.

   Collective

   Input Parameters:
+  pc - the preconditioner context
-  X - block of input vectors

   Output Parameter:
.  Y - block of output vectors

   Level: developer

.seealso: `PC`, `PCApply()`, `KSPMatSolve()`
@*/
PetscErrorCode PCMatApply(PC pc, Mat X, Mat Y)
{
  Mat       A;
  Vec       cy, cx;
  PetscInt  m1, M1, m2, M2, n1, N1, n2, N2, m3, M3, n3, N3;
  PetscBool match;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(X, MAT_CLASSID, 2);
  PetscValidHeaderSpecific(Y, MAT_CLASSID, 3);
  PetscCheckSameComm(pc, 1, X, 2);
  PetscCheckSameComm(pc, 1, Y, 3);
  PetscCheck(Y != X, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_IDN, "Y and X must be different matrices");
  PetscCall(PCGetOperators(pc, NULL, &A));
  PetscCall(MatGetLocalSize(A, &m3, &n3));
  PetscCall(MatGetLocalSize(X, &m2, &n2));
  PetscCall(MatGetLocalSize(Y, &m1, &n1));
  PetscCall(MatGetSize(A, &M3, &N3));
  PetscCall(MatGetSize(X, &M2, &N2));
  PetscCall(MatGetSize(Y, &M1, &N1));
  PetscCheck(n1 == n2 && N1 == N2, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Incompatible number of columns between block of input vectors (n,N) = (%" PetscInt_FMT ",%" PetscInt_FMT ") and block of output vectors (n,N) = (%" PetscInt_FMT ",%" PetscInt_FMT ")", n2, N2, n1, N1);
  PetscCheck(m2 == m3 && M2 == M3, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Incompatible layout between block of input vectors (m,M) = (%" PetscInt_FMT ",%" PetscInt_FMT ") and Pmat (m,M)x(n,N) = (%" PetscInt_FMT ",%" PetscInt_FMT ")x(%" PetscInt_FMT ",%" PetscInt_FMT ")", m2, M2, m3, M3, n3, N3);
  PetscCheck(m1 == n3 && M1 == N3, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Incompatible layout between block of output vectors (m,M) = (%" PetscInt_FMT ",%" PetscInt_FMT ") and Pmat (m,M)x(n,N) = (%" PetscInt_FMT ",%" PetscInt_FMT ")x(%" PetscInt_FMT ",%" PetscInt_FMT ")", m1, M1, m3, M3, n3, N3);
  PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)Y, &match, MATSEQDENSE, MATMPIDENSE, ""));
  PetscCheck(match, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Provided block of output vectors not stored in a dense Mat");
  PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)X, &match, MATSEQDENSE, MATMPIDENSE, ""));
  PetscCheck(match, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Provided block of input vectors not stored in a dense Mat");
  PetscCall(PCSetUp(pc));
  if (pc->ops->matapply) {
    PetscCall(PetscLogEventBegin(PC_MatApply, pc, X, Y, 0));
    PetscUseTypeMethod(pc, matapply, X, Y);
    PetscCall(PetscLogEventEnd(PC_MatApply, pc, X, Y, 0));
  } else {
    PetscCall(PetscInfo(pc, "PC type %s applying column by column\n", ((PetscObject)pc)->type_name));
    for (n1 = 0; n1 < N1; ++n1) {
      PetscCall(MatDenseGetColumnVecRead(X, n1, &cx));
      PetscCall(MatDenseGetColumnVecWrite(Y, n1, &cy));
      PetscCall(PCApply(pc, cx, cy));
      PetscCall(MatDenseRestoreColumnVecWrite(Y, n1, &cy));
      PetscCall(MatDenseRestoreColumnVecRead(X, n1, &cx));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCApplySymmetricLeft - Applies the left part of a symmetric preconditioner to a vector.

   Collective

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

   Output Parameter:
.  y - output vector

   Level: developer

   Note:
   Currently, this routine is implemented only for `PCICC` and `PCJACOBI` preconditioners.

.seealso: `PC`, `PCApply()`, `PCApplySymmetricRight()`
@*/
PetscErrorCode PCApplySymmetricLeft(PC pc, Vec x, Vec y)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(x, VEC_CLASSID, 2);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 3);
  PetscCheck(x != y, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_IDN, "x and y must be different vectors");
  if (pc->erroriffailure) PetscCall(VecValidValues_Internal(x, 2, PETSC_TRUE));
  PetscCall(PCSetUp(pc));
  PetscCall(VecLockReadPush(x));
  PetscCall(PetscLogEventBegin(PC_ApplySymmetricLeft, pc, x, y, 0));
  PetscUseTypeMethod(pc, applysymmetricleft, x, y);
  PetscCall(PetscLogEventEnd(PC_ApplySymmetricLeft, pc, x, y, 0));
  PetscCall(VecLockReadPop(x));
  if (pc->erroriffailure) PetscCall(VecValidValues_Internal(y, 3, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCApplySymmetricRight - Applies the right part of a symmetric preconditioner to a vector.

   Collective

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

   Output Parameter:
.  y - output vector

   Level: developer

   Note:
   Currently, this routine is implemented only for `PCICC` and `PCJACOBI` preconditioners.

.seealso: `PC`, `PCApply()`, `PCApplySymmetricLeft()`
@*/
PetscErrorCode PCApplySymmetricRight(PC pc, Vec x, Vec y)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(x, VEC_CLASSID, 2);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 3);
  PetscCheck(x != y, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_IDN, "x and y must be different vectors");
  if (pc->erroriffailure) PetscCall(VecValidValues_Internal(x, 2, PETSC_TRUE));
  PetscCall(PCSetUp(pc));
  PetscCall(VecLockReadPush(x));
  PetscCall(PetscLogEventBegin(PC_ApplySymmetricRight, pc, x, y, 0));
  PetscUseTypeMethod(pc, applysymmetricright, x, y);
  PetscCall(PetscLogEventEnd(PC_ApplySymmetricRight, pc, x, y, 0));
  PetscCall(VecLockReadPop(x));
  if (pc->erroriffailure) PetscCall(VecValidValues_Internal(y, 3, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCApplyTranspose - Applies the transpose of preconditioner to a vector.

   Collective

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

   Output Parameter:
.  y - output vector

   Level: developer

   Note:
    For complex numbers this applies the non-Hermitian transpose.

   Developer Note:
    We need to implement a `PCApplyHermitianTranspose()`

.seealso: `PC`, `PCApply()`, `PCApplyBAorAB()`, `PCApplyBAorABTranspose()`, `PCApplyTransposeExists()`
@*/
PetscErrorCode PCApplyTranspose(PC pc, Vec x, Vec y)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(x, VEC_CLASSID, 2);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 3);
  PetscCheck(x != y, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_IDN, "x and y must be different vectors");
  if (pc->erroriffailure) PetscCall(VecValidValues_Internal(x, 2, PETSC_TRUE));
  PetscCall(PCSetUp(pc));
  PetscCall(VecLockReadPush(x));
  PetscCall(PetscLogEventBegin(PC_Apply, pc, x, y, 0));
  PetscUseTypeMethod(pc, applytranspose, x, y);
  PetscCall(PetscLogEventEnd(PC_Apply, pc, x, y, 0));
  PetscCall(VecLockReadPop(x));
  if (pc->erroriffailure) PetscCall(VecValidValues_Internal(y, 3, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCApplyTransposeExists - Test whether the preconditioner has a transpose apply operation

   Collective

   Input Parameter:
.  pc - the preconditioner context

   Output Parameter:
.  flg - `PETSC_TRUE` if a transpose operation is defined

   Level: developer

.seealso: `PC`, `PCApplyTranspose()`
@*/
PetscErrorCode PCApplyTransposeExists(PC pc, PetscBool *flg)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidBoolPointer(flg, 2);
  if (pc->ops->applytranspose) *flg = PETSC_TRUE;
  else *flg = PETSC_FALSE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCApplyBAorAB - Applies the preconditioner and operator to a vector. y = B*A*x or y = A*B*x.

   Collective

   Input Parameters:
+  pc - the preconditioner context
.  side - indicates the preconditioner side, one of `PC_LEFT`, `PC_RIGHT`, or `PC_SYMMETRIC`
.  x - input vector
-  work - work vector

   Output Parameter:
.  y - output vector

   Level: developer

   Note:
    If the `PC` has had `PCSetDiagonalScale()` set then D M A D^{-1} for left preconditioning or  D A M D^{-1} is actually applied. Note that the
   specific `KSPSolve()` method must also be written to handle the post-solve "correction" for the diagonal scaling.

.seealso: `PC`, `PCApply()`, `PCApplyTranspose()`, `PCApplyBAorABTranspose()`
@*/
PetscErrorCode PCApplyBAorAB(PC pc, PCSide side, Vec x, Vec y, Vec work)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidLogicalCollectiveEnum(pc, side, 2);
  PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 4);
  PetscValidHeaderSpecific(work, VEC_CLASSID, 5);
  PetscCheckSameComm(pc, 1, x, 3);
  PetscCheckSameComm(pc, 1, y, 4);
  PetscCheckSameComm(pc, 1, work, 5);
  PetscCheck(x != y, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_IDN, "x and y must be different vectors");
  PetscCheck(side == PC_LEFT || side == PC_SYMMETRIC || side == PC_RIGHT, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Side must be right, left, or symmetric");
  PetscCheck(!pc->diagonalscale || side != PC_SYMMETRIC, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Cannot include diagonal scaling with symmetric preconditioner application");
  if (pc->erroriffailure) PetscCall(VecValidValues_Internal(x, 3, PETSC_TRUE));

  PetscCall(PCSetUp(pc));
  if (pc->diagonalscale) {
    if (pc->ops->applyBA) {
      Vec work2; /* this is expensive, but to fix requires a second work vector argument to PCApplyBAorAB() */
      PetscCall(VecDuplicate(x, &work2));
      PetscCall(PCDiagonalScaleRight(pc, x, work2));
      PetscUseTypeMethod(pc, applyBA, side, work2, y, work);
      PetscCall(PCDiagonalScaleLeft(pc, y, y));
      PetscCall(VecDestroy(&work2));
    } else if (side == PC_RIGHT) {
      PetscCall(PCDiagonalScaleRight(pc, x, y));
      PetscCall(PCApply(pc, y, work));
      PetscCall(MatMult(pc->mat, work, y));
      PetscCall(PCDiagonalScaleLeft(pc, y, y));
    } else if (side == PC_LEFT) {
      PetscCall(PCDiagonalScaleRight(pc, x, y));
      PetscCall(MatMult(pc->mat, y, work));
      PetscCall(PCApply(pc, work, y));
      PetscCall(PCDiagonalScaleLeft(pc, y, y));
    } else PetscCheck(side != PC_SYMMETRIC, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Cannot provide diagonal scaling with symmetric application of preconditioner");
  } else {
    if (pc->ops->applyBA) {
      PetscUseTypeMethod(pc, applyBA, side, x, y, work);
    } else if (side == PC_RIGHT) {
      PetscCall(PCApply(pc, x, work));
      PetscCall(MatMult(pc->mat, work, y));
    } else if (side == PC_LEFT) {
      PetscCall(MatMult(pc->mat, x, work));
      PetscCall(PCApply(pc, work, y));
    } else if (side == PC_SYMMETRIC) {
      /* There's an extra copy here; maybe should provide 2 work vectors instead? */
      PetscCall(PCApplySymmetricRight(pc, x, work));
      PetscCall(MatMult(pc->mat, work, y));
      PetscCall(VecCopy(y, work));
      PetscCall(PCApplySymmetricLeft(pc, work, y));
    }
  }
  if (pc->erroriffailure) PetscCall(VecValidValues_Internal(y, 4, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCApplyBAorABTranspose - Applies the transpose of the preconditioner
   and operator to a vector. That is, applies tr(B) * tr(A) with left preconditioning,
   NOT tr(B*A) = tr(A)*tr(B).

   Collective

   Input Parameters:
+  pc - the preconditioner context
.  side - indicates the preconditioner side, one of `PC_LEFT`, `PC_RIGHT`, or `PC_SYMMETRIC`
.  x - input vector
-  work - work vector

   Output Parameter:
.  y - output vector

    Level: developer

   Note:
    This routine is used internally so that the same Krylov code can be used to solve A x = b and A' x = b, with a preconditioner
      defined by B'. This is why this has the funny form that it computes tr(B) * tr(A)

.seealso: `PC`, `PCApply()`, `PCApplyTranspose()`, `PCApplyBAorAB()`
@*/
PetscErrorCode PCApplyBAorABTranspose(PC pc, PCSide side, Vec x, Vec y, Vec work)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 4);
  PetscValidHeaderSpecific(work, VEC_CLASSID, 5);
  PetscCheck(x != y, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_IDN, "x and y must be different vectors");
  if (pc->erroriffailure) PetscCall(VecValidValues_Internal(x, 3, PETSC_TRUE));
  if (pc->ops->applyBAtranspose) {
    PetscUseTypeMethod(pc, applyBAtranspose, side, x, y, work);
    if (pc->erroriffailure) PetscCall(VecValidValues_Internal(y, 4, PETSC_FALSE));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCheck(side == PC_LEFT || side == PC_RIGHT, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Side must be right or left");

  PetscCall(PCSetUp(pc));
  if (side == PC_RIGHT) {
    PetscCall(PCApplyTranspose(pc, x, work));
    PetscCall(MatMultTranspose(pc->mat, work, y));
  } else if (side == PC_LEFT) {
    PetscCall(MatMultTranspose(pc->mat, x, work));
    PetscCall(PCApplyTranspose(pc, work, y));
  }
  /* add support for PC_SYMMETRIC */
  if (pc->erroriffailure) PetscCall(VecValidValues_Internal(y, 4, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCApplyRichardsonExists - Determines whether a particular preconditioner has a
   built-in fast application of Richardson's method.

   Not Collective

   Input Parameter:
.  pc - the preconditioner

   Output Parameter:
.  exists - `PETSC_TRUE` or `PETSC_FALSE`

   Level: developer

.seealso: `PC`, `PCRICHARDSON`, `PCApplyRichardson()`
@*/
PetscErrorCode PCApplyRichardsonExists(PC pc, PetscBool *exists)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidBoolPointer(exists, 2);
  if (pc->ops->applyrichardson) *exists = PETSC_TRUE;
  else *exists = PETSC_FALSE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCApplyRichardson - Applies several steps of Richardson iteration with
   the particular preconditioner. This routine is usually used by the
   Krylov solvers and not the application code directly.

   Collective

   Input Parameters:
+  pc  - the preconditioner context
.  b   - the right hand side
.  w   - one work vector
.  rtol - relative decrease in residual norm convergence criteria
.  abstol - absolute residual norm convergence criteria
.  dtol - divergence residual norm increase criteria
.  its - the number of iterations to apply.
-  guesszero - if the input x contains nonzero initial guess

   Output Parameters:
+  outits - number of iterations actually used (for SOR this always equals its)
.  reason - the reason the apply terminated
-  y - the solution (also contains initial guess if guesszero is `PETSC_FALSE`

   Level: developer

   Notes:
   Most preconditioners do not support this function. Use the command
   `PCApplyRichardsonExists()` to determine if one does.

   Except for the `PCMG` this routine ignores the convergence tolerances
   and always runs for the number of iterations

.seealso: `PC`, `PCApplyRichardsonExists()`
@*/
PetscErrorCode PCApplyRichardson(PC pc, Vec b, Vec y, Vec w, PetscReal rtol, PetscReal abstol, PetscReal dtol, PetscInt its, PetscBool guesszero, PetscInt *outits, PCRichardsonConvergedReason *reason)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(b, VEC_CLASSID, 2);
  PetscValidHeaderSpecific(y, VEC_CLASSID, 3);
  PetscValidHeaderSpecific(w, VEC_CLASSID, 4);
  PetscCheck(b != y, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_IDN, "b and y must be different vectors");
  PetscCall(PCSetUp(pc));
  PetscUseTypeMethod(pc, applyrichardson, b, y, w, rtol, abstol, dtol, its, guesszero, outits, reason);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCSetFailedReason - Sets the reason a `PCSetUp()` failed or `PC_NOERROR` if it did not fail

   Logically Collective

   Input Parameters:
+  pc - the preconditioner context
-  reason - the reason it failedx

   Level: advanced

.seealso: `PC`, `PCCreate()`, `PCApply()`, `PCDestroy()`, `PCFailedReason`
@*/
PetscErrorCode PCSetFailedReason(PC pc, PCFailedReason reason)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  pc->failedreason = reason;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCGetFailedReason - Gets the reason a `PCSetUp()` failed or `PC_NOERROR` if it did not fail

   Logically Collective

   Input Parameter:
.  pc - the preconditioner context

   Output Parameter:
.  reason - the reason it failed

   Level: advanced

   Note:
   This is the maximum over reason over all ranks in the PC communicator. It is only valid after
   a call `KSPCheckDot()` or  `KSPCheckNorm()` inside a `KSPSolve()` or `PCReduceFailedReason()`.
   It is not valid immediately after a `PCSetUp()` or `PCApply()`, then use `PCGetFailedReasonRank()`

.seealso: PC`, ``PCCreate()`, `PCApply()`, `PCDestroy()`, `PCGetFailedReasonRank()`, `PCSetFailedReason()`
@*/
PetscErrorCode PCGetFailedReason(PC pc, PCFailedReason *reason)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  if (pc->setupcalled < 0) *reason = (PCFailedReason)pc->setupcalled;
  else *reason = pc->failedreason;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCGetFailedReasonRank - Gets the reason a `PCSetUp()` failed or `PC_NOERROR` if it did not fail on this MPI rank

   Not Collective

   Input Parameter:
.  pc - the preconditioner context

   Output Parameter:
.  reason - the reason it failed

   Level: advanced

   Note:
     Different ranks may have different reasons or no reason, see `PCGetFailedReason()`

.seealso: `PC`, `PCCreate()`, `PCApply()`, `PCDestroy()`, `PCGetFailedReason()`, `PCSetFailedReason()`, `PCReduceFailedReason()`
@*/
PetscErrorCode PCGetFailedReasonRank(PC pc, PCFailedReason *reason)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  if (pc->setupcalled < 0) *reason = (PCFailedReason)pc->setupcalled;
  else *reason = pc->failedreason;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCReduceFailedReason - Reduce the failed reason among the MPI processes that share the `PC`

   Collective

   Input Parameter:
.  pc - the preconditioner context

   Level: advanced

   Note:
     Different MPI ranks may have different reasons or no reason, see `PCGetFailedReason()`. This routine
     makes them have a common value (failure if any MPI process had a failure).

.seealso: `PC`, `PCCreate()`, `PCApply()`, `PCDestroy()`, `PCGetFailedReason()`, `PCSetFailedReason()`
@*/
PetscErrorCode PCReduceFailedReason(PC pc)
{
  PetscInt buf;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  buf = (PetscInt)pc->failedreason;
  PetscCall(MPIU_Allreduce(MPI_IN_PLACE, &buf, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)pc)));
  pc->failedreason = (PCFailedReason)buf;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*  Next line needed to deactivate KSP_Solve logging */
#include <petsc/private/kspimpl.h>

/*
      a setupcall of 0 indicates never setup,
                     1 indicates has been previously setup
                    -1 indicates a PCSetUp() was attempted and failed
*/
/*@
   PCSetUp - Prepares for the use of a preconditioner.

   Collective

   Input Parameter:
.  pc - the preconditioner context

   Level: developer

.seealso: `PC`, `PCCreate()`, `PCApply()`, `PCDestroy()`
@*/
PetscErrorCode PCSetUp(PC pc)
{
  const char      *def;
  PetscObjectState matstate, matnonzerostate;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscCheck(pc->mat, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Matrix must be set first");

  if (pc->setupcalled && pc->reusepreconditioner) {
    PetscCall(PetscInfo(pc, "Leaving PC with identical preconditioner since reuse preconditioner is set\n"));
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  PetscCall(PetscObjectStateGet((PetscObject)pc->pmat, &matstate));
  PetscCall(MatGetNonzeroState(pc->pmat, &matnonzerostate));
  if (!pc->setupcalled) {
    PetscCall(PetscInfo(pc, "Setting up PC for first time\n"));
    pc->flag = DIFFERENT_NONZERO_PATTERN;
  } else if (matstate == pc->matstate) {
    PetscCall(PetscInfo(pc, "Leaving PC with identical preconditioner since operator is unchanged\n"));
    PetscFunctionReturn(PETSC_SUCCESS);
  } else {
    if (matnonzerostate > pc->matnonzerostate) {
      PetscCall(PetscInfo(pc, "Setting up PC with different nonzero pattern\n"));
      pc->flag = DIFFERENT_NONZERO_PATTERN;
    } else {
      PetscCall(PetscInfo(pc, "Setting up PC with same nonzero pattern\n"));
      pc->flag = SAME_NONZERO_PATTERN;
    }
  }
  pc->matstate        = matstate;
  pc->matnonzerostate = matnonzerostate;

  if (!((PetscObject)pc)->type_name) {
    PetscCall(PCGetDefaultType_Private(pc, &def));
    PetscCall(PCSetType(pc, def));
  }

  PetscCall(MatSetErrorIfFailure(pc->pmat, pc->erroriffailure));
  PetscCall(MatSetErrorIfFailure(pc->mat, pc->erroriffailure));
  PetscCall(PetscLogEventBegin(PC_SetUp, pc, 0, 0, 0));
  if (pc->ops->setup) {
    /* do not log solves and applications of preconditioners while constructing preconditioners; perhaps they should be logged separately from the regular solves */
    PetscCall(KSPInitializePackage());
    PetscCall(PetscLogEventDeactivatePush(KSP_Solve));
    PetscCall(PetscLogEventDeactivatePush(PC_Apply));
    PetscUseTypeMethod(pc, setup);
    PetscCall(PetscLogEventDeactivatePop(KSP_Solve));
    PetscCall(PetscLogEventDeactivatePop(PC_Apply));
  }
  PetscCall(PetscLogEventEnd(PC_SetUp, pc, 0, 0, 0));
  if (!pc->setupcalled) pc->setupcalled = 1;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCSetUpOnBlocks - Sets up the preconditioner for each block in
   the block Jacobi, block Gauss-Seidel, and overlapping Schwarz
   methods.

   Collective

   Input Parameter:
.  pc - the preconditioner context

   Level: developer

   Note:
   For nested preconditioners such as `PCBJACOBI` `PCSetUp()` is not called on each sub-`KSP` when `PCSetUp()` is
   called on the outer `PC`, this routine ensures it is called.

.seealso: `PC`, `PCSetUp()`, `PCCreate()`, `PCApply()`, `PCDestroy()`, `PCSetUp()`
@*/
PetscErrorCode PCSetUpOnBlocks(PC pc)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  if (!pc->ops->setuponblocks) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscLogEventBegin(PC_SetUpOnBlocks, pc, 0, 0, 0));
  PetscUseTypeMethod(pc, setuponblocks);
  PetscCall(PetscLogEventEnd(PC_SetUpOnBlocks, pc, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   PCSetModifySubMatrices - Sets a user-defined routine for modifying the
   submatrices that arise within certain subdomain-based preconditioners.
   The basic submatrices are extracted from the preconditioner matrix as
   usual; the user can then alter these (for example, to set different boundary
   conditions for each submatrix) before they are used for the local solves.

   Logically Collective

   Input Parameters:
+  pc - the preconditioner context
.  func - routine for modifying the submatrices
-  ctx - optional user-defined context (may be null)

   Calling sequence of `func`:
$  PetscErrorCode func(PC pc, PetscInt nsub, IS *row, IS *col, Mat *submat, void *ctx);
+  pc - the preconditioner context
.  row - an array of index sets that contain the global row numbers
         that comprise each local submatrix
.  col - an array of index sets that contain the global column numbers
         that comprise each local submatrix
.  submat - array of local submatrices
-  ctx - optional user-defined context for private data for the
         user-defined func routine (may be null)

   Level: advanced

   Notes:
   `PCSetModifySubMatrices()` MUST be called before `KSPSetUp()` and
   `KSPSolve()`.

   A routine set by `PCSetModifySubMatrices()` is currently called within
   the block Jacobi (`PCBJACOBI`) and additive Schwarz (`PCASM`)
   preconditioners.  All other preconditioners ignore this routine.

.seealso: `PC`, `PCBJACOBI`, `PCASM`, `PCModifySubMatrices()`
@*/
PetscErrorCode PCSetModifySubMatrices(PC pc, PetscErrorCode (*func)(PC, PetscInt, const IS[], const IS[], Mat[], void *), void *ctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  pc->modifysubmatrices  = func;
  pc->modifysubmatricesP = ctx;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   PCModifySubMatrices - Calls an optional user-defined routine within
   certain preconditioners if one has been set with `PCSetModifySubMatrices()`.

   Collective

   Input Parameters:
+  pc - the preconditioner context
.  nsub - the number of local submatrices
.  row - an array of index sets that contain the global row numbers
         that comprise each local submatrix
.  col - an array of index sets that contain the global column numbers
         that comprise each local submatrix
.  submat - array of local submatrices
-  ctx - optional user-defined context for private data for the
         user-defined routine (may be null)

   Output Parameter:
.  submat - array of local submatrices (the entries of which may
            have been modified)

   Level: developer

   Notes:
   The user should NOT generally call this routine, as it will
   automatically be called within certain preconditioners (currently
   block Jacobi, additive Schwarz) if set.

   The basic submatrices are extracted from the preconditioner matrix
   as usual; the user can then alter these (for example, to set different
   boundary conditions for each submatrix) before they are used for the
   local solves.

.seealso: `PC`, `PCSetModifySubMatrices()`
@*/
PetscErrorCode PCModifySubMatrices(PC pc, PetscInt nsub, const IS row[], const IS col[], Mat submat[], void *ctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  if (!pc->modifysubmatrices) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscLogEventBegin(PC_ModifySubMatrices, pc, 0, 0, 0));
  PetscCall((*pc->modifysubmatrices)(pc, nsub, row, col, submat, ctx));
  PetscCall(PetscLogEventEnd(PC_ModifySubMatrices, pc, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCSetOperators - Sets the matrix associated with the linear system and
   a (possibly) different one associated with the preconditioner.

   Logically Collective

   Input Parameters:
+  pc - the preconditioner context
.  Amat - the matrix that defines the linear system
-  Pmat - the matrix to be used in constructing the preconditioner, usually the same as Amat.

   Level: intermediate

   Notes:
    Passing a `NULL` for `Amat` or `Pmat` removes the matrix that is currently used.

    If you wish to replace either `Amat` or `Pmat` but leave the other one untouched then
    first call `KSPGetOperators()` to get the one you wish to keep, call `PetscObjectReference()`
    on it and then pass it back in in your call to `KSPSetOperators()`.

   More Notes about Repeated Solution of Linear Systems:
   PETSc does NOT reset the matrix entries of either `Amat` or `Pmat`
   to zero after a linear solve; the user is completely responsible for
   matrix assembly.  See the routine `MatZeroEntries()` if desiring to
   zero all elements of a matrix.

.seealso: `PC`, `PCGetOperators()`, `MatZeroEntries()`
 @*/
PetscErrorCode PCSetOperators(PC pc, Mat Amat, Mat Pmat)
{
  PetscInt m1, n1, m2, n2;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  if (Amat) PetscValidHeaderSpecific(Amat, MAT_CLASSID, 2);
  if (Pmat) PetscValidHeaderSpecific(Pmat, MAT_CLASSID, 3);
  if (Amat) PetscCheckSameComm(pc, 1, Amat, 2);
  if (Pmat) PetscCheckSameComm(pc, 1, Pmat, 3);
  if (pc->setupcalled && pc->mat && pc->pmat && Amat && Pmat) {
    PetscCall(MatGetLocalSize(Amat, &m1, &n1));
    PetscCall(MatGetLocalSize(pc->mat, &m2, &n2));
    PetscCheck(m1 == m2 && n1 == n2, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Cannot change local size of Amat after use old sizes %" PetscInt_FMT " %" PetscInt_FMT " new sizes %" PetscInt_FMT " %" PetscInt_FMT, m2, n2, m1, n1);
    PetscCall(MatGetLocalSize(Pmat, &m1, &n1));
    PetscCall(MatGetLocalSize(pc->pmat, &m2, &n2));
    PetscCheck(m1 == m2 && n1 == n2, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Cannot change local size of Pmat after use old sizes %" PetscInt_FMT " %" PetscInt_FMT " new sizes %" PetscInt_FMT " %" PetscInt_FMT, m2, n2, m1, n1);
  }

  if (Pmat != pc->pmat) {
    /* changing the operator that defines the preconditioner thus reneed to clear current states so new preconditioner is built */
    pc->matnonzerostate = -1;
    pc->matstate        = -1;
  }

  /* reference first in case the matrices are the same */
  if (Amat) PetscCall(PetscObjectReference((PetscObject)Amat));
  PetscCall(MatDestroy(&pc->mat));
  if (Pmat) PetscCall(PetscObjectReference((PetscObject)Pmat));
  PetscCall(MatDestroy(&pc->pmat));
  pc->mat  = Amat;
  pc->pmat = Pmat;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCSetReusePreconditioner - reuse the current preconditioner even if the operator in the preconditioner has changed.

   Logically Collective

   Input Parameters:
+  pc - the preconditioner context
-  flag - `PETSC_TRUE` do not compute a new preconditioner, `PETSC_FALSE` do compute a new preconditioner

    Level: intermediate

   Note:
   Normally if a matrix inside a `PC` changes the `PC` automatically updates itself using information from the changed matrix. This option
   prevents this.

.seealso: `PC`, `PCGetOperators()`, `MatZeroEntries()`, `PCGetReusePreconditioner()`, `KSPSetReusePreconditioner()`
 @*/
PetscErrorCode PCSetReusePreconditioner(PC pc, PetscBool flag)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidLogicalCollectiveBool(pc, flag, 2);
  pc->reusepreconditioner = flag;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCGetReusePreconditioner - Determines if the `PC` reuses the current preconditioner even if the operator in the preconditioner has changed.

   Not Collective

   Input Parameter:
.  pc - the preconditioner context

   Output Parameter:
.  flag - `PETSC_TRUE` do not compute a new preconditioner, `PETSC_FALSE` do compute a new preconditioner

   Level: intermediate

.seealso: `PC`, `PCGetOperators()`, `MatZeroEntries()`, `PCSetReusePreconditioner()`
 @*/
PetscErrorCode PCGetReusePreconditioner(PC pc, PetscBool *flag)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidBoolPointer(flag, 2);
  *flag = pc->reusepreconditioner;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCGetOperators - Gets the matrix associated with the linear system and
   possibly a different one associated with the preconditioner.

   Not Collective, though parallel mats are returned if pc is parallel

   Input Parameter:
.  pc - the preconditioner context

   Output Parameters:
+  Amat - the matrix defining the linear system
-  Pmat - the matrix from which the preconditioner is constructed, usually the same as Amat.

   Level: intermediate

   Note:
    Does not increase the reference count of the matrices, so you should not destroy them

   Alternative usage: If the operators have NOT been set with `KSPSetOperators()`/`PCSetOperators()` then the operators
      are created in `PC` and returned to the user. In this case, if both operators
      mat and pmat are requested, two DIFFERENT operators will be returned. If
      only one is requested both operators in the PC will be the same (i.e. as
      if one had called `KSPSetOperators()`/`PCSetOperators()` with the same argument for both Mats).
      The user must set the sizes of the returned matrices and their type etc just
      as if the user created them with `MatCreate()`. For example,

.vb
         KSP/PCGetOperators(ksp/pc,&Amat,NULL); is equivalent to
           set size, type, etc of Amat

         MatCreate(comm,&mat);
         KSP/PCSetOperators(ksp/pc,Amat,Amat);
         PetscObjectDereference((PetscObject)mat);
           set size, type, etc of Amat
.ve

     and

.vb
         KSP/PCGetOperators(ksp/pc,&Amat,&Pmat); is equivalent to
           set size, type, etc of Amat and Pmat

         MatCreate(comm,&Amat);
         MatCreate(comm,&Pmat);
         KSP/PCSetOperators(ksp/pc,Amat,Pmat);
         PetscObjectDereference((PetscObject)Amat);
         PetscObjectDereference((PetscObject)Pmat);
           set size, type, etc of Amat and Pmat
.ve

    The rationale for this support is so that when creating a `TS`, `SNES`, or `KSP` the hierarchy
    of underlying objects (i.e. `SNES`, `KSP`, `PC`, `Mat`) and their lifespans can be completely
    managed by the top most level object (i.e. the `TS`, `SNES`, or `KSP`). Another way to look
    at this is when you create a `SNES` you do not NEED to create a `KSP` and attach it to
    the `SNES` object (the `SNES` object manages it for you). Similarly when you create a KSP
    you do not need to attach a `PC` to it (the `KSP` object manages the `PC` object for you).
    Thus, why should YOU have to create the `Mat` and attach it to the `SNES`/`KSP`/`PC`, when
    it can be created for you?

.seealso: `PC`, `PCSetOperators()`, `KSPGetOperators()`, `KSPSetOperators()`, `PCGetOperatorsSet()`
@*/
PetscErrorCode PCGetOperators(PC pc, Mat *Amat, Mat *Pmat)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  if (Amat) {
    if (!pc->mat) {
      if (pc->pmat && !Pmat) { /* Pmat has been set, but user did not request it, so use for Amat */
        pc->mat = pc->pmat;
        PetscCall(PetscObjectReference((PetscObject)pc->mat));
      } else { /* both Amat and Pmat are empty */
        PetscCall(MatCreate(PetscObjectComm((PetscObject)pc), &pc->mat));
        if (!Pmat) { /* user did NOT request Pmat, so make same as Amat */
          pc->pmat = pc->mat;
          PetscCall(PetscObjectReference((PetscObject)pc->pmat));
        }
      }
    }
    *Amat = pc->mat;
  }
  if (Pmat) {
    if (!pc->pmat) {
      if (pc->mat && !Amat) { /* Amat has been set but was not requested, so use for pmat */
        pc->pmat = pc->mat;
        PetscCall(PetscObjectReference((PetscObject)pc->pmat));
      } else {
        PetscCall(MatCreate(PetscObjectComm((PetscObject)pc), &pc->pmat));
        if (!Amat) { /* user did NOT request Amat, so make same as Pmat */
          pc->mat = pc->pmat;
          PetscCall(PetscObjectReference((PetscObject)pc->mat));
        }
      }
    }
    *Pmat = pc->pmat;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   PCGetOperatorsSet - Determines if the matrix associated with the linear system and
   possibly a different one associated with the preconditioner have been set in the `PC`.

   Not Collective, though the results on all processes should be the same

   Input Parameter:
.  pc - the preconditioner context

   Output Parameters:
+  mat - the matrix associated with the linear system was set
-  pmat - matrix associated with the preconditioner was set, usually the same

   Level: intermediate

.seealso: `PC`, `PCSetOperators()`, `KSPGetOperators()`, `KSPSetOperators()`, `PCGetOperators()`
@*/
PetscErrorCode PCGetOperatorsSet(PC pc, PetscBool *mat, PetscBool *pmat)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  if (mat) *mat = (pc->mat) ? PETSC_TRUE : PETSC_FALSE;
  if (pmat) *pmat = (pc->pmat) ? PETSC_TRUE : PETSC_FALSE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCFactorGetMatrix - Gets the factored matrix from the
   preconditioner context.  This routine is valid only for the `PCLU`,
   `PCILU`, `PCCHOLESKY`, and `PCICC` methods.

   Not Collective though mat is parallel if pc is parallel

   Input Parameter:
.  pc - the preconditioner context

   Output parameters:
.  mat - the factored matrix

   Level: advanced

   Note:
    Does not increase the reference count for the matrix so DO NOT destroy it

.seealso: `PC`, `PCLU`, `PCILU`, `PCCHOLESKY`, `PCICC`
@*/
PetscErrorCode PCFactorGetMatrix(PC pc, Mat *mat)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidPointer(mat, 2);
  PetscCall(PCFactorSetUpMatSolverType(pc));
  PetscUseTypeMethod(pc, getfactoredmatrix, mat);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   PCSetOptionsPrefix - Sets the prefix used for searching for all
   `PC` options in the database.

   Logically Collective

   Input Parameters:
+  pc - the preconditioner context
-  prefix - the prefix string to prepend to all `PC` option requests

   Note:
   A hyphen (-) must NOT be given at the beginning of the prefix name.
   The first character of all runtime options is AUTOMATICALLY the
   hyphen.

   Level: advanced

.seealso: `PC`, `PCSetFromOptions`, `PCAppendOptionsPrefix()`, `PCGetOptionsPrefix()`
@*/
PetscErrorCode PCSetOptionsPrefix(PC pc, const char prefix[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscCall(PetscObjectSetOptionsPrefix((PetscObject)pc, prefix));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   PCAppendOptionsPrefix - Appends to the prefix used for searching for all
   `PC` options in the database.

   Logically Collective

   Input Parameters:
+  pc - the preconditioner context
-  prefix - the prefix string to prepend to all `PC` option requests

   Note:
   A hyphen (-) must NOT be given at the beginning of the prefix name.
   The first character of all runtime options is AUTOMATICALLY the
   hyphen.

   Level: advanced

.seealso: `PC`, `PCSetFromOptions`, `PCSetOptionsPrefix()`, `PCGetOptionsPrefix()`
@*/
PetscErrorCode PCAppendOptionsPrefix(PC pc, const char prefix[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscCall(PetscObjectAppendOptionsPrefix((PetscObject)pc, prefix));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   PCGetOptionsPrefix - Gets the prefix used for searching for all
   PC options in the database.

   Not Collective

   Input Parameter:
.  pc - the preconditioner context

   Output Parameter:
.  prefix - pointer to the prefix string used, is returned

   Fortran Note:
   The user should pass in a string 'prefix' of
   sufficient length to hold the prefix.

   Level: advanced

.seealso: `PC`, `PCSetFromOptions`, `PCSetOptionsPrefix()`, `PCAppendOptionsPrefix()`
@*/
PetscErrorCode PCGetOptionsPrefix(PC pc, const char *prefix[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidPointer(prefix, 2);
  PetscCall(PetscObjectGetOptionsPrefix((PetscObject)pc, prefix));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
   Indicates the right hand side will be changed by KSPSolve(), this occurs for a few
  preconditioners including BDDC and Eisentat that transform the equations before applying
  the Krylov methods
*/
PETSC_INTERN PetscErrorCode PCPreSolveChangeRHS(PC pc, PetscBool *change)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidBoolPointer(change, 2);
  *change = PETSC_FALSE;
  PetscTryMethod(pc, "PCPreSolveChangeRHS_C", (PC, PetscBool *), (pc, change));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCPreSolve - Optional pre-solve phase, intended for any
   preconditioner-specific actions that must be performed before
   the iterative solve itself.

   Collective

   Input Parameters:
+  pc - the preconditioner context
-  ksp - the Krylov subspace context

   Level: developer

   Sample of Usage:
.vb
    PCPreSolve(pc,ksp);
    KSPSolve(ksp,b,x);
    PCPostSolve(pc,ksp);
.ve

   Notes:
   The pre-solve phase is distinct from the `PCSetUp()` phase.

   `KSPSolve()` calls this directly, so is rarely called by the user.

.seealso: `PC`, `PCPostSolve()`
@*/
PetscErrorCode PCPreSolve(PC pc, KSP ksp)
{
  Vec x, rhs;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(ksp, KSP_CLASSID, 2);
  pc->presolvedone++;
  PetscCheck(pc->presolvedone <= 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Cannot embed PCPreSolve() more than twice");
  PetscCall(KSPGetSolution(ksp, &x));
  PetscCall(KSPGetRhs(ksp, &rhs));

  if (pc->ops->presolve) PetscUseTypeMethod(pc, presolve, ksp, rhs, x);
  else if (pc->presolve) PetscCall((pc->presolve)(pc, ksp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   PCSetPreSolve - Sets function used by `PCPreSolve()` which is intended for any
   preconditioner-specific actions that must be performed before
   the iterative solve itself.

   Logically Collective

   Input Parameters:
+   pc - the preconditioner object
-   presolve - the function to call before the solve

   Calling sequence of `presolve`:
$  PetscErrorCode presolve(PC pc, KSP ksp)
+  pc - the `PC` context
-  ksp - the `KSP` context

   Level: developer

.seealso: `PC`, `PCSetUp()`, `PCPreSolve()`
@*/
PetscErrorCode PCSetPreSolve(PC pc, PetscErrorCode (*presolve)(PC, KSP))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  pc->presolve = presolve;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCPostSolve - Optional post-solve phase, intended for any
   preconditioner-specific actions that must be performed after
   the iterative solve itself.

   Collective

   Input Parameters:
+  pc - the preconditioner context
-  ksp - the Krylov subspace context

   Sample of Usage:
.vb
    PCPreSolve(pc,ksp);
    KSPSolve(ksp,b,x);
    PCPostSolve(pc,ksp);
.ve

   Note:
   `KSPSolve()` calls this routine directly, so it is rarely called by the user.

   Level: developer

.seealso: `PC`, `PCSetPostSolve()`, `PCSetPresolve()`, `PCPreSolve()`, `KSPSolve()`
@*/
PetscErrorCode PCPostSolve(PC pc, KSP ksp)
{
  Vec x, rhs;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidHeaderSpecific(ksp, KSP_CLASSID, 2);
  pc->presolvedone--;
  PetscCall(KSPGetSolution(ksp, &x));
  PetscCall(KSPGetRhs(ksp, &rhs));
  PetscTryTypeMethod(pc, postsolve, ksp, rhs, x);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PCLoad - Loads a `PC` that has been stored in binary  with `PCView()`.

  Collective

  Input Parameters:
+ newdm - the newly loaded `PC`, this needs to have been created with `PCCreate()` or
           some related function before a call to `PCLoad()`.
- viewer - binary file viewer, obtained from `PetscViewerBinaryOpen()`

   Level: intermediate

  Note:
   The type is determined by the data in the file, any type set into the PC before this call is ignored.

.seealso: `PC`, `PetscViewerBinaryOpen()`, `PCView()`, `MatLoad()`, `VecLoad()`
@*/
PetscErrorCode PCLoad(PC newdm, PetscViewer viewer)
{
  PetscBool isbinary;
  PetscInt  classid;
  char      type[256];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(newdm, PC_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
  PetscCheck(isbinary, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid viewer; open viewer with PetscViewerBinaryOpen()");

  PetscCall(PetscViewerBinaryRead(viewer, &classid, 1, NULL, PETSC_INT));
  PetscCheck(classid == PC_FILE_CLASSID, PetscObjectComm((PetscObject)newdm), PETSC_ERR_ARG_WRONG, "Not PC next in file");
  PetscCall(PetscViewerBinaryRead(viewer, type, 256, NULL, PETSC_CHAR));
  PetscCall(PCSetType(newdm, type));
  PetscTryTypeMethod(newdm, load, viewer);
  PetscFunctionReturn(PETSC_SUCCESS);
}

#include <petscdraw.h>
#if defined(PETSC_HAVE_SAWS)
  #include <petscviewersaws.h>
#endif

/*@C
   PCViewFromOptions - View from the `PC` based on options in the database

   Collective

   Input Parameters:
+  A - the `PC` context
.  obj - Optional object that provides the options prefix
-  name - command line option

   Level: intermediate

.seealso: `PC`, `PCView`, `PetscObjectViewFromOptions()`, `PCCreate()`
@*/
PetscErrorCode PCViewFromOptions(PC A, PetscObject obj, const char name[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, PC_CLASSID, 1);
  PetscCall(PetscObjectViewFromOptions((PetscObject)A, obj, name));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
   PCView - Prints information about the `PC`

   Collective

   Input Parameters:
+  PC - the `PC` context
-  viewer - optional visualization context

   Level: developer

   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.

   The user can open an alternative visualization contexts with
   `PetscViewerASCIIOpen()` (output to a specified file).

.seealso: `PC`, `PetscViewer`, `KSPView()`, `PetscViewerASCIIOpen()`
@*/
PetscErrorCode PCView(PC pc, PetscViewer viewer)
{
  PCType    cstr;
  PetscBool iascii, isstring, isbinary, isdraw;
#if defined(PETSC_HAVE_SAWS)
  PetscBool issaws;
#endif

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

  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSTRING, &isstring));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
#if defined(PETSC_HAVE_SAWS)
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSAWS, &issaws));
#endif

  if (iascii) {
    PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)pc, viewer));
    if (!pc->setupcalled) PetscCall(PetscViewerASCIIPrintf(viewer, "  PC has not been set up so information may be incomplete\n"));
    PetscCall(PetscViewerASCIIPushTab(viewer));
    PetscTryTypeMethod(pc, view, viewer);
    PetscCall(PetscViewerASCIIPopTab(viewer));
    if (pc->mat) {
      PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_INFO));
      if (pc->pmat == pc->mat) {
        PetscCall(PetscViewerASCIIPrintf(viewer, "  linear system matrix = precond matrix:\n"));
        PetscCall(PetscViewerASCIIPushTab(viewer));
        PetscCall(MatView(pc->mat, viewer));
        PetscCall(PetscViewerASCIIPopTab(viewer));
      } else {
        if (pc->pmat) {
          PetscCall(PetscViewerASCIIPrintf(viewer, "  linear system matrix followed by preconditioner matrix:\n"));
        } else {
          PetscCall(PetscViewerASCIIPrintf(viewer, "  linear system matrix:\n"));
        }
        PetscCall(PetscViewerASCIIPushTab(viewer));
        PetscCall(MatView(pc->mat, viewer));
        if (pc->pmat) PetscCall(MatView(pc->pmat, viewer));
        PetscCall(PetscViewerASCIIPopTab(viewer));
      }
      PetscCall(PetscViewerPopFormat(viewer));
    }
  } else if (isstring) {
    PetscCall(PCGetType(pc, &cstr));
    PetscCall(PetscViewerStringSPrintf(viewer, " PCType: %-7.7s", cstr));
    PetscTryTypeMethod(pc, view, viewer);
    if (pc->mat) PetscCall(MatView(pc->mat, viewer));
    if (pc->pmat && pc->pmat != pc->mat) PetscCall(MatView(pc->pmat, viewer));
  } else if (isbinary) {
    PetscInt    classid = PC_FILE_CLASSID;
    MPI_Comm    comm;
    PetscMPIInt rank;
    char        type[256];

    PetscCall(PetscObjectGetComm((PetscObject)pc, &comm));
    PetscCallMPI(MPI_Comm_rank(comm, &rank));
    if (rank == 0) {
      PetscCall(PetscViewerBinaryWrite(viewer, &classid, 1, PETSC_INT));
      PetscCall(PetscStrncpy(type, ((PetscObject)pc)->type_name, 256));
      PetscCall(PetscViewerBinaryWrite(viewer, type, 256, PETSC_CHAR));
    }
    PetscTryTypeMethod(pc, view, viewer);
  } else if (isdraw) {
    PetscDraw draw;
    char      str[25];
    PetscReal x, y, bottom, h;
    PetscInt  n;

    PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
    PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
    if (pc->mat) {
      PetscCall(MatGetSize(pc->mat, &n, NULL));
      PetscCall(PetscSNPrintf(str, 25, "PC: %s (%" PetscInt_FMT ")", ((PetscObject)pc)->type_name, n));
    } else {
      PetscCall(PetscSNPrintf(str, 25, "PC: %s", ((PetscObject)pc)->type_name));
    }
    PetscCall(PetscDrawStringBoxed(draw, x, y, PETSC_DRAW_RED, PETSC_DRAW_BLACK, str, NULL, &h));
    bottom = y - h;
    PetscCall(PetscDrawPushCurrentPoint(draw, x, bottom));
    PetscTryTypeMethod(pc, view, viewer);
    PetscCall(PetscDrawPopCurrentPoint(draw));
#if defined(PETSC_HAVE_SAWS)
  } else if (issaws) {
    PetscMPIInt rank;

    PetscCall(PetscObjectName((PetscObject)pc));
    PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
    if (!((PetscObject)pc)->amsmem && rank == 0) PetscCall(PetscObjectViewSAWs((PetscObject)pc, viewer));
    if (pc->mat) PetscCall(MatView(pc->mat, viewer));
    if (pc->pmat && pc->pmat != pc->mat) PetscCall(MatView(pc->pmat, viewer));
#endif
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  PCRegister -  Adds a method to the preconditioner package.

   Not collective

   Input Parameters:
+  sname - name of a new user-defined solver
-  function - routine to create method context

   Sample usage:
.vb
   PCRegister("my_solver", MySolverCreate);
.ve

   Then, your solver can be chosen with the procedural interface via
$     PCSetType(pc, "my_solver")
   or at runtime via the option
$     -pc_type my_solver

   Level: advanced

   Note:
   `PCRegister()` may be called multiple times to add several user-defined preconditioners.

.seealso: `PC`, `PCType`, `PCRegisterAll()`
@*/
PetscErrorCode PCRegister(const char sname[], PetscErrorCode (*function)(PC))
{
  PetscFunctionBegin;
  PetscCall(PCInitializePackage());
  PetscCall(PetscFunctionListAdd(&PCList, sname, function));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMult_PC(Mat A, Vec X, Vec Y)
{
  PC pc;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(A, &pc));
  PetscCall(PCApply(pc, X, Y));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
    PCComputeOperator - Computes the explicit preconditioned operator.

    Collective

    Input Parameters:
+   pc - the preconditioner object
-   mattype - the matrix type to be used for the operator

    Output Parameter:
.   mat - the explicit preconditioned operator

    Level: advanced

    Note:
    This computation is done by applying the operators to columns of the identity matrix.
    This routine is costly in general, and is recommended for use only with relatively small systems.
    Currently, this routine uses a dense matrix format when mattype == NULL

.seealso: `PC`, `KSPComputeOperator()`, `MatType`
@*/
PetscErrorCode PCComputeOperator(PC pc, MatType mattype, Mat *mat)
{
  PetscInt N, M, m, n;
  Mat      A, Apc;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidPointer(mat, 3);
  PetscCall(PCGetOperators(pc, &A, NULL));
  PetscCall(MatGetLocalSize(A, &m, &n));
  PetscCall(MatGetSize(A, &M, &N));
  PetscCall(MatCreateShell(PetscObjectComm((PetscObject)pc), m, n, M, N, pc, &Apc));
  PetscCall(MatShellSetOperation(Apc, MATOP_MULT, (void (*)(void))MatMult_PC));
  PetscCall(MatComputeOperator(Apc, mattype, mat));
  PetscCall(MatDestroy(&Apc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCSetCoordinates - sets the coordinates of all the nodes on the local process

   Collective

   Input Parameters:
+  pc - the solver context
.  dim - the dimension of the coordinates 1, 2, or 3
.  nloc - the blocked size of the coordinates array
-  coords - the coordinates array

   Level: intermediate

   Note:
   `coords` is an array of the dim coordinates for the nodes on
   the local processor, of size `dim`*`nloc`.
   If there are 108 equation on a processor
   for a displacement finite element discretization of elasticity (so
   that there are nloc = 36 = 108/3 nodes) then the array must have 108
   double precision values (ie, 3 * 36).  These x y z coordinates
   should be ordered for nodes 0 to N-1 like so: [ 0.x, 0.y, 0.z, 1.x,
   ... , N-1.z ].

.seealso: `PC`, `MatSetNearNullSpace()`
@*/
PetscErrorCode PCSetCoordinates(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidLogicalCollectiveInt(pc, dim, 2);
  PetscTryMethod(pc, "PCSetCoordinates_C", (PC, PetscInt, PetscInt, PetscReal[]), (pc, dim, nloc, coords));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCGetInterpolations - Gets interpolation matrices for all levels (except level 0)

   Logically Collective

   Input Parameter:
.  pc - the precondition context

   Output Parameters:
+  num_levels - the number of levels
-  interpolations - the interpolation matrices (size of num_levels-1)

   Level: advanced

   Developer Note:
   Why is this here instead of in `PCMG` etc?

.seealso: `PC`, `PCMG`, `PCMGGetRestriction()`, `PCMGSetInterpolation()`, `PCMGGetInterpolation()`, `PCGetCoarseOperators()`
@*/
PetscErrorCode PCGetInterpolations(PC pc, PetscInt *num_levels, Mat *interpolations[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidIntPointer(num_levels, 2);
  PetscValidPointer(interpolations, 3);
  PetscUseMethod(pc, "PCGetInterpolations_C", (PC, PetscInt *, Mat *[]), (pc, num_levels, interpolations));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   PCGetCoarseOperators - Gets coarse operator matrices for all levels (except the finest level)

   Logically Collective

   Input Parameter:
.  pc - the precondition context

   Output Parameters:
+  num_levels - the number of levels
-  coarseOperators - the coarse operator matrices (size of num_levels-1)

   Level: advanced

   Developer Note:
   Why is this here instead of in `PCMG` etc?

.seealso: `PC`, `PCMG`, `PCMGGetRestriction()`, `PCMGSetInterpolation()`, `PCMGGetRScale()`, `PCMGGetInterpolation()`, `PCGetInterpolations()`
@*/
PetscErrorCode PCGetCoarseOperators(PC pc, PetscInt *num_levels, Mat *coarseOperators[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
  PetscValidIntPointer(num_levels, 2);
  PetscValidPointer(coarseOperators, 3);
  PetscUseMethod(pc, "PCGetCoarseOperators_C", (PC, PetscInt *, Mat *[]), (pc, num_levels, coarseOperators));
  PetscFunctionReturn(PETSC_SUCCESS);
}