factor/lu/lu.c

/*
   Defines a direct factorization preconditioner for any Mat implementation
   Note: this need not be considered a preconditioner since it supplies
         a direct solver.
*/

#include <../src/ksp/pc/impls/factor/lu/lu.h> /*I "petscpc.h" I*/

static PetscErrorCode PCFactorReorderForNonzeroDiagonal_LU(PC pc, PetscReal z)
{
  PC_LU *lu = (PC_LU *)pc->data;

  PetscFunctionBegin;
  lu->nonzerosalongdiagonal = PETSC_TRUE;
  if (z == (PetscReal)PETSC_DECIDE) lu->nonzerosalongdiagonaltol = 1.e-10;
  else lu->nonzerosalongdiagonaltol = z;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCSetFromOptions_LU(PC pc, PetscOptionItems PetscOptionsObject)
{
  PC_LU    *lu  = (PC_LU *)pc->data;
  PetscBool flg = PETSC_FALSE;
  PetscReal tol;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "LU options");
  PetscCall(PCSetFromOptions_Factor(pc, PetscOptionsObject));

  PetscCall(PetscOptionsName("-pc_factor_nonzeros_along_diagonal", "Reorder to remove zeros from diagonal", "PCFactorReorderForNonzeroDiagonal", &flg));
  if (flg) {
    tol = PETSC_DECIDE;
    PetscCall(PetscOptionsReal("-pc_factor_nonzeros_along_diagonal", "Reorder to remove zeros from diagonal", "PCFactorReorderForNonzeroDiagonal", lu->nonzerosalongdiagonaltol, &tol, NULL));
    PetscCall(PCFactorReorderForNonzeroDiagonal(pc, tol));
  }
  PetscOptionsHeadEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCSetUp_LU(PC pc)
{
  PC_LU         *dir = (PC_LU *)pc->data;
  MatSolverType  stype;
  MatFactorError err;
  const char    *prefix;

  PetscFunctionBegin;
  pc->failedreason = PC_NOERROR;
  if (dir->hdr.reusefill && pc->setupcalled) ((PC_Factor *)dir)->info.fill = dir->hdr.actualfill;

  PetscCall(PCGetOptionsPrefix(pc, &prefix));
  PetscCall(MatSetOptionsPrefixFactor(pc->pmat, prefix));

  PetscCall(MatSetErrorIfFailure(pc->pmat, pc->erroriffailure));
  if (dir->hdr.inplace) {
    MatFactorType ftype;

    PetscCall(MatGetFactorType(pc->pmat, &ftype));
    if (ftype == MAT_FACTOR_NONE) {
      if (dir->row && dir->col && dir->row != dir->col) PetscCall(ISDestroy(&dir->row));
      PetscCall(ISDestroy(&dir->col));
      /* This should only get the ordering if needed, but since MatGetFactor() is not called we can't know if it is needed */
      PetscCall(PCFactorSetDefaultOrdering_Factor(pc));
      PetscCall(MatGetOrdering(pc->pmat, ((PC_Factor *)dir)->ordering, &dir->row, &dir->col));
      PetscCall(MatLUFactor(pc->pmat, dir->row, dir->col, &((PC_Factor *)dir)->info));
      PetscCall(MatFactorGetError(pc->pmat, &err));
      if (err) { /* Factor() fails */
        pc->failedreason = (PCFailedReason)err;
        PetscFunctionReturn(PETSC_SUCCESS);
      }
    }
    ((PC_Factor *)dir)->fact = pc->pmat;
  } else {
    MatInfo info;

    if (!pc->setupcalled) {
      PetscBool canuseordering;

      PetscCall(PCFactorSetUpMatSolverType(pc));
      PetscCall(MatFactorGetCanUseOrdering(((PC_Factor *)dir)->fact, &canuseordering));
      if (canuseordering) {
        PetscCall(PCFactorSetDefaultOrdering_Factor(pc));
        PetscCall(MatGetOrdering(pc->pmat, ((PC_Factor *)dir)->ordering, &dir->row, &dir->col));
        if (dir->nonzerosalongdiagonal) PetscCall(MatReorderForNonzeroDiagonal(pc->pmat, dir->nonzerosalongdiagonaltol, dir->row, dir->col));
      }
      PetscCall(MatLUFactorSymbolic(((PC_Factor *)dir)->fact, pc->pmat, dir->row, dir->col, &((PC_Factor *)dir)->info));
      PetscCall(MatGetInfo(((PC_Factor *)dir)->fact, MAT_LOCAL, &info));
      dir->hdr.actualfill = info.fill_ratio_needed;
    } else if (pc->flag != SAME_NONZERO_PATTERN) {
      PetscBool canuseordering;

      if (!dir->hdr.reuseordering) {
        PetscCall(MatDestroy(&((PC_Factor *)dir)->fact));
        PetscCall(PCFactorSetUpMatSolverType(pc));
        PetscCall(MatFactorGetCanUseOrdering(((PC_Factor *)dir)->fact, &canuseordering));
        if (canuseordering) {
          if (dir->row && dir->col && dir->row != dir->col) PetscCall(ISDestroy(&dir->row));
          PetscCall(ISDestroy(&dir->col));
          PetscCall(PCFactorSetDefaultOrdering_Factor(pc));
          PetscCall(MatGetOrdering(pc->pmat, ((PC_Factor *)dir)->ordering, &dir->row, &dir->col));
          if (dir->nonzerosalongdiagonal) PetscCall(MatReorderForNonzeroDiagonal(pc->pmat, dir->nonzerosalongdiagonaltol, dir->row, dir->col));
        }
      }
      PetscCall(MatLUFactorSymbolic(((PC_Factor *)dir)->fact, pc->pmat, dir->row, dir->col, &((PC_Factor *)dir)->info));
      PetscCall(MatGetInfo(((PC_Factor *)dir)->fact, MAT_LOCAL, &info));
      dir->hdr.actualfill = info.fill_ratio_needed;
    } else {
      PetscCall(MatFactorGetError(((PC_Factor *)dir)->fact, &err));
      if (err == MAT_FACTOR_NUMERIC_ZEROPIVOT) {
        PetscCall(MatFactorClearError(((PC_Factor *)dir)->fact));
        pc->failedreason = PC_NOERROR;
      }
    }
    PetscCall(MatFactorGetError(((PC_Factor *)dir)->fact, &err));
    if (err) { /* FactorSymbolic() fails */
      pc->failedreason = (PCFailedReason)err;
      PetscFunctionReturn(PETSC_SUCCESS);
    }

    PetscCall(MatLUFactorNumeric(((PC_Factor *)dir)->fact, pc->pmat, &((PC_Factor *)dir)->info));
    PetscCall(MatFactorGetError(((PC_Factor *)dir)->fact, &err));
    if (err) { /* FactorNumeric() fails */
      pc->failedreason = (PCFailedReason)err;
    }
  }

  PetscCall(PCFactorGetMatSolverType(pc, &stype));
  if (!stype) {
    MatSolverType solverpackage;
    PetscCall(MatFactorGetSolverType(((PC_Factor *)dir)->fact, &solverpackage));
    PetscCall(PCFactorSetMatSolverType(pc, solverpackage));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCReset_LU(PC pc)
{
  PC_LU *dir = (PC_LU *)pc->data;

  PetscFunctionBegin;
  if (!dir->hdr.inplace && ((PC_Factor *)dir)->fact) PetscCall(MatDestroy(&((PC_Factor *)dir)->fact));
  if (dir->row && dir->col && dir->row != dir->col) PetscCall(ISDestroy(&dir->row));
  PetscCall(ISDestroy(&dir->col));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCDestroy_LU(PC pc)
{
  PC_LU *dir = (PC_LU *)pc->data;

  PetscFunctionBegin;
  PetscCall(PCReset_LU(pc));
  PetscCall(PetscFree(((PC_Factor *)dir)->ordering));
  PetscCall(PetscFree(((PC_Factor *)dir)->solvertype));
  PetscCall(PCFactorClearComposedFunctions(pc));
  PetscCall(PetscFree(pc->data));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCApply_LU(PC pc, Vec x, Vec y)
{
  PC_LU *dir = (PC_LU *)pc->data;

  PetscFunctionBegin;
  if (dir->hdr.inplace) {
    PetscCall(MatSolve(pc->pmat, x, y));
  } else {
    PetscCall(MatSolve(((PC_Factor *)dir)->fact, x, y));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCMatApply_LU(PC pc, Mat X, Mat Y)
{
  PC_LU *dir = (PC_LU *)pc->data;

  PetscFunctionBegin;
  if (dir->hdr.inplace) {
    PetscCall(MatMatSolve(pc->pmat, X, Y));
  } else {
    PetscCall(MatMatSolve(((PC_Factor *)dir)->fact, X, Y));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCApplyTranspose_LU(PC pc, Vec x, Vec y)
{
  PC_LU *dir = (PC_LU *)pc->data;

  PetscFunctionBegin;
  if (dir->hdr.inplace) {
    PetscCall(MatSolveTranspose(pc->pmat, x, y));
  } else {
    PetscCall(MatSolveTranspose(((PC_Factor *)dir)->fact, x, y));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCMatApplyTranspose_LU(PC pc, Mat X, Mat Y)
{
  PC_LU *dir = (PC_LU *)pc->data;

  PetscFunctionBegin;
  if (dir->hdr.inplace) {
    PetscCall(MatMatSolveTranspose(pc->pmat, X, Y));
  } else {
    PetscCall(MatMatSolveTranspose(((PC_Factor *)dir)->fact, X, Y));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
   PCLU - Uses a direct solver, based on LU factorization, as a preconditioner

   Options Database Keys:
+  -pc_factor_reuse_ordering - Activate `PCFactorSetReuseOrdering()`
.  -pc_factor_mat_solver_type - Actives `PCFactorSetMatSolverType()` to choose the direct solver, like superlu
.  -pc_factor_reuse_fill - Activates `PCFactorSetReuseFill()`
.  -pc_factor_fill <fill> - Sets fill amount
.  -pc_factor_in_place - Activates in-place factorization
.  -pc_factor_mat_ordering_type <nd,rcm,...> - Sets ordering routine
.  -pc_factor_pivot_in_blocks <true,false> - allow pivoting within the small blocks during factorization (may increase
                                         stability of factorization.
.  -pc_factor_shift_type <shifttype> - Sets shift type or -1 for the default; use '-help' for a list of available types
.  -pc_factor_shift_amount <shiftamount> - Sets shift amount or -1 for the default
.  -pc_factor_nonzeros_along_diagonal - permutes the rows and columns to try to put nonzero value along the diagonal.
.  -pc_factor_mat_solver_type <packagename> - use an external package for the solve, see `MatSolverType` for possibilities
-  -mat_solvertype_optionname - options for a specific solver package, for example -mat_mumps_cntl_1

   Level: beginner

   Notes:
   Not all options work for all matrix formats

   Run with `-help` to see additional options for particular matrix formats or factorization algorithms

   The Cholesky factorization direct solver, `PCCHOLESKY` will be more efficient than `PCLU` for symmetric positive-definite (SPD) matrices

   Usually this will compute an "exact" solution in one iteration and does
   not need a Krylov method (i.e. you can use -ksp_type preonly, or
   `KSPSetType`(ksp,`KSPPREONLY`) for the Krylov method.

.seealso: [](ch_ksp), `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `MatSolverType`, `MatGetFactor()`, `PCQR`, `PCSVD`,
          `PCILU`, `PCCHOLESKY`, `PCICC`, `PCFactorSetReuseOrdering()`, `PCFactorSetReuseFill()`, `PCFactorGetMatrix()`,
          `PCFactorSetFill()`, `PCFactorSetUseInPlace()`, `PCFactorSetMatOrderingType()`, `PCFactorSetColumnPivot()`,
          `PCFactorSetPivotInBlocks()`, `PCFactorSetShiftType()`, `PCFactorSetShiftAmount()`
          `PCFactorReorderForNonzeroDiagonal()`
M*/

PETSC_EXTERN PetscErrorCode PCCreate_LU(PC pc)
{
  PC_LU *dir;

  PetscFunctionBegin;
  PetscCall(PetscNew(&dir));
  pc->data = (void *)dir;
  PetscCall(PCFactorInitialize(pc, MAT_FACTOR_LU));
  dir->nonzerosalongdiagonal = PETSC_FALSE;

  ((PC_Factor *)dir)->info.fill      = 5.0;
  ((PC_Factor *)dir)->info.dtcol     = 1.e-6; /* default to pivoting; this is only thing PETSc LU supports */
  ((PC_Factor *)dir)->info.shifttype = (PetscReal)MAT_SHIFT_NONE;
  dir->col                           = NULL;
  dir->row                           = NULL;

  pc->ops->reset             = PCReset_LU;
  pc->ops->destroy           = PCDestroy_LU;
  pc->ops->apply             = PCApply_LU;
  pc->ops->matapply          = PCMatApply_LU;
  pc->ops->applytranspose    = PCApplyTranspose_LU;
  pc->ops->matapplytranspose = PCMatApplyTranspose_LU;
  pc->ops->setup             = PCSetUp_LU;
  pc->ops->setfromoptions    = PCSetFromOptions_LU;
  pc->ops->view              = PCView_Factor;
  pc->ops->applyrichardson   = NULL;
  PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFactorReorderForNonzeroDiagonal_C", PCFactorReorderForNonzeroDiagonal_LU));
  PetscFunctionReturn(PETSC_SUCCESS);
}