impls/pbjacobi/pbjacobi.c

/*
   Include files needed for the PBJacobi preconditioner:
     pcimpl.h - private include file intended for use by all preconditioners
*/

#include <petsc/private/pcimpl.h> /*I "petscpc.h" I*/

/*
   Private context (data structure) for the PBJacobi preconditioner.
*/
typedef struct {
  const MatScalar *diag;
  PetscInt         bs, mbs;
} PC_PBJacobi;

static PetscErrorCode PCApply_PBJacobi_1(PC pc, Vec x, Vec y) {
  PC_PBJacobi       *jac = (PC_PBJacobi *)pc->data;
  PetscInt           i, m = jac->mbs;
  const MatScalar   *diag = jac->diag;
  const PetscScalar *xx;
  PetscScalar       *yy;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(x, &xx));
  PetscCall(VecGetArray(y, &yy));
  for (i = 0; i < m; i++) yy[i] = diag[i] * xx[i];
  PetscCall(VecRestoreArrayRead(x, &xx));
  PetscCall(VecRestoreArray(y, &yy));
  PetscCall(PetscLogFlops(m));
  PetscFunctionReturn(0);
}

static PetscErrorCode PCApply_PBJacobi_2(PC pc, Vec x, Vec y) {
  PC_PBJacobi       *jac = (PC_PBJacobi *)pc->data;
  PetscInt           i, m = jac->mbs;
  const MatScalar   *diag = jac->diag;
  PetscScalar        x0, x1, *yy;
  const PetscScalar *xx;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(x, &xx));
  PetscCall(VecGetArray(y, &yy));
  for (i = 0; i < m; i++) {
    x0            = xx[2 * i];
    x1            = xx[2 * i + 1];
    yy[2 * i]     = diag[0] * x0 + diag[2] * x1;
    yy[2 * i + 1] = diag[1] * x0 + diag[3] * x1;
    diag += 4;
  }
  PetscCall(VecRestoreArrayRead(x, &xx));
  PetscCall(VecRestoreArray(y, &yy));
  PetscCall(PetscLogFlops(6.0 * m));
  PetscFunctionReturn(0);
}
static PetscErrorCode PCApply_PBJacobi_3(PC pc, Vec x, Vec y) {
  PC_PBJacobi       *jac = (PC_PBJacobi *)pc->data;
  PetscInt           i, m = jac->mbs;
  const MatScalar   *diag = jac->diag;
  PetscScalar        x0, x1, x2, *yy;
  const PetscScalar *xx;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(x, &xx));
  PetscCall(VecGetArray(y, &yy));
  for (i = 0; i < m; i++) {
    x0 = xx[3 * i];
    x1 = xx[3 * i + 1];
    x2 = xx[3 * i + 2];

    yy[3 * i]     = diag[0] * x0 + diag[3] * x1 + diag[6] * x2;
    yy[3 * i + 1] = diag[1] * x0 + diag[4] * x1 + diag[7] * x2;
    yy[3 * i + 2] = diag[2] * x0 + diag[5] * x1 + diag[8] * x2;
    diag += 9;
  }
  PetscCall(VecRestoreArrayRead(x, &xx));
  PetscCall(VecRestoreArray(y, &yy));
  PetscCall(PetscLogFlops(15.0 * m));
  PetscFunctionReturn(0);
}
static PetscErrorCode PCApply_PBJacobi_4(PC pc, Vec x, Vec y) {
  PC_PBJacobi       *jac = (PC_PBJacobi *)pc->data;
  PetscInt           i, m = jac->mbs;
  const MatScalar   *diag = jac->diag;
  PetscScalar        x0, x1, x2, x3, *yy;
  const PetscScalar *xx;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(x, &xx));
  PetscCall(VecGetArray(y, &yy));
  for (i = 0; i < m; i++) {
    x0 = xx[4 * i];
    x1 = xx[4 * i + 1];
    x2 = xx[4 * i + 2];
    x3 = xx[4 * i + 3];

    yy[4 * i]     = diag[0] * x0 + diag[4] * x1 + diag[8] * x2 + diag[12] * x3;
    yy[4 * i + 1] = diag[1] * x0 + diag[5] * x1 + diag[9] * x2 + diag[13] * x3;
    yy[4 * i + 2] = diag[2] * x0 + diag[6] * x1 + diag[10] * x2 + diag[14] * x3;
    yy[4 * i + 3] = diag[3] * x0 + diag[7] * x1 + diag[11] * x2 + diag[15] * x3;
    diag += 16;
  }
  PetscCall(VecRestoreArrayRead(x, &xx));
  PetscCall(VecRestoreArray(y, &yy));
  PetscCall(PetscLogFlops(28.0 * m));
  PetscFunctionReturn(0);
}
static PetscErrorCode PCApply_PBJacobi_5(PC pc, Vec x, Vec y) {
  PC_PBJacobi       *jac = (PC_PBJacobi *)pc->data;
  PetscInt           i, m = jac->mbs;
  const MatScalar   *diag = jac->diag;
  PetscScalar        x0, x1, x2, x3, x4, *yy;
  const PetscScalar *xx;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(x, &xx));
  PetscCall(VecGetArray(y, &yy));
  for (i = 0; i < m; i++) {
    x0 = xx[5 * i];
    x1 = xx[5 * i + 1];
    x2 = xx[5 * i + 2];
    x3 = xx[5 * i + 3];
    x4 = xx[5 * i + 4];

    yy[5 * i]     = diag[0] * x0 + diag[5] * x1 + diag[10] * x2 + diag[15] * x3 + diag[20] * x4;
    yy[5 * i + 1] = diag[1] * x0 + diag[6] * x1 + diag[11] * x2 + diag[16] * x3 + diag[21] * x4;
    yy[5 * i + 2] = diag[2] * x0 + diag[7] * x1 + diag[12] * x2 + diag[17] * x3 + diag[22] * x4;
    yy[5 * i + 3] = diag[3] * x0 + diag[8] * x1 + diag[13] * x2 + diag[18] * x3 + diag[23] * x4;
    yy[5 * i + 4] = diag[4] * x0 + diag[9] * x1 + diag[14] * x2 + diag[19] * x3 + diag[24] * x4;
    diag += 25;
  }
  PetscCall(VecRestoreArrayRead(x, &xx));
  PetscCall(VecRestoreArray(y, &yy));
  PetscCall(PetscLogFlops(45.0 * m));
  PetscFunctionReturn(0);
}
static PetscErrorCode PCApply_PBJacobi_6(PC pc, Vec x, Vec y) {
  PC_PBJacobi       *jac = (PC_PBJacobi *)pc->data;
  PetscInt           i, m = jac->mbs;
  const MatScalar   *diag = jac->diag;
  PetscScalar        x0, x1, x2, x3, x4, x5, *yy;
  const PetscScalar *xx;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(x, &xx));
  PetscCall(VecGetArray(y, &yy));
  for (i = 0; i < m; i++) {
    x0 = xx[6 * i];
    x1 = xx[6 * i + 1];
    x2 = xx[6 * i + 2];
    x3 = xx[6 * i + 3];
    x4 = xx[6 * i + 4];
    x5 = xx[6 * i + 5];

    yy[6 * i]     = diag[0] * x0 + diag[6] * x1 + diag[12] * x2 + diag[18] * x3 + diag[24] * x4 + diag[30] * x5;
    yy[6 * i + 1] = diag[1] * x0 + diag[7] * x1 + diag[13] * x2 + diag[19] * x3 + diag[25] * x4 + diag[31] * x5;
    yy[6 * i + 2] = diag[2] * x0 + diag[8] * x1 + diag[14] * x2 + diag[20] * x3 + diag[26] * x4 + diag[32] * x5;
    yy[6 * i + 3] = diag[3] * x0 + diag[9] * x1 + diag[15] * x2 + diag[21] * x3 + diag[27] * x4 + diag[33] * x5;
    yy[6 * i + 4] = diag[4] * x0 + diag[10] * x1 + diag[16] * x2 + diag[22] * x3 + diag[28] * x4 + diag[34] * x5;
    yy[6 * i + 5] = diag[5] * x0 + diag[11] * x1 + diag[17] * x2 + diag[23] * x3 + diag[29] * x4 + diag[35] * x5;
    diag += 36;
  }
  PetscCall(VecRestoreArrayRead(x, &xx));
  PetscCall(VecRestoreArray(y, &yy));
  PetscCall(PetscLogFlops(66.0 * m));
  PetscFunctionReturn(0);
}
static PetscErrorCode PCApply_PBJacobi_7(PC pc, Vec x, Vec y) {
  PC_PBJacobi       *jac = (PC_PBJacobi *)pc->data;
  PetscInt           i, m = jac->mbs;
  const MatScalar   *diag = jac->diag;
  PetscScalar        x0, x1, x2, x3, x4, x5, x6, *yy;
  const PetscScalar *xx;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(x, &xx));
  PetscCall(VecGetArray(y, &yy));
  for (i = 0; i < m; i++) {
    x0 = xx[7 * i];
    x1 = xx[7 * i + 1];
    x2 = xx[7 * i + 2];
    x3 = xx[7 * i + 3];
    x4 = xx[7 * i + 4];
    x5 = xx[7 * i + 5];
    x6 = xx[7 * i + 6];

    yy[7 * i]     = diag[0] * x0 + diag[7] * x1 + diag[14] * x2 + diag[21] * x3 + diag[28] * x4 + diag[35] * x5 + diag[42] * x6;
    yy[7 * i + 1] = diag[1] * x0 + diag[8] * x1 + diag[15] * x2 + diag[22] * x3 + diag[29] * x4 + diag[36] * x5 + diag[43] * x6;
    yy[7 * i + 2] = diag[2] * x0 + diag[9] * x1 + diag[16] * x2 + diag[23] * x3 + diag[30] * x4 + diag[37] * x5 + diag[44] * x6;
    yy[7 * i + 3] = diag[3] * x0 + diag[10] * x1 + diag[17] * x2 + diag[24] * x3 + diag[31] * x4 + diag[38] * x5 + diag[45] * x6;
    yy[7 * i + 4] = diag[4] * x0 + diag[11] * x1 + diag[18] * x2 + diag[25] * x3 + diag[32] * x4 + diag[39] * x5 + diag[46] * x6;
    yy[7 * i + 5] = diag[5] * x0 + diag[12] * x1 + diag[19] * x2 + diag[26] * x3 + diag[33] * x4 + diag[40] * x5 + diag[47] * x6;
    yy[7 * i + 6] = diag[6] * x0 + diag[13] * x1 + diag[20] * x2 + diag[27] * x3 + diag[34] * x4 + diag[41] * x5 + diag[48] * x6;
    diag += 49;
  }
  PetscCall(VecRestoreArrayRead(x, &xx));
  PetscCall(VecRestoreArray(y, &yy));
  PetscCall(PetscLogFlops(91.0 * m)); /* 2*bs2 - bs */
  PetscFunctionReturn(0);
}
static PetscErrorCode PCApply_PBJacobi_N(PC pc, Vec x, Vec y) {
  PC_PBJacobi       *jac = (PC_PBJacobi *)pc->data;
  PetscInt           i, ib, jb;
  const PetscInt     m    = jac->mbs;
  const PetscInt     bs   = jac->bs;
  const MatScalar   *diag = jac->diag;
  PetscScalar       *yy;
  const PetscScalar *xx;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(x, &xx));
  PetscCall(VecGetArray(y, &yy));
  for (i = 0; i < m; i++) {
    for (ib = 0; ib < bs; ib++) {
      PetscScalar rowsum = 0;
      for (jb = 0; jb < bs; jb++) rowsum += diag[ib + jb * bs] * xx[bs * i + jb];
      yy[bs * i + ib] = rowsum;
    }
    diag += bs * bs;
  }
  PetscCall(VecRestoreArrayRead(x, &xx));
  PetscCall(VecRestoreArray(y, &yy));
  PetscCall(PetscLogFlops((2.0 * bs * bs - bs) * m)); /* 2*bs2 - bs */
  PetscFunctionReturn(0);
}

static PetscErrorCode PCApplyTranspose_PBJacobi_N(PC pc, Vec x, Vec y) {
  PC_PBJacobi       *jac = (PC_PBJacobi *)pc->data;
  PetscInt           i, j, k, m = jac->mbs, bs = jac->bs;
  const MatScalar   *diag = jac->diag;
  const PetscScalar *xx;
  PetscScalar       *yy;

  PetscFunctionBegin;
  PetscCall(VecGetArrayRead(x, &xx));
  PetscCall(VecGetArray(y, &yy));
  for (i = 0; i < m; i++) {
    for (j = 0; j < bs; j++) yy[i * bs + j] = 0.;
    for (j = 0; j < bs; j++) {
      for (k = 0; k < bs; k++) yy[i * bs + k] += diag[k * bs + j] * xx[i * bs + j];
    }
    diag += bs * bs;
  }
  PetscCall(VecRestoreArrayRead(x, &xx));
  PetscCall(VecRestoreArray(y, &yy));
  PetscCall(PetscLogFlops(m * bs * (2 * bs - 1)));
  PetscFunctionReturn(0);
}

static PetscErrorCode PCSetUp_PBJacobi(PC pc) {
  PC_PBJacobi   *jac = (PC_PBJacobi *)pc->data;
  Mat            A   = pc->pmat;
  MatFactorError err;
  PetscInt       nlocal;

  PetscFunctionBegin;
  PetscCall(MatInvertBlockDiagonal(A, &jac->diag));
  PetscCall(MatFactorGetError(A, &err));
  if (err) pc->failedreason = (PCFailedReason)err;

  PetscCall(MatGetBlockSize(A, &jac->bs));
  PetscCall(MatGetLocalSize(A, &nlocal, NULL));
  jac->mbs = nlocal / jac->bs;
  switch (jac->bs) {
  case 1: pc->ops->apply = PCApply_PBJacobi_1; break;
  case 2: pc->ops->apply = PCApply_PBJacobi_2; break;
  case 3: pc->ops->apply = PCApply_PBJacobi_3; break;
  case 4: pc->ops->apply = PCApply_PBJacobi_4; break;
  case 5: pc->ops->apply = PCApply_PBJacobi_5; break;
  case 6: pc->ops->apply = PCApply_PBJacobi_6; break;
  case 7: pc->ops->apply = PCApply_PBJacobi_7; break;
  default: pc->ops->apply = PCApply_PBJacobi_N; break;
  }
  pc->ops->applytranspose = PCApplyTranspose_PBJacobi_N;
  PetscFunctionReturn(0);
}

static PetscErrorCode PCDestroy_PBJacobi(PC pc) {
  PetscFunctionBegin;
  /*
      Free the private data structure that was hanging off the PC
  */
  PetscCall(PetscFree(pc->data));
  PetscFunctionReturn(0);
}

static PetscErrorCode PCView_PBJacobi(PC pc, PetscViewer viewer) {
  PC_PBJacobi *jac = (PC_PBJacobi *)pc->data;
  PetscBool    iascii;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
  if (iascii) PetscCall(PetscViewerASCIIPrintf(viewer, "  point-block size %" PetscInt_FMT "\n", jac->bs));
  PetscFunctionReturn(0);
}

/*MC
     PCPBJACOBI - Point block Jacobi preconditioner

   Notes:
    See `PCJACOBI` for diagonal Jacobi, `PCVPBJACOBI` for variable-size point block, and `PCBJACOBI` for large size blocks

   This works for `MATAIJ` and `MATBAIJ` matrices and uses the blocksize provided to the matrix

   Uses dense LU factorization with partial pivoting to invert the blocks; if a zero pivot
   is detected a PETSc error is generated.

   Developer Notes:
     This should support the `PCSetErrorIfFailure()` flag set to `PETSC_TRUE` to allow
     the factorization to continue even after a zero pivot is found resulting in a Nan and hence
     terminating `KSP` with a `KSP_DIVERGED_NANORIF` allowing
     a nonlinear solver/ODE integrator to recover without stopping the program as currently happens.

     Perhaps should provide an option that allows generation of a valid preconditioner
     even if a block is singular as the `PCJACOBI` does.

   Level: beginner

.seealso: `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCJACOBI`, `PCVPBJACOBI`, `PCBJACOBI`
M*/

PETSC_EXTERN PetscErrorCode PCCreate_PBJacobi(PC pc) {
  PC_PBJacobi *jac;

  PetscFunctionBegin;
  /*
     Creates the private data structure for this preconditioner and
     attach it to the PC object.
  */
  PetscCall(PetscNew(&jac));
  pc->data = (void *)jac;

  /*
     Initialize the pointers to vectors to ZERO; these will be used to store
     diagonal entries of the matrix for fast preconditioner application.
  */
  jac->diag = NULL;

  /*
      Set the pointers for the functions that are provided above.
      Now when the user-level routines (such as PCApply(), PCDestroy(), etc.)
      are called, they will automatically call these functions.  Note we
      choose not to provide a couple of these functions since they are
      not needed.
  */
  pc->ops->apply               = NULL; /*set depending on the block size */
  pc->ops->applytranspose      = NULL;
  pc->ops->setup               = PCSetUp_PBJacobi;
  pc->ops->destroy             = PCDestroy_PBJacobi;
  pc->ops->setfromoptions      = NULL;
  pc->ops->view                = PCView_PBJacobi;
  pc->ops->applyrichardson     = NULL;
  pc->ops->applysymmetricleft  = NULL;
  pc->ops->applysymmetricright = NULL;
  PetscFunctionReturn(0);
}