impls/cp/cp.c

#include <petsc/private/pcimpl.h> /*I "petscpc.h" I*/
#include <../src/mat/impls/aij/seq/aij.h>

/*
   Private context (data structure) for the CP preconditioner.
*/
typedef struct {
  PetscInt     n, m;
  Vec          work;
  PetscScalar *d;     /* sum of squares of each column */
  PetscScalar *a;     /* non-zeros by column */
  PetscInt    *i, *j; /* offsets of nonzeros by column, non-zero indices by column */
} PC_CP;

static PetscErrorCode PCSetUp_CP(PC pc) {
  PC_CP      *cp = (PC_CP *)pc->data;
  PetscInt    i, j, *colcnt;
  PetscBool   flg;
  Mat_SeqAIJ *aij = (Mat_SeqAIJ *)pc->pmat->data;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATSEQAIJ, &flg));
  PetscCheck(flg, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Currently only handles SeqAIJ matrices");

  PetscCall(MatGetLocalSize(pc->pmat, &cp->m, &cp->n));
  PetscCheck(cp->m == cp->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Currently only for square matrices");

  if (!cp->work) PetscCall(MatCreateVecs(pc->pmat, &cp->work, NULL));
  if (!cp->d) PetscCall(PetscMalloc1(cp->n, &cp->d));
  if (cp->a && pc->flag != SAME_NONZERO_PATTERN) {
    PetscCall(PetscFree3(cp->a, cp->i, cp->j));
    cp->a = NULL;
  }

  /* convert to column format */
  if (!cp->a) PetscCall(PetscMalloc3(aij->nz, &cp->a, cp->n + 1, &cp->i, aij->nz, &cp->j));
  PetscCall(PetscCalloc1(cp->n, &colcnt));

  for (i = 0; i < aij->nz; i++) colcnt[aij->j[i]]++;
  cp->i[0] = 0;
  for (i = 0; i < cp->n; i++) cp->i[i + 1] = cp->i[i] + colcnt[i];
  PetscCall(PetscArrayzero(colcnt, cp->n));
  for (i = 0; i < cp->m; i++) {                   /* over rows */
    for (j = aij->i[i]; j < aij->i[i + 1]; j++) { /* over columns in row */
      cp->j[cp->i[aij->j[j]] + colcnt[aij->j[j]]]   = i;
      cp->a[cp->i[aij->j[j]] + colcnt[aij->j[j]]++] = aij->a[j];
    }
  }
  PetscCall(PetscFree(colcnt));

  /* compute sum of squares of each column d[] */
  for (i = 0; i < cp->n; i++) { /* over columns */
    cp->d[i] = 0.;
    for (j = cp->i[i]; j < cp->i[i + 1]; j++) cp->d[i] += cp->a[j] * cp->a[j]; /* over rows in column */
    cp->d[i] = 1.0 / cp->d[i];
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode PCApply_CP(PC pc, Vec bb, Vec xx) {
  PC_CP       *cp = (PC_CP *)pc->data;
  PetscScalar *b, *x, xt;
  PetscInt     i, j;

  PetscFunctionBegin;
  PetscCall(VecCopy(bb, cp->work));
  PetscCall(VecGetArray(cp->work, &b));
  PetscCall(VecGetArray(xx, &x));

  for (i = 0; i < cp->n; i++) { /* over columns */
    xt = 0.;
    for (j = cp->i[i]; j < cp->i[i + 1]; j++) xt += cp->a[j] * b[cp->j[j]]; /* over rows in column */
    xt *= cp->d[i];
    x[i] = xt;
    for (j = cp->i[i]; j < cp->i[i + 1]; j++) b[cp->j[j]] -= xt * cp->a[j]; /* over rows in column updating b*/
  }
  for (i = cp->n - 1; i > -1; i--) { /* over columns */
    xt = 0.;
    for (j = cp->i[i]; j < cp->i[i + 1]; j++) xt += cp->a[j] * b[cp->j[j]]; /* over rows in column */
    xt *= cp->d[i];
    x[i] = xt;
    for (j = cp->i[i]; j < cp->i[i + 1]; j++) b[cp->j[j]] -= xt * cp->a[j]; /* over rows in column updating b*/
  }

  PetscCall(VecRestoreArray(cp->work, &b));
  PetscCall(VecRestoreArray(xx, &x));
  PetscFunctionReturn(0);
}

static PetscErrorCode PCReset_CP(PC pc) {
  PC_CP *cp = (PC_CP *)pc->data;

  PetscFunctionBegin;
  PetscCall(PetscFree(cp->d));
  PetscCall(VecDestroy(&cp->work));
  PetscCall(PetscFree3(cp->a, cp->i, cp->j));
  PetscFunctionReturn(0);
}

static PetscErrorCode PCDestroy_CP(PC pc) {
  PC_CP *cp = (PC_CP *)pc->data;

  PetscFunctionBegin;
  PetscCall(PCReset_CP(pc));
  PetscCall(PetscFree(cp->d));
  PetscCall(PetscFree3(cp->a, cp->i, cp->j));
  PetscCall(PetscFree(pc->data));
  PetscFunctionReturn(0);
}

static PetscErrorCode PCSetFromOptions_CP(PC pc, PetscOptionItems *PetscOptionsObject) {
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

/*MC
     PCCP - a "column-projection" preconditioner

     This is a terrible preconditioner and is not recommended, ever!

     Loops over the entries of x computing dx_i (e_i is the unit vector in the ith direction) to
.vb

        min || b - A(x + dx_i e_i ||_2
        dx_i

    That is, it changes a single entry of x to minimize the new residual norm.
   Let A_i represent the ith column of A, then the minimization can be written as

       min || r - (dx_i) A e_i ||_2
       dx_i
   or   min || r - (dx_i) A_i ||_2
        dx_i

    take the derivative with respect to dx_i to obtain
        dx_i = (A_i^T A_i)^(-1) A_i^T r

    This algorithm can be thought of as Gauss-Seidel on the normal equations
.ve

    Notes:
    This proceedure can also be done with block columns or any groups of columns
    but this is not coded.

    These "projections" can be done simultaneously for all columns (similar to Jacobi)
    or sequentially (similar to Gauss-Seidel/SOR). This is only coded for SOR type.

    This is related to, but not the same as "row projection" methods.

    This is currently coded only for `MATSEQAIJ` matrices

  Level: intermediate

.seealso: `PCCreate()`, `PCSetType()`, `PCType`, `PCJACOBI`, `PCSOR`
M*/

PETSC_EXTERN PetscErrorCode PCCreate_CP(PC pc) {
  PC_CP *cp;

  PetscFunctionBegin;
  PetscCall(PetscNew(&cp));
  pc->data = (void *)cp;

  pc->ops->apply           = PCApply_CP;
  pc->ops->applytranspose  = PCApply_CP;
  pc->ops->setup           = PCSetUp_CP;
  pc->ops->reset           = PCReset_CP;
  pc->ops->destroy         = PCDestroy_CP;
  pc->ops->setfromoptions  = PCSetFromOptions_CP;
  pc->ops->view            = NULL;
  pc->ops->applyrichardson = NULL;
  PetscFunctionReturn(0);
}