Date: 2022-08-02T03:14:34+00:00

Actual source code: cp.c

      2: #include <petsc/private/pcimpl.h>
      3: #include <../src/mat/impls/aij/seq/aij.h>

      5: /*
      6:    Private context (data structure) for the CP preconditioner.
      7: */
      8: typedef struct {
      9:   PetscInt    n,m;
     10:   Vec         work;
     11:   PetscScalar *d;       /* sum of squares of each column */
     12:   PetscScalar *a;       /* non-zeros by column */
     13:   PetscInt    *i,*j;    /* offsets of nonzeros by column, non-zero indices by column */
     14: } PC_CP;

     16: static PetscErrorCode PCSetUp_CP(PC pc)
     17: {
     18:   PC_CP          *cp = (PC_CP*)pc->data;
     19:   PetscInt       i,j,*colcnt;
     20:   PetscBool      flg;
     21:   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)pc->pmat->data;

     23:   PetscObjectTypeCompare((PetscObject)pc->pmat,MATSEQAIJ,&flg);

     26:   MatGetLocalSize(pc->pmat,&cp->m,&cp->n);

     29:   if (!cp->work) MatCreateVecs(pc->pmat,&cp->work,NULL);
     30:   if (!cp->d) PetscMalloc1(cp->n,&cp->d);
     31:   if (cp->a && pc->flag != SAME_NONZERO_PATTERN) {
     32:     PetscFree3(cp->a,cp->i,cp->j);
     33:     cp->a = NULL;
     34:   }

     36:   /* convert to column format */
     37:   if (!cp->a) {
     38:     PetscMalloc3(aij->nz,&cp->a,cp->n+1,&cp->i,aij->nz,&cp->j);
     39:   }
     40:   PetscCalloc1(cp->n,&colcnt);

     42:   for (i=0; i<aij->nz; i++) colcnt[aij->j[i]]++;
     43:   cp->i[0] = 0;
     44:   for (i=0; i<cp->n; i++) cp->i[i+1] = cp->i[i] + colcnt[i];
     45:   PetscArrayzero(colcnt,cp->n);
     46:   for (i=0; i<cp->m; i++) {  /* over rows */
     47:     for (j=aij->i[i]; j<aij->i[i+1]; j++) {  /* over columns in row */
     48:       cp->j[cp->i[aij->j[j]]+colcnt[aij->j[j]]]   = i;
     49:       cp->a[cp->i[aij->j[j]]+colcnt[aij->j[j]]++] = aij->a[j];
     50:     }
     51:   }
     52:   PetscFree(colcnt);

     54:   /* compute sum of squares of each column d[] */
     55:   for (i=0; i<cp->n; i++) {  /* over columns */
     56:     cp->d[i] = 0.;
     57:     for (j=cp->i[i]; j<cp->i[i+1]; j++) cp->d[i] += cp->a[j]*cp->a[j]; /* over rows in column */
     58:     cp->d[i] = 1.0/cp->d[i];
     59:   }
     60:   return 0;
     61: }
     62: /* -------------------------------------------------------------------------- */
     63: static PetscErrorCode PCApply_CP(PC pc,Vec bb,Vec xx)
     64: {
     65:   PC_CP          *cp = (PC_CP*)pc->data;
     66:   PetscScalar    *b,*x,xt;
     67:   PetscInt       i,j;

     69:   VecCopy(bb,cp->work);
     70:   VecGetArray(cp->work,&b);
     71:   VecGetArray(xx,&x);

     73:   for (i=0; i<cp->n; i++) {  /* over columns */
     74:     xt = 0.;
     75:     for (j=cp->i[i]; j<cp->i[i+1]; j++) xt += cp->a[j]*b[cp->j[j]]; /* over rows in column */
     76:     xt  *= cp->d[i];
     77:     x[i] = xt;
     78:     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*/
     79:   }
     80:   for (i=cp->n-1; i>-1; i--) {  /* over columns */
     81:     xt = 0.;
     82:     for (j=cp->i[i]; j<cp->i[i+1]; j++) xt += cp->a[j]*b[cp->j[j]]; /* over rows in column */
     83:     xt  *= cp->d[i];
     84:     x[i] = xt;
     85:     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*/
     86:   }

     88:   VecRestoreArray(cp->work,&b);
     89:   VecRestoreArray(xx,&x);
     90:   return 0;
     91: }
     92: /* -------------------------------------------------------------------------- */
     93: static PetscErrorCode PCReset_CP(PC pc)
     94: {
     95:   PC_CP          *cp = (PC_CP*)pc->data;

     97:   PetscFree(cp->d);
     98:   VecDestroy(&cp->work);
     99:   PetscFree3(cp->a,cp->i,cp->j);
    100:   return 0;
    101: }

    103: static PetscErrorCode PCDestroy_CP(PC pc)
    104: {
    105:   PC_CP          *cp = (PC_CP*)pc->data;

    107:   PCReset_CP(pc);
    108:   PetscFree(cp->d);
    109:   PetscFree3(cp->a,cp->i,cp->j);
    110:   PetscFree(pc->data);
    111:   return 0;
    112: }

    114: static PetscErrorCode PCSetFromOptions_CP(PetscOptionItems *PetscOptionsObject,PC pc)
    115: {
    116:   return 0;
    117: }

    119: /*MC
    120:      PCCP - a "column-projection" preconditioner

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

    124:      Loops over the entries of x computing dx_i (e_i is the unit vector in the ith direction) to
    125: $
    126: $        min || b - A(x + dx_i e_i ||_2
    127: $        dx_i
    128: $
    129: $    That is, it changes a single entry of x to minimize the new residual norm.
    130: $   Let A_i represent the ith column of A, then the minimization can be written as
    131: $
    132: $       min || r - (dx_i) A e_i ||_2
    133: $       dx_i
    134: $   or   min || r - (dx_i) A_i ||_2
    135: $        dx_i
    136: $
    137: $    take the derivative with respect to dx_i to obtain
    138: $        dx_i = (A_i^T A_i)^(-1) A_i^T r
    139: $
    140: $    This algorithm can be thought of as Gauss-Seidel on the normal equations

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

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

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

    151:       This is currently coded only for SeqAIJ matrices in sequential (SOR) form.

    153:   Level: intermediate

    155: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PCJACOBI, PCSOR

    157: M*/

    159: PETSC_EXTERN PetscErrorCode PCCreate_CP(PC pc)
    160: {
    161:   PC_CP          *cp;

    163:   PetscNewLog(pc,&cp);
    164:   pc->data = (void*)cp;

    166:   pc->ops->apply           = PCApply_CP;
    167:   pc->ops->applytranspose  = PCApply_CP;
    168:   pc->ops->setup           = PCSetUp_CP;
    169:   pc->ops->reset           = PCReset_CP;
    170:   pc->ops->destroy         = PCDestroy_CP;
    171:   pc->ops->setfromoptions  = PCSetFromOptions_CP;
    172:   pc->ops->view            = NULL;
    173:   pc->ops->applyrichardson = NULL;
    174:   return 0;
    175: }