Date: 2022-03-04T17:38:54+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;
     21:   PetscBool      flg;
     22:   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)pc->pmat->data;

     25:   PetscObjectTypeCompare((PetscObject)pc->pmat,MATSEQAIJ,&flg);
     26:   if (!flg) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Currently only handles SeqAIJ matrices");

     28:   MatGetLocalSize(pc->pmat,&cp->m,&cp->n);
     29:   if (cp->m != cp->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Currently only for square matrices");

     31:   if (!cp->work) {MatCreateVecs(pc->pmat,&cp->work,NULL);}
     32:   if (!cp->d) {PetscMalloc1(cp->n,&cp->d);}
     33:   if (cp->a && pc->flag != SAME_NONZERO_PATTERN) {
     34:     PetscFree3(cp->a,cp->i,cp->j);
     35:     cp->a = NULL;
     36:   }

     38:   /* convert to column format */
     39:   if (!cp->a) {
     40:     PetscMalloc3(aij->nz,&cp->a,cp->n+1,&cp->i,aij->nz,&cp->j);
     41:   }
     42:   PetscCalloc1(cp->n,&colcnt);

     44:   for (i=0; i<aij->nz; i++) colcnt[aij->j[i]]++;
     45:   cp->i[0] = 0;
     46:   for (i=0; i<cp->n; i++) cp->i[i+1] = cp->i[i] + colcnt[i];
     47:   PetscArrayzero(colcnt,cp->n);
     48:   for (i=0; i<cp->m; i++) {  /* over rows */
     49:     for (j=aij->i[i]; j<aij->i[i+1]; j++) {  /* over columns in row */
     50:       cp->j[cp->i[aij->j[j]]+colcnt[aij->j[j]]]   = i;
     51:       cp->a[cp->i[aij->j[j]]+colcnt[aij->j[j]]++] = aij->a[j];
     52:     }
     53:   }
     54:   PetscFree(colcnt);

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

     73:   VecCopy(bb,cp->work);
     74:   VecGetArray(cp->work,&b);
     75:   VecGetArray(xx,&x);

     77:   for (i=0; i<cp->n; i++) {  /* over columns */
     78:     xt = 0.;
     79:     for (j=cp->i[i]; j<cp->i[i+1]; j++) xt += cp->a[j]*b[cp->j[j]]; /* over rows in column */
     80:     xt  *= cp->d[i];
     81:     x[i] = xt;
     82:     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*/
     83:   }
     84:   for (i=cp->n-1; i>-1; i--) {  /* over columns */
     85:     xt = 0.;
     86:     for (j=cp->i[i]; j<cp->i[i+1]; j++) xt += cp->a[j]*b[cp->j[j]]; /* over rows in column */
     87:     xt  *= cp->d[i];
     88:     x[i] = xt;
     89:     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*/
     90:   }

     92:   VecRestoreArray(cp->work,&b);
     93:   VecRestoreArray(xx,&x);
     94:   return(0);
     95: }
     96: /* -------------------------------------------------------------------------- */
     97: static PetscErrorCode PCReset_CP(PC pc)
     98: {
     99:   PC_CP          *cp = (PC_CP*)pc->data;

    103:   PetscFree(cp->d);
    104:   VecDestroy(&cp->work);
    105:   PetscFree3(cp->a,cp->i,cp->j);
    106:   return(0);
    107: }

    109: static PetscErrorCode PCDestroy_CP(PC pc)
    110: {
    111:   PC_CP          *cp = (PC_CP*)pc->data;

    115:   PCReset_CP(pc);
    116:   PetscFree(cp->d);
    117:   PetscFree3(cp->a,cp->i,cp->j);
    118:   PetscFree(pc->data);
    119:   return(0);
    120: }

    122: static PetscErrorCode PCSetFromOptions_CP(PetscOptionItems *PetscOptionsObject,PC pc)
    123: {
    125:   return(0);
    126: }

    128: /*MC
    129:      PCCP - a "column-projection" preconditioner

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

    133:      Loops over the entries of x computing dx_i (e_i is the unit vector in the ith direction) to
    134: $
    135: $        min || b - A(x + dx_i e_i ||_2
    136: $        dx_i
    137: $
    138: $    That is, it changes a single entry of x to minimize the new residual norm.
    139: $   Let A_i represent the ith column of A, then the minimization can be written as
    140: $
    141: $       min || r - (dx_i) A e_i ||_2
    142: $       dx_i
    143: $   or   min || r - (dx_i) A_i ||_2
    144: $        dx_i
    145: $
    146: $    take the derivative with respect to dx_i to obtain
    147: $        dx_i = (A_i^T A_i)^(-1) A_i^T r
    148: $
    149: $    This algorithm can be thought of as Gauss-Seidel on the normal equations

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

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

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

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

    162:   Level: intermediate

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

    166: M*/

    168: PETSC_EXTERN PetscErrorCode PCCreate_CP(PC pc)
    169: {
    170:   PC_CP          *cp;

    174:   PetscNewLog(pc,&cp);
    175:   pc->data = (void*)cp;

    177:   pc->ops->apply           = PCApply_CP;
    178:   pc->ops->applytranspose  = PCApply_CP;
    179:   pc->ops->setup           = PCSetUp_CP;
    180:   pc->ops->reset           = PCReset_CP;
    181:   pc->ops->destroy         = PCDestroy_CP;
    182:   pc->ops->setfromoptions  = PCSetFromOptions_CP;
    183:   pc->ops->view            = NULL;
    184:   pc->ops->applyrichardson = NULL;
    185:   return(0);
    186: }