Date: 2015-10-02T22:19:05+00:00

Actual source code: cp.c
petsc-3.6.2 2015-10-02
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      2: #include <petsc/private/pcimpl.h>   /*I "petscpc.h" I*/
      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;

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

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

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

     34:   if (!cp->work) {MatCreateVecs(pc->pmat,&cp->work,NULL);}
     35:   if (!cp->d) {PetscMalloc1(cp->n,&cp->d);}
     36:   if (cp->a && pc->flag != SAME_NONZERO_PATTERN) {
     37:     PetscFree3(cp->a,cp->i,cp->j);
     38:     cp->a = 0;
     39:   }

     41:   /* convert to column format */
     42:   if (!cp->a) {
     43:     PetscMalloc3(aij->nz,&cp->a,cp->n+1,&cp->i,aij->nz,&cp->j);
     44:   }
     45:   PetscCalloc1(cp->n,&colcnt);

     47:   for (i=0; i<aij->nz; i++) colcnt[aij->j[i]]++;
     48:   cp->i[0] = 0;
     49:   for (i=0; i<cp->n; i++) cp->i[i+1] = cp->i[i] + colcnt[i];
     50:   PetscMemzero(colcnt,cp->n*sizeof(PetscInt));
     51:   for (i=0; i<cp->m; i++) {  /* over rows */
     52:     for (j=aij->i[i]; j<aij->i[i+1]; j++) {  /* over columns in row */
     53:       cp->j[cp->i[aij->j[j]]+colcnt[aij->j[j]]]   = i;
     54:       cp->a[cp->i[aij->j[j]]+colcnt[aij->j[j]]++] = aij->a[j];
     55:     }
     56:   }
     57:   PetscFree(colcnt);

     59:   /* compute sum of squares of each column d[] */
     60:   for (i=0; i<cp->n; i++) {  /* over columns */
     61:     cp->d[i] = 0.;
     62:     for (j=cp->i[i]; j<cp->i[i+1]; j++) cp->d[i] += cp->a[j]*cp->a[j]; /* over rows in column */
     63:     cp->d[i] = 1.0/cp->d[i];
     64:   }
     65:   return(0);
     66: }
     67: /* -------------------------------------------------------------------------- */
     70: static PetscErrorCode PCApply_CP(PC pc,Vec bb,Vec xx)
     71: {
     72:   PC_CP          *cp = (PC_CP*)pc->data;
     74:   PetscScalar    *b,*x,xt;
     75:   PetscInt       i,j;

     78:   VecCopy(bb,cp->work);
     79:   VecGetArray(cp->work,&b);
     80:   VecGetArray(xx,&x);

     82:   for (i=0; i<cp->n; i++) {  /* over columns */
     83:     xt = 0.;
     84:     for (j=cp->i[i]; j<cp->i[i+1]; j++) xt += cp->a[j]*b[cp->j[j]]; /* over rows in column */
     85:     xt  *= cp->d[i];
     86:     x[i] = xt;
     87:     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*/
     88:   }
     89:   for (i=cp->n-1; i>-1; i--) {  /* over columns */
     90:     xt = 0.;
     91:     for (j=cp->i[i]; j<cp->i[i+1]; j++) xt += cp->a[j]*b[cp->j[j]]; /* over rows in column */
     92:     xt  *= cp->d[i];
     93:     x[i] = xt;
     94:     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*/
     95:   }

     97:   VecRestoreArray(cp->work,&b);
     98:   VecRestoreArray(xx,&x);
     99:   return(0);
    100: }
    101: /* -------------------------------------------------------------------------- */
    104: static PetscErrorCode PCReset_CP(PC pc)
    105: {
    106:   PC_CP          *cp = (PC_CP*)pc->data;

    110:   PetscFree(cp->d);
    111:   VecDestroy(&cp->work);
    112:   PetscFree3(cp->a,cp->i,cp->j);
    113:   return(0);
    114: }

    118: static PetscErrorCode PCDestroy_CP(PC pc)
    119: {
    120:   PC_CP          *cp = (PC_CP*)pc->data;

    124:   PCReset_CP(pc);
    125:   PetscFree(cp->d);
    126:   PetscFree3(cp->a,cp->i,cp->j);
    127:   PetscFree(pc->data);
    128:   return(0);
    129: }

    133: static PetscErrorCode PCSetFromOptions_CP(PetscOptions *PetscOptionsObject,PC pc)
    134: {
    136:   return(0);
    137: }

    140: /*MC
    141:      PCCP - a "column-projection" preconditioner

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

    145:      Loops over the entries of x computing dx_i to
    146: $
    147: $        min || b - A(x + dx_i e_i ||_2
    148: $        dx_i
    149: $
    150: $    That is, it changes a single entry of x to minimize the new residual.
    151: $   Let A_i represent the ith column of A, then the minimization can be written as
    152: $
    153: $       min || r - (dx_i) A e_i ||_2
    154: $       dx_i
    155: $   or   min || r - (dx_i) A_i ||_2
    156: $        dx_i
    157: $
    158: $    take the derivative with respect to dx_i to obtain
    159: $        dx_i = (A_i^T A_i)^(-1) A_i^T r
    160: $
    161: $    This algorithm can be thought of as Gauss-Seidel on the normal equations

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

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

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

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

    173:   Level: intermediate

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

    177: M*/

    181: PETSC_EXTERN PetscErrorCode PCCreate_CP(PC pc)
    182: {
    183:   PC_CP          *cp;

    187:   PetscNewLog(pc,&cp);
    188:   pc->data = (void*)cp;

    190:   pc->ops->apply           = PCApply_CP;
    191:   pc->ops->applytranspose  = PCApply_CP;
    192:   pc->ops->setup           = PCSetUp_CP;
    193:   pc->ops->reset           = PCReset_CP;
    194:   pc->ops->destroy         = PCDestroy_CP;
    195:   pc->ops->setfromoptions  = PCSetFromOptions_CP;
    196:   pc->ops->view            = 0;
    197:   pc->ops->applyrichardson = 0;
    198:   return(0);
    199: }