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: }