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;


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

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

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

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

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

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

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

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

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

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

104:   PetscFree(cp->d);
105:   VecDestroy(&cp->work);
106:   PetscFree3(cp->a,cp->i,cp->j);
107:   return(0);
108: }

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

116:   PCReset_CP(pc);
117:   PetscFree(cp->d);
118:   PetscFree3(cp->a,cp->i,cp->j);
119:   PetscFree(pc->data);
120:   return(0);
121: }

123: static PetscErrorCode PCSetFromOptions_CP(PetscOptionItems *PetscOptionsObject,PC pc)
124: {
126:   return(0);
127: }

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

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

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

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

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

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

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

163:   Level: intermediate

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

167: M*/

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

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

178:   pc->ops->apply           = PCApply_CP;
179:   pc->ops->applytranspose  = PCApply_CP;
180:   pc->ops->setup           = PCSetUp_CP;
181:   pc->ops->reset           = PCReset_CP;
182:   pc->ops->destroy         = PCDestroy_CP;
183:   pc->ops->setfromoptions  = PCSetFromOptions_CP;
184:   pc->ops->view            = NULL;
185:   pc->ops->applyrichardson = NULL;
186:   return(0);
187: }