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(PetscOptionItems *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: }