Actual source code: sbaij2.c

petsc-3.10.3 2018-12-18
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  2:  #include <../src/mat/impls/baij/seq/baij.h>
  3:  #include <petsc/private/kernels/blockinvert.h>
  4:  #include <petscbt.h>
  5:  #include <../src/mat/impls/sbaij/seq/sbaij.h>
  6:  #include <petscblaslapack.h>

  8: PetscErrorCode MatIncreaseOverlap_SeqSBAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
  9: {
 10:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
 12:   PetscInt       brow,i,j,k,l,mbs,n,*nidx,isz,bcol,bcol_max,start,end,*ai,*aj,bs,*nidx2;
 13:   const PetscInt *idx;
 14:   PetscBT        table_out,table_in;

 17:   if (ov < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap specified");
 18:   mbs  = a->mbs;
 19:   ai   = a->i;
 20:   aj   = a->j;
 21:   bs   = A->rmap->bs;
 22:   PetscBTCreate(mbs,&table_out);
 23:   PetscMalloc1(mbs+1,&nidx);
 24:   PetscMalloc1(A->rmap->N+1,&nidx2);
 25:   PetscBTCreate(mbs,&table_in);

 27:   for (i=0; i<is_max; i++) { /* for each is */
 28:     isz  = 0;
 29:     PetscBTMemzero(mbs,table_out);

 31:     /* Extract the indices, assume there can be duplicate entries */
 32:     ISGetIndices(is[i],&idx);
 33:     ISGetLocalSize(is[i],&n);

 35:     /* Enter these into the temp arrays i.e mark table_out[brow], enter brow into new index */
 36:     bcol_max = 0;
 37:     for (j=0; j<n; ++j) {
 38:       brow = idx[j]/bs; /* convert the indices into block indices */
 39:       if (brow >= mbs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"index greater than mat-dim");
 40:       if (!PetscBTLookupSet(table_out,brow)) {
 41:         nidx[isz++] = brow;
 42:         if (bcol_max < brow) bcol_max = brow;
 43:       }
 44:     }
 45:     ISRestoreIndices(is[i],&idx);
 46:     ISDestroy(&is[i]);

 48:     k = 0;
 49:     for (j=0; j<ov; j++) { /* for each overlap */
 50:       /* set table_in for lookup - only mark entries that are added onto nidx in (j-1)-th overlap */
 51:       PetscBTMemzero(mbs,table_in);
 52:       for (l=k; l<isz; l++) { PetscBTSet(table_in,nidx[l]); }

 54:       n = isz;  /* length of the updated is[i] */
 55:       for (brow=0; brow<mbs; brow++) {
 56:         start = ai[brow]; end   = ai[brow+1];
 57:         if (PetscBTLookup(table_in,brow)) { /* brow is on nidx - row search: collect all bcol in this brow */
 58:           for (l = start; l<end; l++) {
 59:             bcol = aj[l];
 60:             if (!PetscBTLookupSet(table_out,bcol)) {
 61:               nidx[isz++] = bcol;
 62:               if (bcol_max < bcol) bcol_max = bcol;
 63:             }
 64:           }
 65:           k++;
 66:           if (k >= n) break; /* for (brow=0; brow<mbs; brow++) */
 67:         } else { /* brow is not on nidx - col serach: add brow onto nidx if there is a bcol in nidx */
 68:           for (l = start; l<end; l++) {
 69:             bcol = aj[l];
 70:             if (bcol > bcol_max) break;
 71:             if (PetscBTLookup(table_in,bcol)) {
 72:               if (!PetscBTLookupSet(table_out,brow)) nidx[isz++] = brow;
 73:               break; /* for l = start; l<end ; l++) */
 74:             }
 75:           }
 76:         }
 77:       }
 78:     } /* for each overlap */

 80:     /* expand the Index Set */
 81:     for (j=0; j<isz; j++) {
 82:       for (k=0; k<bs; k++) nidx2[j*bs+k] = nidx[j]*bs+k;
 83:     }
 84:     ISCreateGeneral(PETSC_COMM_SELF,isz*bs,nidx2,PETSC_COPY_VALUES,is+i);
 85:   }
 86:   PetscBTDestroy(&table_out);
 87:   PetscFree(nidx);
 88:   PetscFree(nidx2);
 89:   PetscBTDestroy(&table_in);
 90:   return(0);
 91: }

 93: /* Bseq is non-symmetric SBAIJ matrix, only used internally by PETSc.
 94:         Zero some ops' to avoid invalid usse */
 95: PetscErrorCode MatSeqSBAIJZeroOps_Private(Mat Bseq)
 96: {

100:   MatSetOption(Bseq,MAT_SYMMETRIC,PETSC_FALSE);
101:   Bseq->ops->mult                   = 0;
102:   Bseq->ops->multadd                = 0;
103:   Bseq->ops->multtranspose          = 0;
104:   Bseq->ops->multtransposeadd       = 0;
105:   Bseq->ops->lufactor               = 0;
106:   Bseq->ops->choleskyfactor         = 0;
107:   Bseq->ops->lufactorsymbolic       = 0;
108:   Bseq->ops->choleskyfactorsymbolic = 0;
109:   Bseq->ops->getinertia             = 0;
110:   return(0);
111: }

113: /* same as MatCreateSubMatrices_SeqBAIJ(), except cast Mat_SeqSBAIJ */
114: PetscErrorCode MatCreateSubMatrix_SeqSBAIJ_Private(Mat A,IS isrow,IS iscol,MatReuse scall,Mat *B)
115: {
116:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*c;
118:   PetscInt       *smap,i,k,kstart,kend,oldcols = a->nbs,*lens;
119:   PetscInt       row,mat_i,*mat_j,tcol,*mat_ilen;
120:   const PetscInt *irow,*icol;
121:   PetscInt       nrows,ncols,*ssmap,bs=A->rmap->bs,bs2=a->bs2;
122:   PetscInt       *aj = a->j,*ai = a->i;
123:   MatScalar      *mat_a;
124:   Mat            C;
125:   PetscBool      flag;


129:   ISGetIndices(isrow,&irow);
130:   ISGetIndices(iscol,&icol);
131:   ISGetLocalSize(isrow,&nrows);
132:   ISGetLocalSize(iscol,&ncols);

134:   PetscCalloc1(1+oldcols,&smap);
135:   ssmap = smap;
136:   PetscMalloc1(1+nrows,&lens);
137:   for (i=0; i<ncols; i++) smap[icol[i]] = i+1;
138:   /* determine lens of each row */
139:   for (i=0; i<nrows; i++) {
140:     kstart  = ai[irow[i]];
141:     kend    = kstart + a->ilen[irow[i]];
142:     lens[i] = 0;
143:     for (k=kstart; k<kend; k++) {
144:       if (ssmap[aj[k]]) lens[i]++;
145:     }
146:   }
147:   /* Create and fill new matrix */
148:   if (scall == MAT_REUSE_MATRIX) {
149:     c = (Mat_SeqSBAIJ*)((*B)->data);

151:     if (c->mbs!=nrows || c->nbs!=ncols || (*B)->rmap->bs!=bs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Submatrix wrong size");
152:     PetscMemcmp(c->ilen,lens,c->mbs *sizeof(PetscInt),&flag);
153:     if (!flag) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
154:     PetscMemzero(c->ilen,c->mbs*sizeof(PetscInt));
155:     C    = *B;
156:   } else {
157:     MatCreate(PetscObjectComm((PetscObject)A),&C);
158:     MatSetSizes(C,nrows*bs,ncols*bs,PETSC_DETERMINE,PETSC_DETERMINE);
159:     MatSetType(C,((PetscObject)A)->type_name);
160:     MatSeqSBAIJSetPreallocation(C,bs,0,lens);
161:   }
162:   c = (Mat_SeqSBAIJ*)(C->data);
163:   for (i=0; i<nrows; i++) {
164:     row      = irow[i];
165:     kstart   = ai[row];
166:     kend     = kstart + a->ilen[row];
167:     mat_i    = c->i[i];
168:     mat_j    = c->j + mat_i;
169:     mat_a    = c->a + mat_i*bs2;
170:     mat_ilen = c->ilen + i;
171:     for (k=kstart; k<kend; k++) {
172:       if ((tcol=ssmap[a->j[k]])) {
173:         *mat_j++ = tcol - 1;
174:         PetscMemcpy(mat_a,a->a+k*bs2,bs2*sizeof(MatScalar));
175:         mat_a   += bs2;
176:         (*mat_ilen)++;
177:       }
178:     }
179:   }
180:   /* sort */
181:   {
182:     MatScalar *work;

184:     PetscMalloc1(bs2,&work);
185:     for (i=0; i<nrows; i++) {
186:       PetscInt ilen;
187:       mat_i = c->i[i];
188:       mat_j = c->j + mat_i;
189:       mat_a = c->a + mat_i*bs2;
190:       ilen  = c->ilen[i];
191:       PetscSortIntWithDataArray(ilen,mat_j,mat_a,bs2*sizeof(MatScalar),work);
192:     }
193:     PetscFree(work);
194:   }

196:   /* Free work space */
197:   ISRestoreIndices(iscol,&icol);
198:   PetscFree(smap);
199:   PetscFree(lens);
200:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
201:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

203:   ISRestoreIndices(isrow,&irow);
204:   *B   = C;
205:   return(0);
206: }

208: PetscErrorCode MatCreateSubMatrix_SeqSBAIJ(Mat A,IS isrow,IS iscol,MatReuse scall,Mat *B)
209: {
210:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;
211:   IS             is1,is2;
213:   PetscInt       *vary,*iary,nrows,ncols,i,bs=A->rmap->bs,count,maxmnbs;
214:   const PetscInt *irow,*icol;

217:   ISGetIndices(isrow,&irow);
218:   ISGetIndices(iscol,&icol);
219:   ISGetLocalSize(isrow,&nrows);
220:   ISGetLocalSize(iscol,&ncols);

222:   /* Verify if the indices corespond to each element in a block
223:    and form the IS with compressed IS */
224:   maxmnbs = PetscMax(a->mbs,a->nbs);
225:   PetscMalloc2(maxmnbs,&vary,maxmnbs,&iary);
226:   PetscMemzero(vary,a->mbs*sizeof(PetscInt));
227:   for (i=0; i<nrows; i++) vary[irow[i]/bs]++;
228:   for (i=0; i<a->mbs; i++) {
229:     if (vary[i]!=0 && vary[i]!=bs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Index set does not match blocks");
230:   }
231:   count = 0;
232:   for (i=0; i<nrows; i++) {
233:     PetscInt j = irow[i] / bs;
234:     if ((vary[j]--)==bs) iary[count++] = j;
235:   }
236:   ISCreateGeneral(PETSC_COMM_SELF,count,iary,PETSC_COPY_VALUES,&is1);

238:   PetscMemzero(vary,(a->nbs)*sizeof(PetscInt));
239:   for (i=0; i<ncols; i++) vary[icol[i]/bs]++;
240:   for (i=0; i<a->nbs; i++) {
241:     if (vary[i]!=0 && vary[i]!=bs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Internal error in PETSc");
242:   }
243:   count = 0;
244:   for (i=0; i<ncols; i++) {
245:     PetscInt j = icol[i] / bs;
246:     if ((vary[j]--)==bs) iary[count++] = j;
247:   }
248:   ISCreateGeneral(PETSC_COMM_SELF,count,iary,PETSC_COPY_VALUES,&is2);
249:   ISRestoreIndices(isrow,&irow);
250:   ISRestoreIndices(iscol,&icol);
251:   PetscFree2(vary,iary);

253:   MatCreateSubMatrix_SeqSBAIJ_Private(A,is1,is2,scall,B);
254:   ISDestroy(&is1);
255:   ISDestroy(&is2);

257:   if (isrow != iscol) {
258:     PetscBool isequal;
259:     ISEqual(isrow,iscol,&isequal);
260:     if (!isequal) {
261:       MatSeqSBAIJZeroOps_Private(*B);
262:     }
263:   }
264:   return(0);
265: }

267: PetscErrorCode MatCreateSubMatrices_SeqSBAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
268: {
270:   PetscInt       i;

273:   if (scall == MAT_INITIAL_MATRIX) {
274:     PetscCalloc1(n+1,B);
275:   }

277:   for (i=0; i<n; i++) {
278:     MatCreateSubMatrix_SeqSBAIJ(A,irow[i],icol[i],scall,&(*B)[i]);
279:   }
280:   return(0);
281: }

283: /* -------------------------------------------------------*/
284: /* Should check that shapes of vectors and matrices match */
285: /* -------------------------------------------------------*/

287: PetscErrorCode MatMult_SeqSBAIJ_2(Mat A,Vec xx,Vec zz)
288: {
289:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
290:   PetscScalar       *z,x1,x2,zero=0.0;
291:   const PetscScalar *x,*xb;
292:   const MatScalar   *v;
293:   PetscErrorCode    ierr;
294:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
295:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
296:   PetscInt          nonzerorow=0;

299:   VecSet(zz,zero);
300:   VecGetArrayRead(xx,&x);
301:   VecGetArray(zz,&z);

303:   v  = a->a;
304:   xb = x;

306:   for (i=0; i<mbs; i++) {
307:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
308:     x1          = xb[0]; x2 = xb[1];
309:     ib          = aj + *ai;
310:     jmin        = 0;
311:     nonzerorow += (n>0);
312:     if (*ib == i) {     /* (diag of A)*x */
313:       z[2*i]   += v[0]*x1 + v[2]*x2;
314:       z[2*i+1] += v[2]*x1 + v[3]*x2;
315:       v        += 4; jmin++;
316:     }
317:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
318:     PetscPrefetchBlock(v+4*n,4*n,0,PETSC_PREFETCH_HINT_NTA);   /* Entries for the next row */
319:     for (j=jmin; j<n; j++) {
320:       /* (strict lower triangular part of A)*x  */
321:       cval       = ib[j]*2;
322:       z[cval]   += v[0]*x1 + v[1]*x2;
323:       z[cval+1] += v[2]*x1 + v[3]*x2;
324:       /* (strict upper triangular part of A)*x  */
325:       z[2*i]   += v[0]*x[cval] + v[2]*x[cval+1];
326:       z[2*i+1] += v[1]*x[cval] + v[3]*x[cval+1];
327:       v        += 4;
328:     }
329:     xb +=2; ai++;
330:   }

332:   VecRestoreArrayRead(xx,&x);
333:   VecRestoreArray(zz,&z);
334:   PetscLogFlops(8.0*(a->nz*2.0 - nonzerorow) - nonzerorow);
335:   return(0);
336: }

338: PetscErrorCode MatMult_SeqSBAIJ_3(Mat A,Vec xx,Vec zz)
339: {
340:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
341:   PetscScalar       *z,x1,x2,x3,zero=0.0;
342:   const PetscScalar *x,*xb;
343:   const MatScalar   *v;
344:   PetscErrorCode    ierr;
345:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
346:   const PetscInt    *aj = a->j,*ai = a->i,*ib;
347:   PetscInt          nonzerorow=0;

350:   VecSet(zz,zero);
351:   VecGetArrayRead(xx,&x);
352:   VecGetArray(zz,&z);

354:   v  = a->a;
355:   xb = x;

357:   for (i=0; i<mbs; i++) {
358:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
359:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2];
360:     ib          = aj + *ai;
361:     jmin        = 0;
362:     nonzerorow += (n>0);
363:     if (*ib == i) {     /* (diag of A)*x */
364:       z[3*i]   += v[0]*x1 + v[3]*x2 + v[6]*x3;
365:       z[3*i+1] += v[3]*x1 + v[4]*x2 + v[7]*x3;
366:       z[3*i+2] += v[6]*x1 + v[7]*x2 + v[8]*x3;
367:       v        += 9; jmin++;
368:     }
369:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
370:     PetscPrefetchBlock(v+9*n,9*n,0,PETSC_PREFETCH_HINT_NTA);   /* Entries for the next row */
371:     for (j=jmin; j<n; j++) {
372:       /* (strict lower triangular part of A)*x  */
373:       cval       = ib[j]*3;
374:       z[cval]   += v[0]*x1 + v[1]*x2 + v[2]*x3;
375:       z[cval+1] += v[3]*x1 + v[4]*x2 + v[5]*x3;
376:       z[cval+2] += v[6]*x1 + v[7]*x2 + v[8]*x3;
377:       /* (strict upper triangular part of A)*x  */
378:       z[3*i]   += v[0]*x[cval] + v[3]*x[cval+1]+ v[6]*x[cval+2];
379:       z[3*i+1] += v[1]*x[cval] + v[4]*x[cval+1]+ v[7]*x[cval+2];
380:       z[3*i+2] += v[2]*x[cval] + v[5]*x[cval+1]+ v[8]*x[cval+2];
381:       v        += 9;
382:     }
383:     xb +=3; ai++;
384:   }

386:   VecRestoreArrayRead(xx,&x);
387:   VecRestoreArray(zz,&z);
388:   PetscLogFlops(18.0*(a->nz*2.0 - nonzerorow) - nonzerorow);
389:   return(0);
390: }

392: PetscErrorCode MatMult_SeqSBAIJ_4(Mat A,Vec xx,Vec zz)
393: {
394:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
395:   PetscScalar       *z,x1,x2,x3,x4,zero=0.0;
396:   const PetscScalar *x,*xb;
397:   const MatScalar   *v;
398:   PetscErrorCode    ierr;
399:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
400:   const PetscInt    *aj = a->j,*ai = a->i,*ib;
401:   PetscInt          nonzerorow = 0;

404:   VecSet(zz,zero);
405:   VecGetArrayRead(xx,&x);
406:   VecGetArray(zz,&z);

408:   v  = a->a;
409:   xb = x;

411:   for (i=0; i<mbs; i++) {
412:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
413:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3];
414:     ib          = aj + *ai;
415:     jmin        = 0;
416:     nonzerorow += (n>0);
417:     if (*ib == i) {     /* (diag of A)*x */
418:       z[4*i]   += v[0]*x1 + v[4]*x2 +  v[8]*x3 + v[12]*x4;
419:       z[4*i+1] += v[4]*x1 + v[5]*x2 +  v[9]*x3 + v[13]*x4;
420:       z[4*i+2] += v[8]*x1 + v[9]*x2 + v[10]*x3 + v[14]*x4;
421:       z[4*i+3] += v[12]*x1+ v[13]*x2+ v[14]*x3 + v[15]*x4;
422:       v        += 16; jmin++;
423:     }
424:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
425:     PetscPrefetchBlock(v+16*n,16*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
426:     for (j=jmin; j<n; j++) {
427:       /* (strict lower triangular part of A)*x  */
428:       cval       = ib[j]*4;
429:       z[cval]   += v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4;
430:       z[cval+1] += v[4]*x1 + v[5]*x2 + v[6]*x3 + v[7]*x4;
431:       z[cval+2] += v[8]*x1 + v[9]*x2 + v[10]*x3 + v[11]*x4;
432:       z[cval+3] += v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4;
433:       /* (strict upper triangular part of A)*x  */
434:       z[4*i]   += v[0]*x[cval] + v[4]*x[cval+1]+ v[8]*x[cval+2] + v[12]*x[cval+3];
435:       z[4*i+1] += v[1]*x[cval] + v[5]*x[cval+1]+ v[9]*x[cval+2] + v[13]*x[cval+3];
436:       z[4*i+2] += v[2]*x[cval] + v[6]*x[cval+1]+ v[10]*x[cval+2]+ v[14]*x[cval+3];
437:       z[4*i+3] += v[3]*x[cval] + v[7]*x[cval+1]+ v[11]*x[cval+2]+ v[15]*x[cval+3];
438:       v        += 16;
439:     }
440:     xb +=4; ai++;
441:   }

443:   VecRestoreArrayRead(xx,&x);
444:   VecRestoreArray(zz,&z);
445:   PetscLogFlops(32.0*(a->nz*2.0 - nonzerorow) - nonzerorow);
446:   return(0);
447: }

449: PetscErrorCode MatMult_SeqSBAIJ_5(Mat A,Vec xx,Vec zz)
450: {
451:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
452:   PetscScalar       *z,x1,x2,x3,x4,x5,zero=0.0;
453:   const PetscScalar *x,*xb;
454:   const MatScalar   *v;
455:   PetscErrorCode    ierr;
456:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
457:   const PetscInt    *aj = a->j,*ai = a->i,*ib;
458:   PetscInt          nonzerorow=0;

461:   VecSet(zz,zero);
462:   VecGetArrayRead(xx,&x);
463:   VecGetArray(zz,&z);

465:   v  = a->a;
466:   xb = x;

468:   for (i=0; i<mbs; i++) {
469:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
470:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4];
471:     ib          = aj + *ai;
472:     jmin        = 0;
473:     nonzerorow += (n>0);
474:     if (*ib == i) {      /* (diag of A)*x */
475:       z[5*i]   += v[0]*x1  + v[5]*x2 + v[10]*x3 + v[15]*x4+ v[20]*x5;
476:       z[5*i+1] += v[5]*x1  + v[6]*x2 + v[11]*x3 + v[16]*x4+ v[21]*x5;
477:       z[5*i+2] += v[10]*x1 +v[11]*x2 + v[12]*x3 + v[17]*x4+ v[22]*x5;
478:       z[5*i+3] += v[15]*x1 +v[16]*x2 + v[17]*x3 + v[18]*x4+ v[23]*x5;
479:       z[5*i+4] += v[20]*x1 +v[21]*x2 + v[22]*x3 + v[23]*x4+ v[24]*x5;
480:       v        += 25; jmin++;
481:     }
482:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
483:     PetscPrefetchBlock(v+25*n,25*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
484:     for (j=jmin; j<n; j++) {
485:       /* (strict lower triangular part of A)*x  */
486:       cval       = ib[j]*5;
487:       z[cval]   += v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4 + v[4]*x5;
488:       z[cval+1] += v[5]*x1 + v[6]*x2 + v[7]*x3 + v[8]*x4 + v[9]*x5;
489:       z[cval+2] += v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4+ v[14]*x5;
490:       z[cval+3] += v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4+ v[19]*x5;
491:       z[cval+4] += v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4+ v[24]*x5;
492:       /* (strict upper triangular part of A)*x  */
493:       z[5*i]   +=v[0]*x[cval]+v[5]*x[cval+1]+v[10]*x[cval+2]+v[15]*x[cval+3]+v[20]*x[cval+4];
494:       z[5*i+1] +=v[1]*x[cval]+v[6]*x[cval+1]+v[11]*x[cval+2]+v[16]*x[cval+3]+v[21]*x[cval+4];
495:       z[5*i+2] +=v[2]*x[cval]+v[7]*x[cval+1]+v[12]*x[cval+2]+v[17]*x[cval+3]+v[22]*x[cval+4];
496:       z[5*i+3] +=v[3]*x[cval]+v[8]*x[cval+1]+v[13]*x[cval+2]+v[18]*x[cval+3]+v[23]*x[cval+4];
497:       z[5*i+4] +=v[4]*x[cval]+v[9]*x[cval+1]+v[14]*x[cval+2]+v[19]*x[cval+3]+v[24]*x[cval+4];
498:       v        += 25;
499:     }
500:     xb +=5; ai++;
501:   }

503:   VecRestoreArrayRead(xx,&x);
504:   VecRestoreArray(zz,&z);
505:   PetscLogFlops(50.0*(a->nz*2.0 - nonzerorow) - nonzerorow);
506:   return(0);
507: }


510: PetscErrorCode MatMult_SeqSBAIJ_6(Mat A,Vec xx,Vec zz)
511: {
512:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
513:   PetscScalar       *z,x1,x2,x3,x4,x5,x6,zero=0.0;
514:   const PetscScalar *x,*xb;
515:   const MatScalar   *v;
516:   PetscErrorCode    ierr;
517:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
518:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
519:   PetscInt          nonzerorow=0;

522:   VecSet(zz,zero);
523:   VecGetArrayRead(xx,&x);
524:   VecGetArray(zz,&z);

526:   v  = a->a;
527:   xb = x;

529:   for (i=0; i<mbs; i++) {
530:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
531:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4]; x6=xb[5];
532:     ib          = aj + *ai;
533:     jmin        = 0;
534:     nonzerorow += (n>0);
535:     if (*ib == i) {      /* (diag of A)*x */
536:       z[6*i]   += v[0]*x1  + v[6]*x2 + v[12]*x3 + v[18]*x4+ v[24]*x5 + v[30]*x6;
537:       z[6*i+1] += v[6]*x1  + v[7]*x2 + v[13]*x3 + v[19]*x4+ v[25]*x5 + v[31]*x6;
538:       z[6*i+2] += v[12]*x1 +v[13]*x2 + v[14]*x3 + v[20]*x4+ v[26]*x5 + v[32]*x6;
539:       z[6*i+3] += v[18]*x1 +v[19]*x2 + v[20]*x3 + v[21]*x4+ v[27]*x5 + v[33]*x6;
540:       z[6*i+4] += v[24]*x1 +v[25]*x2 + v[26]*x3 + v[27]*x4+ v[28]*x5 + v[34]*x6;
541:       z[6*i+5] += v[30]*x1 +v[31]*x2 + v[32]*x3 + v[33]*x4+ v[34]*x5 + v[35]*x6;
542:       v        += 36; jmin++;
543:     }
544:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
545:     PetscPrefetchBlock(v+36*n,36*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
546:     for (j=jmin; j<n; j++) {
547:       /* (strict lower triangular part of A)*x  */
548:       cval       = ib[j]*6;
549:       z[cval]   += v[0]*x1  + v[1]*x2 + v[2]*x3 + v[3]*x4+ v[4]*x5 + v[5]*x6;
550:       z[cval+1] += v[6]*x1  + v[7]*x2 + v[8]*x3 + v[9]*x4+ v[10]*x5 + v[11]*x6;
551:       z[cval+2] += v[12]*x1  + v[13]*x2 + v[14]*x3 + v[15]*x4+ v[16]*x5 + v[17]*x6;
552:       z[cval+3] += v[18]*x1  + v[19]*x2 + v[20]*x3 + v[21]*x4+ v[22]*x5 + v[23]*x6;
553:       z[cval+4] += v[24]*x1  + v[25]*x2 + v[26]*x3 + v[27]*x4+ v[28]*x5 + v[29]*x6;
554:       z[cval+5] += v[30]*x1  + v[31]*x2 + v[32]*x3 + v[33]*x4+ v[34]*x5 + v[35]*x6;
555:       /* (strict upper triangular part of A)*x  */
556:       z[6*i]   +=v[0]*x[cval]+v[6]*x[cval+1]+v[12]*x[cval+2]+v[18]*x[cval+3]+v[24]*x[cval+4]+v[30]*x[cval+5];
557:       z[6*i+1] +=v[1]*x[cval]+v[7]*x[cval+1]+v[13]*x[cval+2]+v[19]*x[cval+3]+v[25]*x[cval+4]+v[31]*x[cval+5];
558:       z[6*i+2] +=v[2]*x[cval]+v[8]*x[cval+1]+v[14]*x[cval+2]+v[20]*x[cval+3]+v[26]*x[cval+4]+v[32]*x[cval+5];
559:       z[6*i+3] +=v[3]*x[cval]+v[9]*x[cval+1]+v[15]*x[cval+2]+v[21]*x[cval+3]+v[27]*x[cval+4]+v[33]*x[cval+5];
560:       z[6*i+4] +=v[4]*x[cval]+v[10]*x[cval+1]+v[16]*x[cval+2]+v[22]*x[cval+3]+v[28]*x[cval+4]+v[34]*x[cval+5];
561:       z[6*i+5] +=v[5]*x[cval]+v[11]*x[cval+1]+v[17]*x[cval+2]+v[23]*x[cval+3]+v[29]*x[cval+4]+v[35]*x[cval+5];
562:       v        += 36;
563:     }
564:     xb +=6; ai++;
565:   }

567:   VecRestoreArrayRead(xx,&x);
568:   VecRestoreArray(zz,&z);
569:   PetscLogFlops(72.0*(a->nz*2.0 - nonzerorow) - nonzerorow);
570:   return(0);
571: }
572: PetscErrorCode MatMult_SeqSBAIJ_7(Mat A,Vec xx,Vec zz)
573: {
574:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
575:   PetscScalar       *z,x1,x2,x3,x4,x5,x6,x7,zero=0.0;
576:   const PetscScalar *x,*xb;
577:   const MatScalar   *v;
578:   PetscErrorCode    ierr;
579:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
580:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
581:   PetscInt          nonzerorow=0;

584:   VecSet(zz,zero);
585:   VecGetArrayRead(xx,&x);
586:   VecGetArray(zz,&z);

588:   v  = a->a;
589:   xb = x;

591:   for (i=0; i<mbs; i++) {
592:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
593:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4]; x6=xb[5]; x7=xb[6];
594:     ib          = aj + *ai;
595:     jmin        = 0;
596:     nonzerorow += (n>0);
597:     if (*ib == i) {      /* (diag of A)*x */
598:       z[7*i]   += v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4+ v[28]*x5 + v[35]*x6+ v[42]*x7;
599:       z[7*i+1] += v[7]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4+ v[29]*x5 + v[36]*x6+ v[43]*x7;
600:       z[7*i+2] += v[14]*x1+ v[15]*x2 +v[16]*x3 + v[23]*x4+ v[30]*x5 + v[37]*x6+ v[44]*x7;
601:       z[7*i+3] += v[21]*x1+ v[22]*x2 +v[23]*x3 + v[24]*x4+ v[31]*x5 + v[38]*x6+ v[45]*x7;
602:       z[7*i+4] += v[28]*x1+ v[29]*x2 +v[30]*x3 + v[31]*x4+ v[32]*x5 + v[39]*x6+ v[46]*x7;
603:       z[7*i+5] += v[35]*x1+ v[36]*x2 +v[37]*x3 + v[38]*x4+ v[39]*x5 + v[40]*x6+ v[47]*x7;
604:       z[7*i+6] += v[42]*x1+ v[43]*x2 +v[44]*x3 + v[45]*x4+ v[46]*x5 + v[47]*x6+ v[48]*x7;
605:       v        += 49; jmin++;
606:     }
607:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
608:     PetscPrefetchBlock(v+49*n,49*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
609:     for (j=jmin; j<n; j++) {
610:       /* (strict lower triangular part of A)*x  */
611:       cval       = ib[j]*7;
612:       z[cval]   += v[0]*x1  + v[1]*x2 + v[2]*x3 + v[3]*x4+ v[4]*x5 + v[5]*x6+ v[6]*x7;
613:       z[cval+1] += v[7]*x1  + v[8]*x2 + v[9]*x3 + v[10]*x4+ v[11]*x5 + v[12]*x6+ v[13]*x7;
614:       z[cval+2] += v[14]*x1  + v[15]*x2 + v[16]*x3 + v[17]*x4+ v[18]*x5 + v[19]*x6+ v[20]*x7;
615:       z[cval+3] += v[21]*x1  + v[22]*x2 + v[23]*x3 + v[24]*x4+ v[25]*x5 + v[26]*x6+ v[27]*x7;
616:       z[cval+4] += v[28]*x1  + v[29]*x2 + v[30]*x3 + v[31]*x4+ v[32]*x5 + v[33]*x6+ v[34]*x7;
617:       z[cval+5] += v[35]*x1  + v[36]*x2 + v[37]*x3 + v[38]*x4+ v[39]*x5 + v[40]*x6+ v[41]*x7;
618:       z[cval+6] += v[42]*x1  + v[43]*x2 + v[44]*x3 + v[45]*x4+ v[46]*x5 + v[47]*x6+ v[48]*x7;
619:       /* (strict upper triangular part of A)*x  */
620:       z[7*i]  +=v[0]*x[cval]+v[7]*x[cval+1]+v[14]*x[cval+2]+v[21]*x[cval+3]+v[28]*x[cval+4]+v[35]*x[cval+5]+v[42]*x[cval+6];
621:       z[7*i+1]+=v[1]*x[cval]+v[8]*x[cval+1]+v[15]*x[cval+2]+v[22]*x[cval+3]+v[29]*x[cval+4]+v[36]*x[cval+5]+v[43]*x[cval+6];
622:       z[7*i+2]+=v[2]*x[cval]+v[9]*x[cval+1]+v[16]*x[cval+2]+v[23]*x[cval+3]+v[30]*x[cval+4]+v[37]*x[cval+5]+v[44]*x[cval+6];
623:       z[7*i+3]+=v[3]*x[cval]+v[10]*x[cval+1]+v[17]*x[cval+2]+v[24]*x[cval+3]+v[31]*x[cval+4]+v[38]*x[cval+5]+v[45]*x[cval+6];
624:       z[7*i+4]+=v[4]*x[cval]+v[11]*x[cval+1]+v[18]*x[cval+2]+v[25]*x[cval+3]+v[32]*x[cval+4]+v[39]*x[cval+5]+v[46]*x[cval+6];
625:       z[7*i+5]+=v[5]*x[cval]+v[12]*x[cval+1]+v[19]*x[cval+2]+v[26]*x[cval+3]+v[33]*x[cval+4]+v[40]*x[cval+5]+v[47]*x[cval+6];
626:       z[7*i+6]+=v[6]*x[cval]+v[13]*x[cval+1]+v[20]*x[cval+2]+v[27]*x[cval+3]+v[34]*x[cval+4]+v[41]*x[cval+5]+v[48]*x[cval+6];
627:       v       += 49;
628:     }
629:     xb +=7; ai++;
630:   }
631:   VecRestoreArrayRead(xx,&x);
632:   VecRestoreArray(zz,&z);
633:   PetscLogFlops(98.0*(a->nz*2.0 - nonzerorow) - nonzerorow);
634:   return(0);
635: }

637: /*
638:     This will not work with MatScalar == float because it calls the BLAS
639: */
640: PetscErrorCode MatMult_SeqSBAIJ_N(Mat A,Vec xx,Vec zz)
641: {
642:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
643:   PetscScalar       *z,*z_ptr,*zb,*work,*workt,zero=0.0;
644:   const PetscScalar *x,*x_ptr,*xb;
645:   const MatScalar   *v;
646:   PetscErrorCode    ierr;
647:   PetscInt          mbs =a->mbs,i,bs=A->rmap->bs,j,n,bs2=a->bs2,ncols,k;
648:   const PetscInt    *idx,*aj,*ii;
649:   PetscInt          nonzerorow=0;

652:   VecSet(zz,zero);
653:   VecGetArrayRead(xx,&x);x_ptr = x;
654:   VecGetArray(zz,&z); z_ptr=z;

656:   aj = a->j;
657:   v  = a->a;
658:   ii = a->i;

660:   if (!a->mult_work) {
661:     PetscMalloc1(A->rmap->N+1,&a->mult_work);
662:   }
663:   work = a->mult_work;

665:   for (i=0; i<mbs; i++) {
666:     n           = ii[1] - ii[0]; ncols = n*bs;
667:     workt       = work; idx=aj+ii[0];
668:     nonzerorow += (n>0);

670:     /* upper triangular part */
671:     for (j=0; j<n; j++) {
672:       xb = x_ptr + bs*(*idx++);
673:       for (k=0; k<bs; k++) workt[k] = xb[k];
674:       workt += bs;
675:     }
676:     /* z(i*bs:(i+1)*bs-1) += A(i,:)*x */
677:     PetscKernel_w_gets_w_plus_Ar_times_v(bs,ncols,work,v,z);

679:     /* strict lower triangular part */
680:     idx = aj+ii[0];
681:     if (*idx == i) {
682:       ncols -= bs; v += bs2; idx++; n--;
683:     }

685:     if (ncols > 0) {
686:       workt = work;
687:       PetscMemzero(workt,ncols*sizeof(PetscScalar));
688:       PetscKernel_w_gets_w_plus_trans_Ar_times_v(bs,ncols,x,v,workt);
689:       for (j=0; j<n; j++) {
690:         zb = z_ptr + bs*(*idx++);
691:         for (k=0; k<bs; k++) zb[k] += workt[k];
692:         workt += bs;
693:       }
694:     }
695:     x += bs; v += n*bs2; z += bs; ii++;
696:   }

698:   VecRestoreArrayRead(xx,&x);
699:   VecRestoreArray(zz,&z);
700:   PetscLogFlops(2.0*(a->nz*2.0 - nonzerorow)*bs2 - nonzerorow);
701:   return(0);
702: }

704: PetscErrorCode MatMultAdd_SeqSBAIJ_1(Mat A,Vec xx,Vec yy,Vec zz)
705: {
706:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
707:   PetscScalar       *z,x1;
708:   const PetscScalar *x,*xb;
709:   const MatScalar   *v;
710:   PetscErrorCode    ierr;
711:   PetscInt          mbs =a->mbs,i,n,cval,j,jmin;
712:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
713:   PetscInt          nonzerorow=0;

716:   VecCopy(yy,zz);
717:   VecGetArrayRead(xx,&x);
718:   VecGetArray(zz,&z);
719:   v    = a->a;
720:   xb   = x;

722:   for (i=0; i<mbs; i++) {
723:     n           = ai[1] - ai[0]; /* length of i_th row of A */
724:     x1          = xb[0];
725:     ib          = aj + *ai;
726:     jmin        = 0;
727:     nonzerorow += (n>0);
728:     if (*ib == i) {            /* (diag of A)*x */
729:       z[i] += *v++ * x[*ib++]; jmin++;
730:     }
731:     for (j=jmin; j<n; j++) {
732:       cval    = *ib;
733:       z[cval] += *v * x1;      /* (strict lower triangular part of A)*x  */
734:       z[i] += *v++ * x[*ib++]; /* (strict upper triangular part of A)*x  */
735:     }
736:     xb++; ai++;
737:   }

739:   VecRestoreArrayRead(xx,&x);
740:   VecRestoreArray(zz,&z);

742:   PetscLogFlops(2.0*(a->nz*2.0 - nonzerorow));
743:   return(0);
744: }

746: PetscErrorCode MatMultAdd_SeqSBAIJ_2(Mat A,Vec xx,Vec yy,Vec zz)
747: {
748:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
749:   PetscScalar       *z,x1,x2;
750:   const PetscScalar *x,*xb;
751:   const MatScalar   *v;
752:   PetscErrorCode    ierr;
753:   PetscInt          mbs =a->mbs,i,n,cval,j,jmin;
754:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
755:   PetscInt          nonzerorow=0;

758:   VecCopy(yy,zz);
759:   VecGetArrayRead(xx,&x);
760:   VecGetArray(zz,&z);

762:   v  = a->a;
763:   xb = x;

765:   for (i=0; i<mbs; i++) {
766:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
767:     x1          = xb[0]; x2 = xb[1];
768:     ib          = aj + *ai;
769:     jmin        = 0;
770:     nonzerorow += (n>0);
771:     if (*ib == i) {      /* (diag of A)*x */
772:       z[2*i]   += v[0]*x1 + v[2]*x2;
773:       z[2*i+1] += v[2]*x1 + v[3]*x2;
774:       v        += 4; jmin++;
775:     }
776:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
777:     PetscPrefetchBlock(v+4*n,4*n,0,PETSC_PREFETCH_HINT_NTA);   /* Entries for the next row */
778:     for (j=jmin; j<n; j++) {
779:       /* (strict lower triangular part of A)*x  */
780:       cval       = ib[j]*2;
781:       z[cval]   += v[0]*x1 + v[1]*x2;
782:       z[cval+1] += v[2]*x1 + v[3]*x2;
783:       /* (strict upper triangular part of A)*x  */
784:       z[2*i]   += v[0]*x[cval] + v[2]*x[cval+1];
785:       z[2*i+1] += v[1]*x[cval] + v[3]*x[cval+1];
786:       v        += 4;
787:     }
788:     xb +=2; ai++;
789:   }
790:   VecRestoreArrayRead(xx,&x);
791:   VecRestoreArray(zz,&z);

793:   PetscLogFlops(4.0*(a->nz*2.0 - nonzerorow));
794:   return(0);
795: }

797: PetscErrorCode MatMultAdd_SeqSBAIJ_3(Mat A,Vec xx,Vec yy,Vec zz)
798: {
799:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
800:   PetscScalar       *z,x1,x2,x3;
801:   const PetscScalar *x,*xb;
802:   const MatScalar   *v;
803:   PetscErrorCode    ierr;
804:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
805:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
806:   PetscInt          nonzerorow=0;

809:   VecCopy(yy,zz);
810:   VecGetArrayRead(xx,&x);
811:   VecGetArray(zz,&z);

813:   v  = a->a;
814:   xb = x;

816:   for (i=0; i<mbs; i++) {
817:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
818:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2];
819:     ib          = aj + *ai;
820:     jmin        = 0;
821:     nonzerorow += (n>0);
822:     if (*ib == i) {     /* (diag of A)*x */
823:       z[3*i]   += v[0]*x1 + v[3]*x2 + v[6]*x3;
824:       z[3*i+1] += v[3]*x1 + v[4]*x2 + v[7]*x3;
825:       z[3*i+2] += v[6]*x1 + v[7]*x2 + v[8]*x3;
826:       v        += 9; jmin++;
827:     }
828:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
829:     PetscPrefetchBlock(v+9*n,9*n,0,PETSC_PREFETCH_HINT_NTA);   /* Entries for the next row */
830:     for (j=jmin; j<n; j++) {
831:       /* (strict lower triangular part of A)*x  */
832:       cval       = ib[j]*3;
833:       z[cval]   += v[0]*x1 + v[1]*x2 + v[2]*x3;
834:       z[cval+1] += v[3]*x1 + v[4]*x2 + v[5]*x3;
835:       z[cval+2] += v[6]*x1 + v[7]*x2 + v[8]*x3;
836:       /* (strict upper triangular part of A)*x  */
837:       z[3*i]   += v[0]*x[cval] + v[3]*x[cval+1]+ v[6]*x[cval+2];
838:       z[3*i+1] += v[1]*x[cval] + v[4]*x[cval+1]+ v[7]*x[cval+2];
839:       z[3*i+2] += v[2]*x[cval] + v[5]*x[cval+1]+ v[8]*x[cval+2];
840:       v        += 9;
841:     }
842:     xb +=3; ai++;
843:   }

845:   VecRestoreArrayRead(xx,&x);
846:   VecRestoreArray(zz,&z);

848:   PetscLogFlops(18.0*(a->nz*2.0 - nonzerorow));
849:   return(0);
850: }

852: PetscErrorCode MatMultAdd_SeqSBAIJ_4(Mat A,Vec xx,Vec yy,Vec zz)
853: {
854:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
855:   PetscScalar       *z,x1,x2,x3,x4;
856:   const PetscScalar *x,*xb;
857:   const MatScalar   *v;
858:   PetscErrorCode    ierr;
859:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
860:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
861:   PetscInt          nonzerorow=0;

864:   VecCopy(yy,zz);
865:   VecGetArrayRead(xx,&x);
866:   VecGetArray(zz,&z);

868:   v  = a->a;
869:   xb = x;

871:   for (i=0; i<mbs; i++) {
872:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
873:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3];
874:     ib          = aj + *ai;
875:     jmin        = 0;
876:     nonzerorow += (n>0);
877:     if (*ib == i) {      /* (diag of A)*x */
878:       z[4*i]   += v[0]*x1 + v[4]*x2 +  v[8]*x3 + v[12]*x4;
879:       z[4*i+1] += v[4]*x1 + v[5]*x2 +  v[9]*x3 + v[13]*x4;
880:       z[4*i+2] += v[8]*x1 + v[9]*x2 + v[10]*x3 + v[14]*x4;
881:       z[4*i+3] += v[12]*x1+ v[13]*x2+ v[14]*x3 + v[15]*x4;
882:       v        += 16; jmin++;
883:     }
884:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
885:     PetscPrefetchBlock(v+16*n,16*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
886:     for (j=jmin; j<n; j++) {
887:       /* (strict lower triangular part of A)*x  */
888:       cval       = ib[j]*4;
889:       z[cval]   += v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4;
890:       z[cval+1] += v[4]*x1 + v[5]*x2 + v[6]*x3 + v[7]*x4;
891:       z[cval+2] += v[8]*x1 + v[9]*x2 + v[10]*x3 + v[11]*x4;
892:       z[cval+3] += v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4;
893:       /* (strict upper triangular part of A)*x  */
894:       z[4*i]   += v[0]*x[cval] + v[4]*x[cval+1]+ v[8]*x[cval+2] + v[12]*x[cval+3];
895:       z[4*i+1] += v[1]*x[cval] + v[5]*x[cval+1]+ v[9]*x[cval+2] + v[13]*x[cval+3];
896:       z[4*i+2] += v[2]*x[cval] + v[6]*x[cval+1]+ v[10]*x[cval+2]+ v[14]*x[cval+3];
897:       z[4*i+3] += v[3]*x[cval] + v[7]*x[cval+1]+ v[11]*x[cval+2]+ v[15]*x[cval+3];
898:       v        += 16;
899:     }
900:     xb +=4; ai++;
901:   }

903:   VecRestoreArrayRead(xx,&x);
904:   VecRestoreArray(zz,&z);

906:   PetscLogFlops(32.0*(a->nz*2.0 - nonzerorow));
907:   return(0);
908: }

910: PetscErrorCode MatMultAdd_SeqSBAIJ_5(Mat A,Vec xx,Vec yy,Vec zz)
911: {
912:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
913:   PetscScalar       *z,x1,x2,x3,x4,x5;
914:   const PetscScalar *x,*xb;
915:   const MatScalar   *v;
916:   PetscErrorCode    ierr;
917:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
918:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
919:   PetscInt          nonzerorow=0;

922:   VecCopy(yy,zz);
923:   VecGetArrayRead(xx,&x);
924:   VecGetArray(zz,&z);

926:   v  = a->a;
927:   xb = x;

929:   for (i=0; i<mbs; i++) {
930:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
931:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4];
932:     ib          = aj + *ai;
933:     jmin        = 0;
934:     nonzerorow += (n>0);
935:     if (*ib == i) {      /* (diag of A)*x */
936:       z[5*i]   += v[0]*x1  + v[5]*x2 + v[10]*x3 + v[15]*x4+ v[20]*x5;
937:       z[5*i+1] += v[5]*x1  + v[6]*x2 + v[11]*x3 + v[16]*x4+ v[21]*x5;
938:       z[5*i+2] += v[10]*x1 +v[11]*x2 + v[12]*x3 + v[17]*x4+ v[22]*x5;
939:       z[5*i+3] += v[15]*x1 +v[16]*x2 + v[17]*x3 + v[18]*x4+ v[23]*x5;
940:       z[5*i+4] += v[20]*x1 +v[21]*x2 + v[22]*x3 + v[23]*x4+ v[24]*x5;
941:       v        += 25; jmin++;
942:     }
943:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
944:     PetscPrefetchBlock(v+25*n,25*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
945:     for (j=jmin; j<n; j++) {
946:       /* (strict lower triangular part of A)*x  */
947:       cval       = ib[j]*5;
948:       z[cval]   += v[0]*x1 + v[1]*x2 + v[2]*x3 + v[3]*x4 + v[4]*x5;
949:       z[cval+1] += v[5]*x1 + v[6]*x2 + v[7]*x3 + v[8]*x4 + v[9]*x5;
950:       z[cval+2] += v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4+ v[14]*x5;
951:       z[cval+3] += v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4+ v[19]*x5;
952:       z[cval+4] += v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4+ v[24]*x5;
953:       /* (strict upper triangular part of A)*x  */
954:       z[5*i]   +=v[0]*x[cval]+v[5]*x[cval+1]+v[10]*x[cval+2]+v[15]*x[cval+3]+v[20]*x[cval+4];
955:       z[5*i+1] +=v[1]*x[cval]+v[6]*x[cval+1]+v[11]*x[cval+2]+v[16]*x[cval+3]+v[21]*x[cval+4];
956:       z[5*i+2] +=v[2]*x[cval]+v[7]*x[cval+1]+v[12]*x[cval+2]+v[17]*x[cval+3]+v[22]*x[cval+4];
957:       z[5*i+3] +=v[3]*x[cval]+v[8]*x[cval+1]+v[13]*x[cval+2]+v[18]*x[cval+3]+v[23]*x[cval+4];
958:       z[5*i+4] +=v[4]*x[cval]+v[9]*x[cval+1]+v[14]*x[cval+2]+v[19]*x[cval+3]+v[24]*x[cval+4];
959:       v        += 25;
960:     }
961:     xb +=5; ai++;
962:   }

964:   VecRestoreArrayRead(xx,&x);
965:   VecRestoreArray(zz,&z);

967:   PetscLogFlops(50.0*(a->nz*2.0 - nonzerorow));
968:   return(0);
969: }
970: PetscErrorCode MatMultAdd_SeqSBAIJ_6(Mat A,Vec xx,Vec yy,Vec zz)
971: {
972:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
973:   PetscScalar       *z,x1,x2,x3,x4,x5,x6;
974:   const PetscScalar *x,*xb;
975:   const MatScalar   *v;
976:   PetscErrorCode    ierr;
977:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
978:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
979:   PetscInt          nonzerorow=0;

982:   VecCopy(yy,zz);
983:   VecGetArrayRead(xx,&x);
984:   VecGetArray(zz,&z);

986:   v  = a->a;
987:   xb = x;

989:   for (i=0; i<mbs; i++) {
990:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
991:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4]; x6=xb[5];
992:     ib          = aj + *ai;
993:     jmin        = 0;
994:     nonzerorow += (n>0);
995:     if (*ib == i) {     /* (diag of A)*x */
996:       z[6*i]   += v[0]*x1  + v[6]*x2 + v[12]*x3 + v[18]*x4+ v[24]*x5 + v[30]*x6;
997:       z[6*i+1] += v[6]*x1  + v[7]*x2 + v[13]*x3 + v[19]*x4+ v[25]*x5 + v[31]*x6;
998:       z[6*i+2] += v[12]*x1 +v[13]*x2 + v[14]*x3 + v[20]*x4+ v[26]*x5 + v[32]*x6;
999:       z[6*i+3] += v[18]*x1 +v[19]*x2 + v[20]*x3 + v[21]*x4+ v[27]*x5 + v[33]*x6;
1000:       z[6*i+4] += v[24]*x1 +v[25]*x2 + v[26]*x3 + v[27]*x4+ v[28]*x5 + v[34]*x6;
1001:       z[6*i+5] += v[30]*x1 +v[31]*x2 + v[32]*x3 + v[33]*x4+ v[34]*x5 + v[35]*x6;
1002:       v        += 36; jmin++;
1003:     }
1004:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
1005:     PetscPrefetchBlock(v+36*n,36*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1006:     for (j=jmin; j<n; j++) {
1007:       /* (strict lower triangular part of A)*x  */
1008:       cval       = ib[j]*6;
1009:       z[cval]   += v[0]*x1  + v[1]*x2 + v[2]*x3 + v[3]*x4+ v[4]*x5 + v[5]*x6;
1010:       z[cval+1] += v[6]*x1  + v[7]*x2 + v[8]*x3 + v[9]*x4+ v[10]*x5 + v[11]*x6;
1011:       z[cval+2] += v[12]*x1  + v[13]*x2 + v[14]*x3 + v[15]*x4+ v[16]*x5 + v[17]*x6;
1012:       z[cval+3] += v[18]*x1  + v[19]*x2 + v[20]*x3 + v[21]*x4+ v[22]*x5 + v[23]*x6;
1013:       z[cval+4] += v[24]*x1  + v[25]*x2 + v[26]*x3 + v[27]*x4+ v[28]*x5 + v[29]*x6;
1014:       z[cval+5] += v[30]*x1  + v[31]*x2 + v[32]*x3 + v[33]*x4+ v[34]*x5 + v[35]*x6;
1015:       /* (strict upper triangular part of A)*x  */
1016:       z[6*i]   +=v[0]*x[cval]+v[6]*x[cval+1]+v[12]*x[cval+2]+v[18]*x[cval+3]+v[24]*x[cval+4]+v[30]*x[cval+5];
1017:       z[6*i+1] +=v[1]*x[cval]+v[7]*x[cval+1]+v[13]*x[cval+2]+v[19]*x[cval+3]+v[25]*x[cval+4]+v[31]*x[cval+5];
1018:       z[6*i+2] +=v[2]*x[cval]+v[8]*x[cval+1]+v[14]*x[cval+2]+v[20]*x[cval+3]+v[26]*x[cval+4]+v[32]*x[cval+5];
1019:       z[6*i+3] +=v[3]*x[cval]+v[9]*x[cval+1]+v[15]*x[cval+2]+v[21]*x[cval+3]+v[27]*x[cval+4]+v[33]*x[cval+5];
1020:       z[6*i+4] +=v[4]*x[cval]+v[10]*x[cval+1]+v[16]*x[cval+2]+v[22]*x[cval+3]+v[28]*x[cval+4]+v[34]*x[cval+5];
1021:       z[6*i+5] +=v[5]*x[cval]+v[11]*x[cval+1]+v[17]*x[cval+2]+v[23]*x[cval+3]+v[29]*x[cval+4]+v[35]*x[cval+5];
1022:       v        += 36;
1023:     }
1024:     xb +=6; ai++;
1025:   }

1027:   VecRestoreArrayRead(xx,&x);
1028:   VecRestoreArray(zz,&z);

1030:   PetscLogFlops(72.0*(a->nz*2.0 - nonzerorow));
1031:   return(0);
1032: }

1034: PetscErrorCode MatMultAdd_SeqSBAIJ_7(Mat A,Vec xx,Vec yy,Vec zz)
1035: {
1036:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
1037:   PetscScalar       *z,x1,x2,x3,x4,x5,x6,x7;
1038:   const PetscScalar *x,*xb;
1039:   const MatScalar   *v;
1040:   PetscErrorCode    ierr;
1041:   PetscInt          mbs = a->mbs,i,n,cval,j,jmin;
1042:   const PetscInt    *aj=a->j,*ai=a->i,*ib;
1043:   PetscInt          nonzerorow=0;

1046:   VecCopy(yy,zz);
1047:   VecGetArrayRead(xx,&x);
1048:   VecGetArray(zz,&z);

1050:   v  = a->a;
1051:   xb = x;

1053:   for (i=0; i<mbs; i++) {
1054:     n           = ai[1] - ai[0]; /* length of i_th block row of A */
1055:     x1          = xb[0]; x2 = xb[1]; x3 = xb[2]; x4 = xb[3]; x5=xb[4]; x6=xb[5]; x7=xb[6];
1056:     ib          = aj + *ai;
1057:     jmin        = 0;
1058:     nonzerorow += (n>0);
1059:     if (*ib == i) {     /* (diag of A)*x */
1060:       z[7*i]   += v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4+ v[28]*x5 + v[35]*x6+ v[42]*x7;
1061:       z[7*i+1] += v[7]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4+ v[29]*x5 + v[36]*x6+ v[43]*x7;
1062:       z[7*i+2] += v[14]*x1+ v[15]*x2 +v[16]*x3 + v[23]*x4+ v[30]*x5 + v[37]*x6+ v[44]*x7;
1063:       z[7*i+3] += v[21]*x1+ v[22]*x2 +v[23]*x3 + v[24]*x4+ v[31]*x5 + v[38]*x6+ v[45]*x7;
1064:       z[7*i+4] += v[28]*x1+ v[29]*x2 +v[30]*x3 + v[31]*x4+ v[32]*x5 + v[39]*x6+ v[46]*x7;
1065:       z[7*i+5] += v[35]*x1+ v[36]*x2 +v[37]*x3 + v[38]*x4+ v[39]*x5 + v[40]*x6+ v[47]*x7;
1066:       z[7*i+6] += v[42]*x1+ v[43]*x2 +v[44]*x3 + v[45]*x4+ v[46]*x5 + v[47]*x6+ v[48]*x7;
1067:       v        += 49; jmin++;
1068:     }
1069:     PetscPrefetchBlock(ib+jmin+n,n,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
1070:     PetscPrefetchBlock(v+49*n,49*n,0,PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1071:     for (j=jmin; j<n; j++) {
1072:       /* (strict lower triangular part of A)*x  */
1073:       cval       = ib[j]*7;
1074:       z[cval]   += v[0]*x1  + v[1]*x2 + v[2]*x3 + v[3]*x4+ v[4]*x5 + v[5]*x6+ v[6]*x7;
1075:       z[cval+1] += v[7]*x1  + v[8]*x2 + v[9]*x3 + v[10]*x4+ v[11]*x5 + v[12]*x6+ v[13]*x7;
1076:       z[cval+2] += v[14]*x1  + v[15]*x2 + v[16]*x3 + v[17]*x4+ v[18]*x5 + v[19]*x6+ v[20]*x7;
1077:       z[cval+3] += v[21]*x1  + v[22]*x2 + v[23]*x3 + v[24]*x4+ v[25]*x5 + v[26]*x6+ v[27]*x7;
1078:       z[cval+4] += v[28]*x1  + v[29]*x2 + v[30]*x3 + v[31]*x4+ v[32]*x5 + v[33]*x6+ v[34]*x7;
1079:       z[cval+5] += v[35]*x1  + v[36]*x2 + v[37]*x3 + v[38]*x4+ v[39]*x5 + v[40]*x6+ v[41]*x7;
1080:       z[cval+6] += v[42]*x1  + v[43]*x2 + v[44]*x3 + v[45]*x4+ v[46]*x5 + v[47]*x6+ v[48]*x7;
1081:       /* (strict upper triangular part of A)*x  */
1082:       z[7*i]  +=v[0]*x[cval]+v[7]*x[cval+1]+v[14]*x[cval+2]+v[21]*x[cval+3]+v[28]*x[cval+4]+v[35]*x[cval+5]+v[42]*x[cval+6];
1083:       z[7*i+1]+=v[1]*x[cval]+v[8]*x[cval+1]+v[15]*x[cval+2]+v[22]*x[cval+3]+v[29]*x[cval+4]+v[36]*x[cval+5]+v[43]*x[cval+6];
1084:       z[7*i+2]+=v[2]*x[cval]+v[9]*x[cval+1]+v[16]*x[cval+2]+v[23]*x[cval+3]+v[30]*x[cval+4]+v[37]*x[cval+5]+v[44]*x[cval+6];
1085:       z[7*i+3]+=v[3]*x[cval]+v[10]*x[cval+1]+v[17]*x[cval+2]+v[24]*x[cval+3]+v[31]*x[cval+4]+v[38]*x[cval+5]+v[45]*x[cval+6];
1086:       z[7*i+4]+=v[4]*x[cval]+v[11]*x[cval+1]+v[18]*x[cval+2]+v[25]*x[cval+3]+v[32]*x[cval+4]+v[39]*x[cval+5]+v[46]*x[cval+6];
1087:       z[7*i+5]+=v[5]*x[cval]+v[12]*x[cval+1]+v[19]*x[cval+2]+v[26]*x[cval+3]+v[33]*x[cval+4]+v[40]*x[cval+5]+v[47]*x[cval+6];
1088:       z[7*i+6]+=v[6]*x[cval]+v[13]*x[cval+1]+v[20]*x[cval+2]+v[27]*x[cval+3]+v[34]*x[cval+4]+v[41]*x[cval+5]+v[48]*x[cval+6];
1089:       v       += 49;
1090:     }
1091:     xb +=7; ai++;
1092:   }

1094:   VecRestoreArrayRead(xx,&x);
1095:   VecRestoreArray(zz,&z);

1097:   PetscLogFlops(98.0*(a->nz*2.0 - nonzerorow));
1098:   return(0);
1099: }

1101: PetscErrorCode MatMultAdd_SeqSBAIJ_N(Mat A,Vec xx,Vec yy,Vec zz)
1102: {
1103:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
1104:   PetscScalar       *z,*z_ptr=0,*zb,*work,*workt;
1105:   const PetscScalar *x,*x_ptr,*xb;
1106:   const MatScalar   *v;
1107:   PetscErrorCode    ierr;
1108:   PetscInt          mbs = a->mbs,i,bs=A->rmap->bs,j,n,bs2=a->bs2,ncols,k;
1109:   const PetscInt    *idx,*aj,*ii;
1110:   PetscInt          nonzerorow=0;

1113:   VecCopy(yy,zz);
1114:   VecGetArrayRead(xx,&x); x_ptr=x;
1115:   VecGetArray(zz,&z); z_ptr=z;

1117:   aj = a->j;
1118:   v  = a->a;
1119:   ii = a->i;

1121:   if (!a->mult_work) {
1122:     PetscMalloc1(A->rmap->n+1,&a->mult_work);
1123:   }
1124:   work = a->mult_work;


1127:   for (i=0; i<mbs; i++) {
1128:     n           = ii[1] - ii[0]; ncols = n*bs;
1129:     workt       = work; idx=aj+ii[0];
1130:     nonzerorow += (n>0);

1132:     /* upper triangular part */
1133:     for (j=0; j<n; j++) {
1134:       xb = x_ptr + bs*(*idx++);
1135:       for (k=0; k<bs; k++) workt[k] = xb[k];
1136:       workt += bs;
1137:     }
1138:     /* z(i*bs:(i+1)*bs-1) += A(i,:)*x */
1139:     PetscKernel_w_gets_w_plus_Ar_times_v(bs,ncols,work,v,z);

1141:     /* strict lower triangular part */
1142:     idx = aj+ii[0];
1143:     if (*idx == i) {
1144:       ncols -= bs; v += bs2; idx++; n--;
1145:     }
1146:     if (ncols > 0) {
1147:       workt = work;
1148:       PetscMemzero(workt,ncols*sizeof(PetscScalar));
1149:       PetscKernel_w_gets_w_plus_trans_Ar_times_v(bs,ncols,x,v,workt);
1150:       for (j=0; j<n; j++) {
1151:         zb = z_ptr + bs*(*idx++);
1152:         for (k=0; k<bs; k++) zb[k] += workt[k];
1153:         workt += bs;
1154:       }
1155:     }

1157:     x += bs; v += n*bs2; z += bs; ii++;
1158:   }

1160:   VecRestoreArrayRead(xx,&x);
1161:   VecRestoreArray(zz,&z);

1163:   PetscLogFlops(2.0*(a->nz*2.0 - nonzerorow));
1164:   return(0);
1165: }

1167: PetscErrorCode MatScale_SeqSBAIJ(Mat inA,PetscScalar alpha)
1168: {
1169:   Mat_SeqSBAIJ   *a     = (Mat_SeqSBAIJ*)inA->data;
1170:   PetscScalar    oalpha = alpha;
1172:   PetscBLASInt   one = 1,totalnz;

1175:   PetscBLASIntCast(a->bs2*a->nz,&totalnz);
1176:   PetscStackCallBLAS("BLASscal",BLASscal_(&totalnz,&oalpha,a->a,&one));
1177:   PetscLogFlops(totalnz);
1178:   return(0);
1179: }

1181: PetscErrorCode MatNorm_SeqSBAIJ(Mat A,NormType type,PetscReal *norm)
1182: {
1183:   Mat_SeqSBAIJ    *a       = (Mat_SeqSBAIJ*)A->data;
1184:   const MatScalar *v       = a->a;
1185:   PetscReal       sum_diag = 0.0, sum_off = 0.0, *sum;
1186:   PetscInt        i,j,k,bs = A->rmap->bs,bs2=a->bs2,k1,mbs=a->mbs,jmin,jmax,nexti,ik,*jl,*il;
1187:   PetscErrorCode  ierr;
1188:   const PetscInt  *aj=a->j,*col;

1191:   if (type == NORM_FROBENIUS) {
1192:     for (k=0; k<mbs; k++) {
1193:       jmin = a->i[k]; jmax = a->i[k+1];
1194:       col  = aj + jmin;
1195:       if (*col == k) {         /* diagonal block */
1196:         for (i=0; i<bs2; i++) {
1197:           sum_diag += PetscRealPart(PetscConj(*v)*(*v)); v++;
1198:         }
1199:         jmin++;
1200:       }
1201:       for (j=jmin; j<jmax; j++) {  /* off-diagonal blocks */
1202:         for (i=0; i<bs2; i++) {
1203:           sum_off += PetscRealPart(PetscConj(*v)*(*v)); v++;
1204:         }
1205:       }
1206:     }
1207:     *norm = PetscSqrtReal(sum_diag + 2*sum_off);
1208:     PetscLogFlops(2*bs2*a->nz);
1209:   } else if (type == NORM_INFINITY || type == NORM_1) {  /* maximum row/column sum */
1210:     PetscMalloc3(bs,&sum,mbs,&il,mbs,&jl);
1211:     for (i=0; i<mbs; i++) jl[i] = mbs;
1212:     il[0] = 0;

1214:     *norm = 0.0;
1215:     for (k=0; k<mbs; k++) { /* k_th block row */
1216:       for (j=0; j<bs; j++) sum[j]=0.0;
1217:       /*-- col sum --*/
1218:       i = jl[k]; /* first |A(i,k)| to be added */
1219:       /* jl[k]=i: first nozero element in row i for submatrix A(1:k,k:n) (active window)
1220:                   at step k */
1221:       while (i<mbs) {
1222:         nexti = jl[i];  /* next block row to be added */
1223:         ik    = il[i];  /* block index of A(i,k) in the array a */
1224:         for (j=0; j<bs; j++) {
1225:           v = a->a + ik*bs2 + j*bs;
1226:           for (k1=0; k1<bs; k1++) {
1227:             sum[j] += PetscAbsScalar(*v); v++;
1228:           }
1229:         }
1230:         /* update il, jl */
1231:         jmin = ik + 1; /* block index of array a: points to the next nonzero of A in row i */
1232:         jmax = a->i[i+1];
1233:         if (jmin < jmax) {
1234:           il[i] = jmin;
1235:           j     = a->j[jmin];
1236:           jl[i] = jl[j]; jl[j]=i;
1237:         }
1238:         i = nexti;
1239:       }
1240:       /*-- row sum --*/
1241:       jmin = a->i[k]; jmax = a->i[k+1];
1242:       for (i=jmin; i<jmax; i++) {
1243:         for (j=0; j<bs; j++) {
1244:           v = a->a + i*bs2 + j;
1245:           for (k1=0; k1<bs; k1++) {
1246:             sum[j] += PetscAbsScalar(*v); v += bs;
1247:           }
1248:         }
1249:       }
1250:       /* add k_th block row to il, jl */
1251:       col = aj+jmin;
1252:       if (*col == k) jmin++;
1253:       if (jmin < jmax) {
1254:         il[k] = jmin;
1255:         j = a->j[jmin]; jl[k] = jl[j]; jl[j] = k;
1256:       }
1257:       for (j=0; j<bs; j++) {
1258:         if (sum[j] > *norm) *norm = sum[j];
1259:       }
1260:     }
1261:     PetscFree3(sum,il,jl);
1262:     PetscLogFlops(PetscMax(mbs*a->nz-1,0));
1263:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for this norm yet");
1264:   return(0);
1265: }

1267: PetscErrorCode MatEqual_SeqSBAIJ(Mat A,Mat B,PetscBool * flg)
1268: {
1269:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)B->data;

1273:   /* If the  matrix/block dimensions are not equal, or no of nonzeros or shift */
1274:   if ((A->rmap->N != B->rmap->N) || (A->cmap->n != B->cmap->n) || (A->rmap->bs != B->rmap->bs)|| (a->nz != b->nz)) {
1275:     *flg = PETSC_FALSE;
1276:     return(0);
1277:   }

1279:   /* if the a->i are the same */
1280:   PetscMemcmp(a->i,b->i,(a->mbs+1)*sizeof(PetscInt),flg);
1281:   if (!*flg) return(0);

1283:   /* if a->j are the same */
1284:   PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);
1285:   if (!*flg) return(0);

1287:   /* if a->a are the same */
1288:   PetscMemcmp(a->a,b->a,(a->nz)*(A->rmap->bs)*(A->rmap->bs)*sizeof(PetscScalar),flg);
1289:   return(0);
1290: }

1292: PetscErrorCode MatGetDiagonal_SeqSBAIJ(Mat A,Vec v)
1293: {
1294:   Mat_SeqSBAIJ    *a = (Mat_SeqSBAIJ*)A->data;
1295:   PetscErrorCode  ierr;
1296:   PetscInt        i,j,k,row,bs,ambs,bs2;
1297:   const PetscInt  *ai,*aj;
1298:   PetscScalar     *x,zero = 0.0;
1299:   const MatScalar *aa,*aa_j;

1302:   bs = A->rmap->bs;
1303:   if (A->factortype && bs>1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix with bs>1");

1305:   aa   = a->a;
1306:   ambs = a->mbs;

1308:   if (A->factortype == MAT_FACTOR_CHOLESKY || A->factortype == MAT_FACTOR_ICC) {
1309:     PetscInt *diag=a->diag;
1310:     aa   = a->a;
1311:     ambs = a->mbs;
1312:     VecGetArray(v,&x);
1313:     for (i=0; i<ambs; i++) x[i] = 1.0/aa[diag[i]];
1314:     VecRestoreArray(v,&x);
1315:     return(0);
1316:   }

1318:   ai   = a->i;
1319:   aj   = a->j;
1320:   bs2  = a->bs2;
1321:   VecSet(v,zero);
1322:   VecGetArray(v,&x);
1323:   for (i=0; i<ambs; i++) {
1324:     j=ai[i];
1325:     if (aj[j] == i) {    /* if this is a diagonal element */
1326:       row  = i*bs;
1327:       aa_j = aa + j*bs2;
1328:       for (k=0; k<bs2; k+=(bs+1),row++) x[row] = aa_j[k];
1329:     }
1330:   }
1331:   VecRestoreArray(v,&x);
1332:   return(0);
1333: }

1335: PetscErrorCode MatDiagonalScale_SeqSBAIJ(Mat A,Vec ll,Vec rr)
1336: {
1337:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
1338:   PetscScalar       x;
1339:   const PetscScalar *l,*li,*ri;
1340:   MatScalar         *aa,*v;
1341:   PetscErrorCode    ierr;
1342:   PetscInt          i,j,k,lm,M,m,mbs,tmp,bs,bs2;
1343:   const PetscInt    *ai,*aj;
1344:   PetscBool         flg;

1347:   if (ll != rr) {
1348:     VecEqual(ll,rr,&flg);
1349:     if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"For symmetric format, left and right scaling vectors must be same\n");
1350:   }
1351:   if (!ll) return(0);
1352:   ai  = a->i;
1353:   aj  = a->j;
1354:   aa  = a->a;
1355:   m   = A->rmap->N;
1356:   bs  = A->rmap->bs;
1357:   mbs = a->mbs;
1358:   bs2 = a->bs2;

1360:   VecGetArrayRead(ll,&l);
1361:   VecGetLocalSize(ll,&lm);
1362:   if (lm != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
1363:   for (i=0; i<mbs; i++) { /* for each block row */
1364:     M  = ai[i+1] - ai[i];
1365:     li = l + i*bs;
1366:     v  = aa + bs2*ai[i];
1367:     for (j=0; j<M; j++) { /* for each block */
1368:       ri = l + bs*aj[ai[i]+j];
1369:       for (k=0; k<bs; k++) {
1370:         x = ri[k];
1371:         for (tmp=0; tmp<bs; tmp++) (*v++) *= li[tmp]*x;
1372:       }
1373:     }
1374:   }
1375:   VecRestoreArrayRead(ll,&l);
1376:   PetscLogFlops(2.0*a->nz);
1377:   return(0);
1378: }

1380: PetscErrorCode MatGetInfo_SeqSBAIJ(Mat A,MatInfoType flag,MatInfo *info)
1381: {
1382:   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data;

1385:   info->block_size   = a->bs2;
1386:   info->nz_allocated = a->bs2*a->maxnz;   /*num. of nonzeros in upper triangular part */
1387:   info->nz_used      = a->bs2*a->nz;   /*num. of nonzeros in upper triangular part */
1388:   info->nz_unneeded  = (double)(info->nz_allocated - info->nz_used);
1389:   info->assemblies   = A->num_ass;
1390:   info->mallocs      = A->info.mallocs;
1391:   info->memory       = ((PetscObject)A)->mem;
1392:   if (A->factortype) {
1393:     info->fill_ratio_given  = A->info.fill_ratio_given;
1394:     info->fill_ratio_needed = A->info.fill_ratio_needed;
1395:     info->factor_mallocs    = A->info.factor_mallocs;
1396:   } else {
1397:     info->fill_ratio_given  = 0;
1398:     info->fill_ratio_needed = 0;
1399:     info->factor_mallocs    = 0;
1400:   }
1401:   return(0);
1402: }


1405: PetscErrorCode MatZeroEntries_SeqSBAIJ(Mat A)
1406: {
1407:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data;

1411:   PetscMemzero(a->a,a->bs2*a->i[a->mbs]*sizeof(MatScalar));
1412:   return(0);
1413: }

1415: /*
1416:    This code does not work since it only checks the upper triangular part of
1417:   the matrix. Hence it is not listed in the function table.
1418: */
1419: PetscErrorCode MatGetRowMaxAbs_SeqSBAIJ(Mat A,Vec v,PetscInt idx[])
1420: {
1421:   Mat_SeqSBAIJ    *a = (Mat_SeqSBAIJ*)A->data;
1422:   PetscErrorCode  ierr;
1423:   PetscInt        i,j,n,row,col,bs,mbs;
1424:   const PetscInt  *ai,*aj;
1425:   PetscReal       atmp;
1426:   const MatScalar *aa;
1427:   PetscScalar     *x;
1428:   PetscInt        ncols,brow,bcol,krow,kcol;

1431:   if (idx) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Send email to petsc-maint@mcs.anl.gov");
1432:   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
1433:   bs  = A->rmap->bs;
1434:   aa  = a->a;
1435:   ai  = a->i;
1436:   aj  = a->j;
1437:   mbs = a->mbs;

1439:   VecSet(v,0.0);
1440:   VecGetArray(v,&x);
1441:   VecGetLocalSize(v,&n);
1442:   if (n != A->rmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
1443:   for (i=0; i<mbs; i++) {
1444:     ncols = ai[1] - ai[0]; ai++;
1445:     brow  = bs*i;
1446:     for (j=0; j<ncols; j++) {
1447:       bcol = bs*(*aj);
1448:       for (kcol=0; kcol<bs; kcol++) {
1449:         col = bcol + kcol;      /* col index */
1450:         for (krow=0; krow<bs; krow++) {
1451:           atmp = PetscAbsScalar(*aa); aa++;
1452:           row  = brow + krow;   /* row index */
1453:           if (PetscRealPart(x[row]) < atmp) x[row] = atmp;
1454:           if (*aj > i && PetscRealPart(x[col]) < atmp) x[col] = atmp;
1455:         }
1456:       }
1457:       aj++;
1458:     }
1459:   }
1460:   VecRestoreArray(v,&x);
1461:   return(0);
1462: }