Date: 2026-05-01T06:11:58+00:00

Actual source code: sbaij2.c

      1: #include <../src/mat/impls/baij/seq/baij.h>
      2: #include <../src/mat/impls/dense/seq/dense.h>
      3: #include <../src/mat/impls/sbaij/seq/sbaij.h>
      4: #include <petsc/private/kernels/blockinvert.h>
      5: #include <petscbt.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;
     11:   PetscInt        brow, i, j, k, l, mbs, n, *nidx, isz, bcol, bcol_max, start, end, *ai, *aj, bs;
     12:   const PetscInt *idx;
     13:   PetscBT         table_out, table_in;

     15:   PetscFunctionBegin;
     16:   PetscCheck(ov >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative overlap specified");
     17:   mbs = a->mbs;
     18:   ai  = a->i;
     19:   aj  = a->j;
     20:   bs  = A->rmap->bs;
     21:   PetscCall(PetscBTCreate(mbs, &table_out));
     22:   PetscCall(PetscMalloc1(mbs + 1, &nidx));
     23:   PetscCall(PetscBTCreate(mbs, &table_in));

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

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

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

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

     52:       n = isz; /* length of the updated is[i] */
     53:       for (brow = 0; brow < mbs; brow++) {
     54:         start = ai[brow];
     55:         end   = ai[brow + 1];
     56:         if (PetscBTLookup(table_in, brow)) { /* brow is on nidx - row search: collect all bcol in this brow */
     57:           for (l = start; l < end; l++) {
     58:             bcol = aj[l];
     59:             if (!PetscBTLookupSet(table_out, bcol)) {
     60:               nidx[isz++] = bcol;
     61:               if (bcol_max < bcol) bcol_max = bcol;
     62:             }
     63:           }
     64:           k++;
     65:           if (k >= n) break; /* for (brow=0; brow<mbs; brow++) */
     66:         } else {             /* brow is not on nidx - col search: add brow onto nidx if there is a bcol in nidx */
     67:           for (l = start; l < end; l++) {
     68:             bcol = aj[l];
     69:             if (bcol > bcol_max) break;
     70:             if (PetscBTLookup(table_in, bcol)) {
     71:               if (!PetscBTLookupSet(table_out, brow)) nidx[isz++] = brow;
     72:               break; /* for l = start; l<end ; l++) */
     73:             }
     74:           }
     75:         }
     76:       }
     77:     } /* for each overlap */
     78:     PetscCall(ISCreateBlock(PETSC_COMM_SELF, bs, isz, nidx, PETSC_COPY_VALUES, is + i));
     79:   } /* for each is */
     80:   PetscCall(PetscBTDestroy(&table_out));
     81:   PetscCall(PetscFree(nidx));
     82:   PetscCall(PetscBTDestroy(&table_in));
     83:   PetscFunctionReturn(PETSC_SUCCESS);
     84: }

     86: /* Bseq is non-symmetric SBAIJ matrix, only used internally by PETSc.
     87:         Zero some ops' to avoid invalid use */
     88: PetscErrorCode MatSeqSBAIJZeroOps_Private(Mat Bseq)
     89: {
     90:   PetscFunctionBegin;
     91:   PetscCall(MatSetOption(Bseq, MAT_SYMMETRIC, PETSC_FALSE));
     92:   Bseq->ops->mult                   = NULL;
     93:   Bseq->ops->multadd                = NULL;
     94:   Bseq->ops->multtranspose          = NULL;
     95:   Bseq->ops->multtransposeadd       = NULL;
     96:   Bseq->ops->lufactor               = NULL;
     97:   Bseq->ops->choleskyfactor         = NULL;
     98:   Bseq->ops->lufactorsymbolic       = NULL;
     99:   Bseq->ops->choleskyfactorsymbolic = NULL;
    100:   Bseq->ops->getinertia             = NULL;
    101:   PetscFunctionReturn(PETSC_SUCCESS);
    102: }

    104: /* same as MatCreateSubMatrices_SeqBAIJ(), except cast Mat_SeqSBAIJ */
    105: static PetscErrorCode MatCreateSubMatrix_SeqSBAIJ_Private(Mat A, IS isrow, IS iscol, MatReuse scall, Mat *B, PetscBool sym)
    106: {
    107:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ *)A->data, *c = NULL;
    108:   Mat_SeqBAIJ    *d = NULL;
    109:   PetscInt       *smap, i, k, kstart, kend, oldcols = a->nbs, *lens;
    110:   PetscInt        row, mat_i, *mat_j, tcol, *mat_ilen;
    111:   const PetscInt *irow, *icol;
    112:   PetscInt        nrows, ncols, *ssmap, bs = A->rmap->bs, bs2 = a->bs2;
    113:   PetscInt       *aj = a->j, *ai = a->i;
    114:   MatScalar      *mat_a;
    115:   Mat             C;
    116:   PetscBool       flag;

    118:   PetscFunctionBegin;
    119:   PetscCall(ISGetIndices(isrow, &irow));
    120:   PetscCall(ISGetIndices(iscol, &icol));
    121:   PetscCall(ISGetLocalSize(isrow, &nrows));
    122:   PetscCall(ISGetLocalSize(iscol, &ncols));

    124:   PetscCall(PetscCalloc1(1 + oldcols, &smap));
    125:   ssmap = smap;
    126:   PetscCall(PetscMalloc1(1 + nrows, &lens));
    127:   for (i = 0; i < ncols; i++) smap[icol[i]] = i + 1;
    128:   /* determine lens of each row */
    129:   for (i = 0; i < nrows; i++) {
    130:     kstart  = ai[irow[i]];
    131:     kend    = kstart + a->ilen[irow[i]];
    132:     lens[i] = 0;
    133:     for (k = kstart; k < kend; k++) {
    134:       if (ssmap[aj[k]]) lens[i]++;
    135:     }
    136:   }
    137:   /* Create and fill new matrix */
    138:   if (scall == MAT_REUSE_MATRIX) {
    139:     if (sym) {
    140:       c = (Mat_SeqSBAIJ *)((*B)->data);

    142:       PetscCheck(c->mbs == nrows && c->nbs == ncols && (*B)->rmap->bs == bs, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Submatrix wrong size");
    143:       PetscCall(PetscArraycmp(c->ilen, lens, c->mbs, &flag));
    144:       PetscCheck(flag, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Cannot reuse matrix. wrong number of nonzeros");
    145:       PetscCall(PetscArrayzero(c->ilen, c->mbs));
    146:     } else {
    147:       d = (Mat_SeqBAIJ *)((*B)->data);

    149:       PetscCheck(d->mbs == nrows && d->nbs == ncols && (*B)->rmap->bs == bs, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Submatrix wrong size");
    150:       PetscCall(PetscArraycmp(d->ilen, lens, d->mbs, &flag));
    151:       PetscCheck(flag, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Cannot reuse matrix. wrong number of nonzeros");
    152:       PetscCall(PetscArrayzero(d->ilen, d->mbs));
    153:     }
    154:     C = *B;
    155:   } else {
    156:     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &C));
    157:     PetscCall(MatSetSizes(C, nrows * bs, ncols * bs, PETSC_DETERMINE, PETSC_DETERMINE));
    158:     if (sym) {
    159:       PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
    160:       PetscCall(MatSeqSBAIJSetPreallocation(C, bs, 0, lens));
    161:     } else {
    162:       PetscCall(MatSetType(C, MATSEQBAIJ));
    163:       PetscCall(MatSeqBAIJSetPreallocation(C, bs, 0, lens));
    164:     }
    165:   }
    166:   if (sym) c = (Mat_SeqSBAIJ *)C->data;
    167:   else d = (Mat_SeqBAIJ *)C->data;
    168:   for (i = 0; i < nrows; i++) {
    169:     row    = irow[i];
    170:     kstart = ai[row];
    171:     kend   = kstart + a->ilen[row];
    172:     if (sym) {
    173:       mat_i    = c->i[i];
    174:       mat_j    = PetscSafePointerPlusOffset(c->j, mat_i);
    175:       mat_a    = PetscSafePointerPlusOffset(c->a, mat_i * bs2);
    176:       mat_ilen = c->ilen + i;
    177:     } else {
    178:       mat_i    = d->i[i];
    179:       mat_j    = PetscSafePointerPlusOffset(d->j, mat_i);
    180:       mat_a    = PetscSafePointerPlusOffset(d->a, mat_i * bs2);
    181:       mat_ilen = d->ilen + i;
    182:     }
    183:     for (k = kstart; k < kend; k++) {
    184:       if ((tcol = ssmap[a->j[k]])) {
    185:         *mat_j++ = tcol - 1;
    186:         PetscCall(PetscArraycpy(mat_a, a->a + k * bs2, bs2));
    187:         mat_a += bs2;
    188:         (*mat_ilen)++;
    189:       }
    190:     }
    191:   }
    192:   /* sort */
    193:   {
    194:     MatScalar *work;

    196:     PetscCall(PetscMalloc1(bs2, &work));
    197:     for (i = 0; i < nrows; i++) {
    198:       PetscInt ilen;
    199:       if (sym) {
    200:         mat_i = c->i[i];
    201:         mat_j = PetscSafePointerPlusOffset(c->j, mat_i);
    202:         mat_a = PetscSafePointerPlusOffset(c->a, mat_i * bs2);
    203:         ilen  = c->ilen[i];
    204:       } else {
    205:         mat_i = d->i[i];
    206:         mat_j = PetscSafePointerPlusOffset(d->j, mat_i);
    207:         mat_a = PetscSafePointerPlusOffset(d->a, mat_i * bs2);
    208:         ilen  = d->ilen[i];
    209:       }
    210:       PetscCall(PetscSortIntWithDataArray(ilen, mat_j, mat_a, bs2 * sizeof(MatScalar), work));
    211:     }
    212:     PetscCall(PetscFree(work));
    213:   }

    215:   /* Free work space */
    216:   PetscCall(ISRestoreIndices(iscol, &icol));
    217:   PetscCall(PetscFree(smap));
    218:   PetscCall(PetscFree(lens));
    219:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    220:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

    222:   PetscCall(ISRestoreIndices(isrow, &irow));
    223:   *B = C;
    224:   PetscFunctionReturn(PETSC_SUCCESS);
    225: }

    227: PetscErrorCode MatCreateSubMatrix_SeqSBAIJ(Mat A, IS isrow, IS iscol, MatReuse scall, Mat *B)
    228: {
    229:   Mat       C[2];
    230:   IS        is1, is2, intersect = NULL;
    231:   PetscInt  n1, n2, ni;
    232:   PetscBool sym = PETSC_TRUE;

    234:   PetscFunctionBegin;
    235:   PetscCall(ISCompressIndicesGeneral(A->rmap->N, A->rmap->n, A->rmap->bs, 1, &isrow, &is1));
    236:   if (isrow == iscol) {
    237:     is2 = is1;
    238:     PetscCall(PetscObjectReference((PetscObject)is2));
    239:   } else {
    240:     PetscCall(ISCompressIndicesGeneral(A->cmap->N, A->cmap->n, A->cmap->bs, 1, &iscol, &is2));
    241:     PetscCall(ISIntersect(is1, is2, &intersect));
    242:     PetscCall(ISGetLocalSize(intersect, &ni));
    243:     PetscCall(ISDestroy(&intersect));
    244:     if (ni == 0) sym = PETSC_FALSE;
    245:     else if (PetscDefined(USE_DEBUG)) {
    246:       PetscCall(ISGetLocalSize(is1, &n1));
    247:       PetscCall(ISGetLocalSize(is2, &n2));
    248:       PetscCheck(ni == n1 && ni == n2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot create such a submatrix");
    249:     }
    250:   }
    251:   if (sym) PetscCall(MatCreateSubMatrix_SeqSBAIJ_Private(A, is1, is2, scall, B, sym));
    252:   else {
    253:     PetscCall(MatCreateSubMatrix_SeqSBAIJ_Private(A, is1, is2, MAT_INITIAL_MATRIX, C, sym));
    254:     PetscCall(MatCreateSubMatrix_SeqSBAIJ_Private(A, is2, is1, MAT_INITIAL_MATRIX, C + 1, sym));
    255:     PetscCall(MatTranspose(C[1], MAT_INPLACE_MATRIX, C + 1));
    256:     PetscCall(MatAXPY(C[0], 1.0, C[1], DIFFERENT_NONZERO_PATTERN));
    257:     PetscCheck(scall != MAT_INPLACE_MATRIX, PETSC_COMM_SELF, PETSC_ERR_SUP, "MAT_INPLACE_MATRIX not supported");
    258:     if (scall == MAT_REUSE_MATRIX) PetscCall(MatCopy(C[0], *B, SAME_NONZERO_PATTERN));
    259:     else if (A->rmap->bs == 1) PetscCall(MatConvert(C[0], MATAIJ, MAT_INITIAL_MATRIX, B));
    260:     else PetscCall(MatCopy(C[0], *B, SAME_NONZERO_PATTERN));
    261:     PetscCall(MatDestroy(C));
    262:     PetscCall(MatDestroy(C + 1));
    263:   }
    264:   PetscCall(ISDestroy(&is1));
    265:   PetscCall(ISDestroy(&is2));

    267:   if (sym && isrow != iscol) {
    268:     PetscBool isequal;
    269:     PetscCall(ISEqual(isrow, iscol, &isequal));
    270:     if (!isequal) PetscCall(MatSeqSBAIJZeroOps_Private(*B));
    271:   }
    272:   PetscFunctionReturn(PETSC_SUCCESS);
    273: }

    275: PetscErrorCode MatCreateSubMatrices_SeqSBAIJ(Mat A, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *B[])
    276: {
    277:   PetscInt i;

    279:   PetscFunctionBegin;
    280:   if (scall == MAT_INITIAL_MATRIX) PetscCall(PetscCalloc1(n, B));

    282:   for (i = 0; i < n; i++) PetscCall(MatCreateSubMatrix_SeqSBAIJ(A, irow[i], icol[i], scall, &(*B)[i]));
    283:   PetscFunctionReturn(PETSC_SUCCESS);
    284: }

    286: /* Should check that shapes of vectors and matrices match */
    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:   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
    294:   const PetscInt    *aj = a->j, *ai = a->i, *ib;
    295:   PetscInt           nonzerorow = 0;

    297:   PetscFunctionBegin;
    298:   PetscCall(VecSet(zz, zero));
    299:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    300:   PetscCall(VecGetArrayRead(xx, &x));
    301:   PetscCall(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];
    309:     x2   = xb[1];
    310:     ib   = aj + *ai;
    311:     jmin = 0;
    312:     nonzerorow += (n > 0);
    313:     if (*ib == i) { /* (diag of A)*x */
    314:       z[2 * i] += v[0] * x1 + v[2] * x2;
    315:       z[2 * i + 1] += v[2] * x1 + v[3] * x2;
    316:       v += 4;
    317:       jmin++;
    318:     }
    319:     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    320:     PetscPrefetchBlock(v + 4 * n, 4 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    321:     for (j = jmin; j < n; j++) {
    322:       /* (strict lower triangular part of A)*x  */
    323:       cval = ib[j] * 2;
    324:       z[cval] += v[0] * x1 + v[1] * x2;
    325:       z[cval + 1] += v[2] * x1 + v[3] * x2;
    326:       /* (strict upper triangular part of A)*x  */
    327:       z[2 * i] += v[0] * x[cval] + v[2] * x[cval + 1];
    328:       z[2 * i + 1] += v[1] * x[cval] + v[3] * x[cval + 1];
    329:       v += 4;
    330:     }
    331:     xb += 2;
    332:     ai++;
    333:   }

    335:   PetscCall(VecRestoreArrayRead(xx, &x));
    336:   PetscCall(VecRestoreArray(zz, &z));
    337:   PetscCall(PetscLogFlops(8.0 * (a->nz * 2.0 - nonzerorow) - nonzerorow));
    338:   PetscFunctionReturn(PETSC_SUCCESS);
    339: }

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

    351:   PetscFunctionBegin;
    352:   PetscCall(VecSet(zz, zero));
    353:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    354:   PetscCall(VecGetArrayRead(xx, &x));
    355:   PetscCall(VecGetArray(zz, &z));

    357:   v  = a->a;
    358:   xb = x;

    360:   for (i = 0; i < mbs; i++) {
    361:     n    = ai[1] - ai[0]; /* length of i_th block row of A */
    362:     x1   = xb[0];
    363:     x2   = xb[1];
    364:     x3   = xb[2];
    365:     ib   = aj + *ai;
    366:     jmin = 0;
    367:     nonzerorow += (n > 0);
    368:     if (*ib == i) { /* (diag of A)*x */
    369:       z[3 * i] += v[0] * x1 + v[3] * x2 + v[6] * x3;
    370:       z[3 * i + 1] += v[3] * x1 + v[4] * x2 + v[7] * x3;
    371:       z[3 * i + 2] += v[6] * x1 + v[7] * x2 + v[8] * x3;
    372:       v += 9;
    373:       jmin++;
    374:     }
    375:     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    376:     PetscPrefetchBlock(v + 9 * n, 9 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    377:     for (j = jmin; j < n; j++) {
    378:       /* (strict lower triangular part of A)*x  */
    379:       cval = ib[j] * 3;
    380:       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3;
    381:       z[cval + 1] += v[3] * x1 + v[4] * x2 + v[5] * x3;
    382:       z[cval + 2] += v[6] * x1 + v[7] * x2 + v[8] * x3;
    383:       /* (strict upper triangular part of A)*x  */
    384:       z[3 * i] += v[0] * x[cval] + v[3] * x[cval + 1] + v[6] * x[cval + 2];
    385:       z[3 * i + 1] += v[1] * x[cval] + v[4] * x[cval + 1] + v[7] * x[cval + 2];
    386:       z[3 * i + 2] += v[2] * x[cval] + v[5] * x[cval + 1] + v[8] * x[cval + 2];
    387:       v += 9;
    388:     }
    389:     xb += 3;
    390:     ai++;
    391:   }

    393:   PetscCall(VecRestoreArrayRead(xx, &x));
    394:   PetscCall(VecRestoreArray(zz, &z));
    395:   PetscCall(PetscLogFlops(18.0 * (a->nz * 2.0 - nonzerorow) - nonzerorow));
    396:   PetscFunctionReturn(PETSC_SUCCESS);
    397: }

    399: PetscErrorCode MatMult_SeqSBAIJ_4(Mat A, Vec xx, Vec zz)
    400: {
    401:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    402:   PetscScalar       *z, x1, x2, x3, x4, zero = 0.0;
    403:   const PetscScalar *x, *xb;
    404:   const MatScalar   *v;
    405:   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
    406:   const PetscInt    *aj = a->j, *ai = a->i, *ib;
    407:   PetscInt           nonzerorow = 0;

    409:   PetscFunctionBegin;
    410:   PetscCall(VecSet(zz, zero));
    411:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    412:   PetscCall(VecGetArrayRead(xx, &x));
    413:   PetscCall(VecGetArray(zz, &z));

    415:   v  = a->a;
    416:   xb = x;

    418:   for (i = 0; i < mbs; i++) {
    419:     n    = ai[1] - ai[0]; /* length of i_th block row of A */
    420:     x1   = xb[0];
    421:     x2   = xb[1];
    422:     x3   = xb[2];
    423:     x4   = xb[3];
    424:     ib   = aj + *ai;
    425:     jmin = 0;
    426:     nonzerorow += (n > 0);
    427:     if (*ib == i) { /* (diag of A)*x */
    428:       z[4 * i] += v[0] * x1 + v[4] * x2 + v[8] * x3 + v[12] * x4;
    429:       z[4 * i + 1] += v[4] * x1 + v[5] * x2 + v[9] * x3 + v[13] * x4;
    430:       z[4 * i + 2] += v[8] * x1 + v[9] * x2 + v[10] * x3 + v[14] * x4;
    431:       z[4 * i + 3] += v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
    432:       v += 16;
    433:       jmin++;
    434:     }
    435:     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
    436:     PetscPrefetchBlock(v + 16 * n, 16 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    437:     for (j = jmin; j < n; j++) {
    438:       /* (strict lower triangular part of A)*x  */
    439:       cval = ib[j] * 4;
    440:       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
    441:       z[cval + 1] += v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
    442:       z[cval + 2] += v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
    443:       z[cval + 3] += v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
    444:       /* (strict upper triangular part of A)*x  */
    445:       z[4 * i] += v[0] * x[cval] + v[4] * x[cval + 1] + v[8] * x[cval + 2] + v[12] * x[cval + 3];
    446:       z[4 * i + 1] += v[1] * x[cval] + v[5] * x[cval + 1] + v[9] * x[cval + 2] + v[13] * x[cval + 3];
    447:       z[4 * i + 2] += v[2] * x[cval] + v[6] * x[cval + 1] + v[10] * x[cval + 2] + v[14] * x[cval + 3];
    448:       z[4 * i + 3] += v[3] * x[cval] + v[7] * x[cval + 1] + v[11] * x[cval + 2] + v[15] * x[cval + 3];
    449:       v += 16;
    450:     }
    451:     xb += 4;
    452:     ai++;
    453:   }

    455:   PetscCall(VecRestoreArrayRead(xx, &x));
    456:   PetscCall(VecRestoreArray(zz, &z));
    457:   PetscCall(PetscLogFlops(32.0 * (a->nz * 2.0 - nonzerorow) - nonzerorow));
    458:   PetscFunctionReturn(PETSC_SUCCESS);
    459: }

    461: PetscErrorCode MatMult_SeqSBAIJ_5(Mat A, Vec xx, Vec zz)
    462: {
    463:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    464:   PetscScalar       *z, x1, x2, x3, x4, x5, zero = 0.0;
    465:   const PetscScalar *x, *xb;
    466:   const MatScalar   *v;
    467:   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
    468:   const PetscInt    *aj = a->j, *ai = a->i, *ib;
    469:   PetscInt           nonzerorow = 0;

    471:   PetscFunctionBegin;
    472:   PetscCall(VecSet(zz, zero));
    473:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    474:   PetscCall(VecGetArrayRead(xx, &x));
    475:   PetscCall(VecGetArray(zz, &z));

    477:   v  = a->a;
    478:   xb = x;

    480:   for (i = 0; i < mbs; i++) {
    481:     n    = ai[1] - ai[0]; /* length of i_th block row of A */
    482:     x1   = xb[0];
    483:     x2   = xb[1];
    484:     x3   = xb[2];
    485:     x4   = xb[3];
    486:     x5   = xb[4];
    487:     ib   = aj + *ai;
    488:     jmin = 0;
    489:     nonzerorow += (n > 0);
    490:     if (*ib == i) { /* (diag of A)*x */
    491:       z[5 * i] += v[0] * x1 + v[5] * x2 + v[10] * x3 + v[15] * x4 + v[20] * x5;
    492:       z[5 * i + 1] += v[5] * x1 + v[6] * x2 + v[11] * x3 + v[16] * x4 + v[21] * x5;
    493:       z[5 * i + 2] += v[10] * x1 + v[11] * x2 + v[12] * x3 + v[17] * x4 + v[22] * x5;
    494:       z[5 * i + 3] += v[15] * x1 + v[16] * x2 + v[17] * x3 + v[18] * x4 + v[23] * x5;
    495:       z[5 * i + 4] += v[20] * x1 + v[21] * x2 + v[22] * x3 + v[23] * x4 + v[24] * x5;
    496:       v += 25;
    497:       jmin++;
    498:     }
    499:     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
    500:     PetscPrefetchBlock(v + 25 * n, 25 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    501:     for (j = jmin; j < n; j++) {
    502:       /* (strict lower triangular part of A)*x  */
    503:       cval = ib[j] * 5;
    504:       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5;
    505:       z[cval + 1] += v[5] * x1 + v[6] * x2 + v[7] * x3 + v[8] * x4 + v[9] * x5;
    506:       z[cval + 2] += v[10] * x1 + v[11] * x2 + v[12] * x3 + v[13] * x4 + v[14] * x5;
    507:       z[cval + 3] += v[15] * x1 + v[16] * x2 + v[17] * x3 + v[18] * x4 + v[19] * x5;
    508:       z[cval + 4] += v[20] * x1 + v[21] * x2 + v[22] * x3 + v[23] * x4 + v[24] * x5;
    509:       /* (strict upper triangular part of A)*x  */
    510:       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];
    511:       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];
    512:       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];
    513:       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];
    514:       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];
    515:       v += 25;
    516:     }
    517:     xb += 5;
    518:     ai++;
    519:   }

    521:   PetscCall(VecRestoreArrayRead(xx, &x));
    522:   PetscCall(VecRestoreArray(zz, &z));
    523:   PetscCall(PetscLogFlops(50.0 * (a->nz * 2.0 - nonzerorow) - nonzerorow));
    524:   PetscFunctionReturn(PETSC_SUCCESS);
    525: }

    527: PetscErrorCode MatMult_SeqSBAIJ_6(Mat A, Vec xx, Vec zz)
    528: {
    529:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    530:   PetscScalar       *z, x1, x2, x3, x4, x5, x6, zero = 0.0;
    531:   const PetscScalar *x, *xb;
    532:   const MatScalar   *v;
    533:   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
    534:   const PetscInt    *aj = a->j, *ai = a->i, *ib;
    535:   PetscInt           nonzerorow = 0;

    537:   PetscFunctionBegin;
    538:   PetscCall(VecSet(zz, zero));
    539:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    540:   PetscCall(VecGetArrayRead(xx, &x));
    541:   PetscCall(VecGetArray(zz, &z));

    543:   v  = a->a;
    544:   xb = x;

    546:   for (i = 0; i < mbs; i++) {
    547:     n    = ai[1] - ai[0]; /* length of i_th block row of A */
    548:     x1   = xb[0];
    549:     x2   = xb[1];
    550:     x3   = xb[2];
    551:     x4   = xb[3];
    552:     x5   = xb[4];
    553:     x6   = xb[5];
    554:     ib   = aj + *ai;
    555:     jmin = 0;
    556:     nonzerorow += (n > 0);
    557:     if (*ib == i) { /* (diag of A)*x */
    558:       z[6 * i] += v[0] * x1 + v[6] * x2 + v[12] * x3 + v[18] * x4 + v[24] * x5 + v[30] * x6;
    559:       z[6 * i + 1] += v[6] * x1 + v[7] * x2 + v[13] * x3 + v[19] * x4 + v[25] * x5 + v[31] * x6;
    560:       z[6 * i + 2] += v[12] * x1 + v[13] * x2 + v[14] * x3 + v[20] * x4 + v[26] * x5 + v[32] * x6;
    561:       z[6 * i + 3] += v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[27] * x5 + v[33] * x6;
    562:       z[6 * i + 4] += v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[34] * x6;
    563:       z[6 * i + 5] += v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
    564:       v += 36;
    565:       jmin++;
    566:     }
    567:     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
    568:     PetscPrefetchBlock(v + 36 * n, 36 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    569:     for (j = jmin; j < n; j++) {
    570:       /* (strict lower triangular part of A)*x  */
    571:       cval = ib[j] * 6;
    572:       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6;
    573:       z[cval + 1] += v[6] * x1 + v[7] * x2 + v[8] * x3 + v[9] * x4 + v[10] * x5 + v[11] * x6;
    574:       z[cval + 2] += v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4 + v[16] * x5 + v[17] * x6;
    575:       z[cval + 3] += v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[22] * x5 + v[23] * x6;
    576:       z[cval + 4] += v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[29] * x6;
    577:       z[cval + 5] += v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
    578:       /* (strict upper triangular part of A)*x  */
    579:       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];
    580:       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];
    581:       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];
    582:       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];
    583:       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];
    584:       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];
    585:       v += 36;
    586:     }
    587:     xb += 6;
    588:     ai++;
    589:   }

    591:   PetscCall(VecRestoreArrayRead(xx, &x));
    592:   PetscCall(VecRestoreArray(zz, &z));
    593:   PetscCall(PetscLogFlops(72.0 * (a->nz * 2.0 - nonzerorow) - nonzerorow));
    594:   PetscFunctionReturn(PETSC_SUCCESS);
    595: }

    597: PetscErrorCode MatMult_SeqSBAIJ_7(Mat A, Vec xx, Vec zz)
    598: {
    599:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    600:   PetscScalar       *z, x1, x2, x3, x4, x5, x6, x7, zero = 0.0;
    601:   const PetscScalar *x, *xb;
    602:   const MatScalar   *v;
    603:   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
    604:   const PetscInt    *aj = a->j, *ai = a->i, *ib;
    605:   PetscInt           nonzerorow = 0;

    607:   PetscFunctionBegin;
    608:   PetscCall(VecSet(zz, zero));
    609:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    610:   PetscCall(VecGetArrayRead(xx, &x));
    611:   PetscCall(VecGetArray(zz, &z));

    613:   v  = a->a;
    614:   xb = x;

    616:   for (i = 0; i < mbs; i++) {
    617:     n    = ai[1] - ai[0]; /* length of i_th block row of A */
    618:     x1   = xb[0];
    619:     x2   = xb[1];
    620:     x3   = xb[2];
    621:     x4   = xb[3];
    622:     x5   = xb[4];
    623:     x6   = xb[5];
    624:     x7   = xb[6];
    625:     ib   = aj + *ai;
    626:     jmin = 0;
    627:     nonzerorow += (n > 0);
    628:     if (*ib == i) { /* (diag of A)*x */
    629:       z[7 * i] += v[0] * x1 + v[7] * x2 + v[14] * x3 + v[21] * x4 + v[28] * x5 + v[35] * x6 + v[42] * x7;
    630:       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;
    631:       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;
    632:       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;
    633:       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;
    634:       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;
    635:       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;
    636:       v += 49;
    637:       jmin++;
    638:     }
    639:     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
    640:     PetscPrefetchBlock(v + 49 * n, 49 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    641:     for (j = jmin; j < n; j++) {
    642:       /* (strict lower triangular part of A)*x  */
    643:       cval = ib[j] * 7;
    644:       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6 + v[6] * x7;
    645:       z[cval + 1] += v[7] * x1 + v[8] * x2 + v[9] * x3 + v[10] * x4 + v[11] * x5 + v[12] * x6 + v[13] * x7;
    646:       z[cval + 2] += v[14] * x1 + v[15] * x2 + v[16] * x3 + v[17] * x4 + v[18] * x5 + v[19] * x6 + v[20] * x7;
    647:       z[cval + 3] += v[21] * x1 + v[22] * x2 + v[23] * x3 + v[24] * x4 + v[25] * x5 + v[26] * x6 + v[27] * x7;
    648:       z[cval + 4] += v[28] * x1 + v[29] * x2 + v[30] * x3 + v[31] * x4 + v[32] * x5 + v[33] * x6 + v[34] * x7;
    649:       z[cval + 5] += v[35] * x1 + v[36] * x2 + v[37] * x3 + v[38] * x4 + v[39] * x5 + v[40] * x6 + v[41] * x7;
    650:       z[cval + 6] += v[42] * x1 + v[43] * x2 + v[44] * x3 + v[45] * x4 + v[46] * x5 + v[47] * x6 + v[48] * x7;
    651:       /* (strict upper triangular part of A)*x  */
    652:       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];
    653:       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];
    654:       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];
    655:       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];
    656:       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];
    657:       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];
    658:       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];
    659:       v += 49;
    660:     }
    661:     xb += 7;
    662:     ai++;
    663:   }
    664:   PetscCall(VecRestoreArrayRead(xx, &x));
    665:   PetscCall(VecRestoreArray(zz, &z));
    666:   PetscCall(PetscLogFlops(98.0 * (a->nz * 2.0 - nonzerorow) - nonzerorow));
    667:   PetscFunctionReturn(PETSC_SUCCESS);
    668: }

    670: /*
    671:     This will not work with MatScalar == float because it calls the BLAS
    672: */
    673: PetscErrorCode MatMult_SeqSBAIJ_N(Mat A, Vec xx, Vec zz)
    674: {
    675:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    676:   PetscScalar       *z, *z_ptr, *zb, *work, *workt, zero = 0.0;
    677:   const PetscScalar *x, *x_ptr, *xb;
    678:   const MatScalar   *v;
    679:   PetscInt           mbs = a->mbs, i, bs = A->rmap->bs, j, n, bs2 = a->bs2, ncols, k;
    680:   const PetscInt    *idx, *aj, *ii;
    681:   PetscInt           nonzerorow = 0;

    683:   PetscFunctionBegin;
    684:   PetscCall(VecSet(zz, zero));
    685:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    686:   PetscCall(VecGetArrayRead(xx, &x));
    687:   PetscCall(VecGetArray(zz, &z));

    689:   x_ptr = x;
    690:   z_ptr = z;

    692:   aj = a->j;
    693:   v  = a->a;
    694:   ii = a->i;

    696:   if (!a->mult_work) PetscCall(PetscMalloc1(A->rmap->N + 1, &a->mult_work));
    697:   work = a->mult_work;

    699:   for (i = 0; i < mbs; i++) {
    700:     n     = ii[1] - ii[0];
    701:     ncols = n * bs;
    702:     workt = work;
    703:     idx   = aj + ii[0];
    704:     nonzerorow += (n > 0);

    706:     /* upper triangular part */
    707:     for (j = 0; j < n; j++) {
    708:       xb = x_ptr + bs * (*idx++);
    709:       for (k = 0; k < bs; k++) workt[k] = xb[k];
    710:       workt += bs;
    711:     }
    712:     /* z(i*bs:(i+1)*bs-1) += A(i,:)*x */
    713:     PetscKernel_w_gets_w_plus_Ar_times_v(bs, ncols, work, v, z);

    715:     /* strict lower triangular part */
    716:     idx = aj + ii[0];
    717:     if (n && *idx == i) {
    718:       ncols -= bs;
    719:       v += bs2;
    720:       idx++;
    721:       n--;
    722:     }

    724:     if (ncols > 0) {
    725:       workt = work;
    726:       PetscCall(PetscArrayzero(workt, ncols));
    727:       PetscKernel_w_gets_w_plus_trans_Ar_times_v(bs, ncols, x, v, workt);
    728:       for (j = 0; j < n; j++) {
    729:         zb = z_ptr + bs * (*idx++);
    730:         for (k = 0; k < bs; k++) zb[k] += workt[k];
    731:         workt += bs;
    732:       }
    733:     }
    734:     x += bs;
    735:     v += n * bs2;
    736:     z += bs;
    737:     ii++;
    738:   }

    740:   PetscCall(VecRestoreArrayRead(xx, &x));
    741:   PetscCall(VecRestoreArray(zz, &z));
    742:   PetscCall(PetscLogFlops(2.0 * (a->nz * 2.0 - nonzerorow) * bs2 - nonzerorow));
    743:   PetscFunctionReturn(PETSC_SUCCESS);
    744: }

    746: PetscErrorCode MatMultAdd_SeqSBAIJ_1(Mat A, Vec xx, Vec yy, Vec zz)
    747: {
    748:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    749:   PetscScalar       *z, x1;
    750:   const PetscScalar *x, *xb;
    751:   const MatScalar   *v;
    752:   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
    753:   const PetscInt    *aj = a->j, *ai = a->i, *ib;
    754:   PetscInt           nonzerorow = 0;
    755:   const int          aconj      = PetscDefined(USE_COMPLEX) && A->hermitian == PETSC_BOOL3_TRUE ? 1 : 0;

    757:   PetscFunctionBegin;
    758:   PetscCall(VecCopy(yy, zz));
    759:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    760:   PetscCall(VecGetArrayRead(xx, &x));
    761:   PetscCall(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 row of A */
    767:     x1   = xb[0];
    768:     ib   = aj + *ai;
    769:     jmin = 0;
    770:     nonzerorow += (n > 0);
    771:     if (n && *ib == i) { /* (diag of A)*x */
    772:       z[i] += *v++ * x[*ib++];
    773:       jmin++;
    774:     }
    775:     if (aconj) {
    776:       for (j = jmin; j < n; j++) {
    777:         cval = *ib;
    778:         z[cval] += PetscConj(*v) * x1; /* (strict lower triangular part of A)*x  */
    779:         z[i] += *v++ * x[*ib++];       /* (strict upper triangular part of A)*x  */
    780:       }
    781:     } else {
    782:       for (j = jmin; j < n; j++) {
    783:         cval = *ib;
    784:         z[cval] += *v * x1;      /* (strict lower triangular part of A)*x  */
    785:         z[i] += *v++ * x[*ib++]; /* (strict upper triangular part of A)*x  */
    786:       }
    787:     }
    788:     xb++;
    789:     ai++;
    790:   }

    792:   PetscCall(VecRestoreArrayRead(xx, &x));
    793:   PetscCall(VecRestoreArray(zz, &z));

    795:   PetscCall(PetscLogFlops(2.0 * (a->nz * 2.0 - nonzerorow)));
    796:   PetscFunctionReturn(PETSC_SUCCESS);
    797: }

    799: PetscErrorCode MatMultAdd_SeqSBAIJ_2(Mat A, Vec xx, Vec yy, Vec zz)
    800: {
    801:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    802:   PetscScalar       *z, x1, x2;
    803:   const PetscScalar *x, *xb;
    804:   const MatScalar   *v;
    805:   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
    806:   const PetscInt    *aj = a->j, *ai = a->i, *ib;
    807:   PetscInt           nonzerorow = 0;

    809:   PetscFunctionBegin;
    810:   PetscCall(VecCopy(yy, zz));
    811:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    812:   PetscCall(VecGetArrayRead(xx, &x));
    813:   PetscCall(VecGetArray(zz, &z));

    815:   v  = a->a;
    816:   xb = x;

    818:   for (i = 0; i < mbs; i++) {
    819:     n    = ai[1] - ai[0]; /* length of i_th block row of A */
    820:     x1   = xb[0];
    821:     x2   = xb[1];
    822:     ib   = aj + *ai;
    823:     jmin = 0;
    824:     nonzerorow += (n > 0);
    825:     if (n && *ib == i) { /* (diag of A)*x */
    826:       z[2 * i] += v[0] * x1 + v[2] * x2;
    827:       z[2 * i + 1] += v[2] * x1 + v[3] * x2;
    828:       v += 4;
    829:       jmin++;
    830:     }
    831:     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    832:     PetscPrefetchBlock(v + 4 * n, 4 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    833:     for (j = jmin; j < n; j++) {
    834:       /* (strict lower triangular part of A)*x  */
    835:       cval = ib[j] * 2;
    836:       z[cval] += v[0] * x1 + v[1] * x2;
    837:       z[cval + 1] += v[2] * x1 + v[3] * x2;
    838:       /* (strict upper triangular part of A)*x  */
    839:       z[2 * i] += v[0] * x[cval] + v[2] * x[cval + 1];
    840:       z[2 * i + 1] += v[1] * x[cval] + v[3] * x[cval + 1];
    841:       v += 4;
    842:     }
    843:     xb += 2;
    844:     ai++;
    845:   }
    846:   PetscCall(VecRestoreArrayRead(xx, &x));
    847:   PetscCall(VecRestoreArray(zz, &z));

    849:   PetscCall(PetscLogFlops(4.0 * (a->nz * 2.0 - nonzerorow)));
    850:   PetscFunctionReturn(PETSC_SUCCESS);
    851: }

    853: PetscErrorCode MatMultAdd_SeqSBAIJ_3(Mat A, Vec xx, Vec yy, Vec zz)
    854: {
    855:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    856:   PetscScalar       *z, x1, x2, x3;
    857:   const PetscScalar *x, *xb;
    858:   const MatScalar   *v;
    859:   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
    860:   const PetscInt    *aj = a->j, *ai = a->i, *ib;
    861:   PetscInt           nonzerorow = 0;

    863:   PetscFunctionBegin;
    864:   PetscCall(VecCopy(yy, zz));
    865:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    866:   PetscCall(VecGetArrayRead(xx, &x));
    867:   PetscCall(VecGetArray(zz, &z));

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

    872:   for (i = 0; i < mbs; i++) {
    873:     n    = ai[1] - ai[0]; /* length of i_th block row of A */
    874:     x1   = xb[0];
    875:     x2   = xb[1];
    876:     x3   = xb[2];
    877:     ib   = aj + *ai;
    878:     jmin = 0;
    879:     nonzerorow += (n > 0);
    880:     if (n && *ib == i) { /* (diag of A)*x */
    881:       z[3 * i] += v[0] * x1 + v[3] * x2 + v[6] * x3;
    882:       z[3 * i + 1] += v[3] * x1 + v[4] * x2 + v[7] * x3;
    883:       z[3 * i + 2] += v[6] * x1 + v[7] * x2 + v[8] * x3;
    884:       v += 9;
    885:       jmin++;
    886:     }
    887:     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    888:     PetscPrefetchBlock(v + 9 * n, 9 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    889:     for (j = jmin; j < n; j++) {
    890:       /* (strict lower triangular part of A)*x  */
    891:       cval = ib[j] * 3;
    892:       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3;
    893:       z[cval + 1] += v[3] * x1 + v[4] * x2 + v[5] * x3;
    894:       z[cval + 2] += v[6] * x1 + v[7] * x2 + v[8] * x3;
    895:       /* (strict upper triangular part of A)*x  */
    896:       z[3 * i] += v[0] * x[cval] + v[3] * x[cval + 1] + v[6] * x[cval + 2];
    897:       z[3 * i + 1] += v[1] * x[cval] + v[4] * x[cval + 1] + v[7] * x[cval + 2];
    898:       z[3 * i + 2] += v[2] * x[cval] + v[5] * x[cval + 1] + v[8] * x[cval + 2];
    899:       v += 9;
    900:     }
    901:     xb += 3;
    902:     ai++;
    903:   }

    905:   PetscCall(VecRestoreArrayRead(xx, &x));
    906:   PetscCall(VecRestoreArray(zz, &z));

    908:   PetscCall(PetscLogFlops(18.0 * (a->nz * 2.0 - nonzerorow)));
    909:   PetscFunctionReturn(PETSC_SUCCESS);
    910: }

    912: PetscErrorCode MatMultAdd_SeqSBAIJ_4(Mat A, Vec xx, Vec yy, Vec zz)
    913: {
    914:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    915:   PetscScalar       *z, x1, x2, x3, x4;
    916:   const PetscScalar *x, *xb;
    917:   const MatScalar   *v;
    918:   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
    919:   const PetscInt    *aj = a->j, *ai = a->i, *ib;
    920:   PetscInt           nonzerorow = 0;

    922:   PetscFunctionBegin;
    923:   PetscCall(VecCopy(yy, zz));
    924:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    925:   PetscCall(VecGetArrayRead(xx, &x));
    926:   PetscCall(VecGetArray(zz, &z));

    928:   v  = a->a;
    929:   xb = x;

    931:   for (i = 0; i < mbs; i++) {
    932:     n    = ai[1] - ai[0]; /* length of i_th block row of A */
    933:     x1   = xb[0];
    934:     x2   = xb[1];
    935:     x3   = xb[2];
    936:     x4   = xb[3];
    937:     ib   = aj + *ai;
    938:     jmin = 0;
    939:     nonzerorow += (n > 0);
    940:     if (n && *ib == i) { /* (diag of A)*x */
    941:       z[4 * i] += v[0] * x1 + v[4] * x2 + v[8] * x3 + v[12] * x4;
    942:       z[4 * i + 1] += v[4] * x1 + v[5] * x2 + v[9] * x3 + v[13] * x4;
    943:       z[4 * i + 2] += v[8] * x1 + v[9] * x2 + v[10] * x3 + v[14] * x4;
    944:       z[4 * i + 3] += v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
    945:       v += 16;
    946:       jmin++;
    947:     }
    948:     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
    949:     PetscPrefetchBlock(v + 16 * n, 16 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    950:     for (j = jmin; j < n; j++) {
    951:       /* (strict lower triangular part of A)*x  */
    952:       cval = ib[j] * 4;
    953:       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
    954:       z[cval + 1] += v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
    955:       z[cval + 2] += v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
    956:       z[cval + 3] += v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
    957:       /* (strict upper triangular part of A)*x  */
    958:       z[4 * i] += v[0] * x[cval] + v[4] * x[cval + 1] + v[8] * x[cval + 2] + v[12] * x[cval + 3];
    959:       z[4 * i + 1] += v[1] * x[cval] + v[5] * x[cval + 1] + v[9] * x[cval + 2] + v[13] * x[cval + 3];
    960:       z[4 * i + 2] += v[2] * x[cval] + v[6] * x[cval + 1] + v[10] * x[cval + 2] + v[14] * x[cval + 3];
    961:       z[4 * i + 3] += v[3] * x[cval] + v[7] * x[cval + 1] + v[11] * x[cval + 2] + v[15] * x[cval + 3];
    962:       v += 16;
    963:     }
    964:     xb += 4;
    965:     ai++;
    966:   }

    968:   PetscCall(VecRestoreArrayRead(xx, &x));
    969:   PetscCall(VecRestoreArray(zz, &z));

    971:   PetscCall(PetscLogFlops(32.0 * (a->nz * 2.0 - nonzerorow)));
    972:   PetscFunctionReturn(PETSC_SUCCESS);
    973: }

    975: PetscErrorCode MatMultAdd_SeqSBAIJ_5(Mat A, Vec xx, Vec yy, Vec zz)
    976: {
    977:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    978:   PetscScalar       *z, x1, x2, x3, x4, x5;
    979:   const PetscScalar *x, *xb;
    980:   const MatScalar   *v;
    981:   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
    982:   const PetscInt    *aj = a->j, *ai = a->i, *ib;
    983:   PetscInt           nonzerorow = 0;

    985:   PetscFunctionBegin;
    986:   PetscCall(VecCopy(yy, zz));
    987:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    988:   PetscCall(VecGetArrayRead(xx, &x));
    989:   PetscCall(VecGetArray(zz, &z));

    991:   v  = a->a;
    992:   xb = x;

    994:   for (i = 0; i < mbs; i++) {
    995:     n    = ai[1] - ai[0]; /* length of i_th block row of A */
    996:     x1   = xb[0];
    997:     x2   = xb[1];
    998:     x3   = xb[2];
    999:     x4   = xb[3];
    1000:     x5   = xb[4];
    1001:     ib   = aj + *ai;
    1002:     jmin = 0;
    1003:     nonzerorow += (n > 0);
    1004:     if (n && *ib == i) { /* (diag of A)*x */
    1005:       z[5 * i] += v[0] * x1 + v[5] * x2 + v[10] * x3 + v[15] * x4 + v[20] * x5;
    1006:       z[5 * i + 1] += v[5] * x1 + v[6] * x2 + v[11] * x3 + v[16] * x4 + v[21] * x5;
    1007:       z[5 * i + 2] += v[10] * x1 + v[11] * x2 + v[12] * x3 + v[17] * x4 + v[22] * x5;
    1008:       z[5 * i + 3] += v[15] * x1 + v[16] * x2 + v[17] * x3 + v[18] * x4 + v[23] * x5;
    1009:       z[5 * i + 4] += v[20] * x1 + v[21] * x2 + v[22] * x3 + v[23] * x4 + v[24] * x5;
    1010:       v += 25;
    1011:       jmin++;
    1012:     }
    1013:     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
    1014:     PetscPrefetchBlock(v + 25 * n, 25 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    1015:     for (j = jmin; j < n; j++) {
    1016:       /* (strict lower triangular part of A)*x  */
    1017:       cval = ib[j] * 5;
    1018:       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5;
    1019:       z[cval + 1] += v[5] * x1 + v[6] * x2 + v[7] * x3 + v[8] * x4 + v[9] * x5;
    1020:       z[cval + 2] += v[10] * x1 + v[11] * x2 + v[12] * x3 + v[13] * x4 + v[14] * x5;
    1021:       z[cval + 3] += v[15] * x1 + v[16] * x2 + v[17] * x3 + v[18] * x4 + v[19] * x5;
    1022:       z[cval + 4] += v[20] * x1 + v[21] * x2 + v[22] * x3 + v[23] * x4 + v[24] * x5;
    1023:       /* (strict upper triangular part of A)*x  */
    1024:       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];
    1025:       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];
    1026:       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];
    1027:       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];
    1028:       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];
    1029:       v += 25;
    1030:     }
    1031:     xb += 5;
    1032:     ai++;
    1033:   }

    1035:   PetscCall(VecRestoreArrayRead(xx, &x));
    1036:   PetscCall(VecRestoreArray(zz, &z));

    1038:   PetscCall(PetscLogFlops(50.0 * (a->nz * 2.0 - nonzerorow)));
    1039:   PetscFunctionReturn(PETSC_SUCCESS);
    1040: }

    1042: PetscErrorCode MatMultAdd_SeqSBAIJ_6(Mat A, Vec xx, Vec yy, Vec zz)
    1043: {
    1044:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    1045:   PetscScalar       *z, x1, x2, x3, x4, x5, x6;
    1046:   const PetscScalar *x, *xb;
    1047:   const MatScalar   *v;
    1048:   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
    1049:   const PetscInt    *aj = a->j, *ai = a->i, *ib;
    1050:   PetscInt           nonzerorow = 0;

    1052:   PetscFunctionBegin;
    1053:   PetscCall(VecCopy(yy, zz));
    1054:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    1055:   PetscCall(VecGetArrayRead(xx, &x));
    1056:   PetscCall(VecGetArray(zz, &z));

    1058:   v  = a->a;
    1059:   xb = x;

    1061:   for (i = 0; i < mbs; i++) {
    1062:     n    = ai[1] - ai[0]; /* length of i_th block row of A */
    1063:     x1   = xb[0];
    1064:     x2   = xb[1];
    1065:     x3   = xb[2];
    1066:     x4   = xb[3];
    1067:     x5   = xb[4];
    1068:     x6   = xb[5];
    1069:     ib   = aj + *ai;
    1070:     jmin = 0;
    1071:     nonzerorow += (n > 0);
    1072:     if (n && *ib == i) { /* (diag of A)*x */
    1073:       z[6 * i] += v[0] * x1 + v[6] * x2 + v[12] * x3 + v[18] * x4 + v[24] * x5 + v[30] * x6;
    1074:       z[6 * i + 1] += v[6] * x1 + v[7] * x2 + v[13] * x3 + v[19] * x4 + v[25] * x5 + v[31] * x6;
    1075:       z[6 * i + 2] += v[12] * x1 + v[13] * x2 + v[14] * x3 + v[20] * x4 + v[26] * x5 + v[32] * x6;
    1076:       z[6 * i + 3] += v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[27] * x5 + v[33] * x6;
    1077:       z[6 * i + 4] += v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[34] * x6;
    1078:       z[6 * i + 5] += v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
    1079:       v += 36;
    1080:       jmin++;
    1081:     }
    1082:     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
    1083:     PetscPrefetchBlock(v + 36 * n, 36 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    1084:     for (j = jmin; j < n; j++) {
    1085:       /* (strict lower triangular part of A)*x  */
    1086:       cval = ib[j] * 6;
    1087:       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6;
    1088:       z[cval + 1] += v[6] * x1 + v[7] * x2 + v[8] * x3 + v[9] * x4 + v[10] * x5 + v[11] * x6;
    1089:       z[cval + 2] += v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4 + v[16] * x5 + v[17] * x6;
    1090:       z[cval + 3] += v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[22] * x5 + v[23] * x6;
    1091:       z[cval + 4] += v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[29] * x6;
    1092:       z[cval + 5] += v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
    1093:       /* (strict upper triangular part of A)*x  */
    1094:       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];
    1095:       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];
    1096:       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];
    1097:       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];
    1098:       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];
    1099:       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];
    1100:       v += 36;
    1101:     }
    1102:     xb += 6;
    1103:     ai++;
    1104:   }

    1106:   PetscCall(VecRestoreArrayRead(xx, &x));
    1107:   PetscCall(VecRestoreArray(zz, &z));

    1109:   PetscCall(PetscLogFlops(72.0 * (a->nz * 2.0 - nonzerorow)));
    1110:   PetscFunctionReturn(PETSC_SUCCESS);
    1111: }

    1113: PetscErrorCode MatMultAdd_SeqSBAIJ_7(Mat A, Vec xx, Vec yy, Vec zz)
    1114: {
    1115:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    1116:   PetscScalar       *z, x1, x2, x3, x4, x5, x6, x7;
    1117:   const PetscScalar *x, *xb;
    1118:   const MatScalar   *v;
    1119:   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
    1120:   const PetscInt    *aj = a->j, *ai = a->i, *ib;
    1121:   PetscInt           nonzerorow = 0;

    1123:   PetscFunctionBegin;
    1124:   PetscCall(VecCopy(yy, zz));
    1125:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    1126:   PetscCall(VecGetArrayRead(xx, &x));
    1127:   PetscCall(VecGetArray(zz, &z));

    1129:   v  = a->a;
    1130:   xb = x;

    1132:   for (i = 0; i < mbs; i++) {
    1133:     n    = ai[1] - ai[0]; /* length of i_th block row of A */
    1134:     x1   = xb[0];
    1135:     x2   = xb[1];
    1136:     x3   = xb[2];
    1137:     x4   = xb[3];
    1138:     x5   = xb[4];
    1139:     x6   = xb[5];
    1140:     x7   = xb[6];
    1141:     ib   = aj + *ai;
    1142:     jmin = 0;
    1143:     nonzerorow += (n > 0);
    1144:     if (n && *ib == i) { /* (diag of A)*x */
    1145:       z[7 * i] += v[0] * x1 + v[7] * x2 + v[14] * x3 + v[21] * x4 + v[28] * x5 + v[35] * x6 + v[42] * x7;
    1146:       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;
    1147:       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;
    1148:       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;
    1149:       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;
    1150:       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;
    1151:       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;
    1152:       v += 49;
    1153:       jmin++;
    1154:     }
    1155:     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
    1156:     PetscPrefetchBlock(v + 49 * n, 49 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    1157:     for (j = jmin; j < n; j++) {
    1158:       /* (strict lower triangular part of A)*x  */
    1159:       cval = ib[j] * 7;
    1160:       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6 + v[6] * x7;
    1161:       z[cval + 1] += v[7] * x1 + v[8] * x2 + v[9] * x3 + v[10] * x4 + v[11] * x5 + v[12] * x6 + v[13] * x7;
    1162:       z[cval + 2] += v[14] * x1 + v[15] * x2 + v[16] * x3 + v[17] * x4 + v[18] * x5 + v[19] * x6 + v[20] * x7;
    1163:       z[cval + 3] += v[21] * x1 + v[22] * x2 + v[23] * x3 + v[24] * x4 + v[25] * x5 + v[26] * x6 + v[27] * x7;
    1164:       z[cval + 4] += v[28] * x1 + v[29] * x2 + v[30] * x3 + v[31] * x4 + v[32] * x5 + v[33] * x6 + v[34] * x7;
    1165:       z[cval + 5] += v[35] * x1 + v[36] * x2 + v[37] * x3 + v[38] * x4 + v[39] * x5 + v[40] * x6 + v[41] * x7;
    1166:       z[cval + 6] += v[42] * x1 + v[43] * x2 + v[44] * x3 + v[45] * x4 + v[46] * x5 + v[47] * x6 + v[48] * x7;
    1167:       /* (strict upper triangular part of A)*x  */
    1168:       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];
    1169:       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];
    1170:       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];
    1171:       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];
    1172:       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];
    1173:       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];
    1174:       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];
    1175:       v += 49;
    1176:     }
    1177:     xb += 7;
    1178:     ai++;
    1179:   }

    1181:   PetscCall(VecRestoreArrayRead(xx, &x));
    1182:   PetscCall(VecRestoreArray(zz, &z));

    1184:   PetscCall(PetscLogFlops(98.0 * (a->nz * 2.0 - nonzerorow)));
    1185:   PetscFunctionReturn(PETSC_SUCCESS);
    1186: }

    1188: PetscErrorCode MatMultAdd_SeqSBAIJ_N(Mat A, Vec xx, Vec yy, Vec zz)
    1189: {
    1190:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    1191:   PetscScalar       *z, *z_ptr = NULL, *zb, *work, *workt;
    1192:   const PetscScalar *x, *x_ptr, *xb;
    1193:   const MatScalar   *v;
    1194:   PetscInt           mbs = a->mbs, i, bs = A->rmap->bs, j, n, bs2 = a->bs2, ncols, k;
    1195:   const PetscInt    *idx, *aj, *ii;
    1196:   PetscInt           nonzerorow = 0;

    1198:   PetscFunctionBegin;
    1199:   PetscCall(VecCopy(yy, zz));
    1200:   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
    1201:   PetscCall(VecGetArrayRead(xx, &x));
    1202:   x_ptr = x;
    1203:   PetscCall(VecGetArray(zz, &z));
    1204:   z_ptr = z;

    1206:   aj = a->j;
    1207:   v  = a->a;
    1208:   ii = a->i;

    1210:   if (!a->mult_work) PetscCall(PetscMalloc1(A->rmap->n + 1, &a->mult_work));
    1211:   work = a->mult_work;

    1213:   for (i = 0; i < mbs; i++) {
    1214:     n     = ii[1] - ii[0];
    1215:     ncols = n * bs;
    1216:     workt = work;
    1217:     idx   = aj + ii[0];
    1218:     nonzerorow += (n > 0);

    1220:     /* upper triangular part */
    1221:     for (j = 0; j < n; j++) {
    1222:       xb = x_ptr + bs * (*idx++);
    1223:       for (k = 0; k < bs; k++) workt[k] = xb[k];
    1224:       workt += bs;
    1225:     }
    1226:     /* z(i*bs:(i+1)*bs-1) += A(i,:)*x */
    1227:     PetscKernel_w_gets_w_plus_Ar_times_v(bs, ncols, work, v, z);

    1229:     /* strict lower triangular part */
    1230:     idx = aj + ii[0];
    1231:     if (n && *idx == i) {
    1232:       ncols -= bs;
    1233:       v += bs2;
    1234:       idx++;
    1235:       n--;
    1236:     }
    1237:     if (ncols > 0) {
    1238:       workt = work;
    1239:       PetscCall(PetscArrayzero(workt, ncols));
    1240:       PetscKernel_w_gets_w_plus_trans_Ar_times_v(bs, ncols, x, v, workt);
    1241:       for (j = 0; j < n; j++) {
    1242:         zb = z_ptr + bs * (*idx++);
    1243:         for (k = 0; k < bs; k++) zb[k] += workt[k];
    1244:         workt += bs;
    1245:       }
    1246:     }

    1248:     x += bs;
    1249:     v += n * bs2;
    1250:     z += bs;
    1251:     ii++;
    1252:   }

    1254:   PetscCall(VecRestoreArrayRead(xx, &x));
    1255:   PetscCall(VecRestoreArray(zz, &z));

    1257:   PetscCall(PetscLogFlops(2.0 * (a->nz * 2.0 - nonzerorow)));
    1258:   PetscFunctionReturn(PETSC_SUCCESS);
    1259: }

    1261: PetscErrorCode MatScale_SeqSBAIJ(Mat inA, PetscScalar alpha)
    1262: {
    1263:   Mat_SeqSBAIJ *a      = (Mat_SeqSBAIJ *)inA->data;
    1264:   PetscScalar   oalpha = alpha;
    1265:   PetscBLASInt  one    = 1, totalnz;

    1267:   PetscFunctionBegin;
    1268:   PetscCall(PetscBLASIntCast(a->bs2 * a->nz, &totalnz));
    1269:   PetscCallBLAS("BLASscal", BLASscal_(&totalnz, &oalpha, a->a, &one));
    1270:   PetscCall(PetscLogFlops(totalnz));
    1271:   PetscFunctionReturn(PETSC_SUCCESS);
    1272: }

    1274: PetscErrorCode MatNorm_SeqSBAIJ(Mat A, NormType type, PetscReal *norm)
    1275: {
    1276:   Mat_SeqSBAIJ    *a        = (Mat_SeqSBAIJ *)A->data;
    1277:   const MatScalar *v        = a->a;
    1278:   PetscReal        sum_diag = 0.0, sum_off = 0.0, *sum;
    1279:   PetscInt         i, j, k, bs = A->rmap->bs, bs2 = a->bs2, k1, mbs = a->mbs, jmin, jmax, nexti, ik, *jl, *il;
    1280:   const PetscInt  *aj = a->j, *col;

    1282:   PetscFunctionBegin;
    1283:   if (!a->nz) {
    1284:     *norm = 0.0;
    1285:     PetscFunctionReturn(PETSC_SUCCESS);
    1286:   }
    1287:   if (type == NORM_FROBENIUS) {
    1288:     for (k = 0; k < mbs; k++) {
    1289:       jmin = a->i[k];
    1290:       jmax = a->i[k + 1];
    1291:       col  = aj + jmin;
    1292:       if (jmax - jmin > 0 && *col == k) { /* diagonal block */
    1293:         for (i = 0; i < bs2; i++) {
    1294:           sum_diag += PetscRealPart(PetscConj(*v) * (*v));
    1295:           v++;
    1296:         }
    1297:         jmin++;
    1298:       }
    1299:       for (j = jmin; j < jmax; j++) { /* off-diagonal blocks */
    1300:         for (i = 0; i < bs2; i++) {
    1301:           sum_off += PetscRealPart(PetscConj(*v) * (*v));
    1302:           v++;
    1303:         }
    1304:       }
    1305:     }
    1306:     *norm = PetscSqrtReal(sum_diag + 2 * sum_off);
    1307:     PetscCall(PetscLogFlops(2.0 * bs2 * a->nz));
    1308:   } else if (type == NORM_INFINITY || type == NORM_1) { /* maximum row/column sum */
    1309:     PetscCall(PetscMalloc3(bs, &sum, mbs, &il, mbs, &jl));
    1310:     for (i = 0; i < mbs; i++) jl[i] = mbs;
    1311:     il[0] = 0;

    1313:     *norm = 0.0;
    1314:     for (k = 0; k < mbs; k++) { /* k_th block row */
    1315:       for (j = 0; j < bs; j++) sum[j] = 0.0;
    1316:       /*-- col sum --*/
    1317:       i = jl[k]; /* first |A(i,k)| to be added */
    1318:       /* jl[k]=i: first nonzero element in row i for submatrix A(1:k,k:n) (active window)
    1319:                   at step k */
    1320:       while (i < mbs) {
    1321:         nexti = jl[i]; /* next block row to be added */
    1322:         ik    = il[i]; /* block index of A(i,k) in the array a */
    1323:         for (j = 0; j < bs; j++) {
    1324:           v = a->a + ik * bs2 + j * bs;
    1325:           for (k1 = 0; k1 < bs; k1++) {
    1326:             sum[j] += PetscAbsScalar(*v);
    1327:             v++;
    1328:           }
    1329:         }
    1330:         /* update il, jl */
    1331:         jmin = ik + 1; /* block index of array a: points to the next nonzero of A in row i */
    1332:         jmax = a->i[i + 1];
    1333:         if (jmin < jmax) {
    1334:           il[i] = jmin;
    1335:           j     = a->j[jmin];
    1336:           jl[i] = jl[j];
    1337:           jl[j] = i;
    1338:         }
    1339:         i = nexti;
    1340:       }
    1341:       /*-- row sum --*/
    1342:       jmin = a->i[k];
    1343:       jmax = a->i[k + 1];
    1344:       for (i = jmin; i < jmax; i++) {
    1345:         for (j = 0; j < bs; j++) {
    1346:           v = a->a + i * bs2 + j;
    1347:           for (k1 = 0; k1 < bs; k1++) {
    1348:             sum[j] += PetscAbsScalar(*v);
    1349:             v += bs;
    1350:           }
    1351:         }
    1352:       }
    1353:       /* add k_th block row to il, jl */
    1354:       col = aj + jmin;
    1355:       if (jmax - jmin > 0 && *col == k) jmin++;
    1356:       if (jmin < jmax) {
    1357:         il[k] = jmin;
    1358:         j     = a->j[jmin];
    1359:         jl[k] = jl[j];
    1360:         jl[j] = k;
    1361:       }
    1362:       for (j = 0; j < bs; j++) {
    1363:         if (sum[j] > *norm) *norm = sum[j];
    1364:       }
    1365:     }
    1366:     PetscCall(PetscFree3(sum, il, jl));
    1367:     PetscCall(PetscLogFlops(PetscMax(mbs * a->nz - 1, 0)));
    1368:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for this norm yet");
    1369:   PetscFunctionReturn(PETSC_SUCCESS);
    1370: }

    1372: PetscErrorCode MatEqual_SeqSBAIJ(Mat A, Mat B, PetscBool *flg)
    1373: {
    1374:   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)B->data;

    1376:   PetscFunctionBegin;
    1377:   /* If the  matrix/block dimensions are not equal, or no of nonzeros or shift */
    1378:   if ((A->rmap->N != B->rmap->N) || (A->cmap->n != B->cmap->n) || (A->rmap->bs != B->rmap->bs) || (a->nz != b->nz)) {
    1379:     *flg = PETSC_FALSE;
    1380:     PetscFunctionReturn(PETSC_SUCCESS);
    1381:   }

    1383:   /* if the a->i are the same */
    1384:   PetscCall(PetscArraycmp(a->i, b->i, a->mbs + 1, flg));
    1385:   if (!*flg) PetscFunctionReturn(PETSC_SUCCESS);

    1387:   /* if a->j are the same */
    1388:   PetscCall(PetscArraycmp(a->j, b->j, a->nz, flg));
    1389:   if (!*flg) PetscFunctionReturn(PETSC_SUCCESS);

    1391:   /* if a->a are the same */
    1392:   PetscCall(PetscArraycmp(a->a, b->a, a->nz * A->rmap->bs * A->rmap->bs, flg));
    1393:   PetscFunctionReturn(PETSC_SUCCESS);
    1394: }

    1396: PetscErrorCode MatGetDiagonal_SeqSBAIJ(Mat A, Vec v)
    1397: {
    1398:   Mat_SeqSBAIJ    *a = (Mat_SeqSBAIJ *)A->data;
    1399:   PetscInt         n;
    1400:   const PetscInt   bs = A->rmap->bs, ambs = a->mbs, bs2 = a->bs2;
    1401:   PetscScalar     *x;
    1402:   const MatScalar *aa = a->a, *aa_j;
    1403:   const PetscInt  *ai = a->i, *adiag;
    1404:   PetscBool        diagDense;

    1406:   PetscFunctionBegin;
    1407:   PetscCheck(!A->factortype || bs <= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix with bs>1");
    1408:   PetscCall(MatGetDiagonalMarkers_SeqSBAIJ(A, &adiag, &diagDense));
    1409:   if (A->factortype == MAT_FACTOR_CHOLESKY || A->factortype == MAT_FACTOR_ICC) {
    1410:     PetscCall(VecGetArrayWrite(v, &x));
    1411:     for (PetscInt i = 0; i < ambs; i++) x[i] = 1.0 / aa[adiag[i]];
    1412:     PetscCall(VecRestoreArrayWrite(v, &x));
    1413:     PetscFunctionReturn(PETSC_SUCCESS);
    1414:   }

    1416:   PetscCall(VecGetLocalSize(v, &n));
    1417:   PetscCheck(n == A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
    1418:   PetscCall(VecGetArrayWrite(v, &x));

    1420:   if (diagDense) {
    1421:     for (PetscInt i = 0, row = 0; i < ambs; i++) {
    1422:       aa_j = aa + adiag[i] * bs2;
    1423:       for (PetscInt k = 0; k < bs2; k += (bs + 1)) x[row++] = aa_j[k];
    1424:     }
    1425:   } else {
    1426:     for (PetscInt i = 0, row = 0; i < ambs; i++) {
    1427:       const PetscInt j = adiag[i];

    1429:       if (j != ai[i + 1]) {
    1430:         aa_j = aa + j * bs2;
    1431:         for (PetscInt k = 0; k < bs2; k += (bs + 1)) x[row++] = aa_j[k];
    1432:       } else {
    1433:         for (PetscInt k = 0; k < bs; k++) x[row++] = 0.0;
    1434:       }
    1435:     }
    1436:   }
    1437:   PetscCall(VecRestoreArrayWrite(v, &x));
    1438:   PetscFunctionReturn(PETSC_SUCCESS);
    1439: }

    1441: PetscErrorCode MatDiagonalScale_SeqSBAIJ(Mat A, Vec ll, Vec rr)
    1442: {
    1443:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    1444:   PetscScalar        x;
    1445:   const PetscScalar *l, *li, *ri;
    1446:   MatScalar         *aa, *v;
    1447:   PetscInt           i, j, k, lm, M, m, mbs, tmp, bs, bs2;
    1448:   const PetscInt    *ai, *aj;

    1450:   PetscFunctionBegin;
    1451:   if (!ll) PetscFunctionReturn(PETSC_SUCCESS);
    1452:   ai  = a->i;
    1453:   aj  = a->j;
    1454:   aa  = a->a;
    1455:   m   = A->rmap->N;
    1456:   bs  = A->rmap->bs;
    1457:   mbs = a->mbs;
    1458:   bs2 = a->bs2;

    1460:   PetscCall(VecGetArrayRead(ll, &l));
    1461:   PetscCall(VecGetLocalSize(ll, &lm));
    1462:   PetscCheck(lm == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Left scaling vector wrong length");
    1463:   for (i = 0; i < mbs; i++) { /* for each block row */
    1464:     M  = ai[i + 1] - ai[i];
    1465:     li = l + i * bs;
    1466:     v  = aa + bs2 * ai[i];
    1467:     for (j = 0; j < M; j++) { /* for each block */
    1468:       ri = l + bs * aj[ai[i] + j];
    1469:       for (k = 0; k < bs; k++) {
    1470:         x = ri[k];
    1471:         for (tmp = 0; tmp < bs; tmp++) (*v++) *= li[tmp] * x;
    1472:       }
    1473:     }
    1474:   }
    1475:   PetscCall(VecRestoreArrayRead(ll, &l));
    1476:   PetscCall(PetscLogFlops(2.0 * a->nz));
    1477:   PetscFunctionReturn(PETSC_SUCCESS);
    1478: }

    1480: PetscErrorCode MatGetInfo_SeqSBAIJ(Mat A, MatInfoType flag, MatInfo *info)
    1481: {
    1482:   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data;

    1484:   PetscFunctionBegin;
    1485:   info->block_size   = a->bs2;
    1486:   info->nz_allocated = a->bs2 * a->maxnz; /*num. of nonzeros in upper triangular part */
    1487:   info->nz_used      = a->bs2 * a->nz;    /*num. of nonzeros in upper triangular part */
    1488:   info->nz_unneeded  = info->nz_allocated - info->nz_used;
    1489:   info->assemblies   = A->num_ass;
    1490:   info->mallocs      = A->info.mallocs;
    1491:   info->memory       = 0; /* REVIEW ME */
    1492:   if (A->factortype) {
    1493:     info->fill_ratio_given  = A->info.fill_ratio_given;
    1494:     info->fill_ratio_needed = A->info.fill_ratio_needed;
    1495:     info->factor_mallocs    = A->info.factor_mallocs;
    1496:   } else {
    1497:     info->fill_ratio_given  = 0;
    1498:     info->fill_ratio_needed = 0;
    1499:     info->factor_mallocs    = 0;
    1500:   }
    1501:   PetscFunctionReturn(PETSC_SUCCESS);
    1502: }

    1504: PetscErrorCode MatZeroEntries_SeqSBAIJ(Mat A)
    1505: {
    1506:   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data;

    1508:   PetscFunctionBegin;
    1509:   PetscCall(PetscArrayzero(a->a, a->bs2 * a->i[a->mbs]));
    1510:   PetscFunctionReturn(PETSC_SUCCESS);
    1511: }

    1513: PetscErrorCode MatGetRowMaxAbs_SeqSBAIJ(Mat A, Vec v, PetscInt idx[])
    1514: {
    1515:   Mat_SeqSBAIJ    *a = (Mat_SeqSBAIJ *)A->data;
    1516:   PetscInt         i, j, n, row, col, bs, mbs;
    1517:   const PetscInt  *ai, *aj;
    1518:   PetscReal        atmp;
    1519:   const MatScalar *aa;
    1520:   PetscScalar     *x;
    1521:   PetscInt         ncols, brow, bcol, krow, kcol;

    1523:   PetscFunctionBegin;
    1524:   PetscCheck(!idx, PETSC_COMM_SELF, PETSC_ERR_SUP, "Send email to petsc-maint@mcs.anl.gov");
    1525:   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    1526:   bs  = A->rmap->bs;
    1527:   aa  = a->a;
    1528:   ai  = a->i;
    1529:   aj  = a->j;
    1530:   mbs = a->mbs;

    1532:   PetscCall(VecSet(v, 0.0));
    1533:   PetscCall(VecGetArray(v, &x));
    1534:   PetscCall(VecGetLocalSize(v, &n));
    1535:   PetscCheck(n == A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
    1536:   for (i = 0; i < mbs; i++) {
    1537:     ncols = ai[1] - ai[0];
    1538:     ai++;
    1539:     brow = bs * i;
    1540:     for (j = 0; j < ncols; j++) {
    1541:       bcol = bs * (*aj);
    1542:       for (kcol = 0; kcol < bs; kcol++) {
    1543:         col = bcol + kcol; /* col index */
    1544:         for (krow = 0; krow < bs; krow++) {
    1545:           atmp = PetscAbsScalar(*aa);
    1546:           aa++;
    1547:           row = brow + krow; /* row index */
    1548:           if (PetscRealPart(x[row]) < atmp) x[row] = atmp;
    1549:           if (*aj > i && PetscRealPart(x[col]) < atmp) x[col] = atmp;
    1550:         }
    1551:       }
    1552:       aj++;
    1553:     }
    1554:   }
    1555:   PetscCall(VecRestoreArray(v, &x));
    1556:   PetscFunctionReturn(PETSC_SUCCESS);
    1557: }

    1559: PetscErrorCode MatMatMultSymbolic_SeqSBAIJ_SeqDense(Mat A, Mat B, PetscReal fill, Mat C)
    1560: {
    1561:   PetscFunctionBegin;
    1562:   PetscCall(MatMatMultSymbolic_SeqDense_SeqDense(A, B, 0.0, C));
    1563:   C->ops->matmultnumeric = MatMatMultNumeric_SeqSBAIJ_SeqDense;
    1564:   PetscFunctionReturn(PETSC_SUCCESS);
    1565: }

    1567: static PetscErrorCode MatMatMult_SeqSBAIJ_1_Private(Mat A, PetscScalar *b, PetscInt bm, PetscScalar *c, PetscInt cm, PetscInt cn)
    1568: {
    1569:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    1570:   PetscScalar       *z = c;
    1571:   const PetscScalar *xb;
    1572:   PetscScalar        x1;
    1573:   const MatScalar   *v   = a->a, *vv;
    1574:   PetscInt           mbs = a->mbs, i, *idx = a->j, *ii = a->i, j, *jj, n, k;
    1575:   const int          aconj = PetscDefined(USE_COMPLEX) && A->hermitian == PETSC_BOOL3_TRUE ? 1 : 0;

    1577:   PetscFunctionBegin;
    1578:   for (i = 0; i < mbs; i++) {
    1579:     n = ii[1] - ii[0];
    1580:     ii++;
    1581:     PetscPrefetchBlock(idx + n, n, 0, PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    1582:     PetscPrefetchBlock(v + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Entries for the next row */
    1583:     jj = idx;
    1584:     vv = v;
    1585:     for (k = 0; k < cn; k++) {
    1586:       idx = jj;
    1587:       v   = vv;
    1588:       for (j = 0; j < n; j++) {
    1589:         xb = b + (*idx);
    1590:         x1 = xb[0 + k * bm];
    1591:         z[0 + k * cm] += v[0] * x1;
    1592:         if (*idx != i) c[(*idx) + k * cm] += (aconj ? PetscConj(v[0]) : v[0]) * b[i + k * bm];
    1593:         v += 1;
    1594:         ++idx;
    1595:       }
    1596:     }
    1597:     z += 1;
    1598:   }
    1599:   PetscFunctionReturn(PETSC_SUCCESS);
    1600: }

    1602: static PetscErrorCode MatMatMult_SeqSBAIJ_2_Private(Mat A, PetscScalar *b, PetscInt bm, PetscScalar *c, PetscInt cm, PetscInt cn)
    1603: {
    1604:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    1605:   PetscScalar       *z = c;
    1606:   const PetscScalar *xb;
    1607:   PetscScalar        x1, x2;
    1608:   const MatScalar   *v   = a->a, *vv;
    1609:   PetscInt           mbs = a->mbs, i, *idx = a->j, *ii = a->i, j, *jj, n, k;

    1611:   PetscFunctionBegin;
    1612:   for (i = 0; i < mbs; i++) {
    1613:     n = ii[1] - ii[0];
    1614:     ii++;
    1615:     PetscPrefetchBlock(idx + n, n, 0, PETSC_PREFETCH_HINT_NTA);       /* Indices for the next row (assumes same size as this one) */
    1616:     PetscPrefetchBlock(v + 4 * n, 4 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    1617:     jj = idx;
    1618:     vv = v;
    1619:     for (k = 0; k < cn; k++) {
    1620:       idx = jj;
    1621:       v   = vv;
    1622:       for (j = 0; j < n; j++) {
    1623:         xb = b + 2 * (*idx);
    1624:         x1 = xb[0 + k * bm];
    1625:         x2 = xb[1 + k * bm];
    1626:         z[0 + k * cm] += v[0] * x1 + v[2] * x2;
    1627:         z[1 + k * cm] += v[1] * x1 + v[3] * x2;
    1628:         if (*idx != i) {
    1629:           c[2 * (*idx) + 0 + k * cm] += v[0] * b[2 * i + k * bm] + v[1] * b[2 * i + 1 + k * bm];
    1630:           c[2 * (*idx) + 1 + k * cm] += v[2] * b[2 * i + k * bm] + v[3] * b[2 * i + 1 + k * bm];
    1631:         }
    1632:         v += 4;
    1633:         ++idx;
    1634:       }
    1635:     }
    1636:     z += 2;
    1637:   }
    1638:   PetscFunctionReturn(PETSC_SUCCESS);
    1639: }

    1641: static PetscErrorCode MatMatMult_SeqSBAIJ_3_Private(Mat A, PetscScalar *b, PetscInt bm, PetscScalar *c, PetscInt cm, PetscInt cn)
    1642: {
    1643:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    1644:   PetscScalar       *z = c;
    1645:   const PetscScalar *xb;
    1646:   PetscScalar        x1, x2, x3;
    1647:   const MatScalar   *v   = a->a, *vv;
    1648:   PetscInt           mbs = a->mbs, i, *idx = a->j, *ii = a->i, j, *jj, n, k;

    1650:   PetscFunctionBegin;
    1651:   for (i = 0; i < mbs; i++) {
    1652:     n = ii[1] - ii[0];
    1653:     ii++;
    1654:     PetscPrefetchBlock(idx + n, n, 0, PETSC_PREFETCH_HINT_NTA);       /* Indices for the next row (assumes same size as this one) */
    1655:     PetscPrefetchBlock(v + 9 * n, 9 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    1656:     jj = idx;
    1657:     vv = v;
    1658:     for (k = 0; k < cn; k++) {
    1659:       idx = jj;
    1660:       v   = vv;
    1661:       for (j = 0; j < n; j++) {
    1662:         xb = b + 3 * (*idx);
    1663:         x1 = xb[0 + k * bm];
    1664:         x2 = xb[1 + k * bm];
    1665:         x3 = xb[2 + k * bm];
    1666:         z[0 + k * cm] += v[0] * x1 + v[3] * x2 + v[6] * x3;
    1667:         z[1 + k * cm] += v[1] * x1 + v[4] * x2 + v[7] * x3;
    1668:         z[2 + k * cm] += v[2] * x1 + v[5] * x2 + v[8] * x3;
    1669:         if (*idx != i) {
    1670:           c[3 * (*idx) + 0 + k * cm] += v[0] * b[3 * i + k * bm] + v[3] * b[3 * i + 1 + k * bm] + v[6] * b[3 * i + 2 + k * bm];
    1671:           c[3 * (*idx) + 1 + k * cm] += v[1] * b[3 * i + k * bm] + v[4] * b[3 * i + 1 + k * bm] + v[7] * b[3 * i + 2 + k * bm];
    1672:           c[3 * (*idx) + 2 + k * cm] += v[2] * b[3 * i + k * bm] + v[5] * b[3 * i + 1 + k * bm] + v[8] * b[3 * i + 2 + k * bm];
    1673:         }
    1674:         v += 9;
    1675:         ++idx;
    1676:       }
    1677:     }
    1678:     z += 3;
    1679:   }
    1680:   PetscFunctionReturn(PETSC_SUCCESS);
    1681: }

    1683: static PetscErrorCode MatMatMult_SeqSBAIJ_4_Private(Mat A, PetscScalar *b, PetscInt bm, PetscScalar *c, PetscInt cm, PetscInt cn)
    1684: {
    1685:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    1686:   PetscScalar       *z = c;
    1687:   const PetscScalar *xb;
    1688:   PetscScalar        x1, x2, x3, x4;
    1689:   const MatScalar   *v   = a->a, *vv;
    1690:   PetscInt           mbs = a->mbs, i, *idx = a->j, *ii = a->i, j, *jj, n, k;

    1692:   PetscFunctionBegin;
    1693:   for (i = 0; i < mbs; i++) {
    1694:     n = ii[1] - ii[0];
    1695:     ii++;
    1696:     PetscPrefetchBlock(idx + n, n, 0, PETSC_PREFETCH_HINT_NTA);         /* Indices for the next row (assumes same size as this one) */
    1697:     PetscPrefetchBlock(v + 16 * n, 16 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    1698:     jj = idx;
    1699:     vv = v;
    1700:     for (k = 0; k < cn; k++) {
    1701:       idx = jj;
    1702:       v   = vv;
    1703:       for (j = 0; j < n; j++) {
    1704:         xb = b + 4 * (*idx);
    1705:         x1 = xb[0 + k * bm];
    1706:         x2 = xb[1 + k * bm];
    1707:         x3 = xb[2 + k * bm];
    1708:         x4 = xb[3 + k * bm];
    1709:         z[0 + k * cm] += v[0] * x1 + v[4] * x2 + v[8] * x3 + v[12] * x4;
    1710:         z[1 + k * cm] += v[1] * x1 + v[5] * x2 + v[9] * x3 + v[13] * x4;
    1711:         z[2 + k * cm] += v[2] * x1 + v[6] * x2 + v[10] * x3 + v[14] * x4;
    1712:         z[3 + k * cm] += v[3] * x1 + v[7] * x2 + v[11] * x3 + v[15] * x4;
    1713:         if (*idx != i) {
    1714:           c[4 * (*idx) + 0 + k * cm] += v[0] * b[4 * i + k * bm] + v[4] * b[4 * i + 1 + k * bm] + v[8] * b[4 * i + 2 + k * bm] + v[12] * b[4 * i + 3 + k * bm];
    1715:           c[4 * (*idx) + 1 + k * cm] += v[1] * b[4 * i + k * bm] + v[5] * b[4 * i + 1 + k * bm] + v[9] * b[4 * i + 2 + k * bm] + v[13] * b[4 * i + 3 + k * bm];
    1716:           c[4 * (*idx) + 2 + k * cm] += v[2] * b[4 * i + k * bm] + v[6] * b[4 * i + 1 + k * bm] + v[10] * b[4 * i + 2 + k * bm] + v[14] * b[4 * i + 3 + k * bm];
    1717:           c[4 * (*idx) + 3 + k * cm] += v[3] * b[4 * i + k * bm] + v[7] * b[4 * i + 1 + k * bm] + v[11] * b[4 * i + 2 + k * bm] + v[15] * b[4 * i + 3 + k * bm];
    1718:         }
    1719:         v += 16;
    1720:         ++idx;
    1721:       }
    1722:     }
    1723:     z += 4;
    1724:   }
    1725:   PetscFunctionReturn(PETSC_SUCCESS);
    1726: }

    1728: static PetscErrorCode MatMatMult_SeqSBAIJ_5_Private(Mat A, PetscScalar *b, PetscInt bm, PetscScalar *c, PetscInt cm, PetscInt cn)
    1729: {
    1730:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
    1731:   PetscScalar       *z = c;
    1732:   const PetscScalar *xb;
    1733:   PetscScalar        x1, x2, x3, x4, x5;
    1734:   const MatScalar   *v   = a->a, *vv;
    1735:   PetscInt           mbs = a->mbs, i, *idx = a->j, *ii = a->i, j, *jj, n, k;

    1737:   PetscFunctionBegin;
    1738:   for (i = 0; i < mbs; i++) {
    1739:     n = ii[1] - ii[0];
    1740:     ii++;
    1741:     PetscPrefetchBlock(idx + n, n, 0, PETSC_PREFETCH_HINT_NTA);         /* Indices for the next row (assumes same size as this one) */
    1742:     PetscPrefetchBlock(v + 25 * n, 25 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
    1743:     jj = idx;
    1744:     vv = v;
    1745:     for (k = 0; k < cn; k++) {
    1746:       idx = jj;
    1747:       v   = vv;
    1748:       for (j = 0; j < n; j++) {
    1749:         xb = b + 5 * (*idx);
    1750:         x1 = xb[0 + k * bm];
    1751:         x2 = xb[1 + k * bm];
    1752:         x3 = xb[2 + k * bm];
    1753:         x4 = xb[3 + k * bm];
    1754:         x5 = xb[4 + k * cm];
    1755:         z[0 + k * cm] += v[0] * x1 + v[5] * x2 + v[10] * x3 + v[15] * x4 + v[20] * x5;
    1756:         z[1 + k * cm] += v[1] * x1 + v[6] * x2 + v[11] * x3 + v[16] * x4 + v[21] * x5;
    1757:         z[2 + k * cm] += v[2] * x1 + v[7] * x2 + v[12] * x3 + v[17] * x4 + v[22] * x5;
    1758:         z[3 + k * cm] += v[3] * x1 + v[8] * x2 + v[13] * x3 + v[18] * x4 + v[23] * x5;
    1759:         z[4 + k * cm] += v[4] * x1 + v[9] * x2 + v[14] * x3 + v[19] * x4 + v[24] * x5;
    1760:         if (*idx != i) {
    1761:           c[5 * (*idx) + 0 + k * cm] += v[0] * b[5 * i + k * bm] + v[5] * b[5 * i + 1 + k * bm] + v[10] * b[5 * i + 2 + k * bm] + v[15] * b[5 * i + 3 + k * bm] + v[20] * b[5 * i + 4 + k * bm];
    1762:           c[5 * (*idx) + 1 + k * cm] += v[1] * b[5 * i + k * bm] + v[6] * b[5 * i + 1 + k * bm] + v[11] * b[5 * i + 2 + k * bm] + v[16] * b[5 * i + 3 + k * bm] + v[21] * b[5 * i + 4 + k * bm];
    1763:           c[5 * (*idx) + 2 + k * cm] += v[2] * b[5 * i + k * bm] + v[7] * b[5 * i + 1 + k * bm] + v[12] * b[5 * i + 2 + k * bm] + v[17] * b[5 * i + 3 + k * bm] + v[22] * b[5 * i + 4 + k * bm];
    1764:           c[5 * (*idx) + 3 + k * cm] += v[3] * b[5 * i + k * bm] + v[8] * b[5 * i + 1 + k * bm] + v[13] * b[5 * i + 2 + k * bm] + v[18] * b[5 * i + 3 + k * bm] + v[23] * b[5 * i + 4 + k * bm];
    1765:           c[5 * (*idx) + 4 + k * cm] += v[4] * b[5 * i + k * bm] + v[9] * b[5 * i + 1 + k * bm] + v[14] * b[5 * i + 2 + k * bm] + v[19] * b[5 * i + 3 + k * bm] + v[24] * b[5 * i + 4 + k * bm];
    1766:         }
    1767:         v += 25;
    1768:         ++idx;
    1769:       }
    1770:     }
    1771:     z += 5;
    1772:   }
    1773:   PetscFunctionReturn(PETSC_SUCCESS);
    1774: }

    1776: PetscErrorCode MatMatMultNumeric_SeqSBAIJ_SeqDense(Mat A, Mat B, Mat C)
    1777: {
    1778:   Mat_SeqSBAIJ    *a  = (Mat_SeqSBAIJ *)A->data;
    1779:   Mat_SeqDense    *bd = (Mat_SeqDense *)B->data;
    1780:   Mat_SeqDense    *cd = (Mat_SeqDense *)C->data;
    1781:   PetscInt         cm = cd->lda, cn = B->cmap->n, bm = bd->lda;
    1782:   PetscInt         mbs, i, bs = A->rmap->bs, j, n, bs2 = a->bs2;
    1783:   PetscBLASInt     bbs, bcn, bbm, bcm;
    1784:   PetscScalar     *z = NULL;
    1785:   PetscScalar     *c, *b;
    1786:   const MatScalar *v;
    1787:   const PetscInt  *idx, *ii;
    1788:   PetscScalar      _DOne = 1.0;

    1790:   PetscFunctionBegin;
    1791:   if (!cm || !cn) PetscFunctionReturn(PETSC_SUCCESS);
    1792:   PetscCheck(B->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number columns in A %" PetscInt_FMT " not equal rows in B %" PetscInt_FMT, A->cmap->n, B->rmap->n);
    1793:   PetscCheck(A->rmap->n == C->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number rows in C %" PetscInt_FMT " not equal rows in A %" PetscInt_FMT, C->rmap->n, A->rmap->n);
    1794:   PetscCheck(B->cmap->n == C->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number columns in B %" PetscInt_FMT " not equal columns in C %" PetscInt_FMT, B->cmap->n, C->cmap->n);
    1795:   b = bd->v;
    1796:   PetscCall(MatZeroEntries(C));
    1797:   PetscCall(MatDenseGetArray(C, &c));
    1798:   switch (bs) {
    1799:   case 1:
    1800:     PetscCall(MatMatMult_SeqSBAIJ_1_Private(A, b, bm, c, cm, cn));
    1801:     break;
    1802:   case 2:
    1803:     PetscCall(MatMatMult_SeqSBAIJ_2_Private(A, b, bm, c, cm, cn));
    1804:     break;
    1805:   case 3:
    1806:     PetscCall(MatMatMult_SeqSBAIJ_3_Private(A, b, bm, c, cm, cn));
    1807:     break;
    1808:   case 4:
    1809:     PetscCall(MatMatMult_SeqSBAIJ_4_Private(A, b, bm, c, cm, cn));
    1810:     break;
    1811:   case 5:
    1812:     PetscCall(MatMatMult_SeqSBAIJ_5_Private(A, b, bm, c, cm, cn));
    1813:     break;
    1814:   default: /* block sizes larger than 5 by 5 are handled by BLAS */
    1815:     PetscCall(PetscBLASIntCast(bs, &bbs));
    1816:     PetscCall(PetscBLASIntCast(cn, &bcn));
    1817:     PetscCall(PetscBLASIntCast(bm, &bbm));
    1818:     PetscCall(PetscBLASIntCast(cm, &bcm));
    1819:     idx = a->j;
    1820:     v   = a->a;
    1821:     mbs = a->mbs;
    1822:     ii  = a->i;
    1823:     z   = c;
    1824:     for (i = 0; i < mbs; i++) {
    1825:       n = ii[1] - ii[0];
    1826:       ii++;
    1827:       for (j = 0; j < n; j++) {
    1828:         if (*idx != i) PetscCallBLAS("BLASgemm", BLASgemm_("T", "N", &bbs, &bcn, &bbs, &_DOne, v, &bbs, b + bs * i, &bbm, &_DOne, c + bs * (*idx), &bcm));
    1829:         PetscCallBLAS("BLASgemm", BLASgemm_("N", "N", &bbs, &bcn, &bbs, &_DOne, v, &bbs, b + bs * (*idx++), &bbm, &_DOne, z, &bcm));
    1830:         v += bs2;
    1831:       }
    1832:       z += bs;
    1833:     }
    1834:   }
    1835:   PetscCall(MatDenseRestoreArray(C, &c));
    1836:   PetscCall(PetscLogFlops((2.0 * (a->nz * 2.0 - a->nonzerorowcnt) * bs2 - a->nonzerorowcnt) * cn));
    1837:   PetscFunctionReturn(PETSC_SUCCESS);
    1838: }