xref: /petsc/src/mat/impls/sbaij/seq/sbaij2.c (revision 8a8e60716cff172efc06305fa00d856443c11202)
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>
7 
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;
14 
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));
24 
25   for (i = 0; i < is_max; i++) { /* for each is */
26     isz = 0;
27     PetscCall(PetscBTMemzero(mbs, table_out));
28 
29     /* Extract the indices, assume there can be duplicate entries */
30     PetscCall(ISGetIndices(is[i], &idx));
31     PetscCall(ISGetLocalSize(is[i], &n));
32 
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]));
45 
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]));
51 
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 }
85 
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 }
103 
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;
117 
118   PetscFunctionBegin;
119   PetscCall(ISGetIndices(isrow, &irow));
120   PetscCall(ISGetIndices(iscol, &icol));
121   PetscCall(ISGetLocalSize(isrow, &nrows));
122   PetscCall(ISGetLocalSize(iscol, &ncols));
123 
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);
141 
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);
148 
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;
195 
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   }
214 
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));
221 
222   PetscCall(ISRestoreIndices(isrow, &irow));
223   *B = C;
224   PetscFunctionReturn(PETSC_SUCCESS);
225 }
226 
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;
233 
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));
266 
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 }
274 
275 PetscErrorCode MatCreateSubMatrices_SeqSBAIJ(Mat A, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *B[])
276 {
277   PetscInt i;
278 
279   PetscFunctionBegin;
280   if (scall == MAT_INITIAL_MATRIX) PetscCall(PetscCalloc1(n, B));
281 
282   for (i = 0; i < n; i++) PetscCall(MatCreateSubMatrix_SeqSBAIJ(A, irow[i], icol[i], scall, &(*B)[i]));
283   PetscFunctionReturn(PETSC_SUCCESS);
284 }
285 
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;
296 
297   PetscFunctionBegin;
298   PetscCall(VecSet(zz, zero));
299   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
300   PetscCall(VecGetArrayRead(xx, &x));
301   PetscCall(VecGetArray(zz, &z));
302 
303   v  = a->a;
304   xb = x;
305 
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   }
334 
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 }
340 
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;
350 
351   PetscFunctionBegin;
352   PetscCall(VecSet(zz, zero));
353   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
354   PetscCall(VecGetArrayRead(xx, &x));
355   PetscCall(VecGetArray(zz, &z));
356 
357   v  = a->a;
358   xb = x;
359 
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   }
392 
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 }
398 
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;
408 
409   PetscFunctionBegin;
410   PetscCall(VecSet(zz, zero));
411   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
412   PetscCall(VecGetArrayRead(xx, &x));
413   PetscCall(VecGetArray(zz, &z));
414 
415   v  = a->a;
416   xb = x;
417 
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   }
454 
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 }
460 
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;
470 
471   PetscFunctionBegin;
472   PetscCall(VecSet(zz, zero));
473   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
474   PetscCall(VecGetArrayRead(xx, &x));
475   PetscCall(VecGetArray(zz, &z));
476 
477   v  = a->a;
478   xb = x;
479 
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   }
520 
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 }
526 
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;
536 
537   PetscFunctionBegin;
538   PetscCall(VecSet(zz, zero));
539   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
540   PetscCall(VecGetArrayRead(xx, &x));
541   PetscCall(VecGetArray(zz, &z));
542 
543   v  = a->a;
544   xb = x;
545 
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   }
590 
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 }
596 
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;
606 
607   PetscFunctionBegin;
608   PetscCall(VecSet(zz, zero));
609   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
610   PetscCall(VecGetArrayRead(xx, &x));
611   PetscCall(VecGetArray(zz, &z));
612 
613   v  = a->a;
614   xb = x;
615 
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 }
669 
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;
682 
683   PetscFunctionBegin;
684   PetscCall(VecSet(zz, zero));
685   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
686   PetscCall(VecGetArrayRead(xx, &x));
687   PetscCall(VecGetArray(zz, &z));
688 
689   x_ptr = x;
690   z_ptr = z;
691 
692   aj = a->j;
693   v  = a->a;
694   ii = a->i;
695 
696   if (!a->mult_work) PetscCall(PetscMalloc1(A->rmap->N + 1, &a->mult_work));
697   work = a->mult_work;
698 
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);
705 
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);
714 
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     }
723 
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   }
739 
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 }
745 
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 #if defined(PETSC_USE_COMPLEX)
756   const int aconj = A->hermitian == PETSC_BOOL3_TRUE;
757 #else
758   const int aconj = 0;
759 #endif
760 
761   PetscFunctionBegin;
762   PetscCall(VecCopy(yy, zz));
763   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
764   PetscCall(VecGetArrayRead(xx, &x));
765   PetscCall(VecGetArray(zz, &z));
766   v  = a->a;
767   xb = x;
768 
769   for (i = 0; i < mbs; i++) {
770     n    = ai[1] - ai[0]; /* length of i_th row of A */
771     x1   = xb[0];
772     ib   = aj + *ai;
773     jmin = 0;
774     nonzerorow += (n > 0);
775     if (n && *ib == i) { /* (diag of A)*x */
776       z[i] += *v++ * x[*ib++];
777       jmin++;
778     }
779     if (aconj) {
780       for (j = jmin; j < n; j++) {
781         cval = *ib;
782         z[cval] += PetscConj(*v) * x1; /* (strict lower triangular part of A)*x  */
783         z[i] += *v++ * x[*ib++];       /* (strict upper triangular part of A)*x  */
784       }
785     } else {
786       for (j = jmin; j < n; j++) {
787         cval = *ib;
788         z[cval] += *v * x1;      /* (strict lower triangular part of A)*x  */
789         z[i] += *v++ * x[*ib++]; /* (strict upper triangular part of A)*x  */
790       }
791     }
792     xb++;
793     ai++;
794   }
795 
796   PetscCall(VecRestoreArrayRead(xx, &x));
797   PetscCall(VecRestoreArray(zz, &z));
798 
799   PetscCall(PetscLogFlops(2.0 * (a->nz * 2.0 - nonzerorow)));
800   PetscFunctionReturn(PETSC_SUCCESS);
801 }
802 
803 PetscErrorCode MatMultAdd_SeqSBAIJ_2(Mat A, Vec xx, Vec yy, Vec zz)
804 {
805   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
806   PetscScalar       *z, x1, x2;
807   const PetscScalar *x, *xb;
808   const MatScalar   *v;
809   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
810   const PetscInt    *aj = a->j, *ai = a->i, *ib;
811   PetscInt           nonzerorow = 0;
812 
813   PetscFunctionBegin;
814   PetscCall(VecCopy(yy, zz));
815   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
816   PetscCall(VecGetArrayRead(xx, &x));
817   PetscCall(VecGetArray(zz, &z));
818 
819   v  = a->a;
820   xb = x;
821 
822   for (i = 0; i < mbs; i++) {
823     n    = ai[1] - ai[0]; /* length of i_th block row of A */
824     x1   = xb[0];
825     x2   = xb[1];
826     ib   = aj + *ai;
827     jmin = 0;
828     nonzerorow += (n > 0);
829     if (n && *ib == i) { /* (diag of A)*x */
830       z[2 * i] += v[0] * x1 + v[2] * x2;
831       z[2 * i + 1] += v[2] * x1 + v[3] * x2;
832       v += 4;
833       jmin++;
834     }
835     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
836     PetscPrefetchBlock(v + 4 * n, 4 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
837     for (j = jmin; j < n; j++) {
838       /* (strict lower triangular part of A)*x  */
839       cval = ib[j] * 2;
840       z[cval] += v[0] * x1 + v[1] * x2;
841       z[cval + 1] += v[2] * x1 + v[3] * x2;
842       /* (strict upper triangular part of A)*x  */
843       z[2 * i] += v[0] * x[cval] + v[2] * x[cval + 1];
844       z[2 * i + 1] += v[1] * x[cval] + v[3] * x[cval + 1];
845       v += 4;
846     }
847     xb += 2;
848     ai++;
849   }
850   PetscCall(VecRestoreArrayRead(xx, &x));
851   PetscCall(VecRestoreArray(zz, &z));
852 
853   PetscCall(PetscLogFlops(4.0 * (a->nz * 2.0 - nonzerorow)));
854   PetscFunctionReturn(PETSC_SUCCESS);
855 }
856 
857 PetscErrorCode MatMultAdd_SeqSBAIJ_3(Mat A, Vec xx, Vec yy, Vec zz)
858 {
859   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
860   PetscScalar       *z, x1, x2, x3;
861   const PetscScalar *x, *xb;
862   const MatScalar   *v;
863   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
864   const PetscInt    *aj = a->j, *ai = a->i, *ib;
865   PetscInt           nonzerorow = 0;
866 
867   PetscFunctionBegin;
868   PetscCall(VecCopy(yy, zz));
869   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
870   PetscCall(VecGetArrayRead(xx, &x));
871   PetscCall(VecGetArray(zz, &z));
872 
873   v  = a->a;
874   xb = x;
875 
876   for (i = 0; i < mbs; i++) {
877     n    = ai[1] - ai[0]; /* length of i_th block row of A */
878     x1   = xb[0];
879     x2   = xb[1];
880     x3   = xb[2];
881     ib   = aj + *ai;
882     jmin = 0;
883     nonzerorow += (n > 0);
884     if (n && *ib == i) { /* (diag of A)*x */
885       z[3 * i] += v[0] * x1 + v[3] * x2 + v[6] * x3;
886       z[3 * i + 1] += v[3] * x1 + v[4] * x2 + v[7] * x3;
887       z[3 * i + 2] += v[6] * x1 + v[7] * x2 + v[8] * x3;
888       v += 9;
889       jmin++;
890     }
891     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
892     PetscPrefetchBlock(v + 9 * n, 9 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
893     for (j = jmin; j < n; j++) {
894       /* (strict lower triangular part of A)*x  */
895       cval = ib[j] * 3;
896       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3;
897       z[cval + 1] += v[3] * x1 + v[4] * x2 + v[5] * x3;
898       z[cval + 2] += v[6] * x1 + v[7] * x2 + v[8] * x3;
899       /* (strict upper triangular part of A)*x  */
900       z[3 * i] += v[0] * x[cval] + v[3] * x[cval + 1] + v[6] * x[cval + 2];
901       z[3 * i + 1] += v[1] * x[cval] + v[4] * x[cval + 1] + v[7] * x[cval + 2];
902       z[3 * i + 2] += v[2] * x[cval] + v[5] * x[cval + 1] + v[8] * x[cval + 2];
903       v += 9;
904     }
905     xb += 3;
906     ai++;
907   }
908 
909   PetscCall(VecRestoreArrayRead(xx, &x));
910   PetscCall(VecRestoreArray(zz, &z));
911 
912   PetscCall(PetscLogFlops(18.0 * (a->nz * 2.0 - nonzerorow)));
913   PetscFunctionReturn(PETSC_SUCCESS);
914 }
915 
916 PetscErrorCode MatMultAdd_SeqSBAIJ_4(Mat A, Vec xx, Vec yy, Vec zz)
917 {
918   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
919   PetscScalar       *z, x1, x2, x3, x4;
920   const PetscScalar *x, *xb;
921   const MatScalar   *v;
922   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
923   const PetscInt    *aj = a->j, *ai = a->i, *ib;
924   PetscInt           nonzerorow = 0;
925 
926   PetscFunctionBegin;
927   PetscCall(VecCopy(yy, zz));
928   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
929   PetscCall(VecGetArrayRead(xx, &x));
930   PetscCall(VecGetArray(zz, &z));
931 
932   v  = a->a;
933   xb = x;
934 
935   for (i = 0; i < mbs; i++) {
936     n    = ai[1] - ai[0]; /* length of i_th block row of A */
937     x1   = xb[0];
938     x2   = xb[1];
939     x3   = xb[2];
940     x4   = xb[3];
941     ib   = aj + *ai;
942     jmin = 0;
943     nonzerorow += (n > 0);
944     if (n && *ib == i) { /* (diag of A)*x */
945       z[4 * i] += v[0] * x1 + v[4] * x2 + v[8] * x3 + v[12] * x4;
946       z[4 * i + 1] += v[4] * x1 + v[5] * x2 + v[9] * x3 + v[13] * x4;
947       z[4 * i + 2] += v[8] * x1 + v[9] * x2 + v[10] * x3 + v[14] * x4;
948       z[4 * i + 3] += v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
949       v += 16;
950       jmin++;
951     }
952     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
953     PetscPrefetchBlock(v + 16 * n, 16 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
954     for (j = jmin; j < n; j++) {
955       /* (strict lower triangular part of A)*x  */
956       cval = ib[j] * 4;
957       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
958       z[cval + 1] += v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
959       z[cval + 2] += v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
960       z[cval + 3] += v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
961       /* (strict upper triangular part of A)*x  */
962       z[4 * i] += v[0] * x[cval] + v[4] * x[cval + 1] + v[8] * x[cval + 2] + v[12] * x[cval + 3];
963       z[4 * i + 1] += v[1] * x[cval] + v[5] * x[cval + 1] + v[9] * x[cval + 2] + v[13] * x[cval + 3];
964       z[4 * i + 2] += v[2] * x[cval] + v[6] * x[cval + 1] + v[10] * x[cval + 2] + v[14] * x[cval + 3];
965       z[4 * i + 3] += v[3] * x[cval] + v[7] * x[cval + 1] + v[11] * x[cval + 2] + v[15] * x[cval + 3];
966       v += 16;
967     }
968     xb += 4;
969     ai++;
970   }
971 
972   PetscCall(VecRestoreArrayRead(xx, &x));
973   PetscCall(VecRestoreArray(zz, &z));
974 
975   PetscCall(PetscLogFlops(32.0 * (a->nz * 2.0 - nonzerorow)));
976   PetscFunctionReturn(PETSC_SUCCESS);
977 }
978 
979 PetscErrorCode MatMultAdd_SeqSBAIJ_5(Mat A, Vec xx, Vec yy, Vec zz)
980 {
981   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
982   PetscScalar       *z, x1, x2, x3, x4, x5;
983   const PetscScalar *x, *xb;
984   const MatScalar   *v;
985   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
986   const PetscInt    *aj = a->j, *ai = a->i, *ib;
987   PetscInt           nonzerorow = 0;
988 
989   PetscFunctionBegin;
990   PetscCall(VecCopy(yy, zz));
991   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
992   PetscCall(VecGetArrayRead(xx, &x));
993   PetscCall(VecGetArray(zz, &z));
994 
995   v  = a->a;
996   xb = x;
997 
998   for (i = 0; i < mbs; i++) {
999     n    = ai[1] - ai[0]; /* length of i_th block row of A */
1000     x1   = xb[0];
1001     x2   = xb[1];
1002     x3   = xb[2];
1003     x4   = xb[3];
1004     x5   = xb[4];
1005     ib   = aj + *ai;
1006     jmin = 0;
1007     nonzerorow += (n > 0);
1008     if (n && *ib == i) { /* (diag of A)*x */
1009       z[5 * i] += v[0] * x1 + v[5] * x2 + v[10] * x3 + v[15] * x4 + v[20] * x5;
1010       z[5 * i + 1] += v[5] * x1 + v[6] * x2 + v[11] * x3 + v[16] * x4 + v[21] * x5;
1011       z[5 * i + 2] += v[10] * x1 + v[11] * x2 + v[12] * x3 + v[17] * x4 + v[22] * x5;
1012       z[5 * i + 3] += v[15] * x1 + v[16] * x2 + v[17] * x3 + v[18] * x4 + v[23] * x5;
1013       z[5 * i + 4] += v[20] * x1 + v[21] * x2 + v[22] * x3 + v[23] * x4 + v[24] * x5;
1014       v += 25;
1015       jmin++;
1016     }
1017     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
1018     PetscPrefetchBlock(v + 25 * n, 25 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1019     for (j = jmin; j < n; j++) {
1020       /* (strict lower triangular part of A)*x  */
1021       cval = ib[j] * 5;
1022       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5;
1023       z[cval + 1] += v[5] * x1 + v[6] * x2 + v[7] * x3 + v[8] * x4 + v[9] * x5;
1024       z[cval + 2] += v[10] * x1 + v[11] * x2 + v[12] * x3 + v[13] * x4 + v[14] * x5;
1025       z[cval + 3] += v[15] * x1 + v[16] * x2 + v[17] * x3 + v[18] * x4 + v[19] * x5;
1026       z[cval + 4] += v[20] * x1 + v[21] * x2 + v[22] * x3 + v[23] * x4 + v[24] * x5;
1027       /* (strict upper triangular part of A)*x  */
1028       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];
1029       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];
1030       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];
1031       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];
1032       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];
1033       v += 25;
1034     }
1035     xb += 5;
1036     ai++;
1037   }
1038 
1039   PetscCall(VecRestoreArrayRead(xx, &x));
1040   PetscCall(VecRestoreArray(zz, &z));
1041 
1042   PetscCall(PetscLogFlops(50.0 * (a->nz * 2.0 - nonzerorow)));
1043   PetscFunctionReturn(PETSC_SUCCESS);
1044 }
1045 
1046 PetscErrorCode MatMultAdd_SeqSBAIJ_6(Mat A, Vec xx, Vec yy, Vec zz)
1047 {
1048   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
1049   PetscScalar       *z, x1, x2, x3, x4, x5, x6;
1050   const PetscScalar *x, *xb;
1051   const MatScalar   *v;
1052   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
1053   const PetscInt    *aj = a->j, *ai = a->i, *ib;
1054   PetscInt           nonzerorow = 0;
1055 
1056   PetscFunctionBegin;
1057   PetscCall(VecCopy(yy, zz));
1058   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
1059   PetscCall(VecGetArrayRead(xx, &x));
1060   PetscCall(VecGetArray(zz, &z));
1061 
1062   v  = a->a;
1063   xb = x;
1064 
1065   for (i = 0; i < mbs; i++) {
1066     n    = ai[1] - ai[0]; /* length of i_th block row of A */
1067     x1   = xb[0];
1068     x2   = xb[1];
1069     x3   = xb[2];
1070     x4   = xb[3];
1071     x5   = xb[4];
1072     x6   = xb[5];
1073     ib   = aj + *ai;
1074     jmin = 0;
1075     nonzerorow += (n > 0);
1076     if (n && *ib == i) { /* (diag of A)*x */
1077       z[6 * i] += v[0] * x1 + v[6] * x2 + v[12] * x3 + v[18] * x4 + v[24] * x5 + v[30] * x6;
1078       z[6 * i + 1] += v[6] * x1 + v[7] * x2 + v[13] * x3 + v[19] * x4 + v[25] * x5 + v[31] * x6;
1079       z[6 * i + 2] += v[12] * x1 + v[13] * x2 + v[14] * x3 + v[20] * x4 + v[26] * x5 + v[32] * x6;
1080       z[6 * i + 3] += v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[27] * x5 + v[33] * x6;
1081       z[6 * i + 4] += v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[34] * x6;
1082       z[6 * i + 5] += v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
1083       v += 36;
1084       jmin++;
1085     }
1086     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
1087     PetscPrefetchBlock(v + 36 * n, 36 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1088     for (j = jmin; j < n; j++) {
1089       /* (strict lower triangular part of A)*x  */
1090       cval = ib[j] * 6;
1091       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6;
1092       z[cval + 1] += v[6] * x1 + v[7] * x2 + v[8] * x3 + v[9] * x4 + v[10] * x5 + v[11] * x6;
1093       z[cval + 2] += v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4 + v[16] * x5 + v[17] * x6;
1094       z[cval + 3] += v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[22] * x5 + v[23] * x6;
1095       z[cval + 4] += v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[29] * x6;
1096       z[cval + 5] += v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
1097       /* (strict upper triangular part of A)*x  */
1098       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];
1099       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];
1100       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];
1101       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];
1102       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];
1103       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];
1104       v += 36;
1105     }
1106     xb += 6;
1107     ai++;
1108   }
1109 
1110   PetscCall(VecRestoreArrayRead(xx, &x));
1111   PetscCall(VecRestoreArray(zz, &z));
1112 
1113   PetscCall(PetscLogFlops(72.0 * (a->nz * 2.0 - nonzerorow)));
1114   PetscFunctionReturn(PETSC_SUCCESS);
1115 }
1116 
1117 PetscErrorCode MatMultAdd_SeqSBAIJ_7(Mat A, Vec xx, Vec yy, Vec zz)
1118 {
1119   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
1120   PetscScalar       *z, x1, x2, x3, x4, x5, x6, x7;
1121   const PetscScalar *x, *xb;
1122   const MatScalar   *v;
1123   PetscInt           mbs = a->mbs, i, n, cval, j, jmin;
1124   const PetscInt    *aj = a->j, *ai = a->i, *ib;
1125   PetscInt           nonzerorow = 0;
1126 
1127   PetscFunctionBegin;
1128   PetscCall(VecCopy(yy, zz));
1129   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
1130   PetscCall(VecGetArrayRead(xx, &x));
1131   PetscCall(VecGetArray(zz, &z));
1132 
1133   v  = a->a;
1134   xb = x;
1135 
1136   for (i = 0; i < mbs; i++) {
1137     n    = ai[1] - ai[0]; /* length of i_th block row of A */
1138     x1   = xb[0];
1139     x2   = xb[1];
1140     x3   = xb[2];
1141     x4   = xb[3];
1142     x5   = xb[4];
1143     x6   = xb[5];
1144     x7   = xb[6];
1145     ib   = aj + *ai;
1146     jmin = 0;
1147     nonzerorow += (n > 0);
1148     if (n && *ib == i) { /* (diag of A)*x */
1149       z[7 * i] += v[0] * x1 + v[7] * x2 + v[14] * x3 + v[21] * x4 + v[28] * x5 + v[35] * x6 + v[42] * x7;
1150       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;
1151       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;
1152       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;
1153       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;
1154       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;
1155       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;
1156       v += 49;
1157       jmin++;
1158     }
1159     PetscPrefetchBlock(ib + jmin + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Indices for the next row (assumes same size as this one) */
1160     PetscPrefetchBlock(v + 49 * n, 49 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1161     for (j = jmin; j < n; j++) {
1162       /* (strict lower triangular part of A)*x  */
1163       cval = ib[j] * 7;
1164       z[cval] += v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6 + v[6] * x7;
1165       z[cval + 1] += v[7] * x1 + v[8] * x2 + v[9] * x3 + v[10] * x4 + v[11] * x5 + v[12] * x6 + v[13] * x7;
1166       z[cval + 2] += v[14] * x1 + v[15] * x2 + v[16] * x3 + v[17] * x4 + v[18] * x5 + v[19] * x6 + v[20] * x7;
1167       z[cval + 3] += v[21] * x1 + v[22] * x2 + v[23] * x3 + v[24] * x4 + v[25] * x5 + v[26] * x6 + v[27] * x7;
1168       z[cval + 4] += v[28] * x1 + v[29] * x2 + v[30] * x3 + v[31] * x4 + v[32] * x5 + v[33] * x6 + v[34] * x7;
1169       z[cval + 5] += v[35] * x1 + v[36] * x2 + v[37] * x3 + v[38] * x4 + v[39] * x5 + v[40] * x6 + v[41] * x7;
1170       z[cval + 6] += v[42] * x1 + v[43] * x2 + v[44] * x3 + v[45] * x4 + v[46] * x5 + v[47] * x6 + v[48] * x7;
1171       /* (strict upper triangular part of A)*x  */
1172       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];
1173       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];
1174       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];
1175       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];
1176       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];
1177       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];
1178       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];
1179       v += 49;
1180     }
1181     xb += 7;
1182     ai++;
1183   }
1184 
1185   PetscCall(VecRestoreArrayRead(xx, &x));
1186   PetscCall(VecRestoreArray(zz, &z));
1187 
1188   PetscCall(PetscLogFlops(98.0 * (a->nz * 2.0 - nonzerorow)));
1189   PetscFunctionReturn(PETSC_SUCCESS);
1190 }
1191 
1192 PetscErrorCode MatMultAdd_SeqSBAIJ_N(Mat A, Vec xx, Vec yy, Vec zz)
1193 {
1194   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
1195   PetscScalar       *z, *z_ptr = NULL, *zb, *work, *workt;
1196   const PetscScalar *x, *x_ptr, *xb;
1197   const MatScalar   *v;
1198   PetscInt           mbs = a->mbs, i, bs = A->rmap->bs, j, n, bs2 = a->bs2, ncols, k;
1199   const PetscInt    *idx, *aj, *ii;
1200   PetscInt           nonzerorow = 0;
1201 
1202   PetscFunctionBegin;
1203   PetscCall(VecCopy(yy, zz));
1204   if (!a->nz) PetscFunctionReturn(PETSC_SUCCESS);
1205   PetscCall(VecGetArrayRead(xx, &x));
1206   x_ptr = x;
1207   PetscCall(VecGetArray(zz, &z));
1208   z_ptr = z;
1209 
1210   aj = a->j;
1211   v  = a->a;
1212   ii = a->i;
1213 
1214   if (!a->mult_work) PetscCall(PetscMalloc1(A->rmap->n + 1, &a->mult_work));
1215   work = a->mult_work;
1216 
1217   for (i = 0; i < mbs; i++) {
1218     n     = ii[1] - ii[0];
1219     ncols = n * bs;
1220     workt = work;
1221     idx   = aj + ii[0];
1222     nonzerorow += (n > 0);
1223 
1224     /* upper triangular part */
1225     for (j = 0; j < n; j++) {
1226       xb = x_ptr + bs * (*idx++);
1227       for (k = 0; k < bs; k++) workt[k] = xb[k];
1228       workt += bs;
1229     }
1230     /* z(i*bs:(i+1)*bs-1) += A(i,:)*x */
1231     PetscKernel_w_gets_w_plus_Ar_times_v(bs, ncols, work, v, z);
1232 
1233     /* strict lower triangular part */
1234     idx = aj + ii[0];
1235     if (n && *idx == i) {
1236       ncols -= bs;
1237       v += bs2;
1238       idx++;
1239       n--;
1240     }
1241     if (ncols > 0) {
1242       workt = work;
1243       PetscCall(PetscArrayzero(workt, ncols));
1244       PetscKernel_w_gets_w_plus_trans_Ar_times_v(bs, ncols, x, v, workt);
1245       for (j = 0; j < n; j++) {
1246         zb = z_ptr + bs * (*idx++);
1247         for (k = 0; k < bs; k++) zb[k] += workt[k];
1248         workt += bs;
1249       }
1250     }
1251 
1252     x += bs;
1253     v += n * bs2;
1254     z += bs;
1255     ii++;
1256   }
1257 
1258   PetscCall(VecRestoreArrayRead(xx, &x));
1259   PetscCall(VecRestoreArray(zz, &z));
1260 
1261   PetscCall(PetscLogFlops(2.0 * (a->nz * 2.0 - nonzerorow)));
1262   PetscFunctionReturn(PETSC_SUCCESS);
1263 }
1264 
1265 PetscErrorCode MatScale_SeqSBAIJ(Mat inA, PetscScalar alpha)
1266 {
1267   Mat_SeqSBAIJ *a      = (Mat_SeqSBAIJ *)inA->data;
1268   PetscScalar   oalpha = alpha;
1269   PetscBLASInt  one    = 1, totalnz;
1270 
1271   PetscFunctionBegin;
1272   PetscCall(PetscBLASIntCast(a->bs2 * a->nz, &totalnz));
1273   PetscCallBLAS("BLASscal", BLASscal_(&totalnz, &oalpha, a->a, &one));
1274   PetscCall(PetscLogFlops(totalnz));
1275   PetscFunctionReturn(PETSC_SUCCESS);
1276 }
1277 
1278 PetscErrorCode MatNorm_SeqSBAIJ(Mat A, NormType type, PetscReal *norm)
1279 {
1280   Mat_SeqSBAIJ    *a        = (Mat_SeqSBAIJ *)A->data;
1281   const MatScalar *v        = a->a;
1282   PetscReal        sum_diag = 0.0, sum_off = 0.0, *sum;
1283   PetscInt         i, j, k, bs = A->rmap->bs, bs2 = a->bs2, k1, mbs = a->mbs, jmin, jmax, nexti, ik, *jl, *il;
1284   const PetscInt  *aj = a->j, *col;
1285 
1286   PetscFunctionBegin;
1287   if (!a->nz) {
1288     *norm = 0.0;
1289     PetscFunctionReturn(PETSC_SUCCESS);
1290   }
1291   if (type == NORM_FROBENIUS) {
1292     for (k = 0; k < mbs; k++) {
1293       jmin = a->i[k];
1294       jmax = a->i[k + 1];
1295       col  = aj + jmin;
1296       if (jmax - jmin > 0 && *col == k) { /* diagonal block */
1297         for (i = 0; i < bs2; i++) {
1298           sum_diag += PetscRealPart(PetscConj(*v) * (*v));
1299           v++;
1300         }
1301         jmin++;
1302       }
1303       for (j = jmin; j < jmax; j++) { /* off-diagonal blocks */
1304         for (i = 0; i < bs2; i++) {
1305           sum_off += PetscRealPart(PetscConj(*v) * (*v));
1306           v++;
1307         }
1308       }
1309     }
1310     *norm = PetscSqrtReal(sum_diag + 2 * sum_off);
1311     PetscCall(PetscLogFlops(2.0 * bs2 * a->nz));
1312   } else if (type == NORM_INFINITY || type == NORM_1) { /* maximum row/column sum */
1313     PetscCall(PetscMalloc3(bs, &sum, mbs, &il, mbs, &jl));
1314     for (i = 0; i < mbs; i++) jl[i] = mbs;
1315     il[0] = 0;
1316 
1317     *norm = 0.0;
1318     for (k = 0; k < mbs; k++) { /* k_th block row */
1319       for (j = 0; j < bs; j++) sum[j] = 0.0;
1320       /*-- col sum --*/
1321       i = jl[k]; /* first |A(i,k)| to be added */
1322       /* jl[k]=i: first nonzero element in row i for submatrix A(1:k,k:n) (active window)
1323                   at step k */
1324       while (i < mbs) {
1325         nexti = jl[i]; /* next block row to be added */
1326         ik    = il[i]; /* block index of A(i,k) in the array a */
1327         for (j = 0; j < bs; j++) {
1328           v = a->a + ik * bs2 + j * bs;
1329           for (k1 = 0; k1 < bs; k1++) {
1330             sum[j] += PetscAbsScalar(*v);
1331             v++;
1332           }
1333         }
1334         /* update il, jl */
1335         jmin = ik + 1; /* block index of array a: points to the next nonzero of A in row i */
1336         jmax = a->i[i + 1];
1337         if (jmin < jmax) {
1338           il[i] = jmin;
1339           j     = a->j[jmin];
1340           jl[i] = jl[j];
1341           jl[j] = i;
1342         }
1343         i = nexti;
1344       }
1345       /*-- row sum --*/
1346       jmin = a->i[k];
1347       jmax = a->i[k + 1];
1348       for (i = jmin; i < jmax; i++) {
1349         for (j = 0; j < bs; j++) {
1350           v = a->a + i * bs2 + j;
1351           for (k1 = 0; k1 < bs; k1++) {
1352             sum[j] += PetscAbsScalar(*v);
1353             v += bs;
1354           }
1355         }
1356       }
1357       /* add k_th block row to il, jl */
1358       col = aj + jmin;
1359       if (jmax - jmin > 0 && *col == k) jmin++;
1360       if (jmin < jmax) {
1361         il[k] = jmin;
1362         j     = a->j[jmin];
1363         jl[k] = jl[j];
1364         jl[j] = k;
1365       }
1366       for (j = 0; j < bs; j++) {
1367         if (sum[j] > *norm) *norm = sum[j];
1368       }
1369     }
1370     PetscCall(PetscFree3(sum, il, jl));
1371     PetscCall(PetscLogFlops(PetscMax(mbs * a->nz - 1, 0)));
1372   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for this norm yet");
1373   PetscFunctionReturn(PETSC_SUCCESS);
1374 }
1375 
1376 PetscErrorCode MatEqual_SeqSBAIJ(Mat A, Mat B, PetscBool *flg)
1377 {
1378   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)B->data;
1379 
1380   PetscFunctionBegin;
1381   /* If the  matrix/block dimensions are not equal, or no of nonzeros or shift */
1382   if ((A->rmap->N != B->rmap->N) || (A->cmap->n != B->cmap->n) || (A->rmap->bs != B->rmap->bs) || (a->nz != b->nz)) {
1383     *flg = PETSC_FALSE;
1384     PetscFunctionReturn(PETSC_SUCCESS);
1385   }
1386 
1387   /* if the a->i are the same */
1388   PetscCall(PetscArraycmp(a->i, b->i, a->mbs + 1, flg));
1389   if (!*flg) PetscFunctionReturn(PETSC_SUCCESS);
1390 
1391   /* if a->j are the same */
1392   PetscCall(PetscArraycmp(a->j, b->j, a->nz, flg));
1393   if (!*flg) PetscFunctionReturn(PETSC_SUCCESS);
1394 
1395   /* if a->a are the same */
1396   PetscCall(PetscArraycmp(a->a, b->a, a->nz * A->rmap->bs * A->rmap->bs, flg));
1397   PetscFunctionReturn(PETSC_SUCCESS);
1398 }
1399 
1400 PetscErrorCode MatGetDiagonal_SeqSBAIJ(Mat A, Vec v)
1401 {
1402   Mat_SeqSBAIJ    *a = (Mat_SeqSBAIJ *)A->data;
1403   PetscInt         n;
1404   const PetscInt   bs = A->rmap->bs, ambs = a->mbs, bs2 = a->bs2;
1405   PetscScalar     *x;
1406   const MatScalar *aa = a->a, *aa_j;
1407   const PetscInt  *ai = a->i, *adiag;
1408   PetscBool        diagDense;
1409 
1410   PetscFunctionBegin;
1411   PetscCheck(!A->factortype || bs <= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix with bs>1");
1412   PetscCall(MatGetDiagonalMarkers_SeqSBAIJ(A, &adiag, &diagDense));
1413   if (A->factortype == MAT_FACTOR_CHOLESKY || A->factortype == MAT_FACTOR_ICC) {
1414     PetscCall(VecGetArrayWrite(v, &x));
1415     for (PetscInt i = 0; i < ambs; i++) x[i] = 1.0 / aa[adiag[i]];
1416     PetscCall(VecRestoreArrayWrite(v, &x));
1417     PetscFunctionReturn(PETSC_SUCCESS);
1418   }
1419 
1420   PetscCall(VecGetLocalSize(v, &n));
1421   PetscCheck(n == A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
1422   PetscCall(VecGetArrayWrite(v, &x));
1423 
1424   if (diagDense) {
1425     for (PetscInt i = 0, row = 0; i < ambs; i++) {
1426       aa_j = aa + adiag[i] * bs2;
1427       for (PetscInt k = 0; k < bs2; k += (bs + 1)) x[row++] = aa_j[k];
1428     }
1429   } else {
1430     for (PetscInt i = 0, row = 0; i < ambs; i++) {
1431       const PetscInt j = adiag[i];
1432 
1433       if (j != ai[i + 1]) {
1434         aa_j = aa + j * bs2;
1435         for (PetscInt k = 0; k < bs2; k += (bs + 1)) x[row++] = aa_j[k];
1436       } else {
1437         for (PetscInt k = 0; k < bs; k++) x[row++] = 0.0;
1438       }
1439     }
1440   }
1441   PetscCall(VecRestoreArrayWrite(v, &x));
1442   PetscFunctionReturn(PETSC_SUCCESS);
1443 }
1444 
1445 PetscErrorCode MatDiagonalScale_SeqSBAIJ(Mat A, Vec ll, Vec rr)
1446 {
1447   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
1448   PetscScalar        x;
1449   const PetscScalar *l, *li, *ri;
1450   MatScalar         *aa, *v;
1451   PetscInt           i, j, k, lm, M, m, mbs, tmp, bs, bs2;
1452   const PetscInt    *ai, *aj;
1453   PetscBool          flg;
1454 
1455   PetscFunctionBegin;
1456   if (ll != rr) {
1457     PetscCall(VecEqual(ll, rr, &flg));
1458     PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "For symmetric format, left and right scaling vectors must be same");
1459   }
1460   if (!ll) PetscFunctionReturn(PETSC_SUCCESS);
1461   ai  = a->i;
1462   aj  = a->j;
1463   aa  = a->a;
1464   m   = A->rmap->N;
1465   bs  = A->rmap->bs;
1466   mbs = a->mbs;
1467   bs2 = a->bs2;
1468 
1469   PetscCall(VecGetArrayRead(ll, &l));
1470   PetscCall(VecGetLocalSize(ll, &lm));
1471   PetscCheck(lm == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Left scaling vector wrong length");
1472   for (i = 0; i < mbs; i++) { /* for each block row */
1473     M  = ai[i + 1] - ai[i];
1474     li = l + i * bs;
1475     v  = aa + bs2 * ai[i];
1476     for (j = 0; j < M; j++) { /* for each block */
1477       ri = l + bs * aj[ai[i] + j];
1478       for (k = 0; k < bs; k++) {
1479         x = ri[k];
1480         for (tmp = 0; tmp < bs; tmp++) (*v++) *= li[tmp] * x;
1481       }
1482     }
1483   }
1484   PetscCall(VecRestoreArrayRead(ll, &l));
1485   PetscCall(PetscLogFlops(2.0 * a->nz));
1486   PetscFunctionReturn(PETSC_SUCCESS);
1487 }
1488 
1489 PetscErrorCode MatGetInfo_SeqSBAIJ(Mat A, MatInfoType flag, MatInfo *info)
1490 {
1491   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data;
1492 
1493   PetscFunctionBegin;
1494   info->block_size   = a->bs2;
1495   info->nz_allocated = a->bs2 * a->maxnz; /*num. of nonzeros in upper triangular part */
1496   info->nz_used      = a->bs2 * a->nz;    /*num. of nonzeros in upper triangular part */
1497   info->nz_unneeded  = info->nz_allocated - info->nz_used;
1498   info->assemblies   = A->num_ass;
1499   info->mallocs      = A->info.mallocs;
1500   info->memory       = 0; /* REVIEW ME */
1501   if (A->factortype) {
1502     info->fill_ratio_given  = A->info.fill_ratio_given;
1503     info->fill_ratio_needed = A->info.fill_ratio_needed;
1504     info->factor_mallocs    = A->info.factor_mallocs;
1505   } else {
1506     info->fill_ratio_given  = 0;
1507     info->fill_ratio_needed = 0;
1508     info->factor_mallocs    = 0;
1509   }
1510   PetscFunctionReturn(PETSC_SUCCESS);
1511 }
1512 
1513 PetscErrorCode MatZeroEntries_SeqSBAIJ(Mat A)
1514 {
1515   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data;
1516 
1517   PetscFunctionBegin;
1518   PetscCall(PetscArrayzero(a->a, a->bs2 * a->i[a->mbs]));
1519   PetscFunctionReturn(PETSC_SUCCESS);
1520 }
1521 
1522 PetscErrorCode MatGetRowMaxAbs_SeqSBAIJ(Mat A, Vec v, PetscInt idx[])
1523 {
1524   Mat_SeqSBAIJ    *a = (Mat_SeqSBAIJ *)A->data;
1525   PetscInt         i, j, n, row, col, bs, mbs;
1526   const PetscInt  *ai, *aj;
1527   PetscReal        atmp;
1528   const MatScalar *aa;
1529   PetscScalar     *x;
1530   PetscInt         ncols, brow, bcol, krow, kcol;
1531 
1532   PetscFunctionBegin;
1533   PetscCheck(!idx, PETSC_COMM_SELF, PETSC_ERR_SUP, "Send email to petsc-maint@mcs.anl.gov");
1534   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
1535   bs  = A->rmap->bs;
1536   aa  = a->a;
1537   ai  = a->i;
1538   aj  = a->j;
1539   mbs = a->mbs;
1540 
1541   PetscCall(VecSet(v, 0.0));
1542   PetscCall(VecGetArray(v, &x));
1543   PetscCall(VecGetLocalSize(v, &n));
1544   PetscCheck(n == A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
1545   for (i = 0; i < mbs; i++) {
1546     ncols = ai[1] - ai[0];
1547     ai++;
1548     brow = bs * i;
1549     for (j = 0; j < ncols; j++) {
1550       bcol = bs * (*aj);
1551       for (kcol = 0; kcol < bs; kcol++) {
1552         col = bcol + kcol; /* col index */
1553         for (krow = 0; krow < bs; krow++) {
1554           atmp = PetscAbsScalar(*aa);
1555           aa++;
1556           row = brow + krow; /* row index */
1557           if (PetscRealPart(x[row]) < atmp) x[row] = atmp;
1558           if (*aj > i && PetscRealPart(x[col]) < atmp) x[col] = atmp;
1559         }
1560       }
1561       aj++;
1562     }
1563   }
1564   PetscCall(VecRestoreArray(v, &x));
1565   PetscFunctionReturn(PETSC_SUCCESS);
1566 }
1567 
1568 PetscErrorCode MatMatMultSymbolic_SeqSBAIJ_SeqDense(Mat A, Mat B, PetscReal fill, Mat C)
1569 {
1570   PetscFunctionBegin;
1571   PetscCall(MatMatMultSymbolic_SeqDense_SeqDense(A, B, 0.0, C));
1572   C->ops->matmultnumeric = MatMatMultNumeric_SeqSBAIJ_SeqDense;
1573   PetscFunctionReturn(PETSC_SUCCESS);
1574 }
1575 
1576 static PetscErrorCode MatMatMult_SeqSBAIJ_1_Private(Mat A, PetscScalar *b, PetscInt bm, PetscScalar *c, PetscInt cm, PetscInt cn)
1577 {
1578   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
1579   PetscScalar       *z = c;
1580   const PetscScalar *xb;
1581   PetscScalar        x1;
1582   const MatScalar   *v   = a->a, *vv;
1583   PetscInt           mbs = a->mbs, i, *idx = a->j, *ii = a->i, j, *jj, n, k;
1584 #if defined(PETSC_USE_COMPLEX)
1585   const int aconj = A->hermitian == PETSC_BOOL3_TRUE;
1586 #else
1587   const int aconj = 0;
1588 #endif
1589 
1590   PetscFunctionBegin;
1591   for (i = 0; i < mbs; i++) {
1592     n = ii[1] - ii[0];
1593     ii++;
1594     PetscPrefetchBlock(idx + n, n, 0, PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
1595     PetscPrefetchBlock(v + n, n, 0, PETSC_PREFETCH_HINT_NTA);   /* Entries for the next row */
1596     jj = idx;
1597     vv = v;
1598     for (k = 0; k < cn; k++) {
1599       idx = jj;
1600       v   = vv;
1601       for (j = 0; j < n; j++) {
1602         xb = b + (*idx);
1603         x1 = xb[0 + k * bm];
1604         z[0 + k * cm] += v[0] * x1;
1605         if (*idx != i) c[(*idx) + k * cm] += (aconj ? PetscConj(v[0]) : v[0]) * b[i + k * bm];
1606         v += 1;
1607         ++idx;
1608       }
1609     }
1610     z += 1;
1611   }
1612   PetscFunctionReturn(PETSC_SUCCESS);
1613 }
1614 
1615 static PetscErrorCode MatMatMult_SeqSBAIJ_2_Private(Mat A, PetscScalar *b, PetscInt bm, PetscScalar *c, PetscInt cm, PetscInt cn)
1616 {
1617   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
1618   PetscScalar       *z = c;
1619   const PetscScalar *xb;
1620   PetscScalar        x1, x2;
1621   const MatScalar   *v   = a->a, *vv;
1622   PetscInt           mbs = a->mbs, i, *idx = a->j, *ii = a->i, j, *jj, n, k;
1623 
1624   PetscFunctionBegin;
1625   for (i = 0; i < mbs; i++) {
1626     n = ii[1] - ii[0];
1627     ii++;
1628     PetscPrefetchBlock(idx + n, n, 0, PETSC_PREFETCH_HINT_NTA);       /* Indices for the next row (assumes same size as this one) */
1629     PetscPrefetchBlock(v + 4 * n, 4 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1630     jj = idx;
1631     vv = v;
1632     for (k = 0; k < cn; k++) {
1633       idx = jj;
1634       v   = vv;
1635       for (j = 0; j < n; j++) {
1636         xb = b + 2 * (*idx);
1637         x1 = xb[0 + k * bm];
1638         x2 = xb[1 + k * bm];
1639         z[0 + k * cm] += v[0] * x1 + v[2] * x2;
1640         z[1 + k * cm] += v[1] * x1 + v[3] * x2;
1641         if (*idx != i) {
1642           c[2 * (*idx) + 0 + k * cm] += v[0] * b[2 * i + k * bm] + v[1] * b[2 * i + 1 + k * bm];
1643           c[2 * (*idx) + 1 + k * cm] += v[2] * b[2 * i + k * bm] + v[3] * b[2 * i + 1 + k * bm];
1644         }
1645         v += 4;
1646         ++idx;
1647       }
1648     }
1649     z += 2;
1650   }
1651   PetscFunctionReturn(PETSC_SUCCESS);
1652 }
1653 
1654 static PetscErrorCode MatMatMult_SeqSBAIJ_3_Private(Mat A, PetscScalar *b, PetscInt bm, PetscScalar *c, PetscInt cm, PetscInt cn)
1655 {
1656   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
1657   PetscScalar       *z = c;
1658   const PetscScalar *xb;
1659   PetscScalar        x1, x2, x3;
1660   const MatScalar   *v   = a->a, *vv;
1661   PetscInt           mbs = a->mbs, i, *idx = a->j, *ii = a->i, j, *jj, n, k;
1662 
1663   PetscFunctionBegin;
1664   for (i = 0; i < mbs; i++) {
1665     n = ii[1] - ii[0];
1666     ii++;
1667     PetscPrefetchBlock(idx + n, n, 0, PETSC_PREFETCH_HINT_NTA);       /* Indices for the next row (assumes same size as this one) */
1668     PetscPrefetchBlock(v + 9 * n, 9 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1669     jj = idx;
1670     vv = v;
1671     for (k = 0; k < cn; k++) {
1672       idx = jj;
1673       v   = vv;
1674       for (j = 0; j < n; j++) {
1675         xb = b + 3 * (*idx);
1676         x1 = xb[0 + k * bm];
1677         x2 = xb[1 + k * bm];
1678         x3 = xb[2 + k * bm];
1679         z[0 + k * cm] += v[0] * x1 + v[3] * x2 + v[6] * x3;
1680         z[1 + k * cm] += v[1] * x1 + v[4] * x2 + v[7] * x3;
1681         z[2 + k * cm] += v[2] * x1 + v[5] * x2 + v[8] * x3;
1682         if (*idx != i) {
1683           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];
1684           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];
1685           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];
1686         }
1687         v += 9;
1688         ++idx;
1689       }
1690     }
1691     z += 3;
1692   }
1693   PetscFunctionReturn(PETSC_SUCCESS);
1694 }
1695 
1696 static PetscErrorCode MatMatMult_SeqSBAIJ_4_Private(Mat A, PetscScalar *b, PetscInt bm, PetscScalar *c, PetscInt cm, PetscInt cn)
1697 {
1698   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
1699   PetscScalar       *z = c;
1700   const PetscScalar *xb;
1701   PetscScalar        x1, x2, x3, x4;
1702   const MatScalar   *v   = a->a, *vv;
1703   PetscInt           mbs = a->mbs, i, *idx = a->j, *ii = a->i, j, *jj, n, k;
1704 
1705   PetscFunctionBegin;
1706   for (i = 0; i < mbs; i++) {
1707     n = ii[1] - ii[0];
1708     ii++;
1709     PetscPrefetchBlock(idx + n, n, 0, PETSC_PREFETCH_HINT_NTA);         /* Indices for the next row (assumes same size as this one) */
1710     PetscPrefetchBlock(v + 16 * n, 16 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1711     jj = idx;
1712     vv = v;
1713     for (k = 0; k < cn; k++) {
1714       idx = jj;
1715       v   = vv;
1716       for (j = 0; j < n; j++) {
1717         xb = b + 4 * (*idx);
1718         x1 = xb[0 + k * bm];
1719         x2 = xb[1 + k * bm];
1720         x3 = xb[2 + k * bm];
1721         x4 = xb[3 + k * bm];
1722         z[0 + k * cm] += v[0] * x1 + v[4] * x2 + v[8] * x3 + v[12] * x4;
1723         z[1 + k * cm] += v[1] * x1 + v[5] * x2 + v[9] * x3 + v[13] * x4;
1724         z[2 + k * cm] += v[2] * x1 + v[6] * x2 + v[10] * x3 + v[14] * x4;
1725         z[3 + k * cm] += v[3] * x1 + v[7] * x2 + v[11] * x3 + v[15] * x4;
1726         if (*idx != i) {
1727           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];
1728           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];
1729           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];
1730           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];
1731         }
1732         v += 16;
1733         ++idx;
1734       }
1735     }
1736     z += 4;
1737   }
1738   PetscFunctionReturn(PETSC_SUCCESS);
1739 }
1740 
1741 static PetscErrorCode MatMatMult_SeqSBAIJ_5_Private(Mat A, PetscScalar *b, PetscInt bm, PetscScalar *c, PetscInt cm, PetscInt cn)
1742 {
1743   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ *)A->data;
1744   PetscScalar       *z = c;
1745   const PetscScalar *xb;
1746   PetscScalar        x1, x2, x3, x4, x5;
1747   const MatScalar   *v   = a->a, *vv;
1748   PetscInt           mbs = a->mbs, i, *idx = a->j, *ii = a->i, j, *jj, n, k;
1749 
1750   PetscFunctionBegin;
1751   for (i = 0; i < mbs; i++) {
1752     n = ii[1] - ii[0];
1753     ii++;
1754     PetscPrefetchBlock(idx + n, n, 0, PETSC_PREFETCH_HINT_NTA);         /* Indices for the next row (assumes same size as this one) */
1755     PetscPrefetchBlock(v + 25 * n, 25 * n, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */
1756     jj = idx;
1757     vv = v;
1758     for (k = 0; k < cn; k++) {
1759       idx = jj;
1760       v   = vv;
1761       for (j = 0; j < n; j++) {
1762         xb = b + 5 * (*idx);
1763         x1 = xb[0 + k * bm];
1764         x2 = xb[1 + k * bm];
1765         x3 = xb[2 + k * bm];
1766         x4 = xb[3 + k * bm];
1767         x5 = xb[4 + k * cm];
1768         z[0 + k * cm] += v[0] * x1 + v[5] * x2 + v[10] * x3 + v[15] * x4 + v[20] * x5;
1769         z[1 + k * cm] += v[1] * x1 + v[6] * x2 + v[11] * x3 + v[16] * x4 + v[21] * x5;
1770         z[2 + k * cm] += v[2] * x1 + v[7] * x2 + v[12] * x3 + v[17] * x4 + v[22] * x5;
1771         z[3 + k * cm] += v[3] * x1 + v[8] * x2 + v[13] * x3 + v[18] * x4 + v[23] * x5;
1772         z[4 + k * cm] += v[4] * x1 + v[9] * x2 + v[14] * x3 + v[19] * x4 + v[24] * x5;
1773         if (*idx != i) {
1774           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];
1775           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];
1776           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];
1777           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];
1778           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];
1779         }
1780         v += 25;
1781         ++idx;
1782       }
1783     }
1784     z += 5;
1785   }
1786   PetscFunctionReturn(PETSC_SUCCESS);
1787 }
1788 
1789 PetscErrorCode MatMatMultNumeric_SeqSBAIJ_SeqDense(Mat A, Mat B, Mat C)
1790 {
1791   Mat_SeqSBAIJ    *a  = (Mat_SeqSBAIJ *)A->data;
1792   Mat_SeqDense    *bd = (Mat_SeqDense *)B->data;
1793   Mat_SeqDense    *cd = (Mat_SeqDense *)C->data;
1794   PetscInt         cm = cd->lda, cn = B->cmap->n, bm = bd->lda;
1795   PetscInt         mbs, i, bs = A->rmap->bs, j, n, bs2 = a->bs2;
1796   PetscBLASInt     bbs, bcn, bbm, bcm;
1797   PetscScalar     *z = NULL;
1798   PetscScalar     *c, *b;
1799   const MatScalar *v;
1800   const PetscInt  *idx, *ii;
1801   PetscScalar      _DOne = 1.0;
1802 
1803   PetscFunctionBegin;
1804   if (!cm || !cn) PetscFunctionReturn(PETSC_SUCCESS);
1805   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);
1806   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);
1807   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);
1808   b = bd->v;
1809   PetscCall(MatZeroEntries(C));
1810   PetscCall(MatDenseGetArray(C, &c));
1811   switch (bs) {
1812   case 1:
1813     PetscCall(MatMatMult_SeqSBAIJ_1_Private(A, b, bm, c, cm, cn));
1814     break;
1815   case 2:
1816     PetscCall(MatMatMult_SeqSBAIJ_2_Private(A, b, bm, c, cm, cn));
1817     break;
1818   case 3:
1819     PetscCall(MatMatMult_SeqSBAIJ_3_Private(A, b, bm, c, cm, cn));
1820     break;
1821   case 4:
1822     PetscCall(MatMatMult_SeqSBAIJ_4_Private(A, b, bm, c, cm, cn));
1823     break;
1824   case 5:
1825     PetscCall(MatMatMult_SeqSBAIJ_5_Private(A, b, bm, c, cm, cn));
1826     break;
1827   default: /* block sizes larger than 5 by 5 are handled by BLAS */
1828     PetscCall(PetscBLASIntCast(bs, &bbs));
1829     PetscCall(PetscBLASIntCast(cn, &bcn));
1830     PetscCall(PetscBLASIntCast(bm, &bbm));
1831     PetscCall(PetscBLASIntCast(cm, &bcm));
1832     idx = a->j;
1833     v   = a->a;
1834     mbs = a->mbs;
1835     ii  = a->i;
1836     z   = c;
1837     for (i = 0; i < mbs; i++) {
1838       n = ii[1] - ii[0];
1839       ii++;
1840       for (j = 0; j < n; j++) {
1841         if (*idx != i) PetscCallBLAS("BLASgemm", BLASgemm_("T", "N", &bbs, &bcn, &bbs, &_DOne, v, &bbs, b + bs * i, &bbm, &_DOne, c + bs * (*idx), &bcm));
1842         PetscCallBLAS("BLASgemm", BLASgemm_("N", "N", &bbs, &bcn, &bbs, &_DOne, v, &bbs, b + bs * (*idx++), &bbm, &_DOne, z, &bcm));
1843         v += bs2;
1844       }
1845       z += bs;
1846     }
1847   }
1848   PetscCall(MatDenseRestoreArray(C, &c));
1849   PetscCall(PetscLogFlops((2.0 * (a->nz * 2.0 - a->nonzerorowcnt) * bs2 - a->nonzerorowcnt) * cn));
1850   PetscFunctionReturn(PETSC_SUCCESS);
1851 }
1852