Actual source code: inode.c

  1: /*
  2:   This file provides high performance routines for the Inode format (compressed sparse row)
  3:   by taking advantage of rows with identical nonzero structure (I-nodes).
  4: */
  5: #include <../src/mat/impls/aij/seq/aij.h>
  6: #if defined(PETSC_HAVE_XMMINTRIN_H)
  7:   #include <xmmintrin.h>
  8: #endif

 10: static PetscErrorCode MatCreateColInode_Private(Mat A, PetscInt *size, PetscInt **ns)
 11: {
 12:   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
 13:   PetscInt    i, count, m, n, min_mn, *ns_row, *ns_col;

 15:   PetscFunctionBegin;
 16:   n = A->cmap->n;
 17:   m = A->rmap->n;
 18:   PetscCheck(a->inode.size_csr, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
 19:   ns_row = a->inode.size_csr;

 21:   min_mn = (m < n) ? m : n;
 22:   if (!ns) {
 23:     for (count = 0, i = 0; count < min_mn; count += (ns_row[i + 1] - ns_row[i]), i++);
 24:     for (; count + 1 < n; count++, i++);
 25:     if (count < n) i++;
 26:     *size = i;
 27:     PetscFunctionReturn(PETSC_SUCCESS);
 28:   }
 29:   PetscCall(PetscMalloc1(n + 1, &ns_col));
 30:   ns_col[0] = 0;

 32:   /* Use the same row structure wherever feasible. */
 33:   for (count = 0, i = 0; count < min_mn; count += (ns_row[i + 1] - ns_row[i]), i++) ns_col[i + 1] = ns_row[i + 1];

 35:   /* if m < n; pad up the remainder with inode_limit */
 36:   for (; count + 1 < n; count++, i++) ns_col[i + 1] = ns_col[i] + 1;
 37:   /* The last node is the odd ball. pad it up with the remaining rows; */
 38:   if (count < n) {
 39:     ns_col[i + 1] = ns_col[i] + (n - count);
 40:     i++;
 41:   } else if (count > n) {
 42:     /* Adjust for the over estimation */
 43:     ns_col[i] += n - count;
 44:   }
 45:   *size = i;
 46:   *ns   = ns_col;
 47:   PetscFunctionReturn(PETSC_SUCCESS);
 48: }

 50: /*
 51:       This builds symmetric version of nonzero structure,
 52: */
 53: static PetscErrorCode MatGetRowIJ_SeqAIJ_Inode_Symmetric(Mat A, const PetscInt *iia[], const PetscInt *jja[], PetscInt ishift, PetscInt oshift)
 54: {
 55:   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
 56:   PetscInt       *work, *ia, *ja, nz, nslim_row, nslim_col, m, row, col, n;
 57:   PetscInt       *tns, *tvc, *ns_row = a->inode.size_csr, *ns_col, nsz, i1, i2;
 58:   const PetscInt *j, *jmax, *ai = a->i, *aj = a->j;

 60:   PetscFunctionBegin;
 61:   nslim_row = a->inode.node_count;
 62:   m         = A->rmap->n;
 63:   n         = A->cmap->n;
 64:   PetscCheck(m == n, PETSC_COMM_SELF, PETSC_ERR_SUP, "MatGetRowIJ_SeqAIJ_Inode_Symmetric: Matrix should be square");
 65:   PetscCheck(a->inode.size_csr, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");

 67:   /* Use the row_inode as column_inode */
 68:   nslim_col = nslim_row;
 69:   ns_col    = ns_row;

 71:   /* allocate space for reformatted inode structure */
 72:   PetscCall(PetscMalloc2(nslim_col + 1, &tns, n + 1, &tvc));
 73:   for (i1 = 0, tns[0] = 0; i1 < nslim_col; ++i1) tns[i1 + 1] = tns[i1] + (ns_row[i1 + 1] - ns_row[i1]);

 75:   for (i1 = 0, col = 0; i1 < nslim_col; ++i1) {
 76:     nsz = ns_col[i1 + 1] - ns_col[i1];
 77:     for (i2 = 0; i2 < nsz; ++i2, ++col) tvc[col] = i1;
 78:   }
 79:   /* allocate space for row pointers */
 80:   PetscCall(PetscCalloc1(nslim_row + 1, &ia));
 81:   *iia = ia;
 82:   PetscCall(PetscMalloc1(nslim_row + 1, &work));

 84:   /* determine the number of columns in each row */
 85:   ia[0] = oshift;
 86:   for (i1 = 0; i1 < nslim_row; i1++) {
 87:     row  = ns_row[i1];
 88:     j    = aj + ai[row] + ishift;
 89:     jmax = aj + ai[row + 1] + ishift;
 90:     if (j == jmax) continue; /* empty row */
 91:     col = *j++ + ishift;
 92:     i2  = tvc[col];
 93:     while (i2 < i1 && j < jmax) { /* 1.[-xx-d-xx--] 2.[-xx-------],off-diagonal elements */
 94:       ia[i1 + 1]++;
 95:       ia[i2 + 1]++;
 96:       i2++; /* Start col of next node */
 97:       while ((j < jmax) && ((col = *j + ishift) < tns[i2])) ++j;
 98:       i2 = tvc[col];
 99:     }
100:     if (i2 == i1) ia[i2 + 1]++; /* now the diagonal element */
101:   }

103:   /* shift ia[i] to point to next row */
104:   for (i1 = 1; i1 < nslim_row + 1; i1++) {
105:     row = ia[i1 - 1];
106:     ia[i1] += row;
107:     work[i1 - 1] = row - oshift;
108:   }

110:   /* allocate space for column pointers */
111:   nz = ia[nslim_row] + (!ishift);
112:   PetscCall(PetscMalloc1(nz, &ja));
113:   *jja = ja;

115:   /* loop over lower triangular part putting into ja */
116:   for (i1 = 0; i1 < nslim_row; i1++) {
117:     row  = ns_row[i1];
118:     j    = aj + ai[row] + ishift;
119:     jmax = aj + ai[row + 1] + ishift;
120:     if (j == jmax) continue; /* empty row */
121:     col = *j++ + ishift;
122:     i2  = tvc[col];
123:     while (i2 < i1 && j < jmax) {
124:       ja[work[i2]++] = i1 + oshift;
125:       ja[work[i1]++] = i2 + oshift;
126:       ++i2;
127:       while ((j < jmax) && ((col = *j + ishift) < tns[i2])) ++j; /* Skip rest col indices in this node */
128:       i2 = tvc[col];
129:     }
130:     if (i2 == i1) ja[work[i1]++] = i2 + oshift;
131:   }
132:   PetscCall(PetscFree(work));
133:   PetscCall(PetscFree2(tns, tvc));
134:   PetscFunctionReturn(PETSC_SUCCESS);
135: }

137: /*
138:       This builds nonsymmetric version of nonzero structure,
139: */
140: static PetscErrorCode MatGetRowIJ_SeqAIJ_Inode_Nonsymmetric(Mat A, const PetscInt *iia[], const PetscInt *jja[], PetscInt ishift, PetscInt oshift)
141: {
142:   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
143:   PetscInt       *work, *ia, *ja, nz, nslim_row, n, row, col, *ns_col, nslim_col;
144:   PetscInt       *tns, *tvc, nsz, i1, i2;
145:   const PetscInt *j, *ai = a->i, *aj = a->j, *ns_row = a->inode.size_csr;

147:   PetscFunctionBegin;
148:   PetscCheck(a->inode.size_csr, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
149:   nslim_row = a->inode.node_count;
150:   n         = A->cmap->n;

152:   /* Create The column_inode for this matrix */
153:   PetscCall(MatCreateColInode_Private(A, &nslim_col, &ns_col));

155:   /* allocate space for reformatted column_inode structure */
156:   PetscCall(PetscMalloc2(nslim_col + 1, &tns, n + 1, &tvc));
157:   for (i1 = 0, tns[0] = 0; i1 < nslim_col; ++i1) tns[i1 + 1] = tns[i1] + (ns_col[i1 + 1] - ns_col[i1]);

159:   for (i1 = 0, col = 0; i1 < nslim_col; ++i1) {
160:     nsz = ns_col[i1 + 1] - ns_col[i1];
161:     for (i2 = 0; i2 < nsz; ++i2, ++col) tvc[col] = i1;
162:   }
163:   /* allocate space for row pointers */
164:   PetscCall(PetscCalloc1(nslim_row + 1, &ia));
165:   *iia = ia;
166:   PetscCall(PetscMalloc1(nslim_row + 1, &work));

168:   /* determine the number of columns in each row */
169:   ia[0] = oshift;
170:   for (i1 = 0; i1 < nslim_row; i1++) {
171:     row = ns_row[i1];
172:     j   = aj + ai[row] + ishift;
173:     nz  = ai[row + 1] - ai[row];
174:     if (!nz) continue; /* empty row */
175:     col = *j++ + ishift;
176:     i2  = tvc[col];
177:     while (nz-- > 0) { /* off-diagonal elements */
178:       ia[i1 + 1]++;
179:       i2++; /* Start col of next node */
180:       while (nz > 0 && ((col = *j++ + ishift) < tns[i2])) nz--;
181:       if (nz > 0) i2 = tvc[col];
182:     }
183:   }

185:   /* shift ia[i] to point to next row */
186:   for (i1 = 1; i1 < nslim_row + 1; i1++) {
187:     row = ia[i1 - 1];
188:     ia[i1] += row;
189:     work[i1 - 1] = row - oshift;
190:   }

192:   /* allocate space for column pointers */
193:   nz = ia[nslim_row] + (!ishift);
194:   PetscCall(PetscMalloc1(nz, &ja));
195:   *jja = ja;

197:   /* loop over matrix putting into ja */
198:   for (i1 = 0; i1 < nslim_row; i1++) {
199:     row = ns_row[i1];
200:     j   = aj + ai[row] + ishift;
201:     nz  = ai[row + 1] - ai[row];
202:     if (!nz) continue; /* empty row */
203:     col = *j++ + ishift;
204:     i2  = tvc[col];
205:     while (nz-- > 0) {
206:       ja[work[i1]++] = i2 + oshift;
207:       ++i2;
208:       while (nz > 0 && ((col = *j++ + ishift) < tns[i2])) nz--;
209:       if (nz > 0) i2 = tvc[col];
210:     }
211:   }
212:   PetscCall(PetscFree(ns_col));
213:   PetscCall(PetscFree(work));
214:   PetscCall(PetscFree2(tns, tvc));
215:   PetscFunctionReturn(PETSC_SUCCESS);
216: }

218: static PetscErrorCode MatGetRowIJ_SeqAIJ_Inode(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool blockcompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
219: {
220:   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;

222:   PetscFunctionBegin;
223:   if (n) *n = a->inode.node_count;
224:   if (!ia) PetscFunctionReturn(PETSC_SUCCESS);
225:   if (!blockcompressed) {
226:     PetscCall(MatGetRowIJ_SeqAIJ(A, oshift, symmetric, blockcompressed, n, ia, ja, done));
227:   } else if (symmetric) {
228:     PetscCall(MatGetRowIJ_SeqAIJ_Inode_Symmetric(A, ia, ja, 0, oshift));
229:   } else {
230:     PetscCall(MatGetRowIJ_SeqAIJ_Inode_Nonsymmetric(A, ia, ja, 0, oshift));
231:   }
232:   PetscFunctionReturn(PETSC_SUCCESS);
233: }

235: static PetscErrorCode MatRestoreRowIJ_SeqAIJ_Inode(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool blockcompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
236: {
237:   PetscFunctionBegin;
238:   if (!ia) PetscFunctionReturn(PETSC_SUCCESS);

240:   if (!blockcompressed) {
241:     PetscCall(MatRestoreRowIJ_SeqAIJ(A, oshift, symmetric, blockcompressed, n, ia, ja, done));
242:   } else {
243:     PetscCall(PetscFree(*ia));
244:     PetscCall(PetscFree(*ja));
245:   }
246:   PetscFunctionReturn(PETSC_SUCCESS);
247: }

249: static PetscErrorCode MatGetColumnIJ_SeqAIJ_Inode_Nonsymmetric(Mat A, const PetscInt *iia[], const PetscInt *jja[], PetscInt ishift, PetscInt oshift)
250: {
251:   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
252:   PetscInt   *work, *ia, *ja, *j, nz, nslim_row, n, row, col, *ns_col, nslim_col;
253:   PetscInt   *tns, *tvc, *ns_row = a->inode.size_csr, nsz, i1, i2, *ai = a->i, *aj = a->j;

255:   PetscFunctionBegin;
256:   PetscCheck(a->inode.size_csr, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
257:   nslim_row = a->inode.node_count;
258:   n         = A->cmap->n;

260:   /* Create The column_inode for this matrix */
261:   PetscCall(MatCreateColInode_Private(A, &nslim_col, &ns_col));

263:   /* allocate space for reformatted column_inode structure */
264:   PetscCall(PetscMalloc2(nslim_col + 1, &tns, n + 1, &tvc));
265:   for (i1 = 0, tns[0] = 0; i1 < nslim_col; ++i1) tns[i1 + 1] = tns[i1] + (ns_col[i1 + 1] - ns_col[i1]);

267:   for (i1 = 0, col = 0; i1 < nslim_col; ++i1) {
268:     nsz = ns_col[i1 + 1] - ns_col[i1];
269:     for (i2 = 0; i2 < nsz; ++i2, ++col) tvc[col] = i1;
270:   }
271:   /* allocate space for column pointers */
272:   PetscCall(PetscCalloc1(nslim_col + 1, &ia));
273:   *iia = ia;
274:   PetscCall(PetscMalloc1(nslim_col + 1, &work));

276:   /* determine the number of columns in each row */
277:   ia[0] = oshift;
278:   for (i1 = 0; i1 < nslim_row; i1++) {
279:     row = ns_row[i1];
280:     j   = aj + ai[row] + ishift;
281:     col = *j++ + ishift;
282:     i2  = tvc[col];
283:     nz  = ai[row + 1] - ai[row];
284:     while (nz-- > 0) { /* off-diagonal elements */
285:       /* ia[i1+1]++; */
286:       ia[i2 + 1]++;
287:       i2++;
288:       while (nz > 0 && ((col = *j++ + ishift) < tns[i2])) nz--;
289:       if (nz > 0) i2 = tvc[col];
290:     }
291:   }

293:   /* shift ia[i] to point to next col */
294:   for (i1 = 1; i1 < nslim_col + 1; i1++) {
295:     col = ia[i1 - 1];
296:     ia[i1] += col;
297:     work[i1 - 1] = col - oshift;
298:   }

300:   /* allocate space for column pointers */
301:   nz = ia[nslim_col] + (!ishift);
302:   PetscCall(PetscMalloc1(nz, &ja));
303:   *jja = ja;

305:   /* loop over matrix putting into ja */
306:   for (i1 = 0; i1 < nslim_row; i1++) {
307:     row = ns_row[i1];
308:     j   = aj + ai[row] + ishift;
309:     col = *j++ + ishift;
310:     i2  = tvc[col];
311:     nz  = ai[row + 1] - ai[row];
312:     while (nz-- > 0) {
313:       /* ja[work[i1]++] = i2 + oshift; */
314:       ja[work[i2]++] = i1 + oshift;
315:       i2++;
316:       while (nz > 0 && ((col = *j++ + ishift) < tns[i2])) nz--;
317:       if (nz > 0) i2 = tvc[col];
318:     }
319:   }
320:   PetscCall(PetscFree(ns_col));
321:   PetscCall(PetscFree(work));
322:   PetscCall(PetscFree2(tns, tvc));
323:   PetscFunctionReturn(PETSC_SUCCESS);
324: }

326: static PetscErrorCode MatGetColumnIJ_SeqAIJ_Inode(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool blockcompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
327: {
328:   PetscFunctionBegin;
329:   PetscCall(MatCreateColInode_Private(A, n, NULL));
330:   if (!ia) PetscFunctionReturn(PETSC_SUCCESS);

332:   if (!blockcompressed) {
333:     PetscCall(MatGetColumnIJ_SeqAIJ(A, oshift, symmetric, blockcompressed, n, ia, ja, done));
334:   } else if (symmetric) {
335:     /* Since the indices are symmetric it doesn't matter */
336:     PetscCall(MatGetRowIJ_SeqAIJ_Inode_Symmetric(A, ia, ja, 0, oshift));
337:   } else {
338:     PetscCall(MatGetColumnIJ_SeqAIJ_Inode_Nonsymmetric(A, ia, ja, 0, oshift));
339:   }
340:   PetscFunctionReturn(PETSC_SUCCESS);
341: }

343: static PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Inode(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool blockcompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
344: {
345:   PetscFunctionBegin;
346:   if (!ia) PetscFunctionReturn(PETSC_SUCCESS);
347:   if (!blockcompressed) {
348:     PetscCall(MatRestoreColumnIJ_SeqAIJ(A, oshift, symmetric, blockcompressed, n, ia, ja, done));
349:   } else {
350:     PetscCall(PetscFree(*ia));
351:     PetscCall(PetscFree(*ja));
352:   }
353:   PetscFunctionReturn(PETSC_SUCCESS);
354: }

356: PetscErrorCode MatMult_SeqAIJ_Inode(Mat A, Vec xx, Vec yy)
357: {
358:   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
359:   PetscScalar       *y;
360:   const PetscScalar *x;
361:   PetscInt           row, node_max, nonzerorow = 0;
362:   PetscInt          *ns;

364:   PetscFunctionBegin;
365:   PetscCheck(a->inode.size_csr, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
366:   node_max = a->inode.node_count;
367:   ns       = a->inode.size_csr; /* Node Size array */
368:   PetscCall(VecGetArrayRead(xx, &x));
369:   PetscCall(VecGetArray(yy, &y));

371:   PetscPragmaUseOMPKernels(parallel for private(row) reduction(+:nonzerorow))
372:   for (PetscInt i = 0; i < node_max; ++i) {
373:     PetscInt         i1, i2, nsz, n, sz;
374:     const MatScalar *v1, *v2, *v3, *v4, *v5;
375:     PetscScalar      sum1, sum2, sum3, sum4, sum5, tmp0, tmp1;
376:     const PetscInt  *idx;

378: #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
379:   #pragma disjoint(*x, *y, *v1, *v2, *v3, *v4, *v5)
380: #endif
381:     row = ns[i];
382:     nsz = ns[i + 1] - ns[i];
383:     n   = a->i[row + 1] - a->i[row];
384:     nonzerorow += (n > 0) * nsz;

386:     idx = &a->j[a->i[row]];
387:     v1  = &a->a[a->i[row]];
388:     PetscPrefetchBlock(idx + nsz * n, n, 0, PETSC_PREFETCH_HINT_NTA);      /* Prefetch the indices for the block row after the current one */
389:     PetscPrefetchBlock(v1 + nsz * n, nsz * n, 0, PETSC_PREFETCH_HINT_NTA); /* Prefetch the values for the block row after the current one  */
390:     sz = n;                                                                /* No of non zeros in this row */
391:                                                                            /* Switch on the size of Node */
392:     switch (nsz) {                                                         /* Each loop in 'case' is unrolled */
393:     case 1:
394:       sum1 = 0.;

396:       for (n = 0; n < sz - 1; n += 2) {
397:         i1 = idx[0]; /* The instructions are ordered to */
398:         i2 = idx[1]; /* make the compiler's job easy */
399:         idx += 2;
400:         tmp0 = x[i1];
401:         tmp1 = x[i2];
402:         sum1 += v1[0] * tmp0 + v1[1] * tmp1;
403:         v1 += 2;
404:       }

406:       if (n == sz - 1) { /* Take care of the last nonzero  */
407:         tmp0 = x[*idx++];
408:         sum1 += *v1++ * tmp0;
409:       }
410:       y[row++] = sum1;
411:       break;
412:     case 2:
413:       sum1 = 0.;
414:       sum2 = 0.;
415:       v2   = v1 + n;

417:       for (n = 0; n < sz - 1; n += 2) {
418:         i1 = idx[0];
419:         i2 = idx[1];
420:         idx += 2;
421:         tmp0 = x[i1];
422:         tmp1 = x[i2];
423:         sum1 += v1[0] * tmp0 + v1[1] * tmp1;
424:         v1 += 2;
425:         sum2 += v2[0] * tmp0 + v2[1] * tmp1;
426:         v2 += 2;
427:       }
428:       if (n == sz - 1) {
429:         tmp0 = x[*idx++];
430:         sum1 += *v1++ * tmp0;
431:         sum2 += *v2++ * tmp0;
432:       }
433:       y[row++] = sum1;
434:       y[row++] = sum2;
435:       v1       = v2; /* Since the next block to be processed starts there*/
436:       idx += sz;
437:       break;
438:     case 3:
439:       sum1 = 0.;
440:       sum2 = 0.;
441:       sum3 = 0.;
442:       v2   = v1 + n;
443:       v3   = v2 + n;

445:       for (n = 0; n < sz - 1; n += 2) {
446:         i1 = idx[0];
447:         i2 = idx[1];
448:         idx += 2;
449:         tmp0 = x[i1];
450:         tmp1 = x[i2];
451:         sum1 += v1[0] * tmp0 + v1[1] * tmp1;
452:         v1 += 2;
453:         sum2 += v2[0] * tmp0 + v2[1] * tmp1;
454:         v2 += 2;
455:         sum3 += v3[0] * tmp0 + v3[1] * tmp1;
456:         v3 += 2;
457:       }
458:       if (n == sz - 1) {
459:         tmp0 = x[*idx++];
460:         sum1 += *v1++ * tmp0;
461:         sum2 += *v2++ * tmp0;
462:         sum3 += *v3++ * tmp0;
463:       }
464:       y[row++] = sum1;
465:       y[row++] = sum2;
466:       y[row++] = sum3;
467:       v1       = v3; /* Since the next block to be processed starts there*/
468:       idx += 2 * sz;
469:       break;
470:     case 4:
471:       sum1 = 0.;
472:       sum2 = 0.;
473:       sum3 = 0.;
474:       sum4 = 0.;
475:       v2   = v1 + n;
476:       v3   = v2 + n;
477:       v4   = v3 + n;

479:       for (n = 0; n < sz - 1; n += 2) {
480:         i1 = idx[0];
481:         i2 = idx[1];
482:         idx += 2;
483:         tmp0 = x[i1];
484:         tmp1 = x[i2];
485:         sum1 += v1[0] * tmp0 + v1[1] * tmp1;
486:         v1 += 2;
487:         sum2 += v2[0] * tmp0 + v2[1] * tmp1;
488:         v2 += 2;
489:         sum3 += v3[0] * tmp0 + v3[1] * tmp1;
490:         v3 += 2;
491:         sum4 += v4[0] * tmp0 + v4[1] * tmp1;
492:         v4 += 2;
493:       }
494:       if (n == sz - 1) {
495:         tmp0 = x[*idx++];
496:         sum1 += *v1++ * tmp0;
497:         sum2 += *v2++ * tmp0;
498:         sum3 += *v3++ * tmp0;
499:         sum4 += *v4++ * tmp0;
500:       }
501:       y[row++] = sum1;
502:       y[row++] = sum2;
503:       y[row++] = sum3;
504:       y[row++] = sum4;
505:       v1       = v4; /* Since the next block to be processed starts there*/
506:       idx += 3 * sz;
507:       break;
508:     case 5:
509:       sum1 = 0.;
510:       sum2 = 0.;
511:       sum3 = 0.;
512:       sum4 = 0.;
513:       sum5 = 0.;
514:       v2   = v1 + n;
515:       v3   = v2 + n;
516:       v4   = v3 + n;
517:       v5   = v4 + n;

519:       for (n = 0; n < sz - 1; n += 2) {
520:         i1 = idx[0];
521:         i2 = idx[1];
522:         idx += 2;
523:         tmp0 = x[i1];
524:         tmp1 = x[i2];
525:         sum1 += v1[0] * tmp0 + v1[1] * tmp1;
526:         v1 += 2;
527:         sum2 += v2[0] * tmp0 + v2[1] * tmp1;
528:         v2 += 2;
529:         sum3 += v3[0] * tmp0 + v3[1] * tmp1;
530:         v3 += 2;
531:         sum4 += v4[0] * tmp0 + v4[1] * tmp1;
532:         v4 += 2;
533:         sum5 += v5[0] * tmp0 + v5[1] * tmp1;
534:         v5 += 2;
535:       }
536:       if (n == sz - 1) {
537:         tmp0 = x[*idx++];
538:         sum1 += *v1++ * tmp0;
539:         sum2 += *v2++ * tmp0;
540:         sum3 += *v3++ * tmp0;
541:         sum4 += *v4++ * tmp0;
542:         sum5 += *v5++ * tmp0;
543:       }
544:       y[row++] = sum1;
545:       y[row++] = sum2;
546:       y[row++] = sum3;
547:       y[row++] = sum4;
548:       y[row++] = sum5;
549:       v1       = v5; /* Since the next block to be processed starts there */
550:       idx += 4 * sz;
551:       break;
552:     default:
553:       SETERRABORT(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not supported, node row %" PetscInt_FMT " size %" PetscInt_FMT, row, nsz);
554:     }
555:   }
556:   PetscCall(VecRestoreArrayRead(xx, &x));
557:   PetscCall(VecRestoreArray(yy, &y));
558:   PetscCall(PetscLogFlops(2.0 * a->nz - nonzerorow));
559:   PetscFunctionReturn(PETSC_SUCCESS);
560: }

562: /* Almost same code as the MatMult_SeqAIJ_Inode() */
563: PetscErrorCode MatMultAdd_SeqAIJ_Inode(Mat A, Vec xx, Vec zz, Vec yy)
564: {
565:   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
566:   PetscScalar        sum1, sum2, sum3, sum4, sum5, tmp0, tmp1;
567:   const MatScalar   *v1, *v2, *v3, *v4, *v5;
568:   const PetscScalar *x;
569:   PetscScalar       *y, *z, *zt;
570:   PetscInt           i1, i2, n, i, row, node_max, nsz, sz;
571:   const PetscInt    *idx, *ns, *ii;

573:   PetscFunctionBegin;
574:   PetscCheck(a->inode.size_csr, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
575:   node_max = a->inode.node_count;
576:   ns       = a->inode.size_csr; /* Node Size array */

578:   PetscCall(VecGetArrayRead(xx, &x));
579:   PetscCall(VecGetArrayPair(zz, yy, &z, &y));
580:   zt = z;

582:   idx = a->j;
583:   v1  = a->a;
584:   ii  = a->i;

586:   for (i = 0; i < node_max; ++i) {
587:     row = ns[i];
588:     nsz = ns[i + 1] - ns[i];
589:     n   = ii[1] - ii[0];
590:     ii += nsz;
591:     sz = n;        /* No of non zeros in this row */
592:                    /* Switch on the size of Node */
593:     switch (nsz) { /* Each loop in 'case' is unrolled */
594:     case 1:
595:       sum1 = *zt++;

597:       for (n = 0; n < sz - 1; n += 2) {
598:         i1 = idx[0]; /* The instructions are ordered to */
599:         i2 = idx[1]; /* make the compiler's job easy */
600:         idx += 2;
601:         tmp0 = x[i1];
602:         tmp1 = x[i2];
603:         sum1 += v1[0] * tmp0 + v1[1] * tmp1;
604:         v1 += 2;
605:       }

607:       if (n == sz - 1) { /* Take care of the last nonzero  */
608:         tmp0 = x[*idx++];
609:         sum1 += *v1++ * tmp0;
610:       }
611:       y[row++] = sum1;
612:       break;
613:     case 2:
614:       sum1 = *zt++;
615:       sum2 = *zt++;
616:       v2   = v1 + n;

618:       for (n = 0; n < sz - 1; n += 2) {
619:         i1 = idx[0];
620:         i2 = idx[1];
621:         idx += 2;
622:         tmp0 = x[i1];
623:         tmp1 = x[i2];
624:         sum1 += v1[0] * tmp0 + v1[1] * tmp1;
625:         v1 += 2;
626:         sum2 += v2[0] * tmp0 + v2[1] * tmp1;
627:         v2 += 2;
628:       }
629:       if (n == sz - 1) {
630:         tmp0 = x[*idx++];
631:         sum1 += *v1++ * tmp0;
632:         sum2 += *v2++ * tmp0;
633:       }
634:       y[row++] = sum1;
635:       y[row++] = sum2;
636:       v1       = v2; /* Since the next block to be processed starts there*/
637:       idx += sz;
638:       break;
639:     case 3:
640:       sum1 = *zt++;
641:       sum2 = *zt++;
642:       sum3 = *zt++;
643:       v2   = v1 + n;
644:       v3   = v2 + n;

646:       for (n = 0; n < sz - 1; n += 2) {
647:         i1 = idx[0];
648:         i2 = idx[1];
649:         idx += 2;
650:         tmp0 = x[i1];
651:         tmp1 = x[i2];
652:         sum1 += v1[0] * tmp0 + v1[1] * tmp1;
653:         v1 += 2;
654:         sum2 += v2[0] * tmp0 + v2[1] * tmp1;
655:         v2 += 2;
656:         sum3 += v3[0] * tmp0 + v3[1] * tmp1;
657:         v3 += 2;
658:       }
659:       if (n == sz - 1) {
660:         tmp0 = x[*idx++];
661:         sum1 += *v1++ * tmp0;
662:         sum2 += *v2++ * tmp0;
663:         sum3 += *v3++ * tmp0;
664:       }
665:       y[row++] = sum1;
666:       y[row++] = sum2;
667:       y[row++] = sum3;
668:       v1       = v3; /* Since the next block to be processed starts there*/
669:       idx += 2 * sz;
670:       break;
671:     case 4:
672:       sum1 = *zt++;
673:       sum2 = *zt++;
674:       sum3 = *zt++;
675:       sum4 = *zt++;
676:       v2   = v1 + n;
677:       v3   = v2 + n;
678:       v4   = v3 + n;

680:       for (n = 0; n < sz - 1; n += 2) {
681:         i1 = idx[0];
682:         i2 = idx[1];
683:         idx += 2;
684:         tmp0 = x[i1];
685:         tmp1 = x[i2];
686:         sum1 += v1[0] * tmp0 + v1[1] * tmp1;
687:         v1 += 2;
688:         sum2 += v2[0] * tmp0 + v2[1] * tmp1;
689:         v2 += 2;
690:         sum3 += v3[0] * tmp0 + v3[1] * tmp1;
691:         v3 += 2;
692:         sum4 += v4[0] * tmp0 + v4[1] * tmp1;
693:         v4 += 2;
694:       }
695:       if (n == sz - 1) {
696:         tmp0 = x[*idx++];
697:         sum1 += *v1++ * tmp0;
698:         sum2 += *v2++ * tmp0;
699:         sum3 += *v3++ * tmp0;
700:         sum4 += *v4++ * tmp0;
701:       }
702:       y[row++] = sum1;
703:       y[row++] = sum2;
704:       y[row++] = sum3;
705:       y[row++] = sum4;
706:       v1       = v4; /* Since the next block to be processed starts there*/
707:       idx += 3 * sz;
708:       break;
709:     case 5:
710:       sum1 = *zt++;
711:       sum2 = *zt++;
712:       sum3 = *zt++;
713:       sum4 = *zt++;
714:       sum5 = *zt++;
715:       v2   = v1 + n;
716:       v3   = v2 + n;
717:       v4   = v3 + n;
718:       v5   = v4 + n;

720:       for (n = 0; n < sz - 1; n += 2) {
721:         i1 = idx[0];
722:         i2 = idx[1];
723:         idx += 2;
724:         tmp0 = x[i1];
725:         tmp1 = x[i2];
726:         sum1 += v1[0] * tmp0 + v1[1] * tmp1;
727:         v1 += 2;
728:         sum2 += v2[0] * tmp0 + v2[1] * tmp1;
729:         v2 += 2;
730:         sum3 += v3[0] * tmp0 + v3[1] * tmp1;
731:         v3 += 2;
732:         sum4 += v4[0] * tmp0 + v4[1] * tmp1;
733:         v4 += 2;
734:         sum5 += v5[0] * tmp0 + v5[1] * tmp1;
735:         v5 += 2;
736:       }
737:       if (n == sz - 1) {
738:         tmp0 = x[*idx++];
739:         sum1 += *v1++ * tmp0;
740:         sum2 += *v2++ * tmp0;
741:         sum3 += *v3++ * tmp0;
742:         sum4 += *v4++ * tmp0;
743:         sum5 += *v5++ * tmp0;
744:       }
745:       y[row++] = sum1;
746:       y[row++] = sum2;
747:       y[row++] = sum3;
748:       y[row++] = sum4;
749:       y[row++] = sum5;
750:       v1       = v5; /* Since the next block to be processed starts there */
751:       idx += 4 * sz;
752:       break;
753:     default:
754:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not yet supported");
755:     }
756:   }
757:   PetscCall(VecRestoreArrayRead(xx, &x));
758:   PetscCall(VecRestoreArrayPair(zz, yy, &z, &y));
759:   PetscCall(PetscLogFlops(2.0 * a->nz));
760:   PetscFunctionReturn(PETSC_SUCCESS);
761: }

763: static PetscErrorCode MatSolve_SeqAIJ_Inode_inplace(Mat A, Vec bb, Vec xx)
764: {
765:   Mat_SeqAIJ        *a     = (Mat_SeqAIJ *)A->data;
766:   IS                 iscol = a->col, isrow = a->row;
767:   const PetscInt    *r, *c, *rout, *cout;
768:   PetscInt           i, j, n = A->rmap->n, nz;
769:   PetscInt           node_max, *ns, row, nsz, aii, i0, i1;
770:   const PetscInt    *ai = a->i, *a_j = a->j, *vi, *ad, *aj;
771:   PetscScalar       *x, *tmp, *tmps, tmp0, tmp1;
772:   PetscScalar        sum1, sum2, sum3, sum4, sum5;
773:   const MatScalar   *v1, *v2, *v3, *v4, *v5, *a_a = a->a, *aa;
774:   const PetscScalar *b;

776:   PetscFunctionBegin;
777:   PetscCheck(a->inode.size_csr, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
778:   node_max = a->inode.node_count;
779:   ns       = a->inode.size_csr; /* Node Size array */

781:   PetscCall(VecGetArrayRead(bb, &b));
782:   PetscCall(VecGetArrayWrite(xx, &x));
783:   tmp = a->solve_work;

785:   PetscCall(ISGetIndices(isrow, &rout));
786:   r = rout;
787:   PetscCall(ISGetIndices(iscol, &cout));
788:   c = cout + (n - 1);

790:   /* forward solve the lower triangular */
791:   tmps = tmp;
792:   aa   = a_a;
793:   aj   = a_j;
794:   ad   = a->diag;

796:   for (i = 0, row = 0; i < node_max; ++i) {
797:     row = ns[i];
798:     nsz = ns[i + 1] - ns[i];
799:     aii = ai[row];
800:     v1  = aa + aii;
801:     vi  = aj + aii;
802:     nz  = ad[row] - aii;
803:     if (i < node_max - 1) {
804:       /* Prefetch the block after the current one, the prefetch itself can't cause a memory error,
805:       * but our indexing to determine its size could. */
806:       PetscPrefetchBlock(aj + ai[row + nsz], ad[row + nsz] - ai[row + nsz], 0, PETSC_PREFETCH_HINT_NTA); /* indices */
807:       /* In my tests, it seems to be better to fetch entire rows instead of just the lower-triangular part */
808:       PetscPrefetchBlock(aa + ai[row + nsz], ad[ns[i + 2] - 1] - ai[row + nsz], 0, PETSC_PREFETCH_HINT_NTA);
809:       /* for (j=0; j<ns[i+1]; j++) PetscPrefetchBlock(aa+ai[row+nsz+j],ad[row+nsz+j]-ai[row+nsz+j],0,0); */
810:     }

812:     switch (nsz) { /* Each loop in 'case' is unrolled */
813:     case 1:
814:       sum1 = b[*r++];
815:       for (j = 0; j < nz - 1; j += 2) {
816:         i0 = vi[0];
817:         i1 = vi[1];
818:         vi += 2;
819:         tmp0 = tmps[i0];
820:         tmp1 = tmps[i1];
821:         sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
822:         v1 += 2;
823:       }
824:       if (j == nz - 1) {
825:         tmp0 = tmps[*vi++];
826:         sum1 -= *v1++ * tmp0;
827:       }
828:       tmp[row++] = sum1;
829:       break;
830:     case 2:
831:       sum1 = b[*r++];
832:       sum2 = b[*r++];
833:       v2   = aa + ai[row + 1];

835:       for (j = 0; j < nz - 1; j += 2) {
836:         i0 = vi[0];
837:         i1 = vi[1];
838:         vi += 2;
839:         tmp0 = tmps[i0];
840:         tmp1 = tmps[i1];
841:         sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
842:         v1 += 2;
843:         sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
844:         v2 += 2;
845:       }
846:       if (j == nz - 1) {
847:         tmp0 = tmps[*vi++];
848:         sum1 -= *v1++ * tmp0;
849:         sum2 -= *v2++ * tmp0;
850:       }
851:       sum2 -= *v2++ * sum1;
852:       tmp[row++] = sum1;
853:       tmp[row++] = sum2;
854:       break;
855:     case 3:
856:       sum1 = b[*r++];
857:       sum2 = b[*r++];
858:       sum3 = b[*r++];
859:       v2   = aa + ai[row + 1];
860:       v3   = aa + ai[row + 2];

862:       for (j = 0; j < nz - 1; j += 2) {
863:         i0 = vi[0];
864:         i1 = vi[1];
865:         vi += 2;
866:         tmp0 = tmps[i0];
867:         tmp1 = tmps[i1];
868:         sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
869:         v1 += 2;
870:         sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
871:         v2 += 2;
872:         sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
873:         v3 += 2;
874:       }
875:       if (j == nz - 1) {
876:         tmp0 = tmps[*vi++];
877:         sum1 -= *v1++ * tmp0;
878:         sum2 -= *v2++ * tmp0;
879:         sum3 -= *v3++ * tmp0;
880:       }
881:       sum2 -= *v2++ * sum1;
882:       sum3 -= *v3++ * sum1;
883:       sum3 -= *v3++ * sum2;

885:       tmp[row++] = sum1;
886:       tmp[row++] = sum2;
887:       tmp[row++] = sum3;
888:       break;

890:     case 4:
891:       sum1 = b[*r++];
892:       sum2 = b[*r++];
893:       sum3 = b[*r++];
894:       sum4 = b[*r++];
895:       v2   = aa + ai[row + 1];
896:       v3   = aa + ai[row + 2];
897:       v4   = aa + ai[row + 3];

899:       for (j = 0; j < nz - 1; j += 2) {
900:         i0 = vi[0];
901:         i1 = vi[1];
902:         vi += 2;
903:         tmp0 = tmps[i0];
904:         tmp1 = tmps[i1];
905:         sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
906:         v1 += 2;
907:         sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
908:         v2 += 2;
909:         sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
910:         v3 += 2;
911:         sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
912:         v4 += 2;
913:       }
914:       if (j == nz - 1) {
915:         tmp0 = tmps[*vi++];
916:         sum1 -= *v1++ * tmp0;
917:         sum2 -= *v2++ * tmp0;
918:         sum3 -= *v3++ * tmp0;
919:         sum4 -= *v4++ * tmp0;
920:       }
921:       sum2 -= *v2++ * sum1;
922:       sum3 -= *v3++ * sum1;
923:       sum4 -= *v4++ * sum1;
924:       sum3 -= *v3++ * sum2;
925:       sum4 -= *v4++ * sum2;
926:       sum4 -= *v4++ * sum3;

928:       tmp[row++] = sum1;
929:       tmp[row++] = sum2;
930:       tmp[row++] = sum3;
931:       tmp[row++] = sum4;
932:       break;
933:     case 5:
934:       sum1 = b[*r++];
935:       sum2 = b[*r++];
936:       sum3 = b[*r++];
937:       sum4 = b[*r++];
938:       sum5 = b[*r++];
939:       v2   = aa + ai[row + 1];
940:       v3   = aa + ai[row + 2];
941:       v4   = aa + ai[row + 3];
942:       v5   = aa + ai[row + 4];

944:       for (j = 0; j < nz - 1; j += 2) {
945:         i0 = vi[0];
946:         i1 = vi[1];
947:         vi += 2;
948:         tmp0 = tmps[i0];
949:         tmp1 = tmps[i1];
950:         sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
951:         v1 += 2;
952:         sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
953:         v2 += 2;
954:         sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
955:         v3 += 2;
956:         sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
957:         v4 += 2;
958:         sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
959:         v5 += 2;
960:       }
961:       if (j == nz - 1) {
962:         tmp0 = tmps[*vi++];
963:         sum1 -= *v1++ * tmp0;
964:         sum2 -= *v2++ * tmp0;
965:         sum3 -= *v3++ * tmp0;
966:         sum4 -= *v4++ * tmp0;
967:         sum5 -= *v5++ * tmp0;
968:       }

970:       sum2 -= *v2++ * sum1;
971:       sum3 -= *v3++ * sum1;
972:       sum4 -= *v4++ * sum1;
973:       sum5 -= *v5++ * sum1;
974:       sum3 -= *v3++ * sum2;
975:       sum4 -= *v4++ * sum2;
976:       sum5 -= *v5++ * sum2;
977:       sum4 -= *v4++ * sum3;
978:       sum5 -= *v5++ * sum3;
979:       sum5 -= *v5++ * sum4;

981:       tmp[row++] = sum1;
982:       tmp[row++] = sum2;
983:       tmp[row++] = sum3;
984:       tmp[row++] = sum4;
985:       tmp[row++] = sum5;
986:       break;
987:     default:
988:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not yet supported ");
989:     }
990:   }
991:   /* backward solve the upper triangular */
992:   for (i = node_max - 1; i >= 0; i--) {
993:     row = ns[i + 1];
994:     nsz = ns[i + 1] - ns[i];
995:     aii = ai[row + 1] - 1;
996:     v1  = aa + aii;
997:     vi  = aj + aii;
998:     nz  = aii - ad[row];
999:     switch (nsz) { /* Each loop in 'case' is unrolled */
1000:     case 1:
1001:       sum1 = tmp[row];

1003:       for (j = nz; j > 1; j -= 2) {
1004:         vi -= 2;
1005:         i0   = vi[2];
1006:         i1   = vi[1];
1007:         tmp0 = tmps[i0];
1008:         tmp1 = tmps[i1];
1009:         v1 -= 2;
1010:         sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
1011:       }
1012:       if (j == 1) {
1013:         tmp0 = tmps[*vi--];
1014:         sum1 -= *v1-- * tmp0;
1015:       }
1016:       x[*c--] = tmp[row] = sum1 * a_a[ad[row]];
1017:       row--;
1018:       break;
1019:     case 2:
1020:       sum1 = tmp[row];
1021:       sum2 = tmp[row - 1];
1022:       v2   = aa + ai[row] - 1;
1023:       for (j = nz; j > 1; j -= 2) {
1024:         vi -= 2;
1025:         i0   = vi[2];
1026:         i1   = vi[1];
1027:         tmp0 = tmps[i0];
1028:         tmp1 = tmps[i1];
1029:         v1 -= 2;
1030:         v2 -= 2;
1031:         sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
1032:         sum2 -= v2[2] * tmp0 + v2[1] * tmp1;
1033:       }
1034:       if (j == 1) {
1035:         tmp0 = tmps[*vi--];
1036:         sum1 -= *v1-- * tmp0;
1037:         sum2 -= *v2-- * tmp0;
1038:       }

1040:       tmp0 = x[*c--] = tmp[row] = sum1 * a_a[ad[row]];
1041:       row--;
1042:       sum2 -= *v2-- * tmp0;
1043:       x[*c--] = tmp[row] = sum2 * a_a[ad[row]];
1044:       row--;
1045:       break;
1046:     case 3:
1047:       sum1 = tmp[row];
1048:       sum2 = tmp[row - 1];
1049:       sum3 = tmp[row - 2];
1050:       v2   = aa + ai[row] - 1;
1051:       v3   = aa + ai[row - 1] - 1;
1052:       for (j = nz; j > 1; j -= 2) {
1053:         vi -= 2;
1054:         i0   = vi[2];
1055:         i1   = vi[1];
1056:         tmp0 = tmps[i0];
1057:         tmp1 = tmps[i1];
1058:         v1 -= 2;
1059:         v2 -= 2;
1060:         v3 -= 2;
1061:         sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
1062:         sum2 -= v2[2] * tmp0 + v2[1] * tmp1;
1063:         sum3 -= v3[2] * tmp0 + v3[1] * tmp1;
1064:       }
1065:       if (j == 1) {
1066:         tmp0 = tmps[*vi--];
1067:         sum1 -= *v1-- * tmp0;
1068:         sum2 -= *v2-- * tmp0;
1069:         sum3 -= *v3-- * tmp0;
1070:       }
1071:       tmp0 = x[*c--] = tmp[row] = sum1 * a_a[ad[row]];
1072:       row--;
1073:       sum2 -= *v2-- * tmp0;
1074:       sum3 -= *v3-- * tmp0;
1075:       tmp0 = x[*c--] = tmp[row] = sum2 * a_a[ad[row]];
1076:       row--;
1077:       sum3 -= *v3-- * tmp0;
1078:       x[*c--] = tmp[row] = sum3 * a_a[ad[row]];
1079:       row--;

1081:       break;
1082:     case 4:
1083:       sum1 = tmp[row];
1084:       sum2 = tmp[row - 1];
1085:       sum3 = tmp[row - 2];
1086:       sum4 = tmp[row - 3];
1087:       v2   = aa + ai[row] - 1;
1088:       v3   = aa + ai[row - 1] - 1;
1089:       v4   = aa + ai[row - 2] - 1;

1091:       for (j = nz; j > 1; j -= 2) {
1092:         vi -= 2;
1093:         i0   = vi[2];
1094:         i1   = vi[1];
1095:         tmp0 = tmps[i0];
1096:         tmp1 = tmps[i1];
1097:         v1 -= 2;
1098:         v2 -= 2;
1099:         v3 -= 2;
1100:         v4 -= 2;
1101:         sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
1102:         sum2 -= v2[2] * tmp0 + v2[1] * tmp1;
1103:         sum3 -= v3[2] * tmp0 + v3[1] * tmp1;
1104:         sum4 -= v4[2] * tmp0 + v4[1] * tmp1;
1105:       }
1106:       if (j == 1) {
1107:         tmp0 = tmps[*vi--];
1108:         sum1 -= *v1-- * tmp0;
1109:         sum2 -= *v2-- * tmp0;
1110:         sum3 -= *v3-- * tmp0;
1111:         sum4 -= *v4-- * tmp0;
1112:       }

1114:       tmp0 = x[*c--] = tmp[row] = sum1 * a_a[ad[row]];
1115:       row--;
1116:       sum2 -= *v2-- * tmp0;
1117:       sum3 -= *v3-- * tmp0;
1118:       sum4 -= *v4-- * tmp0;
1119:       tmp0 = x[*c--] = tmp[row] = sum2 * a_a[ad[row]];
1120:       row--;
1121:       sum3 -= *v3-- * tmp0;
1122:       sum4 -= *v4-- * tmp0;
1123:       tmp0 = x[*c--] = tmp[row] = sum3 * a_a[ad[row]];
1124:       row--;
1125:       sum4 -= *v4-- * tmp0;
1126:       x[*c--] = tmp[row] = sum4 * a_a[ad[row]];
1127:       row--;
1128:       break;
1129:     case 5:
1130:       sum1 = tmp[row];
1131:       sum2 = tmp[row - 1];
1132:       sum3 = tmp[row - 2];
1133:       sum4 = tmp[row - 3];
1134:       sum5 = tmp[row - 4];
1135:       v2   = aa + ai[row] - 1;
1136:       v3   = aa + ai[row - 1] - 1;
1137:       v4   = aa + ai[row - 2] - 1;
1138:       v5   = aa + ai[row - 3] - 1;
1139:       for (j = nz; j > 1; j -= 2) {
1140:         vi -= 2;
1141:         i0   = vi[2];
1142:         i1   = vi[1];
1143:         tmp0 = tmps[i0];
1144:         tmp1 = tmps[i1];
1145:         v1 -= 2;
1146:         v2 -= 2;
1147:         v3 -= 2;
1148:         v4 -= 2;
1149:         v5 -= 2;
1150:         sum1 -= v1[2] * tmp0 + v1[1] * tmp1;
1151:         sum2 -= v2[2] * tmp0 + v2[1] * tmp1;
1152:         sum3 -= v3[2] * tmp0 + v3[1] * tmp1;
1153:         sum4 -= v4[2] * tmp0 + v4[1] * tmp1;
1154:         sum5 -= v5[2] * tmp0 + v5[1] * tmp1;
1155:       }
1156:       if (j == 1) {
1157:         tmp0 = tmps[*vi--];
1158:         sum1 -= *v1-- * tmp0;
1159:         sum2 -= *v2-- * tmp0;
1160:         sum3 -= *v3-- * tmp0;
1161:         sum4 -= *v4-- * tmp0;
1162:         sum5 -= *v5-- * tmp0;
1163:       }

1165:       tmp0 = x[*c--] = tmp[row] = sum1 * a_a[ad[row]];
1166:       row--;
1167:       sum2 -= *v2-- * tmp0;
1168:       sum3 -= *v3-- * tmp0;
1169:       sum4 -= *v4-- * tmp0;
1170:       sum5 -= *v5-- * tmp0;
1171:       tmp0 = x[*c--] = tmp[row] = sum2 * a_a[ad[row]];
1172:       row--;
1173:       sum3 -= *v3-- * tmp0;
1174:       sum4 -= *v4-- * tmp0;
1175:       sum5 -= *v5-- * tmp0;
1176:       tmp0 = x[*c--] = tmp[row] = sum3 * a_a[ad[row]];
1177:       row--;
1178:       sum4 -= *v4-- * tmp0;
1179:       sum5 -= *v5-- * tmp0;
1180:       tmp0 = x[*c--] = tmp[row] = sum4 * a_a[ad[row]];
1181:       row--;
1182:       sum5 -= *v5-- * tmp0;
1183:       x[*c--] = tmp[row] = sum5 * a_a[ad[row]];
1184:       row--;
1185:       break;
1186:     default:
1187:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not yet supported ");
1188:     }
1189:   }
1190:   PetscCall(ISRestoreIndices(isrow, &rout));
1191:   PetscCall(ISRestoreIndices(iscol, &cout));
1192:   PetscCall(VecRestoreArrayRead(bb, &b));
1193:   PetscCall(VecRestoreArrayWrite(xx, &x));
1194:   PetscCall(PetscLogFlops(2.0 * a->nz - A->cmap->n));
1195:   PetscFunctionReturn(PETSC_SUCCESS);
1196: }

1198: PetscErrorCode MatLUFactorNumeric_SeqAIJ_Inode(Mat B, Mat A, const MatFactorInfo *info)
1199: {
1200:   Mat              C = B;
1201:   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)C->data;
1202:   IS               isrow = b->row, isicol = b->icol;
1203:   const PetscInt  *r, *ic, *ics;
1204:   const PetscInt   n = A->rmap->n, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, *bdiag = b->diag;
1205:   PetscInt         i, j, k, nz, nzL, row, *pj;
1206:   const PetscInt  *ajtmp, *bjtmp;
1207:   MatScalar       *pc, *pc1, *pc2, *pc3, *pc4, mul1, mul2, mul3, mul4, *pv, *rtmp1, *rtmp2, *rtmp3, *rtmp4;
1208:   const MatScalar *aa = a->a, *v, *v1, *v2, *v3, *v4;
1209:   FactorShiftCtx   sctx;
1210:   const PetscInt  *ddiag;
1211:   PetscReal        rs;
1212:   MatScalar        d;
1213:   PetscInt         inod, nodesz, node_max, col;
1214:   const PetscInt  *ns;
1215:   PetscInt        *tmp_vec1, *tmp_vec2, *nsmap;

1217:   PetscFunctionBegin;
1218:   /* MatPivotSetUp(): initialize shift context sctx */
1219:   PetscCall(PetscMemzero(&sctx, sizeof(FactorShiftCtx)));

1221:   if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
1222:     ddiag          = a->diag;
1223:     sctx.shift_top = info->zeropivot;
1224:     for (i = 0; i < n; i++) {
1225:       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
1226:       d  = (aa)[ddiag[i]];
1227:       rs = -PetscAbsScalar(d) - PetscRealPart(d);
1228:       v  = aa + ai[i];
1229:       nz = ai[i + 1] - ai[i];
1230:       for (j = 0; j < nz; j++) rs += PetscAbsScalar(v[j]);
1231:       if (rs > sctx.shift_top) sctx.shift_top = rs;
1232:     }
1233:     sctx.shift_top *= 1.1;
1234:     sctx.nshift_max = 5;
1235:     sctx.shift_lo   = 0.;
1236:     sctx.shift_hi   = 1.;
1237:   }

1239:   PetscCall(ISGetIndices(isrow, &r));
1240:   PetscCall(ISGetIndices(isicol, &ic));

1242:   PetscCall(PetscCalloc4(n, &rtmp1, n, &rtmp2, n, &rtmp3, n, &rtmp4));
1243:   ics = ic;

1245:   node_max = a->inode.node_count;
1246:   ns       = a->inode.size_csr;
1247:   PetscCheck(ns, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Matrix without inode information");

1249:   /* If max inode size > 4, split it into two inodes.*/
1250:   /* also map the inode sizes according to the ordering */
1251:   PetscCall(PetscMalloc1(n + 1, &tmp_vec1));
1252:   for (i = 0, j = 0; i < node_max; ++i, ++j) {
1253:     nodesz = ns[i + 1] - ns[i];
1254:     if (nodesz > 4) {
1255:       tmp_vec1[j] = 4;
1256:       ++j;
1257:       tmp_vec1[j] = nodesz - tmp_vec1[j - 1];
1258:     } else {
1259:       tmp_vec1[j] = nodesz;
1260:     }
1261:   }
1262:   /* Use the correct node_max */
1263:   node_max = j;

1265:   /* Now reorder the inode info based on mat re-ordering info */
1266:   /* First create a row -> inode_size_array_index map */
1267:   PetscCall(PetscMalloc1(n + 1, &nsmap));
1268:   PetscCall(PetscMalloc1(node_max + 1, &tmp_vec2));
1269:   tmp_vec2[0] = 0;
1270:   for (i = 0, row = 0; i < node_max; i++) {
1271:     nodesz = tmp_vec1[i];
1272:     for (j = 0; j < nodesz; j++, row++) nsmap[row] = i;
1273:   }
1274:   /* Using nsmap, create a reordered ns structure */
1275:   for (i = 0, j = 0; i < node_max; i++) {
1276:     nodesz          = tmp_vec1[nsmap[r[j]]]; /* here the reordered row_no is in r[] */
1277:     tmp_vec2[i + 1] = tmp_vec2[i] + nodesz;
1278:     j += nodesz;
1279:   }
1280:   PetscCall(PetscFree(nsmap));
1281:   PetscCall(PetscFree(tmp_vec1));

1283:   /* Now use the correct ns */
1284:   ns = tmp_vec2;

1286:   do {
1287:     sctx.newshift = PETSC_FALSE;
1288:     /* Now loop over each block-row, and do the factorization */
1289:     for (inod = 0, i = 0; inod < node_max; inod++) { /* i: row index; inod: inode index */
1290:       nodesz = ns[inod + 1] - ns[inod];

1292:       switch (nodesz) {
1293:       case 1:
1294:         /* zero rtmp1 */
1295:         /* L part */
1296:         nz    = bi[i + 1] - bi[i];
1297:         bjtmp = bj + bi[i];
1298:         for (j = 0; j < nz; j++) rtmp1[bjtmp[j]] = 0.0;

1300:         /* U part */
1301:         nz    = bdiag[i] - bdiag[i + 1];
1302:         bjtmp = bj + bdiag[i + 1] + 1;
1303:         for (j = 0; j < nz; j++) rtmp1[bjtmp[j]] = 0.0;

1305:         /* load in initial (unfactored row) */
1306:         nz    = ai[r[i] + 1] - ai[r[i]];
1307:         ajtmp = aj + ai[r[i]];
1308:         v     = aa + ai[r[i]];
1309:         for (j = 0; j < nz; j++) rtmp1[ics[ajtmp[j]]] = v[j];

1311:         /* ZeropivotApply() */
1312:         rtmp1[i] += sctx.shift_amount; /* shift the diagonal of the matrix */

1314:         /* elimination */
1315:         bjtmp = bj + bi[i];
1316:         row   = *bjtmp++;
1317:         nzL   = bi[i + 1] - bi[i];
1318:         for (k = 0; k < nzL; k++) {
1319:           pc = rtmp1 + row;
1320:           if (*pc != 0.0) {
1321:             pv   = b->a + bdiag[row];
1322:             mul1 = *pc * (*pv);
1323:             *pc  = mul1;
1324:             pj   = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
1325:             pv   = b->a + bdiag[row + 1] + 1;
1326:             nz   = bdiag[row] - bdiag[row + 1] - 1; /* num of entries in U(row,:) excluding diag */
1327:             for (j = 0; j < nz; j++) rtmp1[pj[j]] -= mul1 * pv[j];
1328:             PetscCall(PetscLogFlops(1 + 2.0 * nz));
1329:           }
1330:           row = *bjtmp++;
1331:         }

1333:         /* finished row so stick it into b->a */
1334:         rs = 0.0;
1335:         /* L part */
1336:         pv = b->a + bi[i];
1337:         pj = b->j + bi[i];
1338:         nz = bi[i + 1] - bi[i];
1339:         for (j = 0; j < nz; j++) {
1340:           pv[j] = rtmp1[pj[j]];
1341:           rs += PetscAbsScalar(pv[j]);
1342:         }

1344:         /* U part */
1345:         pv = b->a + bdiag[i + 1] + 1;
1346:         pj = b->j + bdiag[i + 1] + 1;
1347:         nz = bdiag[i] - bdiag[i + 1] - 1;
1348:         for (j = 0; j < nz; j++) {
1349:           pv[j] = rtmp1[pj[j]];
1350:           rs += PetscAbsScalar(pv[j]);
1351:         }

1353:         /* Check zero pivot */
1354:         sctx.rs = rs;
1355:         sctx.pv = rtmp1[i];
1356:         PetscCall(MatPivotCheck(B, A, info, &sctx, i));
1357:         if (sctx.newshift) break;

1359:         /* Mark diagonal and invert diagonal for simpler triangular solves */
1360:         pv  = b->a + bdiag[i];
1361:         *pv = 1.0 / sctx.pv; /* sctx.pv = rtmp1[i]+shiftamount if shifttype==MAT_SHIFT_INBLOCKS */
1362:         break;

1364:       case 2:
1365:         /* zero rtmp1 and rtmp2 */
1366:         /* L part */
1367:         nz    = bi[i + 1] - bi[i];
1368:         bjtmp = bj + bi[i];
1369:         for (j = 0; j < nz; j++) {
1370:           col        = bjtmp[j];
1371:           rtmp1[col] = 0.0;
1372:           rtmp2[col] = 0.0;
1373:         }

1375:         /* U part */
1376:         nz    = bdiag[i] - bdiag[i + 1];
1377:         bjtmp = bj + bdiag[i + 1] + 1;
1378:         for (j = 0; j < nz; j++) {
1379:           col        = bjtmp[j];
1380:           rtmp1[col] = 0.0;
1381:           rtmp2[col] = 0.0;
1382:         }

1384:         /* load in initial (unfactored row) */
1385:         nz    = ai[r[i] + 1] - ai[r[i]];
1386:         ajtmp = aj + ai[r[i]];
1387:         v1    = aa + ai[r[i]];
1388:         v2    = aa + ai[r[i + 1]];
1389:         for (j = 0; j < nz; j++) {
1390:           col        = ics[ajtmp[j]];
1391:           rtmp1[col] = v1[j];
1392:           rtmp2[col] = v2[j];
1393:         }
1394:         /* ZeropivotApply(): shift the diagonal of the matrix  */
1395:         rtmp1[i] += sctx.shift_amount;
1396:         rtmp2[i + 1] += sctx.shift_amount;

1398:         /* elimination */
1399:         bjtmp = bj + bi[i];
1400:         row   = *bjtmp++; /* pivot row */
1401:         nzL   = bi[i + 1] - bi[i];
1402:         for (k = 0; k < nzL; k++) {
1403:           pc1 = rtmp1 + row;
1404:           pc2 = rtmp2 + row;
1405:           if (*pc1 != 0.0 || *pc2 != 0.0) {
1406:             pv   = b->a + bdiag[row];
1407:             mul1 = *pc1 * (*pv);
1408:             mul2 = *pc2 * (*pv);
1409:             *pc1 = mul1;
1410:             *pc2 = mul2;

1412:             pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
1413:             pv = b->a + bdiag[row + 1] + 1;
1414:             nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries in U(row,:) excluding diag */
1415:             for (j = 0; j < nz; j++) {
1416:               col = pj[j];
1417:               rtmp1[col] -= mul1 * pv[j];
1418:               rtmp2[col] -= mul2 * pv[j];
1419:             }
1420:             PetscCall(PetscLogFlops(2 + 4.0 * nz));
1421:           }
1422:           row = *bjtmp++;
1423:         }

1425:         /* finished row i; check zero pivot, then stick row i into b->a */
1426:         rs = 0.0;
1427:         /* L part */
1428:         pc1 = b->a + bi[i];
1429:         pj  = b->j + bi[i];
1430:         nz  = bi[i + 1] - bi[i];
1431:         for (j = 0; j < nz; j++) {
1432:           col    = pj[j];
1433:           pc1[j] = rtmp1[col];
1434:           rs += PetscAbsScalar(pc1[j]);
1435:         }
1436:         /* U part */
1437:         pc1 = b->a + bdiag[i + 1] + 1;
1438:         pj  = b->j + bdiag[i + 1] + 1;
1439:         nz  = bdiag[i] - bdiag[i + 1] - 1; /* exclude diagonal */
1440:         for (j = 0; j < nz; j++) {
1441:           col    = pj[j];
1442:           pc1[j] = rtmp1[col];
1443:           rs += PetscAbsScalar(pc1[j]);
1444:         }

1446:         sctx.rs = rs;
1447:         sctx.pv = rtmp1[i];
1448:         PetscCall(MatPivotCheck(B, A, info, &sctx, i));
1449:         if (sctx.newshift) break;
1450:         pc1  = b->a + bdiag[i]; /* Mark diagonal */
1451:         *pc1 = 1.0 / sctx.pv;

1453:         /* Now take care of diagonal 2x2 block. */
1454:         pc2 = rtmp2 + i;
1455:         if (*pc2 != 0.0) {
1456:           mul1 = (*pc2) * (*pc1);             /* *pc1=diag[i] is inverted! */
1457:           *pc2 = mul1;                        /* insert L entry */
1458:           pj   = b->j + bdiag[i + 1] + 1;     /* beginning of U(i,:) */
1459:           nz   = bdiag[i] - bdiag[i + 1] - 1; /* num of entries in U(i,:) excluding diag */
1460:           for (j = 0; j < nz; j++) {
1461:             col = pj[j];
1462:             rtmp2[col] -= mul1 * rtmp1[col];
1463:           }
1464:           PetscCall(PetscLogFlops(1 + 2.0 * nz));
1465:         }

1467:         /* finished row i+1; check zero pivot, then stick row i+1 into b->a */
1468:         rs = 0.0;
1469:         /* L part */
1470:         pc2 = b->a + bi[i + 1];
1471:         pj  = b->j + bi[i + 1];
1472:         nz  = bi[i + 2] - bi[i + 1];
1473:         for (j = 0; j < nz; j++) {
1474:           col    = pj[j];
1475:           pc2[j] = rtmp2[col];
1476:           rs += PetscAbsScalar(pc2[j]);
1477:         }
1478:         /* U part */
1479:         pc2 = b->a + bdiag[i + 2] + 1;
1480:         pj  = b->j + bdiag[i + 2] + 1;
1481:         nz  = bdiag[i + 1] - bdiag[i + 2] - 1; /* exclude diagonal */
1482:         for (j = 0; j < nz; j++) {
1483:           col    = pj[j];
1484:           pc2[j] = rtmp2[col];
1485:           rs += PetscAbsScalar(pc2[j]);
1486:         }

1488:         sctx.rs = rs;
1489:         sctx.pv = rtmp2[i + 1];
1490:         PetscCall(MatPivotCheck(B, A, info, &sctx, i + 1));
1491:         if (sctx.newshift) break;
1492:         pc2  = b->a + bdiag[i + 1];
1493:         *pc2 = 1.0 / sctx.pv;
1494:         break;

1496:       case 3:
1497:         /* zero rtmp */
1498:         /* L part */
1499:         nz    = bi[i + 1] - bi[i];
1500:         bjtmp = bj + bi[i];
1501:         for (j = 0; j < nz; j++) {
1502:           col        = bjtmp[j];
1503:           rtmp1[col] = 0.0;
1504:           rtmp2[col] = 0.0;
1505:           rtmp3[col] = 0.0;
1506:         }

1508:         /* U part */
1509:         nz    = bdiag[i] - bdiag[i + 1];
1510:         bjtmp = bj + bdiag[i + 1] + 1;
1511:         for (j = 0; j < nz; j++) {
1512:           col        = bjtmp[j];
1513:           rtmp1[col] = 0.0;
1514:           rtmp2[col] = 0.0;
1515:           rtmp3[col] = 0.0;
1516:         }

1518:         /* load in initial (unfactored row) */
1519:         nz    = ai[r[i] + 1] - ai[r[i]];
1520:         ajtmp = aj + ai[r[i]];
1521:         v1    = aa + ai[r[i]];
1522:         v2    = aa + ai[r[i + 1]];
1523:         v3    = aa + ai[r[i + 2]];
1524:         for (j = 0; j < nz; j++) {
1525:           col        = ics[ajtmp[j]];
1526:           rtmp1[col] = v1[j];
1527:           rtmp2[col] = v2[j];
1528:           rtmp3[col] = v3[j];
1529:         }
1530:         /* ZeropivotApply(): shift the diagonal of the matrix  */
1531:         rtmp1[i] += sctx.shift_amount;
1532:         rtmp2[i + 1] += sctx.shift_amount;
1533:         rtmp3[i + 2] += sctx.shift_amount;

1535:         /* elimination */
1536:         bjtmp = bj + bi[i];
1537:         row   = *bjtmp++; /* pivot row */
1538:         nzL   = bi[i + 1] - bi[i];
1539:         for (k = 0; k < nzL; k++) {
1540:           pc1 = rtmp1 + row;
1541:           pc2 = rtmp2 + row;
1542:           pc3 = rtmp3 + row;
1543:           if (*pc1 != 0.0 || *pc2 != 0.0 || *pc3 != 0.0) {
1544:             pv   = b->a + bdiag[row];
1545:             mul1 = *pc1 * (*pv);
1546:             mul2 = *pc2 * (*pv);
1547:             mul3 = *pc3 * (*pv);
1548:             *pc1 = mul1;
1549:             *pc2 = mul2;
1550:             *pc3 = mul3;

1552:             pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
1553:             pv = b->a + bdiag[row + 1] + 1;
1554:             nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries in U(row,:) excluding diag */
1555:             for (j = 0; j < nz; j++) {
1556:               col = pj[j];
1557:               rtmp1[col] -= mul1 * pv[j];
1558:               rtmp2[col] -= mul2 * pv[j];
1559:               rtmp3[col] -= mul3 * pv[j];
1560:             }
1561:             PetscCall(PetscLogFlops(3 + 6.0 * nz));
1562:           }
1563:           row = *bjtmp++;
1564:         }

1566:         /* finished row i; check zero pivot, then stick row i into b->a */
1567:         rs = 0.0;
1568:         /* L part */
1569:         pc1 = b->a + bi[i];
1570:         pj  = b->j + bi[i];
1571:         nz  = bi[i + 1] - bi[i];
1572:         for (j = 0; j < nz; j++) {
1573:           col    = pj[j];
1574:           pc1[j] = rtmp1[col];
1575:           rs += PetscAbsScalar(pc1[j]);
1576:         }
1577:         /* U part */
1578:         pc1 = b->a + bdiag[i + 1] + 1;
1579:         pj  = b->j + bdiag[i + 1] + 1;
1580:         nz  = bdiag[i] - bdiag[i + 1] - 1; /* exclude diagonal */
1581:         for (j = 0; j < nz; j++) {
1582:           col    = pj[j];
1583:           pc1[j] = rtmp1[col];
1584:           rs += PetscAbsScalar(pc1[j]);
1585:         }

1587:         sctx.rs = rs;
1588:         sctx.pv = rtmp1[i];
1589:         PetscCall(MatPivotCheck(B, A, info, &sctx, i));
1590:         if (sctx.newshift) break;
1591:         pc1  = b->a + bdiag[i]; /* Mark diag[i] */
1592:         *pc1 = 1.0 / sctx.pv;

1594:         /* Now take care of 1st column of diagonal 3x3 block. */
1595:         pc2 = rtmp2 + i;
1596:         pc3 = rtmp3 + i;
1597:         if (*pc2 != 0.0 || *pc3 != 0.0) {
1598:           mul2 = (*pc2) * (*pc1);
1599:           *pc2 = mul2;
1600:           mul3 = (*pc3) * (*pc1);
1601:           *pc3 = mul3;
1602:           pj   = b->j + bdiag[i + 1] + 1;     /* beginning of U(i,:) */
1603:           nz   = bdiag[i] - bdiag[i + 1] - 1; /* num of entries in U(i,:) excluding diag */
1604:           for (j = 0; j < nz; j++) {
1605:             col = pj[j];
1606:             rtmp2[col] -= mul2 * rtmp1[col];
1607:             rtmp3[col] -= mul3 * rtmp1[col];
1608:           }
1609:           PetscCall(PetscLogFlops(2 + 4.0 * nz));
1610:         }

1612:         /* finished row i+1; check zero pivot, then stick row i+1 into b->a */
1613:         rs = 0.0;
1614:         /* L part */
1615:         pc2 = b->a + bi[i + 1];
1616:         pj  = b->j + bi[i + 1];
1617:         nz  = bi[i + 2] - bi[i + 1];
1618:         for (j = 0; j < nz; j++) {
1619:           col    = pj[j];
1620:           pc2[j] = rtmp2[col];
1621:           rs += PetscAbsScalar(pc2[j]);
1622:         }
1623:         /* U part */
1624:         pc2 = b->a + bdiag[i + 2] + 1;
1625:         pj  = b->j + bdiag[i + 2] + 1;
1626:         nz  = bdiag[i + 1] - bdiag[i + 2] - 1; /* exclude diagonal */
1627:         for (j = 0; j < nz; j++) {
1628:           col    = pj[j];
1629:           pc2[j] = rtmp2[col];
1630:           rs += PetscAbsScalar(pc2[j]);
1631:         }

1633:         sctx.rs = rs;
1634:         sctx.pv = rtmp2[i + 1];
1635:         PetscCall(MatPivotCheck(B, A, info, &sctx, i + 1));
1636:         if (sctx.newshift) break;
1637:         pc2  = b->a + bdiag[i + 1];
1638:         *pc2 = 1.0 / sctx.pv; /* Mark diag[i+1] */

1640:         /* Now take care of 2nd column of diagonal 3x3 block. */
1641:         pc3 = rtmp3 + i + 1;
1642:         if (*pc3 != 0.0) {
1643:           mul3 = (*pc3) * (*pc2);
1644:           *pc3 = mul3;
1645:           pj   = b->j + bdiag[i + 2] + 1;         /* beginning of U(i+1,:) */
1646:           nz   = bdiag[i + 1] - bdiag[i + 2] - 1; /* num of entries in U(i+1,:) excluding diag */
1647:           for (j = 0; j < nz; j++) {
1648:             col = pj[j];
1649:             rtmp3[col] -= mul3 * rtmp2[col];
1650:           }
1651:           PetscCall(PetscLogFlops(1 + 2.0 * nz));
1652:         }

1654:         /* finished i+2; check zero pivot, then stick row i+2 into b->a */
1655:         rs = 0.0;
1656:         /* L part */
1657:         pc3 = b->a + bi[i + 2];
1658:         pj  = b->j + bi[i + 2];
1659:         nz  = bi[i + 3] - bi[i + 2];
1660:         for (j = 0; j < nz; j++) {
1661:           col    = pj[j];
1662:           pc3[j] = rtmp3[col];
1663:           rs += PetscAbsScalar(pc3[j]);
1664:         }
1665:         /* U part */
1666:         pc3 = b->a + bdiag[i + 3] + 1;
1667:         pj  = b->j + bdiag[i + 3] + 1;
1668:         nz  = bdiag[i + 2] - bdiag[i + 3] - 1; /* exclude diagonal */
1669:         for (j = 0; j < nz; j++) {
1670:           col    = pj[j];
1671:           pc3[j] = rtmp3[col];
1672:           rs += PetscAbsScalar(pc3[j]);
1673:         }

1675:         sctx.rs = rs;
1676:         sctx.pv = rtmp3[i + 2];
1677:         PetscCall(MatPivotCheck(B, A, info, &sctx, i + 2));
1678:         if (sctx.newshift) break;
1679:         pc3  = b->a + bdiag[i + 2];
1680:         *pc3 = 1.0 / sctx.pv; /* Mark diag[i+2] */
1681:         break;
1682:       case 4:
1683:         /* zero rtmp */
1684:         /* L part */
1685:         nz    = bi[i + 1] - bi[i];
1686:         bjtmp = bj + bi[i];
1687:         for (j = 0; j < nz; j++) {
1688:           col        = bjtmp[j];
1689:           rtmp1[col] = 0.0;
1690:           rtmp2[col] = 0.0;
1691:           rtmp3[col] = 0.0;
1692:           rtmp4[col] = 0.0;
1693:         }

1695:         /* U part */
1696:         nz    = bdiag[i] - bdiag[i + 1];
1697:         bjtmp = bj + bdiag[i + 1] + 1;
1698:         for (j = 0; j < nz; j++) {
1699:           col        = bjtmp[j];
1700:           rtmp1[col] = 0.0;
1701:           rtmp2[col] = 0.0;
1702:           rtmp3[col] = 0.0;
1703:           rtmp4[col] = 0.0;
1704:         }

1706:         /* load in initial (unfactored row) */
1707:         nz    = ai[r[i] + 1] - ai[r[i]];
1708:         ajtmp = aj + ai[r[i]];
1709:         v1    = aa + ai[r[i]];
1710:         v2    = aa + ai[r[i + 1]];
1711:         v3    = aa + ai[r[i + 2]];
1712:         v4    = aa + ai[r[i + 3]];
1713:         for (j = 0; j < nz; j++) {
1714:           col        = ics[ajtmp[j]];
1715:           rtmp1[col] = v1[j];
1716:           rtmp2[col] = v2[j];
1717:           rtmp3[col] = v3[j];
1718:           rtmp4[col] = v4[j];
1719:         }
1720:         /* ZeropivotApply(): shift the diagonal of the matrix  */
1721:         rtmp1[i] += sctx.shift_amount;
1722:         rtmp2[i + 1] += sctx.shift_amount;
1723:         rtmp3[i + 2] += sctx.shift_amount;
1724:         rtmp4[i + 3] += sctx.shift_amount;

1726:         /* elimination */
1727:         bjtmp = bj + bi[i];
1728:         row   = *bjtmp++; /* pivot row */
1729:         nzL   = bi[i + 1] - bi[i];
1730:         for (k = 0; k < nzL; k++) {
1731:           pc1 = rtmp1 + row;
1732:           pc2 = rtmp2 + row;
1733:           pc3 = rtmp3 + row;
1734:           pc4 = rtmp4 + row;
1735:           if (*pc1 != 0.0 || *pc2 != 0.0 || *pc3 != 0.0 || *pc4 != 0.0) {
1736:             pv   = b->a + bdiag[row];
1737:             mul1 = *pc1 * (*pv);
1738:             mul2 = *pc2 * (*pv);
1739:             mul3 = *pc3 * (*pv);
1740:             mul4 = *pc4 * (*pv);
1741:             *pc1 = mul1;
1742:             *pc2 = mul2;
1743:             *pc3 = mul3;
1744:             *pc4 = mul4;

1746:             pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
1747:             pv = b->a + bdiag[row + 1] + 1;
1748:             nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries in U(row,:) excluding diag */
1749:             for (j = 0; j < nz; j++) {
1750:               col = pj[j];
1751:               rtmp1[col] -= mul1 * pv[j];
1752:               rtmp2[col] -= mul2 * pv[j];
1753:               rtmp3[col] -= mul3 * pv[j];
1754:               rtmp4[col] -= mul4 * pv[j];
1755:             }
1756:             PetscCall(PetscLogFlops(4 + 8.0 * nz));
1757:           }
1758:           row = *bjtmp++;
1759:         }

1761:         /* finished row i; check zero pivot, then stick row i into b->a */
1762:         rs = 0.0;
1763:         /* L part */
1764:         pc1 = b->a + bi[i];
1765:         pj  = b->j + bi[i];
1766:         nz  = bi[i + 1] - bi[i];
1767:         for (j = 0; j < nz; j++) {
1768:           col    = pj[j];
1769:           pc1[j] = rtmp1[col];
1770:           rs += PetscAbsScalar(pc1[j]);
1771:         }
1772:         /* U part */
1773:         pc1 = b->a + bdiag[i + 1] + 1;
1774:         pj  = b->j + bdiag[i + 1] + 1;
1775:         nz  = bdiag[i] - bdiag[i + 1] - 1; /* exclude diagonal */
1776:         for (j = 0; j < nz; j++) {
1777:           col    = pj[j];
1778:           pc1[j] = rtmp1[col];
1779:           rs += PetscAbsScalar(pc1[j]);
1780:         }

1782:         sctx.rs = rs;
1783:         sctx.pv = rtmp1[i];
1784:         PetscCall(MatPivotCheck(B, A, info, &sctx, i));
1785:         if (sctx.newshift) break;
1786:         pc1  = b->a + bdiag[i]; /* Mark diag[i] */
1787:         *pc1 = 1.0 / sctx.pv;

1789:         /* Now take care of 1st column of diagonal 4x4 block. */
1790:         pc2 = rtmp2 + i;
1791:         pc3 = rtmp3 + i;
1792:         pc4 = rtmp4 + i;
1793:         if (*pc2 != 0.0 || *pc3 != 0.0 || *pc4 != 0.0) {
1794:           mul2 = (*pc2) * (*pc1);
1795:           *pc2 = mul2;
1796:           mul3 = (*pc3) * (*pc1);
1797:           *pc3 = mul3;
1798:           mul4 = (*pc4) * (*pc1);
1799:           *pc4 = mul4;
1800:           pj   = b->j + bdiag[i + 1] + 1;     /* beginning of U(i,:) */
1801:           nz   = bdiag[i] - bdiag[i + 1] - 1; /* num of entries in U(i,:) excluding diag */
1802:           for (j = 0; j < nz; j++) {
1803:             col = pj[j];
1804:             rtmp2[col] -= mul2 * rtmp1[col];
1805:             rtmp3[col] -= mul3 * rtmp1[col];
1806:             rtmp4[col] -= mul4 * rtmp1[col];
1807:           }
1808:           PetscCall(PetscLogFlops(3 + 6.0 * nz));
1809:         }

1811:         /* finished row i+1; check zero pivot, then stick row i+1 into b->a */
1812:         rs = 0.0;
1813:         /* L part */
1814:         pc2 = b->a + bi[i + 1];
1815:         pj  = b->j + bi[i + 1];
1816:         nz  = bi[i + 2] - bi[i + 1];
1817:         for (j = 0; j < nz; j++) {
1818:           col    = pj[j];
1819:           pc2[j] = rtmp2[col];
1820:           rs += PetscAbsScalar(pc2[j]);
1821:         }
1822:         /* U part */
1823:         pc2 = b->a + bdiag[i + 2] + 1;
1824:         pj  = b->j + bdiag[i + 2] + 1;
1825:         nz  = bdiag[i + 1] - bdiag[i + 2] - 1; /* exclude diagonal */
1826:         for (j = 0; j < nz; j++) {
1827:           col    = pj[j];
1828:           pc2[j] = rtmp2[col];
1829:           rs += PetscAbsScalar(pc2[j]);
1830:         }

1832:         sctx.rs = rs;
1833:         sctx.pv = rtmp2[i + 1];
1834:         PetscCall(MatPivotCheck(B, A, info, &sctx, i + 1));
1835:         if (sctx.newshift) break;
1836:         pc2  = b->a + bdiag[i + 1];
1837:         *pc2 = 1.0 / sctx.pv; /* Mark diag[i+1] */

1839:         /* Now take care of 2nd column of diagonal 4x4 block. */
1840:         pc3 = rtmp3 + i + 1;
1841:         pc4 = rtmp4 + i + 1;
1842:         if (*pc3 != 0.0 || *pc4 != 0.0) {
1843:           mul3 = (*pc3) * (*pc2);
1844:           *pc3 = mul3;
1845:           mul4 = (*pc4) * (*pc2);
1846:           *pc4 = mul4;
1847:           pj   = b->j + bdiag[i + 2] + 1;         /* beginning of U(i+1,:) */
1848:           nz   = bdiag[i + 1] - bdiag[i + 2] - 1; /* num of entries in U(i+1,:) excluding diag */
1849:           for (j = 0; j < nz; j++) {
1850:             col = pj[j];
1851:             rtmp3[col] -= mul3 * rtmp2[col];
1852:             rtmp4[col] -= mul4 * rtmp2[col];
1853:           }
1854:           PetscCall(PetscLogFlops(4.0 * nz));
1855:         }

1857:         /* finished i+2; check zero pivot, then stick row i+2 into b->a */
1858:         rs = 0.0;
1859:         /* L part */
1860:         pc3 = b->a + bi[i + 2];
1861:         pj  = b->j + bi[i + 2];
1862:         nz  = bi[i + 3] - bi[i + 2];
1863:         for (j = 0; j < nz; j++) {
1864:           col    = pj[j];
1865:           pc3[j] = rtmp3[col];
1866:           rs += PetscAbsScalar(pc3[j]);
1867:         }
1868:         /* U part */
1869:         pc3 = b->a + bdiag[i + 3] + 1;
1870:         pj  = b->j + bdiag[i + 3] + 1;
1871:         nz  = bdiag[i + 2] - bdiag[i + 3] - 1; /* exclude diagonal */
1872:         for (j = 0; j < nz; j++) {
1873:           col    = pj[j];
1874:           pc3[j] = rtmp3[col];
1875:           rs += PetscAbsScalar(pc3[j]);
1876:         }

1878:         sctx.rs = rs;
1879:         sctx.pv = rtmp3[i + 2];
1880:         PetscCall(MatPivotCheck(B, A, info, &sctx, i + 2));
1881:         if (sctx.newshift) break;
1882:         pc3  = b->a + bdiag[i + 2];
1883:         *pc3 = 1.0 / sctx.pv; /* Mark diag[i+2] */

1885:         /* Now take care of 3rd column of diagonal 4x4 block. */
1886:         pc4 = rtmp4 + i + 2;
1887:         if (*pc4 != 0.0) {
1888:           mul4 = (*pc4) * (*pc3);
1889:           *pc4 = mul4;
1890:           pj   = b->j + bdiag[i + 3] + 1;         /* beginning of U(i+2,:) */
1891:           nz   = bdiag[i + 2] - bdiag[i + 3] - 1; /* num of entries in U(i+2,:) excluding diag */
1892:           for (j = 0; j < nz; j++) {
1893:             col = pj[j];
1894:             rtmp4[col] -= mul4 * rtmp3[col];
1895:           }
1896:           PetscCall(PetscLogFlops(1 + 2.0 * nz));
1897:         }

1899:         /* finished i+3; check zero pivot, then stick row i+3 into b->a */
1900:         rs = 0.0;
1901:         /* L part */
1902:         pc4 = b->a + bi[i + 3];
1903:         pj  = b->j + bi[i + 3];
1904:         nz  = bi[i + 4] - bi[i + 3];
1905:         for (j = 0; j < nz; j++) {
1906:           col    = pj[j];
1907:           pc4[j] = rtmp4[col];
1908:           rs += PetscAbsScalar(pc4[j]);
1909:         }
1910:         /* U part */
1911:         pc4 = b->a + bdiag[i + 4] + 1;
1912:         pj  = b->j + bdiag[i + 4] + 1;
1913:         nz  = bdiag[i + 3] - bdiag[i + 4] - 1; /* exclude diagonal */
1914:         for (j = 0; j < nz; j++) {
1915:           col    = pj[j];
1916:           pc4[j] = rtmp4[col];
1917:           rs += PetscAbsScalar(pc4[j]);
1918:         }

1920:         sctx.rs = rs;
1921:         sctx.pv = rtmp4[i + 3];
1922:         PetscCall(MatPivotCheck(B, A, info, &sctx, i + 3));
1923:         if (sctx.newshift) break;
1924:         pc4  = b->a + bdiag[i + 3];
1925:         *pc4 = 1.0 / sctx.pv; /* Mark diag[i+3] */
1926:         break;

1928:       default:
1929:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Node size not yet supported ");
1930:       }
1931:       if (sctx.newshift) break; /* break for (inod=0,i=0; inod<node_max; inod++) */
1932:       i += nodesz;              /* Update the row */
1933:     }

1935:     /* MatPivotRefine() */
1936:     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction > 0 && sctx.nshift < sctx.nshift_max) {
1937:       /*
1938:        * if no shift in this attempt & shifting & started shifting & can refine,
1939:        * then try lower shift
1940:        */
1941:       sctx.shift_hi       = sctx.shift_fraction;
1942:       sctx.shift_fraction = (sctx.shift_hi + sctx.shift_lo) / 2.;
1943:       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
1944:       sctx.newshift       = PETSC_TRUE;
1945:       sctx.nshift++;
1946:     }
1947:   } while (sctx.newshift);

1949:   PetscCall(PetscFree4(rtmp1, rtmp2, rtmp3, rtmp4));
1950:   PetscCall(PetscFree(tmp_vec2));
1951:   PetscCall(ISRestoreIndices(isicol, &ic));
1952:   PetscCall(ISRestoreIndices(isrow, &r));

1954:   if (b->inode.size_csr) {
1955:     C->ops->solve = MatSolve_SeqAIJ_Inode;
1956:   } else {
1957:     C->ops->solve = MatSolve_SeqAIJ;
1958:   }
1959:   C->ops->solveadd          = MatSolveAdd_SeqAIJ;
1960:   C->ops->solvetranspose    = MatSolveTranspose_SeqAIJ;
1961:   C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
1962:   C->ops->matsolve          = MatMatSolve_SeqAIJ;
1963:   C->ops->matsolvetranspose = MatMatSolveTranspose_SeqAIJ;
1964:   C->assembled              = PETSC_TRUE;
1965:   C->preallocated           = PETSC_TRUE;

1967:   PetscCall(PetscLogFlops(C->cmap->n));

1969:   /* MatShiftView(A,info,&sctx) */
1970:   if (sctx.nshift) {
1971:     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
1972:       PetscCall(PetscInfo(A, "number of shift_pd tries %" PetscInt_FMT ", shift_amount %g, diagonal shifted up by %e fraction top_value %e\n", sctx.nshift, (double)sctx.shift_amount, (double)sctx.shift_fraction, (double)sctx.shift_top));
1973:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
1974:       PetscCall(PetscInfo(A, "number of shift_nz tries %" PetscInt_FMT ", shift_amount %g\n", sctx.nshift, (double)sctx.shift_amount));
1975:     } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
1976:       PetscCall(PetscInfo(A, "number of shift_inblocks applied %" PetscInt_FMT ", each shift_amount %g\n", sctx.nshift, (double)info->shiftamount));
1977:     }
1978:   }
1979:   PetscFunctionReturn(PETSC_SUCCESS);
1980: }

1982: PetscErrorCode MatSolve_SeqAIJ_Inode(Mat A, Vec bb, Vec xx)
1983: {
1984:   Mat_SeqAIJ        *a     = (Mat_SeqAIJ *)A->data;
1985:   IS                 iscol = a->col, isrow = a->row;
1986:   const PetscInt    *r, *c, *rout, *cout;
1987:   PetscInt           i, j;
1988:   PetscInt           node_max, row, nsz, aii, i0, i1, nz;
1989:   const PetscInt    *ai = a->i, *a_j = a->j, *ns, *vi, *ad, *aj;
1990:   PetscScalar       *x, *tmp, *tmps, tmp0, tmp1;
1991:   PetscScalar        sum1, sum2, sum3, sum4, sum5;
1992:   const MatScalar   *v1, *v2, *v3, *v4, *v5, *a_a = a->a, *aa;
1993:   const PetscScalar *b;

1995:   PetscFunctionBegin;
1996:   PetscCheck(a->inode.size_csr, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
1997:   node_max = a->inode.node_count;
1998:   ns       = a->inode.size_csr; /* Node Size array */

2000:   PetscCall(VecGetArrayRead(bb, &b));
2001:   PetscCall(VecGetArrayWrite(xx, &x));
2002:   tmp = a->solve_work;

2004:   PetscCall(ISGetIndices(isrow, &rout));
2005:   r = rout;
2006:   PetscCall(ISGetIndices(iscol, &cout));
2007:   c = cout;

2009:   /* forward solve the lower triangular */
2010:   tmps = tmp;
2011:   aa   = a_a;
2012:   aj   = a_j;
2013:   ad   = a->diag;

2015:   for (i = 0; i < node_max; ++i) {
2016:     row = ns[i];
2017:     nsz = ns[i + 1] - ns[i];
2018:     aii = ai[row];
2019:     v1  = aa + aii;
2020:     vi  = aj + aii;
2021:     nz  = ai[row + 1] - ai[row];

2023:     if (i < node_max - 1) {
2024:       /* Prefetch the indices for the next block */
2025:       PetscPrefetchBlock(aj + ai[row + nsz], ai[row + nsz + 1] - ai[row + nsz], 0, PETSC_PREFETCH_HINT_NTA); /* indices */
2026:       /* Prefetch the data for the next block */
2027:       PetscPrefetchBlock(aa + ai[row + nsz], ai[ns[i + 2]] - ai[row + nsz], 0, PETSC_PREFETCH_HINT_NTA);
2028:     }

2030:     switch (nsz) { /* Each loop in 'case' is unrolled */
2031:     case 1:
2032:       sum1 = b[r[row]];
2033:       for (j = 0; j < nz - 1; j += 2) {
2034:         i0   = vi[j];
2035:         i1   = vi[j + 1];
2036:         tmp0 = tmps[i0];
2037:         tmp1 = tmps[i1];
2038:         sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
2039:       }
2040:       if (j == nz - 1) {
2041:         tmp0 = tmps[vi[j]];
2042:         sum1 -= v1[j] * tmp0;
2043:       }
2044:       tmp[row++] = sum1;
2045:       break;
2046:     case 2:
2047:       sum1 = b[r[row]];
2048:       sum2 = b[r[row + 1]];
2049:       v2   = aa + ai[row + 1];

2051:       for (j = 0; j < nz - 1; j += 2) {
2052:         i0   = vi[j];
2053:         i1   = vi[j + 1];
2054:         tmp0 = tmps[i0];
2055:         tmp1 = tmps[i1];
2056:         sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
2057:         sum2 -= v2[j] * tmp0 + v2[j + 1] * tmp1;
2058:       }
2059:       if (j == nz - 1) {
2060:         tmp0 = tmps[vi[j]];
2061:         sum1 -= v1[j] * tmp0;
2062:         sum2 -= v2[j] * tmp0;
2063:       }
2064:       sum2 -= v2[nz] * sum1;
2065:       tmp[row++] = sum1;
2066:       tmp[row++] = sum2;
2067:       break;
2068:     case 3:
2069:       sum1 = b[r[row]];
2070:       sum2 = b[r[row + 1]];
2071:       sum3 = b[r[row + 2]];
2072:       v2   = aa + ai[row + 1];
2073:       v3   = aa + ai[row + 2];

2075:       for (j = 0; j < nz - 1; j += 2) {
2076:         i0   = vi[j];
2077:         i1   = vi[j + 1];
2078:         tmp0 = tmps[i0];
2079:         tmp1 = tmps[i1];
2080:         sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
2081:         sum2 -= v2[j] * tmp0 + v2[j + 1] * tmp1;
2082:         sum3 -= v3[j] * tmp0 + v3[j + 1] * tmp1;
2083:       }
2084:       if (j == nz - 1) {
2085:         tmp0 = tmps[vi[j]];
2086:         sum1 -= v1[j] * tmp0;
2087:         sum2 -= v2[j] * tmp0;
2088:         sum3 -= v3[j] * tmp0;
2089:       }
2090:       sum2 -= v2[nz] * sum1;
2091:       sum3 -= v3[nz] * sum1;
2092:       sum3 -= v3[nz + 1] * sum2;
2093:       tmp[row++] = sum1;
2094:       tmp[row++] = sum2;
2095:       tmp[row++] = sum3;
2096:       break;

2098:     case 4:
2099:       sum1 = b[r[row]];
2100:       sum2 = b[r[row + 1]];
2101:       sum3 = b[r[row + 2]];
2102:       sum4 = b[r[row + 3]];
2103:       v2   = aa + ai[row + 1];
2104:       v3   = aa + ai[row + 2];
2105:       v4   = aa + ai[row + 3];

2107:       for (j = 0; j < nz - 1; j += 2) {
2108:         i0   = vi[j];
2109:         i1   = vi[j + 1];
2110:         tmp0 = tmps[i0];
2111:         tmp1 = tmps[i1];
2112:         sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
2113:         sum2 -= v2[j] * tmp0 + v2[j + 1] * tmp1;
2114:         sum3 -= v3[j] * tmp0 + v3[j + 1] * tmp1;
2115:         sum4 -= v4[j] * tmp0 + v4[j + 1] * tmp1;
2116:       }
2117:       if (j == nz - 1) {
2118:         tmp0 = tmps[vi[j]];
2119:         sum1 -= v1[j] * tmp0;
2120:         sum2 -= v2[j] * tmp0;
2121:         sum3 -= v3[j] * tmp0;
2122:         sum4 -= v4[j] * tmp0;
2123:       }
2124:       sum2 -= v2[nz] * sum1;
2125:       sum3 -= v3[nz] * sum1;
2126:       sum4 -= v4[nz] * sum1;
2127:       sum3 -= v3[nz + 1] * sum2;
2128:       sum4 -= v4[nz + 1] * sum2;
2129:       sum4 -= v4[nz + 2] * sum3;

2131:       tmp[row++] = sum1;
2132:       tmp[row++] = sum2;
2133:       tmp[row++] = sum3;
2134:       tmp[row++] = sum4;
2135:       break;
2136:     case 5:
2137:       sum1 = b[r[row]];
2138:       sum2 = b[r[row + 1]];
2139:       sum3 = b[r[row + 2]];
2140:       sum4 = b[r[row + 3]];
2141:       sum5 = b[r[row + 4]];
2142:       v2   = aa + ai[row + 1];
2143:       v3   = aa + ai[row + 2];
2144:       v4   = aa + ai[row + 3];
2145:       v5   = aa + ai[row + 4];

2147:       for (j = 0; j < nz - 1; j += 2) {
2148:         i0   = vi[j];
2149:         i1   = vi[j + 1];
2150:         tmp0 = tmps[i0];
2151:         tmp1 = tmps[i1];
2152:         sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
2153:         sum2 -= v2[j] * tmp0 + v2[j + 1] * tmp1;
2154:         sum3 -= v3[j] * tmp0 + v3[j + 1] * tmp1;
2155:         sum4 -= v4[j] * tmp0 + v4[j + 1] * tmp1;
2156:         sum5 -= v5[j] * tmp0 + v5[j + 1] * tmp1;
2157:       }
2158:       if (j == nz - 1) {
2159:         tmp0 = tmps[vi[j]];
2160:         sum1 -= v1[j] * tmp0;
2161:         sum2 -= v2[j] * tmp0;
2162:         sum3 -= v3[j] * tmp0;
2163:         sum4 -= v4[j] * tmp0;
2164:         sum5 -= v5[j] * tmp0;
2165:       }

2167:       sum2 -= v2[nz] * sum1;
2168:       sum3 -= v3[nz] * sum1;
2169:       sum4 -= v4[nz] * sum1;
2170:       sum5 -= v5[nz] * sum1;
2171:       sum3 -= v3[nz + 1] * sum2;
2172:       sum4 -= v4[nz + 1] * sum2;
2173:       sum5 -= v5[nz + 1] * sum2;
2174:       sum4 -= v4[nz + 2] * sum3;
2175:       sum5 -= v5[nz + 2] * sum3;
2176:       sum5 -= v5[nz + 3] * sum4;

2178:       tmp[row++] = sum1;
2179:       tmp[row++] = sum2;
2180:       tmp[row++] = sum3;
2181:       tmp[row++] = sum4;
2182:       tmp[row++] = sum5;
2183:       break;
2184:     default:
2185:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not yet supported ");
2186:     }
2187:   }
2188:   /* backward solve the upper triangular */
2189:   for (i = node_max - 1; i >= 0; i--) {
2190:     row = ns[i + 1] - 1;
2191:     nsz = ns[i + 1] - ns[i];
2192:     aii = ad[row + 1] + 1;
2193:     v1  = aa + aii;
2194:     vi  = aj + aii;
2195:     nz  = ad[row] - ad[row + 1] - 1;

2197:     if (i > 0) {
2198:       /* Prefetch the indices for the next block */
2199:       PetscPrefetchBlock(aj + ad[row - nsz + 1] + 1, ad[row - nsz] - ad[row - nsz + 1], 0, PETSC_PREFETCH_HINT_NTA);
2200:       /* Prefetch the data for the next block */
2201:       PetscPrefetchBlock(aa + ad[row - nsz + 1] + 1, ad[ns[i - 1] + 1] - ad[row - nsz + 1], 0, PETSC_PREFETCH_HINT_NTA);
2202:     }

2204:     switch (nsz) { /* Each loop in 'case' is unrolled */
2205:     case 1:
2206:       sum1 = tmp[row];

2208:       for (j = 0; j < nz - 1; j += 2) {
2209:         i0   = vi[j];
2210:         i1   = vi[j + 1];
2211:         tmp0 = tmps[i0];
2212:         tmp1 = tmps[i1];
2213:         sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
2214:       }
2215:       if (j == nz - 1) {
2216:         tmp0 = tmps[vi[j]];
2217:         sum1 -= v1[j] * tmp0;
2218:       }
2219:       x[c[row]] = tmp[row] = sum1 * v1[nz];
2220:       row--;
2221:       break;
2222:     case 2:
2223:       sum1 = tmp[row];
2224:       sum2 = tmp[row - 1];
2225:       v2   = aa + ad[row] + 1;
2226:       for (j = 0; j < nz - 1; j += 2) {
2227:         i0   = vi[j];
2228:         i1   = vi[j + 1];
2229:         tmp0 = tmps[i0];
2230:         tmp1 = tmps[i1];
2231:         sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
2232:         sum2 -= v2[j + 1] * tmp0 + v2[j + 2] * tmp1;
2233:       }
2234:       if (j == nz - 1) {
2235:         tmp0 = tmps[vi[j]];
2236:         sum1 -= v1[j] * tmp0;
2237:         sum2 -= v2[j + 1] * tmp0;
2238:       }

2240:       tmp0 = x[c[row]] = tmp[row] = sum1 * v1[nz];
2241:       row--;
2242:       sum2 -= v2[0] * tmp0;
2243:       x[c[row]] = tmp[row] = sum2 * v2[nz + 1];
2244:       row--;
2245:       break;
2246:     case 3:
2247:       sum1 = tmp[row];
2248:       sum2 = tmp[row - 1];
2249:       sum3 = tmp[row - 2];
2250:       v2   = aa + ad[row] + 1;
2251:       v3   = aa + ad[row - 1] + 1;
2252:       for (j = 0; j < nz - 1; j += 2) {
2253:         i0   = vi[j];
2254:         i1   = vi[j + 1];
2255:         tmp0 = tmps[i0];
2256:         tmp1 = tmps[i1];
2257:         sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
2258:         sum2 -= v2[j + 1] * tmp0 + v2[j + 2] * tmp1;
2259:         sum3 -= v3[j + 2] * tmp0 + v3[j + 3] * tmp1;
2260:       }
2261:       if (j == nz - 1) {
2262:         tmp0 = tmps[vi[j]];
2263:         sum1 -= v1[j] * tmp0;
2264:         sum2 -= v2[j + 1] * tmp0;
2265:         sum3 -= v3[j + 2] * tmp0;
2266:       }
2267:       tmp0 = x[c[row]] = tmp[row] = sum1 * v1[nz];
2268:       row--;
2269:       sum2 -= v2[0] * tmp0;
2270:       sum3 -= v3[1] * tmp0;
2271:       tmp0 = x[c[row]] = tmp[row] = sum2 * v2[nz + 1];
2272:       row--;
2273:       sum3 -= v3[0] * tmp0;
2274:       x[c[row]] = tmp[row] = sum3 * v3[nz + 2];
2275:       row--;

2277:       break;
2278:     case 4:
2279:       sum1 = tmp[row];
2280:       sum2 = tmp[row - 1];
2281:       sum3 = tmp[row - 2];
2282:       sum4 = tmp[row - 3];
2283:       v2   = aa + ad[row] + 1;
2284:       v3   = aa + ad[row - 1] + 1;
2285:       v4   = aa + ad[row - 2] + 1;

2287:       for (j = 0; j < nz - 1; j += 2) {
2288:         i0   = vi[j];
2289:         i1   = vi[j + 1];
2290:         tmp0 = tmps[i0];
2291:         tmp1 = tmps[i1];
2292:         sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
2293:         sum2 -= v2[j + 1] * tmp0 + v2[j + 2] * tmp1;
2294:         sum3 -= v3[j + 2] * tmp0 + v3[j + 3] * tmp1;
2295:         sum4 -= v4[j + 3] * tmp0 + v4[j + 4] * tmp1;
2296:       }
2297:       if (j == nz - 1) {
2298:         tmp0 = tmps[vi[j]];
2299:         sum1 -= v1[j] * tmp0;
2300:         sum2 -= v2[j + 1] * tmp0;
2301:         sum3 -= v3[j + 2] * tmp0;
2302:         sum4 -= v4[j + 3] * tmp0;
2303:       }

2305:       tmp0 = x[c[row]] = tmp[row] = sum1 * v1[nz];
2306:       row--;
2307:       sum2 -= v2[0] * tmp0;
2308:       sum3 -= v3[1] * tmp0;
2309:       sum4 -= v4[2] * tmp0;
2310:       tmp0 = x[c[row]] = tmp[row] = sum2 * v2[nz + 1];
2311:       row--;
2312:       sum3 -= v3[0] * tmp0;
2313:       sum4 -= v4[1] * tmp0;
2314:       tmp0 = x[c[row]] = tmp[row] = sum3 * v3[nz + 2];
2315:       row--;
2316:       sum4 -= v4[0] * tmp0;
2317:       x[c[row]] = tmp[row] = sum4 * v4[nz + 3];
2318:       row--;
2319:       break;
2320:     case 5:
2321:       sum1 = tmp[row];
2322:       sum2 = tmp[row - 1];
2323:       sum3 = tmp[row - 2];
2324:       sum4 = tmp[row - 3];
2325:       sum5 = tmp[row - 4];
2326:       v2   = aa + ad[row] + 1;
2327:       v3   = aa + ad[row - 1] + 1;
2328:       v4   = aa + ad[row - 2] + 1;
2329:       v5   = aa + ad[row - 3] + 1;
2330:       for (j = 0; j < nz - 1; j += 2) {
2331:         i0   = vi[j];
2332:         i1   = vi[j + 1];
2333:         tmp0 = tmps[i0];
2334:         tmp1 = tmps[i1];
2335:         sum1 -= v1[j] * tmp0 + v1[j + 1] * tmp1;
2336:         sum2 -= v2[j + 1] * tmp0 + v2[j + 2] * tmp1;
2337:         sum3 -= v3[j + 2] * tmp0 + v3[j + 3] * tmp1;
2338:         sum4 -= v4[j + 3] * tmp0 + v4[j + 4] * tmp1;
2339:         sum5 -= v5[j + 4] * tmp0 + v5[j + 5] * tmp1;
2340:       }
2341:       if (j == nz - 1) {
2342:         tmp0 = tmps[vi[j]];
2343:         sum1 -= v1[j] * tmp0;
2344:         sum2 -= v2[j + 1] * tmp0;
2345:         sum3 -= v3[j + 2] * tmp0;
2346:         sum4 -= v4[j + 3] * tmp0;
2347:         sum5 -= v5[j + 4] * tmp0;
2348:       }

2350:       tmp0 = x[c[row]] = tmp[row] = sum1 * v1[nz];
2351:       row--;
2352:       sum2 -= v2[0] * tmp0;
2353:       sum3 -= v3[1] * tmp0;
2354:       sum4 -= v4[2] * tmp0;
2355:       sum5 -= v5[3] * tmp0;
2356:       tmp0 = x[c[row]] = tmp[row] = sum2 * v2[nz + 1];
2357:       row--;
2358:       sum3 -= v3[0] * tmp0;
2359:       sum4 -= v4[1] * tmp0;
2360:       sum5 -= v5[2] * tmp0;
2361:       tmp0 = x[c[row]] = tmp[row] = sum3 * v3[nz + 2];
2362:       row--;
2363:       sum4 -= v4[0] * tmp0;
2364:       sum5 -= v5[1] * tmp0;
2365:       tmp0 = x[c[row]] = tmp[row] = sum4 * v4[nz + 3];
2366:       row--;
2367:       sum5 -= v5[0] * tmp0;
2368:       x[c[row]] = tmp[row] = sum5 * v5[nz + 4];
2369:       row--;
2370:       break;
2371:     default:
2372:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not yet supported ");
2373:     }
2374:   }
2375:   PetscCall(ISRestoreIndices(isrow, &rout));
2376:   PetscCall(ISRestoreIndices(iscol, &cout));
2377:   PetscCall(VecRestoreArrayRead(bb, &b));
2378:   PetscCall(VecRestoreArrayWrite(xx, &x));
2379:   PetscCall(PetscLogFlops(2.0 * a->nz - A->cmap->n));
2380:   PetscFunctionReturn(PETSC_SUCCESS);
2381: }

2383: /*
2384:      Makes a longer coloring[] array and calls the usual code with that
2385: */
2386: static PetscErrorCode MatColoringPatch_SeqAIJ_Inode(Mat mat, PetscInt ncolors, PetscInt nin, ISColoringValue coloring[], ISColoring *iscoloring)
2387: {
2388:   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)mat->data;
2389:   PetscInt         n = mat->cmap->n, m = a->inode.node_count, j, *ns = a->inode.size_csr, row;
2390:   PetscInt        *colorused, i;
2391:   ISColoringValue *newcolor;

2393:   PetscFunctionBegin;
2394:   PetscCheck(a->inode.size_csr, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
2395:   PetscCall(PetscMalloc1(n + 1, &newcolor));
2396:   /* loop over inodes, marking a color for each column*/
2397:   row = 0;
2398:   for (i = 0; i < m; i++) {
2399:     for (j = 0; j < (ns[i + 1] - ns[i]); j++) PetscCall(ISColoringValueCast(coloring[i] + j * ncolors, newcolor + row++));
2400:   }

2402:   /* eliminate unneeded colors */
2403:   PetscCall(PetscCalloc1(5 * ncolors, &colorused));
2404:   for (i = 0; i < n; i++) colorused[newcolor[i]] = 1;

2406:   for (i = 1; i < 5 * ncolors; i++) colorused[i] += colorused[i - 1];
2407:   ncolors = colorused[5 * ncolors - 1];
2408:   for (i = 0; i < n; i++) PetscCall(ISColoringValueCast(colorused[newcolor[i]] - 1, newcolor + i));
2409:   PetscCall(PetscFree(colorused));
2410:   PetscCall(ISColoringCreate(PetscObjectComm((PetscObject)mat), ncolors, n, newcolor, PETSC_OWN_POINTER, iscoloring));
2411:   PetscCall(PetscFree(coloring));
2412:   PetscFunctionReturn(PETSC_SUCCESS);
2413: }

2415: #include <petsc/private/kernels/blockinvert.h>

2417: /*
2418:    Negative shift indicates do not generate an error if there is a zero diagonal, just invert it anyways
2419: */
2420: static PetscErrorCode MatInvertDiagonalForSOR_SeqAIJ_Inode(Mat A, PetscScalar omega, PetscScalar fshift)
2421: {
2422:   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
2423:   MatScalar       *ibdiag, *bdiag, work[25];
2424:   const MatScalar *v         = a->a;
2425:   PetscReal        zeropivot = 100. * PETSC_MACHINE_EPSILON, shift = 0.0;
2426:   PetscInt         m = a->inode.node_count, cnt = 0, i, j, row, nodesz;
2427:   PetscInt         k, ipvt[5];
2428:   PetscBool        allowzeropivot = PetscNot(A->erroriffailure), zeropivotdetected;
2429:   const PetscInt  *sizes          = a->inode.size_csr, *diag;

2431:   PetscFunctionBegin;
2432:   if (a->idiagState == ((PetscObject)A)->state) PetscFunctionReturn(PETSC_SUCCESS);
2433:   PetscCall(MatGetDiagonalMarkers_SeqAIJ(A, &diag, NULL));
2434:   if (!a->inode.ibdiag) {
2435:     /* calculate space needed for diagonal blocks */
2436:     for (i = 0; i < m; i++) {
2437:       nodesz = sizes[i + 1] - sizes[i];
2438:       cnt += nodesz * nodesz;
2439:     }
2440:     a->inode.bdiagsize = cnt;
2441:     PetscCall(PetscMalloc3(cnt, &a->inode.ibdiag, cnt, &a->inode.bdiag, A->rmap->n, &a->inode.ssor_work));
2442:   }

2444:   /* copy over the diagonal blocks and invert them */
2445:   ibdiag = a->inode.ibdiag;
2446:   bdiag  = a->inode.bdiag;
2447:   cnt    = 0;
2448:   for (i = 0, row = 0; i < m; i++) {
2449:     nodesz = sizes[i + 1] - sizes[i];
2450:     for (j = 0; j < nodesz; j++) {
2451:       for (k = 0; k < nodesz; k++) bdiag[cnt + k * nodesz + j] = v[diag[row + j] - j + k];
2452:     }
2453:     PetscCall(PetscArraycpy(ibdiag + cnt, bdiag + cnt, nodesz * nodesz));

2455:     switch (nodesz) {
2456:     case 1:
2457:       /* Create matrix data structure */
2458:       if (PetscAbsScalar(ibdiag[cnt]) < zeropivot) {
2459:         PetscCheck(allowzeropivot, PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot on row %" PetscInt_FMT, row);
2460:         A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
2461:         A->factorerror_zeropivot_value = PetscAbsScalar(ibdiag[cnt]);
2462:         A->factorerror_zeropivot_row   = row;
2463:         PetscCall(PetscInfo(A, "Zero pivot, row %" PetscInt_FMT "\n", row));
2464:       }
2465:       ibdiag[cnt] = 1.0 / ibdiag[cnt];
2466:       break;
2467:     case 2:
2468:       PetscCall(PetscKernel_A_gets_inverse_A_2(ibdiag + cnt, shift, allowzeropivot, &zeropivotdetected));
2469:       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
2470:       break;
2471:     case 3:
2472:       PetscCall(PetscKernel_A_gets_inverse_A_3(ibdiag + cnt, shift, allowzeropivot, &zeropivotdetected));
2473:       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
2474:       break;
2475:     case 4:
2476:       PetscCall(PetscKernel_A_gets_inverse_A_4(ibdiag + cnt, shift, allowzeropivot, &zeropivotdetected));
2477:       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
2478:       break;
2479:     case 5:
2480:       PetscCall(PetscKernel_A_gets_inverse_A_5(ibdiag + cnt, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
2481:       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
2482:       break;
2483:     default:
2484:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not supported, node row %" PetscInt_FMT " size %" PetscInt_FMT, row, nodesz);
2485:     }
2486:     cnt += nodesz * nodesz;
2487:     row += nodesz;
2488:   }
2489:   a->inode.ibdiagState = ((PetscObject)A)->state;
2490:   PetscFunctionReturn(PETSC_SUCCESS);
2491: }

2493: PetscErrorCode MatSOR_SeqAIJ_Inode(Mat A, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
2494: {
2495:   Mat_SeqAIJ        *a    = (Mat_SeqAIJ *)A->data;
2496:   PetscScalar        sum1 = 0.0, sum2 = 0.0, sum3 = 0.0, sum4 = 0.0, sum5 = 0.0, tmp0, tmp1, tmp2, tmp3;
2497:   MatScalar         *ibdiag, *bdiag, *t;
2498:   PetscScalar       *x, tmp4, tmp5, x1, x2, x3, x4, x5;
2499:   const MatScalar   *v1 = NULL, *v2 = NULL, *v3 = NULL, *v4 = NULL, *v5 = NULL;
2500:   const PetscScalar *xb, *b;
2501:   PetscInt           n, m = a->inode.node_count, cnt = 0, i, row, i1, i2, nodesz;
2502:   PetscInt           sz;
2503:   const PetscInt    *sizes = a->inode.size_csr, *idx, *diag, *ii = a->i;

2505:   PetscFunctionBegin;
2506:   PetscCheck(a->inode.size_csr, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
2507:   PetscCheck(omega == 1.0, PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for omega != 1.0; use -mat_no_inode");
2508:   PetscCheck(fshift == 0.0, PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for fshift != 0.0; use -mat_no_inode");
2509:   PetscCall(MatInvertDiagonalForSOR_SeqAIJ_Inode(A, omega, fshift));
2510:   diag = a->diag;

2512:   ibdiag = a->inode.ibdiag;
2513:   bdiag  = a->inode.bdiag;
2514:   t      = a->inode.ssor_work;

2516:   PetscCall(VecGetArray(xx, &x));
2517:   PetscCall(VecGetArrayRead(bb, &b));
2518:   /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
2519:   if (flag & SOR_ZERO_INITIAL_GUESS) {
2520:     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
2521:       for (i = 0, row = 0; i < m; i++) {
2522:         sz  = diag[row] - ii[row];
2523:         v1  = a->a + ii[row];
2524:         idx = a->j + ii[row];

2526:         /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
2527:         nodesz = sizes[i + 1] - sizes[i];
2528:         switch (nodesz) {
2529:         case 1:

2531:           sum1 = b[row];
2532:           for (n = 0; n < sz - 1; n += 2) {
2533:             i1 = idx[0];
2534:             i2 = idx[1];
2535:             idx += 2;
2536:             tmp0 = x[i1];
2537:             tmp1 = x[i2];
2538:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2539:             v1 += 2;
2540:           }

2542:           if (n == sz - 1) {
2543:             tmp0 = x[*idx];
2544:             sum1 -= *v1 * tmp0;
2545:           }
2546:           t[row]   = sum1;
2547:           x[row++] = sum1 * (*ibdiag++);
2548:           break;
2549:         case 2:
2550:           v2   = a->a + ii[row + 1];
2551:           sum1 = b[row];
2552:           sum2 = b[row + 1];
2553:           for (n = 0; n < sz - 1; n += 2) {
2554:             i1 = idx[0];
2555:             i2 = idx[1];
2556:             idx += 2;
2557:             tmp0 = x[i1];
2558:             tmp1 = x[i2];
2559:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2560:             v1 += 2;
2561:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
2562:             v2 += 2;
2563:           }

2565:           if (n == sz - 1) {
2566:             tmp0 = x[*idx];
2567:             sum1 -= v1[0] * tmp0;
2568:             sum2 -= v2[0] * tmp0;
2569:           }
2570:           t[row]     = sum1;
2571:           t[row + 1] = sum2;
2572:           x[row++]   = sum1 * ibdiag[0] + sum2 * ibdiag[2];
2573:           x[row++]   = sum1 * ibdiag[1] + sum2 * ibdiag[3];
2574:           ibdiag += 4;
2575:           break;
2576:         case 3:
2577:           v2   = a->a + ii[row + 1];
2578:           v3   = a->a + ii[row + 2];
2579:           sum1 = b[row];
2580:           sum2 = b[row + 1];
2581:           sum3 = b[row + 2];
2582:           for (n = 0; n < sz - 1; n += 2) {
2583:             i1 = idx[0];
2584:             i2 = idx[1];
2585:             idx += 2;
2586:             tmp0 = x[i1];
2587:             tmp1 = x[i2];
2588:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2589:             v1 += 2;
2590:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
2591:             v2 += 2;
2592:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
2593:             v3 += 2;
2594:           }

2596:           if (n == sz - 1) {
2597:             tmp0 = x[*idx];
2598:             sum1 -= v1[0] * tmp0;
2599:             sum2 -= v2[0] * tmp0;
2600:             sum3 -= v3[0] * tmp0;
2601:           }
2602:           t[row]     = sum1;
2603:           t[row + 1] = sum2;
2604:           t[row + 2] = sum3;
2605:           x[row++]   = sum1 * ibdiag[0] + sum2 * ibdiag[3] + sum3 * ibdiag[6];
2606:           x[row++]   = sum1 * ibdiag[1] + sum2 * ibdiag[4] + sum3 * ibdiag[7];
2607:           x[row++]   = sum1 * ibdiag[2] + sum2 * ibdiag[5] + sum3 * ibdiag[8];
2608:           ibdiag += 9;
2609:           break;
2610:         case 4:
2611:           v2   = a->a + ii[row + 1];
2612:           v3   = a->a + ii[row + 2];
2613:           v4   = a->a + ii[row + 3];
2614:           sum1 = b[row];
2615:           sum2 = b[row + 1];
2616:           sum3 = b[row + 2];
2617:           sum4 = b[row + 3];
2618:           for (n = 0; n < sz - 1; n += 2) {
2619:             i1 = idx[0];
2620:             i2 = idx[1];
2621:             idx += 2;
2622:             tmp0 = x[i1];
2623:             tmp1 = x[i2];
2624:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2625:             v1 += 2;
2626:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
2627:             v2 += 2;
2628:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
2629:             v3 += 2;
2630:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
2631:             v4 += 2;
2632:           }

2634:           if (n == sz - 1) {
2635:             tmp0 = x[*idx];
2636:             sum1 -= v1[0] * tmp0;
2637:             sum2 -= v2[0] * tmp0;
2638:             sum3 -= v3[0] * tmp0;
2639:             sum4 -= v4[0] * tmp0;
2640:           }
2641:           t[row]     = sum1;
2642:           t[row + 1] = sum2;
2643:           t[row + 2] = sum3;
2644:           t[row + 3] = sum4;
2645:           x[row++]   = sum1 * ibdiag[0] + sum2 * ibdiag[4] + sum3 * ibdiag[8] + sum4 * ibdiag[12];
2646:           x[row++]   = sum1 * ibdiag[1] + sum2 * ibdiag[5] + sum3 * ibdiag[9] + sum4 * ibdiag[13];
2647:           x[row++]   = sum1 * ibdiag[2] + sum2 * ibdiag[6] + sum3 * ibdiag[10] + sum4 * ibdiag[14];
2648:           x[row++]   = sum1 * ibdiag[3] + sum2 * ibdiag[7] + sum3 * ibdiag[11] + sum4 * ibdiag[15];
2649:           ibdiag += 16;
2650:           break;
2651:         case 5:
2652:           v2   = a->a + ii[row + 1];
2653:           v3   = a->a + ii[row + 2];
2654:           v4   = a->a + ii[row + 3];
2655:           v5   = a->a + ii[row + 4];
2656:           sum1 = b[row];
2657:           sum2 = b[row + 1];
2658:           sum3 = b[row + 2];
2659:           sum4 = b[row + 3];
2660:           sum5 = b[row + 4];
2661:           for (n = 0; n < sz - 1; n += 2) {
2662:             i1 = idx[0];
2663:             i2 = idx[1];
2664:             idx += 2;
2665:             tmp0 = x[i1];
2666:             tmp1 = x[i2];
2667:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2668:             v1 += 2;
2669:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
2670:             v2 += 2;
2671:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
2672:             v3 += 2;
2673:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
2674:             v4 += 2;
2675:             sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
2676:             v5 += 2;
2677:           }

2679:           if (n == sz - 1) {
2680:             tmp0 = x[*idx];
2681:             sum1 -= v1[0] * tmp0;
2682:             sum2 -= v2[0] * tmp0;
2683:             sum3 -= v3[0] * tmp0;
2684:             sum4 -= v4[0] * tmp0;
2685:             sum5 -= v5[0] * tmp0;
2686:           }
2687:           t[row]     = sum1;
2688:           t[row + 1] = sum2;
2689:           t[row + 2] = sum3;
2690:           t[row + 3] = sum4;
2691:           t[row + 4] = sum5;
2692:           x[row++]   = sum1 * ibdiag[0] + sum2 * ibdiag[5] + sum3 * ibdiag[10] + sum4 * ibdiag[15] + sum5 * ibdiag[20];
2693:           x[row++]   = sum1 * ibdiag[1] + sum2 * ibdiag[6] + sum3 * ibdiag[11] + sum4 * ibdiag[16] + sum5 * ibdiag[21];
2694:           x[row++]   = sum1 * ibdiag[2] + sum2 * ibdiag[7] + sum3 * ibdiag[12] + sum4 * ibdiag[17] + sum5 * ibdiag[22];
2695:           x[row++]   = sum1 * ibdiag[3] + sum2 * ibdiag[8] + sum3 * ibdiag[13] + sum4 * ibdiag[18] + sum5 * ibdiag[23];
2696:           x[row++]   = sum1 * ibdiag[4] + sum2 * ibdiag[9] + sum3 * ibdiag[14] + sum4 * ibdiag[19] + sum5 * ibdiag[24];
2697:           ibdiag += 25;
2698:           break;
2699:         default:
2700:           SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not supported, node row %" PetscInt_FMT " size %" PetscInt_FMT, row, nodesz);
2701:         }
2702:       }

2704:       xb = t;
2705:       PetscCall(PetscLogFlops(a->nz));
2706:     } else xb = b;
2707:     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
2708:       ibdiag = a->inode.ibdiag + a->inode.bdiagsize;
2709:       for (i = m - 1, row = A->rmap->n - 1; i >= 0; i--) {
2710:         nodesz = sizes[i + 1] - sizes[i];
2711:         ibdiag -= nodesz * nodesz;
2712:         sz  = ii[row + 1] - diag[row] - 1;
2713:         v1  = a->a + diag[row] + 1;
2714:         idx = a->j + diag[row] + 1;

2716:         /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
2717:         switch (nodesz) {
2718:         case 1:

2720:           sum1 = xb[row];
2721:           for (n = 0; n < sz - 1; n += 2) {
2722:             i1 = idx[0];
2723:             i2 = idx[1];
2724:             idx += 2;
2725:             tmp0 = x[i1];
2726:             tmp1 = x[i2];
2727:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2728:             v1 += 2;
2729:           }

2731:           if (n == sz - 1) {
2732:             tmp0 = x[*idx];
2733:             sum1 -= *v1 * tmp0;
2734:           }
2735:           x[row--] = sum1 * (*ibdiag);
2736:           break;

2738:         case 2:

2740:           sum1 = xb[row];
2741:           sum2 = xb[row - 1];
2742:           /* note that sum1 is associated with the second of the two rows */
2743:           v2 = a->a + diag[row - 1] + 2;
2744:           for (n = 0; n < sz - 1; n += 2) {
2745:             i1 = idx[0];
2746:             i2 = idx[1];
2747:             idx += 2;
2748:             tmp0 = x[i1];
2749:             tmp1 = x[i2];
2750:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2751:             v1 += 2;
2752:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
2753:             v2 += 2;
2754:           }

2756:           if (n == sz - 1) {
2757:             tmp0 = x[*idx];
2758:             sum1 -= *v1 * tmp0;
2759:             sum2 -= *v2 * tmp0;
2760:           }
2761:           x[row--] = sum2 * ibdiag[1] + sum1 * ibdiag[3];
2762:           x[row--] = sum2 * ibdiag[0] + sum1 * ibdiag[2];
2763:           break;
2764:         case 3:

2766:           sum1 = xb[row];
2767:           sum2 = xb[row - 1];
2768:           sum3 = xb[row - 2];
2769:           v2   = a->a + diag[row - 1] + 2;
2770:           v3   = a->a + diag[row - 2] + 3;
2771:           for (n = 0; n < sz - 1; n += 2) {
2772:             i1 = idx[0];
2773:             i2 = idx[1];
2774:             idx += 2;
2775:             tmp0 = x[i1];
2776:             tmp1 = x[i2];
2777:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2778:             v1 += 2;
2779:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
2780:             v2 += 2;
2781:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
2782:             v3 += 2;
2783:           }

2785:           if (n == sz - 1) {
2786:             tmp0 = x[*idx];
2787:             sum1 -= *v1 * tmp0;
2788:             sum2 -= *v2 * tmp0;
2789:             sum3 -= *v3 * tmp0;
2790:           }
2791:           x[row--] = sum3 * ibdiag[2] + sum2 * ibdiag[5] + sum1 * ibdiag[8];
2792:           x[row--] = sum3 * ibdiag[1] + sum2 * ibdiag[4] + sum1 * ibdiag[7];
2793:           x[row--] = sum3 * ibdiag[0] + sum2 * ibdiag[3] + sum1 * ibdiag[6];
2794:           break;
2795:         case 4:

2797:           sum1 = xb[row];
2798:           sum2 = xb[row - 1];
2799:           sum3 = xb[row - 2];
2800:           sum4 = xb[row - 3];
2801:           v2   = a->a + diag[row - 1] + 2;
2802:           v3   = a->a + diag[row - 2] + 3;
2803:           v4   = a->a + diag[row - 3] + 4;
2804:           for (n = 0; n < sz - 1; n += 2) {
2805:             i1 = idx[0];
2806:             i2 = idx[1];
2807:             idx += 2;
2808:             tmp0 = x[i1];
2809:             tmp1 = x[i2];
2810:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2811:             v1 += 2;
2812:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
2813:             v2 += 2;
2814:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
2815:             v3 += 2;
2816:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
2817:             v4 += 2;
2818:           }

2820:           if (n == sz - 1) {
2821:             tmp0 = x[*idx];
2822:             sum1 -= *v1 * tmp0;
2823:             sum2 -= *v2 * tmp0;
2824:             sum3 -= *v3 * tmp0;
2825:             sum4 -= *v4 * tmp0;
2826:           }
2827:           x[row--] = sum4 * ibdiag[3] + sum3 * ibdiag[7] + sum2 * ibdiag[11] + sum1 * ibdiag[15];
2828:           x[row--] = sum4 * ibdiag[2] + sum3 * ibdiag[6] + sum2 * ibdiag[10] + sum1 * ibdiag[14];
2829:           x[row--] = sum4 * ibdiag[1] + sum3 * ibdiag[5] + sum2 * ibdiag[9] + sum1 * ibdiag[13];
2830:           x[row--] = sum4 * ibdiag[0] + sum3 * ibdiag[4] + sum2 * ibdiag[8] + sum1 * ibdiag[12];
2831:           break;
2832:         case 5:

2834:           sum1 = xb[row];
2835:           sum2 = xb[row - 1];
2836:           sum3 = xb[row - 2];
2837:           sum4 = xb[row - 3];
2838:           sum5 = xb[row - 4];
2839:           v2   = a->a + diag[row - 1] + 2;
2840:           v3   = a->a + diag[row - 2] + 3;
2841:           v4   = a->a + diag[row - 3] + 4;
2842:           v5   = a->a + diag[row - 4] + 5;
2843:           for (n = 0; n < sz - 1; n += 2) {
2844:             i1 = idx[0];
2845:             i2 = idx[1];
2846:             idx += 2;
2847:             tmp0 = x[i1];
2848:             tmp1 = x[i2];
2849:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2850:             v1 += 2;
2851:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
2852:             v2 += 2;
2853:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
2854:             v3 += 2;
2855:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
2856:             v4 += 2;
2857:             sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
2858:             v5 += 2;
2859:           }

2861:           if (n == sz - 1) {
2862:             tmp0 = x[*idx];
2863:             sum1 -= *v1 * tmp0;
2864:             sum2 -= *v2 * tmp0;
2865:             sum3 -= *v3 * tmp0;
2866:             sum4 -= *v4 * tmp0;
2867:             sum5 -= *v5 * tmp0;
2868:           }
2869:           x[row--] = sum5 * ibdiag[4] + sum4 * ibdiag[9] + sum3 * ibdiag[14] + sum2 * ibdiag[19] + sum1 * ibdiag[24];
2870:           x[row--] = sum5 * ibdiag[3] + sum4 * ibdiag[8] + sum3 * ibdiag[13] + sum2 * ibdiag[18] + sum1 * ibdiag[23];
2871:           x[row--] = sum5 * ibdiag[2] + sum4 * ibdiag[7] + sum3 * ibdiag[12] + sum2 * ibdiag[17] + sum1 * ibdiag[22];
2872:           x[row--] = sum5 * ibdiag[1] + sum4 * ibdiag[6] + sum3 * ibdiag[11] + sum2 * ibdiag[16] + sum1 * ibdiag[21];
2873:           x[row--] = sum5 * ibdiag[0] + sum4 * ibdiag[5] + sum3 * ibdiag[10] + sum2 * ibdiag[15] + sum1 * ibdiag[20];
2874:           break;
2875:         default:
2876:           SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not supported, node row %" PetscInt_FMT " size %" PetscInt_FMT, row, nodesz);
2877:         }
2878:       }

2880:       PetscCall(PetscLogFlops(a->nz));
2881:     }
2882:     its--;
2883:   }
2884:   while (its--) {
2885:     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
2886:       for (i = 0, row = 0, ibdiag = a->inode.ibdiag; i < m; row += nodesz, ibdiag += nodesz * nodesz, i++) {
2887:         nodesz = sizes[i + 1] - sizes[i];
2888:         sz     = diag[row] - ii[row];
2889:         v1     = a->a + ii[row];
2890:         idx    = a->j + ii[row];
2891:         /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
2892:         switch (nodesz) {
2893:         case 1:
2894:           sum1 = b[row];
2895:           for (n = 0; n < sz - 1; n += 2) {
2896:             i1 = idx[0];
2897:             i2 = idx[1];
2898:             idx += 2;
2899:             tmp0 = x[i1];
2900:             tmp1 = x[i2];
2901:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2902:             v1 += 2;
2903:           }
2904:           if (n == sz - 1) {
2905:             tmp0 = x[*idx++];
2906:             sum1 -= *v1 * tmp0;
2907:             v1++;
2908:           }
2909:           t[row] = sum1;
2910:           sz     = ii[row + 1] - diag[row] - 1;
2911:           idx    = a->j + diag[row] + 1;
2912:           v1 += 1;
2913:           for (n = 0; n < sz - 1; n += 2) {
2914:             i1 = idx[0];
2915:             i2 = idx[1];
2916:             idx += 2;
2917:             tmp0 = x[i1];
2918:             tmp1 = x[i2];
2919:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2920:             v1 += 2;
2921:           }
2922:           if (n == sz - 1) {
2923:             tmp0 = x[*idx++];
2924:             sum1 -= *v1 * tmp0;
2925:           }
2926:           /* in MatSOR_SeqAIJ this line would be
2927:            *
2928:            * x[row] = (1-omega)*x[row]+(sum1+(*bdiag++)*x[row])*(*ibdiag++);
2929:            *
2930:            * but omega == 1, so this becomes
2931:            *
2932:            * x[row] = sum1*(*ibdiag++);
2933:            *
2934:            */
2935:           x[row] = sum1 * (*ibdiag);
2936:           break;
2937:         case 2:
2938:           v2   = a->a + ii[row + 1];
2939:           sum1 = b[row];
2940:           sum2 = b[row + 1];
2941:           for (n = 0; n < sz - 1; n += 2) {
2942:             i1 = idx[0];
2943:             i2 = idx[1];
2944:             idx += 2;
2945:             tmp0 = x[i1];
2946:             tmp1 = x[i2];
2947:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2948:             v1 += 2;
2949:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
2950:             v2 += 2;
2951:           }
2952:           if (n == sz - 1) {
2953:             tmp0 = x[*idx++];
2954:             sum1 -= v1[0] * tmp0;
2955:             sum2 -= v2[0] * tmp0;
2956:             v1++;
2957:             v2++;
2958:           }
2959:           t[row]     = sum1;
2960:           t[row + 1] = sum2;
2961:           sz         = ii[row + 1] - diag[row] - 2;
2962:           idx        = a->j + diag[row] + 2;
2963:           v1 += 2;
2964:           v2 += 2;
2965:           for (n = 0; n < sz - 1; n += 2) {
2966:             i1 = idx[0];
2967:             i2 = idx[1];
2968:             idx += 2;
2969:             tmp0 = x[i1];
2970:             tmp1 = x[i2];
2971:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2972:             v1 += 2;
2973:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
2974:             v2 += 2;
2975:           }
2976:           if (n == sz - 1) {
2977:             tmp0 = x[*idx];
2978:             sum1 -= v1[0] * tmp0;
2979:             sum2 -= v2[0] * tmp0;
2980:           }
2981:           x[row]     = sum1 * ibdiag[0] + sum2 * ibdiag[2];
2982:           x[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[3];
2983:           break;
2984:         case 3:
2985:           v2   = a->a + ii[row + 1];
2986:           v3   = a->a + ii[row + 2];
2987:           sum1 = b[row];
2988:           sum2 = b[row + 1];
2989:           sum3 = b[row + 2];
2990:           for (n = 0; n < sz - 1; n += 2) {
2991:             i1 = idx[0];
2992:             i2 = idx[1];
2993:             idx += 2;
2994:             tmp0 = x[i1];
2995:             tmp1 = x[i2];
2996:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
2997:             v1 += 2;
2998:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
2999:             v2 += 2;
3000:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3001:             v3 += 2;
3002:           }
3003:           if (n == sz - 1) {
3004:             tmp0 = x[*idx++];
3005:             sum1 -= v1[0] * tmp0;
3006:             sum2 -= v2[0] * tmp0;
3007:             sum3 -= v3[0] * tmp0;
3008:             v1++;
3009:             v2++;
3010:             v3++;
3011:           }
3012:           t[row]     = sum1;
3013:           t[row + 1] = sum2;
3014:           t[row + 2] = sum3;
3015:           sz         = ii[row + 1] - diag[row] - 3;
3016:           idx        = a->j + diag[row] + 3;
3017:           v1 += 3;
3018:           v2 += 3;
3019:           v3 += 3;
3020:           for (n = 0; n < sz - 1; n += 2) {
3021:             i1 = idx[0];
3022:             i2 = idx[1];
3023:             idx += 2;
3024:             tmp0 = x[i1];
3025:             tmp1 = x[i2];
3026:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3027:             v1 += 2;
3028:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3029:             v2 += 2;
3030:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3031:             v3 += 2;
3032:           }
3033:           if (n == sz - 1) {
3034:             tmp0 = x[*idx];
3035:             sum1 -= v1[0] * tmp0;
3036:             sum2 -= v2[0] * tmp0;
3037:             sum3 -= v3[0] * tmp0;
3038:           }
3039:           x[row]     = sum1 * ibdiag[0] + sum2 * ibdiag[3] + sum3 * ibdiag[6];
3040:           x[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[4] + sum3 * ibdiag[7];
3041:           x[row + 2] = sum1 * ibdiag[2] + sum2 * ibdiag[5] + sum3 * ibdiag[8];
3042:           break;
3043:         case 4:
3044:           v2   = a->a + ii[row + 1];
3045:           v3   = a->a + ii[row + 2];
3046:           v4   = a->a + ii[row + 3];
3047:           sum1 = b[row];
3048:           sum2 = b[row + 1];
3049:           sum3 = b[row + 2];
3050:           sum4 = b[row + 3];
3051:           for (n = 0; n < sz - 1; n += 2) {
3052:             i1 = idx[0];
3053:             i2 = idx[1];
3054:             idx += 2;
3055:             tmp0 = x[i1];
3056:             tmp1 = x[i2];
3057:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3058:             v1 += 2;
3059:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3060:             v2 += 2;
3061:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3062:             v3 += 2;
3063:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
3064:             v4 += 2;
3065:           }
3066:           if (n == sz - 1) {
3067:             tmp0 = x[*idx++];
3068:             sum1 -= v1[0] * tmp0;
3069:             sum2 -= v2[0] * tmp0;
3070:             sum3 -= v3[0] * tmp0;
3071:             sum4 -= v4[0] * tmp0;
3072:             v1++;
3073:             v2++;
3074:             v3++;
3075:             v4++;
3076:           }
3077:           t[row]     = sum1;
3078:           t[row + 1] = sum2;
3079:           t[row + 2] = sum3;
3080:           t[row + 3] = sum4;
3081:           sz         = ii[row + 1] - diag[row] - 4;
3082:           idx        = a->j + diag[row] + 4;
3083:           v1 += 4;
3084:           v2 += 4;
3085:           v3 += 4;
3086:           v4 += 4;
3087:           for (n = 0; n < sz - 1; n += 2) {
3088:             i1 = idx[0];
3089:             i2 = idx[1];
3090:             idx += 2;
3091:             tmp0 = x[i1];
3092:             tmp1 = x[i2];
3093:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3094:             v1 += 2;
3095:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3096:             v2 += 2;
3097:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3098:             v3 += 2;
3099:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
3100:             v4 += 2;
3101:           }
3102:           if (n == sz - 1) {
3103:             tmp0 = x[*idx];
3104:             sum1 -= v1[0] * tmp0;
3105:             sum2 -= v2[0] * tmp0;
3106:             sum3 -= v3[0] * tmp0;
3107:             sum4 -= v4[0] * tmp0;
3108:           }
3109:           x[row]     = sum1 * ibdiag[0] + sum2 * ibdiag[4] + sum3 * ibdiag[8] + sum4 * ibdiag[12];
3110:           x[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[5] + sum3 * ibdiag[9] + sum4 * ibdiag[13];
3111:           x[row + 2] = sum1 * ibdiag[2] + sum2 * ibdiag[6] + sum3 * ibdiag[10] + sum4 * ibdiag[14];
3112:           x[row + 3] = sum1 * ibdiag[3] + sum2 * ibdiag[7] + sum3 * ibdiag[11] + sum4 * ibdiag[15];
3113:           break;
3114:         case 5:
3115:           v2   = a->a + ii[row + 1];
3116:           v3   = a->a + ii[row + 2];
3117:           v4   = a->a + ii[row + 3];
3118:           v5   = a->a + ii[row + 4];
3119:           sum1 = b[row];
3120:           sum2 = b[row + 1];
3121:           sum3 = b[row + 2];
3122:           sum4 = b[row + 3];
3123:           sum5 = b[row + 4];
3124:           for (n = 0; n < sz - 1; n += 2) {
3125:             i1 = idx[0];
3126:             i2 = idx[1];
3127:             idx += 2;
3128:             tmp0 = x[i1];
3129:             tmp1 = x[i2];
3130:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3131:             v1 += 2;
3132:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3133:             v2 += 2;
3134:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3135:             v3 += 2;
3136:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
3137:             v4 += 2;
3138:             sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
3139:             v5 += 2;
3140:           }
3141:           if (n == sz - 1) {
3142:             tmp0 = x[*idx++];
3143:             sum1 -= v1[0] * tmp0;
3144:             sum2 -= v2[0] * tmp0;
3145:             sum3 -= v3[0] * tmp0;
3146:             sum4 -= v4[0] * tmp0;
3147:             sum5 -= v5[0] * tmp0;
3148:             v1++;
3149:             v2++;
3150:             v3++;
3151:             v4++;
3152:             v5++;
3153:           }
3154:           t[row]     = sum1;
3155:           t[row + 1] = sum2;
3156:           t[row + 2] = sum3;
3157:           t[row + 3] = sum4;
3158:           t[row + 4] = sum5;
3159:           sz         = ii[row + 1] - diag[row] - 5;
3160:           idx        = a->j + diag[row] + 5;
3161:           v1 += 5;
3162:           v2 += 5;
3163:           v3 += 5;
3164:           v4 += 5;
3165:           v5 += 5;
3166:           for (n = 0; n < sz - 1; n += 2) {
3167:             i1 = idx[0];
3168:             i2 = idx[1];
3169:             idx += 2;
3170:             tmp0 = x[i1];
3171:             tmp1 = x[i2];
3172:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3173:             v1 += 2;
3174:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3175:             v2 += 2;
3176:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3177:             v3 += 2;
3178:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
3179:             v4 += 2;
3180:             sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
3181:             v5 += 2;
3182:           }
3183:           if (n == sz - 1) {
3184:             tmp0 = x[*idx];
3185:             sum1 -= v1[0] * tmp0;
3186:             sum2 -= v2[0] * tmp0;
3187:             sum3 -= v3[0] * tmp0;
3188:             sum4 -= v4[0] * tmp0;
3189:             sum5 -= v5[0] * tmp0;
3190:           }
3191:           x[row]     = sum1 * ibdiag[0] + sum2 * ibdiag[5] + sum3 * ibdiag[10] + sum4 * ibdiag[15] + sum5 * ibdiag[20];
3192:           x[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[6] + sum3 * ibdiag[11] + sum4 * ibdiag[16] + sum5 * ibdiag[21];
3193:           x[row + 2] = sum1 * ibdiag[2] + sum2 * ibdiag[7] + sum3 * ibdiag[12] + sum4 * ibdiag[17] + sum5 * ibdiag[22];
3194:           x[row + 3] = sum1 * ibdiag[3] + sum2 * ibdiag[8] + sum3 * ibdiag[13] + sum4 * ibdiag[18] + sum5 * ibdiag[23];
3195:           x[row + 4] = sum1 * ibdiag[4] + sum2 * ibdiag[9] + sum3 * ibdiag[14] + sum4 * ibdiag[19] + sum5 * ibdiag[24];
3196:           break;
3197:         default:
3198:           SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not supported, node row %" PetscInt_FMT " size %" PetscInt_FMT, row, nodesz);
3199:         }
3200:       }
3201:       xb = t;
3202:       PetscCall(PetscLogFlops(2.0 * a->nz)); /* undercounts diag inverse */
3203:     } else xb = b;

3205:     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
3206:       ibdiag = a->inode.ibdiag + a->inode.bdiagsize;
3207:       for (i = m - 1, row = A->rmap->n - 1; i >= 0; i--) {
3208:         nodesz = sizes[i + 1] - sizes[i];
3209:         ibdiag -= nodesz * nodesz;

3211:         /* set RHS */
3212:         if (xb == b) {
3213:           /* whole (old way) */
3214:           sz  = ii[row + 1] - ii[row];
3215:           idx = a->j + ii[row];
3216:           switch (nodesz) {
3217:           case 5:
3218:             v5 = a->a + ii[row - 4]; /* fall through */
3219:           case 4:
3220:             v4 = a->a + ii[row - 3]; /* fall through */
3221:           case 3:
3222:             v3 = a->a + ii[row - 2]; /* fall through */
3223:           case 2:
3224:             v2 = a->a + ii[row - 1]; /* fall through */
3225:           case 1:
3226:             v1 = a->a + ii[row];
3227:             break;
3228:           default:
3229:             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not supported, node row %" PetscInt_FMT " size %" PetscInt_FMT, row, nodesz);
3230:           }
3231:         } else {
3232:           /* upper, no diag */
3233:           sz  = ii[row + 1] - diag[row] - 1;
3234:           idx = a->j + diag[row] + 1;
3235:           switch (nodesz) {
3236:           case 5:
3237:             v5 = a->a + diag[row - 4] + 5; /* fall through */
3238:           case 4:
3239:             v4 = a->a + diag[row - 3] + 4; /* fall through */
3240:           case 3:
3241:             v3 = a->a + diag[row - 2] + 3; /* fall through */
3242:           case 2:
3243:             v2 = a->a + diag[row - 1] + 2; /* fall through */
3244:           case 1:
3245:             v1 = a->a + diag[row] + 1;
3246:           }
3247:         }
3248:         /* set sum */
3249:         switch (nodesz) {
3250:         case 5:
3251:           sum5 = xb[row - 4]; /* fall through */
3252:         case 4:
3253:           sum4 = xb[row - 3]; /* fall through */
3254:         case 3:
3255:           sum3 = xb[row - 2]; /* fall through */
3256:         case 2:
3257:           sum2 = xb[row - 1]; /* fall through */
3258:         case 1:
3259:           /* note that sum1 is associated with the last row */
3260:           sum1 = xb[row];
3261:         }
3262:         /* do sums */
3263:         for (n = 0; n < sz - 1; n += 2) {
3264:           i1 = idx[0];
3265:           i2 = idx[1];
3266:           idx += 2;
3267:           tmp0 = x[i1];
3268:           tmp1 = x[i2];
3269:           switch (nodesz) {
3270:           case 5:
3271:             sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
3272:             v5 += 2; /* fall through */
3273:           case 4:
3274:             sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
3275:             v4 += 2; /* fall through */
3276:           case 3:
3277:             sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3278:             v3 += 2; /* fall through */
3279:           case 2:
3280:             sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3281:             v2 += 2; /* fall through */
3282:           case 1:
3283:             sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3284:             v1 += 2;
3285:           }
3286:         }
3287:         /* ragged edge */
3288:         if (n == sz - 1) {
3289:           tmp0 = x[*idx];
3290:           switch (nodesz) {
3291:           case 5:
3292:             sum5 -= *v5 * tmp0; /* fall through */
3293:           case 4:
3294:             sum4 -= *v4 * tmp0; /* fall through */
3295:           case 3:
3296:             sum3 -= *v3 * tmp0; /* fall through */
3297:           case 2:
3298:             sum2 -= *v2 * tmp0; /* fall through */
3299:           case 1:
3300:             sum1 -= *v1 * tmp0;
3301:           }
3302:         }
3303:         /* update */
3304:         if (xb == b) {
3305:           /* whole (old way) w/ diag */
3306:           switch (nodesz) {
3307:           case 5:
3308:             x[row--] += sum5 * ibdiag[4] + sum4 * ibdiag[9] + sum3 * ibdiag[14] + sum2 * ibdiag[19] + sum1 * ibdiag[24];
3309:             x[row--] += sum5 * ibdiag[3] + sum4 * ibdiag[8] + sum3 * ibdiag[13] + sum2 * ibdiag[18] + sum1 * ibdiag[23];
3310:             x[row--] += sum5 * ibdiag[2] + sum4 * ibdiag[7] + sum3 * ibdiag[12] + sum2 * ibdiag[17] + sum1 * ibdiag[22];
3311:             x[row--] += sum5 * ibdiag[1] + sum4 * ibdiag[6] + sum3 * ibdiag[11] + sum2 * ibdiag[16] + sum1 * ibdiag[21];
3312:             x[row--] += sum5 * ibdiag[0] + sum4 * ibdiag[5] + sum3 * ibdiag[10] + sum2 * ibdiag[15] + sum1 * ibdiag[20];
3313:             break;
3314:           case 4:
3315:             x[row--] += sum4 * ibdiag[3] + sum3 * ibdiag[7] + sum2 * ibdiag[11] + sum1 * ibdiag[15];
3316:             x[row--] += sum4 * ibdiag[2] + sum3 * ibdiag[6] + sum2 * ibdiag[10] + sum1 * ibdiag[14];
3317:             x[row--] += sum4 * ibdiag[1] + sum3 * ibdiag[5] + sum2 * ibdiag[9] + sum1 * ibdiag[13];
3318:             x[row--] += sum4 * ibdiag[0] + sum3 * ibdiag[4] + sum2 * ibdiag[8] + sum1 * ibdiag[12];
3319:             break;
3320:           case 3:
3321:             x[row--] += sum3 * ibdiag[2] + sum2 * ibdiag[5] + sum1 * ibdiag[8];
3322:             x[row--] += sum3 * ibdiag[1] + sum2 * ibdiag[4] + sum1 * ibdiag[7];
3323:             x[row--] += sum3 * ibdiag[0] + sum2 * ibdiag[3] + sum1 * ibdiag[6];
3324:             break;
3325:           case 2:
3326:             x[row--] += sum2 * ibdiag[1] + sum1 * ibdiag[3];
3327:             x[row--] += sum2 * ibdiag[0] + sum1 * ibdiag[2];
3328:             break;
3329:           case 1:
3330:             x[row--] += sum1 * (*ibdiag);
3331:             break;
3332:           }
3333:         } else {
3334:           /* no diag so set =  */
3335:           switch (nodesz) {
3336:           case 5:
3337:             x[row--] = sum5 * ibdiag[4] + sum4 * ibdiag[9] + sum3 * ibdiag[14] + sum2 * ibdiag[19] + sum1 * ibdiag[24];
3338:             x[row--] = sum5 * ibdiag[3] + sum4 * ibdiag[8] + sum3 * ibdiag[13] + sum2 * ibdiag[18] + sum1 * ibdiag[23];
3339:             x[row--] = sum5 * ibdiag[2] + sum4 * ibdiag[7] + sum3 * ibdiag[12] + sum2 * ibdiag[17] + sum1 * ibdiag[22];
3340:             x[row--] = sum5 * ibdiag[1] + sum4 * ibdiag[6] + sum3 * ibdiag[11] + sum2 * ibdiag[16] + sum1 * ibdiag[21];
3341:             x[row--] = sum5 * ibdiag[0] + sum4 * ibdiag[5] + sum3 * ibdiag[10] + sum2 * ibdiag[15] + sum1 * ibdiag[20];
3342:             break;
3343:           case 4:
3344:             x[row--] = sum4 * ibdiag[3] + sum3 * ibdiag[7] + sum2 * ibdiag[11] + sum1 * ibdiag[15];
3345:             x[row--] = sum4 * ibdiag[2] + sum3 * ibdiag[6] + sum2 * ibdiag[10] + sum1 * ibdiag[14];
3346:             x[row--] = sum4 * ibdiag[1] + sum3 * ibdiag[5] + sum2 * ibdiag[9] + sum1 * ibdiag[13];
3347:             x[row--] = sum4 * ibdiag[0] + sum3 * ibdiag[4] + sum2 * ibdiag[8] + sum1 * ibdiag[12];
3348:             break;
3349:           case 3:
3350:             x[row--] = sum3 * ibdiag[2] + sum2 * ibdiag[5] + sum1 * ibdiag[8];
3351:             x[row--] = sum3 * ibdiag[1] + sum2 * ibdiag[4] + sum1 * ibdiag[7];
3352:             x[row--] = sum3 * ibdiag[0] + sum2 * ibdiag[3] + sum1 * ibdiag[6];
3353:             break;
3354:           case 2:
3355:             x[row--] = sum2 * ibdiag[1] + sum1 * ibdiag[3];
3356:             x[row--] = sum2 * ibdiag[0] + sum1 * ibdiag[2];
3357:             break;
3358:           case 1:
3359:             x[row--] = sum1 * (*ibdiag);
3360:             break;
3361:           }
3362:         }
3363:       }
3364:       if (xb == b) {
3365:         PetscCall(PetscLogFlops(2.0 * a->nz));
3366:       } else {
3367:         PetscCall(PetscLogFlops(a->nz)); /* assumes 1/2 in upper, undercounts diag inverse */
3368:       }
3369:     }
3370:   }
3371:   if (flag & SOR_EISENSTAT) {
3372:     /*
3373:           Apply  (U + D)^-1  where D is now the block diagonal
3374:     */
3375:     ibdiag = a->inode.ibdiag + a->inode.bdiagsize;
3376:     for (i = m - 1, row = A->rmap->n - 1; i >= 0; i--) {
3377:       nodesz = sizes[i + 1] - sizes[i];
3378:       ibdiag -= nodesz * nodesz;
3379:       sz  = ii[row + 1] - diag[row] - 1;
3380:       v1  = a->a + diag[row] + 1;
3381:       idx = a->j + diag[row] + 1;
3382:       /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
3383:       switch (nodesz) {
3384:       case 1:

3386:         sum1 = b[row];
3387:         for (n = 0; n < sz - 1; n += 2) {
3388:           i1 = idx[0];
3389:           i2 = idx[1];
3390:           idx += 2;
3391:           tmp0 = x[i1];
3392:           tmp1 = x[i2];
3393:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3394:           v1 += 2;
3395:         }

3397:         if (n == sz - 1) {
3398:           tmp0 = x[*idx];
3399:           sum1 -= *v1 * tmp0;
3400:         }
3401:         x[row] = sum1 * (*ibdiag);
3402:         row--;
3403:         break;

3405:       case 2:

3407:         sum1 = b[row];
3408:         sum2 = b[row - 1];
3409:         /* note that sum1 is associated with the second of the two rows */
3410:         v2 = a->a + diag[row - 1] + 2;
3411:         for (n = 0; n < sz - 1; n += 2) {
3412:           i1 = idx[0];
3413:           i2 = idx[1];
3414:           idx += 2;
3415:           tmp0 = x[i1];
3416:           tmp1 = x[i2];
3417:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3418:           v1 += 2;
3419:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3420:           v2 += 2;
3421:         }

3423:         if (n == sz - 1) {
3424:           tmp0 = x[*idx];
3425:           sum1 -= *v1 * tmp0;
3426:           sum2 -= *v2 * tmp0;
3427:         }
3428:         x[row]     = sum2 * ibdiag[1] + sum1 * ibdiag[3];
3429:         x[row - 1] = sum2 * ibdiag[0] + sum1 * ibdiag[2];
3430:         row -= 2;
3431:         break;
3432:       case 3:

3434:         sum1 = b[row];
3435:         sum2 = b[row - 1];
3436:         sum3 = b[row - 2];
3437:         v2   = a->a + diag[row - 1] + 2;
3438:         v3   = a->a + diag[row - 2] + 3;
3439:         for (n = 0; n < sz - 1; n += 2) {
3440:           i1 = idx[0];
3441:           i2 = idx[1];
3442:           idx += 2;
3443:           tmp0 = x[i1];
3444:           tmp1 = x[i2];
3445:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3446:           v1 += 2;
3447:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3448:           v2 += 2;
3449:           sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3450:           v3 += 2;
3451:         }

3453:         if (n == sz - 1) {
3454:           tmp0 = x[*idx];
3455:           sum1 -= *v1 * tmp0;
3456:           sum2 -= *v2 * tmp0;
3457:           sum3 -= *v3 * tmp0;
3458:         }
3459:         x[row]     = sum3 * ibdiag[2] + sum2 * ibdiag[5] + sum1 * ibdiag[8];
3460:         x[row - 1] = sum3 * ibdiag[1] + sum2 * ibdiag[4] + sum1 * ibdiag[7];
3461:         x[row - 2] = sum3 * ibdiag[0] + sum2 * ibdiag[3] + sum1 * ibdiag[6];
3462:         row -= 3;
3463:         break;
3464:       case 4:

3466:         sum1 = b[row];
3467:         sum2 = b[row - 1];
3468:         sum3 = b[row - 2];
3469:         sum4 = b[row - 3];
3470:         v2   = a->a + diag[row - 1] + 2;
3471:         v3   = a->a + diag[row - 2] + 3;
3472:         v4   = a->a + diag[row - 3] + 4;
3473:         for (n = 0; n < sz - 1; n += 2) {
3474:           i1 = idx[0];
3475:           i2 = idx[1];
3476:           idx += 2;
3477:           tmp0 = x[i1];
3478:           tmp1 = x[i2];
3479:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3480:           v1 += 2;
3481:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3482:           v2 += 2;
3483:           sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3484:           v3 += 2;
3485:           sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
3486:           v4 += 2;
3487:         }

3489:         if (n == sz - 1) {
3490:           tmp0 = x[*idx];
3491:           sum1 -= *v1 * tmp0;
3492:           sum2 -= *v2 * tmp0;
3493:           sum3 -= *v3 * tmp0;
3494:           sum4 -= *v4 * tmp0;
3495:         }
3496:         x[row]     = sum4 * ibdiag[3] + sum3 * ibdiag[7] + sum2 * ibdiag[11] + sum1 * ibdiag[15];
3497:         x[row - 1] = sum4 * ibdiag[2] + sum3 * ibdiag[6] + sum2 * ibdiag[10] + sum1 * ibdiag[14];
3498:         x[row - 2] = sum4 * ibdiag[1] + sum3 * ibdiag[5] + sum2 * ibdiag[9] + sum1 * ibdiag[13];
3499:         x[row - 3] = sum4 * ibdiag[0] + sum3 * ibdiag[4] + sum2 * ibdiag[8] + sum1 * ibdiag[12];
3500:         row -= 4;
3501:         break;
3502:       case 5:

3504:         sum1 = b[row];
3505:         sum2 = b[row - 1];
3506:         sum3 = b[row - 2];
3507:         sum4 = b[row - 3];
3508:         sum5 = b[row - 4];
3509:         v2   = a->a + diag[row - 1] + 2;
3510:         v3   = a->a + diag[row - 2] + 3;
3511:         v4   = a->a + diag[row - 3] + 4;
3512:         v5   = a->a + diag[row - 4] + 5;
3513:         for (n = 0; n < sz - 1; n += 2) {
3514:           i1 = idx[0];
3515:           i2 = idx[1];
3516:           idx += 2;
3517:           tmp0 = x[i1];
3518:           tmp1 = x[i2];
3519:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3520:           v1 += 2;
3521:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3522:           v2 += 2;
3523:           sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3524:           v3 += 2;
3525:           sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
3526:           v4 += 2;
3527:           sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
3528:           v5 += 2;
3529:         }

3531:         if (n == sz - 1) {
3532:           tmp0 = x[*idx];
3533:           sum1 -= *v1 * tmp0;
3534:           sum2 -= *v2 * tmp0;
3535:           sum3 -= *v3 * tmp0;
3536:           sum4 -= *v4 * tmp0;
3537:           sum5 -= *v5 * tmp0;
3538:         }
3539:         x[row]     = sum5 * ibdiag[4] + sum4 * ibdiag[9] + sum3 * ibdiag[14] + sum2 * ibdiag[19] + sum1 * ibdiag[24];
3540:         x[row - 1] = sum5 * ibdiag[3] + sum4 * ibdiag[8] + sum3 * ibdiag[13] + sum2 * ibdiag[18] + sum1 * ibdiag[23];
3541:         x[row - 2] = sum5 * ibdiag[2] + sum4 * ibdiag[7] + sum3 * ibdiag[12] + sum2 * ibdiag[17] + sum1 * ibdiag[22];
3542:         x[row - 3] = sum5 * ibdiag[1] + sum4 * ibdiag[6] + sum3 * ibdiag[11] + sum2 * ibdiag[16] + sum1 * ibdiag[21];
3543:         x[row - 4] = sum5 * ibdiag[0] + sum4 * ibdiag[5] + sum3 * ibdiag[10] + sum2 * ibdiag[15] + sum1 * ibdiag[20];
3544:         row -= 5;
3545:         break;
3546:       default:
3547:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not supported, node row %" PetscInt_FMT " size %" PetscInt_FMT, row, nodesz);
3548:       }
3549:     }
3550:     PetscCall(PetscLogFlops(a->nz));

3552:     /*
3553:            t = b - D x    where D is the block diagonal
3554:     */
3555:     cnt = 0;
3556:     for (i = 0, row = 0; i < m; i++) {
3557:       nodesz = sizes[i + 1] - sizes[i];
3558:       switch (nodesz) {
3559:       case 1:
3560:         t[row] = b[row] - bdiag[cnt++] * x[row];
3561:         row++;
3562:         break;
3563:       case 2:
3564:         x1         = x[row];
3565:         x2         = x[row + 1];
3566:         tmp1       = x1 * bdiag[cnt] + x2 * bdiag[cnt + 2];
3567:         tmp2       = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 3];
3568:         t[row]     = b[row] - tmp1;
3569:         t[row + 1] = b[row + 1] - tmp2;
3570:         row += 2;
3571:         cnt += 4;
3572:         break;
3573:       case 3:
3574:         x1         = x[row];
3575:         x2         = x[row + 1];
3576:         x3         = x[row + 2];
3577:         tmp1       = x1 * bdiag[cnt] + x2 * bdiag[cnt + 3] + x3 * bdiag[cnt + 6];
3578:         tmp2       = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 4] + x3 * bdiag[cnt + 7];
3579:         tmp3       = x1 * bdiag[cnt + 2] + x2 * bdiag[cnt + 5] + x3 * bdiag[cnt + 8];
3580:         t[row]     = b[row] - tmp1;
3581:         t[row + 1] = b[row + 1] - tmp2;
3582:         t[row + 2] = b[row + 2] - tmp3;
3583:         row += 3;
3584:         cnt += 9;
3585:         break;
3586:       case 4:
3587:         x1         = x[row];
3588:         x2         = x[row + 1];
3589:         x3         = x[row + 2];
3590:         x4         = x[row + 3];
3591:         tmp1       = x1 * bdiag[cnt] + x2 * bdiag[cnt + 4] + x3 * bdiag[cnt + 8] + x4 * bdiag[cnt + 12];
3592:         tmp2       = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 5] + x3 * bdiag[cnt + 9] + x4 * bdiag[cnt + 13];
3593:         tmp3       = x1 * bdiag[cnt + 2] + x2 * bdiag[cnt + 6] + x3 * bdiag[cnt + 10] + x4 * bdiag[cnt + 14];
3594:         tmp4       = x1 * bdiag[cnt + 3] + x2 * bdiag[cnt + 7] + x3 * bdiag[cnt + 11] + x4 * bdiag[cnt + 15];
3595:         t[row]     = b[row] - tmp1;
3596:         t[row + 1] = b[row + 1] - tmp2;
3597:         t[row + 2] = b[row + 2] - tmp3;
3598:         t[row + 3] = b[row + 3] - tmp4;
3599:         row += 4;
3600:         cnt += 16;
3601:         break;
3602:       case 5:
3603:         x1         = x[row];
3604:         x2         = x[row + 1];
3605:         x3         = x[row + 2];
3606:         x4         = x[row + 3];
3607:         x5         = x[row + 4];
3608:         tmp1       = x1 * bdiag[cnt] + x2 * bdiag[cnt + 5] + x3 * bdiag[cnt + 10] + x4 * bdiag[cnt + 15] + x5 * bdiag[cnt + 20];
3609:         tmp2       = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 6] + x3 * bdiag[cnt + 11] + x4 * bdiag[cnt + 16] + x5 * bdiag[cnt + 21];
3610:         tmp3       = x1 * bdiag[cnt + 2] + x2 * bdiag[cnt + 7] + x3 * bdiag[cnt + 12] + x4 * bdiag[cnt + 17] + x5 * bdiag[cnt + 22];
3611:         tmp4       = x1 * bdiag[cnt + 3] + x2 * bdiag[cnt + 8] + x3 * bdiag[cnt + 13] + x4 * bdiag[cnt + 18] + x5 * bdiag[cnt + 23];
3612:         tmp5       = x1 * bdiag[cnt + 4] + x2 * bdiag[cnt + 9] + x3 * bdiag[cnt + 14] + x4 * bdiag[cnt + 19] + x5 * bdiag[cnt + 24];
3613:         t[row]     = b[row] - tmp1;
3614:         t[row + 1] = b[row + 1] - tmp2;
3615:         t[row + 2] = b[row + 2] - tmp3;
3616:         t[row + 3] = b[row + 3] - tmp4;
3617:         t[row + 4] = b[row + 4] - tmp5;
3618:         row += 5;
3619:         cnt += 25;
3620:         break;
3621:       default:
3622:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not supported, node row %" PetscInt_FMT " size %" PetscInt_FMT, row, nodesz);
3623:       }
3624:     }
3625:     PetscCall(PetscLogFlops(m));

3627:     /*
3628:           Apply (L + D)^-1 where D is the block diagonal
3629:     */
3630:     for (i = 0, row = 0; i < m; i++) {
3631:       nodesz = sizes[i + 1] - sizes[i];
3632:       sz     = diag[row] - ii[row];
3633:       v1     = a->a + ii[row];
3634:       idx    = a->j + ii[row];
3635:       /* see comments for MatMult_SeqAIJ_Inode() for how this is coded */
3636:       switch (nodesz) {
3637:       case 1:

3639:         sum1 = t[row];
3640:         for (n = 0; n < sz - 1; n += 2) {
3641:           i1 = idx[0];
3642:           i2 = idx[1];
3643:           idx += 2;
3644:           tmp0 = t[i1];
3645:           tmp1 = t[i2];
3646:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3647:           v1 += 2;
3648:         }

3650:         if (n == sz - 1) {
3651:           tmp0 = t[*idx];
3652:           sum1 -= *v1 * tmp0;
3653:         }
3654:         x[row] += t[row] = sum1 * (*ibdiag++);
3655:         row++;
3656:         break;
3657:       case 2:
3658:         v2   = a->a + ii[row + 1];
3659:         sum1 = t[row];
3660:         sum2 = t[row + 1];
3661:         for (n = 0; n < sz - 1; n += 2) {
3662:           i1 = idx[0];
3663:           i2 = idx[1];
3664:           idx += 2;
3665:           tmp0 = t[i1];
3666:           tmp1 = t[i2];
3667:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3668:           v1 += 2;
3669:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3670:           v2 += 2;
3671:         }

3673:         if (n == sz - 1) {
3674:           tmp0 = t[*idx];
3675:           sum1 -= v1[0] * tmp0;
3676:           sum2 -= v2[0] * tmp0;
3677:         }
3678:         x[row] += t[row]         = sum1 * ibdiag[0] + sum2 * ibdiag[2];
3679:         x[row + 1] += t[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[3];
3680:         ibdiag += 4;
3681:         row += 2;
3682:         break;
3683:       case 3:
3684:         v2   = a->a + ii[row + 1];
3685:         v3   = a->a + ii[row + 2];
3686:         sum1 = t[row];
3687:         sum2 = t[row + 1];
3688:         sum3 = t[row + 2];
3689:         for (n = 0; n < sz - 1; n += 2) {
3690:           i1 = idx[0];
3691:           i2 = idx[1];
3692:           idx += 2;
3693:           tmp0 = t[i1];
3694:           tmp1 = t[i2];
3695:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3696:           v1 += 2;
3697:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3698:           v2 += 2;
3699:           sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3700:           v3 += 2;
3701:         }

3703:         if (n == sz - 1) {
3704:           tmp0 = t[*idx];
3705:           sum1 -= v1[0] * tmp0;
3706:           sum2 -= v2[0] * tmp0;
3707:           sum3 -= v3[0] * tmp0;
3708:         }
3709:         x[row] += t[row]         = sum1 * ibdiag[0] + sum2 * ibdiag[3] + sum3 * ibdiag[6];
3710:         x[row + 1] += t[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[4] + sum3 * ibdiag[7];
3711:         x[row + 2] += t[row + 2] = sum1 * ibdiag[2] + sum2 * ibdiag[5] + sum3 * ibdiag[8];
3712:         ibdiag += 9;
3713:         row += 3;
3714:         break;
3715:       case 4:
3716:         v2   = a->a + ii[row + 1];
3717:         v3   = a->a + ii[row + 2];
3718:         v4   = a->a + ii[row + 3];
3719:         sum1 = t[row];
3720:         sum2 = t[row + 1];
3721:         sum3 = t[row + 2];
3722:         sum4 = t[row + 3];
3723:         for (n = 0; n < sz - 1; n += 2) {
3724:           i1 = idx[0];
3725:           i2 = idx[1];
3726:           idx += 2;
3727:           tmp0 = t[i1];
3728:           tmp1 = t[i2];
3729:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3730:           v1 += 2;
3731:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3732:           v2 += 2;
3733:           sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3734:           v3 += 2;
3735:           sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
3736:           v4 += 2;
3737:         }

3739:         if (n == sz - 1) {
3740:           tmp0 = t[*idx];
3741:           sum1 -= v1[0] * tmp0;
3742:           sum2 -= v2[0] * tmp0;
3743:           sum3 -= v3[0] * tmp0;
3744:           sum4 -= v4[0] * tmp0;
3745:         }
3746:         x[row] += t[row]         = sum1 * ibdiag[0] + sum2 * ibdiag[4] + sum3 * ibdiag[8] + sum4 * ibdiag[12];
3747:         x[row + 1] += t[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[5] + sum3 * ibdiag[9] + sum4 * ibdiag[13];
3748:         x[row + 2] += t[row + 2] = sum1 * ibdiag[2] + sum2 * ibdiag[6] + sum3 * ibdiag[10] + sum4 * ibdiag[14];
3749:         x[row + 3] += t[row + 3] = sum1 * ibdiag[3] + sum2 * ibdiag[7] + sum3 * ibdiag[11] + sum4 * ibdiag[15];
3750:         ibdiag += 16;
3751:         row += 4;
3752:         break;
3753:       case 5:
3754:         v2   = a->a + ii[row + 1];
3755:         v3   = a->a + ii[row + 2];
3756:         v4   = a->a + ii[row + 3];
3757:         v5   = a->a + ii[row + 4];
3758:         sum1 = t[row];
3759:         sum2 = t[row + 1];
3760:         sum3 = t[row + 2];
3761:         sum4 = t[row + 3];
3762:         sum5 = t[row + 4];
3763:         for (n = 0; n < sz - 1; n += 2) {
3764:           i1 = idx[0];
3765:           i2 = idx[1];
3766:           idx += 2;
3767:           tmp0 = t[i1];
3768:           tmp1 = t[i2];
3769:           sum1 -= v1[0] * tmp0 + v1[1] * tmp1;
3770:           v1 += 2;
3771:           sum2 -= v2[0] * tmp0 + v2[1] * tmp1;
3772:           v2 += 2;
3773:           sum3 -= v3[0] * tmp0 + v3[1] * tmp1;
3774:           v3 += 2;
3775:           sum4 -= v4[0] * tmp0 + v4[1] * tmp1;
3776:           v4 += 2;
3777:           sum5 -= v5[0] * tmp0 + v5[1] * tmp1;
3778:           v5 += 2;
3779:         }

3781:         if (n == sz - 1) {
3782:           tmp0 = t[*idx];
3783:           sum1 -= v1[0] * tmp0;
3784:           sum2 -= v2[0] * tmp0;
3785:           sum3 -= v3[0] * tmp0;
3786:           sum4 -= v4[0] * tmp0;
3787:           sum5 -= v5[0] * tmp0;
3788:         }
3789:         x[row] += t[row]         = sum1 * ibdiag[0] + sum2 * ibdiag[5] + sum3 * ibdiag[10] + sum4 * ibdiag[15] + sum5 * ibdiag[20];
3790:         x[row + 1] += t[row + 1] = sum1 * ibdiag[1] + sum2 * ibdiag[6] + sum3 * ibdiag[11] + sum4 * ibdiag[16] + sum5 * ibdiag[21];
3791:         x[row + 2] += t[row + 2] = sum1 * ibdiag[2] + sum2 * ibdiag[7] + sum3 * ibdiag[12] + sum4 * ibdiag[17] + sum5 * ibdiag[22];
3792:         x[row + 3] += t[row + 3] = sum1 * ibdiag[3] + sum2 * ibdiag[8] + sum3 * ibdiag[13] + sum4 * ibdiag[18] + sum5 * ibdiag[23];
3793:         x[row + 4] += t[row + 4] = sum1 * ibdiag[4] + sum2 * ibdiag[9] + sum3 * ibdiag[14] + sum4 * ibdiag[19] + sum5 * ibdiag[24];
3794:         ibdiag += 25;
3795:         row += 5;
3796:         break;
3797:       default:
3798:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not supported, node row %" PetscInt_FMT " size %" PetscInt_FMT, row, nodesz);
3799:       }
3800:     }
3801:     PetscCall(PetscLogFlops(a->nz));
3802:   }
3803:   PetscCall(VecRestoreArray(xx, &x));
3804:   PetscCall(VecRestoreArrayRead(bb, &b));
3805:   PetscFunctionReturn(PETSC_SUCCESS);
3806: }

3808: static PetscErrorCode MatMultDiagonalBlock_SeqAIJ_Inode(Mat A, Vec bb, Vec xx)
3809: {
3810:   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
3811:   PetscScalar       *x, tmp1, tmp2, tmp3, tmp4, tmp5, x1, x2, x3, x4, x5;
3812:   const MatScalar   *bdiag = a->inode.bdiag;
3813:   const PetscScalar *b;
3814:   PetscInt           m = a->inode.node_count, cnt = 0, i, row, nodesz;
3815:   const PetscInt    *sizes = a->inode.size_csr;

3817:   PetscFunctionBegin;
3818:   PetscCheck(a->inode.size_csr, PETSC_COMM_SELF, PETSC_ERR_COR, "Missing Inode Structure");
3819:   PetscCall(VecGetArray(xx, &x));
3820:   PetscCall(VecGetArrayRead(bb, &b));
3821:   cnt = 0;
3822:   for (i = 0, row = 0; i < m; i++) {
3823:     nodesz = sizes[i + 1] - sizes[i];
3824:     switch (nodesz) {
3825:     case 1:
3826:       x[row] = b[row] * bdiag[cnt++];
3827:       row++;
3828:       break;
3829:     case 2:
3830:       x1       = b[row];
3831:       x2       = b[row + 1];
3832:       tmp1     = x1 * bdiag[cnt] + x2 * bdiag[cnt + 2];
3833:       tmp2     = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 3];
3834:       x[row++] = tmp1;
3835:       x[row++] = tmp2;
3836:       cnt += 4;
3837:       break;
3838:     case 3:
3839:       x1       = b[row];
3840:       x2       = b[row + 1];
3841:       x3       = b[row + 2];
3842:       tmp1     = x1 * bdiag[cnt] + x2 * bdiag[cnt + 3] + x3 * bdiag[cnt + 6];
3843:       tmp2     = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 4] + x3 * bdiag[cnt + 7];
3844:       tmp3     = x1 * bdiag[cnt + 2] + x2 * bdiag[cnt + 5] + x3 * bdiag[cnt + 8];
3845:       x[row++] = tmp1;
3846:       x[row++] = tmp2;
3847:       x[row++] = tmp3;
3848:       cnt += 9;
3849:       break;
3850:     case 4:
3851:       x1       = b[row];
3852:       x2       = b[row + 1];
3853:       x3       = b[row + 2];
3854:       x4       = b[row + 3];
3855:       tmp1     = x1 * bdiag[cnt] + x2 * bdiag[cnt + 4] + x3 * bdiag[cnt + 8] + x4 * bdiag[cnt + 12];
3856:       tmp2     = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 5] + x3 * bdiag[cnt + 9] + x4 * bdiag[cnt + 13];
3857:       tmp3     = x1 * bdiag[cnt + 2] + x2 * bdiag[cnt + 6] + x3 * bdiag[cnt + 10] + x4 * bdiag[cnt + 14];
3858:       tmp4     = x1 * bdiag[cnt + 3] + x2 * bdiag[cnt + 7] + x3 * bdiag[cnt + 11] + x4 * bdiag[cnt + 15];
3859:       x[row++] = tmp1;
3860:       x[row++] = tmp2;
3861:       x[row++] = tmp3;
3862:       x[row++] = tmp4;
3863:       cnt += 16;
3864:       break;
3865:     case 5:
3866:       x1       = b[row];
3867:       x2       = b[row + 1];
3868:       x3       = b[row + 2];
3869:       x4       = b[row + 3];
3870:       x5       = b[row + 4];
3871:       tmp1     = x1 * bdiag[cnt] + x2 * bdiag[cnt + 5] + x3 * bdiag[cnt + 10] + x4 * bdiag[cnt + 15] + x5 * bdiag[cnt + 20];
3872:       tmp2     = x1 * bdiag[cnt + 1] + x2 * bdiag[cnt + 6] + x3 * bdiag[cnt + 11] + x4 * bdiag[cnt + 16] + x5 * bdiag[cnt + 21];
3873:       tmp3     = x1 * bdiag[cnt + 2] + x2 * bdiag[cnt + 7] + x3 * bdiag[cnt + 12] + x4 * bdiag[cnt + 17] + x5 * bdiag[cnt + 22];
3874:       tmp4     = x1 * bdiag[cnt + 3] + x2 * bdiag[cnt + 8] + x3 * bdiag[cnt + 13] + x4 * bdiag[cnt + 18] + x5 * bdiag[cnt + 23];
3875:       tmp5     = x1 * bdiag[cnt + 4] + x2 * bdiag[cnt + 9] + x3 * bdiag[cnt + 14] + x4 * bdiag[cnt + 19] + x5 * bdiag[cnt + 24];
3876:       x[row++] = tmp1;
3877:       x[row++] = tmp2;
3878:       x[row++] = tmp3;
3879:       x[row++] = tmp4;
3880:       x[row++] = tmp5;
3881:       cnt += 25;
3882:       break;
3883:     default:
3884:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_COR, "Node size not supported, node row %" PetscInt_FMT " size %" PetscInt_FMT, row, nodesz);
3885:     }
3886:   }
3887:   PetscCall(PetscLogFlops(2.0 * cnt));
3888:   PetscCall(VecRestoreArray(xx, &x));
3889:   PetscCall(VecRestoreArrayRead(bb, &b));
3890:   PetscFunctionReturn(PETSC_SUCCESS);
3891: }

3893: static PetscErrorCode MatSeqAIJ_Inode_ResetOps(Mat A)
3894: {
3895:   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;

3897:   PetscFunctionBegin;
3898:   a->inode.node_count       = 0;
3899:   a->inode.use              = PETSC_FALSE;
3900:   a->inode.checked          = PETSC_FALSE;
3901:   a->inode.mat_nonzerostate = -1;
3902:   A->ops->getrowij          = MatGetRowIJ_SeqAIJ;
3903:   A->ops->restorerowij      = MatRestoreRowIJ_SeqAIJ;
3904:   A->ops->getcolumnij       = MatGetColumnIJ_SeqAIJ;
3905:   A->ops->restorecolumnij   = MatRestoreColumnIJ_SeqAIJ;
3906:   A->ops->coloringpatch     = NULL;
3907:   A->ops->multdiagonalblock = NULL;
3908:   if (A->factortype) A->ops->solve = MatSolve_SeqAIJ_inplace;
3909:   PetscFunctionReturn(PETSC_SUCCESS);
3910: }

3912: /*
3913:     samestructure indicates that the matrix has not changed its nonzero structure so we
3914:     do not need to recompute the inodes
3915: */
3916: PetscErrorCode MatSeqAIJCheckInode(Mat A)
3917: {
3918:   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
3919:   PetscInt        i, j, m, nzx, nzy, *ns, node_count, blk_size;
3920:   PetscBool       flag;
3921:   const PetscInt *idx, *idy, *ii;

3923:   PetscFunctionBegin;
3924:   if (!a->inode.use) {
3925:     PetscCall(MatSeqAIJ_Inode_ResetOps(A));
3926:     PetscCall(PetscFree(a->inode.size_csr));
3927:     PetscFunctionReturn(PETSC_SUCCESS);
3928:   }
3929:   if (a->inode.checked && A->nonzerostate == a->inode.mat_nonzerostate) PetscFunctionReturn(PETSC_SUCCESS);

3931:   m = A->rmap->n;
3932:   if (!a->inode.size_csr) PetscCall(PetscMalloc1(m + 1, &a->inode.size_csr));
3933:   ns    = a->inode.size_csr;
3934:   ns[0] = 0;

3936:   i          = 0;
3937:   node_count = 0;
3938:   idx        = a->j;
3939:   ii         = a->i;
3940:   if (idx) {
3941:     while (i < m) {            /* For each row */
3942:       nzx = ii[i + 1] - ii[i]; /* Number of nonzeros */
3943:       /* Limits the number of elements in a node to 'a->inode.limit' */
3944:       for (j = i + 1, idy = idx, blk_size = 1; j < m && blk_size < a->inode.limit; ++j, ++blk_size) {
3945:         nzy = ii[j + 1] - ii[j]; /* Same number of nonzeros */
3946:         if (nzy != nzx) break;
3947:         idy += nzx; /* Same nonzero pattern */
3948:         PetscCall(PetscArraycmp(idx, idy, nzx, &flag));
3949:         if (!flag) break;
3950:       }
3951:       ns[node_count + 1] = ns[node_count] + blk_size;
3952:       node_count++;
3953:       idx += blk_size * nzx;
3954:       i = j;
3955:     }
3956:   }
3957:   /* If not enough inodes found,, do not use inode version of the routines */
3958:   if (!m || !idx || node_count > .8 * m) {
3959:     PetscCall(MatSeqAIJ_Inode_ResetOps(A));
3960:     PetscCall(PetscFree(a->inode.size_csr));
3961:     PetscCall(PetscInfo(A, "Found %" PetscInt_FMT " nodes out of %" PetscInt_FMT " rows. Not using Inode routines\n", node_count, m));
3962:   } else {
3963:     if (!A->factortype) {
3964:       A->ops->multdiagonalblock = MatMultDiagonalBlock_SeqAIJ_Inode;
3965:       if (A->rmap->n == A->cmap->n) {
3966:         A->ops->getrowij        = MatGetRowIJ_SeqAIJ_Inode;
3967:         A->ops->restorerowij    = MatRestoreRowIJ_SeqAIJ_Inode;
3968:         A->ops->getcolumnij     = MatGetColumnIJ_SeqAIJ_Inode;
3969:         A->ops->restorecolumnij = MatRestoreColumnIJ_SeqAIJ_Inode;
3970:         A->ops->coloringpatch   = MatColoringPatch_SeqAIJ_Inode;
3971:       }
3972:     } else {
3973:       A->ops->solve = MatSolve_SeqAIJ_Inode_inplace;
3974:     }
3975:     a->inode.node_count = node_count;
3976:     PetscCall(PetscInfo(A, "Found %" PetscInt_FMT " nodes of %" PetscInt_FMT ". Limit used: %" PetscInt_FMT ". Using Inode routines\n", node_count, m, a->inode.limit));
3977:   }
3978:   a->inode.checked          = PETSC_TRUE;
3979:   a->inode.mat_nonzerostate = A->nonzerostate;
3980:   PetscFunctionReturn(PETSC_SUCCESS);
3981: }

3983: PetscErrorCode MatDuplicate_SeqAIJ_Inode(Mat A, MatDuplicateOption cpvalues, Mat *C)
3984: {
3985:   Mat         B = *C;
3986:   Mat_SeqAIJ *c = (Mat_SeqAIJ *)B->data, *a = (Mat_SeqAIJ *)A->data;
3987:   PetscInt    m = A->rmap->n;

3989:   PetscFunctionBegin;
3990:   c->inode.use              = a->inode.use;
3991:   c->inode.limit            = a->inode.limit;
3992:   c->inode.max_limit        = a->inode.max_limit;
3993:   c->inode.checked          = PETSC_FALSE;
3994:   c->inode.size_csr         = NULL;
3995:   c->inode.node_count       = 0;
3996:   c->inode.ibdiag           = NULL;
3997:   c->inode.bdiag            = NULL;
3998:   c->inode.mat_nonzerostate = -1;
3999:   if (a->inode.use) {
4000:     if (a->inode.checked && a->inode.size_csr) {
4001:       PetscCall(PetscMalloc1(m + 1, &c->inode.size_csr));
4002:       PetscCall(PetscArraycpy(c->inode.size_csr, a->inode.size_csr, m + 1));

4004:       c->inode.checked          = PETSC_TRUE;
4005:       c->inode.node_count       = a->inode.node_count;
4006:       c->inode.mat_nonzerostate = (*C)->nonzerostate;
4007:     }
4008:     /* note the table of functions below should match that in MatSeqAIJCheckInode() */
4009:     if (!B->factortype) {
4010:       B->ops->getrowij          = MatGetRowIJ_SeqAIJ_Inode;
4011:       B->ops->restorerowij      = MatRestoreRowIJ_SeqAIJ_Inode;
4012:       B->ops->getcolumnij       = MatGetColumnIJ_SeqAIJ_Inode;
4013:       B->ops->restorecolumnij   = MatRestoreColumnIJ_SeqAIJ_Inode;
4014:       B->ops->coloringpatch     = MatColoringPatch_SeqAIJ_Inode;
4015:       B->ops->multdiagonalblock = MatMultDiagonalBlock_SeqAIJ_Inode;
4016:     } else {
4017:       B->ops->solve = MatSolve_SeqAIJ_Inode_inplace;
4018:     }
4019:   }
4020:   PetscFunctionReturn(PETSC_SUCCESS);
4021: }

4023: static inline PetscErrorCode MatGetRow_FactoredLU(PetscInt *cols, PetscInt nzl, PetscInt nzu, PetscInt nz, const PetscInt *ai, const PetscInt *aj, const PetscInt *adiag, PetscInt row)
4024: {
4025:   PetscInt        k;
4026:   const PetscInt *vi;

4028:   PetscFunctionBegin;
4029:   vi = aj + ai[row];
4030:   for (k = 0; k < nzl; k++) cols[k] = vi[k];
4031:   vi        = aj + adiag[row];
4032:   cols[nzl] = vi[0];
4033:   vi        = aj + adiag[row + 1] + 1;
4034:   for (k = 0; k < nzu; k++) cols[nzl + 1 + k] = vi[k];
4035:   PetscFunctionReturn(PETSC_SUCCESS);
4036: }
4037: /*
4038:    MatSeqAIJCheckInode_FactorLU - Check Inode for factored seqaij matrix.
4039:    Modified from MatSeqAIJCheckInode().

4041:    Input Parameters:
4042: .  Mat A - ILU or LU matrix factor

4044: */
4045: PetscErrorCode MatSeqAIJCheckInode_FactorLU(Mat A)
4046: {
4047:   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
4048:   PetscInt        i, j, m, nzl1, nzu1, nzl2, nzu2, nzx, nzy, node_count, blk_size;
4049:   PetscInt       *cols1, *cols2, *ns;
4050:   const PetscInt *ai = a->i, *aj = a->j, *adiag = a->diag;
4051:   PetscBool       flag;

4053:   PetscFunctionBegin;
4054:   if (!a->inode.use) PetscFunctionReturn(PETSC_SUCCESS);
4055:   if (a->inode.checked) PetscFunctionReturn(PETSC_SUCCESS);

4057:   m = A->rmap->n;
4058:   if (a->inode.size_csr) ns = a->inode.size_csr;
4059:   else PetscCall(PetscMalloc1(m + 1, &ns));
4060:   ns[0] = 0;

4062:   i          = 0;
4063:   node_count = 0;
4064:   PetscCall(PetscMalloc2(m, &cols1, m, &cols2));
4065:   while (i < m) {                       /* For each row */
4066:     nzl1 = ai[i + 1] - ai[i];           /* Number of nonzeros in L */
4067:     nzu1 = adiag[i] - adiag[i + 1] - 1; /* Number of nonzeros in U excluding diagonal*/
4068:     nzx  = nzl1 + nzu1 + 1;
4069:     PetscCall(MatGetRow_FactoredLU(cols1, nzl1, nzu1, nzx, ai, aj, adiag, i));

4071:     /* Limits the number of elements in a node to 'a->inode.limit' */
4072:     for (j = i + 1, blk_size = 1; j < m && blk_size < a->inode.limit; ++j, ++blk_size) {
4073:       nzl2 = ai[j + 1] - ai[j];
4074:       nzu2 = adiag[j] - adiag[j + 1] - 1;
4075:       nzy  = nzl2 + nzu2 + 1;
4076:       if (nzy != nzx) break;
4077:       PetscCall(MatGetRow_FactoredLU(cols2, nzl2, nzu2, nzy, ai, aj, adiag, j));
4078:       PetscCall(PetscArraycmp(cols1, cols2, nzx, &flag));
4079:       if (!flag) break;
4080:     }
4081:     ns[node_count + 1] = ns[node_count] + blk_size;
4082:     node_count++;
4083:     i = j;
4084:   }
4085:   PetscCall(PetscFree2(cols1, cols2));
4086:   /* If not enough inodes found,, do not use inode version of the routines */
4087:   if (!m || node_count > .8 * m) {
4088:     PetscCall(PetscFree(ns));

4090:     a->inode.node_count = 0;
4091:     a->inode.size_csr   = NULL;
4092:     a->inode.use        = PETSC_FALSE;

4094:     PetscCall(PetscInfo(A, "Found %" PetscInt_FMT " nodes out of %" PetscInt_FMT " rows. Not using Inode routines\n", node_count, m));
4095:   } else {
4096:     A->ops->mult              = NULL;
4097:     A->ops->sor               = NULL;
4098:     A->ops->multadd           = NULL;
4099:     A->ops->getrowij          = NULL;
4100:     A->ops->restorerowij      = NULL;
4101:     A->ops->getcolumnij       = NULL;
4102:     A->ops->restorecolumnij   = NULL;
4103:     A->ops->coloringpatch     = NULL;
4104:     A->ops->multdiagonalblock = NULL;
4105:     a->inode.node_count       = node_count;
4106:     a->inode.size_csr         = ns;
4107:     PetscCall(PetscInfo(A, "Found %" PetscInt_FMT " nodes of %" PetscInt_FMT ". Limit used: %" PetscInt_FMT ". Using Inode routines\n", node_count, m, a->inode.limit));
4108:   }
4109:   a->inode.checked = PETSC_TRUE;
4110:   PetscFunctionReturn(PETSC_SUCCESS);
4111: }

4113: /*
4114:      This is really ugly. if inodes are used this replaces the
4115:   permutations with ones that correspond to rows/cols of the matrix
4116:   rather than inode blocks
4117: */
4118: PetscErrorCode MatInodeAdjustForInodes(Mat A, IS *rperm, IS *cperm)
4119: {
4120:   PetscFunctionBegin;
4121:   PetscTryMethod(A, "MatInodeAdjustForInodes_C", (Mat, IS *, IS *), (A, rperm, cperm));
4122:   PetscFunctionReturn(PETSC_SUCCESS);
4123: }

4125: PetscErrorCode MatInodeAdjustForInodes_SeqAIJ_Inode(Mat A, IS *rperm, IS *cperm)
4126: {
4127:   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
4128:   PetscInt        m = A->rmap->n, n = A->cmap->n, i, j, nslim_row = a->inode.node_count;
4129:   const PetscInt *ridx, *cidx;
4130:   PetscInt        row, col, *permr, *permc, *ns_row = a->inode.size_csr, *tns, start_val, end_val, indx;
4131:   PetscInt        nslim_col, *ns_col;
4132:   IS              ris = *rperm, cis = *cperm;

4134:   PetscFunctionBegin;
4135:   if (!a->inode.size_csr) PetscFunctionReturn(PETSC_SUCCESS);       /* no inodes so return */
4136:   if (a->inode.node_count == m) PetscFunctionReturn(PETSC_SUCCESS); /* all inodes are of size 1 */

4138:   PetscCall(MatCreateColInode_Private(A, &nslim_col, &ns_col));
4139:   PetscCall(PetscMalloc1(((nslim_row > nslim_col ? nslim_row : nslim_col) + 1), &tns));
4140:   PetscCall(PetscMalloc2(m, &permr, n, &permc));

4142:   PetscCall(ISGetIndices(ris, &ridx));
4143:   PetscCall(ISGetIndices(cis, &cidx));

4145:   /* Form the inode structure for the rows of permuted matrix using inv perm*/
4146:   for (i = 0, tns[0] = 0; i < nslim_row; ++i) tns[i + 1] = tns[i] + (ns_row[i + 1] - ns_row[i]);

4148:   /* Construct the permutations for rows*/
4149:   for (i = 0, row = 0; i < nslim_row; ++i) {
4150:     indx      = ridx[i];
4151:     start_val = tns[indx];
4152:     end_val   = tns[indx + 1];
4153:     for (j = start_val; j < end_val; ++j, ++row) permr[row] = j;
4154:   }

4156:   /* Form the inode structure for the columns of permuted matrix using inv perm*/
4157:   for (i = 0, tns[0] = 0; i < nslim_col; ++i) tns[i + 1] = tns[i] + (ns_col[i + 1] - ns_col[i]);

4159:   /* Construct permutations for columns */
4160:   for (i = 0, col = 0; i < nslim_col; ++i) {
4161:     indx      = cidx[i];
4162:     start_val = tns[indx];
4163:     end_val   = tns[indx + 1];
4164:     for (j = start_val; j < end_val; ++j, ++col) permc[col] = j;
4165:   }

4167:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n, permr, PETSC_COPY_VALUES, rperm));
4168:   PetscCall(ISSetPermutation(*rperm));
4169:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n, permc, PETSC_COPY_VALUES, cperm));
4170:   PetscCall(ISSetPermutation(*cperm));

4172:   PetscCall(ISRestoreIndices(ris, &ridx));
4173:   PetscCall(ISRestoreIndices(cis, &cidx));

4175:   PetscCall(PetscFree(ns_col));
4176:   PetscCall(PetscFree2(permr, permc));
4177:   PetscCall(ISDestroy(&cis));
4178:   PetscCall(ISDestroy(&ris));
4179:   PetscCall(PetscFree(tns));
4180:   PetscFunctionReturn(PETSC_SUCCESS);
4181: }

4183: /*@C
4184:   MatInodeGetInodeSizes - Returns the inode information of a matrix with inodes

4186:   Not Collective

4188:   Input Parameter:
4189: . A - the Inode matrix or matrix derived from the Inode class -- e.g., `MATSEQAIJ`

4191:   Output Parameters:
4192: + node_count - no of inodes present in the matrix.
4193: . sizes      - an array of size `node_count`, with the sizes of each inode.
4194: - limit      - the max size used to generate the inodes.

4196:   Level: advanced

4198:   Note:
4199:   It should be called after the matrix is assembled.
4200:   The contents of the sizes[] array should not be changed.
4201:   `NULL` may be passed for information not needed

4203: .seealso: [](ch_matrices), `Mat`, `MatGetInfo()`
4204: @*/
4205: PetscErrorCode MatInodeGetInodeSizes(Mat A, PetscInt *node_count, PetscInt *sizes[], PetscInt *limit)
4206: {
4207:   PetscErrorCode (*f)(Mat, PetscInt *, PetscInt **, PetscInt *);

4209:   PetscFunctionBegin;
4210:   PetscCheck(A->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
4211:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatInodeGetInodeSizes_C", &f));
4212:   if (f) PetscCall((*f)(A, node_count, sizes, limit));
4213:   PetscFunctionReturn(PETSC_SUCCESS);
4214: }

4216: PetscErrorCode MatInodeGetInodeSizes_SeqAIJ_Inode(Mat A, PetscInt *node_count, PetscInt *sizes[], PetscInt *limit)
4217: {
4218:   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;

4220:   PetscFunctionBegin;
4221:   if (node_count) *node_count = a->inode.node_count;
4222:   if (sizes) *sizes = a->inode.size_csr;
4223:   if (limit) *limit = a->inode.limit;
4224:   PetscFunctionReturn(PETSC_SUCCESS);
4225: }