Actual source code: baijfact2.c

  1: /*
  2:     Factorization code for BAIJ format.
  3: */

  5: #include <../src/mat/impls/baij/seq/baij.h>
  6: #include <petsc/private/kernels/blockinvert.h>
  7: #include <../src/mat/utils/freespace.h>

  9: PETSC_INTERN PetscErrorCode MatDuplicateNoCreate_SeqBAIJ(Mat, Mat, MatDuplicateOption, PetscBool);

 11: /*
 12:    This is not much faster than MatLUFactorNumeric_SeqBAIJ_N() but the solve is faster at least sometimes
 13: */
 14: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_15_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
 15: {
 16:   Mat              C = B;
 17:   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
 18:   PetscInt         i, j, k, ipvt[15];
 19:   const PetscInt   n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, *ajtmp, *bjtmp, *bdiag = b->diag, *pj;
 20:   PetscInt         nz, nzL, row;
 21:   MatScalar       *rtmp, *pc, *mwork, *pv, *vv, work[225];
 22:   const MatScalar *v, *aa = a->a;
 23:   PetscInt         bs2 = a->bs2, bs = A->rmap->bs, flg;
 24:   PetscInt         sol_ver;
 25:   PetscBool        allowzeropivot, zeropivotdetected;

 27:   PetscFunctionBegin;
 28:   allowzeropivot = PetscNot(A->erroriffailure);
 29:   PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)A)->prefix, "-sol_ver", &sol_ver, NULL));

 31:   /* generate work space needed by the factorization */
 32:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
 33:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

 35:   for (i = 0; i < n; i++) {
 36:     /* zero rtmp */
 37:     /* L part */
 38:     nz    = bi[i + 1] - bi[i];
 39:     bjtmp = bj + bi[i];
 40:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

 42:     /* U part */
 43:     nz    = bdiag[i] - bdiag[i + 1];
 44:     bjtmp = bj + bdiag[i + 1] + 1;
 45:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

 47:     /* load in initial (unfactored row) */
 48:     nz    = ai[i + 1] - ai[i];
 49:     ajtmp = aj + ai[i];
 50:     v     = aa + bs2 * ai[i];
 51:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));

 53:     /* elimination */
 54:     bjtmp = bj + bi[i];
 55:     nzL   = bi[i + 1] - bi[i];
 56:     for (k = 0; k < nzL; k++) {
 57:       row = bjtmp[k];
 58:       pc  = rtmp + bs2 * row;
 59:       for (flg = 0, j = 0; j < bs2; j++) {
 60:         if (pc[j] != 0.0) {
 61:           flg = 1;
 62:           break;
 63:         }
 64:       }
 65:       if (flg) {
 66:         pv = b->a + bs2 * bdiag[row];
 67:         PetscKernel_A_gets_A_times_B(bs, pc, pv, mwork);
 68:         /* PetscCall(PetscKernel_A_gets_A_times_B_15(pc,pv,mwork)); */
 69:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
 70:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
 71:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
 72:         for (j = 0; j < nz; j++) {
 73:           vv = rtmp + bs2 * pj[j];
 74:           PetscKernel_A_gets_A_minus_B_times_C(bs, vv, pc, pv);
 75:           /* PetscCall(PetscKernel_A_gets_A_minus_B_times_C_15(vv,pc,pv)); */
 76:           pv += bs2;
 77:         }
 78:         PetscCall(PetscLogFlops(2.0 * bs2 * bs * (nz + 1) - bs2)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
 79:       }
 80:     }

 82:     /* finished row so stick it into b->a */
 83:     /* L part */
 84:     pv = b->a + bs2 * bi[i];
 85:     pj = b->j + bi[i];
 86:     nz = bi[i + 1] - bi[i];
 87:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

 89:     /* Mark diagonal and invert diagonal for simpler triangular solves */
 90:     pv = b->a + bs2 * bdiag[i];
 91:     pj = b->j + bdiag[i];
 92:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
 93:     PetscCall(PetscKernel_A_gets_inverse_A_15(pv, ipvt, work, info->shiftamount, allowzeropivot, &zeropivotdetected));
 94:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

 96:     /* U part */
 97:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
 98:     pj = b->j + bdiag[i + 1] + 1;
 99:     nz = bdiag[i] - bdiag[i + 1] - 1;
100:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
101:   }

103:   PetscCall(PetscFree2(rtmp, mwork));

105:   C->ops->solve          = MatSolve_SeqBAIJ_15_NaturalOrdering_ver1;
106:   C->ops->solvetranspose = MatSolve_SeqBAIJ_N_NaturalOrdering;
107:   C->assembled           = PETSC_TRUE;

109:   PetscCall(PetscLogFlops(1.333333333333 * bs * bs2 * b->mbs)); /* from inverting diagonal blocks */
110:   PetscFunctionReturn(PETSC_SUCCESS);
111: }

113: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_N(Mat B, Mat A, const MatFactorInfo *info)
114: {
115:   Mat             C = B;
116:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
117:   IS              isrow = b->row, isicol = b->icol;
118:   const PetscInt *r, *ic;
119:   PetscInt        i, j, k, n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
120:   PetscInt       *ajtmp, *bjtmp, nz, nzL, row, *bdiag = b->diag, *pj;
121:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa     = a->a;
122:   PetscInt        bs = A->rmap->bs, bs2 = a->bs2, *v_pivots, flg;
123:   MatScalar      *v_work;
124:   PetscBool       col_identity, row_identity, both_identity;
125:   PetscBool       allowzeropivot, zeropivotdetected;

127:   PetscFunctionBegin;
128:   PetscCall(ISGetIndices(isrow, &r));
129:   PetscCall(ISGetIndices(isicol, &ic));
130:   allowzeropivot = PetscNot(A->erroriffailure);

132:   PetscCall(PetscCalloc1(bs2 * n, &rtmp));

134:   /* generate work space needed by dense LU factorization */
135:   PetscCall(PetscMalloc3(bs, &v_work, bs2, &mwork, bs, &v_pivots));

137:   for (i = 0; i < n; i++) {
138:     /* zero rtmp */
139:     /* L part */
140:     nz    = bi[i + 1] - bi[i];
141:     bjtmp = bj + bi[i];
142:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

144:     /* U part */
145:     nz    = bdiag[i] - bdiag[i + 1];
146:     bjtmp = bj + bdiag[i + 1] + 1;
147:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

149:     /* load in initial (unfactored row) */
150:     nz    = ai[r[i] + 1] - ai[r[i]];
151:     ajtmp = aj + ai[r[i]];
152:     v     = aa + bs2 * ai[r[i]];
153:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2));

155:     /* elimination */
156:     bjtmp = bj + bi[i];
157:     nzL   = bi[i + 1] - bi[i];
158:     for (k = 0; k < nzL; k++) {
159:       row = bjtmp[k];
160:       pc  = rtmp + bs2 * row;
161:       for (flg = 0, j = 0; j < bs2; j++) {
162:         if (pc[j] != 0.0) {
163:           flg = 1;
164:           break;
165:         }
166:       }
167:       if (flg) {
168:         pv = b->a + bs2 * bdiag[row];
169:         PetscKernel_A_gets_A_times_B(bs, pc, pv, mwork); /* *pc = *pc * (*pv); */
170:         pj = b->j + bdiag[row + 1] + 1;                  /* beginning of U(row,:) */
171:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
172:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
173:         for (j = 0; j < nz; j++) PetscKernel_A_gets_A_minus_B_times_C(bs, rtmp + bs2 * pj[j], pc, pv + bs2 * j);
174:         PetscCall(PetscLogFlops(2.0 * bs2 * bs * (nz + 1) - bs2)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
175:       }
176:     }

178:     /* finished row so stick it into b->a */
179:     /* L part */
180:     pv = b->a + bs2 * bi[i];
181:     pj = b->j + bi[i];
182:     nz = bi[i + 1] - bi[i];
183:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

185:     /* Mark diagonal and invert diagonal for simpler triangular solves */
186:     pv = b->a + bs2 * bdiag[i];
187:     pj = b->j + bdiag[i];
188:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));

190:     PetscCall(PetscKernel_A_gets_inverse_A(bs, pv, v_pivots, v_work, allowzeropivot, &zeropivotdetected));
191:     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

193:     /* U part */
194:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
195:     pj = b->j + bdiag[i + 1] + 1;
196:     nz = bdiag[i] - bdiag[i + 1] - 1;
197:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
198:   }

200:   PetscCall(PetscFree(rtmp));
201:   PetscCall(PetscFree3(v_work, mwork, v_pivots));
202:   PetscCall(ISRestoreIndices(isicol, &ic));
203:   PetscCall(ISRestoreIndices(isrow, &r));

205:   PetscCall(ISIdentity(isrow, &row_identity));
206:   PetscCall(ISIdentity(isicol, &col_identity));

208:   both_identity = (PetscBool)(row_identity && col_identity);
209:   if (both_identity) {
210:     switch (bs) {
211:     case 9:
212: #if PetscDefined(HAVE_IMMINTRIN_H) && defined(__AVX2__) && defined(__FMA__) && PetscDefined(USE_REAL_DOUBLE) && !PetscDefined(USE_COMPLEX) && !PetscDefined(USE_64BIT_INDICES)
213:       C->ops->solve = MatSolve_SeqBAIJ_9_NaturalOrdering;
214: #else
215:       C->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
216: #endif
217:       break;
218:     case 11:
219:       C->ops->solve = MatSolve_SeqBAIJ_11_NaturalOrdering;
220:       break;
221:     case 12:
222:       C->ops->solve = MatSolve_SeqBAIJ_12_NaturalOrdering;
223:       break;
224:     case 13:
225:       C->ops->solve = MatSolve_SeqBAIJ_13_NaturalOrdering;
226:       break;
227:     case 14:
228:       C->ops->solve = MatSolve_SeqBAIJ_14_NaturalOrdering;
229:       break;
230:     default:
231:       C->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
232:       break;
233:     }
234:   } else {
235:     C->ops->solve = MatSolve_SeqBAIJ_N;
236:   }
237:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_N;

239:   C->assembled = PETSC_TRUE;

241:   PetscCall(PetscLogFlops(1.333333333333 * bs * bs2 * b->mbs)); /* from inverting diagonal blocks */
242:   PetscFunctionReturn(PETSC_SUCCESS);
243: }

245: /*
246:    ilu(0) with natural ordering under new data structure.
247:    See MatILUFactorSymbolic_SeqAIJ_ilu0() for detailed description
248:    because this code is almost identical to MatILUFactorSymbolic_SeqAIJ_ilu0_inplace().
249: */

251: static PetscErrorCode MatILUFactorSymbolic_SeqBAIJ_ilu0(Mat fact, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
252: {
253:   Mat_SeqBAIJ   *a = (Mat_SeqBAIJ *)A->data, *b;
254:   const PetscInt n = a->mbs, *ai = a->i, *aj, *adiag, bs2 = a->bs2;
255:   PetscInt       i, j, nz, *bi, *bj, *bdiag, bi_temp;

257:   PetscFunctionBegin;
258:   PetscCall(MatGetDiagonalMarkers_SeqBAIJ(A, &adiag, NULL));
259:   PetscCall(MatDuplicateNoCreate_SeqBAIJ(fact, A, MAT_DO_NOT_COPY_VALUES, PETSC_FALSE));
260:   b = (Mat_SeqBAIJ *)fact->data;

262:   /* allocate matrix arrays for new data structure */
263:   PetscCall(PetscShmgetAllocateArray(bs2 * ai[n], sizeof(PetscScalar), (void **)&b->a));
264:   PetscCall(PetscShmgetAllocateArray(ai[n], sizeof(PetscInt), (void **)&b->j));
265:   PetscCall(PetscShmgetAllocateArray(n + 1, sizeof(PetscInt), (void **)&b->i));
266:   b->free_a          = PETSC_TRUE;
267:   b->free_ij         = PETSC_TRUE;
268:   fact->preallocated = PETSC_TRUE;
269:   fact->assembled    = PETSC_TRUE;
270:   if (!b->diag) PetscCall(PetscMalloc1(n + 1, &b->diag));
271:   bdiag = b->diag;

273:   if (n > 0) PetscCall(PetscArrayzero(b->a, bs2 * ai[n]));

275:   /* set bi and bj with new data structure */
276:   bi = b->i;
277:   bj = b->j;

279:   /* L part */
280:   bi[0] = 0;
281:   for (i = 0; i < n; i++) {
282:     nz        = adiag[i] - ai[i];
283:     bi[i + 1] = bi[i] + nz;
284:     aj        = a->j + ai[i];
285:     for (j = 0; j < nz; j++) {
286:       *bj = aj[j];
287:       bj++;
288:     }
289:   }

291:   /* U part */
292:   bi_temp  = bi[n];
293:   bdiag[n] = bi[n] - 1;
294:   for (i = n - 1; i >= 0; i--) {
295:     nz      = ai[i + 1] - adiag[i] - 1;
296:     bi_temp = bi_temp + nz + 1;
297:     aj      = a->j + adiag[i] + 1;
298:     for (j = 0; j < nz; j++) {
299:       *bj = aj[j];
300:       bj++;
301:     }
302:     /* diag[i] */
303:     *bj = i;
304:     bj++;
305:     bdiag[i] = bi_temp - 1;
306:   }
307:   PetscFunctionReturn(PETSC_SUCCESS);
308: }

310: PetscErrorCode MatILUFactorSymbolic_SeqBAIJ(Mat fact, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
311: {
312:   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data, *b;
313:   IS                 isicol;
314:   const PetscInt    *r, *ic;
315:   PetscInt           n = a->mbs, *ai = a->i, *aj = a->j;
316:   PetscInt          *bi, *cols, nnz, *cols_lvl;
317:   PetscInt          *bdiag, prow, fm, nzbd, reallocs = 0, dcount = 0;
318:   PetscInt           i, levels, diagonal_fill;
319:   PetscBool          col_identity, row_identity, both_identity;
320:   PetscReal          f;
321:   PetscInt           nlnk, *lnk, *lnk_lvl = NULL;
322:   PetscBT            lnkbt;
323:   PetscInt           nzi, *bj, **bj_ptr, **bjlvl_ptr;
324:   PetscFreeSpaceList free_space = NULL, current_space = NULL;
325:   PetscFreeSpaceList free_space_lvl = NULL, current_space_lvl = NULL;
326:   PetscInt           bs = A->rmap->bs, bs2 = a->bs2;
327:   PetscBool          diagDense;

329:   PetscFunctionBegin;
330:   PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Must be square matrix, rows %" PetscInt_FMT " columns %" PetscInt_FMT, A->rmap->n, A->cmap->n);
331:   if (bs > 1) { /* check shifttype */
332:     PetscCheck(info->shifttype != (PetscReal)MAT_SHIFT_NONZERO && info->shifttype != (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only MAT_SHIFT_NONE and MAT_SHIFT_INBLOCKS are supported for BAIJ matrix");
333:   }
334:   PetscCall(MatGetDiagonalMarkers_SeqBAIJ(A, NULL, &diagDense));
335:   PetscCheck(diagDense, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix is missing diagonal entry");

337:   f             = info->fill;
338:   levels        = (PetscInt)info->levels;
339:   diagonal_fill = (PetscInt)info->diagonal_fill;

341:   PetscCall(ISInvertPermutation(iscol, PETSC_DECIDE, &isicol));

343:   PetscCall(ISIdentity(isrow, &row_identity));
344:   PetscCall(ISIdentity(iscol, &col_identity));

346:   both_identity = (PetscBool)(row_identity && col_identity);

348:   if (!levels && both_identity) {
349:     /* special case: ilu(0) with natural ordering */
350:     PetscCall(MatILUFactorSymbolic_SeqBAIJ_ilu0(fact, A, isrow, iscol, info));
351:     PetscCall(MatSeqBAIJSetNumericFactorization(fact, both_identity));

353:     fact->factortype             = MAT_FACTOR_ILU;
354:     fact->info.factor_mallocs    = 0;
355:     fact->info.fill_ratio_given  = info->fill;
356:     fact->info.fill_ratio_needed = 1.0;

358:     b       = (Mat_SeqBAIJ *)fact->data;
359:     b->row  = isrow;
360:     b->col  = iscol;
361:     b->icol = isicol;
362:     PetscCall(PetscObjectReference((PetscObject)isrow));
363:     PetscCall(PetscObjectReference((PetscObject)iscol));
364:     b->pivotinblocks = info->pivotinblocks ? PETSC_TRUE : PETSC_FALSE;

366:     PetscCall(PetscMalloc1((n + 1) * bs, &b->solve_work));
367:     PetscFunctionReturn(PETSC_SUCCESS);
368:   }

370:   PetscCall(ISGetIndices(isrow, &r));
371:   PetscCall(ISGetIndices(isicol, &ic));

373:   /* get new row pointers */
374:   PetscCall(PetscMalloc1(n + 1, &bi));
375:   bi[0] = 0;
376:   /* bdiag is location of diagonal in factor */
377:   PetscCall(PetscMalloc1(n + 1, &bdiag));
378:   bdiag[0] = 0;

380:   PetscCall(PetscMalloc2(n, &bj_ptr, n, &bjlvl_ptr));

382:   /* create a linked list for storing column indices of the active row */
383:   nlnk = n + 1;
384:   PetscCall(PetscIncompleteLLCreate(n, n, nlnk, lnk, lnk_lvl, lnkbt));

386:   /* initial FreeSpace size is f*(ai[n]+1) */
387:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(f, ai[n] + 1), &free_space));
388:   current_space = free_space;
389:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(f, ai[n] + 1), &free_space_lvl));
390:   current_space_lvl = free_space_lvl;

392:   for (i = 0; i < n; i++) {
393:     nzi = 0;
394:     /* copy current row into linked list */
395:     nnz = ai[r[i] + 1] - ai[r[i]];
396:     PetscCheck(nnz, PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Empty row in matrix: row in original ordering %" PetscInt_FMT " in permuted ordering %" PetscInt_FMT, r[i], i);
397:     cols   = aj + ai[r[i]];
398:     lnk[i] = -1; /* marker to indicate if diagonal exists */
399:     PetscCall(PetscIncompleteLLInit(nnz, cols, n, ic, &nlnk, lnk, lnk_lvl, lnkbt));
400:     nzi += nlnk;

402:     /* make sure diagonal entry is included */
403:     if (diagonal_fill && lnk[i] == -1) {
404:       fm = n;
405:       while (lnk[fm] < i) fm = lnk[fm];
406:       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
407:       lnk[fm]    = i;
408:       lnk_lvl[i] = 0;
409:       nzi++;
410:       dcount++;
411:     }

413:     /* add pivot rows into the active row */
414:     nzbd = 0;
415:     prow = lnk[n];
416:     while (prow < i) {
417:       nnz      = bdiag[prow];
418:       cols     = bj_ptr[prow] + nnz + 1;
419:       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
420:       nnz      = bi[prow + 1] - bi[prow] - nnz - 1;

422:       PetscCall(PetscILULLAddSorted(nnz, cols, levels, cols_lvl, prow, &nlnk, lnk, lnk_lvl, lnkbt, prow));
423:       nzi += nlnk;
424:       prow = lnk[prow];
425:       nzbd++;
426:     }
427:     bdiag[i]  = nzbd;
428:     bi[i + 1] = bi[i] + nzi;

430:     /* if free space is not available, make more free space */
431:     if (current_space->local_remaining < nzi) {
432:       nnz = PetscIntMultTruncate(2, PetscIntMultTruncate(nzi, n - i)); /* estimated and max additional space needed */
433:       PetscCall(PetscFreeSpaceGet(nnz, &current_space));
434:       PetscCall(PetscFreeSpaceGet(nnz, &current_space_lvl));
435:       reallocs++;
436:     }

438:     /* copy data into free_space and free_space_lvl, then initialize lnk */
439:     PetscCall(PetscIncompleteLLClean(n, n, nzi, lnk, lnk_lvl, current_space->array, current_space_lvl->array, lnkbt));

441:     bj_ptr[i]    = current_space->array;
442:     bjlvl_ptr[i] = current_space_lvl->array;

444:     /* make sure the active row i has diagonal entry */
445:     PetscCheck(*(bj_ptr[i] + bdiag[i]) == i, PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Row %" PetscInt_FMT " has missing diagonal in factored matrix, try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill", i);

447:     current_space->array += nzi;
448:     current_space->local_used += nzi;
449:     current_space->local_remaining -= nzi;

451:     current_space_lvl->array += nzi;
452:     current_space_lvl->local_used += nzi;
453:     current_space_lvl->local_remaining -= nzi;
454:   }

456:   PetscCall(ISRestoreIndices(isrow, &r));
457:   PetscCall(ISRestoreIndices(isicol, &ic));

459:   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
460:   PetscCall(PetscMalloc1(bi[n], &bj));
461:   PetscCall(PetscFreeSpaceContiguous_LU(&free_space, bj, n, bi, bdiag));

463:   PetscCall(PetscIncompleteLLDestroy(lnk, lnkbt));
464:   PetscCall(PetscFreeSpaceDestroy(free_space_lvl));
465:   PetscCall(PetscFree2(bj_ptr, bjlvl_ptr));

467: #if PetscDefined(USE_INFO)
468:   {
469:     PetscReal af = ((PetscReal)(bdiag[0] + 1)) / ((PetscReal)ai[n]);
470:     PetscCall(PetscInfo(A, "Reallocs %" PetscInt_FMT " Fill ratio:given %g needed %g\n", reallocs, (double)f, (double)af));
471:     PetscCall(PetscInfo(A, "Run with -[sub_]pc_factor_fill %g or use \n", (double)af));
472:     PetscCall(PetscInfo(A, "PCFactorSetFill([sub]pc,%g);\n", (double)af));
473:     PetscCall(PetscInfo(A, "for best performance.\n"));
474:     if (diagonal_fill) PetscCall(PetscInfo(A, "Detected and replaced %" PetscInt_FMT " missing diagonals\n", dcount));
475:   }
476: #endif

478:   /* put together the new matrix */
479:   PetscCall(MatSeqBAIJSetPreallocation(fact, bs, MAT_SKIP_ALLOCATION, NULL));

481:   b          = (Mat_SeqBAIJ *)fact->data;
482:   b->free_ij = PETSC_TRUE;
483:   PetscCall(PetscShmgetAllocateArray(bs2 * (bdiag[0] + 1), sizeof(PetscScalar), (void **)&b->a));
484:   b->free_a = PETSC_TRUE;

486:   b->j    = bj;
487:   b->i    = bi;
488:   b->diag = bdiag;
489:   b->ilen = NULL;
490:   b->imax = NULL;
491:   b->row  = isrow;
492:   b->col  = iscol;
493:   PetscCall(PetscObjectReference((PetscObject)isrow));
494:   PetscCall(PetscObjectReference((PetscObject)iscol));
495:   b->icol = isicol;

497:   PetscCall(PetscMalloc1(bs * n + bs, &b->solve_work));
498:   /* In b structure:  Free imax, ilen, old a, old j.
499:      Allocate bdiag, solve_work, new a, new j */
500:   b->maxnz = b->nz = bdiag[0] + 1;

502:   fact->info.factor_mallocs    = reallocs;
503:   fact->info.fill_ratio_given  = f;
504:   fact->info.fill_ratio_needed = ((PetscReal)(bdiag[0] + 1)) / ((PetscReal)ai[n]);

506:   PetscCall(MatSeqBAIJSetNumericFactorization(fact, both_identity));
507:   PetscFunctionReturn(PETSC_SUCCESS);
508: }