xref: /petsc/src/mat/impls/baij/seq/baijfact2.c (revision e8c0849ab8fe171bed529bea27238c9b402db591)
1 /*
2     Factorization code for BAIJ format.
3 */
4 
5 #include <../src/mat/impls/baij/seq/baij.h>
6 #include <petsc/private/kernels/blockinvert.h>
7 #include <petscbt.h>
8 #include <../src/mat/utils/freespace.h>
9 
10 PETSC_INTERN PetscErrorCode MatDuplicateNoCreate_SeqBAIJ(Mat, Mat, MatDuplicateOption, PetscBool);
11 
12 /*
13    This is not much faster than MatLUFactorNumeric_SeqBAIJ_N() but the solve is faster at least sometimes
14 */
MatLUFactorNumeric_SeqBAIJ_15_NaturalOrdering(Mat B,Mat A,const MatFactorInfo * info)15 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_15_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
16 {
17   Mat              C = B;
18   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
19   PetscInt         i, j, k, ipvt[15];
20   const PetscInt   n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, *ajtmp, *bjtmp, *bdiag = b->diag, *pj;
21   PetscInt         nz, nzL, row;
22   MatScalar       *rtmp, *pc, *mwork, *pv, *vv, work[225];
23   const MatScalar *v, *aa = a->a;
24   PetscInt         bs2 = a->bs2, bs = A->rmap->bs, flg;
25   PetscInt         sol_ver;
26   PetscBool        allowzeropivot, zeropivotdetected;
27 
28   PetscFunctionBegin;
29   allowzeropivot = PetscNot(A->erroriffailure);
30   PetscCall(PetscOptionsGetInt(NULL, ((PetscObject)A)->prefix, "-sol_ver", &sol_ver, NULL));
31 
32   /* generate work space needed by the factorization */
33   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
34   PetscCall(PetscArrayzero(rtmp, bs2 * n));
35 
36   for (i = 0; i < n; i++) {
37     /* zero rtmp */
38     /* L part */
39     nz    = bi[i + 1] - bi[i];
40     bjtmp = bj + bi[i];
41     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
42 
43     /* U part */
44     nz    = bdiag[i] - bdiag[i + 1];
45     bjtmp = bj + bdiag[i + 1] + 1;
46     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
47 
48     /* load in initial (unfactored row) */
49     nz    = ai[i + 1] - ai[i];
50     ajtmp = aj + ai[i];
51     v     = aa + bs2 * ai[i];
52     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));
53 
54     /* elimination */
55     bjtmp = bj + bi[i];
56     nzL   = bi[i + 1] - bi[i];
57     for (k = 0; k < nzL; k++) {
58       row = bjtmp[k];
59       pc  = rtmp + bs2 * row;
60       for (flg = 0, j = 0; j < bs2; j++) {
61         if (pc[j] != 0.0) {
62           flg = 1;
63           break;
64         }
65       }
66       if (flg) {
67         pv = b->a + bs2 * bdiag[row];
68         PetscKernel_A_gets_A_times_B(bs, pc, pv, mwork);
69         /* PetscCall(PetscKernel_A_gets_A_times_B_15(pc,pv,mwork)); */
70         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
71         pv = b->a + bs2 * (bdiag[row + 1] + 1);
72         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
73         for (j = 0; j < nz; j++) {
74           vv = rtmp + bs2 * pj[j];
75           PetscKernel_A_gets_A_minus_B_times_C(bs, vv, pc, pv);
76           /* PetscCall(PetscKernel_A_gets_A_minus_B_times_C_15(vv,pc,pv)); */
77           pv += bs2;
78         }
79         PetscCall(PetscLogFlops(2.0 * bs2 * bs * (nz + 1) - bs2)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
80       }
81     }
82 
83     /* finished row so stick it into b->a */
84     /* L part */
85     pv = b->a + bs2 * bi[i];
86     pj = b->j + bi[i];
87     nz = bi[i + 1] - bi[i];
88     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
89 
90     /* Mark diagonal and invert diagonal for simpler triangular solves */
91     pv = b->a + bs2 * bdiag[i];
92     pj = b->j + bdiag[i];
93     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
94     PetscCall(PetscKernel_A_gets_inverse_A_15(pv, ipvt, work, info->shiftamount, allowzeropivot, &zeropivotdetected));
95     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
96 
97     /* U part */
98     pv = b->a + bs2 * (bdiag[i + 1] + 1);
99     pj = b->j + bdiag[i + 1] + 1;
100     nz = bdiag[i] - bdiag[i + 1] - 1;
101     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
102   }
103 
104   PetscCall(PetscFree2(rtmp, mwork));
105 
106   C->ops->solve          = MatSolve_SeqBAIJ_15_NaturalOrdering_ver1;
107   C->ops->solvetranspose = MatSolve_SeqBAIJ_N_NaturalOrdering;
108   C->assembled           = PETSC_TRUE;
109 
110   PetscCall(PetscLogFlops(1.333333333333 * bs * bs2 * b->mbs)); /* from inverting diagonal blocks */
111   PetscFunctionReturn(PETSC_SUCCESS);
112 }
113 
MatLUFactorNumeric_SeqBAIJ_N(Mat B,Mat A,const MatFactorInfo * info)114 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_N(Mat B, Mat A, const MatFactorInfo *info)
115 {
116   Mat             C = B;
117   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
118   IS              isrow = b->row, isicol = b->icol;
119   const PetscInt *r, *ic;
120   PetscInt        i, j, k, n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
121   PetscInt       *ajtmp, *bjtmp, nz, nzL, row, *bdiag = b->diag, *pj;
122   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa     = a->a;
123   PetscInt        bs = A->rmap->bs, bs2 = a->bs2, *v_pivots, flg;
124   MatScalar      *v_work;
125   PetscBool       col_identity, row_identity, both_identity;
126   PetscBool       allowzeropivot, zeropivotdetected;
127 
128   PetscFunctionBegin;
129   PetscCall(ISGetIndices(isrow, &r));
130   PetscCall(ISGetIndices(isicol, &ic));
131   allowzeropivot = PetscNot(A->erroriffailure);
132 
133   PetscCall(PetscCalloc1(bs2 * n, &rtmp));
134 
135   /* generate work space needed by dense LU factorization */
136   PetscCall(PetscMalloc3(bs, &v_work, bs2, &mwork, bs, &v_pivots));
137 
138   for (i = 0; i < n; i++) {
139     /* zero rtmp */
140     /* L part */
141     nz    = bi[i + 1] - bi[i];
142     bjtmp = bj + bi[i];
143     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
144 
145     /* U part */
146     nz    = bdiag[i] - bdiag[i + 1];
147     bjtmp = bj + bdiag[i + 1] + 1;
148     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));
149 
150     /* load in initial (unfactored row) */
151     nz    = ai[r[i] + 1] - ai[r[i]];
152     ajtmp = aj + ai[r[i]];
153     v     = aa + bs2 * ai[r[i]];
154     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2));
155 
156     /* elimination */
157     bjtmp = bj + bi[i];
158     nzL   = bi[i + 1] - bi[i];
159     for (k = 0; k < nzL; k++) {
160       row = bjtmp[k];
161       pc  = rtmp + bs2 * row;
162       for (flg = 0, j = 0; j < bs2; j++) {
163         if (pc[j] != 0.0) {
164           flg = 1;
165           break;
166         }
167       }
168       if (flg) {
169         pv = b->a + bs2 * bdiag[row];
170         PetscKernel_A_gets_A_times_B(bs, pc, pv, mwork); /* *pc = *pc * (*pv); */
171         pj = b->j + bdiag[row + 1] + 1;                  /* beginning of U(row,:) */
172         pv = b->a + bs2 * (bdiag[row + 1] + 1);
173         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
174         for (j = 0; j < nz; j++) PetscKernel_A_gets_A_minus_B_times_C(bs, rtmp + bs2 * pj[j], pc, pv + bs2 * j);
175         PetscCall(PetscLogFlops(2.0 * bs2 * bs * (nz + 1) - bs2)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
176       }
177     }
178 
179     /* finished row so stick it into b->a */
180     /* L part */
181     pv = b->a + bs2 * bi[i];
182     pj = b->j + bi[i];
183     nz = bi[i + 1] - bi[i];
184     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
185 
186     /* Mark diagonal and invert diagonal for simpler triangular solves */
187     pv = b->a + bs2 * bdiag[i];
188     pj = b->j + bdiag[i];
189     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
190 
191     PetscCall(PetscKernel_A_gets_inverse_A(bs, pv, v_pivots, v_work, allowzeropivot, &zeropivotdetected));
192     if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
193 
194     /* U part */
195     pv = b->a + bs2 * (bdiag[i + 1] + 1);
196     pj = b->j + bdiag[i + 1] + 1;
197     nz = bdiag[i] - bdiag[i + 1] - 1;
198     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
199   }
200 
201   PetscCall(PetscFree(rtmp));
202   PetscCall(PetscFree3(v_work, mwork, v_pivots));
203   PetscCall(ISRestoreIndices(isicol, &ic));
204   PetscCall(ISRestoreIndices(isrow, &r));
205 
206   PetscCall(ISIdentity(isrow, &row_identity));
207   PetscCall(ISIdentity(isicol, &col_identity));
208 
209   both_identity = (PetscBool)(row_identity && col_identity);
210   if (both_identity) {
211     switch (bs) {
212     case 9:
213 #if defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX2__) && defined(__FMA__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES)
214       C->ops->solve = MatSolve_SeqBAIJ_9_NaturalOrdering;
215 #else
216       C->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
217 #endif
218       break;
219     case 11:
220       C->ops->solve = MatSolve_SeqBAIJ_11_NaturalOrdering;
221       break;
222     case 12:
223       C->ops->solve = MatSolve_SeqBAIJ_12_NaturalOrdering;
224       break;
225     case 13:
226       C->ops->solve = MatSolve_SeqBAIJ_13_NaturalOrdering;
227       break;
228     case 14:
229       C->ops->solve = MatSolve_SeqBAIJ_14_NaturalOrdering;
230       break;
231     default:
232       C->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
233       break;
234     }
235   } else {
236     C->ops->solve = MatSolve_SeqBAIJ_N;
237   }
238   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_N;
239 
240   C->assembled = PETSC_TRUE;
241 
242   PetscCall(PetscLogFlops(1.333333333333 * bs * bs2 * b->mbs)); /* from inverting diagonal blocks */
243   PetscFunctionReturn(PETSC_SUCCESS);
244 }
245 
246 /*
247    ilu(0) with natural ordering under new data structure.
248    See MatILUFactorSymbolic_SeqAIJ_ilu0() for detailed description
249    because this code is almost identical to MatILUFactorSymbolic_SeqAIJ_ilu0_inplace().
250 */
251 
MatILUFactorSymbolic_SeqBAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo * info)252 static PetscErrorCode MatILUFactorSymbolic_SeqBAIJ_ilu0(Mat fact, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
253 {
254   Mat_SeqBAIJ   *a = (Mat_SeqBAIJ *)A->data, *b;
255   const PetscInt n = a->mbs, *ai = a->i, *aj, *adiag, bs2 = a->bs2;
256   PetscInt       i, j, nz, *bi, *bj, *bdiag, bi_temp;
257 
258   PetscFunctionBegin;
259   PetscCall(MatGetDiagonalMarkers_SeqBAIJ(A, &adiag, NULL));
260   PetscCall(MatDuplicateNoCreate_SeqBAIJ(fact, A, MAT_DO_NOT_COPY_VALUES, PETSC_FALSE));
261   b = (Mat_SeqBAIJ *)fact->data;
262 
263   /* allocate matrix arrays for new data structure */
264   PetscCall(PetscShmgetAllocateArray(bs2 * ai[n], sizeof(PetscScalar), (void **)&b->a));
265   PetscCall(PetscShmgetAllocateArray(ai[n], sizeof(PetscInt), (void **)&b->j));
266   PetscCall(PetscShmgetAllocateArray(n + 1, sizeof(PetscInt), (void **)&b->i));
267   b->free_a          = PETSC_TRUE;
268   b->free_ij         = PETSC_TRUE;
269   fact->preallocated = PETSC_TRUE;
270   fact->assembled    = PETSC_TRUE;
271   if (!b->diag) PetscCall(PetscMalloc1(n + 1, &b->diag));
272   bdiag = b->diag;
273 
274   if (n > 0) PetscCall(PetscArrayzero(b->a, bs2 * ai[n]));
275 
276   /* set bi and bj with new data structure */
277   bi = b->i;
278   bj = b->j;
279 
280   /* L part */
281   bi[0] = 0;
282   for (i = 0; i < n; i++) {
283     nz        = adiag[i] - ai[i];
284     bi[i + 1] = bi[i] + nz;
285     aj        = a->j + ai[i];
286     for (j = 0; j < nz; j++) {
287       *bj = aj[j];
288       bj++;
289     }
290   }
291 
292   /* U part */
293   bi_temp  = bi[n];
294   bdiag[n] = bi[n] - 1;
295   for (i = n - 1; i >= 0; i--) {
296     nz      = ai[i + 1] - adiag[i] - 1;
297     bi_temp = bi_temp + nz + 1;
298     aj      = a->j + adiag[i] + 1;
299     for (j = 0; j < nz; j++) {
300       *bj = aj[j];
301       bj++;
302     }
303     /* diag[i] */
304     *bj = i;
305     bj++;
306     bdiag[i] = bi_temp - 1;
307   }
308   PetscFunctionReturn(PETSC_SUCCESS);
309 }
310 
MatILUFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo * info)311 PetscErrorCode MatILUFactorSymbolic_SeqBAIJ(Mat fact, Mat A, IS isrow, IS iscol, const MatFactorInfo *info)
312 {
313   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data, *b;
314   IS                 isicol;
315   const PetscInt    *r, *ic;
316   PetscInt           n = a->mbs, *ai = a->i, *aj = a->j;
317   PetscInt          *bi, *cols, nnz, *cols_lvl;
318   PetscInt          *bdiag, prow, fm, nzbd, reallocs = 0, dcount = 0;
319   PetscInt           i, levels, diagonal_fill;
320   PetscBool          col_identity, row_identity, both_identity;
321   PetscReal          f;
322   PetscInt           nlnk, *lnk, *lnk_lvl = NULL;
323   PetscBT            lnkbt;
324   PetscInt           nzi, *bj, **bj_ptr, **bjlvl_ptr;
325   PetscFreeSpaceList free_space = NULL, current_space = NULL;
326   PetscFreeSpaceList free_space_lvl = NULL, current_space_lvl = NULL;
327   PetscInt           bs = A->rmap->bs, bs2 = a->bs2;
328   PetscBool          diagDense;
329 
330   PetscFunctionBegin;
331   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);
332   if (bs > 1) { /* check shifttype */
333     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");
334   }
335   PetscCall(MatGetDiagonalMarkers_SeqBAIJ(A, NULL, &diagDense));
336   PetscCheck(diagDense, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix is missing diagonal entry");
337 
338   f             = info->fill;
339   levels        = (PetscInt)info->levels;
340   diagonal_fill = (PetscInt)info->diagonal_fill;
341 
342   PetscCall(ISInvertPermutation(iscol, PETSC_DECIDE, &isicol));
343 
344   PetscCall(ISIdentity(isrow, &row_identity));
345   PetscCall(ISIdentity(iscol, &col_identity));
346 
347   both_identity = (PetscBool)(row_identity && col_identity);
348 
349   if (!levels && both_identity) {
350     /* special case: ilu(0) with natural ordering */
351     PetscCall(MatILUFactorSymbolic_SeqBAIJ_ilu0(fact, A, isrow, iscol, info));
352     PetscCall(MatSeqBAIJSetNumericFactorization(fact, both_identity));
353 
354     fact->factortype             = MAT_FACTOR_ILU;
355     fact->info.factor_mallocs    = 0;
356     fact->info.fill_ratio_given  = info->fill;
357     fact->info.fill_ratio_needed = 1.0;
358 
359     b       = (Mat_SeqBAIJ *)fact->data;
360     b->row  = isrow;
361     b->col  = iscol;
362     b->icol = isicol;
363     PetscCall(PetscObjectReference((PetscObject)isrow));
364     PetscCall(PetscObjectReference((PetscObject)iscol));
365     b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;
366 
367     PetscCall(PetscMalloc1((n + 1) * bs, &b->solve_work));
368     PetscFunctionReturn(PETSC_SUCCESS);
369   }
370 
371   PetscCall(ISGetIndices(isrow, &r));
372   PetscCall(ISGetIndices(isicol, &ic));
373 
374   /* get new row pointers */
375   PetscCall(PetscMalloc1(n + 1, &bi));
376   bi[0] = 0;
377   /* bdiag is location of diagonal in factor */
378   PetscCall(PetscMalloc1(n + 1, &bdiag));
379   bdiag[0] = 0;
380 
381   PetscCall(PetscMalloc2(n, &bj_ptr, n, &bjlvl_ptr));
382 
383   /* create a linked list for storing column indices of the active row */
384   nlnk = n + 1;
385   PetscCall(PetscIncompleteLLCreate(n, n, nlnk, lnk, lnk_lvl, lnkbt));
386 
387   /* initial FreeSpace size is f*(ai[n]+1) */
388   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(f, ai[n] + 1), &free_space));
389   current_space = free_space;
390   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(f, ai[n] + 1), &free_space_lvl));
391   current_space_lvl = free_space_lvl;
392 
393   for (i = 0; i < n; i++) {
394     nzi = 0;
395     /* copy current row into linked list */
396     nnz = ai[r[i] + 1] - ai[r[i]];
397     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);
398     cols   = aj + ai[r[i]];
399     lnk[i] = -1; /* marker to indicate if diagonal exists */
400     PetscCall(PetscIncompleteLLInit(nnz, cols, n, ic, &nlnk, lnk, lnk_lvl, lnkbt));
401     nzi += nlnk;
402 
403     /* make sure diagonal entry is included */
404     if (diagonal_fill && lnk[i] == -1) {
405       fm = n;
406       while (lnk[fm] < i) fm = lnk[fm];
407       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
408       lnk[fm]    = i;
409       lnk_lvl[i] = 0;
410       nzi++;
411       dcount++;
412     }
413 
414     /* add pivot rows into the active row */
415     nzbd = 0;
416     prow = lnk[n];
417     while (prow < i) {
418       nnz      = bdiag[prow];
419       cols     = bj_ptr[prow] + nnz + 1;
420       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
421       nnz      = bi[prow + 1] - bi[prow] - nnz - 1;
422 
423       PetscCall(PetscILULLAddSorted(nnz, cols, levels, cols_lvl, prow, &nlnk, lnk, lnk_lvl, lnkbt, prow));
424       nzi += nlnk;
425       prow = lnk[prow];
426       nzbd++;
427     }
428     bdiag[i]  = nzbd;
429     bi[i + 1] = bi[i] + nzi;
430 
431     /* if free space is not available, make more free space */
432     if (current_space->local_remaining < nzi) {
433       nnz = PetscIntMultTruncate(2, PetscIntMultTruncate(nzi, n - i)); /* estimated and max additional space needed */
434       PetscCall(PetscFreeSpaceGet(nnz, &current_space));
435       PetscCall(PetscFreeSpaceGet(nnz, &current_space_lvl));
436       reallocs++;
437     }
438 
439     /* copy data into free_space and free_space_lvl, then initialize lnk */
440     PetscCall(PetscIncompleteLLClean(n, n, nzi, lnk, lnk_lvl, current_space->array, current_space_lvl->array, lnkbt));
441 
442     bj_ptr[i]    = current_space->array;
443     bjlvl_ptr[i] = current_space_lvl->array;
444 
445     /* make sure the active row i has diagonal entry */
446     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 
448     current_space->array += nzi;
449     current_space->local_used += nzi;
450     current_space->local_remaining -= nzi;
451 
452     current_space_lvl->array += nzi;
453     current_space_lvl->local_used += nzi;
454     current_space_lvl->local_remaining -= nzi;
455   }
456 
457   PetscCall(ISRestoreIndices(isrow, &r));
458   PetscCall(ISRestoreIndices(isicol, &ic));
459 
460   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
461   PetscCall(PetscMalloc1(bi[n], &bj));
462   PetscCall(PetscFreeSpaceContiguous_LU(&free_space, bj, n, bi, bdiag));
463 
464   PetscCall(PetscIncompleteLLDestroy(lnk, lnkbt));
465   PetscCall(PetscFreeSpaceDestroy(free_space_lvl));
466   PetscCall(PetscFree2(bj_ptr, bjlvl_ptr));
467 
468 #if defined(PETSC_USE_INFO)
469   {
470     PetscReal af = ((PetscReal)(bdiag[0] + 1)) / ((PetscReal)ai[n]);
471     PetscCall(PetscInfo(A, "Reallocs %" PetscInt_FMT " Fill ratio:given %g needed %g\n", reallocs, (double)f, (double)af));
472     PetscCall(PetscInfo(A, "Run with -[sub_]pc_factor_fill %g or use \n", (double)af));
473     PetscCall(PetscInfo(A, "PCFactorSetFill([sub]pc,%g);\n", (double)af));
474     PetscCall(PetscInfo(A, "for best performance.\n"));
475     if (diagonal_fill) PetscCall(PetscInfo(A, "Detected and replaced %" PetscInt_FMT " missing diagonals\n", dcount));
476   }
477 #endif
478 
479   /* put together the new matrix */
480   PetscCall(MatSeqBAIJSetPreallocation(fact, bs, MAT_SKIP_ALLOCATION, NULL));
481 
482   b          = (Mat_SeqBAIJ *)fact->data;
483   b->free_ij = PETSC_TRUE;
484   PetscCall(PetscShmgetAllocateArray(bs2 * (bdiag[0] + 1), sizeof(PetscScalar), (void **)&b->a));
485   b->free_a = PETSC_TRUE;
486 
487   b->j    = bj;
488   b->i    = bi;
489   b->diag = bdiag;
490   b->ilen = NULL;
491   b->imax = NULL;
492   b->row  = isrow;
493   b->col  = iscol;
494   PetscCall(PetscObjectReference((PetscObject)isrow));
495   PetscCall(PetscObjectReference((PetscObject)iscol));
496   b->icol = isicol;
497 
498   PetscCall(PetscMalloc1(bs * n + bs, &b->solve_work));
499   /* In b structure:  Free imax, ilen, old a, old j.
500      Allocate bdiag, solve_work, new a, new j */
501   b->maxnz = b->nz = bdiag[0] + 1;
502 
503   fact->info.factor_mallocs    = reallocs;
504   fact->info.fill_ratio_given  = f;
505   fact->info.fill_ratio_needed = ((PetscReal)(bdiag[0] + 1)) / ((PetscReal)ai[n]);
506 
507   PetscCall(MatSeqBAIJSetNumericFactorization(fact, both_identity));
508   PetscFunctionReturn(PETSC_SUCCESS);
509 }
510