xref: /petsc/src/mat/impls/aij/seq/aij.c (revision f409f0aa4ada26a4a5b8f25b91c71f4af3eee8e5)
1 /*
2     Defines the basic matrix operations for the AIJ (compressed row)
3   matrix storage format.
4 */
5 
6 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
7 #include <petscblaslapack.h>
8 #include <petscbt.h>
9 #include <petsc/private/kernels/blocktranspose.h>
10 
11 /* defines MatSetValues_Seq_Hash(), MatAssemblyEnd_Seq_Hash(), MatSetUp_Seq_Hash() */
12 #define TYPE AIJ
13 #define TYPE_BS
14 #include "../src/mat/impls/aij/seq/seqhashmatsetvalues.h"
15 #include "../src/mat/impls/aij/seq/seqhashmat.h"
16 #undef TYPE
17 #undef TYPE_BS
18 
19 static PetscErrorCode MatSeqAIJSetTypeFromOptions(Mat A)
20 {
21   PetscBool flg;
22   char      type[256];
23 
24   PetscFunctionBegin;
25   PetscObjectOptionsBegin((PetscObject)A);
26   PetscCall(PetscOptionsFList("-mat_seqaij_type", "Matrix SeqAIJ type", "MatSeqAIJSetType", MatSeqAIJList, "seqaij", type, 256, &flg));
27   if (flg) PetscCall(MatSeqAIJSetType(A, type));
28   PetscOptionsEnd();
29   PetscFunctionReturn(PETSC_SUCCESS);
30 }
31 
32 static PetscErrorCode MatGetColumnReductions_SeqAIJ(Mat A, PetscInt type, PetscReal *reductions)
33 {
34   PetscInt    i, m, n;
35   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
36 
37   PetscFunctionBegin;
38   PetscCall(MatGetSize(A, &m, &n));
39   PetscCall(PetscArrayzero(reductions, n));
40   if (type == NORM_2) {
41     for (i = 0; i < aij->i[m]; i++) reductions[aij->j[i]] += PetscAbsScalar(aij->a[i] * aij->a[i]);
42   } else if (type == NORM_1) {
43     for (i = 0; i < aij->i[m]; i++) reductions[aij->j[i]] += PetscAbsScalar(aij->a[i]);
44   } else if (type == NORM_INFINITY) {
45     for (i = 0; i < aij->i[m]; i++) reductions[aij->j[i]] = PetscMax(PetscAbsScalar(aij->a[i]), reductions[aij->j[i]]);
46   } else if (type == REDUCTION_SUM_REALPART || type == REDUCTION_MEAN_REALPART) {
47     for (i = 0; i < aij->i[m]; i++) reductions[aij->j[i]] += PetscRealPart(aij->a[i]);
48   } else if (type == REDUCTION_SUM_IMAGINARYPART || type == REDUCTION_MEAN_IMAGINARYPART) {
49     for (i = 0; i < aij->i[m]; i++) reductions[aij->j[i]] += PetscImaginaryPart(aij->a[i]);
50   } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Unknown reduction type");
51 
52   if (type == NORM_2) {
53     for (i = 0; i < n; i++) reductions[i] = PetscSqrtReal(reductions[i]);
54   } else if (type == REDUCTION_MEAN_REALPART || type == REDUCTION_MEAN_IMAGINARYPART) {
55     for (i = 0; i < n; i++) reductions[i] /= m;
56   }
57   PetscFunctionReturn(PETSC_SUCCESS);
58 }
59 
60 static PetscErrorCode MatFindOffBlockDiagonalEntries_SeqAIJ(Mat A, IS *is)
61 {
62   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
63   PetscInt        i, m = A->rmap->n, cnt = 0, bs = A->rmap->bs;
64   const PetscInt *jj = a->j, *ii = a->i;
65   PetscInt       *rows;
66 
67   PetscFunctionBegin;
68   for (i = 0; i < m; i++) {
69     if ((ii[i] != ii[i + 1]) && ((jj[ii[i]] < bs * (i / bs)) || (jj[ii[i + 1] - 1] > bs * ((i + bs) / bs) - 1))) cnt++;
70   }
71   PetscCall(PetscMalloc1(cnt, &rows));
72   cnt = 0;
73   for (i = 0; i < m; i++) {
74     if ((ii[i] != ii[i + 1]) && ((jj[ii[i]] < bs * (i / bs)) || (jj[ii[i + 1] - 1] > bs * ((i + bs) / bs) - 1))) {
75       rows[cnt] = i;
76       cnt++;
77     }
78   }
79   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, cnt, rows, PETSC_OWN_POINTER, is));
80   PetscFunctionReturn(PETSC_SUCCESS);
81 }
82 
83 PetscErrorCode MatFindZeroDiagonals_SeqAIJ_Private(Mat A, PetscInt *nrows, PetscInt **zrows)
84 {
85   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
86   const MatScalar *aa;
87   PetscInt         i, m = A->rmap->n, cnt = 0;
88   const PetscInt  *ii = a->i, *jj = a->j, *diag;
89   PetscInt        *rows;
90 
91   PetscFunctionBegin;
92   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
93   PetscCall(MatMarkDiagonal_SeqAIJ(A));
94   diag = a->diag;
95   for (i = 0; i < m; i++) {
96     if ((diag[i] >= ii[i + 1]) || (jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) cnt++;
97   }
98   PetscCall(PetscMalloc1(cnt, &rows));
99   cnt = 0;
100   for (i = 0; i < m; i++) {
101     if ((diag[i] >= ii[i + 1]) || (jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) rows[cnt++] = i;
102   }
103   *nrows = cnt;
104   *zrows = rows;
105   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
106   PetscFunctionReturn(PETSC_SUCCESS);
107 }
108 
109 static PetscErrorCode MatFindZeroDiagonals_SeqAIJ(Mat A, IS *zrows)
110 {
111   PetscInt nrows, *rows;
112 
113   PetscFunctionBegin;
114   *zrows = NULL;
115   PetscCall(MatFindZeroDiagonals_SeqAIJ_Private(A, &nrows, &rows));
116   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)A), nrows, rows, PETSC_OWN_POINTER, zrows));
117   PetscFunctionReturn(PETSC_SUCCESS);
118 }
119 
120 static PetscErrorCode MatFindNonzeroRows_SeqAIJ(Mat A, IS *keptrows)
121 {
122   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
123   const MatScalar *aa;
124   PetscInt         m = A->rmap->n, cnt = 0;
125   const PetscInt  *ii;
126   PetscInt         n, i, j, *rows;
127 
128   PetscFunctionBegin;
129   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
130   *keptrows = NULL;
131   ii        = a->i;
132   for (i = 0; i < m; i++) {
133     n = ii[i + 1] - ii[i];
134     if (!n) {
135       cnt++;
136       goto ok1;
137     }
138     for (j = ii[i]; j < ii[i + 1]; j++) {
139       if (aa[j] != 0.0) goto ok1;
140     }
141     cnt++;
142   ok1:;
143   }
144   if (!cnt) {
145     PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
146     PetscFunctionReturn(PETSC_SUCCESS);
147   }
148   PetscCall(PetscMalloc1(A->rmap->n - cnt, &rows));
149   cnt = 0;
150   for (i = 0; i < m; i++) {
151     n = ii[i + 1] - ii[i];
152     if (!n) continue;
153     for (j = ii[i]; j < ii[i + 1]; j++) {
154       if (aa[j] != 0.0) {
155         rows[cnt++] = i;
156         break;
157       }
158     }
159   }
160   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
161   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, cnt, rows, PETSC_OWN_POINTER, keptrows));
162   PetscFunctionReturn(PETSC_SUCCESS);
163 }
164 
165 PetscErrorCode MatDiagonalSet_SeqAIJ(Mat Y, Vec D, InsertMode is)
166 {
167   Mat_SeqAIJ        *aij = (Mat_SeqAIJ *)Y->data;
168   PetscInt           i, m = Y->rmap->n;
169   const PetscInt    *diag;
170   MatScalar         *aa;
171   const PetscScalar *v;
172   PetscBool          missing;
173 
174   PetscFunctionBegin;
175   if (Y->assembled) {
176     PetscCall(MatMissingDiagonal_SeqAIJ(Y, &missing, NULL));
177     if (!missing) {
178       diag = aij->diag;
179       PetscCall(VecGetArrayRead(D, &v));
180       PetscCall(MatSeqAIJGetArray(Y, &aa));
181       if (is == INSERT_VALUES) {
182         for (i = 0; i < m; i++) aa[diag[i]] = v[i];
183       } else {
184         for (i = 0; i < m; i++) aa[diag[i]] += v[i];
185       }
186       PetscCall(MatSeqAIJRestoreArray(Y, &aa));
187       PetscCall(VecRestoreArrayRead(D, &v));
188       PetscFunctionReturn(PETSC_SUCCESS);
189     }
190     PetscCall(MatSeqAIJInvalidateDiagonal(Y));
191   }
192   PetscCall(MatDiagonalSet_Default(Y, D, is));
193   PetscFunctionReturn(PETSC_SUCCESS);
194 }
195 
196 PetscErrorCode MatGetRowIJ_SeqAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *m, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
197 {
198   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
199   PetscInt    i, ishift;
200 
201   PetscFunctionBegin;
202   if (m) *m = A->rmap->n;
203   if (!ia) PetscFunctionReturn(PETSC_SUCCESS);
204   ishift = 0;
205   if (symmetric && A->structurally_symmetric != PETSC_BOOL3_TRUE) {
206     PetscCall(MatToSymmetricIJ_SeqAIJ(A->rmap->n, a->i, a->j, PETSC_TRUE, ishift, oshift, (PetscInt **)ia, (PetscInt **)ja));
207   } else if (oshift == 1) {
208     PetscInt *tia;
209     PetscInt  nz = a->i[A->rmap->n];
210     /* malloc space and  add 1 to i and j indices */
211     PetscCall(PetscMalloc1(A->rmap->n + 1, &tia));
212     for (i = 0; i < A->rmap->n + 1; i++) tia[i] = a->i[i] + 1;
213     *ia = tia;
214     if (ja) {
215       PetscInt *tja;
216       PetscCall(PetscMalloc1(nz + 1, &tja));
217       for (i = 0; i < nz; i++) tja[i] = a->j[i] + 1;
218       *ja = tja;
219     }
220   } else {
221     *ia = a->i;
222     if (ja) *ja = a->j;
223   }
224   PetscFunctionReturn(PETSC_SUCCESS);
225 }
226 
227 PetscErrorCode MatRestoreRowIJ_SeqAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
228 {
229   PetscFunctionBegin;
230   if (!ia) PetscFunctionReturn(PETSC_SUCCESS);
231   if ((symmetric && A->structurally_symmetric != PETSC_BOOL3_TRUE) || oshift == 1) {
232     PetscCall(PetscFree(*ia));
233     if (ja) PetscCall(PetscFree(*ja));
234   }
235   PetscFunctionReturn(PETSC_SUCCESS);
236 }
237 
238 PetscErrorCode MatGetColumnIJ_SeqAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *nn, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
239 {
240   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
241   PetscInt    i, *collengths, *cia, *cja, n = A->cmap->n, m = A->rmap->n;
242   PetscInt    nz = a->i[m], row, *jj, mr, col;
243 
244   PetscFunctionBegin;
245   *nn = n;
246   if (!ia) PetscFunctionReturn(PETSC_SUCCESS);
247   if (symmetric) {
248     PetscCall(MatToSymmetricIJ_SeqAIJ(A->rmap->n, a->i, a->j, PETSC_TRUE, 0, oshift, (PetscInt **)ia, (PetscInt **)ja));
249   } else {
250     PetscCall(PetscCalloc1(n, &collengths));
251     PetscCall(PetscMalloc1(n + 1, &cia));
252     PetscCall(PetscMalloc1(nz, &cja));
253     jj = a->j;
254     for (i = 0; i < nz; i++) collengths[jj[i]]++;
255     cia[0] = oshift;
256     for (i = 0; i < n; i++) cia[i + 1] = cia[i] + collengths[i];
257     PetscCall(PetscArrayzero(collengths, n));
258     jj = a->j;
259     for (row = 0; row < m; row++) {
260       mr = a->i[row + 1] - a->i[row];
261       for (i = 0; i < mr; i++) {
262         col = *jj++;
263 
264         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
265       }
266     }
267     PetscCall(PetscFree(collengths));
268     *ia = cia;
269     *ja = cja;
270   }
271   PetscFunctionReturn(PETSC_SUCCESS);
272 }
273 
274 PetscErrorCode MatRestoreColumnIJ_SeqAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
275 {
276   PetscFunctionBegin;
277   if (!ia) PetscFunctionReturn(PETSC_SUCCESS);
278 
279   PetscCall(PetscFree(*ia));
280   PetscCall(PetscFree(*ja));
281   PetscFunctionReturn(PETSC_SUCCESS);
282 }
283 
284 /*
285  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
286  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
287  spidx[], index of a->a, to be used in MatTransposeColoringCreate_SeqAIJ() and MatFDColoringCreate_SeqXAIJ()
288 */
289 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *nn, const PetscInt *ia[], const PetscInt *ja[], PetscInt *spidx[], PetscBool *done)
290 {
291   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
292   PetscInt        i, *collengths, *cia, *cja, n = A->cmap->n, m = A->rmap->n;
293   PetscInt        nz = a->i[m], row, mr, col, tmp;
294   PetscInt       *cspidx;
295   const PetscInt *jj;
296 
297   PetscFunctionBegin;
298   *nn = n;
299   if (!ia) PetscFunctionReturn(PETSC_SUCCESS);
300 
301   PetscCall(PetscCalloc1(n, &collengths));
302   PetscCall(PetscMalloc1(n + 1, &cia));
303   PetscCall(PetscMalloc1(nz, &cja));
304   PetscCall(PetscMalloc1(nz, &cspidx));
305   jj = a->j;
306   for (i = 0; i < nz; i++) collengths[jj[i]]++;
307   cia[0] = oshift;
308   for (i = 0; i < n; i++) cia[i + 1] = cia[i] + collengths[i];
309   PetscCall(PetscArrayzero(collengths, n));
310   jj = a->j;
311   for (row = 0; row < m; row++) {
312     mr = a->i[row + 1] - a->i[row];
313     for (i = 0; i < mr; i++) {
314       col         = *jj++;
315       tmp         = cia[col] + collengths[col]++ - oshift;
316       cspidx[tmp] = a->i[row] + i; /* index of a->j */
317       cja[tmp]    = row + oshift;
318     }
319   }
320   PetscCall(PetscFree(collengths));
321   *ia    = cia;
322   *ja    = cja;
323   *spidx = cspidx;
324   PetscFunctionReturn(PETSC_SUCCESS);
325 }
326 
327 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscInt *spidx[], PetscBool *done)
328 {
329   PetscFunctionBegin;
330   PetscCall(MatRestoreColumnIJ_SeqAIJ(A, oshift, symmetric, inodecompressed, n, ia, ja, done));
331   PetscCall(PetscFree(*spidx));
332   PetscFunctionReturn(PETSC_SUCCESS);
333 }
334 
335 static PetscErrorCode MatSetValuesRow_SeqAIJ(Mat A, PetscInt row, const PetscScalar v[])
336 {
337   Mat_SeqAIJ  *a  = (Mat_SeqAIJ *)A->data;
338   PetscInt    *ai = a->i;
339   PetscScalar *aa;
340 
341   PetscFunctionBegin;
342   PetscCall(MatSeqAIJGetArray(A, &aa));
343   PetscCall(PetscArraycpy(aa + ai[row], v, ai[row + 1] - ai[row]));
344   PetscCall(MatSeqAIJRestoreArray(A, &aa));
345   PetscFunctionReturn(PETSC_SUCCESS);
346 }
347 
348 /*
349     MatSeqAIJSetValuesLocalFast - An optimized version of MatSetValuesLocal() for SeqAIJ matrices with several assumptions
350 
351       -   a single row of values is set with each call
352       -   no row or column indices are negative or (in error) larger than the number of rows or columns
353       -   the values are always added to the matrix, not set
354       -   no new locations are introduced in the nonzero structure of the matrix
355 
356      This does NOT assume the global column indices are sorted
357 
358 */
359 
360 #include <petsc/private/isimpl.h>
361 PetscErrorCode MatSeqAIJSetValuesLocalFast(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode is)
362 {
363   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
364   PetscInt        low, high, t, row, nrow, i, col, l;
365   const PetscInt *rp, *ai = a->i, *ailen = a->ilen, *aj = a->j;
366   PetscInt        lastcol = -1;
367   MatScalar      *ap, value, *aa;
368   const PetscInt *ridx = A->rmap->mapping->indices, *cidx = A->cmap->mapping->indices;
369 
370   PetscFunctionBegin;
371   PetscCall(MatSeqAIJGetArray(A, &aa));
372   row  = ridx[im[0]];
373   rp   = aj + ai[row];
374   ap   = aa + ai[row];
375   nrow = ailen[row];
376   low  = 0;
377   high = nrow;
378   for (l = 0; l < n; l++) { /* loop over added columns */
379     col   = cidx[in[l]];
380     value = v[l];
381 
382     if (col <= lastcol) low = 0;
383     else high = nrow;
384     lastcol = col;
385     while (high - low > 5) {
386       t = (low + high) / 2;
387       if (rp[t] > col) high = t;
388       else low = t;
389     }
390     for (i = low; i < high; i++) {
391       if (rp[i] == col) {
392         ap[i] += value;
393         low = i + 1;
394         break;
395       }
396     }
397   }
398   PetscCall(MatSeqAIJRestoreArray(A, &aa));
399   return PETSC_SUCCESS;
400 }
401 
402 PetscErrorCode MatSetValues_SeqAIJ(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode is)
403 {
404   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
405   PetscInt   *rp, k, low, high, t, ii, row, nrow, i, col, l, rmax, N;
406   PetscInt   *imax = a->imax, *ai = a->i, *ailen = a->ilen;
407   PetscInt   *aj = a->j, nonew = a->nonew, lastcol = -1;
408   MatScalar  *ap = NULL, value = 0.0, *aa;
409   PetscBool   ignorezeroentries = a->ignorezeroentries;
410   PetscBool   roworiented       = a->roworiented;
411 
412   PetscFunctionBegin;
413   PetscCall(MatSeqAIJGetArray(A, &aa));
414   for (k = 0; k < m; k++) { /* loop over added rows */
415     row = im[k];
416     if (row < 0) continue;
417     PetscCheck(row < A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, row, A->rmap->n - 1);
418     rp = PetscSafePointerPlusOffset(aj, ai[row]);
419     if (!A->structure_only) ap = PetscSafePointerPlusOffset(aa, ai[row]);
420     rmax = imax[row];
421     nrow = ailen[row];
422     low  = 0;
423     high = nrow;
424     for (l = 0; l < n; l++) { /* loop over added columns */
425       if (in[l] < 0) continue;
426       PetscCheck(in[l] < A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, in[l], A->cmap->n - 1);
427       col = in[l];
428       if (v && !A->structure_only) value = roworiented ? v[l + k * n] : v[k + l * m];
429       if (!A->structure_only && value == 0.0 && ignorezeroentries && is == ADD_VALUES && row != col) continue;
430 
431       if (col <= lastcol) low = 0;
432       else high = nrow;
433       lastcol = col;
434       while (high - low > 5) {
435         t = (low + high) / 2;
436         if (rp[t] > col) high = t;
437         else low = t;
438       }
439       for (i = low; i < high; i++) {
440         if (rp[i] > col) break;
441         if (rp[i] == col) {
442           if (!A->structure_only) {
443             if (is == ADD_VALUES) {
444               ap[i] += value;
445               (void)PetscLogFlops(1.0);
446             } else ap[i] = value;
447           }
448           low = i + 1;
449           goto noinsert;
450         }
451       }
452       if (value == 0.0 && ignorezeroentries && row != col) goto noinsert;
453       if (nonew == 1) goto noinsert;
454       PetscCheck(nonew != -1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero at (%" PetscInt_FMT ",%" PetscInt_FMT ") in the matrix", row, col);
455       if (A->structure_only) {
456         MatSeqXAIJReallocateAIJ_structure_only(A, A->rmap->n, 1, nrow, row, col, rmax, ai, aj, rp, imax, nonew, MatScalar);
457       } else {
458         MatSeqXAIJReallocateAIJ(A, A->rmap->n, 1, nrow, row, col, rmax, aa, ai, aj, rp, ap, imax, nonew, MatScalar);
459       }
460       N = nrow++ - 1;
461       a->nz++;
462       high++;
463       /* shift up all the later entries in this row */
464       PetscCall(PetscArraymove(rp + i + 1, rp + i, N - i + 1));
465       rp[i] = col;
466       if (!A->structure_only) {
467         PetscCall(PetscArraymove(ap + i + 1, ap + i, N - i + 1));
468         ap[i] = value;
469       }
470       low = i + 1;
471     noinsert:;
472     }
473     ailen[row] = nrow;
474   }
475   PetscCall(MatSeqAIJRestoreArray(A, &aa));
476   PetscFunctionReturn(PETSC_SUCCESS);
477 }
478 
479 static PetscErrorCode MatSetValues_SeqAIJ_SortedFullNoPreallocation(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode is)
480 {
481   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
482   PetscInt   *rp, k, row;
483   PetscInt   *ai = a->i;
484   PetscInt   *aj = a->j;
485   MatScalar  *aa, *ap;
486 
487   PetscFunctionBegin;
488   PetscCheck(!A->was_assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot call on assembled matrix.");
489   PetscCheck(m * n + a->nz <= a->maxnz, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of entries in matrix will be larger than maximum nonzeros allocated for %" PetscInt_FMT " in MatSeqAIJSetTotalPreallocation()", a->maxnz);
490 
491   PetscCall(MatSeqAIJGetArray(A, &aa));
492   for (k = 0; k < m; k++) { /* loop over added rows */
493     row = im[k];
494     rp  = aj + ai[row];
495     ap  = PetscSafePointerPlusOffset(aa, ai[row]);
496 
497     PetscCall(PetscMemcpy(rp, in, n * sizeof(PetscInt)));
498     if (!A->structure_only) {
499       if (v) {
500         PetscCall(PetscMemcpy(ap, v, n * sizeof(PetscScalar)));
501         v += n;
502       } else {
503         PetscCall(PetscMemzero(ap, n * sizeof(PetscScalar)));
504       }
505     }
506     a->ilen[row]  = n;
507     a->imax[row]  = n;
508     a->i[row + 1] = a->i[row] + n;
509     a->nz += n;
510   }
511   PetscCall(MatSeqAIJRestoreArray(A, &aa));
512   PetscFunctionReturn(PETSC_SUCCESS);
513 }
514 
515 /*@
516   MatSeqAIJSetTotalPreallocation - Sets an upper bound on the total number of expected nonzeros in the matrix.
517 
518   Input Parameters:
519 + A       - the `MATSEQAIJ` matrix
520 - nztotal - bound on the number of nonzeros
521 
522   Level: advanced
523 
524   Notes:
525   This can be called if you will be provided the matrix row by row (from row zero) with sorted column indices for each row.
526   Simply call `MatSetValues()` after this call to provide the matrix entries in the usual manner. This matrix may be used
527   as always with multiple matrix assemblies.
528 
529 .seealso: [](ch_matrices), `Mat`, `MatSetOption()`, `MAT_SORTED_FULL`, `MatSetValues()`, `MatSeqAIJSetPreallocation()`
530 @*/
531 PetscErrorCode MatSeqAIJSetTotalPreallocation(Mat A, PetscInt nztotal)
532 {
533   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
534 
535   PetscFunctionBegin;
536   PetscCall(PetscLayoutSetUp(A->rmap));
537   PetscCall(PetscLayoutSetUp(A->cmap));
538   a->maxnz = nztotal;
539   if (!a->imax) { PetscCall(PetscMalloc1(A->rmap->n, &a->imax)); }
540   if (!a->ilen) {
541     PetscCall(PetscMalloc1(A->rmap->n, &a->ilen));
542   } else {
543     PetscCall(PetscMemzero(a->ilen, A->rmap->n * sizeof(PetscInt)));
544   }
545 
546   /* allocate the matrix space */
547   PetscCall(PetscShmgetAllocateArray(A->rmap->n + 1, sizeof(PetscInt), (void **)&a->i));
548   PetscCall(PetscShmgetAllocateArray(nztotal, sizeof(PetscInt), (void **)&a->j));
549   a->free_ij = PETSC_TRUE;
550   if (A->structure_only) {
551     a->free_a = PETSC_FALSE;
552   } else {
553     PetscCall(PetscShmgetAllocateArray(nztotal, sizeof(PetscScalar), (void **)&a->a));
554     a->free_a = PETSC_TRUE;
555   }
556   a->i[0]           = 0;
557   A->ops->setvalues = MatSetValues_SeqAIJ_SortedFullNoPreallocation;
558   A->preallocated   = PETSC_TRUE;
559   PetscFunctionReturn(PETSC_SUCCESS);
560 }
561 
562 static PetscErrorCode MatSetValues_SeqAIJ_SortedFull(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode is)
563 {
564   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
565   PetscInt   *rp, k, row;
566   PetscInt   *ai = a->i, *ailen = a->ilen;
567   PetscInt   *aj = a->j;
568   MatScalar  *aa, *ap;
569 
570   PetscFunctionBegin;
571   PetscCall(MatSeqAIJGetArray(A, &aa));
572   for (k = 0; k < m; k++) { /* loop over added rows */
573     row = im[k];
574     PetscCheck(n <= a->imax[row], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Preallocation for row %" PetscInt_FMT " does not match number of columns provided", n);
575     rp = aj + ai[row];
576     ap = aa + ai[row];
577     if (!A->was_assembled) PetscCall(PetscMemcpy(rp, in, n * sizeof(PetscInt)));
578     if (!A->structure_only) {
579       if (v) {
580         PetscCall(PetscMemcpy(ap, v, n * sizeof(PetscScalar)));
581         v += n;
582       } else {
583         PetscCall(PetscMemzero(ap, n * sizeof(PetscScalar)));
584       }
585     }
586     ailen[row] = n;
587     a->nz += n;
588   }
589   PetscCall(MatSeqAIJRestoreArray(A, &aa));
590   PetscFunctionReturn(PETSC_SUCCESS);
591 }
592 
593 static PetscErrorCode MatGetValues_SeqAIJ(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], PetscScalar v[])
594 {
595   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
596   PetscInt        *rp, k, low, high, t, row, nrow, i, col, l, *aj = a->j;
597   PetscInt        *ai = a->i, *ailen = a->ilen;
598   const MatScalar *ap, *aa;
599 
600   PetscFunctionBegin;
601   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
602   for (k = 0; k < m; k++) { /* loop over rows */
603     row = im[k];
604     if (row < 0) {
605       v += n;
606       continue;
607     } /* negative row */
608     PetscCheck(row < A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, row, A->rmap->n - 1);
609     rp   = PetscSafePointerPlusOffset(aj, ai[row]);
610     ap   = PetscSafePointerPlusOffset(aa, ai[row]);
611     nrow = ailen[row];
612     for (l = 0; l < n; l++) { /* loop over columns */
613       if (in[l] < 0) {
614         v++;
615         continue;
616       } /* negative column */
617       PetscCheck(in[l] < A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, in[l], A->cmap->n - 1);
618       col  = in[l];
619       high = nrow;
620       low  = 0; /* assume unsorted */
621       while (high - low > 5) {
622         t = (low + high) / 2;
623         if (rp[t] > col) high = t;
624         else low = t;
625       }
626       for (i = low; i < high; i++) {
627         if (rp[i] > col) break;
628         if (rp[i] == col) {
629           *v++ = ap[i];
630           goto finished;
631         }
632       }
633       *v++ = 0.0;
634     finished:;
635     }
636   }
637   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
638   PetscFunctionReturn(PETSC_SUCCESS);
639 }
640 
641 static PetscErrorCode MatView_SeqAIJ_Binary(Mat mat, PetscViewer viewer)
642 {
643   Mat_SeqAIJ        *A = (Mat_SeqAIJ *)mat->data;
644   const PetscScalar *av;
645   PetscInt           header[4], M, N, m, nz, i;
646   PetscInt          *rowlens;
647 
648   PetscFunctionBegin;
649   PetscCall(PetscViewerSetUp(viewer));
650 
651   M  = mat->rmap->N;
652   N  = mat->cmap->N;
653   m  = mat->rmap->n;
654   nz = A->nz;
655 
656   /* write matrix header */
657   header[0] = MAT_FILE_CLASSID;
658   header[1] = M;
659   header[2] = N;
660   header[3] = nz;
661   PetscCall(PetscViewerBinaryWrite(viewer, header, 4, PETSC_INT));
662 
663   /* fill in and store row lengths */
664   PetscCall(PetscMalloc1(m, &rowlens));
665   for (i = 0; i < m; i++) rowlens[i] = A->i[i + 1] - A->i[i];
666   if (PetscDefined(USE_DEBUG)) {
667     PetscInt mnz = 0;
668 
669     for (i = 0; i < m; i++) mnz += rowlens[i];
670     PetscCheck(nz == mnz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Row lens %" PetscInt_FMT " do not sum to nz %" PetscInt_FMT, mnz, nz);
671   }
672   PetscCall(PetscViewerBinaryWrite(viewer, rowlens, m, PETSC_INT));
673   PetscCall(PetscFree(rowlens));
674   /* store column indices */
675   PetscCall(PetscViewerBinaryWrite(viewer, A->j, nz, PETSC_INT));
676   /* store nonzero values */
677   PetscCall(MatSeqAIJGetArrayRead(mat, &av));
678   PetscCall(PetscViewerBinaryWrite(viewer, av, nz, PETSC_SCALAR));
679   PetscCall(MatSeqAIJRestoreArrayRead(mat, &av));
680 
681   /* write block size option to the viewer's .info file */
682   PetscCall(MatView_Binary_BlockSizes(mat, viewer));
683   PetscFunctionReturn(PETSC_SUCCESS);
684 }
685 
686 static PetscErrorCode MatView_SeqAIJ_ASCII_structonly(Mat A, PetscViewer viewer)
687 {
688   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
689   PetscInt    i, k, m = A->rmap->N;
690 
691   PetscFunctionBegin;
692   PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
693   for (i = 0; i < m; i++) {
694     PetscCall(PetscViewerASCIIPrintf(viewer, "row %" PetscInt_FMT ":", i));
695     for (k = a->i[i]; k < a->i[i + 1]; k++) PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ") ", a->j[k]));
696     PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
697   }
698   PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
699   PetscFunctionReturn(PETSC_SUCCESS);
700 }
701 
702 static PetscErrorCode MatView_SeqAIJ_ASCII(Mat A, PetscViewer viewer)
703 {
704   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
705   const PetscScalar *av;
706   PetscInt           i, j, m = A->rmap->n;
707   const char        *name;
708   PetscViewerFormat  format;
709 
710   PetscFunctionBegin;
711   if (A->structure_only) {
712     PetscCall(MatView_SeqAIJ_ASCII_structonly(A, viewer));
713     PetscFunctionReturn(PETSC_SUCCESS);
714   }
715 
716   PetscCall(PetscViewerGetFormat(viewer, &format));
717   // By petsc's rule, even PETSC_VIEWER_ASCII_INFO_DETAIL doesn't print matrix entries
718   if (format == PETSC_VIEWER_ASCII_FACTOR_INFO || format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscFunctionReturn(PETSC_SUCCESS);
719 
720   /* trigger copy to CPU if needed */
721   PetscCall(MatSeqAIJGetArrayRead(A, &av));
722   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
723   if (format == PETSC_VIEWER_ASCII_MATLAB) {
724     PetscInt nofinalvalue = 0;
725     if (m && ((a->i[m] == a->i[m - 1]) || (a->j[a->nz - 1] != A->cmap->n - 1))) {
726       /* Need a dummy value to ensure the dimension of the matrix. */
727       nofinalvalue = 1;
728     }
729     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
730     PetscCall(PetscViewerASCIIPrintf(viewer, "%% Size = %" PetscInt_FMT " %" PetscInt_FMT " \n", m, A->cmap->n));
731     PetscCall(PetscViewerASCIIPrintf(viewer, "%% Nonzeros = %" PetscInt_FMT " \n", a->nz));
732 #if defined(PETSC_USE_COMPLEX)
733     PetscCall(PetscViewerASCIIPrintf(viewer, "zzz = zeros(%" PetscInt_FMT ",4);\n", a->nz + nofinalvalue));
734 #else
735     PetscCall(PetscViewerASCIIPrintf(viewer, "zzz = zeros(%" PetscInt_FMT ",3);\n", a->nz + nofinalvalue));
736 #endif
737     PetscCall(PetscViewerASCIIPrintf(viewer, "zzz = [\n"));
738 
739     for (i = 0; i < m; i++) {
740       for (j = a->i[i]; j < a->i[i + 1]; j++) {
741 #if defined(PETSC_USE_COMPLEX)
742         PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e %18.16e\n", i + 1, a->j[j] + 1, (double)PetscRealPart(a->a[j]), (double)PetscImaginaryPart(a->a[j])));
743 #else
744         PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n", i + 1, a->j[j] + 1, (double)a->a[j]));
745 #endif
746       }
747     }
748     if (nofinalvalue) {
749 #if defined(PETSC_USE_COMPLEX)
750       PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e %18.16e\n", m, A->cmap->n, 0., 0.));
751 #else
752       PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n", m, A->cmap->n, 0.0));
753 #endif
754     }
755     PetscCall(PetscObjectGetName((PetscObject)A, &name));
756     PetscCall(PetscViewerASCIIPrintf(viewer, "];\n %s = spconvert(zzz);\n", name));
757     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
758   } else if (format == PETSC_VIEWER_ASCII_COMMON) {
759     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
760     for (i = 0; i < m; i++) {
761       PetscCall(PetscViewerASCIIPrintf(viewer, "row %" PetscInt_FMT ":", i));
762       for (j = a->i[i]; j < a->i[i + 1]; j++) {
763 #if defined(PETSC_USE_COMPLEX)
764         if (PetscImaginaryPart(a->a[j]) > 0.0 && PetscRealPart(a->a[j]) != 0.0) {
765           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)PetscImaginaryPart(a->a[j])));
766         } else if (PetscImaginaryPart(a->a[j]) < 0.0 && PetscRealPart(a->a[j]) != 0.0) {
767           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g - %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)-PetscImaginaryPart(a->a[j])));
768         } else if (PetscRealPart(a->a[j]) != 0.0) {
769           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)PetscRealPart(a->a[j])));
770         }
771 #else
772         if (a->a[j] != 0.0) PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)a->a[j]));
773 #endif
774       }
775       PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
776     }
777     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
778   } else if (format == PETSC_VIEWER_ASCII_SYMMODU) {
779     PetscInt nzd = 0, fshift = 1, *sptr;
780     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
781     PetscCall(PetscMalloc1(m + 1, &sptr));
782     for (i = 0; i < m; i++) {
783       sptr[i] = nzd + 1;
784       for (j = a->i[i]; j < a->i[i + 1]; j++) {
785         if (a->j[j] >= i) {
786 #if defined(PETSC_USE_COMPLEX)
787           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) nzd++;
788 #else
789           if (a->a[j] != 0.0) nzd++;
790 #endif
791         }
792       }
793     }
794     sptr[m] = nzd + 1;
795     PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " %" PetscInt_FMT "\n\n", m, nzd));
796     for (i = 0; i < m + 1; i += 6) {
797       if (i + 4 < m) {
798         PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n", sptr[i], sptr[i + 1], sptr[i + 2], sptr[i + 3], sptr[i + 4], sptr[i + 5]));
799       } else if (i + 3 < m) {
800         PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n", sptr[i], sptr[i + 1], sptr[i + 2], sptr[i + 3], sptr[i + 4]));
801       } else if (i + 2 < m) {
802         PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n", sptr[i], sptr[i + 1], sptr[i + 2], sptr[i + 3]));
803       } else if (i + 1 < m) {
804         PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n", sptr[i], sptr[i + 1], sptr[i + 2]));
805       } else if (i < m) {
806         PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " %" PetscInt_FMT "\n", sptr[i], sptr[i + 1]));
807       } else {
808         PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT "\n", sptr[i]));
809       }
810     }
811     PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
812     PetscCall(PetscFree(sptr));
813     for (i = 0; i < m; i++) {
814       for (j = a->i[i]; j < a->i[i + 1]; j++) {
815         if (a->j[j] >= i) PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " ", a->j[j] + fshift));
816       }
817       PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
818     }
819     PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
820     for (i = 0; i < m; i++) {
821       for (j = a->i[i]; j < a->i[i + 1]; j++) {
822         if (a->j[j] >= i) {
823 #if defined(PETSC_USE_COMPLEX)
824           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) PetscCall(PetscViewerASCIIPrintf(viewer, " %18.16e %18.16e ", (double)PetscRealPart(a->a[j]), (double)PetscImaginaryPart(a->a[j])));
825 #else
826           if (a->a[j] != 0.0) PetscCall(PetscViewerASCIIPrintf(viewer, " %18.16e ", (double)a->a[j]));
827 #endif
828         }
829       }
830       PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
831     }
832     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
833   } else if (format == PETSC_VIEWER_ASCII_DENSE) {
834     PetscInt    cnt = 0, jcnt;
835     PetscScalar value;
836 #if defined(PETSC_USE_COMPLEX)
837     PetscBool realonly = PETSC_TRUE;
838 
839     for (i = 0; i < a->i[m]; i++) {
840       if (PetscImaginaryPart(a->a[i]) != 0.0) {
841         realonly = PETSC_FALSE;
842         break;
843       }
844     }
845 #endif
846 
847     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
848     for (i = 0; i < m; i++) {
849       jcnt = 0;
850       for (j = 0; j < A->cmap->n; j++) {
851         if (jcnt < a->i[i + 1] - a->i[i] && j == a->j[cnt]) {
852           value = a->a[cnt++];
853           jcnt++;
854         } else {
855           value = 0.0;
856         }
857 #if defined(PETSC_USE_COMPLEX)
858         if (realonly) {
859           PetscCall(PetscViewerASCIIPrintf(viewer, " %7.5e ", (double)PetscRealPart(value)));
860         } else {
861           PetscCall(PetscViewerASCIIPrintf(viewer, " %7.5e+%7.5e i ", (double)PetscRealPart(value), (double)PetscImaginaryPart(value)));
862         }
863 #else
864         PetscCall(PetscViewerASCIIPrintf(viewer, " %7.5e ", (double)value));
865 #endif
866       }
867       PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
868     }
869     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
870   } else if (format == PETSC_VIEWER_ASCII_MATRIXMARKET) {
871     PetscInt fshift = 1;
872     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
873 #if defined(PETSC_USE_COMPLEX)
874     PetscCall(PetscViewerASCIIPrintf(viewer, "%%%%MatrixMarket matrix coordinate complex general\n"));
875 #else
876     PetscCall(PetscViewerASCIIPrintf(viewer, "%%%%MatrixMarket matrix coordinate real general\n"));
877 #endif
878     PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n", m, A->cmap->n, a->nz));
879     for (i = 0; i < m; i++) {
880       for (j = a->i[i]; j < a->i[i + 1]; j++) {
881 #if defined(PETSC_USE_COMPLEX)
882         PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " %" PetscInt_FMT " %g %g\n", i + fshift, a->j[j] + fshift, (double)PetscRealPart(a->a[j]), (double)PetscImaginaryPart(a->a[j])));
883 #else
884         PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " %" PetscInt_FMT " %g\n", i + fshift, a->j[j] + fshift, (double)a->a[j]));
885 #endif
886       }
887     }
888     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
889   } else {
890     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
891     if (A->factortype) {
892       for (i = 0; i < m; i++) {
893         PetscCall(PetscViewerASCIIPrintf(viewer, "row %" PetscInt_FMT ":", i));
894         /* L part */
895         for (j = a->i[i]; j < a->i[i + 1]; j++) {
896 #if defined(PETSC_USE_COMPLEX)
897           if (PetscImaginaryPart(a->a[j]) > 0.0) {
898             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)PetscImaginaryPart(a->a[j])));
899           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
900             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g - %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)(-PetscImaginaryPart(a->a[j]))));
901           } else {
902             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)PetscRealPart(a->a[j])));
903           }
904 #else
905           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)a->a[j]));
906 #endif
907         }
908         /* diagonal */
909         j = a->diag[i];
910 #if defined(PETSC_USE_COMPLEX)
911         if (PetscImaginaryPart(a->a[j]) > 0.0) {
912           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %g i)", a->j[j], (double)PetscRealPart(1 / a->a[j]), (double)PetscImaginaryPart(1 / a->a[j])));
913         } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
914           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g - %g i)", a->j[j], (double)PetscRealPart(1 / a->a[j]), (double)(-PetscImaginaryPart(1 / a->a[j]))));
915         } else {
916           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)PetscRealPart(1 / a->a[j])));
917         }
918 #else
919         PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)(1 / a->a[j])));
920 #endif
921 
922         /* U part */
923         for (j = a->diag[i + 1] + 1; j < a->diag[i]; j++) {
924 #if defined(PETSC_USE_COMPLEX)
925           if (PetscImaginaryPart(a->a[j]) > 0.0) {
926             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)PetscImaginaryPart(a->a[j])));
927           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
928             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g - %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)(-PetscImaginaryPart(a->a[j]))));
929           } else {
930             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)PetscRealPart(a->a[j])));
931           }
932 #else
933           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)a->a[j]));
934 #endif
935         }
936         PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
937       }
938     } else {
939       for (i = 0; i < m; i++) {
940         PetscCall(PetscViewerASCIIPrintf(viewer, "row %" PetscInt_FMT ":", i));
941         for (j = a->i[i]; j < a->i[i + 1]; j++) {
942 #if defined(PETSC_USE_COMPLEX)
943           if (PetscImaginaryPart(a->a[j]) > 0.0) {
944             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)PetscImaginaryPart(a->a[j])));
945           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
946             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g - %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)-PetscImaginaryPart(a->a[j])));
947           } else {
948             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)PetscRealPart(a->a[j])));
949           }
950 #else
951           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)a->a[j]));
952 #endif
953         }
954         PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
955       }
956     }
957     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
958   }
959   PetscCall(PetscViewerFlush(viewer));
960   PetscFunctionReturn(PETSC_SUCCESS);
961 }
962 
963 #include <petscdraw.h>
964 static PetscErrorCode MatView_SeqAIJ_Draw_Zoom(PetscDraw draw, void *Aa)
965 {
966   Mat                A = (Mat)Aa;
967   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
968   PetscInt           i, j, m = A->rmap->n;
969   int                color;
970   PetscReal          xl, yl, xr, yr, x_l, x_r, y_l, y_r;
971   PetscViewer        viewer;
972   PetscViewerFormat  format;
973   const PetscScalar *aa;
974 
975   PetscFunctionBegin;
976   PetscCall(PetscObjectQuery((PetscObject)A, "Zoomviewer", (PetscObject *)&viewer));
977   PetscCall(PetscViewerGetFormat(viewer, &format));
978   PetscCall(PetscDrawGetCoordinates(draw, &xl, &yl, &xr, &yr));
979 
980   /* loop over matrix elements drawing boxes */
981   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
982   if (format != PETSC_VIEWER_DRAW_CONTOUR) {
983     PetscDrawCollectiveBegin(draw);
984     /* Blue for negative, Cyan for zero and  Red for positive */
985     color = PETSC_DRAW_BLUE;
986     for (i = 0; i < m; i++) {
987       y_l = m - i - 1.0;
988       y_r = y_l + 1.0;
989       for (j = a->i[i]; j < a->i[i + 1]; j++) {
990         x_l = a->j[j];
991         x_r = x_l + 1.0;
992         if (PetscRealPart(aa[j]) >= 0.) continue;
993         PetscCall(PetscDrawRectangle(draw, x_l, y_l, x_r, y_r, color, color, color, color));
994       }
995     }
996     color = PETSC_DRAW_CYAN;
997     for (i = 0; i < m; i++) {
998       y_l = m - i - 1.0;
999       y_r = y_l + 1.0;
1000       for (j = a->i[i]; j < a->i[i + 1]; j++) {
1001         x_l = a->j[j];
1002         x_r = x_l + 1.0;
1003         if (aa[j] != 0.) continue;
1004         PetscCall(PetscDrawRectangle(draw, x_l, y_l, x_r, y_r, color, color, color, color));
1005       }
1006     }
1007     color = PETSC_DRAW_RED;
1008     for (i = 0; i < m; i++) {
1009       y_l = m - i - 1.0;
1010       y_r = y_l + 1.0;
1011       for (j = a->i[i]; j < a->i[i + 1]; j++) {
1012         x_l = a->j[j];
1013         x_r = x_l + 1.0;
1014         if (PetscRealPart(aa[j]) <= 0.) continue;
1015         PetscCall(PetscDrawRectangle(draw, x_l, y_l, x_r, y_r, color, color, color, color));
1016       }
1017     }
1018     PetscDrawCollectiveEnd(draw);
1019   } else {
1020     /* use contour shading to indicate magnitude of values */
1021     /* first determine max of all nonzero values */
1022     PetscReal minv = 0.0, maxv = 0.0;
1023     PetscInt  nz = a->nz, count = 0;
1024     PetscDraw popup;
1025 
1026     for (i = 0; i < nz; i++) {
1027       if (PetscAbsScalar(aa[i]) > maxv) maxv = PetscAbsScalar(aa[i]);
1028     }
1029     if (minv >= maxv) maxv = minv + PETSC_SMALL;
1030     PetscCall(PetscDrawGetPopup(draw, &popup));
1031     PetscCall(PetscDrawScalePopup(popup, minv, maxv));
1032 
1033     PetscDrawCollectiveBegin(draw);
1034     for (i = 0; i < m; i++) {
1035       y_l = m - i - 1.0;
1036       y_r = y_l + 1.0;
1037       for (j = a->i[i]; j < a->i[i + 1]; j++) {
1038         x_l   = a->j[j];
1039         x_r   = x_l + 1.0;
1040         color = PetscDrawRealToColor(PetscAbsScalar(aa[count]), minv, maxv);
1041         PetscCall(PetscDrawRectangle(draw, x_l, y_l, x_r, y_r, color, color, color, color));
1042         count++;
1043       }
1044     }
1045     PetscDrawCollectiveEnd(draw);
1046   }
1047   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
1048   PetscFunctionReturn(PETSC_SUCCESS);
1049 }
1050 
1051 #include <petscdraw.h>
1052 static PetscErrorCode MatView_SeqAIJ_Draw(Mat A, PetscViewer viewer)
1053 {
1054   PetscDraw draw;
1055   PetscReal xr, yr, xl, yl, h, w;
1056   PetscBool isnull;
1057 
1058   PetscFunctionBegin;
1059   PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
1060   PetscCall(PetscDrawIsNull(draw, &isnull));
1061   if (isnull) PetscFunctionReturn(PETSC_SUCCESS);
1062 
1063   xr = A->cmap->n;
1064   yr = A->rmap->n;
1065   h  = yr / 10.0;
1066   w  = xr / 10.0;
1067   xr += w;
1068   yr += h;
1069   xl = -w;
1070   yl = -h;
1071   PetscCall(PetscDrawSetCoordinates(draw, xl, yl, xr, yr));
1072   PetscCall(PetscObjectCompose((PetscObject)A, "Zoomviewer", (PetscObject)viewer));
1073   PetscCall(PetscDrawZoom(draw, MatView_SeqAIJ_Draw_Zoom, A));
1074   PetscCall(PetscObjectCompose((PetscObject)A, "Zoomviewer", NULL));
1075   PetscCall(PetscDrawSave(draw));
1076   PetscFunctionReturn(PETSC_SUCCESS);
1077 }
1078 
1079 PetscErrorCode MatView_SeqAIJ(Mat A, PetscViewer viewer)
1080 {
1081   PetscBool iascii, isbinary, isdraw;
1082 
1083   PetscFunctionBegin;
1084   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1085   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
1086   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
1087   if (iascii) PetscCall(MatView_SeqAIJ_ASCII(A, viewer));
1088   else if (isbinary) PetscCall(MatView_SeqAIJ_Binary(A, viewer));
1089   else if (isdraw) PetscCall(MatView_SeqAIJ_Draw(A, viewer));
1090   PetscCall(MatView_SeqAIJ_Inode(A, viewer));
1091   PetscFunctionReturn(PETSC_SUCCESS);
1092 }
1093 
1094 PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat A, MatAssemblyType mode)
1095 {
1096   Mat_SeqAIJ *a      = (Mat_SeqAIJ *)A->data;
1097   PetscInt    fshift = 0, i, *ai = a->i, *aj = a->j, *imax = a->imax;
1098   PetscInt    m = A->rmap->n, *ip, N, *ailen = a->ilen, rmax = 0, n;
1099   MatScalar  *aa    = a->a, *ap;
1100   PetscReal   ratio = 0.6;
1101 
1102   PetscFunctionBegin;
1103   if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(PETSC_SUCCESS);
1104   PetscCall(MatSeqAIJInvalidateDiagonal(A));
1105   if (A->was_assembled && A->ass_nonzerostate == A->nonzerostate) {
1106     /* we need to respect users asking to use or not the inodes routine in between matrix assemblies */
1107     PetscCall(MatAssemblyEnd_SeqAIJ_Inode(A, mode));
1108     PetscFunctionReturn(PETSC_SUCCESS);
1109   }
1110 
1111   if (m) rmax = ailen[0]; /* determine row with most nonzeros */
1112   for (i = 1; i < m; i++) {
1113     /* move each row back by the amount of empty slots (fshift) before it*/
1114     fshift += imax[i - 1] - ailen[i - 1];
1115     rmax = PetscMax(rmax, ailen[i]);
1116     if (fshift) {
1117       ip = aj + ai[i];
1118       ap = aa + ai[i];
1119       N  = ailen[i];
1120       PetscCall(PetscArraymove(ip - fshift, ip, N));
1121       if (!A->structure_only) PetscCall(PetscArraymove(ap - fshift, ap, N));
1122     }
1123     ai[i] = ai[i - 1] + ailen[i - 1];
1124   }
1125   if (m) {
1126     fshift += imax[m - 1] - ailen[m - 1];
1127     ai[m] = ai[m - 1] + ailen[m - 1];
1128   }
1129   /* reset ilen and imax for each row */
1130   a->nonzerorowcnt = 0;
1131   if (A->structure_only) {
1132     PetscCall(PetscFree(a->imax));
1133     PetscCall(PetscFree(a->ilen));
1134   } else { /* !A->structure_only */
1135     for (i = 0; i < m; i++) {
1136       ailen[i] = imax[i] = ai[i + 1] - ai[i];
1137       a->nonzerorowcnt += ((ai[i + 1] - ai[i]) > 0);
1138     }
1139   }
1140   a->nz = ai[m];
1141   PetscCheck(!fshift || a->nounused != -1, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unused space detected in matrix: %" PetscInt_FMT " X %" PetscInt_FMT ", %" PetscInt_FMT " unneeded", m, A->cmap->n, fshift);
1142   PetscCall(MatMarkDiagonal_SeqAIJ(A)); // since diagonal info is used a lot, it is helpful to set them up at the end of assembly
1143   a->diagonaldense = PETSC_TRUE;
1144   n                = PetscMin(A->rmap->n, A->cmap->n);
1145   for (i = 0; i < n; i++) {
1146     if (a->diag[i] >= ai[i + 1]) {
1147       a->diagonaldense = PETSC_FALSE;
1148       break;
1149     }
1150   }
1151   PetscCall(PetscInfo(A, "Matrix size: %" PetscInt_FMT " X %" PetscInt_FMT "; storage space: %" PetscInt_FMT " unneeded,%" PetscInt_FMT " used\n", m, A->cmap->n, fshift, a->nz));
1152   PetscCall(PetscInfo(A, "Number of mallocs during MatSetValues() is %" PetscInt_FMT "\n", a->reallocs));
1153   PetscCall(PetscInfo(A, "Maximum nonzeros in any row is %" PetscInt_FMT "\n", rmax));
1154 
1155   A->info.mallocs += a->reallocs;
1156   a->reallocs         = 0;
1157   A->info.nz_unneeded = (PetscReal)fshift;
1158   a->rmax             = rmax;
1159 
1160   if (!A->structure_only) PetscCall(MatCheckCompressedRow(A, a->nonzerorowcnt, &a->compressedrow, a->i, m, ratio));
1161   PetscCall(MatAssemblyEnd_SeqAIJ_Inode(A, mode));
1162   PetscFunctionReturn(PETSC_SUCCESS);
1163 }
1164 
1165 static PetscErrorCode MatRealPart_SeqAIJ(Mat A)
1166 {
1167   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1168   PetscInt    i, nz = a->nz;
1169   MatScalar  *aa;
1170 
1171   PetscFunctionBegin;
1172   PetscCall(MatSeqAIJGetArray(A, &aa));
1173   for (i = 0; i < nz; i++) aa[i] = PetscRealPart(aa[i]);
1174   PetscCall(MatSeqAIJRestoreArray(A, &aa));
1175   PetscCall(MatSeqAIJInvalidateDiagonal(A));
1176   PetscFunctionReturn(PETSC_SUCCESS);
1177 }
1178 
1179 static PetscErrorCode MatImaginaryPart_SeqAIJ(Mat A)
1180 {
1181   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1182   PetscInt    i, nz = a->nz;
1183   MatScalar  *aa;
1184 
1185   PetscFunctionBegin;
1186   PetscCall(MatSeqAIJGetArray(A, &aa));
1187   for (i = 0; i < nz; i++) aa[i] = PetscImaginaryPart(aa[i]);
1188   PetscCall(MatSeqAIJRestoreArray(A, &aa));
1189   PetscCall(MatSeqAIJInvalidateDiagonal(A));
1190   PetscFunctionReturn(PETSC_SUCCESS);
1191 }
1192 
1193 PetscErrorCode MatZeroEntries_SeqAIJ(Mat A)
1194 {
1195   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1196   MatScalar  *aa;
1197 
1198   PetscFunctionBegin;
1199   PetscCall(MatSeqAIJGetArrayWrite(A, &aa));
1200   PetscCall(PetscArrayzero(aa, a->i[A->rmap->n]));
1201   PetscCall(MatSeqAIJRestoreArrayWrite(A, &aa));
1202   PetscCall(MatSeqAIJInvalidateDiagonal(A));
1203   PetscFunctionReturn(PETSC_SUCCESS);
1204 }
1205 
1206 static PetscErrorCode MatReset_SeqAIJ(Mat A)
1207 {
1208   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1209 
1210   PetscFunctionBegin;
1211   if (A->hash_active) {
1212     A->ops[0] = a->cops;
1213     PetscCall(PetscHMapIJVDestroy(&a->ht));
1214     PetscCall(PetscFree(a->dnz));
1215     A->hash_active = PETSC_FALSE;
1216   }
1217 
1218   PetscCall(PetscLogObjectState((PetscObject)A, "Rows=%" PetscInt_FMT ", Cols=%" PetscInt_FMT ", NZ=%" PetscInt_FMT, A->rmap->n, A->cmap->n, a->nz));
1219   PetscCall(MatSeqXAIJFreeAIJ(A, &a->a, &a->j, &a->i));
1220   PetscCall(ISDestroy(&a->row));
1221   PetscCall(ISDestroy(&a->col));
1222   PetscCall(PetscFree(a->diag));
1223   PetscCall(PetscFree(a->ibdiag));
1224   PetscCall(PetscFree(a->imax));
1225   PetscCall(PetscFree(a->ilen));
1226   PetscCall(PetscFree(a->ipre));
1227   PetscCall(PetscFree3(a->idiag, a->mdiag, a->ssor_work));
1228   PetscCall(PetscFree(a->solve_work));
1229   PetscCall(ISDestroy(&a->icol));
1230   PetscCall(PetscFree(a->saved_values));
1231   PetscCall(PetscFree2(a->compressedrow.i, a->compressedrow.rindex));
1232   PetscCall(MatDestroy_SeqAIJ_Inode(A));
1233   PetscFunctionReturn(PETSC_SUCCESS);
1234 }
1235 
1236 static PetscErrorCode MatResetHash_SeqAIJ(Mat A)
1237 {
1238   PetscFunctionBegin;
1239   PetscCall(MatReset_SeqAIJ(A));
1240   PetscCall(MatCreate_SeqAIJ_Inode(A));
1241   PetscCall(MatSetUp_Seq_Hash(A));
1242   A->nonzerostate++;
1243   PetscFunctionReturn(PETSC_SUCCESS);
1244 }
1245 
1246 PetscErrorCode MatDestroy_SeqAIJ(Mat A)
1247 {
1248   PetscFunctionBegin;
1249   PetscCall(MatReset_SeqAIJ(A));
1250   PetscCall(PetscFree(A->data));
1251 
1252   /* MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted may allocate this.
1253      That function is so heavily used (sometimes in an hidden way through multnumeric function pointers)
1254      that is hard to properly add this data to the MatProduct data. We free it here to avoid
1255      users reusing the matrix object with different data to incur in obscure segmentation faults
1256      due to different matrix sizes */
1257   PetscCall(PetscObjectCompose((PetscObject)A, "__PETSc__ab_dense", NULL));
1258 
1259   PetscCall(PetscObjectChangeTypeName((PetscObject)A, NULL));
1260   PetscCall(PetscObjectComposeFunction((PetscObject)A, "PetscMatlabEnginePut_C", NULL));
1261   PetscCall(PetscObjectComposeFunction((PetscObject)A, "PetscMatlabEngineGet_C", NULL));
1262   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJSetColumnIndices_C", NULL));
1263   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatStoreValues_C", NULL));
1264   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatRetrieveValues_C", NULL));
1265   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqsbaij_C", NULL));
1266   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqbaij_C", NULL));
1267   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijperm_C", NULL));
1268   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijsell_C", NULL));
1269 #if defined(PETSC_HAVE_MKL_SPARSE)
1270   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijmkl_C", NULL));
1271 #endif
1272 #if defined(PETSC_HAVE_CUDA)
1273   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijcusparse_C", NULL));
1274   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaij_C", NULL));
1275   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaij_seqaijcusparse_C", NULL));
1276 #endif
1277 #if defined(PETSC_HAVE_HIP)
1278   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijhipsparse_C", NULL));
1279   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijhipsparse_seqaij_C", NULL));
1280   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaij_seqaijhipsparse_C", NULL));
1281 #endif
1282 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
1283   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijkokkos_C", NULL));
1284 #endif
1285   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijcrl_C", NULL));
1286 #if defined(PETSC_HAVE_ELEMENTAL)
1287   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_elemental_C", NULL));
1288 #endif
1289 #if defined(PETSC_HAVE_SCALAPACK)
1290   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_scalapack_C", NULL));
1291 #endif
1292 #if defined(PETSC_HAVE_HYPRE)
1293   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_hypre_C", NULL));
1294   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_transpose_seqaij_seqaij_C", NULL));
1295 #endif
1296   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqdense_C", NULL));
1297   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqsell_C", NULL));
1298   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_is_C", NULL));
1299   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatIsTranspose_C", NULL));
1300   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatIsHermitianTranspose_C", NULL));
1301   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJSetPreallocation_C", NULL));
1302   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatResetPreallocation_C", NULL));
1303   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatResetHash_C", NULL));
1304   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJSetPreallocationCSR_C", NULL));
1305   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatReorderForNonzeroDiagonal_C", NULL));
1306   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_is_seqaij_C", NULL));
1307   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqdense_seqaij_C", NULL));
1308   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaij_seqaij_C", NULL));
1309   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJKron_C", NULL));
1310   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", NULL));
1311   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", NULL));
1312   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
1313   /* these calls do not belong here: the subclasses Duplicate/Destroy are wrong */
1314   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaijsell_seqaij_C", NULL));
1315   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaijperm_seqaij_C", NULL));
1316   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijviennacl_C", NULL));
1317   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijviennacl_seqdense_C", NULL));
1318   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijviennacl_seqaij_C", NULL));
1319   PetscFunctionReturn(PETSC_SUCCESS);
1320 }
1321 
1322 PetscErrorCode MatSetOption_SeqAIJ(Mat A, MatOption op, PetscBool flg)
1323 {
1324   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1325 
1326   PetscFunctionBegin;
1327   switch (op) {
1328   case MAT_ROW_ORIENTED:
1329     a->roworiented = flg;
1330     break;
1331   case MAT_KEEP_NONZERO_PATTERN:
1332     a->keepnonzeropattern = flg;
1333     break;
1334   case MAT_NEW_NONZERO_LOCATIONS:
1335     a->nonew = (flg ? 0 : 1);
1336     break;
1337   case MAT_NEW_NONZERO_LOCATION_ERR:
1338     a->nonew = (flg ? -1 : 0);
1339     break;
1340   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1341     a->nonew = (flg ? -2 : 0);
1342     break;
1343   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1344     a->nounused = (flg ? -1 : 0);
1345     break;
1346   case MAT_IGNORE_ZERO_ENTRIES:
1347     a->ignorezeroentries = flg;
1348     break;
1349   case MAT_USE_INODES:
1350     PetscCall(MatSetOption_SeqAIJ_Inode(A, MAT_USE_INODES, flg));
1351     break;
1352   case MAT_SUBMAT_SINGLEIS:
1353     A->submat_singleis = flg;
1354     break;
1355   case MAT_SORTED_FULL:
1356     if (flg) A->ops->setvalues = MatSetValues_SeqAIJ_SortedFull;
1357     else A->ops->setvalues = MatSetValues_SeqAIJ;
1358     break;
1359   case MAT_FORM_EXPLICIT_TRANSPOSE:
1360     A->form_explicit_transpose = flg;
1361     break;
1362   default:
1363     break;
1364   }
1365   PetscFunctionReturn(PETSC_SUCCESS);
1366 }
1367 
1368 static PetscErrorCode MatGetDiagonal_SeqAIJ(Mat A, Vec v)
1369 {
1370   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1371   PetscInt           i, j, n, *ai = a->i, *aj = a->j;
1372   PetscScalar       *x;
1373   const PetscScalar *aa;
1374 
1375   PetscFunctionBegin;
1376   PetscCall(VecGetLocalSize(v, &n));
1377   PetscCheck(n == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
1378   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
1379   if (A->factortype == MAT_FACTOR_ILU || A->factortype == MAT_FACTOR_LU) {
1380     PetscInt *diag = a->diag;
1381     PetscCall(VecGetArrayWrite(v, &x));
1382     for (i = 0; i < n; i++) x[i] = 1.0 / aa[diag[i]];
1383     PetscCall(VecRestoreArrayWrite(v, &x));
1384     PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
1385     PetscFunctionReturn(PETSC_SUCCESS);
1386   }
1387 
1388   PetscCall(VecGetArrayWrite(v, &x));
1389   for (i = 0; i < n; i++) {
1390     x[i] = 0.0;
1391     for (j = ai[i]; j < ai[i + 1]; j++) {
1392       if (aj[j] == i) {
1393         x[i] = aa[j];
1394         break;
1395       }
1396     }
1397   }
1398   PetscCall(VecRestoreArrayWrite(v, &x));
1399   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
1400   PetscFunctionReturn(PETSC_SUCCESS);
1401 }
1402 
1403 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1404 PetscErrorCode MatMultTransposeAdd_SeqAIJ(Mat A, Vec xx, Vec zz, Vec yy)
1405 {
1406   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1407   const MatScalar   *aa;
1408   PetscScalar       *y;
1409   const PetscScalar *x;
1410   PetscInt           m = A->rmap->n;
1411 #if !defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1412   const MatScalar  *v;
1413   PetscScalar       alpha;
1414   PetscInt          n, i, j;
1415   const PetscInt   *idx, *ii, *ridx = NULL;
1416   Mat_CompressedRow cprow    = a->compressedrow;
1417   PetscBool         usecprow = cprow.use;
1418 #endif
1419 
1420   PetscFunctionBegin;
1421   if (zz != yy) PetscCall(VecCopy(zz, yy));
1422   PetscCall(VecGetArrayRead(xx, &x));
1423   PetscCall(VecGetArray(yy, &y));
1424   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
1425 
1426 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1427   fortranmulttransposeaddaij_(&m, x, a->i, a->j, aa, y);
1428 #else
1429   if (usecprow) {
1430     m    = cprow.nrows;
1431     ii   = cprow.i;
1432     ridx = cprow.rindex;
1433   } else {
1434     ii = a->i;
1435   }
1436   for (i = 0; i < m; i++) {
1437     idx = a->j + ii[i];
1438     v   = aa + ii[i];
1439     n   = ii[i + 1] - ii[i];
1440     if (usecprow) {
1441       alpha = x[ridx[i]];
1442     } else {
1443       alpha = x[i];
1444     }
1445     for (j = 0; j < n; j++) y[idx[j]] += alpha * v[j];
1446   }
1447 #endif
1448   PetscCall(PetscLogFlops(2.0 * a->nz));
1449   PetscCall(VecRestoreArrayRead(xx, &x));
1450   PetscCall(VecRestoreArray(yy, &y));
1451   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
1452   PetscFunctionReturn(PETSC_SUCCESS);
1453 }
1454 
1455 PetscErrorCode MatMultTranspose_SeqAIJ(Mat A, Vec xx, Vec yy)
1456 {
1457   PetscFunctionBegin;
1458   PetscCall(VecSet(yy, 0.0));
1459   PetscCall(MatMultTransposeAdd_SeqAIJ(A, xx, yy, yy));
1460   PetscFunctionReturn(PETSC_SUCCESS);
1461 }
1462 
1463 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1464 
1465 PetscErrorCode MatMult_SeqAIJ(Mat A, Vec xx, Vec yy)
1466 {
1467   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1468   PetscScalar       *y;
1469   const PetscScalar *x;
1470   const MatScalar   *a_a;
1471   PetscInt           m = A->rmap->n;
1472   const PetscInt    *ii, *ridx = NULL;
1473   PetscBool          usecprow = a->compressedrow.use;
1474 
1475 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1476   #pragma disjoint(*x, *y, *aa)
1477 #endif
1478 
1479   PetscFunctionBegin;
1480   if (a->inode.use && a->inode.checked) {
1481     PetscCall(MatMult_SeqAIJ_Inode(A, xx, yy));
1482     PetscFunctionReturn(PETSC_SUCCESS);
1483   }
1484   PetscCall(MatSeqAIJGetArrayRead(A, &a_a));
1485   PetscCall(VecGetArrayRead(xx, &x));
1486   PetscCall(VecGetArray(yy, &y));
1487   ii = a->i;
1488   if (usecprow) { /* use compressed row format */
1489     PetscCall(PetscArrayzero(y, m));
1490     m    = a->compressedrow.nrows;
1491     ii   = a->compressedrow.i;
1492     ridx = a->compressedrow.rindex;
1493     PetscPragmaUseOMPKernels(parallel for)
1494     for (PetscInt i = 0; i < m; i++) {
1495       PetscInt           n   = ii[i + 1] - ii[i];
1496       const PetscInt    *aj  = a->j + ii[i];
1497       const PetscScalar *aa  = a_a + ii[i];
1498       PetscScalar        sum = 0.0;
1499       PetscSparseDensePlusDot(sum, x, aa, aj, n);
1500       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1501       y[ridx[i]] = sum;
1502     }
1503   } else { /* do not use compressed row format */
1504 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJ)
1505     fortranmultaij_(&m, x, ii, a->j, a_a, y);
1506 #else
1507     PetscPragmaUseOMPKernels(parallel for)
1508     for (PetscInt i = 0; i < m; i++) {
1509       PetscInt           n   = ii[i + 1] - ii[i];
1510       const PetscInt    *aj  = a->j + ii[i];
1511       const PetscScalar *aa  = a_a + ii[i];
1512       PetscScalar        sum = 0.0;
1513       PetscSparseDensePlusDot(sum, x, aa, aj, n);
1514       y[i] = sum;
1515     }
1516 #endif
1517   }
1518   PetscCall(PetscLogFlops(2.0 * a->nz - a->nonzerorowcnt));
1519   PetscCall(VecRestoreArrayRead(xx, &x));
1520   PetscCall(VecRestoreArray(yy, &y));
1521   PetscCall(MatSeqAIJRestoreArrayRead(A, &a_a));
1522   PetscFunctionReturn(PETSC_SUCCESS);
1523 }
1524 
1525 // HACK!!!!! Used by src/mat/tests/ex170.c
1526 PETSC_EXTERN PetscErrorCode MatMultMax_SeqAIJ(Mat A, Vec xx, Vec yy)
1527 {
1528   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1529   PetscScalar       *y;
1530   const PetscScalar *x;
1531   const MatScalar   *aa, *a_a;
1532   PetscInt           m = A->rmap->n;
1533   const PetscInt    *aj, *ii, *ridx   = NULL;
1534   PetscInt           n, i, nonzerorow = 0;
1535   PetscScalar        sum;
1536   PetscBool          usecprow = a->compressedrow.use;
1537 
1538 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1539   #pragma disjoint(*x, *y, *aa)
1540 #endif
1541 
1542   PetscFunctionBegin;
1543   PetscCall(MatSeqAIJGetArrayRead(A, &a_a));
1544   PetscCall(VecGetArrayRead(xx, &x));
1545   PetscCall(VecGetArray(yy, &y));
1546   if (usecprow) { /* use compressed row format */
1547     m    = a->compressedrow.nrows;
1548     ii   = a->compressedrow.i;
1549     ridx = a->compressedrow.rindex;
1550     for (i = 0; i < m; i++) {
1551       n   = ii[i + 1] - ii[i];
1552       aj  = a->j + ii[i];
1553       aa  = a_a + ii[i];
1554       sum = 0.0;
1555       nonzerorow += (n > 0);
1556       PetscSparseDenseMaxDot(sum, x, aa, aj, n);
1557       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1558       y[*ridx++] = sum;
1559     }
1560   } else { /* do not use compressed row format */
1561     ii = a->i;
1562     for (i = 0; i < m; i++) {
1563       n   = ii[i + 1] - ii[i];
1564       aj  = a->j + ii[i];
1565       aa  = a_a + ii[i];
1566       sum = 0.0;
1567       nonzerorow += (n > 0);
1568       PetscSparseDenseMaxDot(sum, x, aa, aj, n);
1569       y[i] = sum;
1570     }
1571   }
1572   PetscCall(PetscLogFlops(2.0 * a->nz - nonzerorow));
1573   PetscCall(VecRestoreArrayRead(xx, &x));
1574   PetscCall(VecRestoreArray(yy, &y));
1575   PetscCall(MatSeqAIJRestoreArrayRead(A, &a_a));
1576   PetscFunctionReturn(PETSC_SUCCESS);
1577 }
1578 
1579 // HACK!!!!! Used by src/mat/tests/ex170.c
1580 PETSC_EXTERN PetscErrorCode MatMultAddMax_SeqAIJ(Mat A, Vec xx, Vec yy, Vec zz)
1581 {
1582   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1583   PetscScalar       *y, *z;
1584   const PetscScalar *x;
1585   const MatScalar   *aa, *a_a;
1586   PetscInt           m = A->rmap->n, *aj, *ii;
1587   PetscInt           n, i, *ridx = NULL;
1588   PetscScalar        sum;
1589   PetscBool          usecprow = a->compressedrow.use;
1590 
1591   PetscFunctionBegin;
1592   PetscCall(MatSeqAIJGetArrayRead(A, &a_a));
1593   PetscCall(VecGetArrayRead(xx, &x));
1594   PetscCall(VecGetArrayPair(yy, zz, &y, &z));
1595   if (usecprow) { /* use compressed row format */
1596     if (zz != yy) PetscCall(PetscArraycpy(z, y, m));
1597     m    = a->compressedrow.nrows;
1598     ii   = a->compressedrow.i;
1599     ridx = a->compressedrow.rindex;
1600     for (i = 0; i < m; i++) {
1601       n   = ii[i + 1] - ii[i];
1602       aj  = a->j + ii[i];
1603       aa  = a_a + ii[i];
1604       sum = y[*ridx];
1605       PetscSparseDenseMaxDot(sum, x, aa, aj, n);
1606       z[*ridx++] = sum;
1607     }
1608   } else { /* do not use compressed row format */
1609     ii = a->i;
1610     for (i = 0; i < m; i++) {
1611       n   = ii[i + 1] - ii[i];
1612       aj  = a->j + ii[i];
1613       aa  = a_a + ii[i];
1614       sum = y[i];
1615       PetscSparseDenseMaxDot(sum, x, aa, aj, n);
1616       z[i] = sum;
1617     }
1618   }
1619   PetscCall(PetscLogFlops(2.0 * a->nz));
1620   PetscCall(VecRestoreArrayRead(xx, &x));
1621   PetscCall(VecRestoreArrayPair(yy, zz, &y, &z));
1622   PetscCall(MatSeqAIJRestoreArrayRead(A, &a_a));
1623   PetscFunctionReturn(PETSC_SUCCESS);
1624 }
1625 
1626 #include <../src/mat/impls/aij/seq/ftn-kernels/fmultadd.h>
1627 PetscErrorCode MatMultAdd_SeqAIJ(Mat A, Vec xx, Vec yy, Vec zz)
1628 {
1629   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1630   PetscScalar       *y, *z;
1631   const PetscScalar *x;
1632   const MatScalar   *a_a;
1633   const PetscInt    *ii, *ridx = NULL;
1634   PetscInt           m        = A->rmap->n;
1635   PetscBool          usecprow = a->compressedrow.use;
1636 
1637   PetscFunctionBegin;
1638   if (a->inode.use && a->inode.checked) {
1639     PetscCall(MatMultAdd_SeqAIJ_Inode(A, xx, yy, zz));
1640     PetscFunctionReturn(PETSC_SUCCESS);
1641   }
1642   PetscCall(MatSeqAIJGetArrayRead(A, &a_a));
1643   PetscCall(VecGetArrayRead(xx, &x));
1644   PetscCall(VecGetArrayPair(yy, zz, &y, &z));
1645   if (usecprow) { /* use compressed row format */
1646     if (zz != yy) PetscCall(PetscArraycpy(z, y, m));
1647     m    = a->compressedrow.nrows;
1648     ii   = a->compressedrow.i;
1649     ridx = a->compressedrow.rindex;
1650     for (PetscInt i = 0; i < m; i++) {
1651       PetscInt           n   = ii[i + 1] - ii[i];
1652       const PetscInt    *aj  = a->j + ii[i];
1653       const PetscScalar *aa  = a_a + ii[i];
1654       PetscScalar        sum = y[*ridx];
1655       PetscSparseDensePlusDot(sum, x, aa, aj, n);
1656       z[*ridx++] = sum;
1657     }
1658   } else { /* do not use compressed row format */
1659     ii = a->i;
1660 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJ)
1661     fortranmultaddaij_(&m, x, ii, a->j, a_a, y, z);
1662 #else
1663     PetscPragmaUseOMPKernels(parallel for)
1664     for (PetscInt i = 0; i < m; i++) {
1665       PetscInt           n   = ii[i + 1] - ii[i];
1666       const PetscInt    *aj  = a->j + ii[i];
1667       const PetscScalar *aa  = a_a + ii[i];
1668       PetscScalar        sum = y[i];
1669       PetscSparseDensePlusDot(sum, x, aa, aj, n);
1670       z[i] = sum;
1671     }
1672 #endif
1673   }
1674   PetscCall(PetscLogFlops(2.0 * a->nz));
1675   PetscCall(VecRestoreArrayRead(xx, &x));
1676   PetscCall(VecRestoreArrayPair(yy, zz, &y, &z));
1677   PetscCall(MatSeqAIJRestoreArrayRead(A, &a_a));
1678   PetscFunctionReturn(PETSC_SUCCESS);
1679 }
1680 
1681 /*
1682      Adds diagonal pointers to sparse matrix nonzero structure.
1683 */
1684 PetscErrorCode MatMarkDiagonal_SeqAIJ(Mat A)
1685 {
1686   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1687   PetscInt    i, j, m = A->rmap->n;
1688   PetscBool   alreadySet = PETSC_TRUE;
1689 
1690   PetscFunctionBegin;
1691   if (!a->diag) {
1692     PetscCall(PetscMalloc1(m, &a->diag));
1693     alreadySet = PETSC_FALSE;
1694   }
1695   for (i = 0; i < A->rmap->n; i++) {
1696     /* If A's diagonal is already correctly set, this fast track enables cheap and repeated MatMarkDiagonal_SeqAIJ() calls */
1697     if (alreadySet) {
1698       PetscInt pos = a->diag[i];
1699       if (pos >= a->i[i] && pos < a->i[i + 1] && a->j[pos] == i) continue;
1700     }
1701 
1702     a->diag[i] = a->i[i + 1];
1703     for (j = a->i[i]; j < a->i[i + 1]; j++) {
1704       if (a->j[j] == i) {
1705         a->diag[i] = j;
1706         break;
1707       }
1708     }
1709   }
1710   PetscFunctionReturn(PETSC_SUCCESS);
1711 }
1712 
1713 static PetscErrorCode MatShift_SeqAIJ(Mat A, PetscScalar v)
1714 {
1715   Mat_SeqAIJ     *a    = (Mat_SeqAIJ *)A->data;
1716   const PetscInt *diag = (const PetscInt *)a->diag;
1717   const PetscInt *ii   = (const PetscInt *)a->i;
1718   PetscInt        i, *mdiag = NULL;
1719   PetscInt        cnt = 0; /* how many diagonals are missing */
1720 
1721   PetscFunctionBegin;
1722   if (!A->preallocated || !a->nz) {
1723     PetscCall(MatSeqAIJSetPreallocation(A, 1, NULL));
1724     PetscCall(MatShift_Basic(A, v));
1725     PetscFunctionReturn(PETSC_SUCCESS);
1726   }
1727 
1728   if (a->diagonaldense) {
1729     cnt = 0;
1730   } else {
1731     PetscCall(PetscCalloc1(A->rmap->n, &mdiag));
1732     for (i = 0; i < A->rmap->n; i++) {
1733       if (i < A->cmap->n && diag[i] >= ii[i + 1]) { /* 'out of range' rows never have diagonals */
1734         cnt++;
1735         mdiag[i] = 1;
1736       }
1737     }
1738   }
1739   if (!cnt) {
1740     PetscCall(MatShift_Basic(A, v));
1741   } else {
1742     PetscScalar       *olda = a->a; /* preserve pointers to current matrix nonzeros structure and values */
1743     PetscInt          *oldj = a->j, *oldi = a->i;
1744     PetscBool          free_a = a->free_a, free_ij = a->free_ij;
1745     const PetscScalar *Aa;
1746 
1747     PetscCall(MatSeqAIJGetArrayRead(A, &Aa)); // sync the host
1748     PetscCall(MatSeqAIJRestoreArrayRead(A, &Aa));
1749 
1750     a->a = NULL;
1751     a->j = NULL;
1752     a->i = NULL;
1753     /* increase the values in imax for each row where a diagonal is being inserted then reallocate the matrix data structures */
1754     for (i = 0; i < PetscMin(A->rmap->n, A->cmap->n); i++) a->imax[i] += mdiag[i];
1755     PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(A, 0, a->imax));
1756 
1757     /* copy old values into new matrix data structure */
1758     for (i = 0; i < A->rmap->n; i++) {
1759       PetscCall(MatSetValues(A, 1, &i, a->imax[i] - mdiag[i], &oldj[oldi[i]], &olda[oldi[i]], ADD_VALUES));
1760       if (i < A->cmap->n) PetscCall(MatSetValue(A, i, i, v, ADD_VALUES));
1761     }
1762     PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
1763     PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
1764     if (free_a) PetscCall(PetscShmgetDeallocateArray((void **)&olda));
1765     if (free_ij) PetscCall(PetscShmgetDeallocateArray((void **)&oldj));
1766     if (free_ij) PetscCall(PetscShmgetDeallocateArray((void **)&oldi));
1767   }
1768   PetscCall(PetscFree(mdiag));
1769   a->diagonaldense = PETSC_TRUE;
1770   PetscFunctionReturn(PETSC_SUCCESS);
1771 }
1772 
1773 /*
1774      Checks for missing diagonals
1775 */
1776 PetscErrorCode MatMissingDiagonal_SeqAIJ(Mat A, PetscBool *missing, PetscInt *d)
1777 {
1778   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1779   PetscInt   *diag, *ii = a->i, i;
1780 
1781   PetscFunctionBegin;
1782   *missing = PETSC_FALSE;
1783   if (A->rmap->n > 0 && !ii) {
1784     *missing = PETSC_TRUE;
1785     if (d) *d = 0;
1786     PetscCall(PetscInfo(A, "Matrix has no entries therefore is missing diagonal\n"));
1787   } else {
1788     PetscInt n;
1789     n    = PetscMin(A->rmap->n, A->cmap->n);
1790     diag = a->diag;
1791     for (i = 0; i < n; i++) {
1792       if (diag[i] >= ii[i + 1]) {
1793         *missing = PETSC_TRUE;
1794         if (d) *d = i;
1795         PetscCall(PetscInfo(A, "Matrix is missing diagonal number %" PetscInt_FMT "\n", i));
1796         break;
1797       }
1798     }
1799   }
1800   PetscFunctionReturn(PETSC_SUCCESS);
1801 }
1802 
1803 #include <petscblaslapack.h>
1804 #include <petsc/private/kernels/blockinvert.h>
1805 
1806 /*
1807     Note that values is allocated externally by the PC and then passed into this routine
1808 */
1809 static PetscErrorCode MatInvertVariableBlockDiagonal_SeqAIJ(Mat A, PetscInt nblocks, const PetscInt *bsizes, PetscScalar *diag)
1810 {
1811   PetscInt        n = A->rmap->n, i, ncnt = 0, *indx, j, bsizemax = 0, *v_pivots;
1812   PetscBool       allowzeropivot, zeropivotdetected = PETSC_FALSE;
1813   const PetscReal shift = 0.0;
1814   PetscInt        ipvt[5];
1815   PetscCount      flops = 0;
1816   PetscScalar     work[25], *v_work;
1817 
1818   PetscFunctionBegin;
1819   allowzeropivot = PetscNot(A->erroriffailure);
1820   for (i = 0; i < nblocks; i++) ncnt += bsizes[i];
1821   PetscCheck(ncnt == n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Total blocksizes %" PetscInt_FMT " doesn't match number matrix rows %" PetscInt_FMT, ncnt, n);
1822   for (i = 0; i < nblocks; i++) bsizemax = PetscMax(bsizemax, bsizes[i]);
1823   PetscCall(PetscMalloc1(bsizemax, &indx));
1824   if (bsizemax > 7) PetscCall(PetscMalloc2(bsizemax, &v_work, bsizemax, &v_pivots));
1825   ncnt = 0;
1826   for (i = 0; i < nblocks; i++) {
1827     for (j = 0; j < bsizes[i]; j++) indx[j] = ncnt + j;
1828     PetscCall(MatGetValues(A, bsizes[i], indx, bsizes[i], indx, diag));
1829     switch (bsizes[i]) {
1830     case 1:
1831       *diag = 1.0 / (*diag);
1832       break;
1833     case 2:
1834       PetscCall(PetscKernel_A_gets_inverse_A_2(diag, shift, allowzeropivot, &zeropivotdetected));
1835       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1836       PetscCall(PetscKernel_A_gets_transpose_A_2(diag));
1837       break;
1838     case 3:
1839       PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected));
1840       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1841       PetscCall(PetscKernel_A_gets_transpose_A_3(diag));
1842       break;
1843     case 4:
1844       PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected));
1845       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1846       PetscCall(PetscKernel_A_gets_transpose_A_4(diag));
1847       break;
1848     case 5:
1849       PetscCall(PetscKernel_A_gets_inverse_A_5(diag, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
1850       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1851       PetscCall(PetscKernel_A_gets_transpose_A_5(diag));
1852       break;
1853     case 6:
1854       PetscCall(PetscKernel_A_gets_inverse_A_6(diag, shift, allowzeropivot, &zeropivotdetected));
1855       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1856       PetscCall(PetscKernel_A_gets_transpose_A_6(diag));
1857       break;
1858     case 7:
1859       PetscCall(PetscKernel_A_gets_inverse_A_7(diag, shift, allowzeropivot, &zeropivotdetected));
1860       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1861       PetscCall(PetscKernel_A_gets_transpose_A_7(diag));
1862       break;
1863     default:
1864       PetscCall(PetscKernel_A_gets_inverse_A(bsizes[i], diag, v_pivots, v_work, allowzeropivot, &zeropivotdetected));
1865       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1866       PetscCall(PetscKernel_A_gets_transpose_A_N(diag, bsizes[i]));
1867     }
1868     ncnt += bsizes[i];
1869     diag += bsizes[i] * bsizes[i];
1870     flops += 2 * PetscPowInt64(bsizes[i], 3) / 3;
1871   }
1872   PetscCall(PetscLogFlops(flops));
1873   if (bsizemax > 7) PetscCall(PetscFree2(v_work, v_pivots));
1874   PetscCall(PetscFree(indx));
1875   PetscFunctionReturn(PETSC_SUCCESS);
1876 }
1877 
1878 /*
1879    Negative shift indicates do not generate an error if there is a zero diagonal, just invert it anyways
1880 */
1881 static PetscErrorCode MatInvertDiagonal_SeqAIJ(Mat A, PetscScalar omega, PetscScalar fshift)
1882 {
1883   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
1884   PetscInt         i, *diag, m = A->rmap->n;
1885   const MatScalar *v;
1886   PetscScalar     *idiag, *mdiag;
1887 
1888   PetscFunctionBegin;
1889   if (a->idiagvalid) PetscFunctionReturn(PETSC_SUCCESS);
1890   PetscCall(MatMarkDiagonal_SeqAIJ(A));
1891   diag = a->diag;
1892   if (!a->idiag) { PetscCall(PetscMalloc3(m, &a->idiag, m, &a->mdiag, m, &a->ssor_work)); }
1893 
1894   mdiag = a->mdiag;
1895   idiag = a->idiag;
1896   PetscCall(MatSeqAIJGetArrayRead(A, &v));
1897   if (omega == 1.0 && PetscRealPart(fshift) <= 0.0) {
1898     for (i = 0; i < m; i++) {
1899       mdiag[i] = v[diag[i]];
1900       if (!PetscAbsScalar(mdiag[i])) { /* zero diagonal */
1901         if (PetscRealPart(fshift)) {
1902           PetscCall(PetscInfo(A, "Zero diagonal on row %" PetscInt_FMT "\n", i));
1903           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1904           A->factorerror_zeropivot_value = 0.0;
1905           A->factorerror_zeropivot_row   = i;
1906         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Zero diagonal on row %" PetscInt_FMT, i);
1907       }
1908       idiag[i] = 1.0 / v[diag[i]];
1909     }
1910     PetscCall(PetscLogFlops(m));
1911   } else {
1912     for (i = 0; i < m; i++) {
1913       mdiag[i] = v[diag[i]];
1914       idiag[i] = omega / (fshift + v[diag[i]]);
1915     }
1916     PetscCall(PetscLogFlops(2.0 * m));
1917   }
1918   a->idiagvalid = PETSC_TRUE;
1919   PetscCall(MatSeqAIJRestoreArrayRead(A, &v));
1920   PetscFunctionReturn(PETSC_SUCCESS);
1921 }
1922 
1923 PetscErrorCode MatSOR_SeqAIJ(Mat A, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
1924 {
1925   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1926   PetscScalar       *x, d, sum, *t, scale;
1927   const MatScalar   *v, *idiag = NULL, *mdiag, *aa;
1928   const PetscScalar *b, *bs, *xb, *ts;
1929   PetscInt           n, m = A->rmap->n, i;
1930   const PetscInt    *idx, *diag;
1931 
1932   PetscFunctionBegin;
1933   if (a->inode.use && a->inode.checked && omega == 1.0 && fshift == 0.0) {
1934     PetscCall(MatSOR_SeqAIJ_Inode(A, bb, omega, flag, fshift, its, lits, xx));
1935     PetscFunctionReturn(PETSC_SUCCESS);
1936   }
1937   its = its * lits;
1938 
1939   if (fshift != a->fshift || omega != a->omega) a->idiagvalid = PETSC_FALSE; /* must recompute idiag[] */
1940   if (!a->idiagvalid) PetscCall(MatInvertDiagonal_SeqAIJ(A, omega, fshift));
1941   a->fshift = fshift;
1942   a->omega  = omega;
1943 
1944   diag  = a->diag;
1945   t     = a->ssor_work;
1946   idiag = a->idiag;
1947   mdiag = a->mdiag;
1948 
1949   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
1950   PetscCall(VecGetArray(xx, &x));
1951   PetscCall(VecGetArrayRead(bb, &b));
1952   /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
1953   if (flag == SOR_APPLY_UPPER) {
1954     /* apply (U + D/omega) to the vector */
1955     bs = b;
1956     for (i = 0; i < m; i++) {
1957       d   = fshift + mdiag[i];
1958       n   = a->i[i + 1] - diag[i] - 1;
1959       idx = a->j + diag[i] + 1;
1960       v   = aa + diag[i] + 1;
1961       sum = b[i] * d / omega;
1962       PetscSparseDensePlusDot(sum, bs, v, idx, n);
1963       x[i] = sum;
1964     }
1965     PetscCall(VecRestoreArray(xx, &x));
1966     PetscCall(VecRestoreArrayRead(bb, &b));
1967     PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
1968     PetscCall(PetscLogFlops(a->nz));
1969     PetscFunctionReturn(PETSC_SUCCESS);
1970   }
1971 
1972   PetscCheck(flag != SOR_APPLY_LOWER, PETSC_COMM_SELF, PETSC_ERR_SUP, "SOR_APPLY_LOWER is not implemented");
1973   if (flag & SOR_EISENSTAT) {
1974     /* Let  A = L + U + D; where L is lower triangular,
1975     U is upper triangular, E = D/omega; This routine applies
1976 
1977             (L + E)^{-1} A (U + E)^{-1}
1978 
1979     to a vector efficiently using Eisenstat's trick.
1980     */
1981     scale = (2.0 / omega) - 1.0;
1982 
1983     /*  x = (E + U)^{-1} b */
1984     for (i = m - 1; i >= 0; i--) {
1985       n   = a->i[i + 1] - diag[i] - 1;
1986       idx = a->j + diag[i] + 1;
1987       v   = aa + diag[i] + 1;
1988       sum = b[i];
1989       PetscSparseDenseMinusDot(sum, x, v, idx, n);
1990       x[i] = sum * idiag[i];
1991     }
1992 
1993     /*  t = b - (2*E - D)x */
1994     v = aa;
1995     for (i = 0; i < m; i++) t[i] = b[i] - scale * (v[*diag++]) * x[i];
1996 
1997     /*  t = (E + L)^{-1}t */
1998     ts   = t;
1999     diag = a->diag;
2000     for (i = 0; i < m; i++) {
2001       n   = diag[i] - a->i[i];
2002       idx = a->j + a->i[i];
2003       v   = aa + a->i[i];
2004       sum = t[i];
2005       PetscSparseDenseMinusDot(sum, ts, v, idx, n);
2006       t[i] = sum * idiag[i];
2007       /*  x = x + t */
2008       x[i] += t[i];
2009     }
2010 
2011     PetscCall(PetscLogFlops(6.0 * m - 1 + 2.0 * a->nz));
2012     PetscCall(VecRestoreArray(xx, &x));
2013     PetscCall(VecRestoreArrayRead(bb, &b));
2014     PetscFunctionReturn(PETSC_SUCCESS);
2015   }
2016   if (flag & SOR_ZERO_INITIAL_GUESS) {
2017     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
2018       for (i = 0; i < m; i++) {
2019         n   = diag[i] - a->i[i];
2020         idx = a->j + a->i[i];
2021         v   = aa + a->i[i];
2022         sum = b[i];
2023         PetscSparseDenseMinusDot(sum, x, v, idx, n);
2024         t[i] = sum;
2025         x[i] = sum * idiag[i];
2026       }
2027       xb = t;
2028       PetscCall(PetscLogFlops(a->nz));
2029     } else xb = b;
2030     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
2031       for (i = m - 1; i >= 0; i--) {
2032         n   = a->i[i + 1] - diag[i] - 1;
2033         idx = a->j + diag[i] + 1;
2034         v   = aa + diag[i] + 1;
2035         sum = xb[i];
2036         PetscSparseDenseMinusDot(sum, x, v, idx, n);
2037         if (xb == b) {
2038           x[i] = sum * idiag[i];
2039         } else {
2040           x[i] = (1 - omega) * x[i] + sum * idiag[i]; /* omega in idiag */
2041         }
2042       }
2043       PetscCall(PetscLogFlops(a->nz)); /* assumes 1/2 in upper */
2044     }
2045     its--;
2046   }
2047   while (its--) {
2048     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
2049       for (i = 0; i < m; i++) {
2050         /* lower */
2051         n   = diag[i] - a->i[i];
2052         idx = a->j + a->i[i];
2053         v   = aa + a->i[i];
2054         sum = b[i];
2055         PetscSparseDenseMinusDot(sum, x, v, idx, n);
2056         t[i] = sum; /* save application of the lower-triangular part */
2057         /* upper */
2058         n   = a->i[i + 1] - diag[i] - 1;
2059         idx = a->j + diag[i] + 1;
2060         v   = aa + diag[i] + 1;
2061         PetscSparseDenseMinusDot(sum, x, v, idx, n);
2062         x[i] = (1. - omega) * x[i] + sum * idiag[i]; /* omega in idiag */
2063       }
2064       xb = t;
2065       PetscCall(PetscLogFlops(2.0 * a->nz));
2066     } else xb = b;
2067     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
2068       for (i = m - 1; i >= 0; i--) {
2069         sum = xb[i];
2070         if (xb == b) {
2071           /* whole matrix (no checkpointing available) */
2072           n   = a->i[i + 1] - a->i[i];
2073           idx = a->j + a->i[i];
2074           v   = aa + a->i[i];
2075           PetscSparseDenseMinusDot(sum, x, v, idx, n);
2076           x[i] = (1. - omega) * x[i] + (sum + mdiag[i] * x[i]) * idiag[i];
2077         } else { /* lower-triangular part has been saved, so only apply upper-triangular */
2078           n   = a->i[i + 1] - diag[i] - 1;
2079           idx = a->j + diag[i] + 1;
2080           v   = aa + diag[i] + 1;
2081           PetscSparseDenseMinusDot(sum, x, v, idx, n);
2082           x[i] = (1. - omega) * x[i] + sum * idiag[i]; /* omega in idiag */
2083         }
2084       }
2085       if (xb == b) {
2086         PetscCall(PetscLogFlops(2.0 * a->nz));
2087       } else {
2088         PetscCall(PetscLogFlops(a->nz)); /* assumes 1/2 in upper */
2089       }
2090     }
2091   }
2092   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
2093   PetscCall(VecRestoreArray(xx, &x));
2094   PetscCall(VecRestoreArrayRead(bb, &b));
2095   PetscFunctionReturn(PETSC_SUCCESS);
2096 }
2097 
2098 static PetscErrorCode MatGetInfo_SeqAIJ(Mat A, MatInfoType flag, MatInfo *info)
2099 {
2100   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
2101 
2102   PetscFunctionBegin;
2103   info->block_size   = 1.0;
2104   info->nz_allocated = a->maxnz;
2105   info->nz_used      = a->nz;
2106   info->nz_unneeded  = (a->maxnz - a->nz);
2107   info->assemblies   = A->num_ass;
2108   info->mallocs      = A->info.mallocs;
2109   info->memory       = 0; /* REVIEW ME */
2110   if (A->factortype) {
2111     info->fill_ratio_given  = A->info.fill_ratio_given;
2112     info->fill_ratio_needed = A->info.fill_ratio_needed;
2113     info->factor_mallocs    = A->info.factor_mallocs;
2114   } else {
2115     info->fill_ratio_given  = 0;
2116     info->fill_ratio_needed = 0;
2117     info->factor_mallocs    = 0;
2118   }
2119   PetscFunctionReturn(PETSC_SUCCESS);
2120 }
2121 
2122 static PetscErrorCode MatZeroRows_SeqAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
2123 {
2124   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
2125   PetscInt           i, m = A->rmap->n - 1;
2126   const PetscScalar *xx;
2127   PetscScalar       *bb, *aa;
2128   PetscInt           d = 0;
2129 
2130   PetscFunctionBegin;
2131   if (x && b) {
2132     PetscCall(VecGetArrayRead(x, &xx));
2133     PetscCall(VecGetArray(b, &bb));
2134     for (i = 0; i < N; i++) {
2135       PetscCheck(rows[i] >= 0 && rows[i] <= m, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "row %" PetscInt_FMT " out of range", rows[i]);
2136       if (rows[i] >= A->cmap->n) continue;
2137       bb[rows[i]] = diag * xx[rows[i]];
2138     }
2139     PetscCall(VecRestoreArrayRead(x, &xx));
2140     PetscCall(VecRestoreArray(b, &bb));
2141   }
2142 
2143   PetscCall(MatSeqAIJGetArray(A, &aa));
2144   if (a->keepnonzeropattern) {
2145     for (i = 0; i < N; i++) {
2146       PetscCheck(rows[i] >= 0 && rows[i] <= m, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "row %" PetscInt_FMT " out of range", rows[i]);
2147       PetscCall(PetscArrayzero(&aa[a->i[rows[i]]], a->ilen[rows[i]]));
2148     }
2149     if (diag != 0.0) {
2150       for (i = 0; i < N; i++) {
2151         d = rows[i];
2152         if (rows[i] >= A->cmap->n) continue;
2153         PetscCheck(a->diag[d] < a->i[d + 1], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix is missing diagonal entry in the zeroed row %" PetscInt_FMT, d);
2154       }
2155       for (i = 0; i < N; i++) {
2156         if (rows[i] >= A->cmap->n) continue;
2157         aa[a->diag[rows[i]]] = diag;
2158       }
2159     }
2160   } else {
2161     if (diag != 0.0) {
2162       for (i = 0; i < N; i++) {
2163         PetscCheck(rows[i] >= 0 && rows[i] <= m, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "row %" PetscInt_FMT " out of range", rows[i]);
2164         if (a->ilen[rows[i]] > 0) {
2165           if (rows[i] >= A->cmap->n) {
2166             a->ilen[rows[i]] = 0;
2167           } else {
2168             a->ilen[rows[i]]    = 1;
2169             aa[a->i[rows[i]]]   = diag;
2170             a->j[a->i[rows[i]]] = rows[i];
2171           }
2172         } else if (rows[i] < A->cmap->n) { /* in case row was completely empty */
2173           PetscCall(MatSetValues_SeqAIJ(A, 1, &rows[i], 1, &rows[i], &diag, INSERT_VALUES));
2174         }
2175       }
2176     } else {
2177       for (i = 0; i < N; i++) {
2178         PetscCheck(rows[i] >= 0 && rows[i] <= m, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "row %" PetscInt_FMT " out of range", rows[i]);
2179         a->ilen[rows[i]] = 0;
2180       }
2181     }
2182     A->nonzerostate++;
2183   }
2184   PetscCall(MatSeqAIJRestoreArray(A, &aa));
2185   PetscUseTypeMethod(A, assemblyend, MAT_FINAL_ASSEMBLY);
2186   PetscFunctionReturn(PETSC_SUCCESS);
2187 }
2188 
2189 static PetscErrorCode MatZeroRowsColumns_SeqAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
2190 {
2191   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
2192   PetscInt           i, j, m = A->rmap->n - 1, d = 0;
2193   PetscBool          missing, *zeroed, vecs = PETSC_FALSE;
2194   const PetscScalar *xx;
2195   PetscScalar       *bb, *aa;
2196 
2197   PetscFunctionBegin;
2198   if (!N) PetscFunctionReturn(PETSC_SUCCESS);
2199   PetscCall(MatSeqAIJGetArray(A, &aa));
2200   if (x && b) {
2201     PetscCall(VecGetArrayRead(x, &xx));
2202     PetscCall(VecGetArray(b, &bb));
2203     vecs = PETSC_TRUE;
2204   }
2205   PetscCall(PetscCalloc1(A->rmap->n, &zeroed));
2206   for (i = 0; i < N; i++) {
2207     PetscCheck(rows[i] >= 0 && rows[i] <= m, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "row %" PetscInt_FMT " out of range", rows[i]);
2208     PetscCall(PetscArrayzero(PetscSafePointerPlusOffset(aa, a->i[rows[i]]), a->ilen[rows[i]]));
2209 
2210     zeroed[rows[i]] = PETSC_TRUE;
2211   }
2212   for (i = 0; i < A->rmap->n; i++) {
2213     if (!zeroed[i]) {
2214       for (j = a->i[i]; j < a->i[i + 1]; j++) {
2215         if (a->j[j] < A->rmap->n && zeroed[a->j[j]]) {
2216           if (vecs) bb[i] -= aa[j] * xx[a->j[j]];
2217           aa[j] = 0.0;
2218         }
2219       }
2220     } else if (vecs && i < A->cmap->N) bb[i] = diag * xx[i];
2221   }
2222   if (x && b) {
2223     PetscCall(VecRestoreArrayRead(x, &xx));
2224     PetscCall(VecRestoreArray(b, &bb));
2225   }
2226   PetscCall(PetscFree(zeroed));
2227   if (diag != 0.0) {
2228     PetscCall(MatMissingDiagonal_SeqAIJ(A, &missing, &d));
2229     if (missing) {
2230       for (i = 0; i < N; i++) {
2231         if (rows[i] >= A->cmap->N) continue;
2232         PetscCheck(!a->nonew || rows[i] < d, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix is missing diagonal entry in row %" PetscInt_FMT " (%" PetscInt_FMT ")", d, rows[i]);
2233         PetscCall(MatSetValues_SeqAIJ(A, 1, &rows[i], 1, &rows[i], &diag, INSERT_VALUES));
2234       }
2235     } else {
2236       for (i = 0; i < N; i++) aa[a->diag[rows[i]]] = diag;
2237     }
2238   }
2239   PetscCall(MatSeqAIJRestoreArray(A, &aa));
2240   PetscUseTypeMethod(A, assemblyend, MAT_FINAL_ASSEMBLY);
2241   PetscFunctionReturn(PETSC_SUCCESS);
2242 }
2243 
2244 PetscErrorCode MatGetRow_SeqAIJ(Mat A, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
2245 {
2246   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
2247   const PetscScalar *aa;
2248 
2249   PetscFunctionBegin;
2250   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
2251   *nz = a->i[row + 1] - a->i[row];
2252   if (v) *v = PetscSafePointerPlusOffset((PetscScalar *)aa, a->i[row]);
2253   if (idx) {
2254     if (*nz && a->j) *idx = a->j + a->i[row];
2255     else *idx = NULL;
2256   }
2257   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
2258   PetscFunctionReturn(PETSC_SUCCESS);
2259 }
2260 
2261 PetscErrorCode MatRestoreRow_SeqAIJ(Mat A, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
2262 {
2263   PetscFunctionBegin;
2264   PetscFunctionReturn(PETSC_SUCCESS);
2265 }
2266 
2267 static PetscErrorCode MatNorm_SeqAIJ(Mat A, NormType type, PetscReal *nrm)
2268 {
2269   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
2270   const MatScalar *v;
2271   PetscReal        sum = 0.0;
2272   PetscInt         i, j;
2273 
2274   PetscFunctionBegin;
2275   PetscCall(MatSeqAIJGetArrayRead(A, &v));
2276   if (type == NORM_FROBENIUS) {
2277 #if defined(PETSC_USE_REAL___FP16)
2278     PetscBLASInt one = 1, nz = a->nz;
2279     PetscCallBLAS("BLASnrm2", *nrm = BLASnrm2_(&nz, v, &one));
2280 #else
2281     for (i = 0; i < a->nz; i++) {
2282       sum += PetscRealPart(PetscConj(*v) * (*v));
2283       v++;
2284     }
2285     *nrm = PetscSqrtReal(sum);
2286 #endif
2287     PetscCall(PetscLogFlops(2.0 * a->nz));
2288   } else if (type == NORM_1) {
2289     PetscReal *tmp;
2290     PetscInt  *jj = a->j;
2291     PetscCall(PetscCalloc1(A->cmap->n + 1, &tmp));
2292     *nrm = 0.0;
2293     for (j = 0; j < a->nz; j++) {
2294       tmp[*jj++] += PetscAbsScalar(*v);
2295       v++;
2296     }
2297     for (j = 0; j < A->cmap->n; j++) {
2298       if (tmp[j] > *nrm) *nrm = tmp[j];
2299     }
2300     PetscCall(PetscFree(tmp));
2301     PetscCall(PetscLogFlops(PetscMax(a->nz - 1, 0)));
2302   } else if (type == NORM_INFINITY) {
2303     *nrm = 0.0;
2304     for (j = 0; j < A->rmap->n; j++) {
2305       const PetscScalar *v2 = PetscSafePointerPlusOffset(v, a->i[j]);
2306       sum                   = 0.0;
2307       for (i = 0; i < a->i[j + 1] - a->i[j]; i++) {
2308         sum += PetscAbsScalar(*v2);
2309         v2++;
2310       }
2311       if (sum > *nrm) *nrm = sum;
2312     }
2313     PetscCall(PetscLogFlops(PetscMax(a->nz - 1, 0)));
2314   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for two norm");
2315   PetscCall(MatSeqAIJRestoreArrayRead(A, &v));
2316   PetscFunctionReturn(PETSC_SUCCESS);
2317 }
2318 
2319 static PetscErrorCode MatIsTranspose_SeqAIJ(Mat A, Mat B, PetscReal tol, PetscBool *f)
2320 {
2321   Mat_SeqAIJ      *aij = (Mat_SeqAIJ *)A->data, *bij = (Mat_SeqAIJ *)B->data;
2322   PetscInt        *adx, *bdx, *aii, *bii, *aptr, *bptr;
2323   const MatScalar *va, *vb;
2324   PetscInt         ma, na, mb, nb, i;
2325 
2326   PetscFunctionBegin;
2327   PetscCall(MatGetSize(A, &ma, &na));
2328   PetscCall(MatGetSize(B, &mb, &nb));
2329   if (ma != nb || na != mb) {
2330     *f = PETSC_FALSE;
2331     PetscFunctionReturn(PETSC_SUCCESS);
2332   }
2333   PetscCall(MatSeqAIJGetArrayRead(A, &va));
2334   PetscCall(MatSeqAIJGetArrayRead(B, &vb));
2335   aii = aij->i;
2336   bii = bij->i;
2337   adx = aij->j;
2338   bdx = bij->j;
2339   PetscCall(PetscMalloc1(ma, &aptr));
2340   PetscCall(PetscMalloc1(mb, &bptr));
2341   for (i = 0; i < ma; i++) aptr[i] = aii[i];
2342   for (i = 0; i < mb; i++) bptr[i] = bii[i];
2343 
2344   *f = PETSC_TRUE;
2345   for (i = 0; i < ma; i++) {
2346     while (aptr[i] < aii[i + 1]) {
2347       PetscInt    idc, idr;
2348       PetscScalar vc, vr;
2349       /* column/row index/value */
2350       idc = adx[aptr[i]];
2351       idr = bdx[bptr[idc]];
2352       vc  = va[aptr[i]];
2353       vr  = vb[bptr[idc]];
2354       if (i != idr || PetscAbsScalar(vc - vr) > tol) {
2355         *f = PETSC_FALSE;
2356         goto done;
2357       } else {
2358         aptr[i]++;
2359         if (B || i != idc) bptr[idc]++;
2360       }
2361     }
2362   }
2363 done:
2364   PetscCall(PetscFree(aptr));
2365   PetscCall(PetscFree(bptr));
2366   PetscCall(MatSeqAIJRestoreArrayRead(A, &va));
2367   PetscCall(MatSeqAIJRestoreArrayRead(B, &vb));
2368   PetscFunctionReturn(PETSC_SUCCESS);
2369 }
2370 
2371 static PetscErrorCode MatIsHermitianTranspose_SeqAIJ(Mat A, Mat B, PetscReal tol, PetscBool *f)
2372 {
2373   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data, *bij = (Mat_SeqAIJ *)B->data;
2374   PetscInt   *adx, *bdx, *aii, *bii, *aptr, *bptr;
2375   MatScalar  *va, *vb;
2376   PetscInt    ma, na, mb, nb, i;
2377 
2378   PetscFunctionBegin;
2379   PetscCall(MatGetSize(A, &ma, &na));
2380   PetscCall(MatGetSize(B, &mb, &nb));
2381   if (ma != nb || na != mb) {
2382     *f = PETSC_FALSE;
2383     PetscFunctionReturn(PETSC_SUCCESS);
2384   }
2385   aii = aij->i;
2386   bii = bij->i;
2387   adx = aij->j;
2388   bdx = bij->j;
2389   va  = aij->a;
2390   vb  = bij->a;
2391   PetscCall(PetscMalloc1(ma, &aptr));
2392   PetscCall(PetscMalloc1(mb, &bptr));
2393   for (i = 0; i < ma; i++) aptr[i] = aii[i];
2394   for (i = 0; i < mb; i++) bptr[i] = bii[i];
2395 
2396   *f = PETSC_TRUE;
2397   for (i = 0; i < ma; i++) {
2398     while (aptr[i] < aii[i + 1]) {
2399       PetscInt    idc, idr;
2400       PetscScalar vc, vr;
2401       /* column/row index/value */
2402       idc = adx[aptr[i]];
2403       idr = bdx[bptr[idc]];
2404       vc  = va[aptr[i]];
2405       vr  = vb[bptr[idc]];
2406       if (i != idr || PetscAbsScalar(vc - PetscConj(vr)) > tol) {
2407         *f = PETSC_FALSE;
2408         goto done;
2409       } else {
2410         aptr[i]++;
2411         if (B || i != idc) bptr[idc]++;
2412       }
2413     }
2414   }
2415 done:
2416   PetscCall(PetscFree(aptr));
2417   PetscCall(PetscFree(bptr));
2418   PetscFunctionReturn(PETSC_SUCCESS);
2419 }
2420 
2421 PetscErrorCode MatDiagonalScale_SeqAIJ(Mat A, Vec ll, Vec rr)
2422 {
2423   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
2424   const PetscScalar *l, *r;
2425   PetscScalar        x;
2426   MatScalar         *v;
2427   PetscInt           i, j, m = A->rmap->n, n = A->cmap->n, M, nz = a->nz;
2428   const PetscInt    *jj;
2429 
2430   PetscFunctionBegin;
2431   if (ll) {
2432     /* The local size is used so that VecMPI can be passed to this routine
2433        by MatDiagonalScale_MPIAIJ */
2434     PetscCall(VecGetLocalSize(ll, &m));
2435     PetscCheck(m == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Left scaling vector wrong length");
2436     PetscCall(VecGetArrayRead(ll, &l));
2437     PetscCall(MatSeqAIJGetArray(A, &v));
2438     for (i = 0; i < m; i++) {
2439       x = l[i];
2440       M = a->i[i + 1] - a->i[i];
2441       for (j = 0; j < M; j++) (*v++) *= x;
2442     }
2443     PetscCall(VecRestoreArrayRead(ll, &l));
2444     PetscCall(PetscLogFlops(nz));
2445     PetscCall(MatSeqAIJRestoreArray(A, &v));
2446   }
2447   if (rr) {
2448     PetscCall(VecGetLocalSize(rr, &n));
2449     PetscCheck(n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Right scaling vector wrong length");
2450     PetscCall(VecGetArrayRead(rr, &r));
2451     PetscCall(MatSeqAIJGetArray(A, &v));
2452     jj = a->j;
2453     for (i = 0; i < nz; i++) (*v++) *= r[*jj++];
2454     PetscCall(MatSeqAIJRestoreArray(A, &v));
2455     PetscCall(VecRestoreArrayRead(rr, &r));
2456     PetscCall(PetscLogFlops(nz));
2457   }
2458   PetscCall(MatSeqAIJInvalidateDiagonal(A));
2459   PetscFunctionReturn(PETSC_SUCCESS);
2460 }
2461 
2462 PetscErrorCode MatCreateSubMatrix_SeqAIJ(Mat A, IS isrow, IS iscol, PetscInt csize, MatReuse scall, Mat *B)
2463 {
2464   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *c;
2465   PetscInt          *smap, i, k, kstart, kend, oldcols = A->cmap->n, *lens;
2466   PetscInt           row, mat_i, *mat_j, tcol, first, step, *mat_ilen, sum, lensi;
2467   const PetscInt    *irow, *icol;
2468   const PetscScalar *aa;
2469   PetscInt           nrows, ncols;
2470   PetscInt          *starts, *j_new, *i_new, *aj = a->j, *ai = a->i, ii, *ailen = a->ilen;
2471   MatScalar         *a_new, *mat_a, *c_a;
2472   Mat                C;
2473   PetscBool          stride;
2474 
2475   PetscFunctionBegin;
2476   PetscCall(ISGetIndices(isrow, &irow));
2477   PetscCall(ISGetLocalSize(isrow, &nrows));
2478   PetscCall(ISGetLocalSize(iscol, &ncols));
2479 
2480   PetscCall(PetscObjectTypeCompare((PetscObject)iscol, ISSTRIDE, &stride));
2481   if (stride) {
2482     PetscCall(ISStrideGetInfo(iscol, &first, &step));
2483   } else {
2484     first = 0;
2485     step  = 0;
2486   }
2487   if (stride && step == 1) {
2488     /* special case of contiguous rows */
2489     PetscCall(PetscMalloc2(nrows, &lens, nrows, &starts));
2490     /* loop over new rows determining lens and starting points */
2491     for (i = 0; i < nrows; i++) {
2492       kstart    = ai[irow[i]];
2493       kend      = kstart + ailen[irow[i]];
2494       starts[i] = kstart;
2495       for (k = kstart; k < kend; k++) {
2496         if (aj[k] >= first) {
2497           starts[i] = k;
2498           break;
2499         }
2500       }
2501       sum = 0;
2502       while (k < kend) {
2503         if (aj[k++] >= first + ncols) break;
2504         sum++;
2505       }
2506       lens[i] = sum;
2507     }
2508     /* create submatrix */
2509     if (scall == MAT_REUSE_MATRIX) {
2510       PetscInt n_cols, n_rows;
2511       PetscCall(MatGetSize(*B, &n_rows, &n_cols));
2512       PetscCheck(n_rows == nrows && n_cols == ncols, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Reused submatrix wrong size");
2513       PetscCall(MatZeroEntries(*B));
2514       C = *B;
2515     } else {
2516       PetscInt rbs, cbs;
2517       PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &C));
2518       PetscCall(MatSetSizes(C, nrows, ncols, PETSC_DETERMINE, PETSC_DETERMINE));
2519       PetscCall(ISGetBlockSize(isrow, &rbs));
2520       PetscCall(ISGetBlockSize(iscol, &cbs));
2521       PetscCall(MatSetBlockSizes(C, rbs, cbs));
2522       PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
2523       PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(C, 0, lens));
2524     }
2525     c = (Mat_SeqAIJ *)C->data;
2526 
2527     /* loop over rows inserting into submatrix */
2528     PetscCall(MatSeqAIJGetArrayWrite(C, &a_new)); // Not 'a_new = c->a-new', since that raw usage ignores offload state of C
2529     j_new = c->j;
2530     i_new = c->i;
2531     PetscCall(MatSeqAIJGetArrayRead(A, &aa));
2532     for (i = 0; i < nrows; i++) {
2533       ii    = starts[i];
2534       lensi = lens[i];
2535       if (lensi) {
2536         for (k = 0; k < lensi; k++) *j_new++ = aj[ii + k] - first;
2537         PetscCall(PetscArraycpy(a_new, aa + starts[i], lensi));
2538         a_new += lensi;
2539       }
2540       i_new[i + 1] = i_new[i] + lensi;
2541       c->ilen[i]   = lensi;
2542     }
2543     PetscCall(MatSeqAIJRestoreArrayWrite(C, &a_new)); // Set C's offload state properly
2544     PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
2545     PetscCall(PetscFree2(lens, starts));
2546   } else {
2547     PetscCall(ISGetIndices(iscol, &icol));
2548     PetscCall(PetscCalloc1(oldcols, &smap));
2549     PetscCall(PetscMalloc1(1 + nrows, &lens));
2550     for (i = 0; i < ncols; i++) {
2551       PetscCheck(icol[i] < oldcols, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Requesting column beyond largest column icol[%" PetscInt_FMT "] %" PetscInt_FMT " >= A->cmap->n %" PetscInt_FMT, i, icol[i], oldcols);
2552       smap[icol[i]] = i + 1;
2553     }
2554 
2555     /* determine lens of each row */
2556     for (i = 0; i < nrows; i++) {
2557       kstart  = ai[irow[i]];
2558       kend    = kstart + a->ilen[irow[i]];
2559       lens[i] = 0;
2560       for (k = kstart; k < kend; k++) {
2561         if (smap[aj[k]]) lens[i]++;
2562       }
2563     }
2564     /* Create and fill new matrix */
2565     if (scall == MAT_REUSE_MATRIX) {
2566       PetscBool equal;
2567 
2568       c = (Mat_SeqAIJ *)((*B)->data);
2569       PetscCheck((*B)->rmap->n == nrows && (*B)->cmap->n == ncols, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Cannot reuse matrix. wrong size");
2570       PetscCall(PetscArraycmp(c->ilen, lens, (*B)->rmap->n, &equal));
2571       PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Cannot reuse matrix. wrong number of nonzeros");
2572       PetscCall(PetscArrayzero(c->ilen, (*B)->rmap->n));
2573       C = *B;
2574     } else {
2575       PetscInt rbs, cbs;
2576       PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &C));
2577       PetscCall(MatSetSizes(C, nrows, ncols, PETSC_DETERMINE, PETSC_DETERMINE));
2578       PetscCall(ISGetBlockSize(isrow, &rbs));
2579       PetscCall(ISGetBlockSize(iscol, &cbs));
2580       if (rbs > 1 || cbs > 1) PetscCall(MatSetBlockSizes(C, rbs, cbs));
2581       PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
2582       PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(C, 0, lens));
2583     }
2584     PetscCall(MatSeqAIJGetArrayRead(A, &aa));
2585 
2586     c = (Mat_SeqAIJ *)C->data;
2587     PetscCall(MatSeqAIJGetArrayWrite(C, &c_a)); // Not 'c->a', since that raw usage ignores offload state of C
2588     for (i = 0; i < nrows; i++) {
2589       row      = irow[i];
2590       kstart   = ai[row];
2591       kend     = kstart + a->ilen[row];
2592       mat_i    = c->i[i];
2593       mat_j    = PetscSafePointerPlusOffset(c->j, mat_i);
2594       mat_a    = PetscSafePointerPlusOffset(c_a, mat_i);
2595       mat_ilen = c->ilen + i;
2596       for (k = kstart; k < kend; k++) {
2597         if ((tcol = smap[a->j[k]])) {
2598           *mat_j++ = tcol - 1;
2599           *mat_a++ = aa[k];
2600           (*mat_ilen)++;
2601         }
2602       }
2603     }
2604     PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
2605     /* Free work space */
2606     PetscCall(ISRestoreIndices(iscol, &icol));
2607     PetscCall(PetscFree(smap));
2608     PetscCall(PetscFree(lens));
2609     /* sort */
2610     for (i = 0; i < nrows; i++) {
2611       PetscInt ilen;
2612 
2613       mat_i = c->i[i];
2614       mat_j = PetscSafePointerPlusOffset(c->j, mat_i);
2615       mat_a = PetscSafePointerPlusOffset(c_a, mat_i);
2616       ilen  = c->ilen[i];
2617       PetscCall(PetscSortIntWithScalarArray(ilen, mat_j, mat_a));
2618     }
2619     PetscCall(MatSeqAIJRestoreArrayWrite(C, &c_a));
2620   }
2621 #if defined(PETSC_HAVE_DEVICE)
2622   PetscCall(MatBindToCPU(C, A->boundtocpu));
2623 #endif
2624   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2625   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2626 
2627   PetscCall(ISRestoreIndices(isrow, &irow));
2628   *B = C;
2629   PetscFunctionReturn(PETSC_SUCCESS);
2630 }
2631 
2632 static PetscErrorCode MatGetMultiProcBlock_SeqAIJ(Mat mat, MPI_Comm subComm, MatReuse scall, Mat *subMat)
2633 {
2634   Mat B;
2635 
2636   PetscFunctionBegin;
2637   if (scall == MAT_INITIAL_MATRIX) {
2638     PetscCall(MatCreate(subComm, &B));
2639     PetscCall(MatSetSizes(B, mat->rmap->n, mat->cmap->n, mat->rmap->n, mat->cmap->n));
2640     PetscCall(MatSetBlockSizesFromMats(B, mat, mat));
2641     PetscCall(MatSetType(B, MATSEQAIJ));
2642     PetscCall(MatDuplicateNoCreate_SeqAIJ(B, mat, MAT_COPY_VALUES, PETSC_TRUE));
2643     *subMat = B;
2644   } else {
2645     PetscCall(MatCopy_SeqAIJ(mat, *subMat, SAME_NONZERO_PATTERN));
2646   }
2647   PetscFunctionReturn(PETSC_SUCCESS);
2648 }
2649 
2650 static PetscErrorCode MatILUFactor_SeqAIJ(Mat inA, IS row, IS col, const MatFactorInfo *info)
2651 {
2652   Mat_SeqAIJ *a = (Mat_SeqAIJ *)inA->data;
2653   Mat         outA;
2654   PetscBool   row_identity, col_identity;
2655 
2656   PetscFunctionBegin;
2657   PetscCheck(info->levels == 0, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only levels=0 supported for in-place ilu");
2658 
2659   PetscCall(ISIdentity(row, &row_identity));
2660   PetscCall(ISIdentity(col, &col_identity));
2661 
2662   outA             = inA;
2663   outA->factortype = MAT_FACTOR_LU;
2664   PetscCall(PetscFree(inA->solvertype));
2665   PetscCall(PetscStrallocpy(MATSOLVERPETSC, &inA->solvertype));
2666 
2667   PetscCall(PetscObjectReference((PetscObject)row));
2668   PetscCall(ISDestroy(&a->row));
2669 
2670   a->row = row;
2671 
2672   PetscCall(PetscObjectReference((PetscObject)col));
2673   PetscCall(ISDestroy(&a->col));
2674 
2675   a->col = col;
2676 
2677   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
2678   PetscCall(ISDestroy(&a->icol));
2679   PetscCall(ISInvertPermutation(col, PETSC_DECIDE, &a->icol));
2680 
2681   if (!a->solve_work) { /* this matrix may have been factored before */
2682     PetscCall(PetscMalloc1(inA->rmap->n + 1, &a->solve_work));
2683   }
2684 
2685   PetscCall(MatMarkDiagonal_SeqAIJ(inA));
2686   if (row_identity && col_identity) {
2687     PetscCall(MatLUFactorNumeric_SeqAIJ_inplace(outA, inA, info));
2688   } else {
2689     PetscCall(MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA, inA, info));
2690   }
2691   PetscFunctionReturn(PETSC_SUCCESS);
2692 }
2693 
2694 PetscErrorCode MatScale_SeqAIJ(Mat inA, PetscScalar alpha)
2695 {
2696   Mat_SeqAIJ  *a = (Mat_SeqAIJ *)inA->data;
2697   PetscScalar *v;
2698   PetscBLASInt one = 1, bnz;
2699 
2700   PetscFunctionBegin;
2701   PetscCall(MatSeqAIJGetArray(inA, &v));
2702   PetscCall(PetscBLASIntCast(a->nz, &bnz));
2703   PetscCallBLAS("BLASscal", BLASscal_(&bnz, &alpha, v, &one));
2704   PetscCall(PetscLogFlops(a->nz));
2705   PetscCall(MatSeqAIJRestoreArray(inA, &v));
2706   PetscCall(MatSeqAIJInvalidateDiagonal(inA));
2707   PetscFunctionReturn(PETSC_SUCCESS);
2708 }
2709 
2710 PetscErrorCode MatDestroySubMatrix_Private(Mat_SubSppt *submatj)
2711 {
2712   PetscInt i;
2713 
2714   PetscFunctionBegin;
2715   if (!submatj->id) { /* delete data that are linked only to submats[id=0] */
2716     PetscCall(PetscFree4(submatj->sbuf1, submatj->ptr, submatj->tmp, submatj->ctr));
2717 
2718     for (i = 0; i < submatj->nrqr; ++i) PetscCall(PetscFree(submatj->sbuf2[i]));
2719     PetscCall(PetscFree3(submatj->sbuf2, submatj->req_size, submatj->req_source1));
2720 
2721     if (submatj->rbuf1) {
2722       PetscCall(PetscFree(submatj->rbuf1[0]));
2723       PetscCall(PetscFree(submatj->rbuf1));
2724     }
2725 
2726     for (i = 0; i < submatj->nrqs; ++i) PetscCall(PetscFree(submatj->rbuf3[i]));
2727     PetscCall(PetscFree3(submatj->req_source2, submatj->rbuf2, submatj->rbuf3));
2728     PetscCall(PetscFree(submatj->pa));
2729   }
2730 
2731 #if defined(PETSC_USE_CTABLE)
2732   PetscCall(PetscHMapIDestroy(&submatj->rmap));
2733   if (submatj->cmap_loc) PetscCall(PetscFree(submatj->cmap_loc));
2734   PetscCall(PetscFree(submatj->rmap_loc));
2735 #else
2736   PetscCall(PetscFree(submatj->rmap));
2737 #endif
2738 
2739   if (!submatj->allcolumns) {
2740 #if defined(PETSC_USE_CTABLE)
2741     PetscCall(PetscHMapIDestroy(&submatj->cmap));
2742 #else
2743     PetscCall(PetscFree(submatj->cmap));
2744 #endif
2745   }
2746   PetscCall(PetscFree(submatj->row2proc));
2747 
2748   PetscCall(PetscFree(submatj));
2749   PetscFunctionReturn(PETSC_SUCCESS);
2750 }
2751 
2752 PetscErrorCode MatDestroySubMatrix_SeqAIJ(Mat C)
2753 {
2754   Mat_SeqAIJ  *c       = (Mat_SeqAIJ *)C->data;
2755   Mat_SubSppt *submatj = c->submatis1;
2756 
2757   PetscFunctionBegin;
2758   PetscCall((*submatj->destroy)(C));
2759   PetscCall(MatDestroySubMatrix_Private(submatj));
2760   PetscFunctionReturn(PETSC_SUCCESS);
2761 }
2762 
2763 /* Note this has code duplication with MatDestroySubMatrices_SeqBAIJ() */
2764 static PetscErrorCode MatDestroySubMatrices_SeqAIJ(PetscInt n, Mat *mat[])
2765 {
2766   PetscInt     i;
2767   Mat          C;
2768   Mat_SeqAIJ  *c;
2769   Mat_SubSppt *submatj;
2770 
2771   PetscFunctionBegin;
2772   for (i = 0; i < n; i++) {
2773     C       = (*mat)[i];
2774     c       = (Mat_SeqAIJ *)C->data;
2775     submatj = c->submatis1;
2776     if (submatj) {
2777       if (--((PetscObject)C)->refct <= 0) {
2778         PetscCall(PetscFree(C->factorprefix));
2779         PetscCall((*submatj->destroy)(C));
2780         PetscCall(MatDestroySubMatrix_Private(submatj));
2781         PetscCall(PetscFree(C->defaultvectype));
2782         PetscCall(PetscFree(C->defaultrandtype));
2783         PetscCall(PetscLayoutDestroy(&C->rmap));
2784         PetscCall(PetscLayoutDestroy(&C->cmap));
2785         PetscCall(PetscHeaderDestroy(&C));
2786       }
2787     } else {
2788       PetscCall(MatDestroy(&C));
2789     }
2790   }
2791 
2792   /* Destroy Dummy submatrices created for reuse */
2793   PetscCall(MatDestroySubMatrices_Dummy(n, mat));
2794 
2795   PetscCall(PetscFree(*mat));
2796   PetscFunctionReturn(PETSC_SUCCESS);
2797 }
2798 
2799 static PetscErrorCode MatCreateSubMatrices_SeqAIJ(Mat A, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *B[])
2800 {
2801   PetscInt i;
2802 
2803   PetscFunctionBegin;
2804   if (scall == MAT_INITIAL_MATRIX) PetscCall(PetscCalloc1(n + 1, B));
2805 
2806   for (i = 0; i < n; i++) PetscCall(MatCreateSubMatrix_SeqAIJ(A, irow[i], icol[i], PETSC_DECIDE, scall, &(*B)[i]));
2807   PetscFunctionReturn(PETSC_SUCCESS);
2808 }
2809 
2810 static PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A, PetscInt is_max, IS is[], PetscInt ov)
2811 {
2812   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
2813   PetscInt        row, i, j, k, l, ll, m, n, *nidx, isz, val;
2814   const PetscInt *idx;
2815   PetscInt        start, end, *ai, *aj, bs = A->rmap->bs == A->cmap->bs ? A->rmap->bs : 1;
2816   PetscBT         table;
2817 
2818   PetscFunctionBegin;
2819   m  = A->rmap->n / bs;
2820   ai = a->i;
2821   aj = a->j;
2822 
2823   PetscCheck(ov >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "illegal negative overlap value used");
2824 
2825   PetscCall(PetscMalloc1(m + 1, &nidx));
2826   PetscCall(PetscBTCreate(m, &table));
2827 
2828   for (i = 0; i < is_max; i++) {
2829     /* Initialize the two local arrays */
2830     isz = 0;
2831     PetscCall(PetscBTMemzero(m, table));
2832 
2833     /* Extract the indices, assume there can be duplicate entries */
2834     PetscCall(ISGetIndices(is[i], &idx));
2835     PetscCall(ISGetLocalSize(is[i], &n));
2836 
2837     if (bs > 1) {
2838       /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2839       for (j = 0; j < n; ++j) {
2840         if (!PetscBTLookupSet(table, idx[j] / bs)) nidx[isz++] = idx[j] / bs;
2841       }
2842       PetscCall(ISRestoreIndices(is[i], &idx));
2843       PetscCall(ISDestroy(&is[i]));
2844 
2845       k = 0;
2846       for (j = 0; j < ov; j++) { /* for each overlap */
2847         n = isz;
2848         for (; k < n; k++) { /* do only those rows in nidx[k], which are not done yet */
2849           for (ll = 0; ll < bs; ll++) {
2850             row   = bs * nidx[k] + ll;
2851             start = ai[row];
2852             end   = ai[row + 1];
2853             for (l = start; l < end; l++) {
2854               val = aj[l] / bs;
2855               if (!PetscBTLookupSet(table, val)) nidx[isz++] = val;
2856             }
2857           }
2858         }
2859       }
2860       PetscCall(ISCreateBlock(PETSC_COMM_SELF, bs, isz, nidx, PETSC_COPY_VALUES, is + i));
2861     } else {
2862       /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2863       for (j = 0; j < n; ++j) {
2864         if (!PetscBTLookupSet(table, idx[j])) nidx[isz++] = idx[j];
2865       }
2866       PetscCall(ISRestoreIndices(is[i], &idx));
2867       PetscCall(ISDestroy(&is[i]));
2868 
2869       k = 0;
2870       for (j = 0; j < ov; j++) { /* for each overlap */
2871         n = isz;
2872         for (; k < n; k++) { /* do only those rows in nidx[k], which are not done yet */
2873           row   = nidx[k];
2874           start = ai[row];
2875           end   = ai[row + 1];
2876           for (l = start; l < end; l++) {
2877             val = aj[l];
2878             if (!PetscBTLookupSet(table, val)) nidx[isz++] = val;
2879           }
2880         }
2881       }
2882       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, isz, nidx, PETSC_COPY_VALUES, is + i));
2883     }
2884   }
2885   PetscCall(PetscBTDestroy(&table));
2886   PetscCall(PetscFree(nidx));
2887   PetscFunctionReturn(PETSC_SUCCESS);
2888 }
2889 
2890 static PetscErrorCode MatPermute_SeqAIJ(Mat A, IS rowp, IS colp, Mat *B)
2891 {
2892   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
2893   PetscInt        i, nz = 0, m = A->rmap->n, n = A->cmap->n;
2894   const PetscInt *row, *col;
2895   PetscInt       *cnew, j, *lens;
2896   IS              icolp, irowp;
2897   PetscInt       *cwork = NULL;
2898   PetscScalar    *vwork = NULL;
2899 
2900   PetscFunctionBegin;
2901   PetscCall(ISInvertPermutation(rowp, PETSC_DECIDE, &irowp));
2902   PetscCall(ISGetIndices(irowp, &row));
2903   PetscCall(ISInvertPermutation(colp, PETSC_DECIDE, &icolp));
2904   PetscCall(ISGetIndices(icolp, &col));
2905 
2906   /* determine lengths of permuted rows */
2907   PetscCall(PetscMalloc1(m + 1, &lens));
2908   for (i = 0; i < m; i++) lens[row[i]] = a->i[i + 1] - a->i[i];
2909   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), B));
2910   PetscCall(MatSetSizes(*B, m, n, m, n));
2911   PetscCall(MatSetBlockSizesFromMats(*B, A, A));
2912   PetscCall(MatSetType(*B, ((PetscObject)A)->type_name));
2913   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*B, 0, lens));
2914   PetscCall(PetscFree(lens));
2915 
2916   PetscCall(PetscMalloc1(n, &cnew));
2917   for (i = 0; i < m; i++) {
2918     PetscCall(MatGetRow_SeqAIJ(A, i, &nz, &cwork, &vwork));
2919     for (j = 0; j < nz; j++) cnew[j] = col[cwork[j]];
2920     PetscCall(MatSetValues_SeqAIJ(*B, 1, &row[i], nz, cnew, vwork, INSERT_VALUES));
2921     PetscCall(MatRestoreRow_SeqAIJ(A, i, &nz, &cwork, &vwork));
2922   }
2923   PetscCall(PetscFree(cnew));
2924 
2925   (*B)->assembled = PETSC_FALSE;
2926 
2927 #if defined(PETSC_HAVE_DEVICE)
2928   PetscCall(MatBindToCPU(*B, A->boundtocpu));
2929 #endif
2930   PetscCall(MatAssemblyBegin(*B, MAT_FINAL_ASSEMBLY));
2931   PetscCall(MatAssemblyEnd(*B, MAT_FINAL_ASSEMBLY));
2932   PetscCall(ISRestoreIndices(irowp, &row));
2933   PetscCall(ISRestoreIndices(icolp, &col));
2934   PetscCall(ISDestroy(&irowp));
2935   PetscCall(ISDestroy(&icolp));
2936   if (rowp == colp) PetscCall(MatPropagateSymmetryOptions(A, *B));
2937   PetscFunctionReturn(PETSC_SUCCESS);
2938 }
2939 
2940 PetscErrorCode MatCopy_SeqAIJ(Mat A, Mat B, MatStructure str)
2941 {
2942   PetscFunctionBegin;
2943   /* If the two matrices have the same copy implementation, use fast copy. */
2944   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
2945     Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
2946     Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;
2947     const PetscScalar *aa;
2948     PetscScalar       *bb;
2949 
2950     PetscCall(MatSeqAIJGetArrayRead(A, &aa));
2951     PetscCall(MatSeqAIJGetArrayWrite(B, &bb));
2952 
2953     PetscCheck(a->i[A->rmap->n] == b->i[B->rmap->n], PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Number of nonzeros in two matrices are different %" PetscInt_FMT " != %" PetscInt_FMT, a->i[A->rmap->n], b->i[B->rmap->n]);
2954     PetscCall(PetscArraycpy(bb, aa, a->i[A->rmap->n]));
2955     PetscCall(PetscObjectStateIncrease((PetscObject)B));
2956     PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
2957     PetscCall(MatSeqAIJRestoreArrayWrite(B, &bb));
2958   } else {
2959     PetscCall(MatCopy_Basic(A, B, str));
2960   }
2961   PetscFunctionReturn(PETSC_SUCCESS);
2962 }
2963 
2964 PETSC_INTERN PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A, PetscScalar *array[])
2965 {
2966   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
2967 
2968   PetscFunctionBegin;
2969   *array = a->a;
2970   PetscFunctionReturn(PETSC_SUCCESS);
2971 }
2972 
2973 PETSC_INTERN PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A, PetscScalar *array[])
2974 {
2975   PetscFunctionBegin;
2976   *array = NULL;
2977   PetscFunctionReturn(PETSC_SUCCESS);
2978 }
2979 
2980 /*
2981    Computes the number of nonzeros per row needed for preallocation when X and Y
2982    have different nonzero structure.
2983 */
2984 PetscErrorCode MatAXPYGetPreallocation_SeqX_private(PetscInt m, const PetscInt *xi, const PetscInt *xj, const PetscInt *yi, const PetscInt *yj, PetscInt *nnz)
2985 {
2986   PetscInt i, j, k, nzx, nzy;
2987 
2988   PetscFunctionBegin;
2989   /* Set the number of nonzeros in the new matrix */
2990   for (i = 0; i < m; i++) {
2991     const PetscInt *xjj = PetscSafePointerPlusOffset(xj, xi[i]), *yjj = PetscSafePointerPlusOffset(yj, yi[i]);
2992     nzx    = xi[i + 1] - xi[i];
2993     nzy    = yi[i + 1] - yi[i];
2994     nnz[i] = 0;
2995     for (j = 0, k = 0; j < nzx; j++) {                  /* Point in X */
2996       for (; k < nzy && yjj[k] < xjj[j]; k++) nnz[i]++; /* Catch up to X */
2997       if (k < nzy && yjj[k] == xjj[j]) k++;             /* Skip duplicate */
2998       nnz[i]++;
2999     }
3000     for (; k < nzy; k++) nnz[i]++;
3001   }
3002   PetscFunctionReturn(PETSC_SUCCESS);
3003 }
3004 
3005 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y, Mat X, PetscInt *nnz)
3006 {
3007   PetscInt    m = Y->rmap->N;
3008   Mat_SeqAIJ *x = (Mat_SeqAIJ *)X->data;
3009   Mat_SeqAIJ *y = (Mat_SeqAIJ *)Y->data;
3010 
3011   PetscFunctionBegin;
3012   /* Set the number of nonzeros in the new matrix */
3013   PetscCall(MatAXPYGetPreallocation_SeqX_private(m, x->i, x->j, y->i, y->j, nnz));
3014   PetscFunctionReturn(PETSC_SUCCESS);
3015 }
3016 
3017 PetscErrorCode MatAXPY_SeqAIJ(Mat Y, PetscScalar a, Mat X, MatStructure str)
3018 {
3019   Mat_SeqAIJ *x = (Mat_SeqAIJ *)X->data, *y = (Mat_SeqAIJ *)Y->data;
3020 
3021   PetscFunctionBegin;
3022   if (str == UNKNOWN_NONZERO_PATTERN || (PetscDefined(USE_DEBUG) && str == SAME_NONZERO_PATTERN)) {
3023     PetscBool e = x->nz == y->nz ? PETSC_TRUE : PETSC_FALSE;
3024     if (e) {
3025       PetscCall(PetscArraycmp(x->i, y->i, Y->rmap->n + 1, &e));
3026       if (e) {
3027         PetscCall(PetscArraycmp(x->j, y->j, y->nz, &e));
3028         if (e) str = SAME_NONZERO_PATTERN;
3029       }
3030     }
3031     if (!e) PetscCheck(str != SAME_NONZERO_PATTERN, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatStructure is not SAME_NONZERO_PATTERN");
3032   }
3033   if (str == SAME_NONZERO_PATTERN) {
3034     const PetscScalar *xa;
3035     PetscScalar       *ya, alpha = a;
3036     PetscBLASInt       one = 1, bnz;
3037 
3038     PetscCall(PetscBLASIntCast(x->nz, &bnz));
3039     PetscCall(MatSeqAIJGetArray(Y, &ya));
3040     PetscCall(MatSeqAIJGetArrayRead(X, &xa));
3041     PetscCallBLAS("BLASaxpy", BLASaxpy_(&bnz, &alpha, xa, &one, ya, &one));
3042     PetscCall(MatSeqAIJRestoreArrayRead(X, &xa));
3043     PetscCall(MatSeqAIJRestoreArray(Y, &ya));
3044     PetscCall(PetscLogFlops(2.0 * bnz));
3045     PetscCall(MatSeqAIJInvalidateDiagonal(Y));
3046     PetscCall(PetscObjectStateIncrease((PetscObject)Y));
3047   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
3048     PetscCall(MatAXPY_Basic(Y, a, X, str));
3049   } else {
3050     Mat       B;
3051     PetscInt *nnz;
3052     PetscCall(PetscMalloc1(Y->rmap->N, &nnz));
3053     PetscCall(MatCreate(PetscObjectComm((PetscObject)Y), &B));
3054     PetscCall(PetscObjectSetName((PetscObject)B, ((PetscObject)Y)->name));
3055     PetscCall(MatSetLayouts(B, Y->rmap, Y->cmap));
3056     PetscCall(MatSetType(B, ((PetscObject)Y)->type_name));
3057     PetscCall(MatAXPYGetPreallocation_SeqAIJ(Y, X, nnz));
3058     PetscCall(MatSeqAIJSetPreallocation(B, 0, nnz));
3059     PetscCall(MatAXPY_BasicWithPreallocation(B, Y, a, X, str));
3060     PetscCall(MatHeaderMerge(Y, &B));
3061     PetscCall(MatSeqAIJCheckInode(Y));
3062     PetscCall(PetscFree(nnz));
3063   }
3064   PetscFunctionReturn(PETSC_SUCCESS);
3065 }
3066 
3067 PETSC_INTERN PetscErrorCode MatConjugate_SeqAIJ(Mat mat)
3068 {
3069 #if defined(PETSC_USE_COMPLEX)
3070   Mat_SeqAIJ  *aij = (Mat_SeqAIJ *)mat->data;
3071   PetscInt     i, nz;
3072   PetscScalar *a;
3073 
3074   PetscFunctionBegin;
3075   nz = aij->nz;
3076   PetscCall(MatSeqAIJGetArray(mat, &a));
3077   for (i = 0; i < nz; i++) a[i] = PetscConj(a[i]);
3078   PetscCall(MatSeqAIJRestoreArray(mat, &a));
3079 #else
3080   PetscFunctionBegin;
3081 #endif
3082   PetscFunctionReturn(PETSC_SUCCESS);
3083 }
3084 
3085 static PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A, Vec v, PetscInt idx[])
3086 {
3087   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
3088   PetscInt         i, j, m = A->rmap->n, *ai, *aj, ncols, n;
3089   PetscReal        atmp;
3090   PetscScalar     *x;
3091   const MatScalar *aa, *av;
3092 
3093   PetscFunctionBegin;
3094   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3095   PetscCall(MatSeqAIJGetArrayRead(A, &av));
3096   aa = av;
3097   ai = a->i;
3098   aj = a->j;
3099 
3100   PetscCall(VecGetArrayWrite(v, &x));
3101   PetscCall(VecGetLocalSize(v, &n));
3102   PetscCheck(n == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
3103   for (i = 0; i < m; i++) {
3104     ncols = ai[1] - ai[0];
3105     ai++;
3106     x[i] = 0;
3107     for (j = 0; j < ncols; j++) {
3108       atmp = PetscAbsScalar(*aa);
3109       if (PetscAbsScalar(x[i]) < atmp) {
3110         x[i] = atmp;
3111         if (idx) idx[i] = *aj;
3112       }
3113       aa++;
3114       aj++;
3115     }
3116   }
3117   PetscCall(VecRestoreArrayWrite(v, &x));
3118   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
3119   PetscFunctionReturn(PETSC_SUCCESS);
3120 }
3121 
3122 static PetscErrorCode MatGetRowSumAbs_SeqAIJ(Mat A, Vec v)
3123 {
3124   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
3125   PetscInt         i, j, m = A->rmap->n, *ai, ncols, n;
3126   PetscScalar     *x;
3127   const MatScalar *aa, *av;
3128 
3129   PetscFunctionBegin;
3130   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3131   PetscCall(MatSeqAIJGetArrayRead(A, &av));
3132   aa = av;
3133   ai = a->i;
3134 
3135   PetscCall(VecGetArrayWrite(v, &x));
3136   PetscCall(VecGetLocalSize(v, &n));
3137   PetscCheck(n == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
3138   for (i = 0; i < m; i++) {
3139     ncols = ai[1] - ai[0];
3140     ai++;
3141     x[i] = 0;
3142     for (j = 0; j < ncols; j++) {
3143       x[i] += PetscAbsScalar(*aa);
3144       aa++;
3145     }
3146   }
3147   PetscCall(VecRestoreArrayWrite(v, &x));
3148   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
3149   PetscFunctionReturn(PETSC_SUCCESS);
3150 }
3151 
3152 static PetscErrorCode MatGetRowMax_SeqAIJ(Mat A, Vec v, PetscInt idx[])
3153 {
3154   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
3155   PetscInt         i, j, m = A->rmap->n, *ai, *aj, ncols, n;
3156   PetscScalar     *x;
3157   const MatScalar *aa, *av;
3158 
3159   PetscFunctionBegin;
3160   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3161   PetscCall(MatSeqAIJGetArrayRead(A, &av));
3162   aa = av;
3163   ai = a->i;
3164   aj = a->j;
3165 
3166   PetscCall(VecGetArrayWrite(v, &x));
3167   PetscCall(VecGetLocalSize(v, &n));
3168   PetscCheck(n == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
3169   for (i = 0; i < m; i++) {
3170     ncols = ai[1] - ai[0];
3171     ai++;
3172     if (ncols == A->cmap->n) { /* row is dense */
3173       x[i] = *aa;
3174       if (idx) idx[i] = 0;
3175     } else { /* row is sparse so already KNOW maximum is 0.0 or higher */
3176       x[i] = 0.0;
3177       if (idx) {
3178         for (j = 0; j < ncols; j++) { /* find first implicit 0.0 in the row */
3179           if (aj[j] > j) {
3180             idx[i] = j;
3181             break;
3182           }
3183         }
3184         /* in case first implicit 0.0 in the row occurs at ncols-th column */
3185         if (j == ncols && j < A->cmap->n) idx[i] = j;
3186       }
3187     }
3188     for (j = 0; j < ncols; j++) {
3189       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {
3190         x[i] = *aa;
3191         if (idx) idx[i] = *aj;
3192       }
3193       aa++;
3194       aj++;
3195     }
3196   }
3197   PetscCall(VecRestoreArrayWrite(v, &x));
3198   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
3199   PetscFunctionReturn(PETSC_SUCCESS);
3200 }
3201 
3202 static PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A, Vec v, PetscInt idx[])
3203 {
3204   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
3205   PetscInt         i, j, m = A->rmap->n, *ai, *aj, ncols, n;
3206   PetscScalar     *x;
3207   const MatScalar *aa, *av;
3208 
3209   PetscFunctionBegin;
3210   PetscCall(MatSeqAIJGetArrayRead(A, &av));
3211   aa = av;
3212   ai = a->i;
3213   aj = a->j;
3214 
3215   PetscCall(VecGetArrayWrite(v, &x));
3216   PetscCall(VecGetLocalSize(v, &n));
3217   PetscCheck(n == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector, %" PetscInt_FMT " vs. %" PetscInt_FMT " rows", m, n);
3218   for (i = 0; i < m; i++) {
3219     ncols = ai[1] - ai[0];
3220     ai++;
3221     if (ncols == A->cmap->n) { /* row is dense */
3222       x[i] = *aa;
3223       if (idx) idx[i] = 0;
3224     } else { /* row is sparse so already KNOW minimum is 0.0 or higher */
3225       x[i] = 0.0;
3226       if (idx) { /* find first implicit 0.0 in the row */
3227         for (j = 0; j < ncols; j++) {
3228           if (aj[j] > j) {
3229             idx[i] = j;
3230             break;
3231           }
3232         }
3233         /* in case first implicit 0.0 in the row occurs at ncols-th column */
3234         if (j == ncols && j < A->cmap->n) idx[i] = j;
3235       }
3236     }
3237     for (j = 0; j < ncols; j++) {
3238       if (PetscAbsScalar(x[i]) > PetscAbsScalar(*aa)) {
3239         x[i] = *aa;
3240         if (idx) idx[i] = *aj;
3241       }
3242       aa++;
3243       aj++;
3244     }
3245   }
3246   PetscCall(VecRestoreArrayWrite(v, &x));
3247   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
3248   PetscFunctionReturn(PETSC_SUCCESS);
3249 }
3250 
3251 static PetscErrorCode MatGetRowMin_SeqAIJ(Mat A, Vec v, PetscInt idx[])
3252 {
3253   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
3254   PetscInt         i, j, m = A->rmap->n, ncols, n;
3255   const PetscInt  *ai, *aj;
3256   PetscScalar     *x;
3257   const MatScalar *aa, *av;
3258 
3259   PetscFunctionBegin;
3260   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3261   PetscCall(MatSeqAIJGetArrayRead(A, &av));
3262   aa = av;
3263   ai = a->i;
3264   aj = a->j;
3265 
3266   PetscCall(VecGetArrayWrite(v, &x));
3267   PetscCall(VecGetLocalSize(v, &n));
3268   PetscCheck(n == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
3269   for (i = 0; i < m; i++) {
3270     ncols = ai[1] - ai[0];
3271     ai++;
3272     if (ncols == A->cmap->n) { /* row is dense */
3273       x[i] = *aa;
3274       if (idx) idx[i] = 0;
3275     } else { /* row is sparse so already KNOW minimum is 0.0 or lower */
3276       x[i] = 0.0;
3277       if (idx) { /* find first implicit 0.0 in the row */
3278         for (j = 0; j < ncols; j++) {
3279           if (aj[j] > j) {
3280             idx[i] = j;
3281             break;
3282           }
3283         }
3284         /* in case first implicit 0.0 in the row occurs at ncols-th column */
3285         if (j == ncols && j < A->cmap->n) idx[i] = j;
3286       }
3287     }
3288     for (j = 0; j < ncols; j++) {
3289       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {
3290         x[i] = *aa;
3291         if (idx) idx[i] = *aj;
3292       }
3293       aa++;
3294       aj++;
3295     }
3296   }
3297   PetscCall(VecRestoreArrayWrite(v, &x));
3298   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
3299   PetscFunctionReturn(PETSC_SUCCESS);
3300 }
3301 
3302 static PetscErrorCode MatInvertBlockDiagonal_SeqAIJ(Mat A, const PetscScalar **values)
3303 {
3304   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
3305   PetscInt        i, bs = A->rmap->bs, mbs = A->rmap->n / bs, ipvt[5], bs2 = bs * bs, *v_pivots, ij[7], *IJ, j;
3306   MatScalar      *diag, work[25], *v_work;
3307   const PetscReal shift = 0.0;
3308   PetscBool       allowzeropivot, zeropivotdetected = PETSC_FALSE;
3309 
3310   PetscFunctionBegin;
3311   allowzeropivot = PetscNot(A->erroriffailure);
3312   if (a->ibdiagvalid) {
3313     if (values) *values = a->ibdiag;
3314     PetscFunctionReturn(PETSC_SUCCESS);
3315   }
3316   PetscCall(MatMarkDiagonal_SeqAIJ(A));
3317   if (!a->ibdiag) { PetscCall(PetscMalloc1(bs2 * mbs, &a->ibdiag)); }
3318   diag = a->ibdiag;
3319   if (values) *values = a->ibdiag;
3320   /* factor and invert each block */
3321   switch (bs) {
3322   case 1:
3323     for (i = 0; i < mbs; i++) {
3324       PetscCall(MatGetValues(A, 1, &i, 1, &i, diag + i));
3325       if (PetscAbsScalar(diag[i] + shift) < PETSC_MACHINE_EPSILON) {
3326         if (allowzeropivot) {
3327           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3328           A->factorerror_zeropivot_value = PetscAbsScalar(diag[i]);
3329           A->factorerror_zeropivot_row   = i;
3330           PetscCall(PetscInfo(A, "Zero pivot, row %" PetscInt_FMT " pivot %g tolerance %g\n", i, (double)PetscAbsScalar(diag[i]), (double)PETSC_MACHINE_EPSILON));
3331         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT " pivot %g tolerance %g", i, (double)PetscAbsScalar(diag[i]), (double)PETSC_MACHINE_EPSILON);
3332       }
3333       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3334     }
3335     break;
3336   case 2:
3337     for (i = 0; i < mbs; i++) {
3338       ij[0] = 2 * i;
3339       ij[1] = 2 * i + 1;
3340       PetscCall(MatGetValues(A, 2, ij, 2, ij, diag));
3341       PetscCall(PetscKernel_A_gets_inverse_A_2(diag, shift, allowzeropivot, &zeropivotdetected));
3342       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3343       PetscCall(PetscKernel_A_gets_transpose_A_2(diag));
3344       diag += 4;
3345     }
3346     break;
3347   case 3:
3348     for (i = 0; i < mbs; i++) {
3349       ij[0] = 3 * i;
3350       ij[1] = 3 * i + 1;
3351       ij[2] = 3 * i + 2;
3352       PetscCall(MatGetValues(A, 3, ij, 3, ij, diag));
3353       PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected));
3354       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3355       PetscCall(PetscKernel_A_gets_transpose_A_3(diag));
3356       diag += 9;
3357     }
3358     break;
3359   case 4:
3360     for (i = 0; i < mbs; i++) {
3361       ij[0] = 4 * i;
3362       ij[1] = 4 * i + 1;
3363       ij[2] = 4 * i + 2;
3364       ij[3] = 4 * i + 3;
3365       PetscCall(MatGetValues(A, 4, ij, 4, ij, diag));
3366       PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected));
3367       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3368       PetscCall(PetscKernel_A_gets_transpose_A_4(diag));
3369       diag += 16;
3370     }
3371     break;
3372   case 5:
3373     for (i = 0; i < mbs; i++) {
3374       ij[0] = 5 * i;
3375       ij[1] = 5 * i + 1;
3376       ij[2] = 5 * i + 2;
3377       ij[3] = 5 * i + 3;
3378       ij[4] = 5 * i + 4;
3379       PetscCall(MatGetValues(A, 5, ij, 5, ij, diag));
3380       PetscCall(PetscKernel_A_gets_inverse_A_5(diag, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
3381       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3382       PetscCall(PetscKernel_A_gets_transpose_A_5(diag));
3383       diag += 25;
3384     }
3385     break;
3386   case 6:
3387     for (i = 0; i < mbs; i++) {
3388       ij[0] = 6 * i;
3389       ij[1] = 6 * i + 1;
3390       ij[2] = 6 * i + 2;
3391       ij[3] = 6 * i + 3;
3392       ij[4] = 6 * i + 4;
3393       ij[5] = 6 * i + 5;
3394       PetscCall(MatGetValues(A, 6, ij, 6, ij, diag));
3395       PetscCall(PetscKernel_A_gets_inverse_A_6(diag, shift, allowzeropivot, &zeropivotdetected));
3396       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3397       PetscCall(PetscKernel_A_gets_transpose_A_6(diag));
3398       diag += 36;
3399     }
3400     break;
3401   case 7:
3402     for (i = 0; i < mbs; i++) {
3403       ij[0] = 7 * i;
3404       ij[1] = 7 * i + 1;
3405       ij[2] = 7 * i + 2;
3406       ij[3] = 7 * i + 3;
3407       ij[4] = 7 * i + 4;
3408       ij[5] = 7 * i + 5;
3409       ij[6] = 7 * i + 6;
3410       PetscCall(MatGetValues(A, 7, ij, 7, ij, diag));
3411       PetscCall(PetscKernel_A_gets_inverse_A_7(diag, shift, allowzeropivot, &zeropivotdetected));
3412       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3413       PetscCall(PetscKernel_A_gets_transpose_A_7(diag));
3414       diag += 49;
3415     }
3416     break;
3417   default:
3418     PetscCall(PetscMalloc3(bs, &v_work, bs, &v_pivots, bs, &IJ));
3419     for (i = 0; i < mbs; i++) {
3420       for (j = 0; j < bs; j++) IJ[j] = bs * i + j;
3421       PetscCall(MatGetValues(A, bs, IJ, bs, IJ, diag));
3422       PetscCall(PetscKernel_A_gets_inverse_A(bs, diag, v_pivots, v_work, allowzeropivot, &zeropivotdetected));
3423       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3424       PetscCall(PetscKernel_A_gets_transpose_A_N(diag, bs));
3425       diag += bs2;
3426     }
3427     PetscCall(PetscFree3(v_work, v_pivots, IJ));
3428   }
3429   a->ibdiagvalid = PETSC_TRUE;
3430   PetscFunctionReturn(PETSC_SUCCESS);
3431 }
3432 
3433 static PetscErrorCode MatSetRandom_SeqAIJ(Mat x, PetscRandom rctx)
3434 {
3435   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)x->data;
3436   PetscScalar a, *aa;
3437   PetscInt    m, n, i, j, col;
3438 
3439   PetscFunctionBegin;
3440   if (!x->assembled) {
3441     PetscCall(MatGetSize(x, &m, &n));
3442     for (i = 0; i < m; i++) {
3443       for (j = 0; j < aij->imax[i]; j++) {
3444         PetscCall(PetscRandomGetValue(rctx, &a));
3445         col = (PetscInt)(n * PetscRealPart(a));
3446         PetscCall(MatSetValues(x, 1, &i, 1, &col, &a, ADD_VALUES));
3447       }
3448     }
3449   } else {
3450     PetscCall(MatSeqAIJGetArrayWrite(x, &aa));
3451     for (i = 0; i < aij->nz; i++) PetscCall(PetscRandomGetValue(rctx, aa + i));
3452     PetscCall(MatSeqAIJRestoreArrayWrite(x, &aa));
3453   }
3454   PetscCall(MatAssemblyBegin(x, MAT_FINAL_ASSEMBLY));
3455   PetscCall(MatAssemblyEnd(x, MAT_FINAL_ASSEMBLY));
3456   PetscFunctionReturn(PETSC_SUCCESS);
3457 }
3458 
3459 /* Like MatSetRandom_SeqAIJ, but do not set values on columns in range of [low, high) */
3460 PetscErrorCode MatSetRandomSkipColumnRange_SeqAIJ_Private(Mat x, PetscInt low, PetscInt high, PetscRandom rctx)
3461 {
3462   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)x->data;
3463   PetscScalar a;
3464   PetscInt    m, n, i, j, col, nskip;
3465 
3466   PetscFunctionBegin;
3467   nskip = high - low;
3468   PetscCall(MatGetSize(x, &m, &n));
3469   n -= nskip; /* shrink number of columns where nonzeros can be set */
3470   for (i = 0; i < m; i++) {
3471     for (j = 0; j < aij->imax[i]; j++) {
3472       PetscCall(PetscRandomGetValue(rctx, &a));
3473       col = (PetscInt)(n * PetscRealPart(a));
3474       if (col >= low) col += nskip; /* shift col rightward to skip the hole */
3475       PetscCall(MatSetValues(x, 1, &i, 1, &col, &a, ADD_VALUES));
3476     }
3477   }
3478   PetscCall(MatAssemblyBegin(x, MAT_FINAL_ASSEMBLY));
3479   PetscCall(MatAssemblyEnd(x, MAT_FINAL_ASSEMBLY));
3480   PetscFunctionReturn(PETSC_SUCCESS);
3481 }
3482 
3483 static struct _MatOps MatOps_Values = {MatSetValues_SeqAIJ,
3484                                        MatGetRow_SeqAIJ,
3485                                        MatRestoreRow_SeqAIJ,
3486                                        MatMult_SeqAIJ,
3487                                        /*  4*/ MatMultAdd_SeqAIJ,
3488                                        MatMultTranspose_SeqAIJ,
3489                                        MatMultTransposeAdd_SeqAIJ,
3490                                        NULL,
3491                                        NULL,
3492                                        NULL,
3493                                        /* 10*/ NULL,
3494                                        MatLUFactor_SeqAIJ,
3495                                        NULL,
3496                                        MatSOR_SeqAIJ,
3497                                        MatTranspose_SeqAIJ,
3498                                        /*1 5*/ MatGetInfo_SeqAIJ,
3499                                        MatEqual_SeqAIJ,
3500                                        MatGetDiagonal_SeqAIJ,
3501                                        MatDiagonalScale_SeqAIJ,
3502                                        MatNorm_SeqAIJ,
3503                                        /* 20*/ NULL,
3504                                        MatAssemblyEnd_SeqAIJ,
3505                                        MatSetOption_SeqAIJ,
3506                                        MatZeroEntries_SeqAIJ,
3507                                        /* 24*/ MatZeroRows_SeqAIJ,
3508                                        NULL,
3509                                        NULL,
3510                                        NULL,
3511                                        NULL,
3512                                        /* 29*/ MatSetUp_Seq_Hash,
3513                                        NULL,
3514                                        NULL,
3515                                        NULL,
3516                                        NULL,
3517                                        /* 34*/ MatDuplicate_SeqAIJ,
3518                                        NULL,
3519                                        NULL,
3520                                        MatILUFactor_SeqAIJ,
3521                                        NULL,
3522                                        /* 39*/ MatAXPY_SeqAIJ,
3523                                        MatCreateSubMatrices_SeqAIJ,
3524                                        MatIncreaseOverlap_SeqAIJ,
3525                                        MatGetValues_SeqAIJ,
3526                                        MatCopy_SeqAIJ,
3527                                        /* 44*/ MatGetRowMax_SeqAIJ,
3528                                        MatScale_SeqAIJ,
3529                                        MatShift_SeqAIJ,
3530                                        MatDiagonalSet_SeqAIJ,
3531                                        MatZeroRowsColumns_SeqAIJ,
3532                                        /* 49*/ MatSetRandom_SeqAIJ,
3533                                        MatGetRowIJ_SeqAIJ,
3534                                        MatRestoreRowIJ_SeqAIJ,
3535                                        MatGetColumnIJ_SeqAIJ,
3536                                        MatRestoreColumnIJ_SeqAIJ,
3537                                        /* 54*/ MatFDColoringCreate_SeqXAIJ,
3538                                        NULL,
3539                                        NULL,
3540                                        MatPermute_SeqAIJ,
3541                                        NULL,
3542                                        /* 59*/ NULL,
3543                                        MatDestroy_SeqAIJ,
3544                                        MatView_SeqAIJ,
3545                                        NULL,
3546                                        NULL,
3547                                        /* 64*/ NULL,
3548                                        MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3549                                        NULL,
3550                                        NULL,
3551                                        NULL,
3552                                        /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3553                                        MatGetRowMinAbs_SeqAIJ,
3554                                        NULL,
3555                                        NULL,
3556                                        NULL,
3557                                        /* 74*/ NULL,
3558                                        MatFDColoringApply_AIJ,
3559                                        NULL,
3560                                        NULL,
3561                                        NULL,
3562                                        /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3563                                        NULL,
3564                                        NULL,
3565                                        NULL,
3566                                        MatLoad_SeqAIJ,
3567                                        /* 84*/ NULL,
3568                                        NULL,
3569                                        NULL,
3570                                        NULL,
3571                                        NULL,
3572                                        /* 89*/ NULL,
3573                                        NULL,
3574                                        MatMatMultNumeric_SeqAIJ_SeqAIJ,
3575                                        NULL,
3576                                        NULL,
3577                                        /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy,
3578                                        NULL,
3579                                        NULL,
3580                                        MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3581                                        NULL,
3582                                        /* 99*/ MatProductSetFromOptions_SeqAIJ,
3583                                        NULL,
3584                                        NULL,
3585                                        MatConjugate_SeqAIJ,
3586                                        NULL,
3587                                        /*104*/ MatSetValuesRow_SeqAIJ,
3588                                        MatRealPart_SeqAIJ,
3589                                        MatImaginaryPart_SeqAIJ,
3590                                        NULL,
3591                                        NULL,
3592                                        /*109*/ MatMatSolve_SeqAIJ,
3593                                        NULL,
3594                                        MatGetRowMin_SeqAIJ,
3595                                        NULL,
3596                                        MatMissingDiagonal_SeqAIJ,
3597                                        /*114*/ NULL,
3598                                        NULL,
3599                                        NULL,
3600                                        NULL,
3601                                        NULL,
3602                                        /*119*/ NULL,
3603                                        NULL,
3604                                        NULL,
3605                                        NULL,
3606                                        MatGetMultiProcBlock_SeqAIJ,
3607                                        /*124*/ MatFindNonzeroRows_SeqAIJ,
3608                                        MatGetColumnReductions_SeqAIJ,
3609                                        MatInvertBlockDiagonal_SeqAIJ,
3610                                        MatInvertVariableBlockDiagonal_SeqAIJ,
3611                                        NULL,
3612                                        /*129*/ NULL,
3613                                        NULL,
3614                                        NULL,
3615                                        MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3616                                        MatTransposeColoringCreate_SeqAIJ,
3617                                        /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3618                                        MatTransColoringApplyDenToSp_SeqAIJ,
3619                                        NULL,
3620                                        NULL,
3621                                        MatRARtNumeric_SeqAIJ_SeqAIJ,
3622                                        /*139*/ NULL,
3623                                        NULL,
3624                                        NULL,
3625                                        MatFDColoringSetUp_SeqXAIJ,
3626                                        MatFindOffBlockDiagonalEntries_SeqAIJ,
3627                                        MatCreateMPIMatConcatenateSeqMat_SeqAIJ,
3628                                        /*145*/ MatDestroySubMatrices_SeqAIJ,
3629                                        NULL,
3630                                        NULL,
3631                                        MatCreateGraph_Simple_AIJ,
3632                                        NULL,
3633                                        /*150*/ MatTransposeSymbolic_SeqAIJ,
3634                                        MatEliminateZeros_SeqAIJ,
3635                                        MatGetRowSumAbs_SeqAIJ,
3636                                        NULL,
3637                                        NULL,
3638                                        /*155*/ NULL,
3639                                        MatCopyHashToXAIJ_Seq_Hash};
3640 
3641 static PetscErrorCode MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat, PetscInt *indices)
3642 {
3643   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)mat->data;
3644   PetscInt    i, nz, n;
3645 
3646   PetscFunctionBegin;
3647   nz = aij->maxnz;
3648   n  = mat->rmap->n;
3649   for (i = 0; i < nz; i++) aij->j[i] = indices[i];
3650   aij->nz = nz;
3651   for (i = 0; i < n; i++) aij->ilen[i] = aij->imax[i];
3652   PetscFunctionReturn(PETSC_SUCCESS);
3653 }
3654 
3655 /*
3656  * Given a sparse matrix with global column indices, compact it by using a local column space.
3657  * The result matrix helps saving memory in other algorithms, such as MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable()
3658  */
3659 PetscErrorCode MatSeqAIJCompactOutExtraColumns_SeqAIJ(Mat mat, ISLocalToGlobalMapping *mapping)
3660 {
3661   Mat_SeqAIJ   *aij = (Mat_SeqAIJ *)mat->data;
3662   PetscHMapI    gid1_lid1;
3663   PetscHashIter tpos;
3664   PetscInt      gid, lid, i, ec, nz = aij->nz;
3665   PetscInt     *garray, *jj = aij->j;
3666 
3667   PetscFunctionBegin;
3668   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
3669   PetscAssertPointer(mapping, 2);
3670   /* use a table */
3671   PetscCall(PetscHMapICreateWithSize(mat->rmap->n, &gid1_lid1));
3672   ec = 0;
3673   for (i = 0; i < nz; i++) {
3674     PetscInt data, gid1 = jj[i] + 1;
3675     PetscCall(PetscHMapIGetWithDefault(gid1_lid1, gid1, 0, &data));
3676     if (!data) {
3677       /* one based table */
3678       PetscCall(PetscHMapISet(gid1_lid1, gid1, ++ec));
3679     }
3680   }
3681   /* form array of columns we need */
3682   PetscCall(PetscMalloc1(ec, &garray));
3683   PetscHashIterBegin(gid1_lid1, tpos);
3684   while (!PetscHashIterAtEnd(gid1_lid1, tpos)) {
3685     PetscHashIterGetKey(gid1_lid1, tpos, gid);
3686     PetscHashIterGetVal(gid1_lid1, tpos, lid);
3687     PetscHashIterNext(gid1_lid1, tpos);
3688     gid--;
3689     lid--;
3690     garray[lid] = gid;
3691   }
3692   PetscCall(PetscSortInt(ec, garray)); /* sort, and rebuild */
3693   PetscCall(PetscHMapIClear(gid1_lid1));
3694   for (i = 0; i < ec; i++) PetscCall(PetscHMapISet(gid1_lid1, garray[i] + 1, i + 1));
3695   /* compact out the extra columns in B */
3696   for (i = 0; i < nz; i++) {
3697     PetscInt gid1 = jj[i] + 1;
3698     PetscCall(PetscHMapIGetWithDefault(gid1_lid1, gid1, 0, &lid));
3699     lid--;
3700     jj[i] = lid;
3701   }
3702   PetscCall(PetscLayoutDestroy(&mat->cmap));
3703   PetscCall(PetscHMapIDestroy(&gid1_lid1));
3704   PetscCall(PetscLayoutCreateFromSizes(PetscObjectComm((PetscObject)mat), ec, ec, 1, &mat->cmap));
3705   PetscCall(ISLocalToGlobalMappingCreate(PETSC_COMM_SELF, mat->cmap->bs, mat->cmap->n, garray, PETSC_OWN_POINTER, mapping));
3706   PetscCall(ISLocalToGlobalMappingSetType(*mapping, ISLOCALTOGLOBALMAPPINGHASH));
3707   PetscFunctionReturn(PETSC_SUCCESS);
3708 }
3709 
3710 /*@
3711   MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3712   in the matrix.
3713 
3714   Input Parameters:
3715 + mat     - the `MATSEQAIJ` matrix
3716 - indices - the column indices
3717 
3718   Level: advanced
3719 
3720   Notes:
3721   This can be called if you have precomputed the nonzero structure of the
3722   matrix and want to provide it to the matrix object to improve the performance
3723   of the `MatSetValues()` operation.
3724 
3725   You MUST have set the correct numbers of nonzeros per row in the call to
3726   `MatCreateSeqAIJ()`, and the columns indices MUST be sorted.
3727 
3728   MUST be called before any calls to `MatSetValues()`
3729 
3730   The indices should start with zero, not one.
3731 
3732 .seealso: [](ch_matrices), `Mat`, `MATSEQAIJ`
3733 @*/
3734 PetscErrorCode MatSeqAIJSetColumnIndices(Mat mat, PetscInt *indices)
3735 {
3736   PetscFunctionBegin;
3737   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
3738   PetscAssertPointer(indices, 2);
3739   PetscUseMethod(mat, "MatSeqAIJSetColumnIndices_C", (Mat, PetscInt *), (mat, indices));
3740   PetscFunctionReturn(PETSC_SUCCESS);
3741 }
3742 
3743 static PetscErrorCode MatStoreValues_SeqAIJ(Mat mat)
3744 {
3745   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)mat->data;
3746   size_t      nz  = aij->i[mat->rmap->n];
3747 
3748   PetscFunctionBegin;
3749   PetscCheck(aij->nonew, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3750 
3751   /* allocate space for values if not already there */
3752   if (!aij->saved_values) { PetscCall(PetscMalloc1(nz + 1, &aij->saved_values)); }
3753 
3754   /* copy values over */
3755   PetscCall(PetscArraycpy(aij->saved_values, aij->a, nz));
3756   PetscFunctionReturn(PETSC_SUCCESS);
3757 }
3758 
3759 /*@
3760   MatStoreValues - Stashes a copy of the matrix values; this allows reusing of the linear part of a Jacobian, while recomputing only the
3761   nonlinear portion.
3762 
3763   Logically Collect
3764 
3765   Input Parameter:
3766 . mat - the matrix (currently only `MATAIJ` matrices support this option)
3767 
3768   Level: advanced
3769 
3770   Example Usage:
3771 .vb
3772     Using SNES
3773     Create Jacobian matrix
3774     Set linear terms into matrix
3775     Apply boundary conditions to matrix, at this time matrix must have
3776       final nonzero structure (i.e. setting the nonlinear terms and applying
3777       boundary conditions again will not change the nonzero structure
3778     MatSetOption(mat, MAT_NEW_NONZERO_LOCATIONS, PETSC_FALSE);
3779     MatStoreValues(mat);
3780     Call SNESSetJacobian() with matrix
3781     In your Jacobian routine
3782       MatRetrieveValues(mat);
3783       Set nonlinear terms in matrix
3784 
3785     Without `SNESSolve()`, i.e. when you handle nonlinear solve yourself:
3786     // build linear portion of Jacobian
3787     MatSetOption(mat, MAT_NEW_NONZERO_LOCATIONS, PETSC_FALSE);
3788     MatStoreValues(mat);
3789     loop over nonlinear iterations
3790        MatRetrieveValues(mat);
3791        // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3792        // call MatAssemblyBegin/End() on matrix
3793        Solve linear system with Jacobian
3794     endloop
3795 .ve
3796 
3797   Notes:
3798   Matrix must already be assembled before calling this routine
3799   Must set the matrix option `MatSetOption`(mat,`MAT_NEW_NONZERO_LOCATIONS`,`PETSC_FALSE`); before
3800   calling this routine.
3801 
3802   When this is called multiple times it overwrites the previous set of stored values
3803   and does not allocated additional space.
3804 
3805 .seealso: [](ch_matrices), `Mat`, `MatRetrieveValues()`
3806 @*/
3807 PetscErrorCode MatStoreValues(Mat mat)
3808 {
3809   PetscFunctionBegin;
3810   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
3811   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
3812   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3813   PetscUseMethod(mat, "MatStoreValues_C", (Mat), (mat));
3814   PetscFunctionReturn(PETSC_SUCCESS);
3815 }
3816 
3817 static PetscErrorCode MatRetrieveValues_SeqAIJ(Mat mat)
3818 {
3819   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)mat->data;
3820   PetscInt    nz  = aij->i[mat->rmap->n];
3821 
3822   PetscFunctionBegin;
3823   PetscCheck(aij->nonew, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3824   PetscCheck(aij->saved_values, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Must call MatStoreValues(A);first");
3825   /* copy values over */
3826   PetscCall(PetscArraycpy(aij->a, aij->saved_values, nz));
3827   PetscFunctionReturn(PETSC_SUCCESS);
3828 }
3829 
3830 /*@
3831   MatRetrieveValues - Retrieves the copy of the matrix values that was stored with `MatStoreValues()`
3832 
3833   Logically Collect
3834 
3835   Input Parameter:
3836 . mat - the matrix (currently only `MATAIJ` matrices support this option)
3837 
3838   Level: advanced
3839 
3840 .seealso: [](ch_matrices), `Mat`, `MatStoreValues()`
3841 @*/
3842 PetscErrorCode MatRetrieveValues(Mat mat)
3843 {
3844   PetscFunctionBegin;
3845   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
3846   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
3847   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3848   PetscUseMethod(mat, "MatRetrieveValues_C", (Mat), (mat));
3849   PetscFunctionReturn(PETSC_SUCCESS);
3850 }
3851 
3852 /*@
3853   MatCreateSeqAIJ - Creates a sparse matrix in `MATSEQAIJ` (compressed row) format
3854   (the default parallel PETSc format).  For good matrix assembly performance
3855   the user should preallocate the matrix storage by setting the parameter `nz`
3856   (or the array `nnz`).
3857 
3858   Collective
3859 
3860   Input Parameters:
3861 + comm - MPI communicator, set to `PETSC_COMM_SELF`
3862 . m    - number of rows
3863 . n    - number of columns
3864 . nz   - number of nonzeros per row (same for all rows)
3865 - nnz  - array containing the number of nonzeros in the various rows
3866          (possibly different for each row) or NULL
3867 
3868   Output Parameter:
3869 . A - the matrix
3870 
3871   Options Database Keys:
3872 + -mat_no_inode            - Do not use inodes
3873 - -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3874 
3875   Level: intermediate
3876 
3877   Notes:
3878   It is recommend to use `MatCreateFromOptions()` instead of this routine
3879 
3880   If `nnz` is given then `nz` is ignored
3881 
3882   The `MATSEQAIJ` format, also called
3883   compressed row storage, is fully compatible with standard Fortran
3884   storage.  That is, the stored row and column indices can begin at
3885   either one (as in Fortran) or zero.
3886 
3887   Specify the preallocated storage with either `nz` or `nnz` (not both).
3888   Set `nz` = `PETSC_DEFAULT` and `nnz` = `NULL` for PETSc to control dynamic memory
3889   allocation.
3890 
3891   By default, this format uses inodes (identical nodes) when possible, to
3892   improve numerical efficiency of matrix-vector products and solves. We
3893   search for consecutive rows with the same nonzero structure, thereby
3894   reusing matrix information to achieve increased efficiency.
3895 
3896 .seealso: [](ch_matrices), `Mat`, [Sparse Matrix Creation](sec_matsparse), `MatCreate()`, `MatCreateAIJ()`, `MatSetValues()`, `MatSeqAIJSetColumnIndices()`, `MatCreateSeqAIJWithArrays()`
3897 @*/
3898 PetscErrorCode MatCreateSeqAIJ(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt nz, const PetscInt nnz[], Mat *A)
3899 {
3900   PetscFunctionBegin;
3901   PetscCall(MatCreate(comm, A));
3902   PetscCall(MatSetSizes(*A, m, n, m, n));
3903   PetscCall(MatSetType(*A, MATSEQAIJ));
3904   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*A, nz, nnz));
3905   PetscFunctionReturn(PETSC_SUCCESS);
3906 }
3907 
3908 /*@
3909   MatSeqAIJSetPreallocation - For good matrix assembly performance
3910   the user should preallocate the matrix storage by setting the parameter nz
3911   (or the array nnz).  By setting these parameters accurately, performance
3912   during matrix assembly can be increased by more than a factor of 50.
3913 
3914   Collective
3915 
3916   Input Parameters:
3917 + B   - The matrix
3918 . nz  - number of nonzeros per row (same for all rows)
3919 - nnz - array containing the number of nonzeros in the various rows
3920          (possibly different for each row) or NULL
3921 
3922   Options Database Keys:
3923 + -mat_no_inode            - Do not use inodes
3924 - -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3925 
3926   Level: intermediate
3927 
3928   Notes:
3929   If `nnz` is given then `nz` is ignored
3930 
3931   The `MATSEQAIJ` format also called
3932   compressed row storage, is fully compatible with standard Fortran
3933   storage.  That is, the stored row and column indices can begin at
3934   either one (as in Fortran) or zero.  See the users' manual for details.
3935 
3936   Specify the preallocated storage with either `nz` or `nnz` (not both).
3937   Set nz = `PETSC_DEFAULT` and `nnz` = `NULL` for PETSc to control dynamic memory
3938   allocation.
3939 
3940   You can call `MatGetInfo()` to get information on how effective the preallocation was;
3941   for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3942   You can also run with the option -info and look for messages with the string
3943   malloc in them to see if additional memory allocation was needed.
3944 
3945   Developer Notes:
3946   Use nz of `MAT_SKIP_ALLOCATION` to not allocate any space for the matrix
3947   entries or columns indices
3948 
3949   By default, this format uses inodes (identical nodes) when possible, to
3950   improve numerical efficiency of matrix-vector products and solves. We
3951   search for consecutive rows with the same nonzero structure, thereby
3952   reusing matrix information to achieve increased efficiency.
3953 
3954 .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateAIJ()`, `MatSetValues()`, `MatSeqAIJSetColumnIndices()`, `MatCreateSeqAIJWithArrays()`, `MatGetInfo()`,
3955           `MatSeqAIJSetTotalPreallocation()`
3956 @*/
3957 PetscErrorCode MatSeqAIJSetPreallocation(Mat B, PetscInt nz, const PetscInt nnz[])
3958 {
3959   PetscFunctionBegin;
3960   PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
3961   PetscValidType(B, 1);
3962   PetscTryMethod(B, "MatSeqAIJSetPreallocation_C", (Mat, PetscInt, const PetscInt[]), (B, nz, nnz));
3963   PetscFunctionReturn(PETSC_SUCCESS);
3964 }
3965 
3966 PetscErrorCode MatSeqAIJSetPreallocation_SeqAIJ(Mat B, PetscInt nz, const PetscInt *nnz)
3967 {
3968   Mat_SeqAIJ *b              = (Mat_SeqAIJ *)B->data;
3969   PetscBool   skipallocation = PETSC_FALSE, realalloc = PETSC_FALSE;
3970   PetscInt    i;
3971 
3972   PetscFunctionBegin;
3973   if (B->hash_active) {
3974     B->ops[0] = b->cops;
3975     PetscCall(PetscHMapIJVDestroy(&b->ht));
3976     PetscCall(PetscFree(b->dnz));
3977     B->hash_active = PETSC_FALSE;
3978   }
3979   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3980   if (nz == MAT_SKIP_ALLOCATION) {
3981     skipallocation = PETSC_TRUE;
3982     nz             = 0;
3983   }
3984   PetscCall(PetscLayoutSetUp(B->rmap));
3985   PetscCall(PetscLayoutSetUp(B->cmap));
3986 
3987   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3988   PetscCheck(nz >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "nz cannot be less than 0: value %" PetscInt_FMT, nz);
3989   if (nnz) {
3990     for (i = 0; i < B->rmap->n; i++) {
3991       PetscCheck(nnz[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "nnz cannot be less than 0: local row %" PetscInt_FMT " value %" PetscInt_FMT, i, nnz[i]);
3992       PetscCheck(nnz[i] <= B->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "nnz cannot be greater than row length: local row %" PetscInt_FMT " value %" PetscInt_FMT " rowlength %" PetscInt_FMT, i, nnz[i], B->cmap->n);
3993     }
3994   }
3995 
3996   B->preallocated = PETSC_TRUE;
3997   if (!skipallocation) {
3998     if (!b->imax) { PetscCall(PetscMalloc1(B->rmap->n, &b->imax)); }
3999     if (!b->ilen) {
4000       /* b->ilen will count nonzeros in each row so far. */
4001       PetscCall(PetscCalloc1(B->rmap->n, &b->ilen));
4002     } else {
4003       PetscCall(PetscMemzero(b->ilen, B->rmap->n * sizeof(PetscInt)));
4004     }
4005     if (!b->ipre) PetscCall(PetscMalloc1(B->rmap->n, &b->ipre));
4006     if (!nnz) {
4007       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
4008       else if (nz < 0) nz = 1;
4009       nz = PetscMin(nz, B->cmap->n);
4010       for (i = 0; i < B->rmap->n; i++) b->imax[i] = nz;
4011       PetscCall(PetscIntMultError(nz, B->rmap->n, &nz));
4012     } else {
4013       PetscInt64 nz64 = 0;
4014       for (i = 0; i < B->rmap->n; i++) {
4015         b->imax[i] = nnz[i];
4016         nz64 += nnz[i];
4017       }
4018       PetscCall(PetscIntCast(nz64, &nz));
4019     }
4020 
4021     /* allocate the matrix space */
4022     PetscCall(MatSeqXAIJFreeAIJ(B, &b->a, &b->j, &b->i));
4023     PetscCall(PetscShmgetAllocateArray(nz, sizeof(PetscInt), (void **)&b->j));
4024     PetscCall(PetscShmgetAllocateArray(B->rmap->n + 1, sizeof(PetscInt), (void **)&b->i));
4025     b->free_ij = PETSC_TRUE;
4026     if (B->structure_only) {
4027       b->free_a = PETSC_FALSE;
4028     } else {
4029       PetscCall(PetscShmgetAllocateArray(nz, sizeof(PetscScalar), (void **)&b->a));
4030       b->free_a = PETSC_TRUE;
4031     }
4032     b->i[0] = 0;
4033     for (i = 1; i < B->rmap->n + 1; i++) b->i[i] = b->i[i - 1] + b->imax[i - 1];
4034   } else {
4035     b->free_a  = PETSC_FALSE;
4036     b->free_ij = PETSC_FALSE;
4037   }
4038 
4039   if (b->ipre && nnz != b->ipre && b->imax) {
4040     /* reserve user-requested sparsity */
4041     PetscCall(PetscArraycpy(b->ipre, b->imax, B->rmap->n));
4042   }
4043 
4044   b->nz               = 0;
4045   b->maxnz            = nz;
4046   B->info.nz_unneeded = (double)b->maxnz;
4047   if (realalloc) PetscCall(MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE));
4048   B->was_assembled = PETSC_FALSE;
4049   B->assembled     = PETSC_FALSE;
4050   /* We simply deem preallocation has changed nonzero state. Updating the state
4051      will give clients (like AIJKokkos) a chance to know something has happened.
4052   */
4053   B->nonzerostate++;
4054   PetscFunctionReturn(PETSC_SUCCESS);
4055 }
4056 
4057 PetscErrorCode MatResetPreallocation_SeqAIJ_Private(Mat A, PetscBool *memoryreset)
4058 {
4059   Mat_SeqAIJ *a;
4060   PetscInt    i;
4061   PetscBool   skipreset;
4062 
4063   PetscFunctionBegin;
4064   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4065 
4066   PetscCheck(A->insertmode == NOT_SET_VALUES, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot reset preallocation after setting some values but not yet calling MatAssemblyBegin()/MatAssemblyEnd()");
4067   if (A->num_ass == 0) PetscFunctionReturn(PETSC_SUCCESS);
4068 
4069   /* Check local size. If zero, then return */
4070   if (!A->rmap->n) PetscFunctionReturn(PETSC_SUCCESS);
4071 
4072   a = (Mat_SeqAIJ *)A->data;
4073   /* if no saved info, we error out */
4074   PetscCheck(a->ipre, PETSC_COMM_SELF, PETSC_ERR_ARG_NULL, "No saved preallocation info ");
4075 
4076   PetscCheck(a->i && a->imax && a->ilen, PETSC_COMM_SELF, PETSC_ERR_ARG_NULL, "Memory info is incomplete, and cannot reset preallocation ");
4077 
4078   PetscCall(PetscArraycmp(a->ipre, a->ilen, A->rmap->n, &skipreset));
4079   if (skipreset) PetscCall(MatZeroEntries(A));
4080   else {
4081     PetscCall(PetscArraycpy(a->imax, a->ipre, A->rmap->n));
4082     PetscCall(PetscArrayzero(a->ilen, A->rmap->n));
4083     a->i[0] = 0;
4084     for (i = 1; i < A->rmap->n + 1; i++) a->i[i] = a->i[i - 1] + a->imax[i - 1];
4085     A->preallocated     = PETSC_TRUE;
4086     a->nz               = 0;
4087     a->maxnz            = a->i[A->rmap->n];
4088     A->info.nz_unneeded = (double)a->maxnz;
4089     A->was_assembled    = PETSC_FALSE;
4090     A->assembled        = PETSC_FALSE;
4091     A->nonzerostate++;
4092     /* Log that the state of this object has changed; this will help guarantee that preconditioners get re-setup */
4093     PetscCall(PetscObjectStateIncrease((PetscObject)A));
4094   }
4095   if (memoryreset) *memoryreset = (PetscBool)!skipreset;
4096   PetscFunctionReturn(PETSC_SUCCESS);
4097 }
4098 
4099 static PetscErrorCode MatResetPreallocation_SeqAIJ(Mat A)
4100 {
4101   PetscFunctionBegin;
4102   PetscCall(MatResetPreallocation_SeqAIJ_Private(A, NULL));
4103   PetscFunctionReturn(PETSC_SUCCESS);
4104 }
4105 
4106 /*@
4107   MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in `MATSEQAIJ` format.
4108 
4109   Input Parameters:
4110 + B - the matrix
4111 . i - the indices into `j` for the start of each row (indices start with zero)
4112 . j - the column indices for each row (indices start with zero) these must be sorted for each row
4113 - v - optional values in the matrix, use `NULL` if not provided
4114 
4115   Level: developer
4116 
4117   Notes:
4118   The `i`,`j`,`v` values are COPIED with this routine; to avoid the copy use `MatCreateSeqAIJWithArrays()`
4119 
4120   This routine may be called multiple times with different nonzero patterns (or the same nonzero pattern). The nonzero
4121   structure will be the union of all the previous nonzero structures.
4122 
4123   Developer Notes:
4124   An optimization could be added to the implementation where it checks if the `i`, and `j` are identical to the current `i` and `j` and
4125   then just copies the `v` values directly with `PetscMemcpy()`.
4126 
4127   This routine could also take a `PetscCopyMode` argument to allow sharing the values instead of always copying them.
4128 
4129 .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatSeqAIJSetPreallocation()`, `MATSEQAIJ`, `MatResetPreallocation()`
4130 @*/
4131 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B, const PetscInt i[], const PetscInt j[], const PetscScalar v[])
4132 {
4133   PetscFunctionBegin;
4134   PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
4135   PetscValidType(B, 1);
4136   PetscTryMethod(B, "MatSeqAIJSetPreallocationCSR_C", (Mat, const PetscInt[], const PetscInt[], const PetscScalar[]), (B, i, j, v));
4137   PetscFunctionReturn(PETSC_SUCCESS);
4138 }
4139 
4140 static PetscErrorCode MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B, const PetscInt Ii[], const PetscInt J[], const PetscScalar v[])
4141 {
4142   PetscInt  i;
4143   PetscInt  m, n;
4144   PetscInt  nz;
4145   PetscInt *nnz;
4146 
4147   PetscFunctionBegin;
4148   PetscCheck(Ii[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %" PetscInt_FMT, Ii[0]);
4149 
4150   PetscCall(PetscLayoutSetUp(B->rmap));
4151   PetscCall(PetscLayoutSetUp(B->cmap));
4152 
4153   PetscCall(MatGetSize(B, &m, &n));
4154   PetscCall(PetscMalloc1(m + 1, &nnz));
4155   for (i = 0; i < m; i++) {
4156     nz = Ii[i + 1] - Ii[i];
4157     PetscCheck(nz >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local row %" PetscInt_FMT " has a negative number of columns %" PetscInt_FMT, i, nz);
4158     nnz[i] = nz;
4159   }
4160   PetscCall(MatSeqAIJSetPreallocation(B, 0, nnz));
4161   PetscCall(PetscFree(nnz));
4162 
4163   for (i = 0; i < m; i++) PetscCall(MatSetValues_SeqAIJ(B, 1, &i, Ii[i + 1] - Ii[i], J + Ii[i], PetscSafePointerPlusOffset(v, Ii[i]), INSERT_VALUES));
4164 
4165   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
4166   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
4167 
4168   PetscCall(MatSetOption(B, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
4169   PetscFunctionReturn(PETSC_SUCCESS);
4170 }
4171 
4172 /*@
4173   MatSeqAIJKron - Computes `C`, the Kronecker product of `A` and `B`.
4174 
4175   Input Parameters:
4176 + A     - left-hand side matrix
4177 . B     - right-hand side matrix
4178 - reuse - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
4179 
4180   Output Parameter:
4181 . C - Kronecker product of `A` and `B`
4182 
4183   Level: intermediate
4184 
4185   Note:
4186   `MAT_REUSE_MATRIX` can only be used when the nonzero structure of the product matrix has not changed from that last call to `MatSeqAIJKron()`.
4187 
4188 .seealso: [](ch_matrices), `Mat`, `MatCreateSeqAIJ()`, `MATSEQAIJ`, `MATKAIJ`, `MatReuse`
4189 @*/
4190 PetscErrorCode MatSeqAIJKron(Mat A, Mat B, MatReuse reuse, Mat *C)
4191 {
4192   PetscFunctionBegin;
4193   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4194   PetscValidType(A, 1);
4195   PetscValidHeaderSpecific(B, MAT_CLASSID, 2);
4196   PetscValidType(B, 2);
4197   PetscAssertPointer(C, 4);
4198   if (reuse == MAT_REUSE_MATRIX) {
4199     PetscValidHeaderSpecific(*C, MAT_CLASSID, 4);
4200     PetscValidType(*C, 4);
4201   }
4202   PetscTryMethod(A, "MatSeqAIJKron_C", (Mat, Mat, MatReuse, Mat *), (A, B, reuse, C));
4203   PetscFunctionReturn(PETSC_SUCCESS);
4204 }
4205 
4206 static PetscErrorCode MatSeqAIJKron_SeqAIJ(Mat A, Mat B, MatReuse reuse, Mat *C)
4207 {
4208   Mat                newmat;
4209   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
4210   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;
4211   PetscScalar       *v;
4212   const PetscScalar *aa, *ba;
4213   PetscInt          *i, *j, m, n, p, q, nnz = 0, am = A->rmap->n, bm = B->rmap->n, an = A->cmap->n, bn = B->cmap->n;
4214   PetscBool          flg;
4215 
4216   PetscFunctionBegin;
4217   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
4218   PetscCheck(A->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
4219   PetscCheck(!B->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
4220   PetscCheck(B->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
4221   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQAIJ, &flg));
4222   PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "MatType %s", ((PetscObject)B)->type_name);
4223   PetscCheck(reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX, PETSC_COMM_SELF, PETSC_ERR_SUP, "MatReuse %d", (int)reuse);
4224   if (reuse == MAT_INITIAL_MATRIX) {
4225     PetscCall(PetscMalloc2(am * bm + 1, &i, a->i[am] * b->i[bm], &j));
4226     PetscCall(MatCreate(PETSC_COMM_SELF, &newmat));
4227     PetscCall(MatSetSizes(newmat, am * bm, an * bn, am * bm, an * bn));
4228     PetscCall(MatSetType(newmat, MATAIJ));
4229     i[0] = 0;
4230     for (m = 0; m < am; ++m) {
4231       for (p = 0; p < bm; ++p) {
4232         i[m * bm + p + 1] = i[m * bm + p] + (a->i[m + 1] - a->i[m]) * (b->i[p + 1] - b->i[p]);
4233         for (n = a->i[m]; n < a->i[m + 1]; ++n) {
4234           for (q = b->i[p]; q < b->i[p + 1]; ++q) j[nnz++] = a->j[n] * bn + b->j[q];
4235         }
4236       }
4237     }
4238     PetscCall(MatSeqAIJSetPreallocationCSR(newmat, i, j, NULL));
4239     *C = newmat;
4240     PetscCall(PetscFree2(i, j));
4241     nnz = 0;
4242   }
4243   PetscCall(MatSeqAIJGetArray(*C, &v));
4244   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
4245   PetscCall(MatSeqAIJGetArrayRead(B, &ba));
4246   for (m = 0; m < am; ++m) {
4247     for (p = 0; p < bm; ++p) {
4248       for (n = a->i[m]; n < a->i[m + 1]; ++n) {
4249         for (q = b->i[p]; q < b->i[p + 1]; ++q) v[nnz++] = aa[n] * ba[q];
4250       }
4251     }
4252   }
4253   PetscCall(MatSeqAIJRestoreArray(*C, &v));
4254   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
4255   PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
4256   PetscFunctionReturn(PETSC_SUCCESS);
4257 }
4258 
4259 #include <../src/mat/impls/dense/seq/dense.h>
4260 #include <petsc/private/kernels/petscaxpy.h>
4261 
4262 /*
4263     Computes (B'*A')' since computing B*A directly is untenable
4264 
4265                n                       p                          p
4266         [             ]       [             ]         [                 ]
4267       m [      A      ]  *  n [       B     ]   =   m [         C       ]
4268         [             ]       [             ]         [                 ]
4269 
4270 */
4271 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A, Mat B, Mat C)
4272 {
4273   Mat_SeqDense      *sub_a = (Mat_SeqDense *)A->data;
4274   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ *)B->data;
4275   Mat_SeqDense      *sub_c = (Mat_SeqDense *)C->data;
4276   PetscInt           i, j, n, m, q, p;
4277   const PetscInt    *ii, *idx;
4278   const PetscScalar *b, *a, *a_q;
4279   PetscScalar       *c, *c_q;
4280   PetscInt           clda = sub_c->lda;
4281   PetscInt           alda = sub_a->lda;
4282 
4283   PetscFunctionBegin;
4284   m = A->rmap->n;
4285   n = A->cmap->n;
4286   p = B->cmap->n;
4287   a = sub_a->v;
4288   b = sub_b->a;
4289   c = sub_c->v;
4290   if (clda == m) {
4291     PetscCall(PetscArrayzero(c, m * p));
4292   } else {
4293     for (j = 0; j < p; j++)
4294       for (i = 0; i < m; i++) c[j * clda + i] = 0.0;
4295   }
4296   ii  = sub_b->i;
4297   idx = sub_b->j;
4298   for (i = 0; i < n; i++) {
4299     q = ii[i + 1] - ii[i];
4300     while (q-- > 0) {
4301       c_q = c + clda * (*idx);
4302       a_q = a + alda * i;
4303       PetscKernelAXPY(c_q, *b, a_q, m);
4304       idx++;
4305       b++;
4306     }
4307   }
4308   PetscFunctionReturn(PETSC_SUCCESS);
4309 }
4310 
4311 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
4312 {
4313   PetscInt  m = A->rmap->n, n = B->cmap->n;
4314   PetscBool cisdense;
4315 
4316   PetscFunctionBegin;
4317   PetscCheck(A->cmap->n == B->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "A->cmap->n %" PetscInt_FMT " != B->rmap->n %" PetscInt_FMT, A->cmap->n, B->rmap->n);
4318   PetscCall(MatSetSizes(C, m, n, m, n));
4319   PetscCall(MatSetBlockSizesFromMats(C, A, B));
4320   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSECUDA, MATSEQDENSEHIP, ""));
4321   if (!cisdense) PetscCall(MatSetType(C, MATDENSE));
4322   PetscCall(MatSetUp(C));
4323 
4324   C->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
4325   PetscFunctionReturn(PETSC_SUCCESS);
4326 }
4327 
4328 /*MC
4329    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
4330    based on compressed sparse row format.
4331 
4332    Options Database Key:
4333 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
4334 
4335    Level: beginner
4336 
4337    Notes:
4338     `MatSetValues()` may be called for this matrix type with a `NULL` argument for the numerical values,
4339     in this case the values associated with the rows and columns one passes in are set to zero
4340     in the matrix
4341 
4342     `MatSetOptions`(,`MAT_STRUCTURE_ONLY`,`PETSC_TRUE`) may be called for this matrix type. In this no
4343     space is allocated for the nonzero entries and any entries passed with `MatSetValues()` are ignored
4344 
4345   Developer Note:
4346     It would be nice if all matrix formats supported passing `NULL` in for the numerical values
4347 
4348 .seealso: [](ch_matrices), `Mat`, `MatCreateSeqAIJ()`, `MatSetFromOptions()`, `MatSetType()`, `MatCreate()`, `MatType`, `MATSELL`, `MATSEQSELL`, `MATMPISELL`
4349 M*/
4350 
4351 /*MC
4352    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
4353 
4354    This matrix type is identical to `MATSEQAIJ` when constructed with a single process communicator,
4355    and `MATMPIAIJ` otherwise.  As a result, for single process communicators,
4356    `MatSeqAIJSetPreallocation()` is supported, and similarly `MatMPIAIJSetPreallocation()` is supported
4357    for communicators controlling multiple processes.  It is recommended that you call both of
4358    the above preallocation routines for simplicity.
4359 
4360    Options Database Key:
4361 . -mat_type aij - sets the matrix type to "aij" during a call to `MatSetFromOptions()`
4362 
4363   Level: beginner
4364 
4365    Note:
4366    Subclasses include `MATAIJCUSPARSE`, `MATAIJPERM`, `MATAIJSELL`, `MATAIJMKL`, `MATAIJCRL`, and also automatically switches over to use inodes when
4367    enough exist.
4368 
4369 .seealso: [](ch_matrices), `Mat`, `MatCreateAIJ()`, `MatCreateSeqAIJ()`, `MATSEQAIJ`, `MATMPIAIJ`, `MATSELL`, `MATSEQSELL`, `MATMPISELL`
4370 M*/
4371 
4372 /*MC
4373    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
4374 
4375    Options Database Key:
4376 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to `MatSetFromOptions()`
4377 
4378   Level: beginner
4379 
4380    Note:
4381    This matrix type is identical to `MATSEQAIJCRL` when constructed with a single process communicator,
4382    and `MATMPIAIJCRL` otherwise.  As a result, for single process communicators,
4383    `MatSeqAIJSetPreallocation()` is supported, and similarly `MatMPIAIJSetPreallocation()` is supported
4384    for communicators controlling multiple processes.  It is recommended that you call both of
4385    the above preallocation routines for simplicity.
4386 
4387 .seealso: [](ch_matrices), `Mat`, `MatCreateMPIAIJCRL`, `MATSEQAIJCRL`, `MATMPIAIJCRL`, `MATSEQAIJCRL`, `MATMPIAIJCRL`
4388 M*/
4389 
4390 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat, MatType, MatReuse, Mat *);
4391 #if defined(PETSC_HAVE_ELEMENTAL)
4392 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_Elemental(Mat, MatType, MatReuse, Mat *);
4393 #endif
4394 #if defined(PETSC_HAVE_SCALAPACK)
4395 PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat, MatType, MatReuse, Mat *);
4396 #endif
4397 #if defined(PETSC_HAVE_HYPRE)
4398 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat A, MatType, MatReuse, Mat *);
4399 #endif
4400 
4401 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqSELL(Mat, MatType, MatReuse, Mat *);
4402 PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat, MatType, MatReuse, Mat *);
4403 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_IS_XAIJ(Mat);
4404 
4405 /*@C
4406   MatSeqAIJGetArray - gives read/write access to the array where the data for a `MATSEQAIJ` matrix is stored
4407 
4408   Not Collective
4409 
4410   Input Parameter:
4411 . A - a `MATSEQAIJ` matrix
4412 
4413   Output Parameter:
4414 . array - pointer to the data
4415 
4416   Level: intermediate
4417 
4418 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJRestoreArray()`
4419 @*/
4420 PetscErrorCode MatSeqAIJGetArray(Mat A, PetscScalar *array[])
4421 {
4422   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4423 
4424   PetscFunctionBegin;
4425   if (aij->ops->getarray) {
4426     PetscCall((*aij->ops->getarray)(A, array));
4427   } else {
4428     *array = aij->a;
4429   }
4430   PetscFunctionReturn(PETSC_SUCCESS);
4431 }
4432 
4433 /*@C
4434   MatSeqAIJRestoreArray - returns access to the array where the data for a `MATSEQAIJ` matrix is stored obtained by `MatSeqAIJGetArray()`
4435 
4436   Not Collective
4437 
4438   Input Parameters:
4439 + A     - a `MATSEQAIJ` matrix
4440 - array - pointer to the data
4441 
4442   Level: intermediate
4443 
4444 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJGetArray()`
4445 @*/
4446 PetscErrorCode MatSeqAIJRestoreArray(Mat A, PetscScalar *array[])
4447 {
4448   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4449 
4450   PetscFunctionBegin;
4451   if (aij->ops->restorearray) {
4452     PetscCall((*aij->ops->restorearray)(A, array));
4453   } else {
4454     *array = NULL;
4455   }
4456   PetscCall(MatSeqAIJInvalidateDiagonal(A));
4457   PetscCall(PetscObjectStateIncrease((PetscObject)A));
4458   PetscFunctionReturn(PETSC_SUCCESS);
4459 }
4460 
4461 /*@C
4462   MatSeqAIJGetArrayRead - gives read-only access to the array where the data for a `MATSEQAIJ` matrix is stored
4463 
4464   Not Collective; No Fortran Support
4465 
4466   Input Parameter:
4467 . A - a `MATSEQAIJ` matrix
4468 
4469   Output Parameter:
4470 . array - pointer to the data
4471 
4472   Level: intermediate
4473 
4474 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJGetArray()`, `MatSeqAIJRestoreArrayRead()`
4475 @*/
4476 PetscErrorCode MatSeqAIJGetArrayRead(Mat A, const PetscScalar *array[])
4477 {
4478   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4479 
4480   PetscFunctionBegin;
4481   if (aij->ops->getarrayread) {
4482     PetscCall((*aij->ops->getarrayread)(A, array));
4483   } else {
4484     *array = aij->a;
4485   }
4486   PetscFunctionReturn(PETSC_SUCCESS);
4487 }
4488 
4489 /*@C
4490   MatSeqAIJRestoreArrayRead - restore the read-only access array obtained from `MatSeqAIJGetArrayRead()`
4491 
4492   Not Collective; No Fortran Support
4493 
4494   Input Parameter:
4495 . A - a `MATSEQAIJ` matrix
4496 
4497   Output Parameter:
4498 . array - pointer to the data
4499 
4500   Level: intermediate
4501 
4502 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJGetArray()`, `MatSeqAIJGetArrayRead()`
4503 @*/
4504 PetscErrorCode MatSeqAIJRestoreArrayRead(Mat A, const PetscScalar *array[])
4505 {
4506   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4507 
4508   PetscFunctionBegin;
4509   if (aij->ops->restorearrayread) {
4510     PetscCall((*aij->ops->restorearrayread)(A, array));
4511   } else {
4512     *array = NULL;
4513   }
4514   PetscFunctionReturn(PETSC_SUCCESS);
4515 }
4516 
4517 /*@C
4518   MatSeqAIJGetArrayWrite - gives write-only access to the array where the data for a `MATSEQAIJ` matrix is stored
4519 
4520   Not Collective; No Fortran Support
4521 
4522   Input Parameter:
4523 . A - a `MATSEQAIJ` matrix
4524 
4525   Output Parameter:
4526 . array - pointer to the data
4527 
4528   Level: intermediate
4529 
4530 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJGetArray()`, `MatSeqAIJRestoreArrayRead()`
4531 @*/
4532 PetscErrorCode MatSeqAIJGetArrayWrite(Mat A, PetscScalar *array[])
4533 {
4534   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4535 
4536   PetscFunctionBegin;
4537   if (aij->ops->getarraywrite) {
4538     PetscCall((*aij->ops->getarraywrite)(A, array));
4539   } else {
4540     *array = aij->a;
4541   }
4542   PetscCall(MatSeqAIJInvalidateDiagonal(A));
4543   PetscCall(PetscObjectStateIncrease((PetscObject)A));
4544   PetscFunctionReturn(PETSC_SUCCESS);
4545 }
4546 
4547 /*@C
4548   MatSeqAIJRestoreArrayWrite - restore the read-only access array obtained from MatSeqAIJGetArrayRead
4549 
4550   Not Collective; No Fortran Support
4551 
4552   Input Parameter:
4553 . A - a MATSEQAIJ matrix
4554 
4555   Output Parameter:
4556 . array - pointer to the data
4557 
4558   Level: intermediate
4559 
4560 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJGetArray()`, `MatSeqAIJGetArrayRead()`
4561 @*/
4562 PetscErrorCode MatSeqAIJRestoreArrayWrite(Mat A, PetscScalar *array[])
4563 {
4564   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4565 
4566   PetscFunctionBegin;
4567   if (aij->ops->restorearraywrite) {
4568     PetscCall((*aij->ops->restorearraywrite)(A, array));
4569   } else {
4570     *array = NULL;
4571   }
4572   PetscFunctionReturn(PETSC_SUCCESS);
4573 }
4574 
4575 /*@C
4576   MatSeqAIJGetCSRAndMemType - Get the CSR arrays and the memory type of the `MATSEQAIJ` matrix
4577 
4578   Not Collective; No Fortran Support
4579 
4580   Input Parameter:
4581 . mat - a matrix of type `MATSEQAIJ` or its subclasses
4582 
4583   Output Parameters:
4584 + i     - row map array of the matrix
4585 . j     - column index array of the matrix
4586 . a     - data array of the matrix
4587 - mtype - memory type of the arrays
4588 
4589   Level: developer
4590 
4591   Notes:
4592   Any of the output parameters can be `NULL`, in which case the corresponding value is not returned.
4593   If mat is a device matrix, the arrays are on the device. Otherwise, they are on the host.
4594 
4595   One can call this routine on a preallocated but not assembled matrix to just get the memory of the CSR underneath the matrix.
4596   If the matrix is assembled, the data array `a` is guaranteed to have the latest values of the matrix.
4597 
4598 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJGetArray()`, `MatSeqAIJGetArrayRead()`
4599 @*/
4600 PetscErrorCode MatSeqAIJGetCSRAndMemType(Mat mat, const PetscInt *i[], const PetscInt *j[], PetscScalar *a[], PetscMemType *mtype)
4601 {
4602   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)mat->data;
4603 
4604   PetscFunctionBegin;
4605   PetscCheck(mat->preallocated, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "matrix is not preallocated");
4606   if (aij->ops->getcsrandmemtype) {
4607     PetscCall((*aij->ops->getcsrandmemtype)(mat, i, j, a, mtype));
4608   } else {
4609     if (i) *i = aij->i;
4610     if (j) *j = aij->j;
4611     if (a) *a = aij->a;
4612     if (mtype) *mtype = PETSC_MEMTYPE_HOST;
4613   }
4614   PetscFunctionReturn(PETSC_SUCCESS);
4615 }
4616 
4617 /*@
4618   MatSeqAIJGetMaxRowNonzeros - returns the maximum number of nonzeros in any row
4619 
4620   Not Collective
4621 
4622   Input Parameter:
4623 . A - a `MATSEQAIJ` matrix
4624 
4625   Output Parameter:
4626 . nz - the maximum number of nonzeros in any row
4627 
4628   Level: intermediate
4629 
4630 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJRestoreArray()`
4631 @*/
4632 PetscErrorCode MatSeqAIJGetMaxRowNonzeros(Mat A, PetscInt *nz)
4633 {
4634   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4635 
4636   PetscFunctionBegin;
4637   *nz = aij->rmax;
4638   PetscFunctionReturn(PETSC_SUCCESS);
4639 }
4640 
4641 static PetscErrorCode MatCOOStructDestroy_SeqAIJ(void **data)
4642 {
4643   MatCOOStruct_SeqAIJ *coo = (MatCOOStruct_SeqAIJ *)*data;
4644 
4645   PetscFunctionBegin;
4646   PetscCall(PetscFree(coo->perm));
4647   PetscCall(PetscFree(coo->jmap));
4648   PetscCall(PetscFree(coo));
4649   PetscFunctionReturn(PETSC_SUCCESS);
4650 }
4651 
4652 PetscErrorCode MatSetPreallocationCOO_SeqAIJ(Mat mat, PetscCount coo_n, PetscInt coo_i[], PetscInt coo_j[])
4653 {
4654   MPI_Comm             comm;
4655   PetscInt            *i, *j;
4656   PetscInt             M, N, row, iprev;
4657   PetscCount           k, p, q, nneg, nnz, start, end; /* Index the coo array, so use PetscCount as their type */
4658   PetscInt            *Ai;                             /* Change to PetscCount once we use it for row pointers */
4659   PetscInt            *Aj;
4660   PetscScalar         *Aa;
4661   Mat_SeqAIJ          *seqaij = (Mat_SeqAIJ *)mat->data;
4662   MatType              rtype;
4663   PetscCount          *perm, *jmap;
4664   MatCOOStruct_SeqAIJ *coo;
4665   PetscBool            isorted;
4666   PetscBool            hypre;
4667   const char          *name;
4668 
4669   PetscFunctionBegin;
4670   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
4671   PetscCall(MatGetSize(mat, &M, &N));
4672   i = coo_i;
4673   j = coo_j;
4674   PetscCall(PetscMalloc1(coo_n, &perm));
4675 
4676   /* Ignore entries with negative row or col indices; at the same time, check if i[] is already sorted (e.g., MatConvert_AlJ_HYPRE results in this case) */
4677   isorted = PETSC_TRUE;
4678   iprev   = PETSC_INT_MIN;
4679   for (k = 0; k < coo_n; k++) {
4680     if (j[k] < 0) i[k] = -1;
4681     if (isorted) {
4682       if (i[k] < iprev) isorted = PETSC_FALSE;
4683       else iprev = i[k];
4684     }
4685     perm[k] = k;
4686   }
4687 
4688   /* Sort by row if not already */
4689   if (!isorted) PetscCall(PetscSortIntWithIntCountArrayPair(coo_n, i, j, perm));
4690 
4691   /* Advance k to the first row with a non-negative index */
4692   for (k = 0; k < coo_n; k++)
4693     if (i[k] >= 0) break;
4694   nneg = k;
4695   PetscCall(PetscMalloc1(coo_n - nneg + 1, &jmap)); /* +1 to make a CSR-like data structure. jmap[i] originally is the number of repeats for i-th nonzero */
4696   nnz = 0;                                          /* Total number of unique nonzeros to be counted */
4697   jmap++;                                           /* Inc jmap by 1 for convenience */
4698 
4699   PetscCall(PetscShmgetAllocateArray(M + 1, sizeof(PetscInt), (void **)&Ai)); /* CSR of A */
4700   PetscCall(PetscArrayzero(Ai, M + 1));
4701   PetscCall(PetscShmgetAllocateArray(coo_n - nneg, sizeof(PetscInt), (void **)&Aj)); /* We have at most coo_n-nneg unique nonzeros */
4702 
4703   PetscCall(PetscObjectGetName((PetscObject)mat, &name));
4704   PetscCall(PetscStrcmp("_internal_COO_mat_for_hypre", name, &hypre));
4705 
4706   /* In each row, sort by column, then unique column indices to get row length */
4707   Ai++;  /* Inc by 1 for convenience */
4708   q = 0; /* q-th unique nonzero, with q starting from 0 */
4709   while (k < coo_n) {
4710     PetscBool strictly_sorted; // this row is strictly sorted?
4711     PetscInt  jprev;
4712 
4713     /* get [start,end) indices for this row; also check if cols in this row are strictly sorted */
4714     row             = i[k];
4715     start           = k;
4716     jprev           = PETSC_INT_MIN;
4717     strictly_sorted = PETSC_TRUE;
4718     while (k < coo_n && i[k] == row) {
4719       if (strictly_sorted) {
4720         if (j[k] <= jprev) strictly_sorted = PETSC_FALSE;
4721         else jprev = j[k];
4722       }
4723       k++;
4724     }
4725     end = k;
4726 
4727     /* hack for HYPRE: swap min column to diag so that diagonal values will go first */
4728     if (hypre) {
4729       PetscInt  minj    = PETSC_INT_MAX;
4730       PetscBool hasdiag = PETSC_FALSE;
4731 
4732       if (strictly_sorted) { // fast path to swap the first and the diag
4733         PetscCount tmp;
4734         for (p = start; p < end; p++) {
4735           if (j[p] == row && p != start) {
4736             j[p]        = j[start]; // swap j[], so that the diagonal value will go first (manipulated by perm[])
4737             j[start]    = row;
4738             tmp         = perm[start];
4739             perm[start] = perm[p]; // also swap perm[] so we can save the call to PetscSortIntWithCountArray() below
4740             perm[p]     = tmp;
4741             break;
4742           }
4743         }
4744       } else {
4745         for (p = start; p < end; p++) {
4746           hasdiag = (PetscBool)(hasdiag || (j[p] == row));
4747           minj    = PetscMin(minj, j[p]);
4748         }
4749 
4750         if (hasdiag) {
4751           for (p = start; p < end; p++) {
4752             if (j[p] == minj) j[p] = row;
4753             else if (j[p] == row) j[p] = minj;
4754           }
4755         }
4756       }
4757     }
4758     // sort by columns in a row. perm[] indicates their original order
4759     if (!strictly_sorted) PetscCall(PetscSortIntWithCountArray(end - start, j + start, perm + start));
4760 
4761     if (strictly_sorted) { // fast path to set Aj[], jmap[], Ai[], nnz, q
4762       for (p = start; p < end; p++, q++) {
4763         Aj[q]   = j[p];
4764         jmap[q] = 1;
4765       }
4766       PetscCall(PetscIntCast(end - start, Ai + row));
4767       nnz += Ai[row]; // q is already advanced
4768     } else {
4769       /* Find number of unique col entries in this row */
4770       Aj[q]   = j[start]; /* Log the first nonzero in this row */
4771       jmap[q] = 1;        /* Number of repeats of this nonzero entry */
4772       Ai[row] = 1;
4773       nnz++;
4774 
4775       for (p = start + 1; p < end; p++) { /* Scan remaining nonzero in this row */
4776         if (j[p] != j[p - 1]) {           /* Meet a new nonzero */
4777           q++;
4778           jmap[q] = 1;
4779           Aj[q]   = j[p];
4780           Ai[row]++;
4781           nnz++;
4782         } else {
4783           jmap[q]++;
4784         }
4785       }
4786       q++; /* Move to next row and thus next unique nonzero */
4787     }
4788   }
4789 
4790   Ai--; /* Back to the beginning of Ai[] */
4791   for (k = 0; k < M; k++) Ai[k + 1] += Ai[k];
4792   jmap--; // Back to the beginning of jmap[]
4793   jmap[0] = 0;
4794   for (k = 0; k < nnz; k++) jmap[k + 1] += jmap[k];
4795 
4796   if (nnz < coo_n - nneg) { /* Reallocate with actual number of unique nonzeros */
4797     PetscCount *jmap_new;
4798     PetscInt   *Aj_new;
4799 
4800     PetscCall(PetscMalloc1(nnz + 1, &jmap_new));
4801     PetscCall(PetscArraycpy(jmap_new, jmap, nnz + 1));
4802     PetscCall(PetscFree(jmap));
4803     jmap = jmap_new;
4804 
4805     PetscCall(PetscShmgetAllocateArray(nnz, sizeof(PetscInt), (void **)&Aj_new));
4806     PetscCall(PetscArraycpy(Aj_new, Aj, nnz));
4807     PetscCall(PetscShmgetDeallocateArray((void **)&Aj));
4808     Aj = Aj_new;
4809   }
4810 
4811   if (nneg) { /* Discard heading entries with negative indices in perm[], as we'll access it from index 0 in MatSetValuesCOO */
4812     PetscCount *perm_new;
4813 
4814     PetscCall(PetscMalloc1(coo_n - nneg, &perm_new));
4815     PetscCall(PetscArraycpy(perm_new, perm + nneg, coo_n - nneg));
4816     PetscCall(PetscFree(perm));
4817     perm = perm_new;
4818   }
4819 
4820   PetscCall(MatGetRootType_Private(mat, &rtype));
4821   PetscCall(PetscShmgetAllocateArray(nnz, sizeof(PetscScalar), (void **)&Aa));
4822   PetscCall(PetscArrayzero(Aa, nnz));
4823   PetscCall(MatSetSeqAIJWithArrays_private(PETSC_COMM_SELF, M, N, Ai, Aj, Aa, rtype, mat));
4824 
4825   seqaij->free_a = seqaij->free_ij = PETSC_TRUE; /* Let newmat own Ai, Aj and Aa */
4826 
4827   // Put the COO struct in a container and then attach that to the matrix
4828   PetscCall(PetscMalloc1(1, &coo));
4829   PetscCall(PetscIntCast(nnz, &coo->nz));
4830   coo->n    = coo_n;
4831   coo->Atot = coo_n - nneg; // Annz is seqaij->nz, so no need to record that again
4832   coo->jmap = jmap;         // of length nnz+1
4833   coo->perm = perm;
4834   PetscCall(PetscObjectContainerCompose((PetscObject)mat, "__PETSc_MatCOOStruct_Host", coo, MatCOOStructDestroy_SeqAIJ));
4835   PetscFunctionReturn(PETSC_SUCCESS);
4836 }
4837 
4838 static PetscErrorCode MatSetValuesCOO_SeqAIJ(Mat A, const PetscScalar v[], InsertMode imode)
4839 {
4840   Mat_SeqAIJ          *aseq = (Mat_SeqAIJ *)A->data;
4841   PetscCount           i, j, Annz = aseq->nz;
4842   PetscCount          *perm, *jmap;
4843   PetscScalar         *Aa;
4844   PetscContainer       container;
4845   MatCOOStruct_SeqAIJ *coo;
4846 
4847   PetscFunctionBegin;
4848   PetscCall(PetscObjectQuery((PetscObject)A, "__PETSc_MatCOOStruct_Host", (PetscObject *)&container));
4849   PetscCheck(container, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Not found MatCOOStruct on this matrix");
4850   PetscCall(PetscContainerGetPointer(container, (void **)&coo));
4851   perm = coo->perm;
4852   jmap = coo->jmap;
4853   PetscCall(MatSeqAIJGetArray(A, &Aa));
4854   for (i = 0; i < Annz; i++) {
4855     PetscScalar sum = 0.0;
4856     for (j = jmap[i]; j < jmap[i + 1]; j++) sum += v[perm[j]];
4857     Aa[i] = (imode == INSERT_VALUES ? 0.0 : Aa[i]) + sum;
4858   }
4859   PetscCall(MatSeqAIJRestoreArray(A, &Aa));
4860   PetscFunctionReturn(PETSC_SUCCESS);
4861 }
4862 
4863 #if defined(PETSC_HAVE_CUDA)
4864 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat, MatType, MatReuse, Mat *);
4865 #endif
4866 #if defined(PETSC_HAVE_HIP)
4867 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJHIPSPARSE(Mat, MatType, MatReuse, Mat *);
4868 #endif
4869 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
4870 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJKokkos(Mat, MatType, MatReuse, Mat *);
4871 #endif
4872 
4873 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4874 {
4875   Mat_SeqAIJ *b;
4876   PetscMPIInt size;
4877 
4878   PetscFunctionBegin;
4879   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));
4880   PetscCheck(size <= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Comm must be of size 1");
4881 
4882   PetscCall(PetscNew(&b));
4883 
4884   B->data   = (void *)b;
4885   B->ops[0] = MatOps_Values;
4886   if (B->sortedfull) B->ops->setvalues = MatSetValues_SeqAIJ_SortedFull;
4887 
4888   b->row                = NULL;
4889   b->col                = NULL;
4890   b->icol               = NULL;
4891   b->reallocs           = 0;
4892   b->ignorezeroentries  = PETSC_FALSE;
4893   b->roworiented        = PETSC_TRUE;
4894   b->nonew              = 0;
4895   b->diag               = NULL;
4896   b->solve_work         = NULL;
4897   B->spptr              = NULL;
4898   b->saved_values       = NULL;
4899   b->idiag              = NULL;
4900   b->mdiag              = NULL;
4901   b->ssor_work          = NULL;
4902   b->omega              = 1.0;
4903   b->fshift             = 0.0;
4904   b->idiagvalid         = PETSC_FALSE;
4905   b->ibdiagvalid        = PETSC_FALSE;
4906   b->keepnonzeropattern = PETSC_FALSE;
4907 
4908   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQAIJ));
4909 #if defined(PETSC_HAVE_MATLAB)
4910   PetscCall(PetscObjectComposeFunction((PetscObject)B, "PetscMatlabEnginePut_C", MatlabEnginePut_SeqAIJ));
4911   PetscCall(PetscObjectComposeFunction((PetscObject)B, "PetscMatlabEngineGet_C", MatlabEngineGet_SeqAIJ));
4912 #endif
4913   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqAIJSetColumnIndices_C", MatSeqAIJSetColumnIndices_SeqAIJ));
4914   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatStoreValues_C", MatStoreValues_SeqAIJ));
4915   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatRetrieveValues_C", MatRetrieveValues_SeqAIJ));
4916   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqsbaij_C", MatConvert_SeqAIJ_SeqSBAIJ));
4917   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqbaij_C", MatConvert_SeqAIJ_SeqBAIJ));
4918   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijperm_C", MatConvert_SeqAIJ_SeqAIJPERM));
4919   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijsell_C", MatConvert_SeqAIJ_SeqAIJSELL));
4920 #if defined(PETSC_HAVE_MKL_SPARSE)
4921   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijmkl_C", MatConvert_SeqAIJ_SeqAIJMKL));
4922 #endif
4923 #if defined(PETSC_HAVE_CUDA)
4924   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijcusparse_C", MatConvert_SeqAIJ_SeqAIJCUSPARSE));
4925   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqaijcusparse_seqaij_C", MatProductSetFromOptions_SeqAIJ));
4926   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqaij_seqaijcusparse_C", MatProductSetFromOptions_SeqAIJ));
4927 #endif
4928 #if defined(PETSC_HAVE_HIP)
4929   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijhipsparse_C", MatConvert_SeqAIJ_SeqAIJHIPSPARSE));
4930   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqaijhipsparse_seqaij_C", MatProductSetFromOptions_SeqAIJ));
4931   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqaij_seqaijhipsparse_C", MatProductSetFromOptions_SeqAIJ));
4932 #endif
4933 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
4934   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijkokkos_C", MatConvert_SeqAIJ_SeqAIJKokkos));
4935 #endif
4936   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijcrl_C", MatConvert_SeqAIJ_SeqAIJCRL));
4937 #if defined(PETSC_HAVE_ELEMENTAL)
4938   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_elemental_C", MatConvert_SeqAIJ_Elemental));
4939 #endif
4940 #if defined(PETSC_HAVE_SCALAPACK)
4941   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_scalapack_C", MatConvert_AIJ_ScaLAPACK));
4942 #endif
4943 #if defined(PETSC_HAVE_HYPRE)
4944   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_hypre_C", MatConvert_AIJ_HYPRE));
4945   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_transpose_seqaij_seqaij_C", MatProductSetFromOptions_Transpose_AIJ_AIJ));
4946 #endif
4947   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqdense_C", MatConvert_SeqAIJ_SeqDense));
4948   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqsell_C", MatConvert_SeqAIJ_SeqSELL));
4949   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_is_C", MatConvert_XAIJ_IS));
4950   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatIsTranspose_C", MatIsTranspose_SeqAIJ));
4951   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatIsHermitianTranspose_C", MatIsHermitianTranspose_SeqAIJ));
4952   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqAIJSetPreallocation_C", MatSeqAIJSetPreallocation_SeqAIJ));
4953   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatResetPreallocation_C", MatResetPreallocation_SeqAIJ));
4954   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatResetHash_C", MatResetHash_SeqAIJ));
4955   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqAIJSetPreallocationCSR_C", MatSeqAIJSetPreallocationCSR_SeqAIJ));
4956   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatReorderForNonzeroDiagonal_C", MatReorderForNonzeroDiagonal_SeqAIJ));
4957   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_is_seqaij_C", MatProductSetFromOptions_IS_XAIJ));
4958   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdense_seqaij_C", MatProductSetFromOptions_SeqDense_SeqAIJ));
4959   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqaij_seqaij_C", MatProductSetFromOptions_SeqAIJ));
4960   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqAIJKron_C", MatSeqAIJKron_SeqAIJ));
4961   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_SeqAIJ));
4962   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetValuesCOO_C", MatSetValuesCOO_SeqAIJ));
4963   PetscCall(MatCreate_SeqAIJ_Inode(B));
4964   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQAIJ));
4965   PetscCall(MatSeqAIJSetTypeFromOptions(B)); /* this allows changing the matrix subtype to say MATSEQAIJPERM */
4966   PetscFunctionReturn(PETSC_SUCCESS);
4967 }
4968 
4969 /*
4970     Given a matrix generated with MatGetFactor() duplicates all the information in A into C
4971 */
4972 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C, Mat A, MatDuplicateOption cpvalues, PetscBool mallocmatspace)
4973 {
4974   Mat_SeqAIJ *c = (Mat_SeqAIJ *)C->data, *a = (Mat_SeqAIJ *)A->data;
4975   PetscInt    m = A->rmap->n, i;
4976 
4977   PetscFunctionBegin;
4978   PetscCheck(A->assembled || cpvalues == MAT_DO_NOT_COPY_VALUES, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot duplicate unassembled matrix");
4979 
4980   C->factortype    = A->factortype;
4981   c->row           = NULL;
4982   c->col           = NULL;
4983   c->icol          = NULL;
4984   c->reallocs      = 0;
4985   c->diagonaldense = a->diagonaldense;
4986 
4987   C->assembled = A->assembled;
4988 
4989   if (A->preallocated) {
4990     PetscCall(PetscLayoutReference(A->rmap, &C->rmap));
4991     PetscCall(PetscLayoutReference(A->cmap, &C->cmap));
4992 
4993     if (!A->hash_active) {
4994       PetscCall(PetscMalloc1(m, &c->imax));
4995       PetscCall(PetscMemcpy(c->imax, a->imax, m * sizeof(PetscInt)));
4996       PetscCall(PetscMalloc1(m, &c->ilen));
4997       PetscCall(PetscMemcpy(c->ilen, a->ilen, m * sizeof(PetscInt)));
4998 
4999       /* allocate the matrix space */
5000       if (mallocmatspace) {
5001         PetscCall(PetscShmgetAllocateArray(a->i[m], sizeof(PetscScalar), (void **)&c->a));
5002         PetscCall(PetscShmgetAllocateArray(a->i[m], sizeof(PetscInt), (void **)&c->j));
5003         PetscCall(PetscShmgetAllocateArray(m + 1, sizeof(PetscInt), (void **)&c->i));
5004         PetscCall(PetscArraycpy(c->i, a->i, m + 1));
5005         c->free_a  = PETSC_TRUE;
5006         c->free_ij = PETSC_TRUE;
5007         if (m > 0) {
5008           PetscCall(PetscArraycpy(c->j, a->j, a->i[m]));
5009           if (cpvalues == MAT_COPY_VALUES) {
5010             const PetscScalar *aa;
5011 
5012             PetscCall(MatSeqAIJGetArrayRead(A, &aa));
5013             PetscCall(PetscArraycpy(c->a, aa, a->i[m]));
5014             PetscCall(MatSeqAIJGetArrayRead(A, &aa));
5015           } else {
5016             PetscCall(PetscArrayzero(c->a, a->i[m]));
5017           }
5018         }
5019       }
5020       C->preallocated = PETSC_TRUE;
5021     } else {
5022       PetscCheck(mallocmatspace, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Cannot malloc matrix memory from a non-preallocated matrix");
5023       PetscCall(MatSetUp(C));
5024     }
5025 
5026     c->ignorezeroentries = a->ignorezeroentries;
5027     c->roworiented       = a->roworiented;
5028     c->nonew             = a->nonew;
5029     if (a->diag) {
5030       PetscCall(PetscMalloc1(m + 1, &c->diag));
5031       PetscCall(PetscMemcpy(c->diag, a->diag, m * sizeof(PetscInt)));
5032     } else c->diag = NULL;
5033 
5034     c->solve_work         = NULL;
5035     c->saved_values       = NULL;
5036     c->idiag              = NULL;
5037     c->ssor_work          = NULL;
5038     c->keepnonzeropattern = a->keepnonzeropattern;
5039 
5040     c->rmax  = a->rmax;
5041     c->nz    = a->nz;
5042     c->maxnz = a->nz; /* Since we allocate exactly the right amount */
5043 
5044     c->compressedrow.use   = a->compressedrow.use;
5045     c->compressedrow.nrows = a->compressedrow.nrows;
5046     if (a->compressedrow.use) {
5047       i = a->compressedrow.nrows;
5048       PetscCall(PetscMalloc2(i + 1, &c->compressedrow.i, i, &c->compressedrow.rindex));
5049       PetscCall(PetscArraycpy(c->compressedrow.i, a->compressedrow.i, i + 1));
5050       PetscCall(PetscArraycpy(c->compressedrow.rindex, a->compressedrow.rindex, i));
5051     } else {
5052       c->compressedrow.use    = PETSC_FALSE;
5053       c->compressedrow.i      = NULL;
5054       c->compressedrow.rindex = NULL;
5055     }
5056     c->nonzerorowcnt = a->nonzerorowcnt;
5057     C->nonzerostate  = A->nonzerostate;
5058 
5059     PetscCall(MatDuplicate_SeqAIJ_Inode(A, cpvalues, &C));
5060   }
5061   PetscCall(PetscFunctionListDuplicate(((PetscObject)A)->qlist, &((PetscObject)C)->qlist));
5062   PetscFunctionReturn(PETSC_SUCCESS);
5063 }
5064 
5065 PetscErrorCode MatDuplicate_SeqAIJ(Mat A, MatDuplicateOption cpvalues, Mat *B)
5066 {
5067   PetscFunctionBegin;
5068   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), B));
5069   PetscCall(MatSetSizes(*B, A->rmap->n, A->cmap->n, A->rmap->n, A->cmap->n));
5070   if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) PetscCall(MatSetBlockSizesFromMats(*B, A, A));
5071   PetscCall(MatSetType(*B, ((PetscObject)A)->type_name));
5072   PetscCall(MatDuplicateNoCreate_SeqAIJ(*B, A, cpvalues, PETSC_TRUE));
5073   PetscFunctionReturn(PETSC_SUCCESS);
5074 }
5075 
5076 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
5077 {
5078   PetscBool isbinary, ishdf5;
5079 
5080   PetscFunctionBegin;
5081   PetscValidHeaderSpecific(newMat, MAT_CLASSID, 1);
5082   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
5083   /* force binary viewer to load .info file if it has not yet done so */
5084   PetscCall(PetscViewerSetUp(viewer));
5085   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
5086   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
5087   if (isbinary) {
5088     PetscCall(MatLoad_SeqAIJ_Binary(newMat, viewer));
5089   } else if (ishdf5) {
5090 #if defined(PETSC_HAVE_HDF5)
5091     PetscCall(MatLoad_AIJ_HDF5(newMat, viewer));
5092 #else
5093     SETERRQ(PetscObjectComm((PetscObject)newMat), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
5094 #endif
5095   } else {
5096     SETERRQ(PetscObjectComm((PetscObject)newMat), PETSC_ERR_SUP, "Viewer type %s not yet supported for reading %s matrices", ((PetscObject)viewer)->type_name, ((PetscObject)newMat)->type_name);
5097   }
5098   PetscFunctionReturn(PETSC_SUCCESS);
5099 }
5100 
5101 PetscErrorCode MatLoad_SeqAIJ_Binary(Mat mat, PetscViewer viewer)
5102 {
5103   Mat_SeqAIJ *a = (Mat_SeqAIJ *)mat->data;
5104   PetscInt    header[4], *rowlens, M, N, nz, sum, rows, cols, i;
5105 
5106   PetscFunctionBegin;
5107   PetscCall(PetscViewerSetUp(viewer));
5108 
5109   /* read in matrix header */
5110   PetscCall(PetscViewerBinaryRead(viewer, header, 4, NULL, PETSC_INT));
5111   PetscCheck(header[0] == MAT_FILE_CLASSID, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a matrix object in file");
5112   M  = header[1];
5113   N  = header[2];
5114   nz = header[3];
5115   PetscCheck(M >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix row size (%" PetscInt_FMT ") in file is negative", M);
5116   PetscCheck(N >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix column size (%" PetscInt_FMT ") in file is negative", N);
5117   PetscCheck(nz >= 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Matrix stored in special format on disk, cannot load as SeqAIJ");
5118 
5119   /* set block sizes from the viewer's .info file */
5120   PetscCall(MatLoad_Binary_BlockSizes(mat, viewer));
5121   /* set local and global sizes if not set already */
5122   if (mat->rmap->n < 0) mat->rmap->n = M;
5123   if (mat->cmap->n < 0) mat->cmap->n = N;
5124   if (mat->rmap->N < 0) mat->rmap->N = M;
5125   if (mat->cmap->N < 0) mat->cmap->N = N;
5126   PetscCall(PetscLayoutSetUp(mat->rmap));
5127   PetscCall(PetscLayoutSetUp(mat->cmap));
5128 
5129   /* check if the matrix sizes are correct */
5130   PetscCall(MatGetSize(mat, &rows, &cols));
5131   PetscCheck(M == rows && N == cols, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Matrix in file of different sizes (%" PetscInt_FMT ", %" PetscInt_FMT ") than the input matrix (%" PetscInt_FMT ", %" PetscInt_FMT ")", M, N, rows, cols);
5132 
5133   /* read in row lengths */
5134   PetscCall(PetscMalloc1(M, &rowlens));
5135   PetscCall(PetscViewerBinaryRead(viewer, rowlens, M, NULL, PETSC_INT));
5136   /* check if sum(rowlens) is same as nz */
5137   sum = 0;
5138   for (i = 0; i < M; i++) sum += rowlens[i];
5139   PetscCheck(sum == nz, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Inconsistent matrix data in file: nonzeros = %" PetscInt_FMT ", sum-row-lengths = %" PetscInt_FMT, nz, sum);
5140   /* preallocate and check sizes */
5141   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(mat, 0, rowlens));
5142   PetscCall(MatGetSize(mat, &rows, &cols));
5143   PetscCheck(M == rows && N == cols, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Matrix in file of different length (%" PetscInt_FMT ", %" PetscInt_FMT ") than the input matrix (%" PetscInt_FMT ", %" PetscInt_FMT ")", M, N, rows, cols);
5144   /* store row lengths */
5145   PetscCall(PetscArraycpy(a->ilen, rowlens, M));
5146   PetscCall(PetscFree(rowlens));
5147 
5148   /* fill in "i" row pointers */
5149   a->i[0] = 0;
5150   for (i = 0; i < M; i++) a->i[i + 1] = a->i[i] + a->ilen[i];
5151   /* read in "j" column indices */
5152   PetscCall(PetscViewerBinaryRead(viewer, a->j, nz, NULL, PETSC_INT));
5153   /* read in "a" nonzero values */
5154   PetscCall(PetscViewerBinaryRead(viewer, a->a, nz, NULL, PETSC_SCALAR));
5155 
5156   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
5157   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
5158   PetscFunctionReturn(PETSC_SUCCESS);
5159 }
5160 
5161 PetscErrorCode MatEqual_SeqAIJ(Mat A, Mat B, PetscBool *flg)
5162 {
5163   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data;
5164   const PetscScalar *aa, *ba;
5165 #if defined(PETSC_USE_COMPLEX)
5166   PetscInt k;
5167 #endif
5168 
5169   PetscFunctionBegin;
5170   /* If the  matrix dimensions are not equal,or no of nonzeros */
5171   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) || (a->nz != b->nz)) {
5172     *flg = PETSC_FALSE;
5173     PetscFunctionReturn(PETSC_SUCCESS);
5174   }
5175 
5176   /* if the a->i are the same */
5177   PetscCall(PetscArraycmp(a->i, b->i, A->rmap->n + 1, flg));
5178   if (!*flg) PetscFunctionReturn(PETSC_SUCCESS);
5179 
5180   /* if a->j are the same */
5181   PetscCall(PetscArraycmp(a->j, b->j, a->nz, flg));
5182   if (!*flg) PetscFunctionReturn(PETSC_SUCCESS);
5183 
5184   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
5185   PetscCall(MatSeqAIJGetArrayRead(B, &ba));
5186   /* if a->a are the same */
5187 #if defined(PETSC_USE_COMPLEX)
5188   for (k = 0; k < a->nz; k++) {
5189     if (PetscRealPart(aa[k]) != PetscRealPart(ba[k]) || PetscImaginaryPart(aa[k]) != PetscImaginaryPart(ba[k])) {
5190       *flg = PETSC_FALSE;
5191       PetscFunctionReturn(PETSC_SUCCESS);
5192     }
5193   }
5194 #else
5195   PetscCall(PetscArraycmp(aa, ba, a->nz, flg));
5196 #endif
5197   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
5198   PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
5199   PetscFunctionReturn(PETSC_SUCCESS);
5200 }
5201 
5202 /*@
5203   MatCreateSeqAIJWithArrays - Creates an sequential `MATSEQAIJ` matrix using matrix elements (in CSR format)
5204   provided by the user.
5205 
5206   Collective
5207 
5208   Input Parameters:
5209 + comm - must be an MPI communicator of size 1
5210 . m    - number of rows
5211 . n    - number of columns
5212 . i    - row indices; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
5213 . j    - column indices
5214 - a    - matrix values
5215 
5216   Output Parameter:
5217 . mat - the matrix
5218 
5219   Level: intermediate
5220 
5221   Notes:
5222   The `i`, `j`, and `a` arrays are not copied by this routine, the user must free these arrays
5223   once the matrix is destroyed and not before
5224 
5225   You cannot set new nonzero locations into this matrix, that will generate an error.
5226 
5227   The `i` and `j` indices are 0 based
5228 
5229   The format which is used for the sparse matrix input, is equivalent to a
5230   row-major ordering.. i.e for the following matrix, the input data expected is
5231   as shown
5232 .vb
5233         1 0 0
5234         2 0 3
5235         4 5 6
5236 
5237         i =  {0,1,3,6}  [size = nrow+1  = 3+1]
5238         j =  {0,0,2,0,1,2}  [size = 6]; values must be sorted for each row
5239         v =  {1,2,3,4,5,6}  [size = 6]
5240 .ve
5241 
5242 .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateAIJ()`, `MatCreateSeqAIJ()`, `MatCreateMPIAIJWithArrays()`, `MatMPIAIJSetPreallocationCSR()`
5243 @*/
5244 PetscErrorCode MatCreateSeqAIJWithArrays(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt i[], PetscInt j[], PetscScalar a[], Mat *mat)
5245 {
5246   PetscInt    ii;
5247   Mat_SeqAIJ *aij;
5248   PetscInt    jj;
5249 
5250   PetscFunctionBegin;
5251   PetscCheck(m <= 0 || i[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
5252   PetscCall(MatCreate(comm, mat));
5253   PetscCall(MatSetSizes(*mat, m, n, m, n));
5254   /* PetscCall(MatSetBlockSizes(*mat,,)); */
5255   PetscCall(MatSetType(*mat, MATSEQAIJ));
5256   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*mat, MAT_SKIP_ALLOCATION, NULL));
5257   aij = (Mat_SeqAIJ *)(*mat)->data;
5258   PetscCall(PetscMalloc1(m, &aij->imax));
5259   PetscCall(PetscMalloc1(m, &aij->ilen));
5260 
5261   aij->i       = i;
5262   aij->j       = j;
5263   aij->a       = a;
5264   aij->nonew   = -1; /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
5265   aij->free_a  = PETSC_FALSE;
5266   aij->free_ij = PETSC_FALSE;
5267 
5268   for (ii = 0, aij->nonzerorowcnt = 0, aij->rmax = 0; ii < m; ii++) {
5269     aij->ilen[ii] = aij->imax[ii] = i[ii + 1] - i[ii];
5270     if (PetscDefined(USE_DEBUG)) {
5271       PetscCheck(i[ii + 1] - i[ii] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative row length in i (row indices) row = %" PetscInt_FMT " length = %" PetscInt_FMT, ii, i[ii + 1] - i[ii]);
5272       for (jj = i[ii] + 1; jj < i[ii + 1]; jj++) {
5273         PetscCheck(j[jj] >= j[jj - 1], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column entry number %" PetscInt_FMT " (actual column %" PetscInt_FMT ") in row %" PetscInt_FMT " is not sorted", jj - i[ii], j[jj], ii);
5274         PetscCheck(j[jj] != j[jj - 1], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column entry number %" PetscInt_FMT " (actual column %" PetscInt_FMT ") in row %" PetscInt_FMT " is identical to previous entry", jj - i[ii], j[jj], ii);
5275       }
5276     }
5277   }
5278   if (PetscDefined(USE_DEBUG)) {
5279     for (ii = 0; ii < aij->i[m]; ii++) {
5280       PetscCheck(j[ii] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative column index at location = %" PetscInt_FMT " index = %" PetscInt_FMT, ii, j[ii]);
5281       PetscCheck(j[ii] <= n - 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column index to large at location = %" PetscInt_FMT " index = %" PetscInt_FMT " last column = %" PetscInt_FMT, ii, j[ii], n - 1);
5282     }
5283   }
5284 
5285   PetscCall(MatAssemblyBegin(*mat, MAT_FINAL_ASSEMBLY));
5286   PetscCall(MatAssemblyEnd(*mat, MAT_FINAL_ASSEMBLY));
5287   PetscFunctionReturn(PETSC_SUCCESS);
5288 }
5289 
5290 /*@
5291   MatCreateSeqAIJFromTriple - Creates an sequential `MATSEQAIJ` matrix using matrix elements (in COO format)
5292   provided by the user.
5293 
5294   Collective
5295 
5296   Input Parameters:
5297 + comm - must be an MPI communicator of size 1
5298 . m    - number of rows
5299 . n    - number of columns
5300 . i    - row indices
5301 . j    - column indices
5302 . a    - matrix values
5303 . nz   - number of nonzeros
5304 - idx  - if the `i` and `j` indices start with 1 use `PETSC_TRUE` otherwise use `PETSC_FALSE`
5305 
5306   Output Parameter:
5307 . mat - the matrix
5308 
5309   Level: intermediate
5310 
5311   Example:
5312   For the following matrix, the input data expected is as shown (using 0 based indexing)
5313 .vb
5314         1 0 0
5315         2 0 3
5316         4 5 6
5317 
5318         i =  {0,1,1,2,2,2}
5319         j =  {0,0,2,0,1,2}
5320         v =  {1,2,3,4,5,6}
5321 .ve
5322 
5323   Note:
5324   Instead of using this function, users should also consider `MatSetPreallocationCOO()` and `MatSetValuesCOO()`, which allow repeated or remote entries,
5325   and are particularly useful in iterative applications.
5326 
5327 .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateAIJ()`, `MatCreateSeqAIJ()`, `MatCreateSeqAIJWithArrays()`, `MatMPIAIJSetPreallocationCSR()`, `MatSetValuesCOO()`, `MatSetPreallocationCOO()`
5328 @*/
5329 PetscErrorCode MatCreateSeqAIJFromTriple(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt i[], PetscInt j[], PetscScalar a[], Mat *mat, PetscCount nz, PetscBool idx)
5330 {
5331   PetscInt ii, *nnz, one = 1, row, col;
5332 
5333   PetscFunctionBegin;
5334   PetscCall(PetscCalloc1(m, &nnz));
5335   for (ii = 0; ii < nz; ii++) nnz[i[ii] - !!idx] += 1;
5336   PetscCall(MatCreate(comm, mat));
5337   PetscCall(MatSetSizes(*mat, m, n, m, n));
5338   PetscCall(MatSetType(*mat, MATSEQAIJ));
5339   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*mat, 0, nnz));
5340   for (ii = 0; ii < nz; ii++) {
5341     if (idx) {
5342       row = i[ii] - 1;
5343       col = j[ii] - 1;
5344     } else {
5345       row = i[ii];
5346       col = j[ii];
5347     }
5348     PetscCall(MatSetValues(*mat, one, &row, one, &col, &a[ii], ADD_VALUES));
5349   }
5350   PetscCall(MatAssemblyBegin(*mat, MAT_FINAL_ASSEMBLY));
5351   PetscCall(MatAssemblyEnd(*mat, MAT_FINAL_ASSEMBLY));
5352   PetscCall(PetscFree(nnz));
5353   PetscFunctionReturn(PETSC_SUCCESS);
5354 }
5355 
5356 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
5357 {
5358   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
5359 
5360   PetscFunctionBegin;
5361   a->idiagvalid  = PETSC_FALSE;
5362   a->ibdiagvalid = PETSC_FALSE;
5363 
5364   PetscCall(MatSeqAIJInvalidateDiagonal_Inode(A));
5365   PetscFunctionReturn(PETSC_SUCCESS);
5366 }
5367 
5368 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqAIJ(MPI_Comm comm, Mat inmat, PetscInt n, MatReuse scall, Mat *outmat)
5369 {
5370   PetscFunctionBegin;
5371   PetscCall(MatCreateMPIMatConcatenateSeqMat_MPIAIJ(comm, inmat, n, scall, outmat));
5372   PetscFunctionReturn(PETSC_SUCCESS);
5373 }
5374 
5375 /*
5376  Permute A into C's *local* index space using rowemb,colemb.
5377  The embedding are supposed to be injections and the above implies that the range of rowemb is a subset
5378  of [0,m), colemb is in [0,n).
5379  If pattern == DIFFERENT_NONZERO_PATTERN, C is preallocated according to A.
5380  */
5381 PetscErrorCode MatSetSeqMat_SeqAIJ(Mat C, IS rowemb, IS colemb, MatStructure pattern, Mat B)
5382 {
5383   /* If making this function public, change the error returned in this function away from _PLIB. */
5384   Mat_SeqAIJ     *Baij;
5385   PetscBool       seqaij;
5386   PetscInt        m, n, *nz, i, j, count;
5387   PetscScalar     v;
5388   const PetscInt *rowindices, *colindices;
5389 
5390   PetscFunctionBegin;
5391   if (!B) PetscFunctionReturn(PETSC_SUCCESS);
5392   /* Check to make sure the target matrix (and embeddings) are compatible with C and each other. */
5393   PetscCall(PetscObjectBaseTypeCompare((PetscObject)B, MATSEQAIJ, &seqaij));
5394   PetscCheck(seqaij, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Input matrix is of wrong type");
5395   if (rowemb) {
5396     PetscCall(ISGetLocalSize(rowemb, &m));
5397     PetscCheck(m == B->rmap->n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Row IS of size %" PetscInt_FMT " is incompatible with matrix row size %" PetscInt_FMT, m, B->rmap->n);
5398   } else {
5399     PetscCheck(C->rmap->n == B->rmap->n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Input matrix is row-incompatible with the target matrix");
5400   }
5401   if (colemb) {
5402     PetscCall(ISGetLocalSize(colemb, &n));
5403     PetscCheck(n == B->cmap->n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Diag col IS of size %" PetscInt_FMT " is incompatible with input matrix col size %" PetscInt_FMT, n, B->cmap->n);
5404   } else {
5405     PetscCheck(C->cmap->n == B->cmap->n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Input matrix is col-incompatible with the target matrix");
5406   }
5407 
5408   Baij = (Mat_SeqAIJ *)B->data;
5409   if (pattern == DIFFERENT_NONZERO_PATTERN) {
5410     PetscCall(PetscMalloc1(B->rmap->n, &nz));
5411     for (i = 0; i < B->rmap->n; i++) nz[i] = Baij->i[i + 1] - Baij->i[i];
5412     PetscCall(MatSeqAIJSetPreallocation(C, 0, nz));
5413     PetscCall(PetscFree(nz));
5414   }
5415   if (pattern == SUBSET_NONZERO_PATTERN) PetscCall(MatZeroEntries(C));
5416   count      = 0;
5417   rowindices = NULL;
5418   colindices = NULL;
5419   if (rowemb) PetscCall(ISGetIndices(rowemb, &rowindices));
5420   if (colemb) PetscCall(ISGetIndices(colemb, &colindices));
5421   for (i = 0; i < B->rmap->n; i++) {
5422     PetscInt row;
5423     row = i;
5424     if (rowindices) row = rowindices[i];
5425     for (j = Baij->i[i]; j < Baij->i[i + 1]; j++) {
5426       PetscInt col;
5427       col = Baij->j[count];
5428       if (colindices) col = colindices[col];
5429       v = Baij->a[count];
5430       PetscCall(MatSetValues(C, 1, &row, 1, &col, &v, INSERT_VALUES));
5431       ++count;
5432     }
5433   }
5434   /* FIXME: set C's nonzerostate correctly. */
5435   /* Assembly for C is necessary. */
5436   C->preallocated  = PETSC_TRUE;
5437   C->assembled     = PETSC_TRUE;
5438   C->was_assembled = PETSC_FALSE;
5439   PetscFunctionReturn(PETSC_SUCCESS);
5440 }
5441 
5442 PetscErrorCode MatEliminateZeros_SeqAIJ(Mat A, PetscBool keep)
5443 {
5444   Mat_SeqAIJ *a  = (Mat_SeqAIJ *)A->data;
5445   MatScalar  *aa = a->a;
5446   PetscInt    m = A->rmap->n, fshift = 0, fshift_prev = 0, i, k;
5447   PetscInt   *ailen = a->ilen, *imax = a->imax, *ai = a->i, *aj = a->j, rmax = 0;
5448 
5449   PetscFunctionBegin;
5450   PetscCheck(A->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot eliminate zeros for unassembled matrix");
5451   if (m) rmax = ailen[0]; /* determine row with most nonzeros */
5452   for (i = 1; i <= m; i++) {
5453     /* move each nonzero entry back by the amount of zero slots (fshift) before it*/
5454     for (k = ai[i - 1]; k < ai[i]; k++) {
5455       if (aa[k] == 0 && (aj[k] != i - 1 || !keep)) fshift++;
5456       else {
5457         if (aa[k] == 0 && aj[k] == i - 1) PetscCall(PetscInfo(A, "Keep the diagonal zero at row %" PetscInt_FMT "\n", i - 1));
5458         aa[k - fshift] = aa[k];
5459         aj[k - fshift] = aj[k];
5460       }
5461     }
5462     ai[i - 1] -= fshift_prev; // safe to update ai[i-1] now since it will not be used in the next iteration
5463     fshift_prev = fshift;
5464     /* reset ilen and imax for each row */
5465     ailen[i - 1] = imax[i - 1] = ai[i] - fshift - ai[i - 1];
5466     a->nonzerorowcnt += ((ai[i] - fshift - ai[i - 1]) > 0);
5467     rmax = PetscMax(rmax, ailen[i - 1]);
5468   }
5469   if (fshift) {
5470     if (m) {
5471       ai[m] -= fshift;
5472       a->nz = ai[m];
5473     }
5474     PetscCall(PetscInfo(A, "Matrix size: %" PetscInt_FMT " X %" PetscInt_FMT "; zeros eliminated: %" PetscInt_FMT "; nonzeros left: %" PetscInt_FMT "\n", m, A->cmap->n, fshift, a->nz));
5475     A->nonzerostate++;
5476     A->info.nz_unneeded += (PetscReal)fshift;
5477     a->rmax = rmax;
5478     if (a->inode.use && a->inode.checked) PetscCall(MatSeqAIJCheckInode(A));
5479     PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
5480     PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
5481   }
5482   PetscFunctionReturn(PETSC_SUCCESS);
5483 }
5484 
5485 PetscFunctionList MatSeqAIJList = NULL;
5486 
5487 /*@
5488   MatSeqAIJSetType - Converts a `MATSEQAIJ` matrix to a subtype
5489 
5490   Collective
5491 
5492   Input Parameters:
5493 + mat    - the matrix object
5494 - matype - matrix type
5495 
5496   Options Database Key:
5497 . -mat_seqaij_type  <method> - for example seqaijcrl
5498 
5499   Level: intermediate
5500 
5501 .seealso: [](ch_matrices), `Mat`, `PCSetType()`, `VecSetType()`, `MatCreate()`, `MatType`
5502 @*/
5503 PetscErrorCode MatSeqAIJSetType(Mat mat, MatType matype)
5504 {
5505   PetscBool sametype;
5506   PetscErrorCode (*r)(Mat, MatType, MatReuse, Mat *);
5507 
5508   PetscFunctionBegin;
5509   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
5510   PetscCall(PetscObjectTypeCompare((PetscObject)mat, matype, &sametype));
5511   if (sametype) PetscFunctionReturn(PETSC_SUCCESS);
5512 
5513   PetscCall(PetscFunctionListFind(MatSeqAIJList, matype, &r));
5514   PetscCheck(r, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown Mat type given: %s", matype);
5515   PetscCall((*r)(mat, matype, MAT_INPLACE_MATRIX, &mat));
5516   PetscFunctionReturn(PETSC_SUCCESS);
5517 }
5518 
5519 /*@C
5520   MatSeqAIJRegister -  - Adds a new sub-matrix type for sequential `MATSEQAIJ` matrices
5521 
5522   Not Collective, No Fortran Support
5523 
5524   Input Parameters:
5525 + sname    - name of a new user-defined matrix type, for example `MATSEQAIJCRL`
5526 - function - routine to convert to subtype
5527 
5528   Level: advanced
5529 
5530   Notes:
5531   `MatSeqAIJRegister()` may be called multiple times to add several user-defined solvers.
5532 
5533   Then, your matrix can be chosen with the procedural interface at runtime via the option
5534 .vb
5535   -mat_seqaij_type my_mat
5536 .ve
5537 
5538 .seealso: [](ch_matrices), `Mat`, `MatSeqAIJRegisterAll()`
5539 @*/
5540 PetscErrorCode MatSeqAIJRegister(const char sname[], PetscErrorCode (*function)(Mat, MatType, MatReuse, Mat *))
5541 {
5542   PetscFunctionBegin;
5543   PetscCall(MatInitializePackage());
5544   PetscCall(PetscFunctionListAdd(&MatSeqAIJList, sname, function));
5545   PetscFunctionReturn(PETSC_SUCCESS);
5546 }
5547 
5548 PetscBool MatSeqAIJRegisterAllCalled = PETSC_FALSE;
5549 
5550 /*@C
5551   MatSeqAIJRegisterAll - Registers all of the matrix subtypes of `MATSSEQAIJ`
5552 
5553   Not Collective
5554 
5555   Level: advanced
5556 
5557   Note:
5558   This registers the versions of `MATSEQAIJ` for GPUs
5559 
5560 .seealso: [](ch_matrices), `Mat`, `MatRegisterAll()`, `MatSeqAIJRegister()`
5561 @*/
5562 PetscErrorCode MatSeqAIJRegisterAll(void)
5563 {
5564   PetscFunctionBegin;
5565   if (MatSeqAIJRegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
5566   MatSeqAIJRegisterAllCalled = PETSC_TRUE;
5567 
5568   PetscCall(MatSeqAIJRegister(MATSEQAIJCRL, MatConvert_SeqAIJ_SeqAIJCRL));
5569   PetscCall(MatSeqAIJRegister(MATSEQAIJPERM, MatConvert_SeqAIJ_SeqAIJPERM));
5570   PetscCall(MatSeqAIJRegister(MATSEQAIJSELL, MatConvert_SeqAIJ_SeqAIJSELL));
5571 #if defined(PETSC_HAVE_MKL_SPARSE)
5572   PetscCall(MatSeqAIJRegister(MATSEQAIJMKL, MatConvert_SeqAIJ_SeqAIJMKL));
5573 #endif
5574 #if defined(PETSC_HAVE_CUDA)
5575   PetscCall(MatSeqAIJRegister(MATSEQAIJCUSPARSE, MatConvert_SeqAIJ_SeqAIJCUSPARSE));
5576 #endif
5577 #if defined(PETSC_HAVE_HIP)
5578   PetscCall(MatSeqAIJRegister(MATSEQAIJHIPSPARSE, MatConvert_SeqAIJ_SeqAIJHIPSPARSE));
5579 #endif
5580 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
5581   PetscCall(MatSeqAIJRegister(MATSEQAIJKOKKOS, MatConvert_SeqAIJ_SeqAIJKokkos));
5582 #endif
5583 #if defined(PETSC_HAVE_VIENNACL) && defined(PETSC_HAVE_VIENNACL_NO_CUDA)
5584   PetscCall(MatSeqAIJRegister(MATMPIAIJVIENNACL, MatConvert_SeqAIJ_SeqAIJViennaCL));
5585 #endif
5586   PetscFunctionReturn(PETSC_SUCCESS);
5587 }
5588 
5589 /*
5590     Special version for direct calls from Fortran
5591 */
5592 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5593   #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
5594 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5595   #define matsetvaluesseqaij_ matsetvaluesseqaij
5596 #endif
5597 
5598 /* Change these macros so can be used in void function */
5599 
5600 /* Change these macros so can be used in void function */
5601 /* Identical to PetscCallVoid, except it assigns to *_ierr */
5602 #undef PetscCall
5603 #define PetscCall(...) \
5604   do { \
5605     PetscErrorCode ierr_msv_mpiaij = __VA_ARGS__; \
5606     if (PetscUnlikely(ierr_msv_mpiaij)) { \
5607       *_ierr = PetscError(PETSC_COMM_SELF, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr_msv_mpiaij, PETSC_ERROR_REPEAT, " "); \
5608       return; \
5609     } \
5610   } while (0)
5611 
5612 #undef SETERRQ
5613 #define SETERRQ(comm, ierr, ...) \
5614   do { \
5615     *_ierr = PetscError(comm, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr, PETSC_ERROR_INITIAL, __VA_ARGS__); \
5616     return; \
5617   } while (0)
5618 
5619 PETSC_EXTERN void matsetvaluesseqaij_(Mat *AA, PetscInt *mm, const PetscInt im[], PetscInt *nn, const PetscInt in[], const PetscScalar v[], InsertMode *isis, PetscErrorCode *_ierr)
5620 {
5621   Mat         A = *AA;
5622   PetscInt    m = *mm, n = *nn;
5623   InsertMode  is = *isis;
5624   Mat_SeqAIJ *a  = (Mat_SeqAIJ *)A->data;
5625   PetscInt   *rp, k, low, high, t, ii, row, nrow, i, col, l, rmax, N;
5626   PetscInt   *imax, *ai, *ailen;
5627   PetscInt   *aj, nonew = a->nonew, lastcol = -1;
5628   MatScalar  *ap, value, *aa;
5629   PetscBool   ignorezeroentries = a->ignorezeroentries;
5630   PetscBool   roworiented       = a->roworiented;
5631 
5632   PetscFunctionBegin;
5633   MatCheckPreallocated(A, 1);
5634   imax  = a->imax;
5635   ai    = a->i;
5636   ailen = a->ilen;
5637   aj    = a->j;
5638   aa    = a->a;
5639 
5640   for (k = 0; k < m; k++) { /* loop over added rows */
5641     row = im[k];
5642     if (row < 0) continue;
5643     PetscCheck(row < A->rmap->n, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_OUTOFRANGE, "Row too large");
5644     rp   = aj + ai[row];
5645     ap   = aa + ai[row];
5646     rmax = imax[row];
5647     nrow = ailen[row];
5648     low  = 0;
5649     high = nrow;
5650     for (l = 0; l < n; l++) { /* loop over added columns */
5651       if (in[l] < 0) continue;
5652       PetscCheck(in[l] < A->cmap->n, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_OUTOFRANGE, "Column too large");
5653       col = in[l];
5654       if (roworiented) value = v[l + k * n];
5655       else value = v[k + l * m];
5656 
5657       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
5658 
5659       if (col <= lastcol) low = 0;
5660       else high = nrow;
5661       lastcol = col;
5662       while (high - low > 5) {
5663         t = (low + high) / 2;
5664         if (rp[t] > col) high = t;
5665         else low = t;
5666       }
5667       for (i = low; i < high; i++) {
5668         if (rp[i] > col) break;
5669         if (rp[i] == col) {
5670           if (is == ADD_VALUES) ap[i] += value;
5671           else ap[i] = value;
5672           goto noinsert;
5673         }
5674       }
5675       if (value == 0.0 && ignorezeroentries) goto noinsert;
5676       if (nonew == 1) goto noinsert;
5677       PetscCheck(nonew != -1, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero in the matrix");
5678       MatSeqXAIJReallocateAIJ(A, A->rmap->n, 1, nrow, row, col, rmax, aa, ai, aj, rp, ap, imax, nonew, MatScalar);
5679       N = nrow++ - 1;
5680       a->nz++;
5681       high++;
5682       /* shift up all the later entries in this row */
5683       for (ii = N; ii >= i; ii--) {
5684         rp[ii + 1] = rp[ii];
5685         ap[ii + 1] = ap[ii];
5686       }
5687       rp[i] = col;
5688       ap[i] = value;
5689     noinsert:;
5690       low = i + 1;
5691     }
5692     ailen[row] = nrow;
5693   }
5694   PetscFunctionReturnVoid();
5695 }
5696 /* Undefining these here since they were redefined from their original definition above! No
5697  * other PETSc functions should be defined past this point, as it is impossible to recover the
5698  * original definitions */
5699 #undef PetscCall
5700 #undef SETERRQ
5701