xref: /petsc/src/mat/impls/aij/seq/aij.c (revision b699bcadc8a40f01eec44393aa9bff7973422b71)
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 PetscErrorCode MatSeqAIJSetTypeFromOptions(Mat A)
12 {
13   PetscBool flg;
14   char      type[256];
15 
16   PetscFunctionBegin;
17   PetscObjectOptionsBegin((PetscObject)A);
18   PetscCall(PetscOptionsFList("-mat_seqaij_type", "Matrix SeqAIJ type", "MatSeqAIJSetType", MatSeqAIJList, "seqaij", type, 256, &flg));
19   if (flg) PetscCall(MatSeqAIJSetType(A, type));
20   PetscOptionsEnd();
21   PetscFunctionReturn(0);
22 }
23 
24 PetscErrorCode MatGetColumnReductions_SeqAIJ(Mat A, PetscInt type, PetscReal *reductions)
25 {
26   PetscInt    i, m, n;
27   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
28 
29   PetscFunctionBegin;
30   PetscCall(MatGetSize(A, &m, &n));
31   PetscCall(PetscArrayzero(reductions, n));
32   if (type == NORM_2) {
33     for (i = 0; i < aij->i[m]; i++) reductions[aij->j[i]] += PetscAbsScalar(aij->a[i] * aij->a[i]);
34   } else if (type == NORM_1) {
35     for (i = 0; i < aij->i[m]; i++) reductions[aij->j[i]] += PetscAbsScalar(aij->a[i]);
36   } else if (type == NORM_INFINITY) {
37     for (i = 0; i < aij->i[m]; i++) reductions[aij->j[i]] = PetscMax(PetscAbsScalar(aij->a[i]), reductions[aij->j[i]]);
38   } else if (type == REDUCTION_SUM_REALPART || type == REDUCTION_MEAN_REALPART) {
39     for (i = 0; i < aij->i[m]; i++) reductions[aij->j[i]] += PetscRealPart(aij->a[i]);
40   } else if (type == REDUCTION_SUM_IMAGINARYPART || type == REDUCTION_MEAN_IMAGINARYPART) {
41     for (i = 0; i < aij->i[m]; i++) reductions[aij->j[i]] += PetscImaginaryPart(aij->a[i]);
42   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown reduction type");
43 
44   if (type == NORM_2) {
45     for (i = 0; i < n; i++) reductions[i] = PetscSqrtReal(reductions[i]);
46   } else if (type == REDUCTION_MEAN_REALPART || type == REDUCTION_MEAN_IMAGINARYPART) {
47     for (i = 0; i < n; i++) reductions[i] /= m;
48   }
49   PetscFunctionReturn(0);
50 }
51 
52 PetscErrorCode MatFindOffBlockDiagonalEntries_SeqAIJ(Mat A, IS *is)
53 {
54   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
55   PetscInt        i, m = A->rmap->n, cnt = 0, bs = A->rmap->bs;
56   const PetscInt *jj = a->j, *ii = a->i;
57   PetscInt       *rows;
58 
59   PetscFunctionBegin;
60   for (i = 0; i < m; i++) {
61     if ((ii[i] != ii[i + 1]) && ((jj[ii[i]] < bs * (i / bs)) || (jj[ii[i + 1] - 1] > bs * ((i + bs) / bs) - 1))) cnt++;
62   }
63   PetscCall(PetscMalloc1(cnt, &rows));
64   cnt = 0;
65   for (i = 0; i < m; i++) {
66     if ((ii[i] != ii[i + 1]) && ((jj[ii[i]] < bs * (i / bs)) || (jj[ii[i + 1] - 1] > bs * ((i + bs) / bs) - 1))) {
67       rows[cnt] = i;
68       cnt++;
69     }
70   }
71   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, cnt, rows, PETSC_OWN_POINTER, is));
72   PetscFunctionReturn(0);
73 }
74 
75 PetscErrorCode MatFindZeroDiagonals_SeqAIJ_Private(Mat A, PetscInt *nrows, PetscInt **zrows)
76 {
77   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
78   const MatScalar *aa;
79   PetscInt         i, m = A->rmap->n, cnt = 0;
80   const PetscInt  *ii = a->i, *jj = a->j, *diag;
81   PetscInt        *rows;
82 
83   PetscFunctionBegin;
84   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
85   PetscCall(MatMarkDiagonal_SeqAIJ(A));
86   diag = a->diag;
87   for (i = 0; i < m; i++) {
88     if ((diag[i] >= ii[i + 1]) || (jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) cnt++;
89   }
90   PetscCall(PetscMalloc1(cnt, &rows));
91   cnt = 0;
92   for (i = 0; i < m; i++) {
93     if ((diag[i] >= ii[i + 1]) || (jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) rows[cnt++] = i;
94   }
95   *nrows = cnt;
96   *zrows = rows;
97   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
98   PetscFunctionReturn(0);
99 }
100 
101 PetscErrorCode MatFindZeroDiagonals_SeqAIJ(Mat A, IS *zrows)
102 {
103   PetscInt nrows, *rows;
104 
105   PetscFunctionBegin;
106   *zrows = NULL;
107   PetscCall(MatFindZeroDiagonals_SeqAIJ_Private(A, &nrows, &rows));
108   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)A), nrows, rows, PETSC_OWN_POINTER, zrows));
109   PetscFunctionReturn(0);
110 }
111 
112 PetscErrorCode MatFindNonzeroRows_SeqAIJ(Mat A, IS *keptrows)
113 {
114   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
115   const MatScalar *aa;
116   PetscInt         m = A->rmap->n, cnt = 0;
117   const PetscInt  *ii;
118   PetscInt         n, i, j, *rows;
119 
120   PetscFunctionBegin;
121   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
122   *keptrows = NULL;
123   ii        = a->i;
124   for (i = 0; i < m; i++) {
125     n = ii[i + 1] - ii[i];
126     if (!n) {
127       cnt++;
128       goto ok1;
129     }
130     for (j = ii[i]; j < ii[i + 1]; j++) {
131       if (aa[j] != 0.0) goto ok1;
132     }
133     cnt++;
134   ok1:;
135   }
136   if (!cnt) {
137     PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
138     PetscFunctionReturn(0);
139   }
140   PetscCall(PetscMalloc1(A->rmap->n - cnt, &rows));
141   cnt = 0;
142   for (i = 0; i < m; i++) {
143     n = ii[i + 1] - ii[i];
144     if (!n) continue;
145     for (j = ii[i]; j < ii[i + 1]; j++) {
146       if (aa[j] != 0.0) {
147         rows[cnt++] = i;
148         break;
149       }
150     }
151   }
152   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
153   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, cnt, rows, PETSC_OWN_POINTER, keptrows));
154   PetscFunctionReturn(0);
155 }
156 
157 PetscErrorCode MatDiagonalSet_SeqAIJ(Mat Y, Vec D, InsertMode is)
158 {
159   Mat_SeqAIJ        *aij = (Mat_SeqAIJ *)Y->data;
160   PetscInt           i, m = Y->rmap->n;
161   const PetscInt    *diag;
162   MatScalar         *aa;
163   const PetscScalar *v;
164   PetscBool          missing;
165 
166   PetscFunctionBegin;
167   if (Y->assembled) {
168     PetscCall(MatMissingDiagonal_SeqAIJ(Y, &missing, NULL));
169     if (!missing) {
170       diag = aij->diag;
171       PetscCall(VecGetArrayRead(D, &v));
172       PetscCall(MatSeqAIJGetArray(Y, &aa));
173       if (is == INSERT_VALUES) {
174         for (i = 0; i < m; i++) aa[diag[i]] = v[i];
175       } else {
176         for (i = 0; i < m; i++) aa[diag[i]] += v[i];
177       }
178       PetscCall(MatSeqAIJRestoreArray(Y, &aa));
179       PetscCall(VecRestoreArrayRead(D, &v));
180       PetscFunctionReturn(0);
181     }
182     PetscCall(MatSeqAIJInvalidateDiagonal(Y));
183   }
184   PetscCall(MatDiagonalSet_Default(Y, D, is));
185   PetscFunctionReturn(0);
186 }
187 
188 PetscErrorCode MatGetRowIJ_SeqAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *m, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
189 {
190   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
191   PetscInt    i, ishift;
192 
193   PetscFunctionBegin;
194   if (m) *m = A->rmap->n;
195   if (!ia) PetscFunctionReturn(0);
196   ishift = 0;
197   if (symmetric && A->structurally_symmetric != PETSC_BOOL3_TRUE) {
198     PetscCall(MatToSymmetricIJ_SeqAIJ(A->rmap->n, a->i, a->j, PETSC_TRUE, ishift, oshift, (PetscInt **)ia, (PetscInt **)ja));
199   } else if (oshift == 1) {
200     PetscInt *tia;
201     PetscInt  nz = a->i[A->rmap->n];
202     /* malloc space and  add 1 to i and j indices */
203     PetscCall(PetscMalloc1(A->rmap->n + 1, &tia));
204     for (i = 0; i < A->rmap->n + 1; i++) tia[i] = a->i[i] + 1;
205     *ia = tia;
206     if (ja) {
207       PetscInt *tja;
208       PetscCall(PetscMalloc1(nz + 1, &tja));
209       for (i = 0; i < nz; i++) tja[i] = a->j[i] + 1;
210       *ja = tja;
211     }
212   } else {
213     *ia = a->i;
214     if (ja) *ja = a->j;
215   }
216   PetscFunctionReturn(0);
217 }
218 
219 PetscErrorCode MatRestoreRowIJ_SeqAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
220 {
221   PetscFunctionBegin;
222   if (!ia) PetscFunctionReturn(0);
223   if ((symmetric && A->structurally_symmetric != PETSC_BOOL3_TRUE) || oshift == 1) {
224     PetscCall(PetscFree(*ia));
225     if (ja) PetscCall(PetscFree(*ja));
226   }
227   PetscFunctionReturn(0);
228 }
229 
230 PetscErrorCode MatGetColumnIJ_SeqAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *nn, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
231 {
232   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
233   PetscInt    i, *collengths, *cia, *cja, n = A->cmap->n, m = A->rmap->n;
234   PetscInt    nz = a->i[m], row, *jj, mr, col;
235 
236   PetscFunctionBegin;
237   *nn = n;
238   if (!ia) PetscFunctionReturn(0);
239   if (symmetric) {
240     PetscCall(MatToSymmetricIJ_SeqAIJ(A->rmap->n, a->i, a->j, PETSC_TRUE, 0, oshift, (PetscInt **)ia, (PetscInt **)ja));
241   } else {
242     PetscCall(PetscCalloc1(n, &collengths));
243     PetscCall(PetscMalloc1(n + 1, &cia));
244     PetscCall(PetscMalloc1(nz, &cja));
245     jj = a->j;
246     for (i = 0; i < nz; i++) collengths[jj[i]]++;
247     cia[0] = oshift;
248     for (i = 0; i < n; i++) cia[i + 1] = cia[i] + collengths[i];
249     PetscCall(PetscArrayzero(collengths, n));
250     jj = a->j;
251     for (row = 0; row < m; row++) {
252       mr = a->i[row + 1] - a->i[row];
253       for (i = 0; i < mr; i++) {
254         col = *jj++;
255 
256         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
257       }
258     }
259     PetscCall(PetscFree(collengths));
260     *ia = cia;
261     *ja = cja;
262   }
263   PetscFunctionReturn(0);
264 }
265 
266 PetscErrorCode MatRestoreColumnIJ_SeqAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
267 {
268   PetscFunctionBegin;
269   if (!ia) PetscFunctionReturn(0);
270 
271   PetscCall(PetscFree(*ia));
272   PetscCall(PetscFree(*ja));
273   PetscFunctionReturn(0);
274 }
275 
276 /*
277  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
278  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
279  spidx[], index of a->a, to be used in MatTransposeColoringCreate_SeqAIJ() and MatFDColoringCreate_SeqXAIJ()
280 */
281 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *nn, const PetscInt *ia[], const PetscInt *ja[], PetscInt *spidx[], PetscBool *done)
282 {
283   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
284   PetscInt        i, *collengths, *cia, *cja, n = A->cmap->n, m = A->rmap->n;
285   PetscInt        nz = a->i[m], row, mr, col, tmp;
286   PetscInt       *cspidx;
287   const PetscInt *jj;
288 
289   PetscFunctionBegin;
290   *nn = n;
291   if (!ia) PetscFunctionReturn(0);
292 
293   PetscCall(PetscCalloc1(n, &collengths));
294   PetscCall(PetscMalloc1(n + 1, &cia));
295   PetscCall(PetscMalloc1(nz, &cja));
296   PetscCall(PetscMalloc1(nz, &cspidx));
297   jj = a->j;
298   for (i = 0; i < nz; i++) collengths[jj[i]]++;
299   cia[0] = oshift;
300   for (i = 0; i < n; i++) cia[i + 1] = cia[i] + collengths[i];
301   PetscCall(PetscArrayzero(collengths, n));
302   jj = a->j;
303   for (row = 0; row < m; row++) {
304     mr = a->i[row + 1] - a->i[row];
305     for (i = 0; i < mr; i++) {
306       col         = *jj++;
307       tmp         = cia[col] + collengths[col]++ - oshift;
308       cspidx[tmp] = a->i[row] + i; /* index of a->j */
309       cja[tmp]    = row + oshift;
310     }
311   }
312   PetscCall(PetscFree(collengths));
313   *ia    = cia;
314   *ja    = cja;
315   *spidx = cspidx;
316   PetscFunctionReturn(0);
317 }
318 
319 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscInt *spidx[], PetscBool *done)
320 {
321   PetscFunctionBegin;
322   PetscCall(MatRestoreColumnIJ_SeqAIJ(A, oshift, symmetric, inodecompressed, n, ia, ja, done));
323   PetscCall(PetscFree(*spidx));
324   PetscFunctionReturn(0);
325 }
326 
327 PetscErrorCode MatSetValuesRow_SeqAIJ(Mat A, PetscInt row, const PetscScalar v[])
328 {
329   Mat_SeqAIJ  *a  = (Mat_SeqAIJ *)A->data;
330   PetscInt    *ai = a->i;
331   PetscScalar *aa;
332 
333   PetscFunctionBegin;
334   PetscCall(MatSeqAIJGetArray(A, &aa));
335   PetscCall(PetscArraycpy(aa + ai[row], v, ai[row + 1] - ai[row]));
336   PetscCall(MatSeqAIJRestoreArray(A, &aa));
337   PetscFunctionReturn(0);
338 }
339 
340 /*
341     MatSeqAIJSetValuesLocalFast - An optimized version of MatSetValuesLocal() for SeqAIJ matrices with several assumptions
342 
343       -   a single row of values is set with each call
344       -   no row or column indices are negative or (in error) larger than the number of rows or columns
345       -   the values are always added to the matrix, not set
346       -   no new locations are introduced in the nonzero structure of the matrix
347 
348      This does NOT assume the global column indices are sorted
349 
350 */
351 
352 #include <petsc/private/isimpl.h>
353 PetscErrorCode MatSeqAIJSetValuesLocalFast(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode is)
354 {
355   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
356   PetscInt        low, high, t, row, nrow, i, col, l;
357   const PetscInt *rp, *ai = a->i, *ailen = a->ilen, *aj = a->j;
358   PetscInt        lastcol = -1;
359   MatScalar      *ap, value, *aa;
360   const PetscInt *ridx = A->rmap->mapping->indices, *cidx = A->cmap->mapping->indices;
361 
362   PetscFunctionBegin;
363   PetscCall(MatSeqAIJGetArray(A, &aa));
364   row  = ridx[im[0]];
365   rp   = aj + ai[row];
366   ap   = aa + ai[row];
367   nrow = ailen[row];
368   low  = 0;
369   high = nrow;
370   for (l = 0; l < n; l++) { /* loop over added columns */
371     col   = cidx[in[l]];
372     value = v[l];
373 
374     if (col <= lastcol) low = 0;
375     else high = nrow;
376     lastcol = col;
377     while (high - low > 5) {
378       t = (low + high) / 2;
379       if (rp[t] > col) high = t;
380       else low = t;
381     }
382     for (i = low; i < high; i++) {
383       if (rp[i] == col) {
384         ap[i] += value;
385         low = i + 1;
386         break;
387       }
388     }
389   }
390   PetscCall(MatSeqAIJRestoreArray(A, &aa));
391   return 0;
392 }
393 
394 PetscErrorCode MatSetValues_SeqAIJ(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode is)
395 {
396   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
397   PetscInt   *rp, k, low, high, t, ii, row, nrow, i, col, l, rmax, N;
398   PetscInt   *imax = a->imax, *ai = a->i, *ailen = a->ilen;
399   PetscInt   *aj = a->j, nonew = a->nonew, lastcol = -1;
400   MatScalar  *ap = NULL, value = 0.0, *aa;
401   PetscBool   ignorezeroentries = a->ignorezeroentries;
402   PetscBool   roworiented       = a->roworiented;
403 
404   PetscFunctionBegin;
405   PetscCall(MatSeqAIJGetArray(A, &aa));
406   for (k = 0; k < m; k++) { /* loop over added rows */
407     row = im[k];
408     if (row < 0) continue;
409     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);
410     rp = aj + ai[row];
411     if (!A->structure_only) ap = aa + ai[row];
412     rmax = imax[row];
413     nrow = ailen[row];
414     low  = 0;
415     high = nrow;
416     for (l = 0; l < n; l++) { /* loop over added columns */
417       if (in[l] < 0) continue;
418       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);
419       col = in[l];
420       if (v && !A->structure_only) value = roworiented ? v[l + k * n] : v[k + l * m];
421       if (!A->structure_only && value == 0.0 && ignorezeroentries && is == ADD_VALUES && row != col) continue;
422 
423       if (col <= lastcol) low = 0;
424       else high = nrow;
425       lastcol = col;
426       while (high - low > 5) {
427         t = (low + high) / 2;
428         if (rp[t] > col) high = t;
429         else low = t;
430       }
431       for (i = low; i < high; i++) {
432         if (rp[i] > col) break;
433         if (rp[i] == col) {
434           if (!A->structure_only) {
435             if (is == ADD_VALUES) {
436               ap[i] += value;
437               (void)PetscLogFlops(1.0);
438             } else ap[i] = value;
439           }
440           low = i + 1;
441           goto noinsert;
442         }
443       }
444       if (value == 0.0 && ignorezeroentries && row != col) goto noinsert;
445       if (nonew == 1) goto noinsert;
446       PetscCheck(nonew != -1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero at (%" PetscInt_FMT ",%" PetscInt_FMT ") in the matrix", row, col);
447       if (A->structure_only) {
448         MatSeqXAIJReallocateAIJ_structure_only(A, A->rmap->n, 1, nrow, row, col, rmax, ai, aj, rp, imax, nonew, MatScalar);
449       } else {
450         MatSeqXAIJReallocateAIJ(A, A->rmap->n, 1, nrow, row, col, rmax, aa, ai, aj, rp, ap, imax, nonew, MatScalar);
451       }
452       N = nrow++ - 1;
453       a->nz++;
454       high++;
455       /* shift up all the later entries in this row */
456       PetscCall(PetscArraymove(rp + i + 1, rp + i, N - i + 1));
457       rp[i] = col;
458       if (!A->structure_only) {
459         PetscCall(PetscArraymove(ap + i + 1, ap + i, N - i + 1));
460         ap[i] = value;
461       }
462       low = i + 1;
463       A->nonzerostate++;
464     noinsert:;
465     }
466     ailen[row] = nrow;
467   }
468   PetscCall(MatSeqAIJRestoreArray(A, &aa));
469   PetscFunctionReturn(0);
470 }
471 
472 PetscErrorCode MatSetValues_SeqAIJ_SortedFullNoPreallocation(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode is)
473 {
474   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
475   PetscInt   *rp, k, row;
476   PetscInt   *ai = a->i;
477   PetscInt   *aj = a->j;
478   MatScalar  *aa, *ap;
479 
480   PetscFunctionBegin;
481   PetscCheck(!A->was_assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot call on assembled matrix.");
482   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);
483 
484   PetscCall(MatSeqAIJGetArray(A, &aa));
485   for (k = 0; k < m; k++) { /* loop over added rows */
486     row = im[k];
487     rp  = aj + ai[row];
488     ap  = aa + ai[row];
489 
490     PetscCall(PetscMemcpy(rp, in, n * sizeof(PetscInt)));
491     if (!A->structure_only) {
492       if (v) {
493         PetscCall(PetscMemcpy(ap, v, n * sizeof(PetscScalar)));
494         v += n;
495       } else {
496         PetscCall(PetscMemzero(ap, n * sizeof(PetscScalar)));
497       }
498     }
499     a->ilen[row]  = n;
500     a->imax[row]  = n;
501     a->i[row + 1] = a->i[row] + n;
502     a->nz += n;
503   }
504   PetscCall(MatSeqAIJRestoreArray(A, &aa));
505   PetscFunctionReturn(0);
506 }
507 
508 /*@
509     MatSeqAIJSetTotalPreallocation - Sets an upper bound on the total number of expected nonzeros in the matrix.
510 
511   Input Parameters:
512 +  A - the `MATSEQAIJ` matrix
513 -  nztotal - bound on the number of nonzeros
514 
515   Level: advanced
516 
517   Notes:
518     This can be called if you will be provided the matrix row by row (from row zero) with sorted column indices for each row.
519     Simply call `MatSetValues()` after this call to provide the matrix entries in the usual manner. This matrix may be used
520     as always with multiple matrix assemblies.
521 
522 .seealso: `MatSetOption()`, `MAT_SORTED_FULL`, `MatSetValues()`, `MatSeqAIJSetPreallocation()`
523 @*/
524 
525 PetscErrorCode MatSeqAIJSetTotalPreallocation(Mat A, PetscInt nztotal)
526 {
527   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
528 
529   PetscFunctionBegin;
530   PetscCall(PetscLayoutSetUp(A->rmap));
531   PetscCall(PetscLayoutSetUp(A->cmap));
532   a->maxnz = nztotal;
533   if (!a->imax) { PetscCall(PetscMalloc1(A->rmap->n, &a->imax)); }
534   if (!a->ilen) {
535     PetscCall(PetscMalloc1(A->rmap->n, &a->ilen));
536   } else {
537     PetscCall(PetscMemzero(a->ilen, A->rmap->n * sizeof(PetscInt)));
538   }
539 
540   /* allocate the matrix space */
541   if (A->structure_only) {
542     PetscCall(PetscMalloc1(nztotal, &a->j));
543     PetscCall(PetscMalloc1(A->rmap->n + 1, &a->i));
544   } else {
545     PetscCall(PetscMalloc3(nztotal, &a->a, nztotal, &a->j, A->rmap->n + 1, &a->i));
546   }
547   a->i[0] = 0;
548   if (A->structure_only) {
549     a->singlemalloc = PETSC_FALSE;
550     a->free_a       = PETSC_FALSE;
551   } else {
552     a->singlemalloc = PETSC_TRUE;
553     a->free_a       = PETSC_TRUE;
554   }
555   a->free_ij        = PETSC_TRUE;
556   A->ops->setvalues = MatSetValues_SeqAIJ_SortedFullNoPreallocation;
557   A->preallocated   = PETSC_TRUE;
558   PetscFunctionReturn(0);
559 }
560 
561 PetscErrorCode MatSetValues_SeqAIJ_SortedFull(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode is)
562 {
563   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
564   PetscInt   *rp, k, row;
565   PetscInt   *ai = a->i, *ailen = a->ilen;
566   PetscInt   *aj = a->j;
567   MatScalar  *aa, *ap;
568 
569   PetscFunctionBegin;
570   PetscCall(MatSeqAIJGetArray(A, &aa));
571   for (k = 0; k < m; k++) { /* loop over added rows */
572     row = im[k];
573     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);
574     rp = aj + ai[row];
575     ap = aa + ai[row];
576     if (!A->was_assembled) PetscCall(PetscMemcpy(rp, in, n * sizeof(PetscInt)));
577     if (!A->structure_only) {
578       if (v) {
579         PetscCall(PetscMemcpy(ap, v, n * sizeof(PetscScalar)));
580         v += n;
581       } else {
582         PetscCall(PetscMemzero(ap, n * sizeof(PetscScalar)));
583       }
584     }
585     ailen[row] = n;
586     a->nz += n;
587   }
588   PetscCall(MatSeqAIJRestoreArray(A, &aa));
589   PetscFunctionReturn(0);
590 }
591 
592 PetscErrorCode MatGetValues_SeqAIJ(Mat A, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], PetscScalar v[])
593 {
594   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
595   PetscInt   *rp, k, low, high, t, row, nrow, i, col, l, *aj = a->j;
596   PetscInt   *ai = a->i, *ailen = a->ilen;
597   MatScalar  *ap, *aa;
598 
599   PetscFunctionBegin;
600   PetscCall(MatSeqAIJGetArray(A, &aa));
601   for (k = 0; k < m; k++) { /* loop over rows */
602     row = im[k];
603     if (row < 0) {
604       v += n;
605       continue;
606     } /* negative row */
607     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);
608     rp   = aj + ai[row];
609     ap   = aa + ai[row];
610     nrow = ailen[row];
611     for (l = 0; l < n; l++) { /* loop over columns */
612       if (in[l] < 0) {
613         v++;
614         continue;
615       } /* negative column */
616       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);
617       col  = in[l];
618       high = nrow;
619       low  = 0; /* assume unsorted */
620       while (high - low > 5) {
621         t = (low + high) / 2;
622         if (rp[t] > col) high = t;
623         else low = t;
624       }
625       for (i = low; i < high; i++) {
626         if (rp[i] > col) break;
627         if (rp[i] == col) {
628           *v++ = ap[i];
629           goto finished;
630         }
631       }
632       *v++ = 0.0;
633     finished:;
634     }
635   }
636   PetscCall(MatSeqAIJRestoreArray(A, &aa));
637   PetscFunctionReturn(0);
638 }
639 
640 PetscErrorCode MatView_SeqAIJ_Binary(Mat mat, PetscViewer viewer)
641 {
642   Mat_SeqAIJ        *A = (Mat_SeqAIJ *)mat->data;
643   const PetscScalar *av;
644   PetscInt           header[4], M, N, m, nz, i;
645   PetscInt          *rowlens;
646 
647   PetscFunctionBegin;
648   PetscCall(PetscViewerSetUp(viewer));
649 
650   M  = mat->rmap->N;
651   N  = mat->cmap->N;
652   m  = mat->rmap->n;
653   nz = A->nz;
654 
655   /* write matrix header */
656   header[0] = MAT_FILE_CLASSID;
657   header[1] = M;
658   header[2] = N;
659   header[3] = nz;
660   PetscCall(PetscViewerBinaryWrite(viewer, header, 4, PETSC_INT));
661 
662   /* fill in and store row lengths */
663   PetscCall(PetscMalloc1(m, &rowlens));
664   for (i = 0; i < m; i++) rowlens[i] = A->i[i + 1] - A->i[i];
665   PetscCall(PetscViewerBinaryWrite(viewer, rowlens, m, PETSC_INT));
666   PetscCall(PetscFree(rowlens));
667   /* store column indices */
668   PetscCall(PetscViewerBinaryWrite(viewer, A->j, nz, PETSC_INT));
669   /* store nonzero values */
670   PetscCall(MatSeqAIJGetArrayRead(mat, &av));
671   PetscCall(PetscViewerBinaryWrite(viewer, av, nz, PETSC_SCALAR));
672   PetscCall(MatSeqAIJRestoreArrayRead(mat, &av));
673 
674   /* write block size option to the viewer's .info file */
675   PetscCall(MatView_Binary_BlockSizes(mat, viewer));
676   PetscFunctionReturn(0);
677 }
678 
679 static PetscErrorCode MatView_SeqAIJ_ASCII_structonly(Mat A, PetscViewer viewer)
680 {
681   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
682   PetscInt    i, k, m = A->rmap->N;
683 
684   PetscFunctionBegin;
685   PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
686   for (i = 0; i < m; i++) {
687     PetscCall(PetscViewerASCIIPrintf(viewer, "row %" PetscInt_FMT ":", i));
688     for (k = a->i[i]; k < a->i[i + 1]; k++) PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ") ", a->j[k]));
689     PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
690   }
691   PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
692   PetscFunctionReturn(0);
693 }
694 
695 extern PetscErrorCode MatSeqAIJFactorInfo_Matlab(Mat, PetscViewer);
696 
697 PetscErrorCode MatView_SeqAIJ_ASCII(Mat A, PetscViewer viewer)
698 {
699   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
700   const PetscScalar *av;
701   PetscInt           i, j, m = A->rmap->n;
702   const char        *name;
703   PetscViewerFormat  format;
704 
705   PetscFunctionBegin;
706   if (A->structure_only) {
707     PetscCall(MatView_SeqAIJ_ASCII_structonly(A, viewer));
708     PetscFunctionReturn(0);
709   }
710 
711   PetscCall(PetscViewerGetFormat(viewer, &format));
712   if (format == PETSC_VIEWER_ASCII_FACTOR_INFO || format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscFunctionReturn(0);
713 
714   /* trigger copy to CPU if needed */
715   PetscCall(MatSeqAIJGetArrayRead(A, &av));
716   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
717   if (format == PETSC_VIEWER_ASCII_MATLAB) {
718     PetscInt nofinalvalue = 0;
719     if (m && ((a->i[m] == a->i[m - 1]) || (a->j[a->nz - 1] != A->cmap->n - 1))) {
720       /* Need a dummy value to ensure the dimension of the matrix. */
721       nofinalvalue = 1;
722     }
723     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
724     PetscCall(PetscViewerASCIIPrintf(viewer, "%% Size = %" PetscInt_FMT " %" PetscInt_FMT " \n", m, A->cmap->n));
725     PetscCall(PetscViewerASCIIPrintf(viewer, "%% Nonzeros = %" PetscInt_FMT " \n", a->nz));
726 #if defined(PETSC_USE_COMPLEX)
727     PetscCall(PetscViewerASCIIPrintf(viewer, "zzz = zeros(%" PetscInt_FMT ",4);\n", a->nz + nofinalvalue));
728 #else
729     PetscCall(PetscViewerASCIIPrintf(viewer, "zzz = zeros(%" PetscInt_FMT ",3);\n", a->nz + nofinalvalue));
730 #endif
731     PetscCall(PetscViewerASCIIPrintf(viewer, "zzz = [\n"));
732 
733     for (i = 0; i < m; i++) {
734       for (j = a->i[i]; j < a->i[i + 1]; j++) {
735 #if defined(PETSC_USE_COMPLEX)
736         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])));
737 #else
738         PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n", i + 1, a->j[j] + 1, (double)a->a[j]));
739 #endif
740       }
741     }
742     if (nofinalvalue) {
743 #if defined(PETSC_USE_COMPLEX)
744       PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e %18.16e\n", m, A->cmap->n, 0., 0.));
745 #else
746       PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " %" PetscInt_FMT "  %18.16e\n", m, A->cmap->n, 0.0));
747 #endif
748     }
749     PetscCall(PetscObjectGetName((PetscObject)A, &name));
750     PetscCall(PetscViewerASCIIPrintf(viewer, "];\n %s = spconvert(zzz);\n", name));
751     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
752   } else if (format == PETSC_VIEWER_ASCII_COMMON) {
753     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
754     for (i = 0; i < m; i++) {
755       PetscCall(PetscViewerASCIIPrintf(viewer, "row %" PetscInt_FMT ":", i));
756       for (j = a->i[i]; j < a->i[i + 1]; j++) {
757 #if defined(PETSC_USE_COMPLEX)
758         if (PetscImaginaryPart(a->a[j]) > 0.0 && PetscRealPart(a->a[j]) != 0.0) {
759           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)PetscImaginaryPart(a->a[j])));
760         } else if (PetscImaginaryPart(a->a[j]) < 0.0 && PetscRealPart(a->a[j]) != 0.0) {
761           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g - %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)-PetscImaginaryPart(a->a[j])));
762         } else if (PetscRealPart(a->a[j]) != 0.0) {
763           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)PetscRealPart(a->a[j])));
764         }
765 #else
766         if (a->a[j] != 0.0) PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)a->a[j]));
767 #endif
768       }
769       PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
770     }
771     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
772   } else if (format == PETSC_VIEWER_ASCII_SYMMODU) {
773     PetscInt nzd = 0, fshift = 1, *sptr;
774     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
775     PetscCall(PetscMalloc1(m + 1, &sptr));
776     for (i = 0; i < m; i++) {
777       sptr[i] = nzd + 1;
778       for (j = a->i[i]; j < a->i[i + 1]; j++) {
779         if (a->j[j] >= i) {
780 #if defined(PETSC_USE_COMPLEX)
781           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) nzd++;
782 #else
783           if (a->a[j] != 0.0) nzd++;
784 #endif
785         }
786       }
787     }
788     sptr[m] = nzd + 1;
789     PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " %" PetscInt_FMT "\n\n", m, nzd));
790     for (i = 0; i < m + 1; i += 6) {
791       if (i + 4 < m) {
792         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]));
793       } else if (i + 3 < m) {
794         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]));
795       } else if (i + 2 < m) {
796         PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n", sptr[i], sptr[i + 1], sptr[i + 2], sptr[i + 3]));
797       } else if (i + 1 < m) {
798         PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n", sptr[i], sptr[i + 1], sptr[i + 2]));
799       } else if (i < m) {
800         PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " %" PetscInt_FMT "\n", sptr[i], sptr[i + 1]));
801       } else {
802         PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT "\n", sptr[i]));
803       }
804     }
805     PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
806     PetscCall(PetscFree(sptr));
807     for (i = 0; i < m; i++) {
808       for (j = a->i[i]; j < a->i[i + 1]; j++) {
809         if (a->j[j] >= i) PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT " ", a->j[j] + fshift));
810       }
811       PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
812     }
813     PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
814     for (i = 0; i < m; i++) {
815       for (j = a->i[i]; j < a->i[i + 1]; j++) {
816         if (a->j[j] >= i) {
817 #if defined(PETSC_USE_COMPLEX)
818           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])));
819 #else
820           if (a->a[j] != 0.0) PetscCall(PetscViewerASCIIPrintf(viewer, " %18.16e ", (double)a->a[j]));
821 #endif
822         }
823       }
824       PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
825     }
826     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
827   } else if (format == PETSC_VIEWER_ASCII_DENSE) {
828     PetscInt    cnt = 0, jcnt;
829     PetscScalar value;
830 #if defined(PETSC_USE_COMPLEX)
831     PetscBool realonly = PETSC_TRUE;
832 
833     for (i = 0; i < a->i[m]; i++) {
834       if (PetscImaginaryPart(a->a[i]) != 0.0) {
835         realonly = PETSC_FALSE;
836         break;
837       }
838     }
839 #endif
840 
841     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
842     for (i = 0; i < m; i++) {
843       jcnt = 0;
844       for (j = 0; j < A->cmap->n; j++) {
845         if (jcnt < a->i[i + 1] - a->i[i] && j == a->j[cnt]) {
846           value = a->a[cnt++];
847           jcnt++;
848         } else {
849           value = 0.0;
850         }
851 #if defined(PETSC_USE_COMPLEX)
852         if (realonly) {
853           PetscCall(PetscViewerASCIIPrintf(viewer, " %7.5e ", (double)PetscRealPart(value)));
854         } else {
855           PetscCall(PetscViewerASCIIPrintf(viewer, " %7.5e+%7.5e i ", (double)PetscRealPart(value), (double)PetscImaginaryPart(value)));
856         }
857 #else
858         PetscCall(PetscViewerASCIIPrintf(viewer, " %7.5e ", (double)value));
859 #endif
860       }
861       PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
862     }
863     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
864   } else if (format == PETSC_VIEWER_ASCII_MATRIXMARKET) {
865     PetscInt fshift = 1;
866     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
867 #if defined(PETSC_USE_COMPLEX)
868     PetscCall(PetscViewerASCIIPrintf(viewer, "%%%%MatrixMarket matrix coordinate complex general\n"));
869 #else
870     PetscCall(PetscViewerASCIIPrintf(viewer, "%%%%MatrixMarket matrix coordinate real general\n"));
871 #endif
872     PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n", m, A->cmap->n, a->nz));
873     for (i = 0; i < m; i++) {
874       for (j = a->i[i]; j < a->i[i + 1]; j++) {
875 #if defined(PETSC_USE_COMPLEX)
876         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])));
877 #else
878         PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " %" PetscInt_FMT " %g\n", i + fshift, a->j[j] + fshift, (double)a->a[j]));
879 #endif
880       }
881     }
882     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
883   } else {
884     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
885     if (A->factortype) {
886       for (i = 0; i < m; i++) {
887         PetscCall(PetscViewerASCIIPrintf(viewer, "row %" PetscInt_FMT ":", i));
888         /* L part */
889         for (j = a->i[i]; j < a->i[i + 1]; j++) {
890 #if defined(PETSC_USE_COMPLEX)
891           if (PetscImaginaryPart(a->a[j]) > 0.0) {
892             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)PetscImaginaryPart(a->a[j])));
893           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
894             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g - %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)(-PetscImaginaryPart(a->a[j]))));
895           } else {
896             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)PetscRealPart(a->a[j])));
897           }
898 #else
899           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)a->a[j]));
900 #endif
901         }
902         /* diagonal */
903         j = a->diag[i];
904 #if defined(PETSC_USE_COMPLEX)
905         if (PetscImaginaryPart(a->a[j]) > 0.0) {
906           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %g i)", a->j[j], (double)PetscRealPart(1.0 / a->a[j]), (double)PetscImaginaryPart(1.0 / a->a[j])));
907         } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
908           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g - %g i)", a->j[j], (double)PetscRealPart(1.0 / a->a[j]), (double)(-PetscImaginaryPart(1.0 / a->a[j]))));
909         } else {
910           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)PetscRealPart(1.0 / a->a[j])));
911         }
912 #else
913         PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)(1.0 / a->a[j])));
914 #endif
915 
916         /* U part */
917         for (j = a->diag[i + 1] + 1; j < a->diag[i]; j++) {
918 #if defined(PETSC_USE_COMPLEX)
919           if (PetscImaginaryPart(a->a[j]) > 0.0) {
920             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)PetscImaginaryPart(a->a[j])));
921           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
922             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g - %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)(-PetscImaginaryPart(a->a[j]))));
923           } else {
924             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)PetscRealPart(a->a[j])));
925           }
926 #else
927           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)a->a[j]));
928 #endif
929         }
930         PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
931       }
932     } else {
933       for (i = 0; i < m; i++) {
934         PetscCall(PetscViewerASCIIPrintf(viewer, "row %" PetscInt_FMT ":", i));
935         for (j = a->i[i]; j < a->i[i + 1]; j++) {
936 #if defined(PETSC_USE_COMPLEX)
937           if (PetscImaginaryPart(a->a[j]) > 0.0) {
938             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)PetscImaginaryPart(a->a[j])));
939           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
940             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g - %g i)", a->j[j], (double)PetscRealPart(a->a[j]), (double)-PetscImaginaryPart(a->a[j])));
941           } else {
942             PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)PetscRealPart(a->a[j])));
943           }
944 #else
945           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", a->j[j], (double)a->a[j]));
946 #endif
947         }
948         PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
949       }
950     }
951     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
952   }
953   PetscCall(PetscViewerFlush(viewer));
954   PetscFunctionReturn(0);
955 }
956 
957 #include <petscdraw.h>
958 PetscErrorCode MatView_SeqAIJ_Draw_Zoom(PetscDraw draw, void *Aa)
959 {
960   Mat                A = (Mat)Aa;
961   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
962   PetscInt           i, j, m = A->rmap->n;
963   int                color;
964   PetscReal          xl, yl, xr, yr, x_l, x_r, y_l, y_r;
965   PetscViewer        viewer;
966   PetscViewerFormat  format;
967   const PetscScalar *aa;
968 
969   PetscFunctionBegin;
970   PetscCall(PetscObjectQuery((PetscObject)A, "Zoomviewer", (PetscObject *)&viewer));
971   PetscCall(PetscViewerGetFormat(viewer, &format));
972   PetscCall(PetscDrawGetCoordinates(draw, &xl, &yl, &xr, &yr));
973 
974   /* loop over matrix elements drawing boxes */
975   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
976   if (format != PETSC_VIEWER_DRAW_CONTOUR) {
977     PetscDrawCollectiveBegin(draw);
978     /* Blue for negative, Cyan for zero and  Red for positive */
979     color = PETSC_DRAW_BLUE;
980     for (i = 0; i < m; i++) {
981       y_l = m - i - 1.0;
982       y_r = y_l + 1.0;
983       for (j = a->i[i]; j < a->i[i + 1]; j++) {
984         x_l = a->j[j];
985         x_r = x_l + 1.0;
986         if (PetscRealPart(aa[j]) >= 0.) continue;
987         PetscCall(PetscDrawRectangle(draw, x_l, y_l, x_r, y_r, color, color, color, color));
988       }
989     }
990     color = PETSC_DRAW_CYAN;
991     for (i = 0; i < m; i++) {
992       y_l = m - i - 1.0;
993       y_r = y_l + 1.0;
994       for (j = a->i[i]; j < a->i[i + 1]; j++) {
995         x_l = a->j[j];
996         x_r = x_l + 1.0;
997         if (aa[j] != 0.) continue;
998         PetscCall(PetscDrawRectangle(draw, x_l, y_l, x_r, y_r, color, color, color, color));
999       }
1000     }
1001     color = PETSC_DRAW_RED;
1002     for (i = 0; i < m; i++) {
1003       y_l = m - i - 1.0;
1004       y_r = y_l + 1.0;
1005       for (j = a->i[i]; j < a->i[i + 1]; j++) {
1006         x_l = a->j[j];
1007         x_r = x_l + 1.0;
1008         if (PetscRealPart(aa[j]) <= 0.) continue;
1009         PetscCall(PetscDrawRectangle(draw, x_l, y_l, x_r, y_r, color, color, color, color));
1010       }
1011     }
1012     PetscDrawCollectiveEnd(draw);
1013   } else {
1014     /* use contour shading to indicate magnitude of values */
1015     /* first determine max of all nonzero values */
1016     PetscReal minv = 0.0, maxv = 0.0;
1017     PetscInt  nz = a->nz, count = 0;
1018     PetscDraw popup;
1019 
1020     for (i = 0; i < nz; i++) {
1021       if (PetscAbsScalar(aa[i]) > maxv) maxv = PetscAbsScalar(aa[i]);
1022     }
1023     if (minv >= maxv) maxv = minv + PETSC_SMALL;
1024     PetscCall(PetscDrawGetPopup(draw, &popup));
1025     PetscCall(PetscDrawScalePopup(popup, minv, maxv));
1026 
1027     PetscDrawCollectiveBegin(draw);
1028     for (i = 0; i < m; i++) {
1029       y_l = m - i - 1.0;
1030       y_r = y_l + 1.0;
1031       for (j = a->i[i]; j < a->i[i + 1]; j++) {
1032         x_l   = a->j[j];
1033         x_r   = x_l + 1.0;
1034         color = PetscDrawRealToColor(PetscAbsScalar(aa[count]), minv, maxv);
1035         PetscCall(PetscDrawRectangle(draw, x_l, y_l, x_r, y_r, color, color, color, color));
1036         count++;
1037       }
1038     }
1039     PetscDrawCollectiveEnd(draw);
1040   }
1041   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
1042   PetscFunctionReturn(0);
1043 }
1044 
1045 #include <petscdraw.h>
1046 PetscErrorCode MatView_SeqAIJ_Draw(Mat A, PetscViewer viewer)
1047 {
1048   PetscDraw draw;
1049   PetscReal xr, yr, xl, yl, h, w;
1050   PetscBool isnull;
1051 
1052   PetscFunctionBegin;
1053   PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
1054   PetscCall(PetscDrawIsNull(draw, &isnull));
1055   if (isnull) PetscFunctionReturn(0);
1056 
1057   xr = A->cmap->n;
1058   yr = A->rmap->n;
1059   h  = yr / 10.0;
1060   w  = xr / 10.0;
1061   xr += w;
1062   yr += h;
1063   xl = -w;
1064   yl = -h;
1065   PetscCall(PetscDrawSetCoordinates(draw, xl, yl, xr, yr));
1066   PetscCall(PetscObjectCompose((PetscObject)A, "Zoomviewer", (PetscObject)viewer));
1067   PetscCall(PetscDrawZoom(draw, MatView_SeqAIJ_Draw_Zoom, A));
1068   PetscCall(PetscObjectCompose((PetscObject)A, "Zoomviewer", NULL));
1069   PetscCall(PetscDrawSave(draw));
1070   PetscFunctionReturn(0);
1071 }
1072 
1073 PetscErrorCode MatView_SeqAIJ(Mat A, PetscViewer viewer)
1074 {
1075   PetscBool iascii, isbinary, isdraw;
1076 
1077   PetscFunctionBegin;
1078   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1079   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
1080   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
1081   if (iascii) PetscCall(MatView_SeqAIJ_ASCII(A, viewer));
1082   else if (isbinary) PetscCall(MatView_SeqAIJ_Binary(A, viewer));
1083   else if (isdraw) PetscCall(MatView_SeqAIJ_Draw(A, viewer));
1084   PetscCall(MatView_SeqAIJ_Inode(A, viewer));
1085   PetscFunctionReturn(0);
1086 }
1087 
1088 PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat A, MatAssemblyType mode)
1089 {
1090   Mat_SeqAIJ *a      = (Mat_SeqAIJ *)A->data;
1091   PetscInt    fshift = 0, i, *ai = a->i, *aj = a->j, *imax = a->imax;
1092   PetscInt    m = A->rmap->n, *ip, N, *ailen = a->ilen, rmax = 0;
1093   MatScalar  *aa    = a->a, *ap;
1094   PetscReal   ratio = 0.6;
1095 
1096   PetscFunctionBegin;
1097   if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(0);
1098   PetscCall(MatSeqAIJInvalidateDiagonal(A));
1099   if (A->was_assembled && A->ass_nonzerostate == A->nonzerostate) {
1100     /* we need to respect users asking to use or not the inodes routine in between matrix assemblies */
1101     PetscCall(MatAssemblyEnd_SeqAIJ_Inode(A, mode));
1102     PetscFunctionReturn(0);
1103   }
1104 
1105   if (m) rmax = ailen[0]; /* determine row with most nonzeros */
1106   for (i = 1; i < m; i++) {
1107     /* move each row back by the amount of empty slots (fshift) before it*/
1108     fshift += imax[i - 1] - ailen[i - 1];
1109     rmax = PetscMax(rmax, ailen[i]);
1110     if (fshift) {
1111       ip = aj + ai[i];
1112       ap = aa + ai[i];
1113       N  = ailen[i];
1114       PetscCall(PetscArraymove(ip - fshift, ip, N));
1115       if (!A->structure_only) PetscCall(PetscArraymove(ap - fshift, ap, N));
1116     }
1117     ai[i] = ai[i - 1] + ailen[i - 1];
1118   }
1119   if (m) {
1120     fshift += imax[m - 1] - ailen[m - 1];
1121     ai[m] = ai[m - 1] + ailen[m - 1];
1122   }
1123   /* reset ilen and imax for each row */
1124   a->nonzerorowcnt = 0;
1125   if (A->structure_only) {
1126     PetscCall(PetscFree(a->imax));
1127     PetscCall(PetscFree(a->ilen));
1128   } else { /* !A->structure_only */
1129     for (i = 0; i < m; i++) {
1130       ailen[i] = imax[i] = ai[i + 1] - ai[i];
1131       a->nonzerorowcnt += ((ai[i + 1] - ai[i]) > 0);
1132     }
1133   }
1134   a->nz = ai[m];
1135   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);
1136 
1137   PetscCall(MatMarkDiagonal_SeqAIJ(A));
1138   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));
1139   PetscCall(PetscInfo(A, "Number of mallocs during MatSetValues() is %" PetscInt_FMT "\n", a->reallocs));
1140   PetscCall(PetscInfo(A, "Maximum nonzeros in any row is %" PetscInt_FMT "\n", rmax));
1141 
1142   A->info.mallocs += a->reallocs;
1143   a->reallocs         = 0;
1144   A->info.nz_unneeded = (PetscReal)fshift;
1145   a->rmax             = rmax;
1146 
1147   if (!A->structure_only) PetscCall(MatCheckCompressedRow(A, a->nonzerorowcnt, &a->compressedrow, a->i, m, ratio));
1148   PetscCall(MatAssemblyEnd_SeqAIJ_Inode(A, mode));
1149   PetscFunctionReturn(0);
1150 }
1151 
1152 PetscErrorCode MatRealPart_SeqAIJ(Mat A)
1153 {
1154   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1155   PetscInt    i, nz = a->nz;
1156   MatScalar  *aa;
1157 
1158   PetscFunctionBegin;
1159   PetscCall(MatSeqAIJGetArray(A, &aa));
1160   for (i = 0; i < nz; i++) aa[i] = PetscRealPart(aa[i]);
1161   PetscCall(MatSeqAIJRestoreArray(A, &aa));
1162   PetscCall(MatSeqAIJInvalidateDiagonal(A));
1163   PetscFunctionReturn(0);
1164 }
1165 
1166 PetscErrorCode MatImaginaryPart_SeqAIJ(Mat A)
1167 {
1168   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1169   PetscInt    i, nz = a->nz;
1170   MatScalar  *aa;
1171 
1172   PetscFunctionBegin;
1173   PetscCall(MatSeqAIJGetArray(A, &aa));
1174   for (i = 0; i < nz; i++) aa[i] = PetscImaginaryPart(aa[i]);
1175   PetscCall(MatSeqAIJRestoreArray(A, &aa));
1176   PetscCall(MatSeqAIJInvalidateDiagonal(A));
1177   PetscFunctionReturn(0);
1178 }
1179 
1180 PetscErrorCode MatZeroEntries_SeqAIJ(Mat A)
1181 {
1182   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1183   MatScalar  *aa;
1184 
1185   PetscFunctionBegin;
1186   PetscCall(MatSeqAIJGetArrayWrite(A, &aa));
1187   PetscCall(PetscArrayzero(aa, a->i[A->rmap->n]));
1188   PetscCall(MatSeqAIJRestoreArrayWrite(A, &aa));
1189   PetscCall(MatSeqAIJInvalidateDiagonal(A));
1190   PetscFunctionReturn(0);
1191 }
1192 
1193 PETSC_INTERN PetscErrorCode MatResetPreallocationCOO_SeqAIJ(Mat A)
1194 {
1195   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1196 
1197   PetscFunctionBegin;
1198   PetscCall(PetscFree(a->perm));
1199   PetscCall(PetscFree(a->jmap));
1200   PetscFunctionReturn(0);
1201 }
1202 
1203 PetscErrorCode MatDestroy_SeqAIJ(Mat A)
1204 {
1205   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1206 
1207   PetscFunctionBegin;
1208 #if defined(PETSC_USE_LOG)
1209   PetscLogObjectState((PetscObject)A, "Rows=%" PetscInt_FMT ", Cols=%" PetscInt_FMT ", NZ=%" PetscInt_FMT, A->rmap->n, A->cmap->n, a->nz);
1210 #endif
1211   PetscCall(MatSeqXAIJFreeAIJ(A, &a->a, &a->j, &a->i));
1212   PetscCall(MatResetPreallocationCOO_SeqAIJ(A));
1213   PetscCall(ISDestroy(&a->row));
1214   PetscCall(ISDestroy(&a->col));
1215   PetscCall(PetscFree(a->diag));
1216   PetscCall(PetscFree(a->ibdiag));
1217   PetscCall(PetscFree(a->imax));
1218   PetscCall(PetscFree(a->ilen));
1219   PetscCall(PetscFree(a->ipre));
1220   PetscCall(PetscFree3(a->idiag, a->mdiag, a->ssor_work));
1221   PetscCall(PetscFree(a->solve_work));
1222   PetscCall(ISDestroy(&a->icol));
1223   PetscCall(PetscFree(a->saved_values));
1224   PetscCall(PetscFree2(a->compressedrow.i, a->compressedrow.rindex));
1225   PetscCall(MatDestroy_SeqAIJ_Inode(A));
1226   PetscCall(PetscFree(A->data));
1227 
1228   /* MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted may allocate this.
1229      That function is so heavily used (sometimes in an hidden way through multnumeric function pointers)
1230      that is hard to properly add this data to the MatProduct data. We free it here to avoid
1231      users reusing the matrix object with different data to incur in obscure segmentation faults
1232      due to different matrix sizes */
1233   PetscCall(PetscObjectCompose((PetscObject)A, "__PETSc__ab_dense", NULL));
1234 
1235   PetscCall(PetscObjectChangeTypeName((PetscObject)A, NULL));
1236   PetscCall(PetscObjectComposeFunction((PetscObject)A, "PetscMatlabEnginePut_C", NULL));
1237   PetscCall(PetscObjectComposeFunction((PetscObject)A, "PetscMatlabEngineGet_C", NULL));
1238   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJSetColumnIndices_C", NULL));
1239   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatStoreValues_C", NULL));
1240   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatRetrieveValues_C", NULL));
1241   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqsbaij_C", NULL));
1242   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqbaij_C", NULL));
1243   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijperm_C", NULL));
1244   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijsell_C", NULL));
1245 #if defined(PETSC_HAVE_MKL_SPARSE)
1246   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijmkl_C", NULL));
1247 #endif
1248 #if defined(PETSC_HAVE_CUDA)
1249   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijcusparse_C", NULL));
1250   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijcusparse_seqaij_C", NULL));
1251   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaij_seqaijcusparse_C", NULL));
1252 #endif
1253 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
1254   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijkokkos_C", NULL));
1255 #endif
1256   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijcrl_C", NULL));
1257 #if defined(PETSC_HAVE_ELEMENTAL)
1258   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_elemental_C", NULL));
1259 #endif
1260 #if defined(PETSC_HAVE_SCALAPACK)
1261   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_scalapack_C", NULL));
1262 #endif
1263 #if defined(PETSC_HAVE_HYPRE)
1264   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_hypre_C", NULL));
1265   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_transpose_seqaij_seqaij_C", NULL));
1266 #endif
1267   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqdense_C", NULL));
1268   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqsell_C", NULL));
1269   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_is_C", NULL));
1270   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatIsTranspose_C", NULL));
1271   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatIsHermitianTranspose_C", NULL));
1272   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJSetPreallocation_C", NULL));
1273   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatResetPreallocation_C", NULL));
1274   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJSetPreallocationCSR_C", NULL));
1275   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatReorderForNonzeroDiagonal_C", NULL));
1276   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_is_seqaij_C", NULL));
1277   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqdense_seqaij_C", NULL));
1278   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaij_seqaij_C", NULL));
1279   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSeqAIJKron_C", NULL));
1280   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", NULL));
1281   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", NULL));
1282   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
1283   /* these calls do not belong here: the subclasses Duplicate/Destroy are wrong */
1284   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaijsell_seqaij_C", NULL));
1285   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaijperm_seqaij_C", NULL));
1286   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_seqaij_seqaijviennacl_C", NULL));
1287   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijviennacl_seqdense_C", NULL));
1288   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_seqaijviennacl_seqaij_C", NULL));
1289   PetscFunctionReturn(0);
1290 }
1291 
1292 PetscErrorCode MatSetOption_SeqAIJ(Mat A, MatOption op, PetscBool flg)
1293 {
1294   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1295 
1296   PetscFunctionBegin;
1297   switch (op) {
1298   case MAT_ROW_ORIENTED:
1299     a->roworiented = flg;
1300     break;
1301   case MAT_KEEP_NONZERO_PATTERN:
1302     a->keepnonzeropattern = flg;
1303     break;
1304   case MAT_NEW_NONZERO_LOCATIONS:
1305     a->nonew = (flg ? 0 : 1);
1306     break;
1307   case MAT_NEW_NONZERO_LOCATION_ERR:
1308     a->nonew = (flg ? -1 : 0);
1309     break;
1310   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1311     a->nonew = (flg ? -2 : 0);
1312     break;
1313   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1314     a->nounused = (flg ? -1 : 0);
1315     break;
1316   case MAT_IGNORE_ZERO_ENTRIES:
1317     a->ignorezeroentries = flg;
1318     break;
1319   case MAT_SPD:
1320   case MAT_SYMMETRIC:
1321   case MAT_STRUCTURALLY_SYMMETRIC:
1322   case MAT_HERMITIAN:
1323   case MAT_SYMMETRY_ETERNAL:
1324   case MAT_STRUCTURE_ONLY:
1325   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
1326   case MAT_SPD_ETERNAL:
1327     /* if the diagonal matrix is square it inherits some of the properties above */
1328     break;
1329   case MAT_FORCE_DIAGONAL_ENTRIES:
1330   case MAT_IGNORE_OFF_PROC_ENTRIES:
1331   case MAT_USE_HASH_TABLE:
1332     PetscCall(PetscInfo(A, "Option %s ignored\n", MatOptions[op]));
1333     break;
1334   case MAT_USE_INODES:
1335     PetscCall(MatSetOption_SeqAIJ_Inode(A, MAT_USE_INODES, flg));
1336     break;
1337   case MAT_SUBMAT_SINGLEIS:
1338     A->submat_singleis = flg;
1339     break;
1340   case MAT_SORTED_FULL:
1341     if (flg) A->ops->setvalues = MatSetValues_SeqAIJ_SortedFull;
1342     else A->ops->setvalues = MatSetValues_SeqAIJ;
1343     break;
1344   case MAT_FORM_EXPLICIT_TRANSPOSE:
1345     A->form_explicit_transpose = flg;
1346     break;
1347   default:
1348     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "unknown option %d", op);
1349   }
1350   PetscFunctionReturn(0);
1351 }
1352 
1353 PetscErrorCode MatGetDiagonal_SeqAIJ(Mat A, Vec v)
1354 {
1355   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1356   PetscInt           i, j, n, *ai = a->i, *aj = a->j;
1357   PetscScalar       *x;
1358   const PetscScalar *aa;
1359 
1360   PetscFunctionBegin;
1361   PetscCall(VecGetLocalSize(v, &n));
1362   PetscCheck(n == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
1363   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
1364   if (A->factortype == MAT_FACTOR_ILU || A->factortype == MAT_FACTOR_LU) {
1365     PetscInt *diag = a->diag;
1366     PetscCall(VecGetArrayWrite(v, &x));
1367     for (i = 0; i < n; i++) x[i] = 1.0 / aa[diag[i]];
1368     PetscCall(VecRestoreArrayWrite(v, &x));
1369     PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
1370     PetscFunctionReturn(0);
1371   }
1372 
1373   PetscCall(VecGetArrayWrite(v, &x));
1374   for (i = 0; i < n; i++) {
1375     x[i] = 0.0;
1376     for (j = ai[i]; j < ai[i + 1]; j++) {
1377       if (aj[j] == i) {
1378         x[i] = aa[j];
1379         break;
1380       }
1381     }
1382   }
1383   PetscCall(VecRestoreArrayWrite(v, &x));
1384   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
1385   PetscFunctionReturn(0);
1386 }
1387 
1388 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1389 PetscErrorCode MatMultTransposeAdd_SeqAIJ(Mat A, Vec xx, Vec zz, Vec yy)
1390 {
1391   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1392   const MatScalar   *aa;
1393   PetscScalar       *y;
1394   const PetscScalar *x;
1395   PetscInt           m = A->rmap->n;
1396 #if !defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1397   const MatScalar  *v;
1398   PetscScalar       alpha;
1399   PetscInt          n, i, j;
1400   const PetscInt   *idx, *ii, *ridx = NULL;
1401   Mat_CompressedRow cprow    = a->compressedrow;
1402   PetscBool         usecprow = cprow.use;
1403 #endif
1404 
1405   PetscFunctionBegin;
1406   if (zz != yy) PetscCall(VecCopy(zz, yy));
1407   PetscCall(VecGetArrayRead(xx, &x));
1408   PetscCall(VecGetArray(yy, &y));
1409   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
1410 
1411 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1412   fortranmulttransposeaddaij_(&m, x, a->i, a->j, aa, y);
1413 #else
1414   if (usecprow) {
1415     m = cprow.nrows;
1416     ii = cprow.i;
1417     ridx = cprow.rindex;
1418   } else {
1419     ii = a->i;
1420   }
1421   for (i = 0; i < m; i++) {
1422     idx = a->j + ii[i];
1423     v = aa + ii[i];
1424     n = ii[i + 1] - ii[i];
1425     if (usecprow) {
1426       alpha = x[ridx[i]];
1427     } else {
1428       alpha = x[i];
1429     }
1430     for (j = 0; j < n; j++) y[idx[j]] += alpha * v[j];
1431   }
1432 #endif
1433   PetscCall(PetscLogFlops(2.0 * a->nz));
1434   PetscCall(VecRestoreArrayRead(xx, &x));
1435   PetscCall(VecRestoreArray(yy, &y));
1436   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
1437   PetscFunctionReturn(0);
1438 }
1439 
1440 PetscErrorCode MatMultTranspose_SeqAIJ(Mat A, Vec xx, Vec yy)
1441 {
1442   PetscFunctionBegin;
1443   PetscCall(VecSet(yy, 0.0));
1444   PetscCall(MatMultTransposeAdd_SeqAIJ(A, xx, yy, yy));
1445   PetscFunctionReturn(0);
1446 }
1447 
1448 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1449 
1450 PetscErrorCode MatMult_SeqAIJ(Mat A, Vec xx, Vec yy)
1451 {
1452   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1453   PetscScalar       *y;
1454   const PetscScalar *x;
1455   const MatScalar   *aa, *a_a;
1456   PetscInt           m = A->rmap->n;
1457   const PetscInt    *aj, *ii, *ridx = NULL;
1458   PetscInt           n, i;
1459   PetscScalar        sum;
1460   PetscBool          usecprow = a->compressedrow.use;
1461 
1462 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1463   #pragma disjoint(*x, *y, *aa)
1464 #endif
1465 
1466   PetscFunctionBegin;
1467   if (a->inode.use && a->inode.checked) {
1468     PetscCall(MatMult_SeqAIJ_Inode(A, xx, yy));
1469     PetscFunctionReturn(0);
1470   }
1471   PetscCall(MatSeqAIJGetArrayRead(A, &a_a));
1472   PetscCall(VecGetArrayRead(xx, &x));
1473   PetscCall(VecGetArray(yy, &y));
1474   ii = a->i;
1475   if (usecprow) { /* use compressed row format */
1476     PetscCall(PetscArrayzero(y, m));
1477     m    = a->compressedrow.nrows;
1478     ii   = a->compressedrow.i;
1479     ridx = a->compressedrow.rindex;
1480     for (i = 0; i < m; i++) {
1481       n   = ii[i + 1] - ii[i];
1482       aj  = a->j + ii[i];
1483       aa  = a_a + ii[i];
1484       sum = 0.0;
1485       PetscSparseDensePlusDot(sum, x, aa, aj, n);
1486       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1487       y[*ridx++] = sum;
1488     }
1489   } else { /* do not use compressed row format */
1490 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJ)
1491     aj = a->j;
1492     aa = a_a;
1493     fortranmultaij_(&m, x, ii, aj, aa, y);
1494 #else
1495     for (i = 0; i < m; i++) {
1496       n = ii[i + 1] - ii[i];
1497       aj = a->j + ii[i];
1498       aa = a_a + ii[i];
1499       sum = 0.0;
1500       PetscSparseDensePlusDot(sum, x, aa, aj, n);
1501       y[i] = sum;
1502     }
1503 #endif
1504   }
1505   PetscCall(PetscLogFlops(2.0 * a->nz - a->nonzerorowcnt));
1506   PetscCall(VecRestoreArrayRead(xx, &x));
1507   PetscCall(VecRestoreArray(yy, &y));
1508   PetscCall(MatSeqAIJRestoreArrayRead(A, &a_a));
1509   PetscFunctionReturn(0);
1510 }
1511 
1512 PetscErrorCode MatMultMax_SeqAIJ(Mat A, Vec xx, Vec yy)
1513 {
1514   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1515   PetscScalar       *y;
1516   const PetscScalar *x;
1517   const MatScalar   *aa, *a_a;
1518   PetscInt           m = A->rmap->n;
1519   const PetscInt    *aj, *ii, *ridx   = NULL;
1520   PetscInt           n, i, nonzerorow = 0;
1521   PetscScalar        sum;
1522   PetscBool          usecprow = a->compressedrow.use;
1523 
1524 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1525   #pragma disjoint(*x, *y, *aa)
1526 #endif
1527 
1528   PetscFunctionBegin;
1529   PetscCall(MatSeqAIJGetArrayRead(A, &a_a));
1530   PetscCall(VecGetArrayRead(xx, &x));
1531   PetscCall(VecGetArray(yy, &y));
1532   if (usecprow) { /* use compressed row format */
1533     m    = a->compressedrow.nrows;
1534     ii   = a->compressedrow.i;
1535     ridx = a->compressedrow.rindex;
1536     for (i = 0; i < m; i++) {
1537       n   = ii[i + 1] - ii[i];
1538       aj  = a->j + ii[i];
1539       aa  = a_a + ii[i];
1540       sum = 0.0;
1541       nonzerorow += (n > 0);
1542       PetscSparseDenseMaxDot(sum, x, aa, aj, n);
1543       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1544       y[*ridx++] = sum;
1545     }
1546   } else { /* do not use compressed row format */
1547     ii = a->i;
1548     for (i = 0; i < m; i++) {
1549       n   = ii[i + 1] - ii[i];
1550       aj  = a->j + ii[i];
1551       aa  = a_a + ii[i];
1552       sum = 0.0;
1553       nonzerorow += (n > 0);
1554       PetscSparseDenseMaxDot(sum, x, aa, aj, n);
1555       y[i] = sum;
1556     }
1557   }
1558   PetscCall(PetscLogFlops(2.0 * a->nz - nonzerorow));
1559   PetscCall(VecRestoreArrayRead(xx, &x));
1560   PetscCall(VecRestoreArray(yy, &y));
1561   PetscCall(MatSeqAIJRestoreArrayRead(A, &a_a));
1562   PetscFunctionReturn(0);
1563 }
1564 
1565 PetscErrorCode MatMultAddMax_SeqAIJ(Mat A, Vec xx, Vec yy, Vec zz)
1566 {
1567   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1568   PetscScalar       *y, *z;
1569   const PetscScalar *x;
1570   const MatScalar   *aa, *a_a;
1571   PetscInt           m = A->rmap->n, *aj, *ii;
1572   PetscInt           n, i, *ridx = NULL;
1573   PetscScalar        sum;
1574   PetscBool          usecprow = a->compressedrow.use;
1575 
1576   PetscFunctionBegin;
1577   PetscCall(MatSeqAIJGetArrayRead(A, &a_a));
1578   PetscCall(VecGetArrayRead(xx, &x));
1579   PetscCall(VecGetArrayPair(yy, zz, &y, &z));
1580   if (usecprow) { /* use compressed row format */
1581     if (zz != yy) PetscCall(PetscArraycpy(z, y, m));
1582     m    = a->compressedrow.nrows;
1583     ii   = a->compressedrow.i;
1584     ridx = a->compressedrow.rindex;
1585     for (i = 0; i < m; i++) {
1586       n   = ii[i + 1] - ii[i];
1587       aj  = a->j + ii[i];
1588       aa  = a_a + ii[i];
1589       sum = y[*ridx];
1590       PetscSparseDenseMaxDot(sum, x, aa, aj, n);
1591       z[*ridx++] = sum;
1592     }
1593   } else { /* do not use compressed row format */
1594     ii = a->i;
1595     for (i = 0; i < m; i++) {
1596       n   = ii[i + 1] - ii[i];
1597       aj  = a->j + ii[i];
1598       aa  = a_a + ii[i];
1599       sum = y[i];
1600       PetscSparseDenseMaxDot(sum, x, aa, aj, n);
1601       z[i] = sum;
1602     }
1603   }
1604   PetscCall(PetscLogFlops(2.0 * a->nz));
1605   PetscCall(VecRestoreArrayRead(xx, &x));
1606   PetscCall(VecRestoreArrayPair(yy, zz, &y, &z));
1607   PetscCall(MatSeqAIJRestoreArrayRead(A, &a_a));
1608   PetscFunctionReturn(0);
1609 }
1610 
1611 #include <../src/mat/impls/aij/seq/ftn-kernels/fmultadd.h>
1612 PetscErrorCode MatMultAdd_SeqAIJ(Mat A, Vec xx, Vec yy, Vec zz)
1613 {
1614   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1615   PetscScalar       *y, *z;
1616   const PetscScalar *x;
1617   const MatScalar   *aa, *a_a;
1618   const PetscInt    *aj, *ii, *ridx = NULL;
1619   PetscInt           m = A->rmap->n, n, i;
1620   PetscScalar        sum;
1621   PetscBool          usecprow = a->compressedrow.use;
1622 
1623   PetscFunctionBegin;
1624   if (a->inode.use && a->inode.checked) {
1625     PetscCall(MatMultAdd_SeqAIJ_Inode(A, xx, yy, zz));
1626     PetscFunctionReturn(0);
1627   }
1628   PetscCall(MatSeqAIJGetArrayRead(A, &a_a));
1629   PetscCall(VecGetArrayRead(xx, &x));
1630   PetscCall(VecGetArrayPair(yy, zz, &y, &z));
1631   if (usecprow) { /* use compressed row format */
1632     if (zz != yy) PetscCall(PetscArraycpy(z, y, m));
1633     m    = a->compressedrow.nrows;
1634     ii   = a->compressedrow.i;
1635     ridx = a->compressedrow.rindex;
1636     for (i = 0; i < m; i++) {
1637       n   = ii[i + 1] - ii[i];
1638       aj  = a->j + ii[i];
1639       aa  = a_a + ii[i];
1640       sum = y[*ridx];
1641       PetscSparseDensePlusDot(sum, x, aa, aj, n);
1642       z[*ridx++] = sum;
1643     }
1644   } else { /* do not use compressed row format */
1645     ii = a->i;
1646 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJ)
1647     aj = a->j;
1648     aa = a_a;
1649     fortranmultaddaij_(&m, x, ii, aj, aa, y, z);
1650 #else
1651     for (i = 0; i < m; i++) {
1652       n = ii[i + 1] - ii[i];
1653       aj = a->j + ii[i];
1654       aa = a_a + ii[i];
1655       sum = y[i];
1656       PetscSparseDensePlusDot(sum, x, aa, aj, n);
1657       z[i] = sum;
1658     }
1659 #endif
1660   }
1661   PetscCall(PetscLogFlops(2.0 * a->nz));
1662   PetscCall(VecRestoreArrayRead(xx, &x));
1663   PetscCall(VecRestoreArrayPair(yy, zz, &y, &z));
1664   PetscCall(MatSeqAIJRestoreArrayRead(A, &a_a));
1665   PetscFunctionReturn(0);
1666 }
1667 
1668 /*
1669      Adds diagonal pointers to sparse matrix structure.
1670 */
1671 PetscErrorCode MatMarkDiagonal_SeqAIJ(Mat A)
1672 {
1673   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1674   PetscInt    i, j, m = A->rmap->n;
1675   PetscBool   alreadySet = PETSC_TRUE;
1676 
1677   PetscFunctionBegin;
1678   if (!a->diag) {
1679     PetscCall(PetscMalloc1(m, &a->diag));
1680     alreadySet = PETSC_FALSE;
1681   }
1682   for (i = 0; i < A->rmap->n; i++) {
1683     /* If A's diagonal is already correctly set, this fast track enables cheap and repeated MatMarkDiagonal_SeqAIJ() calls */
1684     if (alreadySet) {
1685       PetscInt pos = a->diag[i];
1686       if (pos >= a->i[i] && pos < a->i[i + 1] && a->j[pos] == i) continue;
1687     }
1688 
1689     a->diag[i] = a->i[i + 1];
1690     for (j = a->i[i]; j < a->i[i + 1]; j++) {
1691       if (a->j[j] == i) {
1692         a->diag[i] = j;
1693         break;
1694       }
1695     }
1696   }
1697   PetscFunctionReturn(0);
1698 }
1699 
1700 PetscErrorCode MatShift_SeqAIJ(Mat A, PetscScalar v)
1701 {
1702   Mat_SeqAIJ     *a    = (Mat_SeqAIJ *)A->data;
1703   const PetscInt *diag = (const PetscInt *)a->diag;
1704   const PetscInt *ii   = (const PetscInt *)a->i;
1705   PetscInt        i, *mdiag = NULL;
1706   PetscInt        cnt = 0; /* how many diagonals are missing */
1707 
1708   PetscFunctionBegin;
1709   if (!A->preallocated || !a->nz) {
1710     PetscCall(MatSeqAIJSetPreallocation(A, 1, NULL));
1711     PetscCall(MatShift_Basic(A, v));
1712     PetscFunctionReturn(0);
1713   }
1714 
1715   if (a->diagonaldense) {
1716     cnt = 0;
1717   } else {
1718     PetscCall(PetscCalloc1(A->rmap->n, &mdiag));
1719     for (i = 0; i < A->rmap->n; i++) {
1720       if (i < A->cmap->n && diag[i] >= ii[i + 1]) { /* 'out of range' rows never have diagonals */
1721         cnt++;
1722         mdiag[i] = 1;
1723       }
1724     }
1725   }
1726   if (!cnt) {
1727     PetscCall(MatShift_Basic(A, v));
1728   } else {
1729     PetscScalar *olda = a->a; /* preserve pointers to current matrix nonzeros structure and values */
1730     PetscInt    *oldj = a->j, *oldi = a->i;
1731     PetscBool    singlemalloc = a->singlemalloc, free_a = a->free_a, free_ij = a->free_ij;
1732 
1733     a->a = NULL;
1734     a->j = NULL;
1735     a->i = NULL;
1736     /* increase the values in imax for each row where a diagonal is being inserted then reallocate the matrix data structures */
1737     for (i = 0; i < PetscMin(A->rmap->n, A->cmap->n); i++) a->imax[i] += mdiag[i];
1738     PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(A, 0, a->imax));
1739 
1740     /* copy old values into new matrix data structure */
1741     for (i = 0; i < A->rmap->n; i++) {
1742       PetscCall(MatSetValues(A, 1, &i, a->imax[i] - mdiag[i], &oldj[oldi[i]], &olda[oldi[i]], ADD_VALUES));
1743       if (i < A->cmap->n) PetscCall(MatSetValue(A, i, i, v, ADD_VALUES));
1744     }
1745     PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
1746     PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
1747     if (singlemalloc) {
1748       PetscCall(PetscFree3(olda, oldj, oldi));
1749     } else {
1750       if (free_a) PetscCall(PetscFree(olda));
1751       if (free_ij) PetscCall(PetscFree(oldj));
1752       if (free_ij) PetscCall(PetscFree(oldi));
1753     }
1754   }
1755   PetscCall(PetscFree(mdiag));
1756   a->diagonaldense = PETSC_TRUE;
1757   PetscFunctionReturn(0);
1758 }
1759 
1760 /*
1761      Checks for missing diagonals
1762 */
1763 PetscErrorCode MatMissingDiagonal_SeqAIJ(Mat A, PetscBool *missing, PetscInt *d)
1764 {
1765   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
1766   PetscInt   *diag, *ii = a->i, i;
1767 
1768   PetscFunctionBegin;
1769   *missing = PETSC_FALSE;
1770   if (A->rmap->n > 0 && !ii) {
1771     *missing = PETSC_TRUE;
1772     if (d) *d = 0;
1773     PetscCall(PetscInfo(A, "Matrix has no entries therefore is missing diagonal\n"));
1774   } else {
1775     PetscInt n;
1776     n    = PetscMin(A->rmap->n, A->cmap->n);
1777     diag = a->diag;
1778     for (i = 0; i < n; i++) {
1779       if (diag[i] >= ii[i + 1]) {
1780         *missing = PETSC_TRUE;
1781         if (d) *d = i;
1782         PetscCall(PetscInfo(A, "Matrix is missing diagonal number %" PetscInt_FMT "\n", i));
1783         break;
1784       }
1785     }
1786   }
1787   PetscFunctionReturn(0);
1788 }
1789 
1790 #include <petscblaslapack.h>
1791 #include <petsc/private/kernels/blockinvert.h>
1792 
1793 /*
1794     Note that values is allocated externally by the PC and then passed into this routine
1795 */
1796 PetscErrorCode MatInvertVariableBlockDiagonal_SeqAIJ(Mat A, PetscInt nblocks, const PetscInt *bsizes, PetscScalar *diag)
1797 {
1798   PetscInt        n = A->rmap->n, i, ncnt = 0, *indx, j, bsizemax = 0, *v_pivots;
1799   PetscBool       allowzeropivot, zeropivotdetected = PETSC_FALSE;
1800   const PetscReal shift = 0.0;
1801   PetscInt        ipvt[5];
1802   PetscScalar     work[25], *v_work;
1803 
1804   PetscFunctionBegin;
1805   allowzeropivot = PetscNot(A->erroriffailure);
1806   for (i = 0; i < nblocks; i++) ncnt += bsizes[i];
1807   PetscCheck(ncnt == n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Total blocksizes %" PetscInt_FMT " doesn't match number matrix rows %" PetscInt_FMT, ncnt, n);
1808   for (i = 0; i < nblocks; i++) bsizemax = PetscMax(bsizemax, bsizes[i]);
1809   PetscCall(PetscMalloc1(bsizemax, &indx));
1810   if (bsizemax > 7) PetscCall(PetscMalloc2(bsizemax, &v_work, bsizemax, &v_pivots));
1811   ncnt = 0;
1812   for (i = 0; i < nblocks; i++) {
1813     for (j = 0; j < bsizes[i]; j++) indx[j] = ncnt + j;
1814     PetscCall(MatGetValues(A, bsizes[i], indx, bsizes[i], indx, diag));
1815     switch (bsizes[i]) {
1816     case 1:
1817       *diag = 1.0 / (*diag);
1818       break;
1819     case 2:
1820       PetscCall(PetscKernel_A_gets_inverse_A_2(diag, shift, allowzeropivot, &zeropivotdetected));
1821       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1822       PetscCall(PetscKernel_A_gets_transpose_A_2(diag));
1823       break;
1824     case 3:
1825       PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected));
1826       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1827       PetscCall(PetscKernel_A_gets_transpose_A_3(diag));
1828       break;
1829     case 4:
1830       PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected));
1831       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1832       PetscCall(PetscKernel_A_gets_transpose_A_4(diag));
1833       break;
1834     case 5:
1835       PetscCall(PetscKernel_A_gets_inverse_A_5(diag, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
1836       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1837       PetscCall(PetscKernel_A_gets_transpose_A_5(diag));
1838       break;
1839     case 6:
1840       PetscCall(PetscKernel_A_gets_inverse_A_6(diag, shift, allowzeropivot, &zeropivotdetected));
1841       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1842       PetscCall(PetscKernel_A_gets_transpose_A_6(diag));
1843       break;
1844     case 7:
1845       PetscCall(PetscKernel_A_gets_inverse_A_7(diag, shift, allowzeropivot, &zeropivotdetected));
1846       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1847       PetscCall(PetscKernel_A_gets_transpose_A_7(diag));
1848       break;
1849     default:
1850       PetscCall(PetscKernel_A_gets_inverse_A(bsizes[i], diag, v_pivots, v_work, allowzeropivot, &zeropivotdetected));
1851       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1852       PetscCall(PetscKernel_A_gets_transpose_A_N(diag, bsizes[i]));
1853     }
1854     ncnt += bsizes[i];
1855     diag += bsizes[i] * bsizes[i];
1856   }
1857   if (bsizemax > 7) PetscCall(PetscFree2(v_work, v_pivots));
1858   PetscCall(PetscFree(indx));
1859   PetscFunctionReturn(0);
1860 }
1861 
1862 /*
1863    Negative shift indicates do not generate an error if there is a zero diagonal, just invert it anyways
1864 */
1865 PetscErrorCode MatInvertDiagonal_SeqAIJ(Mat A, PetscScalar omega, PetscScalar fshift)
1866 {
1867   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
1868   PetscInt         i, *diag, m = A->rmap->n;
1869   const MatScalar *v;
1870   PetscScalar     *idiag, *mdiag;
1871 
1872   PetscFunctionBegin;
1873   if (a->idiagvalid) PetscFunctionReturn(0);
1874   PetscCall(MatMarkDiagonal_SeqAIJ(A));
1875   diag = a->diag;
1876   if (!a->idiag) { PetscCall(PetscMalloc3(m, &a->idiag, m, &a->mdiag, m, &a->ssor_work)); }
1877 
1878   mdiag = a->mdiag;
1879   idiag = a->idiag;
1880   PetscCall(MatSeqAIJGetArrayRead(A, &v));
1881   if (omega == 1.0 && PetscRealPart(fshift) <= 0.0) {
1882     for (i = 0; i < m; i++) {
1883       mdiag[i] = v[diag[i]];
1884       if (!PetscAbsScalar(mdiag[i])) { /* zero diagonal */
1885         if (PetscRealPart(fshift)) {
1886           PetscCall(PetscInfo(A, "Zero diagonal on row %" PetscInt_FMT "\n", i));
1887           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1888           A->factorerror_zeropivot_value = 0.0;
1889           A->factorerror_zeropivot_row   = i;
1890         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Zero diagonal on row %" PetscInt_FMT, i);
1891       }
1892       idiag[i] = 1.0 / v[diag[i]];
1893     }
1894     PetscCall(PetscLogFlops(m));
1895   } else {
1896     for (i = 0; i < m; i++) {
1897       mdiag[i] = v[diag[i]];
1898       idiag[i] = omega / (fshift + v[diag[i]]);
1899     }
1900     PetscCall(PetscLogFlops(2.0 * m));
1901   }
1902   a->idiagvalid = PETSC_TRUE;
1903   PetscCall(MatSeqAIJRestoreArrayRead(A, &v));
1904   PetscFunctionReturn(0);
1905 }
1906 
1907 #include <../src/mat/impls/aij/seq/ftn-kernels/frelax.h>
1908 PetscErrorCode MatSOR_SeqAIJ(Mat A, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
1909 {
1910   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1911   PetscScalar       *x, d, sum, *t, scale;
1912   const MatScalar   *v, *idiag = NULL, *mdiag, *aa;
1913   const PetscScalar *b, *bs, *xb, *ts;
1914   PetscInt           n, m = A->rmap->n, i;
1915   const PetscInt    *idx, *diag;
1916 
1917   PetscFunctionBegin;
1918   if (a->inode.use && a->inode.checked && omega == 1.0 && fshift == 0.0) {
1919     PetscCall(MatSOR_SeqAIJ_Inode(A, bb, omega, flag, fshift, its, lits, xx));
1920     PetscFunctionReturn(0);
1921   }
1922   its = its * lits;
1923 
1924   if (fshift != a->fshift || omega != a->omega) a->idiagvalid = PETSC_FALSE; /* must recompute idiag[] */
1925   if (!a->idiagvalid) PetscCall(MatInvertDiagonal_SeqAIJ(A, omega, fshift));
1926   a->fshift = fshift;
1927   a->omega  = omega;
1928 
1929   diag  = a->diag;
1930   t     = a->ssor_work;
1931   idiag = a->idiag;
1932   mdiag = a->mdiag;
1933 
1934   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
1935   PetscCall(VecGetArray(xx, &x));
1936   PetscCall(VecGetArrayRead(bb, &b));
1937   /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
1938   if (flag == SOR_APPLY_UPPER) {
1939     /* apply (U + D/omega) to the vector */
1940     bs = b;
1941     for (i = 0; i < m; i++) {
1942       d   = fshift + mdiag[i];
1943       n   = a->i[i + 1] - diag[i] - 1;
1944       idx = a->j + diag[i] + 1;
1945       v   = aa + diag[i] + 1;
1946       sum = b[i] * d / omega;
1947       PetscSparseDensePlusDot(sum, bs, v, idx, n);
1948       x[i] = sum;
1949     }
1950     PetscCall(VecRestoreArray(xx, &x));
1951     PetscCall(VecRestoreArrayRead(bb, &b));
1952     PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
1953     PetscCall(PetscLogFlops(a->nz));
1954     PetscFunctionReturn(0);
1955   }
1956 
1957   PetscCheck(flag != SOR_APPLY_LOWER, PETSC_COMM_SELF, PETSC_ERR_SUP, "SOR_APPLY_LOWER is not implemented");
1958   if (flag & SOR_EISENSTAT) {
1959     /* Let  A = L + U + D; where L is lower triangular,
1960     U is upper triangular, E = D/omega; This routine applies
1961 
1962             (L + E)^{-1} A (U + E)^{-1}
1963 
1964     to a vector efficiently using Eisenstat's trick.
1965     */
1966     scale = (2.0 / omega) - 1.0;
1967 
1968     /*  x = (E + U)^{-1} b */
1969     for (i = m - 1; i >= 0; i--) {
1970       n   = a->i[i + 1] - diag[i] - 1;
1971       idx = a->j + diag[i] + 1;
1972       v   = aa + diag[i] + 1;
1973       sum = b[i];
1974       PetscSparseDenseMinusDot(sum, x, v, idx, n);
1975       x[i] = sum * idiag[i];
1976     }
1977 
1978     /*  t = b - (2*E - D)x */
1979     v = aa;
1980     for (i = 0; i < m; i++) t[i] = b[i] - scale * (v[*diag++]) * x[i];
1981 
1982     /*  t = (E + L)^{-1}t */
1983     ts   = t;
1984     diag = a->diag;
1985     for (i = 0; i < m; i++) {
1986       n   = diag[i] - a->i[i];
1987       idx = a->j + a->i[i];
1988       v   = aa + a->i[i];
1989       sum = t[i];
1990       PetscSparseDenseMinusDot(sum, ts, v, idx, n);
1991       t[i] = sum * idiag[i];
1992       /*  x = x + t */
1993       x[i] += t[i];
1994     }
1995 
1996     PetscCall(PetscLogFlops(6.0 * m - 1 + 2.0 * a->nz));
1997     PetscCall(VecRestoreArray(xx, &x));
1998     PetscCall(VecRestoreArrayRead(bb, &b));
1999     PetscFunctionReturn(0);
2000   }
2001   if (flag & SOR_ZERO_INITIAL_GUESS) {
2002     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
2003       for (i = 0; i < m; i++) {
2004         n   = diag[i] - a->i[i];
2005         idx = a->j + a->i[i];
2006         v   = aa + a->i[i];
2007         sum = b[i];
2008         PetscSparseDenseMinusDot(sum, x, v, idx, n);
2009         t[i] = sum;
2010         x[i] = sum * idiag[i];
2011       }
2012       xb = t;
2013       PetscCall(PetscLogFlops(a->nz));
2014     } else xb = b;
2015     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
2016       for (i = m - 1; i >= 0; i--) {
2017         n   = a->i[i + 1] - diag[i] - 1;
2018         idx = a->j + diag[i] + 1;
2019         v   = aa + diag[i] + 1;
2020         sum = xb[i];
2021         PetscSparseDenseMinusDot(sum, x, v, idx, n);
2022         if (xb == b) {
2023           x[i] = sum * idiag[i];
2024         } else {
2025           x[i] = (1 - omega) * x[i] + sum * idiag[i]; /* omega in idiag */
2026         }
2027       }
2028       PetscCall(PetscLogFlops(a->nz)); /* assumes 1/2 in upper */
2029     }
2030     its--;
2031   }
2032   while (its--) {
2033     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
2034       for (i = 0; i < m; i++) {
2035         /* lower */
2036         n   = diag[i] - a->i[i];
2037         idx = a->j + a->i[i];
2038         v   = aa + a->i[i];
2039         sum = b[i];
2040         PetscSparseDenseMinusDot(sum, x, v, idx, n);
2041         t[i] = sum; /* save application of the lower-triangular part */
2042         /* upper */
2043         n   = a->i[i + 1] - diag[i] - 1;
2044         idx = a->j + diag[i] + 1;
2045         v   = aa + diag[i] + 1;
2046         PetscSparseDenseMinusDot(sum, x, v, idx, n);
2047         x[i] = (1. - omega) * x[i] + sum * idiag[i]; /* omega in idiag */
2048       }
2049       xb = t;
2050       PetscCall(PetscLogFlops(2.0 * a->nz));
2051     } else xb = b;
2052     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
2053       for (i = m - 1; i >= 0; i--) {
2054         sum = xb[i];
2055         if (xb == b) {
2056           /* whole matrix (no checkpointing available) */
2057           n   = a->i[i + 1] - a->i[i];
2058           idx = a->j + a->i[i];
2059           v   = aa + a->i[i];
2060           PetscSparseDenseMinusDot(sum, x, v, idx, n);
2061           x[i] = (1. - omega) * x[i] + (sum + mdiag[i] * x[i]) * idiag[i];
2062         } else { /* lower-triangular part has been saved, so only apply upper-triangular */
2063           n   = a->i[i + 1] - diag[i] - 1;
2064           idx = a->j + diag[i] + 1;
2065           v   = aa + diag[i] + 1;
2066           PetscSparseDenseMinusDot(sum, x, v, idx, n);
2067           x[i] = (1. - omega) * x[i] + sum * idiag[i]; /* omega in idiag */
2068         }
2069       }
2070       if (xb == b) {
2071         PetscCall(PetscLogFlops(2.0 * a->nz));
2072       } else {
2073         PetscCall(PetscLogFlops(a->nz)); /* assumes 1/2 in upper */
2074       }
2075     }
2076   }
2077   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
2078   PetscCall(VecRestoreArray(xx, &x));
2079   PetscCall(VecRestoreArrayRead(bb, &b));
2080   PetscFunctionReturn(0);
2081 }
2082 
2083 PetscErrorCode MatGetInfo_SeqAIJ(Mat A, MatInfoType flag, MatInfo *info)
2084 {
2085   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
2086 
2087   PetscFunctionBegin;
2088   info->block_size   = 1.0;
2089   info->nz_allocated = a->maxnz;
2090   info->nz_used      = a->nz;
2091   info->nz_unneeded  = (a->maxnz - a->nz);
2092   info->assemblies   = A->num_ass;
2093   info->mallocs      = A->info.mallocs;
2094   info->memory       = 0; /* REVIEW ME */
2095   if (A->factortype) {
2096     info->fill_ratio_given  = A->info.fill_ratio_given;
2097     info->fill_ratio_needed = A->info.fill_ratio_needed;
2098     info->factor_mallocs    = A->info.factor_mallocs;
2099   } else {
2100     info->fill_ratio_given  = 0;
2101     info->fill_ratio_needed = 0;
2102     info->factor_mallocs    = 0;
2103   }
2104   PetscFunctionReturn(0);
2105 }
2106 
2107 PetscErrorCode MatZeroRows_SeqAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
2108 {
2109   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
2110   PetscInt           i, m = A->rmap->n - 1;
2111   const PetscScalar *xx;
2112   PetscScalar       *bb, *aa;
2113   PetscInt           d = 0;
2114 
2115   PetscFunctionBegin;
2116   if (x && b) {
2117     PetscCall(VecGetArrayRead(x, &xx));
2118     PetscCall(VecGetArray(b, &bb));
2119     for (i = 0; i < N; i++) {
2120       PetscCheck(rows[i] >= 0 && rows[i] <= m, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "row %" PetscInt_FMT " out of range", rows[i]);
2121       if (rows[i] >= A->cmap->n) continue;
2122       bb[rows[i]] = diag * xx[rows[i]];
2123     }
2124     PetscCall(VecRestoreArrayRead(x, &xx));
2125     PetscCall(VecRestoreArray(b, &bb));
2126   }
2127 
2128   PetscCall(MatSeqAIJGetArray(A, &aa));
2129   if (a->keepnonzeropattern) {
2130     for (i = 0; i < N; i++) {
2131       PetscCheck(rows[i] >= 0 && rows[i] <= m, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "row %" PetscInt_FMT " out of range", rows[i]);
2132       PetscCall(PetscArrayzero(&aa[a->i[rows[i]]], a->ilen[rows[i]]));
2133     }
2134     if (diag != 0.0) {
2135       for (i = 0; i < N; i++) {
2136         d = rows[i];
2137         if (rows[i] >= A->cmap->n) continue;
2138         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);
2139       }
2140       for (i = 0; i < N; i++) {
2141         if (rows[i] >= A->cmap->n) continue;
2142         aa[a->diag[rows[i]]] = diag;
2143       }
2144     }
2145   } else {
2146     if (diag != 0.0) {
2147       for (i = 0; i < N; i++) {
2148         PetscCheck(rows[i] >= 0 && rows[i] <= m, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "row %" PetscInt_FMT " out of range", rows[i]);
2149         if (a->ilen[rows[i]] > 0) {
2150           if (rows[i] >= A->cmap->n) {
2151             a->ilen[rows[i]] = 0;
2152           } else {
2153             a->ilen[rows[i]]    = 1;
2154             aa[a->i[rows[i]]]   = diag;
2155             a->j[a->i[rows[i]]] = rows[i];
2156           }
2157         } else if (rows[i] < A->cmap->n) { /* in case row was completely empty */
2158           PetscCall(MatSetValues_SeqAIJ(A, 1, &rows[i], 1, &rows[i], &diag, INSERT_VALUES));
2159         }
2160       }
2161     } else {
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         a->ilen[rows[i]] = 0;
2165       }
2166     }
2167     A->nonzerostate++;
2168   }
2169   PetscCall(MatSeqAIJRestoreArray(A, &aa));
2170   PetscUseTypeMethod(A, assemblyend, MAT_FINAL_ASSEMBLY);
2171   PetscFunctionReturn(0);
2172 }
2173 
2174 PetscErrorCode MatZeroRowsColumns_SeqAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
2175 {
2176   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
2177   PetscInt           i, j, m = A->rmap->n - 1, d = 0;
2178   PetscBool          missing, *zeroed, vecs = PETSC_FALSE;
2179   const PetscScalar *xx;
2180   PetscScalar       *bb, *aa;
2181 
2182   PetscFunctionBegin;
2183   if (!N) PetscFunctionReturn(0);
2184   PetscCall(MatSeqAIJGetArray(A, &aa));
2185   if (x && b) {
2186     PetscCall(VecGetArrayRead(x, &xx));
2187     PetscCall(VecGetArray(b, &bb));
2188     vecs = PETSC_TRUE;
2189   }
2190   PetscCall(PetscCalloc1(A->rmap->n, &zeroed));
2191   for (i = 0; i < N; i++) {
2192     PetscCheck(rows[i] >= 0 && rows[i] <= m, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "row %" PetscInt_FMT " out of range", rows[i]);
2193     PetscCall(PetscArrayzero(&aa[a->i[rows[i]]], a->ilen[rows[i]]));
2194 
2195     zeroed[rows[i]] = PETSC_TRUE;
2196   }
2197   for (i = 0; i < A->rmap->n; i++) {
2198     if (!zeroed[i]) {
2199       for (j = a->i[i]; j < a->i[i + 1]; j++) {
2200         if (a->j[j] < A->rmap->n && zeroed[a->j[j]]) {
2201           if (vecs) bb[i] -= aa[j] * xx[a->j[j]];
2202           aa[j] = 0.0;
2203         }
2204       }
2205     } else if (vecs && i < A->cmap->N) bb[i] = diag * xx[i];
2206   }
2207   if (x && b) {
2208     PetscCall(VecRestoreArrayRead(x, &xx));
2209     PetscCall(VecRestoreArray(b, &bb));
2210   }
2211   PetscCall(PetscFree(zeroed));
2212   if (diag != 0.0) {
2213     PetscCall(MatMissingDiagonal_SeqAIJ(A, &missing, &d));
2214     if (missing) {
2215       for (i = 0; i < N; i++) {
2216         if (rows[i] >= A->cmap->N) continue;
2217         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]);
2218         PetscCall(MatSetValues_SeqAIJ(A, 1, &rows[i], 1, &rows[i], &diag, INSERT_VALUES));
2219       }
2220     } else {
2221       for (i = 0; i < N; i++) aa[a->diag[rows[i]]] = diag;
2222     }
2223   }
2224   PetscCall(MatSeqAIJRestoreArray(A, &aa));
2225   PetscUseTypeMethod(A, assemblyend, MAT_FINAL_ASSEMBLY);
2226   PetscFunctionReturn(0);
2227 }
2228 
2229 PetscErrorCode MatGetRow_SeqAIJ(Mat A, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
2230 {
2231   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
2232   const PetscScalar *aa;
2233   PetscInt          *itmp;
2234 
2235   PetscFunctionBegin;
2236   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
2237   *nz = a->i[row + 1] - a->i[row];
2238   if (v) *v = (PetscScalar *)(aa + a->i[row]);
2239   if (idx) {
2240     itmp = a->j + a->i[row];
2241     if (*nz) *idx = itmp;
2242     else *idx = NULL;
2243   }
2244   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
2245   PetscFunctionReturn(0);
2246 }
2247 
2248 PetscErrorCode MatRestoreRow_SeqAIJ(Mat A, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
2249 {
2250   PetscFunctionBegin;
2251   if (nz) *nz = 0;
2252   if (idx) *idx = NULL;
2253   if (v) *v = NULL;
2254   PetscFunctionReturn(0);
2255 }
2256 
2257 PetscErrorCode MatNorm_SeqAIJ(Mat A, NormType type, PetscReal *nrm)
2258 {
2259   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
2260   const MatScalar *v;
2261   PetscReal        sum = 0.0;
2262   PetscInt         i, j;
2263 
2264   PetscFunctionBegin;
2265   PetscCall(MatSeqAIJGetArrayRead(A, &v));
2266   if (type == NORM_FROBENIUS) {
2267 #if defined(PETSC_USE_REAL___FP16)
2268     PetscBLASInt one = 1, nz = a->nz;
2269     PetscCallBLAS("BLASnrm2", *nrm = BLASnrm2_(&nz, v, &one));
2270 #else
2271     for (i = 0; i < a->nz; i++) {
2272       sum += PetscRealPart(PetscConj(*v) * (*v));
2273       v++;
2274     }
2275     *nrm = PetscSqrtReal(sum);
2276 #endif
2277     PetscCall(PetscLogFlops(2.0 * a->nz));
2278   } else if (type == NORM_1) {
2279     PetscReal *tmp;
2280     PetscInt  *jj = a->j;
2281     PetscCall(PetscCalloc1(A->cmap->n + 1, &tmp));
2282     *nrm = 0.0;
2283     for (j = 0; j < a->nz; j++) {
2284       tmp[*jj++] += PetscAbsScalar(*v);
2285       v++;
2286     }
2287     for (j = 0; j < A->cmap->n; j++) {
2288       if (tmp[j] > *nrm) *nrm = tmp[j];
2289     }
2290     PetscCall(PetscFree(tmp));
2291     PetscCall(PetscLogFlops(PetscMax(a->nz - 1, 0)));
2292   } else if (type == NORM_INFINITY) {
2293     *nrm = 0.0;
2294     for (j = 0; j < A->rmap->n; j++) {
2295       const PetscScalar *v2 = v + a->i[j];
2296       sum                   = 0.0;
2297       for (i = 0; i < a->i[j + 1] - a->i[j]; i++) {
2298         sum += PetscAbsScalar(*v2);
2299         v2++;
2300       }
2301       if (sum > *nrm) *nrm = sum;
2302     }
2303     PetscCall(PetscLogFlops(PetscMax(a->nz - 1, 0)));
2304   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No support for two norm");
2305   PetscCall(MatSeqAIJRestoreArrayRead(A, &v));
2306   PetscFunctionReturn(0);
2307 }
2308 
2309 PetscErrorCode MatIsTranspose_SeqAIJ(Mat A, Mat B, PetscReal tol, PetscBool *f)
2310 {
2311   Mat_SeqAIJ      *aij = (Mat_SeqAIJ *)A->data, *bij = (Mat_SeqAIJ *)B->data;
2312   PetscInt        *adx, *bdx, *aii, *bii, *aptr, *bptr;
2313   const MatScalar *va, *vb;
2314   PetscInt         ma, na, mb, nb, i;
2315 
2316   PetscFunctionBegin;
2317   PetscCall(MatGetSize(A, &ma, &na));
2318   PetscCall(MatGetSize(B, &mb, &nb));
2319   if (ma != nb || na != mb) {
2320     *f = PETSC_FALSE;
2321     PetscFunctionReturn(0);
2322   }
2323   PetscCall(MatSeqAIJGetArrayRead(A, &va));
2324   PetscCall(MatSeqAIJGetArrayRead(B, &vb));
2325   aii = aij->i;
2326   bii = bij->i;
2327   adx = aij->j;
2328   bdx = bij->j;
2329   PetscCall(PetscMalloc1(ma, &aptr));
2330   PetscCall(PetscMalloc1(mb, &bptr));
2331   for (i = 0; i < ma; i++) aptr[i] = aii[i];
2332   for (i = 0; i < mb; i++) bptr[i] = bii[i];
2333 
2334   *f = PETSC_TRUE;
2335   for (i = 0; i < ma; i++) {
2336     while (aptr[i] < aii[i + 1]) {
2337       PetscInt    idc, idr;
2338       PetscScalar vc, vr;
2339       /* column/row index/value */
2340       idc = adx[aptr[i]];
2341       idr = bdx[bptr[idc]];
2342       vc  = va[aptr[i]];
2343       vr  = vb[bptr[idc]];
2344       if (i != idr || PetscAbsScalar(vc - vr) > tol) {
2345         *f = PETSC_FALSE;
2346         goto done;
2347       } else {
2348         aptr[i]++;
2349         if (B || i != idc) bptr[idc]++;
2350       }
2351     }
2352   }
2353 done:
2354   PetscCall(PetscFree(aptr));
2355   PetscCall(PetscFree(bptr));
2356   PetscCall(MatSeqAIJRestoreArrayRead(A, &va));
2357   PetscCall(MatSeqAIJRestoreArrayRead(B, &vb));
2358   PetscFunctionReturn(0);
2359 }
2360 
2361 PetscErrorCode MatIsHermitianTranspose_SeqAIJ(Mat A, Mat B, PetscReal tol, PetscBool *f)
2362 {
2363   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data, *bij = (Mat_SeqAIJ *)B->data;
2364   PetscInt   *adx, *bdx, *aii, *bii, *aptr, *bptr;
2365   MatScalar  *va, *vb;
2366   PetscInt    ma, na, mb, nb, i;
2367 
2368   PetscFunctionBegin;
2369   PetscCall(MatGetSize(A, &ma, &na));
2370   PetscCall(MatGetSize(B, &mb, &nb));
2371   if (ma != nb || na != mb) {
2372     *f = PETSC_FALSE;
2373     PetscFunctionReturn(0);
2374   }
2375   aii = aij->i;
2376   bii = bij->i;
2377   adx = aij->j;
2378   bdx = bij->j;
2379   va  = aij->a;
2380   vb  = bij->a;
2381   PetscCall(PetscMalloc1(ma, &aptr));
2382   PetscCall(PetscMalloc1(mb, &bptr));
2383   for (i = 0; i < ma; i++) aptr[i] = aii[i];
2384   for (i = 0; i < mb; i++) bptr[i] = bii[i];
2385 
2386   *f = PETSC_TRUE;
2387   for (i = 0; i < ma; i++) {
2388     while (aptr[i] < aii[i + 1]) {
2389       PetscInt    idc, idr;
2390       PetscScalar vc, vr;
2391       /* column/row index/value */
2392       idc = adx[aptr[i]];
2393       idr = bdx[bptr[idc]];
2394       vc  = va[aptr[i]];
2395       vr  = vb[bptr[idc]];
2396       if (i != idr || PetscAbsScalar(vc - PetscConj(vr)) > tol) {
2397         *f = PETSC_FALSE;
2398         goto done;
2399       } else {
2400         aptr[i]++;
2401         if (B || i != idc) bptr[idc]++;
2402       }
2403     }
2404   }
2405 done:
2406   PetscCall(PetscFree(aptr));
2407   PetscCall(PetscFree(bptr));
2408   PetscFunctionReturn(0);
2409 }
2410 
2411 PetscErrorCode MatIsSymmetric_SeqAIJ(Mat A, PetscReal tol, PetscBool *f)
2412 {
2413   PetscFunctionBegin;
2414   PetscCall(MatIsTranspose_SeqAIJ(A, A, tol, f));
2415   PetscFunctionReturn(0);
2416 }
2417 
2418 PetscErrorCode MatIsHermitian_SeqAIJ(Mat A, PetscReal tol, PetscBool *f)
2419 {
2420   PetscFunctionBegin;
2421   PetscCall(MatIsHermitianTranspose_SeqAIJ(A, A, tol, f));
2422   PetscFunctionReturn(0);
2423 }
2424 
2425 PetscErrorCode MatDiagonalScale_SeqAIJ(Mat A, Vec ll, Vec rr)
2426 {
2427   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
2428   const PetscScalar *l, *r;
2429   PetscScalar        x;
2430   MatScalar         *v;
2431   PetscInt           i, j, m = A->rmap->n, n = A->cmap->n, M, nz = a->nz;
2432   const PetscInt    *jj;
2433 
2434   PetscFunctionBegin;
2435   if (ll) {
2436     /* The local size is used so that VecMPI can be passed to this routine
2437        by MatDiagonalScale_MPIAIJ */
2438     PetscCall(VecGetLocalSize(ll, &m));
2439     PetscCheck(m == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Left scaling vector wrong length");
2440     PetscCall(VecGetArrayRead(ll, &l));
2441     PetscCall(MatSeqAIJGetArray(A, &v));
2442     for (i = 0; i < m; i++) {
2443       x = l[i];
2444       M = a->i[i + 1] - a->i[i];
2445       for (j = 0; j < M; j++) (*v++) *= x;
2446     }
2447     PetscCall(VecRestoreArrayRead(ll, &l));
2448     PetscCall(PetscLogFlops(nz));
2449     PetscCall(MatSeqAIJRestoreArray(A, &v));
2450   }
2451   if (rr) {
2452     PetscCall(VecGetLocalSize(rr, &n));
2453     PetscCheck(n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Right scaling vector wrong length");
2454     PetscCall(VecGetArrayRead(rr, &r));
2455     PetscCall(MatSeqAIJGetArray(A, &v));
2456     jj = a->j;
2457     for (i = 0; i < nz; i++) (*v++) *= r[*jj++];
2458     PetscCall(MatSeqAIJRestoreArray(A, &v));
2459     PetscCall(VecRestoreArrayRead(rr, &r));
2460     PetscCall(PetscLogFlops(nz));
2461   }
2462   PetscCall(MatSeqAIJInvalidateDiagonal(A));
2463   PetscFunctionReturn(0);
2464 }
2465 
2466 PetscErrorCode MatCreateSubMatrix_SeqAIJ(Mat A, IS isrow, IS iscol, PetscInt csize, MatReuse scall, Mat *B)
2467 {
2468   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *c;
2469   PetscInt          *smap, i, k, kstart, kend, oldcols = A->cmap->n, *lens;
2470   PetscInt           row, mat_i, *mat_j, tcol, first, step, *mat_ilen, sum, lensi;
2471   const PetscInt    *irow, *icol;
2472   const PetscScalar *aa;
2473   PetscInt           nrows, ncols;
2474   PetscInt          *starts, *j_new, *i_new, *aj = a->j, *ai = a->i, ii, *ailen = a->ilen;
2475   MatScalar         *a_new, *mat_a;
2476   Mat                C;
2477   PetscBool          stride;
2478 
2479   PetscFunctionBegin;
2480   PetscCall(ISGetIndices(isrow, &irow));
2481   PetscCall(ISGetLocalSize(isrow, &nrows));
2482   PetscCall(ISGetLocalSize(iscol, &ncols));
2483 
2484   PetscCall(PetscObjectTypeCompare((PetscObject)iscol, ISSTRIDE, &stride));
2485   if (stride) {
2486     PetscCall(ISStrideGetInfo(iscol, &first, &step));
2487   } else {
2488     first = 0;
2489     step  = 0;
2490   }
2491   if (stride && step == 1) {
2492     /* special case of contiguous rows */
2493     PetscCall(PetscMalloc2(nrows, &lens, nrows, &starts));
2494     /* loop over new rows determining lens and starting points */
2495     for (i = 0; i < nrows; i++) {
2496       kstart    = ai[irow[i]];
2497       kend      = kstart + ailen[irow[i]];
2498       starts[i] = kstart;
2499       for (k = kstart; k < kend; k++) {
2500         if (aj[k] >= first) {
2501           starts[i] = k;
2502           break;
2503         }
2504       }
2505       sum = 0;
2506       while (k < kend) {
2507         if (aj[k++] >= first + ncols) break;
2508         sum++;
2509       }
2510       lens[i] = sum;
2511     }
2512     /* create submatrix */
2513     if (scall == MAT_REUSE_MATRIX) {
2514       PetscInt n_cols, n_rows;
2515       PetscCall(MatGetSize(*B, &n_rows, &n_cols));
2516       PetscCheck(n_rows == nrows && n_cols == ncols, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Reused submatrix wrong size");
2517       PetscCall(MatZeroEntries(*B));
2518       C = *B;
2519     } else {
2520       PetscInt rbs, cbs;
2521       PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &C));
2522       PetscCall(MatSetSizes(C, nrows, ncols, PETSC_DETERMINE, PETSC_DETERMINE));
2523       PetscCall(ISGetBlockSize(isrow, &rbs));
2524       PetscCall(ISGetBlockSize(iscol, &cbs));
2525       PetscCall(MatSetBlockSizes(C, rbs, cbs));
2526       PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
2527       PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(C, 0, lens));
2528     }
2529     c = (Mat_SeqAIJ *)C->data;
2530 
2531     /* loop over rows inserting into submatrix */
2532     a_new = c->a;
2533     j_new = c->j;
2534     i_new = c->i;
2535     PetscCall(MatSeqAIJGetArrayRead(A, &aa));
2536     for (i = 0; i < nrows; i++) {
2537       ii    = starts[i];
2538       lensi = lens[i];
2539       for (k = 0; k < lensi; k++) *j_new++ = aj[ii + k] - first;
2540       PetscCall(PetscArraycpy(a_new, aa + starts[i], lensi));
2541       a_new += lensi;
2542       i_new[i + 1] = i_new[i] + lensi;
2543       c->ilen[i]   = lensi;
2544     }
2545     PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
2546     PetscCall(PetscFree2(lens, starts));
2547   } else {
2548     PetscCall(ISGetIndices(iscol, &icol));
2549     PetscCall(PetscCalloc1(oldcols, &smap));
2550     PetscCall(PetscMalloc1(1 + nrows, &lens));
2551     for (i = 0; i < ncols; i++) {
2552       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);
2553       smap[icol[i]] = i + 1;
2554     }
2555 
2556     /* determine lens of each row */
2557     for (i = 0; i < nrows; i++) {
2558       kstart  = ai[irow[i]];
2559       kend    = kstart + a->ilen[irow[i]];
2560       lens[i] = 0;
2561       for (k = kstart; k < kend; k++) {
2562         if (smap[aj[k]]) lens[i]++;
2563       }
2564     }
2565     /* Create and fill new matrix */
2566     if (scall == MAT_REUSE_MATRIX) {
2567       PetscBool equal;
2568 
2569       c = (Mat_SeqAIJ *)((*B)->data);
2570       PetscCheck((*B)->rmap->n == nrows && (*B)->cmap->n == ncols, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Cannot reuse matrix. wrong size");
2571       PetscCall(PetscArraycmp(c->ilen, lens, (*B)->rmap->n, &equal));
2572       PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Cannot reuse matrix. wrong no of nonzeros");
2573       PetscCall(PetscArrayzero(c->ilen, (*B)->rmap->n));
2574       C = *B;
2575     } else {
2576       PetscInt rbs, cbs;
2577       PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &C));
2578       PetscCall(MatSetSizes(C, nrows, ncols, PETSC_DETERMINE, PETSC_DETERMINE));
2579       PetscCall(ISGetBlockSize(isrow, &rbs));
2580       PetscCall(ISGetBlockSize(iscol, &cbs));
2581       PetscCall(MatSetBlockSizes(C, rbs, cbs));
2582       PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
2583       PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(C, 0, lens));
2584     }
2585     PetscCall(MatSeqAIJGetArrayRead(A, &aa));
2586     c = (Mat_SeqAIJ *)(C->data);
2587     for (i = 0; i < nrows; i++) {
2588       row      = irow[i];
2589       kstart   = ai[row];
2590       kend     = kstart + a->ilen[row];
2591       mat_i    = c->i[i];
2592       mat_j    = c->j + mat_i;
2593       mat_a    = c->a + mat_i;
2594       mat_ilen = c->ilen + i;
2595       for (k = kstart; k < kend; k++) {
2596         if ((tcol = smap[a->j[k]])) {
2597           *mat_j++ = tcol - 1;
2598           *mat_a++ = aa[k];
2599           (*mat_ilen)++;
2600         }
2601       }
2602     }
2603     PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
2604     /* Free work space */
2605     PetscCall(ISRestoreIndices(iscol, &icol));
2606     PetscCall(PetscFree(smap));
2607     PetscCall(PetscFree(lens));
2608     /* sort */
2609     for (i = 0; i < nrows; i++) {
2610       PetscInt ilen;
2611 
2612       mat_i = c->i[i];
2613       mat_j = c->j + mat_i;
2614       mat_a = c->a + mat_i;
2615       ilen  = c->ilen[i];
2616       PetscCall(PetscSortIntWithScalarArray(ilen, mat_j, mat_a));
2617     }
2618   }
2619 #if defined(PETSC_HAVE_DEVICE)
2620   PetscCall(MatBindToCPU(C, A->boundtocpu));
2621 #endif
2622   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2623   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2624 
2625   PetscCall(ISRestoreIndices(isrow, &irow));
2626   *B = C;
2627   PetscFunctionReturn(0);
2628 }
2629 
2630 PetscErrorCode MatGetMultiProcBlock_SeqAIJ(Mat mat, MPI_Comm subComm, MatReuse scall, Mat *subMat)
2631 {
2632   Mat B;
2633 
2634   PetscFunctionBegin;
2635   if (scall == MAT_INITIAL_MATRIX) {
2636     PetscCall(MatCreate(subComm, &B));
2637     PetscCall(MatSetSizes(B, mat->rmap->n, mat->cmap->n, mat->rmap->n, mat->cmap->n));
2638     PetscCall(MatSetBlockSizesFromMats(B, mat, mat));
2639     PetscCall(MatSetType(B, MATSEQAIJ));
2640     PetscCall(MatDuplicateNoCreate_SeqAIJ(B, mat, MAT_COPY_VALUES, PETSC_TRUE));
2641     *subMat = B;
2642   } else {
2643     PetscCall(MatCopy_SeqAIJ(mat, *subMat, SAME_NONZERO_PATTERN));
2644   }
2645   PetscFunctionReturn(0);
2646 }
2647 
2648 PetscErrorCode MatILUFactor_SeqAIJ(Mat inA, IS row, IS col, const MatFactorInfo *info)
2649 {
2650   Mat_SeqAIJ *a = (Mat_SeqAIJ *)inA->data;
2651   Mat         outA;
2652   PetscBool   row_identity, col_identity;
2653 
2654   PetscFunctionBegin;
2655   PetscCheck(info->levels == 0, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only levels=0 supported for in-place ilu");
2656 
2657   PetscCall(ISIdentity(row, &row_identity));
2658   PetscCall(ISIdentity(col, &col_identity));
2659 
2660   outA             = inA;
2661   outA->factortype = MAT_FACTOR_LU;
2662   PetscCall(PetscFree(inA->solvertype));
2663   PetscCall(PetscStrallocpy(MATSOLVERPETSC, &inA->solvertype));
2664 
2665   PetscCall(PetscObjectReference((PetscObject)row));
2666   PetscCall(ISDestroy(&a->row));
2667 
2668   a->row = row;
2669 
2670   PetscCall(PetscObjectReference((PetscObject)col));
2671   PetscCall(ISDestroy(&a->col));
2672 
2673   a->col = col;
2674 
2675   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
2676   PetscCall(ISDestroy(&a->icol));
2677   PetscCall(ISInvertPermutation(col, PETSC_DECIDE, &a->icol));
2678 
2679   if (!a->solve_work) { /* this matrix may have been factored before */
2680     PetscCall(PetscMalloc1(inA->rmap->n + 1, &a->solve_work));
2681   }
2682 
2683   PetscCall(MatMarkDiagonal_SeqAIJ(inA));
2684   if (row_identity && col_identity) {
2685     PetscCall(MatLUFactorNumeric_SeqAIJ_inplace(outA, inA, info));
2686   } else {
2687     PetscCall(MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA, inA, info));
2688   }
2689   PetscFunctionReturn(0);
2690 }
2691 
2692 PetscErrorCode MatScale_SeqAIJ(Mat inA, PetscScalar alpha)
2693 {
2694   Mat_SeqAIJ  *a = (Mat_SeqAIJ *)inA->data;
2695   PetscScalar *v;
2696   PetscBLASInt one = 1, bnz;
2697 
2698   PetscFunctionBegin;
2699   PetscCall(MatSeqAIJGetArray(inA, &v));
2700   PetscCall(PetscBLASIntCast(a->nz, &bnz));
2701   PetscCallBLAS("BLASscal", BLASscal_(&bnz, &alpha, v, &one));
2702   PetscCall(PetscLogFlops(a->nz));
2703   PetscCall(MatSeqAIJRestoreArray(inA, &v));
2704   PetscCall(MatSeqAIJInvalidateDiagonal(inA));
2705   PetscFunctionReturn(0);
2706 }
2707 
2708 PetscErrorCode MatDestroySubMatrix_Private(Mat_SubSppt *submatj)
2709 {
2710   PetscInt i;
2711 
2712   PetscFunctionBegin;
2713   if (!submatj->id) { /* delete data that are linked only to submats[id=0] */
2714     PetscCall(PetscFree4(submatj->sbuf1, submatj->ptr, submatj->tmp, submatj->ctr));
2715 
2716     for (i = 0; i < submatj->nrqr; ++i) PetscCall(PetscFree(submatj->sbuf2[i]));
2717     PetscCall(PetscFree3(submatj->sbuf2, submatj->req_size, submatj->req_source1));
2718 
2719     if (submatj->rbuf1) {
2720       PetscCall(PetscFree(submatj->rbuf1[0]));
2721       PetscCall(PetscFree(submatj->rbuf1));
2722     }
2723 
2724     for (i = 0; i < submatj->nrqs; ++i) PetscCall(PetscFree(submatj->rbuf3[i]));
2725     PetscCall(PetscFree3(submatj->req_source2, submatj->rbuf2, submatj->rbuf3));
2726     PetscCall(PetscFree(submatj->pa));
2727   }
2728 
2729 #if defined(PETSC_USE_CTABLE)
2730   PetscCall(PetscTableDestroy((PetscTable *)&submatj->rmap));
2731   if (submatj->cmap_loc) PetscCall(PetscFree(submatj->cmap_loc));
2732   PetscCall(PetscFree(submatj->rmap_loc));
2733 #else
2734   PetscCall(PetscFree(submatj->rmap));
2735 #endif
2736 
2737   if (!submatj->allcolumns) {
2738 #if defined(PETSC_USE_CTABLE)
2739     PetscCall(PetscTableDestroy((PetscTable *)&submatj->cmap));
2740 #else
2741     PetscCall(PetscFree(submatj->cmap));
2742 #endif
2743   }
2744   PetscCall(PetscFree(submatj->row2proc));
2745 
2746   PetscCall(PetscFree(submatj));
2747   PetscFunctionReturn(0);
2748 }
2749 
2750 PetscErrorCode MatDestroySubMatrix_SeqAIJ(Mat C)
2751 {
2752   Mat_SeqAIJ  *c       = (Mat_SeqAIJ *)C->data;
2753   Mat_SubSppt *submatj = c->submatis1;
2754 
2755   PetscFunctionBegin;
2756   PetscCall((*submatj->destroy)(C));
2757   PetscCall(MatDestroySubMatrix_Private(submatj));
2758   PetscFunctionReturn(0);
2759 }
2760 
2761 /* Note this has code duplication with MatDestroySubMatrices_SeqBAIJ() */
2762 PetscErrorCode MatDestroySubMatrices_SeqAIJ(PetscInt n, Mat *mat[])
2763 {
2764   PetscInt     i;
2765   Mat          C;
2766   Mat_SeqAIJ  *c;
2767   Mat_SubSppt *submatj;
2768 
2769   PetscFunctionBegin;
2770   for (i = 0; i < n; i++) {
2771     C       = (*mat)[i];
2772     c       = (Mat_SeqAIJ *)C->data;
2773     submatj = c->submatis1;
2774     if (submatj) {
2775       if (--((PetscObject)C)->refct <= 0) {
2776         PetscCall(PetscFree(C->factorprefix));
2777         PetscCall((*submatj->destroy)(C));
2778         PetscCall(MatDestroySubMatrix_Private(submatj));
2779         PetscCall(PetscFree(C->defaultvectype));
2780         PetscCall(PetscFree(C->defaultrandtype));
2781         PetscCall(PetscLayoutDestroy(&C->rmap));
2782         PetscCall(PetscLayoutDestroy(&C->cmap));
2783         PetscCall(PetscHeaderDestroy(&C));
2784       }
2785     } else {
2786       PetscCall(MatDestroy(&C));
2787     }
2788   }
2789 
2790   /* Destroy Dummy submatrices created for reuse */
2791   PetscCall(MatDestroySubMatrices_Dummy(n, mat));
2792 
2793   PetscCall(PetscFree(*mat));
2794   PetscFunctionReturn(0);
2795 }
2796 
2797 PetscErrorCode MatCreateSubMatrices_SeqAIJ(Mat A, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *B[])
2798 {
2799   PetscInt i;
2800 
2801   PetscFunctionBegin;
2802   if (scall == MAT_INITIAL_MATRIX) PetscCall(PetscCalloc1(n + 1, B));
2803 
2804   for (i = 0; i < n; i++) PetscCall(MatCreateSubMatrix_SeqAIJ(A, irow[i], icol[i], PETSC_DECIDE, scall, &(*B)[i]));
2805   PetscFunctionReturn(0);
2806 }
2807 
2808 PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A, PetscInt is_max, IS is[], PetscInt ov)
2809 {
2810   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
2811   PetscInt        row, i, j, k, l, m, n, *nidx, isz, val;
2812   const PetscInt *idx;
2813   PetscInt        start, end, *ai, *aj;
2814   PetscBT         table;
2815 
2816   PetscFunctionBegin;
2817   m  = A->rmap->n;
2818   ai = a->i;
2819   aj = a->j;
2820 
2821   PetscCheck(ov >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "illegal negative overlap value used");
2822 
2823   PetscCall(PetscMalloc1(m + 1, &nidx));
2824   PetscCall(PetscBTCreate(m, &table));
2825 
2826   for (i = 0; i < is_max; i++) {
2827     /* Initialize the two local arrays */
2828     isz = 0;
2829     PetscCall(PetscBTMemzero(m, table));
2830 
2831     /* Extract the indices, assume there can be duplicate entries */
2832     PetscCall(ISGetIndices(is[i], &idx));
2833     PetscCall(ISGetLocalSize(is[i], &n));
2834 
2835     /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2836     for (j = 0; j < n; ++j) {
2837       if (!PetscBTLookupSet(table, idx[j])) nidx[isz++] = idx[j];
2838     }
2839     PetscCall(ISRestoreIndices(is[i], &idx));
2840     PetscCall(ISDestroy(&is[i]));
2841 
2842     k = 0;
2843     for (j = 0; j < ov; j++) { /* for each overlap */
2844       n = isz;
2845       for (; k < n; k++) { /* do only those rows in nidx[k], which are not done yet */
2846         row   = nidx[k];
2847         start = ai[row];
2848         end   = ai[row + 1];
2849         for (l = start; l < end; l++) {
2850           val = aj[l];
2851           if (!PetscBTLookupSet(table, val)) nidx[isz++] = val;
2852         }
2853       }
2854     }
2855     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, isz, nidx, PETSC_COPY_VALUES, (is + i)));
2856   }
2857   PetscCall(PetscBTDestroy(&table));
2858   PetscCall(PetscFree(nidx));
2859   PetscFunctionReturn(0);
2860 }
2861 
2862 /* -------------------------------------------------------------- */
2863 PetscErrorCode MatPermute_SeqAIJ(Mat A, IS rowp, IS colp, Mat *B)
2864 {
2865   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
2866   PetscInt        i, nz = 0, m = A->rmap->n, n = A->cmap->n;
2867   const PetscInt *row, *col;
2868   PetscInt       *cnew, j, *lens;
2869   IS              icolp, irowp;
2870   PetscInt       *cwork = NULL;
2871   PetscScalar    *vwork = NULL;
2872 
2873   PetscFunctionBegin;
2874   PetscCall(ISInvertPermutation(rowp, PETSC_DECIDE, &irowp));
2875   PetscCall(ISGetIndices(irowp, &row));
2876   PetscCall(ISInvertPermutation(colp, PETSC_DECIDE, &icolp));
2877   PetscCall(ISGetIndices(icolp, &col));
2878 
2879   /* determine lengths of permuted rows */
2880   PetscCall(PetscMalloc1(m + 1, &lens));
2881   for (i = 0; i < m; i++) lens[row[i]] = a->i[i + 1] - a->i[i];
2882   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), B));
2883   PetscCall(MatSetSizes(*B, m, n, m, n));
2884   PetscCall(MatSetBlockSizesFromMats(*B, A, A));
2885   PetscCall(MatSetType(*B, ((PetscObject)A)->type_name));
2886   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*B, 0, lens));
2887   PetscCall(PetscFree(lens));
2888 
2889   PetscCall(PetscMalloc1(n, &cnew));
2890   for (i = 0; i < m; i++) {
2891     PetscCall(MatGetRow_SeqAIJ(A, i, &nz, &cwork, &vwork));
2892     for (j = 0; j < nz; j++) cnew[j] = col[cwork[j]];
2893     PetscCall(MatSetValues_SeqAIJ(*B, 1, &row[i], nz, cnew, vwork, INSERT_VALUES));
2894     PetscCall(MatRestoreRow_SeqAIJ(A, i, &nz, &cwork, &vwork));
2895   }
2896   PetscCall(PetscFree(cnew));
2897 
2898   (*B)->assembled = PETSC_FALSE;
2899 
2900 #if defined(PETSC_HAVE_DEVICE)
2901   PetscCall(MatBindToCPU(*B, A->boundtocpu));
2902 #endif
2903   PetscCall(MatAssemblyBegin(*B, MAT_FINAL_ASSEMBLY));
2904   PetscCall(MatAssemblyEnd(*B, MAT_FINAL_ASSEMBLY));
2905   PetscCall(ISRestoreIndices(irowp, &row));
2906   PetscCall(ISRestoreIndices(icolp, &col));
2907   PetscCall(ISDestroy(&irowp));
2908   PetscCall(ISDestroy(&icolp));
2909   if (rowp == colp) PetscCall(MatPropagateSymmetryOptions(A, *B));
2910   PetscFunctionReturn(0);
2911 }
2912 
2913 PetscErrorCode MatCopy_SeqAIJ(Mat A, Mat B, MatStructure str)
2914 {
2915   PetscFunctionBegin;
2916   /* If the two matrices have the same copy implementation, use fast copy. */
2917   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
2918     Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
2919     Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;
2920     const PetscScalar *aa;
2921 
2922     PetscCall(MatSeqAIJGetArrayRead(A, &aa));
2923     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]);
2924     PetscCall(PetscArraycpy(b->a, aa, a->i[A->rmap->n]));
2925     PetscCall(PetscObjectStateIncrease((PetscObject)B));
2926     PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
2927   } else {
2928     PetscCall(MatCopy_Basic(A, B, str));
2929   }
2930   PetscFunctionReturn(0);
2931 }
2932 
2933 PetscErrorCode MatSetUp_SeqAIJ(Mat A)
2934 {
2935   PetscFunctionBegin;
2936   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(A, PETSC_DEFAULT, NULL));
2937   PetscFunctionReturn(0);
2938 }
2939 
2940 PETSC_INTERN PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A, PetscScalar *array[])
2941 {
2942   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
2943 
2944   PetscFunctionBegin;
2945   *array = a->a;
2946   PetscFunctionReturn(0);
2947 }
2948 
2949 PETSC_INTERN PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A, PetscScalar *array[])
2950 {
2951   PetscFunctionBegin;
2952   *array = NULL;
2953   PetscFunctionReturn(0);
2954 }
2955 
2956 /*
2957    Computes the number of nonzeros per row needed for preallocation when X and Y
2958    have different nonzero structure.
2959 */
2960 PetscErrorCode MatAXPYGetPreallocation_SeqX_private(PetscInt m, const PetscInt *xi, const PetscInt *xj, const PetscInt *yi, const PetscInt *yj, PetscInt *nnz)
2961 {
2962   PetscInt i, j, k, nzx, nzy;
2963 
2964   PetscFunctionBegin;
2965   /* Set the number of nonzeros in the new matrix */
2966   for (i = 0; i < m; i++) {
2967     const PetscInt *xjj = xj + xi[i], *yjj = yj + yi[i];
2968     nzx    = xi[i + 1] - xi[i];
2969     nzy    = yi[i + 1] - yi[i];
2970     nnz[i] = 0;
2971     for (j = 0, k = 0; j < nzx; j++) {                  /* Point in X */
2972       for (; k < nzy && yjj[k] < xjj[j]; k++) nnz[i]++; /* Catch up to X */
2973       if (k < nzy && yjj[k] == xjj[j]) k++;             /* Skip duplicate */
2974       nnz[i]++;
2975     }
2976     for (; k < nzy; k++) nnz[i]++;
2977   }
2978   PetscFunctionReturn(0);
2979 }
2980 
2981 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y, Mat X, PetscInt *nnz)
2982 {
2983   PetscInt    m = Y->rmap->N;
2984   Mat_SeqAIJ *x = (Mat_SeqAIJ *)X->data;
2985   Mat_SeqAIJ *y = (Mat_SeqAIJ *)Y->data;
2986 
2987   PetscFunctionBegin;
2988   /* Set the number of nonzeros in the new matrix */
2989   PetscCall(MatAXPYGetPreallocation_SeqX_private(m, x->i, x->j, y->i, y->j, nnz));
2990   PetscFunctionReturn(0);
2991 }
2992 
2993 PetscErrorCode MatAXPY_SeqAIJ(Mat Y, PetscScalar a, Mat X, MatStructure str)
2994 {
2995   Mat_SeqAIJ *x = (Mat_SeqAIJ *)X->data, *y = (Mat_SeqAIJ *)Y->data;
2996 
2997   PetscFunctionBegin;
2998   if (str == UNKNOWN_NONZERO_PATTERN || (PetscDefined(USE_DEBUG) && str == SAME_NONZERO_PATTERN)) {
2999     PetscBool e = x->nz == y->nz ? PETSC_TRUE : PETSC_FALSE;
3000     if (e) {
3001       PetscCall(PetscArraycmp(x->i, y->i, Y->rmap->n + 1, &e));
3002       if (e) {
3003         PetscCall(PetscArraycmp(x->j, y->j, y->nz, &e));
3004         if (e) str = SAME_NONZERO_PATTERN;
3005       }
3006     }
3007     if (!e) PetscCheck(str != SAME_NONZERO_PATTERN, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatStructure is not SAME_NONZERO_PATTERN");
3008   }
3009   if (str == SAME_NONZERO_PATTERN) {
3010     const PetscScalar *xa;
3011     PetscScalar       *ya, alpha = a;
3012     PetscBLASInt       one = 1, bnz;
3013 
3014     PetscCall(PetscBLASIntCast(x->nz, &bnz));
3015     PetscCall(MatSeqAIJGetArray(Y, &ya));
3016     PetscCall(MatSeqAIJGetArrayRead(X, &xa));
3017     PetscCallBLAS("BLASaxpy", BLASaxpy_(&bnz, &alpha, xa, &one, ya, &one));
3018     PetscCall(MatSeqAIJRestoreArrayRead(X, &xa));
3019     PetscCall(MatSeqAIJRestoreArray(Y, &ya));
3020     PetscCall(PetscLogFlops(2.0 * bnz));
3021     PetscCall(MatSeqAIJInvalidateDiagonal(Y));
3022     PetscCall(PetscObjectStateIncrease((PetscObject)Y));
3023   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
3024     PetscCall(MatAXPY_Basic(Y, a, X, str));
3025   } else {
3026     Mat       B;
3027     PetscInt *nnz;
3028     PetscCall(PetscMalloc1(Y->rmap->N, &nnz));
3029     PetscCall(MatCreate(PetscObjectComm((PetscObject)Y), &B));
3030     PetscCall(PetscObjectSetName((PetscObject)B, ((PetscObject)Y)->name));
3031     PetscCall(MatSetLayouts(B, Y->rmap, Y->cmap));
3032     PetscCall(MatSetType(B, ((PetscObject)Y)->type_name));
3033     PetscCall(MatAXPYGetPreallocation_SeqAIJ(Y, X, nnz));
3034     PetscCall(MatSeqAIJSetPreallocation(B, 0, nnz));
3035     PetscCall(MatAXPY_BasicWithPreallocation(B, Y, a, X, str));
3036     PetscCall(MatHeaderMerge(Y, &B));
3037     PetscCall(MatSeqAIJCheckInode(Y));
3038     PetscCall(PetscFree(nnz));
3039   }
3040   PetscFunctionReturn(0);
3041 }
3042 
3043 PETSC_INTERN PetscErrorCode MatConjugate_SeqAIJ(Mat mat)
3044 {
3045 #if defined(PETSC_USE_COMPLEX)
3046   Mat_SeqAIJ  *aij = (Mat_SeqAIJ *)mat->data;
3047   PetscInt     i, nz;
3048   PetscScalar *a;
3049 
3050   PetscFunctionBegin;
3051   nz = aij->nz;
3052   PetscCall(MatSeqAIJGetArray(mat, &a));
3053   for (i = 0; i < nz; i++) a[i] = PetscConj(a[i]);
3054   PetscCall(MatSeqAIJRestoreArray(mat, &a));
3055 #else
3056   PetscFunctionBegin;
3057 #endif
3058   PetscFunctionReturn(0);
3059 }
3060 
3061 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A, Vec v, PetscInt idx[])
3062 {
3063   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
3064   PetscInt         i, j, m = A->rmap->n, *ai, *aj, ncols, n;
3065   PetscReal        atmp;
3066   PetscScalar     *x;
3067   const MatScalar *aa, *av;
3068 
3069   PetscFunctionBegin;
3070   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3071   PetscCall(MatSeqAIJGetArrayRead(A, &av));
3072   aa = av;
3073   ai = a->i;
3074   aj = a->j;
3075 
3076   PetscCall(VecSet(v, 0.0));
3077   PetscCall(VecGetArrayWrite(v, &x));
3078   PetscCall(VecGetLocalSize(v, &n));
3079   PetscCheck(n == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
3080   for (i = 0; i < m; i++) {
3081     ncols = ai[1] - ai[0];
3082     ai++;
3083     for (j = 0; j < ncols; j++) {
3084       atmp = PetscAbsScalar(*aa);
3085       if (PetscAbsScalar(x[i]) < atmp) {
3086         x[i] = atmp;
3087         if (idx) idx[i] = *aj;
3088       }
3089       aa++;
3090       aj++;
3091     }
3092   }
3093   PetscCall(VecRestoreArrayWrite(v, &x));
3094   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
3095   PetscFunctionReturn(0);
3096 }
3097 
3098 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A, Vec v, PetscInt idx[])
3099 {
3100   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
3101   PetscInt         i, j, m = A->rmap->n, *ai, *aj, ncols, n;
3102   PetscScalar     *x;
3103   const MatScalar *aa, *av;
3104 
3105   PetscFunctionBegin;
3106   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3107   PetscCall(MatSeqAIJGetArrayRead(A, &av));
3108   aa = av;
3109   ai = a->i;
3110   aj = a->j;
3111 
3112   PetscCall(VecSet(v, 0.0));
3113   PetscCall(VecGetArrayWrite(v, &x));
3114   PetscCall(VecGetLocalSize(v, &n));
3115   PetscCheck(n == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
3116   for (i = 0; i < m; i++) {
3117     ncols = ai[1] - ai[0];
3118     ai++;
3119     if (ncols == A->cmap->n) { /* row is dense */
3120       x[i] = *aa;
3121       if (idx) idx[i] = 0;
3122     } else { /* row is sparse so already KNOW maximum is 0.0 or higher */
3123       x[i] = 0.0;
3124       if (idx) {
3125         for (j = 0; j < ncols; j++) { /* find first implicit 0.0 in the row */
3126           if (aj[j] > j) {
3127             idx[i] = j;
3128             break;
3129           }
3130         }
3131         /* in case first implicit 0.0 in the row occurs at ncols-th column */
3132         if (j == ncols && j < A->cmap->n) idx[i] = j;
3133       }
3134     }
3135     for (j = 0; j < ncols; j++) {
3136       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {
3137         x[i] = *aa;
3138         if (idx) idx[i] = *aj;
3139       }
3140       aa++;
3141       aj++;
3142     }
3143   }
3144   PetscCall(VecRestoreArrayWrite(v, &x));
3145   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
3146   PetscFunctionReturn(0);
3147 }
3148 
3149 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A, Vec v, PetscInt idx[])
3150 {
3151   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
3152   PetscInt         i, j, m = A->rmap->n, *ai, *aj, ncols, n;
3153   PetscScalar     *x;
3154   const MatScalar *aa, *av;
3155 
3156   PetscFunctionBegin;
3157   PetscCall(MatSeqAIJGetArrayRead(A, &av));
3158   aa = av;
3159   ai = a->i;
3160   aj = a->j;
3161 
3162   PetscCall(VecSet(v, 0.0));
3163   PetscCall(VecGetArrayWrite(v, &x));
3164   PetscCall(VecGetLocalSize(v, &n));
3165   PetscCheck(n == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector, %" PetscInt_FMT " vs. %" PetscInt_FMT " rows", m, n);
3166   for (i = 0; i < m; i++) {
3167     ncols = ai[1] - ai[0];
3168     ai++;
3169     if (ncols == A->cmap->n) { /* row is dense */
3170       x[i] = *aa;
3171       if (idx) idx[i] = 0;
3172     } else { /* row is sparse so already KNOW minimum is 0.0 or higher */
3173       x[i] = 0.0;
3174       if (idx) { /* find first implicit 0.0 in the row */
3175         for (j = 0; j < ncols; j++) {
3176           if (aj[j] > j) {
3177             idx[i] = j;
3178             break;
3179           }
3180         }
3181         /* in case first implicit 0.0 in the row occurs at ncols-th column */
3182         if (j == ncols && j < A->cmap->n) idx[i] = j;
3183       }
3184     }
3185     for (j = 0; j < ncols; j++) {
3186       if (PetscAbsScalar(x[i]) > PetscAbsScalar(*aa)) {
3187         x[i] = *aa;
3188         if (idx) idx[i] = *aj;
3189       }
3190       aa++;
3191       aj++;
3192     }
3193   }
3194   PetscCall(VecRestoreArrayWrite(v, &x));
3195   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
3196   PetscFunctionReturn(0);
3197 }
3198 
3199 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A, Vec v, PetscInt idx[])
3200 {
3201   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
3202   PetscInt         i, j, m = A->rmap->n, ncols, n;
3203   const PetscInt  *ai, *aj;
3204   PetscScalar     *x;
3205   const MatScalar *aa, *av;
3206 
3207   PetscFunctionBegin;
3208   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3209   PetscCall(MatSeqAIJGetArrayRead(A, &av));
3210   aa = av;
3211   ai = a->i;
3212   aj = a->j;
3213 
3214   PetscCall(VecSet(v, 0.0));
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");
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 lower */
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 (PetscRealPart(x[i]) > PetscRealPart(*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(0);
3249 }
3250 
3251 PetscErrorCode MatInvertBlockDiagonal_SeqAIJ(Mat A, const PetscScalar **values)
3252 {
3253   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data;
3254   PetscInt        i, bs = PetscAbs(A->rmap->bs), mbs = A->rmap->n / bs, ipvt[5], bs2 = bs * bs, *v_pivots, ij[7], *IJ, j;
3255   MatScalar      *diag, work[25], *v_work;
3256   const PetscReal shift = 0.0;
3257   PetscBool       allowzeropivot, zeropivotdetected = PETSC_FALSE;
3258 
3259   PetscFunctionBegin;
3260   allowzeropivot = PetscNot(A->erroriffailure);
3261   if (a->ibdiagvalid) {
3262     if (values) *values = a->ibdiag;
3263     PetscFunctionReturn(0);
3264   }
3265   PetscCall(MatMarkDiagonal_SeqAIJ(A));
3266   if (!a->ibdiag) { PetscCall(PetscMalloc1(bs2 * mbs, &a->ibdiag)); }
3267   diag = a->ibdiag;
3268   if (values) *values = a->ibdiag;
3269   /* factor and invert each block */
3270   switch (bs) {
3271   case 1:
3272     for (i = 0; i < mbs; i++) {
3273       PetscCall(MatGetValues(A, 1, &i, 1, &i, diag + i));
3274       if (PetscAbsScalar(diag[i] + shift) < PETSC_MACHINE_EPSILON) {
3275         if (allowzeropivot) {
3276           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3277           A->factorerror_zeropivot_value = PetscAbsScalar(diag[i]);
3278           A->factorerror_zeropivot_row   = i;
3279           PetscCall(PetscInfo(A, "Zero pivot, row %" PetscInt_FMT " pivot %g tolerance %g\n", i, (double)PetscAbsScalar(diag[i]), (double)PETSC_MACHINE_EPSILON));
3280         } 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);
3281       }
3282       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3283     }
3284     break;
3285   case 2:
3286     for (i = 0; i < mbs; i++) {
3287       ij[0] = 2 * i;
3288       ij[1] = 2 * i + 1;
3289       PetscCall(MatGetValues(A, 2, ij, 2, ij, diag));
3290       PetscCall(PetscKernel_A_gets_inverse_A_2(diag, shift, allowzeropivot, &zeropivotdetected));
3291       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3292       PetscCall(PetscKernel_A_gets_transpose_A_2(diag));
3293       diag += 4;
3294     }
3295     break;
3296   case 3:
3297     for (i = 0; i < mbs; i++) {
3298       ij[0] = 3 * i;
3299       ij[1] = 3 * i + 1;
3300       ij[2] = 3 * i + 2;
3301       PetscCall(MatGetValues(A, 3, ij, 3, ij, diag));
3302       PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected));
3303       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3304       PetscCall(PetscKernel_A_gets_transpose_A_3(diag));
3305       diag += 9;
3306     }
3307     break;
3308   case 4:
3309     for (i = 0; i < mbs; i++) {
3310       ij[0] = 4 * i;
3311       ij[1] = 4 * i + 1;
3312       ij[2] = 4 * i + 2;
3313       ij[3] = 4 * i + 3;
3314       PetscCall(MatGetValues(A, 4, ij, 4, ij, diag));
3315       PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected));
3316       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3317       PetscCall(PetscKernel_A_gets_transpose_A_4(diag));
3318       diag += 16;
3319     }
3320     break;
3321   case 5:
3322     for (i = 0; i < mbs; i++) {
3323       ij[0] = 5 * i;
3324       ij[1] = 5 * i + 1;
3325       ij[2] = 5 * i + 2;
3326       ij[3] = 5 * i + 3;
3327       ij[4] = 5 * i + 4;
3328       PetscCall(MatGetValues(A, 5, ij, 5, ij, diag));
3329       PetscCall(PetscKernel_A_gets_inverse_A_5(diag, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
3330       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3331       PetscCall(PetscKernel_A_gets_transpose_A_5(diag));
3332       diag += 25;
3333     }
3334     break;
3335   case 6:
3336     for (i = 0; i < mbs; i++) {
3337       ij[0] = 6 * i;
3338       ij[1] = 6 * i + 1;
3339       ij[2] = 6 * i + 2;
3340       ij[3] = 6 * i + 3;
3341       ij[4] = 6 * i + 4;
3342       ij[5] = 6 * i + 5;
3343       PetscCall(MatGetValues(A, 6, ij, 6, ij, diag));
3344       PetscCall(PetscKernel_A_gets_inverse_A_6(diag, shift, allowzeropivot, &zeropivotdetected));
3345       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3346       PetscCall(PetscKernel_A_gets_transpose_A_6(diag));
3347       diag += 36;
3348     }
3349     break;
3350   case 7:
3351     for (i = 0; i < mbs; i++) {
3352       ij[0] = 7 * i;
3353       ij[1] = 7 * i + 1;
3354       ij[2] = 7 * i + 2;
3355       ij[3] = 7 * i + 3;
3356       ij[4] = 7 * i + 4;
3357       ij[5] = 7 * i + 5;
3358       ij[5] = 7 * i + 6;
3359       PetscCall(MatGetValues(A, 7, ij, 7, ij, diag));
3360       PetscCall(PetscKernel_A_gets_inverse_A_7(diag, shift, allowzeropivot, &zeropivotdetected));
3361       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3362       PetscCall(PetscKernel_A_gets_transpose_A_7(diag));
3363       diag += 49;
3364     }
3365     break;
3366   default:
3367     PetscCall(PetscMalloc3(bs, &v_work, bs, &v_pivots, bs, &IJ));
3368     for (i = 0; i < mbs; i++) {
3369       for (j = 0; j < bs; j++) IJ[j] = bs * i + j;
3370       PetscCall(MatGetValues(A, bs, IJ, bs, IJ, diag));
3371       PetscCall(PetscKernel_A_gets_inverse_A(bs, diag, v_pivots, v_work, allowzeropivot, &zeropivotdetected));
3372       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3373       PetscCall(PetscKernel_A_gets_transpose_A_N(diag, bs));
3374       diag += bs2;
3375     }
3376     PetscCall(PetscFree3(v_work, v_pivots, IJ));
3377   }
3378   a->ibdiagvalid = PETSC_TRUE;
3379   PetscFunctionReturn(0);
3380 }
3381 
3382 static PetscErrorCode MatSetRandom_SeqAIJ(Mat x, PetscRandom rctx)
3383 {
3384   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)x->data;
3385   PetscScalar a, *aa;
3386   PetscInt    m, n, i, j, col;
3387 
3388   PetscFunctionBegin;
3389   if (!x->assembled) {
3390     PetscCall(MatGetSize(x, &m, &n));
3391     for (i = 0; i < m; i++) {
3392       for (j = 0; j < aij->imax[i]; j++) {
3393         PetscCall(PetscRandomGetValue(rctx, &a));
3394         col = (PetscInt)(n * PetscRealPart(a));
3395         PetscCall(MatSetValues(x, 1, &i, 1, &col, &a, ADD_VALUES));
3396       }
3397     }
3398   } else {
3399     PetscCall(MatSeqAIJGetArrayWrite(x, &aa));
3400     for (i = 0; i < aij->nz; i++) PetscCall(PetscRandomGetValue(rctx, aa + i));
3401     PetscCall(MatSeqAIJRestoreArrayWrite(x, &aa));
3402   }
3403   PetscCall(MatAssemblyBegin(x, MAT_FINAL_ASSEMBLY));
3404   PetscCall(MatAssemblyEnd(x, MAT_FINAL_ASSEMBLY));
3405   PetscFunctionReturn(0);
3406 }
3407 
3408 /* Like MatSetRandom_SeqAIJ, but do not set values on columns in range of [low, high) */
3409 PetscErrorCode MatSetRandomSkipColumnRange_SeqAIJ_Private(Mat x, PetscInt low, PetscInt high, PetscRandom rctx)
3410 {
3411   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)x->data;
3412   PetscScalar a;
3413   PetscInt    m, n, i, j, col, nskip;
3414 
3415   PetscFunctionBegin;
3416   nskip = high - low;
3417   PetscCall(MatGetSize(x, &m, &n));
3418   n -= nskip; /* shrink number of columns where nonzeros can be set */
3419   for (i = 0; i < m; i++) {
3420     for (j = 0; j < aij->imax[i]; j++) {
3421       PetscCall(PetscRandomGetValue(rctx, &a));
3422       col = (PetscInt)(n * PetscRealPart(a));
3423       if (col >= low) col += nskip; /* shift col rightward to skip the hole */
3424       PetscCall(MatSetValues(x, 1, &i, 1, &col, &a, ADD_VALUES));
3425     }
3426   }
3427   PetscCall(MatAssemblyBegin(x, MAT_FINAL_ASSEMBLY));
3428   PetscCall(MatAssemblyEnd(x, MAT_FINAL_ASSEMBLY));
3429   PetscFunctionReturn(0);
3430 }
3431 
3432 /* -------------------------------------------------------------------*/
3433 static struct _MatOps MatOps_Values = {MatSetValues_SeqAIJ,
3434                                        MatGetRow_SeqAIJ,
3435                                        MatRestoreRow_SeqAIJ,
3436                                        MatMult_SeqAIJ,
3437                                        /*  4*/ MatMultAdd_SeqAIJ,
3438                                        MatMultTranspose_SeqAIJ,
3439                                        MatMultTransposeAdd_SeqAIJ,
3440                                        NULL,
3441                                        NULL,
3442                                        NULL,
3443                                        /* 10*/ NULL,
3444                                        MatLUFactor_SeqAIJ,
3445                                        NULL,
3446                                        MatSOR_SeqAIJ,
3447                                        MatTranspose_SeqAIJ,
3448                                        /*1 5*/ MatGetInfo_SeqAIJ,
3449                                        MatEqual_SeqAIJ,
3450                                        MatGetDiagonal_SeqAIJ,
3451                                        MatDiagonalScale_SeqAIJ,
3452                                        MatNorm_SeqAIJ,
3453                                        /* 20*/ NULL,
3454                                        MatAssemblyEnd_SeqAIJ,
3455                                        MatSetOption_SeqAIJ,
3456                                        MatZeroEntries_SeqAIJ,
3457                                        /* 24*/ MatZeroRows_SeqAIJ,
3458                                        NULL,
3459                                        NULL,
3460                                        NULL,
3461                                        NULL,
3462                                        /* 29*/ MatSetUp_SeqAIJ,
3463                                        NULL,
3464                                        NULL,
3465                                        NULL,
3466                                        NULL,
3467                                        /* 34*/ MatDuplicate_SeqAIJ,
3468                                        NULL,
3469                                        NULL,
3470                                        MatILUFactor_SeqAIJ,
3471                                        NULL,
3472                                        /* 39*/ MatAXPY_SeqAIJ,
3473                                        MatCreateSubMatrices_SeqAIJ,
3474                                        MatIncreaseOverlap_SeqAIJ,
3475                                        MatGetValues_SeqAIJ,
3476                                        MatCopy_SeqAIJ,
3477                                        /* 44*/ MatGetRowMax_SeqAIJ,
3478                                        MatScale_SeqAIJ,
3479                                        MatShift_SeqAIJ,
3480                                        MatDiagonalSet_SeqAIJ,
3481                                        MatZeroRowsColumns_SeqAIJ,
3482                                        /* 49*/ MatSetRandom_SeqAIJ,
3483                                        MatGetRowIJ_SeqAIJ,
3484                                        MatRestoreRowIJ_SeqAIJ,
3485                                        MatGetColumnIJ_SeqAIJ,
3486                                        MatRestoreColumnIJ_SeqAIJ,
3487                                        /* 54*/ MatFDColoringCreate_SeqXAIJ,
3488                                        NULL,
3489                                        NULL,
3490                                        MatPermute_SeqAIJ,
3491                                        NULL,
3492                                        /* 59*/ NULL,
3493                                        MatDestroy_SeqAIJ,
3494                                        MatView_SeqAIJ,
3495                                        NULL,
3496                                        NULL,
3497                                        /* 64*/ NULL,
3498                                        MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3499                                        NULL,
3500                                        NULL,
3501                                        NULL,
3502                                        /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3503                                        MatGetRowMinAbs_SeqAIJ,
3504                                        NULL,
3505                                        NULL,
3506                                        NULL,
3507                                        /* 74*/ NULL,
3508                                        MatFDColoringApply_AIJ,
3509                                        NULL,
3510                                        NULL,
3511                                        NULL,
3512                                        /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3513                                        NULL,
3514                                        NULL,
3515                                        NULL,
3516                                        MatLoad_SeqAIJ,
3517                                        /* 84*/ MatIsSymmetric_SeqAIJ,
3518                                        MatIsHermitian_SeqAIJ,
3519                                        NULL,
3520                                        NULL,
3521                                        NULL,
3522                                        /* 89*/ NULL,
3523                                        NULL,
3524                                        MatMatMultNumeric_SeqAIJ_SeqAIJ,
3525                                        NULL,
3526                                        NULL,
3527                                        /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy,
3528                                        NULL,
3529                                        NULL,
3530                                        MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3531                                        NULL,
3532                                        /* 99*/ MatProductSetFromOptions_SeqAIJ,
3533                                        NULL,
3534                                        NULL,
3535                                        MatConjugate_SeqAIJ,
3536                                        NULL,
3537                                        /*104*/ MatSetValuesRow_SeqAIJ,
3538                                        MatRealPart_SeqAIJ,
3539                                        MatImaginaryPart_SeqAIJ,
3540                                        NULL,
3541                                        NULL,
3542                                        /*109*/ MatMatSolve_SeqAIJ,
3543                                        NULL,
3544                                        MatGetRowMin_SeqAIJ,
3545                                        NULL,
3546                                        MatMissingDiagonal_SeqAIJ,
3547                                        /*114*/ NULL,
3548                                        NULL,
3549                                        NULL,
3550                                        NULL,
3551                                        NULL,
3552                                        /*119*/ NULL,
3553                                        NULL,
3554                                        NULL,
3555                                        NULL,
3556                                        MatGetMultiProcBlock_SeqAIJ,
3557                                        /*124*/ MatFindNonzeroRows_SeqAIJ,
3558                                        MatGetColumnReductions_SeqAIJ,
3559                                        MatInvertBlockDiagonal_SeqAIJ,
3560                                        MatInvertVariableBlockDiagonal_SeqAIJ,
3561                                        NULL,
3562                                        /*129*/ NULL,
3563                                        NULL,
3564                                        NULL,
3565                                        MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3566                                        MatTransposeColoringCreate_SeqAIJ,
3567                                        /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3568                                        MatTransColoringApplyDenToSp_SeqAIJ,
3569                                        NULL,
3570                                        NULL,
3571                                        MatRARtNumeric_SeqAIJ_SeqAIJ,
3572                                        /*139*/ NULL,
3573                                        NULL,
3574                                        NULL,
3575                                        MatFDColoringSetUp_SeqXAIJ,
3576                                        MatFindOffBlockDiagonalEntries_SeqAIJ,
3577                                        MatCreateMPIMatConcatenateSeqMat_SeqAIJ,
3578                                        /*145*/ MatDestroySubMatrices_SeqAIJ,
3579                                        NULL,
3580                                        NULL,
3581                                        MatCreateGraph_Simple_AIJ,
3582                                        NULL,
3583                                        /*150*/ MatTransposeSymbolic_SeqAIJ,
3584                                        MatEliminateZeros_SeqAIJ};
3585 
3586 PetscErrorCode MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat, PetscInt *indices)
3587 {
3588   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)mat->data;
3589   PetscInt    i, nz, n;
3590 
3591   PetscFunctionBegin;
3592   nz = aij->maxnz;
3593   n  = mat->rmap->n;
3594   for (i = 0; i < nz; i++) aij->j[i] = indices[i];
3595   aij->nz = nz;
3596   for (i = 0; i < n; i++) aij->ilen[i] = aij->imax[i];
3597   PetscFunctionReturn(0);
3598 }
3599 
3600 /*
3601  * Given a sparse matrix with global column indices, compact it by using a local column space.
3602  * The result matrix helps saving memory in other algorithms, such as MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable()
3603  */
3604 PetscErrorCode MatSeqAIJCompactOutExtraColumns_SeqAIJ(Mat mat, ISLocalToGlobalMapping *mapping)
3605 {
3606   Mat_SeqAIJ        *aij = (Mat_SeqAIJ *)mat->data;
3607   PetscTable         gid1_lid1;
3608   PetscTablePosition tpos;
3609   PetscInt           gid, lid, i, ec, nz = aij->nz;
3610   PetscInt          *garray, *jj = aij->j;
3611 
3612   PetscFunctionBegin;
3613   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
3614   PetscValidPointer(mapping, 2);
3615   /* use a table */
3616   PetscCall(PetscTableCreate(mat->rmap->n, mat->cmap->N + 1, &gid1_lid1));
3617   ec = 0;
3618   for (i = 0; i < nz; i++) {
3619     PetscInt data, gid1 = jj[i] + 1;
3620     PetscCall(PetscTableFind(gid1_lid1, gid1, &data));
3621     if (!data) {
3622       /* one based table */
3623       PetscCall(PetscTableAdd(gid1_lid1, gid1, ++ec, INSERT_VALUES));
3624     }
3625   }
3626   /* form array of columns we need */
3627   PetscCall(PetscMalloc1(ec, &garray));
3628   PetscCall(PetscTableGetHeadPosition(gid1_lid1, &tpos));
3629   while (tpos) {
3630     PetscCall(PetscTableGetNext(gid1_lid1, &tpos, &gid, &lid));
3631     gid--;
3632     lid--;
3633     garray[lid] = gid;
3634   }
3635   PetscCall(PetscSortInt(ec, garray)); /* sort, and rebuild */
3636   PetscCall(PetscTableRemoveAll(gid1_lid1));
3637   for (i = 0; i < ec; i++) PetscCall(PetscTableAdd(gid1_lid1, garray[i] + 1, i + 1, INSERT_VALUES));
3638   /* compact out the extra columns in B */
3639   for (i = 0; i < nz; i++) {
3640     PetscInt gid1 = jj[i] + 1;
3641     PetscCall(PetscTableFind(gid1_lid1, gid1, &lid));
3642     lid--;
3643     jj[i] = lid;
3644   }
3645   PetscCall(PetscLayoutDestroy(&mat->cmap));
3646   PetscCall(PetscTableDestroy(&gid1_lid1));
3647   PetscCall(PetscLayoutCreateFromSizes(PetscObjectComm((PetscObject)mat), ec, ec, 1, &mat->cmap));
3648   PetscCall(ISLocalToGlobalMappingCreate(PETSC_COMM_SELF, mat->cmap->bs, mat->cmap->n, garray, PETSC_OWN_POINTER, mapping));
3649   PetscCall(ISLocalToGlobalMappingSetType(*mapping, ISLOCALTOGLOBALMAPPINGHASH));
3650   PetscFunctionReturn(0);
3651 }
3652 
3653 /*@
3654     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3655        in the matrix.
3656 
3657   Input Parameters:
3658 +  mat - the `MATSEQAIJ` matrix
3659 -  indices - the column indices
3660 
3661   Level: advanced
3662 
3663   Notes:
3664     This can be called if you have precomputed the nonzero structure of the
3665   matrix and want to provide it to the matrix object to improve the performance
3666   of the `MatSetValues()` operation.
3667 
3668     You MUST have set the correct numbers of nonzeros per row in the call to
3669   `MatCreateSeqAIJ()`, and the columns indices MUST be sorted.
3670 
3671     MUST be called before any calls to `MatSetValues()`
3672 
3673     The indices should start with zero, not one.
3674 
3675 @*/
3676 PetscErrorCode MatSeqAIJSetColumnIndices(Mat mat, PetscInt *indices)
3677 {
3678   PetscFunctionBegin;
3679   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
3680   PetscValidIntPointer(indices, 2);
3681   PetscUseMethod(mat, "MatSeqAIJSetColumnIndices_C", (Mat, PetscInt *), (mat, indices));
3682   PetscFunctionReturn(0);
3683 }
3684 
3685 /* ----------------------------------------------------------------------------------------*/
3686 
3687 PetscErrorCode MatStoreValues_SeqAIJ(Mat mat)
3688 {
3689   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)mat->data;
3690   size_t      nz  = aij->i[mat->rmap->n];
3691 
3692   PetscFunctionBegin;
3693   PetscCheck(aij->nonew, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3694 
3695   /* allocate space for values if not already there */
3696   if (!aij->saved_values) { PetscCall(PetscMalloc1(nz + 1, &aij->saved_values)); }
3697 
3698   /* copy values over */
3699   PetscCall(PetscArraycpy(aij->saved_values, aij->a, nz));
3700   PetscFunctionReturn(0);
3701 }
3702 
3703 /*@
3704     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3705        example, reuse of the linear part of a Jacobian, while recomputing the
3706        nonlinear portion.
3707 
3708    Collect on mat
3709 
3710   Input Parameters:
3711 .  mat - the matrix (currently only `MATAIJ` matrices support this option)
3712 
3713   Level: advanced
3714 
3715   Common Usage, with `SNESSolve()`:
3716 $    Create Jacobian matrix
3717 $    Set linear terms into matrix
3718 $    Apply boundary conditions to matrix, at this time matrix must have
3719 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3720 $      boundary conditions again will not change the nonzero structure
3721 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3722 $    ierr = MatStoreValues(mat);
3723 $    Call SNESSetJacobian() with matrix
3724 $    In your Jacobian routine
3725 $      ierr = MatRetrieveValues(mat);
3726 $      Set nonlinear terms in matrix
3727 
3728   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3729 $    // build linear portion of Jacobian
3730 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3731 $    ierr = MatStoreValues(mat);
3732 $    loop over nonlinear iterations
3733 $       ierr = MatRetrieveValues(mat);
3734 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3735 $       // call MatAssemblyBegin/End() on matrix
3736 $       Solve linear system with Jacobian
3737 $    endloop
3738 
3739   Notes:
3740     Matrix must already be assemblied before calling this routine
3741     Must set the matrix option `MatSetOption`(mat,`MAT_NEW_NONZERO_LOCATIONS`,`PETSC_FALSE`); before
3742     calling this routine.
3743 
3744     When this is called multiple times it overwrites the previous set of stored values
3745     and does not allocated additional space.
3746 
3747 .seealso: `MatRetrieveValues()`
3748 @*/
3749 PetscErrorCode MatStoreValues(Mat mat)
3750 {
3751   PetscFunctionBegin;
3752   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
3753   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
3754   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3755   PetscUseMethod(mat, "MatStoreValues_C", (Mat), (mat));
3756   PetscFunctionReturn(0);
3757 }
3758 
3759 PetscErrorCode MatRetrieveValues_SeqAIJ(Mat mat)
3760 {
3761   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)mat->data;
3762   PetscInt    nz  = aij->i[mat->rmap->n];
3763 
3764   PetscFunctionBegin;
3765   PetscCheck(aij->nonew, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3766   PetscCheck(aij->saved_values, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Must call MatStoreValues(A);first");
3767   /* copy values over */
3768   PetscCall(PetscArraycpy(aij->a, aij->saved_values, nz));
3769   PetscFunctionReturn(0);
3770 }
3771 
3772 /*@
3773     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3774        example, reuse of the linear part of a Jacobian, while recomputing the
3775        nonlinear portion.
3776 
3777    Collect on mat
3778 
3779   Input Parameters:
3780 .  mat - the matrix (currently only `MATAIJ` matrices support this option)
3781 
3782   Level: advanced
3783 
3784 .seealso: `MatStoreValues()`
3785 @*/
3786 PetscErrorCode MatRetrieveValues(Mat mat)
3787 {
3788   PetscFunctionBegin;
3789   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
3790   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
3791   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3792   PetscUseMethod(mat, "MatRetrieveValues_C", (Mat), (mat));
3793   PetscFunctionReturn(0);
3794 }
3795 
3796 /* --------------------------------------------------------------------------------*/
3797 /*@C
3798    MatCreateSeqAIJ - Creates a sparse matrix in `MATSEQAIJ` (compressed row) format
3799    (the default parallel PETSc format).  For good matrix assembly performance
3800    the user should preallocate the matrix storage by setting the parameter nz
3801    (or the array nnz).  By setting these parameters accurately, performance
3802    during matrix assembly can be increased by more than a factor of 50.
3803 
3804    Collective
3805 
3806    Input Parameters:
3807 +  comm - MPI communicator, set to `PETSC_COMM_SELF`
3808 .  m - number of rows
3809 .  n - number of columns
3810 .  nz - number of nonzeros per row (same for all rows)
3811 -  nnz - array containing the number of nonzeros in the various rows
3812          (possibly different for each row) or NULL
3813 
3814    Output Parameter:
3815 .  A - the matrix
3816 
3817    It is recommended that one use the `MatCreate()`, `MatSetType()` and/or `MatSetFromOptions()`,
3818    MatXXXXSetPreallocation() paradigm instead of this routine directly.
3819    [MatXXXXSetPreallocation() is, for example, `MatSeqAIJSetPreallocation()`]
3820 
3821    Notes:
3822    If nnz is given then nz is ignored
3823 
3824    The AIJ format, also called
3825    compressed row storage, is fully compatible with standard Fortran 77
3826    storage.  That is, the stored row and column indices can begin at
3827    either one (as in Fortran) or zero.  See the users' manual for details.
3828 
3829    Specify the preallocated storage with either nz or nnz (not both).
3830    Set nz = `PETSC_DEFAULT` and nnz = NULL for PETSc to control dynamic memory
3831    allocation.  For large problems you MUST preallocate memory or you
3832    will get TERRIBLE performance, see the users' manual chapter on matrices.
3833 
3834    By default, this format uses inodes (identical nodes) when possible, to
3835    improve numerical efficiency of matrix-vector products and solves. We
3836    search for consecutive rows with the same nonzero structure, thereby
3837    reusing matrix information to achieve increased efficiency.
3838 
3839    Options Database Keys:
3840 +  -mat_no_inode  - Do not use inodes
3841 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3842 
3843    Level: intermediate
3844 
3845 .seealso: [Sparse Matrix Creation](sec_matsparse), `MatCreate()`, `MatCreateAIJ()`, `MatSetValues()`, `MatSeqAIJSetColumnIndices()`, `MatCreateSeqAIJWithArrays()`
3846 @*/
3847 PetscErrorCode MatCreateSeqAIJ(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt nz, const PetscInt nnz[], Mat *A)
3848 {
3849   PetscFunctionBegin;
3850   PetscCall(MatCreate(comm, A));
3851   PetscCall(MatSetSizes(*A, m, n, m, n));
3852   PetscCall(MatSetType(*A, MATSEQAIJ));
3853   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*A, nz, nnz));
3854   PetscFunctionReturn(0);
3855 }
3856 
3857 /*@C
3858    MatSeqAIJSetPreallocation - For good matrix assembly performance
3859    the user should preallocate the matrix storage by setting the parameter nz
3860    (or the array nnz).  By setting these parameters accurately, performance
3861    during matrix assembly can be increased by more than a factor of 50.
3862 
3863    Collective
3864 
3865    Input Parameters:
3866 +  B - The matrix
3867 .  nz - number of nonzeros per row (same for all rows)
3868 -  nnz - array containing the number of nonzeros in the various rows
3869          (possibly different for each row) or NULL
3870 
3871    Notes:
3872      If nnz is given then nz is ignored
3873 
3874     The `MATSEQAIJ` format also called
3875    compressed row storage, is fully compatible with standard Fortran 77
3876    storage.  That is, the stored row and column indices can begin at
3877    either one (as in Fortran) or zero.  See the users' manual for details.
3878 
3879    Specify the preallocated storage with either nz or nnz (not both).
3880    Set nz = `PETSC_DEFAULT` and nnz = NULL for PETSc to control dynamic memory
3881    allocation.  For large problems you MUST preallocate memory or you
3882    will get TERRIBLE performance, see the users' manual chapter on matrices.
3883 
3884    You can call `MatGetInfo()` to get information on how effective the preallocation was;
3885    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3886    You can also run with the option -info and look for messages with the string
3887    malloc in them to see if additional memory allocation was needed.
3888 
3889    Developer Notes:
3890    Use nz of `MAT_SKIP_ALLOCATION` to not allocate any space for the matrix
3891    entries or columns indices
3892 
3893    By default, this format uses inodes (identical nodes) when possible, to
3894    improve numerical efficiency of matrix-vector products and solves. We
3895    search for consecutive rows with the same nonzero structure, thereby
3896    reusing matrix information to achieve increased efficiency.
3897 
3898    Options Database Keys:
3899 +  -mat_no_inode  - Do not use inodes
3900 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3901 
3902    Level: intermediate
3903 
3904 .seealso: `MatCreate()`, `MatCreateAIJ()`, `MatSetValues()`, `MatSeqAIJSetColumnIndices()`, `MatCreateSeqAIJWithArrays()`, `MatGetInfo()`,
3905           `MatSeqAIJSetTotalPreallocation()`
3906 @*/
3907 PetscErrorCode MatSeqAIJSetPreallocation(Mat B, PetscInt nz, const PetscInt nnz[])
3908 {
3909   PetscFunctionBegin;
3910   PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
3911   PetscValidType(B, 1);
3912   PetscTryMethod(B, "MatSeqAIJSetPreallocation_C", (Mat, PetscInt, const PetscInt[]), (B, nz, nnz));
3913   PetscFunctionReturn(0);
3914 }
3915 
3916 PetscErrorCode MatSeqAIJSetPreallocation_SeqAIJ(Mat B, PetscInt nz, const PetscInt *nnz)
3917 {
3918   Mat_SeqAIJ *b;
3919   PetscBool   skipallocation = PETSC_FALSE, realalloc = PETSC_FALSE;
3920   PetscInt    i;
3921 
3922   PetscFunctionBegin;
3923   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3924   if (nz == MAT_SKIP_ALLOCATION) {
3925     skipallocation = PETSC_TRUE;
3926     nz             = 0;
3927   }
3928   PetscCall(PetscLayoutSetUp(B->rmap));
3929   PetscCall(PetscLayoutSetUp(B->cmap));
3930 
3931   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3932   PetscCheck(nz >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "nz cannot be less than 0: value %" PetscInt_FMT, nz);
3933   if (PetscUnlikelyDebug(nnz)) {
3934     for (i = 0; i < B->rmap->n; i++) {
3935       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]);
3936       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);
3937     }
3938   }
3939 
3940   B->preallocated = PETSC_TRUE;
3941 
3942   b = (Mat_SeqAIJ *)B->data;
3943 
3944   if (!skipallocation) {
3945     if (!b->imax) { PetscCall(PetscMalloc1(B->rmap->n, &b->imax)); }
3946     if (!b->ilen) {
3947       /* b->ilen will count nonzeros in each row so far. */
3948       PetscCall(PetscCalloc1(B->rmap->n, &b->ilen));
3949     } else {
3950       PetscCall(PetscMemzero(b->ilen, B->rmap->n * sizeof(PetscInt)));
3951     }
3952     if (!b->ipre) { PetscCall(PetscMalloc1(B->rmap->n, &b->ipre)); }
3953     if (!nnz) {
3954       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3955       else if (nz < 0) nz = 1;
3956       nz = PetscMin(nz, B->cmap->n);
3957       for (i = 0; i < B->rmap->n; i++) b->imax[i] = nz;
3958       nz = nz * B->rmap->n;
3959     } else {
3960       PetscInt64 nz64 = 0;
3961       for (i = 0; i < B->rmap->n; i++) {
3962         b->imax[i] = nnz[i];
3963         nz64 += nnz[i];
3964       }
3965       PetscCall(PetscIntCast(nz64, &nz));
3966     }
3967 
3968     /* allocate the matrix space */
3969     /* FIXME: should B's old memory be unlogged? */
3970     PetscCall(MatSeqXAIJFreeAIJ(B, &b->a, &b->j, &b->i));
3971     if (B->structure_only) {
3972       PetscCall(PetscMalloc1(nz, &b->j));
3973       PetscCall(PetscMalloc1(B->rmap->n + 1, &b->i));
3974     } else {
3975       PetscCall(PetscMalloc3(nz, &b->a, nz, &b->j, B->rmap->n + 1, &b->i));
3976     }
3977     b->i[0] = 0;
3978     for (i = 1; i < B->rmap->n + 1; i++) b->i[i] = b->i[i - 1] + b->imax[i - 1];
3979     if (B->structure_only) {
3980       b->singlemalloc = PETSC_FALSE;
3981       b->free_a       = PETSC_FALSE;
3982     } else {
3983       b->singlemalloc = PETSC_TRUE;
3984       b->free_a       = PETSC_TRUE;
3985     }
3986     b->free_ij = PETSC_TRUE;
3987   } else {
3988     b->free_a  = PETSC_FALSE;
3989     b->free_ij = PETSC_FALSE;
3990   }
3991 
3992   if (b->ipre && nnz != b->ipre && b->imax) {
3993     /* reserve user-requested sparsity */
3994     PetscCall(PetscArraycpy(b->ipre, b->imax, B->rmap->n));
3995   }
3996 
3997   b->nz               = 0;
3998   b->maxnz            = nz;
3999   B->info.nz_unneeded = (double)b->maxnz;
4000   if (realalloc) PetscCall(MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE));
4001   B->was_assembled = PETSC_FALSE;
4002   B->assembled     = PETSC_FALSE;
4003   /* We simply deem preallocation has changed nonzero state. Updating the state
4004      will give clients (like AIJKokkos) a chance to know something has happened.
4005   */
4006   B->nonzerostate++;
4007   PetscFunctionReturn(0);
4008 }
4009 
4010 PetscErrorCode MatResetPreallocation_SeqAIJ(Mat A)
4011 {
4012   Mat_SeqAIJ *a;
4013   PetscInt    i;
4014 
4015   PetscFunctionBegin;
4016   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4017 
4018   /* Check local size. If zero, then return */
4019   if (!A->rmap->n) PetscFunctionReturn(0);
4020 
4021   a = (Mat_SeqAIJ *)A->data;
4022   /* if no saved info, we error out */
4023   PetscCheck(a->ipre, PETSC_COMM_SELF, PETSC_ERR_ARG_NULL, "No saved preallocation info ");
4024 
4025   PetscCheck(a->i && a->j && a->a && a->imax && a->ilen, PETSC_COMM_SELF, PETSC_ERR_ARG_NULL, "Memory info is incomplete, and can not reset preallocation ");
4026 
4027   PetscCall(PetscArraycpy(a->imax, a->ipre, A->rmap->n));
4028   PetscCall(PetscArrayzero(a->ilen, A->rmap->n));
4029   a->i[0] = 0;
4030   for (i = 1; i < A->rmap->n + 1; i++) a->i[i] = a->i[i - 1] + a->imax[i - 1];
4031   A->preallocated     = PETSC_TRUE;
4032   a->nz               = 0;
4033   a->maxnz            = a->i[A->rmap->n];
4034   A->info.nz_unneeded = (double)a->maxnz;
4035   A->was_assembled    = PETSC_FALSE;
4036   A->assembled        = PETSC_FALSE;
4037   PetscFunctionReturn(0);
4038 }
4039 
4040 /*@
4041    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in `MATSEQAIJ` format.
4042 
4043    Input Parameters:
4044 +  B - the matrix
4045 .  i - the indices into j for the start of each row (starts with zero)
4046 .  j - the column indices for each row (starts with zero) these must be sorted for each row
4047 -  v - optional values in the matrix
4048 
4049    Level: developer
4050 
4051    Notes:
4052       The i,j,v values are COPIED with this routine; to avoid the copy use `MatCreateSeqAIJWithArrays()`
4053 
4054       This routine may be called multiple times with different nonzero patterns (or the same nonzero pattern). The nonzero
4055       structure will be the union of all the previous nonzero structures.
4056 
4057     Developer Notes:
4058       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
4059       then just copies the v values directly with `PetscMemcpy()`.
4060 
4061       This routine could also take a `PetscCopyMode` argument to allow sharing the values instead of always copying them.
4062 
4063 .seealso: `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatSeqAIJSetPreallocation()`, `MatCreateSeqAIJ()`, `MATSEQAIJ`, `MatResetPreallocation()`
4064 @*/
4065 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B, const PetscInt i[], const PetscInt j[], const PetscScalar v[])
4066 {
4067   PetscFunctionBegin;
4068   PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
4069   PetscValidType(B, 1);
4070   PetscTryMethod(B, "MatSeqAIJSetPreallocationCSR_C", (Mat, const PetscInt[], const PetscInt[], const PetscScalar[]), (B, i, j, v));
4071   PetscFunctionReturn(0);
4072 }
4073 
4074 PetscErrorCode MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B, const PetscInt Ii[], const PetscInt J[], const PetscScalar v[])
4075 {
4076   PetscInt  i;
4077   PetscInt  m, n;
4078   PetscInt  nz;
4079   PetscInt *nnz;
4080 
4081   PetscFunctionBegin;
4082   PetscCheck(Ii[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %" PetscInt_FMT, Ii[0]);
4083 
4084   PetscCall(PetscLayoutSetUp(B->rmap));
4085   PetscCall(PetscLayoutSetUp(B->cmap));
4086 
4087   PetscCall(MatGetSize(B, &m, &n));
4088   PetscCall(PetscMalloc1(m + 1, &nnz));
4089   for (i = 0; i < m; i++) {
4090     nz = Ii[i + 1] - Ii[i];
4091     PetscCheck(nz >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local row %" PetscInt_FMT " has a negative number of columns %" PetscInt_FMT, i, nz);
4092     nnz[i] = nz;
4093   }
4094   PetscCall(MatSeqAIJSetPreallocation(B, 0, nnz));
4095   PetscCall(PetscFree(nnz));
4096 
4097   for (i = 0; i < m; i++) PetscCall(MatSetValues_SeqAIJ(B, 1, &i, Ii[i + 1] - Ii[i], J + Ii[i], v ? v + Ii[i] : NULL, INSERT_VALUES));
4098 
4099   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
4100   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
4101 
4102   PetscCall(MatSetOption(B, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
4103   PetscFunctionReturn(0);
4104 }
4105 
4106 /*@
4107    MatSeqAIJKron - Computes C, the Kronecker product of A and B.
4108 
4109    Input Parameters:
4110 +  A - left-hand side matrix
4111 .  B - right-hand side matrix
4112 -  reuse - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
4113 
4114    Output Parameter:
4115 .  C - Kronecker product of A and B
4116 
4117    Level: intermediate
4118 
4119    Note:
4120       `MAT_REUSE_MATRIX` can only be used when the nonzero structure of the product matrix has not changed from that last call to `MatSeqAIJKron()`.
4121 
4122 .seealso: `MatCreateSeqAIJ()`, `MATSEQAIJ`, `MATKAIJ`, `MatReuse`
4123 @*/
4124 PetscErrorCode MatSeqAIJKron(Mat A, Mat B, MatReuse reuse, Mat *C)
4125 {
4126   PetscFunctionBegin;
4127   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4128   PetscValidType(A, 1);
4129   PetscValidHeaderSpecific(B, MAT_CLASSID, 2);
4130   PetscValidType(B, 2);
4131   PetscValidPointer(C, 4);
4132   if (reuse == MAT_REUSE_MATRIX) {
4133     PetscValidHeaderSpecific(*C, MAT_CLASSID, 4);
4134     PetscValidType(*C, 4);
4135   }
4136   PetscTryMethod(A, "MatSeqAIJKron_C", (Mat, Mat, MatReuse, Mat *), (A, B, reuse, C));
4137   PetscFunctionReturn(0);
4138 }
4139 
4140 PetscErrorCode MatSeqAIJKron_SeqAIJ(Mat A, Mat B, MatReuse reuse, Mat *C)
4141 {
4142   Mat                newmat;
4143   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
4144   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;
4145   PetscScalar       *v;
4146   const PetscScalar *aa, *ba;
4147   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;
4148   PetscBool          flg;
4149 
4150   PetscFunctionBegin;
4151   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
4152   PetscCheck(A->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
4153   PetscCheck(!B->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
4154   PetscCheck(B->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
4155   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQAIJ, &flg));
4156   PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "MatType %s", ((PetscObject)B)->type_name);
4157   PetscCheck(reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX, PETSC_COMM_SELF, PETSC_ERR_SUP, "MatReuse %d", (int)reuse);
4158   if (reuse == MAT_INITIAL_MATRIX) {
4159     PetscCall(PetscMalloc2(am * bm + 1, &i, a->i[am] * b->i[bm], &j));
4160     PetscCall(MatCreate(PETSC_COMM_SELF, &newmat));
4161     PetscCall(MatSetSizes(newmat, am * bm, an * bn, am * bm, an * bn));
4162     PetscCall(MatSetType(newmat, MATAIJ));
4163     i[0] = 0;
4164     for (m = 0; m < am; ++m) {
4165       for (p = 0; p < bm; ++p) {
4166         i[m * bm + p + 1] = i[m * bm + p] + (a->i[m + 1] - a->i[m]) * (b->i[p + 1] - b->i[p]);
4167         for (n = a->i[m]; n < a->i[m + 1]; ++n) {
4168           for (q = b->i[p]; q < b->i[p + 1]; ++q) j[nnz++] = a->j[n] * bn + b->j[q];
4169         }
4170       }
4171     }
4172     PetscCall(MatSeqAIJSetPreallocationCSR(newmat, i, j, NULL));
4173     *C = newmat;
4174     PetscCall(PetscFree2(i, j));
4175     nnz = 0;
4176   }
4177   PetscCall(MatSeqAIJGetArray(*C, &v));
4178   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
4179   PetscCall(MatSeqAIJGetArrayRead(B, &ba));
4180   for (m = 0; m < am; ++m) {
4181     for (p = 0; p < bm; ++p) {
4182       for (n = a->i[m]; n < a->i[m + 1]; ++n) {
4183         for (q = b->i[p]; q < b->i[p + 1]; ++q) v[nnz++] = aa[n] * ba[q];
4184       }
4185     }
4186   }
4187   PetscCall(MatSeqAIJRestoreArray(*C, &v));
4188   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
4189   PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
4190   PetscFunctionReturn(0);
4191 }
4192 
4193 #include <../src/mat/impls/dense/seq/dense.h>
4194 #include <petsc/private/kernels/petscaxpy.h>
4195 
4196 /*
4197     Computes (B'*A')' since computing B*A directly is untenable
4198 
4199                n                       p                          p
4200         [             ]       [             ]         [                 ]
4201       m [      A      ]  *  n [       B     ]   =   m [         C       ]
4202         [             ]       [             ]         [                 ]
4203 
4204 */
4205 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A, Mat B, Mat C)
4206 {
4207   Mat_SeqDense      *sub_a = (Mat_SeqDense *)A->data;
4208   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ *)B->data;
4209   Mat_SeqDense      *sub_c = (Mat_SeqDense *)C->data;
4210   PetscInt           i, j, n, m, q, p;
4211   const PetscInt    *ii, *idx;
4212   const PetscScalar *b, *a, *a_q;
4213   PetscScalar       *c, *c_q;
4214   PetscInt           clda = sub_c->lda;
4215   PetscInt           alda = sub_a->lda;
4216 
4217   PetscFunctionBegin;
4218   m = A->rmap->n;
4219   n = A->cmap->n;
4220   p = B->cmap->n;
4221   a = sub_a->v;
4222   b = sub_b->a;
4223   c = sub_c->v;
4224   if (clda == m) {
4225     PetscCall(PetscArrayzero(c, m * p));
4226   } else {
4227     for (j = 0; j < p; j++)
4228       for (i = 0; i < m; i++) c[j * clda + i] = 0.0;
4229   }
4230   ii  = sub_b->i;
4231   idx = sub_b->j;
4232   for (i = 0; i < n; i++) {
4233     q = ii[i + 1] - ii[i];
4234     while (q-- > 0) {
4235       c_q = c + clda * (*idx);
4236       a_q = a + alda * i;
4237       PetscKernelAXPY(c_q, *b, a_q, m);
4238       idx++;
4239       b++;
4240     }
4241   }
4242   PetscFunctionReturn(0);
4243 }
4244 
4245 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
4246 {
4247   PetscInt  m = A->rmap->n, n = B->cmap->n;
4248   PetscBool cisdense;
4249 
4250   PetscFunctionBegin;
4251   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);
4252   PetscCall(MatSetSizes(C, m, n, m, n));
4253   PetscCall(MatSetBlockSizesFromMats(C, A, B));
4254   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSECUDA, ""));
4255   if (!cisdense) PetscCall(MatSetType(C, MATDENSE));
4256   PetscCall(MatSetUp(C));
4257 
4258   C->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
4259   PetscFunctionReturn(0);
4260 }
4261 
4262 /* ----------------------------------------------------------------*/
4263 /*MC
4264    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
4265    based on compressed sparse row format.
4266 
4267    Options Database Keys:
4268 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
4269 
4270    Level: beginner
4271 
4272    Notes:
4273     `MatSetValues()` may be called for this matrix type with a NULL argument for the numerical values,
4274     in this case the values associated with the rows and columns one passes in are set to zero
4275     in the matrix
4276 
4277     `MatSetOptions`(,`MAT_STRUCTURE_ONLY`,`PETSC_TRUE`) may be called for this matrix type. In this no
4278     space is allocated for the nonzero entries and any entries passed with `MatSetValues()` are ignored
4279 
4280   Developer Note:
4281     It would be nice if all matrix formats supported passing NULL in for the numerical values
4282 
4283 .seealso: `MatCreateSeqAIJ()`, `MatSetFromOptions()`, `MatSetType()`, `MatCreate()`, `MatType`, `MATSELL`, `MATSEQSELL`, `MATMPISELL`
4284 M*/
4285 
4286 /*MC
4287    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
4288 
4289    This matrix type is identical to `MATSEQAIJ` when constructed with a single process communicator,
4290    and `MATMPIAIJ` otherwise.  As a result, for single process communicators,
4291    `MatSeqAIJSetPreallocation()` is supported, and similarly `MatMPIAIJSetPreallocation()` is supported
4292    for communicators controlling multiple processes.  It is recommended that you call both of
4293    the above preallocation routines for simplicity.
4294 
4295    Options Database Keys:
4296 . -mat_type aij - sets the matrix type to "aij" during a call to `MatSetFromOptions()`
4297 
4298    Note:
4299    Subclasses include `MATAIJCUSPARSE`, `MATAIJPERM`, `MATAIJSELL`, `MATAIJMKL`, `MATAIJCRL`, and also automatically switches over to use inodes when
4300    enough exist.
4301 
4302   Level: beginner
4303 
4304 .seealso: `MatCreateAIJ()`, `MatCreateSeqAIJ()`, `MATSEQAIJ`, `MATMPIAIJ`, `MATSELL`, `MATSEQSELL`, `MATMPISELL`
4305 M*/
4306 
4307 /*MC
4308    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
4309 
4310    This matrix type is identical to `MATSEQAIJCRL` when constructed with a single process communicator,
4311    and `MATMPIAIJCRL` otherwise.  As a result, for single process communicators,
4312    `MatSeqAIJSetPreallocation()` is supported, and similarly `MatMPIAIJSetPreallocation()` is supported
4313    for communicators controlling multiple processes.  It is recommended that you call both of
4314    the above preallocation routines for simplicity.
4315 
4316    Options Database Keys:
4317 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to `MatSetFromOptions()`
4318 
4319   Level: beginner
4320 
4321 .seealso: `MatCreateMPIAIJCRL`, `MATSEQAIJCRL`, `MATMPIAIJCRL`, `MATSEQAIJCRL`, `MATMPIAIJCRL`
4322 M*/
4323 
4324 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat, MatType, MatReuse, Mat *);
4325 #if defined(PETSC_HAVE_ELEMENTAL)
4326 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_Elemental(Mat, MatType, MatReuse, Mat *);
4327 #endif
4328 #if defined(PETSC_HAVE_SCALAPACK)
4329 PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat, MatType, MatReuse, Mat *);
4330 #endif
4331 #if defined(PETSC_HAVE_HYPRE)
4332 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat A, MatType, MatReuse, Mat *);
4333 #endif
4334 
4335 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqSELL(Mat, MatType, MatReuse, Mat *);
4336 PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat, MatType, MatReuse, Mat *);
4337 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_IS_XAIJ(Mat);
4338 
4339 /*@C
4340    MatSeqAIJGetArray - gives read/write access to the array where the data for a `MATSEQAIJ` matrix is stored
4341 
4342    Not Collective
4343 
4344    Input Parameter:
4345 .  mat - a `MATSEQAIJ` matrix
4346 
4347    Output Parameter:
4348 .   array - pointer to the data
4349 
4350    Level: intermediate
4351 
4352 .seealso: `MatSeqAIJRestoreArray()`, `MatSeqAIJGetArrayF90()`
4353 @*/
4354 PetscErrorCode MatSeqAIJGetArray(Mat A, PetscScalar **array)
4355 {
4356   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4357 
4358   PetscFunctionBegin;
4359   if (aij->ops->getarray) {
4360     PetscCall((*aij->ops->getarray)(A, array));
4361   } else {
4362     *array = aij->a;
4363   }
4364   PetscFunctionReturn(0);
4365 }
4366 
4367 /*@C
4368    MatSeqAIJRestoreArray - returns access to the array where the data for a `MATSEQAIJ` matrix is stored obtained by `MatSeqAIJGetArray()`
4369 
4370    Not Collective
4371 
4372    Input Parameters:
4373 +  mat - a `MATSEQAIJ` matrix
4374 -  array - pointer to the data
4375 
4376    Level: intermediate
4377 
4378 .seealso: `MatSeqAIJGetArray()`, `MatSeqAIJRestoreArrayF90()`
4379 @*/
4380 PetscErrorCode MatSeqAIJRestoreArray(Mat A, PetscScalar **array)
4381 {
4382   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4383 
4384   PetscFunctionBegin;
4385   if (aij->ops->restorearray) {
4386     PetscCall((*aij->ops->restorearray)(A, array));
4387   } else {
4388     *array = NULL;
4389   }
4390   PetscCall(MatSeqAIJInvalidateDiagonal(A));
4391   PetscCall(PetscObjectStateIncrease((PetscObject)A));
4392   PetscFunctionReturn(0);
4393 }
4394 
4395 /*@C
4396    MatSeqAIJGetArrayRead - gives read-only access to the array where the data for a `MATSEQAIJ` matrix is stored
4397 
4398    Not Collective
4399 
4400    Input Parameter:
4401 .  mat - a `MATSEQAIJ` matrix
4402 
4403    Output Parameter:
4404 .   array - pointer to the data
4405 
4406    Level: intermediate
4407 
4408 .seealso: `MatSeqAIJGetArray()`, `MatSeqAIJRestoreArrayRead()`
4409 @*/
4410 PetscErrorCode MatSeqAIJGetArrayRead(Mat A, const PetscScalar **array)
4411 {
4412   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4413 
4414   PetscFunctionBegin;
4415   if (aij->ops->getarrayread) {
4416     PetscCall((*aij->ops->getarrayread)(A, array));
4417   } else {
4418     *array = aij->a;
4419   }
4420   PetscFunctionReturn(0);
4421 }
4422 
4423 /*@C
4424    MatSeqAIJRestoreArrayRead - restore the read-only access array obtained from `MatSeqAIJGetArrayRead()`
4425 
4426    Not Collective
4427 
4428    Input Parameter:
4429 .  mat - a `MATSEQAIJ` matrix
4430 
4431    Output Parameter:
4432 .   array - pointer to the data
4433 
4434    Level: intermediate
4435 
4436 .seealso: `MatSeqAIJGetArray()`, `MatSeqAIJGetArrayRead()`
4437 @*/
4438 PetscErrorCode MatSeqAIJRestoreArrayRead(Mat A, const PetscScalar **array)
4439 {
4440   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4441 
4442   PetscFunctionBegin;
4443   if (aij->ops->restorearrayread) {
4444     PetscCall((*aij->ops->restorearrayread)(A, array));
4445   } else {
4446     *array = NULL;
4447   }
4448   PetscFunctionReturn(0);
4449 }
4450 
4451 /*@C
4452    MatSeqAIJGetArrayWrite - gives write-only access to the array where the data for a `MATSEQAIJ` matrix is stored
4453 
4454    Not Collective
4455 
4456    Input Parameter:
4457 .  mat - a `MATSEQAIJ` matrix
4458 
4459    Output Parameter:
4460 .   array - pointer to the data
4461 
4462    Level: intermediate
4463 
4464 .seealso: `MatSeqAIJGetArray()`, `MatSeqAIJRestoreArrayRead()`
4465 @*/
4466 PetscErrorCode MatSeqAIJGetArrayWrite(Mat A, PetscScalar **array)
4467 {
4468   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4469 
4470   PetscFunctionBegin;
4471   if (aij->ops->getarraywrite) {
4472     PetscCall((*aij->ops->getarraywrite)(A, array));
4473   } else {
4474     *array = aij->a;
4475   }
4476   PetscCall(MatSeqAIJInvalidateDiagonal(A));
4477   PetscCall(PetscObjectStateIncrease((PetscObject)A));
4478   PetscFunctionReturn(0);
4479 }
4480 
4481 /*@C
4482    MatSeqAIJRestoreArrayWrite - restore the read-only access array obtained from MatSeqAIJGetArrayRead
4483 
4484    Not Collective
4485 
4486    Input Parameter:
4487 .  mat - a MATSEQAIJ matrix
4488 
4489    Output Parameter:
4490 .   array - pointer to the data
4491 
4492    Level: intermediate
4493 
4494 .seealso: `MatSeqAIJGetArray()`, `MatSeqAIJGetArrayRead()`
4495 @*/
4496 PetscErrorCode MatSeqAIJRestoreArrayWrite(Mat A, PetscScalar **array)
4497 {
4498   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4499 
4500   PetscFunctionBegin;
4501   if (aij->ops->restorearraywrite) {
4502     PetscCall((*aij->ops->restorearraywrite)(A, array));
4503   } else {
4504     *array = NULL;
4505   }
4506   PetscFunctionReturn(0);
4507 }
4508 
4509 /*@C
4510    MatSeqAIJGetCSRAndMemType - Get the CSR arrays and the memory type of the `MATSEQAIJ` matrix
4511 
4512    Not Collective
4513 
4514    Input Parameter:
4515 .  mat - a matrix of type `MATSEQAIJ` or its subclasses
4516 
4517    Output Parameters:
4518 +  i - row map array of the matrix
4519 .  j - column index array of the matrix
4520 .  a - data array of the matrix
4521 -  memtype - memory type of the arrays
4522 
4523   Notes:
4524    Any of the output parameters can be NULL, in which case the corresponding value is not returned.
4525    If mat is a device matrix, the arrays are on the device. Otherwise, they are on the host.
4526 
4527    One can call this routine on a preallocated but not assembled matrix to just get the memory of the CSR underneath the matrix.
4528    If the matrix is assembled, the data array 'a' is guaranteed to have the latest values of the matrix.
4529 
4530    Level: Developer
4531 
4532 .seealso: `MatSeqAIJGetArray()`, `MatSeqAIJGetArrayRead()`
4533 @*/
4534 PetscErrorCode MatSeqAIJGetCSRAndMemType(Mat mat, const PetscInt **i, const PetscInt **j, PetscScalar **a, PetscMemType *mtype)
4535 {
4536   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)mat->data;
4537 
4538   PetscFunctionBegin;
4539   PetscCheck(mat->preallocated, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "matrix is not preallocated");
4540   if (aij->ops->getcsrandmemtype) {
4541     PetscCall((*aij->ops->getcsrandmemtype)(mat, i, j, a, mtype));
4542   } else {
4543     if (i) *i = aij->i;
4544     if (j) *j = aij->j;
4545     if (a) *a = aij->a;
4546     if (mtype) *mtype = PETSC_MEMTYPE_HOST;
4547   }
4548   PetscFunctionReturn(0);
4549 }
4550 
4551 /*@C
4552    MatSeqAIJGetMaxRowNonzeros - returns the maximum number of nonzeros in any row
4553 
4554    Not Collective
4555 
4556    Input Parameter:
4557 .  mat - a `MATSEQAIJ` matrix
4558 
4559    Output Parameter:
4560 .   nz - the maximum number of nonzeros in any row
4561 
4562    Level: intermediate
4563 
4564 .seealso: `MatSeqAIJRestoreArray()`, `MatSeqAIJGetArrayF90()`
4565 @*/
4566 PetscErrorCode MatSeqAIJGetMaxRowNonzeros(Mat A, PetscInt *nz)
4567 {
4568   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)A->data;
4569 
4570   PetscFunctionBegin;
4571   *nz = aij->rmax;
4572   PetscFunctionReturn(0);
4573 }
4574 
4575 PetscErrorCode MatSetPreallocationCOO_SeqAIJ(Mat mat, PetscCount coo_n, PetscInt coo_i[], PetscInt coo_j[])
4576 {
4577   MPI_Comm     comm;
4578   PetscInt    *i, *j;
4579   PetscInt     M, N, row;
4580   PetscCount   k, p, q, nneg, nnz, start, end; /* Index the coo array, so use PetscCount as their type */
4581   PetscInt    *Ai;                             /* Change to PetscCount once we use it for row pointers */
4582   PetscInt    *Aj;
4583   PetscScalar *Aa;
4584   Mat_SeqAIJ  *seqaij = (Mat_SeqAIJ *)(mat->data);
4585   MatType      rtype;
4586   PetscCount  *perm, *jmap;
4587 
4588   PetscFunctionBegin;
4589   PetscCall(MatResetPreallocationCOO_SeqAIJ(mat));
4590   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
4591   PetscCall(MatGetSize(mat, &M, &N));
4592   i = coo_i;
4593   j = coo_j;
4594   PetscCall(PetscMalloc1(coo_n, &perm));
4595   for (k = 0; k < coo_n; k++) { /* Ignore entries with negative row or col indices */
4596     if (j[k] < 0) i[k] = -1;
4597     perm[k] = k;
4598   }
4599 
4600   /* Sort by row */
4601   PetscCall(PetscSortIntWithIntCountArrayPair(coo_n, i, j, perm));
4602   for (k = 0; k < coo_n; k++) {
4603     if (i[k] >= 0) break;
4604   } /* Advance k to the first row with a non-negative index */
4605   nneg = k;
4606   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 */
4607   nnz = 0;                                          /* Total number of unique nonzeros to be counted */
4608   jmap++;                                           /* Inc jmap by 1 for convinience */
4609 
4610   PetscCall(PetscCalloc1(M + 1, &Ai));        /* CSR of A */
4611   PetscCall(PetscMalloc1(coo_n - nneg, &Aj)); /* We have at most coo_n-nneg unique nonzeros */
4612 
4613   /* In each row, sort by column, then unique column indices to get row length */
4614   Ai++;  /* Inc by 1 for convinience */
4615   q = 0; /* q-th unique nonzero, with q starting from 0 */
4616   while (k < coo_n) {
4617     row   = i[k];
4618     start = k; /* [start,end) indices for this row */
4619     while (k < coo_n && i[k] == row) k++;
4620     end = k;
4621     PetscCall(PetscSortIntWithCountArray(end - start, j + start, perm + start));
4622     /* Find number of unique col entries in this row */
4623     Aj[q]   = j[start]; /* Log the first nonzero in this row */
4624     jmap[q] = 1;        /* Number of repeats of this nozero entry */
4625     Ai[row] = 1;
4626     nnz++;
4627 
4628     for (p = start + 1; p < end; p++) { /* Scan remaining nonzero in this row */
4629       if (j[p] != j[p - 1]) {           /* Meet a new nonzero */
4630         q++;
4631         jmap[q] = 1;
4632         Aj[q]   = j[p];
4633         Ai[row]++;
4634         nnz++;
4635       } else {
4636         jmap[q]++;
4637       }
4638     }
4639     q++; /* Move to next row and thus next unique nonzero */
4640   }
4641 
4642   Ai--; /* Back to the beginning of Ai[] */
4643   for (k = 0; k < M; k++) Ai[k + 1] += Ai[k];
4644   jmap--; /* Back to the beginning of jmap[] */
4645   jmap[0] = 0;
4646   for (k = 0; k < nnz; k++) jmap[k + 1] += jmap[k];
4647   if (nnz < coo_n - nneg) { /* Realloc with actual number of unique nonzeros */
4648     PetscCount *jmap_new;
4649     PetscInt   *Aj_new;
4650 
4651     PetscCall(PetscMalloc1(nnz + 1, &jmap_new));
4652     PetscCall(PetscArraycpy(jmap_new, jmap, nnz + 1));
4653     PetscCall(PetscFree(jmap));
4654     jmap = jmap_new;
4655 
4656     PetscCall(PetscMalloc1(nnz, &Aj_new));
4657     PetscCall(PetscArraycpy(Aj_new, Aj, nnz));
4658     PetscCall(PetscFree(Aj));
4659     Aj = Aj_new;
4660   }
4661 
4662   if (nneg) { /* Discard heading entries with negative indices in perm[], as we'll access it from index 0 in MatSetValuesCOO */
4663     PetscCount *perm_new;
4664 
4665     PetscCall(PetscMalloc1(coo_n - nneg, &perm_new));
4666     PetscCall(PetscArraycpy(perm_new, perm + nneg, coo_n - nneg));
4667     PetscCall(PetscFree(perm));
4668     perm = perm_new;
4669   }
4670 
4671   PetscCall(MatGetRootType_Private(mat, &rtype));
4672   PetscCall(PetscCalloc1(nnz, &Aa)); /* Zero the matrix */
4673   PetscCall(MatSetSeqAIJWithArrays_private(PETSC_COMM_SELF, M, N, Ai, Aj, Aa, rtype, mat));
4674 
4675   seqaij->singlemalloc = PETSC_FALSE;            /* Ai, Aj and Aa are not allocated in one big malloc */
4676   seqaij->free_a = seqaij->free_ij = PETSC_TRUE; /* Let newmat own Ai, Aj and Aa */
4677   /* Record COO fields */
4678   seqaij->coo_n = coo_n;
4679   seqaij->Atot  = coo_n - nneg; /* Annz is seqaij->nz, so no need to record that again */
4680   seqaij->jmap  = jmap;         /* of length nnz+1 */
4681   seqaij->perm  = perm;
4682   PetscFunctionReturn(0);
4683 }
4684 
4685 static PetscErrorCode MatSetValuesCOO_SeqAIJ(Mat A, const PetscScalar v[], InsertMode imode)
4686 {
4687   Mat_SeqAIJ  *aseq = (Mat_SeqAIJ *)A->data;
4688   PetscCount   i, j, Annz = aseq->nz;
4689   PetscCount  *perm = aseq->perm, *jmap = aseq->jmap;
4690   PetscScalar *Aa;
4691 
4692   PetscFunctionBegin;
4693   PetscCall(MatSeqAIJGetArray(A, &Aa));
4694   for (i = 0; i < Annz; i++) {
4695     PetscScalar sum = 0.0;
4696     for (j = jmap[i]; j < jmap[i + 1]; j++) sum += v[perm[j]];
4697     Aa[i] = (imode == INSERT_VALUES ? 0.0 : Aa[i]) + sum;
4698   }
4699   PetscCall(MatSeqAIJRestoreArray(A, &Aa));
4700   PetscFunctionReturn(0);
4701 }
4702 
4703 #if defined(PETSC_HAVE_CUDA)
4704 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat, MatType, MatReuse, Mat *);
4705 #endif
4706 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
4707 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJKokkos(Mat, MatType, MatReuse, Mat *);
4708 #endif
4709 
4710 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4711 {
4712   Mat_SeqAIJ *b;
4713   PetscMPIInt size;
4714 
4715   PetscFunctionBegin;
4716   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));
4717   PetscCheck(size <= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Comm must be of size 1");
4718 
4719   PetscCall(PetscNew(&b));
4720 
4721   B->data = (void *)b;
4722 
4723   PetscCall(PetscMemcpy(B->ops, &MatOps_Values, sizeof(struct _MatOps)));
4724   if (B->sortedfull) B->ops->setvalues = MatSetValues_SeqAIJ_SortedFull;
4725 
4726   b->row                = NULL;
4727   b->col                = NULL;
4728   b->icol               = NULL;
4729   b->reallocs           = 0;
4730   b->ignorezeroentries  = PETSC_FALSE;
4731   b->roworiented        = PETSC_TRUE;
4732   b->nonew              = 0;
4733   b->diag               = NULL;
4734   b->solve_work         = NULL;
4735   B->spptr              = NULL;
4736   b->saved_values       = NULL;
4737   b->idiag              = NULL;
4738   b->mdiag              = NULL;
4739   b->ssor_work          = NULL;
4740   b->omega              = 1.0;
4741   b->fshift             = 0.0;
4742   b->idiagvalid         = PETSC_FALSE;
4743   b->ibdiagvalid        = PETSC_FALSE;
4744   b->keepnonzeropattern = PETSC_FALSE;
4745 
4746   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQAIJ));
4747 #if defined(PETSC_HAVE_MATLAB)
4748   PetscCall(PetscObjectComposeFunction((PetscObject)B, "PetscMatlabEnginePut_C", MatlabEnginePut_SeqAIJ));
4749   PetscCall(PetscObjectComposeFunction((PetscObject)B, "PetscMatlabEngineGet_C", MatlabEngineGet_SeqAIJ));
4750 #endif
4751   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqAIJSetColumnIndices_C", MatSeqAIJSetColumnIndices_SeqAIJ));
4752   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatStoreValues_C", MatStoreValues_SeqAIJ));
4753   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatRetrieveValues_C", MatRetrieveValues_SeqAIJ));
4754   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqsbaij_C", MatConvert_SeqAIJ_SeqSBAIJ));
4755   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqbaij_C", MatConvert_SeqAIJ_SeqBAIJ));
4756   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijperm_C", MatConvert_SeqAIJ_SeqAIJPERM));
4757   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijsell_C", MatConvert_SeqAIJ_SeqAIJSELL));
4758 #if defined(PETSC_HAVE_MKL_SPARSE)
4759   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijmkl_C", MatConvert_SeqAIJ_SeqAIJMKL));
4760 #endif
4761 #if defined(PETSC_HAVE_CUDA)
4762   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijcusparse_C", MatConvert_SeqAIJ_SeqAIJCUSPARSE));
4763   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqaijcusparse_seqaij_C", MatProductSetFromOptions_SeqAIJ));
4764   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqaij_seqaijcusparse_C", MatProductSetFromOptions_SeqAIJ));
4765 #endif
4766 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
4767   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijkokkos_C", MatConvert_SeqAIJ_SeqAIJKokkos));
4768 #endif
4769   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqaijcrl_C", MatConvert_SeqAIJ_SeqAIJCRL));
4770 #if defined(PETSC_HAVE_ELEMENTAL)
4771   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_elemental_C", MatConvert_SeqAIJ_Elemental));
4772 #endif
4773 #if defined(PETSC_HAVE_SCALAPACK)
4774   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_scalapack_C", MatConvert_AIJ_ScaLAPACK));
4775 #endif
4776 #if defined(PETSC_HAVE_HYPRE)
4777   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_hypre_C", MatConvert_AIJ_HYPRE));
4778   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_transpose_seqaij_seqaij_C", MatProductSetFromOptions_Transpose_AIJ_AIJ));
4779 #endif
4780   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqdense_C", MatConvert_SeqAIJ_SeqDense));
4781   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_seqsell_C", MatConvert_SeqAIJ_SeqSELL));
4782   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqaij_is_C", MatConvert_XAIJ_IS));
4783   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatIsTranspose_C", MatIsTranspose_SeqAIJ));
4784   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatIsHermitianTranspose_C", MatIsTranspose_SeqAIJ));
4785   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqAIJSetPreallocation_C", MatSeqAIJSetPreallocation_SeqAIJ));
4786   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatResetPreallocation_C", MatResetPreallocation_SeqAIJ));
4787   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqAIJSetPreallocationCSR_C", MatSeqAIJSetPreallocationCSR_SeqAIJ));
4788   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatReorderForNonzeroDiagonal_C", MatReorderForNonzeroDiagonal_SeqAIJ));
4789   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_is_seqaij_C", MatProductSetFromOptions_IS_XAIJ));
4790   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdense_seqaij_C", MatProductSetFromOptions_SeqDense_SeqAIJ));
4791   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqaij_seqaij_C", MatProductSetFromOptions_SeqAIJ));
4792   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqAIJKron_C", MatSeqAIJKron_SeqAIJ));
4793   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_SeqAIJ));
4794   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetValuesCOO_C", MatSetValuesCOO_SeqAIJ));
4795   PetscCall(MatCreate_SeqAIJ_Inode(B));
4796   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQAIJ));
4797   PetscCall(MatSeqAIJSetTypeFromOptions(B)); /* this allows changing the matrix subtype to say MATSEQAIJPERM */
4798   PetscFunctionReturn(0);
4799 }
4800 
4801 /*
4802     Given a matrix generated with MatGetFactor() duplicates all the information in A into C
4803 */
4804 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C, Mat A, MatDuplicateOption cpvalues, PetscBool mallocmatspace)
4805 {
4806   Mat_SeqAIJ *c = (Mat_SeqAIJ *)C->data, *a = (Mat_SeqAIJ *)A->data;
4807   PetscInt    m = A->rmap->n, i;
4808 
4809   PetscFunctionBegin;
4810   PetscCheck(A->assembled || cpvalues == MAT_DO_NOT_COPY_VALUES, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot duplicate unassembled matrix");
4811 
4812   C->factortype = A->factortype;
4813   c->row        = NULL;
4814   c->col        = NULL;
4815   c->icol       = NULL;
4816   c->reallocs   = 0;
4817 
4818   C->assembled    = A->assembled;
4819   C->preallocated = A->preallocated;
4820 
4821   if (A->preallocated) {
4822     PetscCall(PetscLayoutReference(A->rmap, &C->rmap));
4823     PetscCall(PetscLayoutReference(A->cmap, &C->cmap));
4824 
4825     PetscCall(PetscMalloc1(m, &c->imax));
4826     PetscCall(PetscMemcpy(c->imax, a->imax, m * sizeof(PetscInt)));
4827     PetscCall(PetscMalloc1(m, &c->ilen));
4828     PetscCall(PetscMemcpy(c->ilen, a->ilen, m * sizeof(PetscInt)));
4829 
4830     /* allocate the matrix space */
4831     if (mallocmatspace) {
4832       PetscCall(PetscMalloc3(a->i[m], &c->a, a->i[m], &c->j, m + 1, &c->i));
4833 
4834       c->singlemalloc = PETSC_TRUE;
4835 
4836       PetscCall(PetscArraycpy(c->i, a->i, m + 1));
4837       if (m > 0) {
4838         PetscCall(PetscArraycpy(c->j, a->j, a->i[m]));
4839         if (cpvalues == MAT_COPY_VALUES) {
4840           const PetscScalar *aa;
4841 
4842           PetscCall(MatSeqAIJGetArrayRead(A, &aa));
4843           PetscCall(PetscArraycpy(c->a, aa, a->i[m]));
4844           PetscCall(MatSeqAIJGetArrayRead(A, &aa));
4845         } else {
4846           PetscCall(PetscArrayzero(c->a, a->i[m]));
4847         }
4848       }
4849     }
4850 
4851     c->ignorezeroentries = a->ignorezeroentries;
4852     c->roworiented       = a->roworiented;
4853     c->nonew             = a->nonew;
4854     if (a->diag) {
4855       PetscCall(PetscMalloc1(m + 1, &c->diag));
4856       PetscCall(PetscMemcpy(c->diag, a->diag, m * sizeof(PetscInt)));
4857     } else c->diag = NULL;
4858 
4859     c->solve_work         = NULL;
4860     c->saved_values       = NULL;
4861     c->idiag              = NULL;
4862     c->ssor_work          = NULL;
4863     c->keepnonzeropattern = a->keepnonzeropattern;
4864     c->free_a             = PETSC_TRUE;
4865     c->free_ij            = PETSC_TRUE;
4866 
4867     c->rmax  = a->rmax;
4868     c->nz    = a->nz;
4869     c->maxnz = a->nz; /* Since we allocate exactly the right amount */
4870 
4871     c->compressedrow.use   = a->compressedrow.use;
4872     c->compressedrow.nrows = a->compressedrow.nrows;
4873     if (a->compressedrow.use) {
4874       i = a->compressedrow.nrows;
4875       PetscCall(PetscMalloc2(i + 1, &c->compressedrow.i, i, &c->compressedrow.rindex));
4876       PetscCall(PetscArraycpy(c->compressedrow.i, a->compressedrow.i, i + 1));
4877       PetscCall(PetscArraycpy(c->compressedrow.rindex, a->compressedrow.rindex, i));
4878     } else {
4879       c->compressedrow.use    = PETSC_FALSE;
4880       c->compressedrow.i      = NULL;
4881       c->compressedrow.rindex = NULL;
4882     }
4883     c->nonzerorowcnt = a->nonzerorowcnt;
4884     C->nonzerostate  = A->nonzerostate;
4885 
4886     PetscCall(MatDuplicate_SeqAIJ_Inode(A, cpvalues, &C));
4887   }
4888   PetscCall(PetscFunctionListDuplicate(((PetscObject)A)->qlist, &((PetscObject)C)->qlist));
4889   PetscFunctionReturn(0);
4890 }
4891 
4892 PetscErrorCode MatDuplicate_SeqAIJ(Mat A, MatDuplicateOption cpvalues, Mat *B)
4893 {
4894   PetscFunctionBegin;
4895   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), B));
4896   PetscCall(MatSetSizes(*B, A->rmap->n, A->cmap->n, A->rmap->n, A->cmap->n));
4897   if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) PetscCall(MatSetBlockSizesFromMats(*B, A, A));
4898   PetscCall(MatSetType(*B, ((PetscObject)A)->type_name));
4899   PetscCall(MatDuplicateNoCreate_SeqAIJ(*B, A, cpvalues, PETSC_TRUE));
4900   PetscFunctionReturn(0);
4901 }
4902 
4903 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4904 {
4905   PetscBool isbinary, ishdf5;
4906 
4907   PetscFunctionBegin;
4908   PetscValidHeaderSpecific(newMat, MAT_CLASSID, 1);
4909   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
4910   /* force binary viewer to load .info file if it has not yet done so */
4911   PetscCall(PetscViewerSetUp(viewer));
4912   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
4913   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
4914   if (isbinary) {
4915     PetscCall(MatLoad_SeqAIJ_Binary(newMat, viewer));
4916   } else if (ishdf5) {
4917 #if defined(PETSC_HAVE_HDF5)
4918     PetscCall(MatLoad_AIJ_HDF5(newMat, viewer));
4919 #else
4920     SETERRQ(PetscObjectComm((PetscObject)newMat), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
4921 #endif
4922   } else {
4923     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);
4924   }
4925   PetscFunctionReturn(0);
4926 }
4927 
4928 PetscErrorCode MatLoad_SeqAIJ_Binary(Mat mat, PetscViewer viewer)
4929 {
4930   Mat_SeqAIJ *a = (Mat_SeqAIJ *)mat->data;
4931   PetscInt    header[4], *rowlens, M, N, nz, sum, rows, cols, i;
4932 
4933   PetscFunctionBegin;
4934   PetscCall(PetscViewerSetUp(viewer));
4935 
4936   /* read in matrix header */
4937   PetscCall(PetscViewerBinaryRead(viewer, header, 4, NULL, PETSC_INT));
4938   PetscCheck(header[0] == MAT_FILE_CLASSID, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a matrix object in file");
4939   M  = header[1];
4940   N  = header[2];
4941   nz = header[3];
4942   PetscCheck(M >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix row size (%" PetscInt_FMT ") in file is negative", M);
4943   PetscCheck(N >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix column size (%" PetscInt_FMT ") in file is negative", N);
4944   PetscCheck(nz >= 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Matrix stored in special format on disk, cannot load as SeqAIJ");
4945 
4946   /* set block sizes from the viewer's .info file */
4947   PetscCall(MatLoad_Binary_BlockSizes(mat, viewer));
4948   /* set local and global sizes if not set already */
4949   if (mat->rmap->n < 0) mat->rmap->n = M;
4950   if (mat->cmap->n < 0) mat->cmap->n = N;
4951   if (mat->rmap->N < 0) mat->rmap->N = M;
4952   if (mat->cmap->N < 0) mat->cmap->N = N;
4953   PetscCall(PetscLayoutSetUp(mat->rmap));
4954   PetscCall(PetscLayoutSetUp(mat->cmap));
4955 
4956   /* check if the matrix sizes are correct */
4957   PetscCall(MatGetSize(mat, &rows, &cols));
4958   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);
4959 
4960   /* read in row lengths */
4961   PetscCall(PetscMalloc1(M, &rowlens));
4962   PetscCall(PetscViewerBinaryRead(viewer, rowlens, M, NULL, PETSC_INT));
4963   /* check if sum(rowlens) is same as nz */
4964   sum = 0;
4965   for (i = 0; i < M; i++) sum += rowlens[i];
4966   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);
4967   /* preallocate and check sizes */
4968   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(mat, 0, rowlens));
4969   PetscCall(MatGetSize(mat, &rows, &cols));
4970   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);
4971   /* store row lengths */
4972   PetscCall(PetscArraycpy(a->ilen, rowlens, M));
4973   PetscCall(PetscFree(rowlens));
4974 
4975   /* fill in "i" row pointers */
4976   a->i[0] = 0;
4977   for (i = 0; i < M; i++) a->i[i + 1] = a->i[i] + a->ilen[i];
4978   /* read in "j" column indices */
4979   PetscCall(PetscViewerBinaryRead(viewer, a->j, nz, NULL, PETSC_INT));
4980   /* read in "a" nonzero values */
4981   PetscCall(PetscViewerBinaryRead(viewer, a->a, nz, NULL, PETSC_SCALAR));
4982 
4983   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
4984   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
4985   PetscFunctionReturn(0);
4986 }
4987 
4988 PetscErrorCode MatEqual_SeqAIJ(Mat A, Mat B, PetscBool *flg)
4989 {
4990   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data;
4991   const PetscScalar *aa, *ba;
4992 #if defined(PETSC_USE_COMPLEX)
4993   PetscInt k;
4994 #endif
4995 
4996   PetscFunctionBegin;
4997   /* If the  matrix dimensions are not equal,or no of nonzeros */
4998   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) || (a->nz != b->nz)) {
4999     *flg = PETSC_FALSE;
5000     PetscFunctionReturn(0);
5001   }
5002 
5003   /* if the a->i are the same */
5004   PetscCall(PetscArraycmp(a->i, b->i, A->rmap->n + 1, flg));
5005   if (!*flg) PetscFunctionReturn(0);
5006 
5007   /* if a->j are the same */
5008   PetscCall(PetscArraycmp(a->j, b->j, a->nz, flg));
5009   if (!*flg) PetscFunctionReturn(0);
5010 
5011   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
5012   PetscCall(MatSeqAIJGetArrayRead(B, &ba));
5013   /* if a->a are the same */
5014 #if defined(PETSC_USE_COMPLEX)
5015   for (k = 0; k < a->nz; k++) {
5016     if (PetscRealPart(aa[k]) != PetscRealPart(ba[k]) || PetscImaginaryPart(aa[k]) != PetscImaginaryPart(ba[k])) {
5017       *flg = PETSC_FALSE;
5018       PetscFunctionReturn(0);
5019     }
5020   }
5021 #else
5022   PetscCall(PetscArraycmp(aa, ba, a->nz, flg));
5023 #endif
5024   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
5025   PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
5026   PetscFunctionReturn(0);
5027 }
5028 
5029 /*@
5030      MatCreateSeqAIJWithArrays - Creates an sequential `MATSEQAIJ` matrix using matrix elements (in CSR format)
5031               provided by the user.
5032 
5033       Collective
5034 
5035    Input Parameters:
5036 +   comm - must be an MPI communicator of size 1
5037 .   m - number of rows
5038 .   n - number of columns
5039 .   i - row indices; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
5040 .   j - column indices
5041 -   a - matrix values
5042 
5043    Output Parameter:
5044 .   mat - the matrix
5045 
5046    Level: intermediate
5047 
5048    Notes:
5049        The i, j, and a arrays are not copied by this routine, the user must free these arrays
5050     once the matrix is destroyed and not before
5051 
5052        You cannot set new nonzero locations into this matrix, that will generate an error.
5053 
5054        The i and j indices are 0 based
5055 
5056        The format which is used for the sparse matrix input, is equivalent to a
5057     row-major ordering.. i.e for the following matrix, the input data expected is
5058     as shown
5059 
5060 $        1 0 0
5061 $        2 0 3
5062 $        4 5 6
5063 $
5064 $        i =  {0,1,3,6}  [size = nrow+1  = 3+1]
5065 $        j =  {0,0,2,0,1,2}  [size = 6]; values must be sorted for each row
5066 $        v =  {1,2,3,4,5,6}  [size = 6]
5067 
5068 .seealso: `MatCreate()`, `MatCreateAIJ()`, `MatCreateSeqAIJ()`, `MatCreateMPIAIJWithArrays()`, `MatMPIAIJSetPreallocationCSR()`
5069 @*/
5070 PetscErrorCode MatCreateSeqAIJWithArrays(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt i[], PetscInt j[], PetscScalar a[], Mat *mat)
5071 {
5072   PetscInt    ii;
5073   Mat_SeqAIJ *aij;
5074   PetscInt    jj;
5075 
5076   PetscFunctionBegin;
5077   PetscCheck(m <= 0 || i[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
5078   PetscCall(MatCreate(comm, mat));
5079   PetscCall(MatSetSizes(*mat, m, n, m, n));
5080   /* PetscCall(MatSetBlockSizes(*mat,,)); */
5081   PetscCall(MatSetType(*mat, MATSEQAIJ));
5082   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*mat, MAT_SKIP_ALLOCATION, NULL));
5083   aij = (Mat_SeqAIJ *)(*mat)->data;
5084   PetscCall(PetscMalloc1(m, &aij->imax));
5085   PetscCall(PetscMalloc1(m, &aij->ilen));
5086 
5087   aij->i            = i;
5088   aij->j            = j;
5089   aij->a            = a;
5090   aij->singlemalloc = PETSC_FALSE;
5091   aij->nonew        = -1; /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
5092   aij->free_a       = PETSC_FALSE;
5093   aij->free_ij      = PETSC_FALSE;
5094 
5095   for (ii = 0, aij->nonzerorowcnt = 0, aij->rmax = 0; ii < m; ii++) {
5096     aij->ilen[ii] = aij->imax[ii] = i[ii + 1] - i[ii];
5097     if (PetscDefined(USE_DEBUG)) {
5098       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]);
5099       for (jj = i[ii] + 1; jj < i[ii + 1]; jj++) {
5100         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);
5101         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);
5102       }
5103     }
5104   }
5105   if (PetscDefined(USE_DEBUG)) {
5106     for (ii = 0; ii < aij->i[m]; ii++) {
5107       PetscCheck(j[ii] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative column index at location = %" PetscInt_FMT " index = %" PetscInt_FMT, ii, j[ii]);
5108       PetscCheck(j[ii] <= n - 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column index to large at location = %" PetscInt_FMT " index = %" PetscInt_FMT, ii, j[ii]);
5109     }
5110   }
5111 
5112   PetscCall(MatAssemblyBegin(*mat, MAT_FINAL_ASSEMBLY));
5113   PetscCall(MatAssemblyEnd(*mat, MAT_FINAL_ASSEMBLY));
5114   PetscFunctionReturn(0);
5115 }
5116 
5117 /*@
5118      MatCreateSeqAIJFromTriple - Creates an sequential `MATSEQAIJ` matrix using matrix elements (in COO format)
5119               provided by the user.
5120 
5121       Collective
5122 
5123    Input Parameters:
5124 +   comm - must be an MPI communicator of size 1
5125 .   m   - number of rows
5126 .   n   - number of columns
5127 .   i   - row indices
5128 .   j   - column indices
5129 .   a   - matrix values
5130 .   nz  - number of nonzeros
5131 -   idx - if the i and j indices start with 1 use `PETSC_TRUE` otherwise use `PETSC_FALSE`
5132 
5133    Output Parameter:
5134 .   mat - the matrix
5135 
5136    Level: intermediate
5137 
5138    Example:
5139        For the following matrix, the input data expected is as shown (using 0 based indexing)
5140 .vb
5141         1 0 0
5142         2 0 3
5143         4 5 6
5144 
5145         i =  {0,1,1,2,2,2}
5146         j =  {0,0,2,0,1,2}
5147         v =  {1,2,3,4,5,6}
5148 .ve
5149   Notes:
5150     Instead of using this function, users should also consider `MatSetPreallocationCOO()` and `MatSetValuesCOO()`, which allow repeated or remote entries,
5151     and are particularly useful in iterative applications.
5152 
5153 .seealso: `MatCreate()`, `MatCreateAIJ()`, `MatCreateSeqAIJ()`, `MatCreateSeqAIJWithArrays()`, `MatMPIAIJSetPreallocationCSR()`, `MatSetValuesCOO()`, `MatSetPreallocationCOO()`
5154 @*/
5155 PetscErrorCode MatCreateSeqAIJFromTriple(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt i[], PetscInt j[], PetscScalar a[], Mat *mat, PetscInt nz, PetscBool idx)
5156 {
5157   PetscInt ii, *nnz, one = 1, row, col;
5158 
5159   PetscFunctionBegin;
5160   PetscCall(PetscCalloc1(m, &nnz));
5161   for (ii = 0; ii < nz; ii++) nnz[i[ii] - !!idx] += 1;
5162   PetscCall(MatCreate(comm, mat));
5163   PetscCall(MatSetSizes(*mat, m, n, m, n));
5164   PetscCall(MatSetType(*mat, MATSEQAIJ));
5165   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(*mat, 0, nnz));
5166   for (ii = 0; ii < nz; ii++) {
5167     if (idx) {
5168       row = i[ii] - 1;
5169       col = j[ii] - 1;
5170     } else {
5171       row = i[ii];
5172       col = j[ii];
5173     }
5174     PetscCall(MatSetValues(*mat, one, &row, one, &col, &a[ii], ADD_VALUES));
5175   }
5176   PetscCall(MatAssemblyBegin(*mat, MAT_FINAL_ASSEMBLY));
5177   PetscCall(MatAssemblyEnd(*mat, MAT_FINAL_ASSEMBLY));
5178   PetscCall(PetscFree(nnz));
5179   PetscFunctionReturn(0);
5180 }
5181 
5182 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
5183 {
5184   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;
5185 
5186   PetscFunctionBegin;
5187   a->idiagvalid  = PETSC_FALSE;
5188   a->ibdiagvalid = PETSC_FALSE;
5189 
5190   PetscCall(MatSeqAIJInvalidateDiagonal_Inode(A));
5191   PetscFunctionReturn(0);
5192 }
5193 
5194 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqAIJ(MPI_Comm comm, Mat inmat, PetscInt n, MatReuse scall, Mat *outmat)
5195 {
5196   PetscFunctionBegin;
5197   PetscCall(MatCreateMPIMatConcatenateSeqMat_MPIAIJ(comm, inmat, n, scall, outmat));
5198   PetscFunctionReturn(0);
5199 }
5200 
5201 /*
5202  Permute A into C's *local* index space using rowemb,colemb.
5203  The embedding are supposed to be injections and the above implies that the range of rowemb is a subset
5204  of [0,m), colemb is in [0,n).
5205  If pattern == DIFFERENT_NONZERO_PATTERN, C is preallocated according to A.
5206  */
5207 PetscErrorCode MatSetSeqMat_SeqAIJ(Mat C, IS rowemb, IS colemb, MatStructure pattern, Mat B)
5208 {
5209   /* If making this function public, change the error returned in this function away from _PLIB. */
5210   Mat_SeqAIJ     *Baij;
5211   PetscBool       seqaij;
5212   PetscInt        m, n, *nz, i, j, count;
5213   PetscScalar     v;
5214   const PetscInt *rowindices, *colindices;
5215 
5216   PetscFunctionBegin;
5217   if (!B) PetscFunctionReturn(0);
5218   /* Check to make sure the target matrix (and embeddings) are compatible with C and each other. */
5219   PetscCall(PetscObjectBaseTypeCompare((PetscObject)B, MATSEQAIJ, &seqaij));
5220   PetscCheck(seqaij, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Input matrix is of wrong type");
5221   if (rowemb) {
5222     PetscCall(ISGetLocalSize(rowemb, &m));
5223     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);
5224   } else {
5225     PetscCheck(C->rmap->n == B->rmap->n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Input matrix is row-incompatible with the target matrix");
5226   }
5227   if (colemb) {
5228     PetscCall(ISGetLocalSize(colemb, &n));
5229     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);
5230   } else {
5231     PetscCheck(C->cmap->n == B->cmap->n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Input matrix is col-incompatible with the target matrix");
5232   }
5233 
5234   Baij = (Mat_SeqAIJ *)(B->data);
5235   if (pattern == DIFFERENT_NONZERO_PATTERN) {
5236     PetscCall(PetscMalloc1(B->rmap->n, &nz));
5237     for (i = 0; i < B->rmap->n; i++) nz[i] = Baij->i[i + 1] - Baij->i[i];
5238     PetscCall(MatSeqAIJSetPreallocation(C, 0, nz));
5239     PetscCall(PetscFree(nz));
5240   }
5241   if (pattern == SUBSET_NONZERO_PATTERN) PetscCall(MatZeroEntries(C));
5242   count      = 0;
5243   rowindices = NULL;
5244   colindices = NULL;
5245   if (rowemb) PetscCall(ISGetIndices(rowemb, &rowindices));
5246   if (colemb) PetscCall(ISGetIndices(colemb, &colindices));
5247   for (i = 0; i < B->rmap->n; i++) {
5248     PetscInt row;
5249     row = i;
5250     if (rowindices) row = rowindices[i];
5251     for (j = Baij->i[i]; j < Baij->i[i + 1]; j++) {
5252       PetscInt col;
5253       col = Baij->j[count];
5254       if (colindices) col = colindices[col];
5255       v = Baij->a[count];
5256       PetscCall(MatSetValues(C, 1, &row, 1, &col, &v, INSERT_VALUES));
5257       ++count;
5258     }
5259   }
5260   /* FIXME: set C's nonzerostate correctly. */
5261   /* Assembly for C is necessary. */
5262   C->preallocated  = PETSC_TRUE;
5263   C->assembled     = PETSC_TRUE;
5264   C->was_assembled = PETSC_FALSE;
5265   PetscFunctionReturn(0);
5266 }
5267 
5268 PetscErrorCode MatEliminateZeros_SeqAIJ(Mat A)
5269 {
5270   Mat_SeqAIJ *a  = (Mat_SeqAIJ *)A->data;
5271   MatScalar  *aa = a->a;
5272   PetscInt    m = A->rmap->n, fshift = 0, fshift_prev = 0, i, k;
5273   PetscInt   *ailen = a->ilen, *imax = a->imax, *ai = a->i, *aj = a->j, rmax = 0;
5274 
5275   PetscFunctionBegin;
5276   PetscCheck(A->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot eliminate zeros for unassembled matrix");
5277   if (m) rmax = ailen[0]; /* determine row with most nonzeros */
5278   for (i = 1; i <= m; i++) {
5279     /* move each nonzero entry back by the amount of zero slots (fshift) before it*/
5280     for (k = ai[i - 1]; k < ai[i]; k++) {
5281       if (aa[k] == 0 && aj[k] != i - 1) fshift++;
5282       else {
5283         if (aa[k] == 0 && aj[k] == i - 1) PetscCall(PetscInfo(A, "Keep the diagonal zero at row %" PetscInt_FMT "\n", i - 1));
5284         aa[k - fshift] = aa[k];
5285         aj[k - fshift] = aj[k];
5286       }
5287     }
5288     ai[i - 1] -= fshift_prev; // safe to update ai[i-1] now since it will not be used in the next iteration
5289     fshift_prev = fshift;
5290     /* reset ilen and imax for each row */
5291     ailen[i - 1] = imax[i - 1] = ai[i] - fshift - ai[i - 1];
5292     a->nonzerorowcnt += ((ai[i] - fshift - ai[i - 1]) > 0);
5293     rmax = PetscMax(rmax, ailen[i - 1]);
5294   }
5295   if (m) {
5296     ai[m] -= fshift;
5297     a->nz = ai[m];
5298   }
5299   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));
5300   A->nonzerostate -= fshift;
5301   A->info.nz_unneeded += (PetscReal)fshift;
5302   a->rmax = rmax;
5303   if (a->inode.use && a->inode.checked) PetscCall(MatSeqAIJCheckInode(A));
5304   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
5305   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
5306   PetscFunctionReturn(0);
5307 }
5308 
5309 PetscFunctionList MatSeqAIJList = NULL;
5310 
5311 /*@C
5312    MatSeqAIJSetType - Converts a `MATSEQAIJ` matrix to a subtype
5313 
5314    Collective on mat
5315 
5316    Input Parameters:
5317 +  mat      - the matrix object
5318 -  matype   - matrix type
5319 
5320    Options Database Key:
5321 .  -mat_seqai_type  <method> - for example seqaijcrl
5322 
5323   Level: intermediate
5324 
5325 .seealso: `PCSetType()`, `VecSetType()`, `MatCreate()`, `MatType`, `Mat`
5326 @*/
5327 PetscErrorCode MatSeqAIJSetType(Mat mat, MatType matype)
5328 {
5329   PetscBool sametype;
5330   PetscErrorCode (*r)(Mat, MatType, MatReuse, Mat *);
5331 
5332   PetscFunctionBegin;
5333   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
5334   PetscCall(PetscObjectTypeCompare((PetscObject)mat, matype, &sametype));
5335   if (sametype) PetscFunctionReturn(0);
5336 
5337   PetscCall(PetscFunctionListFind(MatSeqAIJList, matype, &r));
5338   PetscCheck(r, PETSC_COMM_SELF, PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown Mat type given: %s", matype);
5339   PetscCall((*r)(mat, matype, MAT_INPLACE_MATRIX, &mat));
5340   PetscFunctionReturn(0);
5341 }
5342 
5343 /*@C
5344   MatSeqAIJRegister -  - Adds a new sub-matrix type for sequential `MATSEQAIJ` matrices
5345 
5346    Not Collective
5347 
5348    Input Parameters:
5349 +  name - name of a new user-defined matrix type, for example `MATSEQAIJCRL`
5350 -  function - routine to convert to subtype
5351 
5352    Notes:
5353    `MatSeqAIJRegister()` may be called multiple times to add several user-defined solvers.
5354 
5355    Then, your matrix can be chosen with the procedural interface at runtime via the option
5356 $     -mat_seqaij_type my_mat
5357 
5358    Level: advanced
5359 
5360 .seealso: `MatSeqAIJRegisterAll()`
5361 @*/
5362 PetscErrorCode MatSeqAIJRegister(const char sname[], PetscErrorCode (*function)(Mat, MatType, MatReuse, Mat *))
5363 {
5364   PetscFunctionBegin;
5365   PetscCall(MatInitializePackage());
5366   PetscCall(PetscFunctionListAdd(&MatSeqAIJList, sname, function));
5367   PetscFunctionReturn(0);
5368 }
5369 
5370 PetscBool MatSeqAIJRegisterAllCalled = PETSC_FALSE;
5371 
5372 /*@C
5373   MatSeqAIJRegisterAll - Registers all of the matrix subtypes of `MATSSEQAIJ`
5374 
5375   Not Collective
5376 
5377   Level: advanced
5378 
5379 .seealso: `MatRegisterAll()`, `MatSeqAIJRegister()`
5380 @*/
5381 PetscErrorCode MatSeqAIJRegisterAll(void)
5382 {
5383   PetscFunctionBegin;
5384   if (MatSeqAIJRegisterAllCalled) PetscFunctionReturn(0);
5385   MatSeqAIJRegisterAllCalled = PETSC_TRUE;
5386 
5387   PetscCall(MatSeqAIJRegister(MATSEQAIJCRL, MatConvert_SeqAIJ_SeqAIJCRL));
5388   PetscCall(MatSeqAIJRegister(MATSEQAIJPERM, MatConvert_SeqAIJ_SeqAIJPERM));
5389   PetscCall(MatSeqAIJRegister(MATSEQAIJSELL, MatConvert_SeqAIJ_SeqAIJSELL));
5390 #if defined(PETSC_HAVE_MKL_SPARSE)
5391   PetscCall(MatSeqAIJRegister(MATSEQAIJMKL, MatConvert_SeqAIJ_SeqAIJMKL));
5392 #endif
5393 #if defined(PETSC_HAVE_CUDA)
5394   PetscCall(MatSeqAIJRegister(MATSEQAIJCUSPARSE, MatConvert_SeqAIJ_SeqAIJCUSPARSE));
5395 #endif
5396 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
5397   PetscCall(MatSeqAIJRegister(MATSEQAIJKOKKOS, MatConvert_SeqAIJ_SeqAIJKokkos));
5398 #endif
5399 #if defined(PETSC_HAVE_VIENNACL) && defined(PETSC_HAVE_VIENNACL_NO_CUDA)
5400   PetscCall(MatSeqAIJRegister(MATMPIAIJVIENNACL, MatConvert_SeqAIJ_SeqAIJViennaCL));
5401 #endif
5402   PetscFunctionReturn(0);
5403 }
5404 
5405 /*
5406     Special version for direct calls from Fortran
5407 */
5408 #include <petsc/private/fortranimpl.h>
5409 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5410   #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
5411 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5412   #define matsetvaluesseqaij_ matsetvaluesseqaij
5413 #endif
5414 
5415 /* Change these macros so can be used in void function */
5416 
5417 /* Change these macros so can be used in void function */
5418 /* Identical to PetscCallVoid, except it assigns to *_ierr */
5419 #undef PetscCall
5420 #define PetscCall(...) \
5421   do { \
5422     PetscErrorCode ierr_msv_mpiaij = __VA_ARGS__; \
5423     if (PetscUnlikely(ierr_msv_mpiaij)) { \
5424       *_ierr = PetscError(PETSC_COMM_SELF, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr_msv_mpiaij, PETSC_ERROR_REPEAT, " "); \
5425       return; \
5426     } \
5427   } while (0)
5428 
5429 #undef SETERRQ
5430 #define SETERRQ(comm, ierr, ...) \
5431   do { \
5432     *_ierr = PetscError(comm, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr, PETSC_ERROR_INITIAL, __VA_ARGS__); \
5433     return; \
5434   } while (0)
5435 
5436 PETSC_EXTERN void matsetvaluesseqaij_(Mat *AA, PetscInt *mm, const PetscInt im[], PetscInt *nn, const PetscInt in[], const PetscScalar v[], InsertMode *isis, PetscErrorCode *_ierr)
5437 {
5438   Mat         A = *AA;
5439   PetscInt    m = *mm, n = *nn;
5440   InsertMode  is = *isis;
5441   Mat_SeqAIJ *a  = (Mat_SeqAIJ *)A->data;
5442   PetscInt   *rp, k, low, high, t, ii, row, nrow, i, col, l, rmax, N;
5443   PetscInt   *imax, *ai, *ailen;
5444   PetscInt   *aj, nonew = a->nonew, lastcol = -1;
5445   MatScalar  *ap, value, *aa;
5446   PetscBool   ignorezeroentries = a->ignorezeroentries;
5447   PetscBool   roworiented       = a->roworiented;
5448 
5449   PetscFunctionBegin;
5450   MatCheckPreallocated(A, 1);
5451   imax  = a->imax;
5452   ai    = a->i;
5453   ailen = a->ilen;
5454   aj    = a->j;
5455   aa    = a->a;
5456 
5457   for (k = 0; k < m; k++) { /* loop over added rows */
5458     row = im[k];
5459     if (row < 0) continue;
5460     PetscCheck(row < A->rmap->n, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_OUTOFRANGE, "Row too large");
5461     rp   = aj + ai[row];
5462     ap   = aa + ai[row];
5463     rmax = imax[row];
5464     nrow = ailen[row];
5465     low  = 0;
5466     high = nrow;
5467     for (l = 0; l < n; l++) { /* loop over added columns */
5468       if (in[l] < 0) continue;
5469       PetscCheck(in[l] < A->cmap->n, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_OUTOFRANGE, "Column too large");
5470       col = in[l];
5471       if (roworiented) value = v[l + k * n];
5472       else value = v[k + l * m];
5473 
5474       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
5475 
5476       if (col <= lastcol) low = 0;
5477       else high = nrow;
5478       lastcol = col;
5479       while (high - low > 5) {
5480         t = (low + high) / 2;
5481         if (rp[t] > col) high = t;
5482         else low = t;
5483       }
5484       for (i = low; i < high; i++) {
5485         if (rp[i] > col) break;
5486         if (rp[i] == col) {
5487           if (is == ADD_VALUES) ap[i] += value;
5488           else ap[i] = value;
5489           goto noinsert;
5490         }
5491       }
5492       if (value == 0.0 && ignorezeroentries) goto noinsert;
5493       if (nonew == 1) goto noinsert;
5494       PetscCheck(nonew != -1, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero in the matrix");
5495       MatSeqXAIJReallocateAIJ(A, A->rmap->n, 1, nrow, row, col, rmax, aa, ai, aj, rp, ap, imax, nonew, MatScalar);
5496       N = nrow++ - 1;
5497       a->nz++;
5498       high++;
5499       /* shift up all the later entries in this row */
5500       for (ii = N; ii >= i; ii--) {
5501         rp[ii + 1] = rp[ii];
5502         ap[ii + 1] = ap[ii];
5503       }
5504       rp[i] = col;
5505       ap[i] = value;
5506       A->nonzerostate++;
5507     noinsert:;
5508       low = i + 1;
5509     }
5510     ailen[row] = nrow;
5511   }
5512   PetscFunctionReturnVoid();
5513 }
5514 /* Undefining these here since they were redefined from their original definition above! No
5515  * other PETSc functions should be defined past this point, as it is impossible to recover the
5516  * original definitions */
5517 #undef PetscCall
5518 #undef SETERRQ
5519