xref: /petsc/src/mat/impls/dense/seq/dense.c (revision 49c2f9045d3a91e7be182f7f53e05380f8af9fad)
1 /*
2      Defines the basic matrix operations for sequential dense.
3      Portions of this code are under:
4      Copyright (c) 2022 Advanced Micro Devices, Inc. All rights reserved.
5 */
6 
7 #include <../src/mat/impls/dense/seq/dense.h> /*I "petscmat.h" I*/
8 #include <../src/mat/impls/dense/mpi/mpidense.h>
9 #include <petscblaslapack.h>
10 #include <../src/mat/impls/aij/seq/aij.h>
11 #include <petsc/private/vecimpl.h>
12 
13 PetscErrorCode MatSeqDenseSymmetrize_Private(Mat A, PetscBool hermitian)
14 {
15   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
16   PetscInt      j, k, n = A->rmap->n;
17   PetscScalar  *v;
18 
19   PetscFunctionBegin;
20   PetscCheck(A->rmap->n == A->cmap->n, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot symmetrize a rectangular matrix");
21   PetscCall(MatDenseGetArray(A, &v));
22   if (!hermitian) {
23     for (k = 0; k < n; k++) {
24       for (j = k; j < n; j++) v[j * mat->lda + k] = v[k * mat->lda + j];
25     }
26   } else {
27     for (k = 0; k < n; k++) {
28       for (j = k; j < n; j++) v[j * mat->lda + k] = PetscConj(v[k * mat->lda + j]);
29     }
30   }
31   PetscCall(MatDenseRestoreArray(A, &v));
32   PetscFunctionReturn(PETSC_SUCCESS);
33 }
34 
35 PetscErrorCode MatSeqDenseInvertFactors_Private(Mat A)
36 {
37   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
38   PetscBLASInt  info, n;
39 
40   PetscFunctionBegin;
41   if (!A->rmap->n || !A->cmap->n) PetscFunctionReturn(PETSC_SUCCESS);
42   PetscCall(PetscBLASIntCast(A->cmap->n, &n));
43   if (A->factortype == MAT_FACTOR_LU) {
44     PetscCheck(mat->pivots, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Pivots not present");
45     if (!mat->fwork) {
46       mat->lfwork = n;
47       PetscCall(PetscMalloc1(mat->lfwork, &mat->fwork));
48     }
49     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
50     PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&n, mat->v, &mat->lda, mat->pivots, mat->fwork, &mat->lfwork, &info));
51     PetscCall(PetscFPTrapPop());
52     PetscCall(PetscLogFlops((1.0 * A->cmap->n * A->cmap->n * A->cmap->n) / 3.0));
53   } else if (A->factortype == MAT_FACTOR_CHOLESKY) {
54     if (A->spd == PETSC_BOOL3_TRUE) {
55       PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
56       PetscCallBLAS("LAPACKpotri", LAPACKpotri_("L", &n, mat->v, &mat->lda, &info));
57       PetscCall(PetscFPTrapPop());
58       PetscCall(MatSeqDenseSymmetrize_Private(A, PETSC_TRUE));
59 #if defined(PETSC_USE_COMPLEX)
60     } else if (A->hermitian == PETSC_BOOL3_TRUE) {
61       PetscCheck(mat->pivots, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Pivots not present");
62       PetscCheck(mat->fwork, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Fwork not present");
63       PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
64       PetscCallBLAS("LAPACKhetri", LAPACKhetri_("L", &n, mat->v, &mat->lda, mat->pivots, mat->fwork, &info));
65       PetscCall(PetscFPTrapPop());
66       PetscCall(MatSeqDenseSymmetrize_Private(A, PETSC_TRUE));
67 #endif
68     } else { /* symmetric case */
69       PetscCheck(mat->pivots, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Pivots not present");
70       PetscCheck(mat->fwork, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Fwork not present");
71       PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
72       PetscCallBLAS("LAPACKsytri", LAPACKsytri_("L", &n, mat->v, &mat->lda, mat->pivots, mat->fwork, &info));
73       PetscCall(PetscFPTrapPop());
74       PetscCall(MatSeqDenseSymmetrize_Private(A, PETSC_FALSE));
75     }
76     PetscCheck(!info, PETSC_COMM_SELF, PETSC_ERR_MAT_CH_ZRPVT, "Bad Inversion: zero pivot in row %" PetscBLASInt_FMT, info - 1);
77     PetscCall(PetscLogFlops((1.0 * A->cmap->n * A->cmap->n * A->cmap->n) / 3.0));
78   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix must be factored to solve");
79 
80   A->ops->solve             = NULL;
81   A->ops->matsolve          = NULL;
82   A->ops->solvetranspose    = NULL;
83   A->ops->matsolvetranspose = NULL;
84   A->ops->solveadd          = NULL;
85   A->ops->solvetransposeadd = NULL;
86   A->factortype             = MAT_FACTOR_NONE;
87   PetscCall(PetscFree(A->solvertype));
88   PetscFunctionReturn(PETSC_SUCCESS);
89 }
90 
91 static PetscErrorCode MatZeroRowsColumns_SeqDense(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
92 {
93   Mat_SeqDense      *l = (Mat_SeqDense *)A->data;
94   PetscInt           m = l->lda, n = A->cmap->n, r = A->rmap->n, i, j;
95   PetscScalar       *slot, *bb, *v;
96   const PetscScalar *xx;
97 
98   PetscFunctionBegin;
99   if (PetscDefined(USE_DEBUG)) {
100     for (i = 0; i < N; i++) {
101       PetscCheck(rows[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative row requested to be zeroed");
102       PetscCheck(rows[i] < A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row %" PetscInt_FMT " requested to be zeroed greater than or equal number of rows %" PetscInt_FMT, rows[i], A->rmap->n);
103       PetscCheck(rows[i] < A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Col %" PetscInt_FMT " requested to be zeroed greater than or equal number of cols %" PetscInt_FMT, rows[i], A->cmap->n);
104     }
105   }
106   if (!N) PetscFunctionReturn(PETSC_SUCCESS);
107 
108   /* fix right-hand side if needed */
109   if (x && b) {
110     Vec xt;
111 
112     PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only coded for square matrices");
113     PetscCall(VecDuplicate(x, &xt));
114     PetscCall(VecCopy(x, xt));
115     PetscCall(VecScale(xt, -1.0));
116     PetscCall(MatMultAdd(A, xt, b, b));
117     PetscCall(VecDestroy(&xt));
118     PetscCall(VecGetArrayRead(x, &xx));
119     PetscCall(VecGetArray(b, &bb));
120     for (i = 0; i < N; i++) bb[rows[i]] = diag * xx[rows[i]];
121     PetscCall(VecRestoreArrayRead(x, &xx));
122     PetscCall(VecRestoreArray(b, &bb));
123   }
124 
125   PetscCall(MatDenseGetArray(A, &v));
126   for (i = 0; i < N; i++) {
127     slot = v + rows[i] * m;
128     PetscCall(PetscArrayzero(slot, r));
129   }
130   for (i = 0; i < N; i++) {
131     slot = v + rows[i];
132     for (j = 0; j < n; j++) {
133       *slot = 0.0;
134       slot += m;
135     }
136   }
137   if (diag != 0.0) {
138     PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only coded for square matrices");
139     for (i = 0; i < N; i++) {
140       slot  = v + (m + 1) * rows[i];
141       *slot = diag;
142     }
143   }
144   PetscCall(MatDenseRestoreArray(A, &v));
145   PetscFunctionReturn(PETSC_SUCCESS);
146 }
147 
148 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqDense(Mat A, MatType newtype, MatReuse reuse, Mat *newmat)
149 {
150   Mat              B = NULL;
151   Mat_SeqAIJ      *a = (Mat_SeqAIJ *)A->data;
152   Mat_SeqDense    *b;
153   PetscInt        *ai = a->i, *aj = a->j, m = A->rmap->N, n = A->cmap->N, i;
154   const MatScalar *av;
155   PetscBool        isseqdense;
156 
157   PetscFunctionBegin;
158   if (reuse == MAT_REUSE_MATRIX) {
159     PetscCall(PetscObjectTypeCompare((PetscObject)*newmat, MATSEQDENSE, &isseqdense));
160     PetscCheck(isseqdense, PetscObjectComm((PetscObject)*newmat), PETSC_ERR_USER, "Cannot reuse matrix of type %s", ((PetscObject)*newmat)->type_name);
161   }
162   if (reuse != MAT_REUSE_MATRIX) {
163     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
164     PetscCall(MatSetSizes(B, m, n, m, n));
165     PetscCall(MatSetType(B, MATSEQDENSE));
166     PetscCall(MatSeqDenseSetPreallocation(B, NULL));
167     b = (Mat_SeqDense *)B->data;
168   } else {
169     b = (Mat_SeqDense *)((*newmat)->data);
170     for (i = 0; i < n; i++) PetscCall(PetscArrayzero(b->v + i * b->lda, m));
171   }
172   PetscCall(MatSeqAIJGetArrayRead(A, &av));
173   for (i = 0; i < m; i++) {
174     PetscInt j;
175     for (j = 0; j < ai[1] - ai[0]; j++) {
176       b->v[*aj * b->lda + i] = *av;
177       aj++;
178       av++;
179     }
180     ai++;
181   }
182   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
183 
184   if (reuse == MAT_INPLACE_MATRIX) {
185     PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
186     PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
187     PetscCall(MatHeaderReplace(A, &B));
188   } else {
189     if (B) *newmat = B;
190     PetscCall(MatAssemblyBegin(*newmat, MAT_FINAL_ASSEMBLY));
191     PetscCall(MatAssemblyEnd(*newmat, MAT_FINAL_ASSEMBLY));
192   }
193   PetscFunctionReturn(PETSC_SUCCESS);
194 }
195 
196 PETSC_INTERN PetscErrorCode MatConvert_SeqDense_SeqAIJ(Mat A, MatType newtype, MatReuse reuse, Mat *newmat)
197 {
198   Mat           B = NULL;
199   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
200   PetscInt      i, j;
201   PetscInt     *rows, *nnz;
202   MatScalar    *aa = a->v, *vals;
203 
204   PetscFunctionBegin;
205   PetscCall(PetscCalloc3(A->rmap->n, &rows, A->rmap->n, &nnz, A->rmap->n, &vals));
206   if (reuse != MAT_REUSE_MATRIX) {
207     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
208     PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
209     PetscCall(MatSetType(B, MATSEQAIJ));
210     for (j = 0; j < A->cmap->n; j++) {
211       for (i = 0; i < A->rmap->n; i++)
212         if (aa[i] != 0.0 || (i == j && A->cmap->n == A->rmap->n)) ++nnz[i];
213       aa += a->lda;
214     }
215     PetscCall(MatSeqAIJSetPreallocation(B, PETSC_DETERMINE, nnz));
216   } else B = *newmat;
217   aa = a->v;
218   for (j = 0; j < A->cmap->n; j++) {
219     PetscInt numRows = 0;
220     for (i = 0; i < A->rmap->n; i++)
221       if (aa[i] != 0.0 || (i == j && A->cmap->n == A->rmap->n)) {
222         rows[numRows]   = i;
223         vals[numRows++] = aa[i];
224       }
225     PetscCall(MatSetValues(B, numRows, rows, 1, &j, vals, INSERT_VALUES));
226     aa += a->lda;
227   }
228   PetscCall(PetscFree3(rows, nnz, vals));
229   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
230   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
231 
232   if (reuse == MAT_INPLACE_MATRIX) {
233     PetscCall(MatHeaderReplace(A, &B));
234   } else if (reuse != MAT_REUSE_MATRIX) *newmat = B;
235   PetscFunctionReturn(PETSC_SUCCESS);
236 }
237 
238 PetscErrorCode MatAXPY_SeqDense(Mat Y, PetscScalar alpha, Mat X, MatStructure str)
239 {
240   Mat_SeqDense      *x = (Mat_SeqDense *)X->data, *y = (Mat_SeqDense *)Y->data;
241   const PetscScalar *xv;
242   PetscScalar       *yv;
243   PetscBLASInt       N, m, ldax = 0, lday = 0, one = 1;
244 
245   PetscFunctionBegin;
246   PetscCall(MatDenseGetArrayRead(X, &xv));
247   PetscCall(MatDenseGetArray(Y, &yv));
248   PetscCall(PetscBLASIntCast(X->rmap->n * X->cmap->n, &N));
249   PetscCall(PetscBLASIntCast(X->rmap->n, &m));
250   PetscCall(PetscBLASIntCast(x->lda, &ldax));
251   PetscCall(PetscBLASIntCast(y->lda, &lday));
252   if (ldax > m || lday > m) {
253     for (PetscInt j = 0; j < X->cmap->n; j++) PetscCallBLAS("BLASaxpy", BLASaxpy_(&m, &alpha, PetscSafePointerPlusOffset(xv, j * ldax), &one, PetscSafePointerPlusOffset(yv, j * lday), &one));
254   } else {
255     PetscCallBLAS("BLASaxpy", BLASaxpy_(&N, &alpha, xv, &one, yv, &one));
256   }
257   PetscCall(MatDenseRestoreArrayRead(X, &xv));
258   PetscCall(MatDenseRestoreArray(Y, &yv));
259   PetscCall(PetscLogFlops(PetscMax(2.0 * N - 1, 0)));
260   PetscFunctionReturn(PETSC_SUCCESS);
261 }
262 
263 static PetscErrorCode MatGetInfo_SeqDense(Mat A, MatInfoType flag, MatInfo *info)
264 {
265   PetscLogDouble N = A->rmap->n * A->cmap->n;
266 
267   PetscFunctionBegin;
268   info->block_size        = 1.0;
269   info->nz_allocated      = N;
270   info->nz_used           = N;
271   info->nz_unneeded       = 0;
272   info->assemblies        = A->num_ass;
273   info->mallocs           = 0;
274   info->memory            = 0; /* REVIEW ME */
275   info->fill_ratio_given  = 0;
276   info->fill_ratio_needed = 0;
277   info->factor_mallocs    = 0;
278   PetscFunctionReturn(PETSC_SUCCESS);
279 }
280 
281 PetscErrorCode MatScale_SeqDense(Mat A, PetscScalar alpha)
282 {
283   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
284   PetscScalar  *v;
285   PetscBLASInt  one = 1, j, nz, lda = 0;
286 
287   PetscFunctionBegin;
288   PetscCall(MatDenseGetArray(A, &v));
289   PetscCall(PetscBLASIntCast(a->lda, &lda));
290   if (lda > A->rmap->n) {
291     PetscCall(PetscBLASIntCast(A->rmap->n, &nz));
292     for (j = 0; j < A->cmap->n; j++) PetscCallBLAS("BLASscal", BLASscal_(&nz, &alpha, v + j * lda, &one));
293   } else {
294     PetscCall(PetscBLASIntCast(A->rmap->n * A->cmap->n, &nz));
295     PetscCallBLAS("BLASscal", BLASscal_(&nz, &alpha, v, &one));
296   }
297   PetscCall(PetscLogFlops(A->rmap->n * A->cmap->n));
298   PetscCall(MatDenseRestoreArray(A, &v));
299   PetscFunctionReturn(PETSC_SUCCESS);
300 }
301 
302 PetscErrorCode MatShift_SeqDense(Mat A, PetscScalar alpha)
303 {
304   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
305   PetscScalar  *v;
306   PetscInt      j, k;
307 
308   PetscFunctionBegin;
309   PetscCall(MatDenseGetArray(A, &v));
310   k = PetscMin(A->rmap->n, A->cmap->n);
311   for (j = 0; j < k; j++) v[j + j * a->lda] += alpha;
312   PetscCall(PetscLogFlops(k));
313   PetscCall(MatDenseRestoreArray(A, &v));
314   PetscFunctionReturn(PETSC_SUCCESS);
315 }
316 
317 static PetscErrorCode MatIsHermitian_SeqDense(Mat A, PetscReal rtol, PetscBool *fl)
318 {
319   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
320   PetscInt           i, j, m = A->rmap->n, N = a->lda;
321   const PetscScalar *v;
322 
323   PetscFunctionBegin;
324   *fl = PETSC_FALSE;
325   if (A->rmap->n != A->cmap->n) PetscFunctionReturn(PETSC_SUCCESS);
326   PetscCall(MatDenseGetArrayRead(A, &v));
327   for (i = 0; i < m; i++) {
328     for (j = i; j < m; j++) {
329       if (PetscAbsScalar(v[i + j * N] - PetscConj(v[j + i * N])) > rtol) goto restore;
330     }
331   }
332   *fl = PETSC_TRUE;
333 restore:
334   PetscCall(MatDenseRestoreArrayRead(A, &v));
335   PetscFunctionReturn(PETSC_SUCCESS);
336 }
337 
338 static PetscErrorCode MatIsSymmetric_SeqDense(Mat A, PetscReal rtol, PetscBool *fl)
339 {
340   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
341   PetscInt           i, j, m = A->rmap->n, N = a->lda;
342   const PetscScalar *v;
343 
344   PetscFunctionBegin;
345   *fl = PETSC_FALSE;
346   if (A->rmap->n != A->cmap->n) PetscFunctionReturn(PETSC_SUCCESS);
347   PetscCall(MatDenseGetArrayRead(A, &v));
348   for (i = 0; i < m; i++) {
349     for (j = i; j < m; j++) {
350       if (PetscAbsScalar(v[i + j * N] - v[j + i * N]) > rtol) goto restore;
351     }
352   }
353   *fl = PETSC_TRUE;
354 restore:
355   PetscCall(MatDenseRestoreArrayRead(A, &v));
356   PetscFunctionReturn(PETSC_SUCCESS);
357 }
358 
359 PetscErrorCode MatDuplicateNoCreate_SeqDense(Mat newi, Mat A, MatDuplicateOption cpvalues)
360 {
361   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
362   PetscInt      lda = mat->lda, j, m, nlda = lda;
363   PetscBool     isdensecpu;
364 
365   PetscFunctionBegin;
366   PetscCall(PetscLayoutReference(A->rmap, &newi->rmap));
367   PetscCall(PetscLayoutReference(A->cmap, &newi->cmap));
368   if (cpvalues == MAT_SHARE_NONZERO_PATTERN) { /* propagate LDA */
369     PetscCall(MatDenseSetLDA(newi, lda));
370   }
371   PetscCall(PetscObjectTypeCompare((PetscObject)newi, MATSEQDENSE, &isdensecpu));
372   if (isdensecpu) PetscCall(MatSeqDenseSetPreallocation(newi, NULL));
373   if (cpvalues == MAT_COPY_VALUES) {
374     const PetscScalar *av;
375     PetscScalar       *v;
376 
377     PetscCall(MatDenseGetArrayRead(A, &av));
378     PetscCall(MatDenseGetArrayWrite(newi, &v));
379     PetscCall(MatDenseGetLDA(newi, &nlda));
380     m = A->rmap->n;
381     if (lda > m || nlda > m) {
382       for (j = 0; j < A->cmap->n; j++) PetscCall(PetscArraycpy(PetscSafePointerPlusOffset(v, j * nlda), PetscSafePointerPlusOffset(av, j * lda), m));
383     } else {
384       PetscCall(PetscArraycpy(v, av, A->rmap->n * A->cmap->n));
385     }
386     PetscCall(MatDenseRestoreArrayWrite(newi, &v));
387     PetscCall(MatDenseRestoreArrayRead(A, &av));
388     PetscCall(MatPropagateSymmetryOptions(A, newi));
389   }
390   PetscFunctionReturn(PETSC_SUCCESS);
391 }
392 
393 PetscErrorCode MatDuplicate_SeqDense(Mat A, MatDuplicateOption cpvalues, Mat *newmat)
394 {
395   PetscFunctionBegin;
396   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), newmat));
397   PetscCall(MatSetSizes(*newmat, A->rmap->n, A->cmap->n, A->rmap->n, A->cmap->n));
398   PetscCall(MatSetType(*newmat, ((PetscObject)A)->type_name));
399   PetscCall(MatDuplicateNoCreate_SeqDense(*newmat, A, cpvalues));
400   PetscFunctionReturn(PETSC_SUCCESS);
401 }
402 
403 static PetscErrorCode MatSolve_SeqDense_Internal_LU(Mat A, PetscScalar *x, PetscBLASInt ldx, PetscBLASInt m, PetscBLASInt nrhs, PetscBLASInt k, PetscBool T)
404 {
405   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
406   PetscBLASInt  info;
407 
408   PetscFunctionBegin;
409   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
410   PetscCallBLAS("LAPACKgetrs", LAPACKgetrs_(T ? "T" : "N", &m, &nrhs, mat->v, &mat->lda, mat->pivots, x, &m, &info));
411   PetscCall(PetscFPTrapPop());
412   PetscCheck(!info, PETSC_COMM_SELF, PETSC_ERR_LIB, "GETRS - Bad solve %" PetscBLASInt_FMT, info);
413   PetscCall(PetscLogFlops(nrhs * (2.0 * m * m - m)));
414   PetscFunctionReturn(PETSC_SUCCESS);
415 }
416 
417 static PetscErrorCode MatConjugate_SeqDense(Mat);
418 
419 static PetscErrorCode MatSolve_SeqDense_Internal_Cholesky(Mat A, PetscScalar *x, PetscBLASInt ldx, PetscBLASInt m, PetscBLASInt nrhs, PetscBLASInt k, PetscBool T)
420 {
421   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
422   PetscBLASInt  info;
423 
424   PetscFunctionBegin;
425   if (A->spd == PETSC_BOOL3_TRUE) {
426     if (PetscDefined(USE_COMPLEX) && T) PetscCall(MatConjugate_SeqDense(A));
427     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
428     PetscCallBLAS("LAPACKpotrs", LAPACKpotrs_("L", &m, &nrhs, mat->v, &mat->lda, x, &m, &info));
429     PetscCall(PetscFPTrapPop());
430     PetscCheck(!info, PETSC_COMM_SELF, PETSC_ERR_LIB, "POTRS Bad solve %" PetscBLASInt_FMT, info);
431     if (PetscDefined(USE_COMPLEX) && T) PetscCall(MatConjugate_SeqDense(A));
432 #if defined(PETSC_USE_COMPLEX)
433   } else if (A->hermitian == PETSC_BOOL3_TRUE) {
434     if (T) PetscCall(MatConjugate_SeqDense(A));
435     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
436     PetscCallBLAS("LAPACKhetrs", LAPACKhetrs_("L", &m, &nrhs, mat->v, &mat->lda, mat->pivots, x, &m, &info));
437     PetscCall(PetscFPTrapPop());
438     PetscCheck(!info, PETSC_COMM_SELF, PETSC_ERR_LIB, "HETRS Bad solve %" PetscBLASInt_FMT, info);
439     if (T) PetscCall(MatConjugate_SeqDense(A));
440 #endif
441   } else { /* symmetric case */
442     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
443     PetscCallBLAS("LAPACKsytrs", LAPACKsytrs_("L", &m, &nrhs, mat->v, &mat->lda, mat->pivots, x, &m, &info));
444     PetscCall(PetscFPTrapPop());
445     PetscCheck(!info, PETSC_COMM_SELF, PETSC_ERR_LIB, "SYTRS Bad solve %" PetscBLASInt_FMT, info);
446   }
447   PetscCall(PetscLogFlops(nrhs * (2.0 * m * m - m)));
448   PetscFunctionReturn(PETSC_SUCCESS);
449 }
450 
451 static PetscErrorCode MatSolve_SeqDense_Internal_QR(Mat A, PetscScalar *x, PetscBLASInt ldx, PetscBLASInt m, PetscBLASInt nrhs, PetscBLASInt k)
452 {
453   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
454   PetscBLASInt  info;
455   char          trans;
456 
457   PetscFunctionBegin;
458   if (PetscDefined(USE_COMPLEX)) {
459     trans = 'C';
460   } else {
461     trans = 'T';
462   }
463   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
464   { /* lwork depends on the number of right-hand sides */
465     PetscBLASInt nlfwork, lfwork = -1;
466     PetscScalar  fwork;
467 
468     PetscCallBLAS("LAPACKormqr", LAPACKormqr_("L", &trans, &m, &nrhs, &mat->rank, mat->v, &mat->lda, mat->tau, x, &ldx, &fwork, &lfwork, &info));
469     nlfwork = (PetscBLASInt)PetscRealPart(fwork);
470     if (nlfwork > mat->lfwork) {
471       mat->lfwork = nlfwork;
472       PetscCall(PetscFree(mat->fwork));
473       PetscCall(PetscMalloc1(mat->lfwork, &mat->fwork));
474     }
475   }
476   PetscCallBLAS("LAPACKormqr", LAPACKormqr_("L", &trans, &m, &nrhs, &mat->rank, mat->v, &mat->lda, mat->tau, x, &ldx, mat->fwork, &mat->lfwork, &info));
477   PetscCall(PetscFPTrapPop());
478   PetscCheck(!info, PETSC_COMM_SELF, PETSC_ERR_LIB, "ORMQR - Bad orthogonal transform %" PetscBLASInt_FMT, info);
479   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
480   PetscCallBLAS("LAPACKtrtrs", LAPACKtrtrs_("U", "N", "N", &mat->rank, &nrhs, mat->v, &mat->lda, x, &ldx, &info));
481   PetscCall(PetscFPTrapPop());
482   PetscCheck(!info, PETSC_COMM_SELF, PETSC_ERR_LIB, "TRTRS - Bad triangular solve %" PetscBLASInt_FMT, info);
483   for (PetscInt j = 0; j < nrhs; j++) {
484     for (PetscInt i = mat->rank; i < k; i++) x[j * ldx + i] = 0.;
485   }
486   PetscCall(PetscLogFlops(nrhs * (4.0 * m * mat->rank - PetscSqr(mat->rank))));
487   PetscFunctionReturn(PETSC_SUCCESS);
488 }
489 
490 static PetscErrorCode MatSolveTranspose_SeqDense_Internal_QR(Mat A, PetscScalar *x, PetscBLASInt ldx, PetscBLASInt m, PetscBLASInt nrhs, PetscBLASInt k)
491 {
492   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
493   PetscBLASInt  info;
494 
495   PetscFunctionBegin;
496   if (A->rmap->n == A->cmap->n && mat->rank == A->rmap->n) {
497     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
498     PetscCallBLAS("LAPACKtrtrs", LAPACKtrtrs_("U", "T", "N", &m, &nrhs, mat->v, &mat->lda, x, &ldx, &info));
499     PetscCall(PetscFPTrapPop());
500     PetscCheck(!info, PETSC_COMM_SELF, PETSC_ERR_LIB, "TRTRS - Bad triangular solve %" PetscBLASInt_FMT, info);
501     if (PetscDefined(USE_COMPLEX)) PetscCall(MatConjugate_SeqDense(A));
502     { /* lwork depends on the number of right-hand sides */
503       PetscBLASInt nlfwork, lfwork = -1;
504       PetscScalar  fwork;
505 
506       PetscCallBLAS("LAPACKormqr", LAPACKormqr_("L", "N", &m, &nrhs, &mat->rank, mat->v, &mat->lda, mat->tau, x, &ldx, &fwork, &lfwork, &info));
507       nlfwork = (PetscBLASInt)PetscRealPart(fwork);
508       if (nlfwork > mat->lfwork) {
509         mat->lfwork = nlfwork;
510         PetscCall(PetscFree(mat->fwork));
511         PetscCall(PetscMalloc1(mat->lfwork, &mat->fwork));
512       }
513     }
514     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
515     PetscCallBLAS("LAPACKormqr", LAPACKormqr_("L", "N", &m, &nrhs, &mat->rank, mat->v, &mat->lda, mat->tau, x, &ldx, mat->fwork, &mat->lfwork, &info));
516     PetscCall(PetscFPTrapPop());
517     PetscCheck(!info, PETSC_COMM_SELF, PETSC_ERR_LIB, "ORMQR - Bad orthogonal transform %" PetscBLASInt_FMT, info);
518     if (PetscDefined(USE_COMPLEX)) PetscCall(MatConjugate_SeqDense(A));
519   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "QR factored matrix cannot be used for transpose solve");
520   PetscCall(PetscLogFlops(nrhs * (4.0 * m * mat->rank - PetscSqr(mat->rank))));
521   PetscFunctionReturn(PETSC_SUCCESS);
522 }
523 
524 static PetscErrorCode MatSolve_SeqDense_SetUp(Mat A, Vec xx, Vec yy, PetscScalar **_y, PetscBLASInt *_m, PetscBLASInt *_k)
525 {
526   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
527   PetscScalar  *y;
528   PetscBLASInt  m = 0, k = 0;
529 
530   PetscFunctionBegin;
531   PetscCall(PetscBLASIntCast(A->rmap->n, &m));
532   PetscCall(PetscBLASIntCast(A->cmap->n, &k));
533   if (k < m) {
534     PetscCall(VecCopy(xx, mat->qrrhs));
535     PetscCall(VecGetArray(mat->qrrhs, &y));
536   } else {
537     PetscCall(VecCopy(xx, yy));
538     PetscCall(VecGetArray(yy, &y));
539   }
540   *_y = y;
541   *_k = k;
542   *_m = m;
543   PetscFunctionReturn(PETSC_SUCCESS);
544 }
545 
546 static PetscErrorCode MatSolve_SeqDense_TearDown(Mat A, Vec xx, Vec yy, PetscScalar **_y, PetscBLASInt *_m, PetscBLASInt *_k)
547 {
548   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
549   PetscScalar  *y   = NULL;
550   PetscBLASInt  m, k;
551 
552   PetscFunctionBegin;
553   y   = *_y;
554   *_y = NULL;
555   k   = *_k;
556   m   = *_m;
557   if (k < m) {
558     PetscScalar *yv;
559     PetscCall(VecGetArray(yy, &yv));
560     PetscCall(PetscArraycpy(yv, y, k));
561     PetscCall(VecRestoreArray(yy, &yv));
562     PetscCall(VecRestoreArray(mat->qrrhs, &y));
563   } else {
564     PetscCall(VecRestoreArray(yy, &y));
565   }
566   PetscFunctionReturn(PETSC_SUCCESS);
567 }
568 
569 static PetscErrorCode MatSolve_SeqDense_LU(Mat A, Vec xx, Vec yy)
570 {
571   PetscScalar *y = NULL;
572   PetscBLASInt m = 0, k = 0;
573 
574   PetscFunctionBegin;
575   PetscCall(MatSolve_SeqDense_SetUp(A, xx, yy, &y, &m, &k));
576   PetscCall(MatSolve_SeqDense_Internal_LU(A, y, m, m, 1, k, PETSC_FALSE));
577   PetscCall(MatSolve_SeqDense_TearDown(A, xx, yy, &y, &m, &k));
578   PetscFunctionReturn(PETSC_SUCCESS);
579 }
580 
581 static PetscErrorCode MatSolveTranspose_SeqDense_LU(Mat A, Vec xx, Vec yy)
582 {
583   PetscScalar *y = NULL;
584   PetscBLASInt m = 0, k = 0;
585 
586   PetscFunctionBegin;
587   PetscCall(MatSolve_SeqDense_SetUp(A, xx, yy, &y, &m, &k));
588   PetscCall(MatSolve_SeqDense_Internal_LU(A, y, m, m, 1, k, PETSC_TRUE));
589   PetscCall(MatSolve_SeqDense_TearDown(A, xx, yy, &y, &m, &k));
590   PetscFunctionReturn(PETSC_SUCCESS);
591 }
592 
593 static PetscErrorCode MatSolve_SeqDense_Cholesky(Mat A, Vec xx, Vec yy)
594 {
595   PetscScalar *y = NULL;
596   PetscBLASInt m = 0, k = 0;
597 
598   PetscFunctionBegin;
599   PetscCall(MatSolve_SeqDense_SetUp(A, xx, yy, &y, &m, &k));
600   PetscCall(MatSolve_SeqDense_Internal_Cholesky(A, y, m, m, 1, k, PETSC_FALSE));
601   PetscCall(MatSolve_SeqDense_TearDown(A, xx, yy, &y, &m, &k));
602   PetscFunctionReturn(PETSC_SUCCESS);
603 }
604 
605 static PetscErrorCode MatSolveTranspose_SeqDense_Cholesky(Mat A, Vec xx, Vec yy)
606 {
607   PetscScalar *y = NULL;
608   PetscBLASInt m = 0, k = 0;
609 
610   PetscFunctionBegin;
611   PetscCall(MatSolve_SeqDense_SetUp(A, xx, yy, &y, &m, &k));
612   PetscCall(MatSolve_SeqDense_Internal_Cholesky(A, y, m, m, 1, k, PETSC_TRUE));
613   PetscCall(MatSolve_SeqDense_TearDown(A, xx, yy, &y, &m, &k));
614   PetscFunctionReturn(PETSC_SUCCESS);
615 }
616 
617 static PetscErrorCode MatSolve_SeqDense_QR(Mat A, Vec xx, Vec yy)
618 {
619   PetscScalar *y = NULL;
620   PetscBLASInt m = 0, k = 0;
621 
622   PetscFunctionBegin;
623   PetscCall(MatSolve_SeqDense_SetUp(A, xx, yy, &y, &m, &k));
624   PetscCall(MatSolve_SeqDense_Internal_QR(A, y, PetscMax(m, k), m, 1, k));
625   PetscCall(MatSolve_SeqDense_TearDown(A, xx, yy, &y, &m, &k));
626   PetscFunctionReturn(PETSC_SUCCESS);
627 }
628 
629 static PetscErrorCode MatSolveTranspose_SeqDense_QR(Mat A, Vec xx, Vec yy)
630 {
631   PetscScalar *y = NULL;
632   PetscBLASInt m = 0, k = 0;
633 
634   PetscFunctionBegin;
635   PetscCall(MatSolve_SeqDense_SetUp(A, xx, yy, &y, &m, &k));
636   PetscCall(MatSolveTranspose_SeqDense_Internal_QR(A, y, PetscMax(m, k), m, 1, k));
637   PetscCall(MatSolve_SeqDense_TearDown(A, xx, yy, &y, &m, &k));
638   PetscFunctionReturn(PETSC_SUCCESS);
639 }
640 
641 static PetscErrorCode MatMatSolve_SeqDense_SetUp(Mat A, Mat B, Mat X, PetscScalar **_y, PetscBLASInt *_ldy, PetscBLASInt *_m, PetscBLASInt *_nrhs, PetscBLASInt *_k)
642 {
643   const PetscScalar *b;
644   PetscScalar       *y;
645   PetscInt           n, _ldb, _ldx;
646   PetscBLASInt       nrhs = 0, m = 0, k = 0, ldb = 0, ldx = 0, ldy = 0;
647 
648   PetscFunctionBegin;
649   *_ldy  = 0;
650   *_m    = 0;
651   *_nrhs = 0;
652   *_k    = 0;
653   *_y    = NULL;
654   PetscCall(PetscBLASIntCast(A->rmap->n, &m));
655   PetscCall(PetscBLASIntCast(A->cmap->n, &k));
656   PetscCall(MatGetSize(B, NULL, &n));
657   PetscCall(PetscBLASIntCast(n, &nrhs));
658   PetscCall(MatDenseGetLDA(B, &_ldb));
659   PetscCall(PetscBLASIntCast(_ldb, &ldb));
660   PetscCall(MatDenseGetLDA(X, &_ldx));
661   PetscCall(PetscBLASIntCast(_ldx, &ldx));
662   if (ldx < m) {
663     PetscCall(MatDenseGetArrayRead(B, &b));
664     PetscCall(PetscMalloc1(nrhs * m, &y));
665     if (ldb == m) {
666       PetscCall(PetscArraycpy(y, b, ldb * nrhs));
667     } else {
668       for (PetscInt j = 0; j < nrhs; j++) PetscCall(PetscArraycpy(&y[j * m], &b[j * ldb], m));
669     }
670     ldy = m;
671     PetscCall(MatDenseRestoreArrayRead(B, &b));
672   } else {
673     if (ldb == ldx) {
674       PetscCall(MatCopy(B, X, SAME_NONZERO_PATTERN));
675       PetscCall(MatDenseGetArray(X, &y));
676     } else {
677       PetscCall(MatDenseGetArray(X, &y));
678       PetscCall(MatDenseGetArrayRead(B, &b));
679       for (PetscInt j = 0; j < nrhs; j++) PetscCall(PetscArraycpy(&y[j * ldx], &b[j * ldb], m));
680       PetscCall(MatDenseRestoreArrayRead(B, &b));
681     }
682     ldy = ldx;
683   }
684   *_y    = y;
685   *_ldy  = ldy;
686   *_k    = k;
687   *_m    = m;
688   *_nrhs = nrhs;
689   PetscFunctionReturn(PETSC_SUCCESS);
690 }
691 
692 static PetscErrorCode MatMatSolve_SeqDense_TearDown(Mat A, Mat B, Mat X, PetscScalar **_y, PetscBLASInt *_ldy, PetscBLASInt *_m, PetscBLASInt *_nrhs, PetscBLASInt *_k)
693 {
694   PetscScalar *y;
695   PetscInt     _ldx;
696   PetscBLASInt k, ldy, nrhs, ldx = 0;
697 
698   PetscFunctionBegin;
699   y    = *_y;
700   *_y  = NULL;
701   k    = *_k;
702   ldy  = *_ldy;
703   nrhs = *_nrhs;
704   PetscCall(MatDenseGetLDA(X, &_ldx));
705   PetscCall(PetscBLASIntCast(_ldx, &ldx));
706   if (ldx != ldy) {
707     PetscScalar *xv;
708     PetscCall(MatDenseGetArray(X, &xv));
709     for (PetscInt j = 0; j < nrhs; j++) PetscCall(PetscArraycpy(&xv[j * ldx], &y[j * ldy], k));
710     PetscCall(MatDenseRestoreArray(X, &xv));
711     PetscCall(PetscFree(y));
712   } else {
713     PetscCall(MatDenseRestoreArray(X, &y));
714   }
715   PetscFunctionReturn(PETSC_SUCCESS);
716 }
717 
718 static PetscErrorCode MatMatSolve_SeqDense_LU(Mat A, Mat B, Mat X)
719 {
720   PetscScalar *y;
721   PetscBLASInt m, k, ldy, nrhs;
722 
723   PetscFunctionBegin;
724   PetscCall(MatMatSolve_SeqDense_SetUp(A, B, X, &y, &ldy, &m, &nrhs, &k));
725   PetscCall(MatSolve_SeqDense_Internal_LU(A, y, ldy, m, nrhs, k, PETSC_FALSE));
726   PetscCall(MatMatSolve_SeqDense_TearDown(A, B, X, &y, &ldy, &m, &nrhs, &k));
727   PetscFunctionReturn(PETSC_SUCCESS);
728 }
729 
730 static PetscErrorCode MatMatSolveTranspose_SeqDense_LU(Mat A, Mat B, Mat X)
731 {
732   PetscScalar *y;
733   PetscBLASInt m, k, ldy, nrhs;
734 
735   PetscFunctionBegin;
736   PetscCall(MatMatSolve_SeqDense_SetUp(A, B, X, &y, &ldy, &m, &nrhs, &k));
737   PetscCall(MatSolve_SeqDense_Internal_LU(A, y, ldy, m, nrhs, k, PETSC_TRUE));
738   PetscCall(MatMatSolve_SeqDense_TearDown(A, B, X, &y, &ldy, &m, &nrhs, &k));
739   PetscFunctionReturn(PETSC_SUCCESS);
740 }
741 
742 static PetscErrorCode MatMatSolve_SeqDense_Cholesky(Mat A, Mat B, Mat X)
743 {
744   PetscScalar *y;
745   PetscBLASInt m, k, ldy, nrhs;
746 
747   PetscFunctionBegin;
748   PetscCall(MatMatSolve_SeqDense_SetUp(A, B, X, &y, &ldy, &m, &nrhs, &k));
749   PetscCall(MatSolve_SeqDense_Internal_Cholesky(A, y, ldy, m, nrhs, k, PETSC_FALSE));
750   PetscCall(MatMatSolve_SeqDense_TearDown(A, B, X, &y, &ldy, &m, &nrhs, &k));
751   PetscFunctionReturn(PETSC_SUCCESS);
752 }
753 
754 static PetscErrorCode MatMatSolveTranspose_SeqDense_Cholesky(Mat A, Mat B, Mat X)
755 {
756   PetscScalar *y;
757   PetscBLASInt m, k, ldy, nrhs;
758 
759   PetscFunctionBegin;
760   PetscCall(MatMatSolve_SeqDense_SetUp(A, B, X, &y, &ldy, &m, &nrhs, &k));
761   PetscCall(MatSolve_SeqDense_Internal_Cholesky(A, y, ldy, m, nrhs, k, PETSC_TRUE));
762   PetscCall(MatMatSolve_SeqDense_TearDown(A, B, X, &y, &ldy, &m, &nrhs, &k));
763   PetscFunctionReturn(PETSC_SUCCESS);
764 }
765 
766 static PetscErrorCode MatMatSolve_SeqDense_QR(Mat A, Mat B, Mat X)
767 {
768   PetscScalar *y;
769   PetscBLASInt m, k, ldy, nrhs;
770 
771   PetscFunctionBegin;
772   PetscCall(MatMatSolve_SeqDense_SetUp(A, B, X, &y, &ldy, &m, &nrhs, &k));
773   PetscCall(MatSolve_SeqDense_Internal_QR(A, y, ldy, m, nrhs, k));
774   PetscCall(MatMatSolve_SeqDense_TearDown(A, B, X, &y, &ldy, &m, &nrhs, &k));
775   PetscFunctionReturn(PETSC_SUCCESS);
776 }
777 
778 static PetscErrorCode MatMatSolveTranspose_SeqDense_QR(Mat A, Mat B, Mat X)
779 {
780   PetscScalar *y;
781   PetscBLASInt m, k, ldy, nrhs;
782 
783   PetscFunctionBegin;
784   PetscCall(MatMatSolve_SeqDense_SetUp(A, B, X, &y, &ldy, &m, &nrhs, &k));
785   PetscCall(MatSolveTranspose_SeqDense_Internal_QR(A, y, ldy, m, nrhs, k));
786   PetscCall(MatMatSolve_SeqDense_TearDown(A, B, X, &y, &ldy, &m, &nrhs, &k));
787   PetscFunctionReturn(PETSC_SUCCESS);
788 }
789 
790 /* COMMENT: I have chosen to hide row permutation in the pivots,
791    rather than put it in the Mat->row slot.*/
792 PetscErrorCode MatLUFactor_SeqDense(Mat A, IS row, IS col, const MatFactorInfo *minfo)
793 {
794   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
795   PetscBLASInt  n, m, info;
796 
797   PetscFunctionBegin;
798   PetscCall(PetscBLASIntCast(A->cmap->n, &n));
799   PetscCall(PetscBLASIntCast(A->rmap->n, &m));
800   if (!mat->pivots) { PetscCall(PetscMalloc1(A->rmap->n, &mat->pivots)); }
801   if (!A->rmap->n || !A->cmap->n) PetscFunctionReturn(PETSC_SUCCESS);
802   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
803   PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&m, &n, mat->v, &mat->lda, mat->pivots, &info));
804   PetscCall(PetscFPTrapPop());
805 
806   PetscCheck(info >= 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to LU factorization %" PetscBLASInt_FMT, info);
807   PetscCheck(info <= 0, PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Bad LU factorization %" PetscBLASInt_FMT, info);
808 
809   A->ops->solve             = MatSolve_SeqDense_LU;
810   A->ops->matsolve          = MatMatSolve_SeqDense_LU;
811   A->ops->solvetranspose    = MatSolveTranspose_SeqDense_LU;
812   A->ops->matsolvetranspose = MatMatSolveTranspose_SeqDense_LU;
813   A->factortype             = MAT_FACTOR_LU;
814 
815   PetscCall(PetscFree(A->solvertype));
816   PetscCall(PetscStrallocpy(MATSOLVERPETSC, &A->solvertype));
817 
818   PetscCall(PetscLogFlops((2.0 * A->cmap->n * A->cmap->n * A->cmap->n) / 3));
819   PetscFunctionReturn(PETSC_SUCCESS);
820 }
821 
822 static PetscErrorCode MatLUFactorNumeric_SeqDense(Mat fact, Mat A, const MatFactorInfo *info_dummy)
823 {
824   MatFactorInfo info;
825 
826   PetscFunctionBegin;
827   PetscCall(MatDuplicateNoCreate_SeqDense(fact, A, MAT_COPY_VALUES));
828   PetscUseTypeMethod(fact, lufactor, NULL, NULL, &info);
829   PetscFunctionReturn(PETSC_SUCCESS);
830 }
831 
832 PetscErrorCode MatLUFactorSymbolic_SeqDense(Mat fact, Mat A, IS row, IS col, const MatFactorInfo *info)
833 {
834   PetscFunctionBegin;
835   fact->preallocated         = PETSC_TRUE;
836   fact->assembled            = PETSC_TRUE;
837   fact->ops->lufactornumeric = MatLUFactorNumeric_SeqDense;
838   PetscFunctionReturn(PETSC_SUCCESS);
839 }
840 
841 /* Cholesky as L*L^T or L*D*L^T and the symmetric/hermitian complex variants */
842 PetscErrorCode MatCholeskyFactor_SeqDense(Mat A, IS perm, const MatFactorInfo *factinfo)
843 {
844   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
845   PetscBLASInt  info, n;
846 
847   PetscFunctionBegin;
848   PetscCall(PetscBLASIntCast(A->cmap->n, &n));
849   if (!A->rmap->n || !A->cmap->n) PetscFunctionReturn(PETSC_SUCCESS);
850   if (A->spd == PETSC_BOOL3_TRUE) {
851     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
852     PetscCallBLAS("LAPACKpotrf", LAPACKpotrf_("L", &n, mat->v, &mat->lda, &info));
853     PetscCall(PetscFPTrapPop());
854 #if defined(PETSC_USE_COMPLEX)
855   } else if (A->hermitian == PETSC_BOOL3_TRUE) {
856     if (!mat->pivots) { PetscCall(PetscMalloc1(A->rmap->n, &mat->pivots)); }
857     if (!mat->fwork) {
858       PetscScalar dummy;
859 
860       mat->lfwork = -1;
861       PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
862       PetscCallBLAS("LAPACKhetrf", LAPACKhetrf_("L", &n, mat->v, &mat->lda, mat->pivots, &dummy, &mat->lfwork, &info));
863       PetscCall(PetscFPTrapPop());
864       PetscCall(PetscBLASIntCast((PetscCount)(PetscRealPart(dummy)), &mat->lfwork));
865       PetscCall(PetscMalloc1(mat->lfwork, &mat->fwork));
866     }
867     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
868     PetscCallBLAS("LAPACKhetrf", LAPACKhetrf_("L", &n, mat->v, &mat->lda, mat->pivots, mat->fwork, &mat->lfwork, &info));
869     PetscCall(PetscFPTrapPop());
870 #endif
871   } else { /* symmetric case */
872     if (!mat->pivots) { PetscCall(PetscMalloc1(A->rmap->n, &mat->pivots)); }
873     if (!mat->fwork) {
874       PetscScalar dummy;
875 
876       mat->lfwork = -1;
877       PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
878       PetscCallBLAS("LAPACKsytrf", LAPACKsytrf_("L", &n, mat->v, &mat->lda, mat->pivots, &dummy, &mat->lfwork, &info));
879       PetscCall(PetscFPTrapPop());
880       PetscCall(PetscBLASIntCast((PetscCount)(PetscRealPart(dummy)), &mat->lfwork));
881       PetscCall(PetscMalloc1(mat->lfwork, &mat->fwork));
882     }
883     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
884     PetscCallBLAS("LAPACKsytrf", LAPACKsytrf_("L", &n, mat->v, &mat->lda, mat->pivots, mat->fwork, &mat->lfwork, &info));
885     PetscCall(PetscFPTrapPop());
886   }
887   PetscCheck(!info, PETSC_COMM_SELF, PETSC_ERR_MAT_CH_ZRPVT, "Bad factorization: zero pivot in row %" PetscBLASInt_FMT, info - 1);
888 
889   A->ops->solve             = MatSolve_SeqDense_Cholesky;
890   A->ops->matsolve          = MatMatSolve_SeqDense_Cholesky;
891   A->ops->solvetranspose    = MatSolveTranspose_SeqDense_Cholesky;
892   A->ops->matsolvetranspose = MatMatSolveTranspose_SeqDense_Cholesky;
893   A->factortype             = MAT_FACTOR_CHOLESKY;
894 
895   PetscCall(PetscFree(A->solvertype));
896   PetscCall(PetscStrallocpy(MATSOLVERPETSC, &A->solvertype));
897 
898   PetscCall(PetscLogFlops((1.0 * A->cmap->n * A->cmap->n * A->cmap->n) / 3.0));
899   PetscFunctionReturn(PETSC_SUCCESS);
900 }
901 
902 static PetscErrorCode MatCholeskyFactorNumeric_SeqDense(Mat fact, Mat A, const MatFactorInfo *info_dummy)
903 {
904   MatFactorInfo info;
905 
906   PetscFunctionBegin;
907   info.fill = 1.0;
908 
909   PetscCall(MatDuplicateNoCreate_SeqDense(fact, A, MAT_COPY_VALUES));
910   PetscUseTypeMethod(fact, choleskyfactor, NULL, &info);
911   PetscFunctionReturn(PETSC_SUCCESS);
912 }
913 
914 PetscErrorCode MatCholeskyFactorSymbolic_SeqDense(Mat fact, Mat A, IS row, const MatFactorInfo *info)
915 {
916   PetscFunctionBegin;
917   fact->assembled                  = PETSC_TRUE;
918   fact->preallocated               = PETSC_TRUE;
919   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqDense;
920   PetscFunctionReturn(PETSC_SUCCESS);
921 }
922 
923 PetscErrorCode MatQRFactor_SeqDense(Mat A, IS col, const MatFactorInfo *minfo)
924 {
925   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
926   PetscBLASInt  n, m, info, min, max;
927 
928   PetscFunctionBegin;
929   PetscCall(PetscBLASIntCast(A->cmap->n, &n));
930   PetscCall(PetscBLASIntCast(A->rmap->n, &m));
931   max = PetscMax(m, n);
932   min = PetscMin(m, n);
933   if (!mat->tau) { PetscCall(PetscMalloc1(min, &mat->tau)); }
934   if (!mat->pivots) { PetscCall(PetscMalloc1(n, &mat->pivots)); }
935   if (!mat->qrrhs) PetscCall(MatCreateVecs(A, NULL, &mat->qrrhs));
936   if (!A->rmap->n || !A->cmap->n) PetscFunctionReturn(PETSC_SUCCESS);
937   if (!mat->fwork) {
938     PetscScalar dummy;
939 
940     mat->lfwork = -1;
941     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
942     PetscCallBLAS("LAPACKgeqrf", LAPACKgeqrf_(&m, &n, mat->v, &mat->lda, mat->tau, &dummy, &mat->lfwork, &info));
943     PetscCall(PetscFPTrapPop());
944     PetscCall(PetscBLASIntCast((PetscCount)(PetscRealPart(dummy)), &mat->lfwork));
945     PetscCall(PetscMalloc1(mat->lfwork, &mat->fwork));
946   }
947   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
948   PetscCallBLAS("LAPACKgeqrf", LAPACKgeqrf_(&m, &n, mat->v, &mat->lda, mat->tau, mat->fwork, &mat->lfwork, &info));
949   PetscCall(PetscFPTrapPop());
950   PetscCheck(!info, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to QR factorization %" PetscBLASInt_FMT, info);
951   // TODO: try to estimate rank or test for and use geqp3 for rank revealing QR.  For now just say rank is min of m and n
952   mat->rank = min;
953 
954   A->ops->solve    = MatSolve_SeqDense_QR;
955   A->ops->matsolve = MatMatSolve_SeqDense_QR;
956   A->factortype    = MAT_FACTOR_QR;
957   if (m == n) {
958     A->ops->solvetranspose    = MatSolveTranspose_SeqDense_QR;
959     A->ops->matsolvetranspose = MatMatSolveTranspose_SeqDense_QR;
960   }
961 
962   PetscCall(PetscFree(A->solvertype));
963   PetscCall(PetscStrallocpy(MATSOLVERPETSC, &A->solvertype));
964 
965   PetscCall(PetscLogFlops(2.0 * min * min * (max - min / 3.0)));
966   PetscFunctionReturn(PETSC_SUCCESS);
967 }
968 
969 static PetscErrorCode MatQRFactorNumeric_SeqDense(Mat fact, Mat A, const MatFactorInfo *info_dummy)
970 {
971   MatFactorInfo info;
972 
973   PetscFunctionBegin;
974   info.fill = 1.0;
975 
976   PetscCall(MatDuplicateNoCreate_SeqDense(fact, A, MAT_COPY_VALUES));
977   PetscUseMethod(fact, "MatQRFactor_C", (Mat, IS, const MatFactorInfo *), (fact, NULL, &info));
978   PetscFunctionReturn(PETSC_SUCCESS);
979 }
980 
981 PetscErrorCode MatQRFactorSymbolic_SeqDense(Mat fact, Mat A, IS row, const MatFactorInfo *info)
982 {
983   PetscFunctionBegin;
984   fact->assembled    = PETSC_TRUE;
985   fact->preallocated = PETSC_TRUE;
986   PetscCall(PetscObjectComposeFunction((PetscObject)fact, "MatQRFactorNumeric_C", MatQRFactorNumeric_SeqDense));
987   PetscFunctionReturn(PETSC_SUCCESS);
988 }
989 
990 /* uses LAPACK */
991 PETSC_INTERN PetscErrorCode MatGetFactor_seqdense_petsc(Mat A, MatFactorType ftype, Mat *fact)
992 {
993   PetscFunctionBegin;
994   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), fact));
995   PetscCall(MatSetSizes(*fact, A->rmap->n, A->cmap->n, A->rmap->n, A->cmap->n));
996   PetscCall(MatSetType(*fact, MATDENSE));
997   (*fact)->trivialsymbolic = PETSC_TRUE;
998   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU) {
999     (*fact)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqDense;
1000     (*fact)->ops->ilufactorsymbolic = MatLUFactorSymbolic_SeqDense;
1001   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
1002     (*fact)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqDense;
1003   } else if (ftype == MAT_FACTOR_QR) {
1004     PetscCall(PetscObjectComposeFunction((PetscObject)*fact, "MatQRFactorSymbolic_C", MatQRFactorSymbolic_SeqDense));
1005   }
1006   (*fact)->factortype = ftype;
1007 
1008   PetscCall(PetscFree((*fact)->solvertype));
1009   PetscCall(PetscStrallocpy(MATSOLVERPETSC, &(*fact)->solvertype));
1010   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&(*fact)->preferredordering[MAT_FACTOR_LU]));
1011   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&(*fact)->preferredordering[MAT_FACTOR_ILU]));
1012   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&(*fact)->preferredordering[MAT_FACTOR_CHOLESKY]));
1013   PetscCall(PetscStrallocpy(MATORDERINGEXTERNAL, (char **)&(*fact)->preferredordering[MAT_FACTOR_ICC]));
1014   PetscFunctionReturn(PETSC_SUCCESS);
1015 }
1016 
1017 static PetscErrorCode MatSOR_SeqDense(Mat A, Vec bb, PetscReal omega, MatSORType flag, PetscReal shift, PetscInt its, PetscInt lits, Vec xx)
1018 {
1019   Mat_SeqDense      *mat = (Mat_SeqDense *)A->data;
1020   PetscScalar       *x, *v = mat->v, zero = 0.0, xt;
1021   const PetscScalar *b;
1022   PetscInt           m = A->rmap->n, i;
1023   PetscBLASInt       o = 1, bm = 0;
1024 
1025   PetscFunctionBegin;
1026 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
1027   PetscCheck(A->offloadmask != PETSC_OFFLOAD_GPU, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented");
1028 #endif
1029   if (shift == -1) shift = 0.0; /* negative shift indicates do not error on zero diagonal; this code never zeros on zero diagonal */
1030   PetscCall(PetscBLASIntCast(m, &bm));
1031   if (flag & SOR_ZERO_INITIAL_GUESS) {
1032     /* this is a hack fix, should have another version without the second BLASdotu */
1033     PetscCall(VecSet(xx, zero));
1034   }
1035   PetscCall(VecGetArray(xx, &x));
1036   PetscCall(VecGetArrayRead(bb, &b));
1037   its = its * lits;
1038   PetscCheck(its > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Relaxation requires global its %" PetscInt_FMT " and local its %" PetscInt_FMT " both positive", its, lits);
1039   while (its--) {
1040     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1041       for (i = 0; i < m; i++) {
1042         PetscCallBLAS("BLASdotu", xt = b[i] - BLASdotu_(&bm, v + i, &bm, x, &o));
1043         x[i] = (1. - omega) * x[i] + omega * (xt + v[i + i * m] * x[i]) / (v[i + i * m] + shift);
1044       }
1045     }
1046     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1047       for (i = m - 1; i >= 0; i--) {
1048         PetscCallBLAS("BLASdotu", xt = b[i] - BLASdotu_(&bm, v + i, &bm, x, &o));
1049         x[i] = (1. - omega) * x[i] + omega * (xt + v[i + i * m] * x[i]) / (v[i + i * m] + shift);
1050       }
1051     }
1052   }
1053   PetscCall(VecRestoreArrayRead(bb, &b));
1054   PetscCall(VecRestoreArray(xx, &x));
1055   PetscFunctionReturn(PETSC_SUCCESS);
1056 }
1057 
1058 static PetscErrorCode MatMultColumnRangeKernel_SeqDense(Mat A, Vec xx, Vec yy, PetscInt c_start, PetscInt c_end, PetscBool trans, PetscBool herm)
1059 {
1060   Mat_SeqDense      *mat = (Mat_SeqDense *)A->data;
1061   PetscScalar       *y, _DOne = 1.0, _DZero = 0.0;
1062   PetscBLASInt       m, n, _One             = 1;
1063   const PetscScalar *v = mat->v, *x;
1064 
1065   PetscFunctionBegin;
1066   PetscCall(PetscBLASIntCast(A->rmap->n, &m));
1067   PetscCall(PetscBLASIntCast(c_end - c_start, &n));
1068   PetscCall(VecGetArrayRead(xx, &x));
1069   PetscCall(VecGetArrayWrite(yy, &y));
1070   if (!m || !n) {
1071     PetscBLASInt i;
1072     if (trans)
1073       for (i = 0; i < n; i++) y[i] = 0.0;
1074     else
1075       for (i = 0; i < m; i++) y[i] = 0.0;
1076   } else {
1077     if (trans) {
1078       if (herm) PetscCallBLAS("BLASgemv", BLASgemv_("C", &m, &n, &_DOne, v + c_start * mat->lda, &mat->lda, x, &_One, &_DZero, y + c_start, &_One));
1079       else PetscCallBLAS("BLASgemv", BLASgemv_("T", &m, &n, &_DOne, v + c_start * mat->lda, &mat->lda, x, &_One, &_DZero, y + c_start, &_One));
1080     } else {
1081       PetscCallBLAS("BLASgemv", BLASgemv_("N", &m, &n, &_DOne, v + c_start * mat->lda, &mat->lda, x + c_start, &_One, &_DZero, y, &_One));
1082     }
1083     PetscCall(PetscLogFlops(2.0 * m * n - n));
1084   }
1085   PetscCall(VecRestoreArrayRead(xx, &x));
1086   PetscCall(VecRestoreArrayWrite(yy, &y));
1087   PetscFunctionReturn(PETSC_SUCCESS);
1088 }
1089 
1090 PetscErrorCode MatMultHermitianTransposeColumnRange_SeqDense(Mat A, Vec xx, Vec yy, PetscInt c_start, PetscInt c_end)
1091 {
1092   PetscFunctionBegin;
1093   PetscCall(MatMultColumnRangeKernel_SeqDense(A, xx, yy, c_start, c_end, PETSC_TRUE, PETSC_TRUE));
1094   PetscFunctionReturn(PETSC_SUCCESS);
1095 }
1096 
1097 PetscErrorCode MatMult_SeqDense(Mat A, Vec xx, Vec yy)
1098 {
1099   PetscFunctionBegin;
1100   PetscCall(MatMultColumnRangeKernel_SeqDense(A, xx, yy, 0, A->cmap->n, PETSC_FALSE, PETSC_FALSE));
1101   PetscFunctionReturn(PETSC_SUCCESS);
1102 }
1103 
1104 PetscErrorCode MatMultTranspose_SeqDense(Mat A, Vec xx, Vec yy)
1105 {
1106   PetscFunctionBegin;
1107   PetscCall(MatMultColumnRangeKernel_SeqDense(A, xx, yy, 0, A->cmap->n, PETSC_TRUE, PETSC_FALSE));
1108   PetscFunctionReturn(PETSC_SUCCESS);
1109 }
1110 
1111 PetscErrorCode MatMultHermitianTranspose_SeqDense(Mat A, Vec xx, Vec yy)
1112 {
1113   PetscFunctionBegin;
1114   PetscCall(MatMultColumnRangeKernel_SeqDense(A, xx, yy, 0, A->cmap->n, PETSC_TRUE, PETSC_TRUE));
1115   PetscFunctionReturn(PETSC_SUCCESS);
1116 }
1117 
1118 static PetscErrorCode MatMultAddColumnRangeKernel_SeqDense(Mat A, Vec xx, Vec zz, Vec yy, PetscInt c_start, PetscInt c_end, PetscBool trans, PetscBool herm)
1119 {
1120   Mat_SeqDense      *mat = (Mat_SeqDense *)A->data;
1121   const PetscScalar *v   = mat->v, *x;
1122   PetscScalar       *y, _DOne = 1.0;
1123   PetscBLASInt       m, n, _One = 1;
1124 
1125   PetscFunctionBegin;
1126   PetscCall(PetscBLASIntCast(A->rmap->n, &m));
1127   PetscCall(PetscBLASIntCast(c_end - c_start, &n));
1128   PetscCall(VecCopy(zz, yy));
1129   if (!m || !n) PetscFunctionReturn(PETSC_SUCCESS);
1130   PetscCall(VecGetArray(yy, &y));
1131   PetscCall(VecGetArrayRead(xx, &x));
1132   if (trans) {
1133     if (herm) PetscCallBLAS("BLASgemv", BLASgemv_("C", &m, &n, &_DOne, v + c_start * mat->lda, &mat->lda, x, &_One, &_DOne, y + c_start, &_One));
1134     else PetscCallBLAS("BLASgemv", BLASgemv_("T", &m, &n, &_DOne, v + c_start * mat->lda, &mat->lda, x, &_One, &_DOne, y + c_start, &_One));
1135   } else {
1136     PetscCallBLAS("BLASgemv", BLASgemv_("N", &m, &n, &_DOne, v + c_start * mat->lda, &mat->lda, x + c_start, &_One, &_DOne, y, &_One));
1137   }
1138   PetscCall(VecRestoreArrayRead(xx, &x));
1139   PetscCall(VecRestoreArray(yy, &y));
1140   PetscCall(PetscLogFlops(2.0 * m * n));
1141   PetscFunctionReturn(PETSC_SUCCESS);
1142 }
1143 
1144 PetscErrorCode MatMultAddColumnRange_SeqDense(Mat A, Vec xx, Vec zz, Vec yy, PetscInt c_start, PetscInt c_end)
1145 {
1146   PetscFunctionBegin;
1147   PetscCall(MatMultAddColumnRangeKernel_SeqDense(A, xx, zz, yy, c_start, c_end, PETSC_FALSE, PETSC_FALSE));
1148   PetscFunctionReturn(PETSC_SUCCESS);
1149 }
1150 
1151 PetscErrorCode MatMultHermitianTransposeAddColumnRange_SeqDense(Mat A, Vec xx, Vec zz, Vec yy, PetscInt c_start, PetscInt c_end)
1152 {
1153   PetscFunctionBegin;
1154   PetscMPIInt rank;
1155   PetscCallMPI(MPI_Comm_rank(MPI_COMM_WORLD, &rank));
1156   PetscCall(MatMultAddColumnRangeKernel_SeqDense(A, xx, zz, yy, c_start, c_end, PETSC_TRUE, PETSC_TRUE));
1157   PetscFunctionReturn(PETSC_SUCCESS);
1158 }
1159 
1160 PetscErrorCode MatMultAdd_SeqDense(Mat A, Vec xx, Vec zz, Vec yy)
1161 {
1162   PetscFunctionBegin;
1163   PetscCall(MatMultAddColumnRangeKernel_SeqDense(A, xx, zz, yy, 0, A->cmap->n, PETSC_FALSE, PETSC_FALSE));
1164   PetscFunctionReturn(PETSC_SUCCESS);
1165 }
1166 
1167 PetscErrorCode MatMultTransposeAdd_SeqDense(Mat A, Vec xx, Vec zz, Vec yy)
1168 {
1169   PetscFunctionBegin;
1170   PetscCall(MatMultAddColumnRangeKernel_SeqDense(A, xx, zz, yy, 0, A->cmap->n, PETSC_TRUE, PETSC_FALSE));
1171   PetscFunctionReturn(PETSC_SUCCESS);
1172 }
1173 
1174 PetscErrorCode MatMultHermitianTransposeAdd_SeqDense(Mat A, Vec xx, Vec zz, Vec yy)
1175 {
1176   PetscFunctionBegin;
1177   PetscCall(MatMultAddColumnRangeKernel_SeqDense(A, xx, zz, yy, 0, A->cmap->n, PETSC_TRUE, PETSC_TRUE));
1178   PetscFunctionReturn(PETSC_SUCCESS);
1179 }
1180 
1181 static PetscErrorCode MatGetRow_SeqDense(Mat A, PetscInt row, PetscInt *ncols, PetscInt **cols, PetscScalar **vals)
1182 {
1183   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
1184   PetscInt      i;
1185 
1186   PetscFunctionBegin;
1187   if (ncols) *ncols = A->cmap->n;
1188   if (cols) {
1189     PetscCall(PetscMalloc1(A->cmap->n, cols));
1190     for (i = 0; i < A->cmap->n; i++) (*cols)[i] = i;
1191   }
1192   if (vals) {
1193     const PetscScalar *v;
1194 
1195     PetscCall(MatDenseGetArrayRead(A, &v));
1196     PetscCall(PetscMalloc1(A->cmap->n, vals));
1197     v += row;
1198     for (i = 0; i < A->cmap->n; i++) {
1199       (*vals)[i] = *v;
1200       v += mat->lda;
1201     }
1202     PetscCall(MatDenseRestoreArrayRead(A, &v));
1203   }
1204   PetscFunctionReturn(PETSC_SUCCESS);
1205 }
1206 
1207 static PetscErrorCode MatRestoreRow_SeqDense(Mat A, PetscInt row, PetscInt *ncols, PetscInt **cols, PetscScalar **vals)
1208 {
1209   PetscFunctionBegin;
1210   if (cols) PetscCall(PetscFree(*cols));
1211   if (vals) PetscCall(PetscFree(*vals));
1212   PetscFunctionReturn(PETSC_SUCCESS);
1213 }
1214 
1215 static PetscErrorCode MatSetValues_SeqDense(Mat A, PetscInt m, const PetscInt indexm[], PetscInt n, const PetscInt indexn[], const PetscScalar v[], InsertMode addv)
1216 {
1217   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
1218   PetscScalar  *av;
1219   PetscInt      i, j, idx = 0;
1220 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
1221   PetscOffloadMask oldf;
1222 #endif
1223 
1224   PetscFunctionBegin;
1225   PetscCall(MatDenseGetArray(A, &av));
1226   if (!mat->roworiented) {
1227     if (addv == INSERT_VALUES) {
1228       for (j = 0; j < n; j++) {
1229         if (indexn[j] < 0) {
1230           idx += m;
1231           continue;
1232         }
1233         PetscCheck(indexn[j] < A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, indexn[j], A->cmap->n - 1);
1234         for (i = 0; i < m; i++) {
1235           if (indexm[i] < 0) {
1236             idx++;
1237             continue;
1238           }
1239           PetscCheck(indexm[i] < A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, indexm[i], A->rmap->n - 1);
1240           av[indexn[j] * mat->lda + indexm[i]] = v ? v[idx++] : (idx++, 0.0);
1241         }
1242       }
1243     } else {
1244       for (j = 0; j < n; j++) {
1245         if (indexn[j] < 0) {
1246           idx += m;
1247           continue;
1248         }
1249         PetscCheck(indexn[j] < A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, indexn[j], A->cmap->n - 1);
1250         for (i = 0; i < m; i++) {
1251           if (indexm[i] < 0) {
1252             idx++;
1253             continue;
1254           }
1255           PetscCheck(indexm[i] < A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, indexm[i], A->rmap->n - 1);
1256           av[indexn[j] * mat->lda + indexm[i]] += v ? v[idx++] : (idx++, 0.0);
1257         }
1258       }
1259     }
1260   } else {
1261     if (addv == INSERT_VALUES) {
1262       for (i = 0; i < m; i++) {
1263         if (indexm[i] < 0) {
1264           idx += n;
1265           continue;
1266         }
1267         PetscCheck(indexm[i] < A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, indexm[i], A->rmap->n - 1);
1268         for (j = 0; j < n; j++) {
1269           if (indexn[j] < 0) {
1270             idx++;
1271             continue;
1272           }
1273           PetscCheck(indexn[j] < A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, indexn[j], A->cmap->n - 1);
1274           av[indexn[j] * mat->lda + indexm[i]] = v ? v[idx++] : (idx++, 0.0);
1275         }
1276       }
1277     } else {
1278       for (i = 0; i < m; i++) {
1279         if (indexm[i] < 0) {
1280           idx += n;
1281           continue;
1282         }
1283         PetscCheck(indexm[i] < A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, indexm[i], A->rmap->n - 1);
1284         for (j = 0; j < n; j++) {
1285           if (indexn[j] < 0) {
1286             idx++;
1287             continue;
1288           }
1289           PetscCheck(indexn[j] < A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, indexn[j], A->cmap->n - 1);
1290           av[indexn[j] * mat->lda + indexm[i]] += v ? v[idx++] : (idx++, 0.0);
1291         }
1292       }
1293     }
1294   }
1295   /* hack to prevent unneeded copy to the GPU while returning the array */
1296 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
1297   oldf           = A->offloadmask;
1298   A->offloadmask = PETSC_OFFLOAD_GPU;
1299 #endif
1300   PetscCall(MatDenseRestoreArray(A, &av));
1301 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
1302   A->offloadmask = (oldf == PETSC_OFFLOAD_UNALLOCATED ? PETSC_OFFLOAD_UNALLOCATED : PETSC_OFFLOAD_CPU);
1303 #endif
1304   PetscFunctionReturn(PETSC_SUCCESS);
1305 }
1306 
1307 static PetscErrorCode MatGetValues_SeqDense(Mat A, PetscInt m, const PetscInt indexm[], PetscInt n, const PetscInt indexn[], PetscScalar v[])
1308 {
1309   Mat_SeqDense      *mat = (Mat_SeqDense *)A->data;
1310   const PetscScalar *vv;
1311   PetscInt           i, j;
1312 
1313   PetscFunctionBegin;
1314   PetscCall(MatDenseGetArrayRead(A, &vv));
1315   /* row-oriented output */
1316   for (i = 0; i < m; i++) {
1317     if (indexm[i] < 0) {
1318       v += n;
1319       continue;
1320     }
1321     PetscCheck(indexm[i] < A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row %" PetscInt_FMT " requested larger than number rows %" PetscInt_FMT, indexm[i], A->rmap->n);
1322     for (j = 0; j < n; j++) {
1323       if (indexn[j] < 0) {
1324         v++;
1325         continue;
1326       }
1327       PetscCheck(indexn[j] < A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column %" PetscInt_FMT " requested larger than number columns %" PetscInt_FMT, indexn[j], A->cmap->n);
1328       *v++ = vv[indexn[j] * mat->lda + indexm[i]];
1329     }
1330   }
1331   PetscCall(MatDenseRestoreArrayRead(A, &vv));
1332   PetscFunctionReturn(PETSC_SUCCESS);
1333 }
1334 
1335 PetscErrorCode MatView_Dense_Binary(Mat mat, PetscViewer viewer)
1336 {
1337   PetscBool          skipHeader;
1338   PetscViewerFormat  format;
1339   PetscInt           header[4], M, N, m, lda, i, j;
1340   PetscCount         k;
1341   const PetscScalar *v;
1342   PetscScalar       *vwork;
1343 
1344   PetscFunctionBegin;
1345   PetscCall(PetscViewerSetUp(viewer));
1346   PetscCall(PetscViewerBinaryGetSkipHeader(viewer, &skipHeader));
1347   PetscCall(PetscViewerGetFormat(viewer, &format));
1348   if (skipHeader) format = PETSC_VIEWER_NATIVE;
1349 
1350   PetscCall(MatGetSize(mat, &M, &N));
1351 
1352   /* write matrix header */
1353   header[0] = MAT_FILE_CLASSID;
1354   header[1] = M;
1355   header[2] = N;
1356   header[3] = (format == PETSC_VIEWER_NATIVE) ? MATRIX_BINARY_FORMAT_DENSE : M * N;
1357   if (!skipHeader) PetscCall(PetscViewerBinaryWrite(viewer, header, 4, PETSC_INT));
1358 
1359   PetscCall(MatGetLocalSize(mat, &m, NULL));
1360   if (format != PETSC_VIEWER_NATIVE) {
1361     PetscInt nnz = m * N, *iwork;
1362     /* store row lengths for each row */
1363     PetscCall(PetscMalloc1(nnz, &iwork));
1364     for (i = 0; i < m; i++) iwork[i] = N;
1365     PetscCall(PetscViewerBinaryWriteAll(viewer, iwork, m, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
1366     /* store column indices (zero start index) */
1367     for (k = 0, i = 0; i < m; i++)
1368       for (j = 0; j < N; j++, k++) iwork[k] = j;
1369     PetscCall(PetscViewerBinaryWriteAll(viewer, iwork, nnz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
1370     PetscCall(PetscFree(iwork));
1371   }
1372   /* store matrix values as a dense matrix in row major order */
1373   PetscCall(PetscMalloc1(m * N, &vwork));
1374   PetscCall(MatDenseGetArrayRead(mat, &v));
1375   PetscCall(MatDenseGetLDA(mat, &lda));
1376   for (k = 0, i = 0; i < m; i++)
1377     for (j = 0; j < N; j++, k++) vwork[k] = v[i + (size_t)lda * j];
1378   PetscCall(MatDenseRestoreArrayRead(mat, &v));
1379   PetscCall(PetscViewerBinaryWriteAll(viewer, vwork, m * N, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
1380   PetscCall(PetscFree(vwork));
1381   PetscFunctionReturn(PETSC_SUCCESS);
1382 }
1383 
1384 PetscErrorCode MatLoad_Dense_Binary(Mat mat, PetscViewer viewer)
1385 {
1386   PetscBool    skipHeader;
1387   PetscInt     header[4], M, N, m, nz, lda, i, j, k;
1388   PetscInt     rows, cols;
1389   PetscScalar *v, *vwork;
1390 
1391   PetscFunctionBegin;
1392   PetscCall(PetscViewerSetUp(viewer));
1393   PetscCall(PetscViewerBinaryGetSkipHeader(viewer, &skipHeader));
1394 
1395   if (!skipHeader) {
1396     PetscCall(PetscViewerBinaryRead(viewer, header, 4, NULL, PETSC_INT));
1397     PetscCheck(header[0] == MAT_FILE_CLASSID, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Not a matrix object in file");
1398     M = header[1];
1399     N = header[2];
1400     PetscCheck(M >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix row size (%" PetscInt_FMT ") in file is negative", M);
1401     PetscCheck(N >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix column size (%" PetscInt_FMT ") in file is negative", N);
1402     nz = header[3];
1403     PetscCheck(nz == MATRIX_BINARY_FORMAT_DENSE || nz >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Unknown matrix format %" PetscInt_FMT " in file", nz);
1404   } else {
1405     PetscCall(MatGetSize(mat, &M, &N));
1406     PetscCheck(M >= 0 && N >= 0, PETSC_COMM_SELF, PETSC_ERR_USER, "Matrix binary file header was skipped, thus the user must specify the global sizes of input matrix");
1407     nz = MATRIX_BINARY_FORMAT_DENSE;
1408   }
1409 
1410   /* setup global sizes if not set */
1411   if (mat->rmap->N < 0) mat->rmap->N = M;
1412   if (mat->cmap->N < 0) mat->cmap->N = N;
1413   PetscCall(MatSetUp(mat));
1414   /* check if global sizes are correct */
1415   PetscCall(MatGetSize(mat, &rows, &cols));
1416   PetscCheck(M == rows && N == cols, PetscObjectComm((PetscObject)viewer), 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);
1417 
1418   PetscCall(MatGetSize(mat, NULL, &N));
1419   PetscCall(MatGetLocalSize(mat, &m, NULL));
1420   PetscCall(MatDenseGetArray(mat, &v));
1421   PetscCall(MatDenseGetLDA(mat, &lda));
1422   if (nz == MATRIX_BINARY_FORMAT_DENSE) { /* matrix in file is dense format */
1423     PetscCount nnz = (size_t)m * N;
1424     /* read in matrix values */
1425     PetscCall(PetscMalloc1(nnz, &vwork));
1426     PetscCall(PetscViewerBinaryReadAll(viewer, vwork, nnz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
1427     /* store values in column major order */
1428     for (j = 0; j < N; j++)
1429       for (i = 0; i < m; i++) v[i + (size_t)lda * j] = vwork[(size_t)i * N + j];
1430     PetscCall(PetscFree(vwork));
1431   } else { /* matrix in file is sparse format */
1432     PetscInt nnz = 0, *rlens, *icols;
1433     /* read in row lengths */
1434     PetscCall(PetscMalloc1(m, &rlens));
1435     PetscCall(PetscViewerBinaryReadAll(viewer, rlens, m, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
1436     for (i = 0; i < m; i++) nnz += rlens[i];
1437     /* read in column indices and values */
1438     PetscCall(PetscMalloc2(nnz, &icols, nnz, &vwork));
1439     PetscCall(PetscViewerBinaryReadAll(viewer, icols, nnz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
1440     PetscCall(PetscViewerBinaryReadAll(viewer, vwork, nnz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
1441     /* store values in column major order */
1442     for (k = 0, i = 0; i < m; i++)
1443       for (j = 0; j < rlens[i]; j++, k++) v[i + lda * icols[k]] = vwork[k];
1444     PetscCall(PetscFree(rlens));
1445     PetscCall(PetscFree2(icols, vwork));
1446   }
1447   PetscCall(MatDenseRestoreArray(mat, &v));
1448   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
1449   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
1450   PetscFunctionReturn(PETSC_SUCCESS);
1451 }
1452 
1453 static PetscErrorCode MatLoad_SeqDense(Mat newMat, PetscViewer viewer)
1454 {
1455   PetscBool isbinary, ishdf5;
1456 
1457   PetscFunctionBegin;
1458   PetscValidHeaderSpecific(newMat, MAT_CLASSID, 1);
1459   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1460   /* force binary viewer to load .info file if it has not yet done so */
1461   PetscCall(PetscViewerSetUp(viewer));
1462   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
1463   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
1464   if (isbinary) {
1465     PetscCall(MatLoad_Dense_Binary(newMat, viewer));
1466   } else if (ishdf5) {
1467 #if defined(PETSC_HAVE_HDF5)
1468     PetscCall(MatLoad_Dense_HDF5(newMat, viewer));
1469 #else
1470     SETERRQ(PetscObjectComm((PetscObject)newMat), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
1471 #endif
1472   } else {
1473     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);
1474   }
1475   PetscFunctionReturn(PETSC_SUCCESS);
1476 }
1477 
1478 static PetscErrorCode MatView_SeqDense_ASCII(Mat A, PetscViewer viewer)
1479 {
1480   Mat_SeqDense     *a = (Mat_SeqDense *)A->data;
1481   PetscInt          i, j;
1482   const char       *name;
1483   PetscScalar      *v, *av;
1484   PetscViewerFormat format;
1485 #if defined(PETSC_USE_COMPLEX)
1486   PetscBool allreal = PETSC_TRUE;
1487 #endif
1488 
1489   PetscFunctionBegin;
1490   PetscCall(MatDenseGetArrayRead(A, (const PetscScalar **)&av));
1491   PetscCall(PetscViewerGetFormat(viewer, &format));
1492   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1493     PetscFunctionReturn(PETSC_SUCCESS); /* do nothing for now */
1494   } else if (format == PETSC_VIEWER_ASCII_COMMON) {
1495     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
1496     for (i = 0; i < A->rmap->n; i++) {
1497       v = av + i;
1498       PetscCall(PetscViewerASCIIPrintf(viewer, "row %" PetscInt_FMT ":", i));
1499       for (j = 0; j < A->cmap->n; j++) {
1500 #if defined(PETSC_USE_COMPLEX)
1501         if (PetscRealPart(*v) != 0.0 && PetscImaginaryPart(*v) != 0.0) {
1502           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g + %g i) ", j, (double)PetscRealPart(*v), (double)PetscImaginaryPart(*v)));
1503         } else if (PetscRealPart(*v)) {
1504           PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", j, (double)PetscRealPart(*v)));
1505         }
1506 #else
1507         if (*v) PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ", %g) ", j, (double)*v));
1508 #endif
1509         v += a->lda;
1510       }
1511       PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
1512     }
1513     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
1514   } else {
1515     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
1516 #if defined(PETSC_USE_COMPLEX)
1517     /* determine if matrix has all real values */
1518     for (j = 0; j < A->cmap->n; j++) {
1519       v = av + j * a->lda;
1520       for (i = 0; i < A->rmap->n; i++) {
1521         if (PetscImaginaryPart(v[i])) {
1522           allreal = PETSC_FALSE;
1523           break;
1524         }
1525       }
1526     }
1527 #endif
1528     if (format == PETSC_VIEWER_ASCII_MATLAB) {
1529       PetscCall(PetscObjectGetName((PetscObject)A, &name));
1530       PetscCall(PetscViewerASCIIPrintf(viewer, "%% Size = %" PetscInt_FMT " %" PetscInt_FMT " \n", A->rmap->n, A->cmap->n));
1531       PetscCall(PetscViewerASCIIPrintf(viewer, "%s = zeros(%" PetscInt_FMT ",%" PetscInt_FMT ");\n", name, A->rmap->n, A->cmap->n));
1532       PetscCall(PetscViewerASCIIPrintf(viewer, "%s = [\n", name));
1533     }
1534 
1535     for (i = 0; i < A->rmap->n; i++) {
1536       v = av + i;
1537       for (j = 0; j < A->cmap->n; j++) {
1538 #if defined(PETSC_USE_COMPLEX)
1539         if (allreal) {
1540           PetscCall(PetscViewerASCIIPrintf(viewer, "%18.16e ", (double)PetscRealPart(*v)));
1541         } else {
1542           PetscCall(PetscViewerASCIIPrintf(viewer, "%18.16e + %18.16ei ", (double)PetscRealPart(*v), (double)PetscImaginaryPart(*v)));
1543         }
1544 #else
1545         PetscCall(PetscViewerASCIIPrintf(viewer, "%18.16e ", (double)*v));
1546 #endif
1547         v += a->lda;
1548       }
1549       PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
1550     }
1551     if (format == PETSC_VIEWER_ASCII_MATLAB) PetscCall(PetscViewerASCIIPrintf(viewer, "];\n"));
1552     PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
1553   }
1554   PetscCall(MatDenseRestoreArrayRead(A, (const PetscScalar **)&av));
1555   PetscCall(PetscViewerFlush(viewer));
1556   PetscFunctionReturn(PETSC_SUCCESS);
1557 }
1558 
1559 #include <petscdraw.h>
1560 static PetscErrorCode MatView_SeqDense_Draw_Zoom(PetscDraw draw, void *Aa)
1561 {
1562   Mat                A = (Mat)Aa;
1563   PetscInt           m = A->rmap->n, n = A->cmap->n, i, j;
1564   int                color = PETSC_DRAW_WHITE;
1565   const PetscScalar *v;
1566   PetscViewer        viewer;
1567   PetscReal          xl, yl, xr, yr, x_l, x_r, y_l, y_r;
1568   PetscViewerFormat  format;
1569 
1570   PetscFunctionBegin;
1571   PetscCall(PetscObjectQuery((PetscObject)A, "Zoomviewer", (PetscObject *)&viewer));
1572   PetscCall(PetscViewerGetFormat(viewer, &format));
1573   PetscCall(PetscDrawGetCoordinates(draw, &xl, &yl, &xr, &yr));
1574 
1575   /* Loop over matrix elements drawing boxes */
1576   PetscCall(MatDenseGetArrayRead(A, &v));
1577   if (format != PETSC_VIEWER_DRAW_CONTOUR) {
1578     PetscDrawCollectiveBegin(draw);
1579     /* Blue for negative and Red for positive */
1580     for (j = 0; j < n; j++) {
1581       x_l = j;
1582       x_r = x_l + 1.0;
1583       for (i = 0; i < m; i++) {
1584         y_l = m - i - 1.0;
1585         y_r = y_l + 1.0;
1586         if (PetscRealPart(v[j * m + i]) > 0.) color = PETSC_DRAW_RED;
1587         else if (PetscRealPart(v[j * m + i]) < 0.) color = PETSC_DRAW_BLUE;
1588         else continue;
1589         PetscCall(PetscDrawRectangle(draw, x_l, y_l, x_r, y_r, color, color, color, color));
1590       }
1591     }
1592     PetscDrawCollectiveEnd(draw);
1593   } else {
1594     /* use contour shading to indicate magnitude of values */
1595     /* first determine max of all nonzero values */
1596     PetscReal minv = 0.0, maxv = 0.0;
1597     PetscDraw popup;
1598 
1599     for (i = 0; i < m * n; i++) {
1600       if (PetscAbsScalar(v[i]) > maxv) maxv = PetscAbsScalar(v[i]);
1601     }
1602     if (minv >= maxv) maxv = minv + PETSC_SMALL;
1603     PetscCall(PetscDrawGetPopup(draw, &popup));
1604     PetscCall(PetscDrawScalePopup(popup, minv, maxv));
1605 
1606     PetscDrawCollectiveBegin(draw);
1607     for (j = 0; j < n; j++) {
1608       x_l = j;
1609       x_r = x_l + 1.0;
1610       for (i = 0; i < m; i++) {
1611         y_l   = m - i - 1.0;
1612         y_r   = y_l + 1.0;
1613         color = PetscDrawRealToColor(PetscAbsScalar(v[j * m + i]), minv, maxv);
1614         PetscCall(PetscDrawRectangle(draw, x_l, y_l, x_r, y_r, color, color, color, color));
1615       }
1616     }
1617     PetscDrawCollectiveEnd(draw);
1618   }
1619   PetscCall(MatDenseRestoreArrayRead(A, &v));
1620   PetscFunctionReturn(PETSC_SUCCESS);
1621 }
1622 
1623 static PetscErrorCode MatView_SeqDense_Draw(Mat A, PetscViewer viewer)
1624 {
1625   PetscDraw draw;
1626   PetscBool isnull;
1627   PetscReal xr, yr, xl, yl, h, w;
1628 
1629   PetscFunctionBegin;
1630   PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
1631   PetscCall(PetscDrawIsNull(draw, &isnull));
1632   if (isnull) PetscFunctionReturn(PETSC_SUCCESS);
1633 
1634   xr = A->cmap->n;
1635   yr = A->rmap->n;
1636   h  = yr / 10.0;
1637   w  = xr / 10.0;
1638   xr += w;
1639   yr += h;
1640   xl = -w;
1641   yl = -h;
1642   PetscCall(PetscDrawSetCoordinates(draw, xl, yl, xr, yr));
1643   PetscCall(PetscObjectCompose((PetscObject)A, "Zoomviewer", (PetscObject)viewer));
1644   PetscCall(PetscDrawZoom(draw, MatView_SeqDense_Draw_Zoom, A));
1645   PetscCall(PetscObjectCompose((PetscObject)A, "Zoomviewer", NULL));
1646   PetscCall(PetscDrawSave(draw));
1647   PetscFunctionReturn(PETSC_SUCCESS);
1648 }
1649 
1650 PetscErrorCode MatView_SeqDense(Mat A, PetscViewer viewer)
1651 {
1652   PetscBool iascii, isbinary, isdraw;
1653 
1654   PetscFunctionBegin;
1655   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1656   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
1657   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
1658   if (iascii) PetscCall(MatView_SeqDense_ASCII(A, viewer));
1659   else if (isbinary) PetscCall(MatView_Dense_Binary(A, viewer));
1660   else if (isdraw) PetscCall(MatView_SeqDense_Draw(A, viewer));
1661   PetscFunctionReturn(PETSC_SUCCESS);
1662 }
1663 
1664 static PetscErrorCode MatDensePlaceArray_SeqDense(Mat A, const PetscScalar *array)
1665 {
1666   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
1667 
1668   PetscFunctionBegin;
1669   PetscCheck(!a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
1670   PetscCheck(!a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
1671   PetscCheck(!a->unplacedarray, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseResetArray() first");
1672   a->unplacedarray       = a->v;
1673   a->unplaced_user_alloc = a->user_alloc;
1674   a->v                   = (PetscScalar *)array;
1675   a->user_alloc          = PETSC_TRUE;
1676 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
1677   A->offloadmask = PETSC_OFFLOAD_CPU;
1678 #endif
1679   PetscFunctionReturn(PETSC_SUCCESS);
1680 }
1681 
1682 static PetscErrorCode MatDenseResetArray_SeqDense(Mat A)
1683 {
1684   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
1685 
1686   PetscFunctionBegin;
1687   PetscCheck(!a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
1688   PetscCheck(!a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
1689   a->v             = a->unplacedarray;
1690   a->user_alloc    = a->unplaced_user_alloc;
1691   a->unplacedarray = NULL;
1692 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
1693   A->offloadmask = PETSC_OFFLOAD_CPU;
1694 #endif
1695   PetscFunctionReturn(PETSC_SUCCESS);
1696 }
1697 
1698 static PetscErrorCode MatDenseReplaceArray_SeqDense(Mat A, const PetscScalar *array)
1699 {
1700   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
1701 
1702   PetscFunctionBegin;
1703   PetscCheck(!a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
1704   PetscCheck(!a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
1705   if (!a->user_alloc) PetscCall(PetscFree(a->v));
1706   a->v          = (PetscScalar *)array;
1707   a->user_alloc = PETSC_FALSE;
1708 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
1709   A->offloadmask = PETSC_OFFLOAD_CPU;
1710 #endif
1711   PetscFunctionReturn(PETSC_SUCCESS);
1712 }
1713 
1714 PetscErrorCode MatDestroy_SeqDense(Mat mat)
1715 {
1716   Mat_SeqDense *l = (Mat_SeqDense *)mat->data;
1717 
1718   PetscFunctionBegin;
1719   PetscCall(PetscLogObjectState((PetscObject)mat, "Rows %" PetscInt_FMT " Cols %" PetscInt_FMT, mat->rmap->n, mat->cmap->n));
1720   PetscCall(VecDestroy(&l->qrrhs));
1721   PetscCall(PetscFree(l->tau));
1722   PetscCall(PetscFree(l->pivots));
1723   PetscCall(PetscFree(l->fwork));
1724   if (!l->user_alloc) PetscCall(PetscFree(l->v));
1725   if (!l->unplaced_user_alloc) PetscCall(PetscFree(l->unplacedarray));
1726   PetscCheck(!l->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
1727   PetscCheck(!l->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
1728   PetscCall(VecDestroy(&l->cvec));
1729   PetscCall(MatDestroy(&l->cmat));
1730   PetscCall(PetscFree(mat->data));
1731 
1732   PetscCall(PetscObjectChangeTypeName((PetscObject)mat, NULL));
1733   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatQRFactor_C", NULL));
1734   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatQRFactorSymbolic_C", NULL));
1735   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatQRFactorNumeric_C", NULL));
1736   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetLDA_C", NULL));
1737   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseSetLDA_C", NULL));
1738   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetArray_C", NULL));
1739   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreArray_C", NULL));
1740   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDensePlaceArray_C", NULL));
1741   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseResetArray_C", NULL));
1742   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseReplaceArray_C", NULL));
1743   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetArrayRead_C", NULL));
1744   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreArrayRead_C", NULL));
1745   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetArrayWrite_C", NULL));
1746   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreArrayWrite_C", NULL));
1747   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_seqdense_seqaij_C", NULL));
1748 #if defined(PETSC_HAVE_ELEMENTAL)
1749   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_seqdense_elemental_C", NULL));
1750 #endif
1751 #if defined(PETSC_HAVE_SCALAPACK)
1752   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_seqdense_scalapack_C", NULL));
1753 #endif
1754 #if defined(PETSC_HAVE_CUDA)
1755   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_seqdense_seqdensecuda_C", NULL));
1756   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_seqdensecuda_seqdensecuda_C", NULL));
1757   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_seqdensecuda_seqdense_C", NULL));
1758   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_seqdense_seqdensecuda_C", NULL));
1759 #endif
1760 #if defined(PETSC_HAVE_HIP)
1761   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_seqdense_seqdensehip_C", NULL));
1762   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_seqdensehip_seqdensehip_C", NULL));
1763   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_seqdensehip_seqdense_C", NULL));
1764   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_seqdense_seqdensehip_C", NULL));
1765 #endif
1766   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSeqDenseSetPreallocation_C", NULL));
1767   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_seqaij_seqdense_C", NULL));
1768   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_seqdense_seqdense_C", NULL));
1769   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_seqbaij_seqdense_C", NULL));
1770   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_seqsbaij_seqdense_C", NULL));
1771 
1772   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetColumn_C", NULL));
1773   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreColumn_C", NULL));
1774   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetColumnVec_C", NULL));
1775   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreColumnVec_C", NULL));
1776   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetColumnVecRead_C", NULL));
1777   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreColumnVecRead_C", NULL));
1778   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetColumnVecWrite_C", NULL));
1779   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreColumnVecWrite_C", NULL));
1780   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetSubMatrix_C", NULL));
1781   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreSubMatrix_C", NULL));
1782   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMultAddColumnRange_C", NULL));
1783   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMultHermitianTransposeColumnRange_C", NULL));
1784   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMultHermitianTransposeAddColumnRange_C", NULL));
1785   PetscFunctionReturn(PETSC_SUCCESS);
1786 }
1787 
1788 static PetscErrorCode MatTranspose_SeqDense(Mat A, MatReuse reuse, Mat *matout)
1789 {
1790   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
1791   PetscInt      k, j, m = A->rmap->n, M = mat->lda, n = A->cmap->n;
1792   PetscScalar  *v, tmp;
1793 
1794   PetscFunctionBegin;
1795   if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *matout));
1796   if (reuse == MAT_INPLACE_MATRIX) {
1797     if (m == n) { /* in place transpose */
1798       PetscCall(MatDenseGetArray(A, &v));
1799       for (j = 0; j < m; j++) {
1800         for (k = 0; k < j; k++) {
1801           tmp          = v[j + k * M];
1802           v[j + k * M] = v[k + j * M];
1803           v[k + j * M] = tmp;
1804         }
1805       }
1806       PetscCall(MatDenseRestoreArray(A, &v));
1807     } else { /* reuse memory, temporary allocates new memory */
1808       PetscScalar *v2;
1809       PetscLayout  tmplayout;
1810 
1811       PetscCall(PetscMalloc1((size_t)m * n, &v2));
1812       PetscCall(MatDenseGetArray(A, &v));
1813       for (j = 0; j < n; j++) {
1814         for (k = 0; k < m; k++) v2[j + (size_t)k * n] = v[k + (size_t)j * M];
1815       }
1816       PetscCall(PetscArraycpy(v, v2, (size_t)m * n));
1817       PetscCall(PetscFree(v2));
1818       PetscCall(MatDenseRestoreArray(A, &v));
1819       /* cleanup size dependent quantities */
1820       PetscCall(VecDestroy(&mat->cvec));
1821       PetscCall(MatDestroy(&mat->cmat));
1822       PetscCall(PetscFree(mat->pivots));
1823       PetscCall(PetscFree(mat->fwork));
1824       /* swap row/col layouts */
1825       PetscCall(PetscBLASIntCast(n, &mat->lda));
1826       tmplayout = A->rmap;
1827       A->rmap   = A->cmap;
1828       A->cmap   = tmplayout;
1829     }
1830   } else { /* out-of-place transpose */
1831     Mat           tmat;
1832     Mat_SeqDense *tmatd;
1833     PetscScalar  *v2;
1834     PetscInt      M2;
1835 
1836     if (reuse == MAT_INITIAL_MATRIX) {
1837       PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &tmat));
1838       PetscCall(MatSetSizes(tmat, A->cmap->n, A->rmap->n, A->cmap->n, A->rmap->n));
1839       PetscCall(MatSetType(tmat, ((PetscObject)A)->type_name));
1840       PetscCall(MatSeqDenseSetPreallocation(tmat, NULL));
1841     } else tmat = *matout;
1842 
1843     PetscCall(MatDenseGetArrayRead(A, (const PetscScalar **)&v));
1844     PetscCall(MatDenseGetArray(tmat, &v2));
1845     tmatd = (Mat_SeqDense *)tmat->data;
1846     M2    = tmatd->lda;
1847     for (j = 0; j < n; j++) {
1848       for (k = 0; k < m; k++) v2[j + k * M2] = v[k + j * M];
1849     }
1850     PetscCall(MatDenseRestoreArray(tmat, &v2));
1851     PetscCall(MatDenseRestoreArrayRead(A, (const PetscScalar **)&v));
1852     PetscCall(MatAssemblyBegin(tmat, MAT_FINAL_ASSEMBLY));
1853     PetscCall(MatAssemblyEnd(tmat, MAT_FINAL_ASSEMBLY));
1854     *matout = tmat;
1855   }
1856   PetscFunctionReturn(PETSC_SUCCESS);
1857 }
1858 
1859 static PetscErrorCode MatEqual_SeqDense(Mat A1, Mat A2, PetscBool *flg)
1860 {
1861   Mat_SeqDense      *mat1 = (Mat_SeqDense *)A1->data;
1862   Mat_SeqDense      *mat2 = (Mat_SeqDense *)A2->data;
1863   PetscInt           i;
1864   const PetscScalar *v1, *v2;
1865 
1866   PetscFunctionBegin;
1867   if (A1->rmap->n != A2->rmap->n) {
1868     *flg = PETSC_FALSE;
1869     PetscFunctionReturn(PETSC_SUCCESS);
1870   }
1871   if (A1->cmap->n != A2->cmap->n) {
1872     *flg = PETSC_FALSE;
1873     PetscFunctionReturn(PETSC_SUCCESS);
1874   }
1875   PetscCall(MatDenseGetArrayRead(A1, &v1));
1876   PetscCall(MatDenseGetArrayRead(A2, &v2));
1877   for (i = 0; i < A1->cmap->n; i++) {
1878     PetscCall(PetscArraycmp(v1, v2, A1->rmap->n, flg));
1879     if (*flg == PETSC_FALSE) PetscFunctionReturn(PETSC_SUCCESS);
1880     v1 += mat1->lda;
1881     v2 += mat2->lda;
1882   }
1883   PetscCall(MatDenseRestoreArrayRead(A1, &v1));
1884   PetscCall(MatDenseRestoreArrayRead(A2, &v2));
1885   *flg = PETSC_TRUE;
1886   PetscFunctionReturn(PETSC_SUCCESS);
1887 }
1888 
1889 PetscErrorCode MatGetDiagonal_SeqDense(Mat A, Vec v)
1890 {
1891   Mat_SeqDense      *mat = (Mat_SeqDense *)A->data;
1892   PetscInt           i, n, len;
1893   PetscScalar       *x;
1894   const PetscScalar *vv;
1895 
1896   PetscFunctionBegin;
1897   PetscCall(VecGetSize(v, &n));
1898   PetscCall(VecGetArray(v, &x));
1899   len = PetscMin(A->rmap->n, A->cmap->n);
1900   PetscCall(MatDenseGetArrayRead(A, &vv));
1901   PetscCheck(n == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming mat and vec");
1902   for (i = 0; i < len; i++) x[i] = vv[i * mat->lda + i];
1903   PetscCall(MatDenseRestoreArrayRead(A, &vv));
1904   PetscCall(VecRestoreArray(v, &x));
1905   PetscFunctionReturn(PETSC_SUCCESS);
1906 }
1907 
1908 static PetscErrorCode MatDiagonalScale_SeqDense(Mat A, Vec ll, Vec rr)
1909 {
1910   Mat_SeqDense      *mat = (Mat_SeqDense *)A->data;
1911   const PetscScalar *l, *r;
1912   PetscScalar        x, *v, *vv;
1913   PetscInt           i, j, m = A->rmap->n, n = A->cmap->n;
1914 
1915   PetscFunctionBegin;
1916   PetscCall(MatDenseGetArray(A, &vv));
1917   if (ll) {
1918     PetscCall(VecGetSize(ll, &m));
1919     PetscCall(VecGetArrayRead(ll, &l));
1920     PetscCheck(m == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Left scaling vec wrong size");
1921     for (i = 0; i < m; i++) {
1922       x = l[i];
1923       v = vv + i;
1924       for (j = 0; j < n; j++) {
1925         (*v) *= x;
1926         v += mat->lda;
1927       }
1928     }
1929     PetscCall(VecRestoreArrayRead(ll, &l));
1930     PetscCall(PetscLogFlops(1.0 * n * m));
1931   }
1932   if (rr) {
1933     PetscCall(VecGetSize(rr, &n));
1934     PetscCall(VecGetArrayRead(rr, &r));
1935     PetscCheck(n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Right scaling vec wrong size");
1936     for (i = 0; i < n; i++) {
1937       x = r[i];
1938       v = vv + i * mat->lda;
1939       for (j = 0; j < m; j++) (*v++) *= x;
1940     }
1941     PetscCall(VecRestoreArrayRead(rr, &r));
1942     PetscCall(PetscLogFlops(1.0 * n * m));
1943   }
1944   PetscCall(MatDenseRestoreArray(A, &vv));
1945   PetscFunctionReturn(PETSC_SUCCESS);
1946 }
1947 
1948 PetscErrorCode MatNorm_SeqDense(Mat A, NormType type, PetscReal *nrm)
1949 {
1950   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
1951   PetscScalar  *v, *vv;
1952   PetscReal     sum = 0.0;
1953   PetscInt      lda, m = A->rmap->n, i, j;
1954 
1955   PetscFunctionBegin;
1956   PetscCall(MatDenseGetArrayRead(A, (const PetscScalar **)&vv));
1957   PetscCall(MatDenseGetLDA(A, &lda));
1958   v = vv;
1959   if (type == NORM_FROBENIUS) {
1960     if (lda > m) {
1961       for (j = 0; j < A->cmap->n; j++) {
1962         v = vv + j * lda;
1963         for (i = 0; i < m; i++) {
1964           sum += PetscRealPart(PetscConj(*v) * (*v));
1965           v++;
1966         }
1967       }
1968     } else {
1969 #if defined(PETSC_USE_REAL___FP16)
1970       PetscBLASInt one = 1, cnt = A->cmap->n * A->rmap->n;
1971       PetscCallBLAS("BLASnrm2", *nrm = BLASnrm2_(&cnt, v, &one));
1972     }
1973 #else
1974       for (i = 0; i < A->cmap->n * A->rmap->n; i++) {
1975         sum += PetscRealPart(PetscConj(*v) * (*v));
1976         v++;
1977       }
1978     }
1979     *nrm = PetscSqrtReal(sum);
1980 #endif
1981     PetscCall(PetscLogFlops(2.0 * A->cmap->n * A->rmap->n));
1982   } else if (type == NORM_1) {
1983     *nrm = 0.0;
1984     for (j = 0; j < A->cmap->n; j++) {
1985       v   = vv + j * mat->lda;
1986       sum = 0.0;
1987       for (i = 0; i < A->rmap->n; i++) {
1988         sum += PetscAbsScalar(*v);
1989         v++;
1990       }
1991       if (sum > *nrm) *nrm = sum;
1992     }
1993     PetscCall(PetscLogFlops(1.0 * A->cmap->n * A->rmap->n));
1994   } else if (type == NORM_INFINITY) {
1995     *nrm = 0.0;
1996     for (j = 0; j < A->rmap->n; j++) {
1997       v   = vv + j;
1998       sum = 0.0;
1999       for (i = 0; i < A->cmap->n; i++) {
2000         sum += PetscAbsScalar(*v);
2001         v += mat->lda;
2002       }
2003       if (sum > *nrm) *nrm = sum;
2004     }
2005     PetscCall(PetscLogFlops(1.0 * A->cmap->n * A->rmap->n));
2006   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No two norm");
2007   PetscCall(MatDenseRestoreArrayRead(A, (const PetscScalar **)&vv));
2008   PetscFunctionReturn(PETSC_SUCCESS);
2009 }
2010 
2011 static PetscErrorCode MatSetOption_SeqDense(Mat A, MatOption op, PetscBool flg)
2012 {
2013   Mat_SeqDense *aij = (Mat_SeqDense *)A->data;
2014 
2015   PetscFunctionBegin;
2016   switch (op) {
2017   case MAT_ROW_ORIENTED:
2018     aij->roworiented = flg;
2019     break;
2020   case MAT_NEW_NONZERO_LOCATIONS:
2021   case MAT_NEW_NONZERO_LOCATION_ERR:
2022   case MAT_NEW_NONZERO_ALLOCATION_ERR:
2023   case MAT_FORCE_DIAGONAL_ENTRIES:
2024   case MAT_KEEP_NONZERO_PATTERN:
2025   case MAT_IGNORE_OFF_PROC_ENTRIES:
2026   case MAT_USE_HASH_TABLE:
2027   case MAT_IGNORE_ZERO_ENTRIES:
2028   case MAT_IGNORE_LOWER_TRIANGULAR:
2029   case MAT_SORTED_FULL:
2030   case MAT_SUBMAT_SINGLEIS:
2031     PetscCall(PetscInfo(A, "Option %s ignored\n", MatOptions[op]));
2032     break;
2033   case MAT_SPD:
2034   case MAT_SYMMETRIC:
2035   case MAT_STRUCTURALLY_SYMMETRIC:
2036   case MAT_HERMITIAN:
2037   case MAT_SYMMETRY_ETERNAL:
2038   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
2039   case MAT_SPD_ETERNAL:
2040     break;
2041   default:
2042     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "unknown option %s", MatOptions[op]);
2043   }
2044   PetscFunctionReturn(PETSC_SUCCESS);
2045 }
2046 
2047 PetscErrorCode MatZeroEntries_SeqDense(Mat A)
2048 {
2049   Mat_SeqDense *l   = (Mat_SeqDense *)A->data;
2050   PetscInt      lda = l->lda, m = A->rmap->n, n = A->cmap->n, j;
2051   PetscScalar  *v;
2052 
2053   PetscFunctionBegin;
2054   PetscCall(MatDenseGetArrayWrite(A, &v));
2055   if (lda > m) {
2056     for (j = 0; j < n; j++) PetscCall(PetscArrayzero(v + j * lda, m));
2057   } else {
2058     PetscCall(PetscArrayzero(v, PetscInt64Mult(m, n)));
2059   }
2060   PetscCall(MatDenseRestoreArrayWrite(A, &v));
2061   PetscFunctionReturn(PETSC_SUCCESS);
2062 }
2063 
2064 static PetscErrorCode MatZeroRows_SeqDense(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
2065 {
2066   Mat_SeqDense      *l = (Mat_SeqDense *)A->data;
2067   PetscInt           m = l->lda, n = A->cmap->n, i, j;
2068   PetscScalar       *slot, *bb, *v;
2069   const PetscScalar *xx;
2070 
2071   PetscFunctionBegin;
2072   if (PetscDefined(USE_DEBUG)) {
2073     for (i = 0; i < N; i++) {
2074       PetscCheck(rows[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative row requested to be zeroed");
2075       PetscCheck(rows[i] < A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row %" PetscInt_FMT " requested to be zeroed greater than or equal number of rows %" PetscInt_FMT, rows[i], A->rmap->n);
2076     }
2077   }
2078   if (!N) PetscFunctionReturn(PETSC_SUCCESS);
2079 
2080   /* fix right-hand side if needed */
2081   if (x && b) {
2082     PetscCall(VecGetArrayRead(x, &xx));
2083     PetscCall(VecGetArray(b, &bb));
2084     for (i = 0; i < N; i++) bb[rows[i]] = diag * xx[rows[i]];
2085     PetscCall(VecRestoreArrayRead(x, &xx));
2086     PetscCall(VecRestoreArray(b, &bb));
2087   }
2088 
2089   PetscCall(MatDenseGetArray(A, &v));
2090   for (i = 0; i < N; i++) {
2091     slot = v + rows[i];
2092     for (j = 0; j < n; j++) {
2093       *slot = 0.0;
2094       slot += m;
2095     }
2096   }
2097   if (diag != 0.0) {
2098     PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only coded for square matrices");
2099     for (i = 0; i < N; i++) {
2100       slot  = v + (m + 1) * rows[i];
2101       *slot = diag;
2102     }
2103   }
2104   PetscCall(MatDenseRestoreArray(A, &v));
2105   PetscFunctionReturn(PETSC_SUCCESS);
2106 }
2107 
2108 static PetscErrorCode MatDenseGetLDA_SeqDense(Mat A, PetscInt *lda)
2109 {
2110   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
2111 
2112   PetscFunctionBegin;
2113   *lda = mat->lda;
2114   PetscFunctionReturn(PETSC_SUCCESS);
2115 }
2116 
2117 PetscErrorCode MatDenseGetArray_SeqDense(Mat A, PetscScalar **array)
2118 {
2119   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
2120 
2121   PetscFunctionBegin;
2122   PetscCheck(!mat->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
2123   *array = mat->v;
2124   PetscFunctionReturn(PETSC_SUCCESS);
2125 }
2126 
2127 PetscErrorCode MatDenseRestoreArray_SeqDense(Mat A, PetscScalar **array)
2128 {
2129   PetscFunctionBegin;
2130   if (array) *array = NULL;
2131   PetscFunctionReturn(PETSC_SUCCESS);
2132 }
2133 
2134 /*@
2135   MatDenseGetLDA - gets the leading dimension of the array returned from `MatDenseGetArray()`
2136 
2137   Not Collective
2138 
2139   Input Parameter:
2140 . A - a `MATDENSE` or `MATDENSECUDA` matrix
2141 
2142   Output Parameter:
2143 . lda - the leading dimension
2144 
2145   Level: intermediate
2146 
2147 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MatDenseGetArray()`, `MatDenseRestoreArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseSetLDA()`
2148 @*/
2149 PetscErrorCode MatDenseGetLDA(Mat A, PetscInt *lda)
2150 {
2151   PetscFunctionBegin;
2152   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2153   PetscAssertPointer(lda, 2);
2154   MatCheckPreallocated(A, 1);
2155   PetscUseMethod(A, "MatDenseGetLDA_C", (Mat, PetscInt *), (A, lda));
2156   PetscFunctionReturn(PETSC_SUCCESS);
2157 }
2158 
2159 /*@
2160   MatDenseSetLDA - Sets the leading dimension of the array used by the `MATDENSE` matrix
2161 
2162   Collective if the matrix layouts have not yet been setup
2163 
2164   Input Parameters:
2165 + A   - a `MATDENSE` or `MATDENSECUDA` matrix
2166 - lda - the leading dimension
2167 
2168   Level: intermediate
2169 
2170 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MatDenseGetArray()`, `MatDenseRestoreArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetLDA()`
2171 @*/
2172 PetscErrorCode MatDenseSetLDA(Mat A, PetscInt lda)
2173 {
2174   PetscFunctionBegin;
2175   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2176   PetscTryMethod(A, "MatDenseSetLDA_C", (Mat, PetscInt), (A, lda));
2177   PetscFunctionReturn(PETSC_SUCCESS);
2178 }
2179 
2180 /*@C
2181   MatDenseGetArray - gives read-write access to the array where the data for a `MATDENSE` matrix is stored
2182 
2183   Logically Collective
2184 
2185   Input Parameter:
2186 . A - a dense matrix
2187 
2188   Output Parameter:
2189 . array - pointer to the data
2190 
2191   Level: intermediate
2192 
2193   Fortran Notes:
2194   `MatDenseGetArray()` Fortran binding is deprecated (since PETSc 3.19), use `MatDenseGetArrayF90()`
2195 
2196 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2197 @*/
2198 PetscErrorCode MatDenseGetArray(Mat A, PetscScalar *array[])
2199 {
2200   PetscFunctionBegin;
2201   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2202   PetscAssertPointer(array, 2);
2203   PetscUseMethod(A, "MatDenseGetArray_C", (Mat, PetscScalar **), (A, array));
2204   PetscFunctionReturn(PETSC_SUCCESS);
2205 }
2206 
2207 /*@C
2208   MatDenseRestoreArray - returns access to the array where the data for a `MATDENSE` matrix is stored obtained by `MatDenseGetArray()`
2209 
2210   Logically Collective
2211 
2212   Input Parameters:
2213 + A     - a dense matrix
2214 - array - pointer to the data (may be `NULL`)
2215 
2216   Level: intermediate
2217 
2218   Fortran Notes:
2219   `MatDenseRestoreArray()` Fortran binding is deprecated (since PETSc 3.19), use `MatDenseRestoreArrayF90()`
2220 
2221 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2222 @*/
2223 PetscErrorCode MatDenseRestoreArray(Mat A, PetscScalar *array[])
2224 {
2225   PetscFunctionBegin;
2226   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2227   if (array) PetscAssertPointer(array, 2);
2228   PetscUseMethod(A, "MatDenseRestoreArray_C", (Mat, PetscScalar **), (A, array));
2229   PetscCall(PetscObjectStateIncrease((PetscObject)A));
2230 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
2231   A->offloadmask = PETSC_OFFLOAD_CPU;
2232 #endif
2233   PetscFunctionReturn(PETSC_SUCCESS);
2234 }
2235 
2236 /*@C
2237   MatDenseGetArrayRead - gives read-only access to the array where the data for a `MATDENSE` matrix is stored
2238 
2239   Not Collective
2240 
2241   Input Parameter:
2242 . A - a dense matrix
2243 
2244   Output Parameter:
2245 . array - pointer to the data
2246 
2247   Level: intermediate
2248 
2249 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreArrayRead()`, `MatDenseGetArray()`, `MatDenseRestoreArray()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2250 @*/
2251 PetscErrorCode MatDenseGetArrayRead(Mat A, const PetscScalar *array[])
2252 {
2253   PetscFunctionBegin;
2254   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2255   PetscAssertPointer(array, 2);
2256   PetscUseMethod(A, "MatDenseGetArrayRead_C", (Mat, PetscScalar **), (A, (PetscScalar **)array));
2257   PetscFunctionReturn(PETSC_SUCCESS);
2258 }
2259 
2260 /*@C
2261   MatDenseRestoreArrayRead - returns access to the array where the data for a `MATDENSE` matrix is stored obtained by `MatDenseGetArrayRead()`
2262 
2263   Not Collective
2264 
2265   Input Parameters:
2266 + A     - a dense matrix
2267 - array - pointer to the data (may be `NULL`)
2268 
2269   Level: intermediate
2270 
2271 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArrayRead()`, `MatDenseGetArray()`, `MatDenseRestoreArray()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2272 @*/
2273 PetscErrorCode MatDenseRestoreArrayRead(Mat A, const PetscScalar *array[])
2274 {
2275   PetscFunctionBegin;
2276   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2277   if (array) PetscAssertPointer(array, 2);
2278   PetscUseMethod(A, "MatDenseRestoreArrayRead_C", (Mat, PetscScalar **), (A, (PetscScalar **)array));
2279   PetscFunctionReturn(PETSC_SUCCESS);
2280 }
2281 
2282 /*@C
2283   MatDenseGetArrayWrite - gives write-only access to the array where the data for a `MATDENSE` matrix is stored
2284 
2285   Not Collective
2286 
2287   Input Parameter:
2288 . A - a dense matrix
2289 
2290   Output Parameter:
2291 . array - pointer to the data
2292 
2293   Level: intermediate
2294 
2295 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreArrayWrite()`, `MatDenseGetArray()`, `MatDenseRestoreArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`
2296 @*/
2297 PetscErrorCode MatDenseGetArrayWrite(Mat A, PetscScalar *array[])
2298 {
2299   PetscFunctionBegin;
2300   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2301   PetscAssertPointer(array, 2);
2302   PetscUseMethod(A, "MatDenseGetArrayWrite_C", (Mat, PetscScalar **), (A, array));
2303   PetscFunctionReturn(PETSC_SUCCESS);
2304 }
2305 
2306 /*@C
2307   MatDenseRestoreArrayWrite - returns access to the array where the data for a `MATDENSE` matrix is stored obtained by `MatDenseGetArrayWrite()`
2308 
2309   Not Collective
2310 
2311   Input Parameters:
2312 + A     - a dense matrix
2313 - array - pointer to the data (may be `NULL`)
2314 
2315   Level: intermediate
2316 
2317 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArrayWrite()`, `MatDenseGetArray()`, `MatDenseRestoreArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`
2318 @*/
2319 PetscErrorCode MatDenseRestoreArrayWrite(Mat A, PetscScalar *array[])
2320 {
2321   PetscFunctionBegin;
2322   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2323   if (array) PetscAssertPointer(array, 2);
2324   PetscUseMethod(A, "MatDenseRestoreArrayWrite_C", (Mat, PetscScalar **), (A, array));
2325   PetscCall(PetscObjectStateIncrease((PetscObject)A));
2326 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
2327   A->offloadmask = PETSC_OFFLOAD_CPU;
2328 #endif
2329   PetscFunctionReturn(PETSC_SUCCESS);
2330 }
2331 
2332 /*@C
2333   MatDenseGetArrayAndMemType - gives read-write access to the array where the data for a `MATDENSE` matrix is stored
2334 
2335   Logically Collective
2336 
2337   Input Parameter:
2338 . A - a dense matrix
2339 
2340   Output Parameters:
2341 + array - pointer to the data
2342 - mtype - memory type of the returned pointer
2343 
2344   Level: intermediate
2345 
2346   Note:
2347   If the matrix is of a device type such as `MATDENSECUDA`, `MATDENSEHIP`, etc.,
2348   an array on device is always returned and is guaranteed to contain the matrix's latest data.
2349 
2350 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreArrayAndMemType()`, `MatDenseGetArrayReadAndMemType()`, `MatDenseGetArrayWriteAndMemType()`, `MatDenseGetArrayRead()`,
2351    `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`, `MatSeqAIJGetCSRAndMemType()`
2352 @*/
2353 PetscErrorCode MatDenseGetArrayAndMemType(Mat A, PetscScalar *array[], PetscMemType *mtype)
2354 {
2355   PetscBool isMPI;
2356 
2357   PetscFunctionBegin;
2358   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2359   PetscAssertPointer(array, 2);
2360   PetscCall(MatBindToCPU(A, PETSC_FALSE)); /* We want device matrices to always return device arrays, so we unbind the matrix if it is bound to CPU */
2361   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &isMPI));
2362   if (isMPI) {
2363     /* Dispatch here so that the code can be reused for all subclasses of MATDENSE */
2364     PetscCall(MatDenseGetArrayAndMemType(((Mat_MPIDense *)A->data)->A, array, mtype));
2365   } else {
2366     PetscErrorCode (*fptr)(Mat, PetscScalar **, PetscMemType *);
2367 
2368     PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatDenseGetArrayAndMemType_C", &fptr));
2369     if (fptr) {
2370       PetscCall((*fptr)(A, array, mtype));
2371     } else {
2372       PetscUseMethod(A, "MatDenseGetArray_C", (Mat, PetscScalar **), (A, array));
2373       if (mtype) *mtype = PETSC_MEMTYPE_HOST;
2374     }
2375   }
2376   PetscFunctionReturn(PETSC_SUCCESS);
2377 }
2378 
2379 /*@C
2380   MatDenseRestoreArrayAndMemType - returns access to the array that is obtained by `MatDenseGetArrayAndMemType()`
2381 
2382   Logically Collective
2383 
2384   Input Parameters:
2385 + A     - a dense matrix
2386 - array - pointer to the data
2387 
2388   Level: intermediate
2389 
2390 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArrayAndMemType()`, `MatDenseGetArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2391 @*/
2392 PetscErrorCode MatDenseRestoreArrayAndMemType(Mat A, PetscScalar *array[])
2393 {
2394   PetscBool isMPI;
2395 
2396   PetscFunctionBegin;
2397   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2398   PetscAssertPointer(array, 2);
2399   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &isMPI));
2400   if (isMPI) {
2401     PetscCall(MatDenseRestoreArrayAndMemType(((Mat_MPIDense *)A->data)->A, array));
2402   } else {
2403     PetscErrorCode (*fptr)(Mat, PetscScalar **);
2404 
2405     PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatDenseRestoreArrayAndMemType_C", &fptr));
2406     if (fptr) {
2407       PetscCall((*fptr)(A, array));
2408     } else {
2409       PetscUseMethod(A, "MatDenseRestoreArray_C", (Mat, PetscScalar **), (A, array));
2410     }
2411     *array = NULL;
2412   }
2413   PetscCall(PetscObjectStateIncrease((PetscObject)A));
2414   PetscFunctionReturn(PETSC_SUCCESS);
2415 }
2416 
2417 /*@C
2418   MatDenseGetArrayReadAndMemType - gives read-only access to the array where the data for a `MATDENSE` matrix is stored
2419 
2420   Logically Collective
2421 
2422   Input Parameter:
2423 . A - a dense matrix
2424 
2425   Output Parameters:
2426 + array - pointer to the data
2427 - mtype - memory type of the returned pointer
2428 
2429   Level: intermediate
2430 
2431   Note:
2432   If the matrix is of a device type such as `MATDENSECUDA`, `MATDENSEHIP`, etc.,
2433   an array on device is always returned and is guaranteed to contain the matrix's latest data.
2434 
2435 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreArrayReadAndMemType()`, `MatDenseGetArrayWriteAndMemType()`,
2436    `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`, `MatSeqAIJGetCSRAndMemType()`
2437 @*/
2438 PetscErrorCode MatDenseGetArrayReadAndMemType(Mat A, const PetscScalar *array[], PetscMemType *mtype)
2439 {
2440   PetscBool isMPI;
2441 
2442   PetscFunctionBegin;
2443   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2444   PetscAssertPointer(array, 2);
2445   PetscCall(MatBindToCPU(A, PETSC_FALSE)); /* We want device matrices to always return device arrays, so we unbind the matrix if it is bound to CPU */
2446   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &isMPI));
2447   if (isMPI) { /* Dispatch here so that the code can be reused for all subclasses of MATDENSE */
2448     PetscCall(MatDenseGetArrayReadAndMemType(((Mat_MPIDense *)A->data)->A, array, mtype));
2449   } else {
2450     PetscErrorCode (*fptr)(Mat, const PetscScalar **, PetscMemType *);
2451 
2452     PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatDenseGetArrayReadAndMemType_C", &fptr));
2453     if (fptr) {
2454       PetscCall((*fptr)(A, array, mtype));
2455     } else {
2456       PetscUseMethod(A, "MatDenseGetArrayRead_C", (Mat, PetscScalar **), (A, (PetscScalar **)array));
2457       if (mtype) *mtype = PETSC_MEMTYPE_HOST;
2458     }
2459   }
2460   PetscFunctionReturn(PETSC_SUCCESS);
2461 }
2462 
2463 /*@C
2464   MatDenseRestoreArrayReadAndMemType - returns access to the array that is obtained by `MatDenseGetArrayReadAndMemType()`
2465 
2466   Logically Collective
2467 
2468   Input Parameters:
2469 + A     - a dense matrix
2470 - array - pointer to the data
2471 
2472   Level: intermediate
2473 
2474 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArrayReadAndMemType()`, `MatDenseGetArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2475 @*/
2476 PetscErrorCode MatDenseRestoreArrayReadAndMemType(Mat A, const PetscScalar *array[])
2477 {
2478   PetscBool isMPI;
2479 
2480   PetscFunctionBegin;
2481   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2482   PetscAssertPointer(array, 2);
2483   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &isMPI));
2484   if (isMPI) {
2485     PetscCall(MatDenseRestoreArrayReadAndMemType(((Mat_MPIDense *)A->data)->A, array));
2486   } else {
2487     PetscErrorCode (*fptr)(Mat, const PetscScalar **);
2488 
2489     PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatDenseRestoreArrayReadAndMemType_C", &fptr));
2490     if (fptr) {
2491       PetscCall((*fptr)(A, array));
2492     } else {
2493       PetscUseMethod(A, "MatDenseRestoreArrayRead_C", (Mat, PetscScalar **), (A, (PetscScalar **)array));
2494     }
2495     *array = NULL;
2496   }
2497   PetscFunctionReturn(PETSC_SUCCESS);
2498 }
2499 
2500 /*@C
2501   MatDenseGetArrayWriteAndMemType - gives write-only access to the array where the data for a `MATDENSE` matrix is stored
2502 
2503   Logically Collective
2504 
2505   Input Parameter:
2506 . A - a dense matrix
2507 
2508   Output Parameters:
2509 + array - pointer to the data
2510 - mtype - memory type of the returned pointer
2511 
2512   Level: intermediate
2513 
2514   Note:
2515   If the matrix is of a device type such as `MATDENSECUDA`, `MATDENSEHIP`, etc.,
2516   an array on device is always returned and is guaranteed to contain the matrix's latest data.
2517 
2518 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreArrayWriteAndMemType()`, `MatDenseGetArrayReadAndMemType()`, `MatDenseGetArrayRead()`,
2519   `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`, `MatSeqAIJGetCSRAndMemType()`
2520 @*/
2521 PetscErrorCode MatDenseGetArrayWriteAndMemType(Mat A, PetscScalar *array[], PetscMemType *mtype)
2522 {
2523   PetscBool isMPI;
2524 
2525   PetscFunctionBegin;
2526   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2527   PetscAssertPointer(array, 2);
2528   PetscCall(MatBindToCPU(A, PETSC_FALSE)); /* We want device matrices to always return device arrays, so we unbind the matrix if it is bound to CPU */
2529   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &isMPI));
2530   if (isMPI) {
2531     PetscCall(MatDenseGetArrayWriteAndMemType(((Mat_MPIDense *)A->data)->A, array, mtype));
2532   } else {
2533     PetscErrorCode (*fptr)(Mat, PetscScalar **, PetscMemType *);
2534 
2535     PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatDenseGetArrayWriteAndMemType_C", &fptr));
2536     if (fptr) {
2537       PetscCall((*fptr)(A, array, mtype));
2538     } else {
2539       PetscUseMethod(A, "MatDenseGetArrayWrite_C", (Mat, PetscScalar **), (A, array));
2540       if (mtype) *mtype = PETSC_MEMTYPE_HOST;
2541     }
2542   }
2543   PetscFunctionReturn(PETSC_SUCCESS);
2544 }
2545 
2546 /*@C
2547   MatDenseRestoreArrayWriteAndMemType - returns access to the array that is obtained by `MatDenseGetArrayReadAndMemType()`
2548 
2549   Logically Collective
2550 
2551   Input Parameters:
2552 + A     - a dense matrix
2553 - array - pointer to the data
2554 
2555   Level: intermediate
2556 
2557 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArrayWriteAndMemType()`, `MatDenseGetArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2558 @*/
2559 PetscErrorCode MatDenseRestoreArrayWriteAndMemType(Mat A, PetscScalar *array[])
2560 {
2561   PetscBool isMPI;
2562 
2563   PetscFunctionBegin;
2564   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2565   PetscAssertPointer(array, 2);
2566   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &isMPI));
2567   if (isMPI) {
2568     PetscCall(MatDenseRestoreArrayWriteAndMemType(((Mat_MPIDense *)A->data)->A, array));
2569   } else {
2570     PetscErrorCode (*fptr)(Mat, PetscScalar **);
2571 
2572     PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatDenseRestoreArrayWriteAndMemType_C", &fptr));
2573     if (fptr) {
2574       PetscCall((*fptr)(A, array));
2575     } else {
2576       PetscUseMethod(A, "MatDenseRestoreArrayWrite_C", (Mat, PetscScalar **), (A, array));
2577     }
2578     *array = NULL;
2579   }
2580   PetscCall(PetscObjectStateIncrease((PetscObject)A));
2581   PetscFunctionReturn(PETSC_SUCCESS);
2582 }
2583 
2584 static PetscErrorCode MatCreateSubMatrix_SeqDense(Mat A, IS isrow, IS iscol, MatReuse scall, Mat *B)
2585 {
2586   Mat_SeqDense   *mat = (Mat_SeqDense *)A->data;
2587   PetscInt        i, j, nrows, ncols, ldb;
2588   const PetscInt *irow, *icol;
2589   PetscScalar    *av, *bv, *v = mat->v;
2590   Mat             newmat;
2591 
2592   PetscFunctionBegin;
2593   PetscCall(ISGetIndices(isrow, &irow));
2594   PetscCall(ISGetIndices(iscol, &icol));
2595   PetscCall(ISGetLocalSize(isrow, &nrows));
2596   PetscCall(ISGetLocalSize(iscol, &ncols));
2597 
2598   /* Check submatrixcall */
2599   if (scall == MAT_REUSE_MATRIX) {
2600     PetscInt n_cols, n_rows;
2601     PetscCall(MatGetSize(*B, &n_rows, &n_cols));
2602     if (n_rows != nrows || n_cols != ncols) {
2603       /* resize the result matrix to match number of requested rows/columns */
2604       PetscCall(MatSetSizes(*B, nrows, ncols, nrows, ncols));
2605     }
2606     newmat = *B;
2607   } else {
2608     /* Create and fill new matrix */
2609     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &newmat));
2610     PetscCall(MatSetSizes(newmat, nrows, ncols, nrows, ncols));
2611     PetscCall(MatSetType(newmat, ((PetscObject)A)->type_name));
2612     PetscCall(MatSeqDenseSetPreallocation(newmat, NULL));
2613   }
2614 
2615   /* Now extract the data pointers and do the copy,column at a time */
2616   PetscCall(MatDenseGetArray(newmat, &bv));
2617   PetscCall(MatDenseGetLDA(newmat, &ldb));
2618   for (i = 0; i < ncols; i++) {
2619     av = v + mat->lda * icol[i];
2620     for (j = 0; j < nrows; j++) bv[j] = av[irow[j]];
2621     bv += ldb;
2622   }
2623   PetscCall(MatDenseRestoreArray(newmat, &bv));
2624 
2625   /* Assemble the matrices so that the correct flags are set */
2626   PetscCall(MatAssemblyBegin(newmat, MAT_FINAL_ASSEMBLY));
2627   PetscCall(MatAssemblyEnd(newmat, MAT_FINAL_ASSEMBLY));
2628 
2629   /* Free work space */
2630   PetscCall(ISRestoreIndices(isrow, &irow));
2631   PetscCall(ISRestoreIndices(iscol, &icol));
2632   *B = newmat;
2633   PetscFunctionReturn(PETSC_SUCCESS);
2634 }
2635 
2636 static PetscErrorCode MatCreateSubMatrices_SeqDense(Mat A, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *B[])
2637 {
2638   PetscInt i;
2639 
2640   PetscFunctionBegin;
2641   if (scall == MAT_INITIAL_MATRIX) PetscCall(PetscCalloc1(n, B));
2642 
2643   for (i = 0; i < n; i++) PetscCall(MatCreateSubMatrix_SeqDense(A, irow[i], icol[i], scall, &(*B)[i]));
2644   PetscFunctionReturn(PETSC_SUCCESS);
2645 }
2646 
2647 PetscErrorCode MatCopy_SeqDense(Mat A, Mat B, MatStructure str)
2648 {
2649   Mat_SeqDense      *a = (Mat_SeqDense *)A->data, *b = (Mat_SeqDense *)B->data;
2650   const PetscScalar *va;
2651   PetscScalar       *vb;
2652   PetscInt           lda1 = a->lda, lda2 = b->lda, m = A->rmap->n, n = A->cmap->n, j;
2653 
2654   PetscFunctionBegin;
2655   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2656   if (A->ops->copy != B->ops->copy) {
2657     PetscCall(MatCopy_Basic(A, B, str));
2658     PetscFunctionReturn(PETSC_SUCCESS);
2659   }
2660   PetscCheck(m == B->rmap->n && n == B->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "size(B) != size(A)");
2661   PetscCall(MatDenseGetArrayRead(A, &va));
2662   PetscCall(MatDenseGetArray(B, &vb));
2663   if (lda1 > m || lda2 > m) {
2664     for (j = 0; j < n; j++) PetscCall(PetscArraycpy(vb + j * lda2, va + j * lda1, m));
2665   } else {
2666     PetscCall(PetscArraycpy(vb, va, A->rmap->n * A->cmap->n));
2667   }
2668   PetscCall(MatDenseRestoreArray(B, &vb));
2669   PetscCall(MatDenseRestoreArrayRead(A, &va));
2670   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
2671   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
2672   PetscFunctionReturn(PETSC_SUCCESS);
2673 }
2674 
2675 PetscErrorCode MatSetUp_SeqDense(Mat A)
2676 {
2677   PetscFunctionBegin;
2678   PetscCall(PetscLayoutSetUp(A->rmap));
2679   PetscCall(PetscLayoutSetUp(A->cmap));
2680   if (!A->preallocated) PetscCall(MatSeqDenseSetPreallocation(A, NULL));
2681   PetscFunctionReturn(PETSC_SUCCESS);
2682 }
2683 
2684 static PetscErrorCode MatConjugate_SeqDense(Mat A)
2685 {
2686   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
2687   PetscInt      i, j;
2688   PetscInt      min = PetscMin(A->rmap->n, A->cmap->n);
2689   PetscScalar  *aa;
2690 
2691   PetscFunctionBegin;
2692   PetscCall(MatDenseGetArray(A, &aa));
2693   for (j = 0; j < A->cmap->n; j++) {
2694     for (i = 0; i < A->rmap->n; i++) aa[i + j * mat->lda] = PetscConj(aa[i + j * mat->lda]);
2695   }
2696   PetscCall(MatDenseRestoreArray(A, &aa));
2697   if (mat->tau)
2698     for (i = 0; i < min; i++) mat->tau[i] = PetscConj(mat->tau[i]);
2699   PetscFunctionReturn(PETSC_SUCCESS);
2700 }
2701 
2702 static PetscErrorCode MatRealPart_SeqDense(Mat A)
2703 {
2704   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
2705   PetscInt      i, j;
2706   PetscScalar  *aa;
2707 
2708   PetscFunctionBegin;
2709   PetscCall(MatDenseGetArray(A, &aa));
2710   for (j = 0; j < A->cmap->n; j++) {
2711     for (i = 0; i < A->rmap->n; i++) aa[i + j * mat->lda] = PetscRealPart(aa[i + j * mat->lda]);
2712   }
2713   PetscCall(MatDenseRestoreArray(A, &aa));
2714   PetscFunctionReturn(PETSC_SUCCESS);
2715 }
2716 
2717 static PetscErrorCode MatImaginaryPart_SeqDense(Mat A)
2718 {
2719   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
2720   PetscInt      i, j;
2721   PetscScalar  *aa;
2722 
2723   PetscFunctionBegin;
2724   PetscCall(MatDenseGetArray(A, &aa));
2725   for (j = 0; j < A->cmap->n; j++) {
2726     for (i = 0; i < A->rmap->n; i++) aa[i + j * mat->lda] = PetscImaginaryPart(aa[i + j * mat->lda]);
2727   }
2728   PetscCall(MatDenseRestoreArray(A, &aa));
2729   PetscFunctionReturn(PETSC_SUCCESS);
2730 }
2731 
2732 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqDense(Mat A, Mat B, PetscReal fill, Mat C)
2733 {
2734   PetscInt  m = A->rmap->n, n = B->cmap->n;
2735   PetscBool cisdense = PETSC_FALSE;
2736 
2737   PetscFunctionBegin;
2738   PetscCall(MatSetSizes(C, m, n, m, n));
2739 #if defined(PETSC_HAVE_CUDA)
2740   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSECUDA, ""));
2741 #endif
2742 #if defined(PETSC_HAVE_HIP)
2743   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSEHIP, ""));
2744 #endif
2745   if (!cisdense) {
2746     PetscBool flg;
2747 
2748     PetscCall(PetscObjectTypeCompare((PetscObject)B, ((PetscObject)A)->type_name, &flg));
2749     PetscCall(MatSetType(C, flg ? ((PetscObject)A)->type_name : MATDENSE));
2750   }
2751   PetscCall(MatSetUp(C));
2752   PetscFunctionReturn(PETSC_SUCCESS);
2753 }
2754 
2755 PetscErrorCode MatMatMultNumeric_SeqDense_SeqDense(Mat A, Mat B, Mat C)
2756 {
2757   Mat_SeqDense      *a = (Mat_SeqDense *)A->data, *b = (Mat_SeqDense *)B->data, *c = (Mat_SeqDense *)C->data;
2758   PetscBLASInt       m, n, k;
2759   const PetscScalar *av, *bv;
2760   PetscScalar       *cv;
2761   PetscScalar        _DOne = 1.0, _DZero = 0.0;
2762 
2763   PetscFunctionBegin;
2764   PetscCall(PetscBLASIntCast(C->rmap->n, &m));
2765   PetscCall(PetscBLASIntCast(C->cmap->n, &n));
2766   PetscCall(PetscBLASIntCast(A->cmap->n, &k));
2767   if (!m || !n || !k) PetscFunctionReturn(PETSC_SUCCESS);
2768   PetscCall(MatDenseGetArrayRead(A, &av));
2769   PetscCall(MatDenseGetArrayRead(B, &bv));
2770   PetscCall(MatDenseGetArrayWrite(C, &cv));
2771   PetscCallBLAS("BLASgemm", BLASgemm_("N", "N", &m, &n, &k, &_DOne, av, &a->lda, bv, &b->lda, &_DZero, cv, &c->lda));
2772   PetscCall(PetscLogFlops(1.0 * m * n * k + 1.0 * m * n * (k - 1)));
2773   PetscCall(MatDenseRestoreArrayRead(A, &av));
2774   PetscCall(MatDenseRestoreArrayRead(B, &bv));
2775   PetscCall(MatDenseRestoreArrayWrite(C, &cv));
2776   PetscFunctionReturn(PETSC_SUCCESS);
2777 }
2778 
2779 PetscErrorCode MatMatTransposeMultSymbolic_SeqDense_SeqDense(Mat A, Mat B, PetscReal fill, Mat C)
2780 {
2781   PetscInt  m = A->rmap->n, n = B->rmap->n;
2782   PetscBool cisdense = PETSC_FALSE;
2783 
2784   PetscFunctionBegin;
2785   PetscCall(MatSetSizes(C, m, n, m, n));
2786 #if defined(PETSC_HAVE_CUDA)
2787   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSECUDA, ""));
2788 #endif
2789 #if defined(PETSC_HAVE_HIP)
2790   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSEHIP, ""));
2791 #endif
2792   if (!cisdense) {
2793     PetscBool flg;
2794 
2795     PetscCall(PetscObjectTypeCompare((PetscObject)B, ((PetscObject)A)->type_name, &flg));
2796     PetscCall(MatSetType(C, flg ? ((PetscObject)A)->type_name : MATDENSE));
2797   }
2798   PetscCall(MatSetUp(C));
2799   PetscFunctionReturn(PETSC_SUCCESS);
2800 }
2801 
2802 PetscErrorCode MatMatTransposeMultNumeric_SeqDense_SeqDense(Mat A, Mat B, Mat C)
2803 {
2804   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
2805   Mat_SeqDense      *b = (Mat_SeqDense *)B->data;
2806   Mat_SeqDense      *c = (Mat_SeqDense *)C->data;
2807   const PetscScalar *av, *bv;
2808   PetscScalar       *cv;
2809   PetscBLASInt       m, n, k;
2810   PetscScalar        _DOne = 1.0, _DZero = 0.0;
2811 
2812   PetscFunctionBegin;
2813   PetscCall(PetscBLASIntCast(C->rmap->n, &m));
2814   PetscCall(PetscBLASIntCast(C->cmap->n, &n));
2815   PetscCall(PetscBLASIntCast(A->cmap->n, &k));
2816   if (!m || !n || !k) PetscFunctionReturn(PETSC_SUCCESS);
2817   PetscCall(MatDenseGetArrayRead(A, &av));
2818   PetscCall(MatDenseGetArrayRead(B, &bv));
2819   PetscCall(MatDenseGetArrayWrite(C, &cv));
2820   PetscCallBLAS("BLASgemm", BLASgemm_("N", "T", &m, &n, &k, &_DOne, av, &a->lda, bv, &b->lda, &_DZero, cv, &c->lda));
2821   PetscCall(MatDenseRestoreArrayRead(A, &av));
2822   PetscCall(MatDenseRestoreArrayRead(B, &bv));
2823   PetscCall(MatDenseRestoreArrayWrite(C, &cv));
2824   PetscCall(PetscLogFlops(1.0 * m * n * k + 1.0 * m * n * (k - 1)));
2825   PetscFunctionReturn(PETSC_SUCCESS);
2826 }
2827 
2828 PetscErrorCode MatTransposeMatMultSymbolic_SeqDense_SeqDense(Mat A, Mat B, PetscReal fill, Mat C)
2829 {
2830   PetscInt  m = A->cmap->n, n = B->cmap->n;
2831   PetscBool cisdense = PETSC_FALSE;
2832 
2833   PetscFunctionBegin;
2834   PetscCall(MatSetSizes(C, m, n, m, n));
2835 #if defined(PETSC_HAVE_CUDA)
2836   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSECUDA, ""));
2837 #endif
2838 #if defined(PETSC_HAVE_HIP)
2839   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSEHIP, ""));
2840 #endif
2841   if (!cisdense) {
2842     PetscBool flg;
2843 
2844     PetscCall(PetscObjectTypeCompare((PetscObject)B, ((PetscObject)A)->type_name, &flg));
2845     PetscCall(MatSetType(C, flg ? ((PetscObject)A)->type_name : MATDENSE));
2846   }
2847   PetscCall(MatSetUp(C));
2848   PetscFunctionReturn(PETSC_SUCCESS);
2849 }
2850 
2851 PetscErrorCode MatTransposeMatMultNumeric_SeqDense_SeqDense(Mat A, Mat B, Mat C)
2852 {
2853   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
2854   Mat_SeqDense      *b = (Mat_SeqDense *)B->data;
2855   Mat_SeqDense      *c = (Mat_SeqDense *)C->data;
2856   const PetscScalar *av, *bv;
2857   PetscScalar       *cv;
2858   PetscBLASInt       m, n, k;
2859   PetscScalar        _DOne = 1.0, _DZero = 0.0;
2860 
2861   PetscFunctionBegin;
2862   PetscCall(PetscBLASIntCast(C->rmap->n, &m));
2863   PetscCall(PetscBLASIntCast(C->cmap->n, &n));
2864   PetscCall(PetscBLASIntCast(A->rmap->n, &k));
2865   if (!m || !n || !k) PetscFunctionReturn(PETSC_SUCCESS);
2866   PetscCall(MatDenseGetArrayRead(A, &av));
2867   PetscCall(MatDenseGetArrayRead(B, &bv));
2868   PetscCall(MatDenseGetArrayWrite(C, &cv));
2869   PetscCallBLAS("BLASgemm", BLASgemm_("T", "N", &m, &n, &k, &_DOne, av, &a->lda, bv, &b->lda, &_DZero, cv, &c->lda));
2870   PetscCall(MatDenseRestoreArrayRead(A, &av));
2871   PetscCall(MatDenseRestoreArrayRead(B, &bv));
2872   PetscCall(MatDenseRestoreArrayWrite(C, &cv));
2873   PetscCall(PetscLogFlops(1.0 * m * n * k + 1.0 * m * n * (k - 1)));
2874   PetscFunctionReturn(PETSC_SUCCESS);
2875 }
2876 
2877 static PetscErrorCode MatProductSetFromOptions_SeqDense_AB(Mat C)
2878 {
2879   PetscFunctionBegin;
2880   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqDense_SeqDense;
2881   C->ops->productsymbolic = MatProductSymbolic_AB;
2882   PetscFunctionReturn(PETSC_SUCCESS);
2883 }
2884 
2885 static PetscErrorCode MatProductSetFromOptions_SeqDense_AtB(Mat C)
2886 {
2887   PetscFunctionBegin;
2888   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_SeqDense_SeqDense;
2889   C->ops->productsymbolic          = MatProductSymbolic_AtB;
2890   PetscFunctionReturn(PETSC_SUCCESS);
2891 }
2892 
2893 static PetscErrorCode MatProductSetFromOptions_SeqDense_ABt(Mat C)
2894 {
2895   PetscFunctionBegin;
2896   C->ops->mattransposemultsymbolic = MatMatTransposeMultSymbolic_SeqDense_SeqDense;
2897   C->ops->productsymbolic          = MatProductSymbolic_ABt;
2898   PetscFunctionReturn(PETSC_SUCCESS);
2899 }
2900 
2901 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqDense(Mat C)
2902 {
2903   Mat_Product *product = C->product;
2904 
2905   PetscFunctionBegin;
2906   switch (product->type) {
2907   case MATPRODUCT_AB:
2908     PetscCall(MatProductSetFromOptions_SeqDense_AB(C));
2909     break;
2910   case MATPRODUCT_AtB:
2911     PetscCall(MatProductSetFromOptions_SeqDense_AtB(C));
2912     break;
2913   case MATPRODUCT_ABt:
2914     PetscCall(MatProductSetFromOptions_SeqDense_ABt(C));
2915     break;
2916   default:
2917     break;
2918   }
2919   PetscFunctionReturn(PETSC_SUCCESS);
2920 }
2921 
2922 static PetscErrorCode MatGetRowMax_SeqDense(Mat A, Vec v, PetscInt idx[])
2923 {
2924   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
2925   PetscInt           i, j, m = A->rmap->n, n = A->cmap->n, p;
2926   PetscScalar       *x;
2927   const PetscScalar *aa;
2928 
2929   PetscFunctionBegin;
2930   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
2931   PetscCall(VecGetArray(v, &x));
2932   PetscCall(VecGetLocalSize(v, &p));
2933   PetscCall(MatDenseGetArrayRead(A, &aa));
2934   PetscCheck(p == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
2935   for (i = 0; i < m; i++) {
2936     x[i] = aa[i];
2937     if (idx) idx[i] = 0;
2938     for (j = 1; j < n; j++) {
2939       if (PetscRealPart(x[i]) < PetscRealPart(aa[i + a->lda * j])) {
2940         x[i] = aa[i + a->lda * j];
2941         if (idx) idx[i] = j;
2942       }
2943     }
2944   }
2945   PetscCall(MatDenseRestoreArrayRead(A, &aa));
2946   PetscCall(VecRestoreArray(v, &x));
2947   PetscFunctionReturn(PETSC_SUCCESS);
2948 }
2949 
2950 static PetscErrorCode MatGetRowMaxAbs_SeqDense(Mat A, Vec v, PetscInt idx[])
2951 {
2952   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
2953   PetscInt           i, j, m = A->rmap->n, n = A->cmap->n, p;
2954   PetscScalar       *x;
2955   PetscReal          atmp;
2956   const PetscScalar *aa;
2957 
2958   PetscFunctionBegin;
2959   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
2960   PetscCall(VecGetArray(v, &x));
2961   PetscCall(VecGetLocalSize(v, &p));
2962   PetscCall(MatDenseGetArrayRead(A, &aa));
2963   PetscCheck(p == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
2964   for (i = 0; i < m; i++) {
2965     x[i] = PetscAbsScalar(aa[i]);
2966     for (j = 1; j < n; j++) {
2967       atmp = PetscAbsScalar(aa[i + a->lda * j]);
2968       if (PetscAbsScalar(x[i]) < atmp) {
2969         x[i] = atmp;
2970         if (idx) idx[i] = j;
2971       }
2972     }
2973   }
2974   PetscCall(MatDenseRestoreArrayRead(A, &aa));
2975   PetscCall(VecRestoreArray(v, &x));
2976   PetscFunctionReturn(PETSC_SUCCESS);
2977 }
2978 
2979 static PetscErrorCode MatGetRowMin_SeqDense(Mat A, Vec v, PetscInt idx[])
2980 {
2981   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
2982   PetscInt           i, j, m = A->rmap->n, n = A->cmap->n, p;
2983   PetscScalar       *x;
2984   const PetscScalar *aa;
2985 
2986   PetscFunctionBegin;
2987   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
2988   PetscCall(MatDenseGetArrayRead(A, &aa));
2989   PetscCall(VecGetArray(v, &x));
2990   PetscCall(VecGetLocalSize(v, &p));
2991   PetscCheck(p == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
2992   for (i = 0; i < m; i++) {
2993     x[i] = aa[i];
2994     if (idx) idx[i] = 0;
2995     for (j = 1; j < n; j++) {
2996       if (PetscRealPart(x[i]) > PetscRealPart(aa[i + a->lda * j])) {
2997         x[i] = aa[i + a->lda * j];
2998         if (idx) idx[i] = j;
2999       }
3000     }
3001   }
3002   PetscCall(VecRestoreArray(v, &x));
3003   PetscCall(MatDenseRestoreArrayRead(A, &aa));
3004   PetscFunctionReturn(PETSC_SUCCESS);
3005 }
3006 
3007 PetscErrorCode MatGetColumnVector_SeqDense(Mat A, Vec v, PetscInt col)
3008 {
3009   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
3010   PetscScalar       *x;
3011   const PetscScalar *aa;
3012 
3013   PetscFunctionBegin;
3014   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3015   PetscCall(MatDenseGetArrayRead(A, &aa));
3016   PetscCall(VecGetArray(v, &x));
3017   PetscCall(PetscArraycpy(x, aa + col * a->lda, A->rmap->n));
3018   PetscCall(VecRestoreArray(v, &x));
3019   PetscCall(MatDenseRestoreArrayRead(A, &aa));
3020   PetscFunctionReturn(PETSC_SUCCESS);
3021 }
3022 
3023 PETSC_INTERN PetscErrorCode MatGetColumnReductions_SeqDense(Mat A, PetscInt type, PetscReal *reductions)
3024 {
3025   PetscInt           i, j, m, n;
3026   const PetscScalar *a;
3027 
3028   PetscFunctionBegin;
3029   PetscCall(MatGetSize(A, &m, &n));
3030   PetscCall(PetscArrayzero(reductions, n));
3031   PetscCall(MatDenseGetArrayRead(A, &a));
3032   if (type == NORM_2) {
3033     for (i = 0; i < n; i++) {
3034       for (j = 0; j < m; j++) reductions[i] += PetscAbsScalar(a[j] * a[j]);
3035       a = PetscSafePointerPlusOffset(a, m);
3036     }
3037   } else if (type == NORM_1) {
3038     for (i = 0; i < n; i++) {
3039       for (j = 0; j < m; j++) reductions[i] += PetscAbsScalar(a[j]);
3040       a = PetscSafePointerPlusOffset(a, m);
3041     }
3042   } else if (type == NORM_INFINITY) {
3043     for (i = 0; i < n; i++) {
3044       for (j = 0; j < m; j++) reductions[i] = PetscMax(PetscAbsScalar(a[j]), reductions[i]);
3045       a = PetscSafePointerPlusOffset(a, m);
3046     }
3047   } else if (type == REDUCTION_SUM_REALPART || type == REDUCTION_MEAN_REALPART) {
3048     for (i = 0; i < n; i++) {
3049       for (j = 0; j < m; j++) reductions[i] += PetscRealPart(a[j]);
3050       a = PetscSafePointerPlusOffset(a, m);
3051     }
3052   } else if (type == REDUCTION_SUM_IMAGINARYPART || type == REDUCTION_MEAN_IMAGINARYPART) {
3053     for (i = 0; i < n; i++) {
3054       for (j = 0; j < m; j++) reductions[i] += PetscImaginaryPart(a[j]);
3055       a = PetscSafePointerPlusOffset(a, m);
3056     }
3057   } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Unknown reduction type");
3058   PetscCall(MatDenseRestoreArrayRead(A, &a));
3059   if (type == NORM_2) {
3060     for (i = 0; i < n; i++) reductions[i] = PetscSqrtReal(reductions[i]);
3061   } else if (type == REDUCTION_MEAN_REALPART || type == REDUCTION_MEAN_IMAGINARYPART) {
3062     for (i = 0; i < n; i++) reductions[i] /= m;
3063   }
3064   PetscFunctionReturn(PETSC_SUCCESS);
3065 }
3066 
3067 PetscErrorCode MatSetRandom_SeqDense(Mat x, PetscRandom rctx)
3068 {
3069   PetscScalar *a;
3070   PetscInt     lda, m, n, i, j;
3071 
3072   PetscFunctionBegin;
3073   PetscCall(MatGetSize(x, &m, &n));
3074   PetscCall(MatDenseGetLDA(x, &lda));
3075   PetscCall(MatDenseGetArrayWrite(x, &a));
3076   for (j = 0; j < n; j++) {
3077     for (i = 0; i < m; i++) PetscCall(PetscRandomGetValue(rctx, a + j * lda + i));
3078   }
3079   PetscCall(MatDenseRestoreArrayWrite(x, &a));
3080   PetscFunctionReturn(PETSC_SUCCESS);
3081 }
3082 
3083 static PetscErrorCode MatMissingDiagonal_SeqDense(Mat A, PetscBool *missing, PetscInt *d)
3084 {
3085   PetscFunctionBegin;
3086   *missing = PETSC_FALSE;
3087   PetscFunctionReturn(PETSC_SUCCESS);
3088 }
3089 
3090 /* vals is not const */
3091 static PetscErrorCode MatDenseGetColumn_SeqDense(Mat A, PetscInt col, PetscScalar **vals)
3092 {
3093   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3094   PetscScalar  *v;
3095 
3096   PetscFunctionBegin;
3097   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3098   PetscCall(MatDenseGetArray(A, &v));
3099   *vals = v + col * a->lda;
3100   PetscCall(MatDenseRestoreArray(A, &v));
3101   PetscFunctionReturn(PETSC_SUCCESS);
3102 }
3103 
3104 static PetscErrorCode MatDenseRestoreColumn_SeqDense(Mat A, PetscScalar **vals)
3105 {
3106   PetscFunctionBegin;
3107   if (vals) *vals = NULL; /* user cannot accidentally use the array later */
3108   PetscFunctionReturn(PETSC_SUCCESS);
3109 }
3110 
3111 static struct _MatOps MatOps_Values = {MatSetValues_SeqDense,
3112                                        MatGetRow_SeqDense,
3113                                        MatRestoreRow_SeqDense,
3114                                        MatMult_SeqDense,
3115                                        /*  4*/ MatMultAdd_SeqDense,
3116                                        MatMultTranspose_SeqDense,
3117                                        MatMultTransposeAdd_SeqDense,
3118                                        NULL,
3119                                        NULL,
3120                                        NULL,
3121                                        /* 10*/ NULL,
3122                                        MatLUFactor_SeqDense,
3123                                        MatCholeskyFactor_SeqDense,
3124                                        MatSOR_SeqDense,
3125                                        MatTranspose_SeqDense,
3126                                        /* 15*/ MatGetInfo_SeqDense,
3127                                        MatEqual_SeqDense,
3128                                        MatGetDiagonal_SeqDense,
3129                                        MatDiagonalScale_SeqDense,
3130                                        MatNorm_SeqDense,
3131                                        /* 20*/ NULL,
3132                                        NULL,
3133                                        MatSetOption_SeqDense,
3134                                        MatZeroEntries_SeqDense,
3135                                        /* 24*/ MatZeroRows_SeqDense,
3136                                        NULL,
3137                                        NULL,
3138                                        NULL,
3139                                        NULL,
3140                                        /* 29*/ MatSetUp_SeqDense,
3141                                        NULL,
3142                                        NULL,
3143                                        NULL,
3144                                        NULL,
3145                                        /* 34*/ MatDuplicate_SeqDense,
3146                                        NULL,
3147                                        NULL,
3148                                        NULL,
3149                                        NULL,
3150                                        /* 39*/ MatAXPY_SeqDense,
3151                                        MatCreateSubMatrices_SeqDense,
3152                                        NULL,
3153                                        MatGetValues_SeqDense,
3154                                        MatCopy_SeqDense,
3155                                        /* 44*/ MatGetRowMax_SeqDense,
3156                                        MatScale_SeqDense,
3157                                        MatShift_SeqDense,
3158                                        NULL,
3159                                        MatZeroRowsColumns_SeqDense,
3160                                        /* 49*/ MatSetRandom_SeqDense,
3161                                        NULL,
3162                                        NULL,
3163                                        NULL,
3164                                        NULL,
3165                                        /* 54*/ NULL,
3166                                        NULL,
3167                                        NULL,
3168                                        NULL,
3169                                        NULL,
3170                                        /* 59*/ MatCreateSubMatrix_SeqDense,
3171                                        MatDestroy_SeqDense,
3172                                        MatView_SeqDense,
3173                                        NULL,
3174                                        NULL,
3175                                        /* 64*/ NULL,
3176                                        NULL,
3177                                        NULL,
3178                                        NULL,
3179                                        NULL,
3180                                        /* 69*/ MatGetRowMaxAbs_SeqDense,
3181                                        NULL,
3182                                        NULL,
3183                                        NULL,
3184                                        NULL,
3185                                        /* 74*/ NULL,
3186                                        NULL,
3187                                        NULL,
3188                                        NULL,
3189                                        NULL,
3190                                        /* 79*/ NULL,
3191                                        NULL,
3192                                        NULL,
3193                                        NULL,
3194                                        /* 83*/ MatLoad_SeqDense,
3195                                        MatIsSymmetric_SeqDense,
3196                                        MatIsHermitian_SeqDense,
3197                                        NULL,
3198                                        NULL,
3199                                        NULL,
3200                                        /* 89*/ NULL,
3201                                        NULL,
3202                                        MatMatMultNumeric_SeqDense_SeqDense,
3203                                        NULL,
3204                                        NULL,
3205                                        /* 94*/ NULL,
3206                                        NULL,
3207                                        NULL,
3208                                        MatMatTransposeMultNumeric_SeqDense_SeqDense,
3209                                        NULL,
3210                                        /* 99*/ MatProductSetFromOptions_SeqDense,
3211                                        NULL,
3212                                        NULL,
3213                                        MatConjugate_SeqDense,
3214                                        NULL,
3215                                        /*104*/ NULL,
3216                                        MatRealPart_SeqDense,
3217                                        MatImaginaryPart_SeqDense,
3218                                        NULL,
3219                                        NULL,
3220                                        /*109*/ NULL,
3221                                        NULL,
3222                                        MatGetRowMin_SeqDense,
3223                                        MatGetColumnVector_SeqDense,
3224                                        MatMissingDiagonal_SeqDense,
3225                                        /*114*/ NULL,
3226                                        NULL,
3227                                        NULL,
3228                                        NULL,
3229                                        NULL,
3230                                        /*119*/ NULL,
3231                                        NULL,
3232                                        MatMultHermitianTranspose_SeqDense,
3233                                        MatMultHermitianTransposeAdd_SeqDense,
3234                                        NULL,
3235                                        /*124*/ NULL,
3236                                        MatGetColumnReductions_SeqDense,
3237                                        NULL,
3238                                        NULL,
3239                                        NULL,
3240                                        /*129*/ NULL,
3241                                        NULL,
3242                                        NULL,
3243                                        MatTransposeMatMultNumeric_SeqDense_SeqDense,
3244                                        NULL,
3245                                        /*134*/ NULL,
3246                                        NULL,
3247                                        NULL,
3248                                        NULL,
3249                                        NULL,
3250                                        /*139*/ NULL,
3251                                        NULL,
3252                                        NULL,
3253                                        NULL,
3254                                        NULL,
3255                                        MatCreateMPIMatConcatenateSeqMat_SeqDense,
3256                                        /*145*/ NULL,
3257                                        NULL,
3258                                        NULL,
3259                                        NULL,
3260                                        NULL,
3261                                        /*150*/ NULL,
3262                                        NULL,
3263                                        NULL,
3264                                        NULL,
3265                                        NULL,
3266                                        /*155*/ NULL,
3267                                        NULL};
3268 
3269 /*@
3270   MatCreateSeqDense - Creates a `MATSEQDENSE` that
3271   is stored in column major order (the usual Fortran format).
3272 
3273   Collective
3274 
3275   Input Parameters:
3276 + comm - MPI communicator, set to `PETSC_COMM_SELF`
3277 . m    - number of rows
3278 . n    - number of columns
3279 - data - optional location of matrix data in column major order.  Use `NULL` for PETSc
3280          to control all matrix memory allocation.
3281 
3282   Output Parameter:
3283 . A - the matrix
3284 
3285   Level: intermediate
3286 
3287   Note:
3288   The data input variable is intended primarily for Fortran programmers
3289   who wish to allocate their own matrix memory space.  Most users should
3290   set `data` = `NULL`.
3291 
3292   Developer Note:
3293   Many of the matrix operations for this variant use the BLAS and LAPACK routines.
3294 
3295 .seealso: [](ch_matrices), `Mat`, `MATSEQDENSE`, `MatCreate()`, `MatCreateDense()`, `MatSetValues()`
3296 @*/
3297 PetscErrorCode MatCreateSeqDense(MPI_Comm comm, PetscInt m, PetscInt n, PetscScalar data[], Mat *A)
3298 {
3299   PetscFunctionBegin;
3300   PetscCall(MatCreate(comm, A));
3301   PetscCall(MatSetSizes(*A, m, n, m, n));
3302   PetscCall(MatSetType(*A, MATSEQDENSE));
3303   PetscCall(MatSeqDenseSetPreallocation(*A, data));
3304   PetscFunctionReturn(PETSC_SUCCESS);
3305 }
3306 
3307 /*@
3308   MatSeqDenseSetPreallocation - Sets the array used for storing the matrix elements of a `MATSEQDENSE` matrix
3309 
3310   Collective
3311 
3312   Input Parameters:
3313 + B    - the matrix
3314 - data - the array (or `NULL`)
3315 
3316   Level: intermediate
3317 
3318   Note:
3319   The data input variable is intended primarily for Fortran programmers
3320   who wish to allocate their own matrix memory space.  Most users should
3321   need not call this routine.
3322 
3323 .seealso: [](ch_matrices), `Mat`, `MATSEQDENSE`, `MatCreate()`, `MatCreateDense()`, `MatSetValues()`, `MatDenseSetLDA()`
3324 @*/
3325 PetscErrorCode MatSeqDenseSetPreallocation(Mat B, PetscScalar data[])
3326 {
3327   PetscFunctionBegin;
3328   PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
3329   PetscTryMethod(B, "MatSeqDenseSetPreallocation_C", (Mat, PetscScalar[]), (B, data));
3330   PetscFunctionReturn(PETSC_SUCCESS);
3331 }
3332 
3333 PetscErrorCode MatSeqDenseSetPreallocation_SeqDense(Mat B, PetscScalar *data)
3334 {
3335   Mat_SeqDense *b = (Mat_SeqDense *)B->data;
3336 
3337   PetscFunctionBegin;
3338   PetscCheck(!b->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
3339   B->preallocated = PETSC_TRUE;
3340 
3341   PetscCall(PetscLayoutSetUp(B->rmap));
3342   PetscCall(PetscLayoutSetUp(B->cmap));
3343 
3344   if (b->lda <= 0) PetscCall(PetscBLASIntCast(B->rmap->n, &b->lda));
3345 
3346   if (!data) { /* petsc-allocated storage */
3347     if (!b->user_alloc) PetscCall(PetscFree(b->v));
3348     PetscCall(PetscCalloc1((size_t)b->lda * B->cmap->n, &b->v));
3349 
3350     b->user_alloc = PETSC_FALSE;
3351   } else { /* user-allocated storage */
3352     if (!b->user_alloc) PetscCall(PetscFree(b->v));
3353     b->v          = data;
3354     b->user_alloc = PETSC_TRUE;
3355   }
3356   B->assembled = PETSC_TRUE;
3357   PetscFunctionReturn(PETSC_SUCCESS);
3358 }
3359 
3360 #if defined(PETSC_HAVE_ELEMENTAL)
3361 PETSC_INTERN PetscErrorCode MatConvert_SeqDense_Elemental(Mat A, MatType newtype, MatReuse reuse, Mat *newmat)
3362 {
3363   Mat                mat_elemental;
3364   const PetscScalar *array;
3365   PetscScalar       *v_colwise;
3366   PetscInt           M = A->rmap->N, N = A->cmap->N, i, j, k, *rows, *cols;
3367 
3368   PetscFunctionBegin;
3369   PetscCall(PetscMalloc3(M * N, &v_colwise, M, &rows, N, &cols));
3370   PetscCall(MatDenseGetArrayRead(A, &array));
3371   /* convert column-wise array into row-wise v_colwise, see MatSetValues_Elemental() */
3372   k = 0;
3373   for (j = 0; j < N; j++) {
3374     cols[j] = j;
3375     for (i = 0; i < M; i++) v_colwise[j * M + i] = array[k++];
3376   }
3377   for (i = 0; i < M; i++) rows[i] = i;
3378   PetscCall(MatDenseRestoreArrayRead(A, &array));
3379 
3380   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &mat_elemental));
3381   PetscCall(MatSetSizes(mat_elemental, PETSC_DECIDE, PETSC_DECIDE, M, N));
3382   PetscCall(MatSetType(mat_elemental, MATELEMENTAL));
3383   PetscCall(MatSetUp(mat_elemental));
3384 
3385   /* PETSc-Elemental interaface uses axpy for setting off-processor entries, only ADD_VALUES is allowed */
3386   PetscCall(MatSetValues(mat_elemental, M, rows, N, cols, v_colwise, ADD_VALUES));
3387   PetscCall(MatAssemblyBegin(mat_elemental, MAT_FINAL_ASSEMBLY));
3388   PetscCall(MatAssemblyEnd(mat_elemental, MAT_FINAL_ASSEMBLY));
3389   PetscCall(PetscFree3(v_colwise, rows, cols));
3390 
3391   if (reuse == MAT_INPLACE_MATRIX) {
3392     PetscCall(MatHeaderReplace(A, &mat_elemental));
3393   } else {
3394     *newmat = mat_elemental;
3395   }
3396   PetscFunctionReturn(PETSC_SUCCESS);
3397 }
3398 #endif
3399 
3400 PetscErrorCode MatDenseSetLDA_SeqDense(Mat B, PetscInt lda)
3401 {
3402   Mat_SeqDense *b = (Mat_SeqDense *)B->data;
3403   PetscBool     data;
3404 
3405   PetscFunctionBegin;
3406   data = (B->rmap->n > 0 && B->cmap->n > 0) ? (b->v ? PETSC_TRUE : PETSC_FALSE) : PETSC_FALSE;
3407   PetscCheck(b->user_alloc || !data || b->lda == lda, PETSC_COMM_SELF, PETSC_ERR_ORDER, "LDA cannot be changed after allocation of internal storage");
3408   PetscCheck(lda >= B->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "LDA %" PetscInt_FMT " must be at least matrix dimension %" PetscInt_FMT, lda, B->rmap->n);
3409   PetscCall(PetscBLASIntCast(lda, &b->lda));
3410   PetscFunctionReturn(PETSC_SUCCESS);
3411 }
3412 
3413 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqDense(MPI_Comm comm, Mat inmat, PetscInt n, MatReuse scall, Mat *outmat)
3414 {
3415   PetscFunctionBegin;
3416   PetscCall(MatCreateMPIMatConcatenateSeqMat_MPIDense(comm, inmat, n, scall, outmat));
3417   PetscFunctionReturn(PETSC_SUCCESS);
3418 }
3419 
3420 PetscErrorCode MatDenseCreateColumnVec_Private(Mat A, Vec *v)
3421 {
3422   PetscBool   isstd, iskok, iscuda, iship;
3423   PetscMPIInt size;
3424 #if PetscDefined(HAVE_CUDA) || PetscDefined(HAVE_HIP)
3425   /* we pass the data of A, to prevent allocating needless GPU memory the first time VecCUPMPlaceArray is called. */
3426   const PetscScalar *a;
3427 #endif
3428 
3429   PetscFunctionBegin;
3430   *v = NULL;
3431   PetscCall(PetscStrcmpAny(A->defaultvectype, &isstd, VECSTANDARD, VECSEQ, VECMPI, ""));
3432   PetscCall(PetscStrcmpAny(A->defaultvectype, &iskok, VECKOKKOS, VECSEQKOKKOS, VECMPIKOKKOS, ""));
3433   PetscCall(PetscStrcmpAny(A->defaultvectype, &iscuda, VECCUDA, VECSEQCUDA, VECMPICUDA, ""));
3434   PetscCall(PetscStrcmpAny(A->defaultvectype, &iship, VECHIP, VECSEQHIP, VECMPIHIP, ""));
3435   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3436   if (isstd) {
3437     if (size > 1) PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, A->rmap->N, NULL, v));
3438     else PetscCall(VecCreateSeqWithArray(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, NULL, v));
3439   } else if (iskok) {
3440     PetscCheck(PetscDefined(HAVE_KOKKOS_KERNELS), PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Reconfigure using KOKKOS kernels support");
3441 #if PetscDefined(HAVE_KOKKOS_KERNELS)
3442     if (size > 1) PetscCall(VecCreateMPIKokkosWithArray(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, A->rmap->N, NULL, v));
3443     else PetscCall(VecCreateSeqKokkosWithArray(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, NULL, v));
3444 #endif
3445   } else if (iscuda) {
3446     PetscCheck(PetscDefined(HAVE_CUDA), PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Reconfigure using CUDA support");
3447 #if PetscDefined(HAVE_CUDA)
3448     PetscCall(MatDenseCUDAGetArrayRead(A, &a));
3449     if (size > 1) PetscCall(VecCreateMPICUDAWithArrays(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, A->rmap->N, NULL, a, v));
3450     else PetscCall(VecCreateSeqCUDAWithArrays(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, NULL, a, v));
3451 #endif
3452   } else if (iship) {
3453     PetscCheck(PetscDefined(HAVE_HIP), PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Reconfigure using HIP support");
3454 #if PetscDefined(HAVE_HIP)
3455     PetscCall(MatDenseHIPGetArrayRead(A, &a));
3456     if (size > 1) PetscCall(VecCreateMPIHIPWithArrays(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, A->rmap->N, NULL, a, v));
3457     else PetscCall(VecCreateSeqHIPWithArrays(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, NULL, a, v));
3458 #endif
3459   }
3460   PetscCheck(*v, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not coded for type %s", A->defaultvectype);
3461   PetscFunctionReturn(PETSC_SUCCESS);
3462 }
3463 
3464 PetscErrorCode MatDenseGetColumnVec_SeqDense(Mat A, PetscInt col, Vec *v)
3465 {
3466   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3467 
3468   PetscFunctionBegin;
3469   PetscCheck(!a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
3470   PetscCheck(!a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
3471   if (!a->cvec) PetscCall(MatDenseCreateColumnVec_Private(A, &a->cvec));
3472   a->vecinuse = col + 1;
3473   PetscCall(MatDenseGetArray(A, (PetscScalar **)&a->ptrinuse));
3474   PetscCall(VecPlaceArray(a->cvec, a->ptrinuse + (size_t)col * (size_t)a->lda));
3475   *v = a->cvec;
3476   PetscFunctionReturn(PETSC_SUCCESS);
3477 }
3478 
3479 PetscErrorCode MatDenseRestoreColumnVec_SeqDense(Mat A, PetscInt col, Vec *v)
3480 {
3481   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3482 
3483   PetscFunctionBegin;
3484   PetscCheck(a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseGetColumnVec() first");
3485   PetscCheck(a->cvec, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing internal column vector");
3486   VecCheckAssembled(a->cvec);
3487   a->vecinuse = 0;
3488   PetscCall(MatDenseRestoreArray(A, (PetscScalar **)&a->ptrinuse));
3489   PetscCall(VecResetArray(a->cvec));
3490   if (v) *v = NULL;
3491   PetscFunctionReturn(PETSC_SUCCESS);
3492 }
3493 
3494 PetscErrorCode MatDenseGetColumnVecRead_SeqDense(Mat A, PetscInt col, Vec *v)
3495 {
3496   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3497 
3498   PetscFunctionBegin;
3499   PetscCheck(!a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
3500   PetscCheck(!a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
3501   if (!a->cvec) PetscCall(MatDenseCreateColumnVec_Private(A, &a->cvec));
3502   a->vecinuse = col + 1;
3503   PetscCall(MatDenseGetArrayRead(A, &a->ptrinuse));
3504   PetscCall(VecPlaceArray(a->cvec, PetscSafePointerPlusOffset(a->ptrinuse, (size_t)col * (size_t)a->lda)));
3505   PetscCall(VecLockReadPush(a->cvec));
3506   *v = a->cvec;
3507   PetscFunctionReturn(PETSC_SUCCESS);
3508 }
3509 
3510 PetscErrorCode MatDenseRestoreColumnVecRead_SeqDense(Mat A, PetscInt col, Vec *v)
3511 {
3512   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3513 
3514   PetscFunctionBegin;
3515   PetscCheck(a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseGetColumnVec() first");
3516   PetscCheck(a->cvec, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing internal column vector");
3517   VecCheckAssembled(a->cvec);
3518   a->vecinuse = 0;
3519   PetscCall(MatDenseRestoreArrayRead(A, &a->ptrinuse));
3520   PetscCall(VecLockReadPop(a->cvec));
3521   PetscCall(VecResetArray(a->cvec));
3522   if (v) *v = NULL;
3523   PetscFunctionReturn(PETSC_SUCCESS);
3524 }
3525 
3526 PetscErrorCode MatDenseGetColumnVecWrite_SeqDense(Mat A, PetscInt col, Vec *v)
3527 {
3528   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3529 
3530   PetscFunctionBegin;
3531   PetscCheck(!a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
3532   PetscCheck(!a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
3533   if (!a->cvec) PetscCall(MatDenseCreateColumnVec_Private(A, &a->cvec));
3534   a->vecinuse = col + 1;
3535   PetscCall(MatDenseGetArrayWrite(A, (PetscScalar **)&a->ptrinuse));
3536   PetscCall(VecPlaceArray(a->cvec, PetscSafePointerPlusOffset(a->ptrinuse, (size_t)col * (size_t)a->lda)));
3537   *v = a->cvec;
3538   PetscFunctionReturn(PETSC_SUCCESS);
3539 }
3540 
3541 PetscErrorCode MatDenseRestoreColumnVecWrite_SeqDense(Mat A, PetscInt col, Vec *v)
3542 {
3543   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3544 
3545   PetscFunctionBegin;
3546   PetscCheck(a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseGetColumnVec() first");
3547   PetscCheck(a->cvec, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing internal column vector");
3548   VecCheckAssembled(a->cvec);
3549   a->vecinuse = 0;
3550   PetscCall(MatDenseRestoreArrayWrite(A, (PetscScalar **)&a->ptrinuse));
3551   PetscCall(VecResetArray(a->cvec));
3552   if (v) *v = NULL;
3553   PetscFunctionReturn(PETSC_SUCCESS);
3554 }
3555 
3556 PetscErrorCode MatDenseGetSubMatrix_SeqDense(Mat A, PetscInt rbegin, PetscInt rend, PetscInt cbegin, PetscInt cend, Mat *v)
3557 {
3558   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3559 
3560   PetscFunctionBegin;
3561   PetscCheck(!a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
3562   PetscCheck(!a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
3563   if (a->cmat && (cend - cbegin != a->cmat->cmap->N || rend - rbegin != a->cmat->rmap->N)) PetscCall(MatDestroy(&a->cmat));
3564   if (!a->cmat) {
3565     PetscCall(MatCreateDense(PetscObjectComm((PetscObject)A), rend - rbegin, PETSC_DECIDE, rend - rbegin, cend - cbegin, PetscSafePointerPlusOffset(a->v, rbegin + (size_t)cbegin * a->lda), &a->cmat));
3566   } else {
3567     PetscCall(MatDensePlaceArray(a->cmat, PetscSafePointerPlusOffset(a->v, rbegin + (size_t)cbegin * a->lda)));
3568   }
3569   PetscCall(MatDenseSetLDA(a->cmat, a->lda));
3570   a->matinuse = cbegin + 1;
3571   *v          = a->cmat;
3572 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
3573   A->offloadmask = PETSC_OFFLOAD_CPU;
3574 #endif
3575   PetscFunctionReturn(PETSC_SUCCESS);
3576 }
3577 
3578 PetscErrorCode MatDenseRestoreSubMatrix_SeqDense(Mat A, Mat *v)
3579 {
3580   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3581 
3582   PetscFunctionBegin;
3583   PetscCheck(a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseGetSubMatrix() first");
3584   PetscCheck(a->cmat, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing internal column matrix");
3585   PetscCheck(*v == a->cmat, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Not the matrix obtained from MatDenseGetSubMatrix()");
3586   a->matinuse = 0;
3587   PetscCall(MatDenseResetArray(a->cmat));
3588   if (v) *v = NULL;
3589 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
3590   A->offloadmask = PETSC_OFFLOAD_CPU;
3591 #endif
3592   PetscFunctionReturn(PETSC_SUCCESS);
3593 }
3594 
3595 /*MC
3596    MATSEQDENSE - MATSEQDENSE = "seqdense" - A matrix type to be used for sequential dense matrices.
3597 
3598    Options Database Key:
3599 . -mat_type seqdense - sets the matrix type to `MATSEQDENSE` during a call to `MatSetFromOptions()`
3600 
3601   Level: beginner
3602 
3603 .seealso: [](ch_matrices), `Mat`, `MATSEQDENSE`, `MatCreateSeqDense()`
3604 M*/
3605 PetscErrorCode MatCreate_SeqDense(Mat B)
3606 {
3607   Mat_SeqDense *b;
3608   PetscMPIInt   size;
3609 
3610   PetscFunctionBegin;
3611   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));
3612   PetscCheck(size <= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Comm must be of size 1");
3613 
3614   PetscCall(PetscNew(&b));
3615   B->data   = (void *)b;
3616   B->ops[0] = MatOps_Values;
3617 
3618   b->roworiented = PETSC_TRUE;
3619 
3620   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatQRFactor_C", MatQRFactor_SeqDense));
3621   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetLDA_C", MatDenseGetLDA_SeqDense));
3622   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseSetLDA_C", MatDenseSetLDA_SeqDense));
3623   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetArray_C", MatDenseGetArray_SeqDense));
3624   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreArray_C", MatDenseRestoreArray_SeqDense));
3625   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDensePlaceArray_C", MatDensePlaceArray_SeqDense));
3626   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseResetArray_C", MatDenseResetArray_SeqDense));
3627   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseReplaceArray_C", MatDenseReplaceArray_SeqDense));
3628   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetArrayRead_C", MatDenseGetArray_SeqDense));
3629   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreArrayRead_C", MatDenseRestoreArray_SeqDense));
3630   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetArrayWrite_C", MatDenseGetArray_SeqDense));
3631   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreArrayWrite_C", MatDenseRestoreArray_SeqDense));
3632   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqdense_seqaij_C", MatConvert_SeqDense_SeqAIJ));
3633 #if defined(PETSC_HAVE_ELEMENTAL)
3634   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqdense_elemental_C", MatConvert_SeqDense_Elemental));
3635 #endif
3636 #if defined(PETSC_HAVE_SCALAPACK)
3637   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqdense_scalapack_C", MatConvert_Dense_ScaLAPACK));
3638 #endif
3639 #if defined(PETSC_HAVE_CUDA)
3640   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqdense_seqdensecuda_C", MatConvert_SeqDense_SeqDenseCUDA));
3641   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdensecuda_seqdensecuda_C", MatProductSetFromOptions_SeqDense));
3642   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdensecuda_seqdense_C", MatProductSetFromOptions_SeqDense));
3643   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdense_seqdensecuda_C", MatProductSetFromOptions_SeqDense));
3644 #endif
3645 #if defined(PETSC_HAVE_HIP)
3646   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqdense_seqdensehip_C", MatConvert_SeqDense_SeqDenseHIP));
3647   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdensehip_seqdensehip_C", MatProductSetFromOptions_SeqDense));
3648   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdensehip_seqdense_C", MatProductSetFromOptions_SeqDense));
3649   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdense_seqdensehip_C", MatProductSetFromOptions_SeqDense));
3650 #endif
3651   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqDenseSetPreallocation_C", MatSeqDenseSetPreallocation_SeqDense));
3652   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqaij_seqdense_C", MatProductSetFromOptions_SeqAIJ_SeqDense));
3653   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdense_seqdense_C", MatProductSetFromOptions_SeqDense));
3654   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqbaij_seqdense_C", MatProductSetFromOptions_SeqXBAIJ_SeqDense));
3655   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqsbaij_seqdense_C", MatProductSetFromOptions_SeqXBAIJ_SeqDense));
3656 
3657   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetColumn_C", MatDenseGetColumn_SeqDense));
3658   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreColumn_C", MatDenseRestoreColumn_SeqDense));
3659   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetColumnVec_C", MatDenseGetColumnVec_SeqDense));
3660   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreColumnVec_C", MatDenseRestoreColumnVec_SeqDense));
3661   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetColumnVecRead_C", MatDenseGetColumnVecRead_SeqDense));
3662   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreColumnVecRead_C", MatDenseRestoreColumnVecRead_SeqDense));
3663   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetColumnVecWrite_C", MatDenseGetColumnVecWrite_SeqDense));
3664   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreColumnVecWrite_C", MatDenseRestoreColumnVecWrite_SeqDense));
3665   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetSubMatrix_C", MatDenseGetSubMatrix_SeqDense));
3666   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreSubMatrix_C", MatDenseRestoreSubMatrix_SeqDense));
3667   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMultAddColumnRange_C", MatMultAddColumnRange_SeqDense));
3668   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMultHermitianTransposeColumnRange_C", MatMultHermitianTransposeColumnRange_SeqDense));
3669   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMultHermitianTransposeAddColumnRange_C", MatMultHermitianTransposeAddColumnRange_SeqDense));
3670   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQDENSE));
3671   PetscFunctionReturn(PETSC_SUCCESS);
3672 }
3673 
3674 /*@C
3675   MatDenseGetColumn - gives access to a column of a dense matrix. This is only the local part of the column. You MUST call `MatDenseRestoreColumn()` to avoid memory bleeding.
3676 
3677   Not Collective
3678 
3679   Input Parameters:
3680 + A   - a `MATSEQDENSE` or `MATMPIDENSE` matrix
3681 - col - column index
3682 
3683   Output Parameter:
3684 . vals - pointer to the data
3685 
3686   Level: intermediate
3687 
3688   Note:
3689   Use `MatDenseGetColumnVec()` to get access to a column of a `MATDENSE` treated as a `Vec`
3690 
3691 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreColumn()`, `MatDenseGetColumnVec()`
3692 @*/
3693 PetscErrorCode MatDenseGetColumn(Mat A, PetscInt col, PetscScalar *vals[])
3694 {
3695   PetscFunctionBegin;
3696   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3697   PetscValidLogicalCollectiveInt(A, col, 2);
3698   PetscAssertPointer(vals, 3);
3699   PetscUseMethod(A, "MatDenseGetColumn_C", (Mat, PetscInt, PetscScalar **), (A, col, vals));
3700   PetscFunctionReturn(PETSC_SUCCESS);
3701 }
3702 
3703 /*@C
3704   MatDenseRestoreColumn - returns access to a column of a `MATDENSE` matrix which is returned by `MatDenseGetColumn()`.
3705 
3706   Not Collective
3707 
3708   Input Parameters:
3709 + A    - a `MATSEQDENSE` or `MATMPIDENSE` matrix
3710 - vals - pointer to the data (may be `NULL`)
3711 
3712   Level: intermediate
3713 
3714 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetColumn()`
3715 @*/
3716 PetscErrorCode MatDenseRestoreColumn(Mat A, PetscScalar *vals[])
3717 {
3718   PetscFunctionBegin;
3719   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3720   PetscAssertPointer(vals, 2);
3721   PetscUseMethod(A, "MatDenseRestoreColumn_C", (Mat, PetscScalar **), (A, vals));
3722   PetscFunctionReturn(PETSC_SUCCESS);
3723 }
3724 
3725 /*@
3726   MatDenseGetColumnVec - Gives read-write access to a column of a `MATDENSE` matrix, represented as a `Vec`.
3727 
3728   Collective
3729 
3730   Input Parameters:
3731 + A   - the `Mat` object
3732 - col - the column index
3733 
3734   Output Parameter:
3735 . v - the vector
3736 
3737   Level: intermediate
3738 
3739   Notes:
3740   The vector is owned by PETSc. Users need to call `MatDenseRestoreColumnVec()` when the vector is no longer needed.
3741 
3742   Use `MatDenseGetColumnVecRead()` to obtain read-only access or `MatDenseGetColumnVecWrite()` for write-only access.
3743 
3744 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVecRead()`, `MatDenseGetColumnVecWrite()`, `MatDenseRestoreColumnVec()`, `MatDenseRestoreColumnVecRead()`, `MatDenseRestoreColumnVecWrite()`, `MatDenseGetColumn()`
3745 @*/
3746 PetscErrorCode MatDenseGetColumnVec(Mat A, PetscInt col, Vec *v)
3747 {
3748   PetscFunctionBegin;
3749   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3750   PetscValidType(A, 1);
3751   PetscValidLogicalCollectiveInt(A, col, 2);
3752   PetscAssertPointer(v, 3);
3753   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3754   PetscCheck(col >= 0 && col < A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Invalid col %" PetscInt_FMT ", should be in [0,%" PetscInt_FMT ")", col, A->cmap->N);
3755   PetscUseMethod(A, "MatDenseGetColumnVec_C", (Mat, PetscInt, Vec *), (A, col, v));
3756   PetscFunctionReturn(PETSC_SUCCESS);
3757 }
3758 
3759 /*@
3760   MatDenseRestoreColumnVec - Returns access to a column of a dense matrix obtained from `MatDenseGetColumnVec()`.
3761 
3762   Collective
3763 
3764   Input Parameters:
3765 + A   - the `Mat` object
3766 . col - the column index
3767 - v   - the `Vec` object (may be `NULL`)
3768 
3769   Level: intermediate
3770 
3771 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseGetColumnVecRead()`, `MatDenseGetColumnVecWrite()`, `MatDenseRestoreColumnVecRead()`, `MatDenseRestoreColumnVecWrite()`
3772 @*/
3773 PetscErrorCode MatDenseRestoreColumnVec(Mat A, PetscInt col, Vec *v)
3774 {
3775   PetscFunctionBegin;
3776   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3777   PetscValidType(A, 1);
3778   PetscValidLogicalCollectiveInt(A, col, 2);
3779   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3780   PetscCheck(col >= 0 && col < A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Invalid col %" PetscInt_FMT ", should be in [0,%" PetscInt_FMT ")", col, A->cmap->N);
3781   PetscUseMethod(A, "MatDenseRestoreColumnVec_C", (Mat, PetscInt, Vec *), (A, col, v));
3782   PetscFunctionReturn(PETSC_SUCCESS);
3783 }
3784 
3785 /*@
3786   MatDenseGetColumnVecRead - Gives read-only access to a column of a dense matrix, represented as a `Vec`.
3787 
3788   Collective
3789 
3790   Input Parameters:
3791 + A   - the `Mat` object
3792 - col - the column index
3793 
3794   Output Parameter:
3795 . v - the vector
3796 
3797   Level: intermediate
3798 
3799   Notes:
3800   The vector is owned by PETSc and users cannot modify it.
3801 
3802   Users need to call `MatDenseRestoreColumnVecRead()` when the vector is no longer needed.
3803 
3804   Use `MatDenseGetColumnVec()` to obtain read-write access or `MatDenseGetColumnVecWrite()` for write-only access.
3805 
3806 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseGetColumnVecWrite()`, `MatDenseRestoreColumnVec()`, `MatDenseRestoreColumnVecRead()`, `MatDenseRestoreColumnVecWrite()`
3807 @*/
3808 PetscErrorCode MatDenseGetColumnVecRead(Mat A, PetscInt col, Vec *v)
3809 {
3810   PetscFunctionBegin;
3811   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3812   PetscValidType(A, 1);
3813   PetscValidLogicalCollectiveInt(A, col, 2);
3814   PetscAssertPointer(v, 3);
3815   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3816   PetscCheck(col >= 0 && col < A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Invalid col %" PetscInt_FMT ", should be in [0,%" PetscInt_FMT ")", col, A->cmap->N);
3817   PetscUseMethod(A, "MatDenseGetColumnVecRead_C", (Mat, PetscInt, Vec *), (A, col, v));
3818   PetscFunctionReturn(PETSC_SUCCESS);
3819 }
3820 
3821 /*@
3822   MatDenseRestoreColumnVecRead - Returns access to a column of a dense matrix obtained from `MatDenseGetColumnVecRead()`.
3823 
3824   Collective
3825 
3826   Input Parameters:
3827 + A   - the `Mat` object
3828 . col - the column index
3829 - v   - the `Vec` object (may be `NULL`)
3830 
3831   Level: intermediate
3832 
3833 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseGetColumnVecRead()`, `MatDenseGetColumnVecWrite()`, `MatDenseRestoreColumnVec()`, `MatDenseRestoreColumnVecWrite()`
3834 @*/
3835 PetscErrorCode MatDenseRestoreColumnVecRead(Mat A, PetscInt col, Vec *v)
3836 {
3837   PetscFunctionBegin;
3838   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3839   PetscValidType(A, 1);
3840   PetscValidLogicalCollectiveInt(A, col, 2);
3841   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3842   PetscCheck(col >= 0 && col < A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Invalid col %" PetscInt_FMT ", should be in [0,%" PetscInt_FMT ")", col, A->cmap->N);
3843   PetscUseMethod(A, "MatDenseRestoreColumnVecRead_C", (Mat, PetscInt, Vec *), (A, col, v));
3844   PetscFunctionReturn(PETSC_SUCCESS);
3845 }
3846 
3847 /*@
3848   MatDenseGetColumnVecWrite - Gives write-only access to a column of a dense matrix, represented as a `Vec`.
3849 
3850   Collective
3851 
3852   Input Parameters:
3853 + A   - the `Mat` object
3854 - col - the column index
3855 
3856   Output Parameter:
3857 . v - the vector
3858 
3859   Level: intermediate
3860 
3861   Notes:
3862   The vector is owned by PETSc. Users need to call `MatDenseRestoreColumnVecWrite()` when the vector is no longer needed.
3863 
3864   Use `MatDenseGetColumnVec()` to obtain read-write access or `MatDenseGetColumnVecRead()` for read-only access.
3865 
3866 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseGetColumnVecRead()`, `MatDenseRestoreColumnVec()`, `MatDenseRestoreColumnVecRead()`, `MatDenseRestoreColumnVecWrite()`
3867 @*/
3868 PetscErrorCode MatDenseGetColumnVecWrite(Mat A, PetscInt col, Vec *v)
3869 {
3870   PetscFunctionBegin;
3871   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3872   PetscValidType(A, 1);
3873   PetscValidLogicalCollectiveInt(A, col, 2);
3874   PetscAssertPointer(v, 3);
3875   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3876   PetscCheck(col >= 0 && col < A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Invalid col %" PetscInt_FMT ", should be in [0,%" PetscInt_FMT ")", col, A->cmap->N);
3877   PetscUseMethod(A, "MatDenseGetColumnVecWrite_C", (Mat, PetscInt, Vec *), (A, col, v));
3878   PetscFunctionReturn(PETSC_SUCCESS);
3879 }
3880 
3881 /*@
3882   MatDenseRestoreColumnVecWrite - Returns access to a column of a dense matrix obtained from `MatDenseGetColumnVecWrite()`.
3883 
3884   Collective
3885 
3886   Input Parameters:
3887 + A   - the `Mat` object
3888 . col - the column index
3889 - v   - the `Vec` object (may be `NULL`)
3890 
3891   Level: intermediate
3892 
3893 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseGetColumnVecRead()`, `MatDenseGetColumnVecWrite()`, `MatDenseRestoreColumnVec()`, `MatDenseRestoreColumnVecRead()`
3894 @*/
3895 PetscErrorCode MatDenseRestoreColumnVecWrite(Mat A, PetscInt col, Vec *v)
3896 {
3897   PetscFunctionBegin;
3898   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3899   PetscValidType(A, 1);
3900   PetscValidLogicalCollectiveInt(A, col, 2);
3901   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3902   PetscCheck(col >= 0 && col < A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Invalid col %" PetscInt_FMT ", should be in [0,%" PetscInt_FMT ")", col, A->cmap->N);
3903   PetscUseMethod(A, "MatDenseRestoreColumnVecWrite_C", (Mat, PetscInt, Vec *), (A, col, v));
3904   PetscFunctionReturn(PETSC_SUCCESS);
3905 }
3906 
3907 /*@
3908   MatDenseGetSubMatrix - Gives access to a block of rows and columns of a dense matrix, represented as a `Mat`.
3909 
3910   Collective
3911 
3912   Input Parameters:
3913 + A      - the `Mat` object
3914 . rbegin - the first global row index in the block (if `PETSC_DECIDE`, is 0)
3915 . rend   - the global row index past the last one in the block (if `PETSC_DECIDE`, is `M`)
3916 . cbegin - the first global column index in the block (if `PETSC_DECIDE`, is 0)
3917 - cend   - the global column index past the last one in the block (if `PETSC_DECIDE`, is `N`)
3918 
3919   Output Parameter:
3920 . v - the matrix
3921 
3922   Level: intermediate
3923 
3924   Notes:
3925   The matrix is owned by PETSc. Users need to call `MatDenseRestoreSubMatrix()` when the matrix is no longer needed.
3926 
3927   The output matrix is not redistributed by PETSc, so depending on the values of `rbegin` and `rend`, some processes may have no local rows.
3928 
3929 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseRestoreColumnVec()`, `MatDenseRestoreSubMatrix()`
3930 @*/
3931 PetscErrorCode MatDenseGetSubMatrix(Mat A, PetscInt rbegin, PetscInt rend, PetscInt cbegin, PetscInt cend, Mat *v)
3932 {
3933   PetscFunctionBegin;
3934   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3935   PetscValidType(A, 1);
3936   PetscValidLogicalCollectiveInt(A, rbegin, 2);
3937   PetscValidLogicalCollectiveInt(A, rend, 3);
3938   PetscValidLogicalCollectiveInt(A, cbegin, 4);
3939   PetscValidLogicalCollectiveInt(A, cend, 5);
3940   PetscAssertPointer(v, 6);
3941   if (rbegin == PETSC_DECIDE) rbegin = 0;
3942   if (rend == PETSC_DECIDE) rend = A->rmap->N;
3943   if (cbegin == PETSC_DECIDE) cbegin = 0;
3944   if (cend == PETSC_DECIDE) cend = A->cmap->N;
3945   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3946   PetscCheck(rbegin >= 0 && rbegin <= A->rmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Invalid rbegin %" PetscInt_FMT ", should be in [0,%" PetscInt_FMT "]", rbegin, A->rmap->N);
3947   PetscCheck(rend >= rbegin && rend <= A->rmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Invalid rend %" PetscInt_FMT ", should be in [%" PetscInt_FMT ",%" PetscInt_FMT "]", rend, rbegin, A->rmap->N);
3948   PetscCheck(cbegin >= 0 && cbegin <= A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Invalid cbegin %" PetscInt_FMT ", should be in [0,%" PetscInt_FMT "]", cbegin, A->cmap->N);
3949   PetscCheck(cend >= cbegin && cend <= A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Invalid cend %" PetscInt_FMT ", should be in [%" PetscInt_FMT ",%" PetscInt_FMT "]", cend, cbegin, A->cmap->N);
3950   PetscUseMethod(A, "MatDenseGetSubMatrix_C", (Mat, PetscInt, PetscInt, PetscInt, PetscInt, Mat *), (A, rbegin, rend, cbegin, cend, v));
3951   PetscFunctionReturn(PETSC_SUCCESS);
3952 }
3953 
3954 /*@
3955   MatDenseRestoreSubMatrix - Returns access to a block of columns of a dense matrix obtained from `MatDenseGetSubMatrix()`.
3956 
3957   Collective
3958 
3959   Input Parameters:
3960 + A - the `Mat` object
3961 - v - the `Mat` object (may be `NULL`)
3962 
3963   Level: intermediate
3964 
3965 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseRestoreColumnVec()`, `MatDenseGetSubMatrix()`
3966 @*/
3967 PetscErrorCode MatDenseRestoreSubMatrix(Mat A, Mat *v)
3968 {
3969   PetscFunctionBegin;
3970   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3971   PetscValidType(A, 1);
3972   PetscAssertPointer(v, 2);
3973   PetscUseMethod(A, "MatDenseRestoreSubMatrix_C", (Mat, Mat *), (A, v));
3974   PetscFunctionReturn(PETSC_SUCCESS);
3975 }
3976 
3977 #include <petscblaslapack.h>
3978 #include <petsc/private/kernels/blockinvert.h>
3979 
3980 PetscErrorCode MatSeqDenseInvert(Mat A)
3981 {
3982   PetscInt        m;
3983   const PetscReal shift = 0.0;
3984   PetscBool       allowzeropivot, zeropivotdetected = PETSC_FALSE;
3985   PetscScalar    *values;
3986 
3987   PetscFunctionBegin;
3988   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3989   PetscCall(MatDenseGetArray(A, &values));
3990   PetscCall(MatGetLocalSize(A, &m, NULL));
3991   allowzeropivot = PetscNot(A->erroriffailure);
3992   /* factor and invert each block */
3993   switch (m) {
3994   case 1:
3995     values[0] = (PetscScalar)1.0 / (values[0] + shift);
3996     break;
3997   case 2:
3998     PetscCall(PetscKernel_A_gets_inverse_A_2(values, shift, allowzeropivot, &zeropivotdetected));
3999     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4000     break;
4001   case 3:
4002     PetscCall(PetscKernel_A_gets_inverse_A_3(values, shift, allowzeropivot, &zeropivotdetected));
4003     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4004     break;
4005   case 4:
4006     PetscCall(PetscKernel_A_gets_inverse_A_4(values, shift, allowzeropivot, &zeropivotdetected));
4007     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4008     break;
4009   case 5: {
4010     PetscScalar work[25];
4011     PetscInt    ipvt[5];
4012 
4013     PetscCall(PetscKernel_A_gets_inverse_A_5(values, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
4014     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4015   } break;
4016   case 6:
4017     PetscCall(PetscKernel_A_gets_inverse_A_6(values, shift, allowzeropivot, &zeropivotdetected));
4018     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4019     break;
4020   case 7:
4021     PetscCall(PetscKernel_A_gets_inverse_A_7(values, shift, allowzeropivot, &zeropivotdetected));
4022     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4023     break;
4024   default: {
4025     PetscInt    *v_pivots, *IJ, j;
4026     PetscScalar *v_work;
4027 
4028     PetscCall(PetscMalloc3(m, &v_work, m, &v_pivots, m, &IJ));
4029     for (j = 0; j < m; j++) IJ[j] = j;
4030     PetscCall(PetscKernel_A_gets_inverse_A(m, values, v_pivots, v_work, allowzeropivot, &zeropivotdetected));
4031     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4032     PetscCall(PetscFree3(v_work, v_pivots, IJ));
4033   }
4034   }
4035   PetscCall(MatDenseRestoreArray(A, &values));
4036   PetscFunctionReturn(PETSC_SUCCESS);
4037 }
4038