xref: /petsc/src/mat/impls/dense/seq/dense.c (revision e6519f9f8d90f4199bf6bb1df3ffafa56045e5d2)
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     PetscCall(PetscInfo(A, "Option %s ignored\n", MatOptions[op]));
2031     break;
2032   case MAT_SPD:
2033   case MAT_SYMMETRIC:
2034   case MAT_STRUCTURALLY_SYMMETRIC:
2035   case MAT_HERMITIAN:
2036   case MAT_SYMMETRY_ETERNAL:
2037   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
2038   case MAT_SPD_ETERNAL:
2039     break;
2040   default:
2041     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "unknown option %s", MatOptions[op]);
2042   }
2043   PetscFunctionReturn(PETSC_SUCCESS);
2044 }
2045 
2046 PetscErrorCode MatZeroEntries_SeqDense(Mat A)
2047 {
2048   Mat_SeqDense *l   = (Mat_SeqDense *)A->data;
2049   PetscInt      lda = l->lda, m = A->rmap->n, n = A->cmap->n, j;
2050   PetscScalar  *v;
2051 
2052   PetscFunctionBegin;
2053   PetscCall(MatDenseGetArrayWrite(A, &v));
2054   if (lda > m) {
2055     for (j = 0; j < n; j++) PetscCall(PetscArrayzero(v + j * lda, m));
2056   } else {
2057     PetscCall(PetscArrayzero(v, PetscInt64Mult(m, n)));
2058   }
2059   PetscCall(MatDenseRestoreArrayWrite(A, &v));
2060   PetscFunctionReturn(PETSC_SUCCESS);
2061 }
2062 
2063 static PetscErrorCode MatZeroRows_SeqDense(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
2064 {
2065   Mat_SeqDense      *l = (Mat_SeqDense *)A->data;
2066   PetscInt           m = l->lda, n = A->cmap->n, i, j;
2067   PetscScalar       *slot, *bb, *v;
2068   const PetscScalar *xx;
2069 
2070   PetscFunctionBegin;
2071   if (PetscDefined(USE_DEBUG)) {
2072     for (i = 0; i < N; i++) {
2073       PetscCheck(rows[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative row requested to be zeroed");
2074       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);
2075     }
2076   }
2077   if (!N) PetscFunctionReturn(PETSC_SUCCESS);
2078 
2079   /* fix right-hand side if needed */
2080   if (x && b) {
2081     PetscCall(VecGetArrayRead(x, &xx));
2082     PetscCall(VecGetArray(b, &bb));
2083     for (i = 0; i < N; i++) bb[rows[i]] = diag * xx[rows[i]];
2084     PetscCall(VecRestoreArrayRead(x, &xx));
2085     PetscCall(VecRestoreArray(b, &bb));
2086   }
2087 
2088   PetscCall(MatDenseGetArray(A, &v));
2089   for (i = 0; i < N; i++) {
2090     slot = v + rows[i];
2091     for (j = 0; j < n; j++) {
2092       *slot = 0.0;
2093       slot += m;
2094     }
2095   }
2096   if (diag != 0.0) {
2097     PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only coded for square matrices");
2098     for (i = 0; i < N; i++) {
2099       slot  = v + (m + 1) * rows[i];
2100       *slot = diag;
2101     }
2102   }
2103   PetscCall(MatDenseRestoreArray(A, &v));
2104   PetscFunctionReturn(PETSC_SUCCESS);
2105 }
2106 
2107 static PetscErrorCode MatDenseGetLDA_SeqDense(Mat A, PetscInt *lda)
2108 {
2109   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
2110 
2111   PetscFunctionBegin;
2112   *lda = mat->lda;
2113   PetscFunctionReturn(PETSC_SUCCESS);
2114 }
2115 
2116 PetscErrorCode MatDenseGetArray_SeqDense(Mat A, PetscScalar **array)
2117 {
2118   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
2119 
2120   PetscFunctionBegin;
2121   PetscCheck(!mat->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
2122   *array = mat->v;
2123   PetscFunctionReturn(PETSC_SUCCESS);
2124 }
2125 
2126 PetscErrorCode MatDenseRestoreArray_SeqDense(Mat A, PetscScalar **array)
2127 {
2128   PetscFunctionBegin;
2129   if (array) *array = NULL;
2130   PetscFunctionReturn(PETSC_SUCCESS);
2131 }
2132 
2133 /*@
2134   MatDenseGetLDA - gets the leading dimension of the array returned from `MatDenseGetArray()`
2135 
2136   Not Collective
2137 
2138   Input Parameter:
2139 . A - a `MATDENSE` or `MATDENSECUDA` matrix
2140 
2141   Output Parameter:
2142 . lda - the leading dimension
2143 
2144   Level: intermediate
2145 
2146 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MatDenseGetArray()`, `MatDenseRestoreArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseSetLDA()`
2147 @*/
2148 PetscErrorCode MatDenseGetLDA(Mat A, PetscInt *lda)
2149 {
2150   PetscFunctionBegin;
2151   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2152   PetscAssertPointer(lda, 2);
2153   MatCheckPreallocated(A, 1);
2154   PetscUseMethod(A, "MatDenseGetLDA_C", (Mat, PetscInt *), (A, lda));
2155   PetscFunctionReturn(PETSC_SUCCESS);
2156 }
2157 
2158 /*@
2159   MatDenseSetLDA - Sets the leading dimension of the array used by the `MATDENSE` matrix
2160 
2161   Collective if the matrix layouts have not yet been setup
2162 
2163   Input Parameters:
2164 + A   - a `MATDENSE` or `MATDENSECUDA` matrix
2165 - lda - the leading dimension
2166 
2167   Level: intermediate
2168 
2169 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MatDenseGetArray()`, `MatDenseRestoreArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetLDA()`
2170 @*/
2171 PetscErrorCode MatDenseSetLDA(Mat A, PetscInt lda)
2172 {
2173   PetscFunctionBegin;
2174   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2175   PetscTryMethod(A, "MatDenseSetLDA_C", (Mat, PetscInt), (A, lda));
2176   PetscFunctionReturn(PETSC_SUCCESS);
2177 }
2178 
2179 /*@C
2180   MatDenseGetArray - gives read-write access to the array where the data for a `MATDENSE` matrix is stored
2181 
2182   Logically Collective
2183 
2184   Input Parameter:
2185 . A - a dense matrix
2186 
2187   Output Parameter:
2188 . array - pointer to the data
2189 
2190   Level: intermediate
2191 
2192   Fortran Notes:
2193   `MatDenseGetArray()` Fortran binding is deprecated (since PETSc 3.19), use `MatDenseGetArrayF90()`
2194 
2195 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2196 @*/
2197 PetscErrorCode MatDenseGetArray(Mat A, PetscScalar *array[])
2198 {
2199   PetscFunctionBegin;
2200   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2201   PetscAssertPointer(array, 2);
2202   PetscUseMethod(A, "MatDenseGetArray_C", (Mat, PetscScalar **), (A, array));
2203   PetscFunctionReturn(PETSC_SUCCESS);
2204 }
2205 
2206 /*@C
2207   MatDenseRestoreArray - returns access to the array where the data for a `MATDENSE` matrix is stored obtained by `MatDenseGetArray()`
2208 
2209   Logically Collective
2210 
2211   Input Parameters:
2212 + A     - a dense matrix
2213 - array - pointer to the data (may be `NULL`)
2214 
2215   Level: intermediate
2216 
2217   Fortran Notes:
2218   `MatDenseRestoreArray()` Fortran binding is deprecated (since PETSc 3.19), use `MatDenseRestoreArrayF90()`
2219 
2220 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2221 @*/
2222 PetscErrorCode MatDenseRestoreArray(Mat A, PetscScalar *array[])
2223 {
2224   PetscFunctionBegin;
2225   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2226   if (array) PetscAssertPointer(array, 2);
2227   PetscUseMethod(A, "MatDenseRestoreArray_C", (Mat, PetscScalar **), (A, array));
2228   PetscCall(PetscObjectStateIncrease((PetscObject)A));
2229 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
2230   A->offloadmask = PETSC_OFFLOAD_CPU;
2231 #endif
2232   PetscFunctionReturn(PETSC_SUCCESS);
2233 }
2234 
2235 /*@C
2236   MatDenseGetArrayRead - gives read-only access to the array where the data for a `MATDENSE` matrix is stored
2237 
2238   Not Collective
2239 
2240   Input Parameter:
2241 . A - a dense matrix
2242 
2243   Output Parameter:
2244 . array - pointer to the data
2245 
2246   Level: intermediate
2247 
2248 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreArrayRead()`, `MatDenseGetArray()`, `MatDenseRestoreArray()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2249 @*/
2250 PetscErrorCode MatDenseGetArrayRead(Mat A, const PetscScalar *array[])
2251 {
2252   PetscFunctionBegin;
2253   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2254   PetscAssertPointer(array, 2);
2255   PetscUseMethod(A, "MatDenseGetArrayRead_C", (Mat, PetscScalar **), (A, (PetscScalar **)array));
2256   PetscFunctionReturn(PETSC_SUCCESS);
2257 }
2258 
2259 /*@C
2260   MatDenseRestoreArrayRead - returns access to the array where the data for a `MATDENSE` matrix is stored obtained by `MatDenseGetArrayRead()`
2261 
2262   Not Collective
2263 
2264   Input Parameters:
2265 + A     - a dense matrix
2266 - array - pointer to the data (may be `NULL`)
2267 
2268   Level: intermediate
2269 
2270 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArrayRead()`, `MatDenseGetArray()`, `MatDenseRestoreArray()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2271 @*/
2272 PetscErrorCode MatDenseRestoreArrayRead(Mat A, const PetscScalar *array[])
2273 {
2274   PetscFunctionBegin;
2275   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2276   if (array) PetscAssertPointer(array, 2);
2277   PetscUseMethod(A, "MatDenseRestoreArrayRead_C", (Mat, PetscScalar **), (A, (PetscScalar **)array));
2278   PetscFunctionReturn(PETSC_SUCCESS);
2279 }
2280 
2281 /*@C
2282   MatDenseGetArrayWrite - gives write-only access to the array where the data for a `MATDENSE` matrix is stored
2283 
2284   Not Collective
2285 
2286   Input Parameter:
2287 . A - a dense matrix
2288 
2289   Output Parameter:
2290 . array - pointer to the data
2291 
2292   Level: intermediate
2293 
2294 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreArrayWrite()`, `MatDenseGetArray()`, `MatDenseRestoreArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`
2295 @*/
2296 PetscErrorCode MatDenseGetArrayWrite(Mat A, PetscScalar *array[])
2297 {
2298   PetscFunctionBegin;
2299   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2300   PetscAssertPointer(array, 2);
2301   PetscUseMethod(A, "MatDenseGetArrayWrite_C", (Mat, PetscScalar **), (A, array));
2302   PetscFunctionReturn(PETSC_SUCCESS);
2303 }
2304 
2305 /*@C
2306   MatDenseRestoreArrayWrite - returns access to the array where the data for a `MATDENSE` matrix is stored obtained by `MatDenseGetArrayWrite()`
2307 
2308   Not Collective
2309 
2310   Input Parameters:
2311 + A     - a dense matrix
2312 - array - pointer to the data (may be `NULL`)
2313 
2314   Level: intermediate
2315 
2316 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArrayWrite()`, `MatDenseGetArray()`, `MatDenseRestoreArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`
2317 @*/
2318 PetscErrorCode MatDenseRestoreArrayWrite(Mat A, PetscScalar *array[])
2319 {
2320   PetscFunctionBegin;
2321   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2322   if (array) PetscAssertPointer(array, 2);
2323   PetscUseMethod(A, "MatDenseRestoreArrayWrite_C", (Mat, PetscScalar **), (A, array));
2324   PetscCall(PetscObjectStateIncrease((PetscObject)A));
2325 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
2326   A->offloadmask = PETSC_OFFLOAD_CPU;
2327 #endif
2328   PetscFunctionReturn(PETSC_SUCCESS);
2329 }
2330 
2331 /*@C
2332   MatDenseGetArrayAndMemType - gives read-write access to the array where the data for a `MATDENSE` matrix is stored
2333 
2334   Logically Collective
2335 
2336   Input Parameter:
2337 . A - a dense matrix
2338 
2339   Output Parameters:
2340 + array - pointer to the data
2341 - mtype - memory type of the returned pointer
2342 
2343   Level: intermediate
2344 
2345   Note:
2346   If the matrix is of a device type such as `MATDENSECUDA`, `MATDENSEHIP`, etc.,
2347   an array on device is always returned and is guaranteed to contain the matrix's latest data.
2348 
2349 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreArrayAndMemType()`, `MatDenseGetArrayReadAndMemType()`, `MatDenseGetArrayWriteAndMemType()`, `MatDenseGetArrayRead()`,
2350    `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`, `MatSeqAIJGetCSRAndMemType()`
2351 @*/
2352 PetscErrorCode MatDenseGetArrayAndMemType(Mat A, PetscScalar *array[], PetscMemType *mtype)
2353 {
2354   PetscBool isMPI;
2355 
2356   PetscFunctionBegin;
2357   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2358   PetscAssertPointer(array, 2);
2359   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 */
2360   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &isMPI));
2361   if (isMPI) {
2362     /* Dispatch here so that the code can be reused for all subclasses of MATDENSE */
2363     PetscCall(MatDenseGetArrayAndMemType(((Mat_MPIDense *)A->data)->A, array, mtype));
2364   } else {
2365     PetscErrorCode (*fptr)(Mat, PetscScalar **, PetscMemType *);
2366 
2367     PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatDenseGetArrayAndMemType_C", &fptr));
2368     if (fptr) {
2369       PetscCall((*fptr)(A, array, mtype));
2370     } else {
2371       PetscUseMethod(A, "MatDenseGetArray_C", (Mat, PetscScalar **), (A, array));
2372       if (mtype) *mtype = PETSC_MEMTYPE_HOST;
2373     }
2374   }
2375   PetscFunctionReturn(PETSC_SUCCESS);
2376 }
2377 
2378 /*@C
2379   MatDenseRestoreArrayAndMemType - returns access to the array that is obtained by `MatDenseGetArrayAndMemType()`
2380 
2381   Logically Collective
2382 
2383   Input Parameters:
2384 + A     - a dense matrix
2385 - array - pointer to the data
2386 
2387   Level: intermediate
2388 
2389 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArrayAndMemType()`, `MatDenseGetArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2390 @*/
2391 PetscErrorCode MatDenseRestoreArrayAndMemType(Mat A, PetscScalar *array[])
2392 {
2393   PetscBool isMPI;
2394 
2395   PetscFunctionBegin;
2396   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2397   PetscAssertPointer(array, 2);
2398   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &isMPI));
2399   if (isMPI) {
2400     PetscCall(MatDenseRestoreArrayAndMemType(((Mat_MPIDense *)A->data)->A, array));
2401   } else {
2402     PetscErrorCode (*fptr)(Mat, PetscScalar **);
2403 
2404     PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatDenseRestoreArrayAndMemType_C", &fptr));
2405     if (fptr) {
2406       PetscCall((*fptr)(A, array));
2407     } else {
2408       PetscUseMethod(A, "MatDenseRestoreArray_C", (Mat, PetscScalar **), (A, array));
2409     }
2410     *array = NULL;
2411   }
2412   PetscCall(PetscObjectStateIncrease((PetscObject)A));
2413   PetscFunctionReturn(PETSC_SUCCESS);
2414 }
2415 
2416 /*@C
2417   MatDenseGetArrayReadAndMemType - gives read-only access to the array where the data for a `MATDENSE` matrix is stored
2418 
2419   Logically Collective
2420 
2421   Input Parameter:
2422 . A - a dense matrix
2423 
2424   Output Parameters:
2425 + array - pointer to the data
2426 - mtype - memory type of the returned pointer
2427 
2428   Level: intermediate
2429 
2430   Note:
2431   If the matrix is of a device type such as `MATDENSECUDA`, `MATDENSEHIP`, etc.,
2432   an array on device is always returned and is guaranteed to contain the matrix's latest data.
2433 
2434 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreArrayReadAndMemType()`, `MatDenseGetArrayWriteAndMemType()`,
2435    `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`, `MatSeqAIJGetCSRAndMemType()`
2436 @*/
2437 PetscErrorCode MatDenseGetArrayReadAndMemType(Mat A, const PetscScalar *array[], PetscMemType *mtype)
2438 {
2439   PetscBool isMPI;
2440 
2441   PetscFunctionBegin;
2442   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2443   PetscAssertPointer(array, 2);
2444   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 */
2445   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &isMPI));
2446   if (isMPI) { /* Dispatch here so that the code can be reused for all subclasses of MATDENSE */
2447     PetscCall(MatDenseGetArrayReadAndMemType(((Mat_MPIDense *)A->data)->A, array, mtype));
2448   } else {
2449     PetscErrorCode (*fptr)(Mat, const PetscScalar **, PetscMemType *);
2450 
2451     PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatDenseGetArrayReadAndMemType_C", &fptr));
2452     if (fptr) {
2453       PetscCall((*fptr)(A, array, mtype));
2454     } else {
2455       PetscUseMethod(A, "MatDenseGetArrayRead_C", (Mat, PetscScalar **), (A, (PetscScalar **)array));
2456       if (mtype) *mtype = PETSC_MEMTYPE_HOST;
2457     }
2458   }
2459   PetscFunctionReturn(PETSC_SUCCESS);
2460 }
2461 
2462 /*@C
2463   MatDenseRestoreArrayReadAndMemType - returns access to the array that is obtained by `MatDenseGetArrayReadAndMemType()`
2464 
2465   Logically Collective
2466 
2467   Input Parameters:
2468 + A     - a dense matrix
2469 - array - pointer to the data
2470 
2471   Level: intermediate
2472 
2473 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArrayReadAndMemType()`, `MatDenseGetArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2474 @*/
2475 PetscErrorCode MatDenseRestoreArrayReadAndMemType(Mat A, const PetscScalar *array[])
2476 {
2477   PetscBool isMPI;
2478 
2479   PetscFunctionBegin;
2480   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2481   PetscAssertPointer(array, 2);
2482   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &isMPI));
2483   if (isMPI) {
2484     PetscCall(MatDenseRestoreArrayReadAndMemType(((Mat_MPIDense *)A->data)->A, array));
2485   } else {
2486     PetscErrorCode (*fptr)(Mat, const PetscScalar **);
2487 
2488     PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatDenseRestoreArrayReadAndMemType_C", &fptr));
2489     if (fptr) {
2490       PetscCall((*fptr)(A, array));
2491     } else {
2492       PetscUseMethod(A, "MatDenseRestoreArrayRead_C", (Mat, PetscScalar **), (A, (PetscScalar **)array));
2493     }
2494     *array = NULL;
2495   }
2496   PetscFunctionReturn(PETSC_SUCCESS);
2497 }
2498 
2499 /*@C
2500   MatDenseGetArrayWriteAndMemType - gives write-only access to the array where the data for a `MATDENSE` matrix is stored
2501 
2502   Logically Collective
2503 
2504   Input Parameter:
2505 . A - a dense matrix
2506 
2507   Output Parameters:
2508 + array - pointer to the data
2509 - mtype - memory type of the returned pointer
2510 
2511   Level: intermediate
2512 
2513   Note:
2514   If the matrix is of a device type such as `MATDENSECUDA`, `MATDENSEHIP`, etc.,
2515   an array on device is always returned and is guaranteed to contain the matrix's latest data.
2516 
2517 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreArrayWriteAndMemType()`, `MatDenseGetArrayReadAndMemType()`, `MatDenseGetArrayRead()`,
2518   `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`, `MatSeqAIJGetCSRAndMemType()`
2519 @*/
2520 PetscErrorCode MatDenseGetArrayWriteAndMemType(Mat A, PetscScalar *array[], PetscMemType *mtype)
2521 {
2522   PetscBool isMPI;
2523 
2524   PetscFunctionBegin;
2525   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2526   PetscAssertPointer(array, 2);
2527   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 */
2528   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &isMPI));
2529   if (isMPI) {
2530     PetscCall(MatDenseGetArrayWriteAndMemType(((Mat_MPIDense *)A->data)->A, array, mtype));
2531   } else {
2532     PetscErrorCode (*fptr)(Mat, PetscScalar **, PetscMemType *);
2533 
2534     PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatDenseGetArrayWriteAndMemType_C", &fptr));
2535     if (fptr) {
2536       PetscCall((*fptr)(A, array, mtype));
2537     } else {
2538       PetscUseMethod(A, "MatDenseGetArrayWrite_C", (Mat, PetscScalar **), (A, array));
2539       if (mtype) *mtype = PETSC_MEMTYPE_HOST;
2540     }
2541   }
2542   PetscFunctionReturn(PETSC_SUCCESS);
2543 }
2544 
2545 /*@C
2546   MatDenseRestoreArrayWriteAndMemType - returns access to the array that is obtained by `MatDenseGetArrayReadAndMemType()`
2547 
2548   Logically Collective
2549 
2550   Input Parameters:
2551 + A     - a dense matrix
2552 - array - pointer to the data
2553 
2554   Level: intermediate
2555 
2556 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArrayWriteAndMemType()`, `MatDenseGetArray()`, `MatDenseGetArrayRead()`, `MatDenseRestoreArrayRead()`, `MatDenseGetArrayWrite()`, `MatDenseRestoreArrayWrite()`
2557 @*/
2558 PetscErrorCode MatDenseRestoreArrayWriteAndMemType(Mat A, PetscScalar *array[])
2559 {
2560   PetscBool isMPI;
2561 
2562   PetscFunctionBegin;
2563   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
2564   PetscAssertPointer(array, 2);
2565   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &isMPI));
2566   if (isMPI) {
2567     PetscCall(MatDenseRestoreArrayWriteAndMemType(((Mat_MPIDense *)A->data)->A, array));
2568   } else {
2569     PetscErrorCode (*fptr)(Mat, PetscScalar **);
2570 
2571     PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatDenseRestoreArrayWriteAndMemType_C", &fptr));
2572     if (fptr) {
2573       PetscCall((*fptr)(A, array));
2574     } else {
2575       PetscUseMethod(A, "MatDenseRestoreArrayWrite_C", (Mat, PetscScalar **), (A, array));
2576     }
2577     *array = NULL;
2578   }
2579   PetscCall(PetscObjectStateIncrease((PetscObject)A));
2580   PetscFunctionReturn(PETSC_SUCCESS);
2581 }
2582 
2583 static PetscErrorCode MatCreateSubMatrix_SeqDense(Mat A, IS isrow, IS iscol, MatReuse scall, Mat *B)
2584 {
2585   Mat_SeqDense   *mat = (Mat_SeqDense *)A->data;
2586   PetscInt        i, j, nrows, ncols, ldb;
2587   const PetscInt *irow, *icol;
2588   PetscScalar    *av, *bv, *v = mat->v;
2589   Mat             newmat;
2590 
2591   PetscFunctionBegin;
2592   PetscCall(ISGetIndices(isrow, &irow));
2593   PetscCall(ISGetIndices(iscol, &icol));
2594   PetscCall(ISGetLocalSize(isrow, &nrows));
2595   PetscCall(ISGetLocalSize(iscol, &ncols));
2596 
2597   /* Check submatrixcall */
2598   if (scall == MAT_REUSE_MATRIX) {
2599     PetscInt n_cols, n_rows;
2600     PetscCall(MatGetSize(*B, &n_rows, &n_cols));
2601     if (n_rows != nrows || n_cols != ncols) {
2602       /* resize the result matrix to match number of requested rows/columns */
2603       PetscCall(MatSetSizes(*B, nrows, ncols, nrows, ncols));
2604     }
2605     newmat = *B;
2606   } else {
2607     /* Create and fill new matrix */
2608     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &newmat));
2609     PetscCall(MatSetSizes(newmat, nrows, ncols, nrows, ncols));
2610     PetscCall(MatSetType(newmat, ((PetscObject)A)->type_name));
2611     PetscCall(MatSeqDenseSetPreallocation(newmat, NULL));
2612   }
2613 
2614   /* Now extract the data pointers and do the copy,column at a time */
2615   PetscCall(MatDenseGetArray(newmat, &bv));
2616   PetscCall(MatDenseGetLDA(newmat, &ldb));
2617   for (i = 0; i < ncols; i++) {
2618     av = v + mat->lda * icol[i];
2619     for (j = 0; j < nrows; j++) bv[j] = av[irow[j]];
2620     bv += ldb;
2621   }
2622   PetscCall(MatDenseRestoreArray(newmat, &bv));
2623 
2624   /* Assemble the matrices so that the correct flags are set */
2625   PetscCall(MatAssemblyBegin(newmat, MAT_FINAL_ASSEMBLY));
2626   PetscCall(MatAssemblyEnd(newmat, MAT_FINAL_ASSEMBLY));
2627 
2628   /* Free work space */
2629   PetscCall(ISRestoreIndices(isrow, &irow));
2630   PetscCall(ISRestoreIndices(iscol, &icol));
2631   *B = newmat;
2632   PetscFunctionReturn(PETSC_SUCCESS);
2633 }
2634 
2635 static PetscErrorCode MatCreateSubMatrices_SeqDense(Mat A, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *B[])
2636 {
2637   PetscInt i;
2638 
2639   PetscFunctionBegin;
2640   if (scall == MAT_INITIAL_MATRIX) PetscCall(PetscCalloc1(n, B));
2641 
2642   for (i = 0; i < n; i++) PetscCall(MatCreateSubMatrix_SeqDense(A, irow[i], icol[i], scall, &(*B)[i]));
2643   PetscFunctionReturn(PETSC_SUCCESS);
2644 }
2645 
2646 PetscErrorCode MatCopy_SeqDense(Mat A, Mat B, MatStructure str)
2647 {
2648   Mat_SeqDense      *a = (Mat_SeqDense *)A->data, *b = (Mat_SeqDense *)B->data;
2649   const PetscScalar *va;
2650   PetscScalar       *vb;
2651   PetscInt           lda1 = a->lda, lda2 = b->lda, m = A->rmap->n, n = A->cmap->n, j;
2652 
2653   PetscFunctionBegin;
2654   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2655   if (A->ops->copy != B->ops->copy) {
2656     PetscCall(MatCopy_Basic(A, B, str));
2657     PetscFunctionReturn(PETSC_SUCCESS);
2658   }
2659   PetscCheck(m == B->rmap->n && n == B->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "size(B) != size(A)");
2660   PetscCall(MatDenseGetArrayRead(A, &va));
2661   PetscCall(MatDenseGetArray(B, &vb));
2662   if (lda1 > m || lda2 > m) {
2663     for (j = 0; j < n; j++) PetscCall(PetscArraycpy(vb + j * lda2, va + j * lda1, m));
2664   } else {
2665     PetscCall(PetscArraycpy(vb, va, A->rmap->n * A->cmap->n));
2666   }
2667   PetscCall(MatDenseRestoreArray(B, &vb));
2668   PetscCall(MatDenseRestoreArrayRead(A, &va));
2669   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
2670   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
2671   PetscFunctionReturn(PETSC_SUCCESS);
2672 }
2673 
2674 PetscErrorCode MatSetUp_SeqDense(Mat A)
2675 {
2676   PetscFunctionBegin;
2677   PetscCall(PetscLayoutSetUp(A->rmap));
2678   PetscCall(PetscLayoutSetUp(A->cmap));
2679   if (!A->preallocated) PetscCall(MatSeqDenseSetPreallocation(A, NULL));
2680   PetscFunctionReturn(PETSC_SUCCESS);
2681 }
2682 
2683 static PetscErrorCode MatConjugate_SeqDense(Mat A)
2684 {
2685   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
2686   PetscInt      i, j;
2687   PetscInt      min = PetscMin(A->rmap->n, A->cmap->n);
2688   PetscScalar  *aa;
2689 
2690   PetscFunctionBegin;
2691   PetscCall(MatDenseGetArray(A, &aa));
2692   for (j = 0; j < A->cmap->n; j++) {
2693     for (i = 0; i < A->rmap->n; i++) aa[i + j * mat->lda] = PetscConj(aa[i + j * mat->lda]);
2694   }
2695   PetscCall(MatDenseRestoreArray(A, &aa));
2696   if (mat->tau)
2697     for (i = 0; i < min; i++) mat->tau[i] = PetscConj(mat->tau[i]);
2698   PetscFunctionReturn(PETSC_SUCCESS);
2699 }
2700 
2701 static PetscErrorCode MatRealPart_SeqDense(Mat A)
2702 {
2703   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
2704   PetscInt      i, j;
2705   PetscScalar  *aa;
2706 
2707   PetscFunctionBegin;
2708   PetscCall(MatDenseGetArray(A, &aa));
2709   for (j = 0; j < A->cmap->n; j++) {
2710     for (i = 0; i < A->rmap->n; i++) aa[i + j * mat->lda] = PetscRealPart(aa[i + j * mat->lda]);
2711   }
2712   PetscCall(MatDenseRestoreArray(A, &aa));
2713   PetscFunctionReturn(PETSC_SUCCESS);
2714 }
2715 
2716 static PetscErrorCode MatImaginaryPart_SeqDense(Mat A)
2717 {
2718   Mat_SeqDense *mat = (Mat_SeqDense *)A->data;
2719   PetscInt      i, j;
2720   PetscScalar  *aa;
2721 
2722   PetscFunctionBegin;
2723   PetscCall(MatDenseGetArray(A, &aa));
2724   for (j = 0; j < A->cmap->n; j++) {
2725     for (i = 0; i < A->rmap->n; i++) aa[i + j * mat->lda] = PetscImaginaryPart(aa[i + j * mat->lda]);
2726   }
2727   PetscCall(MatDenseRestoreArray(A, &aa));
2728   PetscFunctionReturn(PETSC_SUCCESS);
2729 }
2730 
2731 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqDense(Mat A, Mat B, PetscReal fill, Mat C)
2732 {
2733   PetscInt  m = A->rmap->n, n = B->cmap->n;
2734   PetscBool cisdense = PETSC_FALSE;
2735 
2736   PetscFunctionBegin;
2737   PetscCall(MatSetSizes(C, m, n, m, n));
2738 #if defined(PETSC_HAVE_CUDA)
2739   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSECUDA, ""));
2740 #endif
2741 #if defined(PETSC_HAVE_HIP)
2742   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSEHIP, ""));
2743 #endif
2744   if (!cisdense) {
2745     PetscBool flg;
2746 
2747     PetscCall(PetscObjectTypeCompare((PetscObject)B, ((PetscObject)A)->type_name, &flg));
2748     PetscCall(MatSetType(C, flg ? ((PetscObject)A)->type_name : MATDENSE));
2749   }
2750   PetscCall(MatSetUp(C));
2751   PetscFunctionReturn(PETSC_SUCCESS);
2752 }
2753 
2754 PetscErrorCode MatMatMultNumeric_SeqDense_SeqDense(Mat A, Mat B, Mat C)
2755 {
2756   Mat_SeqDense      *a = (Mat_SeqDense *)A->data, *b = (Mat_SeqDense *)B->data, *c = (Mat_SeqDense *)C->data;
2757   PetscBLASInt       m, n, k;
2758   const PetscScalar *av, *bv;
2759   PetscScalar       *cv;
2760   PetscScalar        _DOne = 1.0, _DZero = 0.0;
2761 
2762   PetscFunctionBegin;
2763   PetscCall(PetscBLASIntCast(C->rmap->n, &m));
2764   PetscCall(PetscBLASIntCast(C->cmap->n, &n));
2765   PetscCall(PetscBLASIntCast(A->cmap->n, &k));
2766   if (!m || !n || !k) PetscFunctionReturn(PETSC_SUCCESS);
2767   PetscCall(MatDenseGetArrayRead(A, &av));
2768   PetscCall(MatDenseGetArrayRead(B, &bv));
2769   PetscCall(MatDenseGetArrayWrite(C, &cv));
2770   PetscCallBLAS("BLASgemm", BLASgemm_("N", "N", &m, &n, &k, &_DOne, av, &a->lda, bv, &b->lda, &_DZero, cv, &c->lda));
2771   PetscCall(PetscLogFlops(1.0 * m * n * k + 1.0 * m * n * (k - 1)));
2772   PetscCall(MatDenseRestoreArrayRead(A, &av));
2773   PetscCall(MatDenseRestoreArrayRead(B, &bv));
2774   PetscCall(MatDenseRestoreArrayWrite(C, &cv));
2775   PetscFunctionReturn(PETSC_SUCCESS);
2776 }
2777 
2778 PetscErrorCode MatMatTransposeMultSymbolic_SeqDense_SeqDense(Mat A, Mat B, PetscReal fill, Mat C)
2779 {
2780   PetscInt  m = A->rmap->n, n = B->rmap->n;
2781   PetscBool cisdense = PETSC_FALSE;
2782 
2783   PetscFunctionBegin;
2784   PetscCall(MatSetSizes(C, m, n, m, n));
2785 #if defined(PETSC_HAVE_CUDA)
2786   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSECUDA, ""));
2787 #endif
2788 #if defined(PETSC_HAVE_HIP)
2789   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSEHIP, ""));
2790 #endif
2791   if (!cisdense) {
2792     PetscBool flg;
2793 
2794     PetscCall(PetscObjectTypeCompare((PetscObject)B, ((PetscObject)A)->type_name, &flg));
2795     PetscCall(MatSetType(C, flg ? ((PetscObject)A)->type_name : MATDENSE));
2796   }
2797   PetscCall(MatSetUp(C));
2798   PetscFunctionReturn(PETSC_SUCCESS);
2799 }
2800 
2801 PetscErrorCode MatMatTransposeMultNumeric_SeqDense_SeqDense(Mat A, Mat B, Mat C)
2802 {
2803   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
2804   Mat_SeqDense      *b = (Mat_SeqDense *)B->data;
2805   Mat_SeqDense      *c = (Mat_SeqDense *)C->data;
2806   const PetscScalar *av, *bv;
2807   PetscScalar       *cv;
2808   PetscBLASInt       m, n, k;
2809   PetscScalar        _DOne = 1.0, _DZero = 0.0;
2810 
2811   PetscFunctionBegin;
2812   PetscCall(PetscBLASIntCast(C->rmap->n, &m));
2813   PetscCall(PetscBLASIntCast(C->cmap->n, &n));
2814   PetscCall(PetscBLASIntCast(A->cmap->n, &k));
2815   if (!m || !n || !k) PetscFunctionReturn(PETSC_SUCCESS);
2816   PetscCall(MatDenseGetArrayRead(A, &av));
2817   PetscCall(MatDenseGetArrayRead(B, &bv));
2818   PetscCall(MatDenseGetArrayWrite(C, &cv));
2819   PetscCallBLAS("BLASgemm", BLASgemm_("N", "T", &m, &n, &k, &_DOne, av, &a->lda, bv, &b->lda, &_DZero, cv, &c->lda));
2820   PetscCall(MatDenseRestoreArrayRead(A, &av));
2821   PetscCall(MatDenseRestoreArrayRead(B, &bv));
2822   PetscCall(MatDenseRestoreArrayWrite(C, &cv));
2823   PetscCall(PetscLogFlops(1.0 * m * n * k + 1.0 * m * n * (k - 1)));
2824   PetscFunctionReturn(PETSC_SUCCESS);
2825 }
2826 
2827 PetscErrorCode MatTransposeMatMultSymbolic_SeqDense_SeqDense(Mat A, Mat B, PetscReal fill, Mat C)
2828 {
2829   PetscInt  m = A->cmap->n, n = B->cmap->n;
2830   PetscBool cisdense = PETSC_FALSE;
2831 
2832   PetscFunctionBegin;
2833   PetscCall(MatSetSizes(C, m, n, m, n));
2834 #if defined(PETSC_HAVE_CUDA)
2835   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSECUDA, ""));
2836 #endif
2837 #if defined(PETSC_HAVE_HIP)
2838   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATSEQDENSE, MATSEQDENSEHIP, ""));
2839 #endif
2840   if (!cisdense) {
2841     PetscBool flg;
2842 
2843     PetscCall(PetscObjectTypeCompare((PetscObject)B, ((PetscObject)A)->type_name, &flg));
2844     PetscCall(MatSetType(C, flg ? ((PetscObject)A)->type_name : MATDENSE));
2845   }
2846   PetscCall(MatSetUp(C));
2847   PetscFunctionReturn(PETSC_SUCCESS);
2848 }
2849 
2850 PetscErrorCode MatTransposeMatMultNumeric_SeqDense_SeqDense(Mat A, Mat B, Mat C)
2851 {
2852   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
2853   Mat_SeqDense      *b = (Mat_SeqDense *)B->data;
2854   Mat_SeqDense      *c = (Mat_SeqDense *)C->data;
2855   const PetscScalar *av, *bv;
2856   PetscScalar       *cv;
2857   PetscBLASInt       m, n, k;
2858   PetscScalar        _DOne = 1.0, _DZero = 0.0;
2859 
2860   PetscFunctionBegin;
2861   PetscCall(PetscBLASIntCast(C->rmap->n, &m));
2862   PetscCall(PetscBLASIntCast(C->cmap->n, &n));
2863   PetscCall(PetscBLASIntCast(A->rmap->n, &k));
2864   if (!m || !n || !k) PetscFunctionReturn(PETSC_SUCCESS);
2865   PetscCall(MatDenseGetArrayRead(A, &av));
2866   PetscCall(MatDenseGetArrayRead(B, &bv));
2867   PetscCall(MatDenseGetArrayWrite(C, &cv));
2868   PetscCallBLAS("BLASgemm", BLASgemm_("T", "N", &m, &n, &k, &_DOne, av, &a->lda, bv, &b->lda, &_DZero, cv, &c->lda));
2869   PetscCall(MatDenseRestoreArrayRead(A, &av));
2870   PetscCall(MatDenseRestoreArrayRead(B, &bv));
2871   PetscCall(MatDenseRestoreArrayWrite(C, &cv));
2872   PetscCall(PetscLogFlops(1.0 * m * n * k + 1.0 * m * n * (k - 1)));
2873   PetscFunctionReturn(PETSC_SUCCESS);
2874 }
2875 
2876 static PetscErrorCode MatProductSetFromOptions_SeqDense_AB(Mat C)
2877 {
2878   PetscFunctionBegin;
2879   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqDense_SeqDense;
2880   C->ops->productsymbolic = MatProductSymbolic_AB;
2881   PetscFunctionReturn(PETSC_SUCCESS);
2882 }
2883 
2884 static PetscErrorCode MatProductSetFromOptions_SeqDense_AtB(Mat C)
2885 {
2886   PetscFunctionBegin;
2887   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_SeqDense_SeqDense;
2888   C->ops->productsymbolic          = MatProductSymbolic_AtB;
2889   PetscFunctionReturn(PETSC_SUCCESS);
2890 }
2891 
2892 static PetscErrorCode MatProductSetFromOptions_SeqDense_ABt(Mat C)
2893 {
2894   PetscFunctionBegin;
2895   C->ops->mattransposemultsymbolic = MatMatTransposeMultSymbolic_SeqDense_SeqDense;
2896   C->ops->productsymbolic          = MatProductSymbolic_ABt;
2897   PetscFunctionReturn(PETSC_SUCCESS);
2898 }
2899 
2900 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqDense(Mat C)
2901 {
2902   Mat_Product *product = C->product;
2903 
2904   PetscFunctionBegin;
2905   switch (product->type) {
2906   case MATPRODUCT_AB:
2907     PetscCall(MatProductSetFromOptions_SeqDense_AB(C));
2908     break;
2909   case MATPRODUCT_AtB:
2910     PetscCall(MatProductSetFromOptions_SeqDense_AtB(C));
2911     break;
2912   case MATPRODUCT_ABt:
2913     PetscCall(MatProductSetFromOptions_SeqDense_ABt(C));
2914     break;
2915   default:
2916     break;
2917   }
2918   PetscFunctionReturn(PETSC_SUCCESS);
2919 }
2920 
2921 static PetscErrorCode MatGetRowMax_SeqDense(Mat A, Vec v, PetscInt idx[])
2922 {
2923   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
2924   PetscInt           i, j, m = A->rmap->n, n = A->cmap->n, p;
2925   PetscScalar       *x;
2926   const PetscScalar *aa;
2927 
2928   PetscFunctionBegin;
2929   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
2930   PetscCall(VecGetArray(v, &x));
2931   PetscCall(VecGetLocalSize(v, &p));
2932   PetscCall(MatDenseGetArrayRead(A, &aa));
2933   PetscCheck(p == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
2934   for (i = 0; i < m; i++) {
2935     x[i] = aa[i];
2936     if (idx) idx[i] = 0;
2937     for (j = 1; j < n; j++) {
2938       if (PetscRealPart(x[i]) < PetscRealPart(aa[i + a->lda * j])) {
2939         x[i] = aa[i + a->lda * j];
2940         if (idx) idx[i] = j;
2941       }
2942     }
2943   }
2944   PetscCall(MatDenseRestoreArrayRead(A, &aa));
2945   PetscCall(VecRestoreArray(v, &x));
2946   PetscFunctionReturn(PETSC_SUCCESS);
2947 }
2948 
2949 static PetscErrorCode MatGetRowMaxAbs_SeqDense(Mat A, Vec v, PetscInt idx[])
2950 {
2951   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
2952   PetscInt           i, j, m = A->rmap->n, n = A->cmap->n, p;
2953   PetscScalar       *x;
2954   PetscReal          atmp;
2955   const PetscScalar *aa;
2956 
2957   PetscFunctionBegin;
2958   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
2959   PetscCall(VecGetArray(v, &x));
2960   PetscCall(VecGetLocalSize(v, &p));
2961   PetscCall(MatDenseGetArrayRead(A, &aa));
2962   PetscCheck(p == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
2963   for (i = 0; i < m; i++) {
2964     x[i] = PetscAbsScalar(aa[i]);
2965     for (j = 1; j < n; j++) {
2966       atmp = PetscAbsScalar(aa[i + a->lda * j]);
2967       if (PetscAbsScalar(x[i]) < atmp) {
2968         x[i] = atmp;
2969         if (idx) idx[i] = j;
2970       }
2971     }
2972   }
2973   PetscCall(MatDenseRestoreArrayRead(A, &aa));
2974   PetscCall(VecRestoreArray(v, &x));
2975   PetscFunctionReturn(PETSC_SUCCESS);
2976 }
2977 
2978 static PetscErrorCode MatGetRowMin_SeqDense(Mat A, Vec v, PetscInt idx[])
2979 {
2980   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
2981   PetscInt           i, j, m = A->rmap->n, n = A->cmap->n, p;
2982   PetscScalar       *x;
2983   const PetscScalar *aa;
2984 
2985   PetscFunctionBegin;
2986   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
2987   PetscCall(MatDenseGetArrayRead(A, &aa));
2988   PetscCall(VecGetArray(v, &x));
2989   PetscCall(VecGetLocalSize(v, &p));
2990   PetscCheck(p == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming matrix and vector");
2991   for (i = 0; i < m; i++) {
2992     x[i] = aa[i];
2993     if (idx) idx[i] = 0;
2994     for (j = 1; j < n; j++) {
2995       if (PetscRealPart(x[i]) > PetscRealPart(aa[i + a->lda * j])) {
2996         x[i] = aa[i + a->lda * j];
2997         if (idx) idx[i] = j;
2998       }
2999     }
3000   }
3001   PetscCall(VecRestoreArray(v, &x));
3002   PetscCall(MatDenseRestoreArrayRead(A, &aa));
3003   PetscFunctionReturn(PETSC_SUCCESS);
3004 }
3005 
3006 PetscErrorCode MatGetColumnVector_SeqDense(Mat A, Vec v, PetscInt col)
3007 {
3008   Mat_SeqDense      *a = (Mat_SeqDense *)A->data;
3009   PetscScalar       *x;
3010   const PetscScalar *aa;
3011 
3012   PetscFunctionBegin;
3013   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3014   PetscCall(MatDenseGetArrayRead(A, &aa));
3015   PetscCall(VecGetArray(v, &x));
3016   PetscCall(PetscArraycpy(x, aa + col * a->lda, A->rmap->n));
3017   PetscCall(VecRestoreArray(v, &x));
3018   PetscCall(MatDenseRestoreArrayRead(A, &aa));
3019   PetscFunctionReturn(PETSC_SUCCESS);
3020 }
3021 
3022 PETSC_INTERN PetscErrorCode MatGetColumnReductions_SeqDense(Mat A, PetscInt type, PetscReal *reductions)
3023 {
3024   PetscInt           i, j, m, n;
3025   const PetscScalar *a;
3026 
3027   PetscFunctionBegin;
3028   PetscCall(MatGetSize(A, &m, &n));
3029   PetscCall(PetscArrayzero(reductions, n));
3030   PetscCall(MatDenseGetArrayRead(A, &a));
3031   if (type == NORM_2) {
3032     for (i = 0; i < n; i++) {
3033       for (j = 0; j < m; j++) reductions[i] += PetscAbsScalar(a[j] * a[j]);
3034       a = PetscSafePointerPlusOffset(a, m);
3035     }
3036   } else if (type == NORM_1) {
3037     for (i = 0; i < n; i++) {
3038       for (j = 0; j < m; j++) reductions[i] += PetscAbsScalar(a[j]);
3039       a = PetscSafePointerPlusOffset(a, m);
3040     }
3041   } else if (type == NORM_INFINITY) {
3042     for (i = 0; i < n; i++) {
3043       for (j = 0; j < m; j++) reductions[i] = PetscMax(PetscAbsScalar(a[j]), reductions[i]);
3044       a = PetscSafePointerPlusOffset(a, m);
3045     }
3046   } else if (type == REDUCTION_SUM_REALPART || type == REDUCTION_MEAN_REALPART) {
3047     for (i = 0; i < n; i++) {
3048       for (j = 0; j < m; j++) reductions[i] += PetscRealPart(a[j]);
3049       a = PetscSafePointerPlusOffset(a, m);
3050     }
3051   } else if (type == REDUCTION_SUM_IMAGINARYPART || type == REDUCTION_MEAN_IMAGINARYPART) {
3052     for (i = 0; i < n; i++) {
3053       for (j = 0; j < m; j++) reductions[i] += PetscImaginaryPart(a[j]);
3054       a = PetscSafePointerPlusOffset(a, m);
3055     }
3056   } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Unknown reduction type");
3057   PetscCall(MatDenseRestoreArrayRead(A, &a));
3058   if (type == NORM_2) {
3059     for (i = 0; i < n; i++) reductions[i] = PetscSqrtReal(reductions[i]);
3060   } else if (type == REDUCTION_MEAN_REALPART || type == REDUCTION_MEAN_IMAGINARYPART) {
3061     for (i = 0; i < n; i++) reductions[i] /= m;
3062   }
3063   PetscFunctionReturn(PETSC_SUCCESS);
3064 }
3065 
3066 PetscErrorCode MatSetRandom_SeqDense(Mat x, PetscRandom rctx)
3067 {
3068   PetscScalar *a;
3069   PetscInt     lda, m, n, i, j;
3070 
3071   PetscFunctionBegin;
3072   PetscCall(MatGetSize(x, &m, &n));
3073   PetscCall(MatDenseGetLDA(x, &lda));
3074   PetscCall(MatDenseGetArrayWrite(x, &a));
3075   for (j = 0; j < n; j++) {
3076     for (i = 0; i < m; i++) PetscCall(PetscRandomGetValue(rctx, a + j * lda + i));
3077   }
3078   PetscCall(MatDenseRestoreArrayWrite(x, &a));
3079   PetscFunctionReturn(PETSC_SUCCESS);
3080 }
3081 
3082 static PetscErrorCode MatMissingDiagonal_SeqDense(Mat A, PetscBool *missing, PetscInt *d)
3083 {
3084   PetscFunctionBegin;
3085   *missing = PETSC_FALSE;
3086   PetscFunctionReturn(PETSC_SUCCESS);
3087 }
3088 
3089 /* vals is not const */
3090 static PetscErrorCode MatDenseGetColumn_SeqDense(Mat A, PetscInt col, PetscScalar **vals)
3091 {
3092   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3093   PetscScalar  *v;
3094 
3095   PetscFunctionBegin;
3096   PetscCheck(!A->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
3097   PetscCall(MatDenseGetArray(A, &v));
3098   *vals = v + col * a->lda;
3099   PetscCall(MatDenseRestoreArray(A, &v));
3100   PetscFunctionReturn(PETSC_SUCCESS);
3101 }
3102 
3103 static PetscErrorCode MatDenseRestoreColumn_SeqDense(Mat A, PetscScalar **vals)
3104 {
3105   PetscFunctionBegin;
3106   if (vals) *vals = NULL; /* user cannot accidentally use the array later */
3107   PetscFunctionReturn(PETSC_SUCCESS);
3108 }
3109 
3110 static struct _MatOps MatOps_Values = {MatSetValues_SeqDense,
3111                                        MatGetRow_SeqDense,
3112                                        MatRestoreRow_SeqDense,
3113                                        MatMult_SeqDense,
3114                                        /*  4*/ MatMultAdd_SeqDense,
3115                                        MatMultTranspose_SeqDense,
3116                                        MatMultTransposeAdd_SeqDense,
3117                                        NULL,
3118                                        NULL,
3119                                        NULL,
3120                                        /* 10*/ NULL,
3121                                        MatLUFactor_SeqDense,
3122                                        MatCholeskyFactor_SeqDense,
3123                                        MatSOR_SeqDense,
3124                                        MatTranspose_SeqDense,
3125                                        /* 15*/ MatGetInfo_SeqDense,
3126                                        MatEqual_SeqDense,
3127                                        MatGetDiagonal_SeqDense,
3128                                        MatDiagonalScale_SeqDense,
3129                                        MatNorm_SeqDense,
3130                                        /* 20*/ NULL,
3131                                        NULL,
3132                                        MatSetOption_SeqDense,
3133                                        MatZeroEntries_SeqDense,
3134                                        /* 24*/ MatZeroRows_SeqDense,
3135                                        NULL,
3136                                        NULL,
3137                                        NULL,
3138                                        NULL,
3139                                        /* 29*/ MatSetUp_SeqDense,
3140                                        NULL,
3141                                        NULL,
3142                                        NULL,
3143                                        NULL,
3144                                        /* 34*/ MatDuplicate_SeqDense,
3145                                        NULL,
3146                                        NULL,
3147                                        NULL,
3148                                        NULL,
3149                                        /* 39*/ MatAXPY_SeqDense,
3150                                        MatCreateSubMatrices_SeqDense,
3151                                        NULL,
3152                                        MatGetValues_SeqDense,
3153                                        MatCopy_SeqDense,
3154                                        /* 44*/ MatGetRowMax_SeqDense,
3155                                        MatScale_SeqDense,
3156                                        MatShift_SeqDense,
3157                                        NULL,
3158                                        MatZeroRowsColumns_SeqDense,
3159                                        /* 49*/ MatSetRandom_SeqDense,
3160                                        NULL,
3161                                        NULL,
3162                                        NULL,
3163                                        NULL,
3164                                        /* 54*/ NULL,
3165                                        NULL,
3166                                        NULL,
3167                                        NULL,
3168                                        NULL,
3169                                        /* 59*/ MatCreateSubMatrix_SeqDense,
3170                                        MatDestroy_SeqDense,
3171                                        MatView_SeqDense,
3172                                        NULL,
3173                                        NULL,
3174                                        /* 64*/ NULL,
3175                                        NULL,
3176                                        NULL,
3177                                        NULL,
3178                                        NULL,
3179                                        /* 69*/ MatGetRowMaxAbs_SeqDense,
3180                                        NULL,
3181                                        NULL,
3182                                        NULL,
3183                                        NULL,
3184                                        /* 74*/ NULL,
3185                                        NULL,
3186                                        NULL,
3187                                        NULL,
3188                                        NULL,
3189                                        /* 79*/ NULL,
3190                                        NULL,
3191                                        NULL,
3192                                        NULL,
3193                                        /* 83*/ MatLoad_SeqDense,
3194                                        MatIsSymmetric_SeqDense,
3195                                        MatIsHermitian_SeqDense,
3196                                        NULL,
3197                                        NULL,
3198                                        NULL,
3199                                        /* 89*/ NULL,
3200                                        NULL,
3201                                        MatMatMultNumeric_SeqDense_SeqDense,
3202                                        NULL,
3203                                        NULL,
3204                                        /* 94*/ NULL,
3205                                        NULL,
3206                                        NULL,
3207                                        MatMatTransposeMultNumeric_SeqDense_SeqDense,
3208                                        NULL,
3209                                        /* 99*/ MatProductSetFromOptions_SeqDense,
3210                                        NULL,
3211                                        NULL,
3212                                        MatConjugate_SeqDense,
3213                                        NULL,
3214                                        /*104*/ NULL,
3215                                        MatRealPart_SeqDense,
3216                                        MatImaginaryPart_SeqDense,
3217                                        NULL,
3218                                        NULL,
3219                                        /*109*/ NULL,
3220                                        NULL,
3221                                        MatGetRowMin_SeqDense,
3222                                        MatGetColumnVector_SeqDense,
3223                                        MatMissingDiagonal_SeqDense,
3224                                        /*114*/ NULL,
3225                                        NULL,
3226                                        NULL,
3227                                        NULL,
3228                                        NULL,
3229                                        /*119*/ NULL,
3230                                        NULL,
3231                                        MatMultHermitianTranspose_SeqDense,
3232                                        MatMultHermitianTransposeAdd_SeqDense,
3233                                        NULL,
3234                                        /*124*/ NULL,
3235                                        MatGetColumnReductions_SeqDense,
3236                                        NULL,
3237                                        NULL,
3238                                        NULL,
3239                                        /*129*/ NULL,
3240                                        NULL,
3241                                        NULL,
3242                                        MatTransposeMatMultNumeric_SeqDense_SeqDense,
3243                                        NULL,
3244                                        /*134*/ NULL,
3245                                        NULL,
3246                                        NULL,
3247                                        NULL,
3248                                        NULL,
3249                                        /*139*/ NULL,
3250                                        NULL,
3251                                        NULL,
3252                                        NULL,
3253                                        NULL,
3254                                        MatCreateMPIMatConcatenateSeqMat_SeqDense,
3255                                        /*145*/ NULL,
3256                                        NULL,
3257                                        NULL,
3258                                        NULL,
3259                                        NULL,
3260                                        /*150*/ NULL,
3261                                        NULL,
3262                                        NULL,
3263                                        NULL,
3264                                        NULL,
3265                                        /*155*/ NULL,
3266                                        NULL};
3267 
3268 /*@
3269   MatCreateSeqDense - Creates a `MATSEQDENSE` that
3270   is stored in column major order (the usual Fortran format).
3271 
3272   Collective
3273 
3274   Input Parameters:
3275 + comm - MPI communicator, set to `PETSC_COMM_SELF`
3276 . m    - number of rows
3277 . n    - number of columns
3278 - data - optional location of matrix data in column major order.  Use `NULL` for PETSc
3279          to control all matrix memory allocation.
3280 
3281   Output Parameter:
3282 . A - the matrix
3283 
3284   Level: intermediate
3285 
3286   Note:
3287   The data input variable is intended primarily for Fortran programmers
3288   who wish to allocate their own matrix memory space.  Most users should
3289   set `data` = `NULL`.
3290 
3291   Developer Note:
3292   Many of the matrix operations for this variant use the BLAS and LAPACK routines.
3293 
3294 .seealso: [](ch_matrices), `Mat`, `MATSEQDENSE`, `MatCreate()`, `MatCreateDense()`, `MatSetValues()`
3295 @*/
3296 PetscErrorCode MatCreateSeqDense(MPI_Comm comm, PetscInt m, PetscInt n, PetscScalar data[], Mat *A)
3297 {
3298   PetscFunctionBegin;
3299   PetscCall(MatCreate(comm, A));
3300   PetscCall(MatSetSizes(*A, m, n, m, n));
3301   PetscCall(MatSetType(*A, MATSEQDENSE));
3302   PetscCall(MatSeqDenseSetPreallocation(*A, data));
3303   PetscFunctionReturn(PETSC_SUCCESS);
3304 }
3305 
3306 /*@
3307   MatSeqDenseSetPreallocation - Sets the array used for storing the matrix elements of a `MATSEQDENSE` matrix
3308 
3309   Collective
3310 
3311   Input Parameters:
3312 + B    - the matrix
3313 - data - the array (or `NULL`)
3314 
3315   Level: intermediate
3316 
3317   Note:
3318   The data input variable is intended primarily for Fortran programmers
3319   who wish to allocate their own matrix memory space.  Most users should
3320   need not call this routine.
3321 
3322 .seealso: [](ch_matrices), `Mat`, `MATSEQDENSE`, `MatCreate()`, `MatCreateDense()`, `MatSetValues()`, `MatDenseSetLDA()`
3323 @*/
3324 PetscErrorCode MatSeqDenseSetPreallocation(Mat B, PetscScalar data[])
3325 {
3326   PetscFunctionBegin;
3327   PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
3328   PetscTryMethod(B, "MatSeqDenseSetPreallocation_C", (Mat, PetscScalar[]), (B, data));
3329   PetscFunctionReturn(PETSC_SUCCESS);
3330 }
3331 
3332 PetscErrorCode MatSeqDenseSetPreallocation_SeqDense(Mat B, PetscScalar *data)
3333 {
3334   Mat_SeqDense *b = (Mat_SeqDense *)B->data;
3335 
3336   PetscFunctionBegin;
3337   PetscCheck(!b->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
3338   B->preallocated = PETSC_TRUE;
3339 
3340   PetscCall(PetscLayoutSetUp(B->rmap));
3341   PetscCall(PetscLayoutSetUp(B->cmap));
3342 
3343   if (b->lda <= 0) PetscCall(PetscBLASIntCast(B->rmap->n, &b->lda));
3344 
3345   if (!data) { /* petsc-allocated storage */
3346     if (!b->user_alloc) PetscCall(PetscFree(b->v));
3347     PetscCall(PetscCalloc1((size_t)b->lda * B->cmap->n, &b->v));
3348 
3349     b->user_alloc = PETSC_FALSE;
3350   } else { /* user-allocated storage */
3351     if (!b->user_alloc) PetscCall(PetscFree(b->v));
3352     b->v          = data;
3353     b->user_alloc = PETSC_TRUE;
3354   }
3355   B->assembled = PETSC_TRUE;
3356   PetscFunctionReturn(PETSC_SUCCESS);
3357 }
3358 
3359 #if defined(PETSC_HAVE_ELEMENTAL)
3360 PETSC_INTERN PetscErrorCode MatConvert_SeqDense_Elemental(Mat A, MatType newtype, MatReuse reuse, Mat *newmat)
3361 {
3362   Mat                mat_elemental;
3363   const PetscScalar *array;
3364   PetscScalar       *v_colwise;
3365   PetscInt           M = A->rmap->N, N = A->cmap->N, i, j, k, *rows, *cols;
3366 
3367   PetscFunctionBegin;
3368   PetscCall(PetscMalloc3(M * N, &v_colwise, M, &rows, N, &cols));
3369   PetscCall(MatDenseGetArrayRead(A, &array));
3370   /* convert column-wise array into row-wise v_colwise, see MatSetValues_Elemental() */
3371   k = 0;
3372   for (j = 0; j < N; j++) {
3373     cols[j] = j;
3374     for (i = 0; i < M; i++) v_colwise[j * M + i] = array[k++];
3375   }
3376   for (i = 0; i < M; i++) rows[i] = i;
3377   PetscCall(MatDenseRestoreArrayRead(A, &array));
3378 
3379   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &mat_elemental));
3380   PetscCall(MatSetSizes(mat_elemental, PETSC_DECIDE, PETSC_DECIDE, M, N));
3381   PetscCall(MatSetType(mat_elemental, MATELEMENTAL));
3382   PetscCall(MatSetUp(mat_elemental));
3383 
3384   /* PETSc-Elemental interaface uses axpy for setting off-processor entries, only ADD_VALUES is allowed */
3385   PetscCall(MatSetValues(mat_elemental, M, rows, N, cols, v_colwise, ADD_VALUES));
3386   PetscCall(MatAssemblyBegin(mat_elemental, MAT_FINAL_ASSEMBLY));
3387   PetscCall(MatAssemblyEnd(mat_elemental, MAT_FINAL_ASSEMBLY));
3388   PetscCall(PetscFree3(v_colwise, rows, cols));
3389 
3390   if (reuse == MAT_INPLACE_MATRIX) {
3391     PetscCall(MatHeaderReplace(A, &mat_elemental));
3392   } else {
3393     *newmat = mat_elemental;
3394   }
3395   PetscFunctionReturn(PETSC_SUCCESS);
3396 }
3397 #endif
3398 
3399 PetscErrorCode MatDenseSetLDA_SeqDense(Mat B, PetscInt lda)
3400 {
3401   Mat_SeqDense *b = (Mat_SeqDense *)B->data;
3402   PetscBool     data;
3403 
3404   PetscFunctionBegin;
3405   data = (B->rmap->n > 0 && B->cmap->n > 0) ? (b->v ? PETSC_TRUE : PETSC_FALSE) : PETSC_FALSE;
3406   PetscCheck(b->user_alloc || !data || b->lda == lda, PETSC_COMM_SELF, PETSC_ERR_ORDER, "LDA cannot be changed after allocation of internal storage");
3407   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);
3408   PetscCall(PetscBLASIntCast(lda, &b->lda));
3409   PetscFunctionReturn(PETSC_SUCCESS);
3410 }
3411 
3412 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqDense(MPI_Comm comm, Mat inmat, PetscInt n, MatReuse scall, Mat *outmat)
3413 {
3414   PetscFunctionBegin;
3415   PetscCall(MatCreateMPIMatConcatenateSeqMat_MPIDense(comm, inmat, n, scall, outmat));
3416   PetscFunctionReturn(PETSC_SUCCESS);
3417 }
3418 
3419 PetscErrorCode MatDenseCreateColumnVec_Private(Mat A, Vec *v)
3420 {
3421   PetscBool   isstd, iskok, iscuda, iship;
3422   PetscMPIInt size;
3423 #if PetscDefined(HAVE_CUDA) || PetscDefined(HAVE_HIP)
3424   /* we pass the data of A, to prevent allocating needless GPU memory the first time VecCUPMPlaceArray is called. */
3425   const PetscScalar *a;
3426 #endif
3427 
3428   PetscFunctionBegin;
3429   *v = NULL;
3430   PetscCall(PetscStrcmpAny(A->defaultvectype, &isstd, VECSTANDARD, VECSEQ, VECMPI, ""));
3431   PetscCall(PetscStrcmpAny(A->defaultvectype, &iskok, VECKOKKOS, VECSEQKOKKOS, VECMPIKOKKOS, ""));
3432   PetscCall(PetscStrcmpAny(A->defaultvectype, &iscuda, VECCUDA, VECSEQCUDA, VECMPICUDA, ""));
3433   PetscCall(PetscStrcmpAny(A->defaultvectype, &iship, VECHIP, VECSEQHIP, VECMPIHIP, ""));
3434   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
3435   if (isstd) {
3436     if (size > 1) PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, A->rmap->N, NULL, v));
3437     else PetscCall(VecCreateSeqWithArray(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, NULL, v));
3438   } else if (iskok) {
3439     PetscCheck(PetscDefined(HAVE_KOKKOS_KERNELS), PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Reconfigure using KOKKOS kernels support");
3440 #if PetscDefined(HAVE_KOKKOS_KERNELS)
3441     if (size > 1) PetscCall(VecCreateMPIKokkosWithArray(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, A->rmap->N, NULL, v));
3442     else PetscCall(VecCreateSeqKokkosWithArray(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, NULL, v));
3443 #endif
3444   } else if (iscuda) {
3445     PetscCheck(PetscDefined(HAVE_CUDA), PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Reconfigure using CUDA support");
3446 #if PetscDefined(HAVE_CUDA)
3447     PetscCall(MatDenseCUDAGetArrayRead(A, &a));
3448     if (size > 1) PetscCall(VecCreateMPICUDAWithArrays(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, A->rmap->N, NULL, a, v));
3449     else PetscCall(VecCreateSeqCUDAWithArrays(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, NULL, a, v));
3450 #endif
3451   } else if (iship) {
3452     PetscCheck(PetscDefined(HAVE_HIP), PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Reconfigure using HIP support");
3453 #if PetscDefined(HAVE_HIP)
3454     PetscCall(MatDenseHIPGetArrayRead(A, &a));
3455     if (size > 1) PetscCall(VecCreateMPIHIPWithArrays(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, A->rmap->N, NULL, a, v));
3456     else PetscCall(VecCreateSeqHIPWithArrays(PetscObjectComm((PetscObject)A), A->rmap->bs, A->rmap->n, NULL, a, v));
3457 #endif
3458   }
3459   PetscCheck(*v, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not coded for type %s", A->defaultvectype);
3460   PetscFunctionReturn(PETSC_SUCCESS);
3461 }
3462 
3463 PetscErrorCode MatDenseGetColumnVec_SeqDense(Mat A, PetscInt col, Vec *v)
3464 {
3465   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3466 
3467   PetscFunctionBegin;
3468   PetscCheck(!a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
3469   PetscCheck(!a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
3470   if (!a->cvec) PetscCall(MatDenseCreateColumnVec_Private(A, &a->cvec));
3471   a->vecinuse = col + 1;
3472   PetscCall(MatDenseGetArray(A, (PetscScalar **)&a->ptrinuse));
3473   PetscCall(VecPlaceArray(a->cvec, a->ptrinuse + (size_t)col * (size_t)a->lda));
3474   *v = a->cvec;
3475   PetscFunctionReturn(PETSC_SUCCESS);
3476 }
3477 
3478 PetscErrorCode MatDenseRestoreColumnVec_SeqDense(Mat A, PetscInt col, Vec *v)
3479 {
3480   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3481 
3482   PetscFunctionBegin;
3483   PetscCheck(a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseGetColumnVec() first");
3484   PetscCheck(a->cvec, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing internal column vector");
3485   VecCheckAssembled(a->cvec);
3486   a->vecinuse = 0;
3487   PetscCall(MatDenseRestoreArray(A, (PetscScalar **)&a->ptrinuse));
3488   PetscCall(VecResetArray(a->cvec));
3489   if (v) *v = NULL;
3490   PetscFunctionReturn(PETSC_SUCCESS);
3491 }
3492 
3493 PetscErrorCode MatDenseGetColumnVecRead_SeqDense(Mat A, PetscInt col, Vec *v)
3494 {
3495   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3496 
3497   PetscFunctionBegin;
3498   PetscCheck(!a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
3499   PetscCheck(!a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
3500   if (!a->cvec) PetscCall(MatDenseCreateColumnVec_Private(A, &a->cvec));
3501   a->vecinuse = col + 1;
3502   PetscCall(MatDenseGetArrayRead(A, &a->ptrinuse));
3503   PetscCall(VecPlaceArray(a->cvec, PetscSafePointerPlusOffset(a->ptrinuse, (size_t)col * (size_t)a->lda)));
3504   PetscCall(VecLockReadPush(a->cvec));
3505   *v = a->cvec;
3506   PetscFunctionReturn(PETSC_SUCCESS);
3507 }
3508 
3509 PetscErrorCode MatDenseRestoreColumnVecRead_SeqDense(Mat A, PetscInt col, Vec *v)
3510 {
3511   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3512 
3513   PetscFunctionBegin;
3514   PetscCheck(a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseGetColumnVec() first");
3515   PetscCheck(a->cvec, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing internal column vector");
3516   VecCheckAssembled(a->cvec);
3517   a->vecinuse = 0;
3518   PetscCall(MatDenseRestoreArrayRead(A, &a->ptrinuse));
3519   PetscCall(VecLockReadPop(a->cvec));
3520   PetscCall(VecResetArray(a->cvec));
3521   if (v) *v = NULL;
3522   PetscFunctionReturn(PETSC_SUCCESS);
3523 }
3524 
3525 PetscErrorCode MatDenseGetColumnVecWrite_SeqDense(Mat A, PetscInt col, Vec *v)
3526 {
3527   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3528 
3529   PetscFunctionBegin;
3530   PetscCheck(!a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
3531   PetscCheck(!a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
3532   if (!a->cvec) PetscCall(MatDenseCreateColumnVec_Private(A, &a->cvec));
3533   a->vecinuse = col + 1;
3534   PetscCall(MatDenseGetArrayWrite(A, (PetscScalar **)&a->ptrinuse));
3535   PetscCall(VecPlaceArray(a->cvec, PetscSafePointerPlusOffset(a->ptrinuse, (size_t)col * (size_t)a->lda)));
3536   *v = a->cvec;
3537   PetscFunctionReturn(PETSC_SUCCESS);
3538 }
3539 
3540 PetscErrorCode MatDenseRestoreColumnVecWrite_SeqDense(Mat A, PetscInt col, Vec *v)
3541 {
3542   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3543 
3544   PetscFunctionBegin;
3545   PetscCheck(a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseGetColumnVec() first");
3546   PetscCheck(a->cvec, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing internal column vector");
3547   VecCheckAssembled(a->cvec);
3548   a->vecinuse = 0;
3549   PetscCall(MatDenseRestoreArrayWrite(A, (PetscScalar **)&a->ptrinuse));
3550   PetscCall(VecResetArray(a->cvec));
3551   if (v) *v = NULL;
3552   PetscFunctionReturn(PETSC_SUCCESS);
3553 }
3554 
3555 PetscErrorCode MatDenseGetSubMatrix_SeqDense(Mat A, PetscInt rbegin, PetscInt rend, PetscInt cbegin, PetscInt cend, Mat *v)
3556 {
3557   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3558 
3559   PetscFunctionBegin;
3560   PetscCheck(!a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
3561   PetscCheck(!a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
3562   if (a->cmat && (cend - cbegin != a->cmat->cmap->N || rend - rbegin != a->cmat->rmap->N)) PetscCall(MatDestroy(&a->cmat));
3563   if (!a->cmat) {
3564     PetscCall(MatCreateDense(PetscObjectComm((PetscObject)A), rend - rbegin, PETSC_DECIDE, rend - rbegin, cend - cbegin, PetscSafePointerPlusOffset(a->v, rbegin + (size_t)cbegin * a->lda), &a->cmat));
3565   } else {
3566     PetscCall(MatDensePlaceArray(a->cmat, PetscSafePointerPlusOffset(a->v, rbegin + (size_t)cbegin * a->lda)));
3567   }
3568   PetscCall(MatDenseSetLDA(a->cmat, a->lda));
3569   a->matinuse = cbegin + 1;
3570   *v          = a->cmat;
3571 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
3572   A->offloadmask = PETSC_OFFLOAD_CPU;
3573 #endif
3574   PetscFunctionReturn(PETSC_SUCCESS);
3575 }
3576 
3577 PetscErrorCode MatDenseRestoreSubMatrix_SeqDense(Mat A, Mat *v)
3578 {
3579   Mat_SeqDense *a = (Mat_SeqDense *)A->data;
3580 
3581   PetscFunctionBegin;
3582   PetscCheck(a->matinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseGetSubMatrix() first");
3583   PetscCheck(a->cmat, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing internal column matrix");
3584   PetscCheck(*v == a->cmat, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Not the matrix obtained from MatDenseGetSubMatrix()");
3585   a->matinuse = 0;
3586   PetscCall(MatDenseResetArray(a->cmat));
3587   if (v) *v = NULL;
3588 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
3589   A->offloadmask = PETSC_OFFLOAD_CPU;
3590 #endif
3591   PetscFunctionReturn(PETSC_SUCCESS);
3592 }
3593 
3594 /*MC
3595    MATSEQDENSE - MATSEQDENSE = "seqdense" - A matrix type to be used for sequential dense matrices.
3596 
3597    Options Database Key:
3598 . -mat_type seqdense - sets the matrix type to `MATSEQDENSE` during a call to `MatSetFromOptions()`
3599 
3600   Level: beginner
3601 
3602 .seealso: [](ch_matrices), `Mat`, `MATSEQDENSE`, `MatCreateSeqDense()`
3603 M*/
3604 PetscErrorCode MatCreate_SeqDense(Mat B)
3605 {
3606   Mat_SeqDense *b;
3607   PetscMPIInt   size;
3608 
3609   PetscFunctionBegin;
3610   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));
3611   PetscCheck(size <= 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Comm must be of size 1");
3612 
3613   PetscCall(PetscNew(&b));
3614   B->data   = (void *)b;
3615   B->ops[0] = MatOps_Values;
3616 
3617   b->roworiented = PETSC_TRUE;
3618 
3619   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatQRFactor_C", MatQRFactor_SeqDense));
3620   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetLDA_C", MatDenseGetLDA_SeqDense));
3621   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseSetLDA_C", MatDenseSetLDA_SeqDense));
3622   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetArray_C", MatDenseGetArray_SeqDense));
3623   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreArray_C", MatDenseRestoreArray_SeqDense));
3624   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDensePlaceArray_C", MatDensePlaceArray_SeqDense));
3625   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseResetArray_C", MatDenseResetArray_SeqDense));
3626   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseReplaceArray_C", MatDenseReplaceArray_SeqDense));
3627   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetArrayRead_C", MatDenseGetArray_SeqDense));
3628   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreArrayRead_C", MatDenseRestoreArray_SeqDense));
3629   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetArrayWrite_C", MatDenseGetArray_SeqDense));
3630   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreArrayWrite_C", MatDenseRestoreArray_SeqDense));
3631   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqdense_seqaij_C", MatConvert_SeqDense_SeqAIJ));
3632 #if defined(PETSC_HAVE_ELEMENTAL)
3633   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqdense_elemental_C", MatConvert_SeqDense_Elemental));
3634 #endif
3635 #if defined(PETSC_HAVE_SCALAPACK)
3636   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqdense_scalapack_C", MatConvert_Dense_ScaLAPACK));
3637 #endif
3638 #if defined(PETSC_HAVE_CUDA)
3639   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqdense_seqdensecuda_C", MatConvert_SeqDense_SeqDenseCUDA));
3640   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdensecuda_seqdensecuda_C", MatProductSetFromOptions_SeqDense));
3641   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdensecuda_seqdense_C", MatProductSetFromOptions_SeqDense));
3642   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdense_seqdensecuda_C", MatProductSetFromOptions_SeqDense));
3643 #endif
3644 #if defined(PETSC_HAVE_HIP)
3645   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_seqdense_seqdensehip_C", MatConvert_SeqDense_SeqDenseHIP));
3646   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdensehip_seqdensehip_C", MatProductSetFromOptions_SeqDense));
3647   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdensehip_seqdense_C", MatProductSetFromOptions_SeqDense));
3648   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdense_seqdensehip_C", MatProductSetFromOptions_SeqDense));
3649 #endif
3650   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSeqDenseSetPreallocation_C", MatSeqDenseSetPreallocation_SeqDense));
3651   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqaij_seqdense_C", MatProductSetFromOptions_SeqAIJ_SeqDense));
3652   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqdense_seqdense_C", MatProductSetFromOptions_SeqDense));
3653   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqbaij_seqdense_C", MatProductSetFromOptions_SeqXBAIJ_SeqDense));
3654   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_seqsbaij_seqdense_C", MatProductSetFromOptions_SeqXBAIJ_SeqDense));
3655 
3656   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetColumn_C", MatDenseGetColumn_SeqDense));
3657   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreColumn_C", MatDenseRestoreColumn_SeqDense));
3658   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetColumnVec_C", MatDenseGetColumnVec_SeqDense));
3659   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreColumnVec_C", MatDenseRestoreColumnVec_SeqDense));
3660   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetColumnVecRead_C", MatDenseGetColumnVecRead_SeqDense));
3661   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreColumnVecRead_C", MatDenseRestoreColumnVecRead_SeqDense));
3662   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetColumnVecWrite_C", MatDenseGetColumnVecWrite_SeqDense));
3663   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreColumnVecWrite_C", MatDenseRestoreColumnVecWrite_SeqDense));
3664   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseGetSubMatrix_C", MatDenseGetSubMatrix_SeqDense));
3665   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDenseRestoreSubMatrix_C", MatDenseRestoreSubMatrix_SeqDense));
3666   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMultAddColumnRange_C", MatMultAddColumnRange_SeqDense));
3667   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMultHermitianTransposeColumnRange_C", MatMultHermitianTransposeColumnRange_SeqDense));
3668   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMultHermitianTransposeAddColumnRange_C", MatMultHermitianTransposeAddColumnRange_SeqDense));
3669   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATSEQDENSE));
3670   PetscFunctionReturn(PETSC_SUCCESS);
3671 }
3672 
3673 /*@C
3674   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.
3675 
3676   Not Collective
3677 
3678   Input Parameters:
3679 + A   - a `MATSEQDENSE` or `MATMPIDENSE` matrix
3680 - col - column index
3681 
3682   Output Parameter:
3683 . vals - pointer to the data
3684 
3685   Level: intermediate
3686 
3687   Note:
3688   Use `MatDenseGetColumnVec()` to get access to a column of a `MATDENSE` treated as a `Vec`
3689 
3690 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseRestoreColumn()`, `MatDenseGetColumnVec()`
3691 @*/
3692 PetscErrorCode MatDenseGetColumn(Mat A, PetscInt col, PetscScalar *vals[])
3693 {
3694   PetscFunctionBegin;
3695   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3696   PetscValidLogicalCollectiveInt(A, col, 2);
3697   PetscAssertPointer(vals, 3);
3698   PetscUseMethod(A, "MatDenseGetColumn_C", (Mat, PetscInt, PetscScalar **), (A, col, vals));
3699   PetscFunctionReturn(PETSC_SUCCESS);
3700 }
3701 
3702 /*@C
3703   MatDenseRestoreColumn - returns access to a column of a `MATDENSE` matrix which is returned by `MatDenseGetColumn()`.
3704 
3705   Not Collective
3706 
3707   Input Parameters:
3708 + A    - a `MATSEQDENSE` or `MATMPIDENSE` matrix
3709 - vals - pointer to the data (may be `NULL`)
3710 
3711   Level: intermediate
3712 
3713 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetColumn()`
3714 @*/
3715 PetscErrorCode MatDenseRestoreColumn(Mat A, PetscScalar *vals[])
3716 {
3717   PetscFunctionBegin;
3718   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3719   PetscAssertPointer(vals, 2);
3720   PetscUseMethod(A, "MatDenseRestoreColumn_C", (Mat, PetscScalar **), (A, vals));
3721   PetscFunctionReturn(PETSC_SUCCESS);
3722 }
3723 
3724 /*@
3725   MatDenseGetColumnVec - Gives read-write access to a column of a `MATDENSE` matrix, represented as a `Vec`.
3726 
3727   Collective
3728 
3729   Input Parameters:
3730 + A   - the `Mat` object
3731 - col - the column index
3732 
3733   Output Parameter:
3734 . v - the vector
3735 
3736   Level: intermediate
3737 
3738   Notes:
3739   The vector is owned by PETSc. Users need to call `MatDenseRestoreColumnVec()` when the vector is no longer needed.
3740 
3741   Use `MatDenseGetColumnVecRead()` to obtain read-only access or `MatDenseGetColumnVecWrite()` for write-only access.
3742 
3743 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVecRead()`, `MatDenseGetColumnVecWrite()`, `MatDenseRestoreColumnVec()`, `MatDenseRestoreColumnVecRead()`, `MatDenseRestoreColumnVecWrite()`, `MatDenseGetColumn()`
3744 @*/
3745 PetscErrorCode MatDenseGetColumnVec(Mat A, PetscInt col, Vec *v)
3746 {
3747   PetscFunctionBegin;
3748   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3749   PetscValidType(A, 1);
3750   PetscValidLogicalCollectiveInt(A, col, 2);
3751   PetscAssertPointer(v, 3);
3752   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3753   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);
3754   PetscUseMethod(A, "MatDenseGetColumnVec_C", (Mat, PetscInt, Vec *), (A, col, v));
3755   PetscFunctionReturn(PETSC_SUCCESS);
3756 }
3757 
3758 /*@
3759   MatDenseRestoreColumnVec - Returns access to a column of a dense matrix obtained from `MatDenseGetColumnVec()`.
3760 
3761   Collective
3762 
3763   Input Parameters:
3764 + A   - the `Mat` object
3765 . col - the column index
3766 - v   - the `Vec` object (may be `NULL`)
3767 
3768   Level: intermediate
3769 
3770 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseGetColumnVecRead()`, `MatDenseGetColumnVecWrite()`, `MatDenseRestoreColumnVecRead()`, `MatDenseRestoreColumnVecWrite()`
3771 @*/
3772 PetscErrorCode MatDenseRestoreColumnVec(Mat A, PetscInt col, Vec *v)
3773 {
3774   PetscFunctionBegin;
3775   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3776   PetscValidType(A, 1);
3777   PetscValidLogicalCollectiveInt(A, col, 2);
3778   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3779   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);
3780   PetscUseMethod(A, "MatDenseRestoreColumnVec_C", (Mat, PetscInt, Vec *), (A, col, v));
3781   PetscFunctionReturn(PETSC_SUCCESS);
3782 }
3783 
3784 /*@
3785   MatDenseGetColumnVecRead - Gives read-only access to a column of a dense matrix, represented as a `Vec`.
3786 
3787   Collective
3788 
3789   Input Parameters:
3790 + A   - the `Mat` object
3791 - col - the column index
3792 
3793   Output Parameter:
3794 . v - the vector
3795 
3796   Level: intermediate
3797 
3798   Notes:
3799   The vector is owned by PETSc and users cannot modify it.
3800 
3801   Users need to call `MatDenseRestoreColumnVecRead()` when the vector is no longer needed.
3802 
3803   Use `MatDenseGetColumnVec()` to obtain read-write access or `MatDenseGetColumnVecWrite()` for write-only access.
3804 
3805 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseGetColumnVecWrite()`, `MatDenseRestoreColumnVec()`, `MatDenseRestoreColumnVecRead()`, `MatDenseRestoreColumnVecWrite()`
3806 @*/
3807 PetscErrorCode MatDenseGetColumnVecRead(Mat A, PetscInt col, Vec *v)
3808 {
3809   PetscFunctionBegin;
3810   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3811   PetscValidType(A, 1);
3812   PetscValidLogicalCollectiveInt(A, col, 2);
3813   PetscAssertPointer(v, 3);
3814   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3815   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);
3816   PetscUseMethod(A, "MatDenseGetColumnVecRead_C", (Mat, PetscInt, Vec *), (A, col, v));
3817   PetscFunctionReturn(PETSC_SUCCESS);
3818 }
3819 
3820 /*@
3821   MatDenseRestoreColumnVecRead - Returns access to a column of a dense matrix obtained from `MatDenseGetColumnVecRead()`.
3822 
3823   Collective
3824 
3825   Input Parameters:
3826 + A   - the `Mat` object
3827 . col - the column index
3828 - v   - the `Vec` object (may be `NULL`)
3829 
3830   Level: intermediate
3831 
3832 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseGetColumnVecRead()`, `MatDenseGetColumnVecWrite()`, `MatDenseRestoreColumnVec()`, `MatDenseRestoreColumnVecWrite()`
3833 @*/
3834 PetscErrorCode MatDenseRestoreColumnVecRead(Mat A, PetscInt col, Vec *v)
3835 {
3836   PetscFunctionBegin;
3837   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3838   PetscValidType(A, 1);
3839   PetscValidLogicalCollectiveInt(A, col, 2);
3840   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3841   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);
3842   PetscUseMethod(A, "MatDenseRestoreColumnVecRead_C", (Mat, PetscInt, Vec *), (A, col, v));
3843   PetscFunctionReturn(PETSC_SUCCESS);
3844 }
3845 
3846 /*@
3847   MatDenseGetColumnVecWrite - Gives write-only access to a column of a dense matrix, represented as a `Vec`.
3848 
3849   Collective
3850 
3851   Input Parameters:
3852 + A   - the `Mat` object
3853 - col - the column index
3854 
3855   Output Parameter:
3856 . v - the vector
3857 
3858   Level: intermediate
3859 
3860   Notes:
3861   The vector is owned by PETSc. Users need to call `MatDenseRestoreColumnVecWrite()` when the vector is no longer needed.
3862 
3863   Use `MatDenseGetColumnVec()` to obtain read-write access or `MatDenseGetColumnVecRead()` for read-only access.
3864 
3865 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseGetColumnVecRead()`, `MatDenseRestoreColumnVec()`, `MatDenseRestoreColumnVecRead()`, `MatDenseRestoreColumnVecWrite()`
3866 @*/
3867 PetscErrorCode MatDenseGetColumnVecWrite(Mat A, PetscInt col, Vec *v)
3868 {
3869   PetscFunctionBegin;
3870   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3871   PetscValidType(A, 1);
3872   PetscValidLogicalCollectiveInt(A, col, 2);
3873   PetscAssertPointer(v, 3);
3874   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3875   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);
3876   PetscUseMethod(A, "MatDenseGetColumnVecWrite_C", (Mat, PetscInt, Vec *), (A, col, v));
3877   PetscFunctionReturn(PETSC_SUCCESS);
3878 }
3879 
3880 /*@
3881   MatDenseRestoreColumnVecWrite - Returns access to a column of a dense matrix obtained from `MatDenseGetColumnVecWrite()`.
3882 
3883   Collective
3884 
3885   Input Parameters:
3886 + A   - the `Mat` object
3887 . col - the column index
3888 - v   - the `Vec` object (may be `NULL`)
3889 
3890   Level: intermediate
3891 
3892 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseGetColumnVecRead()`, `MatDenseGetColumnVecWrite()`, `MatDenseRestoreColumnVec()`, `MatDenseRestoreColumnVecRead()`
3893 @*/
3894 PetscErrorCode MatDenseRestoreColumnVecWrite(Mat A, PetscInt col, Vec *v)
3895 {
3896   PetscFunctionBegin;
3897   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3898   PetscValidType(A, 1);
3899   PetscValidLogicalCollectiveInt(A, col, 2);
3900   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3901   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);
3902   PetscUseMethod(A, "MatDenseRestoreColumnVecWrite_C", (Mat, PetscInt, Vec *), (A, col, v));
3903   PetscFunctionReturn(PETSC_SUCCESS);
3904 }
3905 
3906 /*@
3907   MatDenseGetSubMatrix - Gives access to a block of rows and columns of a dense matrix, represented as a `Mat`.
3908 
3909   Collective
3910 
3911   Input Parameters:
3912 + A      - the `Mat` object
3913 . rbegin - the first global row index in the block (if `PETSC_DECIDE`, is 0)
3914 . rend   - the global row index past the last one in the block (if `PETSC_DECIDE`, is `M`)
3915 . cbegin - the first global column index in the block (if `PETSC_DECIDE`, is 0)
3916 - cend   - the global column index past the last one in the block (if `PETSC_DECIDE`, is `N`)
3917 
3918   Output Parameter:
3919 . v - the matrix
3920 
3921   Level: intermediate
3922 
3923   Notes:
3924   The matrix is owned by PETSc. Users need to call `MatDenseRestoreSubMatrix()` when the matrix is no longer needed.
3925 
3926   The output matrix is not redistributed by PETSc, so depending on the values of `rbegin` and `rend`, some processes may have no local rows.
3927 
3928 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseRestoreColumnVec()`, `MatDenseRestoreSubMatrix()`
3929 @*/
3930 PetscErrorCode MatDenseGetSubMatrix(Mat A, PetscInt rbegin, PetscInt rend, PetscInt cbegin, PetscInt cend, Mat *v)
3931 {
3932   PetscFunctionBegin;
3933   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3934   PetscValidType(A, 1);
3935   PetscValidLogicalCollectiveInt(A, rbegin, 2);
3936   PetscValidLogicalCollectiveInt(A, rend, 3);
3937   PetscValidLogicalCollectiveInt(A, cbegin, 4);
3938   PetscValidLogicalCollectiveInt(A, cend, 5);
3939   PetscAssertPointer(v, 6);
3940   if (rbegin == PETSC_DECIDE) rbegin = 0;
3941   if (rend == PETSC_DECIDE) rend = A->rmap->N;
3942   if (cbegin == PETSC_DECIDE) cbegin = 0;
3943   if (cend == PETSC_DECIDE) cend = A->cmap->N;
3944   PetscCheck(A->preallocated, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Matrix not preallocated");
3945   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);
3946   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);
3947   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);
3948   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);
3949   PetscUseMethod(A, "MatDenseGetSubMatrix_C", (Mat, PetscInt, PetscInt, PetscInt, PetscInt, Mat *), (A, rbegin, rend, cbegin, cend, v));
3950   PetscFunctionReturn(PETSC_SUCCESS);
3951 }
3952 
3953 /*@
3954   MatDenseRestoreSubMatrix - Returns access to a block of columns of a dense matrix obtained from `MatDenseGetSubMatrix()`.
3955 
3956   Collective
3957 
3958   Input Parameters:
3959 + A - the `Mat` object
3960 - v - the `Mat` object (may be `NULL`)
3961 
3962   Level: intermediate
3963 
3964 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATDENSECUDA`, `MATDENSEHIP`, `MatDenseGetColumnVec()`, `MatDenseRestoreColumnVec()`, `MatDenseGetSubMatrix()`
3965 @*/
3966 PetscErrorCode MatDenseRestoreSubMatrix(Mat A, Mat *v)
3967 {
3968   PetscFunctionBegin;
3969   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3970   PetscValidType(A, 1);
3971   PetscAssertPointer(v, 2);
3972   PetscUseMethod(A, "MatDenseRestoreSubMatrix_C", (Mat, Mat *), (A, v));
3973   PetscFunctionReturn(PETSC_SUCCESS);
3974 }
3975 
3976 #include <petscblaslapack.h>
3977 #include <petsc/private/kernels/blockinvert.h>
3978 
3979 PetscErrorCode MatSeqDenseInvert(Mat A)
3980 {
3981   PetscInt        m;
3982   const PetscReal shift = 0.0;
3983   PetscBool       allowzeropivot, zeropivotdetected = PETSC_FALSE;
3984   PetscScalar    *values;
3985 
3986   PetscFunctionBegin;
3987   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
3988   PetscCall(MatDenseGetArray(A, &values));
3989   PetscCall(MatGetLocalSize(A, &m, NULL));
3990   allowzeropivot = PetscNot(A->erroriffailure);
3991   /* factor and invert each block */
3992   switch (m) {
3993   case 1:
3994     values[0] = (PetscScalar)1.0 / (values[0] + shift);
3995     break;
3996   case 2:
3997     PetscCall(PetscKernel_A_gets_inverse_A_2(values, shift, allowzeropivot, &zeropivotdetected));
3998     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3999     break;
4000   case 3:
4001     PetscCall(PetscKernel_A_gets_inverse_A_3(values, shift, allowzeropivot, &zeropivotdetected));
4002     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4003     break;
4004   case 4:
4005     PetscCall(PetscKernel_A_gets_inverse_A_4(values, shift, allowzeropivot, &zeropivotdetected));
4006     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4007     break;
4008   case 5: {
4009     PetscScalar work[25];
4010     PetscInt    ipvt[5];
4011 
4012     PetscCall(PetscKernel_A_gets_inverse_A_5(values, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
4013     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4014   } break;
4015   case 6:
4016     PetscCall(PetscKernel_A_gets_inverse_A_6(values, shift, allowzeropivot, &zeropivotdetected));
4017     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4018     break;
4019   case 7:
4020     PetscCall(PetscKernel_A_gets_inverse_A_7(values, shift, allowzeropivot, &zeropivotdetected));
4021     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4022     break;
4023   default: {
4024     PetscInt    *v_pivots, *IJ, j;
4025     PetscScalar *v_work;
4026 
4027     PetscCall(PetscMalloc3(m, &v_work, m, &v_pivots, m, &IJ));
4028     for (j = 0; j < m; j++) IJ[j] = j;
4029     PetscCall(PetscKernel_A_gets_inverse_A(m, values, v_pivots, v_work, allowzeropivot, &zeropivotdetected));
4030     if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
4031     PetscCall(PetscFree3(v_work, v_pivots, IJ));
4032   }
4033   }
4034   PetscCall(MatDenseRestoreArray(A, &values));
4035   PetscFunctionReturn(PETSC_SUCCESS);
4036 }
4037