xref: /petsc/src/mat/impls/dense/seq/dense.c (revision 5ea7661a5c6ebfe94618efd9ae12232cbd7a6c1a)
1 
2 /*
3      Defines the basic matrix operations for sequential dense.
4 */
5 
6 #include <../src/mat/impls/dense/seq/dense.h> /*I "petscmat.h" I*/
7 #include <petscblaslapack.h>
8 
9 #include <../src/mat/impls/aij/seq/aij.h>
10 
11 PetscErrorCode MatSeqDenseSymmetrize_Private(Mat A, PetscBool hermitian)
12 {
13   Mat_SeqDense   *mat = (Mat_SeqDense*)A->data;
14   PetscInt       j, k, n = A->rmap->n;
15   PetscScalar    *v;
16   PetscErrorCode ierr;
17 
18   PetscFunctionBegin;
19   if (A->rmap->n != A->cmap->n) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Cannot symmetrize a rectangular matrix");
20   ierr = MatDenseGetArray(A,&v);CHKERRQ(ierr);
21   if (!hermitian) {
22     for (k=0;k<n;k++) {
23       for (j=k;j<n;j++) {
24         v[j*mat->lda + k] = v[k*mat->lda + j];
25       }
26     }
27   } else {
28     for (k=0;k<n;k++) {
29       for (j=k;j<n;j++) {
30         v[j*mat->lda + k] = PetscConj(v[k*mat->lda + j]);
31       }
32     }
33   }
34   ierr = MatDenseRestoreArray(A,&v);CHKERRQ(ierr);
35   PetscFunctionReturn(0);
36 }
37 
38 PETSC_EXTERN PetscErrorCode MatSeqDenseInvertFactors_Private(Mat A)
39 {
40   Mat_SeqDense   *mat = (Mat_SeqDense*)A->data;
41   PetscErrorCode ierr;
42   PetscBLASInt   info,n;
43 
44   PetscFunctionBegin;
45   if (!A->rmap->n || !A->cmap->n) PetscFunctionReturn(0);
46   ierr = PetscBLASIntCast(A->cmap->n,&n);CHKERRQ(ierr);
47   if (A->factortype == MAT_FACTOR_LU) {
48     if (!mat->pivots) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Pivots not present");
49     if (!mat->fwork) {
50       mat->lfwork = n;
51       ierr = PetscMalloc1(mat->lfwork,&mat->fwork);CHKERRQ(ierr);
52       ierr = PetscLogObjectMemory((PetscObject)A,mat->lfwork*sizeof(PetscBLASInt));CHKERRQ(ierr);
53     }
54     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
55     PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&n,mat->v,&mat->lda,mat->pivots,mat->fwork,&mat->lfwork,&info));
56     ierr = PetscFPTrapPop();CHKERRQ(ierr);
57     ierr = PetscLogFlops((1.0*A->cmap->n*A->cmap->n*A->cmap->n)/3.0);CHKERRQ(ierr);
58   } else if (A->factortype == MAT_FACTOR_CHOLESKY) {
59     if (A->spd) {
60       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
61       PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&n,mat->v,&mat->lda,&info));
62       ierr = PetscFPTrapPop();CHKERRQ(ierr);
63       ierr = MatSeqDenseSymmetrize_Private(A,PETSC_TRUE);CHKERRQ(ierr);
64 #if defined(PETSC_USE_COMPLEX)
65     } else if (A->hermitian) {
66       if (!mat->pivots) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Pivots not present");
67       if (!mat->fwork) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Fwork not present");
68       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
69       PetscStackCallBLAS("LAPACKhetri",LAPACKhetri_("L",&n,mat->v,&mat->lda,mat->pivots,mat->fwork,&info));
70       ierr = PetscFPTrapPop();CHKERRQ(ierr);
71       ierr = MatSeqDenseSymmetrize_Private(A,PETSC_TRUE);CHKERRQ(ierr);
72 #endif
73     } else { /* symmetric case */
74       if (!mat->pivots) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Pivots not present");
75       if (!mat->fwork) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Fwork not present");
76       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
77       PetscStackCallBLAS("LAPACKsytri",LAPACKsytri_("L",&n,mat->v,&mat->lda,mat->pivots,mat->fwork,&info));
78       ierr = PetscFPTrapPop();CHKERRQ(ierr);
79       ierr = MatSeqDenseSymmetrize_Private(A,PETSC_FALSE);CHKERRQ(ierr);
80     }
81     if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Bad Inversion: zero pivot in row %D",(PetscInt)info-1);
82     ierr = PetscLogFlops((1.0*A->cmap->n*A->cmap->n*A->cmap->n)/3.0);CHKERRQ(ierr);
83   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix must be factored to solve");
84 
85   A->ops->solve             = NULL;
86   A->ops->matsolve          = NULL;
87   A->ops->solvetranspose    = NULL;
88   A->ops->matsolvetranspose = NULL;
89   A->ops->solveadd          = NULL;
90   A->ops->solvetransposeadd = NULL;
91   A->factortype             = MAT_FACTOR_NONE;
92   ierr                      = PetscFree(A->solvertype);CHKERRQ(ierr);
93   PetscFunctionReturn(0);
94 }
95 
96 PetscErrorCode MatZeroRowsColumns_SeqDense(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
97 {
98   PetscErrorCode    ierr;
99   Mat_SeqDense      *l = (Mat_SeqDense*)A->data;
100   PetscInt          m  = l->lda, n = A->cmap->n,r = A->rmap->n, i,j;
101   PetscScalar       *slot,*bb,*v;
102   const PetscScalar *xx;
103 
104   PetscFunctionBegin;
105   if (PetscDefined(USE_DEBUG)) {
106     for (i=0; i<N; i++) {
107       if (rows[i] < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row requested to be zeroed");
108       if (rows[i] >= A->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D requested to be zeroed greater than or equal number of rows %D",rows[i],A->rmap->n);
109       if (rows[i] >= A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Col %D requested to be zeroed greater than or equal number of cols %D",rows[i],A->cmap->n);
110     }
111   }
112   if (!N) PetscFunctionReturn(0);
113 
114   /* fix right hand side if needed */
115   if (x && b) {
116     Vec xt;
117 
118     if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only coded for square matrices");
119     ierr = VecDuplicate(x,&xt);CHKERRQ(ierr);
120     ierr = VecCopy(x,xt);CHKERRQ(ierr);
121     ierr = VecScale(xt,-1.0);CHKERRQ(ierr);
122     ierr = MatMultAdd(A,xt,b,b);CHKERRQ(ierr);
123     ierr = VecDestroy(&xt);CHKERRQ(ierr);
124     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
125     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
126     for (i=0; i<N; i++) bb[rows[i]] = diag*xx[rows[i]];
127     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
128     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
129   }
130 
131   ierr = MatDenseGetArray(A,&v);CHKERRQ(ierr);
132   for (i=0; i<N; i++) {
133     slot = v + rows[i]*m;
134     ierr = PetscArrayzero(slot,r);CHKERRQ(ierr);
135   }
136   for (i=0; i<N; i++) {
137     slot = v + rows[i];
138     for (j=0; j<n; j++) { *slot = 0.0; slot += m;}
139   }
140   if (diag != 0.0) {
141     if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only coded for square matrices");
142     for (i=0; i<N; i++) {
143       slot  = v + (m+1)*rows[i];
144       *slot = diag;
145     }
146   }
147   ierr = MatDenseRestoreArray(A,&v);CHKERRQ(ierr);
148   PetscFunctionReturn(0);
149 }
150 
151 PetscErrorCode MatPtAPNumeric_SeqDense_SeqDense(Mat A,Mat P,Mat C)
152 {
153   Mat_SeqDense   *c = (Mat_SeqDense*)(C->data);
154   PetscErrorCode ierr;
155 
156   PetscFunctionBegin;
157   if (c->ptapwork) {
158     ierr = (*C->ops->matmultnumeric)(A,P,c->ptapwork);CHKERRQ(ierr);
159     ierr = (*C->ops->transposematmultnumeric)(P,c->ptapwork,C);CHKERRQ(ierr);
160   } else SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"Must call MatPtAPSymbolic_SeqDense_SeqDense() first");
161   PetscFunctionReturn(0);
162 }
163 
164 PetscErrorCode MatPtAPSymbolic_SeqDense_SeqDense(Mat A,Mat P,PetscReal fill,Mat C)
165 {
166   Mat_SeqDense   *c;
167   PetscBool      cisdense;
168   PetscErrorCode ierr;
169 
170   PetscFunctionBegin;
171   ierr = MatSetSizes(C,P->cmap->n,P->cmap->n,P->cmap->N,P->cmap->N);CHKERRQ(ierr);
172   ierr = PetscObjectTypeCompareAny((PetscObject)C,&cisdense,MATSEQDENSE,MATSEQDENSECUDA,"");CHKERRQ(ierr);
173   if (!cisdense) {
174     PetscBool flg;
175 
176     ierr = PetscObjectTypeCompare((PetscObject)P,((PetscObject)A)->type_name,&flg);CHKERRQ(ierr);
177     ierr = MatSetType(C,flg ? ((PetscObject)A)->type_name : MATDENSE);CHKERRQ(ierr);
178   }
179   ierr = MatSetUp(C);CHKERRQ(ierr);
180   c    = (Mat_SeqDense*)C->data;
181   ierr = MatCreate(PetscObjectComm((PetscObject)A),&c->ptapwork);CHKERRQ(ierr);
182   ierr = MatSetSizes(c->ptapwork,A->rmap->n,P->cmap->n,A->rmap->N,P->cmap->N);CHKERRQ(ierr);
183   ierr = MatSetType(c->ptapwork,((PetscObject)C)->type_name);CHKERRQ(ierr);
184   ierr = MatSetUp(c->ptapwork);CHKERRQ(ierr);
185   PetscFunctionReturn(0);
186 }
187 
188 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqDense(Mat A,MatType newtype,MatReuse reuse,Mat *newmat)
189 {
190   Mat            B = NULL;
191   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
192   Mat_SeqDense   *b;
193   PetscErrorCode ierr;
194   PetscInt       *ai=a->i,*aj=a->j,m=A->rmap->N,n=A->cmap->N,i;
195   MatScalar      *av=a->a;
196   PetscBool      isseqdense;
197 
198   PetscFunctionBegin;
199   if (reuse == MAT_REUSE_MATRIX) {
200     ierr = PetscObjectTypeCompare((PetscObject)*newmat,MATSEQDENSE,&isseqdense);CHKERRQ(ierr);
201     if (!isseqdense) SETERRQ1(PetscObjectComm((PetscObject)*newmat),PETSC_ERR_USER,"Cannot reuse matrix of type %s",((PetscObject)(*newmat))->type_name);
202   }
203   if (reuse != MAT_REUSE_MATRIX) {
204     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
205     ierr = MatSetSizes(B,m,n,m,n);CHKERRQ(ierr);
206     ierr = MatSetType(B,MATSEQDENSE);CHKERRQ(ierr);
207     ierr = MatSeqDenseSetPreallocation(B,NULL);CHKERRQ(ierr);
208     b    = (Mat_SeqDense*)(B->data);
209   } else {
210     b    = (Mat_SeqDense*)((*newmat)->data);
211     ierr = PetscArrayzero(b->v,m*n);CHKERRQ(ierr);
212   }
213   for (i=0; i<m; i++) {
214     PetscInt j;
215     for (j=0;j<ai[1]-ai[0];j++) {
216       b->v[*aj*m+i] = *av;
217       aj++;
218       av++;
219     }
220     ai++;
221   }
222 
223   if (reuse == MAT_INPLACE_MATRIX) {
224     ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
225     ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
226     ierr = MatHeaderReplace(A,&B);CHKERRQ(ierr);
227   } else {
228     if (B) *newmat = B;
229     ierr = MatAssemblyBegin(*newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
230     ierr = MatAssemblyEnd(*newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
231   }
232   PetscFunctionReturn(0);
233 }
234 
235 PETSC_INTERN PetscErrorCode MatConvert_SeqDense_SeqAIJ(Mat A, MatType newtype,MatReuse reuse,Mat *newmat)
236 {
237   Mat            B;
238   Mat_SeqDense   *a = (Mat_SeqDense*)A->data;
239   PetscErrorCode ierr;
240   PetscInt       i, j;
241   PetscInt       *rows, *nnz;
242   MatScalar      *aa = a->v, *vals;
243 
244   PetscFunctionBegin;
245   ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
246   ierr = MatSetSizes(B,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);CHKERRQ(ierr);
247   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
248   ierr = PetscCalloc3(A->rmap->n,&rows,A->rmap->n,&nnz,A->rmap->n,&vals);CHKERRQ(ierr);
249   for (j=0; j<A->cmap->n; j++) {
250     for (i=0; i<A->rmap->n; i++) if (aa[i] != 0.0 || i == j) ++nnz[i];
251     aa += a->lda;
252   }
253   ierr = MatSeqAIJSetPreallocation(B,PETSC_DETERMINE,nnz);CHKERRQ(ierr);
254   aa = a->v;
255   for (j=0; j<A->cmap->n; j++) {
256     PetscInt numRows = 0;
257     for (i=0; i<A->rmap->n; i++) if (aa[i] != 0.0 || i == j) {rows[numRows] = i; vals[numRows++] = aa[i];}
258     ierr = MatSetValues(B,numRows,rows,1,&j,vals,INSERT_VALUES);CHKERRQ(ierr);
259     aa  += a->lda;
260   }
261   ierr = PetscFree3(rows,nnz,vals);CHKERRQ(ierr);
262   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
263   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
264 
265   if (reuse == MAT_INPLACE_MATRIX) {
266     ierr = MatHeaderReplace(A,&B);CHKERRQ(ierr);
267   } else {
268     *newmat = B;
269   }
270   PetscFunctionReturn(0);
271 }
272 
273 PetscErrorCode MatAXPY_SeqDense(Mat Y,PetscScalar alpha,Mat X,MatStructure str)
274 {
275   Mat_SeqDense      *x = (Mat_SeqDense*)X->data,*y = (Mat_SeqDense*)Y->data;
276   const PetscScalar *xv;
277   PetscScalar       *yv;
278   PetscBLASInt      N,m,ldax,lday,one = 1;
279   PetscErrorCode    ierr;
280 
281   PetscFunctionBegin;
282   ierr = MatDenseGetArrayRead(X,&xv);CHKERRQ(ierr);
283   ierr = MatDenseGetArray(Y,&yv);CHKERRQ(ierr);
284   ierr = PetscBLASIntCast(X->rmap->n*X->cmap->n,&N);CHKERRQ(ierr);
285   ierr = PetscBLASIntCast(X->rmap->n,&m);CHKERRQ(ierr);
286   ierr = PetscBLASIntCast(x->lda,&ldax);CHKERRQ(ierr);
287   ierr = PetscBLASIntCast(y->lda,&lday);CHKERRQ(ierr);
288   if (ldax>m || lday>m) {
289     PetscInt j;
290 
291     for (j=0; j<X->cmap->n; j++) {
292       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&m,&alpha,xv+j*ldax,&one,yv+j*lday,&one));
293     }
294   } else {
295     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&N,&alpha,xv,&one,yv,&one));
296   }
297   ierr = MatDenseRestoreArrayRead(X,&xv);CHKERRQ(ierr);
298   ierr = MatDenseRestoreArray(Y,&yv);CHKERRQ(ierr);
299   ierr = PetscLogFlops(PetscMax(2*N-1,0));CHKERRQ(ierr);
300   PetscFunctionReturn(0);
301 }
302 
303 static PetscErrorCode MatGetInfo_SeqDense(Mat A,MatInfoType flag,MatInfo *info)
304 {
305   PetscLogDouble N = A->rmap->n*A->cmap->n;
306 
307   PetscFunctionBegin;
308   info->block_size        = 1.0;
309   info->nz_allocated      = N;
310   info->nz_used           = N;
311   info->nz_unneeded       = 0;
312   info->assemblies        = A->num_ass;
313   info->mallocs           = 0;
314   info->memory            = ((PetscObject)A)->mem;
315   info->fill_ratio_given  = 0;
316   info->fill_ratio_needed = 0;
317   info->factor_mallocs    = 0;
318   PetscFunctionReturn(0);
319 }
320 
321 PetscErrorCode MatScale_SeqDense(Mat A,PetscScalar alpha)
322 {
323   Mat_SeqDense   *a = (Mat_SeqDense*)A->data;
324   PetscScalar    *v;
325   PetscErrorCode ierr;
326   PetscBLASInt   one = 1,j,nz,lda;
327 
328   PetscFunctionBegin;
329   ierr = MatDenseGetArray(A,&v);CHKERRQ(ierr);
330   ierr = PetscBLASIntCast(a->lda,&lda);CHKERRQ(ierr);
331   if (lda>A->rmap->n) {
332     ierr = PetscBLASIntCast(A->rmap->n,&nz);CHKERRQ(ierr);
333     for (j=0; j<A->cmap->n; j++) {
334       PetscStackCallBLAS("BLASscal",BLASscal_(&nz,&alpha,v+j*lda,&one));
335     }
336   } else {
337     ierr = PetscBLASIntCast(A->rmap->n*A->cmap->n,&nz);CHKERRQ(ierr);
338     PetscStackCallBLAS("BLASscal",BLASscal_(&nz,&alpha,v,&one));
339   }
340   ierr = PetscLogFlops(nz);CHKERRQ(ierr);
341   ierr = MatDenseRestoreArray(A,&v);CHKERRQ(ierr);
342   PetscFunctionReturn(0);
343 }
344 
345 static PetscErrorCode MatIsHermitian_SeqDense(Mat A,PetscReal rtol,PetscBool  *fl)
346 {
347   Mat_SeqDense      *a = (Mat_SeqDense*)A->data;
348   PetscInt          i,j,m = A->rmap->n,N = a->lda;
349   const PetscScalar *v;
350   PetscErrorCode    ierr;
351 
352   PetscFunctionBegin;
353   *fl = PETSC_FALSE;
354   if (A->rmap->n != A->cmap->n) PetscFunctionReturn(0);
355   ierr = MatDenseGetArrayRead(A,&v);CHKERRQ(ierr);
356   for (i=0; i<m; i++) {
357     for (j=i; j<m; j++) {
358       if (PetscAbsScalar(v[i+j*N] - PetscConj(v[j+i*N])) > rtol) {
359         goto restore;
360       }
361     }
362   }
363   *fl  = PETSC_TRUE;
364 restore:
365   ierr = MatDenseRestoreArrayRead(A,&v);CHKERRQ(ierr);
366   PetscFunctionReturn(0);
367 }
368 
369 static PetscErrorCode MatIsSymmetric_SeqDense(Mat A,PetscReal rtol,PetscBool  *fl)
370 {
371   Mat_SeqDense      *a = (Mat_SeqDense*)A->data;
372   PetscInt          i,j,m = A->rmap->n,N = a->lda;
373   const PetscScalar *v;
374   PetscErrorCode    ierr;
375 
376   PetscFunctionBegin;
377   *fl = PETSC_FALSE;
378   if (A->rmap->n != A->cmap->n) PetscFunctionReturn(0);
379   ierr = MatDenseGetArrayRead(A,&v);CHKERRQ(ierr);
380   for (i=0; i<m; i++) {
381     for (j=i; j<m; j++) {
382       if (PetscAbsScalar(v[i+j*N] - v[j+i*N]) > rtol) {
383         goto restore;
384       }
385     }
386   }
387   *fl  = PETSC_TRUE;
388 restore:
389   ierr = MatDenseRestoreArrayRead(A,&v);CHKERRQ(ierr);
390   PetscFunctionReturn(0);
391 }
392 
393 PetscErrorCode MatDuplicateNoCreate_SeqDense(Mat newi,Mat A,MatDuplicateOption cpvalues)
394 {
395   Mat_SeqDense   *mat = (Mat_SeqDense*)A->data;
396   PetscErrorCode ierr;
397   PetscInt       lda = (PetscInt)mat->lda,j,m,nlda = lda;
398 
399   PetscFunctionBegin;
400   ierr = PetscLayoutReference(A->rmap,&newi->rmap);CHKERRQ(ierr);
401   ierr = PetscLayoutReference(A->cmap,&newi->cmap);CHKERRQ(ierr);
402   if (cpvalues == MAT_SHARE_NONZERO_PATTERN) { /* propagate LDA */
403     ierr = MatDenseSetLDA(newi,lda);CHKERRQ(ierr);
404   }
405   ierr = MatSeqDenseSetPreallocation(newi,NULL);CHKERRQ(ierr);
406   if (cpvalues == MAT_COPY_VALUES) {
407     const PetscScalar *av;
408     PetscScalar       *v;
409 
410     ierr = MatDenseGetArrayRead(A,&av);CHKERRQ(ierr);
411     ierr = MatDenseGetArray(newi,&v);CHKERRQ(ierr);
412     ierr = MatDenseGetLDA(newi,&nlda);CHKERRQ(ierr);
413     m    = A->rmap->n;
414     if (lda>m || nlda>m) {
415       for (j=0; j<A->cmap->n; j++) {
416         ierr = PetscArraycpy(v+j*nlda,av+j*lda,m);CHKERRQ(ierr);
417       }
418     } else {
419       ierr = PetscArraycpy(v,av,A->rmap->n*A->cmap->n);CHKERRQ(ierr);
420     }
421     ierr = MatDenseRestoreArray(newi,&v);CHKERRQ(ierr);
422     ierr = MatDenseRestoreArrayRead(A,&av);CHKERRQ(ierr);
423   }
424   PetscFunctionReturn(0);
425 }
426 
427 PetscErrorCode MatDuplicate_SeqDense(Mat A,MatDuplicateOption cpvalues,Mat *newmat)
428 {
429   PetscErrorCode ierr;
430 
431   PetscFunctionBegin;
432   ierr = MatCreate(PetscObjectComm((PetscObject)A),newmat);CHKERRQ(ierr);
433   ierr = MatSetSizes(*newmat,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
434   ierr = MatSetType(*newmat,((PetscObject)A)->type_name);CHKERRQ(ierr);
435   ierr = MatDuplicateNoCreate_SeqDense(*newmat,A,cpvalues);CHKERRQ(ierr);
436   PetscFunctionReturn(0);
437 }
438 
439 static PetscErrorCode MatLUFactorNumeric_SeqDense(Mat fact,Mat A,const MatFactorInfo *info_dummy)
440 {
441   MatFactorInfo  info;
442   PetscErrorCode ierr;
443 
444   PetscFunctionBegin;
445   ierr = MatDuplicateNoCreate_SeqDense(fact,A,MAT_COPY_VALUES);CHKERRQ(ierr);
446   ierr = (*fact->ops->lufactor)(fact,0,0,&info);CHKERRQ(ierr);
447   PetscFunctionReturn(0);
448 }
449 
450 static PetscErrorCode MatSolve_SeqDense(Mat A,Vec xx,Vec yy)
451 {
452   Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
453   PetscErrorCode    ierr;
454   const PetscScalar *x;
455   PetscScalar       *y;
456   PetscBLASInt      one = 1,info,m;
457 
458   PetscFunctionBegin;
459   ierr = PetscBLASIntCast(A->rmap->n,&m);CHKERRQ(ierr);
460   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
461   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
462   ierr = PetscArraycpy(y,x,A->rmap->n);CHKERRQ(ierr);
463   if (A->factortype == MAT_FACTOR_LU) {
464     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
465     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("N",&m,&one,mat->v,&mat->lda,mat->pivots,y,&m,&info));
466     ierr = PetscFPTrapPop();CHKERRQ(ierr);
467     if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"GETRS - Bad solve");
468   } else if (A->factortype == MAT_FACTOR_CHOLESKY) {
469     if (A->spd) {
470       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
471       PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("L",&m,&one,mat->v,&mat->lda,y,&m,&info));
472       ierr = PetscFPTrapPop();CHKERRQ(ierr);
473       if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"POTRS Bad solve");
474 #if defined(PETSC_USE_COMPLEX)
475     } else if (A->hermitian) {
476       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
477       PetscStackCallBLAS("LAPACKhetrs",LAPACKhetrs_("L",&m,&one,mat->v,&mat->lda,mat->pivots,y,&m,&info));
478       ierr = PetscFPTrapPop();CHKERRQ(ierr);
479       if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"HETRS Bad solve");
480 #endif
481     } else { /* symmetric case */
482       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
483       PetscStackCallBLAS("LAPACKsytrs",LAPACKsytrs_("L",&m,&one,mat->v,&mat->lda,mat->pivots,y,&m,&info));
484       ierr = PetscFPTrapPop();CHKERRQ(ierr);
485       if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"SYTRS Bad solve");
486     }
487   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix must be factored to solve");
488   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
489   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
490   ierr = PetscLogFlops(2.0*A->cmap->n*A->cmap->n - A->cmap->n);CHKERRQ(ierr);
491   PetscFunctionReturn(0);
492 }
493 
494 static PetscErrorCode MatMatSolve_SeqDense(Mat A,Mat B,Mat X)
495 {
496   Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
497   PetscErrorCode    ierr;
498   const PetscScalar *b;
499   PetscScalar       *x;
500   PetscInt          n;
501   PetscBLASInt      nrhs,info,m;
502 
503   PetscFunctionBegin;
504   ierr = PetscBLASIntCast(A->rmap->n,&m);CHKERRQ(ierr);
505   ierr = MatGetSize(B,NULL,&n);CHKERRQ(ierr);
506   ierr = PetscBLASIntCast(n,&nrhs);CHKERRQ(ierr);
507   ierr = MatDenseGetArrayRead(B,&b);CHKERRQ(ierr);
508   ierr = MatDenseGetArray(X,&x);CHKERRQ(ierr);
509 
510   ierr = PetscArraycpy(x,b,m*nrhs);CHKERRQ(ierr);
511 
512   if (A->factortype == MAT_FACTOR_LU) {
513     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
514     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("N",&m,&nrhs,mat->v,&mat->lda,mat->pivots,x,&m,&info));
515     ierr = PetscFPTrapPop();CHKERRQ(ierr);
516     if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"GETRS - Bad solve");
517   } else if (A->factortype == MAT_FACTOR_CHOLESKY) {
518     if (A->spd) {
519       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
520       PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("L",&m,&nrhs,mat->v,&mat->lda,x,&m,&info));
521       ierr = PetscFPTrapPop();CHKERRQ(ierr);
522       if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"POTRS Bad solve");
523 #if defined(PETSC_USE_COMPLEX)
524     } else if (A->hermitian) {
525       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
526       PetscStackCallBLAS("LAPACKhetrs",LAPACKhetrs_("L",&m,&nrhs,mat->v,&mat->lda,mat->pivots,x,&m,&info));
527       ierr = PetscFPTrapPop();CHKERRQ(ierr);
528       if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"HETRS Bad solve");
529 #endif
530     } else { /* symmetric case */
531       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
532       PetscStackCallBLAS("LAPACKsytrs",LAPACKsytrs_("L",&m,&nrhs,mat->v,&mat->lda,mat->pivots,x,&m,&info));
533       ierr = PetscFPTrapPop();CHKERRQ(ierr);
534       if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"SYTRS Bad solve");
535     }
536   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix must be factored to solve");
537 
538   ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr);
539   ierr = MatDenseRestoreArray(X,&x);CHKERRQ(ierr);
540   ierr = PetscLogFlops(nrhs*(2.0*m*m - m));CHKERRQ(ierr);
541   PetscFunctionReturn(0);
542 }
543 
544 static PetscErrorCode MatConjugate_SeqDense(Mat);
545 
546 static PetscErrorCode MatSolveTranspose_SeqDense(Mat A,Vec xx,Vec yy)
547 {
548   Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
549   PetscErrorCode    ierr;
550   const PetscScalar *x;
551   PetscScalar       *y;
552   PetscBLASInt      one = 1,info,m;
553 
554   PetscFunctionBegin;
555   ierr = PetscBLASIntCast(A->rmap->n,&m);CHKERRQ(ierr);
556   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
557   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
558   ierr = PetscArraycpy(y,x,A->rmap->n);CHKERRQ(ierr);
559   if (A->factortype == MAT_FACTOR_LU) {
560     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
561     PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("T",&m,&one,mat->v,&mat->lda,mat->pivots,y,&m,&info));
562     ierr = PetscFPTrapPop();CHKERRQ(ierr);
563     if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"POTRS - Bad solve");
564   } else if (A->factortype == MAT_FACTOR_CHOLESKY) {
565     if (A->spd) {
566 #if defined(PETSC_USE_COMPLEX)
567       ierr = MatConjugate_SeqDense(A);CHKERRQ(ierr);
568 #endif
569       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
570       PetscStackCallBLAS("LAPACKpotrs",LAPACKpotrs_("L",&m,&one,mat->v,&mat->lda,y,&m,&info));
571       ierr = PetscFPTrapPop();CHKERRQ(ierr);
572 #if defined(PETSC_USE_COMPLEX)
573       ierr = MatConjugate_SeqDense(A);CHKERRQ(ierr);
574 #endif
575       if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"POTRS Bad solve");
576 #if defined(PETSC_USE_COMPLEX)
577     } else if (A->hermitian) {
578       ierr = MatConjugate_SeqDense(A);CHKERRQ(ierr);
579       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
580       PetscStackCallBLAS("LAPACKhetrs",LAPACKhetrs_("L",&m,&one,mat->v,&mat->lda,mat->pivots,y,&m,&info));
581       ierr = PetscFPTrapPop();CHKERRQ(ierr);
582       ierr = MatConjugate_SeqDense(A);CHKERRQ(ierr);
583 #endif
584     } else { /* symmetric case */
585       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
586       PetscStackCallBLAS("LAPACKsytrs",LAPACKsytrs_("L",&m,&one,mat->v,&mat->lda,mat->pivots,y,&m,&info));
587       ierr = PetscFPTrapPop();CHKERRQ(ierr);
588       if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"SYTRS Bad solve");
589     }
590   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix must be factored to solve");
591   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
592   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
593   ierr = PetscLogFlops(2.0*A->cmap->n*A->cmap->n - A->cmap->n);CHKERRQ(ierr);
594   PetscFunctionReturn(0);
595 }
596 
597 /* ---------------------------------------------------------------*/
598 /* COMMENT: I have chosen to hide row permutation in the pivots,
599    rather than put it in the Mat->row slot.*/
600 PetscErrorCode MatLUFactor_SeqDense(Mat A,IS row,IS col,const MatFactorInfo *minfo)
601 {
602   Mat_SeqDense   *mat = (Mat_SeqDense*)A->data;
603   PetscErrorCode ierr;
604   PetscBLASInt   n,m,info;
605 
606   PetscFunctionBegin;
607   ierr = PetscBLASIntCast(A->cmap->n,&n);CHKERRQ(ierr);
608   ierr = PetscBLASIntCast(A->rmap->n,&m);CHKERRQ(ierr);
609   if (!mat->pivots) {
610     ierr = PetscMalloc1(A->rmap->n,&mat->pivots);CHKERRQ(ierr);
611     ierr = PetscLogObjectMemory((PetscObject)A,A->rmap->n*sizeof(PetscBLASInt));CHKERRQ(ierr);
612   }
613   if (!A->rmap->n || !A->cmap->n) PetscFunctionReturn(0);
614   ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
615   PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&m,&n,mat->v,&mat->lda,mat->pivots,&info));
616   ierr = PetscFPTrapPop();CHKERRQ(ierr);
617 
618   if (info<0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to LU factorization");
619   if (info>0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Bad LU factorization");
620 
621   A->ops->solve             = MatSolve_SeqDense;
622   A->ops->matsolve          = MatMatSolve_SeqDense;
623   A->ops->solvetranspose    = MatSolveTranspose_SeqDense;
624   A->factortype             = MAT_FACTOR_LU;
625 
626   ierr = PetscFree(A->solvertype);CHKERRQ(ierr);
627   ierr = PetscStrallocpy(MATSOLVERPETSC,&A->solvertype);CHKERRQ(ierr);
628 
629   ierr = PetscLogFlops((2.0*A->cmap->n*A->cmap->n*A->cmap->n)/3);CHKERRQ(ierr);
630   PetscFunctionReturn(0);
631 }
632 
633 /* Cholesky as L*L^T or L*D*L^T and the symmetric/hermitian complex variants */
634 PetscErrorCode MatCholeskyFactor_SeqDense(Mat A,IS perm,const MatFactorInfo *factinfo)
635 {
636   Mat_SeqDense   *mat = (Mat_SeqDense*)A->data;
637   PetscErrorCode ierr;
638   PetscBLASInt   info,n;
639 
640   PetscFunctionBegin;
641   ierr = PetscBLASIntCast(A->cmap->n,&n);CHKERRQ(ierr);
642   if (!A->rmap->n || !A->cmap->n) PetscFunctionReturn(0);
643   if (A->spd) {
644     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
645     PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&n,mat->v,&mat->lda,&info));
646     ierr = PetscFPTrapPop();CHKERRQ(ierr);
647 #if defined(PETSC_USE_COMPLEX)
648   } else if (A->hermitian) {
649     if (!mat->pivots) {
650       ierr = PetscMalloc1(A->rmap->n,&mat->pivots);CHKERRQ(ierr);
651       ierr = PetscLogObjectMemory((PetscObject)A,A->rmap->n*sizeof(PetscBLASInt));CHKERRQ(ierr);
652     }
653     if (!mat->fwork) {
654       PetscScalar dummy;
655 
656       mat->lfwork = -1;
657       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
658       PetscStackCallBLAS("LAPACKhetrf",LAPACKhetrf_("L",&n,mat->v,&mat->lda,mat->pivots,&dummy,&mat->lfwork,&info));
659       ierr = PetscFPTrapPop();CHKERRQ(ierr);
660       mat->lfwork = (PetscInt)PetscRealPart(dummy);
661       ierr = PetscMalloc1(mat->lfwork,&mat->fwork);CHKERRQ(ierr);
662       ierr = PetscLogObjectMemory((PetscObject)A,mat->lfwork*sizeof(PetscBLASInt));CHKERRQ(ierr);
663     }
664     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
665     PetscStackCallBLAS("LAPACKhetrf",LAPACKhetrf_("L",&n,mat->v,&mat->lda,mat->pivots,mat->fwork,&mat->lfwork,&info));
666     ierr = PetscFPTrapPop();CHKERRQ(ierr);
667 #endif
668   } else { /* symmetric case */
669     if (!mat->pivots) {
670       ierr = PetscMalloc1(A->rmap->n,&mat->pivots);CHKERRQ(ierr);
671       ierr = PetscLogObjectMemory((PetscObject)A,A->rmap->n*sizeof(PetscBLASInt));CHKERRQ(ierr);
672     }
673     if (!mat->fwork) {
674       PetscScalar dummy;
675 
676       mat->lfwork = -1;
677       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
678       PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&n,mat->v,&mat->lda,mat->pivots,&dummy,&mat->lfwork,&info));
679       ierr = PetscFPTrapPop();CHKERRQ(ierr);
680       mat->lfwork = (PetscInt)PetscRealPart(dummy);
681       ierr = PetscMalloc1(mat->lfwork,&mat->fwork);CHKERRQ(ierr);
682       ierr = PetscLogObjectMemory((PetscObject)A,mat->lfwork*sizeof(PetscBLASInt));CHKERRQ(ierr);
683     }
684     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
685     PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&n,mat->v,&mat->lda,mat->pivots,mat->fwork,&mat->lfwork,&info));
686     ierr = PetscFPTrapPop();CHKERRQ(ierr);
687   }
688   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Bad factorization: zero pivot in row %D",(PetscInt)info-1);
689 
690   A->ops->solve             = MatSolve_SeqDense;
691   A->ops->matsolve          = MatMatSolve_SeqDense;
692   A->ops->solvetranspose    = MatSolveTranspose_SeqDense;
693   A->factortype             = MAT_FACTOR_CHOLESKY;
694 
695   ierr = PetscFree(A->solvertype);CHKERRQ(ierr);
696   ierr = PetscStrallocpy(MATSOLVERPETSC,&A->solvertype);CHKERRQ(ierr);
697 
698   ierr = PetscLogFlops((1.0*A->cmap->n*A->cmap->n*A->cmap->n)/3.0);CHKERRQ(ierr);
699   PetscFunctionReturn(0);
700 }
701 
702 PetscErrorCode MatCholeskyFactorNumeric_SeqDense(Mat fact,Mat A,const MatFactorInfo *info_dummy)
703 {
704   PetscErrorCode ierr;
705   MatFactorInfo  info;
706 
707   PetscFunctionBegin;
708   info.fill = 1.0;
709 
710   ierr = MatDuplicateNoCreate_SeqDense(fact,A,MAT_COPY_VALUES);CHKERRQ(ierr);
711   ierr = (*fact->ops->choleskyfactor)(fact,0,&info);CHKERRQ(ierr);
712   PetscFunctionReturn(0);
713 }
714 
715 PetscErrorCode MatCholeskyFactorSymbolic_SeqDense(Mat fact,Mat A,IS row,const MatFactorInfo *info)
716 {
717   PetscFunctionBegin;
718   fact->assembled                  = PETSC_TRUE;
719   fact->preallocated               = PETSC_TRUE;
720   fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqDense;
721   fact->ops->solve                 = MatSolve_SeqDense;
722   fact->ops->matsolve              = MatMatSolve_SeqDense;
723   fact->ops->solvetranspose        = MatSolveTranspose_SeqDense;
724   PetscFunctionReturn(0);
725 }
726 
727 PetscErrorCode MatLUFactorSymbolic_SeqDense(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
728 {
729   PetscFunctionBegin;
730   fact->preallocated           = PETSC_TRUE;
731   fact->assembled              = PETSC_TRUE;
732   fact->ops->lufactornumeric   = MatLUFactorNumeric_SeqDense;
733   fact->ops->solve             = MatSolve_SeqDense;
734   fact->ops->matsolve          = MatMatSolve_SeqDense;
735   fact->ops->solvetranspose    = MatSolveTranspose_SeqDense;
736   PetscFunctionReturn(0);
737 }
738 
739 /* uses LAPACK */
740 PETSC_INTERN PetscErrorCode MatGetFactor_seqdense_petsc(Mat A,MatFactorType ftype,Mat *fact)
741 {
742   PetscErrorCode ierr;
743 
744   PetscFunctionBegin;
745   ierr = MatCreate(PetscObjectComm((PetscObject)A),fact);CHKERRQ(ierr);
746   ierr = MatSetSizes(*fact,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
747   ierr = MatSetType(*fact,MATDENSE);CHKERRQ(ierr);
748   if (ftype == MAT_FACTOR_LU) {
749     (*fact)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqDense;
750   } else {
751     (*fact)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqDense;
752   }
753   (*fact)->factortype = ftype;
754 
755   ierr = PetscFree((*fact)->solvertype);CHKERRQ(ierr);
756   ierr = PetscStrallocpy(MATSOLVERPETSC,&(*fact)->solvertype);CHKERRQ(ierr);
757   PetscFunctionReturn(0);
758 }
759 
760 /* ------------------------------------------------------------------*/
761 static PetscErrorCode MatSOR_SeqDense(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal shift,PetscInt its,PetscInt lits,Vec xx)
762 {
763   Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
764   PetscScalar       *x,*v = mat->v,zero = 0.0,xt;
765   const PetscScalar *b;
766   PetscErrorCode    ierr;
767   PetscInt          m = A->rmap->n,i;
768   PetscBLASInt      o = 1,bm;
769 
770   PetscFunctionBegin;
771 #if defined(PETSC_HAVE_CUDA)
772   if (A->offloadmask == PETSC_OFFLOAD_GPU) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented");
773 #endif
774   if (shift == -1) shift = 0.0; /* negative shift indicates do not error on zero diagonal; this code never zeros on zero diagonal */
775   ierr = PetscBLASIntCast(m,&bm);CHKERRQ(ierr);
776   if (flag & SOR_ZERO_INITIAL_GUESS) {
777     /* this is a hack fix, should have another version without the second BLASdotu */
778     ierr = VecSet(xx,zero);CHKERRQ(ierr);
779   }
780   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
781   ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
782   its  = its*lits;
783   if (its <= 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %D and local its %D both positive",its,lits);
784   while (its--) {
785     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
786       for (i=0; i<m; i++) {
787         PetscStackCallBLAS("BLASdotu",xt   = b[i] - BLASdotu_(&bm,v+i,&bm,x,&o));
788         x[i] = (1. - omega)*x[i] + omega*(xt+v[i + i*m]*x[i])/(v[i + i*m]+shift);
789       }
790     }
791     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
792       for (i=m-1; i>=0; i--) {
793         PetscStackCallBLAS("BLASdotu",xt   = b[i] - BLASdotu_(&bm,v+i,&bm,x,&o));
794         x[i] = (1. - omega)*x[i] + omega*(xt+v[i + i*m]*x[i])/(v[i + i*m]+shift);
795       }
796     }
797   }
798   ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
799   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
800   PetscFunctionReturn(0);
801 }
802 
803 /* -----------------------------------------------------------------*/
804 PetscErrorCode MatMultTranspose_SeqDense(Mat A,Vec xx,Vec yy)
805 {
806   Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
807   const PetscScalar *v   = mat->v,*x;
808   PetscScalar       *y;
809   PetscErrorCode    ierr;
810   PetscBLASInt      m, n,_One=1;
811   PetscScalar       _DOne=1.0,_DZero=0.0;
812 
813   PetscFunctionBegin;
814   ierr = PetscBLASIntCast(A->rmap->n,&m);CHKERRQ(ierr);
815   ierr = PetscBLASIntCast(A->cmap->n,&n);CHKERRQ(ierr);
816   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
817   ierr = VecGetArrayWrite(yy,&y);CHKERRQ(ierr);
818   if (!A->rmap->n || !A->cmap->n) {
819     PetscBLASInt i;
820     for (i=0; i<n; i++) y[i] = 0.0;
821   } else {
822     PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&m,&n,&_DOne,v,&mat->lda,x,&_One,&_DZero,y,&_One));
823     ierr = PetscLogFlops(2.0*A->rmap->n*A->cmap->n - A->cmap->n);CHKERRQ(ierr);
824   }
825   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
826   ierr = VecRestoreArrayWrite(yy,&y);CHKERRQ(ierr);
827   PetscFunctionReturn(0);
828 }
829 
830 PetscErrorCode MatMult_SeqDense(Mat A,Vec xx,Vec yy)
831 {
832   Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
833   PetscScalar       *y,_DOne=1.0,_DZero=0.0;
834   PetscErrorCode    ierr;
835   PetscBLASInt      m, n, _One=1;
836   const PetscScalar *v = mat->v,*x;
837 
838   PetscFunctionBegin;
839   ierr = PetscBLASIntCast(A->rmap->n,&m);CHKERRQ(ierr);
840   ierr = PetscBLASIntCast(A->cmap->n,&n);CHKERRQ(ierr);
841   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
842   ierr = VecGetArrayWrite(yy,&y);CHKERRQ(ierr);
843   if (!A->rmap->n || !A->cmap->n) {
844     PetscBLASInt i;
845     for (i=0; i<m; i++) y[i] = 0.0;
846   } else {
847     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&m,&n,&_DOne,v,&(mat->lda),x,&_One,&_DZero,y,&_One));
848     ierr = PetscLogFlops(2.0*A->rmap->n*A->cmap->n - A->rmap->n);CHKERRQ(ierr);
849   }
850   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
851   ierr = VecRestoreArrayWrite(yy,&y);CHKERRQ(ierr);
852   PetscFunctionReturn(0);
853 }
854 
855 PetscErrorCode MatMultAdd_SeqDense(Mat A,Vec xx,Vec zz,Vec yy)
856 {
857   Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
858   const PetscScalar *v = mat->v,*x;
859   PetscScalar       *y,_DOne=1.0;
860   PetscErrorCode    ierr;
861   PetscBLASInt      m, n, _One=1;
862 
863   PetscFunctionBegin;
864   ierr = PetscBLASIntCast(A->rmap->n,&m);CHKERRQ(ierr);
865   ierr = PetscBLASIntCast(A->cmap->n,&n);CHKERRQ(ierr);
866   if (!A->rmap->n || !A->cmap->n) PetscFunctionReturn(0);
867   if (zz != yy) {ierr = VecCopy(zz,yy);CHKERRQ(ierr);}
868   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
869   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
870   PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&m,&n,&_DOne,v,&(mat->lda),x,&_One,&_DOne,y,&_One));
871   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
872   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
873   ierr = PetscLogFlops(2.0*A->rmap->n*A->cmap->n);CHKERRQ(ierr);
874   PetscFunctionReturn(0);
875 }
876 
877 PetscErrorCode MatMultTransposeAdd_SeqDense(Mat A,Vec xx,Vec zz,Vec yy)
878 {
879   Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
880   const PetscScalar *v = mat->v,*x;
881   PetscScalar       *y;
882   PetscErrorCode    ierr;
883   PetscBLASInt      m, n, _One=1;
884   PetscScalar       _DOne=1.0;
885 
886   PetscFunctionBegin;
887   ierr = PetscBLASIntCast(A->rmap->n,&m);CHKERRQ(ierr);
888   ierr = PetscBLASIntCast(A->cmap->n,&n);CHKERRQ(ierr);
889   if (!A->rmap->n || !A->cmap->n) PetscFunctionReturn(0);
890   if (zz != yy) {ierr = VecCopy(zz,yy);CHKERRQ(ierr);}
891   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
892   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
893   PetscStackCallBLAS("BLASgemv",BLASgemv_("T",&m,&n,&_DOne,v,&(mat->lda),x,&_One,&_DOne,y,&_One));
894   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
895   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
896   ierr = PetscLogFlops(2.0*A->rmap->n*A->cmap->n);CHKERRQ(ierr);
897   PetscFunctionReturn(0);
898 }
899 
900 /* -----------------------------------------------------------------*/
901 static PetscErrorCode MatGetRow_SeqDense(Mat A,PetscInt row,PetscInt *ncols,PetscInt **cols,PetscScalar **vals)
902 {
903   Mat_SeqDense   *mat = (Mat_SeqDense*)A->data;
904   PetscErrorCode ierr;
905   PetscInt       i;
906 
907   PetscFunctionBegin;
908   *ncols = A->cmap->n;
909   if (cols) {
910     ierr = PetscMalloc1(A->cmap->n+1,cols);CHKERRQ(ierr);
911     for (i=0; i<A->cmap->n; i++) (*cols)[i] = i;
912   }
913   if (vals) {
914     const PetscScalar *v;
915 
916     ierr = MatDenseGetArrayRead(A,&v);CHKERRQ(ierr);
917     ierr = PetscMalloc1(A->cmap->n+1,vals);CHKERRQ(ierr);
918     v   += row;
919     for (i=0; i<A->cmap->n; i++) {(*vals)[i] = *v; v += mat->lda;}
920     ierr = MatDenseRestoreArrayRead(A,&v);CHKERRQ(ierr);
921   }
922   PetscFunctionReturn(0);
923 }
924 
925 static PetscErrorCode MatRestoreRow_SeqDense(Mat A,PetscInt row,PetscInt *ncols,PetscInt **cols,PetscScalar **vals)
926 {
927   PetscErrorCode ierr;
928 
929   PetscFunctionBegin;
930   if (cols) {ierr = PetscFree(*cols);CHKERRQ(ierr);}
931   if (vals) {ierr = PetscFree(*vals);CHKERRQ(ierr); }
932   PetscFunctionReturn(0);
933 }
934 /* ----------------------------------------------------------------*/
935 static PetscErrorCode MatSetValues_SeqDense(Mat A,PetscInt m,const PetscInt indexm[],PetscInt n,const PetscInt indexn[],const PetscScalar v[],InsertMode addv)
936 {
937   Mat_SeqDense     *mat = (Mat_SeqDense*)A->data;
938   PetscScalar      *av;
939   PetscInt         i,j,idx=0;
940 #if defined(PETSC_HAVE_CUDA)
941   PetscOffloadMask oldf;
942 #endif
943   PetscErrorCode   ierr;
944 
945   PetscFunctionBegin;
946   ierr = MatDenseGetArray(A,&av);CHKERRQ(ierr);
947   if (!mat->roworiented) {
948     if (addv == INSERT_VALUES) {
949       for (j=0; j<n; j++) {
950         if (indexn[j] < 0) {idx += m; continue;}
951         if (PetscUnlikelyDebug(indexn[j] >= A->cmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",indexn[j],A->cmap->n-1);
952         for (i=0; i<m; i++) {
953           if (indexm[i] < 0) {idx++; continue;}
954           if (PetscUnlikelyDebug(indexm[i] >= A->rmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",indexm[i],A->rmap->n-1);
955           av[indexn[j]*mat->lda + indexm[i]] = v[idx++];
956         }
957       }
958     } else {
959       for (j=0; j<n; j++) {
960         if (indexn[j] < 0) {idx += m; continue;}
961         if (PetscUnlikelyDebug(indexn[j] >= A->cmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",indexn[j],A->cmap->n-1);
962         for (i=0; i<m; i++) {
963           if (indexm[i] < 0) {idx++; continue;}
964           if (PetscUnlikelyDebug(indexm[i] >= A->rmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",indexm[i],A->rmap->n-1);
965           av[indexn[j]*mat->lda + indexm[i]] += v[idx++];
966         }
967       }
968     }
969   } else {
970     if (addv == INSERT_VALUES) {
971       for (i=0; i<m; i++) {
972         if (indexm[i] < 0) { idx += n; continue;}
973         if (PetscUnlikelyDebug(indexm[i] >= A->rmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",indexm[i],A->rmap->n-1);
974         for (j=0; j<n; j++) {
975           if (indexn[j] < 0) { idx++; continue;}
976           if (PetscUnlikelyDebug(indexn[j] >= A->cmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",indexn[j],A->cmap->n-1);
977           av[indexn[j]*mat->lda + indexm[i]] = v[idx++];
978         }
979       }
980     } else {
981       for (i=0; i<m; i++) {
982         if (indexm[i] < 0) { idx += n; continue;}
983         if (PetscUnlikelyDebug(indexm[i] >= A->rmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",indexm[i],A->rmap->n-1);
984         for (j=0; j<n; j++) {
985           if (indexn[j] < 0) { idx++; continue;}
986           if (PetscUnlikelyDebug(indexn[j] >= A->cmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",indexn[j],A->cmap->n-1);
987           av[indexn[j]*mat->lda + indexm[i]] += v[idx++];
988         }
989       }
990     }
991   }
992   /* hack to prevent unneeded copy to the GPU while returning the array */
993 #if defined(PETSC_HAVE_CUDA)
994   oldf = A->offloadmask;
995   A->offloadmask = PETSC_OFFLOAD_GPU;
996 #endif
997   ierr = MatDenseRestoreArray(A,&av);CHKERRQ(ierr);
998 #if defined(PETSC_HAVE_CUDA)
999   A->offloadmask = (oldf == PETSC_OFFLOAD_UNALLOCATED ? PETSC_OFFLOAD_UNALLOCATED : PETSC_OFFLOAD_CPU);
1000 #endif
1001   PetscFunctionReturn(0);
1002 }
1003 
1004 static PetscErrorCode MatGetValues_SeqDense(Mat A,PetscInt m,const PetscInt indexm[],PetscInt n,const PetscInt indexn[],PetscScalar v[])
1005 {
1006   Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
1007   const PetscScalar *vv;
1008   PetscInt          i,j;
1009   PetscErrorCode    ierr;
1010 
1011   PetscFunctionBegin;
1012   ierr = MatDenseGetArrayRead(A,&vv);CHKERRQ(ierr);
1013   /* row-oriented output */
1014   for (i=0; i<m; i++) {
1015     if (indexm[i] < 0) {v += n;continue;}
1016     if (indexm[i] >= A->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D requested larger than number rows %D",indexm[i],A->rmap->n);
1017     for (j=0; j<n; j++) {
1018       if (indexn[j] < 0) {v++; continue;}
1019       if (indexn[j] >= A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column %D requested larger than number columns %D",indexn[j],A->cmap->n);
1020       *v++ = vv[indexn[j]*mat->lda + indexm[i]];
1021     }
1022   }
1023   ierr = MatDenseRestoreArrayRead(A,&vv);CHKERRQ(ierr);
1024   PetscFunctionReturn(0);
1025 }
1026 
1027 /* -----------------------------------------------------------------*/
1028 
1029 PetscErrorCode MatView_Dense_Binary(Mat mat,PetscViewer viewer)
1030 {
1031   PetscErrorCode    ierr;
1032   PetscBool         skipHeader;
1033   PetscViewerFormat format;
1034   PetscInt          header[4],M,N,m,lda,i,j,k;
1035   const PetscScalar *v;
1036   PetscScalar       *vwork;
1037 
1038   PetscFunctionBegin;
1039   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
1040   ierr = PetscViewerBinaryGetSkipHeader(viewer,&skipHeader);CHKERRQ(ierr);
1041   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1042   if (skipHeader) format = PETSC_VIEWER_NATIVE;
1043 
1044   ierr = MatGetSize(mat,&M,&N);CHKERRQ(ierr);
1045 
1046   /* write matrix header */
1047   header[0] = MAT_FILE_CLASSID; header[1] = M; header[2] = N;
1048   header[3] = (format == PETSC_VIEWER_NATIVE) ? MATRIX_BINARY_FORMAT_DENSE : M*N;
1049   if (!skipHeader) {ierr = PetscViewerBinaryWrite(viewer,header,4,PETSC_INT);CHKERRQ(ierr);}
1050 
1051   ierr = MatGetLocalSize(mat,&m,NULL);CHKERRQ(ierr);
1052   if (format != PETSC_VIEWER_NATIVE) {
1053     PetscInt nnz = m*N, *iwork;
1054     /* store row lengths for each row */
1055     ierr = PetscMalloc1(nnz,&iwork);CHKERRQ(ierr);
1056     for (i=0; i<m; i++) iwork[i] = N;
1057     ierr = PetscViewerBinaryWriteAll(viewer,iwork,m,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_INT);CHKERRQ(ierr);
1058     /* store column indices (zero start index) */
1059     for (k=0, i=0; i<m; i++)
1060       for (j=0; j<N; j++, k++)
1061         iwork[k] = j;
1062     ierr = PetscViewerBinaryWriteAll(viewer,iwork,nnz,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_INT);CHKERRQ(ierr);
1063     ierr = PetscFree(iwork);CHKERRQ(ierr);
1064   }
1065   /* store matrix values as a dense matrix in row major order */
1066   ierr = PetscMalloc1(m*N,&vwork);CHKERRQ(ierr);
1067   ierr = MatDenseGetArrayRead(mat,&v);CHKERRQ(ierr);
1068   ierr = MatDenseGetLDA(mat,&lda);CHKERRQ(ierr);
1069   for (k=0, i=0; i<m; i++)
1070     for (j=0; j<N; j++, k++)
1071       vwork[k] = v[i+lda*j];
1072   ierr = MatDenseRestoreArrayRead(mat,&v);CHKERRQ(ierr);
1073   ierr = PetscViewerBinaryWriteAll(viewer,vwork,m*N,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_SCALAR);CHKERRQ(ierr);
1074   ierr = PetscFree(vwork);CHKERRQ(ierr);
1075   PetscFunctionReturn(0);
1076 }
1077 
1078 PetscErrorCode MatLoad_Dense_Binary(Mat mat,PetscViewer viewer)
1079 {
1080   PetscErrorCode ierr;
1081   PetscBool      skipHeader;
1082   PetscInt       header[4],M,N,m,nz,lda,i,j,k;
1083   PetscInt       rows,cols;
1084   PetscScalar    *v,*vwork;
1085 
1086   PetscFunctionBegin;
1087   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
1088   ierr = PetscViewerBinaryGetSkipHeader(viewer,&skipHeader);CHKERRQ(ierr);
1089 
1090   if (!skipHeader) {
1091     ierr = PetscViewerBinaryRead(viewer,header,4,NULL,PETSC_INT);CHKERRQ(ierr);
1092     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Not a matrix object in file");
1093     M = header[1]; N = header[2];
1094     if (M < 0) SETERRQ1(PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Matrix row size (%D) in file is negative",M);
1095     if (N < 0) SETERRQ1(PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Matrix column size (%D) in file is negative",N);
1096     nz = header[3];
1097     if (nz != MATRIX_BINARY_FORMAT_DENSE && nz < 0) SETERRQ1(PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Unknown matrix format %D in file",nz);
1098   } else {
1099     ierr = MatGetSize(mat,&M,&N);CHKERRQ(ierr);
1100     if (M < 0 || N < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Matrix binary file header was skipped, thus the user must specify the global sizes of input matrix");
1101     nz = MATRIX_BINARY_FORMAT_DENSE;
1102   }
1103 
1104   /* setup global sizes if not set */
1105   if (mat->rmap->N < 0) mat->rmap->N = M;
1106   if (mat->cmap->N < 0) mat->cmap->N = N;
1107   ierr = MatSetUp(mat);CHKERRQ(ierr);
1108   /* check if global sizes are correct */
1109   ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
1110   if (M != rows || N != cols) SETERRQ4(PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED, "Matrix in file of different sizes (%d, %d) than the input matrix (%d, %d)",M,N,rows,cols);
1111 
1112   ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
1113   ierr = MatGetLocalSize(mat,&m,NULL);CHKERRQ(ierr);
1114   ierr = MatDenseGetArray(mat,&v);CHKERRQ(ierr);
1115   ierr = MatDenseGetLDA(mat,&lda);CHKERRQ(ierr);
1116   if (nz == MATRIX_BINARY_FORMAT_DENSE) {  /* matrix in file is dense format */
1117     PetscInt nnz = m*N;
1118     /* read in matrix values */
1119     ierr = PetscMalloc1(nnz,&vwork);CHKERRQ(ierr);
1120     ierr = PetscViewerBinaryReadAll(viewer,vwork,nnz,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_SCALAR);CHKERRQ(ierr);
1121     /* store values in column major order */
1122     for (j=0; j<N; j++)
1123       for (i=0; i<m; i++)
1124         v[i+lda*j] = vwork[i*N+j];
1125     ierr = PetscFree(vwork);CHKERRQ(ierr);
1126   } else { /* matrix in file is sparse format */
1127     PetscInt nnz = 0, *rlens, *icols;
1128     /* read in row lengths */
1129     ierr = PetscMalloc1(m,&rlens);CHKERRQ(ierr);
1130     ierr = PetscViewerBinaryReadAll(viewer,rlens,m,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_INT);CHKERRQ(ierr);
1131     for (i=0; i<m; i++) nnz += rlens[i];
1132     /* read in column indices and values */
1133     ierr = PetscMalloc2(nnz,&icols,nnz,&vwork);CHKERRQ(ierr);
1134     ierr = PetscViewerBinaryReadAll(viewer,icols,nnz,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_INT);CHKERRQ(ierr);
1135     ierr = PetscViewerBinaryReadAll(viewer,vwork,nnz,PETSC_DETERMINE,PETSC_DETERMINE,PETSC_SCALAR);CHKERRQ(ierr);
1136     /* store values in column major order */
1137     for (k=0, i=0; i<m; i++)
1138       for (j=0; j<rlens[i]; j++, k++)
1139         v[i+lda*icols[k]] = vwork[k];
1140     ierr = PetscFree(rlens);CHKERRQ(ierr);
1141     ierr = PetscFree2(icols,vwork);CHKERRQ(ierr);
1142   }
1143   ierr = MatDenseRestoreArray(mat,&v);CHKERRQ(ierr);
1144   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1145   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1146   PetscFunctionReturn(0);
1147 }
1148 
1149 PetscErrorCode MatLoad_SeqDense(Mat newMat, PetscViewer viewer)
1150 {
1151   PetscBool      isbinary, ishdf5;
1152   PetscErrorCode ierr;
1153 
1154   PetscFunctionBegin;
1155   PetscValidHeaderSpecific(newMat,MAT_CLASSID,1);
1156   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
1157   /* force binary viewer to load .info file if it has not yet done so */
1158   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
1159   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1160   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,  &ishdf5);CHKERRQ(ierr);
1161   if (isbinary) {
1162     ierr = MatLoad_Dense_Binary(newMat,viewer);CHKERRQ(ierr);
1163   } else if (ishdf5) {
1164 #if defined(PETSC_HAVE_HDF5)
1165     ierr = MatLoad_Dense_HDF5(newMat,viewer);CHKERRQ(ierr);
1166 #else
1167     SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
1168 #endif
1169   } else {
1170     SETERRQ2(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"Viewer type %s not yet supported for reading %s matrices",((PetscObject)viewer)->type_name,((PetscObject)newMat)->type_name);
1171   }
1172   PetscFunctionReturn(0);
1173 }
1174 
1175 static PetscErrorCode MatView_SeqDense_ASCII(Mat A,PetscViewer viewer)
1176 {
1177   Mat_SeqDense      *a = (Mat_SeqDense*)A->data;
1178   PetscErrorCode    ierr;
1179   PetscInt          i,j;
1180   const char        *name;
1181   PetscScalar       *v,*av;
1182   PetscViewerFormat format;
1183 #if defined(PETSC_USE_COMPLEX)
1184   PetscBool         allreal = PETSC_TRUE;
1185 #endif
1186 
1187   PetscFunctionBegin;
1188   ierr = MatDenseGetArrayRead(A,(const PetscScalar**)&av);CHKERRQ(ierr);
1189   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1190   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1191     PetscFunctionReturn(0);  /* do nothing for now */
1192   } else if (format == PETSC_VIEWER_ASCII_COMMON) {
1193     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
1194     for (i=0; i<A->rmap->n; i++) {
1195       v    = av + i;
1196       ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
1197       for (j=0; j<A->cmap->n; j++) {
1198 #if defined(PETSC_USE_COMPLEX)
1199         if (PetscRealPart(*v) != 0.0 && PetscImaginaryPart(*v) != 0.0) {
1200           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i) ",j,(double)PetscRealPart(*v),(double)PetscImaginaryPart(*v));CHKERRQ(ierr);
1201         } else if (PetscRealPart(*v)) {
1202           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",j,(double)PetscRealPart(*v));CHKERRQ(ierr);
1203         }
1204 #else
1205         if (*v) {
1206           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",j,(double)*v);CHKERRQ(ierr);
1207         }
1208 #endif
1209         v += a->lda;
1210       }
1211       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
1212     }
1213     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
1214   } else {
1215     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
1216 #if defined(PETSC_USE_COMPLEX)
1217     /* determine if matrix has all real values */
1218     v = av;
1219     for (i=0; i<A->rmap->n*A->cmap->n; i++) {
1220       if (PetscImaginaryPart(v[i])) { allreal = PETSC_FALSE; break;}
1221     }
1222 #endif
1223     if (format == PETSC_VIEWER_ASCII_MATLAB) {
1224       ierr = PetscObjectGetName((PetscObject)A,&name);CHKERRQ(ierr);
1225       ierr = PetscViewerASCIIPrintf(viewer,"%% Size = %D %D \n",A->rmap->n,A->cmap->n);CHKERRQ(ierr);
1226       ierr = PetscViewerASCIIPrintf(viewer,"%s = zeros(%D,%D);\n",name,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
1227       ierr = PetscViewerASCIIPrintf(viewer,"%s = [\n",name);CHKERRQ(ierr);
1228     }
1229 
1230     for (i=0; i<A->rmap->n; i++) {
1231       v = av + i;
1232       for (j=0; j<A->cmap->n; j++) {
1233 #if defined(PETSC_USE_COMPLEX)
1234         if (allreal) {
1235           ierr = PetscViewerASCIIPrintf(viewer,"%18.16e ",(double)PetscRealPart(*v));CHKERRQ(ierr);
1236         } else {
1237           ierr = PetscViewerASCIIPrintf(viewer,"%18.16e + %18.16ei ",(double)PetscRealPart(*v),(double)PetscImaginaryPart(*v));CHKERRQ(ierr);
1238         }
1239 #else
1240         ierr = PetscViewerASCIIPrintf(viewer,"%18.16e ",(double)*v);CHKERRQ(ierr);
1241 #endif
1242         v += a->lda;
1243       }
1244       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
1245     }
1246     if (format == PETSC_VIEWER_ASCII_MATLAB) {
1247       ierr = PetscViewerASCIIPrintf(viewer,"];\n");CHKERRQ(ierr);
1248     }
1249     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
1250   }
1251   ierr = MatDenseRestoreArrayRead(A,(const PetscScalar**)&av);CHKERRQ(ierr);
1252   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1253   PetscFunctionReturn(0);
1254 }
1255 
1256 #include <petscdraw.h>
1257 static PetscErrorCode MatView_SeqDense_Draw_Zoom(PetscDraw draw,void *Aa)
1258 {
1259   Mat               A  = (Mat) Aa;
1260   PetscErrorCode    ierr;
1261   PetscInt          m  = A->rmap->n,n = A->cmap->n,i,j;
1262   int               color = PETSC_DRAW_WHITE;
1263   const PetscScalar *v;
1264   PetscViewer       viewer;
1265   PetscReal         xl,yl,xr,yr,x_l,x_r,y_l,y_r;
1266   PetscViewerFormat format;
1267 
1268   PetscFunctionBegin;
1269   ierr = PetscObjectQuery((PetscObject)A,"Zoomviewer",(PetscObject*)&viewer);CHKERRQ(ierr);
1270   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1271   ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
1272 
1273   /* Loop over matrix elements drawing boxes */
1274   ierr = MatDenseGetArrayRead(A,&v);CHKERRQ(ierr);
1275   if (format != PETSC_VIEWER_DRAW_CONTOUR) {
1276     ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
1277     /* Blue for negative and Red for positive */
1278     for (j = 0; j < n; j++) {
1279       x_l = j; x_r = x_l + 1.0;
1280       for (i = 0; i < m; i++) {
1281         y_l = m - i - 1.0;
1282         y_r = y_l + 1.0;
1283         if (PetscRealPart(v[j*m+i]) >  0.) color = PETSC_DRAW_RED;
1284         else if (PetscRealPart(v[j*m+i]) <  0.) color = PETSC_DRAW_BLUE;
1285         else continue;
1286         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
1287       }
1288     }
1289     ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
1290   } else {
1291     /* use contour shading to indicate magnitude of values */
1292     /* first determine max of all nonzero values */
1293     PetscReal minv = 0.0, maxv = 0.0;
1294     PetscDraw popup;
1295 
1296     for (i=0; i < m*n; i++) {
1297       if (PetscAbsScalar(v[i]) > maxv) maxv = PetscAbsScalar(v[i]);
1298     }
1299     if (minv >= maxv) maxv = minv + PETSC_SMALL;
1300     ierr = PetscDrawGetPopup(draw,&popup);CHKERRQ(ierr);
1301     ierr = PetscDrawScalePopup(popup,minv,maxv);CHKERRQ(ierr);
1302 
1303     ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
1304     for (j=0; j<n; j++) {
1305       x_l = j;
1306       x_r = x_l + 1.0;
1307       for (i=0; i<m; i++) {
1308         y_l   = m - i - 1.0;
1309         y_r   = y_l + 1.0;
1310         color = PetscDrawRealToColor(PetscAbsScalar(v[j*m+i]),minv,maxv);
1311         ierr  = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
1312       }
1313     }
1314     ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
1315   }
1316   ierr = MatDenseRestoreArrayRead(A,&v);CHKERRQ(ierr);
1317   PetscFunctionReturn(0);
1318 }
1319 
1320 static PetscErrorCode MatView_SeqDense_Draw(Mat A,PetscViewer viewer)
1321 {
1322   PetscDraw      draw;
1323   PetscBool      isnull;
1324   PetscReal      xr,yr,xl,yl,h,w;
1325   PetscErrorCode ierr;
1326 
1327   PetscFunctionBegin;
1328   ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1329   ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
1330   if (isnull) PetscFunctionReturn(0);
1331 
1332   xr   = A->cmap->n; yr = A->rmap->n; h = yr/10.0; w = xr/10.0;
1333   xr  += w;          yr += h;        xl = -w;     yl = -h;
1334   ierr = PetscDrawSetCoordinates(draw,xl,yl,xr,yr);CHKERRQ(ierr);
1335   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",(PetscObject)viewer);CHKERRQ(ierr);
1336   ierr = PetscDrawZoom(draw,MatView_SeqDense_Draw_Zoom,A);CHKERRQ(ierr);
1337   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",NULL);CHKERRQ(ierr);
1338   ierr = PetscDrawSave(draw);CHKERRQ(ierr);
1339   PetscFunctionReturn(0);
1340 }
1341 
1342 PetscErrorCode MatView_SeqDense(Mat A,PetscViewer viewer)
1343 {
1344   PetscErrorCode ierr;
1345   PetscBool      iascii,isbinary,isdraw;
1346 
1347   PetscFunctionBegin;
1348   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1349   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1350   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1351 
1352   if (iascii) {
1353     ierr = MatView_SeqDense_ASCII(A,viewer);CHKERRQ(ierr);
1354   } else if (isbinary) {
1355     ierr = MatView_Dense_Binary(A,viewer);CHKERRQ(ierr);
1356   } else if (isdraw) {
1357     ierr = MatView_SeqDense_Draw(A,viewer);CHKERRQ(ierr);
1358   }
1359   PetscFunctionReturn(0);
1360 }
1361 
1362 static PetscErrorCode MatDensePlaceArray_SeqDense(Mat A,const PetscScalar *array)
1363 {
1364   Mat_SeqDense *a = (Mat_SeqDense*)A->data;
1365 
1366   PetscFunctionBegin;
1367   if (a->vecinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreColumnVec() first");
1368   if (a->matinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreSubMatrix() first");
1369   if (a->unplacedarray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreArray() first");
1370   a->unplacedarray       = a->v;
1371   a->unplaced_user_alloc = a->user_alloc;
1372   a->v                   = (PetscScalar*) array;
1373   a->user_alloc          = PETSC_TRUE;
1374 #if defined(PETSC_HAVE_CUDA)
1375   A->offloadmask = PETSC_OFFLOAD_CPU;
1376 #endif
1377   PetscFunctionReturn(0);
1378 }
1379 
1380 static PetscErrorCode MatDenseResetArray_SeqDense(Mat A)
1381 {
1382   Mat_SeqDense *a = (Mat_SeqDense*)A->data;
1383 
1384   PetscFunctionBegin;
1385   if (a->vecinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreColumnVec() first");
1386   if (a->matinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreSubMatrix() first");
1387   a->v             = a->unplacedarray;
1388   a->user_alloc    = a->unplaced_user_alloc;
1389   a->unplacedarray = NULL;
1390 #if defined(PETSC_HAVE_CUDA)
1391   A->offloadmask = PETSC_OFFLOAD_CPU;
1392 #endif
1393   PetscFunctionReturn(0);
1394 }
1395 
1396 static PetscErrorCode MatDenseReplaceArray_SeqDense(Mat A,const PetscScalar *array)
1397 {
1398   Mat_SeqDense   *a = (Mat_SeqDense*)A->data;
1399   PetscErrorCode ierr;
1400 
1401   PetscFunctionBegin;
1402   if (a->vecinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreColumnVec() first");
1403   if (a->matinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreSubMatrix() first");
1404   if (!a->user_alloc) { ierr = PetscFree(a->v);CHKERRQ(ierr); }
1405   a->v           = (PetscScalar*) array;
1406   a->user_alloc  = PETSC_FALSE;
1407 #if defined(PETSC_HAVE_CUDA)
1408   A->offloadmask = PETSC_OFFLOAD_CPU;
1409 #endif
1410   PetscFunctionReturn(0);
1411 }
1412 
1413 PetscErrorCode MatDestroy_SeqDense(Mat mat)
1414 {
1415   Mat_SeqDense   *l = (Mat_SeqDense*)mat->data;
1416   PetscErrorCode ierr;
1417 
1418   PetscFunctionBegin;
1419 #if defined(PETSC_USE_LOG)
1420   PetscLogObjectState((PetscObject)mat,"Rows %D Cols %D",mat->rmap->n,mat->cmap->n);
1421 #endif
1422   ierr = PetscFree(l->pivots);CHKERRQ(ierr);
1423   ierr = PetscFree(l->fwork);CHKERRQ(ierr);
1424   ierr = MatDestroy(&l->ptapwork);CHKERRQ(ierr);
1425   if (!l->user_alloc) {ierr = PetscFree(l->v);CHKERRQ(ierr);}
1426   if (!l->unplaced_user_alloc) {ierr = PetscFree(l->unplacedarray);CHKERRQ(ierr);}
1427   if (l->vecinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreColumnVec() first");
1428   if (l->matinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreSubMatrix() first");
1429   ierr = VecDestroy(&l->cvec);CHKERRQ(ierr);
1430   ierr = MatDestroy(&l->cmat);CHKERRQ(ierr);
1431   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1432 
1433   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1434   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseGetLDA_C",NULL);CHKERRQ(ierr);
1435   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseSetLDA_C",NULL);CHKERRQ(ierr);
1436   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseGetArray_C",NULL);CHKERRQ(ierr);
1437   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseRestoreArray_C",NULL);CHKERRQ(ierr);
1438   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDensePlaceArray_C",NULL);CHKERRQ(ierr);
1439   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseResetArray_C",NULL);CHKERRQ(ierr);
1440   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseReplaceArray_C",NULL);CHKERRQ(ierr);
1441   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseGetArrayRead_C",NULL);CHKERRQ(ierr);
1442   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseRestoreArrayRead_C",NULL);CHKERRQ(ierr);
1443   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseGetArrayWrite_C",NULL);CHKERRQ(ierr);
1444   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseRestoreArrayWrite_C",NULL);CHKERRQ(ierr);
1445   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_seqdense_seqaij_C",NULL);CHKERRQ(ierr);
1446 #if defined(PETSC_HAVE_ELEMENTAL)
1447   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_seqdense_elemental_C",NULL);CHKERRQ(ierr);
1448 #endif
1449 #if defined(PETSC_HAVE_CUDA)
1450   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_seqdense_seqdensecuda_C",NULL);CHKERRQ(ierr);
1451   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatProductSetFromOptions_seqdensecuda_seqdensecuda_C",NULL);CHKERRQ(ierr);
1452   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatProductSetFromOptions_seqdensecuda_seqdense_C",NULL);CHKERRQ(ierr);
1453 #endif
1454   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatSeqDenseSetPreallocation_C",NULL);CHKERRQ(ierr);
1455   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatProductSetFromOptions_seqaij_seqdense_C",NULL);CHKERRQ(ierr);
1456   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatProductSetFromOptions_seqdense_seqdense_C",NULL);CHKERRQ(ierr);
1457   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatProductSetFromOptions_seqbaij_seqdense_C",NULL);CHKERRQ(ierr);
1458   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatProductSetFromOptions_seqsbaij_seqdense_C",NULL);CHKERRQ(ierr);
1459 
1460   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseGetColumn_C",NULL);CHKERRQ(ierr);
1461   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseRestoreColumn_C",NULL);CHKERRQ(ierr);
1462   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseGetColumnVec_C",NULL);CHKERRQ(ierr);
1463   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseRestoreColumnVec_C",NULL);CHKERRQ(ierr);
1464   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseGetColumnVecRead_C",NULL);CHKERRQ(ierr);
1465   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseRestoreColumnVecRead_C",NULL);CHKERRQ(ierr);
1466   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseGetColumnVecWrite_C",NULL);CHKERRQ(ierr);
1467   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseRestoreColumnVecWrite_C",NULL);CHKERRQ(ierr);
1468   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseGetSubMatrix_C",NULL);CHKERRQ(ierr);
1469   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDenseRestoreSubMatrix_C",NULL);CHKERRQ(ierr);
1470   PetscFunctionReturn(0);
1471 }
1472 
1473 static PetscErrorCode MatTranspose_SeqDense(Mat A,MatReuse reuse,Mat *matout)
1474 {
1475   Mat_SeqDense   *mat = (Mat_SeqDense*)A->data;
1476   PetscErrorCode ierr;
1477   PetscInt       k,j,m,n,M;
1478   PetscScalar    *v,tmp;
1479 
1480   PetscFunctionBegin;
1481   m = A->rmap->n; M = mat->lda; n = A->cmap->n;
1482   if (reuse == MAT_INPLACE_MATRIX && m == n) { /* in place transpose */
1483     ierr = MatDenseGetArray(A,&v);CHKERRQ(ierr);
1484     for (j=0; j<m; j++) {
1485       for (k=0; k<j; k++) {
1486         tmp        = v[j + k*M];
1487         v[j + k*M] = v[k + j*M];
1488         v[k + j*M] = tmp;
1489       }
1490     }
1491     ierr = MatDenseRestoreArray(A,&v);CHKERRQ(ierr);
1492   } else { /* out-of-place transpose */
1493     Mat          tmat;
1494     Mat_SeqDense *tmatd;
1495     PetscScalar  *v2;
1496     PetscInt     M2;
1497 
1498     if (reuse != MAT_REUSE_MATRIX) {
1499       ierr = MatCreate(PetscObjectComm((PetscObject)A),&tmat);CHKERRQ(ierr);
1500       ierr = MatSetSizes(tmat,A->cmap->n,A->rmap->n,A->cmap->n,A->rmap->n);CHKERRQ(ierr);
1501       ierr = MatSetType(tmat,((PetscObject)A)->type_name);CHKERRQ(ierr);
1502       ierr = MatSeqDenseSetPreallocation(tmat,NULL);CHKERRQ(ierr);
1503     } else tmat = *matout;
1504 
1505     ierr  = MatDenseGetArrayRead(A,(const PetscScalar**)&v);CHKERRQ(ierr);
1506     ierr  = MatDenseGetArray(tmat,&v2);CHKERRQ(ierr);
1507     tmatd = (Mat_SeqDense*)tmat->data;
1508     M2    = tmatd->lda;
1509     for (j=0; j<n; j++) {
1510       for (k=0; k<m; k++) v2[j + k*M2] = v[k + j*M];
1511     }
1512     ierr = MatDenseRestoreArray(tmat,&v2);CHKERRQ(ierr);
1513     ierr = MatDenseRestoreArrayRead(A,(const PetscScalar**)&v);CHKERRQ(ierr);
1514     ierr = MatAssemblyBegin(tmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1515     ierr = MatAssemblyEnd(tmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1516     if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) *matout = tmat;
1517     else {
1518       ierr = MatHeaderMerge(A,&tmat);CHKERRQ(ierr);
1519     }
1520   }
1521   PetscFunctionReturn(0);
1522 }
1523 
1524 static PetscErrorCode MatEqual_SeqDense(Mat A1,Mat A2,PetscBool  *flg)
1525 {
1526   Mat_SeqDense      *mat1 = (Mat_SeqDense*)A1->data;
1527   Mat_SeqDense      *mat2 = (Mat_SeqDense*)A2->data;
1528   PetscInt          i;
1529   const PetscScalar *v1,*v2;
1530   PetscErrorCode    ierr;
1531 
1532   PetscFunctionBegin;
1533   if (A1->rmap->n != A2->rmap->n) {*flg = PETSC_FALSE; PetscFunctionReturn(0);}
1534   if (A1->cmap->n != A2->cmap->n) {*flg = PETSC_FALSE; PetscFunctionReturn(0);}
1535   ierr = MatDenseGetArrayRead(A1,&v1);CHKERRQ(ierr);
1536   ierr = MatDenseGetArrayRead(A2,&v2);CHKERRQ(ierr);
1537   for (i=0; i<A1->cmap->n; i++) {
1538     ierr = PetscArraycmp(v1,v2,A1->rmap->n,flg);CHKERRQ(ierr);
1539     if (*flg == PETSC_FALSE) PetscFunctionReturn(0);
1540     v1 += mat1->lda;
1541     v2 += mat2->lda;
1542   }
1543   ierr = MatDenseRestoreArrayRead(A1,&v1);CHKERRQ(ierr);
1544   ierr = MatDenseRestoreArrayRead(A2,&v2);CHKERRQ(ierr);
1545   *flg = PETSC_TRUE;
1546   PetscFunctionReturn(0);
1547 }
1548 
1549 static PetscErrorCode MatGetDiagonal_SeqDense(Mat A,Vec v)
1550 {
1551   Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
1552   PetscInt          i,n,len;
1553   PetscScalar       *x;
1554   const PetscScalar *vv;
1555   PetscErrorCode    ierr;
1556 
1557   PetscFunctionBegin;
1558   ierr = VecGetSize(v,&n);CHKERRQ(ierr);
1559   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
1560   len  = PetscMin(A->rmap->n,A->cmap->n);
1561   ierr = MatDenseGetArrayRead(A,&vv);CHKERRQ(ierr);
1562   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming mat and vec");
1563   for (i=0; i<len; i++) {
1564     x[i] = vv[i*mat->lda + i];
1565   }
1566   ierr = MatDenseRestoreArrayRead(A,&vv);CHKERRQ(ierr);
1567   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1568   PetscFunctionReturn(0);
1569 }
1570 
1571 static PetscErrorCode MatDiagonalScale_SeqDense(Mat A,Vec ll,Vec rr)
1572 {
1573   Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
1574   const PetscScalar *l,*r;
1575   PetscScalar       x,*v,*vv;
1576   PetscErrorCode    ierr;
1577   PetscInt          i,j,m = A->rmap->n,n = A->cmap->n;
1578 
1579   PetscFunctionBegin;
1580   ierr = MatDenseGetArray(A,&vv);CHKERRQ(ierr);
1581   if (ll) {
1582     ierr = VecGetSize(ll,&m);CHKERRQ(ierr);
1583     ierr = VecGetArrayRead(ll,&l);CHKERRQ(ierr);
1584     if (m != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vec wrong size");
1585     for (i=0; i<m; i++) {
1586       x = l[i];
1587       v = vv + i;
1588       for (j=0; j<n; j++) { (*v) *= x; v+= mat->lda;}
1589     }
1590     ierr = VecRestoreArrayRead(ll,&l);CHKERRQ(ierr);
1591     ierr = PetscLogFlops(1.0*n*m);CHKERRQ(ierr);
1592   }
1593   if (rr) {
1594     ierr = VecGetSize(rr,&n);CHKERRQ(ierr);
1595     ierr = VecGetArrayRead(rr,&r);CHKERRQ(ierr);
1596     if (n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vec wrong size");
1597     for (i=0; i<n; i++) {
1598       x = r[i];
1599       v = vv + i*mat->lda;
1600       for (j=0; j<m; j++) (*v++) *= x;
1601     }
1602     ierr = VecRestoreArrayRead(rr,&r);CHKERRQ(ierr);
1603     ierr = PetscLogFlops(1.0*n*m);CHKERRQ(ierr);
1604   }
1605   ierr = MatDenseRestoreArray(A,&vv);CHKERRQ(ierr);
1606   PetscFunctionReturn(0);
1607 }
1608 
1609 PetscErrorCode MatNorm_SeqDense(Mat A,NormType type,PetscReal *nrm)
1610 {
1611   Mat_SeqDense      *mat = (Mat_SeqDense*)A->data;
1612   PetscScalar       *v,*vv;
1613   PetscReal         sum  = 0.0;
1614   PetscInt          lda  =mat->lda,m=A->rmap->n,i,j;
1615   PetscErrorCode    ierr;
1616 
1617   PetscFunctionBegin;
1618   ierr = MatDenseGetArrayRead(A,(const PetscScalar**)&vv);CHKERRQ(ierr);
1619   v    = vv;
1620   if (type == NORM_FROBENIUS) {
1621     if (lda>m) {
1622       for (j=0; j<A->cmap->n; j++) {
1623         v = vv+j*lda;
1624         for (i=0; i<m; i++) {
1625           sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1626         }
1627       }
1628     } else {
1629 #if defined(PETSC_USE_REAL___FP16)
1630       PetscBLASInt one = 1,cnt = A->cmap->n*A->rmap->n;
1631       *nrm = BLASnrm2_(&cnt,v,&one);
1632     }
1633 #else
1634       for (i=0; i<A->cmap->n*A->rmap->n; i++) {
1635         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1636       }
1637     }
1638     *nrm = PetscSqrtReal(sum);
1639 #endif
1640     ierr = PetscLogFlops(2.0*A->cmap->n*A->rmap->n);CHKERRQ(ierr);
1641   } else if (type == NORM_1) {
1642     *nrm = 0.0;
1643     for (j=0; j<A->cmap->n; j++) {
1644       v   = vv + j*mat->lda;
1645       sum = 0.0;
1646       for (i=0; i<A->rmap->n; i++) {
1647         sum += PetscAbsScalar(*v);  v++;
1648       }
1649       if (sum > *nrm) *nrm = sum;
1650     }
1651     ierr = PetscLogFlops(1.0*A->cmap->n*A->rmap->n);CHKERRQ(ierr);
1652   } else if (type == NORM_INFINITY) {
1653     *nrm = 0.0;
1654     for (j=0; j<A->rmap->n; j++) {
1655       v   = vv + j;
1656       sum = 0.0;
1657       for (i=0; i<A->cmap->n; i++) {
1658         sum += PetscAbsScalar(*v); v += mat->lda;
1659       }
1660       if (sum > *nrm) *nrm = sum;
1661     }
1662     ierr = PetscLogFlops(1.0*A->cmap->n*A->rmap->n);CHKERRQ(ierr);
1663   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No two norm");
1664   ierr = MatDenseRestoreArrayRead(A,(const PetscScalar**)&vv);CHKERRQ(ierr);
1665   PetscFunctionReturn(0);
1666 }
1667 
1668 static PetscErrorCode MatSetOption_SeqDense(Mat A,MatOption op,PetscBool flg)
1669 {
1670   Mat_SeqDense   *aij = (Mat_SeqDense*)A->data;
1671   PetscErrorCode ierr;
1672 
1673   PetscFunctionBegin;
1674   switch (op) {
1675   case MAT_ROW_ORIENTED:
1676     aij->roworiented = flg;
1677     break;
1678   case MAT_NEW_NONZERO_LOCATIONS:
1679   case MAT_NEW_NONZERO_LOCATION_ERR:
1680   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1681   case MAT_NEW_DIAGONALS:
1682   case MAT_KEEP_NONZERO_PATTERN:
1683   case MAT_IGNORE_OFF_PROC_ENTRIES:
1684   case MAT_USE_HASH_TABLE:
1685   case MAT_IGNORE_ZERO_ENTRIES:
1686   case MAT_IGNORE_LOWER_TRIANGULAR:
1687   case MAT_SORTED_FULL:
1688     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1689     break;
1690   case MAT_SPD:
1691   case MAT_SYMMETRIC:
1692   case MAT_STRUCTURALLY_SYMMETRIC:
1693   case MAT_HERMITIAN:
1694   case MAT_SYMMETRY_ETERNAL:
1695     /* These options are handled directly by MatSetOption() */
1696     break;
1697   default:
1698     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %s",MatOptions[op]);
1699   }
1700   PetscFunctionReturn(0);
1701 }
1702 
1703 static PetscErrorCode MatZeroEntries_SeqDense(Mat A)
1704 {
1705   Mat_SeqDense   *l = (Mat_SeqDense*)A->data;
1706   PetscErrorCode ierr;
1707   PetscInt       lda=l->lda,m=A->rmap->n,j;
1708   PetscScalar    *v;
1709 
1710   PetscFunctionBegin;
1711   ierr = MatDenseGetArray(A,&v);CHKERRQ(ierr);
1712   if (lda>m) {
1713     for (j=0; j<A->cmap->n; j++) {
1714       ierr = PetscArrayzero(v+j*lda,m);CHKERRQ(ierr);
1715     }
1716   } else {
1717     ierr = PetscArrayzero(v,A->rmap->n*A->cmap->n);CHKERRQ(ierr);
1718   }
1719   ierr = MatDenseRestoreArray(A,&v);CHKERRQ(ierr);
1720   PetscFunctionReturn(0);
1721 }
1722 
1723 static PetscErrorCode MatZeroRows_SeqDense(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
1724 {
1725   PetscErrorCode    ierr;
1726   Mat_SeqDense      *l = (Mat_SeqDense*)A->data;
1727   PetscInt          m  = l->lda, n = A->cmap->n, i,j;
1728   PetscScalar       *slot,*bb,*v;
1729   const PetscScalar *xx;
1730 
1731   PetscFunctionBegin;
1732   if (PetscDefined(USE_DEBUG)) {
1733     for (i=0; i<N; i++) {
1734       if (rows[i] < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row requested to be zeroed");
1735       if (rows[i] >= A->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D requested to be zeroed greater than or equal number of rows %D",rows[i],A->rmap->n);
1736     }
1737   }
1738   if (!N) PetscFunctionReturn(0);
1739 
1740   /* fix right hand side if needed */
1741   if (x && b) {
1742     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
1743     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
1744     for (i=0; i<N; i++) bb[rows[i]] = diag*xx[rows[i]];
1745     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
1746     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
1747   }
1748 
1749   ierr = MatDenseGetArray(A,&v);CHKERRQ(ierr);
1750   for (i=0; i<N; i++) {
1751     slot = v + rows[i];
1752     for (j=0; j<n; j++) { *slot = 0.0; slot += m;}
1753   }
1754   if (diag != 0.0) {
1755     if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only coded for square matrices");
1756     for (i=0; i<N; i++) {
1757       slot  = v + (m+1)*rows[i];
1758       *slot = diag;
1759     }
1760   }
1761   ierr = MatDenseRestoreArray(A,&v);CHKERRQ(ierr);
1762   PetscFunctionReturn(0);
1763 }
1764 
1765 static PetscErrorCode MatDenseGetLDA_SeqDense(Mat A,PetscInt *lda)
1766 {
1767   Mat_SeqDense *mat = (Mat_SeqDense*)A->data;
1768 
1769   PetscFunctionBegin;
1770   *lda = mat->lda;
1771   PetscFunctionReturn(0);
1772 }
1773 
1774 PetscErrorCode MatDenseGetArray_SeqDense(Mat A,PetscScalar **array)
1775 {
1776   Mat_SeqDense *mat = (Mat_SeqDense*)A->data;
1777 
1778   PetscFunctionBegin;
1779   *array = mat->v;
1780   PetscFunctionReturn(0);
1781 }
1782 
1783 PetscErrorCode MatDenseRestoreArray_SeqDense(Mat A,PetscScalar **array)
1784 {
1785   PetscFunctionBegin;
1786   *array = NULL;
1787   PetscFunctionReturn(0);
1788 }
1789 
1790 /*@C
1791    MatDenseGetLDA - gets the leading dimension of the array returned from MatDenseGetArray()
1792 
1793    Not collective
1794 
1795    Input Parameter:
1796 .  mat - a MATSEQDENSE or MATMPIDENSE matrix
1797 
1798    Output Parameter:
1799 .   lda - the leading dimension
1800 
1801    Level: intermediate
1802 
1803 .seealso: MatDenseGetArray(), MatDenseRestoreArray(), MatDenseGetArrayRead(), MatDenseRestoreArrayRead(), MatDenseSetLDA()
1804 @*/
1805 PetscErrorCode  MatDenseGetLDA(Mat A,PetscInt *lda)
1806 {
1807   PetscErrorCode ierr;
1808 
1809   PetscFunctionBegin;
1810   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
1811   PetscValidPointer(lda,2);
1812   ierr = PetscUseMethod(A,"MatDenseGetLDA_C",(Mat,PetscInt*),(A,lda));CHKERRQ(ierr);
1813   PetscFunctionReturn(0);
1814 }
1815 
1816 /*@C
1817    MatDenseSetLDA - Sets the leading dimension of the array used by the dense matrix
1818 
1819    Not collective
1820 
1821    Input Parameter:
1822 +  mat - a MATSEQDENSE or MATMPIDENSE matrix
1823 -  lda - the leading dimension
1824 
1825    Level: intermediate
1826 
1827 .seealso: MatDenseGetArray(), MatDenseRestoreArray(), MatDenseGetArrayRead(), MatDenseRestoreArrayRead(), MatDenseGetLDA()
1828 @*/
1829 PetscErrorCode  MatDenseSetLDA(Mat A,PetscInt lda)
1830 {
1831   PetscErrorCode ierr;
1832 
1833   PetscFunctionBegin;
1834   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
1835   ierr = PetscTryMethod(A,"MatDenseSetLDA_C",(Mat,PetscInt),(A,lda));CHKERRQ(ierr);
1836   PetscFunctionReturn(0);
1837 }
1838 
1839 /*@C
1840    MatDenseGetArray - gives read-write access to the array where the data for a dense matrix is stored
1841 
1842    Logically Collective on Mat
1843 
1844    Input Parameter:
1845 .  mat - a dense matrix
1846 
1847    Output Parameter:
1848 .   array - pointer to the data
1849 
1850    Level: intermediate
1851 
1852 .seealso: MatDenseRestoreArray(), MatDenseGetArrayRead(), MatDenseRestoreArrayRead(), MatDenseGetArrayWrite(), MatDenseRestoreArrayWrite()
1853 @*/
1854 PetscErrorCode  MatDenseGetArray(Mat A,PetscScalar **array)
1855 {
1856   PetscErrorCode ierr;
1857 
1858   PetscFunctionBegin;
1859   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
1860   PetscValidPointer(array,2);
1861   ierr = PetscUseMethod(A,"MatDenseGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
1862   PetscFunctionReturn(0);
1863 }
1864 
1865 /*@C
1866    MatDenseRestoreArray - returns access to the array where the data for a dense matrix is stored obtained by MatDenseGetArray()
1867 
1868    Logically Collective on Mat
1869 
1870    Input Parameters:
1871 +  mat - a dense matrix
1872 -  array - pointer to the data
1873 
1874    Level: intermediate
1875 
1876 .seealso: MatDenseGetArray(), MatDenseGetArrayRead(), MatDenseRestoreArrayRead(), MatDenseGetArrayWrite(), MatDenseRestoreArrayWrite()
1877 @*/
1878 PetscErrorCode  MatDenseRestoreArray(Mat A,PetscScalar **array)
1879 {
1880   PetscErrorCode ierr;
1881 
1882   PetscFunctionBegin;
1883   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
1884   PetscValidPointer(array,2);
1885   ierr = PetscUseMethod(A,"MatDenseRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
1886   ierr = PetscObjectStateIncrease((PetscObject)A);CHKERRQ(ierr);
1887 #if defined(PETSC_HAVE_CUDA)
1888   A->offloadmask = PETSC_OFFLOAD_CPU;
1889 #endif
1890   PetscFunctionReturn(0);
1891 }
1892 
1893 /*@C
1894    MatDenseGetArrayRead - gives read-only access to the array where the data for a dense matrix is stored
1895 
1896    Not Collective
1897 
1898    Input Parameter:
1899 .  mat - a dense matrix
1900 
1901    Output Parameter:
1902 .   array - pointer to the data
1903 
1904    Level: intermediate
1905 
1906 .seealso: MatDenseRestoreArrayRead(), MatDenseGetArray(), MatDenseRestoreArray(), MatDenseGetArrayWrite(), MatDenseRestoreArrayWrite()
1907 @*/
1908 PetscErrorCode  MatDenseGetArrayRead(Mat A,const PetscScalar **array)
1909 {
1910   PetscErrorCode ierr;
1911 
1912   PetscFunctionBegin;
1913   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
1914   PetscValidPointer(array,2);
1915   ierr = PetscUseMethod(A,"MatDenseGetArrayRead_C",(Mat,const PetscScalar**),(A,array));CHKERRQ(ierr);
1916   PetscFunctionReturn(0);
1917 }
1918 
1919 /*@C
1920    MatDenseRestoreArrayRead - returns access to the array where the data for a dense matrix is stored obtained by MatDenseGetArrayRead()
1921 
1922    Not Collective
1923 
1924    Input Parameters:
1925 +  mat - a dense matrix
1926 -  array - pointer to the data
1927 
1928    Level: intermediate
1929 
1930 .seealso: MatDenseGetArrayRead(), MatDenseGetArray(), MatDenseRestoreArray(), MatDenseGetArrayWrite(), MatDenseRestoreArrayWrite()
1931 @*/
1932 PetscErrorCode  MatDenseRestoreArrayRead(Mat A,const PetscScalar **array)
1933 {
1934   PetscErrorCode ierr;
1935 
1936   PetscFunctionBegin;
1937   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
1938   PetscValidPointer(array,2);
1939   ierr = PetscUseMethod(A,"MatDenseRestoreArrayRead_C",(Mat,const PetscScalar**),(A,array));CHKERRQ(ierr);
1940   PetscFunctionReturn(0);
1941 }
1942 
1943 /*@C
1944    MatDenseGetArrayWrite - gives write-only access to the array where the data for a dense matrix is stored
1945 
1946    Not Collective
1947 
1948    Input Parameter:
1949 .  mat - a dense matrix
1950 
1951    Output Parameter:
1952 .   array - pointer to the data
1953 
1954    Level: intermediate
1955 
1956 .seealso: MatDenseRestoreArrayWrite(), MatDenseGetArray(), MatDenseRestoreArray(), MatDenseGetArrayRead(), MatDenseRestoreArrayRead()
1957 @*/
1958 PetscErrorCode  MatDenseGetArrayWrite(Mat A,PetscScalar **array)
1959 {
1960   PetscErrorCode ierr;
1961 
1962   PetscFunctionBegin;
1963   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
1964   PetscValidPointer(array,2);
1965   ierr = PetscUseMethod(A,"MatDenseGetArrayWrite_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
1966   PetscFunctionReturn(0);
1967 }
1968 
1969 /*@C
1970    MatDenseRestoreArrayWrite - returns access to the array where the data for a dense matrix is stored obtained by MatDenseGetArrayWrite()
1971 
1972    Not Collective
1973 
1974    Input Parameters:
1975 +  mat - a dense matrix
1976 -  array - pointer to the data
1977 
1978    Level: intermediate
1979 
1980 .seealso: MatDenseGetArrayWrite(), MatDenseGetArray(), MatDenseRestoreArray(), MatDenseGetArrayRead(), MatDenseRestoreArrayRead()
1981 @*/
1982 PetscErrorCode  MatDenseRestoreArrayWrite(Mat A,PetscScalar **array)
1983 {
1984   PetscErrorCode ierr;
1985 
1986   PetscFunctionBegin;
1987   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
1988   PetscValidPointer(array,2);
1989   ierr = PetscUseMethod(A,"MatDenseRestoreArrayWrite_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
1990   ierr = PetscObjectStateIncrease((PetscObject)A);CHKERRQ(ierr);
1991 #if defined(PETSC_HAVE_CUDA)
1992   A->offloadmask = PETSC_OFFLOAD_CPU;
1993 #endif
1994   PetscFunctionReturn(0);
1995 }
1996 
1997 static PetscErrorCode MatCreateSubMatrix_SeqDense(Mat A,IS isrow,IS iscol,PetscInt cs,MatReuse scall,Mat *B)
1998 {
1999   Mat_SeqDense   *mat = (Mat_SeqDense*)A->data;
2000   PetscErrorCode ierr;
2001   PetscInt       i,j,nrows,ncols,blda;
2002   const PetscInt *irow,*icol;
2003   PetscScalar    *av,*bv,*v = mat->v;
2004   Mat            newmat;
2005 
2006   PetscFunctionBegin;
2007   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
2008   ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
2009   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
2010   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
2011 
2012   /* Check submatrixcall */
2013   if (scall == MAT_REUSE_MATRIX) {
2014     PetscInt n_cols,n_rows;
2015     ierr = MatGetSize(*B,&n_rows,&n_cols);CHKERRQ(ierr);
2016     if (n_rows != nrows || n_cols != ncols) {
2017       /* resize the result matrix to match number of requested rows/columns */
2018       ierr = MatSetSizes(*B,nrows,ncols,nrows,ncols);CHKERRQ(ierr);
2019     }
2020     newmat = *B;
2021   } else {
2022     /* Create and fill new matrix */
2023     ierr = MatCreate(PetscObjectComm((PetscObject)A),&newmat);CHKERRQ(ierr);
2024     ierr = MatSetSizes(newmat,nrows,ncols,nrows,ncols);CHKERRQ(ierr);
2025     ierr = MatSetType(newmat,((PetscObject)A)->type_name);CHKERRQ(ierr);
2026     ierr = MatSeqDenseSetPreallocation(newmat,NULL);CHKERRQ(ierr);
2027   }
2028 
2029   /* Now extract the data pointers and do the copy,column at a time */
2030   ierr = MatDenseGetArray(newmat,&bv);CHKERRQ(ierr);
2031   ierr = MatDenseGetLDA(newmat,&blda);CHKERRQ(ierr);
2032   for (i=0; i<ncols; i++) {
2033     av = v + mat->lda*icol[i];
2034     for (j=0; j<nrows; j++) bv[j] = av[irow[j]];
2035     bv += blda;
2036   }
2037   ierr = MatDenseRestoreArray(newmat,&bv);CHKERRQ(ierr);
2038 
2039   /* Assemble the matrices so that the correct flags are set */
2040   ierr = MatAssemblyBegin(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2041   ierr = MatAssemblyEnd(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2042 
2043   /* Free work space */
2044   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
2045   ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
2046   *B   = newmat;
2047   PetscFunctionReturn(0);
2048 }
2049 
2050 static PetscErrorCode MatCreateSubMatrices_SeqDense(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
2051 {
2052   PetscErrorCode ierr;
2053   PetscInt       i;
2054 
2055   PetscFunctionBegin;
2056   if (scall == MAT_INITIAL_MATRIX) {
2057     ierr = PetscCalloc1(n+1,B);CHKERRQ(ierr);
2058   }
2059 
2060   for (i=0; i<n; i++) {
2061     ierr = MatCreateSubMatrix_SeqDense(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]);CHKERRQ(ierr);
2062   }
2063   PetscFunctionReturn(0);
2064 }
2065 
2066 static PetscErrorCode MatAssemblyBegin_SeqDense(Mat mat,MatAssemblyType mode)
2067 {
2068   PetscFunctionBegin;
2069   PetscFunctionReturn(0);
2070 }
2071 
2072 static PetscErrorCode MatAssemblyEnd_SeqDense(Mat mat,MatAssemblyType mode)
2073 {
2074   PetscFunctionBegin;
2075   PetscFunctionReturn(0);
2076 }
2077 
2078 static PetscErrorCode MatCopy_SeqDense(Mat A,Mat B,MatStructure str)
2079 {
2080   Mat_SeqDense      *a = (Mat_SeqDense*)A->data,*b = (Mat_SeqDense*)B->data;
2081   PetscErrorCode    ierr;
2082   const PetscScalar *va;
2083   PetscScalar       *vb;
2084   PetscInt          lda1=a->lda,lda2=b->lda, m=A->rmap->n,n=A->cmap->n, j;
2085 
2086   PetscFunctionBegin;
2087   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2088   if (A->ops->copy != B->ops->copy) {
2089     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2090     PetscFunctionReturn(0);
2091   }
2092   if (m != B->rmap->n || n != B->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"size(B) != size(A)");
2093   ierr = MatDenseGetArrayRead(A,&va);CHKERRQ(ierr);
2094   ierr = MatDenseGetArray(B,&vb);CHKERRQ(ierr);
2095   if (lda1>m || lda2>m) {
2096     for (j=0; j<n; j++) {
2097       ierr = PetscArraycpy(vb+j*lda2,va+j*lda1,m);CHKERRQ(ierr);
2098     }
2099   } else {
2100     ierr = PetscArraycpy(vb,va,A->rmap->n*A->cmap->n);CHKERRQ(ierr);
2101   }
2102   ierr = MatDenseRestoreArray(B,&vb);CHKERRQ(ierr);
2103   ierr = MatDenseRestoreArrayRead(A,&va);CHKERRQ(ierr);
2104   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2105   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2106   PetscFunctionReturn(0);
2107 }
2108 
2109 static PetscErrorCode MatSetUp_SeqDense(Mat A)
2110 {
2111   PetscErrorCode ierr;
2112 
2113   PetscFunctionBegin;
2114   ierr = PetscLayoutSetUp(A->rmap);CHKERRQ(ierr);
2115   ierr = PetscLayoutSetUp(A->cmap);CHKERRQ(ierr);
2116   if (!A->preallocated) {
2117     ierr = MatSeqDenseSetPreallocation(A,0);CHKERRQ(ierr);
2118   }
2119   PetscFunctionReturn(0);
2120 }
2121 
2122 static PetscErrorCode MatConjugate_SeqDense(Mat A)
2123 {
2124   PetscInt       i,nz = A->rmap->n*A->cmap->n;
2125   PetscScalar    *aa;
2126   PetscErrorCode ierr;
2127 
2128   PetscFunctionBegin;
2129   ierr = MatDenseGetArray(A,&aa);CHKERRQ(ierr);
2130   for (i=0; i<nz; i++) aa[i] = PetscConj(aa[i]);
2131   ierr = MatDenseRestoreArray(A,&aa);CHKERRQ(ierr);
2132   PetscFunctionReturn(0);
2133 }
2134 
2135 static PetscErrorCode MatRealPart_SeqDense(Mat A)
2136 {
2137   PetscInt       i,nz = A->rmap->n*A->cmap->n;
2138   PetscScalar    *aa;
2139   PetscErrorCode ierr;
2140 
2141   PetscFunctionBegin;
2142   ierr = MatDenseGetArray(A,&aa);CHKERRQ(ierr);
2143   for (i=0; i<nz; i++) aa[i] = PetscRealPart(aa[i]);
2144   ierr = MatDenseRestoreArray(A,&aa);CHKERRQ(ierr);
2145   PetscFunctionReturn(0);
2146 }
2147 
2148 static PetscErrorCode MatImaginaryPart_SeqDense(Mat A)
2149 {
2150   PetscInt       i,nz = A->rmap->n*A->cmap->n;
2151   PetscScalar    *aa;
2152   PetscErrorCode ierr;
2153 
2154   PetscFunctionBegin;
2155   ierr = MatDenseGetArray(A,&aa);CHKERRQ(ierr);
2156   for (i=0; i<nz; i++) aa[i] = PetscImaginaryPart(aa[i]);
2157   ierr = MatDenseRestoreArray(A,&aa);CHKERRQ(ierr);
2158   PetscFunctionReturn(0);
2159 }
2160 
2161 /* ----------------------------------------------------------------*/
2162 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqDense(Mat A,Mat B,PetscReal fill,Mat C)
2163 {
2164   PetscErrorCode ierr;
2165   PetscInt       m=A->rmap->n,n=B->cmap->n;
2166   PetscBool      cisdense;
2167 
2168   PetscFunctionBegin;
2169   ierr = MatSetSizes(C,m,n,m,n);CHKERRQ(ierr);
2170   ierr = PetscObjectTypeCompareAny((PetscObject)C,&cisdense,MATSEQDENSE,MATSEQDENSECUDA,"");CHKERRQ(ierr);
2171   if (!cisdense) {
2172     PetscBool flg;
2173 
2174     ierr = PetscObjectTypeCompare((PetscObject)B,((PetscObject)A)->type_name,&flg);CHKERRQ(ierr);
2175     ierr = MatSetType(C,flg ? ((PetscObject)A)->type_name : MATDENSE);CHKERRQ(ierr);
2176   }
2177   ierr = MatSetUp(C);CHKERRQ(ierr);
2178   PetscFunctionReturn(0);
2179 }
2180 
2181 PetscErrorCode MatMatMultNumeric_SeqDense_SeqDense(Mat A,Mat B,Mat C)
2182 {
2183   Mat_SeqDense       *a=(Mat_SeqDense*)A->data,*b=(Mat_SeqDense*)B->data,*c=(Mat_SeqDense*)C->data;
2184   PetscBLASInt       m,n,k;
2185   const PetscScalar *av,*bv;
2186   PetscScalar       *cv;
2187   PetscScalar       _DOne=1.0,_DZero=0.0;
2188   PetscErrorCode    ierr;
2189 
2190   PetscFunctionBegin;
2191   ierr = PetscBLASIntCast(C->rmap->n,&m);CHKERRQ(ierr);
2192   ierr = PetscBLASIntCast(C->cmap->n,&n);CHKERRQ(ierr);
2193   ierr = PetscBLASIntCast(A->cmap->n,&k);CHKERRQ(ierr);
2194   if (!m || !n || !k) PetscFunctionReturn(0);
2195   ierr = MatDenseGetArrayRead(A,&av);CHKERRQ(ierr);
2196   ierr = MatDenseGetArrayRead(B,&bv);CHKERRQ(ierr);
2197   ierr = MatDenseGetArrayWrite(C,&cv);CHKERRQ(ierr);
2198   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&m,&n,&k,&_DOne,av,&a->lda,bv,&b->lda,&_DZero,cv,&c->lda));
2199   ierr = PetscLogFlops(1.0*m*n*k + 1.0*m*n*(k-1));CHKERRQ(ierr);
2200   ierr = MatDenseRestoreArrayRead(A,&av);CHKERRQ(ierr);
2201   ierr = MatDenseRestoreArrayRead(B,&bv);CHKERRQ(ierr);
2202   ierr = MatDenseRestoreArrayWrite(C,&cv);CHKERRQ(ierr);
2203   PetscFunctionReturn(0);
2204 }
2205 
2206 PetscErrorCode MatMatTransposeMultSymbolic_SeqDense_SeqDense(Mat A,Mat B,PetscReal fill,Mat C)
2207 {
2208   PetscErrorCode ierr;
2209   PetscInt       m=A->rmap->n,n=B->rmap->n;
2210   PetscBool      cisdense;
2211 
2212   PetscFunctionBegin;
2213   ierr = MatSetSizes(C,m,n,m,n);CHKERRQ(ierr);
2214   ierr = PetscObjectTypeCompareAny((PetscObject)C,&cisdense,MATSEQDENSE,MATSEQDENSECUDA,"");CHKERRQ(ierr);
2215   if (!cisdense) {
2216     PetscBool flg;
2217 
2218     ierr = PetscObjectTypeCompare((PetscObject)B,((PetscObject)A)->type_name,&flg);CHKERRQ(ierr);
2219     ierr = MatSetType(C,flg ? ((PetscObject)A)->type_name : MATDENSE);CHKERRQ(ierr);
2220   }
2221   ierr = MatSetUp(C);CHKERRQ(ierr);
2222   PetscFunctionReturn(0);
2223 }
2224 
2225 PetscErrorCode MatMatTransposeMultNumeric_SeqDense_SeqDense(Mat A,Mat B,Mat C)
2226 {
2227   Mat_SeqDense      *a = (Mat_SeqDense*)A->data;
2228   Mat_SeqDense      *b = (Mat_SeqDense*)B->data;
2229   Mat_SeqDense      *c = (Mat_SeqDense*)C->data;
2230   const PetscScalar *av,*bv;
2231   PetscScalar       *cv;
2232   PetscBLASInt      m,n,k;
2233   PetscScalar       _DOne=1.0,_DZero=0.0;
2234   PetscErrorCode    ierr;
2235 
2236   PetscFunctionBegin;
2237   ierr = PetscBLASIntCast(C->rmap->n,&m);CHKERRQ(ierr);
2238   ierr = PetscBLASIntCast(C->cmap->n,&n);CHKERRQ(ierr);
2239   ierr = PetscBLASIntCast(A->cmap->n,&k);CHKERRQ(ierr);
2240   if (!m || !n || !k) PetscFunctionReturn(0);
2241   ierr = MatDenseGetArrayRead(A,&av);CHKERRQ(ierr);
2242   ierr = MatDenseGetArrayRead(B,&bv);CHKERRQ(ierr);
2243   ierr = MatDenseGetArrayWrite(C,&cv);CHKERRQ(ierr);
2244   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&m,&n,&k,&_DOne,av,&a->lda,bv,&b->lda,&_DZero,cv,&c->lda));
2245   ierr = MatDenseRestoreArrayRead(A,&av);CHKERRQ(ierr);
2246   ierr = MatDenseRestoreArrayRead(B,&bv);CHKERRQ(ierr);
2247   ierr = MatDenseRestoreArrayWrite(C,&cv);CHKERRQ(ierr);
2248   ierr = PetscLogFlops(1.0*m*n*k + 1.0*m*n*(k-1));CHKERRQ(ierr);
2249   PetscFunctionReturn(0);
2250 }
2251 
2252 PetscErrorCode MatTransposeMatMultSymbolic_SeqDense_SeqDense(Mat A,Mat B,PetscReal fill,Mat C)
2253 {
2254   PetscErrorCode ierr;
2255   PetscInt       m=A->cmap->n,n=B->cmap->n;
2256   PetscBool      cisdense;
2257 
2258   PetscFunctionBegin;
2259   ierr = MatSetSizes(C,m,n,m,n);CHKERRQ(ierr);
2260   ierr = PetscObjectTypeCompareAny((PetscObject)C,&cisdense,MATSEQDENSE,MATSEQDENSECUDA,"");CHKERRQ(ierr);
2261   if (!cisdense) {
2262     PetscBool flg;
2263 
2264     ierr = PetscObjectTypeCompare((PetscObject)B,((PetscObject)A)->type_name,&flg);CHKERRQ(ierr);
2265     ierr = MatSetType(C,flg ? ((PetscObject)A)->type_name : MATDENSE);CHKERRQ(ierr);
2266   }
2267   ierr = MatSetUp(C);CHKERRQ(ierr);
2268   PetscFunctionReturn(0);
2269 }
2270 
2271 PetscErrorCode MatTransposeMatMultNumeric_SeqDense_SeqDense(Mat A,Mat B,Mat C)
2272 {
2273   Mat_SeqDense      *a = (Mat_SeqDense*)A->data;
2274   Mat_SeqDense      *b = (Mat_SeqDense*)B->data;
2275   Mat_SeqDense      *c = (Mat_SeqDense*)C->data;
2276   const PetscScalar *av,*bv;
2277   PetscScalar       *cv;
2278   PetscBLASInt      m,n,k;
2279   PetscScalar       _DOne=1.0,_DZero=0.0;
2280   PetscErrorCode    ierr;
2281 
2282   PetscFunctionBegin;
2283   ierr = PetscBLASIntCast(C->rmap->n,&m);CHKERRQ(ierr);
2284   ierr = PetscBLASIntCast(C->cmap->n,&n);CHKERRQ(ierr);
2285   ierr = PetscBLASIntCast(A->rmap->n,&k);CHKERRQ(ierr);
2286   if (!m || !n || !k) PetscFunctionReturn(0);
2287   ierr = MatDenseGetArrayRead(A,&av);CHKERRQ(ierr);
2288   ierr = MatDenseGetArrayRead(B,&bv);CHKERRQ(ierr);
2289   ierr = MatDenseGetArrayWrite(C,&cv);CHKERRQ(ierr);
2290   PetscStackCallBLAS("BLASgemm",BLASgemm_("T","N",&m,&n,&k,&_DOne,av,&a->lda,bv,&b->lda,&_DZero,cv,&c->lda));
2291   ierr = MatDenseRestoreArrayRead(A,&av);CHKERRQ(ierr);
2292   ierr = MatDenseRestoreArrayRead(B,&bv);CHKERRQ(ierr);
2293   ierr = MatDenseRestoreArrayWrite(C,&cv);CHKERRQ(ierr);
2294   ierr = PetscLogFlops(1.0*m*n*k + 1.0*m*n*(k-1));CHKERRQ(ierr);
2295   PetscFunctionReturn(0);
2296 }
2297 
2298 /* ----------------------------------------------- */
2299 static PetscErrorCode MatProductSetFromOptions_SeqDense_AB(Mat C)
2300 {
2301   PetscFunctionBegin;
2302   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqDense_SeqDense;
2303   C->ops->productsymbolic = MatProductSymbolic_AB;
2304   PetscFunctionReturn(0);
2305 }
2306 
2307 static PetscErrorCode MatProductSetFromOptions_SeqDense_AtB(Mat C)
2308 {
2309   PetscFunctionBegin;
2310   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_SeqDense_SeqDense;
2311   C->ops->productsymbolic          = MatProductSymbolic_AtB;
2312   PetscFunctionReturn(0);
2313 }
2314 
2315 static PetscErrorCode MatProductSetFromOptions_SeqDense_ABt(Mat C)
2316 {
2317   PetscFunctionBegin;
2318   C->ops->mattransposemultsymbolic = MatMatTransposeMultSymbolic_SeqDense_SeqDense;
2319   C->ops->productsymbolic          = MatProductSymbolic_ABt;
2320   PetscFunctionReturn(0);
2321 }
2322 
2323 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqDense(Mat C)
2324 {
2325   PetscErrorCode ierr;
2326   Mat_Product    *product = C->product;
2327 
2328   PetscFunctionBegin;
2329   switch (product->type) {
2330   case MATPRODUCT_AB:
2331     ierr = MatProductSetFromOptions_SeqDense_AB(C);CHKERRQ(ierr);
2332     break;
2333   case MATPRODUCT_AtB:
2334     ierr = MatProductSetFromOptions_SeqDense_AtB(C);CHKERRQ(ierr);
2335     break;
2336   case MATPRODUCT_ABt:
2337     ierr = MatProductSetFromOptions_SeqDense_ABt(C);CHKERRQ(ierr);
2338     break;
2339   default:
2340     break;
2341   }
2342   PetscFunctionReturn(0);
2343 }
2344 /* ----------------------------------------------- */
2345 
2346 static PetscErrorCode MatGetRowMax_SeqDense(Mat A,Vec v,PetscInt idx[])
2347 {
2348   Mat_SeqDense       *a = (Mat_SeqDense*)A->data;
2349   PetscErrorCode     ierr;
2350   PetscInt           i,j,m = A->rmap->n,n = A->cmap->n,p;
2351   PetscScalar        *x;
2352   const PetscScalar *aa;
2353 
2354   PetscFunctionBegin;
2355   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2356   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2357   ierr = VecGetLocalSize(v,&p);CHKERRQ(ierr);
2358   ierr = MatDenseGetArrayRead(A,&aa);CHKERRQ(ierr);
2359   if (p != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2360   for (i=0; i<m; i++) {
2361     x[i] = aa[i]; if (idx) idx[i] = 0;
2362     for (j=1; j<n; j++) {
2363       if (PetscRealPart(x[i]) < PetscRealPart(aa[i+a->lda*j])) {x[i] = aa[i + a->lda*j]; if (idx) idx[i] = j;}
2364     }
2365   }
2366   ierr = MatDenseRestoreArrayRead(A,&aa);CHKERRQ(ierr);
2367   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2368   PetscFunctionReturn(0);
2369 }
2370 
2371 static PetscErrorCode MatGetRowMaxAbs_SeqDense(Mat A,Vec v,PetscInt idx[])
2372 {
2373   Mat_SeqDense      *a = (Mat_SeqDense*)A->data;
2374   PetscErrorCode    ierr;
2375   PetscInt          i,j,m = A->rmap->n,n = A->cmap->n,p;
2376   PetscScalar       *x;
2377   PetscReal         atmp;
2378   const PetscScalar *aa;
2379 
2380   PetscFunctionBegin;
2381   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2382   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2383   ierr = VecGetLocalSize(v,&p);CHKERRQ(ierr);
2384   ierr = MatDenseGetArrayRead(A,&aa);CHKERRQ(ierr);
2385   if (p != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2386   for (i=0; i<m; i++) {
2387     x[i] = PetscAbsScalar(aa[i]);
2388     for (j=1; j<n; j++) {
2389       atmp = PetscAbsScalar(aa[i+a->lda*j]);
2390       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = j;}
2391     }
2392   }
2393   ierr = MatDenseRestoreArrayRead(A,&aa);CHKERRQ(ierr);
2394   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2395   PetscFunctionReturn(0);
2396 }
2397 
2398 static PetscErrorCode MatGetRowMin_SeqDense(Mat A,Vec v,PetscInt idx[])
2399 {
2400   Mat_SeqDense      *a = (Mat_SeqDense*)A->data;
2401   PetscErrorCode    ierr;
2402   PetscInt          i,j,m = A->rmap->n,n = A->cmap->n,p;
2403   PetscScalar       *x;
2404   const PetscScalar *aa;
2405 
2406   PetscFunctionBegin;
2407   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2408   ierr = MatDenseGetArrayRead(A,&aa);CHKERRQ(ierr);
2409   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2410   ierr = VecGetLocalSize(v,&p);CHKERRQ(ierr);
2411   if (p != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2412   for (i=0; i<m; i++) {
2413     x[i] = aa[i]; if (idx) idx[i] = 0;
2414     for (j=1; j<n; j++) {
2415       if (PetscRealPart(x[i]) > PetscRealPart(aa[i+a->lda*j])) {x[i] = aa[i + a->lda*j]; if (idx) idx[i] = j;}
2416     }
2417   }
2418   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2419   ierr = MatDenseRestoreArrayRead(A,&aa);CHKERRQ(ierr);
2420   PetscFunctionReturn(0);
2421 }
2422 
2423 PetscErrorCode MatGetColumnVector_SeqDense(Mat A,Vec v,PetscInt col)
2424 {
2425   Mat_SeqDense      *a = (Mat_SeqDense*)A->data;
2426   PetscErrorCode    ierr;
2427   PetscScalar       *x;
2428   const PetscScalar *aa;
2429 
2430   PetscFunctionBegin;
2431   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2432   ierr = MatDenseGetArrayRead(A,&aa);CHKERRQ(ierr);
2433   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2434   ierr = PetscArraycpy(x,aa+col*a->lda,A->rmap->n);CHKERRQ(ierr);
2435   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2436   ierr = MatDenseRestoreArrayRead(A,&aa);CHKERRQ(ierr);
2437   PetscFunctionReturn(0);
2438 }
2439 
2440 PETSC_INTERN PetscErrorCode MatGetColumnNorms_SeqDense(Mat A,NormType type,PetscReal *norms)
2441 {
2442   PetscErrorCode    ierr;
2443   PetscInt          i,j,m,n;
2444   const PetscScalar *a;
2445 
2446   PetscFunctionBegin;
2447   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
2448   ierr = PetscArrayzero(norms,n);CHKERRQ(ierr);
2449   ierr = MatDenseGetArrayRead(A,&a);CHKERRQ(ierr);
2450   if (type == NORM_2) {
2451     for (i=0; i<n; i++) {
2452       for (j=0; j<m; j++) {
2453         norms[i] += PetscAbsScalar(a[j]*a[j]);
2454       }
2455       a += m;
2456     }
2457   } else if (type == NORM_1) {
2458     for (i=0; i<n; i++) {
2459       for (j=0; j<m; j++) {
2460         norms[i] += PetscAbsScalar(a[j]);
2461       }
2462       a += m;
2463     }
2464   } else if (type == NORM_INFINITY) {
2465     for (i=0; i<n; i++) {
2466       for (j=0; j<m; j++) {
2467         norms[i] = PetscMax(PetscAbsScalar(a[j]),norms[i]);
2468       }
2469       a += m;
2470     }
2471   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown NormType");
2472   ierr = MatDenseRestoreArrayRead(A,&a);CHKERRQ(ierr);
2473   if (type == NORM_2) {
2474     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
2475   }
2476   PetscFunctionReturn(0);
2477 }
2478 
2479 static PetscErrorCode  MatSetRandom_SeqDense(Mat x,PetscRandom rctx)
2480 {
2481   PetscErrorCode ierr;
2482   PetscScalar    *a;
2483   PetscInt       lda,m,n,i,j;
2484 
2485   PetscFunctionBegin;
2486   ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
2487   ierr = MatDenseGetLDA(x,&lda);CHKERRQ(ierr);
2488   ierr = MatDenseGetArray(x,&a);CHKERRQ(ierr);
2489   for (j=0; j<n; j++) {
2490     for (i=0; i<m; i++) {
2491       ierr = PetscRandomGetValue(rctx,a+j*lda+i);CHKERRQ(ierr);
2492     }
2493   }
2494   ierr = MatDenseRestoreArray(x,&a);CHKERRQ(ierr);
2495   PetscFunctionReturn(0);
2496 }
2497 
2498 static PetscErrorCode MatMissingDiagonal_SeqDense(Mat A,PetscBool  *missing,PetscInt *d)
2499 {
2500   PetscFunctionBegin;
2501   *missing = PETSC_FALSE;
2502   PetscFunctionReturn(0);
2503 }
2504 
2505 /* vals is not const */
2506 static PetscErrorCode MatDenseGetColumn_SeqDense(Mat A,PetscInt col,PetscScalar **vals)
2507 {
2508   PetscErrorCode ierr;
2509   Mat_SeqDense   *a = (Mat_SeqDense*)A->data;
2510   PetscScalar    *v;
2511 
2512   PetscFunctionBegin;
2513   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2514   ierr  = MatDenseGetArray(A,&v);CHKERRQ(ierr);
2515   *vals = v+col*a->lda;
2516   ierr  = MatDenseRestoreArray(A,&v);CHKERRQ(ierr);
2517   PetscFunctionReturn(0);
2518 }
2519 
2520 static PetscErrorCode MatDenseRestoreColumn_SeqDense(Mat A,PetscScalar **vals)
2521 {
2522   PetscFunctionBegin;
2523   *vals = 0; /* user cannot accidently use the array later */
2524   PetscFunctionReturn(0);
2525 }
2526 
2527 /* -------------------------------------------------------------------*/
2528 static struct _MatOps MatOps_Values = { MatSetValues_SeqDense,
2529                                         MatGetRow_SeqDense,
2530                                         MatRestoreRow_SeqDense,
2531                                         MatMult_SeqDense,
2532                                 /*  4*/ MatMultAdd_SeqDense,
2533                                         MatMultTranspose_SeqDense,
2534                                         MatMultTransposeAdd_SeqDense,
2535                                         0,
2536                                         0,
2537                                         0,
2538                                 /* 10*/ 0,
2539                                         MatLUFactor_SeqDense,
2540                                         MatCholeskyFactor_SeqDense,
2541                                         MatSOR_SeqDense,
2542                                         MatTranspose_SeqDense,
2543                                 /* 15*/ MatGetInfo_SeqDense,
2544                                         MatEqual_SeqDense,
2545                                         MatGetDiagonal_SeqDense,
2546                                         MatDiagonalScale_SeqDense,
2547                                         MatNorm_SeqDense,
2548                                 /* 20*/ MatAssemblyBegin_SeqDense,
2549                                         MatAssemblyEnd_SeqDense,
2550                                         MatSetOption_SeqDense,
2551                                         MatZeroEntries_SeqDense,
2552                                 /* 24*/ MatZeroRows_SeqDense,
2553                                         0,
2554                                         0,
2555                                         0,
2556                                         0,
2557                                 /* 29*/ MatSetUp_SeqDense,
2558                                         0,
2559                                         0,
2560                                         0,
2561                                         0,
2562                                 /* 34*/ MatDuplicate_SeqDense,
2563                                         0,
2564                                         0,
2565                                         0,
2566                                         0,
2567                                 /* 39*/ MatAXPY_SeqDense,
2568                                         MatCreateSubMatrices_SeqDense,
2569                                         0,
2570                                         MatGetValues_SeqDense,
2571                                         MatCopy_SeqDense,
2572                                 /* 44*/ MatGetRowMax_SeqDense,
2573                                         MatScale_SeqDense,
2574                                         MatShift_Basic,
2575                                         0,
2576                                         MatZeroRowsColumns_SeqDense,
2577                                 /* 49*/ MatSetRandom_SeqDense,
2578                                         0,
2579                                         0,
2580                                         0,
2581                                         0,
2582                                 /* 54*/ 0,
2583                                         0,
2584                                         0,
2585                                         0,
2586                                         0,
2587                                 /* 59*/ 0,
2588                                         MatDestroy_SeqDense,
2589                                         MatView_SeqDense,
2590                                         0,
2591                                         0,
2592                                 /* 64*/ 0,
2593                                         0,
2594                                         0,
2595                                         0,
2596                                         0,
2597                                 /* 69*/ MatGetRowMaxAbs_SeqDense,
2598                                         0,
2599                                         0,
2600                                         0,
2601                                         0,
2602                                 /* 74*/ 0,
2603                                         0,
2604                                         0,
2605                                         0,
2606                                         0,
2607                                 /* 79*/ 0,
2608                                         0,
2609                                         0,
2610                                         0,
2611                                 /* 83*/ MatLoad_SeqDense,
2612                                         MatIsSymmetric_SeqDense,
2613                                         MatIsHermitian_SeqDense,
2614                                         0,
2615                                         0,
2616                                         0,
2617                                 /* 89*/ 0,
2618                                         0,
2619                                         MatMatMultNumeric_SeqDense_SeqDense,
2620                                         0,
2621                                         0,
2622                                 /* 94*/ 0,
2623                                         0,
2624                                         0,
2625                                         MatMatTransposeMultNumeric_SeqDense_SeqDense,
2626                                         0,
2627                                 /* 99*/ MatProductSetFromOptions_SeqDense,
2628                                         0,
2629                                         0,
2630                                         MatConjugate_SeqDense,
2631                                         0,
2632                                 /*104*/ 0,
2633                                         MatRealPart_SeqDense,
2634                                         MatImaginaryPart_SeqDense,
2635                                         0,
2636                                         0,
2637                                 /*109*/ 0,
2638                                         0,
2639                                         MatGetRowMin_SeqDense,
2640                                         MatGetColumnVector_SeqDense,
2641                                         MatMissingDiagonal_SeqDense,
2642                                 /*114*/ 0,
2643                                         0,
2644                                         0,
2645                                         0,
2646                                         0,
2647                                 /*119*/ 0,
2648                                         0,
2649                                         0,
2650                                         0,
2651                                         0,
2652                                 /*124*/ 0,
2653                                         MatGetColumnNorms_SeqDense,
2654                                         0,
2655                                         0,
2656                                         0,
2657                                 /*129*/ 0,
2658                                         0,
2659                                         0,
2660                                         MatTransposeMatMultNumeric_SeqDense_SeqDense,
2661                                         0,
2662                                 /*134*/ 0,
2663                                         0,
2664                                         0,
2665                                         0,
2666                                         0,
2667                                 /*139*/ 0,
2668                                         0,
2669                                         0,
2670                                         0,
2671                                         0,
2672                                         MatCreateMPIMatConcatenateSeqMat_SeqDense,
2673                                 /*145*/ 0,
2674                                         0,
2675                                         0
2676 };
2677 
2678 /*@C
2679    MatCreateSeqDense - Creates a sequential dense matrix that
2680    is stored in column major order (the usual Fortran 77 manner). Many
2681    of the matrix operations use the BLAS and LAPACK routines.
2682 
2683    Collective
2684 
2685    Input Parameters:
2686 +  comm - MPI communicator, set to PETSC_COMM_SELF
2687 .  m - number of rows
2688 .  n - number of columns
2689 -  data - optional location of matrix data in column major order.  Set data=NULL for PETSc
2690    to control all matrix memory allocation.
2691 
2692    Output Parameter:
2693 .  A - the matrix
2694 
2695    Notes:
2696    The data input variable is intended primarily for Fortran programmers
2697    who wish to allocate their own matrix memory space.  Most users should
2698    set data=NULL.
2699 
2700    Level: intermediate
2701 
2702 .seealso: MatCreate(), MatCreateDense(), MatSetValues()
2703 @*/
2704 PetscErrorCode  MatCreateSeqDense(MPI_Comm comm,PetscInt m,PetscInt n,PetscScalar *data,Mat *A)
2705 {
2706   PetscErrorCode ierr;
2707 
2708   PetscFunctionBegin;
2709   ierr = MatCreate(comm,A);CHKERRQ(ierr);
2710   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
2711   ierr = MatSetType(*A,MATSEQDENSE);CHKERRQ(ierr);
2712   ierr = MatSeqDenseSetPreallocation(*A,data);CHKERRQ(ierr);
2713   PetscFunctionReturn(0);
2714 }
2715 
2716 /*@C
2717    MatSeqDenseSetPreallocation - Sets the array used for storing the matrix elements
2718 
2719    Collective
2720 
2721    Input Parameters:
2722 +  B - the matrix
2723 -  data - the array (or NULL)
2724 
2725    Notes:
2726    The data input variable is intended primarily for Fortran programmers
2727    who wish to allocate their own matrix memory space.  Most users should
2728    need not call this routine.
2729 
2730    Level: intermediate
2731 
2732 .seealso: MatCreate(), MatCreateDense(), MatSetValues(), MatDenseSetLDA()
2733 
2734 @*/
2735 PetscErrorCode  MatSeqDenseSetPreallocation(Mat B,PetscScalar data[])
2736 {
2737   PetscErrorCode ierr;
2738 
2739   PetscFunctionBegin;
2740   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
2741   ierr = PetscTryMethod(B,"MatSeqDenseSetPreallocation_C",(Mat,PetscScalar[]),(B,data));CHKERRQ(ierr);
2742   PetscFunctionReturn(0);
2743 }
2744 
2745 PetscErrorCode  MatSeqDenseSetPreallocation_SeqDense(Mat B,PetscScalar *data)
2746 {
2747   Mat_SeqDense   *b = (Mat_SeqDense*)B->data;
2748   PetscErrorCode ierr;
2749 
2750   PetscFunctionBegin;
2751   B->preallocated = PETSC_TRUE;
2752 
2753   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2754   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2755 
2756   if (b->lda <= 0) b->lda = B->rmap->n;
2757 
2758   ierr = PetscIntMultError(b->lda,B->cmap->n,NULL);CHKERRQ(ierr);
2759   if (!data) { /* petsc-allocated storage */
2760     if (!b->user_alloc) { ierr = PetscFree(b->v);CHKERRQ(ierr); }
2761     ierr = PetscCalloc1((size_t)b->lda*B->cmap->n,&b->v);CHKERRQ(ierr);
2762     ierr = PetscLogObjectMemory((PetscObject)B,b->lda*B->cmap->n*sizeof(PetscScalar));CHKERRQ(ierr);
2763 
2764     b->user_alloc = PETSC_FALSE;
2765   } else { /* user-allocated storage */
2766     if (!b->user_alloc) { ierr = PetscFree(b->v);CHKERRQ(ierr); }
2767     b->v          = data;
2768     b->user_alloc = PETSC_TRUE;
2769   }
2770   B->assembled = PETSC_TRUE;
2771   PetscFunctionReturn(0);
2772 }
2773 
2774 #if defined(PETSC_HAVE_ELEMENTAL)
2775 PETSC_INTERN PetscErrorCode MatConvert_SeqDense_Elemental(Mat A, MatType newtype,MatReuse reuse,Mat *newmat)
2776 {
2777   Mat               mat_elemental;
2778   PetscErrorCode    ierr;
2779   const PetscScalar *array;
2780   PetscScalar       *v_colwise;
2781   PetscInt          M=A->rmap->N,N=A->cmap->N,i,j,k,*rows,*cols;
2782 
2783   PetscFunctionBegin;
2784   ierr = PetscMalloc3(M*N,&v_colwise,M,&rows,N,&cols);CHKERRQ(ierr);
2785   ierr = MatDenseGetArrayRead(A,&array);CHKERRQ(ierr);
2786   /* convert column-wise array into row-wise v_colwise, see MatSetValues_Elemental() */
2787   k = 0;
2788   for (j=0; j<N; j++) {
2789     cols[j] = j;
2790     for (i=0; i<M; i++) {
2791       v_colwise[j*M+i] = array[k++];
2792     }
2793   }
2794   for (i=0; i<M; i++) {
2795     rows[i] = i;
2796   }
2797   ierr = MatDenseRestoreArrayRead(A,&array);CHKERRQ(ierr);
2798 
2799   ierr = MatCreate(PetscObjectComm((PetscObject)A), &mat_elemental);CHKERRQ(ierr);
2800   ierr = MatSetSizes(mat_elemental,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
2801   ierr = MatSetType(mat_elemental,MATELEMENTAL);CHKERRQ(ierr);
2802   ierr = MatSetUp(mat_elemental);CHKERRQ(ierr);
2803 
2804   /* PETSc-Elemental interaface uses axpy for setting off-processor entries, only ADD_VALUES is allowed */
2805   ierr = MatSetValues(mat_elemental,M,rows,N,cols,v_colwise,ADD_VALUES);CHKERRQ(ierr);
2806   ierr = MatAssemblyBegin(mat_elemental, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2807   ierr = MatAssemblyEnd(mat_elemental, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2808   ierr = PetscFree3(v_colwise,rows,cols);CHKERRQ(ierr);
2809 
2810   if (reuse == MAT_INPLACE_MATRIX) {
2811     ierr = MatHeaderReplace(A,&mat_elemental);CHKERRQ(ierr);
2812   } else {
2813     *newmat = mat_elemental;
2814   }
2815   PetscFunctionReturn(0);
2816 }
2817 #endif
2818 
2819 static PetscErrorCode  MatDenseSetLDA_SeqDense(Mat B,PetscInt lda)
2820 {
2821   Mat_SeqDense *b = (Mat_SeqDense*)B->data;
2822 
2823   PetscFunctionBegin;
2824   if (lda < B->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"LDA %D must be at least matrix dimension %D",lda,B->rmap->n);
2825   b->lda = lda;
2826   PetscFunctionReturn(0);
2827 }
2828 
2829 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqDense(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
2830 {
2831   PetscErrorCode ierr;
2832   PetscMPIInt    size;
2833 
2834   PetscFunctionBegin;
2835   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2836   if (size == 1) {
2837     if (scall == MAT_INITIAL_MATRIX) {
2838       ierr = MatDuplicate(inmat,MAT_COPY_VALUES,outmat);CHKERRQ(ierr);
2839     } else {
2840       ierr = MatCopy(inmat,*outmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2841     }
2842   } else {
2843     ierr = MatCreateMPIMatConcatenateSeqMat_MPIDense(comm,inmat,n,scall,outmat);CHKERRQ(ierr);
2844   }
2845   PetscFunctionReturn(0);
2846 }
2847 
2848 PetscErrorCode MatDenseGetColumnVec_SeqDense(Mat A,PetscInt col,Vec *v)
2849 {
2850   Mat_SeqDense   *a = (Mat_SeqDense*)A->data;
2851   PetscErrorCode ierr;
2852 
2853   PetscFunctionBegin;
2854   if (a->vecinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreColumnVec() first");
2855   if (a->matinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreSubMatrix() first");
2856   if (!a->cvec) {
2857     ierr = VecCreateSeqWithArray(PetscObjectComm((PetscObject)A),A->rmap->bs,A->rmap->n,NULL,&a->cvec);CHKERRQ(ierr);
2858   }
2859   a->vecinuse = col + 1;
2860   ierr = MatDenseGetArray(A,(PetscScalar**)&a->ptrinuse);CHKERRQ(ierr);
2861   ierr = VecPlaceArray(a->cvec,a->ptrinuse + (size_t)col * (size_t)a->lda);CHKERRQ(ierr);
2862   *v   = a->cvec;
2863   PetscFunctionReturn(0);
2864 }
2865 
2866 PetscErrorCode MatDenseRestoreColumnVec_SeqDense(Mat A,PetscInt col,Vec *v)
2867 {
2868   Mat_SeqDense   *a = (Mat_SeqDense*)A->data;
2869   PetscErrorCode ierr;
2870 
2871   PetscFunctionBegin;
2872   if (!a->vecinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseGetColumnVec() first");
2873   if (!a->cvec) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing internal column vector");
2874   a->vecinuse = 0;
2875   ierr = MatDenseRestoreArray(A,(PetscScalar**)&a->ptrinuse);CHKERRQ(ierr);
2876   ierr = VecResetArray(a->cvec);CHKERRQ(ierr);
2877   *v   = NULL;
2878   PetscFunctionReturn(0);
2879 }
2880 
2881 PetscErrorCode MatDenseGetColumnVecRead_SeqDense(Mat A,PetscInt col,Vec *v)
2882 {
2883   Mat_SeqDense   *a = (Mat_SeqDense*)A->data;
2884   PetscErrorCode ierr;
2885 
2886   PetscFunctionBegin;
2887   if (a->vecinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreColumnVec() first");
2888   if (a->matinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreSubMatrix() first");
2889   if (!a->cvec) {
2890     ierr = VecCreateSeqWithArray(PetscObjectComm((PetscObject)A),A->rmap->bs,A->rmap->n,NULL,&a->cvec);CHKERRQ(ierr);
2891   }
2892   a->vecinuse = col + 1;
2893   ierr = MatDenseGetArrayRead(A,&a->ptrinuse);CHKERRQ(ierr);
2894   ierr = VecPlaceArray(a->cvec,a->ptrinuse + (size_t)col * (size_t)a->lda);CHKERRQ(ierr);
2895   ierr = VecLockReadPush(a->cvec);CHKERRQ(ierr);
2896   *v   = a->cvec;
2897   PetscFunctionReturn(0);
2898 }
2899 
2900 PetscErrorCode MatDenseRestoreColumnVecRead_SeqDense(Mat A,PetscInt col,Vec *v)
2901 {
2902   Mat_SeqDense   *a = (Mat_SeqDense*)A->data;
2903   PetscErrorCode ierr;
2904 
2905   PetscFunctionBegin;
2906   if (!a->vecinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseGetColumnVec() first");
2907   if (!a->cvec) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing internal column vector");
2908   a->vecinuse = 0;
2909   ierr = MatDenseRestoreArrayRead(A,&a->ptrinuse);CHKERRQ(ierr);
2910   ierr = VecLockReadPop(a->cvec);CHKERRQ(ierr);
2911   ierr = VecResetArray(a->cvec);CHKERRQ(ierr);
2912   *v   = NULL;
2913   PetscFunctionReturn(0);
2914 }
2915 
2916 PetscErrorCode MatDenseGetColumnVecWrite_SeqDense(Mat A,PetscInt col,Vec *v)
2917 {
2918   Mat_SeqDense   *a = (Mat_SeqDense*)A->data;
2919   PetscErrorCode ierr;
2920 
2921   PetscFunctionBegin;
2922   if (a->vecinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreColumnVec() first");
2923   if (a->matinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreSubMatrix() first");
2924   if (!a->cvec) {
2925     ierr = VecCreateSeqWithArray(PetscObjectComm((PetscObject)A),A->rmap->bs,A->rmap->n,NULL,&a->cvec);CHKERRQ(ierr);
2926   }
2927   a->vecinuse = col + 1;
2928   ierr = MatDenseGetArrayWrite(A,(PetscScalar**)&a->ptrinuse);CHKERRQ(ierr);
2929   ierr = VecPlaceArray(a->cvec,a->ptrinuse + (size_t)col * (size_t)a->lda);CHKERRQ(ierr);
2930   *v   = a->cvec;
2931   PetscFunctionReturn(0);
2932 }
2933 
2934 PetscErrorCode MatDenseRestoreColumnVecWrite_SeqDense(Mat A,PetscInt col,Vec *v)
2935 {
2936   Mat_SeqDense   *a = (Mat_SeqDense*)A->data;
2937   PetscErrorCode ierr;
2938 
2939   PetscFunctionBegin;
2940   if (!a->vecinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseGetColumnVec() first");
2941   if (!a->cvec) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing internal column vector");
2942   a->vecinuse = 0;
2943   ierr = MatDenseRestoreArrayWrite(A,(PetscScalar**)&a->ptrinuse);CHKERRQ(ierr);
2944   ierr = VecResetArray(a->cvec);CHKERRQ(ierr);
2945   *v   = NULL;
2946   PetscFunctionReturn(0);
2947 }
2948 
2949 PetscErrorCode MatDenseGetSubMatrix_SeqDense(Mat A,PetscInt cbegin,PetscInt cend,Mat *v)
2950 {
2951   Mat_SeqDense   *a = (Mat_SeqDense*)A->data;
2952   PetscErrorCode ierr;
2953 
2954   PetscFunctionBegin;
2955   if (a->vecinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreColumnVec() first");
2956   if (a->matinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseRestoreSubMatrix() first");
2957   if (a->cmat && cend-cbegin != a->cmat->cmap->N) {
2958     ierr = MatDestroy(&a->cmat);CHKERRQ(ierr);
2959   }
2960   ierr = MatDenseGetArray(A,(PetscScalar**)&a->ptrinuse);CHKERRQ(ierr);
2961   if (!a->cmat) {
2962     ierr = MatCreateDense(PetscObjectComm((PetscObject)A),A->rmap->n,PETSC_DECIDE,A->rmap->N,cend-cbegin,(PetscScalar*)a->ptrinuse + (size_t)cbegin * (size_t)a->lda,&a->cmat);CHKERRQ(ierr);
2963     ierr = MatDenseSetLDA(a->cmat,a->lda);CHKERRQ(ierr);
2964   } else {
2965     ierr = MatDensePlaceArray(a->cmat,a->ptrinuse + (size_t)cbegin * (size_t)a->lda);CHKERRQ(ierr);
2966   }
2967   a->matinuse = cbegin + 1;
2968   *v = a->cmat;
2969   PetscFunctionReturn(0);
2970 }
2971 
2972 PetscErrorCode MatDenseRestoreSubMatrix_SeqDense(Mat A,Mat *v)
2973 {
2974   Mat_SeqDense   *a = (Mat_SeqDense*)A->data;
2975   PetscErrorCode ierr;
2976 
2977   PetscFunctionBegin;
2978   if (!a->matinuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Need to call MatDenseGetSubMatrix() first");
2979   if (!a->cmat) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing internal column matrix");
2980   a->matinuse = 0;
2981   ierr = MatDenseRestoreArray(A,(PetscScalar**)&a->ptrinuse);CHKERRQ(ierr);
2982   ierr = MatDenseResetArray(a->cmat);CHKERRQ(ierr);
2983   *v   = NULL;
2984   PetscFunctionReturn(0);
2985 }
2986 
2987 /*MC
2988    MATSEQDENSE - MATSEQDENSE = "seqdense" - A matrix type to be used for sequential dense matrices.
2989 
2990    Options Database Keys:
2991 . -mat_type seqdense - sets the matrix type to "seqdense" during a call to MatSetFromOptions()
2992 
2993   Level: beginner
2994 
2995 .seealso: MatCreateSeqDense()
2996 
2997 M*/
2998 PetscErrorCode MatCreate_SeqDense(Mat B)
2999 {
3000   Mat_SeqDense   *b;
3001   PetscErrorCode ierr;
3002   PetscMPIInt    size;
3003 
3004   PetscFunctionBegin;
3005   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
3006   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Comm must be of size 1");
3007 
3008   ierr    = PetscNewLog(B,&b);CHKERRQ(ierr);
3009   ierr    = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
3010   B->data = (void*)b;
3011 
3012   b->roworiented = PETSC_TRUE;
3013 
3014   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseGetLDA_C",MatDenseGetLDA_SeqDense);CHKERRQ(ierr);
3015   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseSetLDA_C",MatDenseSetLDA_SeqDense);CHKERRQ(ierr);
3016   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseGetArray_C",MatDenseGetArray_SeqDense);CHKERRQ(ierr);
3017   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseRestoreArray_C",MatDenseRestoreArray_SeqDense);CHKERRQ(ierr);
3018   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDensePlaceArray_C",MatDensePlaceArray_SeqDense);CHKERRQ(ierr);
3019   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseResetArray_C",MatDenseResetArray_SeqDense);CHKERRQ(ierr);
3020   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseReplaceArray_C",MatDenseReplaceArray_SeqDense);CHKERRQ(ierr);
3021   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseGetArrayRead_C",MatDenseGetArray_SeqDense);CHKERRQ(ierr);
3022   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseRestoreArrayRead_C",MatDenseRestoreArray_SeqDense);CHKERRQ(ierr);
3023   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseGetArrayWrite_C",MatDenseGetArray_SeqDense);CHKERRQ(ierr);
3024   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseRestoreArrayWrite_C",MatDenseRestoreArray_SeqDense);CHKERRQ(ierr);
3025   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqdense_seqaij_C",MatConvert_SeqDense_SeqAIJ);CHKERRQ(ierr);
3026 #if defined(PETSC_HAVE_ELEMENTAL)
3027   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqdense_elemental_C",MatConvert_SeqDense_Elemental);CHKERRQ(ierr);
3028 #endif
3029 #if defined(PETSC_HAVE_CUDA)
3030   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqdense_seqdensecuda_C",MatConvert_SeqDense_SeqDenseCUDA);CHKERRQ(ierr);
3031   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqdensecuda_seqdensecuda_C",MatProductSetFromOptions_SeqDense);CHKERRQ(ierr);
3032   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqdensecuda_seqdense_C",MatProductSetFromOptions_SeqDense);CHKERRQ(ierr);
3033   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqdense_seqdensecuda_C",MatProductSetFromOptions_SeqDense);CHKERRQ(ierr);
3034 #endif
3035   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqDenseSetPreallocation_C",MatSeqDenseSetPreallocation_SeqDense);CHKERRQ(ierr);
3036   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqaij_seqdense_C",MatProductSetFromOptions_SeqAIJ_SeqDense);CHKERRQ(ierr);
3037   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqdense_seqdense_C",MatProductSetFromOptions_SeqDense);CHKERRQ(ierr);
3038   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqbaij_seqdense_C",MatProductSetFromOptions_SeqXBAIJ_SeqDense);CHKERRQ(ierr);
3039   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqsbaij_seqdense_C",MatProductSetFromOptions_SeqXBAIJ_SeqDense);CHKERRQ(ierr);
3040 
3041   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseGetColumn_C",MatDenseGetColumn_SeqDense);CHKERRQ(ierr);
3042   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseRestoreColumn_C",MatDenseRestoreColumn_SeqDense);CHKERRQ(ierr);
3043   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseGetColumnVec_C",MatDenseGetColumnVec_SeqDense);CHKERRQ(ierr);
3044   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseRestoreColumnVec_C",MatDenseRestoreColumnVec_SeqDense);CHKERRQ(ierr);
3045   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseGetColumnVecRead_C",MatDenseGetColumnVecRead_SeqDense);CHKERRQ(ierr);
3046   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseRestoreColumnVecRead_C",MatDenseRestoreColumnVecRead_SeqDense);CHKERRQ(ierr);
3047   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseGetColumnVecWrite_C",MatDenseGetColumnVecWrite_SeqDense);CHKERRQ(ierr);
3048   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseRestoreColumnVecWrite_C",MatDenseRestoreColumnVecWrite_SeqDense);CHKERRQ(ierr);
3049   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseGetSubMatrix_C",MatDenseGetSubMatrix_SeqDense);CHKERRQ(ierr);
3050   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDenseRestoreSubMatrix_C",MatDenseRestoreSubMatrix_SeqDense);CHKERRQ(ierr);
3051   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQDENSE);CHKERRQ(ierr);
3052   PetscFunctionReturn(0);
3053 }
3054 
3055 /*@C
3056    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.
3057 
3058    Not Collective
3059 
3060    Input Parameters:
3061 +  mat - a MATSEQDENSE or MATMPIDENSE matrix
3062 -  col - column index
3063 
3064    Output Parameter:
3065 .  vals - pointer to the data
3066 
3067    Level: intermediate
3068 
3069 .seealso: MatDenseRestoreColumn()
3070 @*/
3071 PetscErrorCode MatDenseGetColumn(Mat A,PetscInt col,PetscScalar **vals)
3072 {
3073   PetscErrorCode ierr;
3074 
3075   PetscFunctionBegin;
3076   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3077   PetscValidLogicalCollectiveInt(A,col,2);
3078   PetscValidPointer(vals,3);
3079   ierr = PetscUseMethod(A,"MatDenseGetColumn_C",(Mat,PetscInt,PetscScalar**),(A,col,vals));CHKERRQ(ierr);
3080   PetscFunctionReturn(0);
3081 }
3082 
3083 /*@C
3084    MatDenseRestoreColumn - returns access to a column of a dense matrix which is returned by MatDenseGetColumn().
3085 
3086    Not Collective
3087 
3088    Input Parameter:
3089 .  mat - a MATSEQDENSE or MATMPIDENSE matrix
3090 
3091    Output Parameter:
3092 .  vals - pointer to the data
3093 
3094    Level: intermediate
3095 
3096 .seealso: MatDenseGetColumn()
3097 @*/
3098 PetscErrorCode MatDenseRestoreColumn(Mat A,PetscScalar **vals)
3099 {
3100   PetscErrorCode ierr;
3101 
3102   PetscFunctionBegin;
3103   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3104   PetscValidPointer(vals,2);
3105   ierr = PetscUseMethod(A,"MatDenseRestoreColumn_C",(Mat,PetscScalar**),(A,vals));CHKERRQ(ierr);
3106   PetscFunctionReturn(0);
3107 }
3108 
3109 /*@C
3110    MatDenseGetColumnVec - Gives read-write access to a column of a dense matrix, represented as a Vec.
3111 
3112    Collective
3113 
3114    Input Parameters:
3115 +  mat - the Mat object
3116 -  col - the column index
3117 
3118    Output Parameter:
3119 .  v - the vector
3120 
3121    Notes:
3122      The vector is owned by PETSc. Users need to call MatDenseRestoreColumnVec() when the vector is no longer needed.
3123      Use MatDenseGetColumnVecRead() to obtain read-only access or MatDenseGetColumnVecWrite() for write-only access.
3124 
3125    Level: intermediate
3126 
3127 .seealso: MATDENSE, MATDENSECUDA, MatDenseGetColumnVecRead(), MatDenseGetColumnVecWrite(), MatDenseRestoreColumnVec(), MatDenseRestoreColumnVecRead(), MatDenseRestoreColumnVecWrite()
3128 @*/
3129 PetscErrorCode MatDenseGetColumnVec(Mat A,PetscInt col,Vec *v)
3130 {
3131   PetscErrorCode ierr;
3132 
3133   PetscFunctionBegin;
3134   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3135   PetscValidType(A,1);
3136   PetscValidLogicalCollectiveInt(A,col,2);
3137   PetscValidPointer(v,3);
3138   if (!A->preallocated) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ORDER,"Matrix not preallocated");
3139   if (col < 0 || col > A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Invalid col %D, should be in [0,%D)",col,A->cmap->N);
3140   ierr = PetscUseMethod(A,"MatDenseGetColumnVec_C",(Mat,PetscInt,Vec*),(A,col,v));CHKERRQ(ierr);
3141   PetscFunctionReturn(0);
3142 }
3143 
3144 /*@C
3145    MatDenseRestoreColumnVec - Returns access to a column of a dense matrix obtained from MatDenseGetColumnVec().
3146 
3147    Collective
3148 
3149    Input Parameters:
3150 +  mat - the Mat object
3151 .  col - the column index
3152 -  v - the Vec object
3153 
3154    Level: intermediate
3155 
3156 .seealso: MATDENSE, MATDENSECUDA, MatDenseGetColumnVec(), MatDenseGetColumnVecRead(), MatDenseGetColumnVecWrite(), MatDenseRestoreColumnVecRead(), MatDenseRestoreColumnVecWrite()
3157 @*/
3158 PetscErrorCode MatDenseRestoreColumnVec(Mat A,PetscInt col,Vec *v)
3159 {
3160   PetscErrorCode ierr;
3161 
3162   PetscFunctionBegin;
3163   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3164   PetscValidType(A,1);
3165   PetscValidLogicalCollectiveInt(A,col,2);
3166   PetscValidPointer(v,3);
3167   if (!A->preallocated) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ORDER,"Matrix not preallocated");
3168   if (col < 0 || col > A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Invalid col %D, should be in [0,%D)",col,A->cmap->N);
3169   ierr = PetscUseMethod(A,"MatDenseRestoreColumnVec_C",(Mat,PetscInt,Vec*),(A,col,v));CHKERRQ(ierr);
3170   PetscFunctionReturn(0);
3171 }
3172 
3173 /*@C
3174    MatDenseGetColumnVecRead - Gives read-only access to a column of a dense matrix, represented as a Vec.
3175 
3176    Collective
3177 
3178    Input Parameters:
3179 +  mat - the Mat object
3180 -  col - the column index
3181 
3182    Output Parameter:
3183 .  v - the vector
3184 
3185    Notes:
3186      The vector is owned by PETSc and users cannot modify it.
3187      Users need to call MatDenseRestoreColumnVecRead() when the vector is no longer needed.
3188      Use MatDenseGetColumnVec() to obtain read-write access or MatDenseGetColumnVecWrite() for write-only access.
3189 
3190    Level: intermediate
3191 
3192 .seealso: MATDENSE, MATDENSECUDA, MatDenseGetColumnVec(), MatDenseGetColumnVecWrite(), MatDenseRestoreColumnVec(), MatDenseRestoreColumnVecRead(), MatDenseRestoreColumnVecWrite()
3193 @*/
3194 PetscErrorCode MatDenseGetColumnVecRead(Mat A,PetscInt col,Vec *v)
3195 {
3196   PetscErrorCode ierr;
3197 
3198   PetscFunctionBegin;
3199   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3200   PetscValidType(A,1);
3201   PetscValidLogicalCollectiveInt(A,col,2);
3202   PetscValidPointer(v,3);
3203   if (!A->preallocated) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ORDER,"Matrix not preallocated");
3204   if (col < 0 || col > A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Invalid col %D, should be in [0,%D)",col,A->cmap->N);
3205   ierr = PetscUseMethod(A,"MatDenseGetColumnVecRead_C",(Mat,PetscInt,Vec*),(A,col,v));CHKERRQ(ierr);
3206   PetscFunctionReturn(0);
3207 }
3208 
3209 /*@C
3210    MatDenseRestoreColumnVecRead - Returns access to a column of a dense matrix obtained from MatDenseGetColumnVecRead().
3211 
3212    Collective
3213 
3214    Input Parameters:
3215 +  mat - the Mat object
3216 .  col - the column index
3217 -  v - the Vec object
3218 
3219    Level: intermediate
3220 
3221 .seealso: MATDENSE, MATDENSECUDA, MatDenseGetColumnVec(), MatDenseGetColumnVecRead(), MatDenseGetColumnVecWrite(), MatDenseRestoreColumnVec(), MatDenseRestoreColumnVecWrite()
3222 @*/
3223 PetscErrorCode MatDenseRestoreColumnVecRead(Mat A,PetscInt col,Vec *v)
3224 {
3225   PetscErrorCode ierr;
3226 
3227   PetscFunctionBegin;
3228   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3229   PetscValidType(A,1);
3230   PetscValidLogicalCollectiveInt(A,col,2);
3231   PetscValidPointer(v,3);
3232   if (!A->preallocated) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ORDER,"Matrix not preallocated");
3233   if (col < 0 || col > A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Invalid col %D, should be in [0,%D)",col,A->cmap->N);
3234   ierr = PetscUseMethod(A,"MatDenseRestoreColumnVecRead_C",(Mat,PetscInt,Vec*),(A,col,v));CHKERRQ(ierr);
3235   PetscFunctionReturn(0);
3236 }
3237 
3238 /*@C
3239    MatDenseGetColumnVecWrite - Gives write-only access to a column of a dense matrix, represented as a Vec.
3240 
3241    Collective
3242 
3243    Input Parameters:
3244 +  mat - the Mat object
3245 -  col - the column index
3246 
3247    Output Parameter:
3248 .  v - the vector
3249 
3250    Notes:
3251      The vector is owned by PETSc. Users need to call MatDenseRestoreColumnVecWrite() when the vector is no longer needed.
3252      Use MatDenseGetColumnVec() to obtain read-write access or MatDenseGetColumnVecRead() for read-only access.
3253 
3254    Level: intermediate
3255 
3256 .seealso: MATDENSE, MATDENSECUDA, MatDenseGetColumnVec(), MatDenseGetColumnVecRead(), MatDenseRestoreColumnVec(), MatDenseRestoreColumnVecRead(), MatDenseRestoreColumnVecWrite()
3257 @*/
3258 PetscErrorCode MatDenseGetColumnVecWrite(Mat A,PetscInt col,Vec *v)
3259 {
3260   PetscErrorCode ierr;
3261 
3262   PetscFunctionBegin;
3263   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3264   PetscValidType(A,1);
3265   PetscValidLogicalCollectiveInt(A,col,2);
3266   PetscValidPointer(v,3);
3267   if (!A->preallocated) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ORDER,"Matrix not preallocated");
3268   if (col < 0 || col > A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Invalid col %D, should be in [0,%D)",col,A->cmap->N);
3269   ierr = PetscUseMethod(A,"MatDenseGetColumnVecWrite_C",(Mat,PetscInt,Vec*),(A,col,v));CHKERRQ(ierr);
3270   PetscFunctionReturn(0);
3271 }
3272 
3273 /*@C
3274    MatDenseRestoreColumnVecWrite - Returns access to a column of a dense matrix obtained from MatDenseGetColumnVecWrite().
3275 
3276    Collective
3277 
3278    Input Parameters:
3279 +  mat - the Mat object
3280 .  col - the column index
3281 -  v - the Vec object
3282 
3283    Level: intermediate
3284 
3285 .seealso: MATDENSE, MATDENSECUDA, MatDenseGetColumnVec(), MatDenseGetColumnVecRead(), MatDenseGetColumnVecWrite(), MatDenseRestoreColumnVec(), MatDenseRestoreColumnVecRead()
3286 @*/
3287 PetscErrorCode MatDenseRestoreColumnVecWrite(Mat A,PetscInt col,Vec *v)
3288 {
3289   PetscErrorCode ierr;
3290 
3291   PetscFunctionBegin;
3292   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3293   PetscValidType(A,1);
3294   PetscValidLogicalCollectiveInt(A,col,2);
3295   PetscValidPointer(v,3);
3296   if (!A->preallocated) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ORDER,"Matrix not preallocated");
3297   if (col < 0 || col > A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Invalid col %D, should be in [0,%D)",col,A->cmap->N);
3298   ierr = PetscUseMethod(A,"MatDenseRestoreColumnVecWrite_C",(Mat,PetscInt,Vec*),(A,col,v));CHKERRQ(ierr);
3299   PetscFunctionReturn(0);
3300 }
3301 
3302 /*@C
3303    MatDenseGetSubMatrix - Gives access to a block of columns of a dense matrix, represented as a Mat.
3304 
3305    Collective
3306 
3307    Input Parameters:
3308 +  mat - the Mat object
3309 .  cbegin - the first index in the block
3310 -  cend - the last index in the block
3311 
3312    Output Parameter:
3313 .  v - the matrix
3314 
3315    Notes:
3316      The matrix is owned by PETSc. Users need to call MatDenseRestoreSubMatrix() when the matrix is no longer needed.
3317 
3318    Level: intermediate
3319 
3320 .seealso: MATDENSE, MATDENSECUDA, MatDenseGetColumnVec(), MatDenseRestoreColumnVec(), MatDenseRestoreSubMatrix()
3321 @*/
3322 PetscErrorCode MatDenseGetSubMatrix(Mat A,PetscInt cbegin,PetscInt cend,Mat *v)
3323 {
3324   PetscErrorCode ierr;
3325 
3326   PetscFunctionBegin;
3327   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3328   PetscValidType(A,1);
3329   PetscValidLogicalCollectiveInt(A,cbegin,2);
3330   PetscValidLogicalCollectiveInt(A,cend,3);
3331   PetscValidPointer(v,4);
3332   if (!A->preallocated) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ORDER,"Matrix not preallocated");
3333   if (cbegin < 0 || cbegin > A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Invalid cbegin %D, should be in [0,%D)",cbegin,A->cmap->N);
3334   if (cend < 0 || cend > A->cmap->N || cend <= cbegin) SETERRQ3(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Invalid cend %D, should be in [0,%D) and strictly greater than cbegin %D",cend,A->cmap->N,cbegin);
3335   ierr = PetscUseMethod(A,"MatDenseGetSubMatrix_C",(Mat,PetscInt,PetscInt,Mat*),(A,cbegin,cend,v));CHKERRQ(ierr);
3336   PetscFunctionReturn(0);
3337 }
3338 
3339 /*@C
3340    MatDenseRestoreSubMatrix - Returns access to a block of columns of a dense matrix obtained from MatDenseGetSubMatrix().
3341 
3342    Collective
3343 
3344    Input Parameters:
3345 +  mat - the Mat object
3346 -  v - the Mat object
3347 
3348    Level: intermediate
3349 
3350 .seealso: MATDENSE, MATDENSECUDA, MatDenseGetColumnVec(), MatDenseRestoreColumnVec(), MatDenseGetSubMatrix()
3351 @*/
3352 PetscErrorCode MatDenseRestoreSubMatrix(Mat A,Mat *v)
3353 {
3354   PetscErrorCode ierr;
3355 
3356   PetscFunctionBegin;
3357   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3358   PetscValidType(A,1);
3359   PetscValidPointer(v,2);
3360   if (!A->preallocated) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ORDER,"Matrix not preallocated");
3361   ierr = PetscUseMethod(A,"MatDenseRestoreSubMatrix_C",(Mat,Mat*),(A,v));CHKERRQ(ierr);
3362   PetscFunctionReturn(0);
3363 }
3364