xref: /petsc/src/mat/impls/aij/seq/aij.c (revision 29b3c8a1c1d29fc05018f23f4f087a3ebe1dff6f)
1 
2 /*
3     Defines the basic matrix operations for the AIJ (compressed row)
4   matrix storage format.
5 */
6 
7 
8 #include <../src/mat/impls/aij/seq/aij.h>          /*I "petscmat.h" I*/
9 #include <petscblaslapack.h>
10 #include <petscbt.h>
11 #include <petsc/private/kernels/blocktranspose.h>
12 
13 PetscErrorCode MatSeqAIJSetTypeFromOptions(Mat A)
14 {
15   PetscErrorCode       ierr;
16   PetscBool            flg;
17   char                 type[256];
18 
19   PetscFunctionBegin;
20   ierr = PetscObjectOptionsBegin((PetscObject)A);
21   ierr = PetscOptionsFList("-mat_seqaij_type","Matrix SeqAIJ type","MatSeqAIJSetType",MatSeqAIJList,"seqaij",type,256,&flg);CHKERRQ(ierr);
22   if (flg) {
23     ierr = MatSeqAIJSetType(A,type);CHKERRQ(ierr);
24   }
25   ierr = PetscOptionsEnd();CHKERRQ(ierr);
26   PetscFunctionReturn(0);
27 }
28 
29 PetscErrorCode MatGetColumnNorms_SeqAIJ(Mat A,NormType type,PetscReal *norms)
30 {
31   PetscErrorCode ierr;
32   PetscInt       i,m,n;
33   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
34 
35   PetscFunctionBegin;
36   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
37   ierr = PetscArrayzero(norms,n);CHKERRQ(ierr);
38   if (type == NORM_2) {
39     for (i=0; i<aij->i[m]; i++) {
40       norms[aij->j[i]] += PetscAbsScalar(aij->a[i]*aij->a[i]);
41     }
42   } else if (type == NORM_1) {
43     for (i=0; i<aij->i[m]; i++) {
44       norms[aij->j[i]] += PetscAbsScalar(aij->a[i]);
45     }
46   } else if (type == NORM_INFINITY) {
47     for (i=0; i<aij->i[m]; i++) {
48       norms[aij->j[i]] = PetscMax(PetscAbsScalar(aij->a[i]),norms[aij->j[i]]);
49     }
50   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unknown NormType");
51 
52   if (type == NORM_2) {
53     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
54   }
55   PetscFunctionReturn(0);
56 }
57 
58 PetscErrorCode MatFindOffBlockDiagonalEntries_SeqAIJ(Mat A,IS *is)
59 {
60   Mat_SeqAIJ      *a  = (Mat_SeqAIJ*)A->data;
61   PetscInt        i,m=A->rmap->n,cnt = 0, bs = A->rmap->bs;
62   const PetscInt  *jj = a->j,*ii = a->i;
63   PetscInt        *rows;
64   PetscErrorCode  ierr;
65 
66   PetscFunctionBegin;
67   for (i=0; i<m; i++) {
68     if ((ii[i] != ii[i+1]) && ((jj[ii[i]] < bs*(i/bs)) || (jj[ii[i+1]-1] > bs*((i+bs)/bs)-1))) {
69       cnt++;
70     }
71   }
72   ierr = PetscMalloc1(cnt,&rows);CHKERRQ(ierr);
73   cnt  = 0;
74   for (i=0; i<m; i++) {
75     if ((ii[i] != ii[i+1]) && ((jj[ii[i]] < bs*(i/bs)) || (jj[ii[i+1]-1] > bs*((i+bs)/bs)-1))) {
76       rows[cnt] = i;
77       cnt++;
78     }
79   }
80   ierr = ISCreateGeneral(PETSC_COMM_SELF,cnt,rows,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
81   PetscFunctionReturn(0);
82 }
83 
84 PetscErrorCode MatFindZeroDiagonals_SeqAIJ_Private(Mat A,PetscInt *nrows,PetscInt **zrows)
85 {
86   Mat_SeqAIJ      *a  = (Mat_SeqAIJ*)A->data;
87   const MatScalar *aa = a->a;
88   PetscInt        i,m=A->rmap->n,cnt = 0;
89   const PetscInt  *ii = a->i,*jj = a->j,*diag;
90   PetscInt        *rows;
91   PetscErrorCode  ierr;
92 
93   PetscFunctionBegin;
94   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
95   diag = a->diag;
96   for (i=0; i<m; i++) {
97     if ((diag[i] >= ii[i+1]) || (jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) {
98       cnt++;
99     }
100   }
101   ierr = PetscMalloc1(cnt,&rows);CHKERRQ(ierr);
102   cnt  = 0;
103   for (i=0; i<m; i++) {
104     if ((diag[i] >= ii[i+1]) || (jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) {
105       rows[cnt++] = i;
106     }
107   }
108   *nrows = cnt;
109   *zrows = rows;
110   PetscFunctionReturn(0);
111 }
112 
113 PetscErrorCode MatFindZeroDiagonals_SeqAIJ(Mat A,IS *zrows)
114 {
115   PetscInt       nrows,*rows;
116   PetscErrorCode ierr;
117 
118   PetscFunctionBegin;
119   *zrows = NULL;
120   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(A,&nrows,&rows);CHKERRQ(ierr);
121   ierr   = ISCreateGeneral(PetscObjectComm((PetscObject)A),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
122   PetscFunctionReturn(0);
123 }
124 
125 PetscErrorCode MatFindNonzeroRows_SeqAIJ(Mat A,IS *keptrows)
126 {
127   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
128   const MatScalar *aa;
129   PetscInt        m=A->rmap->n,cnt = 0;
130   const PetscInt  *ii;
131   PetscInt        n,i,j,*rows;
132   PetscErrorCode  ierr;
133 
134   PetscFunctionBegin;
135   *keptrows = 0;
136   ii        = a->i;
137   for (i=0; i<m; i++) {
138     n = ii[i+1] - ii[i];
139     if (!n) {
140       cnt++;
141       goto ok1;
142     }
143     aa = a->a + ii[i];
144     for (j=0; j<n; j++) {
145       if (aa[j] != 0.0) goto ok1;
146     }
147     cnt++;
148 ok1:;
149   }
150   if (!cnt) PetscFunctionReturn(0);
151   ierr = PetscMalloc1(A->rmap->n-cnt,&rows);CHKERRQ(ierr);
152   cnt  = 0;
153   for (i=0; i<m; i++) {
154     n = ii[i+1] - ii[i];
155     if (!n) continue;
156     aa = a->a + ii[i];
157     for (j=0; j<n; j++) {
158       if (aa[j] != 0.0) {
159         rows[cnt++] = i;
160         break;
161       }
162     }
163   }
164   ierr = ISCreateGeneral(PETSC_COMM_SELF,cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
165   PetscFunctionReturn(0);
166 }
167 
168 PetscErrorCode  MatDiagonalSet_SeqAIJ(Mat Y,Vec D,InsertMode is)
169 {
170   PetscErrorCode    ierr;
171   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*) Y->data;
172   PetscInt          i,m = Y->rmap->n;
173   const PetscInt    *diag;
174   MatScalar         *aa = aij->a;
175   const PetscScalar *v;
176   PetscBool         missing;
177 
178   PetscFunctionBegin;
179   if (Y->assembled) {
180     ierr = MatMissingDiagonal_SeqAIJ(Y,&missing,NULL);CHKERRQ(ierr);
181     if (!missing) {
182       diag = aij->diag;
183       ierr = VecGetArrayRead(D,&v);CHKERRQ(ierr);
184       if (is == INSERT_VALUES) {
185         for (i=0; i<m; i++) {
186           aa[diag[i]] = v[i];
187         }
188       } else {
189         for (i=0; i<m; i++) {
190           aa[diag[i]] += v[i];
191         }
192       }
193       ierr = VecRestoreArrayRead(D,&v);CHKERRQ(ierr);
194       PetscFunctionReturn(0);
195     }
196     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
197   }
198   ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
199   PetscFunctionReturn(0);
200 }
201 
202 PetscErrorCode MatGetRowIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *m,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
203 {
204   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
205   PetscErrorCode ierr;
206   PetscInt       i,ishift;
207 
208   PetscFunctionBegin;
209   *m = A->rmap->n;
210   if (!ia) PetscFunctionReturn(0);
211   ishift = 0;
212   if (symmetric && !A->structurally_symmetric) {
213     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,PETSC_TRUE,ishift,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
214   } else if (oshift == 1) {
215     PetscInt *tia;
216     PetscInt nz = a->i[A->rmap->n];
217     /* malloc space and  add 1 to i and j indices */
218     ierr = PetscMalloc1(A->rmap->n+1,&tia);CHKERRQ(ierr);
219     for (i=0; i<A->rmap->n+1; i++) tia[i] = a->i[i] + 1;
220     *ia = tia;
221     if (ja) {
222       PetscInt *tja;
223       ierr = PetscMalloc1(nz+1,&tja);CHKERRQ(ierr);
224       for (i=0; i<nz; i++) tja[i] = a->j[i] + 1;
225       *ja = tja;
226     }
227   } else {
228     *ia = a->i;
229     if (ja) *ja = a->j;
230   }
231   PetscFunctionReturn(0);
232 }
233 
234 PetscErrorCode MatRestoreRowIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
235 {
236   PetscErrorCode ierr;
237 
238   PetscFunctionBegin;
239   if (!ia) PetscFunctionReturn(0);
240   if ((symmetric && !A->structurally_symmetric) || oshift == 1) {
241     ierr = PetscFree(*ia);CHKERRQ(ierr);
242     if (ja) {ierr = PetscFree(*ja);CHKERRQ(ierr);}
243   }
244   PetscFunctionReturn(0);
245 }
246 
247 PetscErrorCode MatGetColumnIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
248 {
249   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
250   PetscErrorCode ierr;
251   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
252   PetscInt       nz = a->i[m],row,*jj,mr,col;
253 
254   PetscFunctionBegin;
255   *nn = n;
256   if (!ia) PetscFunctionReturn(0);
257   if (symmetric) {
258     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,PETSC_TRUE,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
259   } else {
260     ierr = PetscCalloc1(n,&collengths);CHKERRQ(ierr);
261     ierr = PetscMalloc1(n+1,&cia);CHKERRQ(ierr);
262     ierr = PetscMalloc1(nz,&cja);CHKERRQ(ierr);
263     jj   = a->j;
264     for (i=0; i<nz; i++) {
265       collengths[jj[i]]++;
266     }
267     cia[0] = oshift;
268     for (i=0; i<n; i++) {
269       cia[i+1] = cia[i] + collengths[i];
270     }
271     ierr = PetscArrayzero(collengths,n);CHKERRQ(ierr);
272     jj   = a->j;
273     for (row=0; row<m; row++) {
274       mr = a->i[row+1] - a->i[row];
275       for (i=0; i<mr; i++) {
276         col = *jj++;
277 
278         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
279       }
280     }
281     ierr = PetscFree(collengths);CHKERRQ(ierr);
282     *ia  = cia; *ja = cja;
283   }
284   PetscFunctionReturn(0);
285 }
286 
287 PetscErrorCode MatRestoreColumnIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
288 {
289   PetscErrorCode ierr;
290 
291   PetscFunctionBegin;
292   if (!ia) PetscFunctionReturn(0);
293 
294   ierr = PetscFree(*ia);CHKERRQ(ierr);
295   ierr = PetscFree(*ja);CHKERRQ(ierr);
296   PetscFunctionReturn(0);
297 }
298 
299 /*
300  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
301  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
302  spidx[], index of a->a, to be used in MatTransposeColoringCreate_SeqAIJ() and MatFDColoringCreate_SeqXAIJ()
303 */
304 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
305 {
306   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
307   PetscErrorCode ierr;
308   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
309   PetscInt       nz = a->i[m],row,mr,col,tmp;
310   PetscInt       *cspidx;
311   const PetscInt *jj;
312 
313   PetscFunctionBegin;
314   *nn = n;
315   if (!ia) PetscFunctionReturn(0);
316 
317   ierr = PetscCalloc1(n,&collengths);CHKERRQ(ierr);
318   ierr = PetscMalloc1(n+1,&cia);CHKERRQ(ierr);
319   ierr = PetscMalloc1(nz,&cja);CHKERRQ(ierr);
320   ierr = PetscMalloc1(nz,&cspidx);CHKERRQ(ierr);
321   jj   = a->j;
322   for (i=0; i<nz; i++) {
323     collengths[jj[i]]++;
324   }
325   cia[0] = oshift;
326   for (i=0; i<n; i++) {
327     cia[i+1] = cia[i] + collengths[i];
328   }
329   ierr = PetscArrayzero(collengths,n);CHKERRQ(ierr);
330   jj   = a->j;
331   for (row=0; row<m; row++) {
332     mr = a->i[row+1] - a->i[row];
333     for (i=0; i<mr; i++) {
334       col         = *jj++;
335       tmp         = cia[col] + collengths[col]++ - oshift;
336       cspidx[tmp] = a->i[row] + i; /* index of a->j */
337       cja[tmp]    = row + oshift;
338     }
339   }
340   ierr   = PetscFree(collengths);CHKERRQ(ierr);
341   *ia    = cia;
342   *ja    = cja;
343   *spidx = cspidx;
344   PetscFunctionReturn(0);
345 }
346 
347 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
348 {
349   PetscErrorCode ierr;
350 
351   PetscFunctionBegin;
352   ierr = MatRestoreColumnIJ_SeqAIJ(A,oshift,symmetric,inodecompressed,n,ia,ja,done);CHKERRQ(ierr);
353   ierr = PetscFree(*spidx);CHKERRQ(ierr);
354   PetscFunctionReturn(0);
355 }
356 
357 PetscErrorCode MatSetValuesRow_SeqAIJ(Mat A,PetscInt row,const PetscScalar v[])
358 {
359   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
360   PetscInt       *ai = a->i;
361   PetscErrorCode ierr;
362 
363   PetscFunctionBegin;
364   ierr = PetscArraycpy(a->a+ai[row],v,ai[row+1]-ai[row]);CHKERRQ(ierr);
365 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
366   if (A->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED && ai[row+1]-ai[row]) A->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
367 #endif
368   PetscFunctionReturn(0);
369 }
370 
371 /*
372     MatSeqAIJSetValuesLocalFast - An optimized version of MatSetValuesLocal() for SeqAIJ matrices with several assumptions
373 
374       -   a single row of values is set with each call
375       -   no row or column indices are negative or (in error) larger than the number of rows or columns
376       -   the values are always added to the matrix, not set
377       -   no new locations are introduced in the nonzero structure of the matrix
378 
379      This does NOT assume the global column indices are sorted
380 
381 */
382 
383 #include <petsc/private/isimpl.h>
384 PetscErrorCode MatSeqAIJSetValuesLocalFast(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
385 {
386   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
387   PetscInt       low,high,t,row,nrow,i,col,l;
388   const PetscInt *rp,*ai = a->i,*ailen = a->ilen,*aj = a->j;
389   PetscInt       lastcol = -1;
390   MatScalar      *ap,value,*aa = a->a;
391   const PetscInt *ridx = A->rmap->mapping->indices,*cidx = A->cmap->mapping->indices;
392 
393   row  = ridx[im[0]];
394   rp   = aj + ai[row];
395   ap   = aa + ai[row];
396   nrow = ailen[row];
397   low  = 0;
398   high = nrow;
399   for (l=0; l<n; l++) { /* loop over added columns */
400     col = cidx[in[l]];
401     value = v[l];
402 
403     if (col <= lastcol) low = 0;
404     else high = nrow;
405     lastcol = col;
406     while (high-low > 5) {
407       t = (low+high)/2;
408       if (rp[t] > col) high = t;
409       else low = t;
410     }
411     for (i=low; i<high; i++) {
412       if (rp[i] == col) {
413         ap[i] += value;
414         low = i + 1;
415         break;
416       }
417     }
418   }
419 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
420   if (A->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED && m*n) A->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
421 #endif
422   return 0;
423 }
424 
425 PetscErrorCode MatSetValues_SeqAIJ(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
426 {
427   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
428   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
429   PetscInt       *imax = a->imax,*ai = a->i,*ailen = a->ilen;
430   PetscErrorCode ierr;
431   PetscInt       *aj = a->j,nonew = a->nonew,lastcol = -1;
432   MatScalar      *ap=NULL,value=0.0,*aa = a->a;
433   PetscBool      ignorezeroentries = a->ignorezeroentries;
434   PetscBool      roworiented       = a->roworiented;
435 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
436   PetscBool      inserted          = PETSC_FALSE;
437 #endif
438 
439   PetscFunctionBegin;
440   for (k=0; k<m; k++) { /* loop over added rows */
441     row = im[k];
442     if (row < 0) continue;
443 #if defined(PETSC_USE_DEBUG)
444     if (row >= A->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",row,A->rmap->n-1);
445 #endif
446     rp   = aj + ai[row];
447     if (!A->structure_only) ap = aa + ai[row];
448     rmax = imax[row]; nrow = ailen[row];
449     low  = 0;
450     high = nrow;
451     for (l=0; l<n; l++) { /* loop over added columns */
452       if (in[l] < 0) continue;
453 #if defined(PETSC_USE_DEBUG)
454       if (in[l] >= A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",in[l],A->cmap->n-1);
455 #endif
456       col = in[l];
457       if (v && !A->structure_only) value = roworiented ? v[l + k*n] : v[k + l*m];
458       if (!A->structure_only && value == 0.0 && ignorezeroentries && is == ADD_VALUES && row != col) continue;
459 
460       if (col <= lastcol) low = 0;
461       else high = nrow;
462       lastcol = col;
463       while (high-low > 5) {
464         t = (low+high)/2;
465         if (rp[t] > col) high = t;
466         else low = t;
467       }
468       for (i=low; i<high; i++) {
469         if (rp[i] > col) break;
470         if (rp[i] == col) {
471           if (!A->structure_only) {
472             if (is == ADD_VALUES) {
473               ap[i] += value;
474               (void)PetscLogFlops(1.0);
475             }
476             else ap[i] = value;
477 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
478             inserted = PETSC_TRUE;
479 #endif
480           }
481           low = i + 1;
482           goto noinsert;
483         }
484       }
485       if (value == 0.0 && ignorezeroentries && row != col) goto noinsert;
486       if (nonew == 1) goto noinsert;
487       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at (%D,%D) in the matrix",row,col);
488       if (A->structure_only) {
489         MatSeqXAIJReallocateAIJ_structure_only(A,A->rmap->n,1,nrow,row,col,rmax,ai,aj,rp,imax,nonew,MatScalar);
490       } else {
491         MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
492       }
493       N = nrow++ - 1; a->nz++; high++;
494       /* shift up all the later entries in this row */
495       ierr  = PetscArraymove(rp+i+1,rp+i,N-i+1);CHKERRQ(ierr);
496       rp[i] = col;
497       if (!A->structure_only){
498         ierr  = PetscArraymove(ap+i+1,ap+i,N-i+1);CHKERRQ(ierr);
499         ap[i] = value;
500       }
501       low = i + 1;
502       A->nonzerostate++;
503 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
504       inserted = PETSC_TRUE;
505 #endif
506 noinsert:;
507     }
508     ailen[row] = nrow;
509   }
510 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
511   if (A->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED && inserted) A->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
512 #endif
513   PetscFunctionReturn(0);
514 }
515 
516 PetscErrorCode MatSetValues_SeqAIJ_SortedFull(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
517 {
518   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
519   PetscInt       *rp,k,row;
520   PetscInt       *ai = a->i,*ailen = a->ilen;
521   PetscErrorCode ierr;
522   PetscInt       *aj = a->j;
523   MatScalar      *aa = a->a,*ap;
524 
525   PetscFunctionBegin;
526   for (k=0; k<m; k++) { /* loop over added rows */
527     row  = im[k];
528     rp   = aj + ai[row];
529     ap   = aa + ai[row];
530     if (!A->was_assembled) {
531       ierr = PetscMemcpy(rp,in,n*sizeof(PetscInt));CHKERRQ(ierr);
532     }
533     if (!A->structure_only) {
534       if (v) {
535         ierr = PetscMemcpy(ap,v,n*sizeof(PetscScalar));CHKERRQ(ierr);
536         v   += n;
537       } else {
538         ierr = PetscMemzero(ap,n*sizeof(PetscScalar));CHKERRQ(ierr);
539       }
540     }
541     ailen[row] = n;
542     a->nz      += n;
543   }
544 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
545   if (A->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED && m*n) A->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
546 #endif
547   PetscFunctionReturn(0);
548 }
549 
550 
551 PetscErrorCode MatGetValues_SeqAIJ(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],PetscScalar v[])
552 {
553   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
554   PetscInt   *rp,k,low,high,t,row,nrow,i,col,l,*aj = a->j;
555   PetscInt   *ai = a->i,*ailen = a->ilen;
556   MatScalar  *ap,*aa = a->a;
557 
558   PetscFunctionBegin;
559   for (k=0; k<m; k++) { /* loop over rows */
560     row = im[k];
561     if (row < 0) {v += n; continue;} /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",row); */
562     if (row >= A->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",row,A->rmap->n-1);
563     rp   = aj + ai[row]; ap = aa + ai[row];
564     nrow = ailen[row];
565     for (l=0; l<n; l++) { /* loop over columns */
566       if (in[l] < 0) {v++; continue;} /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",in[l]); */
567       if (in[l] >= A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",in[l],A->cmap->n-1);
568       col  = in[l];
569       high = nrow; low = 0; /* assume unsorted */
570       while (high-low > 5) {
571         t = (low+high)/2;
572         if (rp[t] > col) high = t;
573         else low = t;
574       }
575       for (i=low; i<high; i++) {
576         if (rp[i] > col) break;
577         if (rp[i] == col) {
578           *v++ = ap[i];
579           goto finished;
580         }
581       }
582       *v++ = 0.0;
583 finished:;
584     }
585   }
586   PetscFunctionReturn(0);
587 }
588 
589 
590 PetscErrorCode MatView_SeqAIJ_Binary(Mat A,PetscViewer viewer)
591 {
592   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
593   PetscErrorCode ierr;
594   PetscInt       i,*col_lens;
595   int            fd;
596   FILE           *file;
597 
598   PetscFunctionBegin;
599   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
600   ierr = PetscMalloc1(4+A->rmap->n,&col_lens);CHKERRQ(ierr);
601 
602   col_lens[0] = MAT_FILE_CLASSID;
603   col_lens[1] = A->rmap->n;
604   col_lens[2] = A->cmap->n;
605   col_lens[3] = a->nz;
606 
607   /* store lengths of each row and write (including header) to file */
608   for (i=0; i<A->rmap->n; i++) {
609     col_lens[4+i] = a->i[i+1] - a->i[i];
610   }
611   ierr = PetscBinaryWrite(fd,col_lens,4+A->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
612   ierr = PetscFree(col_lens);CHKERRQ(ierr);
613 
614   /* store column indices (zero start index) */
615   ierr = PetscBinaryWrite(fd,a->j,a->nz,PETSC_INT,PETSC_FALSE);CHKERRQ(ierr);
616 
617   /* store nonzero values */
618   ierr = PetscBinaryWrite(fd,a->a,a->nz,PETSC_SCALAR,PETSC_FALSE);CHKERRQ(ierr);
619 
620   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
621   if (file) {
622     fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(A->rmap->bs));
623   }
624   PetscFunctionReturn(0);
625 }
626 
627 static PetscErrorCode MatView_SeqAIJ_ASCII_structonly(Mat A,PetscViewer viewer)
628 {
629   PetscErrorCode ierr;
630   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
631   PetscInt       i,k,m=A->rmap->N;
632 
633   PetscFunctionBegin;
634   ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
635   for (i=0; i<m; i++) {
636     ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
637     for (k=a->i[i]; k<a->i[i+1]; k++) {
638       ierr = PetscViewerASCIIPrintf(viewer," (%D) ",a->j[k]);CHKERRQ(ierr);
639     }
640     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
641   }
642   ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
643   PetscFunctionReturn(0);
644 }
645 
646 extern PetscErrorCode MatSeqAIJFactorInfo_Matlab(Mat,PetscViewer);
647 
648 PetscErrorCode MatView_SeqAIJ_ASCII(Mat A,PetscViewer viewer)
649 {
650   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
651   PetscErrorCode    ierr;
652   PetscInt          i,j,m = A->rmap->n;
653   const char        *name;
654   PetscViewerFormat format;
655 
656   PetscFunctionBegin;
657   if (A->structure_only) {
658     ierr = MatView_SeqAIJ_ASCII_structonly(A,viewer);CHKERRQ(ierr);
659     PetscFunctionReturn(0);
660   }
661 
662   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
663   if (format == PETSC_VIEWER_ASCII_MATLAB) {
664     PetscInt nofinalvalue = 0;
665     if (m && ((a->i[m] == a->i[m-1]) || (a->j[a->nz-1] != A->cmap->n-1))) {
666       /* Need a dummy value to ensure the dimension of the matrix. */
667       nofinalvalue = 1;
668     }
669     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
670     ierr = PetscViewerASCIIPrintf(viewer,"%% Size = %D %D \n",m,A->cmap->n);CHKERRQ(ierr);
671     ierr = PetscViewerASCIIPrintf(viewer,"%% Nonzeros = %D \n",a->nz);CHKERRQ(ierr);
672 #if defined(PETSC_USE_COMPLEX)
673     ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,4);\n",a->nz+nofinalvalue);CHKERRQ(ierr);
674 #else
675     ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",a->nz+nofinalvalue);CHKERRQ(ierr);
676 #endif
677     ierr = PetscViewerASCIIPrintf(viewer,"zzz = [\n");CHKERRQ(ierr);
678 
679     for (i=0; i<m; i++) {
680       for (j=a->i[i]; j<a->i[i+1]; j++) {
681 #if defined(PETSC_USE_COMPLEX)
682         ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e %18.16e\n",i+1,a->j[j]+1,(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
683 #else
684         ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,a->j[j]+1,(double)a->a[j]);CHKERRQ(ierr);
685 #endif
686       }
687     }
688     if (nofinalvalue) {
689 #if defined(PETSC_USE_COMPLEX)
690       ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e %18.16e\n",m,A->cmap->n,0.,0.);CHKERRQ(ierr);
691 #else
692       ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",m,A->cmap->n,0.0);CHKERRQ(ierr);
693 #endif
694     }
695     ierr = PetscObjectGetName((PetscObject)A,&name);CHKERRQ(ierr);
696     ierr = PetscViewerASCIIPrintf(viewer,"];\n %s = spconvert(zzz);\n",name);CHKERRQ(ierr);
697     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
698   } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO || format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
699     PetscFunctionReturn(0);
700   } else if (format == PETSC_VIEWER_ASCII_COMMON) {
701     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
702     for (i=0; i<m; i++) {
703       ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
704       for (j=a->i[i]; j<a->i[i+1]; j++) {
705 #if defined(PETSC_USE_COMPLEX)
706         if (PetscImaginaryPart(a->a[j]) > 0.0 && PetscRealPart(a->a[j]) != 0.0) {
707           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
708         } else if (PetscImaginaryPart(a->a[j]) < 0.0 && PetscRealPart(a->a[j]) != 0.0) {
709           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
710         } else if (PetscRealPart(a->a[j]) != 0.0) {
711           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
712         }
713 #else
714         if (a->a[j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);}
715 #endif
716       }
717       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
718     }
719     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
720   } else if (format == PETSC_VIEWER_ASCII_SYMMODU) {
721     PetscInt nzd=0,fshift=1,*sptr;
722     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
723     ierr = PetscMalloc1(m+1,&sptr);CHKERRQ(ierr);
724     for (i=0; i<m; i++) {
725       sptr[i] = nzd+1;
726       for (j=a->i[i]; j<a->i[i+1]; j++) {
727         if (a->j[j] >= i) {
728 #if defined(PETSC_USE_COMPLEX)
729           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) nzd++;
730 #else
731           if (a->a[j] != 0.0) nzd++;
732 #endif
733         }
734       }
735     }
736     sptr[m] = nzd+1;
737     ierr    = PetscViewerASCIIPrintf(viewer," %D %D\n\n",m,nzd);CHKERRQ(ierr);
738     for (i=0; i<m+1; i+=6) {
739       if (i+4<m) {
740         ierr = PetscViewerASCIIPrintf(viewer," %D %D %D %D %D %D\n",sptr[i],sptr[i+1],sptr[i+2],sptr[i+3],sptr[i+4],sptr[i+5]);CHKERRQ(ierr);
741       } else if (i+3<m) {
742         ierr = PetscViewerASCIIPrintf(viewer," %D %D %D %D %D\n",sptr[i],sptr[i+1],sptr[i+2],sptr[i+3],sptr[i+4]);CHKERRQ(ierr);
743       } else if (i+2<m) {
744         ierr = PetscViewerASCIIPrintf(viewer," %D %D %D %D\n",sptr[i],sptr[i+1],sptr[i+2],sptr[i+3]);CHKERRQ(ierr);
745       } else if (i+1<m) {
746         ierr = PetscViewerASCIIPrintf(viewer," %D %D %D\n",sptr[i],sptr[i+1],sptr[i+2]);CHKERRQ(ierr);
747       } else if (i<m) {
748         ierr = PetscViewerASCIIPrintf(viewer," %D %D\n",sptr[i],sptr[i+1]);CHKERRQ(ierr);
749       } else {
750         ierr = PetscViewerASCIIPrintf(viewer," %D\n",sptr[i]);CHKERRQ(ierr);
751       }
752     }
753     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
754     ierr = PetscFree(sptr);CHKERRQ(ierr);
755     for (i=0; i<m; i++) {
756       for (j=a->i[i]; j<a->i[i+1]; j++) {
757         if (a->j[j] >= i) {ierr = PetscViewerASCIIPrintf(viewer," %D ",a->j[j]+fshift);CHKERRQ(ierr);}
758       }
759       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
760     }
761     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
762     for (i=0; i<m; i++) {
763       for (j=a->i[i]; j<a->i[i+1]; j++) {
764         if (a->j[j] >= i) {
765 #if defined(PETSC_USE_COMPLEX)
766           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) {
767             ierr = PetscViewerASCIIPrintf(viewer," %18.16e %18.16e ",(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
768           }
769 #else
770           if (a->a[j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," %18.16e ",(double)a->a[j]);CHKERRQ(ierr);}
771 #endif
772         }
773       }
774       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
775     }
776     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
777   } else if (format == PETSC_VIEWER_ASCII_DENSE) {
778     PetscInt    cnt = 0,jcnt;
779     PetscScalar value;
780 #if defined(PETSC_USE_COMPLEX)
781     PetscBool   realonly = PETSC_TRUE;
782 
783     for (i=0; i<a->i[m]; i++) {
784       if (PetscImaginaryPart(a->a[i]) != 0.0) {
785         realonly = PETSC_FALSE;
786         break;
787       }
788     }
789 #endif
790 
791     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
792     for (i=0; i<m; i++) {
793       jcnt = 0;
794       for (j=0; j<A->cmap->n; j++) {
795         if (jcnt < a->i[i+1]-a->i[i] && j == a->j[cnt]) {
796           value = a->a[cnt++];
797           jcnt++;
798         } else {
799           value = 0.0;
800         }
801 #if defined(PETSC_USE_COMPLEX)
802         if (realonly) {
803           ierr = PetscViewerASCIIPrintf(viewer," %7.5e ",(double)PetscRealPart(value));CHKERRQ(ierr);
804         } else {
805           ierr = PetscViewerASCIIPrintf(viewer," %7.5e+%7.5e i ",(double)PetscRealPart(value),(double)PetscImaginaryPart(value));CHKERRQ(ierr);
806         }
807 #else
808         ierr = PetscViewerASCIIPrintf(viewer," %7.5e ",(double)value);CHKERRQ(ierr);
809 #endif
810       }
811       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
812     }
813     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
814   } else if (format == PETSC_VIEWER_ASCII_MATRIXMARKET) {
815     PetscInt fshift=1;
816     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
817 #if defined(PETSC_USE_COMPLEX)
818     ierr = PetscViewerASCIIPrintf(viewer,"%%%%MatrixMarket matrix coordinate complex general\n");CHKERRQ(ierr);
819 #else
820     ierr = PetscViewerASCIIPrintf(viewer,"%%%%MatrixMarket matrix coordinate real general\n");CHKERRQ(ierr);
821 #endif
822     ierr = PetscViewerASCIIPrintf(viewer,"%D %D %D\n", m, A->cmap->n, a->nz);CHKERRQ(ierr);
823     for (i=0; i<m; i++) {
824       for (j=a->i[i]; j<a->i[i+1]; j++) {
825 #if defined(PETSC_USE_COMPLEX)
826         ierr = PetscViewerASCIIPrintf(viewer,"%D %D %g %g\n", i+fshift,a->j[j]+fshift,(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
827 #else
828         ierr = PetscViewerASCIIPrintf(viewer,"%D %D %g\n", i+fshift, a->j[j]+fshift, (double)a->a[j]);CHKERRQ(ierr);
829 #endif
830       }
831     }
832     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
833   } else {
834     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
835     if (A->factortype) {
836       for (i=0; i<m; i++) {
837         ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
838         /* L part */
839         for (j=a->i[i]; j<a->i[i+1]; j++) {
840 #if defined(PETSC_USE_COMPLEX)
841           if (PetscImaginaryPart(a->a[j]) > 0.0) {
842             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
843           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
844             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)(-PetscImaginaryPart(a->a[j])));CHKERRQ(ierr);
845           } else {
846             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
847           }
848 #else
849           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);
850 #endif
851         }
852         /* diagonal */
853         j = a->diag[i];
854 #if defined(PETSC_USE_COMPLEX)
855         if (PetscImaginaryPart(a->a[j]) > 0.0) {
856           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(1.0/a->a[j]),(double)PetscImaginaryPart(1.0/a->a[j]));CHKERRQ(ierr);
857         } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
858           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(1.0/a->a[j]),(double)(-PetscImaginaryPart(1.0/a->a[j])));CHKERRQ(ierr);
859         } else {
860           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(1.0/a->a[j]));CHKERRQ(ierr);
861         }
862 #else
863         ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)(1.0/a->a[j]));CHKERRQ(ierr);
864 #endif
865 
866         /* U part */
867         for (j=a->diag[i+1]+1; j<a->diag[i]; j++) {
868 #if defined(PETSC_USE_COMPLEX)
869           if (PetscImaginaryPart(a->a[j]) > 0.0) {
870             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
871           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
872             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)(-PetscImaginaryPart(a->a[j])));CHKERRQ(ierr);
873           } else {
874             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
875           }
876 #else
877           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);
878 #endif
879         }
880         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
881       }
882     } else {
883       for (i=0; i<m; i++) {
884         ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
885         for (j=a->i[i]; j<a->i[i+1]; j++) {
886 #if defined(PETSC_USE_COMPLEX)
887           if (PetscImaginaryPart(a->a[j]) > 0.0) {
888             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
889           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
890             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
891           } else {
892             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
893           }
894 #else
895           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);
896 #endif
897         }
898         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
899       }
900     }
901     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
902   }
903   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
904   PetscFunctionReturn(0);
905 }
906 
907 #include <petscdraw.h>
908 PetscErrorCode MatView_SeqAIJ_Draw_Zoom(PetscDraw draw,void *Aa)
909 {
910   Mat               A  = (Mat) Aa;
911   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
912   PetscErrorCode    ierr;
913   PetscInt          i,j,m = A->rmap->n;
914   int               color;
915   PetscReal         xl,yl,xr,yr,x_l,x_r,y_l,y_r;
916   PetscViewer       viewer;
917   PetscViewerFormat format;
918 
919   PetscFunctionBegin;
920   ierr = PetscObjectQuery((PetscObject)A,"Zoomviewer",(PetscObject*)&viewer);CHKERRQ(ierr);
921   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
922   ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
923 
924   /* loop over matrix elements drawing boxes */
925 
926   if (format != PETSC_VIEWER_DRAW_CONTOUR) {
927     ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
928     /* Blue for negative, Cyan for zero and  Red for positive */
929     color = PETSC_DRAW_BLUE;
930     for (i=0; i<m; i++) {
931       y_l = m - i - 1.0; y_r = y_l + 1.0;
932       for (j=a->i[i]; j<a->i[i+1]; j++) {
933         x_l = a->j[j]; x_r = x_l + 1.0;
934         if (PetscRealPart(a->a[j]) >=  0.) continue;
935         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
936       }
937     }
938     color = PETSC_DRAW_CYAN;
939     for (i=0; i<m; i++) {
940       y_l = m - i - 1.0; y_r = y_l + 1.0;
941       for (j=a->i[i]; j<a->i[i+1]; j++) {
942         x_l = a->j[j]; x_r = x_l + 1.0;
943         if (a->a[j] !=  0.) continue;
944         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
945       }
946     }
947     color = PETSC_DRAW_RED;
948     for (i=0; i<m; i++) {
949       y_l = m - i - 1.0; y_r = y_l + 1.0;
950       for (j=a->i[i]; j<a->i[i+1]; j++) {
951         x_l = a->j[j]; x_r = x_l + 1.0;
952         if (PetscRealPart(a->a[j]) <=  0.) continue;
953         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
954       }
955     }
956     ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
957   } else {
958     /* use contour shading to indicate magnitude of values */
959     /* first determine max of all nonzero values */
960     PetscReal minv = 0.0, maxv = 0.0;
961     PetscInt  nz = a->nz, count = 0;
962     PetscDraw popup;
963 
964     for (i=0; i<nz; i++) {
965       if (PetscAbsScalar(a->a[i]) > maxv) maxv = PetscAbsScalar(a->a[i]);
966     }
967     if (minv >= maxv) maxv = minv + PETSC_SMALL;
968     ierr = PetscDrawGetPopup(draw,&popup);CHKERRQ(ierr);
969     ierr = PetscDrawScalePopup(popup,minv,maxv);CHKERRQ(ierr);
970 
971     ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
972     for (i=0; i<m; i++) {
973       y_l = m - i - 1.0;
974       y_r = y_l + 1.0;
975       for (j=a->i[i]; j<a->i[i+1]; j++) {
976         x_l = a->j[j];
977         x_r = x_l + 1.0;
978         color = PetscDrawRealToColor(PetscAbsScalar(a->a[count]),minv,maxv);
979         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
980         count++;
981       }
982     }
983     ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
984   }
985   PetscFunctionReturn(0);
986 }
987 
988 #include <petscdraw.h>
989 PetscErrorCode MatView_SeqAIJ_Draw(Mat A,PetscViewer viewer)
990 {
991   PetscErrorCode ierr;
992   PetscDraw      draw;
993   PetscReal      xr,yr,xl,yl,h,w;
994   PetscBool      isnull;
995 
996   PetscFunctionBegin;
997   ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
998   ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
999   if (isnull) PetscFunctionReturn(0);
1000 
1001   xr   = A->cmap->n; yr  = A->rmap->n; h = yr/10.0; w = xr/10.0;
1002   xr  += w;          yr += h;         xl = -w;     yl = -h;
1003   ierr = PetscDrawSetCoordinates(draw,xl,yl,xr,yr);CHKERRQ(ierr);
1004   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",(PetscObject)viewer);CHKERRQ(ierr);
1005   ierr = PetscDrawZoom(draw,MatView_SeqAIJ_Draw_Zoom,A);CHKERRQ(ierr);
1006   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",NULL);CHKERRQ(ierr);
1007   ierr = PetscDrawSave(draw);CHKERRQ(ierr);
1008   PetscFunctionReturn(0);
1009 }
1010 
1011 PetscErrorCode MatView_SeqAIJ(Mat A,PetscViewer viewer)
1012 {
1013   PetscErrorCode ierr;
1014   PetscBool      iascii,isbinary,isdraw;
1015 
1016   PetscFunctionBegin;
1017   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1018   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1019   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1020   if (iascii) {
1021     ierr = MatView_SeqAIJ_ASCII(A,viewer);CHKERRQ(ierr);
1022   } else if (isbinary) {
1023     ierr = MatView_SeqAIJ_Binary(A,viewer);CHKERRQ(ierr);
1024   } else if (isdraw) {
1025     ierr = MatView_SeqAIJ_Draw(A,viewer);CHKERRQ(ierr);
1026   }
1027   ierr = MatView_SeqAIJ_Inode(A,viewer);CHKERRQ(ierr);
1028   PetscFunctionReturn(0);
1029 }
1030 
1031 PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat A,MatAssemblyType mode)
1032 {
1033   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1034   PetscErrorCode ierr;
1035   PetscInt       fshift = 0,i,*ai = a->i,*aj = a->j,*imax = a->imax;
1036   PetscInt       m      = A->rmap->n,*ip,N,*ailen = a->ilen,rmax = 0;
1037   MatScalar      *aa    = a->a,*ap;
1038   PetscReal      ratio  = 0.6;
1039 
1040   PetscFunctionBegin;
1041   if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(0);
1042   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1043   if (A->was_assembled && A->ass_nonzerostate == A->nonzerostate) PetscFunctionReturn(0);
1044 
1045   if (m) rmax = ailen[0]; /* determine row with most nonzeros */
1046   for (i=1; i<m; i++) {
1047     /* move each row back by the amount of empty slots (fshift) before it*/
1048     fshift += imax[i-1] - ailen[i-1];
1049     rmax    = PetscMax(rmax,ailen[i]);
1050     if (fshift) {
1051       ip = aj + ai[i];
1052       ap = aa + ai[i];
1053       N  = ailen[i];
1054       ierr = PetscArraymove(ip-fshift,ip,N);CHKERRQ(ierr);
1055       if (!A->structure_only) {
1056         ierr = PetscArraymove(ap-fshift,ap,N);CHKERRQ(ierr);
1057       }
1058     }
1059     ai[i] = ai[i-1] + ailen[i-1];
1060   }
1061   if (m) {
1062     fshift += imax[m-1] - ailen[m-1];
1063     ai[m]   = ai[m-1] + ailen[m-1];
1064   }
1065 
1066   /* reset ilen and imax for each row */
1067   a->nonzerorowcnt = 0;
1068   if (A->structure_only) {
1069     ierr = PetscFree(a->imax);CHKERRQ(ierr);
1070     ierr = PetscFree(a->ilen);CHKERRQ(ierr);
1071   } else { /* !A->structure_only */
1072     for (i=0; i<m; i++) {
1073       ailen[i] = imax[i] = ai[i+1] - ai[i];
1074       a->nonzerorowcnt += ((ai[i+1] - ai[i]) > 0);
1075     }
1076   }
1077   a->nz = ai[m];
1078   if (fshift && a->nounused == -1) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB, "Unused space detected in matrix: %D X %D, %D unneeded", m, A->cmap->n, fshift);
1079 
1080   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1081   ierr = PetscInfo4(A,"Matrix size: %D X %D; storage space: %D unneeded,%D used\n",m,A->cmap->n,fshift,a->nz);CHKERRQ(ierr);
1082   ierr = PetscInfo1(A,"Number of mallocs during MatSetValues() is %D\n",a->reallocs);CHKERRQ(ierr);
1083   ierr = PetscInfo1(A,"Maximum nonzeros in any row is %D\n",rmax);CHKERRQ(ierr);
1084 
1085   A->info.mallocs    += a->reallocs;
1086   a->reallocs         = 0;
1087   A->info.nz_unneeded = (PetscReal)fshift;
1088   a->rmax             = rmax;
1089 
1090   if (!A->structure_only) {
1091     ierr = MatCheckCompressedRow(A,a->nonzerorowcnt,&a->compressedrow,a->i,m,ratio);CHKERRQ(ierr);
1092   }
1093   ierr = MatAssemblyEnd_SeqAIJ_Inode(A,mode);CHKERRQ(ierr);
1094   PetscFunctionReturn(0);
1095 }
1096 
1097 PetscErrorCode MatRealPart_SeqAIJ(Mat A)
1098 {
1099   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1100   PetscInt       i,nz = a->nz;
1101   MatScalar      *aa = a->a;
1102   PetscErrorCode ierr;
1103 
1104   PetscFunctionBegin;
1105   for (i=0; i<nz; i++) aa[i] = PetscRealPart(aa[i]);
1106   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1107 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
1108   if (A->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED) A->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
1109 #endif
1110   PetscFunctionReturn(0);
1111 }
1112 
1113 PetscErrorCode MatImaginaryPart_SeqAIJ(Mat A)
1114 {
1115   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1116   PetscInt       i,nz = a->nz;
1117   MatScalar      *aa = a->a;
1118   PetscErrorCode ierr;
1119 
1120   PetscFunctionBegin;
1121   for (i=0; i<nz; i++) aa[i] = PetscImaginaryPart(aa[i]);
1122   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1123 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
1124   if (A->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED) A->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
1125 #endif
1126   PetscFunctionReturn(0);
1127 }
1128 
1129 PetscErrorCode MatZeroEntries_SeqAIJ(Mat A)
1130 {
1131   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1132   PetscErrorCode ierr;
1133 
1134   PetscFunctionBegin;
1135   ierr = PetscArrayzero(a->a,a->i[A->rmap->n]);CHKERRQ(ierr);
1136   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1137 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
1138   if (A->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED) A->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
1139 #endif
1140   PetscFunctionReturn(0);
1141 }
1142 
1143 PetscErrorCode MatDestroy_SeqAIJ(Mat A)
1144 {
1145   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1146   PetscErrorCode ierr;
1147 
1148   PetscFunctionBegin;
1149 #if defined(PETSC_USE_LOG)
1150   PetscLogObjectState((PetscObject)A,"Rows=%D, Cols=%D, NZ=%D",A->rmap->n,A->cmap->n,a->nz);
1151 #endif
1152   ierr = MatSeqXAIJFreeAIJ(A,&a->a,&a->j,&a->i);CHKERRQ(ierr);
1153   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
1154   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
1155   ierr = PetscFree(a->diag);CHKERRQ(ierr);
1156   ierr = PetscFree(a->ibdiag);CHKERRQ(ierr);
1157   ierr = PetscFree(a->imax);CHKERRQ(ierr);
1158   ierr = PetscFree(a->ilen);CHKERRQ(ierr);
1159   ierr = PetscFree(a->ipre);CHKERRQ(ierr);
1160   ierr = PetscFree3(a->idiag,a->mdiag,a->ssor_work);CHKERRQ(ierr);
1161   ierr = PetscFree(a->solve_work);CHKERRQ(ierr);
1162   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
1163   ierr = PetscFree(a->saved_values);CHKERRQ(ierr);
1164   ierr = ISColoringDestroy(&a->coloring);CHKERRQ(ierr);
1165   ierr = PetscFree2(a->compressedrow.i,a->compressedrow.rindex);CHKERRQ(ierr);
1166   ierr = PetscFree(a->matmult_abdense);CHKERRQ(ierr);
1167 
1168   ierr = MatDestroy_SeqAIJ_Inode(A);CHKERRQ(ierr);
1169   ierr = PetscFree(A->data);CHKERRQ(ierr);
1170 
1171   ierr = PetscObjectChangeTypeName((PetscObject)A,0);CHKERRQ(ierr);
1172   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetColumnIndices_C",NULL);CHKERRQ(ierr);
1173   ierr = PetscObjectComposeFunction((PetscObject)A,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1174   ierr = PetscObjectComposeFunction((PetscObject)A,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1175   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqsbaij_C",NULL);CHKERRQ(ierr);
1176   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqbaij_C",NULL);CHKERRQ(ierr);
1177   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqaijperm_C",NULL);CHKERRQ(ierr);
1178 #if defined(PETSC_HAVE_ELEMENTAL)
1179   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_elemental_C",NULL);CHKERRQ(ierr);
1180 #endif
1181 #if defined(PETSC_HAVE_HYPRE)
1182   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_hypre_C",NULL);CHKERRQ(ierr);
1183   ierr = PetscObjectComposeFunction((PetscObject)A,"MatMatMatMult_transpose_seqaij_seqaij_C",NULL);CHKERRQ(ierr);
1184 #endif
1185   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqdense_C",NULL);CHKERRQ(ierr);
1186   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqsell_C",NULL);CHKERRQ(ierr);
1187   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_is_C",NULL);CHKERRQ(ierr);
1188   ierr = PetscObjectComposeFunction((PetscObject)A,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1189   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1190   ierr = PetscObjectComposeFunction((PetscObject)A,"MatResetPreallocation_C",NULL);CHKERRQ(ierr);
1191   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1192   ierr = PetscObjectComposeFunction((PetscObject)A,"MatReorderForNonzeroDiagonal_C",NULL);CHKERRQ(ierr);
1193   ierr = PetscObjectComposeFunction((PetscObject)A,"MatPtAP_is_seqaij_C",NULL);CHKERRQ(ierr);
1194   PetscFunctionReturn(0);
1195 }
1196 
1197 PetscErrorCode MatSetOption_SeqAIJ(Mat A,MatOption op,PetscBool flg)
1198 {
1199   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1200   PetscErrorCode ierr;
1201 
1202   PetscFunctionBegin;
1203   switch (op) {
1204   case MAT_ROW_ORIENTED:
1205     a->roworiented = flg;
1206     break;
1207   case MAT_KEEP_NONZERO_PATTERN:
1208     a->keepnonzeropattern = flg;
1209     break;
1210   case MAT_NEW_NONZERO_LOCATIONS:
1211     a->nonew = (flg ? 0 : 1);
1212     break;
1213   case MAT_NEW_NONZERO_LOCATION_ERR:
1214     a->nonew = (flg ? -1 : 0);
1215     break;
1216   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1217     a->nonew = (flg ? -2 : 0);
1218     break;
1219   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1220     a->nounused = (flg ? -1 : 0);
1221     break;
1222   case MAT_IGNORE_ZERO_ENTRIES:
1223     a->ignorezeroentries = flg;
1224     break;
1225   case MAT_SPD:
1226   case MAT_SYMMETRIC:
1227   case MAT_STRUCTURALLY_SYMMETRIC:
1228   case MAT_HERMITIAN:
1229   case MAT_SYMMETRY_ETERNAL:
1230   case MAT_STRUCTURE_ONLY:
1231     /* These options are handled directly by MatSetOption() */
1232     break;
1233   case MAT_NEW_DIAGONALS:
1234   case MAT_IGNORE_OFF_PROC_ENTRIES:
1235   case MAT_USE_HASH_TABLE:
1236     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1237     break;
1238   case MAT_USE_INODES:
1239     /* Not an error because MatSetOption_SeqAIJ_Inode handles this one */
1240     break;
1241   case MAT_SUBMAT_SINGLEIS:
1242     A->submat_singleis = flg;
1243     break;
1244   case MAT_SORTED_FULL:
1245     if (flg) A->ops->setvalues = MatSetValues_SeqAIJ_SortedFull;
1246     else     A->ops->setvalues = MatSetValues_SeqAIJ;
1247     break;
1248   default:
1249     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1250   }
1251   ierr = MatSetOption_SeqAIJ_Inode(A,op,flg);CHKERRQ(ierr);
1252   PetscFunctionReturn(0);
1253 }
1254 
1255 PetscErrorCode MatGetDiagonal_SeqAIJ(Mat A,Vec v)
1256 {
1257   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1258   PetscErrorCode ierr;
1259   PetscInt       i,j,n,*ai=a->i,*aj=a->j;
1260   PetscScalar    *aa=a->a,*x;
1261 
1262   PetscFunctionBegin;
1263   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
1264   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
1265 
1266   if (A->factortype == MAT_FACTOR_ILU || A->factortype == MAT_FACTOR_LU) {
1267     PetscInt *diag=a->diag;
1268     ierr = VecGetArrayWrite(v,&x);CHKERRQ(ierr);
1269     for (i=0; i<n; i++) x[i] = 1.0/aa[diag[i]];
1270     ierr = VecRestoreArrayWrite(v,&x);CHKERRQ(ierr);
1271     PetscFunctionReturn(0);
1272   }
1273 
1274   ierr = VecGetArrayWrite(v,&x);CHKERRQ(ierr);
1275   for (i=0; i<n; i++) {
1276     x[i] = 0.0;
1277     for (j=ai[i]; j<ai[i+1]; j++) {
1278       if (aj[j] == i) {
1279         x[i] = aa[j];
1280         break;
1281       }
1282     }
1283   }
1284   ierr = VecRestoreArrayWrite(v,&x);CHKERRQ(ierr);
1285   PetscFunctionReturn(0);
1286 }
1287 
1288 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1289 PetscErrorCode MatMultTransposeAdd_SeqAIJ(Mat A,Vec xx,Vec zz,Vec yy)
1290 {
1291   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1292   PetscScalar       *y;
1293   const PetscScalar *x;
1294   PetscErrorCode    ierr;
1295   PetscInt          m = A->rmap->n;
1296 #if !defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1297   const MatScalar   *v;
1298   PetscScalar       alpha;
1299   PetscInt          n,i,j;
1300   const PetscInt    *idx,*ii,*ridx=NULL;
1301   Mat_CompressedRow cprow    = a->compressedrow;
1302   PetscBool         usecprow = cprow.use;
1303 #endif
1304 
1305   PetscFunctionBegin;
1306   if (zz != yy) {ierr = VecCopy(zz,yy);CHKERRQ(ierr);}
1307   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1308   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1309 
1310 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1311   fortranmulttransposeaddaij_(&m,x,a->i,a->j,a->a,y);
1312 #else
1313   if (usecprow) {
1314     m    = cprow.nrows;
1315     ii   = cprow.i;
1316     ridx = cprow.rindex;
1317   } else {
1318     ii = a->i;
1319   }
1320   for (i=0; i<m; i++) {
1321     idx = a->j + ii[i];
1322     v   = a->a + ii[i];
1323     n   = ii[i+1] - ii[i];
1324     if (usecprow) {
1325       alpha = x[ridx[i]];
1326     } else {
1327       alpha = x[i];
1328     }
1329     for (j=0; j<n; j++) y[idx[j]] += alpha*v[j];
1330   }
1331 #endif
1332   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1333   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1334   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1335   PetscFunctionReturn(0);
1336 }
1337 
1338 PetscErrorCode MatMultTranspose_SeqAIJ(Mat A,Vec xx,Vec yy)
1339 {
1340   PetscErrorCode ierr;
1341 
1342   PetscFunctionBegin;
1343   ierr = VecSet(yy,0.0);CHKERRQ(ierr);
1344   ierr = MatMultTransposeAdd_SeqAIJ(A,xx,yy,yy);CHKERRQ(ierr);
1345   PetscFunctionReturn(0);
1346 }
1347 
1348 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1349 
1350 PetscErrorCode MatMult_SeqAIJ(Mat A,Vec xx,Vec yy)
1351 {
1352   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1353   PetscScalar       *y;
1354   const PetscScalar *x;
1355   const MatScalar   *aa;
1356   PetscErrorCode    ierr;
1357   PetscInt          m=A->rmap->n;
1358   const PetscInt    *aj,*ii,*ridx=NULL;
1359   PetscInt          n,i;
1360   PetscScalar       sum;
1361   PetscBool         usecprow=a->compressedrow.use;
1362 
1363 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1364 #pragma disjoint(*x,*y,*aa)
1365 #endif
1366 
1367   PetscFunctionBegin;
1368   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1369   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1370   ii   = a->i;
1371   if (usecprow) { /* use compressed row format */
1372     ierr = PetscArrayzero(y,m);CHKERRQ(ierr);
1373     m    = a->compressedrow.nrows;
1374     ii   = a->compressedrow.i;
1375     ridx = a->compressedrow.rindex;
1376     for (i=0; i<m; i++) {
1377       n           = ii[i+1] - ii[i];
1378       aj          = a->j + ii[i];
1379       aa          = a->a + ii[i];
1380       sum         = 0.0;
1381       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1382       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1383       y[*ridx++] = sum;
1384     }
1385   } else { /* do not use compressed row format */
1386 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJ)
1387     aj   = a->j;
1388     aa   = a->a;
1389     fortranmultaij_(&m,x,ii,aj,aa,y);
1390 #else
1391     for (i=0; i<m; i++) {
1392       n           = ii[i+1] - ii[i];
1393       aj          = a->j + ii[i];
1394       aa          = a->a + ii[i];
1395       sum         = 0.0;
1396       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1397       y[i] = sum;
1398     }
1399 #endif
1400   }
1401   ierr = PetscLogFlops(2.0*a->nz - a->nonzerorowcnt);CHKERRQ(ierr);
1402   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1403   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1404   PetscFunctionReturn(0);
1405 }
1406 
1407 PetscErrorCode MatMultMax_SeqAIJ(Mat A,Vec xx,Vec yy)
1408 {
1409   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1410   PetscScalar       *y;
1411   const PetscScalar *x;
1412   const MatScalar   *aa;
1413   PetscErrorCode    ierr;
1414   PetscInt          m=A->rmap->n;
1415   const PetscInt    *aj,*ii,*ridx=NULL;
1416   PetscInt          n,i,nonzerorow=0;
1417   PetscScalar       sum;
1418   PetscBool         usecprow=a->compressedrow.use;
1419 
1420 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1421 #pragma disjoint(*x,*y,*aa)
1422 #endif
1423 
1424   PetscFunctionBegin;
1425   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1426   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1427   if (usecprow) { /* use compressed row format */
1428     m    = a->compressedrow.nrows;
1429     ii   = a->compressedrow.i;
1430     ridx = a->compressedrow.rindex;
1431     for (i=0; i<m; i++) {
1432       n           = ii[i+1] - ii[i];
1433       aj          = a->j + ii[i];
1434       aa          = a->a + ii[i];
1435       sum         = 0.0;
1436       nonzerorow += (n>0);
1437       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1438       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1439       y[*ridx++] = sum;
1440     }
1441   } else { /* do not use compressed row format */
1442     ii = a->i;
1443     for (i=0; i<m; i++) {
1444       n           = ii[i+1] - ii[i];
1445       aj          = a->j + ii[i];
1446       aa          = a->a + ii[i];
1447       sum         = 0.0;
1448       nonzerorow += (n>0);
1449       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1450       y[i] = sum;
1451     }
1452   }
1453   ierr = PetscLogFlops(2.0*a->nz - nonzerorow);CHKERRQ(ierr);
1454   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1455   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1456   PetscFunctionReturn(0);
1457 }
1458 
1459 PetscErrorCode MatMultAddMax_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1460 {
1461   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1462   PetscScalar       *y,*z;
1463   const PetscScalar *x;
1464   const MatScalar   *aa;
1465   PetscErrorCode    ierr;
1466   PetscInt          m = A->rmap->n,*aj,*ii;
1467   PetscInt          n,i,*ridx=NULL;
1468   PetscScalar       sum;
1469   PetscBool         usecprow=a->compressedrow.use;
1470 
1471   PetscFunctionBegin;
1472   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1473   ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1474   if (usecprow) { /* use compressed row format */
1475     if (zz != yy) {
1476       ierr = PetscArraycpy(z,y,m);CHKERRQ(ierr);
1477     }
1478     m    = a->compressedrow.nrows;
1479     ii   = a->compressedrow.i;
1480     ridx = a->compressedrow.rindex;
1481     for (i=0; i<m; i++) {
1482       n   = ii[i+1] - ii[i];
1483       aj  = a->j + ii[i];
1484       aa  = a->a + ii[i];
1485       sum = y[*ridx];
1486       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1487       z[*ridx++] = sum;
1488     }
1489   } else { /* do not use compressed row format */
1490     ii = a->i;
1491     for (i=0; i<m; i++) {
1492       n   = ii[i+1] - ii[i];
1493       aj  = a->j + ii[i];
1494       aa  = a->a + ii[i];
1495       sum = y[i];
1496       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1497       z[i] = sum;
1498     }
1499   }
1500   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1501   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1502   ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1503   PetscFunctionReturn(0);
1504 }
1505 
1506 #include <../src/mat/impls/aij/seq/ftn-kernels/fmultadd.h>
1507 PetscErrorCode MatMultAdd_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1508 {
1509   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1510   PetscScalar       *y,*z;
1511   const PetscScalar *x;
1512   const MatScalar   *aa;
1513   PetscErrorCode    ierr;
1514   const PetscInt    *aj,*ii,*ridx=NULL;
1515   PetscInt          m = A->rmap->n,n,i;
1516   PetscScalar       sum;
1517   PetscBool         usecprow=a->compressedrow.use;
1518 
1519   PetscFunctionBegin;
1520   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1521   ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1522   if (usecprow) { /* use compressed row format */
1523     if (zz != yy) {
1524       ierr = PetscArraycpy(z,y,m);CHKERRQ(ierr);
1525     }
1526     m    = a->compressedrow.nrows;
1527     ii   = a->compressedrow.i;
1528     ridx = a->compressedrow.rindex;
1529     for (i=0; i<m; i++) {
1530       n   = ii[i+1] - ii[i];
1531       aj  = a->j + ii[i];
1532       aa  = a->a + ii[i];
1533       sum = y[*ridx];
1534       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1535       z[*ridx++] = sum;
1536     }
1537   } else { /* do not use compressed row format */
1538     ii = a->i;
1539 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJ)
1540     aj = a->j;
1541     aa = a->a;
1542     fortranmultaddaij_(&m,x,ii,aj,aa,y,z);
1543 #else
1544     for (i=0; i<m; i++) {
1545       n   = ii[i+1] - ii[i];
1546       aj  = a->j + ii[i];
1547       aa  = a->a + ii[i];
1548       sum = y[i];
1549       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1550       z[i] = sum;
1551     }
1552 #endif
1553   }
1554   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1555   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1556   ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1557   PetscFunctionReturn(0);
1558 }
1559 
1560 /*
1561      Adds diagonal pointers to sparse matrix structure.
1562 */
1563 PetscErrorCode MatMarkDiagonal_SeqAIJ(Mat A)
1564 {
1565   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1566   PetscErrorCode ierr;
1567   PetscInt       i,j,m = A->rmap->n;
1568 
1569   PetscFunctionBegin;
1570   if (!a->diag) {
1571     ierr = PetscMalloc1(m,&a->diag);CHKERRQ(ierr);
1572     ierr = PetscLogObjectMemory((PetscObject)A, m*sizeof(PetscInt));CHKERRQ(ierr);
1573   }
1574   for (i=0; i<A->rmap->n; i++) {
1575     a->diag[i] = a->i[i+1];
1576     for (j=a->i[i]; j<a->i[i+1]; j++) {
1577       if (a->j[j] == i) {
1578         a->diag[i] = j;
1579         break;
1580       }
1581     }
1582   }
1583   PetscFunctionReturn(0);
1584 }
1585 
1586 PetscErrorCode MatShift_SeqAIJ(Mat A,PetscScalar v)
1587 {
1588   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1589   const PetscInt    *diag = (const PetscInt*)a->diag;
1590   const PetscInt    *ii = (const PetscInt*) a->i;
1591   PetscInt          i,*mdiag = NULL;
1592   PetscErrorCode    ierr;
1593   PetscInt          cnt = 0; /* how many diagonals are missing */
1594 
1595   PetscFunctionBegin;
1596   if (!A->preallocated || !a->nz) {
1597     ierr = MatSeqAIJSetPreallocation(A,1,NULL);CHKERRQ(ierr);
1598     ierr = MatShift_Basic(A,v);CHKERRQ(ierr);
1599     PetscFunctionReturn(0);
1600   }
1601 
1602   if (a->diagonaldense) {
1603     cnt = 0;
1604   } else {
1605     ierr = PetscCalloc1(A->rmap->n,&mdiag);CHKERRQ(ierr);
1606     for (i=0; i<A->rmap->n; i++) {
1607       if (diag[i] >= ii[i+1]) {
1608         cnt++;
1609         mdiag[i] = 1;
1610       }
1611     }
1612   }
1613   if (!cnt) {
1614     ierr = MatShift_Basic(A,v);CHKERRQ(ierr);
1615   } else {
1616     PetscScalar *olda = a->a;  /* preserve pointers to current matrix nonzeros structure and values */
1617     PetscInt    *oldj = a->j, *oldi = a->i;
1618     PetscBool   singlemalloc = a->singlemalloc,free_a = a->free_a,free_ij = a->free_ij;
1619 
1620     a->a = NULL;
1621     a->j = NULL;
1622     a->i = NULL;
1623     /* increase the values in imax for each row where a diagonal is being inserted then reallocate the matrix data structures */
1624     for (i=0; i<A->rmap->n; i++) {
1625       a->imax[i] += mdiag[i];
1626       a->imax[i] = PetscMin(a->imax[i],A->cmap->n);
1627     }
1628     ierr = MatSeqAIJSetPreallocation_SeqAIJ(A,0,a->imax);CHKERRQ(ierr);
1629 
1630     /* copy old values into new matrix data structure */
1631     for (i=0; i<A->rmap->n; i++) {
1632       ierr = MatSetValues(A,1,&i,a->imax[i] - mdiag[i],&oldj[oldi[i]],&olda[oldi[i]],ADD_VALUES);CHKERRQ(ierr);
1633       if (i < A->cmap->n) {
1634         ierr = MatSetValue(A,i,i,v,ADD_VALUES);CHKERRQ(ierr);
1635       }
1636     }
1637     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1638     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1639     if (singlemalloc) {
1640       ierr = PetscFree3(olda,oldj,oldi);CHKERRQ(ierr);
1641     } else {
1642       if (free_a)  {ierr = PetscFree(olda);CHKERRQ(ierr);}
1643       if (free_ij) {ierr = PetscFree(oldj);CHKERRQ(ierr);}
1644       if (free_ij) {ierr = PetscFree(oldi);CHKERRQ(ierr);}
1645     }
1646   }
1647   ierr = PetscFree(mdiag);CHKERRQ(ierr);
1648   a->diagonaldense = PETSC_TRUE;
1649   PetscFunctionReturn(0);
1650 }
1651 
1652 /*
1653      Checks for missing diagonals
1654 */
1655 PetscErrorCode MatMissingDiagonal_SeqAIJ(Mat A,PetscBool  *missing,PetscInt *d)
1656 {
1657   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1658   PetscInt       *diag,*ii = a->i,i;
1659   PetscErrorCode ierr;
1660 
1661   PetscFunctionBegin;
1662   *missing = PETSC_FALSE;
1663   if (A->rmap->n > 0 && !ii) {
1664     *missing = PETSC_TRUE;
1665     if (d) *d = 0;
1666     ierr = PetscInfo(A,"Matrix has no entries therefore is missing diagonal\n");CHKERRQ(ierr);
1667   } else {
1668     PetscInt n;
1669     n = PetscMin(A->rmap->n, A->cmap->n);
1670     diag = a->diag;
1671     for (i=0; i<n; i++) {
1672       if (diag[i] >= ii[i+1]) {
1673         *missing = PETSC_TRUE;
1674         if (d) *d = i;
1675         ierr = PetscInfo1(A,"Matrix is missing diagonal number %D\n",i);CHKERRQ(ierr);
1676         break;
1677       }
1678     }
1679   }
1680   PetscFunctionReturn(0);
1681 }
1682 
1683 #include <petscblaslapack.h>
1684 #include <petsc/private/kernels/blockinvert.h>
1685 
1686 /*
1687     Note that values is allocated externally by the PC and then passed into this routine
1688 */
1689 PetscErrorCode MatInvertVariableBlockDiagonal_SeqAIJ(Mat A,PetscInt nblocks,const PetscInt *bsizes,PetscScalar *diag)
1690 {
1691   PetscErrorCode  ierr;
1692   PetscInt        n = A->rmap->n, i, ncnt = 0, *indx,j,bsizemax = 0,*v_pivots;
1693   PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;
1694   const PetscReal shift = 0.0;
1695   PetscInt        ipvt[5];
1696   PetscScalar     work[25],*v_work;
1697 
1698   PetscFunctionBegin;
1699   allowzeropivot = PetscNot(A->erroriffailure);
1700   for (i=0; i<nblocks; i++) ncnt += bsizes[i];
1701   if (ncnt != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Total blocksizes %D doesn't match number matrix rows %D",ncnt,n);
1702   for (i=0; i<nblocks; i++) {
1703     bsizemax = PetscMax(bsizemax,bsizes[i]);
1704   }
1705   ierr = PetscMalloc1(bsizemax,&indx);CHKERRQ(ierr);
1706   if (bsizemax > 7) {
1707     ierr = PetscMalloc2(bsizemax,&v_work,bsizemax,&v_pivots);CHKERRQ(ierr);
1708   }
1709   ncnt = 0;
1710   for (i=0; i<nblocks; i++) {
1711     for (j=0; j<bsizes[i]; j++) indx[j] = ncnt+j;
1712     ierr    = MatGetValues(A,bsizes[i],indx,bsizes[i],indx,diag);CHKERRQ(ierr);
1713     switch (bsizes[i]) {
1714     case 1:
1715       *diag = 1.0/(*diag);
1716       break;
1717     case 2:
1718       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1719       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1720       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
1721       break;
1722     case 3:
1723       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1724       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1725       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
1726       break;
1727     case 4:
1728       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1729       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1730       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
1731       break;
1732     case 5:
1733       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1734       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1735       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
1736       break;
1737     case 6:
1738       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1739       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1740       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
1741       break;
1742     case 7:
1743       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1744       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1745       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
1746       break;
1747     default:
1748       ierr  = PetscKernel_A_gets_inverse_A(bsizes[i],diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1749       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1750       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bsizes[i]);CHKERRQ(ierr);
1751     }
1752     ncnt   += bsizes[i];
1753     diag += bsizes[i]*bsizes[i];
1754   }
1755   if (bsizemax > 7) {
1756     ierr = PetscFree2(v_work,v_pivots);CHKERRQ(ierr);
1757   }
1758   ierr = PetscFree(indx);CHKERRQ(ierr);
1759   PetscFunctionReturn(0);
1760 }
1761 
1762 /*
1763    Negative shift indicates do not generate an error if there is a zero diagonal, just invert it anyways
1764 */
1765 PetscErrorCode  MatInvertDiagonal_SeqAIJ(Mat A,PetscScalar omega,PetscScalar fshift)
1766 {
1767   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
1768   PetscErrorCode ierr;
1769   PetscInt       i,*diag,m = A->rmap->n;
1770   MatScalar      *v = a->a;
1771   PetscScalar    *idiag,*mdiag;
1772 
1773   PetscFunctionBegin;
1774   if (a->idiagvalid) PetscFunctionReturn(0);
1775   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1776   diag = a->diag;
1777   if (!a->idiag) {
1778     ierr = PetscMalloc3(m,&a->idiag,m,&a->mdiag,m,&a->ssor_work);CHKERRQ(ierr);
1779     ierr = PetscLogObjectMemory((PetscObject)A, 3*m*sizeof(PetscScalar));CHKERRQ(ierr);
1780     v    = a->a;
1781   }
1782   mdiag = a->mdiag;
1783   idiag = a->idiag;
1784 
1785   if (omega == 1.0 && PetscRealPart(fshift) <= 0.0) {
1786     for (i=0; i<m; i++) {
1787       mdiag[i] = v[diag[i]];
1788       if (!PetscAbsScalar(mdiag[i])) { /* zero diagonal */
1789         if (PetscRealPart(fshift)) {
1790           ierr = PetscInfo1(A,"Zero diagonal on row %D\n",i);CHKERRQ(ierr);
1791           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1792           A->factorerror_zeropivot_value = 0.0;
1793           A->factorerror_zeropivot_row   = i;
1794         } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Zero diagonal on row %D",i);
1795       }
1796       idiag[i] = 1.0/v[diag[i]];
1797     }
1798     ierr = PetscLogFlops(m);CHKERRQ(ierr);
1799   } else {
1800     for (i=0; i<m; i++) {
1801       mdiag[i] = v[diag[i]];
1802       idiag[i] = omega/(fshift + v[diag[i]]);
1803     }
1804     ierr = PetscLogFlops(2.0*m);CHKERRQ(ierr);
1805   }
1806   a->idiagvalid = PETSC_TRUE;
1807   PetscFunctionReturn(0);
1808 }
1809 
1810 #include <../src/mat/impls/aij/seq/ftn-kernels/frelax.h>
1811 PetscErrorCode MatSOR_SeqAIJ(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1812 {
1813   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1814   PetscScalar       *x,d,sum,*t,scale;
1815   const MatScalar   *v,*idiag=0,*mdiag;
1816   const PetscScalar *b, *bs,*xb, *ts;
1817   PetscErrorCode    ierr;
1818   PetscInt          n,m = A->rmap->n,i;
1819   const PetscInt    *idx,*diag;
1820 
1821   PetscFunctionBegin;
1822   its = its*lits;
1823 
1824   if (fshift != a->fshift || omega != a->omega) a->idiagvalid = PETSC_FALSE; /* must recompute idiag[] */
1825   if (!a->idiagvalid) {ierr = MatInvertDiagonal_SeqAIJ(A,omega,fshift);CHKERRQ(ierr);}
1826   a->fshift = fshift;
1827   a->omega  = omega;
1828 
1829   diag  = a->diag;
1830   t     = a->ssor_work;
1831   idiag = a->idiag;
1832   mdiag = a->mdiag;
1833 
1834   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1835   ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
1836   /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
1837   if (flag == SOR_APPLY_UPPER) {
1838     /* apply (U + D/omega) to the vector */
1839     bs = b;
1840     for (i=0; i<m; i++) {
1841       d   = fshift + mdiag[i];
1842       n   = a->i[i+1] - diag[i] - 1;
1843       idx = a->j + diag[i] + 1;
1844       v   = a->a + diag[i] + 1;
1845       sum = b[i]*d/omega;
1846       PetscSparseDensePlusDot(sum,bs,v,idx,n);
1847       x[i] = sum;
1848     }
1849     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1850     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1851     ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1852     PetscFunctionReturn(0);
1853   }
1854 
1855   if (flag == SOR_APPLY_LOWER) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SOR_APPLY_LOWER is not implemented");
1856   else if (flag & SOR_EISENSTAT) {
1857     /* Let  A = L + U + D; where L is lower triangular,
1858     U is upper triangular, E = D/omega; This routine applies
1859 
1860             (L + E)^{-1} A (U + E)^{-1}
1861 
1862     to a vector efficiently using Eisenstat's trick.
1863     */
1864     scale = (2.0/omega) - 1.0;
1865 
1866     /*  x = (E + U)^{-1} b */
1867     for (i=m-1; i>=0; i--) {
1868       n   = a->i[i+1] - diag[i] - 1;
1869       idx = a->j + diag[i] + 1;
1870       v   = a->a + diag[i] + 1;
1871       sum = b[i];
1872       PetscSparseDenseMinusDot(sum,x,v,idx,n);
1873       x[i] = sum*idiag[i];
1874     }
1875 
1876     /*  t = b - (2*E - D)x */
1877     v = a->a;
1878     for (i=0; i<m; i++) t[i] = b[i] - scale*(v[*diag++])*x[i];
1879 
1880     /*  t = (E + L)^{-1}t */
1881     ts   = t;
1882     diag = a->diag;
1883     for (i=0; i<m; i++) {
1884       n   = diag[i] - a->i[i];
1885       idx = a->j + a->i[i];
1886       v   = a->a + a->i[i];
1887       sum = t[i];
1888       PetscSparseDenseMinusDot(sum,ts,v,idx,n);
1889       t[i] = sum*idiag[i];
1890       /*  x = x + t */
1891       x[i] += t[i];
1892     }
1893 
1894     ierr = PetscLogFlops(6.0*m-1 + 2.0*a->nz);CHKERRQ(ierr);
1895     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1896     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1897     PetscFunctionReturn(0);
1898   }
1899   if (flag & SOR_ZERO_INITIAL_GUESS) {
1900     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1901       for (i=0; i<m; i++) {
1902         n   = diag[i] - a->i[i];
1903         idx = a->j + a->i[i];
1904         v   = a->a + a->i[i];
1905         sum = b[i];
1906         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1907         t[i] = sum;
1908         x[i] = sum*idiag[i];
1909       }
1910       xb   = t;
1911       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1912     } else xb = b;
1913     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1914       for (i=m-1; i>=0; i--) {
1915         n   = a->i[i+1] - diag[i] - 1;
1916         idx = a->j + diag[i] + 1;
1917         v   = a->a + diag[i] + 1;
1918         sum = xb[i];
1919         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1920         if (xb == b) {
1921           x[i] = sum*idiag[i];
1922         } else {
1923           x[i] = (1-omega)*x[i] + sum*idiag[i];  /* omega in idiag */
1924         }
1925       }
1926       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
1927     }
1928     its--;
1929   }
1930   while (its--) {
1931     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1932       for (i=0; i<m; i++) {
1933         /* lower */
1934         n   = diag[i] - a->i[i];
1935         idx = a->j + a->i[i];
1936         v   = a->a + a->i[i];
1937         sum = b[i];
1938         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1939         t[i] = sum;             /* save application of the lower-triangular part */
1940         /* upper */
1941         n   = a->i[i+1] - diag[i] - 1;
1942         idx = a->j + diag[i] + 1;
1943         v   = a->a + diag[i] + 1;
1944         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1945         x[i] = (1. - omega)*x[i] + sum*idiag[i]; /* omega in idiag */
1946       }
1947       xb   = t;
1948       ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1949     } else xb = b;
1950     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1951       for (i=m-1; i>=0; i--) {
1952         sum = xb[i];
1953         if (xb == b) {
1954           /* whole matrix (no checkpointing available) */
1955           n   = a->i[i+1] - a->i[i];
1956           idx = a->j + a->i[i];
1957           v   = a->a + a->i[i];
1958           PetscSparseDenseMinusDot(sum,x,v,idx,n);
1959           x[i] = (1. - omega)*x[i] + (sum + mdiag[i]*x[i])*idiag[i];
1960         } else { /* lower-triangular part has been saved, so only apply upper-triangular */
1961           n   = a->i[i+1] - diag[i] - 1;
1962           idx = a->j + diag[i] + 1;
1963           v   = a->a + diag[i] + 1;
1964           PetscSparseDenseMinusDot(sum,x,v,idx,n);
1965           x[i] = (1. - omega)*x[i] + sum*idiag[i];  /* omega in idiag */
1966         }
1967       }
1968       if (xb == b) {
1969         ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1970       } else {
1971         ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
1972       }
1973     }
1974   }
1975   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1976   ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1977   PetscFunctionReturn(0);
1978 }
1979 
1980 
1981 PetscErrorCode MatGetInfo_SeqAIJ(Mat A,MatInfoType flag,MatInfo *info)
1982 {
1983   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1984 
1985   PetscFunctionBegin;
1986   info->block_size   = 1.0;
1987   info->nz_allocated = (double)a->maxnz;
1988   info->nz_used      = (double)a->nz;
1989   info->nz_unneeded  = (double)(a->maxnz - a->nz);
1990   info->assemblies   = (double)A->num_ass;
1991   info->mallocs      = (double)A->info.mallocs;
1992   info->memory       = ((PetscObject)A)->mem;
1993   if (A->factortype) {
1994     info->fill_ratio_given  = A->info.fill_ratio_given;
1995     info->fill_ratio_needed = A->info.fill_ratio_needed;
1996     info->factor_mallocs    = A->info.factor_mallocs;
1997   } else {
1998     info->fill_ratio_given  = 0;
1999     info->fill_ratio_needed = 0;
2000     info->factor_mallocs    = 0;
2001   }
2002   PetscFunctionReturn(0);
2003 }
2004 
2005 PetscErrorCode MatZeroRows_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
2006 {
2007   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2008   PetscInt          i,m = A->rmap->n - 1;
2009   PetscErrorCode    ierr;
2010   const PetscScalar *xx;
2011   PetscScalar       *bb;
2012   PetscInt          d = 0;
2013 
2014   PetscFunctionBegin;
2015   if (x && b) {
2016     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
2017     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
2018     for (i=0; i<N; i++) {
2019       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2020       if (rows[i] >= A->cmap->n) continue;
2021       bb[rows[i]] = diag*xx[rows[i]];
2022     }
2023     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
2024     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
2025   }
2026 
2027   if (a->keepnonzeropattern) {
2028     for (i=0; i<N; i++) {
2029       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2030       ierr = PetscArrayzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]);CHKERRQ(ierr);
2031     }
2032     if (diag != 0.0) {
2033       for (i=0; i<N; i++) {
2034         d = rows[i];
2035         if (rows[i] >= A->cmap->n) continue;
2036         if (a->diag[d] >= a->i[d+1]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in the zeroed row %D",d);
2037       }
2038       for (i=0; i<N; i++) {
2039         if (rows[i] >= A->cmap->n) continue;
2040         a->a[a->diag[rows[i]]] = diag;
2041       }
2042     }
2043   } else {
2044     if (diag != 0.0) {
2045       for (i=0; i<N; i++) {
2046         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2047         if (a->ilen[rows[i]] > 0) {
2048 	  if (rows[i] >= A->cmap->n) {
2049             a->ilen[rows[i]] = 0;
2050           } else {
2051             a->ilen[rows[i]]    = 1;
2052             a->a[a->i[rows[i]]] = diag;
2053             a->j[a->i[rows[i]]] = rows[i];
2054           }
2055         } else if (rows[i] < A->cmap->n) { /* in case row was completely empty */
2056           ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES);CHKERRQ(ierr);
2057         }
2058       }
2059     } else {
2060       for (i=0; i<N; i++) {
2061         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2062         a->ilen[rows[i]] = 0;
2063       }
2064     }
2065     A->nonzerostate++;
2066   }
2067 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
2068   if (A->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED) A->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
2069 #endif
2070   ierr = (*A->ops->assemblyend)(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2071   PetscFunctionReturn(0);
2072 }
2073 
2074 PetscErrorCode MatZeroRowsColumns_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
2075 {
2076   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2077   PetscInt          i,j,m = A->rmap->n - 1,d = 0;
2078   PetscErrorCode    ierr;
2079   PetscBool         missing,*zeroed,vecs = PETSC_FALSE;
2080   const PetscScalar *xx;
2081   PetscScalar       *bb;
2082 
2083   PetscFunctionBegin;
2084   if (x && b) {
2085     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
2086     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
2087     vecs = PETSC_TRUE;
2088   }
2089   ierr = PetscCalloc1(A->rmap->n,&zeroed);CHKERRQ(ierr);
2090   for (i=0; i<N; i++) {
2091     if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2092     ierr = PetscArrayzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]);CHKERRQ(ierr);
2093 
2094     zeroed[rows[i]] = PETSC_TRUE;
2095   }
2096   for (i=0; i<A->rmap->n; i++) {
2097     if (!zeroed[i]) {
2098       for (j=a->i[i]; j<a->i[i+1]; j++) {
2099         if (a->j[j] < A->rmap->n && zeroed[a->j[j]]) {
2100           if (vecs) bb[i] -= a->a[j]*xx[a->j[j]];
2101           a->a[j] = 0.0;
2102         }
2103       }
2104     } else if (vecs && i < A->cmap->N) bb[i] = diag*xx[i];
2105   }
2106   if (x && b) {
2107     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
2108     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
2109   }
2110   ierr = PetscFree(zeroed);CHKERRQ(ierr);
2111   if (diag != 0.0) {
2112     ierr = MatMissingDiagonal_SeqAIJ(A,&missing,&d);CHKERRQ(ierr);
2113     if (missing) {
2114       for (i=0; i<N; i++) {
2115         if (rows[i] >= A->cmap->N) continue;
2116         if (a->nonew && rows[i] >= d) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in row %D (%D)",d,rows[i]);
2117         ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES);CHKERRQ(ierr);
2118       }
2119     } else {
2120       for (i=0; i<N; i++) {
2121         a->a[a->diag[rows[i]]] = diag;
2122       }
2123     }
2124   }
2125 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
2126   if (A->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED) A->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
2127 #endif
2128   ierr = (*A->ops->assemblyend)(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2129   PetscFunctionReturn(0);
2130 }
2131 
2132 PetscErrorCode MatGetRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
2133 {
2134   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2135   PetscInt   *itmp;
2136 
2137   PetscFunctionBegin;
2138   if (row < 0 || row >= A->rmap->n) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range",row);
2139 
2140   *nz = a->i[row+1] - a->i[row];
2141   if (v) *v = a->a + a->i[row];
2142   if (idx) {
2143     itmp = a->j + a->i[row];
2144     if (*nz) *idx = itmp;
2145     else *idx = 0;
2146   }
2147   PetscFunctionReturn(0);
2148 }
2149 
2150 /* remove this function? */
2151 PetscErrorCode MatRestoreRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
2152 {
2153   PetscFunctionBegin;
2154   PetscFunctionReturn(0);
2155 }
2156 
2157 PetscErrorCode MatNorm_SeqAIJ(Mat A,NormType type,PetscReal *nrm)
2158 {
2159   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
2160   MatScalar      *v  = a->a;
2161   PetscReal      sum = 0.0;
2162   PetscErrorCode ierr;
2163   PetscInt       i,j;
2164 
2165   PetscFunctionBegin;
2166   if (type == NORM_FROBENIUS) {
2167 #if defined(PETSC_USE_REAL___FP16)
2168     PetscBLASInt one = 1,nz = a->nz;
2169     *nrm = BLASnrm2_(&nz,v,&one);
2170 #else
2171     for (i=0; i<a->nz; i++) {
2172       sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
2173     }
2174     *nrm = PetscSqrtReal(sum);
2175 #endif
2176     ierr = PetscLogFlops(2*a->nz);CHKERRQ(ierr);
2177   } else if (type == NORM_1) {
2178     PetscReal *tmp;
2179     PetscInt  *jj = a->j;
2180     ierr = PetscCalloc1(A->cmap->n+1,&tmp);CHKERRQ(ierr);
2181     *nrm = 0.0;
2182     for (j=0; j<a->nz; j++) {
2183       tmp[*jj++] += PetscAbsScalar(*v);  v++;
2184     }
2185     for (j=0; j<A->cmap->n; j++) {
2186       if (tmp[j] > *nrm) *nrm = tmp[j];
2187     }
2188     ierr = PetscFree(tmp);CHKERRQ(ierr);
2189     ierr = PetscLogFlops(PetscMax(a->nz-1,0));CHKERRQ(ierr);
2190   } else if (type == NORM_INFINITY) {
2191     *nrm = 0.0;
2192     for (j=0; j<A->rmap->n; j++) {
2193       v   = a->a + a->i[j];
2194       sum = 0.0;
2195       for (i=0; i<a->i[j+1]-a->i[j]; i++) {
2196         sum += PetscAbsScalar(*v); v++;
2197       }
2198       if (sum > *nrm) *nrm = sum;
2199     }
2200     ierr = PetscLogFlops(PetscMax(a->nz-1,0));CHKERRQ(ierr);
2201   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for two norm");
2202   PetscFunctionReturn(0);
2203 }
2204 
2205 /* Merged from MatGetSymbolicTranspose_SeqAIJ() - replace MatGetSymbolicTranspose_SeqAIJ()? */
2206 PetscErrorCode MatTransposeSymbolic_SeqAIJ(Mat A,Mat *B)
2207 {
2208   PetscErrorCode ierr;
2209   PetscInt       i,j,anzj;
2210   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b;
2211   PetscInt       an=A->cmap->N,am=A->rmap->N;
2212   PetscInt       *ati,*atj,*atfill,*ai=a->i,*aj=a->j;
2213 
2214   PetscFunctionBegin;
2215   /* Allocate space for symbolic transpose info and work array */
2216   ierr = PetscCalloc1(an+1,&ati);CHKERRQ(ierr);
2217   ierr = PetscMalloc1(ai[am],&atj);CHKERRQ(ierr);
2218   ierr = PetscMalloc1(an,&atfill);CHKERRQ(ierr);
2219 
2220   /* Walk through aj and count ## of non-zeros in each row of A^T. */
2221   /* Note: offset by 1 for fast conversion into csr format. */
2222   for (i=0;i<ai[am];i++) ati[aj[i]+1] += 1;
2223   /* Form ati for csr format of A^T. */
2224   for (i=0;i<an;i++) ati[i+1] += ati[i];
2225 
2226   /* Copy ati into atfill so we have locations of the next free space in atj */
2227   ierr = PetscArraycpy(atfill,ati,an);CHKERRQ(ierr);
2228 
2229   /* Walk through A row-wise and mark nonzero entries of A^T. */
2230   for (i=0;i<am;i++) {
2231     anzj = ai[i+1] - ai[i];
2232     for (j=0;j<anzj;j++) {
2233       atj[atfill[*aj]] = i;
2234       atfill[*aj++]   += 1;
2235     }
2236   }
2237 
2238   /* Clean up temporary space and complete requests. */
2239   ierr = PetscFree(atfill);CHKERRQ(ierr);
2240   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),an,am,ati,atj,NULL,B);CHKERRQ(ierr);
2241   ierr = MatSetBlockSizes(*B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2242   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2243 
2244   b          = (Mat_SeqAIJ*)((*B)->data);
2245   b->free_a  = PETSC_FALSE;
2246   b->free_ij = PETSC_TRUE;
2247   b->nonew   = 0;
2248   PetscFunctionReturn(0);
2249 }
2250 
2251 PetscErrorCode  MatIsTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2252 {
2253   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) B->data;
2254   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2255   MatScalar      *va,*vb;
2256   PetscErrorCode ierr;
2257   PetscInt       ma,na,mb,nb, i;
2258 
2259   PetscFunctionBegin;
2260   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2261   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2262   if (ma!=nb || na!=mb) {
2263     *f = PETSC_FALSE;
2264     PetscFunctionReturn(0);
2265   }
2266   aii  = aij->i; bii = bij->i;
2267   adx  = aij->j; bdx = bij->j;
2268   va   = aij->a; vb = bij->a;
2269   ierr = PetscMalloc1(ma,&aptr);CHKERRQ(ierr);
2270   ierr = PetscMalloc1(mb,&bptr);CHKERRQ(ierr);
2271   for (i=0; i<ma; i++) aptr[i] = aii[i];
2272   for (i=0; i<mb; i++) bptr[i] = bii[i];
2273 
2274   *f = PETSC_TRUE;
2275   for (i=0; i<ma; i++) {
2276     while (aptr[i]<aii[i+1]) {
2277       PetscInt    idc,idr;
2278       PetscScalar vc,vr;
2279       /* column/row index/value */
2280       idc = adx[aptr[i]];
2281       idr = bdx[bptr[idc]];
2282       vc  = va[aptr[i]];
2283       vr  = vb[bptr[idc]];
2284       if (i!=idr || PetscAbsScalar(vc-vr) > tol) {
2285         *f = PETSC_FALSE;
2286         goto done;
2287       } else {
2288         aptr[i]++;
2289         if (B || i!=idc) bptr[idc]++;
2290       }
2291     }
2292   }
2293 done:
2294   ierr = PetscFree(aptr);CHKERRQ(ierr);
2295   ierr = PetscFree(bptr);CHKERRQ(ierr);
2296   PetscFunctionReturn(0);
2297 }
2298 
2299 PetscErrorCode  MatIsHermitianTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2300 {
2301   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) B->data;
2302   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2303   MatScalar      *va,*vb;
2304   PetscErrorCode ierr;
2305   PetscInt       ma,na,mb,nb, i;
2306 
2307   PetscFunctionBegin;
2308   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2309   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2310   if (ma!=nb || na!=mb) {
2311     *f = PETSC_FALSE;
2312     PetscFunctionReturn(0);
2313   }
2314   aii  = aij->i; bii = bij->i;
2315   adx  = aij->j; bdx = bij->j;
2316   va   = aij->a; vb = bij->a;
2317   ierr = PetscMalloc1(ma,&aptr);CHKERRQ(ierr);
2318   ierr = PetscMalloc1(mb,&bptr);CHKERRQ(ierr);
2319   for (i=0; i<ma; i++) aptr[i] = aii[i];
2320   for (i=0; i<mb; i++) bptr[i] = bii[i];
2321 
2322   *f = PETSC_TRUE;
2323   for (i=0; i<ma; i++) {
2324     while (aptr[i]<aii[i+1]) {
2325       PetscInt    idc,idr;
2326       PetscScalar vc,vr;
2327       /* column/row index/value */
2328       idc = adx[aptr[i]];
2329       idr = bdx[bptr[idc]];
2330       vc  = va[aptr[i]];
2331       vr  = vb[bptr[idc]];
2332       if (i!=idr || PetscAbsScalar(vc-PetscConj(vr)) > tol) {
2333         *f = PETSC_FALSE;
2334         goto done;
2335       } else {
2336         aptr[i]++;
2337         if (B || i!=idc) bptr[idc]++;
2338       }
2339     }
2340   }
2341 done:
2342   ierr = PetscFree(aptr);CHKERRQ(ierr);
2343   ierr = PetscFree(bptr);CHKERRQ(ierr);
2344   PetscFunctionReturn(0);
2345 }
2346 
2347 PetscErrorCode MatIsSymmetric_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2348 {
2349   PetscErrorCode ierr;
2350 
2351   PetscFunctionBegin;
2352   ierr = MatIsTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2353   PetscFunctionReturn(0);
2354 }
2355 
2356 PetscErrorCode MatIsHermitian_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2357 {
2358   PetscErrorCode ierr;
2359 
2360   PetscFunctionBegin;
2361   ierr = MatIsHermitianTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2362   PetscFunctionReturn(0);
2363 }
2364 
2365 PetscErrorCode MatDiagonalScale_SeqAIJ(Mat A,Vec ll,Vec rr)
2366 {
2367   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2368   const PetscScalar *l,*r;
2369   PetscScalar       x;
2370   MatScalar         *v;
2371   PetscErrorCode    ierr;
2372   PetscInt          i,j,m = A->rmap->n,n = A->cmap->n,M,nz = a->nz;
2373   const PetscInt    *jj;
2374 
2375   PetscFunctionBegin;
2376   if (ll) {
2377     /* The local size is used so that VecMPI can be passed to this routine
2378        by MatDiagonalScale_MPIAIJ */
2379     ierr = VecGetLocalSize(ll,&m);CHKERRQ(ierr);
2380     if (m != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
2381     ierr = VecGetArrayRead(ll,&l);CHKERRQ(ierr);
2382     v    = a->a;
2383     for (i=0; i<m; i++) {
2384       x = l[i];
2385       M = a->i[i+1] - a->i[i];
2386       for (j=0; j<M; j++) (*v++) *= x;
2387     }
2388     ierr = VecRestoreArrayRead(ll,&l);CHKERRQ(ierr);
2389     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2390   }
2391   if (rr) {
2392     ierr = VecGetLocalSize(rr,&n);CHKERRQ(ierr);
2393     if (n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vector wrong length");
2394     ierr = VecGetArrayRead(rr,&r);CHKERRQ(ierr);
2395     v    = a->a; jj = a->j;
2396     for (i=0; i<nz; i++) (*v++) *= r[*jj++];
2397     ierr = VecRestoreArrayRead(rr,&r);CHKERRQ(ierr);
2398     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2399   }
2400   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
2401 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
2402   if (A->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED) A->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
2403 #endif
2404   PetscFunctionReturn(0);
2405 }
2406 
2407 PetscErrorCode MatCreateSubMatrix_SeqAIJ(Mat A,IS isrow,IS iscol,PetscInt csize,MatReuse scall,Mat *B)
2408 {
2409   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*c;
2410   PetscErrorCode ierr;
2411   PetscInt       *smap,i,k,kstart,kend,oldcols = A->cmap->n,*lens;
2412   PetscInt       row,mat_i,*mat_j,tcol,first,step,*mat_ilen,sum,lensi;
2413   const PetscInt *irow,*icol;
2414   PetscInt       nrows,ncols;
2415   PetscInt       *starts,*j_new,*i_new,*aj = a->j,*ai = a->i,ii,*ailen = a->ilen;
2416   MatScalar      *a_new,*mat_a;
2417   Mat            C;
2418   PetscBool      stride;
2419 
2420   PetscFunctionBegin;
2421 
2422   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
2423   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
2424   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
2425 
2426   ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&stride);CHKERRQ(ierr);
2427   if (stride) {
2428     ierr = ISStrideGetInfo(iscol,&first,&step);CHKERRQ(ierr);
2429   } else {
2430     first = 0;
2431     step  = 0;
2432   }
2433   if (stride && step == 1) {
2434     /* special case of contiguous rows */
2435     ierr = PetscMalloc2(nrows,&lens,nrows,&starts);CHKERRQ(ierr);
2436     /* loop over new rows determining lens and starting points */
2437     for (i=0; i<nrows; i++) {
2438       kstart = ai[irow[i]];
2439       kend   = kstart + ailen[irow[i]];
2440       starts[i] = kstart;
2441       for (k=kstart; k<kend; k++) {
2442         if (aj[k] >= first) {
2443           starts[i] = k;
2444           break;
2445         }
2446       }
2447       sum = 0;
2448       while (k < kend) {
2449         if (aj[k++] >= first+ncols) break;
2450         sum++;
2451       }
2452       lens[i] = sum;
2453     }
2454     /* create submatrix */
2455     if (scall == MAT_REUSE_MATRIX) {
2456       PetscInt n_cols,n_rows;
2457       ierr = MatGetSize(*B,&n_rows,&n_cols);CHKERRQ(ierr);
2458       if (n_rows != nrows || n_cols != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
2459       ierr = MatZeroEntries(*B);CHKERRQ(ierr);
2460       C    = *B;
2461     } else {
2462       PetscInt rbs,cbs;
2463       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2464       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2465       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2466       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2467       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2468       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2469       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2470     }
2471     c = (Mat_SeqAIJ*)C->data;
2472 
2473     /* loop over rows inserting into submatrix */
2474     a_new = c->a;
2475     j_new = c->j;
2476     i_new = c->i;
2477 
2478     for (i=0; i<nrows; i++) {
2479       ii    = starts[i];
2480       lensi = lens[i];
2481       for (k=0; k<lensi; k++) {
2482         *j_new++ = aj[ii+k] - first;
2483       }
2484       ierr       = PetscArraycpy(a_new,a->a + starts[i],lensi);CHKERRQ(ierr);
2485       a_new     += lensi;
2486       i_new[i+1] = i_new[i] + lensi;
2487       c->ilen[i] = lensi;
2488     }
2489     ierr = PetscFree2(lens,starts);CHKERRQ(ierr);
2490   } else {
2491     ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
2492     ierr = PetscCalloc1(oldcols,&smap);CHKERRQ(ierr);
2493     ierr = PetscMalloc1(1+nrows,&lens);CHKERRQ(ierr);
2494     for (i=0; i<ncols; i++) {
2495 #if defined(PETSC_USE_DEBUG)
2496       if (icol[i] >= oldcols) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Requesting column beyond largest column icol[%D] %D <= A->cmap->n %D",i,icol[i],oldcols);
2497 #endif
2498       smap[icol[i]] = i+1;
2499     }
2500 
2501     /* determine lens of each row */
2502     for (i=0; i<nrows; i++) {
2503       kstart  = ai[irow[i]];
2504       kend    = kstart + a->ilen[irow[i]];
2505       lens[i] = 0;
2506       for (k=kstart; k<kend; k++) {
2507         if (smap[aj[k]]) {
2508           lens[i]++;
2509         }
2510       }
2511     }
2512     /* Create and fill new matrix */
2513     if (scall == MAT_REUSE_MATRIX) {
2514       PetscBool equal;
2515 
2516       c = (Mat_SeqAIJ*)((*B)->data);
2517       if ((*B)->rmap->n  != nrows || (*B)->cmap->n != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
2518       ierr = PetscArraycmp(c->ilen,lens,(*B)->rmap->n,&equal);CHKERRQ(ierr);
2519       if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
2520       ierr = PetscArrayzero(c->ilen,(*B)->rmap->n);CHKERRQ(ierr);
2521       C    = *B;
2522     } else {
2523       PetscInt rbs,cbs;
2524       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2525       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2526       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2527       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2528       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2529       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2530       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2531     }
2532     c = (Mat_SeqAIJ*)(C->data);
2533     for (i=0; i<nrows; i++) {
2534       row      = irow[i];
2535       kstart   = ai[row];
2536       kend     = kstart + a->ilen[row];
2537       mat_i    = c->i[i];
2538       mat_j    = c->j + mat_i;
2539       mat_a    = c->a + mat_i;
2540       mat_ilen = c->ilen + i;
2541       for (k=kstart; k<kend; k++) {
2542         if ((tcol=smap[a->j[k]])) {
2543           *mat_j++ = tcol - 1;
2544           *mat_a++ = a->a[k];
2545           (*mat_ilen)++;
2546 
2547         }
2548       }
2549     }
2550     /* Free work space */
2551     ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
2552     ierr = PetscFree(smap);CHKERRQ(ierr);
2553     ierr = PetscFree(lens);CHKERRQ(ierr);
2554     /* sort */
2555     for (i = 0; i < nrows; i++) {
2556       PetscInt ilen;
2557 
2558       mat_i = c->i[i];
2559       mat_j = c->j + mat_i;
2560       mat_a = c->a + mat_i;
2561       ilen  = c->ilen[i];
2562       ierr  = PetscSortIntWithScalarArray(ilen,mat_j,mat_a);CHKERRQ(ierr);
2563     }
2564   }
2565   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2566   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2567 
2568   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
2569   *B   = C;
2570   PetscFunctionReturn(0);
2571 }
2572 
2573 PetscErrorCode  MatGetMultiProcBlock_SeqAIJ(Mat mat,MPI_Comm subComm,MatReuse scall,Mat *subMat)
2574 {
2575   PetscErrorCode ierr;
2576   Mat            B;
2577 
2578   PetscFunctionBegin;
2579   if (scall == MAT_INITIAL_MATRIX) {
2580     ierr    = MatCreate(subComm,&B);CHKERRQ(ierr);
2581     ierr    = MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->n,mat->cmap->n);CHKERRQ(ierr);
2582     ierr    = MatSetBlockSizesFromMats(B,mat,mat);CHKERRQ(ierr);
2583     ierr    = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
2584     ierr    = MatDuplicateNoCreate_SeqAIJ(B,mat,MAT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
2585     *subMat = B;
2586   } else {
2587     ierr = MatCopy_SeqAIJ(mat,*subMat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2588   }
2589   PetscFunctionReturn(0);
2590 }
2591 
2592 PetscErrorCode MatILUFactor_SeqAIJ(Mat inA,IS row,IS col,const MatFactorInfo *info)
2593 {
2594   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)inA->data;
2595   PetscErrorCode ierr;
2596   Mat            outA;
2597   PetscBool      row_identity,col_identity;
2598 
2599   PetscFunctionBegin;
2600   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels=0 supported for in-place ilu");
2601 
2602   ierr = ISIdentity(row,&row_identity);CHKERRQ(ierr);
2603   ierr = ISIdentity(col,&col_identity);CHKERRQ(ierr);
2604 
2605   outA             = inA;
2606   outA->factortype = MAT_FACTOR_LU;
2607   ierr = PetscFree(inA->solvertype);CHKERRQ(ierr);
2608   ierr = PetscStrallocpy(MATSOLVERPETSC,&inA->solvertype);CHKERRQ(ierr);
2609 
2610   ierr = PetscObjectReference((PetscObject)row);CHKERRQ(ierr);
2611   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
2612 
2613   a->row = row;
2614 
2615   ierr = PetscObjectReference((PetscObject)col);CHKERRQ(ierr);
2616   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
2617 
2618   a->col = col;
2619 
2620   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
2621   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
2622   ierr = ISInvertPermutation(col,PETSC_DECIDE,&a->icol);CHKERRQ(ierr);
2623   ierr = PetscLogObjectParent((PetscObject)inA,(PetscObject)a->icol);CHKERRQ(ierr);
2624 
2625   if (!a->solve_work) { /* this matrix may have been factored before */
2626     ierr = PetscMalloc1(inA->rmap->n+1,&a->solve_work);CHKERRQ(ierr);
2627     ierr = PetscLogObjectMemory((PetscObject)inA, (inA->rmap->n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2628   }
2629 
2630   ierr = MatMarkDiagonal_SeqAIJ(inA);CHKERRQ(ierr);
2631   if (row_identity && col_identity) {
2632     ierr = MatLUFactorNumeric_SeqAIJ_inplace(outA,inA,info);CHKERRQ(ierr);
2633   } else {
2634     ierr = MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA,inA,info);CHKERRQ(ierr);
2635   }
2636   PetscFunctionReturn(0);
2637 }
2638 
2639 PetscErrorCode MatScale_SeqAIJ(Mat inA,PetscScalar alpha)
2640 {
2641   Mat_SeqAIJ     *a     = (Mat_SeqAIJ*)inA->data;
2642   PetscScalar    oalpha = alpha;
2643   PetscErrorCode ierr;
2644   PetscBLASInt   one = 1,bnz;
2645 
2646   PetscFunctionBegin;
2647   ierr = PetscBLASIntCast(a->nz,&bnz);CHKERRQ(ierr);
2648   PetscStackCallBLAS("BLASscal",BLASscal_(&bnz,&oalpha,a->a,&one));
2649   ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2650   ierr = MatSeqAIJInvalidateDiagonal(inA);CHKERRQ(ierr);
2651 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
2652   if (inA->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED) inA->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
2653 #endif
2654   PetscFunctionReturn(0);
2655 }
2656 
2657 PetscErrorCode MatDestroySubMatrix_Private(Mat_SubSppt *submatj)
2658 {
2659   PetscErrorCode ierr;
2660   PetscInt       i;
2661 
2662   PetscFunctionBegin;
2663   if (!submatj->id) { /* delete data that are linked only to submats[id=0] */
2664     ierr = PetscFree4(submatj->sbuf1,submatj->ptr,submatj->tmp,submatj->ctr);CHKERRQ(ierr);
2665 
2666     for (i=0; i<submatj->nrqr; ++i) {
2667       ierr = PetscFree(submatj->sbuf2[i]);CHKERRQ(ierr);
2668     }
2669     ierr = PetscFree3(submatj->sbuf2,submatj->req_size,submatj->req_source1);CHKERRQ(ierr);
2670 
2671     if (submatj->rbuf1) {
2672       ierr = PetscFree(submatj->rbuf1[0]);CHKERRQ(ierr);
2673       ierr = PetscFree(submatj->rbuf1);CHKERRQ(ierr);
2674     }
2675 
2676     for (i=0; i<submatj->nrqs; ++i) {
2677       ierr = PetscFree(submatj->rbuf3[i]);CHKERRQ(ierr);
2678     }
2679     ierr = PetscFree3(submatj->req_source2,submatj->rbuf2,submatj->rbuf3);CHKERRQ(ierr);
2680     ierr = PetscFree(submatj->pa);CHKERRQ(ierr);
2681   }
2682 
2683 #if defined(PETSC_USE_CTABLE)
2684   ierr = PetscTableDestroy((PetscTable*)&submatj->rmap);CHKERRQ(ierr);
2685   if (submatj->cmap_loc) {ierr = PetscFree(submatj->cmap_loc);CHKERRQ(ierr);}
2686   ierr = PetscFree(submatj->rmap_loc);CHKERRQ(ierr);
2687 #else
2688   ierr = PetscFree(submatj->rmap);CHKERRQ(ierr);
2689 #endif
2690 
2691   if (!submatj->allcolumns) {
2692 #if defined(PETSC_USE_CTABLE)
2693     ierr = PetscTableDestroy((PetscTable*)&submatj->cmap);CHKERRQ(ierr);
2694 #else
2695     ierr = PetscFree(submatj->cmap);CHKERRQ(ierr);
2696 #endif
2697   }
2698   ierr = PetscFree(submatj->row2proc);CHKERRQ(ierr);
2699 
2700   ierr = PetscFree(submatj);CHKERRQ(ierr);
2701   PetscFunctionReturn(0);
2702 }
2703 
2704 PetscErrorCode MatDestroySubMatrix_SeqAIJ(Mat C)
2705 {
2706   PetscErrorCode ierr;
2707   Mat_SeqAIJ     *c = (Mat_SeqAIJ*)C->data;
2708   Mat_SubSppt    *submatj = c->submatis1;
2709 
2710   PetscFunctionBegin;
2711   ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
2712   ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
2713   PetscFunctionReturn(0);
2714 }
2715 
2716 PetscErrorCode MatDestroySubMatrices_SeqAIJ(PetscInt n,Mat *mat[])
2717 {
2718   PetscErrorCode ierr;
2719   PetscInt       i;
2720   Mat            C;
2721   Mat_SeqAIJ     *c;
2722   Mat_SubSppt    *submatj;
2723 
2724   PetscFunctionBegin;
2725   for (i=0; i<n; i++) {
2726     C       = (*mat)[i];
2727     c       = (Mat_SeqAIJ*)C->data;
2728     submatj = c->submatis1;
2729     if (submatj) {
2730       if (--((PetscObject)C)->refct <= 0) {
2731         ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
2732         ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
2733         ierr = PetscFree(C->defaultvectype);CHKERRQ(ierr);
2734         ierr = PetscLayoutDestroy(&C->rmap);CHKERRQ(ierr);
2735         ierr = PetscLayoutDestroy(&C->cmap);CHKERRQ(ierr);
2736         ierr = PetscHeaderDestroy(&C);CHKERRQ(ierr);
2737       }
2738     } else {
2739       ierr = MatDestroy(&C);CHKERRQ(ierr);
2740     }
2741   }
2742 
2743   /* Destroy Dummy submatrices created for reuse */
2744   ierr = MatDestroySubMatrices_Dummy(n,mat);CHKERRQ(ierr);
2745 
2746   ierr = PetscFree(*mat);CHKERRQ(ierr);
2747   PetscFunctionReturn(0);
2748 }
2749 
2750 PetscErrorCode MatCreateSubMatrices_SeqAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
2751 {
2752   PetscErrorCode ierr;
2753   PetscInt       i;
2754 
2755   PetscFunctionBegin;
2756   if (scall == MAT_INITIAL_MATRIX) {
2757     ierr = PetscCalloc1(n+1,B);CHKERRQ(ierr);
2758   }
2759 
2760   for (i=0; i<n; i++) {
2761     ierr = MatCreateSubMatrix_SeqAIJ(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]);CHKERRQ(ierr);
2762   }
2763   PetscFunctionReturn(0);
2764 }
2765 
2766 PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
2767 {
2768   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2769   PetscErrorCode ierr;
2770   PetscInt       row,i,j,k,l,m,n,*nidx,isz,val;
2771   const PetscInt *idx;
2772   PetscInt       start,end,*ai,*aj;
2773   PetscBT        table;
2774 
2775   PetscFunctionBegin;
2776   m  = A->rmap->n;
2777   ai = a->i;
2778   aj = a->j;
2779 
2780   if (ov < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"illegal negative overlap value used");
2781 
2782   ierr = PetscMalloc1(m+1,&nidx);CHKERRQ(ierr);
2783   ierr = PetscBTCreate(m,&table);CHKERRQ(ierr);
2784 
2785   for (i=0; i<is_max; i++) {
2786     /* Initialize the two local arrays */
2787     isz  = 0;
2788     ierr = PetscBTMemzero(m,table);CHKERRQ(ierr);
2789 
2790     /* Extract the indices, assume there can be duplicate entries */
2791     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
2792     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
2793 
2794     /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2795     for (j=0; j<n; ++j) {
2796       if (!PetscBTLookupSet(table,idx[j])) nidx[isz++] = idx[j];
2797     }
2798     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
2799     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
2800 
2801     k = 0;
2802     for (j=0; j<ov; j++) { /* for each overlap */
2803       n = isz;
2804       for (; k<n; k++) { /* do only those rows in nidx[k], which are not done yet */
2805         row   = nidx[k];
2806         start = ai[row];
2807         end   = ai[row+1];
2808         for (l = start; l<end; l++) {
2809           val = aj[l];
2810           if (!PetscBTLookupSet(table,val)) nidx[isz++] = val;
2811         }
2812       }
2813     }
2814     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz,nidx,PETSC_COPY_VALUES,(is+i));CHKERRQ(ierr);
2815   }
2816   ierr = PetscBTDestroy(&table);CHKERRQ(ierr);
2817   ierr = PetscFree(nidx);CHKERRQ(ierr);
2818   PetscFunctionReturn(0);
2819 }
2820 
2821 /* -------------------------------------------------------------- */
2822 PetscErrorCode MatPermute_SeqAIJ(Mat A,IS rowp,IS colp,Mat *B)
2823 {
2824   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2825   PetscErrorCode ierr;
2826   PetscInt       i,nz = 0,m = A->rmap->n,n = A->cmap->n;
2827   const PetscInt *row,*col;
2828   PetscInt       *cnew,j,*lens;
2829   IS             icolp,irowp;
2830   PetscInt       *cwork = NULL;
2831   PetscScalar    *vwork = NULL;
2832 
2833   PetscFunctionBegin;
2834   ierr = ISInvertPermutation(rowp,PETSC_DECIDE,&irowp);CHKERRQ(ierr);
2835   ierr = ISGetIndices(irowp,&row);CHKERRQ(ierr);
2836   ierr = ISInvertPermutation(colp,PETSC_DECIDE,&icolp);CHKERRQ(ierr);
2837   ierr = ISGetIndices(icolp,&col);CHKERRQ(ierr);
2838 
2839   /* determine lengths of permuted rows */
2840   ierr = PetscMalloc1(m+1,&lens);CHKERRQ(ierr);
2841   for (i=0; i<m; i++) lens[row[i]] = a->i[i+1] - a->i[i];
2842   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
2843   ierr = MatSetSizes(*B,m,n,m,n);CHKERRQ(ierr);
2844   ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
2845   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2846   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*B,0,lens);CHKERRQ(ierr);
2847   ierr = PetscFree(lens);CHKERRQ(ierr);
2848 
2849   ierr = PetscMalloc1(n,&cnew);CHKERRQ(ierr);
2850   for (i=0; i<m; i++) {
2851     ierr = MatGetRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2852     for (j=0; j<nz; j++) cnew[j] = col[cwork[j]];
2853     ierr = MatSetValues_SeqAIJ(*B,1,&row[i],nz,cnew,vwork,INSERT_VALUES);CHKERRQ(ierr);
2854     ierr = MatRestoreRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2855   }
2856   ierr = PetscFree(cnew);CHKERRQ(ierr);
2857 
2858   (*B)->assembled = PETSC_FALSE;
2859 
2860   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2861   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2862   ierr = ISRestoreIndices(irowp,&row);CHKERRQ(ierr);
2863   ierr = ISRestoreIndices(icolp,&col);CHKERRQ(ierr);
2864   ierr = ISDestroy(&irowp);CHKERRQ(ierr);
2865   ierr = ISDestroy(&icolp);CHKERRQ(ierr);
2866   PetscFunctionReturn(0);
2867 }
2868 
2869 PetscErrorCode MatCopy_SeqAIJ(Mat A,Mat B,MatStructure str)
2870 {
2871   PetscErrorCode ierr;
2872 
2873   PetscFunctionBegin;
2874   /* If the two matrices have the same copy implementation, use fast copy. */
2875   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
2876     Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2877     Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data;
2878 
2879     if (a->i[A->rmap->n] != b->i[B->rmap->n]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Number of nonzeros in two matrices are different");
2880     ierr = PetscArraycpy(b->a,a->a,a->i[A->rmap->n]);CHKERRQ(ierr);
2881     ierr = PetscObjectStateIncrease((PetscObject)B);CHKERRQ(ierr);
2882   } else {
2883     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2884   }
2885   PetscFunctionReturn(0);
2886 }
2887 
2888 PetscErrorCode MatSetUp_SeqAIJ(Mat A)
2889 {
2890   PetscErrorCode ierr;
2891 
2892   PetscFunctionBegin;
2893   ierr =  MatSeqAIJSetPreallocation_SeqAIJ(A,PETSC_DEFAULT,0);CHKERRQ(ierr);
2894   PetscFunctionReturn(0);
2895 }
2896 
2897 PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A,PetscScalar *array[])
2898 {
2899   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2900 
2901   PetscFunctionBegin;
2902   *array = a->a;
2903   PetscFunctionReturn(0);
2904 }
2905 
2906 PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A,PetscScalar *array[])
2907 {
2908   PetscFunctionBegin;
2909   PetscFunctionReturn(0);
2910 }
2911 
2912 /*
2913    Computes the number of nonzeros per row needed for preallocation when X and Y
2914    have different nonzero structure.
2915 */
2916 PetscErrorCode MatAXPYGetPreallocation_SeqX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *yi,const PetscInt *yj,PetscInt *nnz)
2917 {
2918   PetscInt       i,j,k,nzx,nzy;
2919 
2920   PetscFunctionBegin;
2921   /* Set the number of nonzeros in the new matrix */
2922   for (i=0; i<m; i++) {
2923     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2924     nzx = xi[i+1] - xi[i];
2925     nzy = yi[i+1] - yi[i];
2926     nnz[i] = 0;
2927     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2928       for (; k<nzy && yjj[k]<xjj[j]; k++) nnz[i]++; /* Catch up to X */
2929       if (k<nzy && yjj[k]==xjj[j]) k++;             /* Skip duplicate */
2930       nnz[i]++;
2931     }
2932     for (; k<nzy; k++) nnz[i]++;
2933   }
2934   PetscFunctionReturn(0);
2935 }
2936 
2937 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
2938 {
2939   PetscInt       m = Y->rmap->N;
2940   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2941   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2942   PetscErrorCode ierr;
2943 
2944   PetscFunctionBegin;
2945   /* Set the number of nonzeros in the new matrix */
2946   ierr = MatAXPYGetPreallocation_SeqX_private(m,x->i,x->j,y->i,y->j,nnz);CHKERRQ(ierr);
2947   PetscFunctionReturn(0);
2948 }
2949 
2950 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2951 {
2952   PetscErrorCode ierr;
2953   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
2954   PetscBLASInt   one=1,bnz;
2955 
2956   PetscFunctionBegin;
2957   ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2958   if (str == SAME_NONZERO_PATTERN) {
2959     PetscScalar alpha = a;
2960     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2961     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
2962     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2963     /* the MatAXPY_Basic* subroutines calls MatAssembly, so the matrix on the GPU
2964        will be updated */
2965 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
2966     if (Y->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED) {
2967       Y->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
2968     }
2969 #endif
2970   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2971     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2972   } else {
2973     Mat      B;
2974     PetscInt *nnz;
2975     ierr = PetscMalloc1(Y->rmap->N,&nnz);CHKERRQ(ierr);
2976     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2977     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2978     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2979     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2980     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
2981     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
2982     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
2983     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2984     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2985     ierr = PetscFree(nnz);CHKERRQ(ierr);
2986   }
2987   PetscFunctionReturn(0);
2988 }
2989 
2990 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
2991 {
2992 #if defined(PETSC_USE_COMPLEX)
2993   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
2994   PetscInt    i,nz;
2995   PetscScalar *a;
2996 
2997   PetscFunctionBegin;
2998   nz = aij->nz;
2999   a  = aij->a;
3000   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
3001 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
3002   if (mat->valid_GPU_matrix != PETSC_OFFLOAD_UNALLOCATED) mat->valid_GPU_matrix = PETSC_OFFLOAD_CPU;
3003 #endif
3004 #else
3005   PetscFunctionBegin;
3006 #endif
3007   PetscFunctionReturn(0);
3008 }
3009 
3010 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3011 {
3012   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3013   PetscErrorCode ierr;
3014   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3015   PetscReal      atmp;
3016   PetscScalar    *x;
3017   MatScalar      *aa;
3018 
3019   PetscFunctionBegin;
3020   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3021   aa = a->a;
3022   ai = a->i;
3023   aj = a->j;
3024 
3025   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3026   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3027   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3028   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3029   for (i=0; i<m; i++) {
3030     ncols = ai[1] - ai[0]; ai++;
3031     x[i]  = 0.0;
3032     for (j=0; j<ncols; j++) {
3033       atmp = PetscAbsScalar(*aa);
3034       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3035       aa++; aj++;
3036     }
3037   }
3038   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3039   PetscFunctionReturn(0);
3040 }
3041 
3042 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3043 {
3044   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3045   PetscErrorCode ierr;
3046   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3047   PetscScalar    *x;
3048   MatScalar      *aa;
3049 
3050   PetscFunctionBegin;
3051   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3052   aa = a->a;
3053   ai = a->i;
3054   aj = a->j;
3055 
3056   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3057   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3058   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3059   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3060   for (i=0; i<m; i++) {
3061     ncols = ai[1] - ai[0]; ai++;
3062     if (ncols == A->cmap->n) { /* row is dense */
3063       x[i] = *aa; if (idx) idx[i] = 0;
3064     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
3065       x[i] = 0.0;
3066       if (idx) {
3067         idx[i] = 0; /* in case ncols is zero */
3068         for (j=0;j<ncols;j++) { /* find first implicit 0.0 in the row */
3069           if (aj[j] > j) {
3070             idx[i] = j;
3071             break;
3072           }
3073         }
3074       }
3075     }
3076     for (j=0; j<ncols; j++) {
3077       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3078       aa++; aj++;
3079     }
3080   }
3081   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3082   PetscFunctionReturn(0);
3083 }
3084 
3085 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3086 {
3087   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3088   PetscErrorCode ierr;
3089   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3090   PetscReal      atmp;
3091   PetscScalar    *x;
3092   MatScalar      *aa;
3093 
3094   PetscFunctionBegin;
3095   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3096   aa = a->a;
3097   ai = a->i;
3098   aj = a->j;
3099 
3100   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3101   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3102   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3103   if (n != A->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector, %D vs. %D rows", A->rmap->n, n);
3104   for (i=0; i<m; i++) {
3105     ncols = ai[1] - ai[0]; ai++;
3106     if (ncols) {
3107       /* Get first nonzero */
3108       for (j = 0; j < ncols; j++) {
3109         atmp = PetscAbsScalar(aa[j]);
3110         if (atmp > 1.0e-12) {
3111           x[i] = atmp;
3112           if (idx) idx[i] = aj[j];
3113           break;
3114         }
3115       }
3116       if (j == ncols) {x[i] = PetscAbsScalar(*aa); if (idx) idx[i] = *aj;}
3117     } else {
3118       x[i] = 0.0; if (idx) idx[i] = 0;
3119     }
3120     for (j = 0; j < ncols; j++) {
3121       atmp = PetscAbsScalar(*aa);
3122       if (atmp > 1.0e-12 && PetscAbsScalar(x[i]) > atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3123       aa++; aj++;
3124     }
3125   }
3126   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3127   PetscFunctionReturn(0);
3128 }
3129 
3130 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3131 {
3132   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
3133   PetscErrorCode  ierr;
3134   PetscInt        i,j,m = A->rmap->n,ncols,n;
3135   const PetscInt  *ai,*aj;
3136   PetscScalar     *x;
3137   const MatScalar *aa;
3138 
3139   PetscFunctionBegin;
3140   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3141   aa = a->a;
3142   ai = a->i;
3143   aj = a->j;
3144 
3145   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3146   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3147   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3148   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3149   for (i=0; i<m; i++) {
3150     ncols = ai[1] - ai[0]; ai++;
3151     if (ncols == A->cmap->n) { /* row is dense */
3152       x[i] = *aa; if (idx) idx[i] = 0;
3153     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3154       x[i] = 0.0;
3155       if (idx) {   /* find first implicit 0.0 in the row */
3156         idx[i] = 0; /* in case ncols is zero */
3157         for (j=0; j<ncols; j++) {
3158           if (aj[j] > j) {
3159             idx[i] = j;
3160             break;
3161           }
3162         }
3163       }
3164     }
3165     for (j=0; j<ncols; j++) {
3166       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3167       aa++; aj++;
3168     }
3169   }
3170   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3171   PetscFunctionReturn(0);
3172 }
3173 
3174 PetscErrorCode MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3175 {
3176   Mat_SeqAIJ      *a = (Mat_SeqAIJ*) A->data;
3177   PetscErrorCode  ierr;
3178   PetscInt        i,bs = PetscAbs(A->rmap->bs),mbs = A->rmap->n/bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3179   MatScalar       *diag,work[25],*v_work;
3180   const PetscReal shift = 0.0;
3181   PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;
3182 
3183   PetscFunctionBegin;
3184   allowzeropivot = PetscNot(A->erroriffailure);
3185   if (a->ibdiagvalid) {
3186     if (values) *values = a->ibdiag;
3187     PetscFunctionReturn(0);
3188   }
3189   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3190   if (!a->ibdiag) {
3191     ierr = PetscMalloc1(bs2*mbs,&a->ibdiag);CHKERRQ(ierr);
3192     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3193   }
3194   diag = a->ibdiag;
3195   if (values) *values = a->ibdiag;
3196   /* factor and invert each block */
3197   switch (bs) {
3198   case 1:
3199     for (i=0; i<mbs; i++) {
3200       ierr = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3201       if (PetscAbsScalar(diag[i] + shift) < PETSC_MACHINE_EPSILON) {
3202         if (allowzeropivot) {
3203           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3204           A->factorerror_zeropivot_value = PetscAbsScalar(diag[i]);
3205           A->factorerror_zeropivot_row   = i;
3206           ierr = PetscInfo3(A,"Zero pivot, row %D pivot %g tolerance %g\n",i,(double)PetscAbsScalar(diag[i]),(double)PETSC_MACHINE_EPSILON);CHKERRQ(ierr);
3207         } else SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D pivot %g tolerance %g",i,(double)PetscAbsScalar(diag[i]),(double)PETSC_MACHINE_EPSILON);
3208       }
3209       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3210     }
3211     break;
3212   case 2:
3213     for (i=0; i<mbs; i++) {
3214       ij[0] = 2*i; ij[1] = 2*i + 1;
3215       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3216       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3217       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3218       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
3219       diag += 4;
3220     }
3221     break;
3222   case 3:
3223     for (i=0; i<mbs; i++) {
3224       ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
3225       ierr  = MatGetValues(A,3,ij,3,ij,diag);CHKERRQ(ierr);
3226       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3227       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3228       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3229       diag += 9;
3230     }
3231     break;
3232   case 4:
3233     for (i=0; i<mbs; i++) {
3234       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3235       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3236       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3237       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3238       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3239       diag += 16;
3240     }
3241     break;
3242   case 5:
3243     for (i=0; i<mbs; i++) {
3244       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3245       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3246       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3247       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3248       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3249       diag += 25;
3250     }
3251     break;
3252   case 6:
3253     for (i=0; i<mbs; i++) {
3254       ij[0] = 6*i; ij[1] = 6*i + 1; ij[2] = 6*i + 2; ij[3] = 6*i + 3; ij[4] = 6*i + 4; ij[5] = 6*i + 5;
3255       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3256       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3257       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3258       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3259       diag += 36;
3260     }
3261     break;
3262   case 7:
3263     for (i=0; i<mbs; i++) {
3264       ij[0] = 7*i; ij[1] = 7*i + 1; ij[2] = 7*i + 2; ij[3] = 7*i + 3; ij[4] = 7*i + 4; ij[5] = 7*i + 5; ij[5] = 7*i + 6;
3265       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3266       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3267       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3268       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3269       diag += 49;
3270     }
3271     break;
3272   default:
3273     ierr = PetscMalloc3(bs,&v_work,bs,&v_pivots,bs,&IJ);CHKERRQ(ierr);
3274     for (i=0; i<mbs; i++) {
3275       for (j=0; j<bs; j++) {
3276         IJ[j] = bs*i + j;
3277       }
3278       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3279       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3280       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3281       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3282       diag += bs2;
3283     }
3284     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3285   }
3286   a->ibdiagvalid = PETSC_TRUE;
3287   PetscFunctionReturn(0);
3288 }
3289 
3290 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3291 {
3292   PetscErrorCode ierr;
3293   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3294   PetscScalar    a;
3295   PetscInt       m,n,i,j,col;
3296 
3297   PetscFunctionBegin;
3298   if (!x->assembled) {
3299     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3300     for (i=0; i<m; i++) {
3301       for (j=0; j<aij->imax[i]; j++) {
3302         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3303         col  = (PetscInt)(n*PetscRealPart(a));
3304         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3305       }
3306     }
3307   } else {
3308     for (i=0; i<aij->nz; i++) {ierr = PetscRandomGetValue(rctx,aij->a+i);CHKERRQ(ierr);}
3309   }
3310   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3311   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3312   PetscFunctionReturn(0);
3313 }
3314 
3315 /* Like MatSetRandom_SeqAIJ, but do not set values on columns in range of [low, high) */
3316 PetscErrorCode  MatSetRandomSkipColumnRange_SeqAIJ_Private(Mat x,PetscInt low,PetscInt high,PetscRandom rctx)
3317 {
3318   PetscErrorCode ierr;
3319   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3320   PetscScalar    a;
3321   PetscInt       m,n,i,j,col,nskip;
3322 
3323   PetscFunctionBegin;
3324   nskip = high - low;
3325   ierr  = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3326   n    -= nskip; /* shrink number of columns where nonzeros can be set */
3327   for (i=0; i<m; i++) {
3328     for (j=0; j<aij->imax[i]; j++) {
3329       ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3330       col  = (PetscInt)(n*PetscRealPart(a));
3331       if (col >= low) col += nskip; /* shift col rightward to skip the hole */
3332       ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3333     }
3334   }
3335   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3336   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3337   PetscFunctionReturn(0);
3338 }
3339 
3340 
3341 /* -------------------------------------------------------------------*/
3342 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3343                                         MatGetRow_SeqAIJ,
3344                                         MatRestoreRow_SeqAIJ,
3345                                         MatMult_SeqAIJ,
3346                                 /*  4*/ MatMultAdd_SeqAIJ,
3347                                         MatMultTranspose_SeqAIJ,
3348                                         MatMultTransposeAdd_SeqAIJ,
3349                                         0,
3350                                         0,
3351                                         0,
3352                                 /* 10*/ 0,
3353                                         MatLUFactor_SeqAIJ,
3354                                         0,
3355                                         MatSOR_SeqAIJ,
3356                                         MatTranspose_SeqAIJ,
3357                                 /*1 5*/ MatGetInfo_SeqAIJ,
3358                                         MatEqual_SeqAIJ,
3359                                         MatGetDiagonal_SeqAIJ,
3360                                         MatDiagonalScale_SeqAIJ,
3361                                         MatNorm_SeqAIJ,
3362                                 /* 20*/ 0,
3363                                         MatAssemblyEnd_SeqAIJ,
3364                                         MatSetOption_SeqAIJ,
3365                                         MatZeroEntries_SeqAIJ,
3366                                 /* 24*/ MatZeroRows_SeqAIJ,
3367                                         0,
3368                                         0,
3369                                         0,
3370                                         0,
3371                                 /* 29*/ MatSetUp_SeqAIJ,
3372                                         0,
3373                                         0,
3374                                         0,
3375                                         0,
3376                                 /* 34*/ MatDuplicate_SeqAIJ,
3377                                         0,
3378                                         0,
3379                                         MatILUFactor_SeqAIJ,
3380                                         0,
3381                                 /* 39*/ MatAXPY_SeqAIJ,
3382                                         MatCreateSubMatrices_SeqAIJ,
3383                                         MatIncreaseOverlap_SeqAIJ,
3384                                         MatGetValues_SeqAIJ,
3385                                         MatCopy_SeqAIJ,
3386                                 /* 44*/ MatGetRowMax_SeqAIJ,
3387                                         MatScale_SeqAIJ,
3388                                         MatShift_SeqAIJ,
3389                                         MatDiagonalSet_SeqAIJ,
3390                                         MatZeroRowsColumns_SeqAIJ,
3391                                 /* 49*/ MatSetRandom_SeqAIJ,
3392                                         MatGetRowIJ_SeqAIJ,
3393                                         MatRestoreRowIJ_SeqAIJ,
3394                                         MatGetColumnIJ_SeqAIJ,
3395                                         MatRestoreColumnIJ_SeqAIJ,
3396                                 /* 54*/ MatFDColoringCreate_SeqXAIJ,
3397                                         0,
3398                                         0,
3399                                         MatPermute_SeqAIJ,
3400                                         0,
3401                                 /* 59*/ 0,
3402                                         MatDestroy_SeqAIJ,
3403                                         MatView_SeqAIJ,
3404                                         0,
3405                                         MatMatMatMult_SeqAIJ_SeqAIJ_SeqAIJ,
3406                                 /* 64*/ MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ,
3407                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3408                                         0,
3409                                         0,
3410                                         0,
3411                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3412                                         MatGetRowMinAbs_SeqAIJ,
3413                                         0,
3414                                         0,
3415                                         0,
3416                                 /* 74*/ 0,
3417                                         MatFDColoringApply_AIJ,
3418                                         0,
3419                                         0,
3420                                         0,
3421                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3422                                         0,
3423                                         0,
3424                                         0,
3425                                         MatLoad_SeqAIJ,
3426                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3427                                         MatIsHermitian_SeqAIJ,
3428                                         0,
3429                                         0,
3430                                         0,
3431                                 /* 89*/ MatMatMult_SeqAIJ_SeqAIJ,
3432                                         MatMatMultSymbolic_SeqAIJ_SeqAIJ,
3433                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3434                                         MatPtAP_SeqAIJ_SeqAIJ,
3435                                         MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy,
3436                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy,
3437                                         MatMatTransposeMult_SeqAIJ_SeqAIJ,
3438                                         MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ,
3439                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3440                                         0,
3441                                 /* 99*/ 0,
3442                                         0,
3443                                         0,
3444                                         MatConjugate_SeqAIJ,
3445                                         0,
3446                                 /*104*/ MatSetValuesRow_SeqAIJ,
3447                                         MatRealPart_SeqAIJ,
3448                                         MatImaginaryPart_SeqAIJ,
3449                                         0,
3450                                         0,
3451                                 /*109*/ MatMatSolve_SeqAIJ,
3452                                         0,
3453                                         MatGetRowMin_SeqAIJ,
3454                                         0,
3455                                         MatMissingDiagonal_SeqAIJ,
3456                                 /*114*/ 0,
3457                                         0,
3458                                         0,
3459                                         0,
3460                                         0,
3461                                 /*119*/ 0,
3462                                         0,
3463                                         0,
3464                                         0,
3465                                         MatGetMultiProcBlock_SeqAIJ,
3466                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3467                                         MatGetColumnNorms_SeqAIJ,
3468                                         MatInvertBlockDiagonal_SeqAIJ,
3469                                         MatInvertVariableBlockDiagonal_SeqAIJ,
3470                                         0,
3471                                 /*129*/ 0,
3472                                         MatTransposeMatMult_SeqAIJ_SeqAIJ,
3473                                         MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ,
3474                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3475                                         MatTransposeColoringCreate_SeqAIJ,
3476                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3477                                         MatTransColoringApplyDenToSp_SeqAIJ,
3478                                         MatRARt_SeqAIJ_SeqAIJ,
3479                                         MatRARtSymbolic_SeqAIJ_SeqAIJ,
3480                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3481                                  /*139*/0,
3482                                         0,
3483                                         0,
3484                                         MatFDColoringSetUp_SeqXAIJ,
3485                                         MatFindOffBlockDiagonalEntries_SeqAIJ,
3486                                  /*144*/MatCreateMPIMatConcatenateSeqMat_SeqAIJ,
3487                                         MatDestroySubMatrices_SeqAIJ
3488 };
3489 
3490 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3491 {
3492   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3493   PetscInt   i,nz,n;
3494 
3495   PetscFunctionBegin;
3496   nz = aij->maxnz;
3497   n  = mat->rmap->n;
3498   for (i=0; i<nz; i++) {
3499     aij->j[i] = indices[i];
3500   }
3501   aij->nz = nz;
3502   for (i=0; i<n; i++) {
3503     aij->ilen[i] = aij->imax[i];
3504   }
3505   PetscFunctionReturn(0);
3506 }
3507 
3508 /*
3509  * When a sparse matrix has many zero columns, we should compact them out to save the space
3510  * This happens in MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable()
3511  * */
3512 PetscErrorCode  MatSeqAIJCompactOutExtraColumns_SeqAIJ(Mat mat, ISLocalToGlobalMapping *mapping)
3513 {
3514   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3515   PetscTable         gid1_lid1;
3516   PetscTablePosition tpos;
3517   PetscInt           gid,lid,i,j,ncols,ec;
3518   PetscInt           *garray;
3519   PetscErrorCode  ierr;
3520 
3521   PetscFunctionBegin;
3522   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3523   PetscValidPointer(mapping,2);
3524   /* use a table */
3525   ierr = PetscTableCreate(mat->rmap->n,mat->cmap->N+1,&gid1_lid1);CHKERRQ(ierr);
3526   ec = 0;
3527   for (i=0; i<mat->rmap->n; i++) {
3528     ncols = aij->i[i+1] - aij->i[i];
3529     for (j=0; j<ncols; j++) {
3530       PetscInt data,gid1 = aij->j[aij->i[i] + j] + 1;
3531       ierr = PetscTableFind(gid1_lid1,gid1,&data);CHKERRQ(ierr);
3532       if (!data) {
3533         /* one based table */
3534         ierr = PetscTableAdd(gid1_lid1,gid1,++ec,INSERT_VALUES);CHKERRQ(ierr);
3535       }
3536     }
3537   }
3538   /* form array of columns we need */
3539   ierr = PetscMalloc1(ec+1,&garray);CHKERRQ(ierr);
3540   ierr = PetscTableGetHeadPosition(gid1_lid1,&tpos);CHKERRQ(ierr);
3541   while (tpos) {
3542     ierr = PetscTableGetNext(gid1_lid1,&tpos,&gid,&lid);CHKERRQ(ierr);
3543     gid--;
3544     lid--;
3545     garray[lid] = gid;
3546   }
3547   ierr = PetscSortInt(ec,garray);CHKERRQ(ierr); /* sort, and rebuild */
3548   ierr = PetscTableRemoveAll(gid1_lid1);CHKERRQ(ierr);
3549   for (i=0; i<ec; i++) {
3550     ierr = PetscTableAdd(gid1_lid1,garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
3551   }
3552   /* compact out the extra columns in B */
3553   for (i=0; i<mat->rmap->n; i++) {
3554 	ncols = aij->i[i+1] - aij->i[i];
3555     for (j=0; j<ncols; j++) {
3556       PetscInt gid1 = aij->j[aij->i[i] + j] + 1;
3557       ierr = PetscTableFind(gid1_lid1,gid1,&lid);CHKERRQ(ierr);
3558       lid--;
3559       aij->j[aij->i[i] + j] = lid;
3560     }
3561   }
3562   ierr = PetscLayoutDestroy(&mat->cmap);CHKERRQ(ierr);
3563   ierr = PetscLayoutCreateFromSizes(PetscObjectComm((PetscObject)mat),ec,ec,1,&mat->cmap);CHKERRQ(ierr);
3564   ierr = PetscTableDestroy(&gid1_lid1);CHKERRQ(ierr);
3565   ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,mat->cmap->bs,mat->cmap->n,garray,PETSC_OWN_POINTER,mapping);CHKERRQ(ierr);
3566   ierr = ISLocalToGlobalMappingSetType(*mapping,ISLOCALTOGLOBALMAPPINGHASH);CHKERRQ(ierr);
3567   PetscFunctionReturn(0);
3568 }
3569 
3570 /*@
3571     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3572        in the matrix.
3573 
3574   Input Parameters:
3575 +  mat - the SeqAIJ matrix
3576 -  indices - the column indices
3577 
3578   Level: advanced
3579 
3580   Notes:
3581     This can be called if you have precomputed the nonzero structure of the
3582   matrix and want to provide it to the matrix object to improve the performance
3583   of the MatSetValues() operation.
3584 
3585     You MUST have set the correct numbers of nonzeros per row in the call to
3586   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3587 
3588     MUST be called before any calls to MatSetValues();
3589 
3590     The indices should start with zero, not one.
3591 
3592 @*/
3593 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3594 {
3595   PetscErrorCode ierr;
3596 
3597   PetscFunctionBegin;
3598   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3599   PetscValidPointer(indices,2);
3600   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3601   PetscFunctionReturn(0);
3602 }
3603 
3604 /* ----------------------------------------------------------------------------------------*/
3605 
3606 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3607 {
3608   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3609   PetscErrorCode ierr;
3610   size_t         nz = aij->i[mat->rmap->n];
3611 
3612   PetscFunctionBegin;
3613   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3614 
3615   /* allocate space for values if not already there */
3616   if (!aij->saved_values) {
3617     ierr = PetscMalloc1(nz+1,&aij->saved_values);CHKERRQ(ierr);
3618     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3619   }
3620 
3621   /* copy values over */
3622   ierr = PetscArraycpy(aij->saved_values,aij->a,nz);CHKERRQ(ierr);
3623   PetscFunctionReturn(0);
3624 }
3625 
3626 /*@
3627     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3628        example, reuse of the linear part of a Jacobian, while recomputing the
3629        nonlinear portion.
3630 
3631    Collect on Mat
3632 
3633   Input Parameters:
3634 .  mat - the matrix (currently only AIJ matrices support this option)
3635 
3636   Level: advanced
3637 
3638   Common Usage, with SNESSolve():
3639 $    Create Jacobian matrix
3640 $    Set linear terms into matrix
3641 $    Apply boundary conditions to matrix, at this time matrix must have
3642 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3643 $      boundary conditions again will not change the nonzero structure
3644 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3645 $    ierr = MatStoreValues(mat);
3646 $    Call SNESSetJacobian() with matrix
3647 $    In your Jacobian routine
3648 $      ierr = MatRetrieveValues(mat);
3649 $      Set nonlinear terms in matrix
3650 
3651   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3652 $    // build linear portion of Jacobian
3653 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3654 $    ierr = MatStoreValues(mat);
3655 $    loop over nonlinear iterations
3656 $       ierr = MatRetrieveValues(mat);
3657 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3658 $       // call MatAssemblyBegin/End() on matrix
3659 $       Solve linear system with Jacobian
3660 $    endloop
3661 
3662   Notes:
3663     Matrix must already be assemblied before calling this routine
3664     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3665     calling this routine.
3666 
3667     When this is called multiple times it overwrites the previous set of stored values
3668     and does not allocated additional space.
3669 
3670 .seealso: MatRetrieveValues()
3671 
3672 @*/
3673 PetscErrorCode  MatStoreValues(Mat mat)
3674 {
3675   PetscErrorCode ierr;
3676 
3677   PetscFunctionBegin;
3678   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3679   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3680   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3681   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3682   PetscFunctionReturn(0);
3683 }
3684 
3685 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3686 {
3687   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3688   PetscErrorCode ierr;
3689   PetscInt       nz = aij->i[mat->rmap->n];
3690 
3691   PetscFunctionBegin;
3692   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3693   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3694   /* copy values over */
3695   ierr = PetscArraycpy(aij->a,aij->saved_values,nz);CHKERRQ(ierr);
3696   PetscFunctionReturn(0);
3697 }
3698 
3699 /*@
3700     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3701        example, reuse of the linear part of a Jacobian, while recomputing the
3702        nonlinear portion.
3703 
3704    Collect on Mat
3705 
3706   Input Parameters:
3707 .  mat - the matrix (currently only AIJ matrices support this option)
3708 
3709   Level: advanced
3710 
3711 .seealso: MatStoreValues()
3712 
3713 @*/
3714 PetscErrorCode  MatRetrieveValues(Mat mat)
3715 {
3716   PetscErrorCode ierr;
3717 
3718   PetscFunctionBegin;
3719   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3720   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3721   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3722   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3723   PetscFunctionReturn(0);
3724 }
3725 
3726 
3727 /* --------------------------------------------------------------------------------*/
3728 /*@C
3729    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3730    (the default parallel PETSc format).  For good matrix assembly performance
3731    the user should preallocate the matrix storage by setting the parameter nz
3732    (or the array nnz).  By setting these parameters accurately, performance
3733    during matrix assembly can be increased by more than a factor of 50.
3734 
3735    Collective
3736 
3737    Input Parameters:
3738 +  comm - MPI communicator, set to PETSC_COMM_SELF
3739 .  m - number of rows
3740 .  n - number of columns
3741 .  nz - number of nonzeros per row (same for all rows)
3742 -  nnz - array containing the number of nonzeros in the various rows
3743          (possibly different for each row) or NULL
3744 
3745    Output Parameter:
3746 .  A - the matrix
3747 
3748    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3749    MatXXXXSetPreallocation() paradigm instead of this routine directly.
3750    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3751 
3752    Notes:
3753    If nnz is given then nz is ignored
3754 
3755    The AIJ format (also called the Yale sparse matrix format or
3756    compressed row storage), is fully compatible with standard Fortran 77
3757    storage.  That is, the stored row and column indices can begin at
3758    either one (as in Fortran) or zero.  See the users' manual for details.
3759 
3760    Specify the preallocated storage with either nz or nnz (not both).
3761    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3762    allocation.  For large problems you MUST preallocate memory or you
3763    will get TERRIBLE performance, see the users' manual chapter on matrices.
3764 
3765    By default, this format uses inodes (identical nodes) when possible, to
3766    improve numerical efficiency of matrix-vector products and solves. We
3767    search for consecutive rows with the same nonzero structure, thereby
3768    reusing matrix information to achieve increased efficiency.
3769 
3770    Options Database Keys:
3771 +  -mat_no_inode  - Do not use inodes
3772 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3773 
3774    Level: intermediate
3775 
3776 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3777 
3778 @*/
3779 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3780 {
3781   PetscErrorCode ierr;
3782 
3783   PetscFunctionBegin;
3784   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3785   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3786   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3787   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3788   PetscFunctionReturn(0);
3789 }
3790 
3791 /*@C
3792    MatSeqAIJSetPreallocation - For good matrix assembly performance
3793    the user should preallocate the matrix storage by setting the parameter nz
3794    (or the array nnz).  By setting these parameters accurately, performance
3795    during matrix assembly can be increased by more than a factor of 50.
3796 
3797    Collective
3798 
3799    Input Parameters:
3800 +  B - The matrix
3801 .  nz - number of nonzeros per row (same for all rows)
3802 -  nnz - array containing the number of nonzeros in the various rows
3803          (possibly different for each row) or NULL
3804 
3805    Notes:
3806      If nnz is given then nz is ignored
3807 
3808     The AIJ format (also called the Yale sparse matrix format or
3809    compressed row storage), is fully compatible with standard Fortran 77
3810    storage.  That is, the stored row and column indices can begin at
3811    either one (as in Fortran) or zero.  See the users' manual for details.
3812 
3813    Specify the preallocated storage with either nz or nnz (not both).
3814    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3815    allocation.  For large problems you MUST preallocate memory or you
3816    will get TERRIBLE performance, see the users' manual chapter on matrices.
3817 
3818    You can call MatGetInfo() to get information on how effective the preallocation was;
3819    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3820    You can also run with the option -info and look for messages with the string
3821    malloc in them to see if additional memory allocation was needed.
3822 
3823    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3824    entries or columns indices
3825 
3826    By default, this format uses inodes (identical nodes) when possible, to
3827    improve numerical efficiency of matrix-vector products and solves. We
3828    search for consecutive rows with the same nonzero structure, thereby
3829    reusing matrix information to achieve increased efficiency.
3830 
3831    Options Database Keys:
3832 +  -mat_no_inode  - Do not use inodes
3833 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3834 
3835    Level: intermediate
3836 
3837 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatGetInfo()
3838 
3839 @*/
3840 PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
3841 {
3842   PetscErrorCode ierr;
3843 
3844   PetscFunctionBegin;
3845   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3846   PetscValidType(B,1);
3847   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));CHKERRQ(ierr);
3848   PetscFunctionReturn(0);
3849 }
3850 
3851 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3852 {
3853   Mat_SeqAIJ     *b;
3854   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3855   PetscErrorCode ierr;
3856   PetscInt       i;
3857 
3858   PetscFunctionBegin;
3859   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3860   if (nz == MAT_SKIP_ALLOCATION) {
3861     skipallocation = PETSC_TRUE;
3862     nz             = 0;
3863   }
3864   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3865   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3866 
3867   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3868   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %D",nz);
3869 #if defined(PETSC_USE_DEBUG)
3870   if (nnz) {
3871     for (i=0; i<B->rmap->n; i++) {
3872       if (nnz[i] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nnz cannot be less than 0: local row %D value %D",i,nnz[i]);
3873       if (nnz[i] > B->cmap->n) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nnz cannot be greater than row length: local row %D value %d rowlength %D",i,nnz[i],B->cmap->n);
3874     }
3875   }
3876 #endif
3877 
3878   B->preallocated = PETSC_TRUE;
3879 
3880   b = (Mat_SeqAIJ*)B->data;
3881 
3882   if (!skipallocation) {
3883     if (!b->imax) {
3884       ierr = PetscMalloc1(B->rmap->n,&b->imax);CHKERRQ(ierr);
3885       ierr = PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3886     }
3887     if (!b->ilen) {
3888       /* b->ilen will count nonzeros in each row so far. */
3889       ierr = PetscCalloc1(B->rmap->n,&b->ilen);CHKERRQ(ierr);
3890       ierr = PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3891     } else {
3892       ierr = PetscMemzero(b->ilen,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3893     }
3894     if (!b->ipre) {
3895       ierr = PetscMalloc1(B->rmap->n,&b->ipre);CHKERRQ(ierr);
3896       ierr = PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3897     }
3898     if (!nnz) {
3899       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3900       else if (nz < 0) nz = 1;
3901       nz = PetscMin(nz,B->cmap->n);
3902       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
3903       nz = nz*B->rmap->n;
3904     } else {
3905       PetscInt64 nz64 = 0;
3906       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz64 += nnz[i];}
3907       ierr = PetscIntCast(nz64,&nz);CHKERRQ(ierr);
3908     }
3909 
3910     /* allocate the matrix space */
3911     /* FIXME: should B's old memory be unlogged? */
3912     ierr = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
3913     if (B->structure_only) {
3914       ierr = PetscMalloc1(nz,&b->j);CHKERRQ(ierr);
3915       ierr = PetscMalloc1(B->rmap->n+1,&b->i);CHKERRQ(ierr);
3916       ierr = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*sizeof(PetscInt));CHKERRQ(ierr);
3917     } else {
3918       ierr = PetscMalloc3(nz,&b->a,nz,&b->j,B->rmap->n+1,&b->i);CHKERRQ(ierr);
3919       ierr = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
3920     }
3921     b->i[0] = 0;
3922     for (i=1; i<B->rmap->n+1; i++) {
3923       b->i[i] = b->i[i-1] + b->imax[i-1];
3924     }
3925     if (B->structure_only) {
3926       b->singlemalloc = PETSC_FALSE;
3927       b->free_a       = PETSC_FALSE;
3928     } else {
3929       b->singlemalloc = PETSC_TRUE;
3930       b->free_a       = PETSC_TRUE;
3931     }
3932     b->free_ij      = PETSC_TRUE;
3933   } else {
3934     b->free_a  = PETSC_FALSE;
3935     b->free_ij = PETSC_FALSE;
3936   }
3937 
3938   if (b->ipre && nnz != b->ipre  && b->imax) {
3939     /* reserve user-requested sparsity */
3940     ierr = PetscArraycpy(b->ipre,b->imax,B->rmap->n);CHKERRQ(ierr);
3941   }
3942 
3943 
3944   b->nz               = 0;
3945   b->maxnz            = nz;
3946   B->info.nz_unneeded = (double)b->maxnz;
3947   if (realalloc) {
3948     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3949   }
3950   B->was_assembled = PETSC_FALSE;
3951   B->assembled     = PETSC_FALSE;
3952   PetscFunctionReturn(0);
3953 }
3954 
3955 
3956 PetscErrorCode MatResetPreallocation_SeqAIJ(Mat A)
3957 {
3958   Mat_SeqAIJ     *a;
3959   PetscInt       i;
3960   PetscErrorCode ierr;
3961 
3962   PetscFunctionBegin;
3963   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3964 
3965   /* Check local size. If zero, then return */
3966   if (!A->rmap->n) PetscFunctionReturn(0);
3967 
3968   a = (Mat_SeqAIJ*)A->data;
3969   /* if no saved info, we error out */
3970   if (!a->ipre) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"No saved preallocation info \n");
3971 
3972   if (!a->i || !a->j || !a->a || !a->imax || !a->ilen) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"Memory info is incomplete, and can not reset preallocation \n");
3973 
3974   ierr = PetscArraycpy(a->imax,a->ipre,A->rmap->n);CHKERRQ(ierr);
3975   ierr = PetscArrayzero(a->ilen,A->rmap->n);CHKERRQ(ierr);
3976   a->i[0] = 0;
3977   for (i=1; i<A->rmap->n+1; i++) {
3978     a->i[i] = a->i[i-1] + a->imax[i-1];
3979   }
3980   A->preallocated     = PETSC_TRUE;
3981   a->nz               = 0;
3982   a->maxnz            = a->i[A->rmap->n];
3983   A->info.nz_unneeded = (double)a->maxnz;
3984   A->was_assembled    = PETSC_FALSE;
3985   A->assembled        = PETSC_FALSE;
3986   PetscFunctionReturn(0);
3987 }
3988 
3989 /*@
3990    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
3991 
3992    Input Parameters:
3993 +  B - the matrix
3994 .  i - the indices into j for the start of each row (starts with zero)
3995 .  j - the column indices for each row (starts with zero) these must be sorted for each row
3996 -  v - optional values in the matrix
3997 
3998    Level: developer
3999 
4000    The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
4001 
4002 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), MATSEQAIJ
4003 @*/
4004 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
4005 {
4006   PetscErrorCode ierr;
4007 
4008   PetscFunctionBegin;
4009   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
4010   PetscValidType(B,1);
4011   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
4012   PetscFunctionReturn(0);
4013 }
4014 
4015 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
4016 {
4017   PetscInt       i;
4018   PetscInt       m,n;
4019   PetscInt       nz;
4020   PetscInt       *nnz, nz_max = 0;
4021   PetscErrorCode ierr;
4022 
4023   PetscFunctionBegin;
4024   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
4025 
4026   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
4027   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
4028 
4029   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
4030   ierr = PetscMalloc1(m+1, &nnz);CHKERRQ(ierr);
4031   for (i = 0; i < m; i++) {
4032     nz     = Ii[i+1]- Ii[i];
4033     nz_max = PetscMax(nz_max, nz);
4034     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
4035     nnz[i] = nz;
4036   }
4037   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
4038   ierr = PetscFree(nnz);CHKERRQ(ierr);
4039 
4040   for (i = 0; i < m; i++) {
4041     ierr = MatSetValues_SeqAIJ(B, 1, &i, Ii[i+1] - Ii[i], J+Ii[i], v ? v + Ii[i] : NULL, INSERT_VALUES);CHKERRQ(ierr);
4042   }
4043 
4044   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4045   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4046 
4047   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
4048   PetscFunctionReturn(0);
4049 }
4050 
4051 #include <../src/mat/impls/dense/seq/dense.h>
4052 #include <petsc/private/kernels/petscaxpy.h>
4053 
4054 /*
4055     Computes (B'*A')' since computing B*A directly is untenable
4056 
4057                n                       p                          p
4058         (              )       (              )         (                  )
4059       m (      A       )  *  n (       B      )   =   m (         C        )
4060         (              )       (              )         (                  )
4061 
4062 */
4063 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
4064 {
4065   PetscErrorCode    ierr;
4066   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
4067   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
4068   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
4069   PetscInt          i,n,m,q,p;
4070   const PetscInt    *ii,*idx;
4071   const PetscScalar *b,*a,*a_q;
4072   PetscScalar       *c,*c_q;
4073 
4074   PetscFunctionBegin;
4075   m    = A->rmap->n;
4076   n    = A->cmap->n;
4077   p    = B->cmap->n;
4078   a    = sub_a->v;
4079   b    = sub_b->a;
4080   c    = sub_c->v;
4081   ierr = PetscArrayzero(c,m*p);CHKERRQ(ierr);
4082 
4083   ii  = sub_b->i;
4084   idx = sub_b->j;
4085   for (i=0; i<n; i++) {
4086     q = ii[i+1] - ii[i];
4087     while (q-->0) {
4088       c_q = c + m*(*idx);
4089       a_q = a + m*i;
4090       PetscKernelAXPY(c_q,*b,a_q,m);
4091       idx++;
4092       b++;
4093     }
4094   }
4095   PetscFunctionReturn(0);
4096 }
4097 
4098 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4099 {
4100   PetscErrorCode ierr;
4101   PetscInt       m=A->rmap->n,n=B->cmap->n;
4102   Mat            Cmat;
4103 
4104   PetscFunctionBegin;
4105   if (A->cmap->n != B->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"A->cmap->n %D != B->rmap->n %D\n",A->cmap->n,B->rmap->n);
4106   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4107   ierr = MatSetSizes(Cmat,m,n,m,n);CHKERRQ(ierr);
4108   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
4109   ierr = MatSetType(Cmat,MATSEQDENSE);CHKERRQ(ierr);
4110   ierr = MatSeqDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4111 
4112   Cmat->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
4113 
4114   *C = Cmat;
4115   PetscFunctionReturn(0);
4116 }
4117 
4118 /* ----------------------------------------------------------------*/
4119 PETSC_INTERN PetscErrorCode MatMatMult_SeqDense_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4120 {
4121   PetscErrorCode ierr;
4122 
4123   PetscFunctionBegin;
4124   if (scall == MAT_INITIAL_MATRIX) {
4125     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4126     ierr = MatMatMultSymbolic_SeqDense_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
4127     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4128   }
4129   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4130   ierr = MatMatMultNumeric_SeqDense_SeqAIJ(A,B,*C);CHKERRQ(ierr);
4131   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4132   PetscFunctionReturn(0);
4133 }
4134 
4135 
4136 /*MC
4137    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
4138    based on compressed sparse row format.
4139 
4140    Options Database Keys:
4141 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
4142 
4143    Level: beginner
4144 
4145    Notes:
4146     MatSetValues() may be called for this matrix type with a NULL argument for the numerical values,
4147     in this case the values associated with the rows and columns one passes in are set to zero
4148     in the matrix
4149 
4150     MatSetOptions(,MAT_STRUCTURE_ONLY,PETSC_TRUE) may be called for this matrix type. In this no
4151     space is allocated for the nonzero entries and any entries passed with MatSetValues() are ignored
4152 
4153   Developer Notes:
4154     It would be nice if all matrix formats supported passing NULL in for the numerical values
4155 
4156 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
4157 M*/
4158 
4159 /*MC
4160    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
4161 
4162    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
4163    and MATMPIAIJ otherwise.  As a result, for single process communicators,
4164   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation() is supported
4165   for communicators controlling multiple processes.  It is recommended that you call both of
4166   the above preallocation routines for simplicity.
4167 
4168    Options Database Keys:
4169 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
4170 
4171   Developer Notes:
4172     Subclasses include MATAIJCUSPARSE, MATAIJPERM, MATAIJSELL, MATAIJMKL, MATAIJCRL, and also automatically switches over to use inodes when
4173    enough exist.
4174 
4175   Level: beginner
4176 
4177 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
4178 M*/
4179 
4180 /*MC
4181    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
4182 
4183    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
4184    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
4185    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
4186   for communicators controlling multiple processes.  It is recommended that you call both of
4187   the above preallocation routines for simplicity.
4188 
4189    Options Database Keys:
4190 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
4191 
4192   Level: beginner
4193 
4194 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
4195 M*/
4196 
4197 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
4198 #if defined(PETSC_HAVE_ELEMENTAL)
4199 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4200 #endif
4201 #if defined(PETSC_HAVE_HYPRE)
4202 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat A,MatType,MatReuse,Mat*);
4203 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
4204 #endif
4205 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqDense(Mat,MatType,MatReuse,Mat*);
4206 
4207 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqSELL(Mat,MatType,MatReuse,Mat*);
4208 PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat,MatType,MatReuse,Mat*);
4209 PETSC_INTERN PetscErrorCode MatPtAP_IS_XAIJ(Mat,Mat,MatReuse,PetscReal,Mat*);
4210 
4211 /*@C
4212    MatSeqAIJGetArray - gives access to the array where the data for a MATSEQAIJ matrix is stored
4213 
4214    Not Collective
4215 
4216    Input Parameter:
4217 .  mat - a MATSEQAIJ matrix
4218 
4219    Output Parameter:
4220 .   array - pointer to the data
4221 
4222    Level: intermediate
4223 
4224 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4225 @*/
4226 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4227 {
4228   PetscErrorCode ierr;
4229 
4230   PetscFunctionBegin;
4231   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4232   PetscFunctionReturn(0);
4233 }
4234 
4235 /*@C
4236    MatSeqAIJGetMaxRowNonzeros - returns the maximum number of nonzeros in any row
4237 
4238    Not Collective
4239 
4240    Input Parameter:
4241 .  mat - a MATSEQAIJ matrix
4242 
4243    Output Parameter:
4244 .   nz - the maximum number of nonzeros in any row
4245 
4246    Level: intermediate
4247 
4248 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4249 @*/
4250 PetscErrorCode  MatSeqAIJGetMaxRowNonzeros(Mat A,PetscInt *nz)
4251 {
4252   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
4253 
4254   PetscFunctionBegin;
4255   *nz = aij->rmax;
4256   PetscFunctionReturn(0);
4257 }
4258 
4259 /*@C
4260    MatSeqAIJRestoreArray - returns access to the array where the data for a MATSEQAIJ matrix is stored obtained by MatSeqAIJGetArray()
4261 
4262    Not Collective
4263 
4264    Input Parameters:
4265 +  mat - a MATSEQAIJ matrix
4266 -  array - pointer to the data
4267 
4268    Level: intermediate
4269 
4270 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4271 @*/
4272 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4273 {
4274   PetscErrorCode ierr;
4275 
4276   PetscFunctionBegin;
4277   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4278   PetscFunctionReturn(0);
4279 }
4280 
4281 #if defined(PETSC_HAVE_CUDA)
4282 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat);
4283 #endif
4284 
4285 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4286 {
4287   Mat_SeqAIJ     *b;
4288   PetscErrorCode ierr;
4289   PetscMPIInt    size;
4290 
4291   PetscFunctionBegin;
4292   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4293   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4294 
4295   ierr = PetscNewLog(B,&b);CHKERRQ(ierr);
4296 
4297   B->data = (void*)b;
4298 
4299   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4300   if (B->sortedfull) B->ops->setvalues = MatSetValues_SeqAIJ_SortedFull;
4301 
4302   b->row                = 0;
4303   b->col                = 0;
4304   b->icol               = 0;
4305   b->reallocs           = 0;
4306   b->ignorezeroentries  = PETSC_FALSE;
4307   b->roworiented        = PETSC_TRUE;
4308   b->nonew              = 0;
4309   b->diag               = 0;
4310   b->solve_work         = 0;
4311   B->spptr              = 0;
4312   b->saved_values       = 0;
4313   b->idiag              = 0;
4314   b->mdiag              = 0;
4315   b->ssor_work          = 0;
4316   b->omega              = 1.0;
4317   b->fshift             = 0.0;
4318   b->idiagvalid         = PETSC_FALSE;
4319   b->ibdiagvalid        = PETSC_FALSE;
4320   b->keepnonzeropattern = PETSC_FALSE;
4321 
4322   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4323   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4324   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4325 
4326 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4327   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4328   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4329 #endif
4330 
4331   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4332   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4333   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4334   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4335   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4336   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4337   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijsell_C",MatConvert_SeqAIJ_SeqAIJSELL);CHKERRQ(ierr);
4338 #if defined(PETSC_HAVE_MKL_SPARSE)
4339   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijmkl_C",MatConvert_SeqAIJ_SeqAIJMKL);CHKERRQ(ierr);
4340 #endif
4341 #if defined(PETSC_HAVE_CUDA)
4342   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcusparse_C",MatConvert_SeqAIJ_SeqAIJCUSPARSE);CHKERRQ(ierr);
4343 #endif
4344   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4345 #if defined(PETSC_HAVE_ELEMENTAL)
4346   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_elemental_C",MatConvert_SeqAIJ_Elemental);CHKERRQ(ierr);
4347 #endif
4348 #if defined(PETSC_HAVE_HYPRE)
4349   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
4350   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_seqaij_seqaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
4351 #endif
4352   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqdense_C",MatConvert_SeqAIJ_SeqDense);CHKERRQ(ierr);
4353   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsell_C",MatConvert_SeqAIJ_SeqSELL);CHKERRQ(ierr);
4354   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_is_C",MatConvert_XAIJ_IS);CHKERRQ(ierr);
4355   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4356   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4357   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4358   ierr = PetscObjectComposeFunction((PetscObject)B,"MatResetPreallocation_C",MatResetPreallocation_SeqAIJ);CHKERRQ(ierr);
4359   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4360   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4361   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaij_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
4362   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaij_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
4363   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaij_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
4364   ierr = PetscObjectComposeFunction((PetscObject)B,"MatPtAP_is_seqaij_C",MatPtAP_IS_XAIJ);CHKERRQ(ierr);
4365   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4366   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4367   ierr = MatSeqAIJSetTypeFromOptions(B);CHKERRQ(ierr);  /* this allows changing the matrix subtype to say MATSEQAIJPERM */
4368   PetscFunctionReturn(0);
4369 }
4370 
4371 /*
4372     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4373 */
4374 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4375 {
4376   Mat_SeqAIJ     *c,*a = (Mat_SeqAIJ*)A->data;
4377   PetscErrorCode ierr;
4378   PetscInt       m = A->rmap->n,i;
4379 
4380   PetscFunctionBegin;
4381   c = (Mat_SeqAIJ*)C->data;
4382 
4383   C->factortype = A->factortype;
4384   c->row        = 0;
4385   c->col        = 0;
4386   c->icol       = 0;
4387   c->reallocs   = 0;
4388 
4389   C->assembled = PETSC_TRUE;
4390 
4391   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4392   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4393 
4394   ierr = PetscMalloc1(m,&c->imax);CHKERRQ(ierr);
4395   ierr = PetscMemcpy(c->imax,a->imax,m*sizeof(PetscInt));CHKERRQ(ierr);
4396   ierr = PetscMalloc1(m,&c->ilen);CHKERRQ(ierr);
4397   ierr = PetscMemcpy(c->ilen,a->ilen,m*sizeof(PetscInt));CHKERRQ(ierr);
4398   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4399 
4400   /* allocate the matrix space */
4401   if (mallocmatspace) {
4402     ierr = PetscMalloc3(a->i[m],&c->a,a->i[m],&c->j,m+1,&c->i);CHKERRQ(ierr);
4403     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4404 
4405     c->singlemalloc = PETSC_TRUE;
4406 
4407     ierr = PetscArraycpy(c->i,a->i,m+1);CHKERRQ(ierr);
4408     if (m > 0) {
4409       ierr = PetscArraycpy(c->j,a->j,a->i[m]);CHKERRQ(ierr);
4410       if (cpvalues == MAT_COPY_VALUES) {
4411         ierr = PetscArraycpy(c->a,a->a,a->i[m]);CHKERRQ(ierr);
4412       } else {
4413         ierr = PetscArrayzero(c->a,a->i[m]);CHKERRQ(ierr);
4414       }
4415     }
4416   }
4417 
4418   c->ignorezeroentries = a->ignorezeroentries;
4419   c->roworiented       = a->roworiented;
4420   c->nonew             = a->nonew;
4421   if (a->diag) {
4422     ierr = PetscMalloc1(m+1,&c->diag);CHKERRQ(ierr);
4423     ierr = PetscMemcpy(c->diag,a->diag,m*sizeof(PetscInt));CHKERRQ(ierr);
4424     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4425   } else c->diag = NULL;
4426 
4427   c->solve_work         = 0;
4428   c->saved_values       = 0;
4429   c->idiag              = 0;
4430   c->ssor_work          = 0;
4431   c->keepnonzeropattern = a->keepnonzeropattern;
4432   c->free_a             = PETSC_TRUE;
4433   c->free_ij            = PETSC_TRUE;
4434 
4435   c->rmax         = a->rmax;
4436   c->nz           = a->nz;
4437   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4438   C->preallocated = PETSC_TRUE;
4439 
4440   c->compressedrow.use   = a->compressedrow.use;
4441   c->compressedrow.nrows = a->compressedrow.nrows;
4442   if (a->compressedrow.use) {
4443     i    = a->compressedrow.nrows;
4444     ierr = PetscMalloc2(i+1,&c->compressedrow.i,i,&c->compressedrow.rindex);CHKERRQ(ierr);
4445     ierr = PetscArraycpy(c->compressedrow.i,a->compressedrow.i,i+1);CHKERRQ(ierr);
4446     ierr = PetscArraycpy(c->compressedrow.rindex,a->compressedrow.rindex,i);CHKERRQ(ierr);
4447   } else {
4448     c->compressedrow.use    = PETSC_FALSE;
4449     c->compressedrow.i      = NULL;
4450     c->compressedrow.rindex = NULL;
4451   }
4452   c->nonzerorowcnt = a->nonzerorowcnt;
4453   C->nonzerostate  = A->nonzerostate;
4454 
4455   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4456   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4457   PetscFunctionReturn(0);
4458 }
4459 
4460 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4461 {
4462   PetscErrorCode ierr;
4463 
4464   PetscFunctionBegin;
4465   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4466   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4467   if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) {
4468     ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
4469   }
4470   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4471   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4472   PetscFunctionReturn(0);
4473 }
4474 
4475 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4476 {
4477   PetscBool      isbinary, ishdf5;
4478   PetscErrorCode ierr;
4479 
4480   PetscFunctionBegin;
4481   PetscValidHeaderSpecific(newMat,MAT_CLASSID,1);
4482   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
4483   /* force binary viewer to load .info file if it has not yet done so */
4484   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
4485   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
4486   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,  &ishdf5);CHKERRQ(ierr);
4487   if (isbinary) {
4488     ierr = MatLoad_SeqAIJ_Binary(newMat,viewer);CHKERRQ(ierr);
4489   } else if (ishdf5) {
4490 #if defined(PETSC_HAVE_HDF5)
4491     ierr = MatLoad_AIJ_HDF5(newMat,viewer);CHKERRQ(ierr);
4492 #else
4493     SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
4494 #endif
4495   } else {
4496     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);
4497   }
4498   PetscFunctionReturn(0);
4499 }
4500 
4501 PetscErrorCode MatLoad_SeqAIJ_Binary(Mat newMat, PetscViewer viewer)
4502 {
4503   Mat_SeqAIJ     *a;
4504   PetscErrorCode ierr;
4505   PetscInt       i,sum,nz,header[4],*rowlengths = 0,M,N,rows,cols;
4506   int            fd;
4507   PetscMPIInt    size;
4508   MPI_Comm       comm;
4509   PetscInt       bs = newMat->rmap->bs;
4510 
4511   PetscFunctionBegin;
4512   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
4513   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4514   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"view must have one processor");
4515 
4516   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
4517   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
4518   ierr = PetscOptionsEnd();CHKERRQ(ierr);
4519   if (bs < 0) bs = 1;
4520   ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);
4521 
4522   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
4523   ierr = PetscBinaryRead(fd,header,4,NULL,PETSC_INT);CHKERRQ(ierr);
4524   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
4525   M = header[1]; N = header[2]; nz = header[3];
4526 
4527   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
4528 
4529   /* read in row lengths */
4530   ierr = PetscMalloc1(M,&rowlengths);CHKERRQ(ierr);
4531   ierr = PetscBinaryRead(fd,rowlengths,M,NULL,PETSC_INT);CHKERRQ(ierr);
4532 
4533   /* check if sum of rowlengths is same as nz */
4534   for (i=0,sum=0; i< M; i++) sum +=rowlengths[i];
4535   if (sum != nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Inconsistant matrix data in file. no-nonzeros = %dD, sum-row-lengths = %D\n",nz,sum);
4536 
4537   /* set global size if not set already*/
4538   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) {
4539     ierr = MatSetSizes(newMat,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
4540   } else {
4541     /* if sizes and type are already set, check if the matrix  global sizes are correct */
4542     ierr = MatGetSize(newMat,&rows,&cols);CHKERRQ(ierr);
4543     if (rows < 0 && cols < 0) { /* user might provide local size instead of global size */
4544       ierr = MatGetLocalSize(newMat,&rows,&cols);CHKERRQ(ierr);
4545     }
4546     if (M != rows ||  N != cols) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Matrix in file of different length (%D, %D) than the input matrix (%D, %D)",M,N,rows,cols);
4547   }
4548   ierr = MatSeqAIJSetPreallocation_SeqAIJ(newMat,0,rowlengths);CHKERRQ(ierr);
4549   a    = (Mat_SeqAIJ*)newMat->data;
4550 
4551   ierr = PetscBinaryRead(fd,a->j,nz,NULL,PETSC_INT);CHKERRQ(ierr);
4552 
4553   /* read in nonzero values */
4554   ierr = PetscBinaryRead(fd,a->a,nz,NULL,PETSC_SCALAR);CHKERRQ(ierr);
4555 
4556   /* set matrix "i" values */
4557   a->i[0] = 0;
4558   for (i=1; i<= M; i++) {
4559     a->i[i]      = a->i[i-1] + rowlengths[i-1];
4560     a->ilen[i-1] = rowlengths[i-1];
4561   }
4562   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
4563 
4564   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4565   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4566   PetscFunctionReturn(0);
4567 }
4568 
4569 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4570 {
4571   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4572   PetscErrorCode ierr;
4573 #if defined(PETSC_USE_COMPLEX)
4574   PetscInt k;
4575 #endif
4576 
4577   PetscFunctionBegin;
4578   /* If the  matrix dimensions are not equal,or no of nonzeros */
4579   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4580     *flg = PETSC_FALSE;
4581     PetscFunctionReturn(0);
4582   }
4583 
4584   /* if the a->i are the same */
4585   ierr = PetscArraycmp(a->i,b->i,A->rmap->n+1,flg);CHKERRQ(ierr);
4586   if (!*flg) PetscFunctionReturn(0);
4587 
4588   /* if a->j are the same */
4589   ierr = PetscArraycmp(a->j,b->j,a->nz,flg);CHKERRQ(ierr);
4590   if (!*flg) PetscFunctionReturn(0);
4591 
4592   /* if a->a are the same */
4593 #if defined(PETSC_USE_COMPLEX)
4594   for (k=0; k<a->nz; k++) {
4595     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4596       *flg = PETSC_FALSE;
4597       PetscFunctionReturn(0);
4598     }
4599   }
4600 #else
4601   ierr = PetscArraycmp(a->a,b->a,a->nz,flg);CHKERRQ(ierr);
4602 #endif
4603   PetscFunctionReturn(0);
4604 }
4605 
4606 /*@
4607      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4608               provided by the user.
4609 
4610       Collective
4611 
4612    Input Parameters:
4613 +   comm - must be an MPI communicator of size 1
4614 .   m - number of rows
4615 .   n - number of columns
4616 .   i - row indices; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
4617 .   j - column indices
4618 -   a - matrix values
4619 
4620    Output Parameter:
4621 .   mat - the matrix
4622 
4623    Level: intermediate
4624 
4625    Notes:
4626        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4627     once the matrix is destroyed and not before
4628 
4629        You cannot set new nonzero locations into this matrix, that will generate an error.
4630 
4631        The i and j indices are 0 based
4632 
4633        The format which is used for the sparse matrix input, is equivalent to a
4634     row-major ordering.. i.e for the following matrix, the input data expected is
4635     as shown
4636 
4637 $        1 0 0
4638 $        2 0 3
4639 $        4 5 6
4640 $
4641 $        i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4642 $        j =  {0,0,2,0,1,2}  [size = 6]; values must be sorted for each row
4643 $        v =  {1,2,3,4,5,6}  [size = 6]
4644 
4645 
4646 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4647 
4648 @*/
4649 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat)
4650 {
4651   PetscErrorCode ierr;
4652   PetscInt       ii;
4653   Mat_SeqAIJ     *aij;
4654 #if defined(PETSC_USE_DEBUG)
4655   PetscInt jj;
4656 #endif
4657 
4658   PetscFunctionBegin;
4659   if (m > 0 && i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4660   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4661   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4662   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4663   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4664   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,0);CHKERRQ(ierr);
4665   aij  = (Mat_SeqAIJ*)(*mat)->data;
4666   ierr = PetscMalloc1(m,&aij->imax);CHKERRQ(ierr);
4667   ierr = PetscMalloc1(m,&aij->ilen);CHKERRQ(ierr);
4668 
4669   aij->i            = i;
4670   aij->j            = j;
4671   aij->a            = a;
4672   aij->singlemalloc = PETSC_FALSE;
4673   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4674   aij->free_a       = PETSC_FALSE;
4675   aij->free_ij      = PETSC_FALSE;
4676 
4677   for (ii=0; ii<m; ii++) {
4678     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4679 #if defined(PETSC_USE_DEBUG)
4680     if (i[ii+1] - i[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row length in i (row indices) row = %D length = %D",ii,i[ii+1] - i[ii]);
4681     for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4682       if (j[jj] < j[jj-1]) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column entry number %D (actual column %D) in row %D is not sorted",jj-i[ii],j[jj],ii);
4683       if (j[jj] == j[jj-1]) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column entry number %D (actual column %D) in row %D is identical to previous entry",jj-i[ii],j[jj],ii);
4684     }
4685 #endif
4686   }
4687 #if defined(PETSC_USE_DEBUG)
4688   for (ii=0; ii<aij->i[m]; ii++) {
4689     if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %D index = %D",ii,j[ii]);
4690     if (j[ii] > n - 1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column index to large at location = %D index = %D",ii,j[ii]);
4691   }
4692 #endif
4693 
4694   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4695   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4696   PetscFunctionReturn(0);
4697 }
4698 /*@C
4699      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4700               provided by the user.
4701 
4702       Collective
4703 
4704    Input Parameters:
4705 +   comm - must be an MPI communicator of size 1
4706 .   m   - number of rows
4707 .   n   - number of columns
4708 .   i   - row indices
4709 .   j   - column indices
4710 .   a   - matrix values
4711 .   nz  - number of nonzeros
4712 -   idx - 0 or 1 based
4713 
4714    Output Parameter:
4715 .   mat - the matrix
4716 
4717    Level: intermediate
4718 
4719    Notes:
4720        The i and j indices are 0 based
4721 
4722        The format which is used for the sparse matrix input, is equivalent to a
4723     row-major ordering.. i.e for the following matrix, the input data expected is
4724     as shown:
4725 
4726         1 0 0
4727         2 0 3
4728         4 5 6
4729 
4730         i =  {0,1,1,2,2,2}
4731         j =  {0,0,2,0,1,2}
4732         v =  {1,2,3,4,5,6}
4733 
4734 
4735 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4736 
4737 @*/
4738 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat,PetscInt nz,PetscBool idx)
4739 {
4740   PetscErrorCode ierr;
4741   PetscInt       ii, *nnz, one = 1,row,col;
4742 
4743 
4744   PetscFunctionBegin;
4745   ierr = PetscCalloc1(m,&nnz);CHKERRQ(ierr);
4746   for (ii = 0; ii < nz; ii++) {
4747     nnz[i[ii] - !!idx] += 1;
4748   }
4749   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4750   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4751   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4752   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4753   for (ii = 0; ii < nz; ii++) {
4754     if (idx) {
4755       row = i[ii] - 1;
4756       col = j[ii] - 1;
4757     } else {
4758       row = i[ii];
4759       col = j[ii];
4760     }
4761     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4762   }
4763   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4764   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4765   ierr = PetscFree(nnz);CHKERRQ(ierr);
4766   PetscFunctionReturn(0);
4767 }
4768 
4769 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4770 {
4771   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4772   PetscErrorCode ierr;
4773 
4774   PetscFunctionBegin;
4775   a->idiagvalid  = PETSC_FALSE;
4776   a->ibdiagvalid = PETSC_FALSE;
4777 
4778   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4779   PetscFunctionReturn(0);
4780 }
4781 
4782 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4783 {
4784   PetscErrorCode ierr;
4785   PetscMPIInt    size;
4786 
4787   PetscFunctionBegin;
4788   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4789   if (size == 1) {
4790     if (scall == MAT_INITIAL_MATRIX) {
4791       ierr = MatDuplicate(inmat,MAT_COPY_VALUES,outmat);CHKERRQ(ierr);
4792     } else {
4793       ierr = MatCopy(inmat,*outmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4794     }
4795   } else {
4796     ierr = MatCreateMPIMatConcatenateSeqMat_MPIAIJ(comm,inmat,n,scall,outmat);CHKERRQ(ierr);
4797   }
4798   PetscFunctionReturn(0);
4799 }
4800 
4801 /*
4802  Permute A into C's *local* index space using rowemb,colemb.
4803  The embedding are supposed to be injections and the above implies that the range of rowemb is a subset
4804  of [0,m), colemb is in [0,n).
4805  If pattern == DIFFERENT_NONZERO_PATTERN, C is preallocated according to A.
4806  */
4807 PetscErrorCode MatSetSeqMat_SeqAIJ(Mat C,IS rowemb,IS colemb,MatStructure pattern,Mat B)
4808 {
4809   /* If making this function public, change the error returned in this function away from _PLIB. */
4810   PetscErrorCode ierr;
4811   Mat_SeqAIJ     *Baij;
4812   PetscBool      seqaij;
4813   PetscInt       m,n,*nz,i,j,count;
4814   PetscScalar    v;
4815   const PetscInt *rowindices,*colindices;
4816 
4817   PetscFunctionBegin;
4818   if (!B) PetscFunctionReturn(0);
4819   /* Check to make sure the target matrix (and embeddings) are compatible with C and each other. */
4820   ierr = PetscObjectBaseTypeCompare((PetscObject)B,MATSEQAIJ,&seqaij);CHKERRQ(ierr);
4821   if (!seqaij) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is of wrong type");
4822   if (rowemb) {
4823     ierr = ISGetLocalSize(rowemb,&m);CHKERRQ(ierr);
4824     if (m != B->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Row IS of size %D is incompatible with matrix row size %D",m,B->rmap->n);
4825   } else {
4826     if (C->rmap->n != B->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is row-incompatible with the target matrix");
4827   }
4828   if (colemb) {
4829     ierr = ISGetLocalSize(colemb,&n);CHKERRQ(ierr);
4830     if (n != B->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diag col IS of size %D is incompatible with input matrix col size %D",n,B->cmap->n);
4831   } else {
4832     if (C->cmap->n != B->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is col-incompatible with the target matrix");
4833   }
4834 
4835   Baij = (Mat_SeqAIJ*)(B->data);
4836   if (pattern == DIFFERENT_NONZERO_PATTERN) {
4837     ierr = PetscMalloc1(B->rmap->n,&nz);CHKERRQ(ierr);
4838     for (i=0; i<B->rmap->n; i++) {
4839       nz[i] = Baij->i[i+1] - Baij->i[i];
4840     }
4841     ierr = MatSeqAIJSetPreallocation(C,0,nz);CHKERRQ(ierr);
4842     ierr = PetscFree(nz);CHKERRQ(ierr);
4843   }
4844   if (pattern == SUBSET_NONZERO_PATTERN) {
4845     ierr = MatZeroEntries(C);CHKERRQ(ierr);
4846   }
4847   count = 0;
4848   rowindices = NULL;
4849   colindices = NULL;
4850   if (rowemb) {
4851     ierr = ISGetIndices(rowemb,&rowindices);CHKERRQ(ierr);
4852   }
4853   if (colemb) {
4854     ierr = ISGetIndices(colemb,&colindices);CHKERRQ(ierr);
4855   }
4856   for (i=0; i<B->rmap->n; i++) {
4857     PetscInt row;
4858     row = i;
4859     if (rowindices) row = rowindices[i];
4860     for (j=Baij->i[i]; j<Baij->i[i+1]; j++) {
4861       PetscInt col;
4862       col  = Baij->j[count];
4863       if (colindices) col = colindices[col];
4864       v    = Baij->a[count];
4865       ierr = MatSetValues(C,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
4866       ++count;
4867     }
4868   }
4869   /* FIXME: set C's nonzerostate correctly. */
4870   /* Assembly for C is necessary. */
4871   C->preallocated = PETSC_TRUE;
4872   C->assembled     = PETSC_TRUE;
4873   C->was_assembled = PETSC_FALSE;
4874   PetscFunctionReturn(0);
4875 }
4876 
4877 PetscFunctionList MatSeqAIJList = NULL;
4878 
4879 /*@C
4880    MatSeqAIJSetType - Converts a MATSEQAIJ matrix to a subtype
4881 
4882    Collective on Mat
4883 
4884    Input Parameters:
4885 +  mat      - the matrix object
4886 -  matype   - matrix type
4887 
4888    Options Database Key:
4889 .  -mat_seqai_type  <method> - for example seqaijcrl
4890 
4891 
4892   Level: intermediate
4893 
4894 .seealso: PCSetType(), VecSetType(), MatCreate(), MatType, Mat
4895 @*/
4896 PetscErrorCode  MatSeqAIJSetType(Mat mat, MatType matype)
4897 {
4898   PetscErrorCode ierr,(*r)(Mat,MatType,MatReuse,Mat*);
4899   PetscBool      sametype;
4900 
4901   PetscFunctionBegin;
4902   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
4903   ierr = PetscObjectTypeCompare((PetscObject)mat,matype,&sametype);CHKERRQ(ierr);
4904   if (sametype) PetscFunctionReturn(0);
4905 
4906   ierr =  PetscFunctionListFind(MatSeqAIJList,matype,&r);CHKERRQ(ierr);
4907   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown Mat type given: %s",matype);
4908   ierr = (*r)(mat,matype,MAT_INPLACE_MATRIX,&mat);CHKERRQ(ierr);
4909   PetscFunctionReturn(0);
4910 }
4911 
4912 
4913 /*@C
4914   MatSeqAIJRegister -  - Adds a new sub-matrix type for sequential AIJ matrices
4915 
4916    Not Collective
4917 
4918    Input Parameters:
4919 +  name - name of a new user-defined matrix type, for example MATSEQAIJCRL
4920 -  function - routine to convert to subtype
4921 
4922    Notes:
4923    MatSeqAIJRegister() may be called multiple times to add several user-defined solvers.
4924 
4925 
4926    Then, your matrix can be chosen with the procedural interface at runtime via the option
4927 $     -mat_seqaij_type my_mat
4928 
4929    Level: advanced
4930 
4931 .seealso: MatSeqAIJRegisterAll()
4932 
4933 
4934   Level: advanced
4935 @*/
4936 PetscErrorCode  MatSeqAIJRegister(const char sname[],PetscErrorCode (*function)(Mat,MatType,MatReuse,Mat *))
4937 {
4938   PetscErrorCode ierr;
4939 
4940   PetscFunctionBegin;
4941   ierr = MatInitializePackage();CHKERRQ(ierr);
4942   ierr = PetscFunctionListAdd(&MatSeqAIJList,sname,function);CHKERRQ(ierr);
4943   PetscFunctionReturn(0);
4944 }
4945 
4946 PetscBool MatSeqAIJRegisterAllCalled = PETSC_FALSE;
4947 
4948 /*@C
4949   MatSeqAIJRegisterAll - Registers all of the matrix subtypes of SeqAIJ
4950 
4951   Not Collective
4952 
4953   Level: advanced
4954 
4955   Developers Note: CUSP and CUSPARSE do not yet support the  MatConvert_SeqAIJ..() paradigm and thus cannot be registered here
4956 
4957 .seealso:  MatRegisterAll(), MatSeqAIJRegister()
4958 @*/
4959 PetscErrorCode  MatSeqAIJRegisterAll(void)
4960 {
4961   PetscErrorCode ierr;
4962 
4963   PetscFunctionBegin;
4964   if (MatSeqAIJRegisterAllCalled) PetscFunctionReturn(0);
4965   MatSeqAIJRegisterAllCalled = PETSC_TRUE;
4966 
4967   ierr = MatSeqAIJRegister(MATSEQAIJCRL,      MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4968   ierr = MatSeqAIJRegister(MATSEQAIJPERM,     MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4969   ierr = MatSeqAIJRegister(MATSEQAIJSELL,     MatConvert_SeqAIJ_SeqAIJSELL);CHKERRQ(ierr);
4970 #if defined(PETSC_HAVE_MKL_SPARSE)
4971   ierr = MatSeqAIJRegister(MATSEQAIJMKL,      MatConvert_SeqAIJ_SeqAIJMKL);CHKERRQ(ierr);
4972 #endif
4973 #if defined(PETSC_HAVE_VIENNACL) && defined(PETSC_HAVE_VIENNACL_NO_CUDA)
4974   ierr = MatSeqAIJRegister(MATMPIAIJVIENNACL, MatConvert_SeqAIJ_SeqAIJViennaCL);CHKERRQ(ierr);
4975 #endif
4976   PetscFunctionReturn(0);
4977 }
4978 
4979 /*
4980     Special version for direct calls from Fortran
4981 */
4982 #include <petsc/private/fortranimpl.h>
4983 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4984 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
4985 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4986 #define matsetvaluesseqaij_ matsetvaluesseqaij
4987 #endif
4988 
4989 /* Change these macros so can be used in void function */
4990 #undef CHKERRQ
4991 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
4992 #undef SETERRQ2
4993 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4994 #undef SETERRQ3
4995 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4996 
4997 PETSC_EXTERN void PETSC_STDCALL matsetvaluesseqaij_(Mat *AA,PetscInt *mm,const PetscInt im[],PetscInt *nn,const PetscInt in[],const PetscScalar v[],InsertMode *isis, PetscErrorCode *_ierr)
4998 {
4999   Mat            A  = *AA;
5000   PetscInt       m  = *mm, n = *nn;
5001   InsertMode     is = *isis;
5002   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
5003   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
5004   PetscInt       *imax,*ai,*ailen;
5005   PetscErrorCode ierr;
5006   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
5007   MatScalar      *ap,value,*aa;
5008   PetscBool      ignorezeroentries = a->ignorezeroentries;
5009   PetscBool      roworiented       = a->roworiented;
5010 
5011   PetscFunctionBegin;
5012   MatCheckPreallocated(A,1);
5013   imax  = a->imax;
5014   ai    = a->i;
5015   ailen = a->ilen;
5016   aj    = a->j;
5017   aa    = a->a;
5018 
5019   for (k=0; k<m; k++) { /* loop over added rows */
5020     row = im[k];
5021     if (row < 0) continue;
5022 #if defined(PETSC_USE_DEBUG)
5023     if (row >= A->rmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
5024 #endif
5025     rp   = aj + ai[row]; ap = aa + ai[row];
5026     rmax = imax[row]; nrow = ailen[row];
5027     low  = 0;
5028     high = nrow;
5029     for (l=0; l<n; l++) { /* loop over added columns */
5030       if (in[l] < 0) continue;
5031 #if defined(PETSC_USE_DEBUG)
5032       if (in[l] >= A->cmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
5033 #endif
5034       col = in[l];
5035       if (roworiented) value = v[l + k*n];
5036       else value = v[k + l*m];
5037 
5038       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
5039 
5040       if (col <= lastcol) low = 0;
5041       else high = nrow;
5042       lastcol = col;
5043       while (high-low > 5) {
5044         t = (low+high)/2;
5045         if (rp[t] > col) high = t;
5046         else             low  = t;
5047       }
5048       for (i=low; i<high; i++) {
5049         if (rp[i] > col) break;
5050         if (rp[i] == col) {
5051           if (is == ADD_VALUES) ap[i] += value;
5052           else                  ap[i] = value;
5053           goto noinsert;
5054         }
5055       }
5056       if (value == 0.0 && ignorezeroentries) goto noinsert;
5057       if (nonew == 1) goto noinsert;
5058       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
5059       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
5060       N = nrow++ - 1; a->nz++; high++;
5061       /* shift up all the later entries in this row */
5062       for (ii=N; ii>=i; ii--) {
5063         rp[ii+1] = rp[ii];
5064         ap[ii+1] = ap[ii];
5065       }
5066       rp[i] = col;
5067       ap[i] = value;
5068       A->nonzerostate++;
5069 noinsert:;
5070       low = i + 1;
5071     }
5072     ailen[row] = nrow;
5073   }
5074   PetscFunctionReturnVoid();
5075 }
5076