xref: /petsc/src/mat/impls/aij/seq/aij.c (revision 1873fc9fedfc3bd8fc2f82ccd29ab8b44a80f1db)
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->offloadmask != PETSC_OFFLOAD_UNALLOCATED && ai[row+1]-ai[row]) A->offloadmask = 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->offloadmask != PETSC_OFFLOAD_UNALLOCATED && m && n) A->offloadmask = 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->offloadmask != PETSC_OFFLOAD_UNALLOCATED && inserted) A->offloadmask = 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->offloadmask != PETSC_OFFLOAD_UNALLOCATED && m && n) A->offloadmask = 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->offloadmask != PETSC_OFFLOAD_UNALLOCATED) A->offloadmask = 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->offloadmask != PETSC_OFFLOAD_UNALLOCATED) A->offloadmask = 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->offloadmask != PETSC_OFFLOAD_UNALLOCATED) A->offloadmask = 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 = a->maxnz;
1988   info->nz_used      = a->nz;
1989   info->nz_unneeded  = (a->maxnz - a->nz);
1990   info->assemblies   = A->num_ass;
1991   info->mallocs      = 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->offloadmask != PETSC_OFFLOAD_UNALLOCATED) A->offloadmask = 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->offloadmask != PETSC_OFFLOAD_UNALLOCATED) A->offloadmask = 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->offloadmask != PETSC_OFFLOAD_UNALLOCATED) A->offloadmask = 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 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
2566   ierr = MatPinToCPU(C,A->pinnedtocpu);CHKERRQ(ierr);
2567 #endif
2568   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2569   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2570 
2571   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
2572   *B   = C;
2573   PetscFunctionReturn(0);
2574 }
2575 
2576 PetscErrorCode  MatGetMultiProcBlock_SeqAIJ(Mat mat,MPI_Comm subComm,MatReuse scall,Mat *subMat)
2577 {
2578   PetscErrorCode ierr;
2579   Mat            B;
2580 
2581   PetscFunctionBegin;
2582   if (scall == MAT_INITIAL_MATRIX) {
2583     ierr    = MatCreate(subComm,&B);CHKERRQ(ierr);
2584     ierr    = MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->n,mat->cmap->n);CHKERRQ(ierr);
2585     ierr    = MatSetBlockSizesFromMats(B,mat,mat);CHKERRQ(ierr);
2586     ierr    = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
2587     ierr    = MatDuplicateNoCreate_SeqAIJ(B,mat,MAT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
2588     *subMat = B;
2589   } else {
2590     ierr = MatCopy_SeqAIJ(mat,*subMat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2591   }
2592   PetscFunctionReturn(0);
2593 }
2594 
2595 PetscErrorCode MatILUFactor_SeqAIJ(Mat inA,IS row,IS col,const MatFactorInfo *info)
2596 {
2597   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)inA->data;
2598   PetscErrorCode ierr;
2599   Mat            outA;
2600   PetscBool      row_identity,col_identity;
2601 
2602   PetscFunctionBegin;
2603   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels=0 supported for in-place ilu");
2604 
2605   ierr = ISIdentity(row,&row_identity);CHKERRQ(ierr);
2606   ierr = ISIdentity(col,&col_identity);CHKERRQ(ierr);
2607 
2608   outA             = inA;
2609   outA->factortype = MAT_FACTOR_LU;
2610   ierr = PetscFree(inA->solvertype);CHKERRQ(ierr);
2611   ierr = PetscStrallocpy(MATSOLVERPETSC,&inA->solvertype);CHKERRQ(ierr);
2612 
2613   ierr = PetscObjectReference((PetscObject)row);CHKERRQ(ierr);
2614   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
2615 
2616   a->row = row;
2617 
2618   ierr = PetscObjectReference((PetscObject)col);CHKERRQ(ierr);
2619   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
2620 
2621   a->col = col;
2622 
2623   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
2624   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
2625   ierr = ISInvertPermutation(col,PETSC_DECIDE,&a->icol);CHKERRQ(ierr);
2626   ierr = PetscLogObjectParent((PetscObject)inA,(PetscObject)a->icol);CHKERRQ(ierr);
2627 
2628   if (!a->solve_work) { /* this matrix may have been factored before */
2629     ierr = PetscMalloc1(inA->rmap->n+1,&a->solve_work);CHKERRQ(ierr);
2630     ierr = PetscLogObjectMemory((PetscObject)inA, (inA->rmap->n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2631   }
2632 
2633   ierr = MatMarkDiagonal_SeqAIJ(inA);CHKERRQ(ierr);
2634   if (row_identity && col_identity) {
2635     ierr = MatLUFactorNumeric_SeqAIJ_inplace(outA,inA,info);CHKERRQ(ierr);
2636   } else {
2637     ierr = MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA,inA,info);CHKERRQ(ierr);
2638   }
2639   PetscFunctionReturn(0);
2640 }
2641 
2642 PetscErrorCode MatScale_SeqAIJ(Mat inA,PetscScalar alpha)
2643 {
2644   Mat_SeqAIJ     *a     = (Mat_SeqAIJ*)inA->data;
2645   PetscScalar    oalpha = alpha;
2646   PetscErrorCode ierr;
2647   PetscBLASInt   one = 1,bnz;
2648 
2649   PetscFunctionBegin;
2650   ierr = PetscBLASIntCast(a->nz,&bnz);CHKERRQ(ierr);
2651   PetscStackCallBLAS("BLASscal",BLASscal_(&bnz,&oalpha,a->a,&one));
2652   ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2653   ierr = MatSeqAIJInvalidateDiagonal(inA);CHKERRQ(ierr);
2654 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
2655   if (inA->offloadmask != PETSC_OFFLOAD_UNALLOCATED) inA->offloadmask = PETSC_OFFLOAD_CPU;
2656 #endif
2657   PetscFunctionReturn(0);
2658 }
2659 
2660 PetscErrorCode MatDestroySubMatrix_Private(Mat_SubSppt *submatj)
2661 {
2662   PetscErrorCode ierr;
2663   PetscInt       i;
2664 
2665   PetscFunctionBegin;
2666   if (!submatj->id) { /* delete data that are linked only to submats[id=0] */
2667     ierr = PetscFree4(submatj->sbuf1,submatj->ptr,submatj->tmp,submatj->ctr);CHKERRQ(ierr);
2668 
2669     for (i=0; i<submatj->nrqr; ++i) {
2670       ierr = PetscFree(submatj->sbuf2[i]);CHKERRQ(ierr);
2671     }
2672     ierr = PetscFree3(submatj->sbuf2,submatj->req_size,submatj->req_source1);CHKERRQ(ierr);
2673 
2674     if (submatj->rbuf1) {
2675       ierr = PetscFree(submatj->rbuf1[0]);CHKERRQ(ierr);
2676       ierr = PetscFree(submatj->rbuf1);CHKERRQ(ierr);
2677     }
2678 
2679     for (i=0; i<submatj->nrqs; ++i) {
2680       ierr = PetscFree(submatj->rbuf3[i]);CHKERRQ(ierr);
2681     }
2682     ierr = PetscFree3(submatj->req_source2,submatj->rbuf2,submatj->rbuf3);CHKERRQ(ierr);
2683     ierr = PetscFree(submatj->pa);CHKERRQ(ierr);
2684   }
2685 
2686 #if defined(PETSC_USE_CTABLE)
2687   ierr = PetscTableDestroy((PetscTable*)&submatj->rmap);CHKERRQ(ierr);
2688   if (submatj->cmap_loc) {ierr = PetscFree(submatj->cmap_loc);CHKERRQ(ierr);}
2689   ierr = PetscFree(submatj->rmap_loc);CHKERRQ(ierr);
2690 #else
2691   ierr = PetscFree(submatj->rmap);CHKERRQ(ierr);
2692 #endif
2693 
2694   if (!submatj->allcolumns) {
2695 #if defined(PETSC_USE_CTABLE)
2696     ierr = PetscTableDestroy((PetscTable*)&submatj->cmap);CHKERRQ(ierr);
2697 #else
2698     ierr = PetscFree(submatj->cmap);CHKERRQ(ierr);
2699 #endif
2700   }
2701   ierr = PetscFree(submatj->row2proc);CHKERRQ(ierr);
2702 
2703   ierr = PetscFree(submatj);CHKERRQ(ierr);
2704   PetscFunctionReturn(0);
2705 }
2706 
2707 PetscErrorCode MatDestroySubMatrix_SeqAIJ(Mat C)
2708 {
2709   PetscErrorCode ierr;
2710   Mat_SeqAIJ     *c = (Mat_SeqAIJ*)C->data;
2711   Mat_SubSppt    *submatj = c->submatis1;
2712 
2713   PetscFunctionBegin;
2714   ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
2715   ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
2716   PetscFunctionReturn(0);
2717 }
2718 
2719 PetscErrorCode MatDestroySubMatrices_SeqAIJ(PetscInt n,Mat *mat[])
2720 {
2721   PetscErrorCode ierr;
2722   PetscInt       i;
2723   Mat            C;
2724   Mat_SeqAIJ     *c;
2725   Mat_SubSppt    *submatj;
2726 
2727   PetscFunctionBegin;
2728   for (i=0; i<n; i++) {
2729     C       = (*mat)[i];
2730     c       = (Mat_SeqAIJ*)C->data;
2731     submatj = c->submatis1;
2732     if (submatj) {
2733       if (--((PetscObject)C)->refct <= 0) {
2734         ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
2735         ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
2736         ierr = PetscFree(C->defaultvectype);CHKERRQ(ierr);
2737         ierr = PetscLayoutDestroy(&C->rmap);CHKERRQ(ierr);
2738         ierr = PetscLayoutDestroy(&C->cmap);CHKERRQ(ierr);
2739         ierr = PetscHeaderDestroy(&C);CHKERRQ(ierr);
2740       }
2741     } else {
2742       ierr = MatDestroy(&C);CHKERRQ(ierr);
2743     }
2744   }
2745 
2746   /* Destroy Dummy submatrices created for reuse */
2747   ierr = MatDestroySubMatrices_Dummy(n,mat);CHKERRQ(ierr);
2748 
2749   ierr = PetscFree(*mat);CHKERRQ(ierr);
2750   PetscFunctionReturn(0);
2751 }
2752 
2753 PetscErrorCode MatCreateSubMatrices_SeqAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
2754 {
2755   PetscErrorCode ierr;
2756   PetscInt       i;
2757 
2758   PetscFunctionBegin;
2759   if (scall == MAT_INITIAL_MATRIX) {
2760     ierr = PetscCalloc1(n+1,B);CHKERRQ(ierr);
2761   }
2762 
2763   for (i=0; i<n; i++) {
2764     ierr = MatCreateSubMatrix_SeqAIJ(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]);CHKERRQ(ierr);
2765   }
2766   PetscFunctionReturn(0);
2767 }
2768 
2769 PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
2770 {
2771   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2772   PetscErrorCode ierr;
2773   PetscInt       row,i,j,k,l,m,n,*nidx,isz,val;
2774   const PetscInt *idx;
2775   PetscInt       start,end,*ai,*aj;
2776   PetscBT        table;
2777 
2778   PetscFunctionBegin;
2779   m  = A->rmap->n;
2780   ai = a->i;
2781   aj = a->j;
2782 
2783   if (ov < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"illegal negative overlap value used");
2784 
2785   ierr = PetscMalloc1(m+1,&nidx);CHKERRQ(ierr);
2786   ierr = PetscBTCreate(m,&table);CHKERRQ(ierr);
2787 
2788   for (i=0; i<is_max; i++) {
2789     /* Initialize the two local arrays */
2790     isz  = 0;
2791     ierr = PetscBTMemzero(m,table);CHKERRQ(ierr);
2792 
2793     /* Extract the indices, assume there can be duplicate entries */
2794     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
2795     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
2796 
2797     /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2798     for (j=0; j<n; ++j) {
2799       if (!PetscBTLookupSet(table,idx[j])) nidx[isz++] = idx[j];
2800     }
2801     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
2802     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
2803 
2804     k = 0;
2805     for (j=0; j<ov; j++) { /* for each overlap */
2806       n = isz;
2807       for (; k<n; k++) { /* do only those rows in nidx[k], which are not done yet */
2808         row   = nidx[k];
2809         start = ai[row];
2810         end   = ai[row+1];
2811         for (l = start; l<end; l++) {
2812           val = aj[l];
2813           if (!PetscBTLookupSet(table,val)) nidx[isz++] = val;
2814         }
2815       }
2816     }
2817     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz,nidx,PETSC_COPY_VALUES,(is+i));CHKERRQ(ierr);
2818   }
2819   ierr = PetscBTDestroy(&table);CHKERRQ(ierr);
2820   ierr = PetscFree(nidx);CHKERRQ(ierr);
2821   PetscFunctionReturn(0);
2822 }
2823 
2824 /* -------------------------------------------------------------- */
2825 PetscErrorCode MatPermute_SeqAIJ(Mat A,IS rowp,IS colp,Mat *B)
2826 {
2827   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2828   PetscErrorCode ierr;
2829   PetscInt       i,nz = 0,m = A->rmap->n,n = A->cmap->n;
2830   const PetscInt *row,*col;
2831   PetscInt       *cnew,j,*lens;
2832   IS             icolp,irowp;
2833   PetscInt       *cwork = NULL;
2834   PetscScalar    *vwork = NULL;
2835 
2836   PetscFunctionBegin;
2837   ierr = ISInvertPermutation(rowp,PETSC_DECIDE,&irowp);CHKERRQ(ierr);
2838   ierr = ISGetIndices(irowp,&row);CHKERRQ(ierr);
2839   ierr = ISInvertPermutation(colp,PETSC_DECIDE,&icolp);CHKERRQ(ierr);
2840   ierr = ISGetIndices(icolp,&col);CHKERRQ(ierr);
2841 
2842   /* determine lengths of permuted rows */
2843   ierr = PetscMalloc1(m+1,&lens);CHKERRQ(ierr);
2844   for (i=0; i<m; i++) lens[row[i]] = a->i[i+1] - a->i[i];
2845   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
2846   ierr = MatSetSizes(*B,m,n,m,n);CHKERRQ(ierr);
2847   ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
2848   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2849   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*B,0,lens);CHKERRQ(ierr);
2850   ierr = PetscFree(lens);CHKERRQ(ierr);
2851 
2852   ierr = PetscMalloc1(n,&cnew);CHKERRQ(ierr);
2853   for (i=0; i<m; i++) {
2854     ierr = MatGetRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2855     for (j=0; j<nz; j++) cnew[j] = col[cwork[j]];
2856     ierr = MatSetValues_SeqAIJ(*B,1,&row[i],nz,cnew,vwork,INSERT_VALUES);CHKERRQ(ierr);
2857     ierr = MatRestoreRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2858   }
2859   ierr = PetscFree(cnew);CHKERRQ(ierr);
2860 
2861   (*B)->assembled = PETSC_FALSE;
2862 
2863 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
2864   ierr = MatPinToCPU(*B,A->pinnedtocpu);CHKERRQ(ierr);
2865 #endif
2866   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2867   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2868   ierr = ISRestoreIndices(irowp,&row);CHKERRQ(ierr);
2869   ierr = ISRestoreIndices(icolp,&col);CHKERRQ(ierr);
2870   ierr = ISDestroy(&irowp);CHKERRQ(ierr);
2871   ierr = ISDestroy(&icolp);CHKERRQ(ierr);
2872   PetscFunctionReturn(0);
2873 }
2874 
2875 PetscErrorCode MatCopy_SeqAIJ(Mat A,Mat B,MatStructure str)
2876 {
2877   PetscErrorCode ierr;
2878 
2879   PetscFunctionBegin;
2880   /* If the two matrices have the same copy implementation, use fast copy. */
2881   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
2882     Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2883     Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data;
2884 
2885     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");
2886     ierr = PetscArraycpy(b->a,a->a,a->i[A->rmap->n]);CHKERRQ(ierr);
2887     ierr = PetscObjectStateIncrease((PetscObject)B);CHKERRQ(ierr);
2888   } else {
2889     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2890   }
2891   PetscFunctionReturn(0);
2892 }
2893 
2894 PetscErrorCode MatSetUp_SeqAIJ(Mat A)
2895 {
2896   PetscErrorCode ierr;
2897 
2898   PetscFunctionBegin;
2899   ierr =  MatSeqAIJSetPreallocation_SeqAIJ(A,PETSC_DEFAULT,0);CHKERRQ(ierr);
2900   PetscFunctionReturn(0);
2901 }
2902 
2903 PETSC_INTERN PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A,PetscScalar *array[])
2904 {
2905   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2906 
2907   PetscFunctionBegin;
2908   *array = a->a;
2909   PetscFunctionReturn(0);
2910 }
2911 
2912 PETSC_INTERN PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A,PetscScalar *array[])
2913 {
2914   PetscFunctionBegin;
2915   *array = NULL;
2916   PetscFunctionReturn(0);
2917 }
2918 
2919 /*
2920    Computes the number of nonzeros per row needed for preallocation when X and Y
2921    have different nonzero structure.
2922 */
2923 PetscErrorCode MatAXPYGetPreallocation_SeqX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *yi,const PetscInt *yj,PetscInt *nnz)
2924 {
2925   PetscInt       i,j,k,nzx,nzy;
2926 
2927   PetscFunctionBegin;
2928   /* Set the number of nonzeros in the new matrix */
2929   for (i=0; i<m; i++) {
2930     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2931     nzx = xi[i+1] - xi[i];
2932     nzy = yi[i+1] - yi[i];
2933     nnz[i] = 0;
2934     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2935       for (; k<nzy && yjj[k]<xjj[j]; k++) nnz[i]++; /* Catch up to X */
2936       if (k<nzy && yjj[k]==xjj[j]) k++;             /* Skip duplicate */
2937       nnz[i]++;
2938     }
2939     for (; k<nzy; k++) nnz[i]++;
2940   }
2941   PetscFunctionReturn(0);
2942 }
2943 
2944 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
2945 {
2946   PetscInt       m = Y->rmap->N;
2947   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2948   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2949   PetscErrorCode ierr;
2950 
2951   PetscFunctionBegin;
2952   /* Set the number of nonzeros in the new matrix */
2953   ierr = MatAXPYGetPreallocation_SeqX_private(m,x->i,x->j,y->i,y->j,nnz);CHKERRQ(ierr);
2954   PetscFunctionReturn(0);
2955 }
2956 
2957 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2958 {
2959   PetscErrorCode ierr;
2960   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
2961   PetscBLASInt   one=1,bnz;
2962 
2963   PetscFunctionBegin;
2964   ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2965   if (str == SAME_NONZERO_PATTERN) {
2966     PetscScalar alpha = a;
2967     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2968     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
2969     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2970     /* the MatAXPY_Basic* subroutines calls MatAssembly, so the matrix on the GPU
2971        will be updated */
2972 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
2973     if (Y->offloadmask != PETSC_OFFLOAD_UNALLOCATED) {
2974       Y->offloadmask = PETSC_OFFLOAD_CPU;
2975     }
2976 #endif
2977   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2978     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2979   } else {
2980     Mat      B;
2981     PetscInt *nnz;
2982     ierr = PetscMalloc1(Y->rmap->N,&nnz);CHKERRQ(ierr);
2983     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2984     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2985     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2986     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2987     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
2988     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
2989     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
2990     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2991     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2992     ierr = PetscFree(nnz);CHKERRQ(ierr);
2993   }
2994   PetscFunctionReturn(0);
2995 }
2996 
2997 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
2998 {
2999 #if defined(PETSC_USE_COMPLEX)
3000   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
3001   PetscInt    i,nz;
3002   PetscScalar *a;
3003 
3004   PetscFunctionBegin;
3005   nz = aij->nz;
3006   a  = aij->a;
3007   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
3008 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
3009   if (mat->offloadmask != PETSC_OFFLOAD_UNALLOCATED) mat->offloadmask = PETSC_OFFLOAD_CPU;
3010 #endif
3011 #else
3012   PetscFunctionBegin;
3013 #endif
3014   PetscFunctionReturn(0);
3015 }
3016 
3017 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3018 {
3019   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3020   PetscErrorCode ierr;
3021   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3022   PetscReal      atmp;
3023   PetscScalar    *x;
3024   MatScalar      *aa;
3025 
3026   PetscFunctionBegin;
3027   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3028   aa = a->a;
3029   ai = a->i;
3030   aj = a->j;
3031 
3032   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3033   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3034   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3035   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3036   for (i=0; i<m; i++) {
3037     ncols = ai[1] - ai[0]; ai++;
3038     x[i]  = 0.0;
3039     for (j=0; j<ncols; j++) {
3040       atmp = PetscAbsScalar(*aa);
3041       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3042       aa++; aj++;
3043     }
3044   }
3045   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3046   PetscFunctionReturn(0);
3047 }
3048 
3049 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3050 {
3051   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3052   PetscErrorCode ierr;
3053   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3054   PetscScalar    *x;
3055   MatScalar      *aa;
3056 
3057   PetscFunctionBegin;
3058   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3059   aa = a->a;
3060   ai = a->i;
3061   aj = a->j;
3062 
3063   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3064   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3065   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3066   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3067   for (i=0; i<m; i++) {
3068     ncols = ai[1] - ai[0]; ai++;
3069     if (ncols == A->cmap->n) { /* row is dense */
3070       x[i] = *aa; if (idx) idx[i] = 0;
3071     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
3072       x[i] = 0.0;
3073       if (idx) {
3074         idx[i] = 0; /* in case ncols is zero */
3075         for (j=0;j<ncols;j++) { /* find first implicit 0.0 in the row */
3076           if (aj[j] > j) {
3077             idx[i] = j;
3078             break;
3079           }
3080         }
3081       }
3082     }
3083     for (j=0; j<ncols; j++) {
3084       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3085       aa++; aj++;
3086     }
3087   }
3088   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3089   PetscFunctionReturn(0);
3090 }
3091 
3092 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3093 {
3094   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3095   PetscErrorCode ierr;
3096   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3097   PetscReal      atmp;
3098   PetscScalar    *x;
3099   MatScalar      *aa;
3100 
3101   PetscFunctionBegin;
3102   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3103   aa = a->a;
3104   ai = a->i;
3105   aj = a->j;
3106 
3107   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3108   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3109   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3110   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);
3111   for (i=0; i<m; i++) {
3112     ncols = ai[1] - ai[0]; ai++;
3113     if (ncols) {
3114       /* Get first nonzero */
3115       for (j = 0; j < ncols; j++) {
3116         atmp = PetscAbsScalar(aa[j]);
3117         if (atmp > 1.0e-12) {
3118           x[i] = atmp;
3119           if (idx) idx[i] = aj[j];
3120           break;
3121         }
3122       }
3123       if (j == ncols) {x[i] = PetscAbsScalar(*aa); if (idx) idx[i] = *aj;}
3124     } else {
3125       x[i] = 0.0; if (idx) idx[i] = 0;
3126     }
3127     for (j = 0; j < ncols; j++) {
3128       atmp = PetscAbsScalar(*aa);
3129       if (atmp > 1.0e-12 && PetscAbsScalar(x[i]) > atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3130       aa++; aj++;
3131     }
3132   }
3133   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3134   PetscFunctionReturn(0);
3135 }
3136 
3137 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3138 {
3139   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
3140   PetscErrorCode  ierr;
3141   PetscInt        i,j,m = A->rmap->n,ncols,n;
3142   const PetscInt  *ai,*aj;
3143   PetscScalar     *x;
3144   const MatScalar *aa;
3145 
3146   PetscFunctionBegin;
3147   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3148   aa = a->a;
3149   ai = a->i;
3150   aj = a->j;
3151 
3152   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3153   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3154   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3155   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3156   for (i=0; i<m; i++) {
3157     ncols = ai[1] - ai[0]; ai++;
3158     if (ncols == A->cmap->n) { /* row is dense */
3159       x[i] = *aa; if (idx) idx[i] = 0;
3160     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3161       x[i] = 0.0;
3162       if (idx) {   /* find first implicit 0.0 in the row */
3163         idx[i] = 0; /* in case ncols is zero */
3164         for (j=0; j<ncols; j++) {
3165           if (aj[j] > j) {
3166             idx[i] = j;
3167             break;
3168           }
3169         }
3170       }
3171     }
3172     for (j=0; j<ncols; j++) {
3173       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3174       aa++; aj++;
3175     }
3176   }
3177   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3178   PetscFunctionReturn(0);
3179 }
3180 
3181 PetscErrorCode MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3182 {
3183   Mat_SeqAIJ      *a = (Mat_SeqAIJ*) A->data;
3184   PetscErrorCode  ierr;
3185   PetscInt        i,bs = PetscAbs(A->rmap->bs),mbs = A->rmap->n/bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3186   MatScalar       *diag,work[25],*v_work;
3187   const PetscReal shift = 0.0;
3188   PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;
3189 
3190   PetscFunctionBegin;
3191   allowzeropivot = PetscNot(A->erroriffailure);
3192   if (a->ibdiagvalid) {
3193     if (values) *values = a->ibdiag;
3194     PetscFunctionReturn(0);
3195   }
3196   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3197   if (!a->ibdiag) {
3198     ierr = PetscMalloc1(bs2*mbs,&a->ibdiag);CHKERRQ(ierr);
3199     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3200   }
3201   diag = a->ibdiag;
3202   if (values) *values = a->ibdiag;
3203   /* factor and invert each block */
3204   switch (bs) {
3205   case 1:
3206     for (i=0; i<mbs; i++) {
3207       ierr = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3208       if (PetscAbsScalar(diag[i] + shift) < PETSC_MACHINE_EPSILON) {
3209         if (allowzeropivot) {
3210           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3211           A->factorerror_zeropivot_value = PetscAbsScalar(diag[i]);
3212           A->factorerror_zeropivot_row   = i;
3213           ierr = PetscInfo3(A,"Zero pivot, row %D pivot %g tolerance %g\n",i,(double)PetscAbsScalar(diag[i]),(double)PETSC_MACHINE_EPSILON);CHKERRQ(ierr);
3214         } 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);
3215       }
3216       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3217     }
3218     break;
3219   case 2:
3220     for (i=0; i<mbs; i++) {
3221       ij[0] = 2*i; ij[1] = 2*i + 1;
3222       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3223       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3224       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3225       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
3226       diag += 4;
3227     }
3228     break;
3229   case 3:
3230     for (i=0; i<mbs; i++) {
3231       ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
3232       ierr  = MatGetValues(A,3,ij,3,ij,diag);CHKERRQ(ierr);
3233       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3234       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3235       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3236       diag += 9;
3237     }
3238     break;
3239   case 4:
3240     for (i=0; i<mbs; i++) {
3241       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3242       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3243       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3244       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3245       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3246       diag += 16;
3247     }
3248     break;
3249   case 5:
3250     for (i=0; i<mbs; i++) {
3251       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3252       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3253       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3254       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3255       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3256       diag += 25;
3257     }
3258     break;
3259   case 6:
3260     for (i=0; i<mbs; i++) {
3261       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;
3262       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3263       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3264       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3265       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3266       diag += 36;
3267     }
3268     break;
3269   case 7:
3270     for (i=0; i<mbs; i++) {
3271       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;
3272       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3273       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3274       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3275       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3276       diag += 49;
3277     }
3278     break;
3279   default:
3280     ierr = PetscMalloc3(bs,&v_work,bs,&v_pivots,bs,&IJ);CHKERRQ(ierr);
3281     for (i=0; i<mbs; i++) {
3282       for (j=0; j<bs; j++) {
3283         IJ[j] = bs*i + j;
3284       }
3285       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3286       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3287       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3288       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3289       diag += bs2;
3290     }
3291     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3292   }
3293   a->ibdiagvalid = PETSC_TRUE;
3294   PetscFunctionReturn(0);
3295 }
3296 
3297 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3298 {
3299   PetscErrorCode ierr;
3300   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3301   PetscScalar    a;
3302   PetscInt       m,n,i,j,col;
3303 
3304   PetscFunctionBegin;
3305   if (!x->assembled) {
3306     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3307     for (i=0; i<m; i++) {
3308       for (j=0; j<aij->imax[i]; j++) {
3309         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3310         col  = (PetscInt)(n*PetscRealPart(a));
3311         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3312       }
3313     }
3314   } else {
3315     for (i=0; i<aij->nz; i++) {ierr = PetscRandomGetValue(rctx,aij->a+i);CHKERRQ(ierr);}
3316   }
3317   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3318   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3319   PetscFunctionReturn(0);
3320 }
3321 
3322 /* Like MatSetRandom_SeqAIJ, but do not set values on columns in range of [low, high) */
3323 PetscErrorCode  MatSetRandomSkipColumnRange_SeqAIJ_Private(Mat x,PetscInt low,PetscInt high,PetscRandom rctx)
3324 {
3325   PetscErrorCode ierr;
3326   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3327   PetscScalar    a;
3328   PetscInt       m,n,i,j,col,nskip;
3329 
3330   PetscFunctionBegin;
3331   nskip = high - low;
3332   ierr  = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3333   n    -= nskip; /* shrink number of columns where nonzeros can be set */
3334   for (i=0; i<m; i++) {
3335     for (j=0; j<aij->imax[i]; j++) {
3336       ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3337       col  = (PetscInt)(n*PetscRealPart(a));
3338       if (col >= low) col += nskip; /* shift col rightward to skip the hole */
3339       ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3340     }
3341   }
3342   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3343   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3344   PetscFunctionReturn(0);
3345 }
3346 
3347 
3348 /* -------------------------------------------------------------------*/
3349 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3350                                         MatGetRow_SeqAIJ,
3351                                         MatRestoreRow_SeqAIJ,
3352                                         MatMult_SeqAIJ,
3353                                 /*  4*/ MatMultAdd_SeqAIJ,
3354                                         MatMultTranspose_SeqAIJ,
3355                                         MatMultTransposeAdd_SeqAIJ,
3356                                         0,
3357                                         0,
3358                                         0,
3359                                 /* 10*/ 0,
3360                                         MatLUFactor_SeqAIJ,
3361                                         0,
3362                                         MatSOR_SeqAIJ,
3363                                         MatTranspose_SeqAIJ,
3364                                 /*1 5*/ MatGetInfo_SeqAIJ,
3365                                         MatEqual_SeqAIJ,
3366                                         MatGetDiagonal_SeqAIJ,
3367                                         MatDiagonalScale_SeqAIJ,
3368                                         MatNorm_SeqAIJ,
3369                                 /* 20*/ 0,
3370                                         MatAssemblyEnd_SeqAIJ,
3371                                         MatSetOption_SeqAIJ,
3372                                         MatZeroEntries_SeqAIJ,
3373                                 /* 24*/ MatZeroRows_SeqAIJ,
3374                                         0,
3375                                         0,
3376                                         0,
3377                                         0,
3378                                 /* 29*/ MatSetUp_SeqAIJ,
3379                                         0,
3380                                         0,
3381                                         0,
3382                                         0,
3383                                 /* 34*/ MatDuplicate_SeqAIJ,
3384                                         0,
3385                                         0,
3386                                         MatILUFactor_SeqAIJ,
3387                                         0,
3388                                 /* 39*/ MatAXPY_SeqAIJ,
3389                                         MatCreateSubMatrices_SeqAIJ,
3390                                         MatIncreaseOverlap_SeqAIJ,
3391                                         MatGetValues_SeqAIJ,
3392                                         MatCopy_SeqAIJ,
3393                                 /* 44*/ MatGetRowMax_SeqAIJ,
3394                                         MatScale_SeqAIJ,
3395                                         MatShift_SeqAIJ,
3396                                         MatDiagonalSet_SeqAIJ,
3397                                         MatZeroRowsColumns_SeqAIJ,
3398                                 /* 49*/ MatSetRandom_SeqAIJ,
3399                                         MatGetRowIJ_SeqAIJ,
3400                                         MatRestoreRowIJ_SeqAIJ,
3401                                         MatGetColumnIJ_SeqAIJ,
3402                                         MatRestoreColumnIJ_SeqAIJ,
3403                                 /* 54*/ MatFDColoringCreate_SeqXAIJ,
3404                                         0,
3405                                         0,
3406                                         MatPermute_SeqAIJ,
3407                                         0,
3408                                 /* 59*/ 0,
3409                                         MatDestroy_SeqAIJ,
3410                                         MatView_SeqAIJ,
3411                                         0,
3412                                         MatMatMatMult_SeqAIJ_SeqAIJ_SeqAIJ,
3413                                 /* 64*/ MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ,
3414                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3415                                         0,
3416                                         0,
3417                                         0,
3418                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3419                                         MatGetRowMinAbs_SeqAIJ,
3420                                         0,
3421                                         0,
3422                                         0,
3423                                 /* 74*/ 0,
3424                                         MatFDColoringApply_AIJ,
3425                                         0,
3426                                         0,
3427                                         0,
3428                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3429                                         0,
3430                                         0,
3431                                         0,
3432                                         MatLoad_SeqAIJ,
3433                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3434                                         MatIsHermitian_SeqAIJ,
3435                                         0,
3436                                         0,
3437                                         0,
3438                                 /* 89*/ MatMatMult_SeqAIJ_SeqAIJ,
3439                                         MatMatMultSymbolic_SeqAIJ_SeqAIJ,
3440                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3441                                         MatPtAP_SeqAIJ_SeqAIJ,
3442                                         MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy,
3443                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy,
3444                                         MatMatTransposeMult_SeqAIJ_SeqAIJ,
3445                                         MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ,
3446                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3447                                         0,
3448                                 /* 99*/ 0,
3449                                         0,
3450                                         0,
3451                                         MatConjugate_SeqAIJ,
3452                                         0,
3453                                 /*104*/ MatSetValuesRow_SeqAIJ,
3454                                         MatRealPart_SeqAIJ,
3455                                         MatImaginaryPart_SeqAIJ,
3456                                         0,
3457                                         0,
3458                                 /*109*/ MatMatSolve_SeqAIJ,
3459                                         0,
3460                                         MatGetRowMin_SeqAIJ,
3461                                         0,
3462                                         MatMissingDiagonal_SeqAIJ,
3463                                 /*114*/ 0,
3464                                         0,
3465                                         0,
3466                                         0,
3467                                         0,
3468                                 /*119*/ 0,
3469                                         0,
3470                                         0,
3471                                         0,
3472                                         MatGetMultiProcBlock_SeqAIJ,
3473                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3474                                         MatGetColumnNorms_SeqAIJ,
3475                                         MatInvertBlockDiagonal_SeqAIJ,
3476                                         MatInvertVariableBlockDiagonal_SeqAIJ,
3477                                         0,
3478                                 /*129*/ 0,
3479                                         MatTransposeMatMult_SeqAIJ_SeqAIJ,
3480                                         MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ,
3481                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3482                                         MatTransposeColoringCreate_SeqAIJ,
3483                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3484                                         MatTransColoringApplyDenToSp_SeqAIJ,
3485                                         MatRARt_SeqAIJ_SeqAIJ,
3486                                         MatRARtSymbolic_SeqAIJ_SeqAIJ,
3487                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3488                                  /*139*/0,
3489                                         0,
3490                                         0,
3491                                         MatFDColoringSetUp_SeqXAIJ,
3492                                         MatFindOffBlockDiagonalEntries_SeqAIJ,
3493                                  /*144*/MatCreateMPIMatConcatenateSeqMat_SeqAIJ,
3494                                         MatDestroySubMatrices_SeqAIJ
3495 };
3496 
3497 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3498 {
3499   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3500   PetscInt   i,nz,n;
3501 
3502   PetscFunctionBegin;
3503   nz = aij->maxnz;
3504   n  = mat->rmap->n;
3505   for (i=0; i<nz; i++) {
3506     aij->j[i] = indices[i];
3507   }
3508   aij->nz = nz;
3509   for (i=0; i<n; i++) {
3510     aij->ilen[i] = aij->imax[i];
3511   }
3512   PetscFunctionReturn(0);
3513 }
3514 
3515 /*
3516  * When a sparse matrix has many zero columns, we should compact them out to save the space
3517  * This happens in MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable()
3518  * */
3519 PetscErrorCode  MatSeqAIJCompactOutExtraColumns_SeqAIJ(Mat mat, ISLocalToGlobalMapping *mapping)
3520 {
3521   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3522   PetscTable         gid1_lid1;
3523   PetscTablePosition tpos;
3524   PetscInt           gid,lid,i,j,ncols,ec;
3525   PetscInt           *garray;
3526   PetscErrorCode  ierr;
3527 
3528   PetscFunctionBegin;
3529   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3530   PetscValidPointer(mapping,2);
3531   /* use a table */
3532   ierr = PetscTableCreate(mat->rmap->n,mat->cmap->N+1,&gid1_lid1);CHKERRQ(ierr);
3533   ec = 0;
3534   for (i=0; i<mat->rmap->n; i++) {
3535     ncols = aij->i[i+1] - aij->i[i];
3536     for (j=0; j<ncols; j++) {
3537       PetscInt data,gid1 = aij->j[aij->i[i] + j] + 1;
3538       ierr = PetscTableFind(gid1_lid1,gid1,&data);CHKERRQ(ierr);
3539       if (!data) {
3540         /* one based table */
3541         ierr = PetscTableAdd(gid1_lid1,gid1,++ec,INSERT_VALUES);CHKERRQ(ierr);
3542       }
3543     }
3544   }
3545   /* form array of columns we need */
3546   ierr = PetscMalloc1(ec+1,&garray);CHKERRQ(ierr);
3547   ierr = PetscTableGetHeadPosition(gid1_lid1,&tpos);CHKERRQ(ierr);
3548   while (tpos) {
3549     ierr = PetscTableGetNext(gid1_lid1,&tpos,&gid,&lid);CHKERRQ(ierr);
3550     gid--;
3551     lid--;
3552     garray[lid] = gid;
3553   }
3554   ierr = PetscSortInt(ec,garray);CHKERRQ(ierr); /* sort, and rebuild */
3555   ierr = PetscTableRemoveAll(gid1_lid1);CHKERRQ(ierr);
3556   for (i=0; i<ec; i++) {
3557     ierr = PetscTableAdd(gid1_lid1,garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
3558   }
3559   /* compact out the extra columns in B */
3560   for (i=0; i<mat->rmap->n; i++) {
3561 	ncols = aij->i[i+1] - aij->i[i];
3562     for (j=0; j<ncols; j++) {
3563       PetscInt gid1 = aij->j[aij->i[i] + j] + 1;
3564       ierr = PetscTableFind(gid1_lid1,gid1,&lid);CHKERRQ(ierr);
3565       lid--;
3566       aij->j[aij->i[i] + j] = lid;
3567     }
3568   }
3569   ierr = PetscLayoutDestroy(&mat->cmap);CHKERRQ(ierr);
3570   ierr = PetscLayoutCreateFromSizes(PetscObjectComm((PetscObject)mat),ec,ec,1,&mat->cmap);CHKERRQ(ierr);
3571   ierr = PetscTableDestroy(&gid1_lid1);CHKERRQ(ierr);
3572   ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,mat->cmap->bs,mat->cmap->n,garray,PETSC_OWN_POINTER,mapping);CHKERRQ(ierr);
3573   ierr = ISLocalToGlobalMappingSetType(*mapping,ISLOCALTOGLOBALMAPPINGHASH);CHKERRQ(ierr);
3574   PetscFunctionReturn(0);
3575 }
3576 
3577 /*@
3578     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3579        in the matrix.
3580 
3581   Input Parameters:
3582 +  mat - the SeqAIJ matrix
3583 -  indices - the column indices
3584 
3585   Level: advanced
3586 
3587   Notes:
3588     This can be called if you have precomputed the nonzero structure of the
3589   matrix and want to provide it to the matrix object to improve the performance
3590   of the MatSetValues() operation.
3591 
3592     You MUST have set the correct numbers of nonzeros per row in the call to
3593   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3594 
3595     MUST be called before any calls to MatSetValues();
3596 
3597     The indices should start with zero, not one.
3598 
3599 @*/
3600 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3601 {
3602   PetscErrorCode ierr;
3603 
3604   PetscFunctionBegin;
3605   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3606   PetscValidPointer(indices,2);
3607   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3608   PetscFunctionReturn(0);
3609 }
3610 
3611 /* ----------------------------------------------------------------------------------------*/
3612 
3613 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3614 {
3615   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3616   PetscErrorCode ierr;
3617   size_t         nz = aij->i[mat->rmap->n];
3618 
3619   PetscFunctionBegin;
3620   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3621 
3622   /* allocate space for values if not already there */
3623   if (!aij->saved_values) {
3624     ierr = PetscMalloc1(nz+1,&aij->saved_values);CHKERRQ(ierr);
3625     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3626   }
3627 
3628   /* copy values over */
3629   ierr = PetscArraycpy(aij->saved_values,aij->a,nz);CHKERRQ(ierr);
3630   PetscFunctionReturn(0);
3631 }
3632 
3633 /*@
3634     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3635        example, reuse of the linear part of a Jacobian, while recomputing the
3636        nonlinear portion.
3637 
3638    Collect on Mat
3639 
3640   Input Parameters:
3641 .  mat - the matrix (currently only AIJ matrices support this option)
3642 
3643   Level: advanced
3644 
3645   Common Usage, with SNESSolve():
3646 $    Create Jacobian matrix
3647 $    Set linear terms into matrix
3648 $    Apply boundary conditions to matrix, at this time matrix must have
3649 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3650 $      boundary conditions again will not change the nonzero structure
3651 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3652 $    ierr = MatStoreValues(mat);
3653 $    Call SNESSetJacobian() with matrix
3654 $    In your Jacobian routine
3655 $      ierr = MatRetrieveValues(mat);
3656 $      Set nonlinear terms in matrix
3657 
3658   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3659 $    // build linear portion of Jacobian
3660 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3661 $    ierr = MatStoreValues(mat);
3662 $    loop over nonlinear iterations
3663 $       ierr = MatRetrieveValues(mat);
3664 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3665 $       // call MatAssemblyBegin/End() on matrix
3666 $       Solve linear system with Jacobian
3667 $    endloop
3668 
3669   Notes:
3670     Matrix must already be assemblied before calling this routine
3671     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3672     calling this routine.
3673 
3674     When this is called multiple times it overwrites the previous set of stored values
3675     and does not allocated additional space.
3676 
3677 .seealso: MatRetrieveValues()
3678 
3679 @*/
3680 PetscErrorCode  MatStoreValues(Mat mat)
3681 {
3682   PetscErrorCode ierr;
3683 
3684   PetscFunctionBegin;
3685   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3686   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3687   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3688   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3689   PetscFunctionReturn(0);
3690 }
3691 
3692 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3693 {
3694   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3695   PetscErrorCode ierr;
3696   PetscInt       nz = aij->i[mat->rmap->n];
3697 
3698   PetscFunctionBegin;
3699   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3700   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3701   /* copy values over */
3702   ierr = PetscArraycpy(aij->a,aij->saved_values,nz);CHKERRQ(ierr);
3703   PetscFunctionReturn(0);
3704 }
3705 
3706 /*@
3707     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3708        example, reuse of the linear part of a Jacobian, while recomputing the
3709        nonlinear portion.
3710 
3711    Collect on Mat
3712 
3713   Input Parameters:
3714 .  mat - the matrix (currently only AIJ matrices support this option)
3715 
3716   Level: advanced
3717 
3718 .seealso: MatStoreValues()
3719 
3720 @*/
3721 PetscErrorCode  MatRetrieveValues(Mat mat)
3722 {
3723   PetscErrorCode ierr;
3724 
3725   PetscFunctionBegin;
3726   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3727   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3728   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3729   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3730   PetscFunctionReturn(0);
3731 }
3732 
3733 
3734 /* --------------------------------------------------------------------------------*/
3735 /*@C
3736    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3737    (the default parallel PETSc format).  For good matrix assembly performance
3738    the user should preallocate the matrix storage by setting the parameter nz
3739    (or the array nnz).  By setting these parameters accurately, performance
3740    during matrix assembly can be increased by more than a factor of 50.
3741 
3742    Collective
3743 
3744    Input Parameters:
3745 +  comm - MPI communicator, set to PETSC_COMM_SELF
3746 .  m - number of rows
3747 .  n - number of columns
3748 .  nz - number of nonzeros per row (same for all rows)
3749 -  nnz - array containing the number of nonzeros in the various rows
3750          (possibly different for each row) or NULL
3751 
3752    Output Parameter:
3753 .  A - the matrix
3754 
3755    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3756    MatXXXXSetPreallocation() paradigm instead of this routine directly.
3757    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3758 
3759    Notes:
3760    If nnz is given then nz is ignored
3761 
3762    The AIJ format (also called the Yale sparse matrix format or
3763    compressed row storage), is fully compatible with standard Fortran 77
3764    storage.  That is, the stored row and column indices can begin at
3765    either one (as in Fortran) or zero.  See the users' manual for details.
3766 
3767    Specify the preallocated storage with either nz or nnz (not both).
3768    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3769    allocation.  For large problems you MUST preallocate memory or you
3770    will get TERRIBLE performance, see the users' manual chapter on matrices.
3771 
3772    By default, this format uses inodes (identical nodes) when possible, to
3773    improve numerical efficiency of matrix-vector products and solves. We
3774    search for consecutive rows with the same nonzero structure, thereby
3775    reusing matrix information to achieve increased efficiency.
3776 
3777    Options Database Keys:
3778 +  -mat_no_inode  - Do not use inodes
3779 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3780 
3781    Level: intermediate
3782 
3783 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3784 
3785 @*/
3786 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3787 {
3788   PetscErrorCode ierr;
3789 
3790   PetscFunctionBegin;
3791   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3792   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3793   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3794   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3795   PetscFunctionReturn(0);
3796 }
3797 
3798 /*@C
3799    MatSeqAIJSetPreallocation - For good matrix assembly performance
3800    the user should preallocate the matrix storage by setting the parameter nz
3801    (or the array nnz).  By setting these parameters accurately, performance
3802    during matrix assembly can be increased by more than a factor of 50.
3803 
3804    Collective
3805 
3806    Input Parameters:
3807 +  B - The matrix
3808 .  nz - number of nonzeros per row (same for all rows)
3809 -  nnz - array containing the number of nonzeros in the various rows
3810          (possibly different for each row) or NULL
3811 
3812    Notes:
3813      If nnz is given then nz is ignored
3814 
3815     The AIJ format (also called the Yale sparse matrix format or
3816    compressed row storage), is fully compatible with standard Fortran 77
3817    storage.  That is, the stored row and column indices can begin at
3818    either one (as in Fortran) or zero.  See the users' manual for details.
3819 
3820    Specify the preallocated storage with either nz or nnz (not both).
3821    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3822    allocation.  For large problems you MUST preallocate memory or you
3823    will get TERRIBLE performance, see the users' manual chapter on matrices.
3824 
3825    You can call MatGetInfo() to get information on how effective the preallocation was;
3826    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3827    You can also run with the option -info and look for messages with the string
3828    malloc in them to see if additional memory allocation was needed.
3829 
3830    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3831    entries or columns indices
3832 
3833    By default, this format uses inodes (identical nodes) when possible, to
3834    improve numerical efficiency of matrix-vector products and solves. We
3835    search for consecutive rows with the same nonzero structure, thereby
3836    reusing matrix information to achieve increased efficiency.
3837 
3838    Options Database Keys:
3839 +  -mat_no_inode  - Do not use inodes
3840 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3841 
3842    Level: intermediate
3843 
3844 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatGetInfo()
3845 
3846 @*/
3847 PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
3848 {
3849   PetscErrorCode ierr;
3850 
3851   PetscFunctionBegin;
3852   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3853   PetscValidType(B,1);
3854   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));CHKERRQ(ierr);
3855   PetscFunctionReturn(0);
3856 }
3857 
3858 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3859 {
3860   Mat_SeqAIJ     *b;
3861   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3862   PetscErrorCode ierr;
3863   PetscInt       i;
3864 
3865   PetscFunctionBegin;
3866   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3867   if (nz == MAT_SKIP_ALLOCATION) {
3868     skipallocation = PETSC_TRUE;
3869     nz             = 0;
3870   }
3871   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3872   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3873 
3874   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3875   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %D",nz);
3876 #if defined(PETSC_USE_DEBUG)
3877   if (nnz) {
3878     for (i=0; i<B->rmap->n; i++) {
3879       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]);
3880       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);
3881     }
3882   }
3883 #endif
3884 
3885   B->preallocated = PETSC_TRUE;
3886 
3887   b = (Mat_SeqAIJ*)B->data;
3888 
3889   if (!skipallocation) {
3890     if (!b->imax) {
3891       ierr = PetscMalloc1(B->rmap->n,&b->imax);CHKERRQ(ierr);
3892       ierr = PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3893     }
3894     if (!b->ilen) {
3895       /* b->ilen will count nonzeros in each row so far. */
3896       ierr = PetscCalloc1(B->rmap->n,&b->ilen);CHKERRQ(ierr);
3897       ierr = PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3898     } else {
3899       ierr = PetscMemzero(b->ilen,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3900     }
3901     if (!b->ipre) {
3902       ierr = PetscMalloc1(B->rmap->n,&b->ipre);CHKERRQ(ierr);
3903       ierr = PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3904     }
3905     if (!nnz) {
3906       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3907       else if (nz < 0) nz = 1;
3908       nz = PetscMin(nz,B->cmap->n);
3909       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
3910       nz = nz*B->rmap->n;
3911     } else {
3912       PetscInt64 nz64 = 0;
3913       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz64 += nnz[i];}
3914       ierr = PetscIntCast(nz64,&nz);CHKERRQ(ierr);
3915     }
3916 
3917     /* allocate the matrix space */
3918     /* FIXME: should B's old memory be unlogged? */
3919     ierr = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
3920     if (B->structure_only) {
3921       ierr = PetscMalloc1(nz,&b->j);CHKERRQ(ierr);
3922       ierr = PetscMalloc1(B->rmap->n+1,&b->i);CHKERRQ(ierr);
3923       ierr = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*sizeof(PetscInt));CHKERRQ(ierr);
3924     } else {
3925       ierr = PetscMalloc3(nz,&b->a,nz,&b->j,B->rmap->n+1,&b->i);CHKERRQ(ierr);
3926       ierr = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
3927     }
3928     b->i[0] = 0;
3929     for (i=1; i<B->rmap->n+1; i++) {
3930       b->i[i] = b->i[i-1] + b->imax[i-1];
3931     }
3932     if (B->structure_only) {
3933       b->singlemalloc = PETSC_FALSE;
3934       b->free_a       = PETSC_FALSE;
3935     } else {
3936       b->singlemalloc = PETSC_TRUE;
3937       b->free_a       = PETSC_TRUE;
3938     }
3939     b->free_ij      = PETSC_TRUE;
3940   } else {
3941     b->free_a  = PETSC_FALSE;
3942     b->free_ij = PETSC_FALSE;
3943   }
3944 
3945   if (b->ipre && nnz != b->ipre  && b->imax) {
3946     /* reserve user-requested sparsity */
3947     ierr = PetscArraycpy(b->ipre,b->imax,B->rmap->n);CHKERRQ(ierr);
3948   }
3949 
3950 
3951   b->nz               = 0;
3952   b->maxnz            = nz;
3953   B->info.nz_unneeded = (double)b->maxnz;
3954   if (realalloc) {
3955     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3956   }
3957   B->was_assembled = PETSC_FALSE;
3958   B->assembled     = PETSC_FALSE;
3959   PetscFunctionReturn(0);
3960 }
3961 
3962 
3963 PetscErrorCode MatResetPreallocation_SeqAIJ(Mat A)
3964 {
3965   Mat_SeqAIJ     *a;
3966   PetscInt       i;
3967   PetscErrorCode ierr;
3968 
3969   PetscFunctionBegin;
3970   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3971 
3972   /* Check local size. If zero, then return */
3973   if (!A->rmap->n) PetscFunctionReturn(0);
3974 
3975   a = (Mat_SeqAIJ*)A->data;
3976   /* if no saved info, we error out */
3977   if (!a->ipre) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"No saved preallocation info \n");
3978 
3979   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");
3980 
3981   ierr = PetscArraycpy(a->imax,a->ipre,A->rmap->n);CHKERRQ(ierr);
3982   ierr = PetscArrayzero(a->ilen,A->rmap->n);CHKERRQ(ierr);
3983   a->i[0] = 0;
3984   for (i=1; i<A->rmap->n+1; i++) {
3985     a->i[i] = a->i[i-1] + a->imax[i-1];
3986   }
3987   A->preallocated     = PETSC_TRUE;
3988   a->nz               = 0;
3989   a->maxnz            = a->i[A->rmap->n];
3990   A->info.nz_unneeded = (double)a->maxnz;
3991   A->was_assembled    = PETSC_FALSE;
3992   A->assembled        = PETSC_FALSE;
3993   PetscFunctionReturn(0);
3994 }
3995 
3996 /*@
3997    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
3998 
3999    Input Parameters:
4000 +  B - the matrix
4001 .  i - the indices into j for the start of each row (starts with zero)
4002 .  j - the column indices for each row (starts with zero) these must be sorted for each row
4003 -  v - optional values in the matrix
4004 
4005    Level: developer
4006 
4007    The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
4008 
4009 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), MATSEQAIJ
4010 @*/
4011 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
4012 {
4013   PetscErrorCode ierr;
4014 
4015   PetscFunctionBegin;
4016   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
4017   PetscValidType(B,1);
4018   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
4019   PetscFunctionReturn(0);
4020 }
4021 
4022 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
4023 {
4024   PetscInt       i;
4025   PetscInt       m,n;
4026   PetscInt       nz;
4027   PetscInt       *nnz, nz_max = 0;
4028   PetscErrorCode ierr;
4029 
4030   PetscFunctionBegin;
4031   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
4032 
4033   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
4034   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
4035 
4036   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
4037   ierr = PetscMalloc1(m+1, &nnz);CHKERRQ(ierr);
4038   for (i = 0; i < m; i++) {
4039     nz     = Ii[i+1]- Ii[i];
4040     nz_max = PetscMax(nz_max, nz);
4041     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
4042     nnz[i] = nz;
4043   }
4044   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
4045   ierr = PetscFree(nnz);CHKERRQ(ierr);
4046 
4047   for (i = 0; i < m; i++) {
4048     ierr = MatSetValues_SeqAIJ(B, 1, &i, Ii[i+1] - Ii[i], J+Ii[i], v ? v + Ii[i] : NULL, INSERT_VALUES);CHKERRQ(ierr);
4049   }
4050 
4051   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4052   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4053 
4054   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
4055   PetscFunctionReturn(0);
4056 }
4057 
4058 #include <../src/mat/impls/dense/seq/dense.h>
4059 #include <petsc/private/kernels/petscaxpy.h>
4060 
4061 /*
4062     Computes (B'*A')' since computing B*A directly is untenable
4063 
4064                n                       p                          p
4065         (              )       (              )         (                  )
4066       m (      A       )  *  n (       B      )   =   m (         C        )
4067         (              )       (              )         (                  )
4068 
4069 */
4070 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
4071 {
4072   PetscErrorCode    ierr;
4073   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
4074   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
4075   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
4076   PetscInt          i,n,m,q,p;
4077   const PetscInt    *ii,*idx;
4078   const PetscScalar *b,*a,*a_q;
4079   PetscScalar       *c,*c_q;
4080 
4081   PetscFunctionBegin;
4082   m    = A->rmap->n;
4083   n    = A->cmap->n;
4084   p    = B->cmap->n;
4085   a    = sub_a->v;
4086   b    = sub_b->a;
4087   c    = sub_c->v;
4088   ierr = PetscArrayzero(c,m*p);CHKERRQ(ierr);
4089 
4090   ii  = sub_b->i;
4091   idx = sub_b->j;
4092   for (i=0; i<n; i++) {
4093     q = ii[i+1] - ii[i];
4094     while (q-->0) {
4095       c_q = c + m*(*idx);
4096       a_q = a + m*i;
4097       PetscKernelAXPY(c_q,*b,a_q,m);
4098       idx++;
4099       b++;
4100     }
4101   }
4102   PetscFunctionReturn(0);
4103 }
4104 
4105 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4106 {
4107   PetscErrorCode ierr;
4108   PetscInt       m=A->rmap->n,n=B->cmap->n;
4109   Mat            Cmat;
4110 
4111   PetscFunctionBegin;
4112   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);
4113   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4114   ierr = MatSetSizes(Cmat,m,n,m,n);CHKERRQ(ierr);
4115   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
4116   ierr = MatSetType(Cmat,MATSEQDENSE);CHKERRQ(ierr);
4117   ierr = MatSeqDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4118 
4119   Cmat->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
4120 
4121   *C = Cmat;
4122   PetscFunctionReturn(0);
4123 }
4124 
4125 /* ----------------------------------------------------------------*/
4126 PETSC_INTERN PetscErrorCode MatMatMult_SeqDense_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4127 {
4128   PetscErrorCode ierr;
4129 
4130   PetscFunctionBegin;
4131   if (scall == MAT_INITIAL_MATRIX) {
4132     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4133     ierr = MatMatMultSymbolic_SeqDense_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
4134     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4135   }
4136   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4137   ierr = MatMatMultNumeric_SeqDense_SeqAIJ(A,B,*C);CHKERRQ(ierr);
4138   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4139   PetscFunctionReturn(0);
4140 }
4141 
4142 
4143 /*MC
4144    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
4145    based on compressed sparse row format.
4146 
4147    Options Database Keys:
4148 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
4149 
4150    Level: beginner
4151 
4152    Notes:
4153     MatSetValues() may be called for this matrix type with a NULL argument for the numerical values,
4154     in this case the values associated with the rows and columns one passes in are set to zero
4155     in the matrix
4156 
4157     MatSetOptions(,MAT_STRUCTURE_ONLY,PETSC_TRUE) may be called for this matrix type. In this no
4158     space is allocated for the nonzero entries and any entries passed with MatSetValues() are ignored
4159 
4160   Developer Notes:
4161     It would be nice if all matrix formats supported passing NULL in for the numerical values
4162 
4163 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
4164 M*/
4165 
4166 /*MC
4167    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
4168 
4169    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
4170    and MATMPIAIJ otherwise.  As a result, for single process communicators,
4171   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation() is supported
4172   for communicators controlling multiple processes.  It is recommended that you call both of
4173   the above preallocation routines for simplicity.
4174 
4175    Options Database Keys:
4176 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
4177 
4178   Developer Notes:
4179     Subclasses include MATAIJCUSPARSE, MATAIJPERM, MATAIJSELL, MATAIJMKL, MATAIJCRL, and also automatically switches over to use inodes when
4180    enough exist.
4181 
4182   Level: beginner
4183 
4184 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
4185 M*/
4186 
4187 /*MC
4188    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
4189 
4190    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
4191    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
4192    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
4193   for communicators controlling multiple processes.  It is recommended that you call both of
4194   the above preallocation routines for simplicity.
4195 
4196    Options Database Keys:
4197 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
4198 
4199   Level: beginner
4200 
4201 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
4202 M*/
4203 
4204 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
4205 #if defined(PETSC_HAVE_ELEMENTAL)
4206 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4207 #endif
4208 #if defined(PETSC_HAVE_HYPRE)
4209 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat A,MatType,MatReuse,Mat*);
4210 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
4211 #endif
4212 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqDense(Mat,MatType,MatReuse,Mat*);
4213 
4214 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqSELL(Mat,MatType,MatReuse,Mat*);
4215 PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat,MatType,MatReuse,Mat*);
4216 PETSC_INTERN PetscErrorCode MatPtAP_IS_XAIJ(Mat,Mat,MatReuse,PetscReal,Mat*);
4217 
4218 /*@C
4219    MatSeqAIJGetArray - gives read/write access to the array where the data for a MATSEQAIJ matrix is stored
4220 
4221    Not Collective
4222 
4223    Input Parameter:
4224 .  mat - a MATSEQAIJ matrix
4225 
4226    Output Parameter:
4227 .   array - pointer to the data
4228 
4229    Level: intermediate
4230 
4231 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4232 @*/
4233 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4234 {
4235   PetscErrorCode ierr;
4236 
4237   PetscFunctionBegin;
4238   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4239   PetscFunctionReturn(0);
4240 }
4241 
4242 /*@C
4243    MatSeqAIJGetArrayRead - gives read-only access to the array where the data for a MATSEQAIJ matrix is stored
4244 
4245    Not Collective
4246 
4247    Input Parameter:
4248 .  mat - a MATSEQAIJ matrix
4249 
4250    Output Parameter:
4251 .   array - pointer to the data
4252 
4253    Level: intermediate
4254 
4255 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayRead()
4256 @*/
4257 PetscErrorCode  MatSeqAIJGetArrayRead(Mat A,const PetscScalar **array)
4258 {
4259 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_VIENNACL)
4260   PetscOffloadMask oval;
4261 #endif
4262   PetscErrorCode ierr;
4263 
4264   PetscFunctionBegin;
4265 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_VIENNACL)
4266   oval = A->offloadmask;
4267 #endif
4268   ierr = MatSeqAIJGetArray(A,(PetscScalar**)array);CHKERRQ(ierr);
4269 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_VIENNACL)
4270   if (oval == PETSC_OFFLOAD_GPU || oval == PETSC_OFFLOAD_BOTH) A->offloadmask = PETSC_OFFLOAD_BOTH;
4271 #endif
4272   PetscFunctionReturn(0);
4273 }
4274 
4275 /*@C
4276    MatSeqAIJRestoreArrayRead - restore the read-only access array obtained from MatSeqAIJGetArrayRead
4277 
4278    Not Collective
4279 
4280    Input Parameter:
4281 .  mat - a MATSEQAIJ matrix
4282 
4283    Output Parameter:
4284 .   array - pointer to the data
4285 
4286    Level: intermediate
4287 
4288 .seealso: MatSeqAIJGetArray(), MatSeqAIJGetArrayRead()
4289 @*/
4290 PetscErrorCode  MatSeqAIJRestoreArrayRead(Mat A,const PetscScalar **array)
4291 {
4292 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_VIENNACL)
4293   PetscOffloadMask oval;
4294 #endif
4295   PetscErrorCode ierr;
4296 
4297   PetscFunctionBegin;
4298 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_VIENNACL)
4299   oval = A->offloadmask;
4300 #endif
4301   ierr = MatSeqAIJRestoreArray(A,(PetscScalar**)array);CHKERRQ(ierr);
4302 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_VIENNACL)
4303   A->offloadmask = oval;
4304 #endif
4305   PetscFunctionReturn(0);
4306 }
4307 
4308 /*@C
4309    MatSeqAIJGetMaxRowNonzeros - returns the maximum number of nonzeros in any row
4310 
4311    Not Collective
4312 
4313    Input Parameter:
4314 .  mat - a MATSEQAIJ matrix
4315 
4316    Output Parameter:
4317 .   nz - the maximum number of nonzeros in any row
4318 
4319    Level: intermediate
4320 
4321 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4322 @*/
4323 PetscErrorCode  MatSeqAIJGetMaxRowNonzeros(Mat A,PetscInt *nz)
4324 {
4325   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
4326 
4327   PetscFunctionBegin;
4328   *nz = aij->rmax;
4329   PetscFunctionReturn(0);
4330 }
4331 
4332 /*@C
4333    MatSeqAIJRestoreArray - returns access to the array where the data for a MATSEQAIJ matrix is stored obtained by MatSeqAIJGetArray()
4334 
4335    Not Collective
4336 
4337    Input Parameters:
4338 +  mat - a MATSEQAIJ matrix
4339 -  array - pointer to the data
4340 
4341    Level: intermediate
4342 
4343 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4344 @*/
4345 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4346 {
4347   PetscErrorCode ierr;
4348 
4349   PetscFunctionBegin;
4350   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4351   PetscFunctionReturn(0);
4352 }
4353 
4354 #if defined(PETSC_HAVE_CUDA)
4355 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat);
4356 #endif
4357 
4358 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4359 {
4360   Mat_SeqAIJ     *b;
4361   PetscErrorCode ierr;
4362   PetscMPIInt    size;
4363 
4364   PetscFunctionBegin;
4365   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4366   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4367 
4368   ierr = PetscNewLog(B,&b);CHKERRQ(ierr);
4369 
4370   B->data = (void*)b;
4371 
4372   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4373   if (B->sortedfull) B->ops->setvalues = MatSetValues_SeqAIJ_SortedFull;
4374 
4375   b->row                = 0;
4376   b->col                = 0;
4377   b->icol               = 0;
4378   b->reallocs           = 0;
4379   b->ignorezeroentries  = PETSC_FALSE;
4380   b->roworiented        = PETSC_TRUE;
4381   b->nonew              = 0;
4382   b->diag               = 0;
4383   b->solve_work         = 0;
4384   B->spptr              = 0;
4385   b->saved_values       = 0;
4386   b->idiag              = 0;
4387   b->mdiag              = 0;
4388   b->ssor_work          = 0;
4389   b->omega              = 1.0;
4390   b->fshift             = 0.0;
4391   b->idiagvalid         = PETSC_FALSE;
4392   b->ibdiagvalid        = PETSC_FALSE;
4393   b->keepnonzeropattern = PETSC_FALSE;
4394 
4395   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4396   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4397   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4398 
4399 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4400   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4401   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4402 #endif
4403 
4404   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4405   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4406   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4407   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4408   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4409   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4410   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijsell_C",MatConvert_SeqAIJ_SeqAIJSELL);CHKERRQ(ierr);
4411 #if defined(PETSC_HAVE_MKL_SPARSE)
4412   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijmkl_C",MatConvert_SeqAIJ_SeqAIJMKL);CHKERRQ(ierr);
4413 #endif
4414 #if defined(PETSC_HAVE_CUDA)
4415   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcusparse_C",MatConvert_SeqAIJ_SeqAIJCUSPARSE);CHKERRQ(ierr);
4416 #endif
4417   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4418 #if defined(PETSC_HAVE_ELEMENTAL)
4419   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_elemental_C",MatConvert_SeqAIJ_Elemental);CHKERRQ(ierr);
4420 #endif
4421 #if defined(PETSC_HAVE_HYPRE)
4422   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
4423   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_seqaij_seqaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
4424 #endif
4425   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqdense_C",MatConvert_SeqAIJ_SeqDense);CHKERRQ(ierr);
4426   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsell_C",MatConvert_SeqAIJ_SeqSELL);CHKERRQ(ierr);
4427   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_is_C",MatConvert_XAIJ_IS);CHKERRQ(ierr);
4428   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4429   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4430   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4431   ierr = PetscObjectComposeFunction((PetscObject)B,"MatResetPreallocation_C",MatResetPreallocation_SeqAIJ);CHKERRQ(ierr);
4432   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4433   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4434   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaij_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
4435   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaij_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
4436   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaij_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
4437   ierr = PetscObjectComposeFunction((PetscObject)B,"MatPtAP_is_seqaij_C",MatPtAP_IS_XAIJ);CHKERRQ(ierr);
4438   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4439   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4440   ierr = MatSeqAIJSetTypeFromOptions(B);CHKERRQ(ierr);  /* this allows changing the matrix subtype to say MATSEQAIJPERM */
4441   PetscFunctionReturn(0);
4442 }
4443 
4444 /*
4445     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4446 */
4447 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4448 {
4449   Mat_SeqAIJ     *c,*a = (Mat_SeqAIJ*)A->data;
4450   PetscErrorCode ierr;
4451   PetscInt       m = A->rmap->n,i;
4452 
4453   PetscFunctionBegin;
4454   c = (Mat_SeqAIJ*)C->data;
4455 
4456   C->factortype = A->factortype;
4457   c->row        = 0;
4458   c->col        = 0;
4459   c->icol       = 0;
4460   c->reallocs   = 0;
4461 
4462   C->assembled = PETSC_TRUE;
4463 
4464   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4465   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4466 
4467   ierr = PetscMalloc1(m,&c->imax);CHKERRQ(ierr);
4468   ierr = PetscMemcpy(c->imax,a->imax,m*sizeof(PetscInt));CHKERRQ(ierr);
4469   ierr = PetscMalloc1(m,&c->ilen);CHKERRQ(ierr);
4470   ierr = PetscMemcpy(c->ilen,a->ilen,m*sizeof(PetscInt));CHKERRQ(ierr);
4471   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4472 
4473   /* allocate the matrix space */
4474   if (mallocmatspace) {
4475     ierr = PetscMalloc3(a->i[m],&c->a,a->i[m],&c->j,m+1,&c->i);CHKERRQ(ierr);
4476     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4477 
4478     c->singlemalloc = PETSC_TRUE;
4479 
4480     ierr = PetscArraycpy(c->i,a->i,m+1);CHKERRQ(ierr);
4481     if (m > 0) {
4482       ierr = PetscArraycpy(c->j,a->j,a->i[m]);CHKERRQ(ierr);
4483       if (cpvalues == MAT_COPY_VALUES) {
4484         ierr = PetscArraycpy(c->a,a->a,a->i[m]);CHKERRQ(ierr);
4485       } else {
4486         ierr = PetscArrayzero(c->a,a->i[m]);CHKERRQ(ierr);
4487       }
4488     }
4489   }
4490 
4491   c->ignorezeroentries = a->ignorezeroentries;
4492   c->roworiented       = a->roworiented;
4493   c->nonew             = a->nonew;
4494   if (a->diag) {
4495     ierr = PetscMalloc1(m+1,&c->diag);CHKERRQ(ierr);
4496     ierr = PetscMemcpy(c->diag,a->diag,m*sizeof(PetscInt));CHKERRQ(ierr);
4497     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4498   } else c->diag = NULL;
4499 
4500   c->solve_work         = 0;
4501   c->saved_values       = 0;
4502   c->idiag              = 0;
4503   c->ssor_work          = 0;
4504   c->keepnonzeropattern = a->keepnonzeropattern;
4505   c->free_a             = PETSC_TRUE;
4506   c->free_ij            = PETSC_TRUE;
4507 
4508   c->rmax         = a->rmax;
4509   c->nz           = a->nz;
4510   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4511   C->preallocated = PETSC_TRUE;
4512 
4513   c->compressedrow.use   = a->compressedrow.use;
4514   c->compressedrow.nrows = a->compressedrow.nrows;
4515   if (a->compressedrow.use) {
4516     i    = a->compressedrow.nrows;
4517     ierr = PetscMalloc2(i+1,&c->compressedrow.i,i,&c->compressedrow.rindex);CHKERRQ(ierr);
4518     ierr = PetscArraycpy(c->compressedrow.i,a->compressedrow.i,i+1);CHKERRQ(ierr);
4519     ierr = PetscArraycpy(c->compressedrow.rindex,a->compressedrow.rindex,i);CHKERRQ(ierr);
4520   } else {
4521     c->compressedrow.use    = PETSC_FALSE;
4522     c->compressedrow.i      = NULL;
4523     c->compressedrow.rindex = NULL;
4524   }
4525   c->nonzerorowcnt = a->nonzerorowcnt;
4526   C->nonzerostate  = A->nonzerostate;
4527 
4528   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4529   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4530   PetscFunctionReturn(0);
4531 }
4532 
4533 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4534 {
4535   PetscErrorCode ierr;
4536 
4537   PetscFunctionBegin;
4538   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4539   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4540   if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) {
4541     ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
4542   }
4543   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4544   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4545   PetscFunctionReturn(0);
4546 }
4547 
4548 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4549 {
4550   PetscBool      isbinary, ishdf5;
4551   PetscErrorCode ierr;
4552 
4553   PetscFunctionBegin;
4554   PetscValidHeaderSpecific(newMat,MAT_CLASSID,1);
4555   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
4556   /* force binary viewer to load .info file if it has not yet done so */
4557   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
4558   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
4559   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,  &ishdf5);CHKERRQ(ierr);
4560   if (isbinary) {
4561     ierr = MatLoad_SeqAIJ_Binary(newMat,viewer);CHKERRQ(ierr);
4562   } else if (ishdf5) {
4563 #if defined(PETSC_HAVE_HDF5)
4564     ierr = MatLoad_AIJ_HDF5(newMat,viewer);CHKERRQ(ierr);
4565 #else
4566     SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
4567 #endif
4568   } else {
4569     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);
4570   }
4571   PetscFunctionReturn(0);
4572 }
4573 
4574 PetscErrorCode MatLoad_SeqAIJ_Binary(Mat newMat, PetscViewer viewer)
4575 {
4576   Mat_SeqAIJ     *a;
4577   PetscErrorCode ierr;
4578   PetscInt       i,sum,nz,header[4],*rowlengths = 0,M,N,rows,cols;
4579   int            fd;
4580   PetscMPIInt    size;
4581   MPI_Comm       comm;
4582   PetscInt       bs = newMat->rmap->bs;
4583 
4584   PetscFunctionBegin;
4585   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
4586   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4587   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"view must have one processor");
4588 
4589   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
4590   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
4591   ierr = PetscOptionsEnd();CHKERRQ(ierr);
4592   if (bs < 0) bs = 1;
4593   ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);
4594 
4595   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
4596   ierr = PetscBinaryRead(fd,header,4,NULL,PETSC_INT);CHKERRQ(ierr);
4597   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
4598   M = header[1]; N = header[2]; nz = header[3];
4599 
4600   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
4601 
4602   /* read in row lengths */
4603   ierr = PetscMalloc1(M,&rowlengths);CHKERRQ(ierr);
4604   ierr = PetscBinaryRead(fd,rowlengths,M,NULL,PETSC_INT);CHKERRQ(ierr);
4605 
4606   /* check if sum of rowlengths is same as nz */
4607   for (i=0,sum=0; i< M; i++) sum +=rowlengths[i];
4608   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);
4609 
4610   /* set global size if not set already*/
4611   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) {
4612     ierr = MatSetSizes(newMat,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
4613   } else {
4614     /* if sizes and type are already set, check if the matrix  global sizes are correct */
4615     ierr = MatGetSize(newMat,&rows,&cols);CHKERRQ(ierr);
4616     if (rows < 0 && cols < 0) { /* user might provide local size instead of global size */
4617       ierr = MatGetLocalSize(newMat,&rows,&cols);CHKERRQ(ierr);
4618     }
4619     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);
4620   }
4621   ierr = MatSeqAIJSetPreallocation_SeqAIJ(newMat,0,rowlengths);CHKERRQ(ierr);
4622   a    = (Mat_SeqAIJ*)newMat->data;
4623 
4624   ierr = PetscBinaryRead(fd,a->j,nz,NULL,PETSC_INT);CHKERRQ(ierr);
4625 
4626   /* read in nonzero values */
4627   ierr = PetscBinaryRead(fd,a->a,nz,NULL,PETSC_SCALAR);CHKERRQ(ierr);
4628 
4629   /* set matrix "i" values */
4630   a->i[0] = 0;
4631   for (i=1; i<= M; i++) {
4632     a->i[i]      = a->i[i-1] + rowlengths[i-1];
4633     a->ilen[i-1] = rowlengths[i-1];
4634   }
4635   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
4636 
4637   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4638   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4639   PetscFunctionReturn(0);
4640 }
4641 
4642 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4643 {
4644   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4645   PetscErrorCode ierr;
4646 #if defined(PETSC_USE_COMPLEX)
4647   PetscInt k;
4648 #endif
4649 
4650   PetscFunctionBegin;
4651   /* If the  matrix dimensions are not equal,or no of nonzeros */
4652   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4653     *flg = PETSC_FALSE;
4654     PetscFunctionReturn(0);
4655   }
4656 
4657   /* if the a->i are the same */
4658   ierr = PetscArraycmp(a->i,b->i,A->rmap->n+1,flg);CHKERRQ(ierr);
4659   if (!*flg) PetscFunctionReturn(0);
4660 
4661   /* if a->j are the same */
4662   ierr = PetscArraycmp(a->j,b->j,a->nz,flg);CHKERRQ(ierr);
4663   if (!*flg) PetscFunctionReturn(0);
4664 
4665   /* if a->a are the same */
4666 #if defined(PETSC_USE_COMPLEX)
4667   for (k=0; k<a->nz; k++) {
4668     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4669       *flg = PETSC_FALSE;
4670       PetscFunctionReturn(0);
4671     }
4672   }
4673 #else
4674   ierr = PetscArraycmp(a->a,b->a,a->nz,flg);CHKERRQ(ierr);
4675 #endif
4676   PetscFunctionReturn(0);
4677 }
4678 
4679 /*@
4680      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4681               provided by the user.
4682 
4683       Collective
4684 
4685    Input Parameters:
4686 +   comm - must be an MPI communicator of size 1
4687 .   m - number of rows
4688 .   n - number of columns
4689 .   i - row indices; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
4690 .   j - column indices
4691 -   a - matrix values
4692 
4693    Output Parameter:
4694 .   mat - the matrix
4695 
4696    Level: intermediate
4697 
4698    Notes:
4699        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4700     once the matrix is destroyed and not before
4701 
4702        You cannot set new nonzero locations into this matrix, that will generate an error.
4703 
4704        The i and j indices are 0 based
4705 
4706        The format which is used for the sparse matrix input, is equivalent to a
4707     row-major ordering.. i.e for the following matrix, the input data expected is
4708     as shown
4709 
4710 $        1 0 0
4711 $        2 0 3
4712 $        4 5 6
4713 $
4714 $        i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4715 $        j =  {0,0,2,0,1,2}  [size = 6]; values must be sorted for each row
4716 $        v =  {1,2,3,4,5,6}  [size = 6]
4717 
4718 
4719 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4720 
4721 @*/
4722 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat)
4723 {
4724   PetscErrorCode ierr;
4725   PetscInt       ii;
4726   Mat_SeqAIJ     *aij;
4727 #if defined(PETSC_USE_DEBUG)
4728   PetscInt jj;
4729 #endif
4730 
4731   PetscFunctionBegin;
4732   if (m > 0 && i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4733   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4734   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4735   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4736   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4737   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,0);CHKERRQ(ierr);
4738   aij  = (Mat_SeqAIJ*)(*mat)->data;
4739   ierr = PetscMalloc1(m,&aij->imax);CHKERRQ(ierr);
4740   ierr = PetscMalloc1(m,&aij->ilen);CHKERRQ(ierr);
4741 
4742   aij->i            = i;
4743   aij->j            = j;
4744   aij->a            = a;
4745   aij->singlemalloc = PETSC_FALSE;
4746   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4747   aij->free_a       = PETSC_FALSE;
4748   aij->free_ij      = PETSC_FALSE;
4749 
4750   for (ii=0; ii<m; ii++) {
4751     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4752 #if defined(PETSC_USE_DEBUG)
4753     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]);
4754     for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4755       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);
4756       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);
4757     }
4758 #endif
4759   }
4760 #if defined(PETSC_USE_DEBUG)
4761   for (ii=0; ii<aij->i[m]; ii++) {
4762     if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %D index = %D",ii,j[ii]);
4763     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]);
4764   }
4765 #endif
4766 
4767   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4768   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4769   PetscFunctionReturn(0);
4770 }
4771 /*@C
4772      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4773               provided by the user.
4774 
4775       Collective
4776 
4777    Input Parameters:
4778 +   comm - must be an MPI communicator of size 1
4779 .   m   - number of rows
4780 .   n   - number of columns
4781 .   i   - row indices
4782 .   j   - column indices
4783 .   a   - matrix values
4784 .   nz  - number of nonzeros
4785 -   idx - 0 or 1 based
4786 
4787    Output Parameter:
4788 .   mat - the matrix
4789 
4790    Level: intermediate
4791 
4792    Notes:
4793        The i and j indices are 0 based
4794 
4795        The format which is used for the sparse matrix input, is equivalent to a
4796     row-major ordering.. i.e for the following matrix, the input data expected is
4797     as shown:
4798 
4799         1 0 0
4800         2 0 3
4801         4 5 6
4802 
4803         i =  {0,1,1,2,2,2}
4804         j =  {0,0,2,0,1,2}
4805         v =  {1,2,3,4,5,6}
4806 
4807 
4808 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4809 
4810 @*/
4811 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat,PetscInt nz,PetscBool idx)
4812 {
4813   PetscErrorCode ierr;
4814   PetscInt       ii, *nnz, one = 1,row,col;
4815 
4816 
4817   PetscFunctionBegin;
4818   ierr = PetscCalloc1(m,&nnz);CHKERRQ(ierr);
4819   for (ii = 0; ii < nz; ii++) {
4820     nnz[i[ii] - !!idx] += 1;
4821   }
4822   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4823   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4824   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4825   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4826   for (ii = 0; ii < nz; ii++) {
4827     if (idx) {
4828       row = i[ii] - 1;
4829       col = j[ii] - 1;
4830     } else {
4831       row = i[ii];
4832       col = j[ii];
4833     }
4834     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4835   }
4836   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4837   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4838   ierr = PetscFree(nnz);CHKERRQ(ierr);
4839   PetscFunctionReturn(0);
4840 }
4841 
4842 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4843 {
4844   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4845   PetscErrorCode ierr;
4846 
4847   PetscFunctionBegin;
4848   a->idiagvalid  = PETSC_FALSE;
4849   a->ibdiagvalid = PETSC_FALSE;
4850 
4851   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4852   PetscFunctionReturn(0);
4853 }
4854 
4855 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4856 {
4857   PetscErrorCode ierr;
4858   PetscMPIInt    size;
4859 
4860   PetscFunctionBegin;
4861   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4862   if (size == 1) {
4863     if (scall == MAT_INITIAL_MATRIX) {
4864       ierr = MatDuplicate(inmat,MAT_COPY_VALUES,outmat);CHKERRQ(ierr);
4865     } else {
4866       ierr = MatCopy(inmat,*outmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4867     }
4868   } else {
4869     ierr = MatCreateMPIMatConcatenateSeqMat_MPIAIJ(comm,inmat,n,scall,outmat);CHKERRQ(ierr);
4870   }
4871   PetscFunctionReturn(0);
4872 }
4873 
4874 /*
4875  Permute A into C's *local* index space using rowemb,colemb.
4876  The embedding are supposed to be injections and the above implies that the range of rowemb is a subset
4877  of [0,m), colemb is in [0,n).
4878  If pattern == DIFFERENT_NONZERO_PATTERN, C is preallocated according to A.
4879  */
4880 PetscErrorCode MatSetSeqMat_SeqAIJ(Mat C,IS rowemb,IS colemb,MatStructure pattern,Mat B)
4881 {
4882   /* If making this function public, change the error returned in this function away from _PLIB. */
4883   PetscErrorCode ierr;
4884   Mat_SeqAIJ     *Baij;
4885   PetscBool      seqaij;
4886   PetscInt       m,n,*nz,i,j,count;
4887   PetscScalar    v;
4888   const PetscInt *rowindices,*colindices;
4889 
4890   PetscFunctionBegin;
4891   if (!B) PetscFunctionReturn(0);
4892   /* Check to make sure the target matrix (and embeddings) are compatible with C and each other. */
4893   ierr = PetscObjectBaseTypeCompare((PetscObject)B,MATSEQAIJ,&seqaij);CHKERRQ(ierr);
4894   if (!seqaij) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is of wrong type");
4895   if (rowemb) {
4896     ierr = ISGetLocalSize(rowemb,&m);CHKERRQ(ierr);
4897     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);
4898   } else {
4899     if (C->rmap->n != B->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is row-incompatible with the target matrix");
4900   }
4901   if (colemb) {
4902     ierr = ISGetLocalSize(colemb,&n);CHKERRQ(ierr);
4903     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);
4904   } else {
4905     if (C->cmap->n != B->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is col-incompatible with the target matrix");
4906   }
4907 
4908   Baij = (Mat_SeqAIJ*)(B->data);
4909   if (pattern == DIFFERENT_NONZERO_PATTERN) {
4910     ierr = PetscMalloc1(B->rmap->n,&nz);CHKERRQ(ierr);
4911     for (i=0; i<B->rmap->n; i++) {
4912       nz[i] = Baij->i[i+1] - Baij->i[i];
4913     }
4914     ierr = MatSeqAIJSetPreallocation(C,0,nz);CHKERRQ(ierr);
4915     ierr = PetscFree(nz);CHKERRQ(ierr);
4916   }
4917   if (pattern == SUBSET_NONZERO_PATTERN) {
4918     ierr = MatZeroEntries(C);CHKERRQ(ierr);
4919   }
4920   count = 0;
4921   rowindices = NULL;
4922   colindices = NULL;
4923   if (rowemb) {
4924     ierr = ISGetIndices(rowemb,&rowindices);CHKERRQ(ierr);
4925   }
4926   if (colemb) {
4927     ierr = ISGetIndices(colemb,&colindices);CHKERRQ(ierr);
4928   }
4929   for (i=0; i<B->rmap->n; i++) {
4930     PetscInt row;
4931     row = i;
4932     if (rowindices) row = rowindices[i];
4933     for (j=Baij->i[i]; j<Baij->i[i+1]; j++) {
4934       PetscInt col;
4935       col  = Baij->j[count];
4936       if (colindices) col = colindices[col];
4937       v    = Baij->a[count];
4938       ierr = MatSetValues(C,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
4939       ++count;
4940     }
4941   }
4942   /* FIXME: set C's nonzerostate correctly. */
4943   /* Assembly for C is necessary. */
4944   C->preallocated = PETSC_TRUE;
4945   C->assembled     = PETSC_TRUE;
4946   C->was_assembled = PETSC_FALSE;
4947   PetscFunctionReturn(0);
4948 }
4949 
4950 PetscFunctionList MatSeqAIJList = NULL;
4951 
4952 /*@C
4953    MatSeqAIJSetType - Converts a MATSEQAIJ matrix to a subtype
4954 
4955    Collective on Mat
4956 
4957    Input Parameters:
4958 +  mat      - the matrix object
4959 -  matype   - matrix type
4960 
4961    Options Database Key:
4962 .  -mat_seqai_type  <method> - for example seqaijcrl
4963 
4964 
4965   Level: intermediate
4966 
4967 .seealso: PCSetType(), VecSetType(), MatCreate(), MatType, Mat
4968 @*/
4969 PetscErrorCode  MatSeqAIJSetType(Mat mat, MatType matype)
4970 {
4971   PetscErrorCode ierr,(*r)(Mat,MatType,MatReuse,Mat*);
4972   PetscBool      sametype;
4973 
4974   PetscFunctionBegin;
4975   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
4976   ierr = PetscObjectTypeCompare((PetscObject)mat,matype,&sametype);CHKERRQ(ierr);
4977   if (sametype) PetscFunctionReturn(0);
4978 
4979   ierr =  PetscFunctionListFind(MatSeqAIJList,matype,&r);CHKERRQ(ierr);
4980   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown Mat type given: %s",matype);
4981   ierr = (*r)(mat,matype,MAT_INPLACE_MATRIX,&mat);CHKERRQ(ierr);
4982   PetscFunctionReturn(0);
4983 }
4984 
4985 
4986 /*@C
4987   MatSeqAIJRegister -  - Adds a new sub-matrix type for sequential AIJ matrices
4988 
4989    Not Collective
4990 
4991    Input Parameters:
4992 +  name - name of a new user-defined matrix type, for example MATSEQAIJCRL
4993 -  function - routine to convert to subtype
4994 
4995    Notes:
4996    MatSeqAIJRegister() may be called multiple times to add several user-defined solvers.
4997 
4998 
4999    Then, your matrix can be chosen with the procedural interface at runtime via the option
5000 $     -mat_seqaij_type my_mat
5001 
5002    Level: advanced
5003 
5004 .seealso: MatSeqAIJRegisterAll()
5005 
5006 
5007   Level: advanced
5008 @*/
5009 PetscErrorCode  MatSeqAIJRegister(const char sname[],PetscErrorCode (*function)(Mat,MatType,MatReuse,Mat *))
5010 {
5011   PetscErrorCode ierr;
5012 
5013   PetscFunctionBegin;
5014   ierr = MatInitializePackage();CHKERRQ(ierr);
5015   ierr = PetscFunctionListAdd(&MatSeqAIJList,sname,function);CHKERRQ(ierr);
5016   PetscFunctionReturn(0);
5017 }
5018 
5019 PetscBool MatSeqAIJRegisterAllCalled = PETSC_FALSE;
5020 
5021 /*@C
5022   MatSeqAIJRegisterAll - Registers all of the matrix subtypes of SeqAIJ
5023 
5024   Not Collective
5025 
5026   Level: advanced
5027 
5028   Developers Note: CUSP and CUSPARSE do not yet support the  MatConvert_SeqAIJ..() paradigm and thus cannot be registered here
5029 
5030 .seealso:  MatRegisterAll(), MatSeqAIJRegister()
5031 @*/
5032 PetscErrorCode  MatSeqAIJRegisterAll(void)
5033 {
5034   PetscErrorCode ierr;
5035 
5036   PetscFunctionBegin;
5037   if (MatSeqAIJRegisterAllCalled) PetscFunctionReturn(0);
5038   MatSeqAIJRegisterAllCalled = PETSC_TRUE;
5039 
5040   ierr = MatSeqAIJRegister(MATSEQAIJCRL,      MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
5041   ierr = MatSeqAIJRegister(MATSEQAIJPERM,     MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
5042   ierr = MatSeqAIJRegister(MATSEQAIJSELL,     MatConvert_SeqAIJ_SeqAIJSELL);CHKERRQ(ierr);
5043 #if defined(PETSC_HAVE_MKL_SPARSE)
5044   ierr = MatSeqAIJRegister(MATSEQAIJMKL,      MatConvert_SeqAIJ_SeqAIJMKL);CHKERRQ(ierr);
5045 #endif
5046 #if defined(PETSC_HAVE_VIENNACL) && defined(PETSC_HAVE_VIENNACL_NO_CUDA)
5047   ierr = MatSeqAIJRegister(MATMPIAIJVIENNACL, MatConvert_SeqAIJ_SeqAIJViennaCL);CHKERRQ(ierr);
5048 #endif
5049   PetscFunctionReturn(0);
5050 }
5051 
5052 /*
5053     Special version for direct calls from Fortran
5054 */
5055 #include <petsc/private/fortranimpl.h>
5056 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5057 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
5058 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5059 #define matsetvaluesseqaij_ matsetvaluesseqaij
5060 #endif
5061 
5062 /* Change these macros so can be used in void function */
5063 #undef CHKERRQ
5064 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
5065 #undef SETERRQ2
5066 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5067 #undef SETERRQ3
5068 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5069 
5070 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)
5071 {
5072   Mat            A  = *AA;
5073   PetscInt       m  = *mm, n = *nn;
5074   InsertMode     is = *isis;
5075   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
5076   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
5077   PetscInt       *imax,*ai,*ailen;
5078   PetscErrorCode ierr;
5079   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
5080   MatScalar      *ap,value,*aa;
5081   PetscBool      ignorezeroentries = a->ignorezeroentries;
5082   PetscBool      roworiented       = a->roworiented;
5083 
5084   PetscFunctionBegin;
5085   MatCheckPreallocated(A,1);
5086   imax  = a->imax;
5087   ai    = a->i;
5088   ailen = a->ilen;
5089   aj    = a->j;
5090   aa    = a->a;
5091 
5092   for (k=0; k<m; k++) { /* loop over added rows */
5093     row = im[k];
5094     if (row < 0) continue;
5095 #if defined(PETSC_USE_DEBUG)
5096     if (row >= A->rmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
5097 #endif
5098     rp   = aj + ai[row]; ap = aa + ai[row];
5099     rmax = imax[row]; nrow = ailen[row];
5100     low  = 0;
5101     high = nrow;
5102     for (l=0; l<n; l++) { /* loop over added columns */
5103       if (in[l] < 0) continue;
5104 #if defined(PETSC_USE_DEBUG)
5105       if (in[l] >= A->cmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
5106 #endif
5107       col = in[l];
5108       if (roworiented) value = v[l + k*n];
5109       else value = v[k + l*m];
5110 
5111       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
5112 
5113       if (col <= lastcol) low = 0;
5114       else high = nrow;
5115       lastcol = col;
5116       while (high-low > 5) {
5117         t = (low+high)/2;
5118         if (rp[t] > col) high = t;
5119         else             low  = t;
5120       }
5121       for (i=low; i<high; i++) {
5122         if (rp[i] > col) break;
5123         if (rp[i] == col) {
5124           if (is == ADD_VALUES) ap[i] += value;
5125           else                  ap[i] = value;
5126           goto noinsert;
5127         }
5128       }
5129       if (value == 0.0 && ignorezeroentries) goto noinsert;
5130       if (nonew == 1) goto noinsert;
5131       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
5132       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
5133       N = nrow++ - 1; a->nz++; high++;
5134       /* shift up all the later entries in this row */
5135       for (ii=N; ii>=i; ii--) {
5136         rp[ii+1] = rp[ii];
5137         ap[ii+1] = ap[ii];
5138       }
5139       rp[i] = col;
5140       ap[i] = value;
5141       A->nonzerostate++;
5142 noinsert:;
5143       low = i + 1;
5144     }
5145     ailen[row] = nrow;
5146   }
5147   PetscFunctionReturnVoid();
5148 }
5149