xref: /petsc/src/mat/impls/aij/seq/aij.c (revision ba67282182bbff18a5c2e8153be2769e671cfaf7)
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 = PetscMemzero(norms,n*sizeof(PetscReal));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+1,&collengths);CHKERRQ(ierr);
261     ierr = PetscMalloc1(n+1,&cia);CHKERRQ(ierr);
262     ierr = PetscMalloc1(nz+1,&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 = PetscMemzero(collengths,n*sizeof(PetscInt));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,*jj,mr,col;
310   PetscInt       *cspidx;
311 
312   PetscFunctionBegin;
313   *nn = n;
314   if (!ia) PetscFunctionReturn(0);
315 
316   ierr = PetscCalloc1(n+1,&collengths);CHKERRQ(ierr);
317   ierr = PetscMalloc1(n+1,&cia);CHKERRQ(ierr);
318   ierr = PetscMalloc1(nz+1,&cja);CHKERRQ(ierr);
319   ierr = PetscMalloc1(nz+1,&cspidx);CHKERRQ(ierr);
320   jj   = a->j;
321   for (i=0; i<nz; i++) {
322     collengths[jj[i]]++;
323   }
324   cia[0] = oshift;
325   for (i=0; i<n; i++) {
326     cia[i+1] = cia[i] + collengths[i];
327   }
328   ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
329   jj   = a->j;
330   for (row=0; row<m; row++) {
331     mr = a->i[row+1] - a->i[row];
332     for (i=0; i<mr; i++) {
333       col = *jj++;
334       cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
335       cja[cia[col] + collengths[col]++ - oshift]  = row + oshift;
336     }
337   }
338   ierr   = PetscFree(collengths);CHKERRQ(ierr);
339   *ia    = cia; *ja = cja;
340   *spidx = cspidx;
341   PetscFunctionReturn(0);
342 }
343 
344 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
345 {
346   PetscErrorCode ierr;
347 
348   PetscFunctionBegin;
349   ierr = MatRestoreColumnIJ_SeqAIJ(A,oshift,symmetric,inodecompressed,n,ia,ja,done);CHKERRQ(ierr);
350   ierr = PetscFree(*spidx);CHKERRQ(ierr);
351   PetscFunctionReturn(0);
352 }
353 
354 PetscErrorCode MatSetValuesRow_SeqAIJ(Mat A,PetscInt row,const PetscScalar v[])
355 {
356   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
357   PetscInt       *ai = a->i;
358   PetscErrorCode ierr;
359 
360   PetscFunctionBegin;
361   ierr = PetscMemcpy(a->a+ai[row],v,(ai[row+1]-ai[row])*sizeof(PetscScalar));CHKERRQ(ierr);
362   PetscFunctionReturn(0);
363 }
364 
365 /*
366     MatSeqAIJSetValuesLocalFast - An optimized version of MatSetValuesLocal() for SeqAIJ matrices with several assumptions
367 
368       -   a single row of values is set with each call
369       -   no row or column indices are negative or (in error) larger than the number of rows or columns
370       -   the values are always added to the matrix, not set
371       -   no new locations are introduced in the nonzero structure of the matrix
372 
373      This does NOT assume the global column indices are sorted
374 
375 */
376 
377 #include <petsc/private/isimpl.h>
378 PetscErrorCode MatSeqAIJSetValuesLocalFast(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
379 {
380   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
381   PetscInt       low,high,t,row,nrow,i,col,l;
382   const PetscInt *rp,*ai = a->i,*ailen = a->ilen,*aj = a->j;
383   PetscInt       lastcol = -1;
384   MatScalar      *ap,value,*aa = a->a;
385   const PetscInt *ridx = A->rmap->mapping->indices,*cidx = A->cmap->mapping->indices;
386 
387   row = ridx[im[0]];
388   rp   = aj + ai[row];
389   ap = aa + ai[row];
390   nrow = ailen[row];
391   low  = 0;
392   high = nrow;
393   for (l=0; l<n; l++) { /* loop over added columns */
394     col = cidx[in[l]];
395     value = v[l];
396 
397     if (col <= lastcol) low = 0;
398     else high = nrow;
399     lastcol = col;
400     while (high-low > 5) {
401       t = (low+high)/2;
402       if (rp[t] > col) high = t;
403       else low = t;
404     }
405     for (i=low; i<high; i++) {
406       if (rp[i] == col) {
407         ap[i] += value;
408         low = i + 1;
409         break;
410       }
411     }
412   }
413   return 0;
414 }
415 
416 PetscErrorCode MatSetValues_SeqAIJ(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
417 {
418   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
419   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
420   PetscInt       *imax = a->imax,*ai = a->i,*ailen = a->ilen;
421   PetscErrorCode ierr;
422   PetscInt       *aj = a->j,nonew = a->nonew,lastcol = -1;
423   MatScalar      *ap=NULL,value=0.0,*aa = a->a;
424   PetscBool      ignorezeroentries = a->ignorezeroentries;
425   PetscBool      roworiented       = a->roworiented;
426 
427   PetscFunctionBegin;
428   for (k=0; k<m; k++) { /* loop over added rows */
429     row = im[k];
430     if (row < 0) continue;
431 #if defined(PETSC_USE_DEBUG)
432     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);
433 #endif
434     rp   = aj + ai[row];
435     if (!A->structure_only) ap = aa + ai[row];
436     rmax = imax[row]; nrow = ailen[row];
437     low  = 0;
438     high = nrow;
439     for (l=0; l<n; l++) { /* loop over added columns */
440       if (in[l] < 0) continue;
441 #if defined(PETSC_USE_DEBUG)
442       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);
443 #endif
444       col = in[l];
445       if (!A->structure_only) {
446         if (roworiented) {
447           value = v[l + k*n];
448         } else {
449           value = v[k + l*m];
450         }
451       } else { /* A->structure_only */
452         value = 1; /* avoid 'continue' below?  */
453       }
454       if ((value == 0.0 && ignorezeroentries) && (is == ADD_VALUES) && row != col) continue;
455 
456       if (col <= lastcol) low = 0;
457       else high = nrow;
458       lastcol = col;
459       while (high-low > 5) {
460         t = (low+high)/2;
461         if (rp[t] > col) high = t;
462         else low = t;
463       }
464       for (i=low; i<high; i++) {
465         if (rp[i] > col) break;
466         if (rp[i] == col) {
467           if (!A->structure_only) {
468             if (is == ADD_VALUES) ap[i] += value;
469             else ap[i] = value;
470           }
471           low = i + 1;
472           goto noinsert;
473         }
474       }
475       if (value == 0.0 && ignorezeroentries && row != col) goto noinsert;
476       if (nonew == 1) goto noinsert;
477       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at (%D,%D) in the matrix",row,col);
478       if (A->structure_only) {
479         MatSeqXAIJReallocateAIJ_structure_only(A,A->rmap->n,1,nrow,row,col,rmax,ai,aj,rp,imax,nonew,MatScalar);
480       } else {
481         MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
482       }
483       N = nrow++ - 1; a->nz++; high++;
484       /* shift up all the later entries in this row */
485       for (ii=N; ii>=i; ii--) {
486         rp[ii+1] = rp[ii];
487         if (!A->structure_only) ap[ii+1] = ap[ii];
488       }
489       rp[i] = col;
490       if (!A->structure_only) ap[i] = value;
491       low   = i + 1;
492       A->nonzerostate++;
493 noinsert:;
494     }
495     ailen[row] = nrow;
496   }
497   PetscFunctionReturn(0);
498 }
499 
500 
501 PetscErrorCode MatGetValues_SeqAIJ(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],PetscScalar v[])
502 {
503   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
504   PetscInt   *rp,k,low,high,t,row,nrow,i,col,l,*aj = a->j;
505   PetscInt   *ai = a->i,*ailen = a->ilen;
506   MatScalar  *ap,*aa = a->a;
507 
508   PetscFunctionBegin;
509   for (k=0; k<m; k++) { /* loop over rows */
510     row = im[k];
511     if (row < 0) {v += n; continue;} /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",row); */
512     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);
513     rp   = aj + ai[row]; ap = aa + ai[row];
514     nrow = ailen[row];
515     for (l=0; l<n; l++) { /* loop over columns */
516       if (in[l] < 0) {v++; continue;} /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",in[l]); */
517       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);
518       col  = in[l];
519       high = nrow; low = 0; /* assume unsorted */
520       while (high-low > 5) {
521         t = (low+high)/2;
522         if (rp[t] > col) high = t;
523         else low = t;
524       }
525       for (i=low; i<high; i++) {
526         if (rp[i] > col) break;
527         if (rp[i] == col) {
528           *v++ = ap[i];
529           goto finished;
530         }
531       }
532       *v++ = 0.0;
533 finished:;
534     }
535   }
536   PetscFunctionReturn(0);
537 }
538 
539 
540 PetscErrorCode MatView_SeqAIJ_Binary(Mat A,PetscViewer viewer)
541 {
542   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
543   PetscErrorCode ierr;
544   PetscInt       i,*col_lens;
545   int            fd;
546   FILE           *file;
547 
548   PetscFunctionBegin;
549   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
550   ierr = PetscMalloc1(4+A->rmap->n,&col_lens);CHKERRQ(ierr);
551 
552   col_lens[0] = MAT_FILE_CLASSID;
553   col_lens[1] = A->rmap->n;
554   col_lens[2] = A->cmap->n;
555   col_lens[3] = a->nz;
556 
557   /* store lengths of each row and write (including header) to file */
558   for (i=0; i<A->rmap->n; i++) {
559     col_lens[4+i] = a->i[i+1] - a->i[i];
560   }
561   ierr = PetscBinaryWrite(fd,col_lens,4+A->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
562   ierr = PetscFree(col_lens);CHKERRQ(ierr);
563 
564   /* store column indices (zero start index) */
565   ierr = PetscBinaryWrite(fd,a->j,a->nz,PETSC_INT,PETSC_FALSE);CHKERRQ(ierr);
566 
567   /* store nonzero values */
568   ierr = PetscBinaryWrite(fd,a->a,a->nz,PETSC_SCALAR,PETSC_FALSE);CHKERRQ(ierr);
569 
570   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
571   if (file) {
572     fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(A->rmap->bs));
573   }
574   PetscFunctionReturn(0);
575 }
576 
577 static PetscErrorCode MatView_SeqAIJ_ASCII_structonly(Mat A,PetscViewer viewer)
578 {
579   PetscErrorCode ierr;
580   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
581   PetscInt       i,k,m=A->rmap->N;
582 
583   PetscFunctionBegin;
584   ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
585   for (i=0; i<m; i++) {
586     ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
587     for (k=a->i[i]; k<a->i[i+1]; k++) {
588       ierr = PetscViewerASCIIPrintf(viewer," (%D) ",a->j[k]);CHKERRQ(ierr);
589     }
590     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
591   }
592   ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
593   PetscFunctionReturn(0);
594 }
595 
596 extern PetscErrorCode MatSeqAIJFactorInfo_Matlab(Mat,PetscViewer);
597 
598 PetscErrorCode MatView_SeqAIJ_ASCII(Mat A,PetscViewer viewer)
599 {
600   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
601   PetscErrorCode    ierr;
602   PetscInt          i,j,m = A->rmap->n;
603   const char        *name;
604   PetscViewerFormat format;
605 
606   PetscFunctionBegin;
607   if (A->structure_only) {
608     ierr = MatView_SeqAIJ_ASCII_structonly(A,viewer);CHKERRQ(ierr);
609     PetscFunctionReturn(0);
610   }
611 
612   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
613   if (format == PETSC_VIEWER_ASCII_MATLAB) {
614     PetscInt nofinalvalue = 0;
615     if (m && ((a->i[m] == a->i[m-1]) || (a->j[a->nz-1] != A->cmap->n-1))) {
616       /* Need a dummy value to ensure the dimension of the matrix. */
617       nofinalvalue = 1;
618     }
619     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
620     ierr = PetscViewerASCIIPrintf(viewer,"%% Size = %D %D \n",m,A->cmap->n);CHKERRQ(ierr);
621     ierr = PetscViewerASCIIPrintf(viewer,"%% Nonzeros = %D \n",a->nz);CHKERRQ(ierr);
622 #if defined(PETSC_USE_COMPLEX)
623     ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,4);\n",a->nz+nofinalvalue);CHKERRQ(ierr);
624 #else
625     ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",a->nz+nofinalvalue);CHKERRQ(ierr);
626 #endif
627     ierr = PetscViewerASCIIPrintf(viewer,"zzz = [\n");CHKERRQ(ierr);
628 
629     for (i=0; i<m; i++) {
630       for (j=a->i[i]; j<a->i[i+1]; j++) {
631 #if defined(PETSC_USE_COMPLEX)
632         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);
633 #else
634         ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,a->j[j]+1,(double)a->a[j]);CHKERRQ(ierr);
635 #endif
636       }
637     }
638     if (nofinalvalue) {
639 #if defined(PETSC_USE_COMPLEX)
640       ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e %18.16e\n",m,A->cmap->n,0.,0.);CHKERRQ(ierr);
641 #else
642       ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",m,A->cmap->n,0.0);CHKERRQ(ierr);
643 #endif
644     }
645     ierr = PetscObjectGetName((PetscObject)A,&name);CHKERRQ(ierr);
646     ierr = PetscViewerASCIIPrintf(viewer,"];\n %s = spconvert(zzz);\n",name);CHKERRQ(ierr);
647     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
648   } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO || format == PETSC_VIEWER_ASCII_INFO) {
649     PetscFunctionReturn(0);
650   } else if (format == PETSC_VIEWER_ASCII_COMMON) {
651     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
652     for (i=0; i<m; i++) {
653       ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
654       for (j=a->i[i]; j<a->i[i+1]; j++) {
655 #if defined(PETSC_USE_COMPLEX)
656         if (PetscImaginaryPart(a->a[j]) > 0.0 && PetscRealPart(a->a[j]) != 0.0) {
657           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
658         } else if (PetscImaginaryPart(a->a[j]) < 0.0 && PetscRealPart(a->a[j]) != 0.0) {
659           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
660         } else if (PetscRealPart(a->a[j]) != 0.0) {
661           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
662         }
663 #else
664         if (a->a[j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);}
665 #endif
666       }
667       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
668     }
669     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
670   } else if (format == PETSC_VIEWER_ASCII_SYMMODU) {
671     PetscInt nzd=0,fshift=1,*sptr;
672     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
673     ierr = PetscMalloc1(m+1,&sptr);CHKERRQ(ierr);
674     for (i=0; i<m; i++) {
675       sptr[i] = nzd+1;
676       for (j=a->i[i]; j<a->i[i+1]; j++) {
677         if (a->j[j] >= i) {
678 #if defined(PETSC_USE_COMPLEX)
679           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) nzd++;
680 #else
681           if (a->a[j] != 0.0) nzd++;
682 #endif
683         }
684       }
685     }
686     sptr[m] = nzd+1;
687     ierr    = PetscViewerASCIIPrintf(viewer," %D %D\n\n",m,nzd);CHKERRQ(ierr);
688     for (i=0; i<m+1; i+=6) {
689       if (i+4<m) {
690         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);
691       } else if (i+3<m) {
692         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);
693       } else if (i+2<m) {
694         ierr = PetscViewerASCIIPrintf(viewer," %D %D %D %D\n",sptr[i],sptr[i+1],sptr[i+2],sptr[i+3]);CHKERRQ(ierr);
695       } else if (i+1<m) {
696         ierr = PetscViewerASCIIPrintf(viewer," %D %D %D\n",sptr[i],sptr[i+1],sptr[i+2]);CHKERRQ(ierr);
697       } else if (i<m) {
698         ierr = PetscViewerASCIIPrintf(viewer," %D %D\n",sptr[i],sptr[i+1]);CHKERRQ(ierr);
699       } else {
700         ierr = PetscViewerASCIIPrintf(viewer," %D\n",sptr[i]);CHKERRQ(ierr);
701       }
702     }
703     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
704     ierr = PetscFree(sptr);CHKERRQ(ierr);
705     for (i=0; i<m; i++) {
706       for (j=a->i[i]; j<a->i[i+1]; j++) {
707         if (a->j[j] >= i) {ierr = PetscViewerASCIIPrintf(viewer," %D ",a->j[j]+fshift);CHKERRQ(ierr);}
708       }
709       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
710     }
711     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
712     for (i=0; i<m; i++) {
713       for (j=a->i[i]; j<a->i[i+1]; j++) {
714         if (a->j[j] >= i) {
715 #if defined(PETSC_USE_COMPLEX)
716           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) {
717             ierr = PetscViewerASCIIPrintf(viewer," %18.16e %18.16e ",(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
718           }
719 #else
720           if (a->a[j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," %18.16e ",(double)a->a[j]);CHKERRQ(ierr);}
721 #endif
722         }
723       }
724       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
725     }
726     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
727   } else if (format == PETSC_VIEWER_ASCII_DENSE) {
728     PetscInt    cnt = 0,jcnt;
729     PetscScalar value;
730 #if defined(PETSC_USE_COMPLEX)
731     PetscBool   realonly = PETSC_TRUE;
732 
733     for (i=0; i<a->i[m]; i++) {
734       if (PetscImaginaryPart(a->a[i]) != 0.0) {
735         realonly = PETSC_FALSE;
736         break;
737       }
738     }
739 #endif
740 
741     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
742     for (i=0; i<m; i++) {
743       jcnt = 0;
744       for (j=0; j<A->cmap->n; j++) {
745         if (jcnt < a->i[i+1]-a->i[i] && j == a->j[cnt]) {
746           value = a->a[cnt++];
747           jcnt++;
748         } else {
749           value = 0.0;
750         }
751 #if defined(PETSC_USE_COMPLEX)
752         if (realonly) {
753           ierr = PetscViewerASCIIPrintf(viewer," %7.5e ",(double)PetscRealPart(value));CHKERRQ(ierr);
754         } else {
755           ierr = PetscViewerASCIIPrintf(viewer," %7.5e+%7.5e i ",(double)PetscRealPart(value),(double)PetscImaginaryPart(value));CHKERRQ(ierr);
756         }
757 #else
758         ierr = PetscViewerASCIIPrintf(viewer," %7.5e ",(double)value);CHKERRQ(ierr);
759 #endif
760       }
761       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
762     }
763     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
764   } else if (format == PETSC_VIEWER_ASCII_MATRIXMARKET) {
765     PetscInt fshift=1;
766     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
767 #if defined(PETSC_USE_COMPLEX)
768     ierr = PetscViewerASCIIPrintf(viewer,"%%%%MatrixMarket matrix coordinate complex general\n");CHKERRQ(ierr);
769 #else
770     ierr = PetscViewerASCIIPrintf(viewer,"%%%%MatrixMarket matrix coordinate real general\n");CHKERRQ(ierr);
771 #endif
772     ierr = PetscViewerASCIIPrintf(viewer,"%D %D %D\n", m, A->cmap->n, a->nz);CHKERRQ(ierr);
773     for (i=0; i<m; i++) {
774       for (j=a->i[i]; j<a->i[i+1]; j++) {
775 #if defined(PETSC_USE_COMPLEX)
776         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);
777 #else
778         ierr = PetscViewerASCIIPrintf(viewer,"%D %D %g\n", i+fshift, a->j[j]+fshift, (double)a->a[j]);CHKERRQ(ierr);
779 #endif
780       }
781     }
782     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
783   } else {
784     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
785     if (A->factortype) {
786       for (i=0; i<m; i++) {
787         ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
788         /* L part */
789         for (j=a->i[i]; j<a->i[i+1]; j++) {
790 #if defined(PETSC_USE_COMPLEX)
791           if (PetscImaginaryPart(a->a[j]) > 0.0) {
792             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
793           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
794             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)(-PetscImaginaryPart(a->a[j])));CHKERRQ(ierr);
795           } else {
796             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
797           }
798 #else
799           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);
800 #endif
801         }
802         /* diagonal */
803         j = a->diag[i];
804 #if defined(PETSC_USE_COMPLEX)
805         if (PetscImaginaryPart(a->a[j]) > 0.0) {
806           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);
807         } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
808           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);
809         } else {
810           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(1.0/a->a[j]));CHKERRQ(ierr);
811         }
812 #else
813         ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)(1.0/a->a[j]));CHKERRQ(ierr);
814 #endif
815 
816         /* U part */
817         for (j=a->diag[i+1]+1; j<a->diag[i]; j++) {
818 #if defined(PETSC_USE_COMPLEX)
819           if (PetscImaginaryPart(a->a[j]) > 0.0) {
820             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
821           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
822             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)(-PetscImaginaryPart(a->a[j])));CHKERRQ(ierr);
823           } else {
824             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
825           }
826 #else
827           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);
828 #endif
829         }
830         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
831       }
832     } else {
833       for (i=0; i<m; i++) {
834         ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
835         for (j=a->i[i]; j<a->i[i+1]; j++) {
836 #if defined(PETSC_USE_COMPLEX)
837           if (PetscImaginaryPart(a->a[j]) > 0.0) {
838             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
839           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
840             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
841           } else {
842             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
843           }
844 #else
845           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);
846 #endif
847         }
848         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
849       }
850     }
851     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
852   }
853   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
854   PetscFunctionReturn(0);
855 }
856 
857 #include <petscdraw.h>
858 PetscErrorCode MatView_SeqAIJ_Draw_Zoom(PetscDraw draw,void *Aa)
859 {
860   Mat               A  = (Mat) Aa;
861   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
862   PetscErrorCode    ierr;
863   PetscInt          i,j,m = A->rmap->n;
864   int               color;
865   PetscReal         xl,yl,xr,yr,x_l,x_r,y_l,y_r;
866   PetscViewer       viewer;
867   PetscViewerFormat format;
868 
869   PetscFunctionBegin;
870   ierr = PetscObjectQuery((PetscObject)A,"Zoomviewer",(PetscObject*)&viewer);CHKERRQ(ierr);
871   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
872   ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
873 
874   /* loop over matrix elements drawing boxes */
875 
876   if (format != PETSC_VIEWER_DRAW_CONTOUR) {
877     ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
878     /* Blue for negative, Cyan for zero and  Red for positive */
879     color = PETSC_DRAW_BLUE;
880     for (i=0; i<m; i++) {
881       y_l = m - i - 1.0; y_r = y_l + 1.0;
882       for (j=a->i[i]; j<a->i[i+1]; j++) {
883         x_l = a->j[j]; x_r = x_l + 1.0;
884         if (PetscRealPart(a->a[j]) >=  0.) continue;
885         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
886       }
887     }
888     color = PETSC_DRAW_CYAN;
889     for (i=0; i<m; i++) {
890       y_l = m - i - 1.0; y_r = y_l + 1.0;
891       for (j=a->i[i]; j<a->i[i+1]; j++) {
892         x_l = a->j[j]; x_r = x_l + 1.0;
893         if (a->a[j] !=  0.) continue;
894         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
895       }
896     }
897     color = PETSC_DRAW_RED;
898     for (i=0; i<m; i++) {
899       y_l = m - i - 1.0; y_r = y_l + 1.0;
900       for (j=a->i[i]; j<a->i[i+1]; j++) {
901         x_l = a->j[j]; x_r = x_l + 1.0;
902         if (PetscRealPart(a->a[j]) <=  0.) continue;
903         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
904       }
905     }
906     ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
907   } else {
908     /* use contour shading to indicate magnitude of values */
909     /* first determine max of all nonzero values */
910     PetscReal minv = 0.0, maxv = 0.0;
911     PetscInt  nz = a->nz, count = 0;
912     PetscDraw popup;
913 
914     for (i=0; i<nz; i++) {
915       if (PetscAbsScalar(a->a[i]) > maxv) maxv = PetscAbsScalar(a->a[i]);
916     }
917     if (minv >= maxv) maxv = minv + PETSC_SMALL;
918     ierr = PetscDrawGetPopup(draw,&popup);CHKERRQ(ierr);
919     ierr = PetscDrawScalePopup(popup,minv,maxv);CHKERRQ(ierr);
920 
921     ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
922     for (i=0; i<m; i++) {
923       y_l = m - i - 1.0;
924       y_r = y_l + 1.0;
925       for (j=a->i[i]; j<a->i[i+1]; j++) {
926         x_l = a->j[j];
927         x_r = x_l + 1.0;
928         color = PetscDrawRealToColor(PetscAbsScalar(a->a[count]),minv,maxv);
929         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
930         count++;
931       }
932     }
933     ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
934   }
935   PetscFunctionReturn(0);
936 }
937 
938 #include <petscdraw.h>
939 PetscErrorCode MatView_SeqAIJ_Draw(Mat A,PetscViewer viewer)
940 {
941   PetscErrorCode ierr;
942   PetscDraw      draw;
943   PetscReal      xr,yr,xl,yl,h,w;
944   PetscBool      isnull;
945 
946   PetscFunctionBegin;
947   ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
948   ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
949   if (isnull) PetscFunctionReturn(0);
950 
951   xr   = A->cmap->n; yr  = A->rmap->n; h = yr/10.0; w = xr/10.0;
952   xr  += w;          yr += h;         xl = -w;     yl = -h;
953   ierr = PetscDrawSetCoordinates(draw,xl,yl,xr,yr);CHKERRQ(ierr);
954   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",(PetscObject)viewer);CHKERRQ(ierr);
955   ierr = PetscDrawZoom(draw,MatView_SeqAIJ_Draw_Zoom,A);CHKERRQ(ierr);
956   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",NULL);CHKERRQ(ierr);
957   ierr = PetscDrawSave(draw);CHKERRQ(ierr);
958   PetscFunctionReturn(0);
959 }
960 
961 PetscErrorCode MatView_SeqAIJ(Mat A,PetscViewer viewer)
962 {
963   PetscErrorCode ierr;
964   PetscBool      iascii,isbinary,isdraw;
965 
966   PetscFunctionBegin;
967   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
968   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
969   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
970   if (iascii) {
971     ierr = MatView_SeqAIJ_ASCII(A,viewer);CHKERRQ(ierr);
972   } else if (isbinary) {
973     ierr = MatView_SeqAIJ_Binary(A,viewer);CHKERRQ(ierr);
974   } else if (isdraw) {
975     ierr = MatView_SeqAIJ_Draw(A,viewer);CHKERRQ(ierr);
976   }
977   ierr = MatView_SeqAIJ_Inode(A,viewer);CHKERRQ(ierr);
978   PetscFunctionReturn(0);
979 }
980 
981 PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat A,MatAssemblyType mode)
982 {
983   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
984   PetscErrorCode ierr;
985   PetscInt       fshift = 0,i,j,*ai = a->i,*aj = a->j,*imax = a->imax;
986   PetscInt       m      = A->rmap->n,*ip,N,*ailen = a->ilen,rmax = 0;
987   MatScalar      *aa    = a->a,*ap;
988   PetscReal      ratio  = 0.6;
989 
990   PetscFunctionBegin;
991   if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(0);
992 
993   if (m) rmax = ailen[0]; /* determine row with most nonzeros */
994   for (i=1; i<m; i++) {
995     /* move each row back by the amount of empty slots (fshift) before it*/
996     fshift += imax[i-1] - ailen[i-1];
997     rmax    = PetscMax(rmax,ailen[i]);
998     if (fshift) {
999       ip = aj + ai[i];
1000       ap = aa + ai[i];
1001       N  = ailen[i];
1002       for (j=0; j<N; j++) {
1003         ip[j-fshift] = ip[j];
1004         if (!A->structure_only) ap[j-fshift] = ap[j];
1005       }
1006     }
1007     ai[i] = ai[i-1] + ailen[i-1];
1008   }
1009   if (m) {
1010     fshift += imax[m-1] - ailen[m-1];
1011     ai[m]   = ai[m-1] + ailen[m-1];
1012   }
1013 
1014   /* reset ilen and imax for each row */
1015   a->nonzerorowcnt = 0;
1016   if (A->structure_only) {
1017     ierr = PetscFree2(a->imax,a->ilen);CHKERRQ(ierr);
1018   } else { /* !A->structure_only */
1019     for (i=0; i<m; i++) {
1020       ailen[i] = imax[i] = ai[i+1] - ai[i];
1021       a->nonzerorowcnt += ((ai[i+1] - ai[i]) > 0);
1022     }
1023   }
1024   a->nz = ai[m];
1025   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);
1026 
1027   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1028   ierr = PetscInfo4(A,"Matrix size: %D X %D; storage space: %D unneeded,%D used\n",m,A->cmap->n,fshift,a->nz);CHKERRQ(ierr);
1029   ierr = PetscInfo1(A,"Number of mallocs during MatSetValues() is %D\n",a->reallocs);CHKERRQ(ierr);
1030   ierr = PetscInfo1(A,"Maximum nonzeros in any row is %D\n",rmax);CHKERRQ(ierr);
1031 
1032   A->info.mallocs    += a->reallocs;
1033   a->reallocs         = 0;
1034   A->info.nz_unneeded = (PetscReal)fshift;
1035   a->rmax             = rmax;
1036 
1037   if (!A->structure_only) {
1038     ierr = MatCheckCompressedRow(A,a->nonzerorowcnt,&a->compressedrow,a->i,m,ratio);CHKERRQ(ierr);
1039   }
1040   ierr = MatAssemblyEnd_SeqAIJ_Inode(A,mode);CHKERRQ(ierr);
1041   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1042   PetscFunctionReturn(0);
1043 }
1044 
1045 PetscErrorCode MatRealPart_SeqAIJ(Mat A)
1046 {
1047   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1048   PetscInt       i,nz = a->nz;
1049   MatScalar      *aa = a->a;
1050   PetscErrorCode ierr;
1051 
1052   PetscFunctionBegin;
1053   for (i=0; i<nz; i++) aa[i] = PetscRealPart(aa[i]);
1054   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1055   PetscFunctionReturn(0);
1056 }
1057 
1058 PetscErrorCode MatImaginaryPart_SeqAIJ(Mat A)
1059 {
1060   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1061   PetscInt       i,nz = a->nz;
1062   MatScalar      *aa = a->a;
1063   PetscErrorCode ierr;
1064 
1065   PetscFunctionBegin;
1066   for (i=0; i<nz; i++) aa[i] = PetscImaginaryPart(aa[i]);
1067   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1068   PetscFunctionReturn(0);
1069 }
1070 
1071 PetscErrorCode MatZeroEntries_SeqAIJ(Mat A)
1072 {
1073   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1074   PetscErrorCode ierr;
1075 
1076   PetscFunctionBegin;
1077   ierr = PetscMemzero(a->a,(a->i[A->rmap->n])*sizeof(PetscScalar));CHKERRQ(ierr);
1078   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1079   PetscFunctionReturn(0);
1080 }
1081 
1082 PetscErrorCode MatDestroy_SeqAIJ(Mat A)
1083 {
1084   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1085   PetscErrorCode ierr;
1086 
1087   PetscFunctionBegin;
1088 #if defined(PETSC_USE_LOG)
1089   PetscLogObjectState((PetscObject)A,"Rows=%D, Cols=%D, NZ=%D",A->rmap->n,A->cmap->n,a->nz);
1090 #endif
1091   ierr = MatSeqXAIJFreeAIJ(A,&a->a,&a->j,&a->i);CHKERRQ(ierr);
1092   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
1093   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
1094   ierr = PetscFree(a->diag);CHKERRQ(ierr);
1095   ierr = PetscFree(a->ibdiag);CHKERRQ(ierr);
1096   ierr = PetscFree2(a->imax,a->ilen);CHKERRQ(ierr);
1097   ierr = PetscFree(a->ipre);CHKERRQ(ierr);
1098   ierr = PetscFree3(a->idiag,a->mdiag,a->ssor_work);CHKERRQ(ierr);
1099   ierr = PetscFree(a->solve_work);CHKERRQ(ierr);
1100   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
1101   ierr = PetscFree(a->saved_values);CHKERRQ(ierr);
1102   ierr = ISColoringDestroy(&a->coloring);CHKERRQ(ierr);
1103   ierr = PetscFree2(a->compressedrow.i,a->compressedrow.rindex);CHKERRQ(ierr);
1104   ierr = PetscFree(a->matmult_abdense);CHKERRQ(ierr);
1105 
1106   ierr = MatDestroy_SeqAIJ_Inode(A);CHKERRQ(ierr);
1107   ierr = PetscFree(A->data);CHKERRQ(ierr);
1108 
1109   ierr = PetscObjectChangeTypeName((PetscObject)A,0);CHKERRQ(ierr);
1110   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetColumnIndices_C",NULL);CHKERRQ(ierr);
1111   ierr = PetscObjectComposeFunction((PetscObject)A,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1112   ierr = PetscObjectComposeFunction((PetscObject)A,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1113   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqsbaij_C",NULL);CHKERRQ(ierr);
1114   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqbaij_C",NULL);CHKERRQ(ierr);
1115   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqaijperm_C",NULL);CHKERRQ(ierr);
1116 #if defined(PETSC_HAVE_ELEMENTAL)
1117   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_elemental_C",NULL);CHKERRQ(ierr);
1118 #endif
1119 #if defined(PETSC_HAVE_HYPRE)
1120   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_hypre_C",NULL);CHKERRQ(ierr);
1121   ierr = PetscObjectComposeFunction((PetscObject)A,"MatMatMatMult_transpose_seqaij_seqaij_C",NULL);CHKERRQ(ierr);
1122 #endif
1123   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqdense_C",NULL);CHKERRQ(ierr);
1124   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqsell_C",NULL);CHKERRQ(ierr);
1125   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_is_C",NULL);CHKERRQ(ierr);
1126   ierr = PetscObjectComposeFunction((PetscObject)A,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1127   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1128   ierr = PetscObjectComposeFunction((PetscObject)A,"MatResetPreallocation_C",NULL);CHKERRQ(ierr);
1129   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1130   ierr = PetscObjectComposeFunction((PetscObject)A,"MatReorderForNonzeroDiagonal_C",NULL);CHKERRQ(ierr);
1131   ierr = PetscObjectComposeFunction((PetscObject)A,"MatPtAP_is_seqaij_C",NULL);CHKERRQ(ierr);
1132   PetscFunctionReturn(0);
1133 }
1134 
1135 PetscErrorCode MatSetOption_SeqAIJ(Mat A,MatOption op,PetscBool flg)
1136 {
1137   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1138   PetscErrorCode ierr;
1139 
1140   PetscFunctionBegin;
1141   switch (op) {
1142   case MAT_ROW_ORIENTED:
1143     a->roworiented = flg;
1144     break;
1145   case MAT_KEEP_NONZERO_PATTERN:
1146     a->keepnonzeropattern = flg;
1147     break;
1148   case MAT_NEW_NONZERO_LOCATIONS:
1149     a->nonew = (flg ? 0 : 1);
1150     break;
1151   case MAT_NEW_NONZERO_LOCATION_ERR:
1152     a->nonew = (flg ? -1 : 0);
1153     break;
1154   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1155     a->nonew = (flg ? -2 : 0);
1156     break;
1157   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1158     a->nounused = (flg ? -1 : 0);
1159     break;
1160   case MAT_IGNORE_ZERO_ENTRIES:
1161     a->ignorezeroentries = flg;
1162     break;
1163   case MAT_SPD:
1164   case MAT_SYMMETRIC:
1165   case MAT_STRUCTURALLY_SYMMETRIC:
1166   case MAT_HERMITIAN:
1167   case MAT_SYMMETRY_ETERNAL:
1168   case MAT_STRUCTURE_ONLY:
1169     /* These options are handled directly by MatSetOption() */
1170     break;
1171   case MAT_NEW_DIAGONALS:
1172   case MAT_IGNORE_OFF_PROC_ENTRIES:
1173   case MAT_USE_HASH_TABLE:
1174     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1175     break;
1176   case MAT_USE_INODES:
1177     /* Not an error because MatSetOption_SeqAIJ_Inode handles this one */
1178     break;
1179   case MAT_SUBMAT_SINGLEIS:
1180     A->submat_singleis = flg;
1181     break;
1182   default:
1183     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1184   }
1185   ierr = MatSetOption_SeqAIJ_Inode(A,op,flg);CHKERRQ(ierr);
1186   PetscFunctionReturn(0);
1187 }
1188 
1189 PetscErrorCode MatGetDiagonal_SeqAIJ(Mat A,Vec v)
1190 {
1191   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1192   PetscErrorCode ierr;
1193   PetscInt       i,j,n,*ai=a->i,*aj=a->j,nz;
1194   PetscScalar    *aa=a->a,*x,zero=0.0;
1195 
1196   PetscFunctionBegin;
1197   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
1198   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
1199 
1200   if (A->factortype == MAT_FACTOR_ILU || A->factortype == MAT_FACTOR_LU) {
1201     PetscInt *diag=a->diag;
1202     ierr = VecGetArray(v,&x);CHKERRQ(ierr);
1203     for (i=0; i<n; i++) x[i] = 1.0/aa[diag[i]];
1204     ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1205     PetscFunctionReturn(0);
1206   }
1207 
1208   ierr = VecSet(v,zero);CHKERRQ(ierr);
1209   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
1210   for (i=0; i<n; i++) {
1211     nz = ai[i+1] - ai[i];
1212     if (!nz) x[i] = 0.0;
1213     for (j=ai[i]; j<ai[i+1]; j++) {
1214       if (aj[j] == i) {
1215         x[i] = aa[j];
1216         break;
1217       }
1218     }
1219   }
1220   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1221   PetscFunctionReturn(0);
1222 }
1223 
1224 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1225 PetscErrorCode MatMultTransposeAdd_SeqAIJ(Mat A,Vec xx,Vec zz,Vec yy)
1226 {
1227   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1228   PetscScalar       *y;
1229   const PetscScalar *x;
1230   PetscErrorCode    ierr;
1231   PetscInt          m = A->rmap->n;
1232 #if !defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1233   const MatScalar   *v;
1234   PetscScalar       alpha;
1235   PetscInt          n,i,j;
1236   const PetscInt    *idx,*ii,*ridx=NULL;
1237   Mat_CompressedRow cprow    = a->compressedrow;
1238   PetscBool         usecprow = cprow.use;
1239 #endif
1240 
1241   PetscFunctionBegin;
1242   if (zz != yy) {ierr = VecCopy(zz,yy);CHKERRQ(ierr);}
1243   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1244   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1245 
1246 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1247   fortranmulttransposeaddaij_(&m,x,a->i,a->j,a->a,y);
1248 #else
1249   if (usecprow) {
1250     m    = cprow.nrows;
1251     ii   = cprow.i;
1252     ridx = cprow.rindex;
1253   } else {
1254     ii = a->i;
1255   }
1256   for (i=0; i<m; i++) {
1257     idx = a->j + ii[i];
1258     v   = a->a + ii[i];
1259     n   = ii[i+1] - ii[i];
1260     if (usecprow) {
1261       alpha = x[ridx[i]];
1262     } else {
1263       alpha = x[i];
1264     }
1265     for (j=0; j<n; j++) y[idx[j]] += alpha*v[j];
1266   }
1267 #endif
1268   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1269   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1270   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1271   PetscFunctionReturn(0);
1272 }
1273 
1274 PetscErrorCode MatMultTranspose_SeqAIJ(Mat A,Vec xx,Vec yy)
1275 {
1276   PetscErrorCode ierr;
1277 
1278   PetscFunctionBegin;
1279   ierr = VecSet(yy,0.0);CHKERRQ(ierr);
1280   ierr = MatMultTransposeAdd_SeqAIJ(A,xx,yy,yy);CHKERRQ(ierr);
1281   PetscFunctionReturn(0);
1282 }
1283 
1284 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1285 
1286 PetscErrorCode MatMult_SeqAIJ(Mat A,Vec xx,Vec yy)
1287 {
1288   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1289   PetscScalar       *y;
1290   const PetscScalar *x;
1291   const MatScalar   *aa;
1292   PetscErrorCode    ierr;
1293   PetscInt          m=A->rmap->n;
1294   const PetscInt    *aj,*ii,*ridx=NULL;
1295   PetscInt          n,i;
1296   PetscScalar       sum;
1297   PetscBool         usecprow=a->compressedrow.use;
1298 
1299 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1300 #pragma disjoint(*x,*y,*aa)
1301 #endif
1302 
1303   PetscFunctionBegin;
1304   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1305   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1306   ii   = a->i;
1307   if (usecprow) { /* use compressed row format */
1308     ierr = PetscMemzero(y,m*sizeof(PetscScalar));CHKERRQ(ierr);
1309     m    = a->compressedrow.nrows;
1310     ii   = a->compressedrow.i;
1311     ridx = a->compressedrow.rindex;
1312     for (i=0; i<m; i++) {
1313       n           = ii[i+1] - ii[i];
1314       aj          = a->j + ii[i];
1315       aa          = a->a + ii[i];
1316       sum         = 0.0;
1317       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1318       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1319       y[*ridx++] = sum;
1320     }
1321   } else { /* do not use compressed row format */
1322 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJ)
1323     aj   = a->j;
1324     aa   = a->a;
1325     fortranmultaij_(&m,x,ii,aj,aa,y);
1326 #else
1327     for (i=0; i<m; i++) {
1328       n           = ii[i+1] - ii[i];
1329       aj          = a->j + ii[i];
1330       aa          = a->a + ii[i];
1331       sum         = 0.0;
1332       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1333       y[i] = sum;
1334     }
1335 #endif
1336   }
1337   ierr = PetscLogFlops(2.0*a->nz - a->nonzerorowcnt);CHKERRQ(ierr);
1338   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1339   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1340   PetscFunctionReturn(0);
1341 }
1342 
1343 PetscErrorCode MatMultMax_SeqAIJ(Mat A,Vec xx,Vec yy)
1344 {
1345   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1346   PetscScalar       *y;
1347   const PetscScalar *x;
1348   const MatScalar   *aa;
1349   PetscErrorCode    ierr;
1350   PetscInt          m=A->rmap->n;
1351   const PetscInt    *aj,*ii,*ridx=NULL;
1352   PetscInt          n,i,nonzerorow=0;
1353   PetscScalar       sum;
1354   PetscBool         usecprow=a->compressedrow.use;
1355 
1356 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1357 #pragma disjoint(*x,*y,*aa)
1358 #endif
1359 
1360   PetscFunctionBegin;
1361   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1362   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1363   if (usecprow) { /* use compressed row format */
1364     m    = a->compressedrow.nrows;
1365     ii   = a->compressedrow.i;
1366     ridx = a->compressedrow.rindex;
1367     for (i=0; i<m; i++) {
1368       n           = ii[i+1] - ii[i];
1369       aj          = a->j + ii[i];
1370       aa          = a->a + ii[i];
1371       sum         = 0.0;
1372       nonzerorow += (n>0);
1373       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1374       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1375       y[*ridx++] = sum;
1376     }
1377   } else { /* do not use compressed row format */
1378     ii = a->i;
1379     for (i=0; i<m; i++) {
1380       n           = ii[i+1] - ii[i];
1381       aj          = a->j + ii[i];
1382       aa          = a->a + ii[i];
1383       sum         = 0.0;
1384       nonzerorow += (n>0);
1385       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1386       y[i] = sum;
1387     }
1388   }
1389   ierr = PetscLogFlops(2.0*a->nz - nonzerorow);CHKERRQ(ierr);
1390   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1391   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1392   PetscFunctionReturn(0);
1393 }
1394 
1395 PetscErrorCode MatMultAddMax_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1396 {
1397   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1398   PetscScalar       *y,*z;
1399   const PetscScalar *x;
1400   const MatScalar   *aa;
1401   PetscErrorCode    ierr;
1402   PetscInt          m = A->rmap->n,*aj,*ii;
1403   PetscInt          n,i,*ridx=NULL;
1404   PetscScalar       sum;
1405   PetscBool         usecprow=a->compressedrow.use;
1406 
1407   PetscFunctionBegin;
1408   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1409   ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1410   if (usecprow) { /* use compressed row format */
1411     if (zz != yy) {
1412       ierr = PetscMemcpy(z,y,m*sizeof(PetscScalar));CHKERRQ(ierr);
1413     }
1414     m    = a->compressedrow.nrows;
1415     ii   = a->compressedrow.i;
1416     ridx = a->compressedrow.rindex;
1417     for (i=0; i<m; i++) {
1418       n   = ii[i+1] - ii[i];
1419       aj  = a->j + ii[i];
1420       aa  = a->a + ii[i];
1421       sum = y[*ridx];
1422       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1423       z[*ridx++] = sum;
1424     }
1425   } else { /* do not use compressed row format */
1426     ii = a->i;
1427     for (i=0; i<m; i++) {
1428       n   = ii[i+1] - ii[i];
1429       aj  = a->j + ii[i];
1430       aa  = a->a + ii[i];
1431       sum = y[i];
1432       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1433       z[i] = sum;
1434     }
1435   }
1436   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1437   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1438   ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1439   PetscFunctionReturn(0);
1440 }
1441 
1442 #include <../src/mat/impls/aij/seq/ftn-kernels/fmultadd.h>
1443 PetscErrorCode MatMultAdd_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1444 {
1445   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1446   PetscScalar       *y,*z;
1447   const PetscScalar *x;
1448   const MatScalar   *aa;
1449   PetscErrorCode    ierr;
1450   const PetscInt    *aj,*ii,*ridx=NULL;
1451   PetscInt          m = A->rmap->n,n,i;
1452   PetscScalar       sum;
1453   PetscBool         usecprow=a->compressedrow.use;
1454 
1455   PetscFunctionBegin;
1456   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1457   ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1458   if (usecprow) { /* use compressed row format */
1459     if (zz != yy) {
1460       ierr = PetscMemcpy(z,y,m*sizeof(PetscScalar));CHKERRQ(ierr);
1461     }
1462     m    = a->compressedrow.nrows;
1463     ii   = a->compressedrow.i;
1464     ridx = a->compressedrow.rindex;
1465     for (i=0; i<m; i++) {
1466       n   = ii[i+1] - ii[i];
1467       aj  = a->j + ii[i];
1468       aa  = a->a + ii[i];
1469       sum = y[*ridx];
1470       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1471       z[*ridx++] = sum;
1472     }
1473   } else { /* do not use compressed row format */
1474     ii = a->i;
1475 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJ)
1476     aj = a->j;
1477     aa = a->a;
1478     fortranmultaddaij_(&m,x,ii,aj,aa,y,z);
1479 #else
1480     for (i=0; i<m; i++) {
1481       n   = ii[i+1] - ii[i];
1482       aj  = a->j + ii[i];
1483       aa  = a->a + ii[i];
1484       sum = y[i];
1485       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1486       z[i] = sum;
1487     }
1488 #endif
1489   }
1490   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1491   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1492   ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1493   PetscFunctionReturn(0);
1494 }
1495 
1496 /*
1497      Adds diagonal pointers to sparse matrix structure.
1498 */
1499 PetscErrorCode MatMarkDiagonal_SeqAIJ(Mat A)
1500 {
1501   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1502   PetscErrorCode ierr;
1503   PetscInt       i,j,m = A->rmap->n;
1504 
1505   PetscFunctionBegin;
1506   if (!a->diag) {
1507     ierr = PetscMalloc1(m,&a->diag);CHKERRQ(ierr);
1508     ierr = PetscLogObjectMemory((PetscObject)A, m*sizeof(PetscInt));CHKERRQ(ierr);
1509   }
1510   for (i=0; i<A->rmap->n; i++) {
1511     a->diag[i] = a->i[i+1];
1512     for (j=a->i[i]; j<a->i[i+1]; j++) {
1513       if (a->j[j] == i) {
1514         a->diag[i] = j;
1515         break;
1516       }
1517     }
1518   }
1519   PetscFunctionReturn(0);
1520 }
1521 
1522 PetscErrorCode MatShift_SeqAIJ(Mat A,PetscScalar v)
1523 {
1524   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1525   const PetscInt    *diag = (const PetscInt*)a->diag;
1526   const PetscInt    *ii = (const PetscInt*) a->i;
1527   PetscInt          i,*mdiag = NULL;
1528   PetscErrorCode    ierr;
1529   PetscInt          cnt = 0; /* how many diagonals are missing */
1530 
1531   PetscFunctionBegin;
1532   if (!A->preallocated || !a->nz) {
1533     ierr = MatSeqAIJSetPreallocation(A,1,NULL);CHKERRQ(ierr);
1534     ierr = MatShift_Basic(A,v);CHKERRQ(ierr);
1535     PetscFunctionReturn(0);
1536   }
1537 
1538   if (a->diagonaldense) {
1539     cnt = 0;
1540   } else {
1541     ierr = PetscCalloc1(A->rmap->n,&mdiag);CHKERRQ(ierr);
1542     for (i=0; i<A->rmap->n; i++) {
1543       if (diag[i] >= ii[i+1]) {
1544         cnt++;
1545         mdiag[i] = 1;
1546       }
1547     }
1548   }
1549   if (!cnt) {
1550     ierr = MatShift_Basic(A,v);CHKERRQ(ierr);
1551   } else {
1552     PetscScalar *olda = a->a;  /* preserve pointers to current matrix nonzeros structure and values */
1553     PetscInt    *oldj = a->j, *oldi = a->i;
1554     PetscBool   singlemalloc = a->singlemalloc,free_a = a->free_a,free_ij = a->free_ij;
1555 
1556     a->a = NULL;
1557     a->j = NULL;
1558     a->i = NULL;
1559     /* increase the values in imax for each row where a diagonal is being inserted then reallocate the matrix data structures */
1560     for (i=0; i<A->rmap->n; i++) {
1561       a->imax[i] += mdiag[i];
1562     }
1563     ierr = MatSeqAIJSetPreallocation_SeqAIJ(A,0,a->imax);CHKERRQ(ierr);
1564 
1565     /* copy old values into new matrix data structure */
1566     for (i=0; i<A->rmap->n; i++) {
1567       ierr = MatSetValues(A,1,&i,a->imax[i] - mdiag[i],&oldj[oldi[i]],&olda[oldi[i]],ADD_VALUES);CHKERRQ(ierr);
1568       ierr = MatSetValue(A,i,i,v,ADD_VALUES);CHKERRQ(ierr);
1569     }
1570     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1571     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1572     if (singlemalloc) {
1573       ierr = PetscFree3(olda,oldj,oldi);CHKERRQ(ierr);
1574     } else {
1575       if (free_a)  {ierr = PetscFree(olda);CHKERRQ(ierr);}
1576       if (free_ij) {ierr = PetscFree(oldj);CHKERRQ(ierr);}
1577       if (free_ij) {ierr = PetscFree(oldi);CHKERRQ(ierr);}
1578     }
1579   }
1580   ierr = PetscFree(mdiag);CHKERRQ(ierr);
1581   a->diagonaldense = PETSC_TRUE;
1582   PetscFunctionReturn(0);
1583 }
1584 
1585 /*
1586      Checks for missing diagonals
1587 */
1588 PetscErrorCode MatMissingDiagonal_SeqAIJ(Mat A,PetscBool  *missing,PetscInt *d)
1589 {
1590   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1591   PetscInt       *diag,*ii = a->i,i;
1592   PetscErrorCode ierr;
1593 
1594   PetscFunctionBegin;
1595   *missing = PETSC_FALSE;
1596   if (A->rmap->n > 0 && !ii) {
1597     *missing = PETSC_TRUE;
1598     if (d) *d = 0;
1599     ierr = PetscInfo(A,"Matrix has no entries therefore is missing diagonal\n");CHKERRQ(ierr);
1600   } else {
1601     diag = a->diag;
1602     for (i=0; i<A->rmap->n; i++) {
1603       if (diag[i] >= ii[i+1]) {
1604         *missing = PETSC_TRUE;
1605         if (d) *d = i;
1606         ierr = PetscInfo1(A,"Matrix is missing diagonal number %D\n",i);CHKERRQ(ierr);
1607         break;
1608       }
1609     }
1610   }
1611   PetscFunctionReturn(0);
1612 }
1613 
1614 #include <petscblaslapack.h>
1615 #include <petsc/private/kernels/blockinvert.h>
1616 
1617 /*
1618     Note that values is allocated externally by the PC and then passed into this routine
1619 */
1620 PetscErrorCode MatInvertVariableBlockDiagonal_SeqAIJ(Mat A,PetscInt nblocks,const PetscInt *bsizes,PetscScalar *diag)
1621 {
1622   PetscErrorCode  ierr;
1623   PetscInt        n = A->rmap->n, i, ncnt = 0, *indx,j,bsizemax = 0,*v_pivots;
1624   PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;
1625   const PetscReal shift = 0.0;
1626   PetscInt        ipvt[5];
1627   PetscScalar     work[25],*v_work;
1628 
1629   PetscFunctionBegin;
1630   allowzeropivot = PetscNot(A->erroriffailure);
1631   for (i=0; i<nblocks; i++) ncnt += bsizes[i];
1632   if (ncnt != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Total blocksizes %D doesn't match number matrix rows %D",ncnt,n);
1633   for (i=0; i<nblocks; i++) {
1634     bsizemax = PetscMax(bsizemax,bsizes[i]);
1635   }
1636   ierr = PetscMalloc1(bsizemax,&indx);CHKERRQ(ierr);
1637   if (bsizemax > 7) {
1638     ierr = PetscMalloc2(bsizemax,&v_work,bsizemax,&v_pivots);CHKERRQ(ierr);
1639   }
1640   ncnt = 0;
1641   for (i=0; i<nblocks; i++) {
1642     for (j=0; j<bsizes[i]; j++) indx[j] = ncnt+j;
1643     ierr    = MatGetValues(A,bsizes[i],indx,bsizes[i],indx,diag);CHKERRQ(ierr);
1644     switch (bsizes[i]) {
1645     case 1:
1646       *diag = 1.0/(*diag);
1647       break;
1648     case 2:
1649       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1650       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1651       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
1652       break;
1653     case 3:
1654       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1655       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1656       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
1657       break;
1658     case 4:
1659       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1660       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1661       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
1662       break;
1663     case 5:
1664       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1665       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1666       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
1667       break;
1668     case 6:
1669       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1670       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1671       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
1672       break;
1673     case 7:
1674       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1675       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1676       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
1677       break;
1678     default:
1679       ierr  = PetscKernel_A_gets_inverse_A(bsizes[i],diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1680       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1681       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bsizes[i]);CHKERRQ(ierr);
1682     }
1683     ncnt   += bsizes[i];
1684     diag += bsizes[i]*bsizes[i];
1685   }
1686   if (bsizemax > 7) {
1687     ierr = PetscFree2(v_work,v_pivots);CHKERRQ(ierr);
1688   }
1689   ierr = PetscFree(indx);CHKERRQ(ierr);
1690   PetscFunctionReturn(0);
1691 }
1692 
1693 /*
1694    Negative shift indicates do not generate an error if there is a zero diagonal, just invert it anyways
1695 */
1696 PetscErrorCode  MatInvertDiagonal_SeqAIJ(Mat A,PetscScalar omega,PetscScalar fshift)
1697 {
1698   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
1699   PetscErrorCode ierr;
1700   PetscInt       i,*diag,m = A->rmap->n;
1701   MatScalar      *v = a->a;
1702   PetscScalar    *idiag,*mdiag;
1703 
1704   PetscFunctionBegin;
1705   if (a->idiagvalid) PetscFunctionReturn(0);
1706   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1707   diag = a->diag;
1708   if (!a->idiag) {
1709     ierr = PetscMalloc3(m,&a->idiag,m,&a->mdiag,m,&a->ssor_work);CHKERRQ(ierr);
1710     ierr = PetscLogObjectMemory((PetscObject)A, 3*m*sizeof(PetscScalar));CHKERRQ(ierr);
1711     v    = a->a;
1712   }
1713   mdiag = a->mdiag;
1714   idiag = a->idiag;
1715 
1716   if (omega == 1.0 && PetscRealPart(fshift) <= 0.0) {
1717     for (i=0; i<m; i++) {
1718       mdiag[i] = v[diag[i]];
1719       if (!PetscAbsScalar(mdiag[i])) { /* zero diagonal */
1720         if (PetscRealPart(fshift)) {
1721           ierr = PetscInfo1(A,"Zero diagonal on row %D\n",i);CHKERRQ(ierr);
1722           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1723           A->factorerror_zeropivot_value = 0.0;
1724           A->factorerror_zeropivot_row   = i;
1725         } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Zero diagonal on row %D",i);
1726       }
1727       idiag[i] = 1.0/v[diag[i]];
1728     }
1729     ierr = PetscLogFlops(m);CHKERRQ(ierr);
1730   } else {
1731     for (i=0; i<m; i++) {
1732       mdiag[i] = v[diag[i]];
1733       idiag[i] = omega/(fshift + v[diag[i]]);
1734     }
1735     ierr = PetscLogFlops(2.0*m);CHKERRQ(ierr);
1736   }
1737   a->idiagvalid = PETSC_TRUE;
1738   PetscFunctionReturn(0);
1739 }
1740 
1741 #include <../src/mat/impls/aij/seq/ftn-kernels/frelax.h>
1742 PetscErrorCode MatSOR_SeqAIJ(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1743 {
1744   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1745   PetscScalar       *x,d,sum,*t,scale;
1746   const MatScalar   *v,*idiag=0,*mdiag;
1747   const PetscScalar *b, *bs,*xb, *ts;
1748   PetscErrorCode    ierr;
1749   PetscInt          n,m = A->rmap->n,i;
1750   const PetscInt    *idx,*diag;
1751 
1752   PetscFunctionBegin;
1753   its = its*lits;
1754 
1755   if (fshift != a->fshift || omega != a->omega) a->idiagvalid = PETSC_FALSE; /* must recompute idiag[] */
1756   if (!a->idiagvalid) {ierr = MatInvertDiagonal_SeqAIJ(A,omega,fshift);CHKERRQ(ierr);}
1757   a->fshift = fshift;
1758   a->omega  = omega;
1759 
1760   diag  = a->diag;
1761   t     = a->ssor_work;
1762   idiag = a->idiag;
1763   mdiag = a->mdiag;
1764 
1765   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1766   ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
1767   /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
1768   if (flag == SOR_APPLY_UPPER) {
1769     /* apply (U + D/omega) to the vector */
1770     bs = b;
1771     for (i=0; i<m; i++) {
1772       d   = fshift + mdiag[i];
1773       n   = a->i[i+1] - diag[i] - 1;
1774       idx = a->j + diag[i] + 1;
1775       v   = a->a + diag[i] + 1;
1776       sum = b[i]*d/omega;
1777       PetscSparseDensePlusDot(sum,bs,v,idx,n);
1778       x[i] = sum;
1779     }
1780     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1781     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1782     ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1783     PetscFunctionReturn(0);
1784   }
1785 
1786   if (flag == SOR_APPLY_LOWER) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SOR_APPLY_LOWER is not implemented");
1787   else if (flag & SOR_EISENSTAT) {
1788     /* Let  A = L + U + D; where L is lower trianglar,
1789     U is upper triangular, E = D/omega; This routine applies
1790 
1791             (L + E)^{-1} A (U + E)^{-1}
1792 
1793     to a vector efficiently using Eisenstat's trick.
1794     */
1795     scale = (2.0/omega) - 1.0;
1796 
1797     /*  x = (E + U)^{-1} b */
1798     for (i=m-1; i>=0; i--) {
1799       n   = a->i[i+1] - diag[i] - 1;
1800       idx = a->j + diag[i] + 1;
1801       v   = a->a + diag[i] + 1;
1802       sum = b[i];
1803       PetscSparseDenseMinusDot(sum,x,v,idx,n);
1804       x[i] = sum*idiag[i];
1805     }
1806 
1807     /*  t = b - (2*E - D)x */
1808     v = a->a;
1809     for (i=0; i<m; i++) t[i] = b[i] - scale*(v[*diag++])*x[i];
1810 
1811     /*  t = (E + L)^{-1}t */
1812     ts   = t;
1813     diag = a->diag;
1814     for (i=0; i<m; i++) {
1815       n   = diag[i] - a->i[i];
1816       idx = a->j + a->i[i];
1817       v   = a->a + a->i[i];
1818       sum = t[i];
1819       PetscSparseDenseMinusDot(sum,ts,v,idx,n);
1820       t[i] = sum*idiag[i];
1821       /*  x = x + t */
1822       x[i] += t[i];
1823     }
1824 
1825     ierr = PetscLogFlops(6.0*m-1 + 2.0*a->nz);CHKERRQ(ierr);
1826     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1827     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1828     PetscFunctionReturn(0);
1829   }
1830   if (flag & SOR_ZERO_INITIAL_GUESS) {
1831     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1832       for (i=0; i<m; i++) {
1833         n   = diag[i] - a->i[i];
1834         idx = a->j + a->i[i];
1835         v   = a->a + a->i[i];
1836         sum = b[i];
1837         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1838         t[i] = sum;
1839         x[i] = sum*idiag[i];
1840       }
1841       xb   = t;
1842       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1843     } else xb = b;
1844     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1845       for (i=m-1; i>=0; i--) {
1846         n   = a->i[i+1] - diag[i] - 1;
1847         idx = a->j + diag[i] + 1;
1848         v   = a->a + diag[i] + 1;
1849         sum = xb[i];
1850         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1851         if (xb == b) {
1852           x[i] = sum*idiag[i];
1853         } else {
1854           x[i] = (1-omega)*x[i] + sum*idiag[i];  /* omega in idiag */
1855         }
1856       }
1857       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
1858     }
1859     its--;
1860   }
1861   while (its--) {
1862     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1863       for (i=0; i<m; i++) {
1864         /* lower */
1865         n   = diag[i] - a->i[i];
1866         idx = a->j + a->i[i];
1867         v   = a->a + a->i[i];
1868         sum = b[i];
1869         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1870         t[i] = sum;             /* save application of the lower-triangular part */
1871         /* upper */
1872         n   = a->i[i+1] - diag[i] - 1;
1873         idx = a->j + diag[i] + 1;
1874         v   = a->a + diag[i] + 1;
1875         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1876         x[i] = (1. - omega)*x[i] + sum*idiag[i]; /* omega in idiag */
1877       }
1878       xb   = t;
1879       ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1880     } else xb = b;
1881     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1882       for (i=m-1; i>=0; i--) {
1883         sum = xb[i];
1884         if (xb == b) {
1885           /* whole matrix (no checkpointing available) */
1886           n   = a->i[i+1] - a->i[i];
1887           idx = a->j + a->i[i];
1888           v   = a->a + a->i[i];
1889           PetscSparseDenseMinusDot(sum,x,v,idx,n);
1890           x[i] = (1. - omega)*x[i] + (sum + mdiag[i]*x[i])*idiag[i];
1891         } else { /* lower-triangular part has been saved, so only apply upper-triangular */
1892           n   = a->i[i+1] - diag[i] - 1;
1893           idx = a->j + diag[i] + 1;
1894           v   = a->a + diag[i] + 1;
1895           PetscSparseDenseMinusDot(sum,x,v,idx,n);
1896           x[i] = (1. - omega)*x[i] + sum*idiag[i];  /* omega in idiag */
1897         }
1898       }
1899       if (xb == b) {
1900         ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1901       } else {
1902         ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
1903       }
1904     }
1905   }
1906   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1907   ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1908   PetscFunctionReturn(0);
1909 }
1910 
1911 
1912 PetscErrorCode MatGetInfo_SeqAIJ(Mat A,MatInfoType flag,MatInfo *info)
1913 {
1914   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1915 
1916   PetscFunctionBegin;
1917   info->block_size   = 1.0;
1918   info->nz_allocated = (double)a->maxnz;
1919   info->nz_used      = (double)a->nz;
1920   info->nz_unneeded  = (double)(a->maxnz - a->nz);
1921   info->assemblies   = (double)A->num_ass;
1922   info->mallocs      = (double)A->info.mallocs;
1923   info->memory       = ((PetscObject)A)->mem;
1924   if (A->factortype) {
1925     info->fill_ratio_given  = A->info.fill_ratio_given;
1926     info->fill_ratio_needed = A->info.fill_ratio_needed;
1927     info->factor_mallocs    = A->info.factor_mallocs;
1928   } else {
1929     info->fill_ratio_given  = 0;
1930     info->fill_ratio_needed = 0;
1931     info->factor_mallocs    = 0;
1932   }
1933   PetscFunctionReturn(0);
1934 }
1935 
1936 PetscErrorCode MatZeroRows_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
1937 {
1938   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1939   PetscInt          i,m = A->rmap->n - 1;
1940   PetscErrorCode    ierr;
1941   const PetscScalar *xx;
1942   PetscScalar       *bb;
1943   PetscInt          d = 0;
1944 
1945   PetscFunctionBegin;
1946   if (x && b) {
1947     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
1948     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
1949     for (i=0; i<N; i++) {
1950       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1951       bb[rows[i]] = diag*xx[rows[i]];
1952     }
1953     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
1954     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
1955   }
1956 
1957   if (a->keepnonzeropattern) {
1958     for (i=0; i<N; i++) {
1959       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1960       ierr = PetscMemzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]*sizeof(PetscScalar));CHKERRQ(ierr);
1961     }
1962     if (diag != 0.0) {
1963       for (i=0; i<N; i++) {
1964         d = rows[i];
1965         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);
1966       }
1967       for (i=0; i<N; i++) {
1968         a->a[a->diag[rows[i]]] = diag;
1969       }
1970     }
1971   } else {
1972     if (diag != 0.0) {
1973       for (i=0; i<N; i++) {
1974         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1975         if (a->ilen[rows[i]] > 0) {
1976           a->ilen[rows[i]]    = 1;
1977           a->a[a->i[rows[i]]] = diag;
1978           a->j[a->i[rows[i]]] = rows[i];
1979         } else { /* in case row was completely empty */
1980           ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES);CHKERRQ(ierr);
1981         }
1982       }
1983     } else {
1984       for (i=0; i<N; i++) {
1985         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1986         a->ilen[rows[i]] = 0;
1987       }
1988     }
1989     A->nonzerostate++;
1990   }
1991   ierr = (*A->ops->assemblyend)(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1992   PetscFunctionReturn(0);
1993 }
1994 
1995 PetscErrorCode MatZeroRowsColumns_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
1996 {
1997   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1998   PetscInt          i,j,m = A->rmap->n - 1,d = 0;
1999   PetscErrorCode    ierr;
2000   PetscBool         missing,*zeroed,vecs = PETSC_FALSE;
2001   const PetscScalar *xx;
2002   PetscScalar       *bb;
2003 
2004   PetscFunctionBegin;
2005   if (x && b) {
2006     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
2007     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
2008     vecs = PETSC_TRUE;
2009   }
2010   ierr = PetscCalloc1(A->rmap->n,&zeroed);CHKERRQ(ierr);
2011   for (i=0; i<N; i++) {
2012     if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2013     ierr = PetscMemzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]*sizeof(PetscScalar));CHKERRQ(ierr);
2014 
2015     zeroed[rows[i]] = PETSC_TRUE;
2016   }
2017   for (i=0; i<A->rmap->n; i++) {
2018     if (!zeroed[i]) {
2019       for (j=a->i[i]; j<a->i[i+1]; j++) {
2020         if (zeroed[a->j[j]]) {
2021           if (vecs) bb[i] -= a->a[j]*xx[a->j[j]];
2022           a->a[j] = 0.0;
2023         }
2024       }
2025     } else if (vecs) bb[i] = diag*xx[i];
2026   }
2027   if (x && b) {
2028     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
2029     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
2030   }
2031   ierr = PetscFree(zeroed);CHKERRQ(ierr);
2032   if (diag != 0.0) {
2033     ierr = MatMissingDiagonal_SeqAIJ(A,&missing,&d);CHKERRQ(ierr);
2034     if (missing) {
2035       if (a->nonew) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in row %D",d);
2036       else {
2037         for (i=0; i<N; i++) {
2038           ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES);CHKERRQ(ierr);
2039         }
2040       }
2041     } else {
2042       for (i=0; i<N; i++) {
2043         a->a[a->diag[rows[i]]] = diag;
2044       }
2045     }
2046   }
2047   ierr = (*A->ops->assemblyend)(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2048   PetscFunctionReturn(0);
2049 }
2050 
2051 PetscErrorCode MatGetRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
2052 {
2053   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2054   PetscInt   *itmp;
2055 
2056   PetscFunctionBegin;
2057   if (row < 0 || row >= A->rmap->n) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range",row);
2058 
2059   *nz = a->i[row+1] - a->i[row];
2060   if (v) *v = a->a + a->i[row];
2061   if (idx) {
2062     itmp = a->j + a->i[row];
2063     if (*nz) *idx = itmp;
2064     else *idx = 0;
2065   }
2066   PetscFunctionReturn(0);
2067 }
2068 
2069 /* remove this function? */
2070 PetscErrorCode MatRestoreRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
2071 {
2072   PetscFunctionBegin;
2073   PetscFunctionReturn(0);
2074 }
2075 
2076 PetscErrorCode MatNorm_SeqAIJ(Mat A,NormType type,PetscReal *nrm)
2077 {
2078   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
2079   MatScalar      *v  = a->a;
2080   PetscReal      sum = 0.0;
2081   PetscErrorCode ierr;
2082   PetscInt       i,j;
2083 
2084   PetscFunctionBegin;
2085   if (type == NORM_FROBENIUS) {
2086 #if defined(PETSC_USE_REAL___FP16)
2087     PetscBLASInt one = 1,nz = a->nz;
2088     *nrm = BLASnrm2_(&nz,v,&one);
2089 #else
2090     for (i=0; i<a->nz; i++) {
2091       sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
2092     }
2093     *nrm = PetscSqrtReal(sum);
2094 #endif
2095     ierr = PetscLogFlops(2*a->nz);CHKERRQ(ierr);
2096   } else if (type == NORM_1) {
2097     PetscReal *tmp;
2098     PetscInt  *jj = a->j;
2099     ierr = PetscCalloc1(A->cmap->n+1,&tmp);CHKERRQ(ierr);
2100     *nrm = 0.0;
2101     for (j=0; j<a->nz; j++) {
2102       tmp[*jj++] += PetscAbsScalar(*v);  v++;
2103     }
2104     for (j=0; j<A->cmap->n; j++) {
2105       if (tmp[j] > *nrm) *nrm = tmp[j];
2106     }
2107     ierr = PetscFree(tmp);CHKERRQ(ierr);
2108     ierr = PetscLogFlops(PetscMax(a->nz-1,0));CHKERRQ(ierr);
2109   } else if (type == NORM_INFINITY) {
2110     *nrm = 0.0;
2111     for (j=0; j<A->rmap->n; j++) {
2112       v   = a->a + a->i[j];
2113       sum = 0.0;
2114       for (i=0; i<a->i[j+1]-a->i[j]; i++) {
2115         sum += PetscAbsScalar(*v); v++;
2116       }
2117       if (sum > *nrm) *nrm = sum;
2118     }
2119     ierr = PetscLogFlops(PetscMax(a->nz-1,0));CHKERRQ(ierr);
2120   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for two norm");
2121   PetscFunctionReturn(0);
2122 }
2123 
2124 /* Merged from MatGetSymbolicTranspose_SeqAIJ() - replace MatGetSymbolicTranspose_SeqAIJ()? */
2125 PetscErrorCode MatTransposeSymbolic_SeqAIJ(Mat A,Mat *B)
2126 {
2127   PetscErrorCode ierr;
2128   PetscInt       i,j,anzj;
2129   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b;
2130   PetscInt       an=A->cmap->N,am=A->rmap->N;
2131   PetscInt       *ati,*atj,*atfill,*ai=a->i,*aj=a->j;
2132 
2133   PetscFunctionBegin;
2134   /* Allocate space for symbolic transpose info and work array */
2135   ierr = PetscCalloc1(an+1,&ati);CHKERRQ(ierr);
2136   ierr = PetscMalloc1(ai[am],&atj);CHKERRQ(ierr);
2137   ierr = PetscMalloc1(an,&atfill);CHKERRQ(ierr);
2138 
2139   /* Walk through aj and count ## of non-zeros in each row of A^T. */
2140   /* Note: offset by 1 for fast conversion into csr format. */
2141   for (i=0;i<ai[am];i++) ati[aj[i]+1] += 1;
2142   /* Form ati for csr format of A^T. */
2143   for (i=0;i<an;i++) ati[i+1] += ati[i];
2144 
2145   /* Copy ati into atfill so we have locations of the next free space in atj */
2146   ierr = PetscMemcpy(atfill,ati,an*sizeof(PetscInt));CHKERRQ(ierr);
2147 
2148   /* Walk through A row-wise and mark nonzero entries of A^T. */
2149   for (i=0;i<am;i++) {
2150     anzj = ai[i+1] - ai[i];
2151     for (j=0;j<anzj;j++) {
2152       atj[atfill[*aj]] = i;
2153       atfill[*aj++]   += 1;
2154     }
2155   }
2156 
2157   /* Clean up temporary space and complete requests. */
2158   ierr = PetscFree(atfill);CHKERRQ(ierr);
2159   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),an,am,ati,atj,NULL,B);CHKERRQ(ierr);
2160   ierr = MatSetBlockSizes(*B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2161 
2162   b          = (Mat_SeqAIJ*)((*B)->data);
2163   b->free_a  = PETSC_FALSE;
2164   b->free_ij = PETSC_TRUE;
2165   b->nonew   = 0;
2166   PetscFunctionReturn(0);
2167 }
2168 
2169 PetscErrorCode MatTranspose_SeqAIJ(Mat A,MatReuse reuse,Mat *B)
2170 {
2171   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2172   Mat            C;
2173   PetscErrorCode ierr;
2174   PetscInt       i,*aj = a->j,*ai = a->i,m = A->rmap->n,len,*col;
2175   MatScalar      *array = a->a;
2176 
2177   PetscFunctionBegin;
2178   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_INPLACE_MATRIX) {
2179     ierr = PetscCalloc1(1+A->cmap->n,&col);CHKERRQ(ierr);
2180 
2181     for (i=0; i<ai[m]; i++) col[aj[i]] += 1;
2182     ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2183     ierr = MatSetSizes(C,A->cmap->n,m,A->cmap->n,m);CHKERRQ(ierr);
2184     ierr = MatSetBlockSizes(C,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2185     ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2186     ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,col);CHKERRQ(ierr);
2187     ierr = PetscFree(col);CHKERRQ(ierr);
2188   } else {
2189     C = *B;
2190   }
2191 
2192   for (i=0; i<m; i++) {
2193     len    = ai[i+1]-ai[i];
2194     ierr   = MatSetValues_SeqAIJ(C,len,aj,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2195     array += len;
2196     aj    += len;
2197   }
2198   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2199   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2200 
2201   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
2202     *B = C;
2203   } else {
2204     ierr = MatHeaderMerge(A,&C);CHKERRQ(ierr);
2205   }
2206   PetscFunctionReturn(0);
2207 }
2208 
2209 PetscErrorCode  MatIsTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2210 {
2211   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) B->data;
2212   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2213   MatScalar      *va,*vb;
2214   PetscErrorCode ierr;
2215   PetscInt       ma,na,mb,nb, i;
2216 
2217   PetscFunctionBegin;
2218   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2219   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2220   if (ma!=nb || na!=mb) {
2221     *f = PETSC_FALSE;
2222     PetscFunctionReturn(0);
2223   }
2224   aii  = aij->i; bii = bij->i;
2225   adx  = aij->j; bdx = bij->j;
2226   va   = aij->a; vb = bij->a;
2227   ierr = PetscMalloc1(ma,&aptr);CHKERRQ(ierr);
2228   ierr = PetscMalloc1(mb,&bptr);CHKERRQ(ierr);
2229   for (i=0; i<ma; i++) aptr[i] = aii[i];
2230   for (i=0; i<mb; i++) bptr[i] = bii[i];
2231 
2232   *f = PETSC_TRUE;
2233   for (i=0; i<ma; i++) {
2234     while (aptr[i]<aii[i+1]) {
2235       PetscInt    idc,idr;
2236       PetscScalar vc,vr;
2237       /* column/row index/value */
2238       idc = adx[aptr[i]];
2239       idr = bdx[bptr[idc]];
2240       vc  = va[aptr[i]];
2241       vr  = vb[bptr[idc]];
2242       if (i!=idr || PetscAbsScalar(vc-vr) > tol) {
2243         *f = PETSC_FALSE;
2244         goto done;
2245       } else {
2246         aptr[i]++;
2247         if (B || i!=idc) bptr[idc]++;
2248       }
2249     }
2250   }
2251 done:
2252   ierr = PetscFree(aptr);CHKERRQ(ierr);
2253   ierr = PetscFree(bptr);CHKERRQ(ierr);
2254   PetscFunctionReturn(0);
2255 }
2256 
2257 PetscErrorCode  MatIsHermitianTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2258 {
2259   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) B->data;
2260   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2261   MatScalar      *va,*vb;
2262   PetscErrorCode ierr;
2263   PetscInt       ma,na,mb,nb, i;
2264 
2265   PetscFunctionBegin;
2266   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2267   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2268   if (ma!=nb || na!=mb) {
2269     *f = PETSC_FALSE;
2270     PetscFunctionReturn(0);
2271   }
2272   aii  = aij->i; bii = bij->i;
2273   adx  = aij->j; bdx = bij->j;
2274   va   = aij->a; vb = bij->a;
2275   ierr = PetscMalloc1(ma,&aptr);CHKERRQ(ierr);
2276   ierr = PetscMalloc1(mb,&bptr);CHKERRQ(ierr);
2277   for (i=0; i<ma; i++) aptr[i] = aii[i];
2278   for (i=0; i<mb; i++) bptr[i] = bii[i];
2279 
2280   *f = PETSC_TRUE;
2281   for (i=0; i<ma; i++) {
2282     while (aptr[i]<aii[i+1]) {
2283       PetscInt    idc,idr;
2284       PetscScalar vc,vr;
2285       /* column/row index/value */
2286       idc = adx[aptr[i]];
2287       idr = bdx[bptr[idc]];
2288       vc  = va[aptr[i]];
2289       vr  = vb[bptr[idc]];
2290       if (i!=idr || PetscAbsScalar(vc-PetscConj(vr)) > tol) {
2291         *f = PETSC_FALSE;
2292         goto done;
2293       } else {
2294         aptr[i]++;
2295         if (B || i!=idc) bptr[idc]++;
2296       }
2297     }
2298   }
2299 done:
2300   ierr = PetscFree(aptr);CHKERRQ(ierr);
2301   ierr = PetscFree(bptr);CHKERRQ(ierr);
2302   PetscFunctionReturn(0);
2303 }
2304 
2305 PetscErrorCode MatIsSymmetric_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2306 {
2307   PetscErrorCode ierr;
2308 
2309   PetscFunctionBegin;
2310   ierr = MatIsTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2311   PetscFunctionReturn(0);
2312 }
2313 
2314 PetscErrorCode MatIsHermitian_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2315 {
2316   PetscErrorCode ierr;
2317 
2318   PetscFunctionBegin;
2319   ierr = MatIsHermitianTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2320   PetscFunctionReturn(0);
2321 }
2322 
2323 PetscErrorCode MatDiagonalScale_SeqAIJ(Mat A,Vec ll,Vec rr)
2324 {
2325   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2326   const PetscScalar *l,*r;
2327   PetscScalar       x;
2328   MatScalar         *v;
2329   PetscErrorCode    ierr;
2330   PetscInt          i,j,m = A->rmap->n,n = A->cmap->n,M,nz = a->nz;
2331   const PetscInt    *jj;
2332 
2333   PetscFunctionBegin;
2334   if (ll) {
2335     /* The local size is used so that VecMPI can be passed to this routine
2336        by MatDiagonalScale_MPIAIJ */
2337     ierr = VecGetLocalSize(ll,&m);CHKERRQ(ierr);
2338     if (m != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
2339     ierr = VecGetArrayRead(ll,&l);CHKERRQ(ierr);
2340     v    = a->a;
2341     for (i=0; i<m; i++) {
2342       x = l[i];
2343       M = a->i[i+1] - a->i[i];
2344       for (j=0; j<M; j++) (*v++) *= x;
2345     }
2346     ierr = VecRestoreArrayRead(ll,&l);CHKERRQ(ierr);
2347     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2348   }
2349   if (rr) {
2350     ierr = VecGetLocalSize(rr,&n);CHKERRQ(ierr);
2351     if (n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vector wrong length");
2352     ierr = VecGetArrayRead(rr,&r);CHKERRQ(ierr);
2353     v    = a->a; jj = a->j;
2354     for (i=0; i<nz; i++) (*v++) *= r[*jj++];
2355     ierr = VecRestoreArrayRead(rr,&r);CHKERRQ(ierr);
2356     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2357   }
2358   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
2359   PetscFunctionReturn(0);
2360 }
2361 
2362 PetscErrorCode MatCreateSubMatrix_SeqAIJ(Mat A,IS isrow,IS iscol,PetscInt csize,MatReuse scall,Mat *B)
2363 {
2364   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*c;
2365   PetscErrorCode ierr;
2366   PetscInt       *smap,i,k,kstart,kend,oldcols = A->cmap->n,*lens;
2367   PetscInt       row,mat_i,*mat_j,tcol,first,step,*mat_ilen,sum,lensi;
2368   const PetscInt *irow,*icol;
2369   PetscInt       nrows,ncols;
2370   PetscInt       *starts,*j_new,*i_new,*aj = a->j,*ai = a->i,ii,*ailen = a->ilen;
2371   MatScalar      *a_new,*mat_a;
2372   Mat            C;
2373   PetscBool      stride;
2374 
2375   PetscFunctionBegin;
2376 
2377   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
2378   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
2379   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
2380 
2381   ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&stride);CHKERRQ(ierr);
2382   if (stride) {
2383     ierr = ISStrideGetInfo(iscol,&first,&step);CHKERRQ(ierr);
2384   } else {
2385     first = 0;
2386     step  = 0;
2387   }
2388   if (stride && step == 1) {
2389     /* special case of contiguous rows */
2390     ierr = PetscMalloc2(nrows,&lens,nrows,&starts);CHKERRQ(ierr);
2391     /* loop over new rows determining lens and starting points */
2392     for (i=0; i<nrows; i++) {
2393       kstart = ai[irow[i]];
2394       kend   = kstart + ailen[irow[i]];
2395       starts[i] = kstart;
2396       for (k=kstart; k<kend; k++) {
2397         if (aj[k] >= first) {
2398           starts[i] = k;
2399           break;
2400         }
2401       }
2402       sum = 0;
2403       while (k < kend) {
2404         if (aj[k++] >= first+ncols) break;
2405         sum++;
2406       }
2407       lens[i] = sum;
2408     }
2409     /* create submatrix */
2410     if (scall == MAT_REUSE_MATRIX) {
2411       PetscInt n_cols,n_rows;
2412       ierr = MatGetSize(*B,&n_rows,&n_cols);CHKERRQ(ierr);
2413       if (n_rows != nrows || n_cols != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
2414       ierr = MatZeroEntries(*B);CHKERRQ(ierr);
2415       C    = *B;
2416     } else {
2417       PetscInt rbs,cbs;
2418       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2419       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2420       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2421       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2422       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2423       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2424       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2425     }
2426     c = (Mat_SeqAIJ*)C->data;
2427 
2428     /* loop over rows inserting into submatrix */
2429     a_new = c->a;
2430     j_new = c->j;
2431     i_new = c->i;
2432 
2433     for (i=0; i<nrows; i++) {
2434       ii    = starts[i];
2435       lensi = lens[i];
2436       for (k=0; k<lensi; k++) {
2437         *j_new++ = aj[ii+k] - first;
2438       }
2439       ierr       = PetscMemcpy(a_new,a->a + starts[i],lensi*sizeof(PetscScalar));CHKERRQ(ierr);
2440       a_new     += lensi;
2441       i_new[i+1] = i_new[i] + lensi;
2442       c->ilen[i] = lensi;
2443     }
2444     ierr = PetscFree2(lens,starts);CHKERRQ(ierr);
2445   } else {
2446     ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
2447     ierr = PetscCalloc1(oldcols,&smap);CHKERRQ(ierr);
2448     ierr = PetscMalloc1(1+nrows,&lens);CHKERRQ(ierr);
2449     for (i=0; i<ncols; i++) {
2450 #if defined(PETSC_USE_DEBUG)
2451       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);
2452 #endif
2453       smap[icol[i]] = i+1;
2454     }
2455 
2456     /* determine lens of each row */
2457     for (i=0; i<nrows; i++) {
2458       kstart  = ai[irow[i]];
2459       kend    = kstart + a->ilen[irow[i]];
2460       lens[i] = 0;
2461       for (k=kstart; k<kend; k++) {
2462         if (smap[aj[k]]) {
2463           lens[i]++;
2464         }
2465       }
2466     }
2467     /* Create and fill new matrix */
2468     if (scall == MAT_REUSE_MATRIX) {
2469       PetscBool equal;
2470 
2471       c = (Mat_SeqAIJ*)((*B)->data);
2472       if ((*B)->rmap->n  != nrows || (*B)->cmap->n != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
2473       ierr = PetscMemcmp(c->ilen,lens,(*B)->rmap->n*sizeof(PetscInt),&equal);CHKERRQ(ierr);
2474       if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
2475       ierr = PetscMemzero(c->ilen,(*B)->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
2476       C    = *B;
2477     } else {
2478       PetscInt rbs,cbs;
2479       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2480       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2481       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2482       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2483       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2484       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2485       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2486     }
2487     c = (Mat_SeqAIJ*)(C->data);
2488     for (i=0; i<nrows; i++) {
2489       row      = irow[i];
2490       kstart   = ai[row];
2491       kend     = kstart + a->ilen[row];
2492       mat_i    = c->i[i];
2493       mat_j    = c->j + mat_i;
2494       mat_a    = c->a + mat_i;
2495       mat_ilen = c->ilen + i;
2496       for (k=kstart; k<kend; k++) {
2497         if ((tcol=smap[a->j[k]])) {
2498           *mat_j++ = tcol - 1;
2499           *mat_a++ = a->a[k];
2500           (*mat_ilen)++;
2501 
2502         }
2503       }
2504     }
2505     /* Free work space */
2506     ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
2507     ierr = PetscFree(smap);CHKERRQ(ierr);
2508     ierr = PetscFree(lens);CHKERRQ(ierr);
2509     /* sort */
2510     for (i = 0; i < nrows; i++) {
2511       PetscInt ilen;
2512 
2513       mat_i = c->i[i];
2514       mat_j = c->j + mat_i;
2515       mat_a = c->a + mat_i;
2516       ilen  = c->ilen[i];
2517       ierr  = PetscSortIntWithScalarArray(ilen,mat_j,mat_a);CHKERRQ(ierr);
2518     }
2519   }
2520   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2521   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2522 
2523   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
2524   *B   = C;
2525   PetscFunctionReturn(0);
2526 }
2527 
2528 PetscErrorCode  MatGetMultiProcBlock_SeqAIJ(Mat mat,MPI_Comm subComm,MatReuse scall,Mat *subMat)
2529 {
2530   PetscErrorCode ierr;
2531   Mat            B;
2532 
2533   PetscFunctionBegin;
2534   if (scall == MAT_INITIAL_MATRIX) {
2535     ierr    = MatCreate(subComm,&B);CHKERRQ(ierr);
2536     ierr    = MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->n,mat->cmap->n);CHKERRQ(ierr);
2537     ierr    = MatSetBlockSizesFromMats(B,mat,mat);CHKERRQ(ierr);
2538     ierr    = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
2539     ierr    = MatDuplicateNoCreate_SeqAIJ(B,mat,MAT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
2540     *subMat = B;
2541   } else {
2542     ierr = MatCopy_SeqAIJ(mat,*subMat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2543   }
2544   PetscFunctionReturn(0);
2545 }
2546 
2547 PetscErrorCode MatILUFactor_SeqAIJ(Mat inA,IS row,IS col,const MatFactorInfo *info)
2548 {
2549   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)inA->data;
2550   PetscErrorCode ierr;
2551   Mat            outA;
2552   PetscBool      row_identity,col_identity;
2553 
2554   PetscFunctionBegin;
2555   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels=0 supported for in-place ilu");
2556 
2557   ierr = ISIdentity(row,&row_identity);CHKERRQ(ierr);
2558   ierr = ISIdentity(col,&col_identity);CHKERRQ(ierr);
2559 
2560   outA             = inA;
2561   outA->factortype = MAT_FACTOR_LU;
2562   ierr = PetscFree(inA->solvertype);CHKERRQ(ierr);
2563   ierr = PetscStrallocpy(MATSOLVERPETSC,&inA->solvertype);CHKERRQ(ierr);
2564 
2565   ierr = PetscObjectReference((PetscObject)row);CHKERRQ(ierr);
2566   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
2567 
2568   a->row = row;
2569 
2570   ierr = PetscObjectReference((PetscObject)col);CHKERRQ(ierr);
2571   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
2572 
2573   a->col = col;
2574 
2575   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
2576   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
2577   ierr = ISInvertPermutation(col,PETSC_DECIDE,&a->icol);CHKERRQ(ierr);
2578   ierr = PetscLogObjectParent((PetscObject)inA,(PetscObject)a->icol);CHKERRQ(ierr);
2579 
2580   if (!a->solve_work) { /* this matrix may have been factored before */
2581     ierr = PetscMalloc1(inA->rmap->n+1,&a->solve_work);CHKERRQ(ierr);
2582     ierr = PetscLogObjectMemory((PetscObject)inA, (inA->rmap->n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2583   }
2584 
2585   ierr = MatMarkDiagonal_SeqAIJ(inA);CHKERRQ(ierr);
2586   if (row_identity && col_identity) {
2587     ierr = MatLUFactorNumeric_SeqAIJ_inplace(outA,inA,info);CHKERRQ(ierr);
2588   } else {
2589     ierr = MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA,inA,info);CHKERRQ(ierr);
2590   }
2591   PetscFunctionReturn(0);
2592 }
2593 
2594 PetscErrorCode MatScale_SeqAIJ(Mat inA,PetscScalar alpha)
2595 {
2596   Mat_SeqAIJ     *a     = (Mat_SeqAIJ*)inA->data;
2597   PetscScalar    oalpha = alpha;
2598   PetscErrorCode ierr;
2599   PetscBLASInt   one = 1,bnz;
2600 
2601   PetscFunctionBegin;
2602   ierr = PetscBLASIntCast(a->nz,&bnz);CHKERRQ(ierr);
2603   PetscStackCallBLAS("BLASscal",BLASscal_(&bnz,&oalpha,a->a,&one));
2604   ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2605   ierr = MatSeqAIJInvalidateDiagonal(inA);CHKERRQ(ierr);
2606   PetscFunctionReturn(0);
2607 }
2608 
2609 PetscErrorCode MatDestroySubMatrix_Private(Mat_SubSppt *submatj)
2610 {
2611   PetscErrorCode ierr;
2612   PetscInt       i;
2613 
2614   PetscFunctionBegin;
2615   if (!submatj->id) { /* delete data that are linked only to submats[id=0] */
2616     ierr = PetscFree4(submatj->sbuf1,submatj->ptr,submatj->tmp,submatj->ctr);CHKERRQ(ierr);
2617 
2618     for (i=0; i<submatj->nrqr; ++i) {
2619       ierr = PetscFree(submatj->sbuf2[i]);CHKERRQ(ierr);
2620     }
2621     ierr = PetscFree3(submatj->sbuf2,submatj->req_size,submatj->req_source1);CHKERRQ(ierr);
2622 
2623     if (submatj->rbuf1) {
2624       ierr = PetscFree(submatj->rbuf1[0]);CHKERRQ(ierr);
2625       ierr = PetscFree(submatj->rbuf1);CHKERRQ(ierr);
2626     }
2627 
2628     for (i=0; i<submatj->nrqs; ++i) {
2629       ierr = PetscFree(submatj->rbuf3[i]);CHKERRQ(ierr);
2630     }
2631     ierr = PetscFree3(submatj->req_source2,submatj->rbuf2,submatj->rbuf3);CHKERRQ(ierr);
2632     ierr = PetscFree(submatj->pa);CHKERRQ(ierr);
2633   }
2634 
2635 #if defined(PETSC_USE_CTABLE)
2636   ierr = PetscTableDestroy((PetscTable*)&submatj->rmap);CHKERRQ(ierr);
2637   if (submatj->cmap_loc) {ierr = PetscFree(submatj->cmap_loc);CHKERRQ(ierr);}
2638   ierr = PetscFree(submatj->rmap_loc);CHKERRQ(ierr);
2639 #else
2640   ierr = PetscFree(submatj->rmap);CHKERRQ(ierr);
2641 #endif
2642 
2643   if (!submatj->allcolumns) {
2644 #if defined(PETSC_USE_CTABLE)
2645     ierr = PetscTableDestroy((PetscTable*)&submatj->cmap);CHKERRQ(ierr);
2646 #else
2647     ierr = PetscFree(submatj->cmap);CHKERRQ(ierr);
2648 #endif
2649   }
2650   ierr = PetscFree(submatj->row2proc);CHKERRQ(ierr);
2651 
2652   ierr = PetscFree(submatj);CHKERRQ(ierr);
2653   PetscFunctionReturn(0);
2654 }
2655 
2656 PetscErrorCode MatDestroySubMatrix_SeqAIJ(Mat C)
2657 {
2658   PetscErrorCode ierr;
2659   Mat_SeqAIJ     *c = (Mat_SeqAIJ*)C->data;
2660   Mat_SubSppt    *submatj = c->submatis1;
2661 
2662   PetscFunctionBegin;
2663   ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
2664   ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
2665   PetscFunctionReturn(0);
2666 }
2667 
2668 PetscErrorCode MatDestroySubMatrices_SeqAIJ(PetscInt n,Mat *mat[])
2669 {
2670   PetscErrorCode ierr;
2671   PetscInt       i;
2672   Mat            C;
2673   Mat_SeqAIJ     *c;
2674   Mat_SubSppt    *submatj;
2675 
2676   PetscFunctionBegin;
2677   for (i=0; i<n; i++) {
2678     C       = (*mat)[i];
2679     c       = (Mat_SeqAIJ*)C->data;
2680     submatj = c->submatis1;
2681     if (submatj) {
2682       if (--((PetscObject)C)->refct <= 0) {
2683         ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
2684         ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
2685         ierr = PetscFree(C->defaultvectype);CHKERRQ(ierr);
2686         ierr = PetscLayoutDestroy(&C->rmap);CHKERRQ(ierr);
2687         ierr = PetscLayoutDestroy(&C->cmap);CHKERRQ(ierr);
2688         ierr = PetscHeaderDestroy(&C);CHKERRQ(ierr);
2689       }
2690     } else {
2691       ierr = MatDestroy(&C);CHKERRQ(ierr);
2692     }
2693   }
2694 
2695   /* Destroy Dummy submatrices created for reuse */
2696   ierr = MatDestroySubMatrices_Dummy(n,mat);CHKERRQ(ierr);
2697 
2698   ierr = PetscFree(*mat);CHKERRQ(ierr);
2699   PetscFunctionReturn(0);
2700 }
2701 
2702 PetscErrorCode MatCreateSubMatrices_SeqAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
2703 {
2704   PetscErrorCode ierr;
2705   PetscInt       i;
2706 
2707   PetscFunctionBegin;
2708   if (scall == MAT_INITIAL_MATRIX) {
2709     ierr = PetscCalloc1(n+1,B);CHKERRQ(ierr);
2710   }
2711 
2712   for (i=0; i<n; i++) {
2713     ierr = MatCreateSubMatrix_SeqAIJ(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]);CHKERRQ(ierr);
2714   }
2715   PetscFunctionReturn(0);
2716 }
2717 
2718 PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
2719 {
2720   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2721   PetscErrorCode ierr;
2722   PetscInt       row,i,j,k,l,m,n,*nidx,isz,val;
2723   const PetscInt *idx;
2724   PetscInt       start,end,*ai,*aj;
2725   PetscBT        table;
2726 
2727   PetscFunctionBegin;
2728   m  = A->rmap->n;
2729   ai = a->i;
2730   aj = a->j;
2731 
2732   if (ov < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"illegal negative overlap value used");
2733 
2734   ierr = PetscMalloc1(m+1,&nidx);CHKERRQ(ierr);
2735   ierr = PetscBTCreate(m,&table);CHKERRQ(ierr);
2736 
2737   for (i=0; i<is_max; i++) {
2738     /* Initialize the two local arrays */
2739     isz  = 0;
2740     ierr = PetscBTMemzero(m,table);CHKERRQ(ierr);
2741 
2742     /* Extract the indices, assume there can be duplicate entries */
2743     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
2744     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
2745 
2746     /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2747     for (j=0; j<n; ++j) {
2748       if (!PetscBTLookupSet(table,idx[j])) nidx[isz++] = idx[j];
2749     }
2750     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
2751     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
2752 
2753     k = 0;
2754     for (j=0; j<ov; j++) { /* for each overlap */
2755       n = isz;
2756       for (; k<n; k++) { /* do only those rows in nidx[k], which are not done yet */
2757         row   = nidx[k];
2758         start = ai[row];
2759         end   = ai[row+1];
2760         for (l = start; l<end; l++) {
2761           val = aj[l];
2762           if (!PetscBTLookupSet(table,val)) nidx[isz++] = val;
2763         }
2764       }
2765     }
2766     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz,nidx,PETSC_COPY_VALUES,(is+i));CHKERRQ(ierr);
2767   }
2768   ierr = PetscBTDestroy(&table);CHKERRQ(ierr);
2769   ierr = PetscFree(nidx);CHKERRQ(ierr);
2770   PetscFunctionReturn(0);
2771 }
2772 
2773 /* -------------------------------------------------------------- */
2774 PetscErrorCode MatPermute_SeqAIJ(Mat A,IS rowp,IS colp,Mat *B)
2775 {
2776   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2777   PetscErrorCode ierr;
2778   PetscInt       i,nz = 0,m = A->rmap->n,n = A->cmap->n;
2779   const PetscInt *row,*col;
2780   PetscInt       *cnew,j,*lens;
2781   IS             icolp,irowp;
2782   PetscInt       *cwork = NULL;
2783   PetscScalar    *vwork = NULL;
2784 
2785   PetscFunctionBegin;
2786   ierr = ISInvertPermutation(rowp,PETSC_DECIDE,&irowp);CHKERRQ(ierr);
2787   ierr = ISGetIndices(irowp,&row);CHKERRQ(ierr);
2788   ierr = ISInvertPermutation(colp,PETSC_DECIDE,&icolp);CHKERRQ(ierr);
2789   ierr = ISGetIndices(icolp,&col);CHKERRQ(ierr);
2790 
2791   /* determine lengths of permuted rows */
2792   ierr = PetscMalloc1(m+1,&lens);CHKERRQ(ierr);
2793   for (i=0; i<m; i++) lens[row[i]] = a->i[i+1] - a->i[i];
2794   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
2795   ierr = MatSetSizes(*B,m,n,m,n);CHKERRQ(ierr);
2796   ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
2797   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2798   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*B,0,lens);CHKERRQ(ierr);
2799   ierr = PetscFree(lens);CHKERRQ(ierr);
2800 
2801   ierr = PetscMalloc1(n,&cnew);CHKERRQ(ierr);
2802   for (i=0; i<m; i++) {
2803     ierr = MatGetRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2804     for (j=0; j<nz; j++) cnew[j] = col[cwork[j]];
2805     ierr = MatSetValues_SeqAIJ(*B,1,&row[i],nz,cnew,vwork,INSERT_VALUES);CHKERRQ(ierr);
2806     ierr = MatRestoreRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2807   }
2808   ierr = PetscFree(cnew);CHKERRQ(ierr);
2809 
2810   (*B)->assembled = PETSC_FALSE;
2811 
2812   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2813   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2814   ierr = ISRestoreIndices(irowp,&row);CHKERRQ(ierr);
2815   ierr = ISRestoreIndices(icolp,&col);CHKERRQ(ierr);
2816   ierr = ISDestroy(&irowp);CHKERRQ(ierr);
2817   ierr = ISDestroy(&icolp);CHKERRQ(ierr);
2818   PetscFunctionReturn(0);
2819 }
2820 
2821 PetscErrorCode MatCopy_SeqAIJ(Mat A,Mat B,MatStructure str)
2822 {
2823   PetscErrorCode ierr;
2824 
2825   PetscFunctionBegin;
2826   /* If the two matrices have the same copy implementation, use fast copy. */
2827   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
2828     Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2829     Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data;
2830 
2831     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");
2832     ierr = PetscMemcpy(b->a,a->a,(a->i[A->rmap->n])*sizeof(PetscScalar));CHKERRQ(ierr);
2833     ierr = PetscObjectStateIncrease((PetscObject)B);CHKERRQ(ierr);
2834   } else {
2835     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2836   }
2837   PetscFunctionReturn(0);
2838 }
2839 
2840 PetscErrorCode MatSetUp_SeqAIJ(Mat A)
2841 {
2842   PetscErrorCode ierr;
2843 
2844   PetscFunctionBegin;
2845   ierr =  MatSeqAIJSetPreallocation_SeqAIJ(A,PETSC_DEFAULT,0);CHKERRQ(ierr);
2846   PetscFunctionReturn(0);
2847 }
2848 
2849 PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A,PetscScalar *array[])
2850 {
2851   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2852 
2853   PetscFunctionBegin;
2854   *array = a->a;
2855   PetscFunctionReturn(0);
2856 }
2857 
2858 PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A,PetscScalar *array[])
2859 {
2860   PetscFunctionBegin;
2861   PetscFunctionReturn(0);
2862 }
2863 
2864 /*
2865    Computes the number of nonzeros per row needed for preallocation when X and Y
2866    have different nonzero structure.
2867 */
2868 PetscErrorCode MatAXPYGetPreallocation_SeqX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *yi,const PetscInt *yj,PetscInt *nnz)
2869 {
2870   PetscInt       i,j,k,nzx,nzy;
2871 
2872   PetscFunctionBegin;
2873   /* Set the number of nonzeros in the new matrix */
2874   for (i=0; i<m; i++) {
2875     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2876     nzx = xi[i+1] - xi[i];
2877     nzy = yi[i+1] - yi[i];
2878     nnz[i] = 0;
2879     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2880       for (; k<nzy && yjj[k]<xjj[j]; k++) nnz[i]++; /* Catch up to X */
2881       if (k<nzy && yjj[k]==xjj[j]) k++;             /* Skip duplicate */
2882       nnz[i]++;
2883     }
2884     for (; k<nzy; k++) nnz[i]++;
2885   }
2886   PetscFunctionReturn(0);
2887 }
2888 
2889 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
2890 {
2891   PetscInt       m = Y->rmap->N;
2892   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2893   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2894   PetscErrorCode ierr;
2895 
2896   PetscFunctionBegin;
2897   /* Set the number of nonzeros in the new matrix */
2898   ierr = MatAXPYGetPreallocation_SeqX_private(m,x->i,x->j,y->i,y->j,nnz);CHKERRQ(ierr);
2899   PetscFunctionReturn(0);
2900 }
2901 
2902 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2903 {
2904   PetscErrorCode ierr;
2905   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
2906   PetscBLASInt   one=1,bnz;
2907 
2908   PetscFunctionBegin;
2909   ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2910   if (str == SAME_NONZERO_PATTERN) {
2911     PetscScalar alpha = a;
2912     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2913     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
2914     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2915   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2916     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2917   } else {
2918     Mat      B;
2919     PetscInt *nnz;
2920     ierr = PetscMalloc1(Y->rmap->N,&nnz);CHKERRQ(ierr);
2921     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2922     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2923     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2924     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2925     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
2926     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
2927     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
2928     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2929     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2930     ierr = PetscFree(nnz);CHKERRQ(ierr);
2931   }
2932   PetscFunctionReturn(0);
2933 }
2934 
2935 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
2936 {
2937 #if defined(PETSC_USE_COMPLEX)
2938   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
2939   PetscInt    i,nz;
2940   PetscScalar *a;
2941 
2942   PetscFunctionBegin;
2943   nz = aij->nz;
2944   a  = aij->a;
2945   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
2946 #else
2947   PetscFunctionBegin;
2948 #endif
2949   PetscFunctionReturn(0);
2950 }
2951 
2952 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2953 {
2954   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2955   PetscErrorCode ierr;
2956   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2957   PetscReal      atmp;
2958   PetscScalar    *x;
2959   MatScalar      *aa;
2960 
2961   PetscFunctionBegin;
2962   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2963   aa = a->a;
2964   ai = a->i;
2965   aj = a->j;
2966 
2967   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2968   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2969   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2970   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2971   for (i=0; i<m; i++) {
2972     ncols = ai[1] - ai[0]; ai++;
2973     x[i]  = 0.0;
2974     for (j=0; j<ncols; j++) {
2975       atmp = PetscAbsScalar(*aa);
2976       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
2977       aa++; aj++;
2978     }
2979   }
2980   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2981   PetscFunctionReturn(0);
2982 }
2983 
2984 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2985 {
2986   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2987   PetscErrorCode ierr;
2988   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2989   PetscScalar    *x;
2990   MatScalar      *aa;
2991 
2992   PetscFunctionBegin;
2993   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2994   aa = a->a;
2995   ai = a->i;
2996   aj = a->j;
2997 
2998   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2999   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3000   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3001   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3002   for (i=0; i<m; i++) {
3003     ncols = ai[1] - ai[0]; ai++;
3004     if (ncols == A->cmap->n) { /* row is dense */
3005       x[i] = *aa; if (idx) idx[i] = 0;
3006     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
3007       x[i] = 0.0;
3008       if (idx) {
3009         idx[i] = 0; /* in case ncols is zero */
3010         for (j=0;j<ncols;j++) { /* find first implicit 0.0 in the row */
3011           if (aj[j] > j) {
3012             idx[i] = j;
3013             break;
3014           }
3015         }
3016       }
3017     }
3018     for (j=0; j<ncols; j++) {
3019       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3020       aa++; aj++;
3021     }
3022   }
3023   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3024   PetscFunctionReturn(0);
3025 }
3026 
3027 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3028 {
3029   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3030   PetscErrorCode ierr;
3031   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3032   PetscReal      atmp;
3033   PetscScalar    *x;
3034   MatScalar      *aa;
3035 
3036   PetscFunctionBegin;
3037   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3038   aa = a->a;
3039   ai = a->i;
3040   aj = a->j;
3041 
3042   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3043   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3044   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3045   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);
3046   for (i=0; i<m; i++) {
3047     ncols = ai[1] - ai[0]; ai++;
3048     if (ncols) {
3049       /* Get first nonzero */
3050       for (j = 0; j < ncols; j++) {
3051         atmp = PetscAbsScalar(aa[j]);
3052         if (atmp > 1.0e-12) {
3053           x[i] = atmp;
3054           if (idx) idx[i] = aj[j];
3055           break;
3056         }
3057       }
3058       if (j == ncols) {x[i] = PetscAbsScalar(*aa); if (idx) idx[i] = *aj;}
3059     } else {
3060       x[i] = 0.0; if (idx) idx[i] = 0;
3061     }
3062     for (j = 0; j < ncols; j++) {
3063       atmp = PetscAbsScalar(*aa);
3064       if (atmp > 1.0e-12 && PetscAbsScalar(x[i]) > atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3065       aa++; aj++;
3066     }
3067   }
3068   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3069   PetscFunctionReturn(0);
3070 }
3071 
3072 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3073 {
3074   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
3075   PetscErrorCode  ierr;
3076   PetscInt        i,j,m = A->rmap->n,ncols,n;
3077   const PetscInt  *ai,*aj;
3078   PetscScalar     *x;
3079   const MatScalar *aa;
3080 
3081   PetscFunctionBegin;
3082   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3083   aa = a->a;
3084   ai = a->i;
3085   aj = a->j;
3086 
3087   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3088   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3089   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3090   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3091   for (i=0; i<m; i++) {
3092     ncols = ai[1] - ai[0]; ai++;
3093     if (ncols == A->cmap->n) { /* row is dense */
3094       x[i] = *aa; if (idx) idx[i] = 0;
3095     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3096       x[i] = 0.0;
3097       if (idx) {   /* find first implicit 0.0 in the row */
3098         idx[i] = 0; /* in case ncols is zero */
3099         for (j=0; j<ncols; j++) {
3100           if (aj[j] > j) {
3101             idx[i] = j;
3102             break;
3103           }
3104         }
3105       }
3106     }
3107     for (j=0; j<ncols; j++) {
3108       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3109       aa++; aj++;
3110     }
3111   }
3112   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3113   PetscFunctionReturn(0);
3114 }
3115 
3116 PetscErrorCode MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3117 {
3118   Mat_SeqAIJ      *a = (Mat_SeqAIJ*) A->data;
3119   PetscErrorCode  ierr;
3120   PetscInt        i,bs = PetscAbs(A->rmap->bs),mbs = A->rmap->n/bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3121   MatScalar       *diag,work[25],*v_work;
3122   const PetscReal shift = 0.0;
3123   PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;
3124 
3125   PetscFunctionBegin;
3126   allowzeropivot = PetscNot(A->erroriffailure);
3127   if (a->ibdiagvalid) {
3128     if (values) *values = a->ibdiag;
3129     PetscFunctionReturn(0);
3130   }
3131   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3132   if (!a->ibdiag) {
3133     ierr = PetscMalloc1(bs2*mbs,&a->ibdiag);CHKERRQ(ierr);
3134     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3135   }
3136   diag = a->ibdiag;
3137   if (values) *values = a->ibdiag;
3138   /* factor and invert each block */
3139   switch (bs) {
3140   case 1:
3141     for (i=0; i<mbs; i++) {
3142       ierr = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3143       if (PetscAbsScalar(diag[i] + shift) < PETSC_MACHINE_EPSILON) {
3144         if (allowzeropivot) {
3145           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3146           A->factorerror_zeropivot_value = PetscAbsScalar(diag[i]);
3147           A->factorerror_zeropivot_row   = i;
3148           ierr = PetscInfo3(A,"Zero pivot, row %D pivot %g tolerance %g\n",i,(double)PetscAbsScalar(diag[i]),(double)PETSC_MACHINE_EPSILON);CHKERRQ(ierr);
3149         } 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);
3150       }
3151       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3152     }
3153     break;
3154   case 2:
3155     for (i=0; i<mbs; i++) {
3156       ij[0] = 2*i; ij[1] = 2*i + 1;
3157       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3158       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3159       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3160       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
3161       diag += 4;
3162     }
3163     break;
3164   case 3:
3165     for (i=0; i<mbs; i++) {
3166       ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
3167       ierr  = MatGetValues(A,3,ij,3,ij,diag);CHKERRQ(ierr);
3168       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3169       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3170       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3171       diag += 9;
3172     }
3173     break;
3174   case 4:
3175     for (i=0; i<mbs; i++) {
3176       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3177       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3178       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3179       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3180       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3181       diag += 16;
3182     }
3183     break;
3184   case 5:
3185     for (i=0; i<mbs; i++) {
3186       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3187       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3188       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3189       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3190       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3191       diag += 25;
3192     }
3193     break;
3194   case 6:
3195     for (i=0; i<mbs; i++) {
3196       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;
3197       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3198       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3199       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3200       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3201       diag += 36;
3202     }
3203     break;
3204   case 7:
3205     for (i=0; i<mbs; i++) {
3206       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;
3207       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3208       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3209       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3210       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3211       diag += 49;
3212     }
3213     break;
3214   default:
3215     ierr = PetscMalloc3(bs,&v_work,bs,&v_pivots,bs,&IJ);CHKERRQ(ierr);
3216     for (i=0; i<mbs; i++) {
3217       for (j=0; j<bs; j++) {
3218         IJ[j] = bs*i + j;
3219       }
3220       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3221       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3222       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3223       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3224       diag += bs2;
3225     }
3226     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3227   }
3228   a->ibdiagvalid = PETSC_TRUE;
3229   PetscFunctionReturn(0);
3230 }
3231 
3232 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3233 {
3234   PetscErrorCode ierr;
3235   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3236   PetscScalar    a;
3237   PetscInt       m,n,i,j,col;
3238 
3239   PetscFunctionBegin;
3240   if (!x->assembled) {
3241     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3242     for (i=0; i<m; i++) {
3243       for (j=0; j<aij->imax[i]; j++) {
3244         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3245         col  = (PetscInt)(n*PetscRealPart(a));
3246         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3247       }
3248     }
3249   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet coded");
3250   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3251   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3252   PetscFunctionReturn(0);
3253 }
3254 
3255 /* -------------------------------------------------------------------*/
3256 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3257                                         MatGetRow_SeqAIJ,
3258                                         MatRestoreRow_SeqAIJ,
3259                                         MatMult_SeqAIJ,
3260                                 /*  4*/ MatMultAdd_SeqAIJ,
3261                                         MatMultTranspose_SeqAIJ,
3262                                         MatMultTransposeAdd_SeqAIJ,
3263                                         0,
3264                                         0,
3265                                         0,
3266                                 /* 10*/ 0,
3267                                         MatLUFactor_SeqAIJ,
3268                                         0,
3269                                         MatSOR_SeqAIJ,
3270                                         MatTranspose_SeqAIJ_FAST,
3271                                 /*1 5*/ MatGetInfo_SeqAIJ,
3272                                         MatEqual_SeqAIJ,
3273                                         MatGetDiagonal_SeqAIJ,
3274                                         MatDiagonalScale_SeqAIJ,
3275                                         MatNorm_SeqAIJ,
3276                                 /* 20*/ 0,
3277                                         MatAssemblyEnd_SeqAIJ,
3278                                         MatSetOption_SeqAIJ,
3279                                         MatZeroEntries_SeqAIJ,
3280                                 /* 24*/ MatZeroRows_SeqAIJ,
3281                                         0,
3282                                         0,
3283                                         0,
3284                                         0,
3285                                 /* 29*/ MatSetUp_SeqAIJ,
3286                                         0,
3287                                         0,
3288                                         0,
3289                                         0,
3290                                 /* 34*/ MatDuplicate_SeqAIJ,
3291                                         0,
3292                                         0,
3293                                         MatILUFactor_SeqAIJ,
3294                                         0,
3295                                 /* 39*/ MatAXPY_SeqAIJ,
3296                                         MatCreateSubMatrices_SeqAIJ,
3297                                         MatIncreaseOverlap_SeqAIJ,
3298                                         MatGetValues_SeqAIJ,
3299                                         MatCopy_SeqAIJ,
3300                                 /* 44*/ MatGetRowMax_SeqAIJ,
3301                                         MatScale_SeqAIJ,
3302                                         MatShift_SeqAIJ,
3303                                         MatDiagonalSet_SeqAIJ,
3304                                         MatZeroRowsColumns_SeqAIJ,
3305                                 /* 49*/ MatSetRandom_SeqAIJ,
3306                                         MatGetRowIJ_SeqAIJ,
3307                                         MatRestoreRowIJ_SeqAIJ,
3308                                         MatGetColumnIJ_SeqAIJ,
3309                                         MatRestoreColumnIJ_SeqAIJ,
3310                                 /* 54*/ MatFDColoringCreate_SeqXAIJ,
3311                                         0,
3312                                         0,
3313                                         MatPermute_SeqAIJ,
3314                                         0,
3315                                 /* 59*/ 0,
3316                                         MatDestroy_SeqAIJ,
3317                                         MatView_SeqAIJ,
3318                                         0,
3319                                         MatMatMatMult_SeqAIJ_SeqAIJ_SeqAIJ,
3320                                 /* 64*/ MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ,
3321                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3322                                         0,
3323                                         0,
3324                                         0,
3325                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3326                                         MatGetRowMinAbs_SeqAIJ,
3327                                         0,
3328                                         0,
3329                                         0,
3330                                 /* 74*/ 0,
3331                                         MatFDColoringApply_AIJ,
3332                                         0,
3333                                         0,
3334                                         0,
3335                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3336                                         0,
3337                                         0,
3338                                         0,
3339                                         MatLoad_SeqAIJ,
3340                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3341                                         MatIsHermitian_SeqAIJ,
3342                                         0,
3343                                         0,
3344                                         0,
3345                                 /* 89*/ MatMatMult_SeqAIJ_SeqAIJ,
3346                                         MatMatMultSymbolic_SeqAIJ_SeqAIJ,
3347                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3348                                         MatPtAP_SeqAIJ_SeqAIJ,
3349                                         MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy,
3350                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy,
3351                                         MatMatTransposeMult_SeqAIJ_SeqAIJ,
3352                                         MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ,
3353                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3354                                         0,
3355                                 /* 99*/ 0,
3356                                         0,
3357                                         0,
3358                                         MatConjugate_SeqAIJ,
3359                                         0,
3360                                 /*104*/ MatSetValuesRow_SeqAIJ,
3361                                         MatRealPart_SeqAIJ,
3362                                         MatImaginaryPart_SeqAIJ,
3363                                         0,
3364                                         0,
3365                                 /*109*/ MatMatSolve_SeqAIJ,
3366                                         0,
3367                                         MatGetRowMin_SeqAIJ,
3368                                         0,
3369                                         MatMissingDiagonal_SeqAIJ,
3370                                 /*114*/ 0,
3371                                         0,
3372                                         0,
3373                                         0,
3374                                         0,
3375                                 /*119*/ 0,
3376                                         0,
3377                                         0,
3378                                         0,
3379                                         MatGetMultiProcBlock_SeqAIJ,
3380                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3381                                         MatGetColumnNorms_SeqAIJ,
3382                                         MatInvertBlockDiagonal_SeqAIJ,
3383                                         MatInvertVariableBlockDiagonal_SeqAIJ,
3384                                         0,
3385                                 /*129*/ 0,
3386                                         MatTransposeMatMult_SeqAIJ_SeqAIJ,
3387                                         MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ,
3388                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3389                                         MatTransposeColoringCreate_SeqAIJ,
3390                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3391                                         MatTransColoringApplyDenToSp_SeqAIJ,
3392                                         MatRARt_SeqAIJ_SeqAIJ,
3393                                         MatRARtSymbolic_SeqAIJ_SeqAIJ,
3394                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3395                                  /*139*/0,
3396                                         0,
3397                                         0,
3398                                         MatFDColoringSetUp_SeqXAIJ,
3399                                         MatFindOffBlockDiagonalEntries_SeqAIJ,
3400                                  /*144*/MatCreateMPIMatConcatenateSeqMat_SeqAIJ,
3401                                         MatDestroySubMatrices_SeqAIJ
3402 };
3403 
3404 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3405 {
3406   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3407   PetscInt   i,nz,n;
3408 
3409   PetscFunctionBegin;
3410   nz = aij->maxnz;
3411   n  = mat->rmap->n;
3412   for (i=0; i<nz; i++) {
3413     aij->j[i] = indices[i];
3414   }
3415   aij->nz = nz;
3416   for (i=0; i<n; i++) {
3417     aij->ilen[i] = aij->imax[i];
3418   }
3419   PetscFunctionReturn(0);
3420 }
3421 
3422 /*
3423  * When a sparse matrix has many zero columns, we should compact them out to save the space
3424  * This happens in MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable()
3425  * */
3426 PetscErrorCode  MatSeqAIJCompactOutExtraColumns_SeqAIJ(Mat mat, ISLocalToGlobalMapping *mapping)
3427 {
3428   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3429   PetscTable         gid1_lid1;
3430   PetscTablePosition tpos;
3431   PetscInt           gid,lid,i,j,ncols,ec;
3432   PetscInt           *garray;
3433   PetscErrorCode  ierr;
3434 
3435   PetscFunctionBegin;
3436   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3437   PetscValidPointer(mapping,2);
3438   /* use a table */
3439   ierr = PetscTableCreate(mat->rmap->n,mat->cmap->N+1,&gid1_lid1);CHKERRQ(ierr);
3440   ec = 0;
3441   for (i=0; i<mat->rmap->n; i++) {
3442     ncols = aij->i[i+1] - aij->i[i];
3443     for (j=0; j<ncols; j++) {
3444       PetscInt data,gid1 = aij->j[aij->i[i] + j] + 1;
3445       ierr = PetscTableFind(gid1_lid1,gid1,&data);CHKERRQ(ierr);
3446       if (!data) {
3447         /* one based table */
3448         ierr = PetscTableAdd(gid1_lid1,gid1,++ec,INSERT_VALUES);CHKERRQ(ierr);
3449       }
3450     }
3451   }
3452   /* form array of columns we need */
3453   ierr = PetscMalloc1(ec+1,&garray);CHKERRQ(ierr);
3454   ierr = PetscTableGetHeadPosition(gid1_lid1,&tpos);CHKERRQ(ierr);
3455   while (tpos) {
3456     ierr = PetscTableGetNext(gid1_lid1,&tpos,&gid,&lid);CHKERRQ(ierr);
3457     gid--;
3458     lid--;
3459     garray[lid] = gid;
3460   }
3461   ierr = PetscSortInt(ec,garray);CHKERRQ(ierr); /* sort, and rebuild */
3462   ierr = PetscTableRemoveAll(gid1_lid1);CHKERRQ(ierr);
3463   for (i=0; i<ec; i++) {
3464     ierr = PetscTableAdd(gid1_lid1,garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
3465   }
3466   /* compact out the extra columns in B */
3467   for (i=0; i<mat->rmap->n; i++) {
3468 	ncols = aij->i[i+1] - aij->i[i];
3469     for (j=0; j<ncols; j++) {
3470       PetscInt gid1 = aij->j[aij->i[i] + j] + 1;
3471       ierr = PetscTableFind(gid1_lid1,gid1,&lid);CHKERRQ(ierr);
3472       lid--;
3473       aij->j[aij->i[i] + j] = lid;
3474     }
3475   }
3476   mat->cmap->n = mat->cmap->N = ec;
3477   mat->cmap->bs = 1;
3478 
3479   ierr = PetscTableDestroy(&gid1_lid1);CHKERRQ(ierr);
3480   ierr = PetscLayoutSetUp((mat->cmap));CHKERRQ(ierr);
3481   ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,mat->cmap->bs,mat->cmap->n,garray,PETSC_OWN_POINTER,mapping);CHKERRQ(ierr);
3482   ierr = ISLocalToGlobalMappingSetType(*mapping,ISLOCALTOGLOBALMAPPINGHASH);CHKERRQ(ierr);
3483   PetscFunctionReturn(0);
3484 }
3485 
3486 /*@
3487     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3488        in the matrix.
3489 
3490   Input Parameters:
3491 +  mat - the SeqAIJ matrix
3492 -  indices - the column indices
3493 
3494   Level: advanced
3495 
3496   Notes:
3497     This can be called if you have precomputed the nonzero structure of the
3498   matrix and want to provide it to the matrix object to improve the performance
3499   of the MatSetValues() operation.
3500 
3501     You MUST have set the correct numbers of nonzeros per row in the call to
3502   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3503 
3504     MUST be called before any calls to MatSetValues();
3505 
3506     The indices should start with zero, not one.
3507 
3508 @*/
3509 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3510 {
3511   PetscErrorCode ierr;
3512 
3513   PetscFunctionBegin;
3514   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3515   PetscValidPointer(indices,2);
3516   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3517   PetscFunctionReturn(0);
3518 }
3519 
3520 /* ----------------------------------------------------------------------------------------*/
3521 
3522 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3523 {
3524   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3525   PetscErrorCode ierr;
3526   size_t         nz = aij->i[mat->rmap->n];
3527 
3528   PetscFunctionBegin;
3529   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3530 
3531   /* allocate space for values if not already there */
3532   if (!aij->saved_values) {
3533     ierr = PetscMalloc1(nz+1,&aij->saved_values);CHKERRQ(ierr);
3534     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3535   }
3536 
3537   /* copy values over */
3538   ierr = PetscMemcpy(aij->saved_values,aij->a,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3539   PetscFunctionReturn(0);
3540 }
3541 
3542 /*@
3543     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3544        example, reuse of the linear part of a Jacobian, while recomputing the
3545        nonlinear portion.
3546 
3547    Collect on Mat
3548 
3549   Input Parameters:
3550 .  mat - the matrix (currently only AIJ matrices support this option)
3551 
3552   Level: advanced
3553 
3554   Common Usage, with SNESSolve():
3555 $    Create Jacobian matrix
3556 $    Set linear terms into matrix
3557 $    Apply boundary conditions to matrix, at this time matrix must have
3558 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3559 $      boundary conditions again will not change the nonzero structure
3560 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3561 $    ierr = MatStoreValues(mat);
3562 $    Call SNESSetJacobian() with matrix
3563 $    In your Jacobian routine
3564 $      ierr = MatRetrieveValues(mat);
3565 $      Set nonlinear terms in matrix
3566 
3567   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3568 $    // build linear portion of Jacobian
3569 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3570 $    ierr = MatStoreValues(mat);
3571 $    loop over nonlinear iterations
3572 $       ierr = MatRetrieveValues(mat);
3573 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3574 $       // call MatAssemblyBegin/End() on matrix
3575 $       Solve linear system with Jacobian
3576 $    endloop
3577 
3578   Notes:
3579     Matrix must already be assemblied before calling this routine
3580     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3581     calling this routine.
3582 
3583     When this is called multiple times it overwrites the previous set of stored values
3584     and does not allocated additional space.
3585 
3586 .seealso: MatRetrieveValues()
3587 
3588 @*/
3589 PetscErrorCode  MatStoreValues(Mat mat)
3590 {
3591   PetscErrorCode ierr;
3592 
3593   PetscFunctionBegin;
3594   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3595   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3596   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3597   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3598   PetscFunctionReturn(0);
3599 }
3600 
3601 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3602 {
3603   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3604   PetscErrorCode ierr;
3605   PetscInt       nz = aij->i[mat->rmap->n];
3606 
3607   PetscFunctionBegin;
3608   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3609   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3610   /* copy values over */
3611   ierr = PetscMemcpy(aij->a,aij->saved_values,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3612   PetscFunctionReturn(0);
3613 }
3614 
3615 /*@
3616     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3617        example, reuse of the linear part of a Jacobian, while recomputing the
3618        nonlinear portion.
3619 
3620    Collect on Mat
3621 
3622   Input Parameters:
3623 .  mat - the matrix (currently only AIJ matrices support this option)
3624 
3625   Level: advanced
3626 
3627 .seealso: MatStoreValues()
3628 
3629 @*/
3630 PetscErrorCode  MatRetrieveValues(Mat mat)
3631 {
3632   PetscErrorCode ierr;
3633 
3634   PetscFunctionBegin;
3635   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3636   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3637   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3638   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3639   PetscFunctionReturn(0);
3640 }
3641 
3642 
3643 /* --------------------------------------------------------------------------------*/
3644 /*@C
3645    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3646    (the default parallel PETSc format).  For good matrix assembly performance
3647    the user should preallocate the matrix storage by setting the parameter nz
3648    (or the array nnz).  By setting these parameters accurately, performance
3649    during matrix assembly can be increased by more than a factor of 50.
3650 
3651    Collective on MPI_Comm
3652 
3653    Input Parameters:
3654 +  comm - MPI communicator, set to PETSC_COMM_SELF
3655 .  m - number of rows
3656 .  n - number of columns
3657 .  nz - number of nonzeros per row (same for all rows)
3658 -  nnz - array containing the number of nonzeros in the various rows
3659          (possibly different for each row) or NULL
3660 
3661    Output Parameter:
3662 .  A - the matrix
3663 
3664    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3665    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3666    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3667 
3668    Notes:
3669    If nnz is given then nz is ignored
3670 
3671    The AIJ format (also called the Yale sparse matrix format or
3672    compressed row storage), is fully compatible with standard Fortran 77
3673    storage.  That is, the stored row and column indices can begin at
3674    either one (as in Fortran) or zero.  See the users' manual for details.
3675 
3676    Specify the preallocated storage with either nz or nnz (not both).
3677    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3678    allocation.  For large problems you MUST preallocate memory or you
3679    will get TERRIBLE performance, see the users' manual chapter on matrices.
3680 
3681    By default, this format uses inodes (identical nodes) when possible, to
3682    improve numerical efficiency of matrix-vector products and solves. We
3683    search for consecutive rows with the same nonzero structure, thereby
3684    reusing matrix information to achieve increased efficiency.
3685 
3686    Options Database Keys:
3687 +  -mat_no_inode  - Do not use inodes
3688 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3689 
3690    Level: intermediate
3691 
3692 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3693 
3694 @*/
3695 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3696 {
3697   PetscErrorCode ierr;
3698 
3699   PetscFunctionBegin;
3700   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3701   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3702   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3703   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3704   PetscFunctionReturn(0);
3705 }
3706 
3707 /*@C
3708    MatSeqAIJSetPreallocation - For good matrix assembly performance
3709    the user should preallocate the matrix storage by setting the parameter nz
3710    (or the array nnz).  By setting these parameters accurately, performance
3711    during matrix assembly can be increased by more than a factor of 50.
3712 
3713    Collective on MPI_Comm
3714 
3715    Input Parameters:
3716 +  B - The matrix
3717 .  nz - number of nonzeros per row (same for all rows)
3718 -  nnz - array containing the number of nonzeros in the various rows
3719          (possibly different for each row) or NULL
3720 
3721    Notes:
3722      If nnz is given then nz is ignored
3723 
3724     The AIJ format (also called the Yale sparse matrix format or
3725    compressed row storage), is fully compatible with standard Fortran 77
3726    storage.  That is, the stored row and column indices can begin at
3727    either one (as in Fortran) or zero.  See the users' manual for details.
3728 
3729    Specify the preallocated storage with either nz or nnz (not both).
3730    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3731    allocation.  For large problems you MUST preallocate memory or you
3732    will get TERRIBLE performance, see the users' manual chapter on matrices.
3733 
3734    You can call MatGetInfo() to get information on how effective the preallocation was;
3735    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3736    You can also run with the option -info and look for messages with the string
3737    malloc in them to see if additional memory allocation was needed.
3738 
3739    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3740    entries or columns indices
3741 
3742    By default, this format uses inodes (identical nodes) when possible, to
3743    improve numerical efficiency of matrix-vector products and solves. We
3744    search for consecutive rows with the same nonzero structure, thereby
3745    reusing matrix information to achieve increased efficiency.
3746 
3747    Options Database Keys:
3748 +  -mat_no_inode  - Do not use inodes
3749 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3750 
3751    Level: intermediate
3752 
3753 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatGetInfo()
3754 
3755 @*/
3756 PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
3757 {
3758   PetscErrorCode ierr;
3759 
3760   PetscFunctionBegin;
3761   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3762   PetscValidType(B,1);
3763   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));CHKERRQ(ierr);
3764   PetscFunctionReturn(0);
3765 }
3766 
3767 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3768 {
3769   Mat_SeqAIJ     *b;
3770   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3771   PetscErrorCode ierr;
3772   PetscInt       i;
3773 
3774   PetscFunctionBegin;
3775   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3776   if (nz == MAT_SKIP_ALLOCATION) {
3777     skipallocation = PETSC_TRUE;
3778     nz             = 0;
3779   }
3780   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3781   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3782 
3783   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3784   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %D",nz);
3785   if (nnz) {
3786     for (i=0; i<B->rmap->n; i++) {
3787       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]);
3788       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);
3789     }
3790   }
3791 
3792   B->preallocated = PETSC_TRUE;
3793 
3794   b = (Mat_SeqAIJ*)B->data;
3795 
3796   if (!skipallocation) {
3797     if (!b->imax) {
3798       ierr = PetscMalloc2(B->rmap->n,&b->imax,B->rmap->n,&b->ilen);CHKERRQ(ierr);
3799       ierr = PetscLogObjectMemory((PetscObject)B,2*B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3800     }
3801     if (!b->ipre) {
3802       ierr = PetscMalloc1(B->rmap->n,&b->ipre);CHKERRQ(ierr);
3803       ierr = PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3804     }
3805     if (!nnz) {
3806       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3807       else if (nz < 0) nz = 1;
3808       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
3809       nz = nz*B->rmap->n;
3810     } else {
3811       nz = 0;
3812       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz += nnz[i];}
3813     }
3814     /* b->ilen will count nonzeros in each row so far. */
3815     for (i=0; i<B->rmap->n; i++) b->ilen[i] = 0;
3816 
3817     /* allocate the matrix space */
3818     /* FIXME: should B's old memory be unlogged? */
3819     ierr = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
3820     if (B->structure_only) {
3821       ierr = PetscMalloc1(nz,&b->j);CHKERRQ(ierr);
3822       ierr = PetscMalloc1(B->rmap->n+1,&b->i);CHKERRQ(ierr);
3823       ierr = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*sizeof(PetscInt));CHKERRQ(ierr);
3824     } else {
3825       ierr = PetscMalloc3(nz,&b->a,nz,&b->j,B->rmap->n+1,&b->i);CHKERRQ(ierr);
3826       ierr = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
3827     }
3828     b->i[0] = 0;
3829     for (i=1; i<B->rmap->n+1; i++) {
3830       b->i[i] = b->i[i-1] + b->imax[i-1];
3831     }
3832     if (B->structure_only) {
3833       b->singlemalloc = PETSC_FALSE;
3834       b->free_a       = PETSC_FALSE;
3835     } else {
3836       b->singlemalloc = PETSC_TRUE;
3837       b->free_a       = PETSC_TRUE;
3838     }
3839     b->free_ij      = PETSC_TRUE;
3840   } else {
3841     b->free_a  = PETSC_FALSE;
3842     b->free_ij = PETSC_FALSE;
3843   }
3844 
3845   if (b->ipre && nnz != b->ipre  && b->imax) {
3846     /* reserve user-requested sparsity */
3847     ierr = PetscMemcpy(b->ipre,b->imax,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3848   }
3849 
3850 
3851   b->nz               = 0;
3852   b->maxnz            = nz;
3853   B->info.nz_unneeded = (double)b->maxnz;
3854   if (realalloc) {
3855     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3856   }
3857   B->was_assembled = PETSC_FALSE;
3858   B->assembled     = PETSC_FALSE;
3859   PetscFunctionReturn(0);
3860 }
3861 
3862 
3863 PetscErrorCode MatResetPreallocation_SeqAIJ(Mat A)
3864 {
3865   Mat_SeqAIJ     *a;
3866   PetscInt       i;
3867   PetscErrorCode ierr;
3868 
3869   PetscFunctionBegin;
3870   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3871   a = (Mat_SeqAIJ*)A->data;
3872   /* if no saved info, we error out */
3873   if (!a->ipre) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_NULL,"No saved preallocation info \n");
3874 
3875   if (!a->i || !a->j || !a->a || !a->imax || !a->ilen) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_NULL,"Memory info is incomplete, and can not reset preallocation \n");
3876 
3877   ierr = PetscMemcpy(a->imax,a->ipre,A->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3878   ierr = PetscMemzero(a->ilen,A->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3879   a->i[0] = 0;
3880   for (i=1; i<A->rmap->n+1; i++) {
3881     a->i[i] = a->i[i-1] + a->imax[i-1];
3882   }
3883   A->preallocated     = PETSC_TRUE;
3884   a->nz               = 0;
3885   a->maxnz            = a->i[A->rmap->n];
3886   A->info.nz_unneeded = (double)a->maxnz;
3887   A->was_assembled    = PETSC_FALSE;
3888   A->assembled        = PETSC_FALSE;
3889   PetscFunctionReturn(0);
3890 }
3891 
3892 /*@
3893    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
3894 
3895    Input Parameters:
3896 +  B - the matrix
3897 .  i - the indices into j for the start of each row (starts with zero)
3898 .  j - the column indices for each row (starts with zero) these must be sorted for each row
3899 -  v - optional values in the matrix
3900 
3901    Level: developer
3902 
3903    The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
3904 
3905 .keywords: matrix, aij, compressed row, sparse, sequential
3906 
3907 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), MATSEQAIJ
3908 @*/
3909 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
3910 {
3911   PetscErrorCode ierr;
3912 
3913   PetscFunctionBegin;
3914   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3915   PetscValidType(B,1);
3916   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3917   PetscFunctionReturn(0);
3918 }
3919 
3920 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3921 {
3922   PetscInt       i;
3923   PetscInt       m,n;
3924   PetscInt       nz;
3925   PetscInt       *nnz, nz_max = 0;
3926   PetscScalar    *values;
3927   PetscErrorCode ierr;
3928 
3929   PetscFunctionBegin;
3930   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
3931 
3932   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3933   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3934 
3935   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
3936   ierr = PetscMalloc1(m+1, &nnz);CHKERRQ(ierr);
3937   for (i = 0; i < m; i++) {
3938     nz     = Ii[i+1]- Ii[i];
3939     nz_max = PetscMax(nz_max, nz);
3940     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
3941     nnz[i] = nz;
3942   }
3943   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
3944   ierr = PetscFree(nnz);CHKERRQ(ierr);
3945 
3946   if (v) {
3947     values = (PetscScalar*) v;
3948   } else {
3949     ierr = PetscCalloc1(nz_max, &values);CHKERRQ(ierr);
3950   }
3951 
3952   for (i = 0; i < m; i++) {
3953     nz   = Ii[i+1] - Ii[i];
3954     ierr = MatSetValues_SeqAIJ(B, 1, &i, nz, J+Ii[i], values + (v ? Ii[i] : 0), INSERT_VALUES);CHKERRQ(ierr);
3955   }
3956 
3957   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3958   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3959 
3960   if (!v) {
3961     ierr = PetscFree(values);CHKERRQ(ierr);
3962   }
3963   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3964   PetscFunctionReturn(0);
3965 }
3966 
3967 #include <../src/mat/impls/dense/seq/dense.h>
3968 #include <petsc/private/kernels/petscaxpy.h>
3969 
3970 /*
3971     Computes (B'*A')' since computing B*A directly is untenable
3972 
3973                n                       p                          p
3974         (              )       (              )         (                  )
3975       m (      A       )  *  n (       B      )   =   m (         C        )
3976         (              )       (              )         (                  )
3977 
3978 */
3979 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
3980 {
3981   PetscErrorCode    ierr;
3982   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
3983   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
3984   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
3985   PetscInt          i,n,m,q,p;
3986   const PetscInt    *ii,*idx;
3987   const PetscScalar *b,*a,*a_q;
3988   PetscScalar       *c,*c_q;
3989 
3990   PetscFunctionBegin;
3991   m    = A->rmap->n;
3992   n    = A->cmap->n;
3993   p    = B->cmap->n;
3994   a    = sub_a->v;
3995   b    = sub_b->a;
3996   c    = sub_c->v;
3997   ierr = PetscMemzero(c,m*p*sizeof(PetscScalar));CHKERRQ(ierr);
3998 
3999   ii  = sub_b->i;
4000   idx = sub_b->j;
4001   for (i=0; i<n; i++) {
4002     q = ii[i+1] - ii[i];
4003     while (q-->0) {
4004       c_q = c + m*(*idx);
4005       a_q = a + m*i;
4006       PetscKernelAXPY(c_q,*b,a_q,m);
4007       idx++;
4008       b++;
4009     }
4010   }
4011   PetscFunctionReturn(0);
4012 }
4013 
4014 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4015 {
4016   PetscErrorCode ierr;
4017   PetscInt       m=A->rmap->n,n=B->cmap->n;
4018   Mat            Cmat;
4019 
4020   PetscFunctionBegin;
4021   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);
4022   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4023   ierr = MatSetSizes(Cmat,m,n,m,n);CHKERRQ(ierr);
4024   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
4025   ierr = MatSetType(Cmat,MATSEQDENSE);CHKERRQ(ierr);
4026   ierr = MatSeqDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4027 
4028   Cmat->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
4029 
4030   *C = Cmat;
4031   PetscFunctionReturn(0);
4032 }
4033 
4034 /* ----------------------------------------------------------------*/
4035 PETSC_INTERN PetscErrorCode MatMatMult_SeqDense_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4036 {
4037   PetscErrorCode ierr;
4038 
4039   PetscFunctionBegin;
4040   if (scall == MAT_INITIAL_MATRIX) {
4041     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4042     ierr = MatMatMultSymbolic_SeqDense_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
4043     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4044   }
4045   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4046   ierr = MatMatMultNumeric_SeqDense_SeqAIJ(A,B,*C);CHKERRQ(ierr);
4047   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4048   PetscFunctionReturn(0);
4049 }
4050 
4051 
4052 /*MC
4053    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
4054    based on compressed sparse row format.
4055 
4056    Options Database Keys:
4057 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
4058 
4059   Level: beginner
4060 
4061 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
4062 M*/
4063 
4064 /*MC
4065    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
4066 
4067    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
4068    and MATMPIAIJ otherwise.  As a result, for single process communicators,
4069   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
4070   for communicators controlling multiple processes.  It is recommended that you call both of
4071   the above preallocation routines for simplicity.
4072 
4073    Options Database Keys:
4074 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
4075 
4076   Developer Notes:
4077     Subclasses include MATAIJCUSPARSE, MATAIJPERM, MATAIJSELL, MATAIJMKL, MATAIJCRL, and also automatically switches over to use inodes when
4078    enough exist.
4079 
4080   Level: beginner
4081 
4082 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
4083 M*/
4084 
4085 /*MC
4086    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
4087 
4088    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
4089    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
4090    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
4091   for communicators controlling multiple processes.  It is recommended that you call both of
4092   the above preallocation routines for simplicity.
4093 
4094    Options Database Keys:
4095 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
4096 
4097   Level: beginner
4098 
4099 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
4100 M*/
4101 
4102 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
4103 #if defined(PETSC_HAVE_ELEMENTAL)
4104 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4105 #endif
4106 #if defined(PETSC_HAVE_HYPRE)
4107 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat A,MatType,MatReuse,Mat*);
4108 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
4109 #endif
4110 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqDense(Mat,MatType,MatReuse,Mat*);
4111 
4112 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqSELL(Mat,MatType,MatReuse,Mat*);
4113 PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat,MatType,MatReuse,Mat*);
4114 PETSC_INTERN PetscErrorCode MatPtAP_IS_XAIJ(Mat,Mat,MatReuse,PetscReal,Mat*);
4115 
4116 /*@C
4117    MatSeqAIJGetArray - gives access to the array where the data for a MATSEQAIJ matrix is stored
4118 
4119    Not Collective
4120 
4121    Input Parameter:
4122 .  mat - a MATSEQAIJ matrix
4123 
4124    Output Parameter:
4125 .   array - pointer to the data
4126 
4127    Level: intermediate
4128 
4129 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4130 @*/
4131 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4132 {
4133   PetscErrorCode ierr;
4134 
4135   PetscFunctionBegin;
4136   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4137   PetscFunctionReturn(0);
4138 }
4139 
4140 /*@C
4141    MatSeqAIJGetMaxRowNonzeros - returns the maximum number of nonzeros in any row
4142 
4143    Not Collective
4144 
4145    Input Parameter:
4146 .  mat - a MATSEQAIJ matrix
4147 
4148    Output Parameter:
4149 .   nz - the maximum number of nonzeros in any row
4150 
4151    Level: intermediate
4152 
4153 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4154 @*/
4155 PetscErrorCode  MatSeqAIJGetMaxRowNonzeros(Mat A,PetscInt *nz)
4156 {
4157   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
4158 
4159   PetscFunctionBegin;
4160   *nz = aij->rmax;
4161   PetscFunctionReturn(0);
4162 }
4163 
4164 /*@C
4165    MatSeqAIJRestoreArray - returns access to the array where the data for a MATSEQAIJ matrix is stored obtained by MatSeqAIJGetArray()
4166 
4167    Not Collective
4168 
4169    Input Parameters:
4170 .  mat - a MATSEQAIJ matrix
4171 .  array - pointer to the data
4172 
4173    Level: intermediate
4174 
4175 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4176 @*/
4177 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4178 {
4179   PetscErrorCode ierr;
4180 
4181   PetscFunctionBegin;
4182   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4183   PetscFunctionReturn(0);
4184 }
4185 
4186 #if defined(PETSC_HAVE_CUDA)
4187 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat);
4188 #endif
4189 
4190 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4191 {
4192   Mat_SeqAIJ     *b;
4193   PetscErrorCode ierr;
4194   PetscMPIInt    size;
4195 
4196   PetscFunctionBegin;
4197   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4198   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4199 
4200   ierr = PetscNewLog(B,&b);CHKERRQ(ierr);
4201 
4202   B->data = (void*)b;
4203 
4204   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4205 
4206   b->row                = 0;
4207   b->col                = 0;
4208   b->icol               = 0;
4209   b->reallocs           = 0;
4210   b->ignorezeroentries  = PETSC_FALSE;
4211   b->roworiented        = PETSC_TRUE;
4212   b->nonew              = 0;
4213   b->diag               = 0;
4214   b->solve_work         = 0;
4215   B->spptr              = 0;
4216   b->saved_values       = 0;
4217   b->idiag              = 0;
4218   b->mdiag              = 0;
4219   b->ssor_work          = 0;
4220   b->omega              = 1.0;
4221   b->fshift             = 0.0;
4222   b->idiagvalid         = PETSC_FALSE;
4223   b->ibdiagvalid        = PETSC_FALSE;
4224   b->keepnonzeropattern = PETSC_FALSE;
4225 
4226   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4227   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4228   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4229 
4230 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4231   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4232   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4233 #endif
4234 
4235   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4236   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4237   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4238   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4239   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4240   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4241   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijsell_C",MatConvert_SeqAIJ_SeqAIJSELL);CHKERRQ(ierr);
4242 #if defined(PETSC_HAVE_MKL_SPARSE)
4243   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijmkl_C",MatConvert_SeqAIJ_SeqAIJMKL);CHKERRQ(ierr);
4244 #endif
4245 #if defined(PETSC_HAVE_CUDA)
4246   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcusparse_C",MatConvert_SeqAIJ_SeqAIJCUSPARSE);CHKERRQ(ierr);
4247 #endif
4248   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4249 #if defined(PETSC_HAVE_ELEMENTAL)
4250   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_elemental_C",MatConvert_SeqAIJ_Elemental);CHKERRQ(ierr);
4251 #endif
4252 #if defined(PETSC_HAVE_HYPRE)
4253   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
4254   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_seqaij_seqaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
4255 #endif
4256   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqdense_C",MatConvert_SeqAIJ_SeqDense);CHKERRQ(ierr);
4257   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsell_C",MatConvert_SeqAIJ_SeqSELL);CHKERRQ(ierr);
4258   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_is_C",MatConvert_XAIJ_IS);CHKERRQ(ierr);
4259   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4260   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4261   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4262   ierr = PetscObjectComposeFunction((PetscObject)B,"MatResetPreallocation_C",MatResetPreallocation_SeqAIJ);CHKERRQ(ierr);
4263   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4264   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4265   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaij_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
4266   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaij_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
4267   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaij_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
4268   ierr = PetscObjectComposeFunction((PetscObject)B,"MatPtAP_is_seqaij_C",MatPtAP_IS_XAIJ);CHKERRQ(ierr);
4269   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4270   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4271   ierr = MatSeqAIJSetTypeFromOptions(B);CHKERRQ(ierr);  /* this allows changing the matrix subtype to say MATSEQAIJPERM */
4272   PetscFunctionReturn(0);
4273 }
4274 
4275 /*
4276     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4277 */
4278 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4279 {
4280   Mat_SeqAIJ     *c,*a = (Mat_SeqAIJ*)A->data;
4281   PetscErrorCode ierr;
4282   PetscInt       i,m = A->rmap->n;
4283 
4284   PetscFunctionBegin;
4285   c = (Mat_SeqAIJ*)C->data;
4286 
4287   C->factortype = A->factortype;
4288   c->row        = 0;
4289   c->col        = 0;
4290   c->icol       = 0;
4291   c->reallocs   = 0;
4292 
4293   C->assembled = PETSC_TRUE;
4294 
4295   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4296   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4297 
4298   ierr = PetscMalloc2(m,&c->imax,m,&c->ilen);CHKERRQ(ierr);
4299   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4300   for (i=0; i<m; i++) {
4301     c->imax[i] = a->imax[i];
4302     c->ilen[i] = a->ilen[i];
4303   }
4304 
4305   /* allocate the matrix space */
4306   if (mallocmatspace) {
4307     ierr = PetscMalloc3(a->i[m],&c->a,a->i[m],&c->j,m+1,&c->i);CHKERRQ(ierr);
4308     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4309 
4310     c->singlemalloc = PETSC_TRUE;
4311 
4312     ierr = PetscMemcpy(c->i,a->i,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4313     if (m > 0) {
4314       ierr = PetscMemcpy(c->j,a->j,(a->i[m])*sizeof(PetscInt));CHKERRQ(ierr);
4315       if (cpvalues == MAT_COPY_VALUES) {
4316         ierr = PetscMemcpy(c->a,a->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4317       } else {
4318         ierr = PetscMemzero(c->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4319       }
4320     }
4321   }
4322 
4323   c->ignorezeroentries = a->ignorezeroentries;
4324   c->roworiented       = a->roworiented;
4325   c->nonew             = a->nonew;
4326   if (a->diag) {
4327     ierr = PetscMalloc1(m+1,&c->diag);CHKERRQ(ierr);
4328     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4329     for (i=0; i<m; i++) {
4330       c->diag[i] = a->diag[i];
4331     }
4332   } else c->diag = 0;
4333 
4334   c->solve_work         = 0;
4335   c->saved_values       = 0;
4336   c->idiag              = 0;
4337   c->ssor_work          = 0;
4338   c->keepnonzeropattern = a->keepnonzeropattern;
4339   c->free_a             = PETSC_TRUE;
4340   c->free_ij            = PETSC_TRUE;
4341 
4342   c->rmax         = a->rmax;
4343   c->nz           = a->nz;
4344   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4345   C->preallocated = PETSC_TRUE;
4346 
4347   c->compressedrow.use   = a->compressedrow.use;
4348   c->compressedrow.nrows = a->compressedrow.nrows;
4349   if (a->compressedrow.use) {
4350     i    = a->compressedrow.nrows;
4351     ierr = PetscMalloc2(i+1,&c->compressedrow.i,i,&c->compressedrow.rindex);CHKERRQ(ierr);
4352     ierr = PetscMemcpy(c->compressedrow.i,a->compressedrow.i,(i+1)*sizeof(PetscInt));CHKERRQ(ierr);
4353     ierr = PetscMemcpy(c->compressedrow.rindex,a->compressedrow.rindex,i*sizeof(PetscInt));CHKERRQ(ierr);
4354   } else {
4355     c->compressedrow.use    = PETSC_FALSE;
4356     c->compressedrow.i      = NULL;
4357     c->compressedrow.rindex = NULL;
4358   }
4359   c->nonzerorowcnt = a->nonzerorowcnt;
4360   C->nonzerostate  = A->nonzerostate;
4361 
4362   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4363   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4364   PetscFunctionReturn(0);
4365 }
4366 
4367 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4368 {
4369   PetscErrorCode ierr;
4370 
4371   PetscFunctionBegin;
4372   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4373   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4374   if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) {
4375     ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
4376   }
4377   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4378   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4379   PetscFunctionReturn(0);
4380 }
4381 
4382 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4383 {
4384   PetscBool      isbinary, ishdf5;
4385   PetscErrorCode ierr;
4386 
4387   PetscFunctionBegin;
4388   PetscValidHeaderSpecific(newMat,MAT_CLASSID,1);
4389   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
4390   /* force binary viewer to load .info file if it has not yet done so */
4391   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
4392   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
4393   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,  &ishdf5);CHKERRQ(ierr);
4394   if (isbinary) {
4395     ierr = MatLoad_SeqAIJ_Binary(newMat,viewer);CHKERRQ(ierr);
4396   } else if (ishdf5) {
4397 #if defined(PETSC_HAVE_HDF5)
4398     ierr = MatLoad_AIJ_HDF5(newMat,viewer);CHKERRQ(ierr);
4399 #else
4400     SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
4401 #endif
4402   } else {
4403     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);
4404   }
4405   PetscFunctionReturn(0);
4406 }
4407 
4408 PetscErrorCode MatLoad_SeqAIJ_Binary(Mat newMat, PetscViewer viewer)
4409 {
4410   Mat_SeqAIJ     *a;
4411   PetscErrorCode ierr;
4412   PetscInt       i,sum,nz,header[4],*rowlengths = 0,M,N,rows,cols;
4413   int            fd;
4414   PetscMPIInt    size;
4415   MPI_Comm       comm;
4416   PetscInt       bs = newMat->rmap->bs;
4417 
4418   PetscFunctionBegin;
4419   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
4420   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4421   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"view must have one processor");
4422 
4423   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
4424   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
4425   ierr = PetscOptionsEnd();CHKERRQ(ierr);
4426   if (bs < 0) bs = 1;
4427   ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);
4428 
4429   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
4430   ierr = PetscBinaryRead(fd,header,4,PETSC_INT);CHKERRQ(ierr);
4431   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
4432   M = header[1]; N = header[2]; nz = header[3];
4433 
4434   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
4435 
4436   /* read in row lengths */
4437   ierr = PetscMalloc1(M,&rowlengths);CHKERRQ(ierr);
4438   ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
4439 
4440   /* check if sum of rowlengths is same as nz */
4441   for (i=0,sum=0; i< M; i++) sum +=rowlengths[i];
4442   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);
4443 
4444   /* set global size if not set already*/
4445   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) {
4446     ierr = MatSetSizes(newMat,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
4447   } else {
4448     /* if sizes and type are already set, check if the matrix  global sizes are correct */
4449     ierr = MatGetSize(newMat,&rows,&cols);CHKERRQ(ierr);
4450     if (rows < 0 && cols < 0) { /* user might provide local size instead of global size */
4451       ierr = MatGetLocalSize(newMat,&rows,&cols);CHKERRQ(ierr);
4452     }
4453     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);
4454   }
4455   ierr = MatSeqAIJSetPreallocation_SeqAIJ(newMat,0,rowlengths);CHKERRQ(ierr);
4456   a    = (Mat_SeqAIJ*)newMat->data;
4457 
4458   ierr = PetscBinaryRead(fd,a->j,nz,PETSC_INT);CHKERRQ(ierr);
4459 
4460   /* read in nonzero values */
4461   ierr = PetscBinaryRead(fd,a->a,nz,PETSC_SCALAR);CHKERRQ(ierr);
4462 
4463   /* set matrix "i" values */
4464   a->i[0] = 0;
4465   for (i=1; i<= M; i++) {
4466     a->i[i]      = a->i[i-1] + rowlengths[i-1];
4467     a->ilen[i-1] = rowlengths[i-1];
4468   }
4469   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
4470 
4471   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4472   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4473   PetscFunctionReturn(0);
4474 }
4475 
4476 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4477 {
4478   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4479   PetscErrorCode ierr;
4480 #if defined(PETSC_USE_COMPLEX)
4481   PetscInt k;
4482 #endif
4483 
4484   PetscFunctionBegin;
4485   /* If the  matrix dimensions are not equal,or no of nonzeros */
4486   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4487     *flg = PETSC_FALSE;
4488     PetscFunctionReturn(0);
4489   }
4490 
4491   /* if the a->i are the same */
4492   ierr = PetscMemcmp(a->i,b->i,(A->rmap->n+1)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4493   if (!*flg) PetscFunctionReturn(0);
4494 
4495   /* if a->j are the same */
4496   ierr = PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4497   if (!*flg) PetscFunctionReturn(0);
4498 
4499   /* if a->a are the same */
4500 #if defined(PETSC_USE_COMPLEX)
4501   for (k=0; k<a->nz; k++) {
4502     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4503       *flg = PETSC_FALSE;
4504       PetscFunctionReturn(0);
4505     }
4506   }
4507 #else
4508   ierr = PetscMemcmp(a->a,b->a,(a->nz)*sizeof(PetscScalar),flg);CHKERRQ(ierr);
4509 #endif
4510   PetscFunctionReturn(0);
4511 }
4512 
4513 /*@
4514      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4515               provided by the user.
4516 
4517       Collective on MPI_Comm
4518 
4519    Input Parameters:
4520 +   comm - must be an MPI communicator of size 1
4521 .   m - number of rows
4522 .   n - number of columns
4523 .   i - row indices; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
4524 .   j - column indices
4525 -   a - matrix values
4526 
4527    Output Parameter:
4528 .   mat - the matrix
4529 
4530    Level: intermediate
4531 
4532    Notes:
4533        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4534     once the matrix is destroyed and not before
4535 
4536        You cannot set new nonzero locations into this matrix, that will generate an error.
4537 
4538        The i and j indices are 0 based
4539 
4540        The format which is used for the sparse matrix input, is equivalent to a
4541     row-major ordering.. i.e for the following matrix, the input data expected is
4542     as shown
4543 
4544 $        1 0 0
4545 $        2 0 3
4546 $        4 5 6
4547 $
4548 $        i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4549 $        j =  {0,0,2,0,1,2}  [size = 6]; values must be sorted for each row
4550 $        v =  {1,2,3,4,5,6}  [size = 6]
4551 
4552 
4553 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4554 
4555 @*/
4556 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat)
4557 {
4558   PetscErrorCode ierr;
4559   PetscInt       ii;
4560   Mat_SeqAIJ     *aij;
4561 #if defined(PETSC_USE_DEBUG)
4562   PetscInt jj;
4563 #endif
4564 
4565   PetscFunctionBegin;
4566   if (m > 0 && i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4567   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4568   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4569   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4570   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4571   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,0);CHKERRQ(ierr);
4572   aij  = (Mat_SeqAIJ*)(*mat)->data;
4573   ierr = PetscMalloc2(m,&aij->imax,m,&aij->ilen);CHKERRQ(ierr);
4574 
4575   aij->i            = i;
4576   aij->j            = j;
4577   aij->a            = a;
4578   aij->singlemalloc = PETSC_FALSE;
4579   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4580   aij->free_a       = PETSC_FALSE;
4581   aij->free_ij      = PETSC_FALSE;
4582 
4583   for (ii=0; ii<m; ii++) {
4584     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4585 #if defined(PETSC_USE_DEBUG)
4586     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]);
4587     for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4588       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);
4589       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);
4590     }
4591 #endif
4592   }
4593 #if defined(PETSC_USE_DEBUG)
4594   for (ii=0; ii<aij->i[m]; ii++) {
4595     if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %D index = %D",ii,j[ii]);
4596     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]);
4597   }
4598 #endif
4599 
4600   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4601   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4602   PetscFunctionReturn(0);
4603 }
4604 /*@C
4605      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4606               provided by the user.
4607 
4608       Collective on MPI_Comm
4609 
4610    Input Parameters:
4611 +   comm - must be an MPI communicator of size 1
4612 .   m   - number of rows
4613 .   n   - number of columns
4614 .   i   - row indices
4615 .   j   - column indices
4616 .   a   - matrix values
4617 .   nz  - number of nonzeros
4618 -   idx - 0 or 1 based
4619 
4620    Output Parameter:
4621 .   mat - the matrix
4622 
4623    Level: intermediate
4624 
4625    Notes:
4626        The i and j indices are 0 based
4627 
4628        The format which is used for the sparse matrix input, is equivalent to a
4629     row-major ordering.. i.e for the following matrix, the input data expected is
4630     as shown:
4631 
4632         1 0 0
4633         2 0 3
4634         4 5 6
4635 
4636         i =  {0,1,1,2,2,2}
4637         j =  {0,0,2,0,1,2}
4638         v =  {1,2,3,4,5,6}
4639 
4640 
4641 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4642 
4643 @*/
4644 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat,PetscInt nz,PetscBool idx)
4645 {
4646   PetscErrorCode ierr;
4647   PetscInt       ii, *nnz, one = 1,row,col;
4648 
4649 
4650   PetscFunctionBegin;
4651   ierr = PetscCalloc1(m,&nnz);CHKERRQ(ierr);
4652   for (ii = 0; ii < nz; ii++) {
4653     nnz[i[ii] - !!idx] += 1;
4654   }
4655   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4656   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4657   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4658   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4659   for (ii = 0; ii < nz; ii++) {
4660     if (idx) {
4661       row = i[ii] - 1;
4662       col = j[ii] - 1;
4663     } else {
4664       row = i[ii];
4665       col = j[ii];
4666     }
4667     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4668   }
4669   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4670   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4671   ierr = PetscFree(nnz);CHKERRQ(ierr);
4672   PetscFunctionReturn(0);
4673 }
4674 
4675 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4676 {
4677   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4678   PetscErrorCode ierr;
4679 
4680   PetscFunctionBegin;
4681   a->idiagvalid  = PETSC_FALSE;
4682   a->ibdiagvalid = PETSC_FALSE;
4683 
4684   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4685   PetscFunctionReturn(0);
4686 }
4687 
4688 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4689 {
4690   PetscErrorCode ierr;
4691   PetscMPIInt    size;
4692 
4693   PetscFunctionBegin;
4694   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4695   if (size == 1) {
4696     if (scall == MAT_INITIAL_MATRIX) {
4697       ierr = MatDuplicate(inmat,MAT_COPY_VALUES,outmat);CHKERRQ(ierr);
4698     } else {
4699       ierr = MatCopy(inmat,*outmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4700     }
4701   } else {
4702     ierr = MatCreateMPIMatConcatenateSeqMat_MPIAIJ(comm,inmat,n,scall,outmat);CHKERRQ(ierr);
4703   }
4704   PetscFunctionReturn(0);
4705 }
4706 
4707 /*
4708  Permute A into C's *local* index space using rowemb,colemb.
4709  The embedding are supposed to be injections and the above implies that the range of rowemb is a subset
4710  of [0,m), colemb is in [0,n).
4711  If pattern == DIFFERENT_NONZERO_PATTERN, C is preallocated according to A.
4712  */
4713 PetscErrorCode MatSetSeqMat_SeqAIJ(Mat C,IS rowemb,IS colemb,MatStructure pattern,Mat B)
4714 {
4715   /* If making this function public, change the error returned in this function away from _PLIB. */
4716   PetscErrorCode ierr;
4717   Mat_SeqAIJ     *Baij;
4718   PetscBool      seqaij;
4719   PetscInt       m,n,*nz,i,j,count;
4720   PetscScalar    v;
4721   const PetscInt *rowindices,*colindices;
4722 
4723   PetscFunctionBegin;
4724   if (!B) PetscFunctionReturn(0);
4725   /* Check to make sure the target matrix (and embeddings) are compatible with C and each other. */
4726   ierr = PetscObjectBaseTypeCompare((PetscObject)B,MATSEQAIJ,&seqaij);CHKERRQ(ierr);
4727   if (!seqaij) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is of wrong type");
4728   if (rowemb) {
4729     ierr = ISGetLocalSize(rowemb,&m);CHKERRQ(ierr);
4730     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);
4731   } else {
4732     if (C->rmap->n != B->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is row-incompatible with the target matrix");
4733   }
4734   if (colemb) {
4735     ierr = ISGetLocalSize(colemb,&n);CHKERRQ(ierr);
4736     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);
4737   } else {
4738     if (C->cmap->n != B->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is col-incompatible with the target matrix");
4739   }
4740 
4741   Baij = (Mat_SeqAIJ*)(B->data);
4742   if (pattern == DIFFERENT_NONZERO_PATTERN) {
4743     ierr = PetscMalloc1(B->rmap->n,&nz);CHKERRQ(ierr);
4744     for (i=0; i<B->rmap->n; i++) {
4745       nz[i] = Baij->i[i+1] - Baij->i[i];
4746     }
4747     ierr = MatSeqAIJSetPreallocation(C,0,nz);CHKERRQ(ierr);
4748     ierr = PetscFree(nz);CHKERRQ(ierr);
4749   }
4750   if (pattern == SUBSET_NONZERO_PATTERN) {
4751     ierr = MatZeroEntries(C);CHKERRQ(ierr);
4752   }
4753   count = 0;
4754   rowindices = NULL;
4755   colindices = NULL;
4756   if (rowemb) {
4757     ierr = ISGetIndices(rowemb,&rowindices);CHKERRQ(ierr);
4758   }
4759   if (colemb) {
4760     ierr = ISGetIndices(colemb,&colindices);CHKERRQ(ierr);
4761   }
4762   for (i=0; i<B->rmap->n; i++) {
4763     PetscInt row;
4764     row = i;
4765     if (rowindices) row = rowindices[i];
4766     for (j=Baij->i[i]; j<Baij->i[i+1]; j++) {
4767       PetscInt col;
4768       col  = Baij->j[count];
4769       if (colindices) col = colindices[col];
4770       v    = Baij->a[count];
4771       ierr = MatSetValues(C,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
4772       ++count;
4773     }
4774   }
4775   /* FIXME: set C's nonzerostate correctly. */
4776   /* Assembly for C is necessary. */
4777   C->preallocated = PETSC_TRUE;
4778   C->assembled     = PETSC_TRUE;
4779   C->was_assembled = PETSC_FALSE;
4780   PetscFunctionReturn(0);
4781 }
4782 
4783 PetscFunctionList MatSeqAIJList = NULL;
4784 
4785 /*@C
4786    MatSeqAIJSetType - Converts a MATSEQAIJ matrix to a subtype
4787 
4788    Collective on Mat
4789 
4790    Input Parameters:
4791 +  mat      - the matrix object
4792 -  matype   - matrix type
4793 
4794    Options Database Key:
4795 .  -mat_seqai_type  <method> - for example seqaijcrl
4796 
4797 
4798   Level: intermediate
4799 
4800 .keywords: Mat, MatType, set, method
4801 
4802 .seealso: PCSetType(), VecSetType(), MatCreate(), MatType, Mat
4803 @*/
4804 PetscErrorCode  MatSeqAIJSetType(Mat mat, MatType matype)
4805 {
4806   PetscErrorCode ierr,(*r)(Mat,MatType,MatReuse,Mat*);
4807   PetscBool      sametype;
4808 
4809   PetscFunctionBegin;
4810   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
4811   ierr = PetscObjectTypeCompare((PetscObject)mat,matype,&sametype);CHKERRQ(ierr);
4812   if (sametype) PetscFunctionReturn(0);
4813 
4814   ierr =  PetscFunctionListFind(MatSeqAIJList,matype,&r);CHKERRQ(ierr);
4815   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown Mat type given: %s",matype);
4816   ierr = (*r)(mat,matype,MAT_INPLACE_MATRIX,&mat);CHKERRQ(ierr);
4817   PetscFunctionReturn(0);
4818 }
4819 
4820 
4821 /*@C
4822   MatSeqAIJRegister -  - Adds a new sub-matrix type for sequential AIJ matrices
4823 
4824    Not Collective
4825 
4826    Input Parameters:
4827 +  name - name of a new user-defined matrix type, for example MATSEQAIJCRL
4828 -  function - routine to convert to subtype
4829 
4830    Notes:
4831    MatSeqAIJRegister() may be called multiple times to add several user-defined solvers.
4832 
4833 
4834    Then, your matrix can be chosen with the procedural interface at runtime via the option
4835 $     -mat_seqaij_type my_mat
4836 
4837    Level: advanced
4838 
4839 .keywords: Mat, register
4840 
4841 .seealso: MatSeqAIJRegisterAll()
4842 
4843 
4844   Level: advanced
4845 @*/
4846 PetscErrorCode  MatSeqAIJRegister(const char sname[],PetscErrorCode (*function)(Mat,MatType,MatReuse,Mat *))
4847 {
4848   PetscErrorCode ierr;
4849 
4850   PetscFunctionBegin;
4851   ierr = MatInitializePackage();CHKERRQ(ierr);
4852   ierr = PetscFunctionListAdd(&MatSeqAIJList,sname,function);CHKERRQ(ierr);
4853   PetscFunctionReturn(0);
4854 }
4855 
4856 PetscBool MatSeqAIJRegisterAllCalled = PETSC_FALSE;
4857 
4858 /*@C
4859   MatSeqAIJRegisterAll - Registers all of the matrix subtypes of SeqAIJ
4860 
4861   Not Collective
4862 
4863   Level: advanced
4864 
4865   Developers Note: CUSP and CUSPARSE do not yet support the  MatConvert_SeqAIJ..() paradigm and thus cannot be registered here
4866 
4867 .keywords: KSP, register, all
4868 
4869 .seealso:  MatRegisterAll(), MatSeqAIJRegister()
4870 @*/
4871 PetscErrorCode  MatSeqAIJRegisterAll(void)
4872 {
4873   PetscErrorCode ierr;
4874 
4875   PetscFunctionBegin;
4876   if (MatSeqAIJRegisterAllCalled) PetscFunctionReturn(0);
4877   MatSeqAIJRegisterAllCalled = PETSC_TRUE;
4878 
4879   ierr = MatSeqAIJRegister(MATSEQAIJCRL,      MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4880   ierr = MatSeqAIJRegister(MATSEQAIJPERM,     MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4881   ierr = MatSeqAIJRegister(MATSEQAIJSELL,     MatConvert_SeqAIJ_SeqAIJSELL);CHKERRQ(ierr);
4882 #if defined(PETSC_HAVE_MKL_SPARSE)
4883   ierr = MatSeqAIJRegister(MATSEQAIJMKL,      MatConvert_SeqAIJ_SeqAIJMKL);CHKERRQ(ierr);
4884 #endif
4885 #if defined(PETSC_HAVE_VIENNACL) && defined(PETSC_HAVE_VIENNACL_NO_CUDA)
4886   ierr = MatSeqAIJRegister(MATMPIAIJVIENNACL, MatConvert_SeqAIJ_SeqAIJViennaCL);CHKERRQ(ierr);
4887 #endif
4888   PetscFunctionReturn(0);
4889 }
4890 
4891 /*
4892     Special version for direct calls from Fortran
4893 */
4894 #include <petsc/private/fortranimpl.h>
4895 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4896 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
4897 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4898 #define matsetvaluesseqaij_ matsetvaluesseqaij
4899 #endif
4900 
4901 /* Change these macros so can be used in void function */
4902 #undef CHKERRQ
4903 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
4904 #undef SETERRQ2
4905 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4906 #undef SETERRQ3
4907 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4908 
4909 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)
4910 {
4911   Mat            A  = *AA;
4912   PetscInt       m  = *mm, n = *nn;
4913   InsertMode     is = *isis;
4914   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4915   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
4916   PetscInt       *imax,*ai,*ailen;
4917   PetscErrorCode ierr;
4918   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
4919   MatScalar      *ap,value,*aa;
4920   PetscBool      ignorezeroentries = a->ignorezeroentries;
4921   PetscBool      roworiented       = a->roworiented;
4922 
4923   PetscFunctionBegin;
4924   MatCheckPreallocated(A,1);
4925   imax  = a->imax;
4926   ai    = a->i;
4927   ailen = a->ilen;
4928   aj    = a->j;
4929   aa    = a->a;
4930 
4931   for (k=0; k<m; k++) { /* loop over added rows */
4932     row = im[k];
4933     if (row < 0) continue;
4934 #if defined(PETSC_USE_DEBUG)
4935     if (row >= A->rmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
4936 #endif
4937     rp   = aj + ai[row]; ap = aa + ai[row];
4938     rmax = imax[row]; nrow = ailen[row];
4939     low  = 0;
4940     high = nrow;
4941     for (l=0; l<n; l++) { /* loop over added columns */
4942       if (in[l] < 0) continue;
4943 #if defined(PETSC_USE_DEBUG)
4944       if (in[l] >= A->cmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
4945 #endif
4946       col = in[l];
4947       if (roworiented) value = v[l + k*n];
4948       else value = v[k + l*m];
4949 
4950       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
4951 
4952       if (col <= lastcol) low = 0;
4953       else high = nrow;
4954       lastcol = col;
4955       while (high-low > 5) {
4956         t = (low+high)/2;
4957         if (rp[t] > col) high = t;
4958         else             low  = t;
4959       }
4960       for (i=low; i<high; i++) {
4961         if (rp[i] > col) break;
4962         if (rp[i] == col) {
4963           if (is == ADD_VALUES) ap[i] += value;
4964           else                  ap[i] = value;
4965           goto noinsert;
4966         }
4967       }
4968       if (value == 0.0 && ignorezeroentries) goto noinsert;
4969       if (nonew == 1) goto noinsert;
4970       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
4971       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
4972       N = nrow++ - 1; a->nz++; high++;
4973       /* shift up all the later entries in this row */
4974       for (ii=N; ii>=i; ii--) {
4975         rp[ii+1] = rp[ii];
4976         ap[ii+1] = ap[ii];
4977       }
4978       rp[i] = col;
4979       ap[i] = value;
4980       A->nonzerostate++;
4981 noinsert:;
4982       low = i + 1;
4983     }
4984     ailen[row] = nrow;
4985   }
4986   PetscFunctionReturnVoid();
4987 }
4988