xref: /petsc/src/mat/impls/aij/seq/aij.c (revision 5dc64a9727a0cc1147601b21df2b9dcd374fa7c9)
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       a->imax[i] = PetscMin(a->imax[i],A->cmap->n);
1563     }
1564     ierr = MatSeqAIJSetPreallocation_SeqAIJ(A,0,a->imax);CHKERRQ(ierr);
1565 
1566     /* copy old values into new matrix data structure */
1567     for (i=0; i<A->rmap->n; i++) {
1568       ierr = MatSetValues(A,1,&i,a->imax[i] - mdiag[i],&oldj[oldi[i]],&olda[oldi[i]],ADD_VALUES);CHKERRQ(ierr);
1569       if (i < A->cmap->n) {
1570         ierr = MatSetValue(A,i,i,v,ADD_VALUES);CHKERRQ(ierr);
1571       }
1572     }
1573     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1574     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1575     if (singlemalloc) {
1576       ierr = PetscFree3(olda,oldj,oldi);CHKERRQ(ierr);
1577     } else {
1578       if (free_a)  {ierr = PetscFree(olda);CHKERRQ(ierr);}
1579       if (free_ij) {ierr = PetscFree(oldj);CHKERRQ(ierr);}
1580       if (free_ij) {ierr = PetscFree(oldi);CHKERRQ(ierr);}
1581     }
1582   }
1583   ierr = PetscFree(mdiag);CHKERRQ(ierr);
1584   a->diagonaldense = PETSC_TRUE;
1585   PetscFunctionReturn(0);
1586 }
1587 
1588 /*
1589      Checks for missing diagonals
1590 */
1591 PetscErrorCode MatMissingDiagonal_SeqAIJ(Mat A,PetscBool  *missing,PetscInt *d)
1592 {
1593   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1594   PetscInt       *diag,*ii = a->i,i;
1595   PetscErrorCode ierr;
1596 
1597   PetscFunctionBegin;
1598   *missing = PETSC_FALSE;
1599   if (A->rmap->n > 0 && !ii) {
1600     *missing = PETSC_TRUE;
1601     if (d) *d = 0;
1602     ierr = PetscInfo(A,"Matrix has no entries therefore is missing diagonal\n");CHKERRQ(ierr);
1603   } else {
1604     diag = a->diag;
1605     for (i=0; i<A->rmap->n; i++) {
1606       if (diag[i] >= ii[i+1]) {
1607         *missing = PETSC_TRUE;
1608         if (d) *d = i;
1609         ierr = PetscInfo1(A,"Matrix is missing diagonal number %D\n",i);CHKERRQ(ierr);
1610         break;
1611       }
1612     }
1613   }
1614   PetscFunctionReturn(0);
1615 }
1616 
1617 #include <petscblaslapack.h>
1618 #include <petsc/private/kernels/blockinvert.h>
1619 
1620 /*
1621     Note that values is allocated externally by the PC and then passed into this routine
1622 */
1623 PetscErrorCode MatInvertVariableBlockDiagonal_SeqAIJ(Mat A,PetscInt nblocks,const PetscInt *bsizes,PetscScalar *diag)
1624 {
1625   PetscErrorCode  ierr;
1626   PetscInt        n = A->rmap->n, i, ncnt = 0, *indx,j,bsizemax = 0,*v_pivots;
1627   PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;
1628   const PetscReal shift = 0.0;
1629   PetscInt        ipvt[5];
1630   PetscScalar     work[25],*v_work;
1631 
1632   PetscFunctionBegin;
1633   allowzeropivot = PetscNot(A->erroriffailure);
1634   for (i=0; i<nblocks; i++) ncnt += bsizes[i];
1635   if (ncnt != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Total blocksizes %D doesn't match number matrix rows %D",ncnt,n);
1636   for (i=0; i<nblocks; i++) {
1637     bsizemax = PetscMax(bsizemax,bsizes[i]);
1638   }
1639   ierr = PetscMalloc1(bsizemax,&indx);CHKERRQ(ierr);
1640   if (bsizemax > 7) {
1641     ierr = PetscMalloc2(bsizemax,&v_work,bsizemax,&v_pivots);CHKERRQ(ierr);
1642   }
1643   ncnt = 0;
1644   for (i=0; i<nblocks; i++) {
1645     for (j=0; j<bsizes[i]; j++) indx[j] = ncnt+j;
1646     ierr    = MatGetValues(A,bsizes[i],indx,bsizes[i],indx,diag);CHKERRQ(ierr);
1647     switch (bsizes[i]) {
1648     case 1:
1649       *diag = 1.0/(*diag);
1650       break;
1651     case 2:
1652       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1653       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1654       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
1655       break;
1656     case 3:
1657       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1658       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1659       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
1660       break;
1661     case 4:
1662       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1663       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1664       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
1665       break;
1666     case 5:
1667       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1668       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1669       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
1670       break;
1671     case 6:
1672       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1673       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1674       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
1675       break;
1676     case 7:
1677       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1678       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1679       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
1680       break;
1681     default:
1682       ierr  = PetscKernel_A_gets_inverse_A(bsizes[i],diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1683       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1684       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bsizes[i]);CHKERRQ(ierr);
1685     }
1686     ncnt   += bsizes[i];
1687     diag += bsizes[i]*bsizes[i];
1688   }
1689   if (bsizemax > 7) {
1690     ierr = PetscFree2(v_work,v_pivots);CHKERRQ(ierr);
1691   }
1692   ierr = PetscFree(indx);CHKERRQ(ierr);
1693   PetscFunctionReturn(0);
1694 }
1695 
1696 /*
1697    Negative shift indicates do not generate an error if there is a zero diagonal, just invert it anyways
1698 */
1699 PetscErrorCode  MatInvertDiagonal_SeqAIJ(Mat A,PetscScalar omega,PetscScalar fshift)
1700 {
1701   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
1702   PetscErrorCode ierr;
1703   PetscInt       i,*diag,m = A->rmap->n;
1704   MatScalar      *v = a->a;
1705   PetscScalar    *idiag,*mdiag;
1706 
1707   PetscFunctionBegin;
1708   if (a->idiagvalid) PetscFunctionReturn(0);
1709   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1710   diag = a->diag;
1711   if (!a->idiag) {
1712     ierr = PetscMalloc3(m,&a->idiag,m,&a->mdiag,m,&a->ssor_work);CHKERRQ(ierr);
1713     ierr = PetscLogObjectMemory((PetscObject)A, 3*m*sizeof(PetscScalar));CHKERRQ(ierr);
1714     v    = a->a;
1715   }
1716   mdiag = a->mdiag;
1717   idiag = a->idiag;
1718 
1719   if (omega == 1.0 && PetscRealPart(fshift) <= 0.0) {
1720     for (i=0; i<m; i++) {
1721       mdiag[i] = v[diag[i]];
1722       if (!PetscAbsScalar(mdiag[i])) { /* zero diagonal */
1723         if (PetscRealPart(fshift)) {
1724           ierr = PetscInfo1(A,"Zero diagonal on row %D\n",i);CHKERRQ(ierr);
1725           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1726           A->factorerror_zeropivot_value = 0.0;
1727           A->factorerror_zeropivot_row   = i;
1728         } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Zero diagonal on row %D",i);
1729       }
1730       idiag[i] = 1.0/v[diag[i]];
1731     }
1732     ierr = PetscLogFlops(m);CHKERRQ(ierr);
1733   } else {
1734     for (i=0; i<m; i++) {
1735       mdiag[i] = v[diag[i]];
1736       idiag[i] = omega/(fshift + v[diag[i]]);
1737     }
1738     ierr = PetscLogFlops(2.0*m);CHKERRQ(ierr);
1739   }
1740   a->idiagvalid = PETSC_TRUE;
1741   PetscFunctionReturn(0);
1742 }
1743 
1744 #include <../src/mat/impls/aij/seq/ftn-kernels/frelax.h>
1745 PetscErrorCode MatSOR_SeqAIJ(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1746 {
1747   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1748   PetscScalar       *x,d,sum,*t,scale;
1749   const MatScalar   *v,*idiag=0,*mdiag;
1750   const PetscScalar *b, *bs,*xb, *ts;
1751   PetscErrorCode    ierr;
1752   PetscInt          n,m = A->rmap->n,i;
1753   const PetscInt    *idx,*diag;
1754 
1755   PetscFunctionBegin;
1756   its = its*lits;
1757 
1758   if (fshift != a->fshift || omega != a->omega) a->idiagvalid = PETSC_FALSE; /* must recompute idiag[] */
1759   if (!a->idiagvalid) {ierr = MatInvertDiagonal_SeqAIJ(A,omega,fshift);CHKERRQ(ierr);}
1760   a->fshift = fshift;
1761   a->omega  = omega;
1762 
1763   diag  = a->diag;
1764   t     = a->ssor_work;
1765   idiag = a->idiag;
1766   mdiag = a->mdiag;
1767 
1768   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1769   ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
1770   /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
1771   if (flag == SOR_APPLY_UPPER) {
1772     /* apply (U + D/omega) to the vector */
1773     bs = b;
1774     for (i=0; i<m; i++) {
1775       d   = fshift + mdiag[i];
1776       n   = a->i[i+1] - diag[i] - 1;
1777       idx = a->j + diag[i] + 1;
1778       v   = a->a + diag[i] + 1;
1779       sum = b[i]*d/omega;
1780       PetscSparseDensePlusDot(sum,bs,v,idx,n);
1781       x[i] = sum;
1782     }
1783     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1784     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1785     ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1786     PetscFunctionReturn(0);
1787   }
1788 
1789   if (flag == SOR_APPLY_LOWER) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SOR_APPLY_LOWER is not implemented");
1790   else if (flag & SOR_EISENSTAT) {
1791     /* Let  A = L + U + D; where L is lower trianglar,
1792     U is upper triangular, E = D/omega; This routine applies
1793 
1794             (L + E)^{-1} A (U + E)^{-1}
1795 
1796     to a vector efficiently using Eisenstat's trick.
1797     */
1798     scale = (2.0/omega) - 1.0;
1799 
1800     /*  x = (E + U)^{-1} b */
1801     for (i=m-1; i>=0; i--) {
1802       n   = a->i[i+1] - diag[i] - 1;
1803       idx = a->j + diag[i] + 1;
1804       v   = a->a + diag[i] + 1;
1805       sum = b[i];
1806       PetscSparseDenseMinusDot(sum,x,v,idx,n);
1807       x[i] = sum*idiag[i];
1808     }
1809 
1810     /*  t = b - (2*E - D)x */
1811     v = a->a;
1812     for (i=0; i<m; i++) t[i] = b[i] - scale*(v[*diag++])*x[i];
1813 
1814     /*  t = (E + L)^{-1}t */
1815     ts   = t;
1816     diag = a->diag;
1817     for (i=0; i<m; i++) {
1818       n   = diag[i] - a->i[i];
1819       idx = a->j + a->i[i];
1820       v   = a->a + a->i[i];
1821       sum = t[i];
1822       PetscSparseDenseMinusDot(sum,ts,v,idx,n);
1823       t[i] = sum*idiag[i];
1824       /*  x = x + t */
1825       x[i] += t[i];
1826     }
1827 
1828     ierr = PetscLogFlops(6.0*m-1 + 2.0*a->nz);CHKERRQ(ierr);
1829     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1830     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1831     PetscFunctionReturn(0);
1832   }
1833   if (flag & SOR_ZERO_INITIAL_GUESS) {
1834     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1835       for (i=0; i<m; i++) {
1836         n   = diag[i] - a->i[i];
1837         idx = a->j + a->i[i];
1838         v   = a->a + a->i[i];
1839         sum = b[i];
1840         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1841         t[i] = sum;
1842         x[i] = sum*idiag[i];
1843       }
1844       xb   = t;
1845       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1846     } else xb = b;
1847     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1848       for (i=m-1; i>=0; i--) {
1849         n   = a->i[i+1] - diag[i] - 1;
1850         idx = a->j + diag[i] + 1;
1851         v   = a->a + diag[i] + 1;
1852         sum = xb[i];
1853         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1854         if (xb == b) {
1855           x[i] = sum*idiag[i];
1856         } else {
1857           x[i] = (1-omega)*x[i] + sum*idiag[i];  /* omega in idiag */
1858         }
1859       }
1860       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
1861     }
1862     its--;
1863   }
1864   while (its--) {
1865     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1866       for (i=0; i<m; i++) {
1867         /* lower */
1868         n   = diag[i] - a->i[i];
1869         idx = a->j + a->i[i];
1870         v   = a->a + a->i[i];
1871         sum = b[i];
1872         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1873         t[i] = sum;             /* save application of the lower-triangular part */
1874         /* upper */
1875         n   = a->i[i+1] - diag[i] - 1;
1876         idx = a->j + diag[i] + 1;
1877         v   = a->a + diag[i] + 1;
1878         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1879         x[i] = (1. - omega)*x[i] + sum*idiag[i]; /* omega in idiag */
1880       }
1881       xb   = t;
1882       ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1883     } else xb = b;
1884     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1885       for (i=m-1; i>=0; i--) {
1886         sum = xb[i];
1887         if (xb == b) {
1888           /* whole matrix (no checkpointing available) */
1889           n   = a->i[i+1] - a->i[i];
1890           idx = a->j + a->i[i];
1891           v   = a->a + a->i[i];
1892           PetscSparseDenseMinusDot(sum,x,v,idx,n);
1893           x[i] = (1. - omega)*x[i] + (sum + mdiag[i]*x[i])*idiag[i];
1894         } else { /* lower-triangular part has been saved, so only apply upper-triangular */
1895           n   = a->i[i+1] - diag[i] - 1;
1896           idx = a->j + diag[i] + 1;
1897           v   = a->a + diag[i] + 1;
1898           PetscSparseDenseMinusDot(sum,x,v,idx,n);
1899           x[i] = (1. - omega)*x[i] + sum*idiag[i];  /* omega in idiag */
1900         }
1901       }
1902       if (xb == b) {
1903         ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1904       } else {
1905         ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
1906       }
1907     }
1908   }
1909   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1910   ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1911   PetscFunctionReturn(0);
1912 }
1913 
1914 
1915 PetscErrorCode MatGetInfo_SeqAIJ(Mat A,MatInfoType flag,MatInfo *info)
1916 {
1917   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1918 
1919   PetscFunctionBegin;
1920   info->block_size   = 1.0;
1921   info->nz_allocated = (double)a->maxnz;
1922   info->nz_used      = (double)a->nz;
1923   info->nz_unneeded  = (double)(a->maxnz - a->nz);
1924   info->assemblies   = (double)A->num_ass;
1925   info->mallocs      = (double)A->info.mallocs;
1926   info->memory       = ((PetscObject)A)->mem;
1927   if (A->factortype) {
1928     info->fill_ratio_given  = A->info.fill_ratio_given;
1929     info->fill_ratio_needed = A->info.fill_ratio_needed;
1930     info->factor_mallocs    = A->info.factor_mallocs;
1931   } else {
1932     info->fill_ratio_given  = 0;
1933     info->fill_ratio_needed = 0;
1934     info->factor_mallocs    = 0;
1935   }
1936   PetscFunctionReturn(0);
1937 }
1938 
1939 PetscErrorCode MatZeroRows_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
1940 {
1941   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1942   PetscInt          i,m = A->rmap->n - 1;
1943   PetscErrorCode    ierr;
1944   const PetscScalar *xx;
1945   PetscScalar       *bb;
1946   PetscInt          d = 0;
1947 
1948   PetscFunctionBegin;
1949   if (x && b) {
1950     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
1951     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
1952     for (i=0; i<N; i++) {
1953       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1954       if (rows[i] >= A->cmap->n) continue;
1955       bb[rows[i]] = diag*xx[rows[i]];
1956     }
1957     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
1958     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
1959   }
1960 
1961   if (a->keepnonzeropattern) {
1962     for (i=0; i<N; i++) {
1963       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1964       ierr = PetscMemzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]*sizeof(PetscScalar));CHKERRQ(ierr);
1965     }
1966     if (diag != 0.0) {
1967       for (i=0; i<N; i++) {
1968         d = rows[i];
1969         if (rows[i] >= A->cmap->n) continue;
1970         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);
1971       }
1972       for (i=0; i<N; i++) {
1973         if (rows[i] >= A->cmap->n) continue;
1974         a->a[a->diag[rows[i]]] = diag;
1975       }
1976     }
1977   } else {
1978     if (diag != 0.0) {
1979       for (i=0; i<N; i++) {
1980         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1981         if (a->ilen[rows[i]] > 0) {
1982 	  if (rows[i] >= A->cmap->n) {
1983             a->ilen[rows[i]] = 0;
1984           } else {
1985             a->ilen[rows[i]]    = 1;
1986             a->a[a->i[rows[i]]] = diag;
1987             a->j[a->i[rows[i]]] = rows[i];
1988           }
1989         } else if (rows[i] < A->cmap->n) { /* in case row was completely empty */
1990           ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES);CHKERRQ(ierr);
1991         }
1992       }
1993     } else {
1994       for (i=0; i<N; i++) {
1995         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1996         a->ilen[rows[i]] = 0;
1997       }
1998     }
1999     A->nonzerostate++;
2000   }
2001   ierr = (*A->ops->assemblyend)(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2002   PetscFunctionReturn(0);
2003 }
2004 
2005 PetscErrorCode MatZeroRowsColumns_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
2006 {
2007   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2008   PetscInt          i,j,m = A->rmap->n - 1,d = 0;
2009   PetscErrorCode    ierr;
2010   PetscBool         missing,*zeroed,vecs = PETSC_FALSE;
2011   const PetscScalar *xx;
2012   PetscScalar       *bb;
2013 
2014   PetscFunctionBegin;
2015   if (x && b) {
2016     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
2017     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
2018     vecs = PETSC_TRUE;
2019   }
2020   ierr = PetscCalloc1(A->rmap->n,&zeroed);CHKERRQ(ierr);
2021   for (i=0; i<N; i++) {
2022     if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2023     ierr = PetscMemzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]*sizeof(PetscScalar));CHKERRQ(ierr);
2024 
2025     zeroed[rows[i]] = PETSC_TRUE;
2026   }
2027   for (i=0; i<A->rmap->n; i++) {
2028     if (!zeroed[i]) {
2029       for (j=a->i[i]; j<a->i[i+1]; j++) {
2030         if (a->j[j] < A->rmap->n && zeroed[a->j[j]]) {
2031           if (vecs) bb[i] -= a->a[j]*xx[a->j[j]];
2032           a->a[j] = 0.0;
2033         }
2034       }
2035     } else if (vecs && i < A->cmap->N) bb[i] = diag*xx[i];
2036   }
2037   if (x && b) {
2038     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
2039     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
2040   }
2041   ierr = PetscFree(zeroed);CHKERRQ(ierr);
2042   if (diag != 0.0) {
2043     ierr = MatMissingDiagonal_SeqAIJ(A,&missing,&d);CHKERRQ(ierr);
2044     if (missing) {
2045       for (i=0; i<N; i++) {
2046         if (rows[i] >= A->cmap->N) continue;
2047         if (a->nonew && rows[i] >= d) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in row %D (%D)",d,rows[i]);
2048         ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES);CHKERRQ(ierr);
2049       }
2050     } else {
2051       for (i=0; i<N; i++) {
2052         a->a[a->diag[rows[i]]] = diag;
2053       }
2054     }
2055   }
2056   ierr = (*A->ops->assemblyend)(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2057   PetscFunctionReturn(0);
2058 }
2059 
2060 PetscErrorCode MatGetRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
2061 {
2062   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2063   PetscInt   *itmp;
2064 
2065   PetscFunctionBegin;
2066   if (row < 0 || row >= A->rmap->n) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range",row);
2067 
2068   *nz = a->i[row+1] - a->i[row];
2069   if (v) *v = a->a + a->i[row];
2070   if (idx) {
2071     itmp = a->j + a->i[row];
2072     if (*nz) *idx = itmp;
2073     else *idx = 0;
2074   }
2075   PetscFunctionReturn(0);
2076 }
2077 
2078 /* remove this function? */
2079 PetscErrorCode MatRestoreRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
2080 {
2081   PetscFunctionBegin;
2082   PetscFunctionReturn(0);
2083 }
2084 
2085 PetscErrorCode MatNorm_SeqAIJ(Mat A,NormType type,PetscReal *nrm)
2086 {
2087   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
2088   MatScalar      *v  = a->a;
2089   PetscReal      sum = 0.0;
2090   PetscErrorCode ierr;
2091   PetscInt       i,j;
2092 
2093   PetscFunctionBegin;
2094   if (type == NORM_FROBENIUS) {
2095 #if defined(PETSC_USE_REAL___FP16)
2096     PetscBLASInt one = 1,nz = a->nz;
2097     *nrm = BLASnrm2_(&nz,v,&one);
2098 #else
2099     for (i=0; i<a->nz; i++) {
2100       sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
2101     }
2102     *nrm = PetscSqrtReal(sum);
2103 #endif
2104     ierr = PetscLogFlops(2*a->nz);CHKERRQ(ierr);
2105   } else if (type == NORM_1) {
2106     PetscReal *tmp;
2107     PetscInt  *jj = a->j;
2108     ierr = PetscCalloc1(A->cmap->n+1,&tmp);CHKERRQ(ierr);
2109     *nrm = 0.0;
2110     for (j=0; j<a->nz; j++) {
2111       tmp[*jj++] += PetscAbsScalar(*v);  v++;
2112     }
2113     for (j=0; j<A->cmap->n; j++) {
2114       if (tmp[j] > *nrm) *nrm = tmp[j];
2115     }
2116     ierr = PetscFree(tmp);CHKERRQ(ierr);
2117     ierr = PetscLogFlops(PetscMax(a->nz-1,0));CHKERRQ(ierr);
2118   } else if (type == NORM_INFINITY) {
2119     *nrm = 0.0;
2120     for (j=0; j<A->rmap->n; j++) {
2121       v   = a->a + a->i[j];
2122       sum = 0.0;
2123       for (i=0; i<a->i[j+1]-a->i[j]; i++) {
2124         sum += PetscAbsScalar(*v); v++;
2125       }
2126       if (sum > *nrm) *nrm = sum;
2127     }
2128     ierr = PetscLogFlops(PetscMax(a->nz-1,0));CHKERRQ(ierr);
2129   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for two norm");
2130   PetscFunctionReturn(0);
2131 }
2132 
2133 /* Merged from MatGetSymbolicTranspose_SeqAIJ() - replace MatGetSymbolicTranspose_SeqAIJ()? */
2134 PetscErrorCode MatTransposeSymbolic_SeqAIJ(Mat A,Mat *B)
2135 {
2136   PetscErrorCode ierr;
2137   PetscInt       i,j,anzj;
2138   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b;
2139   PetscInt       an=A->cmap->N,am=A->rmap->N;
2140   PetscInt       *ati,*atj,*atfill,*ai=a->i,*aj=a->j;
2141 
2142   PetscFunctionBegin;
2143   /* Allocate space for symbolic transpose info and work array */
2144   ierr = PetscCalloc1(an+1,&ati);CHKERRQ(ierr);
2145   ierr = PetscMalloc1(ai[am],&atj);CHKERRQ(ierr);
2146   ierr = PetscMalloc1(an,&atfill);CHKERRQ(ierr);
2147 
2148   /* Walk through aj and count ## of non-zeros in each row of A^T. */
2149   /* Note: offset by 1 for fast conversion into csr format. */
2150   for (i=0;i<ai[am];i++) ati[aj[i]+1] += 1;
2151   /* Form ati for csr format of A^T. */
2152   for (i=0;i<an;i++) ati[i+1] += ati[i];
2153 
2154   /* Copy ati into atfill so we have locations of the next free space in atj */
2155   ierr = PetscMemcpy(atfill,ati,an*sizeof(PetscInt));CHKERRQ(ierr);
2156 
2157   /* Walk through A row-wise and mark nonzero entries of A^T. */
2158   for (i=0;i<am;i++) {
2159     anzj = ai[i+1] - ai[i];
2160     for (j=0;j<anzj;j++) {
2161       atj[atfill[*aj]] = i;
2162       atfill[*aj++]   += 1;
2163     }
2164   }
2165 
2166   /* Clean up temporary space and complete requests. */
2167   ierr = PetscFree(atfill);CHKERRQ(ierr);
2168   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),an,am,ati,atj,NULL,B);CHKERRQ(ierr);
2169   ierr = MatSetBlockSizes(*B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2170 
2171   b          = (Mat_SeqAIJ*)((*B)->data);
2172   b->free_a  = PETSC_FALSE;
2173   b->free_ij = PETSC_TRUE;
2174   b->nonew   = 0;
2175   PetscFunctionReturn(0);
2176 }
2177 
2178 PetscErrorCode  MatIsTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2179 {
2180   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) B->data;
2181   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2182   MatScalar      *va,*vb;
2183   PetscErrorCode ierr;
2184   PetscInt       ma,na,mb,nb, i;
2185 
2186   PetscFunctionBegin;
2187   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2188   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2189   if (ma!=nb || na!=mb) {
2190     *f = PETSC_FALSE;
2191     PetscFunctionReturn(0);
2192   }
2193   aii  = aij->i; bii = bij->i;
2194   adx  = aij->j; bdx = bij->j;
2195   va   = aij->a; vb = bij->a;
2196   ierr = PetscMalloc1(ma,&aptr);CHKERRQ(ierr);
2197   ierr = PetscMalloc1(mb,&bptr);CHKERRQ(ierr);
2198   for (i=0; i<ma; i++) aptr[i] = aii[i];
2199   for (i=0; i<mb; i++) bptr[i] = bii[i];
2200 
2201   *f = PETSC_TRUE;
2202   for (i=0; i<ma; i++) {
2203     while (aptr[i]<aii[i+1]) {
2204       PetscInt    idc,idr;
2205       PetscScalar vc,vr;
2206       /* column/row index/value */
2207       idc = adx[aptr[i]];
2208       idr = bdx[bptr[idc]];
2209       vc  = va[aptr[i]];
2210       vr  = vb[bptr[idc]];
2211       if (i!=idr || PetscAbsScalar(vc-vr) > tol) {
2212         *f = PETSC_FALSE;
2213         goto done;
2214       } else {
2215         aptr[i]++;
2216         if (B || i!=idc) bptr[idc]++;
2217       }
2218     }
2219   }
2220 done:
2221   ierr = PetscFree(aptr);CHKERRQ(ierr);
2222   ierr = PetscFree(bptr);CHKERRQ(ierr);
2223   PetscFunctionReturn(0);
2224 }
2225 
2226 PetscErrorCode  MatIsHermitianTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2227 {
2228   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) B->data;
2229   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2230   MatScalar      *va,*vb;
2231   PetscErrorCode ierr;
2232   PetscInt       ma,na,mb,nb, i;
2233 
2234   PetscFunctionBegin;
2235   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2236   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2237   if (ma!=nb || na!=mb) {
2238     *f = PETSC_FALSE;
2239     PetscFunctionReturn(0);
2240   }
2241   aii  = aij->i; bii = bij->i;
2242   adx  = aij->j; bdx = bij->j;
2243   va   = aij->a; vb = bij->a;
2244   ierr = PetscMalloc1(ma,&aptr);CHKERRQ(ierr);
2245   ierr = PetscMalloc1(mb,&bptr);CHKERRQ(ierr);
2246   for (i=0; i<ma; i++) aptr[i] = aii[i];
2247   for (i=0; i<mb; i++) bptr[i] = bii[i];
2248 
2249   *f = PETSC_TRUE;
2250   for (i=0; i<ma; i++) {
2251     while (aptr[i]<aii[i+1]) {
2252       PetscInt    idc,idr;
2253       PetscScalar vc,vr;
2254       /* column/row index/value */
2255       idc = adx[aptr[i]];
2256       idr = bdx[bptr[idc]];
2257       vc  = va[aptr[i]];
2258       vr  = vb[bptr[idc]];
2259       if (i!=idr || PetscAbsScalar(vc-PetscConj(vr)) > tol) {
2260         *f = PETSC_FALSE;
2261         goto done;
2262       } else {
2263         aptr[i]++;
2264         if (B || i!=idc) bptr[idc]++;
2265       }
2266     }
2267   }
2268 done:
2269   ierr = PetscFree(aptr);CHKERRQ(ierr);
2270   ierr = PetscFree(bptr);CHKERRQ(ierr);
2271   PetscFunctionReturn(0);
2272 }
2273 
2274 PetscErrorCode MatIsSymmetric_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2275 {
2276   PetscErrorCode ierr;
2277 
2278   PetscFunctionBegin;
2279   ierr = MatIsTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2280   PetscFunctionReturn(0);
2281 }
2282 
2283 PetscErrorCode MatIsHermitian_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2284 {
2285   PetscErrorCode ierr;
2286 
2287   PetscFunctionBegin;
2288   ierr = MatIsHermitianTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2289   PetscFunctionReturn(0);
2290 }
2291 
2292 PetscErrorCode MatDiagonalScale_SeqAIJ(Mat A,Vec ll,Vec rr)
2293 {
2294   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2295   const PetscScalar *l,*r;
2296   PetscScalar       x;
2297   MatScalar         *v;
2298   PetscErrorCode    ierr;
2299   PetscInt          i,j,m = A->rmap->n,n = A->cmap->n,M,nz = a->nz;
2300   const PetscInt    *jj;
2301 
2302   PetscFunctionBegin;
2303   if (ll) {
2304     /* The local size is used so that VecMPI can be passed to this routine
2305        by MatDiagonalScale_MPIAIJ */
2306     ierr = VecGetLocalSize(ll,&m);CHKERRQ(ierr);
2307     if (m != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
2308     ierr = VecGetArrayRead(ll,&l);CHKERRQ(ierr);
2309     v    = a->a;
2310     for (i=0; i<m; i++) {
2311       x = l[i];
2312       M = a->i[i+1] - a->i[i];
2313       for (j=0; j<M; j++) (*v++) *= x;
2314     }
2315     ierr = VecRestoreArrayRead(ll,&l);CHKERRQ(ierr);
2316     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2317   }
2318   if (rr) {
2319     ierr = VecGetLocalSize(rr,&n);CHKERRQ(ierr);
2320     if (n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vector wrong length");
2321     ierr = VecGetArrayRead(rr,&r);CHKERRQ(ierr);
2322     v    = a->a; jj = a->j;
2323     for (i=0; i<nz; i++) (*v++) *= r[*jj++];
2324     ierr = VecRestoreArrayRead(rr,&r);CHKERRQ(ierr);
2325     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2326   }
2327   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
2328   PetscFunctionReturn(0);
2329 }
2330 
2331 PetscErrorCode MatCreateSubMatrix_SeqAIJ(Mat A,IS isrow,IS iscol,PetscInt csize,MatReuse scall,Mat *B)
2332 {
2333   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*c;
2334   PetscErrorCode ierr;
2335   PetscInt       *smap,i,k,kstart,kend,oldcols = A->cmap->n,*lens;
2336   PetscInt       row,mat_i,*mat_j,tcol,first,step,*mat_ilen,sum,lensi;
2337   const PetscInt *irow,*icol;
2338   PetscInt       nrows,ncols;
2339   PetscInt       *starts,*j_new,*i_new,*aj = a->j,*ai = a->i,ii,*ailen = a->ilen;
2340   MatScalar      *a_new,*mat_a;
2341   Mat            C;
2342   PetscBool      stride;
2343 
2344   PetscFunctionBegin;
2345 
2346   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
2347   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
2348   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
2349 
2350   ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&stride);CHKERRQ(ierr);
2351   if (stride) {
2352     ierr = ISStrideGetInfo(iscol,&first,&step);CHKERRQ(ierr);
2353   } else {
2354     first = 0;
2355     step  = 0;
2356   }
2357   if (stride && step == 1) {
2358     /* special case of contiguous rows */
2359     ierr = PetscMalloc2(nrows,&lens,nrows,&starts);CHKERRQ(ierr);
2360     /* loop over new rows determining lens and starting points */
2361     for (i=0; i<nrows; i++) {
2362       kstart = ai[irow[i]];
2363       kend   = kstart + ailen[irow[i]];
2364       starts[i] = kstart;
2365       for (k=kstart; k<kend; k++) {
2366         if (aj[k] >= first) {
2367           starts[i] = k;
2368           break;
2369         }
2370       }
2371       sum = 0;
2372       while (k < kend) {
2373         if (aj[k++] >= first+ncols) break;
2374         sum++;
2375       }
2376       lens[i] = sum;
2377     }
2378     /* create submatrix */
2379     if (scall == MAT_REUSE_MATRIX) {
2380       PetscInt n_cols,n_rows;
2381       ierr = MatGetSize(*B,&n_rows,&n_cols);CHKERRQ(ierr);
2382       if (n_rows != nrows || n_cols != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
2383       ierr = MatZeroEntries(*B);CHKERRQ(ierr);
2384       C    = *B;
2385     } else {
2386       PetscInt rbs,cbs;
2387       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2388       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2389       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2390       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2391       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2392       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2393       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2394     }
2395     c = (Mat_SeqAIJ*)C->data;
2396 
2397     /* loop over rows inserting into submatrix */
2398     a_new = c->a;
2399     j_new = c->j;
2400     i_new = c->i;
2401 
2402     for (i=0; i<nrows; i++) {
2403       ii    = starts[i];
2404       lensi = lens[i];
2405       for (k=0; k<lensi; k++) {
2406         *j_new++ = aj[ii+k] - first;
2407       }
2408       ierr       = PetscMemcpy(a_new,a->a + starts[i],lensi*sizeof(PetscScalar));CHKERRQ(ierr);
2409       a_new     += lensi;
2410       i_new[i+1] = i_new[i] + lensi;
2411       c->ilen[i] = lensi;
2412     }
2413     ierr = PetscFree2(lens,starts);CHKERRQ(ierr);
2414   } else {
2415     ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
2416     ierr = PetscCalloc1(oldcols,&smap);CHKERRQ(ierr);
2417     ierr = PetscMalloc1(1+nrows,&lens);CHKERRQ(ierr);
2418     for (i=0; i<ncols; i++) {
2419 #if defined(PETSC_USE_DEBUG)
2420       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);
2421 #endif
2422       smap[icol[i]] = i+1;
2423     }
2424 
2425     /* determine lens of each row */
2426     for (i=0; i<nrows; i++) {
2427       kstart  = ai[irow[i]];
2428       kend    = kstart + a->ilen[irow[i]];
2429       lens[i] = 0;
2430       for (k=kstart; k<kend; k++) {
2431         if (smap[aj[k]]) {
2432           lens[i]++;
2433         }
2434       }
2435     }
2436     /* Create and fill new matrix */
2437     if (scall == MAT_REUSE_MATRIX) {
2438       PetscBool equal;
2439 
2440       c = (Mat_SeqAIJ*)((*B)->data);
2441       if ((*B)->rmap->n  != nrows || (*B)->cmap->n != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
2442       ierr = PetscMemcmp(c->ilen,lens,(*B)->rmap->n*sizeof(PetscInt),&equal);CHKERRQ(ierr);
2443       if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
2444       ierr = PetscMemzero(c->ilen,(*B)->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
2445       C    = *B;
2446     } else {
2447       PetscInt rbs,cbs;
2448       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2449       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2450       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2451       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2452       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2453       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2454       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2455     }
2456     c = (Mat_SeqAIJ*)(C->data);
2457     for (i=0; i<nrows; i++) {
2458       row      = irow[i];
2459       kstart   = ai[row];
2460       kend     = kstart + a->ilen[row];
2461       mat_i    = c->i[i];
2462       mat_j    = c->j + mat_i;
2463       mat_a    = c->a + mat_i;
2464       mat_ilen = c->ilen + i;
2465       for (k=kstart; k<kend; k++) {
2466         if ((tcol=smap[a->j[k]])) {
2467           *mat_j++ = tcol - 1;
2468           *mat_a++ = a->a[k];
2469           (*mat_ilen)++;
2470 
2471         }
2472       }
2473     }
2474     /* Free work space */
2475     ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
2476     ierr = PetscFree(smap);CHKERRQ(ierr);
2477     ierr = PetscFree(lens);CHKERRQ(ierr);
2478     /* sort */
2479     for (i = 0; i < nrows; i++) {
2480       PetscInt ilen;
2481 
2482       mat_i = c->i[i];
2483       mat_j = c->j + mat_i;
2484       mat_a = c->a + mat_i;
2485       ilen  = c->ilen[i];
2486       ierr  = PetscSortIntWithScalarArray(ilen,mat_j,mat_a);CHKERRQ(ierr);
2487     }
2488   }
2489   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2490   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2491 
2492   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
2493   *B   = C;
2494   PetscFunctionReturn(0);
2495 }
2496 
2497 PetscErrorCode  MatGetMultiProcBlock_SeqAIJ(Mat mat,MPI_Comm subComm,MatReuse scall,Mat *subMat)
2498 {
2499   PetscErrorCode ierr;
2500   Mat            B;
2501 
2502   PetscFunctionBegin;
2503   if (scall == MAT_INITIAL_MATRIX) {
2504     ierr    = MatCreate(subComm,&B);CHKERRQ(ierr);
2505     ierr    = MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->n,mat->cmap->n);CHKERRQ(ierr);
2506     ierr    = MatSetBlockSizesFromMats(B,mat,mat);CHKERRQ(ierr);
2507     ierr    = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
2508     ierr    = MatDuplicateNoCreate_SeqAIJ(B,mat,MAT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
2509     *subMat = B;
2510   } else {
2511     ierr = MatCopy_SeqAIJ(mat,*subMat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2512   }
2513   PetscFunctionReturn(0);
2514 }
2515 
2516 PetscErrorCode MatILUFactor_SeqAIJ(Mat inA,IS row,IS col,const MatFactorInfo *info)
2517 {
2518   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)inA->data;
2519   PetscErrorCode ierr;
2520   Mat            outA;
2521   PetscBool      row_identity,col_identity;
2522 
2523   PetscFunctionBegin;
2524   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels=0 supported for in-place ilu");
2525 
2526   ierr = ISIdentity(row,&row_identity);CHKERRQ(ierr);
2527   ierr = ISIdentity(col,&col_identity);CHKERRQ(ierr);
2528 
2529   outA             = inA;
2530   outA->factortype = MAT_FACTOR_LU;
2531   ierr = PetscFree(inA->solvertype);CHKERRQ(ierr);
2532   ierr = PetscStrallocpy(MATSOLVERPETSC,&inA->solvertype);CHKERRQ(ierr);
2533 
2534   ierr = PetscObjectReference((PetscObject)row);CHKERRQ(ierr);
2535   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
2536 
2537   a->row = row;
2538 
2539   ierr = PetscObjectReference((PetscObject)col);CHKERRQ(ierr);
2540   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
2541 
2542   a->col = col;
2543 
2544   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
2545   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
2546   ierr = ISInvertPermutation(col,PETSC_DECIDE,&a->icol);CHKERRQ(ierr);
2547   ierr = PetscLogObjectParent((PetscObject)inA,(PetscObject)a->icol);CHKERRQ(ierr);
2548 
2549   if (!a->solve_work) { /* this matrix may have been factored before */
2550     ierr = PetscMalloc1(inA->rmap->n+1,&a->solve_work);CHKERRQ(ierr);
2551     ierr = PetscLogObjectMemory((PetscObject)inA, (inA->rmap->n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2552   }
2553 
2554   ierr = MatMarkDiagonal_SeqAIJ(inA);CHKERRQ(ierr);
2555   if (row_identity && col_identity) {
2556     ierr = MatLUFactorNumeric_SeqAIJ_inplace(outA,inA,info);CHKERRQ(ierr);
2557   } else {
2558     ierr = MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA,inA,info);CHKERRQ(ierr);
2559   }
2560   PetscFunctionReturn(0);
2561 }
2562 
2563 PetscErrorCode MatScale_SeqAIJ(Mat inA,PetscScalar alpha)
2564 {
2565   Mat_SeqAIJ     *a     = (Mat_SeqAIJ*)inA->data;
2566   PetscScalar    oalpha = alpha;
2567   PetscErrorCode ierr;
2568   PetscBLASInt   one = 1,bnz;
2569 
2570   PetscFunctionBegin;
2571   ierr = PetscBLASIntCast(a->nz,&bnz);CHKERRQ(ierr);
2572   PetscStackCallBLAS("BLASscal",BLASscal_(&bnz,&oalpha,a->a,&one));
2573   ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2574   ierr = MatSeqAIJInvalidateDiagonal(inA);CHKERRQ(ierr);
2575   PetscFunctionReturn(0);
2576 }
2577 
2578 PetscErrorCode MatDestroySubMatrix_Private(Mat_SubSppt *submatj)
2579 {
2580   PetscErrorCode ierr;
2581   PetscInt       i;
2582 
2583   PetscFunctionBegin;
2584   if (!submatj->id) { /* delete data that are linked only to submats[id=0] */
2585     ierr = PetscFree4(submatj->sbuf1,submatj->ptr,submatj->tmp,submatj->ctr);CHKERRQ(ierr);
2586 
2587     for (i=0; i<submatj->nrqr; ++i) {
2588       ierr = PetscFree(submatj->sbuf2[i]);CHKERRQ(ierr);
2589     }
2590     ierr = PetscFree3(submatj->sbuf2,submatj->req_size,submatj->req_source1);CHKERRQ(ierr);
2591 
2592     if (submatj->rbuf1) {
2593       ierr = PetscFree(submatj->rbuf1[0]);CHKERRQ(ierr);
2594       ierr = PetscFree(submatj->rbuf1);CHKERRQ(ierr);
2595     }
2596 
2597     for (i=0; i<submatj->nrqs; ++i) {
2598       ierr = PetscFree(submatj->rbuf3[i]);CHKERRQ(ierr);
2599     }
2600     ierr = PetscFree3(submatj->req_source2,submatj->rbuf2,submatj->rbuf3);CHKERRQ(ierr);
2601     ierr = PetscFree(submatj->pa);CHKERRQ(ierr);
2602   }
2603 
2604 #if defined(PETSC_USE_CTABLE)
2605   ierr = PetscTableDestroy((PetscTable*)&submatj->rmap);CHKERRQ(ierr);
2606   if (submatj->cmap_loc) {ierr = PetscFree(submatj->cmap_loc);CHKERRQ(ierr);}
2607   ierr = PetscFree(submatj->rmap_loc);CHKERRQ(ierr);
2608 #else
2609   ierr = PetscFree(submatj->rmap);CHKERRQ(ierr);
2610 #endif
2611 
2612   if (!submatj->allcolumns) {
2613 #if defined(PETSC_USE_CTABLE)
2614     ierr = PetscTableDestroy((PetscTable*)&submatj->cmap);CHKERRQ(ierr);
2615 #else
2616     ierr = PetscFree(submatj->cmap);CHKERRQ(ierr);
2617 #endif
2618   }
2619   ierr = PetscFree(submatj->row2proc);CHKERRQ(ierr);
2620 
2621   ierr = PetscFree(submatj);CHKERRQ(ierr);
2622   PetscFunctionReturn(0);
2623 }
2624 
2625 PetscErrorCode MatDestroySubMatrix_SeqAIJ(Mat C)
2626 {
2627   PetscErrorCode ierr;
2628   Mat_SeqAIJ     *c = (Mat_SeqAIJ*)C->data;
2629   Mat_SubSppt    *submatj = c->submatis1;
2630 
2631   PetscFunctionBegin;
2632   ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
2633   ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
2634   PetscFunctionReturn(0);
2635 }
2636 
2637 PetscErrorCode MatDestroySubMatrices_SeqAIJ(PetscInt n,Mat *mat[])
2638 {
2639   PetscErrorCode ierr;
2640   PetscInt       i;
2641   Mat            C;
2642   Mat_SeqAIJ     *c;
2643   Mat_SubSppt    *submatj;
2644 
2645   PetscFunctionBegin;
2646   for (i=0; i<n; i++) {
2647     C       = (*mat)[i];
2648     c       = (Mat_SeqAIJ*)C->data;
2649     submatj = c->submatis1;
2650     if (submatj) {
2651       if (--((PetscObject)C)->refct <= 0) {
2652         ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
2653         ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
2654         ierr = PetscFree(C->defaultvectype);CHKERRQ(ierr);
2655         ierr = PetscLayoutDestroy(&C->rmap);CHKERRQ(ierr);
2656         ierr = PetscLayoutDestroy(&C->cmap);CHKERRQ(ierr);
2657         ierr = PetscHeaderDestroy(&C);CHKERRQ(ierr);
2658       }
2659     } else {
2660       ierr = MatDestroy(&C);CHKERRQ(ierr);
2661     }
2662   }
2663 
2664   /* Destroy Dummy submatrices created for reuse */
2665   ierr = MatDestroySubMatrices_Dummy(n,mat);CHKERRQ(ierr);
2666 
2667   ierr = PetscFree(*mat);CHKERRQ(ierr);
2668   PetscFunctionReturn(0);
2669 }
2670 
2671 PetscErrorCode MatCreateSubMatrices_SeqAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
2672 {
2673   PetscErrorCode ierr;
2674   PetscInt       i;
2675 
2676   PetscFunctionBegin;
2677   if (scall == MAT_INITIAL_MATRIX) {
2678     ierr = PetscCalloc1(n+1,B);CHKERRQ(ierr);
2679   }
2680 
2681   for (i=0; i<n; i++) {
2682     ierr = MatCreateSubMatrix_SeqAIJ(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]);CHKERRQ(ierr);
2683   }
2684   PetscFunctionReturn(0);
2685 }
2686 
2687 PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
2688 {
2689   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2690   PetscErrorCode ierr;
2691   PetscInt       row,i,j,k,l,m,n,*nidx,isz,val;
2692   const PetscInt *idx;
2693   PetscInt       start,end,*ai,*aj;
2694   PetscBT        table;
2695 
2696   PetscFunctionBegin;
2697   m  = A->rmap->n;
2698   ai = a->i;
2699   aj = a->j;
2700 
2701   if (ov < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"illegal negative overlap value used");
2702 
2703   ierr = PetscMalloc1(m+1,&nidx);CHKERRQ(ierr);
2704   ierr = PetscBTCreate(m,&table);CHKERRQ(ierr);
2705 
2706   for (i=0; i<is_max; i++) {
2707     /* Initialize the two local arrays */
2708     isz  = 0;
2709     ierr = PetscBTMemzero(m,table);CHKERRQ(ierr);
2710 
2711     /* Extract the indices, assume there can be duplicate entries */
2712     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
2713     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
2714 
2715     /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2716     for (j=0; j<n; ++j) {
2717       if (!PetscBTLookupSet(table,idx[j])) nidx[isz++] = idx[j];
2718     }
2719     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
2720     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
2721 
2722     k = 0;
2723     for (j=0; j<ov; j++) { /* for each overlap */
2724       n = isz;
2725       for (; k<n; k++) { /* do only those rows in nidx[k], which are not done yet */
2726         row   = nidx[k];
2727         start = ai[row];
2728         end   = ai[row+1];
2729         for (l = start; l<end; l++) {
2730           val = aj[l];
2731           if (!PetscBTLookupSet(table,val)) nidx[isz++] = val;
2732         }
2733       }
2734     }
2735     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz,nidx,PETSC_COPY_VALUES,(is+i));CHKERRQ(ierr);
2736   }
2737   ierr = PetscBTDestroy(&table);CHKERRQ(ierr);
2738   ierr = PetscFree(nidx);CHKERRQ(ierr);
2739   PetscFunctionReturn(0);
2740 }
2741 
2742 /* -------------------------------------------------------------- */
2743 PetscErrorCode MatPermute_SeqAIJ(Mat A,IS rowp,IS colp,Mat *B)
2744 {
2745   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2746   PetscErrorCode ierr;
2747   PetscInt       i,nz = 0,m = A->rmap->n,n = A->cmap->n;
2748   const PetscInt *row,*col;
2749   PetscInt       *cnew,j,*lens;
2750   IS             icolp,irowp;
2751   PetscInt       *cwork = NULL;
2752   PetscScalar    *vwork = NULL;
2753 
2754   PetscFunctionBegin;
2755   ierr = ISInvertPermutation(rowp,PETSC_DECIDE,&irowp);CHKERRQ(ierr);
2756   ierr = ISGetIndices(irowp,&row);CHKERRQ(ierr);
2757   ierr = ISInvertPermutation(colp,PETSC_DECIDE,&icolp);CHKERRQ(ierr);
2758   ierr = ISGetIndices(icolp,&col);CHKERRQ(ierr);
2759 
2760   /* determine lengths of permuted rows */
2761   ierr = PetscMalloc1(m+1,&lens);CHKERRQ(ierr);
2762   for (i=0; i<m; i++) lens[row[i]] = a->i[i+1] - a->i[i];
2763   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
2764   ierr = MatSetSizes(*B,m,n,m,n);CHKERRQ(ierr);
2765   ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
2766   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2767   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*B,0,lens);CHKERRQ(ierr);
2768   ierr = PetscFree(lens);CHKERRQ(ierr);
2769 
2770   ierr = PetscMalloc1(n,&cnew);CHKERRQ(ierr);
2771   for (i=0; i<m; i++) {
2772     ierr = MatGetRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2773     for (j=0; j<nz; j++) cnew[j] = col[cwork[j]];
2774     ierr = MatSetValues_SeqAIJ(*B,1,&row[i],nz,cnew,vwork,INSERT_VALUES);CHKERRQ(ierr);
2775     ierr = MatRestoreRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2776   }
2777   ierr = PetscFree(cnew);CHKERRQ(ierr);
2778 
2779   (*B)->assembled = PETSC_FALSE;
2780 
2781   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2782   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2783   ierr = ISRestoreIndices(irowp,&row);CHKERRQ(ierr);
2784   ierr = ISRestoreIndices(icolp,&col);CHKERRQ(ierr);
2785   ierr = ISDestroy(&irowp);CHKERRQ(ierr);
2786   ierr = ISDestroy(&icolp);CHKERRQ(ierr);
2787   PetscFunctionReturn(0);
2788 }
2789 
2790 PetscErrorCode MatCopy_SeqAIJ(Mat A,Mat B,MatStructure str)
2791 {
2792   PetscErrorCode ierr;
2793 
2794   PetscFunctionBegin;
2795   /* If the two matrices have the same copy implementation, use fast copy. */
2796   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
2797     Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2798     Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data;
2799 
2800     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");
2801     ierr = PetscMemcpy(b->a,a->a,(a->i[A->rmap->n])*sizeof(PetscScalar));CHKERRQ(ierr);
2802     ierr = PetscObjectStateIncrease((PetscObject)B);CHKERRQ(ierr);
2803   } else {
2804     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2805   }
2806   PetscFunctionReturn(0);
2807 }
2808 
2809 PetscErrorCode MatSetUp_SeqAIJ(Mat A)
2810 {
2811   PetscErrorCode ierr;
2812 
2813   PetscFunctionBegin;
2814   ierr =  MatSeqAIJSetPreallocation_SeqAIJ(A,PETSC_DEFAULT,0);CHKERRQ(ierr);
2815   PetscFunctionReturn(0);
2816 }
2817 
2818 PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A,PetscScalar *array[])
2819 {
2820   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2821 
2822   PetscFunctionBegin;
2823   *array = a->a;
2824   PetscFunctionReturn(0);
2825 }
2826 
2827 PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A,PetscScalar *array[])
2828 {
2829   PetscFunctionBegin;
2830   PetscFunctionReturn(0);
2831 }
2832 
2833 /*
2834    Computes the number of nonzeros per row needed for preallocation when X and Y
2835    have different nonzero structure.
2836 */
2837 PetscErrorCode MatAXPYGetPreallocation_SeqX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *yi,const PetscInt *yj,PetscInt *nnz)
2838 {
2839   PetscInt       i,j,k,nzx,nzy;
2840 
2841   PetscFunctionBegin;
2842   /* Set the number of nonzeros in the new matrix */
2843   for (i=0; i<m; i++) {
2844     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2845     nzx = xi[i+1] - xi[i];
2846     nzy = yi[i+1] - yi[i];
2847     nnz[i] = 0;
2848     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2849       for (; k<nzy && yjj[k]<xjj[j]; k++) nnz[i]++; /* Catch up to X */
2850       if (k<nzy && yjj[k]==xjj[j]) k++;             /* Skip duplicate */
2851       nnz[i]++;
2852     }
2853     for (; k<nzy; k++) nnz[i]++;
2854   }
2855   PetscFunctionReturn(0);
2856 }
2857 
2858 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
2859 {
2860   PetscInt       m = Y->rmap->N;
2861   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2862   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2863   PetscErrorCode ierr;
2864 
2865   PetscFunctionBegin;
2866   /* Set the number of nonzeros in the new matrix */
2867   ierr = MatAXPYGetPreallocation_SeqX_private(m,x->i,x->j,y->i,y->j,nnz);CHKERRQ(ierr);
2868   PetscFunctionReturn(0);
2869 }
2870 
2871 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2872 {
2873   PetscErrorCode ierr;
2874   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
2875   PetscBLASInt   one=1,bnz;
2876 
2877   PetscFunctionBegin;
2878   ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2879   if (str == SAME_NONZERO_PATTERN) {
2880     PetscScalar alpha = a;
2881     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2882     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
2883     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2884   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2885     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2886   } else {
2887     Mat      B;
2888     PetscInt *nnz;
2889     ierr = PetscMalloc1(Y->rmap->N,&nnz);CHKERRQ(ierr);
2890     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2891     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2892     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2893     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2894     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
2895     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
2896     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
2897     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2898     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2899     ierr = PetscFree(nnz);CHKERRQ(ierr);
2900   }
2901   PetscFunctionReturn(0);
2902 }
2903 
2904 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
2905 {
2906 #if defined(PETSC_USE_COMPLEX)
2907   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
2908   PetscInt    i,nz;
2909   PetscScalar *a;
2910 
2911   PetscFunctionBegin;
2912   nz = aij->nz;
2913   a  = aij->a;
2914   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
2915 #else
2916   PetscFunctionBegin;
2917 #endif
2918   PetscFunctionReturn(0);
2919 }
2920 
2921 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2922 {
2923   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2924   PetscErrorCode ierr;
2925   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2926   PetscReal      atmp;
2927   PetscScalar    *x;
2928   MatScalar      *aa;
2929 
2930   PetscFunctionBegin;
2931   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2932   aa = a->a;
2933   ai = a->i;
2934   aj = a->j;
2935 
2936   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2937   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2938   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2939   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2940   for (i=0; i<m; i++) {
2941     ncols = ai[1] - ai[0]; ai++;
2942     x[i]  = 0.0;
2943     for (j=0; j<ncols; j++) {
2944       atmp = PetscAbsScalar(*aa);
2945       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
2946       aa++; aj++;
2947     }
2948   }
2949   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2950   PetscFunctionReturn(0);
2951 }
2952 
2953 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2954 {
2955   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2956   PetscErrorCode ierr;
2957   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
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     if (ncols == A->cmap->n) { /* row is dense */
2974       x[i] = *aa; if (idx) idx[i] = 0;
2975     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
2976       x[i] = 0.0;
2977       if (idx) {
2978         idx[i] = 0; /* in case ncols is zero */
2979         for (j=0;j<ncols;j++) { /* find first implicit 0.0 in the row */
2980           if (aj[j] > j) {
2981             idx[i] = j;
2982             break;
2983           }
2984         }
2985       }
2986     }
2987     for (j=0; j<ncols; j++) {
2988       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
2989       aa++; aj++;
2990     }
2991   }
2992   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2993   PetscFunctionReturn(0);
2994 }
2995 
2996 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2997 {
2998   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2999   PetscErrorCode ierr;
3000   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3001   PetscReal      atmp;
3002   PetscScalar    *x;
3003   MatScalar      *aa;
3004 
3005   PetscFunctionBegin;
3006   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3007   aa = a->a;
3008   ai = a->i;
3009   aj = a->j;
3010 
3011   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3012   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3013   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3014   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);
3015   for (i=0; i<m; i++) {
3016     ncols = ai[1] - ai[0]; ai++;
3017     if (ncols) {
3018       /* Get first nonzero */
3019       for (j = 0; j < ncols; j++) {
3020         atmp = PetscAbsScalar(aa[j]);
3021         if (atmp > 1.0e-12) {
3022           x[i] = atmp;
3023           if (idx) idx[i] = aj[j];
3024           break;
3025         }
3026       }
3027       if (j == ncols) {x[i] = PetscAbsScalar(*aa); if (idx) idx[i] = *aj;}
3028     } else {
3029       x[i] = 0.0; if (idx) idx[i] = 0;
3030     }
3031     for (j = 0; j < ncols; j++) {
3032       atmp = PetscAbsScalar(*aa);
3033       if (atmp > 1.0e-12 && PetscAbsScalar(x[i]) > atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3034       aa++; aj++;
3035     }
3036   }
3037   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3038   PetscFunctionReturn(0);
3039 }
3040 
3041 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3042 {
3043   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
3044   PetscErrorCode  ierr;
3045   PetscInt        i,j,m = A->rmap->n,ncols,n;
3046   const PetscInt  *ai,*aj;
3047   PetscScalar     *x;
3048   const MatScalar *aa;
3049 
3050   PetscFunctionBegin;
3051   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3052   aa = a->a;
3053   ai = a->i;
3054   aj = a->j;
3055 
3056   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3057   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3058   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3059   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3060   for (i=0; i<m; i++) {
3061     ncols = ai[1] - ai[0]; ai++;
3062     if (ncols == A->cmap->n) { /* row is dense */
3063       x[i] = *aa; if (idx) idx[i] = 0;
3064     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3065       x[i] = 0.0;
3066       if (idx) {   /* find first implicit 0.0 in the row */
3067         idx[i] = 0; /* in case ncols is zero */
3068         for (j=0; j<ncols; j++) {
3069           if (aj[j] > j) {
3070             idx[i] = j;
3071             break;
3072           }
3073         }
3074       }
3075     }
3076     for (j=0; j<ncols; j++) {
3077       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3078       aa++; aj++;
3079     }
3080   }
3081   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3082   PetscFunctionReturn(0);
3083 }
3084 
3085 PetscErrorCode MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3086 {
3087   Mat_SeqAIJ      *a = (Mat_SeqAIJ*) A->data;
3088   PetscErrorCode  ierr;
3089   PetscInt        i,bs = PetscAbs(A->rmap->bs),mbs = A->rmap->n/bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3090   MatScalar       *diag,work[25],*v_work;
3091   const PetscReal shift = 0.0;
3092   PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;
3093 
3094   PetscFunctionBegin;
3095   allowzeropivot = PetscNot(A->erroriffailure);
3096   if (a->ibdiagvalid) {
3097     if (values) *values = a->ibdiag;
3098     PetscFunctionReturn(0);
3099   }
3100   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3101   if (!a->ibdiag) {
3102     ierr = PetscMalloc1(bs2*mbs,&a->ibdiag);CHKERRQ(ierr);
3103     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3104   }
3105   diag = a->ibdiag;
3106   if (values) *values = a->ibdiag;
3107   /* factor and invert each block */
3108   switch (bs) {
3109   case 1:
3110     for (i=0; i<mbs; i++) {
3111       ierr = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3112       if (PetscAbsScalar(diag[i] + shift) < PETSC_MACHINE_EPSILON) {
3113         if (allowzeropivot) {
3114           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3115           A->factorerror_zeropivot_value = PetscAbsScalar(diag[i]);
3116           A->factorerror_zeropivot_row   = i;
3117           ierr = PetscInfo3(A,"Zero pivot, row %D pivot %g tolerance %g\n",i,(double)PetscAbsScalar(diag[i]),(double)PETSC_MACHINE_EPSILON);CHKERRQ(ierr);
3118         } 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);
3119       }
3120       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3121     }
3122     break;
3123   case 2:
3124     for (i=0; i<mbs; i++) {
3125       ij[0] = 2*i; ij[1] = 2*i + 1;
3126       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3127       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3128       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3129       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
3130       diag += 4;
3131     }
3132     break;
3133   case 3:
3134     for (i=0; i<mbs; i++) {
3135       ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
3136       ierr  = MatGetValues(A,3,ij,3,ij,diag);CHKERRQ(ierr);
3137       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3138       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3139       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3140       diag += 9;
3141     }
3142     break;
3143   case 4:
3144     for (i=0; i<mbs; i++) {
3145       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3146       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3147       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3148       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3149       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3150       diag += 16;
3151     }
3152     break;
3153   case 5:
3154     for (i=0; i<mbs; i++) {
3155       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3156       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3157       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3158       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3159       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3160       diag += 25;
3161     }
3162     break;
3163   case 6:
3164     for (i=0; i<mbs; i++) {
3165       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;
3166       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3167       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3168       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3169       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3170       diag += 36;
3171     }
3172     break;
3173   case 7:
3174     for (i=0; i<mbs; i++) {
3175       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;
3176       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3177       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3178       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3179       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3180       diag += 49;
3181     }
3182     break;
3183   default:
3184     ierr = PetscMalloc3(bs,&v_work,bs,&v_pivots,bs,&IJ);CHKERRQ(ierr);
3185     for (i=0; i<mbs; i++) {
3186       for (j=0; j<bs; j++) {
3187         IJ[j] = bs*i + j;
3188       }
3189       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3190       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3191       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3192       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3193       diag += bs2;
3194     }
3195     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3196   }
3197   a->ibdiagvalid = PETSC_TRUE;
3198   PetscFunctionReturn(0);
3199 }
3200 
3201 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3202 {
3203   PetscErrorCode ierr;
3204   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3205   PetscScalar    a;
3206   PetscInt       m,n,i,j,col;
3207 
3208   PetscFunctionBegin;
3209   if (!x->assembled) {
3210     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3211     for (i=0; i<m; i++) {
3212       for (j=0; j<aij->imax[i]; j++) {
3213         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3214         col  = (PetscInt)(n*PetscRealPart(a));
3215         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3216       }
3217     }
3218   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet coded");
3219   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3220   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3221   PetscFunctionReturn(0);
3222 }
3223 
3224 /* -------------------------------------------------------------------*/
3225 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3226                                         MatGetRow_SeqAIJ,
3227                                         MatRestoreRow_SeqAIJ,
3228                                         MatMult_SeqAIJ,
3229                                 /*  4*/ MatMultAdd_SeqAIJ,
3230                                         MatMultTranspose_SeqAIJ,
3231                                         MatMultTransposeAdd_SeqAIJ,
3232                                         0,
3233                                         0,
3234                                         0,
3235                                 /* 10*/ 0,
3236                                         MatLUFactor_SeqAIJ,
3237                                         0,
3238                                         MatSOR_SeqAIJ,
3239                                         MatTranspose_SeqAIJ,
3240                                 /*1 5*/ MatGetInfo_SeqAIJ,
3241                                         MatEqual_SeqAIJ,
3242                                         MatGetDiagonal_SeqAIJ,
3243                                         MatDiagonalScale_SeqAIJ,
3244                                         MatNorm_SeqAIJ,
3245                                 /* 20*/ 0,
3246                                         MatAssemblyEnd_SeqAIJ,
3247                                         MatSetOption_SeqAIJ,
3248                                         MatZeroEntries_SeqAIJ,
3249                                 /* 24*/ MatZeroRows_SeqAIJ,
3250                                         0,
3251                                         0,
3252                                         0,
3253                                         0,
3254                                 /* 29*/ MatSetUp_SeqAIJ,
3255                                         0,
3256                                         0,
3257                                         0,
3258                                         0,
3259                                 /* 34*/ MatDuplicate_SeqAIJ,
3260                                         0,
3261                                         0,
3262                                         MatILUFactor_SeqAIJ,
3263                                         0,
3264                                 /* 39*/ MatAXPY_SeqAIJ,
3265                                         MatCreateSubMatrices_SeqAIJ,
3266                                         MatIncreaseOverlap_SeqAIJ,
3267                                         MatGetValues_SeqAIJ,
3268                                         MatCopy_SeqAIJ,
3269                                 /* 44*/ MatGetRowMax_SeqAIJ,
3270                                         MatScale_SeqAIJ,
3271                                         MatShift_SeqAIJ,
3272                                         MatDiagonalSet_SeqAIJ,
3273                                         MatZeroRowsColumns_SeqAIJ,
3274                                 /* 49*/ MatSetRandom_SeqAIJ,
3275                                         MatGetRowIJ_SeqAIJ,
3276                                         MatRestoreRowIJ_SeqAIJ,
3277                                         MatGetColumnIJ_SeqAIJ,
3278                                         MatRestoreColumnIJ_SeqAIJ,
3279                                 /* 54*/ MatFDColoringCreate_SeqXAIJ,
3280                                         0,
3281                                         0,
3282                                         MatPermute_SeqAIJ,
3283                                         0,
3284                                 /* 59*/ 0,
3285                                         MatDestroy_SeqAIJ,
3286                                         MatView_SeqAIJ,
3287                                         0,
3288                                         MatMatMatMult_SeqAIJ_SeqAIJ_SeqAIJ,
3289                                 /* 64*/ MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ,
3290                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3291                                         0,
3292                                         0,
3293                                         0,
3294                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3295                                         MatGetRowMinAbs_SeqAIJ,
3296                                         0,
3297                                         0,
3298                                         0,
3299                                 /* 74*/ 0,
3300                                         MatFDColoringApply_AIJ,
3301                                         0,
3302                                         0,
3303                                         0,
3304                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3305                                         0,
3306                                         0,
3307                                         0,
3308                                         MatLoad_SeqAIJ,
3309                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3310                                         MatIsHermitian_SeqAIJ,
3311                                         0,
3312                                         0,
3313                                         0,
3314                                 /* 89*/ MatMatMult_SeqAIJ_SeqAIJ,
3315                                         MatMatMultSymbolic_SeqAIJ_SeqAIJ,
3316                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3317                                         MatPtAP_SeqAIJ_SeqAIJ,
3318                                         MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy,
3319                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy,
3320                                         MatMatTransposeMult_SeqAIJ_SeqAIJ,
3321                                         MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ,
3322                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3323                                         0,
3324                                 /* 99*/ 0,
3325                                         0,
3326                                         0,
3327                                         MatConjugate_SeqAIJ,
3328                                         0,
3329                                 /*104*/ MatSetValuesRow_SeqAIJ,
3330                                         MatRealPart_SeqAIJ,
3331                                         MatImaginaryPart_SeqAIJ,
3332                                         0,
3333                                         0,
3334                                 /*109*/ MatMatSolve_SeqAIJ,
3335                                         0,
3336                                         MatGetRowMin_SeqAIJ,
3337                                         0,
3338                                         MatMissingDiagonal_SeqAIJ,
3339                                 /*114*/ 0,
3340                                         0,
3341                                         0,
3342                                         0,
3343                                         0,
3344                                 /*119*/ 0,
3345                                         0,
3346                                         0,
3347                                         0,
3348                                         MatGetMultiProcBlock_SeqAIJ,
3349                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3350                                         MatGetColumnNorms_SeqAIJ,
3351                                         MatInvertBlockDiagonal_SeqAIJ,
3352                                         MatInvertVariableBlockDiagonal_SeqAIJ,
3353                                         0,
3354                                 /*129*/ 0,
3355                                         MatTransposeMatMult_SeqAIJ_SeqAIJ,
3356                                         MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ,
3357                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3358                                         MatTransposeColoringCreate_SeqAIJ,
3359                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3360                                         MatTransColoringApplyDenToSp_SeqAIJ,
3361                                         MatRARt_SeqAIJ_SeqAIJ,
3362                                         MatRARtSymbolic_SeqAIJ_SeqAIJ,
3363                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3364                                  /*139*/0,
3365                                         0,
3366                                         0,
3367                                         MatFDColoringSetUp_SeqXAIJ,
3368                                         MatFindOffBlockDiagonalEntries_SeqAIJ,
3369                                  /*144*/MatCreateMPIMatConcatenateSeqMat_SeqAIJ,
3370                                         MatDestroySubMatrices_SeqAIJ
3371 };
3372 
3373 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3374 {
3375   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3376   PetscInt   i,nz,n;
3377 
3378   PetscFunctionBegin;
3379   nz = aij->maxnz;
3380   n  = mat->rmap->n;
3381   for (i=0; i<nz; i++) {
3382     aij->j[i] = indices[i];
3383   }
3384   aij->nz = nz;
3385   for (i=0; i<n; i++) {
3386     aij->ilen[i] = aij->imax[i];
3387   }
3388   PetscFunctionReturn(0);
3389 }
3390 
3391 /*
3392  * When a sparse matrix has many zero columns, we should compact them out to save the space
3393  * This happens in MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable()
3394  * */
3395 PetscErrorCode  MatSeqAIJCompactOutExtraColumns_SeqAIJ(Mat mat, ISLocalToGlobalMapping *mapping)
3396 {
3397   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3398   PetscTable         gid1_lid1;
3399   PetscTablePosition tpos;
3400   PetscInt           gid,lid,i,j,ncols,ec;
3401   PetscInt           *garray;
3402   PetscErrorCode  ierr;
3403 
3404   PetscFunctionBegin;
3405   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3406   PetscValidPointer(mapping,2);
3407   /* use a table */
3408   ierr = PetscTableCreate(mat->rmap->n,mat->cmap->N+1,&gid1_lid1);CHKERRQ(ierr);
3409   ec = 0;
3410   for (i=0; i<mat->rmap->n; i++) {
3411     ncols = aij->i[i+1] - aij->i[i];
3412     for (j=0; j<ncols; j++) {
3413       PetscInt data,gid1 = aij->j[aij->i[i] + j] + 1;
3414       ierr = PetscTableFind(gid1_lid1,gid1,&data);CHKERRQ(ierr);
3415       if (!data) {
3416         /* one based table */
3417         ierr = PetscTableAdd(gid1_lid1,gid1,++ec,INSERT_VALUES);CHKERRQ(ierr);
3418       }
3419     }
3420   }
3421   /* form array of columns we need */
3422   ierr = PetscMalloc1(ec+1,&garray);CHKERRQ(ierr);
3423   ierr = PetscTableGetHeadPosition(gid1_lid1,&tpos);CHKERRQ(ierr);
3424   while (tpos) {
3425     ierr = PetscTableGetNext(gid1_lid1,&tpos,&gid,&lid);CHKERRQ(ierr);
3426     gid--;
3427     lid--;
3428     garray[lid] = gid;
3429   }
3430   ierr = PetscSortInt(ec,garray);CHKERRQ(ierr); /* sort, and rebuild */
3431   ierr = PetscTableRemoveAll(gid1_lid1);CHKERRQ(ierr);
3432   for (i=0; i<ec; i++) {
3433     ierr = PetscTableAdd(gid1_lid1,garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
3434   }
3435   /* compact out the extra columns in B */
3436   for (i=0; i<mat->rmap->n; i++) {
3437 	ncols = aij->i[i+1] - aij->i[i];
3438     for (j=0; j<ncols; j++) {
3439       PetscInt gid1 = aij->j[aij->i[i] + j] + 1;
3440       ierr = PetscTableFind(gid1_lid1,gid1,&lid);CHKERRQ(ierr);
3441       lid--;
3442       aij->j[aij->i[i] + j] = lid;
3443     }
3444   }
3445   mat->cmap->n = mat->cmap->N = ec;
3446   mat->cmap->bs = 1;
3447 
3448   ierr = PetscTableDestroy(&gid1_lid1);CHKERRQ(ierr);
3449   ierr = PetscLayoutSetUp((mat->cmap));CHKERRQ(ierr);
3450   ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,mat->cmap->bs,mat->cmap->n,garray,PETSC_OWN_POINTER,mapping);CHKERRQ(ierr);
3451   ierr = ISLocalToGlobalMappingSetType(*mapping,ISLOCALTOGLOBALMAPPINGHASH);CHKERRQ(ierr);
3452   PetscFunctionReturn(0);
3453 }
3454 
3455 /*@
3456     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3457        in the matrix.
3458 
3459   Input Parameters:
3460 +  mat - the SeqAIJ matrix
3461 -  indices - the column indices
3462 
3463   Level: advanced
3464 
3465   Notes:
3466     This can be called if you have precomputed the nonzero structure of the
3467   matrix and want to provide it to the matrix object to improve the performance
3468   of the MatSetValues() operation.
3469 
3470     You MUST have set the correct numbers of nonzeros per row in the call to
3471   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3472 
3473     MUST be called before any calls to MatSetValues();
3474 
3475     The indices should start with zero, not one.
3476 
3477 @*/
3478 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3479 {
3480   PetscErrorCode ierr;
3481 
3482   PetscFunctionBegin;
3483   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3484   PetscValidPointer(indices,2);
3485   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3486   PetscFunctionReturn(0);
3487 }
3488 
3489 /* ----------------------------------------------------------------------------------------*/
3490 
3491 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3492 {
3493   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3494   PetscErrorCode ierr;
3495   size_t         nz = aij->i[mat->rmap->n];
3496 
3497   PetscFunctionBegin;
3498   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3499 
3500   /* allocate space for values if not already there */
3501   if (!aij->saved_values) {
3502     ierr = PetscMalloc1(nz+1,&aij->saved_values);CHKERRQ(ierr);
3503     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3504   }
3505 
3506   /* copy values over */
3507   ierr = PetscMemcpy(aij->saved_values,aij->a,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3508   PetscFunctionReturn(0);
3509 }
3510 
3511 /*@
3512     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3513        example, reuse of the linear part of a Jacobian, while recomputing the
3514        nonlinear portion.
3515 
3516    Collect on Mat
3517 
3518   Input Parameters:
3519 .  mat - the matrix (currently only AIJ matrices support this option)
3520 
3521   Level: advanced
3522 
3523   Common Usage, with SNESSolve():
3524 $    Create Jacobian matrix
3525 $    Set linear terms into matrix
3526 $    Apply boundary conditions to matrix, at this time matrix must have
3527 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3528 $      boundary conditions again will not change the nonzero structure
3529 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3530 $    ierr = MatStoreValues(mat);
3531 $    Call SNESSetJacobian() with matrix
3532 $    In your Jacobian routine
3533 $      ierr = MatRetrieveValues(mat);
3534 $      Set nonlinear terms in matrix
3535 
3536   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3537 $    // build linear portion of Jacobian
3538 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3539 $    ierr = MatStoreValues(mat);
3540 $    loop over nonlinear iterations
3541 $       ierr = MatRetrieveValues(mat);
3542 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3543 $       // call MatAssemblyBegin/End() on matrix
3544 $       Solve linear system with Jacobian
3545 $    endloop
3546 
3547   Notes:
3548     Matrix must already be assemblied before calling this routine
3549     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3550     calling this routine.
3551 
3552     When this is called multiple times it overwrites the previous set of stored values
3553     and does not allocated additional space.
3554 
3555 .seealso: MatRetrieveValues()
3556 
3557 @*/
3558 PetscErrorCode  MatStoreValues(Mat mat)
3559 {
3560   PetscErrorCode ierr;
3561 
3562   PetscFunctionBegin;
3563   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3564   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3565   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3566   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3567   PetscFunctionReturn(0);
3568 }
3569 
3570 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3571 {
3572   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3573   PetscErrorCode ierr;
3574   PetscInt       nz = aij->i[mat->rmap->n];
3575 
3576   PetscFunctionBegin;
3577   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3578   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3579   /* copy values over */
3580   ierr = PetscMemcpy(aij->a,aij->saved_values,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3581   PetscFunctionReturn(0);
3582 }
3583 
3584 /*@
3585     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3586        example, reuse of the linear part of a Jacobian, while recomputing the
3587        nonlinear portion.
3588 
3589    Collect on Mat
3590 
3591   Input Parameters:
3592 .  mat - the matrix (currently only AIJ matrices support this option)
3593 
3594   Level: advanced
3595 
3596 .seealso: MatStoreValues()
3597 
3598 @*/
3599 PetscErrorCode  MatRetrieveValues(Mat mat)
3600 {
3601   PetscErrorCode ierr;
3602 
3603   PetscFunctionBegin;
3604   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3605   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3606   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3607   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3608   PetscFunctionReturn(0);
3609 }
3610 
3611 
3612 /* --------------------------------------------------------------------------------*/
3613 /*@C
3614    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3615    (the default parallel PETSc format).  For good matrix assembly performance
3616    the user should preallocate the matrix storage by setting the parameter nz
3617    (or the array nnz).  By setting these parameters accurately, performance
3618    during matrix assembly can be increased by more than a factor of 50.
3619 
3620    Collective on MPI_Comm
3621 
3622    Input Parameters:
3623 +  comm - MPI communicator, set to PETSC_COMM_SELF
3624 .  m - number of rows
3625 .  n - number of columns
3626 .  nz - number of nonzeros per row (same for all rows)
3627 -  nnz - array containing the number of nonzeros in the various rows
3628          (possibly different for each row) or NULL
3629 
3630    Output Parameter:
3631 .  A - the matrix
3632 
3633    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3634    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3635    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3636 
3637    Notes:
3638    If nnz is given then nz is ignored
3639 
3640    The AIJ format (also called the Yale sparse matrix format or
3641    compressed row storage), is fully compatible with standard Fortran 77
3642    storage.  That is, the stored row and column indices can begin at
3643    either one (as in Fortran) or zero.  See the users' manual for details.
3644 
3645    Specify the preallocated storage with either nz or nnz (not both).
3646    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3647    allocation.  For large problems you MUST preallocate memory or you
3648    will get TERRIBLE performance, see the users' manual chapter on matrices.
3649 
3650    By default, this format uses inodes (identical nodes) when possible, to
3651    improve numerical efficiency of matrix-vector products and solves. We
3652    search for consecutive rows with the same nonzero structure, thereby
3653    reusing matrix information to achieve increased efficiency.
3654 
3655    Options Database Keys:
3656 +  -mat_no_inode  - Do not use inodes
3657 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3658 
3659    Level: intermediate
3660 
3661 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3662 
3663 @*/
3664 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3665 {
3666   PetscErrorCode ierr;
3667 
3668   PetscFunctionBegin;
3669   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3670   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3671   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3672   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3673   PetscFunctionReturn(0);
3674 }
3675 
3676 /*@C
3677    MatSeqAIJSetPreallocation - For good matrix assembly performance
3678    the user should preallocate the matrix storage by setting the parameter nz
3679    (or the array nnz).  By setting these parameters accurately, performance
3680    during matrix assembly can be increased by more than a factor of 50.
3681 
3682    Collective on MPI_Comm
3683 
3684    Input Parameters:
3685 +  B - The matrix
3686 .  nz - number of nonzeros per row (same for all rows)
3687 -  nnz - array containing the number of nonzeros in the various rows
3688          (possibly different for each row) or NULL
3689 
3690    Notes:
3691      If nnz is given then nz is ignored
3692 
3693     The AIJ format (also called the Yale sparse matrix format or
3694    compressed row storage), is fully compatible with standard Fortran 77
3695    storage.  That is, the stored row and column indices can begin at
3696    either one (as in Fortran) or zero.  See the users' manual for details.
3697 
3698    Specify the preallocated storage with either nz or nnz (not both).
3699    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3700    allocation.  For large problems you MUST preallocate memory or you
3701    will get TERRIBLE performance, see the users' manual chapter on matrices.
3702 
3703    You can call MatGetInfo() to get information on how effective the preallocation was;
3704    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3705    You can also run with the option -info and look for messages with the string
3706    malloc in them to see if additional memory allocation was needed.
3707 
3708    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3709    entries or columns indices
3710 
3711    By default, this format uses inodes (identical nodes) when possible, to
3712    improve numerical efficiency of matrix-vector products and solves. We
3713    search for consecutive rows with the same nonzero structure, thereby
3714    reusing matrix information to achieve increased efficiency.
3715 
3716    Options Database Keys:
3717 +  -mat_no_inode  - Do not use inodes
3718 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3719 
3720    Level: intermediate
3721 
3722 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatGetInfo()
3723 
3724 @*/
3725 PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
3726 {
3727   PetscErrorCode ierr;
3728 
3729   PetscFunctionBegin;
3730   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3731   PetscValidType(B,1);
3732   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));CHKERRQ(ierr);
3733   PetscFunctionReturn(0);
3734 }
3735 
3736 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3737 {
3738   Mat_SeqAIJ     *b;
3739   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3740   PetscErrorCode ierr;
3741   PetscInt       i;
3742 
3743   PetscFunctionBegin;
3744   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3745   if (nz == MAT_SKIP_ALLOCATION) {
3746     skipallocation = PETSC_TRUE;
3747     nz             = 0;
3748   }
3749   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3750   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3751 
3752   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3753   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %D",nz);
3754   if (nnz) {
3755     for (i=0; i<B->rmap->n; i++) {
3756       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]);
3757       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);
3758     }
3759   }
3760 
3761   B->preallocated = PETSC_TRUE;
3762 
3763   b = (Mat_SeqAIJ*)B->data;
3764 
3765   if (!skipallocation) {
3766     if (!b->imax) {
3767       ierr = PetscMalloc2(B->rmap->n,&b->imax,B->rmap->n,&b->ilen);CHKERRQ(ierr);
3768       ierr = PetscLogObjectMemory((PetscObject)B,2*B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3769     }
3770     if (!b->ipre) {
3771       ierr = PetscMalloc1(B->rmap->n,&b->ipre);CHKERRQ(ierr);
3772       ierr = PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3773     }
3774     if (!nnz) {
3775       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3776       else if (nz < 0) nz = 1;
3777       nz = PetscMin(nz,B->cmap->n);
3778       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
3779       nz = nz*B->rmap->n;
3780     } else {
3781       nz = 0;
3782       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz += nnz[i];}
3783     }
3784     /* b->ilen will count nonzeros in each row so far. */
3785     for (i=0; i<B->rmap->n; i++) b->ilen[i] = 0;
3786 
3787     /* allocate the matrix space */
3788     /* FIXME: should B's old memory be unlogged? */
3789     ierr = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
3790     if (B->structure_only) {
3791       ierr = PetscMalloc1(nz,&b->j);CHKERRQ(ierr);
3792       ierr = PetscMalloc1(B->rmap->n+1,&b->i);CHKERRQ(ierr);
3793       ierr = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*sizeof(PetscInt));CHKERRQ(ierr);
3794     } else {
3795       ierr = PetscMalloc3(nz,&b->a,nz,&b->j,B->rmap->n+1,&b->i);CHKERRQ(ierr);
3796       ierr = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
3797     }
3798     b->i[0] = 0;
3799     for (i=1; i<B->rmap->n+1; i++) {
3800       b->i[i] = b->i[i-1] + b->imax[i-1];
3801     }
3802     if (B->structure_only) {
3803       b->singlemalloc = PETSC_FALSE;
3804       b->free_a       = PETSC_FALSE;
3805     } else {
3806       b->singlemalloc = PETSC_TRUE;
3807       b->free_a       = PETSC_TRUE;
3808     }
3809     b->free_ij      = PETSC_TRUE;
3810   } else {
3811     b->free_a  = PETSC_FALSE;
3812     b->free_ij = PETSC_FALSE;
3813   }
3814 
3815   if (b->ipre && nnz != b->ipre  && b->imax) {
3816     /* reserve user-requested sparsity */
3817     ierr = PetscMemcpy(b->ipre,b->imax,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3818   }
3819 
3820 
3821   b->nz               = 0;
3822   b->maxnz            = nz;
3823   B->info.nz_unneeded = (double)b->maxnz;
3824   if (realalloc) {
3825     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3826   }
3827   B->was_assembled = PETSC_FALSE;
3828   B->assembled     = PETSC_FALSE;
3829   PetscFunctionReturn(0);
3830 }
3831 
3832 
3833 PetscErrorCode MatResetPreallocation_SeqAIJ(Mat A)
3834 {
3835   Mat_SeqAIJ     *a;
3836   PetscInt       i;
3837   PetscErrorCode ierr;
3838 
3839   PetscFunctionBegin;
3840   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3841   a = (Mat_SeqAIJ*)A->data;
3842   /* if no saved info, we error out */
3843   if (!a->ipre) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_NULL,"No saved preallocation info \n");
3844 
3845   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");
3846 
3847   ierr = PetscMemcpy(a->imax,a->ipre,A->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3848   ierr = PetscMemzero(a->ilen,A->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3849   a->i[0] = 0;
3850   for (i=1; i<A->rmap->n+1; i++) {
3851     a->i[i] = a->i[i-1] + a->imax[i-1];
3852   }
3853   A->preallocated     = PETSC_TRUE;
3854   a->nz               = 0;
3855   a->maxnz            = a->i[A->rmap->n];
3856   A->info.nz_unneeded = (double)a->maxnz;
3857   A->was_assembled    = PETSC_FALSE;
3858   A->assembled        = PETSC_FALSE;
3859   PetscFunctionReturn(0);
3860 }
3861 
3862 /*@
3863    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
3864 
3865    Input Parameters:
3866 +  B - the matrix
3867 .  i - the indices into j for the start of each row (starts with zero)
3868 .  j - the column indices for each row (starts with zero) these must be sorted for each row
3869 -  v - optional values in the matrix
3870 
3871    Level: developer
3872 
3873    The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
3874 
3875 .keywords: matrix, aij, compressed row, sparse, sequential
3876 
3877 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), MATSEQAIJ
3878 @*/
3879 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
3880 {
3881   PetscErrorCode ierr;
3882 
3883   PetscFunctionBegin;
3884   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3885   PetscValidType(B,1);
3886   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3887   PetscFunctionReturn(0);
3888 }
3889 
3890 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3891 {
3892   PetscInt       i;
3893   PetscInt       m,n;
3894   PetscInt       nz;
3895   PetscInt       *nnz, nz_max = 0;
3896   PetscScalar    *values;
3897   PetscErrorCode ierr;
3898 
3899   PetscFunctionBegin;
3900   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
3901 
3902   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3903   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3904 
3905   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
3906   ierr = PetscMalloc1(m+1, &nnz);CHKERRQ(ierr);
3907   for (i = 0; i < m; i++) {
3908     nz     = Ii[i+1]- Ii[i];
3909     nz_max = PetscMax(nz_max, nz);
3910     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
3911     nnz[i] = nz;
3912   }
3913   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
3914   ierr = PetscFree(nnz);CHKERRQ(ierr);
3915 
3916   if (v) {
3917     values = (PetscScalar*) v;
3918   } else {
3919     ierr = PetscCalloc1(nz_max, &values);CHKERRQ(ierr);
3920   }
3921 
3922   for (i = 0; i < m; i++) {
3923     nz   = Ii[i+1] - Ii[i];
3924     ierr = MatSetValues_SeqAIJ(B, 1, &i, nz, J+Ii[i], values + (v ? Ii[i] : 0), INSERT_VALUES);CHKERRQ(ierr);
3925   }
3926 
3927   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3928   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3929 
3930   if (!v) {
3931     ierr = PetscFree(values);CHKERRQ(ierr);
3932   }
3933   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3934   PetscFunctionReturn(0);
3935 }
3936 
3937 #include <../src/mat/impls/dense/seq/dense.h>
3938 #include <petsc/private/kernels/petscaxpy.h>
3939 
3940 /*
3941     Computes (B'*A')' since computing B*A directly is untenable
3942 
3943                n                       p                          p
3944         (              )       (              )         (                  )
3945       m (      A       )  *  n (       B      )   =   m (         C        )
3946         (              )       (              )         (                  )
3947 
3948 */
3949 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
3950 {
3951   PetscErrorCode    ierr;
3952   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
3953   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
3954   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
3955   PetscInt          i,n,m,q,p;
3956   const PetscInt    *ii,*idx;
3957   const PetscScalar *b,*a,*a_q;
3958   PetscScalar       *c,*c_q;
3959 
3960   PetscFunctionBegin;
3961   m    = A->rmap->n;
3962   n    = A->cmap->n;
3963   p    = B->cmap->n;
3964   a    = sub_a->v;
3965   b    = sub_b->a;
3966   c    = sub_c->v;
3967   ierr = PetscMemzero(c,m*p*sizeof(PetscScalar));CHKERRQ(ierr);
3968 
3969   ii  = sub_b->i;
3970   idx = sub_b->j;
3971   for (i=0; i<n; i++) {
3972     q = ii[i+1] - ii[i];
3973     while (q-->0) {
3974       c_q = c + m*(*idx);
3975       a_q = a + m*i;
3976       PetscKernelAXPY(c_q,*b,a_q,m);
3977       idx++;
3978       b++;
3979     }
3980   }
3981   PetscFunctionReturn(0);
3982 }
3983 
3984 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
3985 {
3986   PetscErrorCode ierr;
3987   PetscInt       m=A->rmap->n,n=B->cmap->n;
3988   Mat            Cmat;
3989 
3990   PetscFunctionBegin;
3991   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);
3992   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
3993   ierr = MatSetSizes(Cmat,m,n,m,n);CHKERRQ(ierr);
3994   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
3995   ierr = MatSetType(Cmat,MATSEQDENSE);CHKERRQ(ierr);
3996   ierr = MatSeqDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
3997 
3998   Cmat->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
3999 
4000   *C = Cmat;
4001   PetscFunctionReturn(0);
4002 }
4003 
4004 /* ----------------------------------------------------------------*/
4005 PETSC_INTERN PetscErrorCode MatMatMult_SeqDense_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4006 {
4007   PetscErrorCode ierr;
4008 
4009   PetscFunctionBegin;
4010   if (scall == MAT_INITIAL_MATRIX) {
4011     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4012     ierr = MatMatMultSymbolic_SeqDense_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
4013     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4014   }
4015   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4016   ierr = MatMatMultNumeric_SeqDense_SeqAIJ(A,B,*C);CHKERRQ(ierr);
4017   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4018   PetscFunctionReturn(0);
4019 }
4020 
4021 
4022 /*MC
4023    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
4024    based on compressed sparse row format.
4025 
4026    Options Database Keys:
4027 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
4028 
4029   Level: beginner
4030 
4031 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
4032 M*/
4033 
4034 /*MC
4035    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
4036 
4037    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
4038    and MATMPIAIJ otherwise.  As a result, for single process communicators,
4039   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
4040   for communicators controlling multiple processes.  It is recommended that you call both of
4041   the above preallocation routines for simplicity.
4042 
4043    Options Database Keys:
4044 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
4045 
4046   Developer Notes:
4047     Subclasses include MATAIJCUSPARSE, MATAIJPERM, MATAIJSELL, MATAIJMKL, MATAIJCRL, and also automatically switches over to use inodes when
4048    enough exist.
4049 
4050   Level: beginner
4051 
4052 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
4053 M*/
4054 
4055 /*MC
4056    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
4057 
4058    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
4059    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
4060    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
4061   for communicators controlling multiple processes.  It is recommended that you call both of
4062   the above preallocation routines for simplicity.
4063 
4064    Options Database Keys:
4065 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
4066 
4067   Level: beginner
4068 
4069 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
4070 M*/
4071 
4072 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
4073 #if defined(PETSC_HAVE_ELEMENTAL)
4074 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4075 #endif
4076 #if defined(PETSC_HAVE_HYPRE)
4077 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat A,MatType,MatReuse,Mat*);
4078 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
4079 #endif
4080 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqDense(Mat,MatType,MatReuse,Mat*);
4081 
4082 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqSELL(Mat,MatType,MatReuse,Mat*);
4083 PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat,MatType,MatReuse,Mat*);
4084 PETSC_INTERN PetscErrorCode MatPtAP_IS_XAIJ(Mat,Mat,MatReuse,PetscReal,Mat*);
4085 
4086 /*@C
4087    MatSeqAIJGetArray - gives access to the array where the data for a MATSEQAIJ matrix is stored
4088 
4089    Not Collective
4090 
4091    Input Parameter:
4092 .  mat - a MATSEQAIJ matrix
4093 
4094    Output Parameter:
4095 .   array - pointer to the data
4096 
4097    Level: intermediate
4098 
4099 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4100 @*/
4101 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4102 {
4103   PetscErrorCode ierr;
4104 
4105   PetscFunctionBegin;
4106   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4107   PetscFunctionReturn(0);
4108 }
4109 
4110 /*@C
4111    MatSeqAIJGetMaxRowNonzeros - returns the maximum number of nonzeros in any row
4112 
4113    Not Collective
4114 
4115    Input Parameter:
4116 .  mat - a MATSEQAIJ matrix
4117 
4118    Output Parameter:
4119 .   nz - the maximum number of nonzeros in any row
4120 
4121    Level: intermediate
4122 
4123 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4124 @*/
4125 PetscErrorCode  MatSeqAIJGetMaxRowNonzeros(Mat A,PetscInt *nz)
4126 {
4127   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
4128 
4129   PetscFunctionBegin;
4130   *nz = aij->rmax;
4131   PetscFunctionReturn(0);
4132 }
4133 
4134 /*@C
4135    MatSeqAIJRestoreArray - returns access to the array where the data for a MATSEQAIJ matrix is stored obtained by MatSeqAIJGetArray()
4136 
4137    Not Collective
4138 
4139    Input Parameters:
4140 .  mat - a MATSEQAIJ matrix
4141 .  array - pointer to the data
4142 
4143    Level: intermediate
4144 
4145 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4146 @*/
4147 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4148 {
4149   PetscErrorCode ierr;
4150 
4151   PetscFunctionBegin;
4152   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4153   PetscFunctionReturn(0);
4154 }
4155 
4156 #if defined(PETSC_HAVE_CUDA)
4157 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat);
4158 #endif
4159 
4160 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4161 {
4162   Mat_SeqAIJ     *b;
4163   PetscErrorCode ierr;
4164   PetscMPIInt    size;
4165 
4166   PetscFunctionBegin;
4167   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4168   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4169 
4170   ierr = PetscNewLog(B,&b);CHKERRQ(ierr);
4171 
4172   B->data = (void*)b;
4173 
4174   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4175 
4176   b->row                = 0;
4177   b->col                = 0;
4178   b->icol               = 0;
4179   b->reallocs           = 0;
4180   b->ignorezeroentries  = PETSC_FALSE;
4181   b->roworiented        = PETSC_TRUE;
4182   b->nonew              = 0;
4183   b->diag               = 0;
4184   b->solve_work         = 0;
4185   B->spptr              = 0;
4186   b->saved_values       = 0;
4187   b->idiag              = 0;
4188   b->mdiag              = 0;
4189   b->ssor_work          = 0;
4190   b->omega              = 1.0;
4191   b->fshift             = 0.0;
4192   b->idiagvalid         = PETSC_FALSE;
4193   b->ibdiagvalid        = PETSC_FALSE;
4194   b->keepnonzeropattern = PETSC_FALSE;
4195 
4196   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4197   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4198   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4199 
4200 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4201   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4202   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4203 #endif
4204 
4205   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4206   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4207   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4208   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4209   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4210   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4211   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijsell_C",MatConvert_SeqAIJ_SeqAIJSELL);CHKERRQ(ierr);
4212 #if defined(PETSC_HAVE_MKL_SPARSE)
4213   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijmkl_C",MatConvert_SeqAIJ_SeqAIJMKL);CHKERRQ(ierr);
4214 #endif
4215 #if defined(PETSC_HAVE_CUDA)
4216   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcusparse_C",MatConvert_SeqAIJ_SeqAIJCUSPARSE);CHKERRQ(ierr);
4217 #endif
4218   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4219 #if defined(PETSC_HAVE_ELEMENTAL)
4220   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_elemental_C",MatConvert_SeqAIJ_Elemental);CHKERRQ(ierr);
4221 #endif
4222 #if defined(PETSC_HAVE_HYPRE)
4223   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
4224   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_seqaij_seqaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
4225 #endif
4226   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqdense_C",MatConvert_SeqAIJ_SeqDense);CHKERRQ(ierr);
4227   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsell_C",MatConvert_SeqAIJ_SeqSELL);CHKERRQ(ierr);
4228   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_is_C",MatConvert_XAIJ_IS);CHKERRQ(ierr);
4229   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4230   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4231   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4232   ierr = PetscObjectComposeFunction((PetscObject)B,"MatResetPreallocation_C",MatResetPreallocation_SeqAIJ);CHKERRQ(ierr);
4233   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4234   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4235   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaij_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
4236   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaij_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
4237   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaij_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
4238   ierr = PetscObjectComposeFunction((PetscObject)B,"MatPtAP_is_seqaij_C",MatPtAP_IS_XAIJ);CHKERRQ(ierr);
4239   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4240   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4241   ierr = MatSeqAIJSetTypeFromOptions(B);CHKERRQ(ierr);  /* this allows changing the matrix subtype to say MATSEQAIJPERM */
4242   PetscFunctionReturn(0);
4243 }
4244 
4245 /*
4246     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4247 */
4248 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4249 {
4250   Mat_SeqAIJ     *c,*a = (Mat_SeqAIJ*)A->data;
4251   PetscErrorCode ierr;
4252   PetscInt       i,m = A->rmap->n;
4253 
4254   PetscFunctionBegin;
4255   c = (Mat_SeqAIJ*)C->data;
4256 
4257   C->factortype = A->factortype;
4258   c->row        = 0;
4259   c->col        = 0;
4260   c->icol       = 0;
4261   c->reallocs   = 0;
4262 
4263   C->assembled = PETSC_TRUE;
4264 
4265   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4266   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4267 
4268   ierr = PetscMalloc2(m,&c->imax,m,&c->ilen);CHKERRQ(ierr);
4269   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4270   for (i=0; i<m; i++) {
4271     c->imax[i] = a->imax[i];
4272     c->ilen[i] = a->ilen[i];
4273   }
4274 
4275   /* allocate the matrix space */
4276   if (mallocmatspace) {
4277     ierr = PetscMalloc3(a->i[m],&c->a,a->i[m],&c->j,m+1,&c->i);CHKERRQ(ierr);
4278     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4279 
4280     c->singlemalloc = PETSC_TRUE;
4281 
4282     ierr = PetscMemcpy(c->i,a->i,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4283     if (m > 0) {
4284       ierr = PetscMemcpy(c->j,a->j,(a->i[m])*sizeof(PetscInt));CHKERRQ(ierr);
4285       if (cpvalues == MAT_COPY_VALUES) {
4286         ierr = PetscMemcpy(c->a,a->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4287       } else {
4288         ierr = PetscMemzero(c->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4289       }
4290     }
4291   }
4292 
4293   c->ignorezeroentries = a->ignorezeroentries;
4294   c->roworiented       = a->roworiented;
4295   c->nonew             = a->nonew;
4296   if (a->diag) {
4297     ierr = PetscMalloc1(m+1,&c->diag);CHKERRQ(ierr);
4298     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4299     for (i=0; i<m; i++) {
4300       c->diag[i] = a->diag[i];
4301     }
4302   } else c->diag = 0;
4303 
4304   c->solve_work         = 0;
4305   c->saved_values       = 0;
4306   c->idiag              = 0;
4307   c->ssor_work          = 0;
4308   c->keepnonzeropattern = a->keepnonzeropattern;
4309   c->free_a             = PETSC_TRUE;
4310   c->free_ij            = PETSC_TRUE;
4311 
4312   c->rmax         = a->rmax;
4313   c->nz           = a->nz;
4314   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4315   C->preallocated = PETSC_TRUE;
4316 
4317   c->compressedrow.use   = a->compressedrow.use;
4318   c->compressedrow.nrows = a->compressedrow.nrows;
4319   if (a->compressedrow.use) {
4320     i    = a->compressedrow.nrows;
4321     ierr = PetscMalloc2(i+1,&c->compressedrow.i,i,&c->compressedrow.rindex);CHKERRQ(ierr);
4322     ierr = PetscMemcpy(c->compressedrow.i,a->compressedrow.i,(i+1)*sizeof(PetscInt));CHKERRQ(ierr);
4323     ierr = PetscMemcpy(c->compressedrow.rindex,a->compressedrow.rindex,i*sizeof(PetscInt));CHKERRQ(ierr);
4324   } else {
4325     c->compressedrow.use    = PETSC_FALSE;
4326     c->compressedrow.i      = NULL;
4327     c->compressedrow.rindex = NULL;
4328   }
4329   c->nonzerorowcnt = a->nonzerorowcnt;
4330   C->nonzerostate  = A->nonzerostate;
4331 
4332   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4333   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4334   PetscFunctionReturn(0);
4335 }
4336 
4337 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4338 {
4339   PetscErrorCode ierr;
4340 
4341   PetscFunctionBegin;
4342   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4343   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4344   if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) {
4345     ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
4346   }
4347   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4348   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4349   PetscFunctionReturn(0);
4350 }
4351 
4352 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4353 {
4354   PetscBool      isbinary, ishdf5;
4355   PetscErrorCode ierr;
4356 
4357   PetscFunctionBegin;
4358   PetscValidHeaderSpecific(newMat,MAT_CLASSID,1);
4359   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
4360   /* force binary viewer to load .info file if it has not yet done so */
4361   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
4362   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
4363   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,  &ishdf5);CHKERRQ(ierr);
4364   if (isbinary) {
4365     ierr = MatLoad_SeqAIJ_Binary(newMat,viewer);CHKERRQ(ierr);
4366   } else if (ishdf5) {
4367 #if defined(PETSC_HAVE_HDF5)
4368     ierr = MatLoad_AIJ_HDF5(newMat,viewer);CHKERRQ(ierr);
4369 #else
4370     SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
4371 #endif
4372   } else {
4373     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);
4374   }
4375   PetscFunctionReturn(0);
4376 }
4377 
4378 PetscErrorCode MatLoad_SeqAIJ_Binary(Mat newMat, PetscViewer viewer)
4379 {
4380   Mat_SeqAIJ     *a;
4381   PetscErrorCode ierr;
4382   PetscInt       i,sum,nz,header[4],*rowlengths = 0,M,N,rows,cols;
4383   int            fd;
4384   PetscMPIInt    size;
4385   MPI_Comm       comm;
4386   PetscInt       bs = newMat->rmap->bs;
4387 
4388   PetscFunctionBegin;
4389   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
4390   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4391   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"view must have one processor");
4392 
4393   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
4394   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
4395   ierr = PetscOptionsEnd();CHKERRQ(ierr);
4396   if (bs < 0) bs = 1;
4397   ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);
4398 
4399   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
4400   ierr = PetscBinaryRead(fd,header,4,PETSC_INT);CHKERRQ(ierr);
4401   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
4402   M = header[1]; N = header[2]; nz = header[3];
4403 
4404   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
4405 
4406   /* read in row lengths */
4407   ierr = PetscMalloc1(M,&rowlengths);CHKERRQ(ierr);
4408   ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
4409 
4410   /* check if sum of rowlengths is same as nz */
4411   for (i=0,sum=0; i< M; i++) sum +=rowlengths[i];
4412   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);
4413 
4414   /* set global size if not set already*/
4415   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) {
4416     ierr = MatSetSizes(newMat,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
4417   } else {
4418     /* if sizes and type are already set, check if the matrix  global sizes are correct */
4419     ierr = MatGetSize(newMat,&rows,&cols);CHKERRQ(ierr);
4420     if (rows < 0 && cols < 0) { /* user might provide local size instead of global size */
4421       ierr = MatGetLocalSize(newMat,&rows,&cols);CHKERRQ(ierr);
4422     }
4423     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);
4424   }
4425   ierr = MatSeqAIJSetPreallocation_SeqAIJ(newMat,0,rowlengths);CHKERRQ(ierr);
4426   a    = (Mat_SeqAIJ*)newMat->data;
4427 
4428   ierr = PetscBinaryRead(fd,a->j,nz,PETSC_INT);CHKERRQ(ierr);
4429 
4430   /* read in nonzero values */
4431   ierr = PetscBinaryRead(fd,a->a,nz,PETSC_SCALAR);CHKERRQ(ierr);
4432 
4433   /* set matrix "i" values */
4434   a->i[0] = 0;
4435   for (i=1; i<= M; i++) {
4436     a->i[i]      = a->i[i-1] + rowlengths[i-1];
4437     a->ilen[i-1] = rowlengths[i-1];
4438   }
4439   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
4440 
4441   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4442   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4443   PetscFunctionReturn(0);
4444 }
4445 
4446 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4447 {
4448   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4449   PetscErrorCode ierr;
4450 #if defined(PETSC_USE_COMPLEX)
4451   PetscInt k;
4452 #endif
4453 
4454   PetscFunctionBegin;
4455   /* If the  matrix dimensions are not equal,or no of nonzeros */
4456   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4457     *flg = PETSC_FALSE;
4458     PetscFunctionReturn(0);
4459   }
4460 
4461   /* if the a->i are the same */
4462   ierr = PetscMemcmp(a->i,b->i,(A->rmap->n+1)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4463   if (!*flg) PetscFunctionReturn(0);
4464 
4465   /* if a->j are the same */
4466   ierr = PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4467   if (!*flg) PetscFunctionReturn(0);
4468 
4469   /* if a->a are the same */
4470 #if defined(PETSC_USE_COMPLEX)
4471   for (k=0; k<a->nz; k++) {
4472     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4473       *flg = PETSC_FALSE;
4474       PetscFunctionReturn(0);
4475     }
4476   }
4477 #else
4478   ierr = PetscMemcmp(a->a,b->a,(a->nz)*sizeof(PetscScalar),flg);CHKERRQ(ierr);
4479 #endif
4480   PetscFunctionReturn(0);
4481 }
4482 
4483 /*@
4484      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4485               provided by the user.
4486 
4487       Collective on MPI_Comm
4488 
4489    Input Parameters:
4490 +   comm - must be an MPI communicator of size 1
4491 .   m - number of rows
4492 .   n - number of columns
4493 .   i - row indices; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
4494 .   j - column indices
4495 -   a - matrix values
4496 
4497    Output Parameter:
4498 .   mat - the matrix
4499 
4500    Level: intermediate
4501 
4502    Notes:
4503        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4504     once the matrix is destroyed and not before
4505 
4506        You cannot set new nonzero locations into this matrix, that will generate an error.
4507 
4508        The i and j indices are 0 based
4509 
4510        The format which is used for the sparse matrix input, is equivalent to a
4511     row-major ordering.. i.e for the following matrix, the input data expected is
4512     as shown
4513 
4514 $        1 0 0
4515 $        2 0 3
4516 $        4 5 6
4517 $
4518 $        i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4519 $        j =  {0,0,2,0,1,2}  [size = 6]; values must be sorted for each row
4520 $        v =  {1,2,3,4,5,6}  [size = 6]
4521 
4522 
4523 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4524 
4525 @*/
4526 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat)
4527 {
4528   PetscErrorCode ierr;
4529   PetscInt       ii;
4530   Mat_SeqAIJ     *aij;
4531 #if defined(PETSC_USE_DEBUG)
4532   PetscInt jj;
4533 #endif
4534 
4535   PetscFunctionBegin;
4536   if (m > 0 && i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4537   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4538   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4539   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4540   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4541   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,0);CHKERRQ(ierr);
4542   aij  = (Mat_SeqAIJ*)(*mat)->data;
4543   ierr = PetscMalloc2(m,&aij->imax,m,&aij->ilen);CHKERRQ(ierr);
4544 
4545   aij->i            = i;
4546   aij->j            = j;
4547   aij->a            = a;
4548   aij->singlemalloc = PETSC_FALSE;
4549   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4550   aij->free_a       = PETSC_FALSE;
4551   aij->free_ij      = PETSC_FALSE;
4552 
4553   for (ii=0; ii<m; ii++) {
4554     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4555 #if defined(PETSC_USE_DEBUG)
4556     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]);
4557     for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4558       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);
4559       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);
4560     }
4561 #endif
4562   }
4563 #if defined(PETSC_USE_DEBUG)
4564   for (ii=0; ii<aij->i[m]; ii++) {
4565     if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %D index = %D",ii,j[ii]);
4566     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]);
4567   }
4568 #endif
4569 
4570   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4571   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4572   PetscFunctionReturn(0);
4573 }
4574 /*@C
4575      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4576               provided by the user.
4577 
4578       Collective on MPI_Comm
4579 
4580    Input Parameters:
4581 +   comm - must be an MPI communicator of size 1
4582 .   m   - number of rows
4583 .   n   - number of columns
4584 .   i   - row indices
4585 .   j   - column indices
4586 .   a   - matrix values
4587 .   nz  - number of nonzeros
4588 -   idx - 0 or 1 based
4589 
4590    Output Parameter:
4591 .   mat - the matrix
4592 
4593    Level: intermediate
4594 
4595    Notes:
4596        The i and j indices are 0 based
4597 
4598        The format which is used for the sparse matrix input, is equivalent to a
4599     row-major ordering.. i.e for the following matrix, the input data expected is
4600     as shown:
4601 
4602         1 0 0
4603         2 0 3
4604         4 5 6
4605 
4606         i =  {0,1,1,2,2,2}
4607         j =  {0,0,2,0,1,2}
4608         v =  {1,2,3,4,5,6}
4609 
4610 
4611 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4612 
4613 @*/
4614 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat,PetscInt nz,PetscBool idx)
4615 {
4616   PetscErrorCode ierr;
4617   PetscInt       ii, *nnz, one = 1,row,col;
4618 
4619 
4620   PetscFunctionBegin;
4621   ierr = PetscCalloc1(m,&nnz);CHKERRQ(ierr);
4622   for (ii = 0; ii < nz; ii++) {
4623     nnz[i[ii] - !!idx] += 1;
4624   }
4625   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4626   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4627   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4628   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4629   for (ii = 0; ii < nz; ii++) {
4630     if (idx) {
4631       row = i[ii] - 1;
4632       col = j[ii] - 1;
4633     } else {
4634       row = i[ii];
4635       col = j[ii];
4636     }
4637     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4638   }
4639   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4640   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4641   ierr = PetscFree(nnz);CHKERRQ(ierr);
4642   PetscFunctionReturn(0);
4643 }
4644 
4645 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4646 {
4647   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4648   PetscErrorCode ierr;
4649 
4650   PetscFunctionBegin;
4651   a->idiagvalid  = PETSC_FALSE;
4652   a->ibdiagvalid = PETSC_FALSE;
4653 
4654   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4655   PetscFunctionReturn(0);
4656 }
4657 
4658 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4659 {
4660   PetscErrorCode ierr;
4661   PetscMPIInt    size;
4662 
4663   PetscFunctionBegin;
4664   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4665   if (size == 1) {
4666     if (scall == MAT_INITIAL_MATRIX) {
4667       ierr = MatDuplicate(inmat,MAT_COPY_VALUES,outmat);CHKERRQ(ierr);
4668     } else {
4669       ierr = MatCopy(inmat,*outmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4670     }
4671   } else {
4672     ierr = MatCreateMPIMatConcatenateSeqMat_MPIAIJ(comm,inmat,n,scall,outmat);CHKERRQ(ierr);
4673   }
4674   PetscFunctionReturn(0);
4675 }
4676 
4677 /*
4678  Permute A into C's *local* index space using rowemb,colemb.
4679  The embedding are supposed to be injections and the above implies that the range of rowemb is a subset
4680  of [0,m), colemb is in [0,n).
4681  If pattern == DIFFERENT_NONZERO_PATTERN, C is preallocated according to A.
4682  */
4683 PetscErrorCode MatSetSeqMat_SeqAIJ(Mat C,IS rowemb,IS colemb,MatStructure pattern,Mat B)
4684 {
4685   /* If making this function public, change the error returned in this function away from _PLIB. */
4686   PetscErrorCode ierr;
4687   Mat_SeqAIJ     *Baij;
4688   PetscBool      seqaij;
4689   PetscInt       m,n,*nz,i,j,count;
4690   PetscScalar    v;
4691   const PetscInt *rowindices,*colindices;
4692 
4693   PetscFunctionBegin;
4694   if (!B) PetscFunctionReturn(0);
4695   /* Check to make sure the target matrix (and embeddings) are compatible with C and each other. */
4696   ierr = PetscObjectBaseTypeCompare((PetscObject)B,MATSEQAIJ,&seqaij);CHKERRQ(ierr);
4697   if (!seqaij) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is of wrong type");
4698   if (rowemb) {
4699     ierr = ISGetLocalSize(rowemb,&m);CHKERRQ(ierr);
4700     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);
4701   } else {
4702     if (C->rmap->n != B->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is row-incompatible with the target matrix");
4703   }
4704   if (colemb) {
4705     ierr = ISGetLocalSize(colemb,&n);CHKERRQ(ierr);
4706     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);
4707   } else {
4708     if (C->cmap->n != B->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is col-incompatible with the target matrix");
4709   }
4710 
4711   Baij = (Mat_SeqAIJ*)(B->data);
4712   if (pattern == DIFFERENT_NONZERO_PATTERN) {
4713     ierr = PetscMalloc1(B->rmap->n,&nz);CHKERRQ(ierr);
4714     for (i=0; i<B->rmap->n; i++) {
4715       nz[i] = Baij->i[i+1] - Baij->i[i];
4716     }
4717     ierr = MatSeqAIJSetPreallocation(C,0,nz);CHKERRQ(ierr);
4718     ierr = PetscFree(nz);CHKERRQ(ierr);
4719   }
4720   if (pattern == SUBSET_NONZERO_PATTERN) {
4721     ierr = MatZeroEntries(C);CHKERRQ(ierr);
4722   }
4723   count = 0;
4724   rowindices = NULL;
4725   colindices = NULL;
4726   if (rowemb) {
4727     ierr = ISGetIndices(rowemb,&rowindices);CHKERRQ(ierr);
4728   }
4729   if (colemb) {
4730     ierr = ISGetIndices(colemb,&colindices);CHKERRQ(ierr);
4731   }
4732   for (i=0; i<B->rmap->n; i++) {
4733     PetscInt row;
4734     row = i;
4735     if (rowindices) row = rowindices[i];
4736     for (j=Baij->i[i]; j<Baij->i[i+1]; j++) {
4737       PetscInt col;
4738       col  = Baij->j[count];
4739       if (colindices) col = colindices[col];
4740       v    = Baij->a[count];
4741       ierr = MatSetValues(C,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
4742       ++count;
4743     }
4744   }
4745   /* FIXME: set C's nonzerostate correctly. */
4746   /* Assembly for C is necessary. */
4747   C->preallocated = PETSC_TRUE;
4748   C->assembled     = PETSC_TRUE;
4749   C->was_assembled = PETSC_FALSE;
4750   PetscFunctionReturn(0);
4751 }
4752 
4753 PetscFunctionList MatSeqAIJList = NULL;
4754 
4755 /*@C
4756    MatSeqAIJSetType - Converts a MATSEQAIJ matrix to a subtype
4757 
4758    Collective on Mat
4759 
4760    Input Parameters:
4761 +  mat      - the matrix object
4762 -  matype   - matrix type
4763 
4764    Options Database Key:
4765 .  -mat_seqai_type  <method> - for example seqaijcrl
4766 
4767 
4768   Level: intermediate
4769 
4770 .keywords: Mat, MatType, set, method
4771 
4772 .seealso: PCSetType(), VecSetType(), MatCreate(), MatType, Mat
4773 @*/
4774 PetscErrorCode  MatSeqAIJSetType(Mat mat, MatType matype)
4775 {
4776   PetscErrorCode ierr,(*r)(Mat,MatType,MatReuse,Mat*);
4777   PetscBool      sametype;
4778 
4779   PetscFunctionBegin;
4780   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
4781   ierr = PetscObjectTypeCompare((PetscObject)mat,matype,&sametype);CHKERRQ(ierr);
4782   if (sametype) PetscFunctionReturn(0);
4783 
4784   ierr =  PetscFunctionListFind(MatSeqAIJList,matype,&r);CHKERRQ(ierr);
4785   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown Mat type given: %s",matype);
4786   ierr = (*r)(mat,matype,MAT_INPLACE_MATRIX,&mat);CHKERRQ(ierr);
4787   PetscFunctionReturn(0);
4788 }
4789 
4790 
4791 /*@C
4792   MatSeqAIJRegister -  - Adds a new sub-matrix type for sequential AIJ matrices
4793 
4794    Not Collective
4795 
4796    Input Parameters:
4797 +  name - name of a new user-defined matrix type, for example MATSEQAIJCRL
4798 -  function - routine to convert to subtype
4799 
4800    Notes:
4801    MatSeqAIJRegister() may be called multiple times to add several user-defined solvers.
4802 
4803 
4804    Then, your matrix can be chosen with the procedural interface at runtime via the option
4805 $     -mat_seqaij_type my_mat
4806 
4807    Level: advanced
4808 
4809 .keywords: Mat, register
4810 
4811 .seealso: MatSeqAIJRegisterAll()
4812 
4813 
4814   Level: advanced
4815 @*/
4816 PetscErrorCode  MatSeqAIJRegister(const char sname[],PetscErrorCode (*function)(Mat,MatType,MatReuse,Mat *))
4817 {
4818   PetscErrorCode ierr;
4819 
4820   PetscFunctionBegin;
4821   ierr = MatInitializePackage();CHKERRQ(ierr);
4822   ierr = PetscFunctionListAdd(&MatSeqAIJList,sname,function);CHKERRQ(ierr);
4823   PetscFunctionReturn(0);
4824 }
4825 
4826 PetscBool MatSeqAIJRegisterAllCalled = PETSC_FALSE;
4827 
4828 /*@C
4829   MatSeqAIJRegisterAll - Registers all of the matrix subtypes of SeqAIJ
4830 
4831   Not Collective
4832 
4833   Level: advanced
4834 
4835   Developers Note: CUSP and CUSPARSE do not yet support the  MatConvert_SeqAIJ..() paradigm and thus cannot be registered here
4836 
4837 .keywords: KSP, register, all
4838 
4839 .seealso:  MatRegisterAll(), MatSeqAIJRegister()
4840 @*/
4841 PetscErrorCode  MatSeqAIJRegisterAll(void)
4842 {
4843   PetscErrorCode ierr;
4844 
4845   PetscFunctionBegin;
4846   if (MatSeqAIJRegisterAllCalled) PetscFunctionReturn(0);
4847   MatSeqAIJRegisterAllCalled = PETSC_TRUE;
4848 
4849   ierr = MatSeqAIJRegister(MATSEQAIJCRL,      MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4850   ierr = MatSeqAIJRegister(MATSEQAIJPERM,     MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4851   ierr = MatSeqAIJRegister(MATSEQAIJSELL,     MatConvert_SeqAIJ_SeqAIJSELL);CHKERRQ(ierr);
4852 #if defined(PETSC_HAVE_MKL_SPARSE)
4853   ierr = MatSeqAIJRegister(MATSEQAIJMKL,      MatConvert_SeqAIJ_SeqAIJMKL);CHKERRQ(ierr);
4854 #endif
4855 #if defined(PETSC_HAVE_VIENNACL) && defined(PETSC_HAVE_VIENNACL_NO_CUDA)
4856   ierr = MatSeqAIJRegister(MATMPIAIJVIENNACL, MatConvert_SeqAIJ_SeqAIJViennaCL);CHKERRQ(ierr);
4857 #endif
4858   PetscFunctionReturn(0);
4859 }
4860 
4861 /*
4862     Special version for direct calls from Fortran
4863 */
4864 #include <petsc/private/fortranimpl.h>
4865 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4866 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
4867 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4868 #define matsetvaluesseqaij_ matsetvaluesseqaij
4869 #endif
4870 
4871 /* Change these macros so can be used in void function */
4872 #undef CHKERRQ
4873 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
4874 #undef SETERRQ2
4875 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4876 #undef SETERRQ3
4877 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4878 
4879 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)
4880 {
4881   Mat            A  = *AA;
4882   PetscInt       m  = *mm, n = *nn;
4883   InsertMode     is = *isis;
4884   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4885   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
4886   PetscInt       *imax,*ai,*ailen;
4887   PetscErrorCode ierr;
4888   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
4889   MatScalar      *ap,value,*aa;
4890   PetscBool      ignorezeroentries = a->ignorezeroentries;
4891   PetscBool      roworiented       = a->roworiented;
4892 
4893   PetscFunctionBegin;
4894   MatCheckPreallocated(A,1);
4895   imax  = a->imax;
4896   ai    = a->i;
4897   ailen = a->ilen;
4898   aj    = a->j;
4899   aa    = a->a;
4900 
4901   for (k=0; k<m; k++) { /* loop over added rows */
4902     row = im[k];
4903     if (row < 0) continue;
4904 #if defined(PETSC_USE_DEBUG)
4905     if (row >= A->rmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
4906 #endif
4907     rp   = aj + ai[row]; ap = aa + ai[row];
4908     rmax = imax[row]; nrow = ailen[row];
4909     low  = 0;
4910     high = nrow;
4911     for (l=0; l<n; l++) { /* loop over added columns */
4912       if (in[l] < 0) continue;
4913 #if defined(PETSC_USE_DEBUG)
4914       if (in[l] >= A->cmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
4915 #endif
4916       col = in[l];
4917       if (roworiented) value = v[l + k*n];
4918       else value = v[k + l*m];
4919 
4920       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
4921 
4922       if (col <= lastcol) low = 0;
4923       else high = nrow;
4924       lastcol = col;
4925       while (high-low > 5) {
4926         t = (low+high)/2;
4927         if (rp[t] > col) high = t;
4928         else             low  = t;
4929       }
4930       for (i=low; i<high; i++) {
4931         if (rp[i] > col) break;
4932         if (rp[i] == col) {
4933           if (is == ADD_VALUES) ap[i] += value;
4934           else                  ap[i] = value;
4935           goto noinsert;
4936         }
4937       }
4938       if (value == 0.0 && ignorezeroentries) goto noinsert;
4939       if (nonew == 1) goto noinsert;
4940       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
4941       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
4942       N = nrow++ - 1; a->nz++; high++;
4943       /* shift up all the later entries in this row */
4944       for (ii=N; ii>=i; ii--) {
4945         rp[ii+1] = rp[ii];
4946         ap[ii+1] = ap[ii];
4947       }
4948       rp[i] = col;
4949       ap[i] = value;
4950       A->nonzerostate++;
4951 noinsert:;
4952       low = i + 1;
4953     }
4954     ailen[row] = nrow;
4955   }
4956   PetscFunctionReturnVoid();
4957 }
4958