xref: /petsc/src/mat/impls/aij/seq/aij.c (revision 55e7fe800d976e85ed2b5cd8bfdef564daa37bd9)
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 /*
1523      Checks for missing diagonals
1524 */
1525 PetscErrorCode MatMissingDiagonal_SeqAIJ(Mat A,PetscBool  *missing,PetscInt *d)
1526 {
1527   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1528   PetscInt       *diag,*ii = a->i,i;
1529   PetscErrorCode ierr;
1530 
1531   PetscFunctionBegin;
1532   *missing = PETSC_FALSE;
1533   if (A->rmap->n > 0 && !ii) {
1534     *missing = PETSC_TRUE;
1535     if (d) *d = 0;
1536     ierr = PetscInfo(A,"Matrix has no entries therefore is missing diagonal\n");CHKERRQ(ierr);
1537   } else {
1538     diag = a->diag;
1539     for (i=0; i<A->rmap->n; i++) {
1540       if (diag[i] >= ii[i+1]) {
1541         *missing = PETSC_TRUE;
1542         if (d) *d = i;
1543         ierr = PetscInfo1(A,"Matrix is missing diagonal number %D\n",i);CHKERRQ(ierr);
1544         break;
1545       }
1546     }
1547   }
1548   PetscFunctionReturn(0);
1549 }
1550 
1551 #include <petscblaslapack.h>
1552 #include <petsc/private/kernels/blockinvert.h>
1553 
1554 /*
1555     Note that values is allocated externally by the PC and then passed into this routine
1556 */
1557 PetscErrorCode MatInvertVariableBlockDiagonal_SeqAIJ(Mat A,PetscInt nblocks,const PetscInt *bsizes,PetscScalar *diag)
1558 {
1559   PetscErrorCode  ierr;
1560   PetscInt        n = A->rmap->n, i, ncnt = 0, *indx,j,bsizemax = 0,*v_pivots;
1561   PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;
1562   const PetscReal shift = 0.0;
1563   PetscInt        ipvt[5];
1564   PetscScalar     work[25],*v_work;
1565 
1566   PetscFunctionBegin;
1567   allowzeropivot = PetscNot(A->erroriffailure);
1568   for (i=0; i<nblocks; i++) ncnt += bsizes[i];
1569   if (ncnt != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Total blocksizes %D doesn't match number matrix rows %D",ncnt,n);
1570   for (i=0; i<nblocks; i++) {
1571     bsizemax = PetscMax(bsizemax,bsizes[i]);
1572   }
1573   ierr = PetscMalloc1(bsizemax,&indx);CHKERRQ(ierr);
1574   if (bsizemax > 7) {
1575     ierr = PetscMalloc2(bsizemax,&v_work,bsizemax,&v_pivots);CHKERRQ(ierr);
1576   }
1577   ncnt = 0;
1578   for (i=0; i<nblocks; i++) {
1579     for (j=0; j<bsizes[i]; j++) indx[j] = ncnt+j;
1580     ierr    = MatGetValues(A,bsizes[i],indx,bsizes[i],indx,diag);CHKERRQ(ierr);
1581     switch (bsizes[i]) {
1582     case 1:
1583       *diag = 1.0/(*diag);
1584       break;
1585     case 2:
1586       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1587       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1588       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
1589       break;
1590     case 3:
1591       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1592       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1593       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
1594       break;
1595     case 4:
1596       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1597       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1598       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
1599       break;
1600     case 5:
1601       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1602       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1603       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
1604       break;
1605     case 6:
1606       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1607       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1608       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
1609       break;
1610     case 7:
1611       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1612       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1613       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
1614       break;
1615     default:
1616       ierr  = PetscKernel_A_gets_inverse_A(bsizes[i],diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1617       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1618       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bsizes[i]);CHKERRQ(ierr);
1619     }
1620     ncnt   += bsizes[i];
1621     diag += bsizes[i]*bsizes[i];
1622   }
1623   if (bsizemax > 7) {
1624     ierr = PetscFree2(v_work,v_pivots);CHKERRQ(ierr);
1625   }
1626   ierr = PetscFree(indx);CHKERRQ(ierr);
1627   PetscFunctionReturn(0);
1628 }
1629 
1630 /*
1631    Negative shift indicates do not generate an error if there is a zero diagonal, just invert it anyways
1632 */
1633 PetscErrorCode  MatInvertDiagonal_SeqAIJ(Mat A,PetscScalar omega,PetscScalar fshift)
1634 {
1635   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
1636   PetscErrorCode ierr;
1637   PetscInt       i,*diag,m = A->rmap->n;
1638   MatScalar      *v = a->a;
1639   PetscScalar    *idiag,*mdiag;
1640 
1641   PetscFunctionBegin;
1642   if (a->idiagvalid) PetscFunctionReturn(0);
1643   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1644   diag = a->diag;
1645   if (!a->idiag) {
1646     ierr = PetscMalloc3(m,&a->idiag,m,&a->mdiag,m,&a->ssor_work);CHKERRQ(ierr);
1647     ierr = PetscLogObjectMemory((PetscObject)A, 3*m*sizeof(PetscScalar));CHKERRQ(ierr);
1648     v    = a->a;
1649   }
1650   mdiag = a->mdiag;
1651   idiag = a->idiag;
1652 
1653   if (omega == 1.0 && PetscRealPart(fshift) <= 0.0) {
1654     for (i=0; i<m; i++) {
1655       mdiag[i] = v[diag[i]];
1656       if (!PetscAbsScalar(mdiag[i])) { /* zero diagonal */
1657         if (PetscRealPart(fshift)) {
1658           ierr = PetscInfo1(A,"Zero diagonal on row %D\n",i);CHKERRQ(ierr);
1659           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1660           A->factorerror_zeropivot_value = 0.0;
1661           A->factorerror_zeropivot_row   = i;
1662         } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Zero diagonal on row %D",i);
1663       }
1664       idiag[i] = 1.0/v[diag[i]];
1665     }
1666     ierr = PetscLogFlops(m);CHKERRQ(ierr);
1667   } else {
1668     for (i=0; i<m; i++) {
1669       mdiag[i] = v[diag[i]];
1670       idiag[i] = omega/(fshift + v[diag[i]]);
1671     }
1672     ierr = PetscLogFlops(2.0*m);CHKERRQ(ierr);
1673   }
1674   a->idiagvalid = PETSC_TRUE;
1675   PetscFunctionReturn(0);
1676 }
1677 
1678 #include <../src/mat/impls/aij/seq/ftn-kernels/frelax.h>
1679 PetscErrorCode MatSOR_SeqAIJ(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1680 {
1681   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1682   PetscScalar       *x,d,sum,*t,scale;
1683   const MatScalar   *v,*idiag=0,*mdiag;
1684   const PetscScalar *b, *bs,*xb, *ts;
1685   PetscErrorCode    ierr;
1686   PetscInt          n,m = A->rmap->n,i;
1687   const PetscInt    *idx,*diag;
1688 
1689   PetscFunctionBegin;
1690   its = its*lits;
1691 
1692   if (fshift != a->fshift || omega != a->omega) a->idiagvalid = PETSC_FALSE; /* must recompute idiag[] */
1693   if (!a->idiagvalid) {ierr = MatInvertDiagonal_SeqAIJ(A,omega,fshift);CHKERRQ(ierr);}
1694   a->fshift = fshift;
1695   a->omega  = omega;
1696 
1697   diag  = a->diag;
1698   t     = a->ssor_work;
1699   idiag = a->idiag;
1700   mdiag = a->mdiag;
1701 
1702   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1703   ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
1704   /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
1705   if (flag == SOR_APPLY_UPPER) {
1706     /* apply (U + D/omega) to the vector */
1707     bs = b;
1708     for (i=0; i<m; i++) {
1709       d   = fshift + mdiag[i];
1710       n   = a->i[i+1] - diag[i] - 1;
1711       idx = a->j + diag[i] + 1;
1712       v   = a->a + diag[i] + 1;
1713       sum = b[i]*d/omega;
1714       PetscSparseDensePlusDot(sum,bs,v,idx,n);
1715       x[i] = sum;
1716     }
1717     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1718     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1719     ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1720     PetscFunctionReturn(0);
1721   }
1722 
1723   if (flag == SOR_APPLY_LOWER) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SOR_APPLY_LOWER is not implemented");
1724   else if (flag & SOR_EISENSTAT) {
1725     /* Let  A = L + U + D; where L is lower trianglar,
1726     U is upper triangular, E = D/omega; This routine applies
1727 
1728             (L + E)^{-1} A (U + E)^{-1}
1729 
1730     to a vector efficiently using Eisenstat's trick.
1731     */
1732     scale = (2.0/omega) - 1.0;
1733 
1734     /*  x = (E + U)^{-1} b */
1735     for (i=m-1; i>=0; i--) {
1736       n   = a->i[i+1] - diag[i] - 1;
1737       idx = a->j + diag[i] + 1;
1738       v   = a->a + diag[i] + 1;
1739       sum = b[i];
1740       PetscSparseDenseMinusDot(sum,x,v,idx,n);
1741       x[i] = sum*idiag[i];
1742     }
1743 
1744     /*  t = b - (2*E - D)x */
1745     v = a->a;
1746     for (i=0; i<m; i++) t[i] = b[i] - scale*(v[*diag++])*x[i];
1747 
1748     /*  t = (E + L)^{-1}t */
1749     ts   = t;
1750     diag = a->diag;
1751     for (i=0; i<m; i++) {
1752       n   = diag[i] - a->i[i];
1753       idx = a->j + a->i[i];
1754       v   = a->a + a->i[i];
1755       sum = t[i];
1756       PetscSparseDenseMinusDot(sum,ts,v,idx,n);
1757       t[i] = sum*idiag[i];
1758       /*  x = x + t */
1759       x[i] += t[i];
1760     }
1761 
1762     ierr = PetscLogFlops(6.0*m-1 + 2.0*a->nz);CHKERRQ(ierr);
1763     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1764     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1765     PetscFunctionReturn(0);
1766   }
1767   if (flag & SOR_ZERO_INITIAL_GUESS) {
1768     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1769       for (i=0; i<m; i++) {
1770         n   = diag[i] - a->i[i];
1771         idx = a->j + a->i[i];
1772         v   = a->a + a->i[i];
1773         sum = b[i];
1774         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1775         t[i] = sum;
1776         x[i] = sum*idiag[i];
1777       }
1778       xb   = t;
1779       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1780     } else xb = b;
1781     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1782       for (i=m-1; i>=0; i--) {
1783         n   = a->i[i+1] - diag[i] - 1;
1784         idx = a->j + diag[i] + 1;
1785         v   = a->a + diag[i] + 1;
1786         sum = xb[i];
1787         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1788         if (xb == b) {
1789           x[i] = sum*idiag[i];
1790         } else {
1791           x[i] = (1-omega)*x[i] + sum*idiag[i];  /* omega in idiag */
1792         }
1793       }
1794       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
1795     }
1796     its--;
1797   }
1798   while (its--) {
1799     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1800       for (i=0; i<m; i++) {
1801         /* lower */
1802         n   = diag[i] - a->i[i];
1803         idx = a->j + a->i[i];
1804         v   = a->a + a->i[i];
1805         sum = b[i];
1806         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1807         t[i] = sum;             /* save application of the lower-triangular part */
1808         /* upper */
1809         n   = a->i[i+1] - diag[i] - 1;
1810         idx = a->j + diag[i] + 1;
1811         v   = a->a + diag[i] + 1;
1812         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1813         x[i] = (1. - omega)*x[i] + sum*idiag[i]; /* omega in idiag */
1814       }
1815       xb   = t;
1816       ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1817     } else xb = b;
1818     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1819       for (i=m-1; i>=0; i--) {
1820         sum = xb[i];
1821         if (xb == b) {
1822           /* whole matrix (no checkpointing available) */
1823           n   = a->i[i+1] - a->i[i];
1824           idx = a->j + a->i[i];
1825           v   = a->a + a->i[i];
1826           PetscSparseDenseMinusDot(sum,x,v,idx,n);
1827           x[i] = (1. - omega)*x[i] + (sum + mdiag[i]*x[i])*idiag[i];
1828         } else { /* lower-triangular part has been saved, so only apply upper-triangular */
1829           n   = a->i[i+1] - diag[i] - 1;
1830           idx = a->j + diag[i] + 1;
1831           v   = a->a + diag[i] + 1;
1832           PetscSparseDenseMinusDot(sum,x,v,idx,n);
1833           x[i] = (1. - omega)*x[i] + sum*idiag[i];  /* omega in idiag */
1834         }
1835       }
1836       if (xb == b) {
1837         ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1838       } else {
1839         ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
1840       }
1841     }
1842   }
1843   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1844   ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1845   PetscFunctionReturn(0);
1846 }
1847 
1848 
1849 PetscErrorCode MatGetInfo_SeqAIJ(Mat A,MatInfoType flag,MatInfo *info)
1850 {
1851   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1852 
1853   PetscFunctionBegin;
1854   info->block_size   = 1.0;
1855   info->nz_allocated = (double)a->maxnz;
1856   info->nz_used      = (double)a->nz;
1857   info->nz_unneeded  = (double)(a->maxnz - a->nz);
1858   info->assemblies   = (double)A->num_ass;
1859   info->mallocs      = (double)A->info.mallocs;
1860   info->memory       = ((PetscObject)A)->mem;
1861   if (A->factortype) {
1862     info->fill_ratio_given  = A->info.fill_ratio_given;
1863     info->fill_ratio_needed = A->info.fill_ratio_needed;
1864     info->factor_mallocs    = A->info.factor_mallocs;
1865   } else {
1866     info->fill_ratio_given  = 0;
1867     info->fill_ratio_needed = 0;
1868     info->factor_mallocs    = 0;
1869   }
1870   PetscFunctionReturn(0);
1871 }
1872 
1873 PetscErrorCode MatZeroRows_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
1874 {
1875   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1876   PetscInt          i,m = A->rmap->n - 1;
1877   PetscErrorCode    ierr;
1878   const PetscScalar *xx;
1879   PetscScalar       *bb;
1880   PetscInt          d = 0;
1881 
1882   PetscFunctionBegin;
1883   if (x && b) {
1884     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
1885     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
1886     for (i=0; i<N; i++) {
1887       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1888       bb[rows[i]] = diag*xx[rows[i]];
1889     }
1890     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
1891     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
1892   }
1893 
1894   if (a->keepnonzeropattern) {
1895     for (i=0; i<N; i++) {
1896       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1897       ierr = PetscMemzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]*sizeof(PetscScalar));CHKERRQ(ierr);
1898     }
1899     if (diag != 0.0) {
1900       for (i=0; i<N; i++) {
1901         d = rows[i];
1902         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);
1903       }
1904       for (i=0; i<N; i++) {
1905         a->a[a->diag[rows[i]]] = diag;
1906       }
1907     }
1908   } else {
1909     if (diag != 0.0) {
1910       for (i=0; i<N; i++) {
1911         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1912         if (a->ilen[rows[i]] > 0) {
1913           a->ilen[rows[i]]    = 1;
1914           a->a[a->i[rows[i]]] = diag;
1915           a->j[a->i[rows[i]]] = rows[i];
1916         } else { /* in case row was completely empty */
1917           ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES);CHKERRQ(ierr);
1918         }
1919       }
1920     } else {
1921       for (i=0; i<N; i++) {
1922         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1923         a->ilen[rows[i]] = 0;
1924       }
1925     }
1926     A->nonzerostate++;
1927   }
1928   ierr = (*A->ops->assemblyend)(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1929   PetscFunctionReturn(0);
1930 }
1931 
1932 PetscErrorCode MatZeroRowsColumns_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
1933 {
1934   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1935   PetscInt          i,j,m = A->rmap->n - 1,d = 0;
1936   PetscErrorCode    ierr;
1937   PetscBool         missing,*zeroed,vecs = PETSC_FALSE;
1938   const PetscScalar *xx;
1939   PetscScalar       *bb;
1940 
1941   PetscFunctionBegin;
1942   if (x && b) {
1943     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
1944     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
1945     vecs = PETSC_TRUE;
1946   }
1947   ierr = PetscCalloc1(A->rmap->n,&zeroed);CHKERRQ(ierr);
1948   for (i=0; i<N; i++) {
1949     if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1950     ierr = PetscMemzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]*sizeof(PetscScalar));CHKERRQ(ierr);
1951 
1952     zeroed[rows[i]] = PETSC_TRUE;
1953   }
1954   for (i=0; i<A->rmap->n; i++) {
1955     if (!zeroed[i]) {
1956       for (j=a->i[i]; j<a->i[i+1]; j++) {
1957         if (zeroed[a->j[j]]) {
1958           if (vecs) bb[i] -= a->a[j]*xx[a->j[j]];
1959           a->a[j] = 0.0;
1960         }
1961       }
1962     } else if (vecs) bb[i] = diag*xx[i];
1963   }
1964   if (x && b) {
1965     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
1966     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
1967   }
1968   ierr = PetscFree(zeroed);CHKERRQ(ierr);
1969   if (diag != 0.0) {
1970     ierr = MatMissingDiagonal_SeqAIJ(A,&missing,&d);CHKERRQ(ierr);
1971     if (missing) {
1972       if (a->nonew) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in row %D",d);
1973       else {
1974         for (i=0; i<N; i++) {
1975           ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES);CHKERRQ(ierr);
1976         }
1977       }
1978     } else {
1979       for (i=0; i<N; i++) {
1980         a->a[a->diag[rows[i]]] = diag;
1981       }
1982     }
1983   }
1984   ierr = (*A->ops->assemblyend)(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1985   PetscFunctionReturn(0);
1986 }
1987 
1988 PetscErrorCode MatGetRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1989 {
1990   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1991   PetscInt   *itmp;
1992 
1993   PetscFunctionBegin;
1994   if (row < 0 || row >= A->rmap->n) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range",row);
1995 
1996   *nz = a->i[row+1] - a->i[row];
1997   if (v) *v = a->a + a->i[row];
1998   if (idx) {
1999     itmp = a->j + a->i[row];
2000     if (*nz) *idx = itmp;
2001     else *idx = 0;
2002   }
2003   PetscFunctionReturn(0);
2004 }
2005 
2006 /* remove this function? */
2007 PetscErrorCode MatRestoreRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
2008 {
2009   PetscFunctionBegin;
2010   PetscFunctionReturn(0);
2011 }
2012 
2013 PetscErrorCode MatNorm_SeqAIJ(Mat A,NormType type,PetscReal *nrm)
2014 {
2015   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
2016   MatScalar      *v  = a->a;
2017   PetscReal      sum = 0.0;
2018   PetscErrorCode ierr;
2019   PetscInt       i,j;
2020 
2021   PetscFunctionBegin;
2022   if (type == NORM_FROBENIUS) {
2023 #if defined(PETSC_USE_REAL___FP16)
2024     PetscBLASInt one = 1,nz = a->nz;
2025     *nrm = BLASnrm2_(&nz,v,&one);
2026 #else
2027     for (i=0; i<a->nz; i++) {
2028       sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
2029     }
2030     *nrm = PetscSqrtReal(sum);
2031 #endif
2032     ierr = PetscLogFlops(2*a->nz);CHKERRQ(ierr);
2033   } else if (type == NORM_1) {
2034     PetscReal *tmp;
2035     PetscInt  *jj = a->j;
2036     ierr = PetscCalloc1(A->cmap->n+1,&tmp);CHKERRQ(ierr);
2037     *nrm = 0.0;
2038     for (j=0; j<a->nz; j++) {
2039       tmp[*jj++] += PetscAbsScalar(*v);  v++;
2040     }
2041     for (j=0; j<A->cmap->n; j++) {
2042       if (tmp[j] > *nrm) *nrm = tmp[j];
2043     }
2044     ierr = PetscFree(tmp);CHKERRQ(ierr);
2045     ierr = PetscLogFlops(PetscMax(a->nz-1,0));CHKERRQ(ierr);
2046   } else if (type == NORM_INFINITY) {
2047     *nrm = 0.0;
2048     for (j=0; j<A->rmap->n; j++) {
2049       v   = a->a + a->i[j];
2050       sum = 0.0;
2051       for (i=0; i<a->i[j+1]-a->i[j]; i++) {
2052         sum += PetscAbsScalar(*v); v++;
2053       }
2054       if (sum > *nrm) *nrm = sum;
2055     }
2056     ierr = PetscLogFlops(PetscMax(a->nz-1,0));CHKERRQ(ierr);
2057   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for two norm");
2058   PetscFunctionReturn(0);
2059 }
2060 
2061 /* Merged from MatGetSymbolicTranspose_SeqAIJ() - replace MatGetSymbolicTranspose_SeqAIJ()? */
2062 PetscErrorCode MatTransposeSymbolic_SeqAIJ(Mat A,Mat *B)
2063 {
2064   PetscErrorCode ierr;
2065   PetscInt       i,j,anzj;
2066   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b;
2067   PetscInt       an=A->cmap->N,am=A->rmap->N;
2068   PetscInt       *ati,*atj,*atfill,*ai=a->i,*aj=a->j;
2069 
2070   PetscFunctionBegin;
2071   /* Allocate space for symbolic transpose info and work array */
2072   ierr = PetscCalloc1(an+1,&ati);CHKERRQ(ierr);
2073   ierr = PetscMalloc1(ai[am],&atj);CHKERRQ(ierr);
2074   ierr = PetscMalloc1(an,&atfill);CHKERRQ(ierr);
2075 
2076   /* Walk through aj and count ## of non-zeros in each row of A^T. */
2077   /* Note: offset by 1 for fast conversion into csr format. */
2078   for (i=0;i<ai[am];i++) ati[aj[i]+1] += 1;
2079   /* Form ati for csr format of A^T. */
2080   for (i=0;i<an;i++) ati[i+1] += ati[i];
2081 
2082   /* Copy ati into atfill so we have locations of the next free space in atj */
2083   ierr = PetscMemcpy(atfill,ati,an*sizeof(PetscInt));CHKERRQ(ierr);
2084 
2085   /* Walk through A row-wise and mark nonzero entries of A^T. */
2086   for (i=0;i<am;i++) {
2087     anzj = ai[i+1] - ai[i];
2088     for (j=0;j<anzj;j++) {
2089       atj[atfill[*aj]] = i;
2090       atfill[*aj++]   += 1;
2091     }
2092   }
2093 
2094   /* Clean up temporary space and complete requests. */
2095   ierr = PetscFree(atfill);CHKERRQ(ierr);
2096   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),an,am,ati,atj,NULL,B);CHKERRQ(ierr);
2097   ierr = MatSetBlockSizes(*B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2098 
2099   b          = (Mat_SeqAIJ*)((*B)->data);
2100   b->free_a  = PETSC_FALSE;
2101   b->free_ij = PETSC_TRUE;
2102   b->nonew   = 0;
2103   PetscFunctionReturn(0);
2104 }
2105 
2106 PetscErrorCode MatTranspose_SeqAIJ(Mat A,MatReuse reuse,Mat *B)
2107 {
2108   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2109   Mat            C;
2110   PetscErrorCode ierr;
2111   PetscInt       i,*aj = a->j,*ai = a->i,m = A->rmap->n,len,*col;
2112   MatScalar      *array = a->a;
2113 
2114   PetscFunctionBegin;
2115   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_INPLACE_MATRIX) {
2116     ierr = PetscCalloc1(1+A->cmap->n,&col);CHKERRQ(ierr);
2117 
2118     for (i=0; i<ai[m]; i++) col[aj[i]] += 1;
2119     ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2120     ierr = MatSetSizes(C,A->cmap->n,m,A->cmap->n,m);CHKERRQ(ierr);
2121     ierr = MatSetBlockSizes(C,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2122     ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2123     ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,col);CHKERRQ(ierr);
2124     ierr = PetscFree(col);CHKERRQ(ierr);
2125   } else {
2126     C = *B;
2127   }
2128 
2129   for (i=0; i<m; i++) {
2130     len    = ai[i+1]-ai[i];
2131     ierr   = MatSetValues_SeqAIJ(C,len,aj,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2132     array += len;
2133     aj    += len;
2134   }
2135   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2136   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2137 
2138   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
2139     *B = C;
2140   } else {
2141     ierr = MatHeaderMerge(A,&C);CHKERRQ(ierr);
2142   }
2143   PetscFunctionReturn(0);
2144 }
2145 
2146 PetscErrorCode  MatIsTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2147 {
2148   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) B->data;
2149   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2150   MatScalar      *va,*vb;
2151   PetscErrorCode ierr;
2152   PetscInt       ma,na,mb,nb, i;
2153 
2154   PetscFunctionBegin;
2155   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2156   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2157   if (ma!=nb || na!=mb) {
2158     *f = PETSC_FALSE;
2159     PetscFunctionReturn(0);
2160   }
2161   aii  = aij->i; bii = bij->i;
2162   adx  = aij->j; bdx = bij->j;
2163   va   = aij->a; vb = bij->a;
2164   ierr = PetscMalloc1(ma,&aptr);CHKERRQ(ierr);
2165   ierr = PetscMalloc1(mb,&bptr);CHKERRQ(ierr);
2166   for (i=0; i<ma; i++) aptr[i] = aii[i];
2167   for (i=0; i<mb; i++) bptr[i] = bii[i];
2168 
2169   *f = PETSC_TRUE;
2170   for (i=0; i<ma; i++) {
2171     while (aptr[i]<aii[i+1]) {
2172       PetscInt    idc,idr;
2173       PetscScalar vc,vr;
2174       /* column/row index/value */
2175       idc = adx[aptr[i]];
2176       idr = bdx[bptr[idc]];
2177       vc  = va[aptr[i]];
2178       vr  = vb[bptr[idc]];
2179       if (i!=idr || PetscAbsScalar(vc-vr) > tol) {
2180         *f = PETSC_FALSE;
2181         goto done;
2182       } else {
2183         aptr[i]++;
2184         if (B || i!=idc) bptr[idc]++;
2185       }
2186     }
2187   }
2188 done:
2189   ierr = PetscFree(aptr);CHKERRQ(ierr);
2190   ierr = PetscFree(bptr);CHKERRQ(ierr);
2191   PetscFunctionReturn(0);
2192 }
2193 
2194 PetscErrorCode  MatIsHermitianTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2195 {
2196   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) B->data;
2197   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2198   MatScalar      *va,*vb;
2199   PetscErrorCode ierr;
2200   PetscInt       ma,na,mb,nb, i;
2201 
2202   PetscFunctionBegin;
2203   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2204   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2205   if (ma!=nb || na!=mb) {
2206     *f = PETSC_FALSE;
2207     PetscFunctionReturn(0);
2208   }
2209   aii  = aij->i; bii = bij->i;
2210   adx  = aij->j; bdx = bij->j;
2211   va   = aij->a; vb = bij->a;
2212   ierr = PetscMalloc1(ma,&aptr);CHKERRQ(ierr);
2213   ierr = PetscMalloc1(mb,&bptr);CHKERRQ(ierr);
2214   for (i=0; i<ma; i++) aptr[i] = aii[i];
2215   for (i=0; i<mb; i++) bptr[i] = bii[i];
2216 
2217   *f = PETSC_TRUE;
2218   for (i=0; i<ma; i++) {
2219     while (aptr[i]<aii[i+1]) {
2220       PetscInt    idc,idr;
2221       PetscScalar vc,vr;
2222       /* column/row index/value */
2223       idc = adx[aptr[i]];
2224       idr = bdx[bptr[idc]];
2225       vc  = va[aptr[i]];
2226       vr  = vb[bptr[idc]];
2227       if (i!=idr || PetscAbsScalar(vc-PetscConj(vr)) > tol) {
2228         *f = PETSC_FALSE;
2229         goto done;
2230       } else {
2231         aptr[i]++;
2232         if (B || i!=idc) bptr[idc]++;
2233       }
2234     }
2235   }
2236 done:
2237   ierr = PetscFree(aptr);CHKERRQ(ierr);
2238   ierr = PetscFree(bptr);CHKERRQ(ierr);
2239   PetscFunctionReturn(0);
2240 }
2241 
2242 PetscErrorCode MatIsSymmetric_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2243 {
2244   PetscErrorCode ierr;
2245 
2246   PetscFunctionBegin;
2247   ierr = MatIsTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2248   PetscFunctionReturn(0);
2249 }
2250 
2251 PetscErrorCode MatIsHermitian_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2252 {
2253   PetscErrorCode ierr;
2254 
2255   PetscFunctionBegin;
2256   ierr = MatIsHermitianTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2257   PetscFunctionReturn(0);
2258 }
2259 
2260 PetscErrorCode MatDiagonalScale_SeqAIJ(Mat A,Vec ll,Vec rr)
2261 {
2262   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2263   const PetscScalar *l,*r;
2264   PetscScalar       x;
2265   MatScalar         *v;
2266   PetscErrorCode    ierr;
2267   PetscInt          i,j,m = A->rmap->n,n = A->cmap->n,M,nz = a->nz;
2268   const PetscInt    *jj;
2269 
2270   PetscFunctionBegin;
2271   if (ll) {
2272     /* The local size is used so that VecMPI can be passed to this routine
2273        by MatDiagonalScale_MPIAIJ */
2274     ierr = VecGetLocalSize(ll,&m);CHKERRQ(ierr);
2275     if (m != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
2276     ierr = VecGetArrayRead(ll,&l);CHKERRQ(ierr);
2277     v    = a->a;
2278     for (i=0; i<m; i++) {
2279       x = l[i];
2280       M = a->i[i+1] - a->i[i];
2281       for (j=0; j<M; j++) (*v++) *= x;
2282     }
2283     ierr = VecRestoreArrayRead(ll,&l);CHKERRQ(ierr);
2284     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2285   }
2286   if (rr) {
2287     ierr = VecGetLocalSize(rr,&n);CHKERRQ(ierr);
2288     if (n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vector wrong length");
2289     ierr = VecGetArrayRead(rr,&r);CHKERRQ(ierr);
2290     v    = a->a; jj = a->j;
2291     for (i=0; i<nz; i++) (*v++) *= r[*jj++];
2292     ierr = VecRestoreArrayRead(rr,&r);CHKERRQ(ierr);
2293     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2294   }
2295   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
2296   PetscFunctionReturn(0);
2297 }
2298 
2299 PetscErrorCode MatCreateSubMatrix_SeqAIJ(Mat A,IS isrow,IS iscol,PetscInt csize,MatReuse scall,Mat *B)
2300 {
2301   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*c;
2302   PetscErrorCode ierr;
2303   PetscInt       *smap,i,k,kstart,kend,oldcols = A->cmap->n,*lens;
2304   PetscInt       row,mat_i,*mat_j,tcol,first,step,*mat_ilen,sum,lensi;
2305   const PetscInt *irow,*icol;
2306   PetscInt       nrows,ncols;
2307   PetscInt       *starts,*j_new,*i_new,*aj = a->j,*ai = a->i,ii,*ailen = a->ilen;
2308   MatScalar      *a_new,*mat_a;
2309   Mat            C;
2310   PetscBool      stride;
2311 
2312   PetscFunctionBegin;
2313 
2314   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
2315   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
2316   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
2317 
2318   ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&stride);CHKERRQ(ierr);
2319   if (stride) {
2320     ierr = ISStrideGetInfo(iscol,&first,&step);CHKERRQ(ierr);
2321   } else {
2322     first = 0;
2323     step  = 0;
2324   }
2325   if (stride && step == 1) {
2326     /* special case of contiguous rows */
2327     ierr = PetscMalloc2(nrows,&lens,nrows,&starts);CHKERRQ(ierr);
2328     /* loop over new rows determining lens and starting points */
2329     for (i=0; i<nrows; i++) {
2330       kstart = ai[irow[i]];
2331       kend   = kstart + ailen[irow[i]];
2332       starts[i] = kstart;
2333       for (k=kstart; k<kend; k++) {
2334         if (aj[k] >= first) {
2335           starts[i] = k;
2336           break;
2337         }
2338       }
2339       sum = 0;
2340       while (k < kend) {
2341         if (aj[k++] >= first+ncols) break;
2342         sum++;
2343       }
2344       lens[i] = sum;
2345     }
2346     /* create submatrix */
2347     if (scall == MAT_REUSE_MATRIX) {
2348       PetscInt n_cols,n_rows;
2349       ierr = MatGetSize(*B,&n_rows,&n_cols);CHKERRQ(ierr);
2350       if (n_rows != nrows || n_cols != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
2351       ierr = MatZeroEntries(*B);CHKERRQ(ierr);
2352       C    = *B;
2353     } else {
2354       PetscInt rbs,cbs;
2355       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2356       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2357       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2358       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2359       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2360       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2361       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2362     }
2363     c = (Mat_SeqAIJ*)C->data;
2364 
2365     /* loop over rows inserting into submatrix */
2366     a_new = c->a;
2367     j_new = c->j;
2368     i_new = c->i;
2369 
2370     for (i=0; i<nrows; i++) {
2371       ii    = starts[i];
2372       lensi = lens[i];
2373       for (k=0; k<lensi; k++) {
2374         *j_new++ = aj[ii+k] - first;
2375       }
2376       ierr       = PetscMemcpy(a_new,a->a + starts[i],lensi*sizeof(PetscScalar));CHKERRQ(ierr);
2377       a_new     += lensi;
2378       i_new[i+1] = i_new[i] + lensi;
2379       c->ilen[i] = lensi;
2380     }
2381     ierr = PetscFree2(lens,starts);CHKERRQ(ierr);
2382   } else {
2383     ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
2384     ierr = PetscCalloc1(oldcols,&smap);CHKERRQ(ierr);
2385     ierr = PetscMalloc1(1+nrows,&lens);CHKERRQ(ierr);
2386     for (i=0; i<ncols; i++) {
2387 #if defined(PETSC_USE_DEBUG)
2388       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);
2389 #endif
2390       smap[icol[i]] = i+1;
2391     }
2392 
2393     /* determine lens of each row */
2394     for (i=0; i<nrows; i++) {
2395       kstart  = ai[irow[i]];
2396       kend    = kstart + a->ilen[irow[i]];
2397       lens[i] = 0;
2398       for (k=kstart; k<kend; k++) {
2399         if (smap[aj[k]]) {
2400           lens[i]++;
2401         }
2402       }
2403     }
2404     /* Create and fill new matrix */
2405     if (scall == MAT_REUSE_MATRIX) {
2406       PetscBool equal;
2407 
2408       c = (Mat_SeqAIJ*)((*B)->data);
2409       if ((*B)->rmap->n  != nrows || (*B)->cmap->n != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
2410       ierr = PetscMemcmp(c->ilen,lens,(*B)->rmap->n*sizeof(PetscInt),&equal);CHKERRQ(ierr);
2411       if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
2412       ierr = PetscMemzero(c->ilen,(*B)->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
2413       C    = *B;
2414     } else {
2415       PetscInt rbs,cbs;
2416       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2417       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2418       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2419       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2420       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2421       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2422       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2423     }
2424     c = (Mat_SeqAIJ*)(C->data);
2425     for (i=0; i<nrows; i++) {
2426       row      = irow[i];
2427       kstart   = ai[row];
2428       kend     = kstart + a->ilen[row];
2429       mat_i    = c->i[i];
2430       mat_j    = c->j + mat_i;
2431       mat_a    = c->a + mat_i;
2432       mat_ilen = c->ilen + i;
2433       for (k=kstart; k<kend; k++) {
2434         if ((tcol=smap[a->j[k]])) {
2435           *mat_j++ = tcol - 1;
2436           *mat_a++ = a->a[k];
2437           (*mat_ilen)++;
2438 
2439         }
2440       }
2441     }
2442     /* Free work space */
2443     ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
2444     ierr = PetscFree(smap);CHKERRQ(ierr);
2445     ierr = PetscFree(lens);CHKERRQ(ierr);
2446     /* sort */
2447     for (i = 0; i < nrows; i++) {
2448       PetscInt ilen;
2449 
2450       mat_i = c->i[i];
2451       mat_j = c->j + mat_i;
2452       mat_a = c->a + mat_i;
2453       ilen  = c->ilen[i];
2454       ierr  = PetscSortIntWithScalarArray(ilen,mat_j,mat_a);CHKERRQ(ierr);
2455     }
2456   }
2457   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2458   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2459 
2460   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
2461   *B   = C;
2462   PetscFunctionReturn(0);
2463 }
2464 
2465 PetscErrorCode  MatGetMultiProcBlock_SeqAIJ(Mat mat,MPI_Comm subComm,MatReuse scall,Mat *subMat)
2466 {
2467   PetscErrorCode ierr;
2468   Mat            B;
2469 
2470   PetscFunctionBegin;
2471   if (scall == MAT_INITIAL_MATRIX) {
2472     ierr    = MatCreate(subComm,&B);CHKERRQ(ierr);
2473     ierr    = MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->n,mat->cmap->n);CHKERRQ(ierr);
2474     ierr    = MatSetBlockSizesFromMats(B,mat,mat);CHKERRQ(ierr);
2475     ierr    = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
2476     ierr    = MatDuplicateNoCreate_SeqAIJ(B,mat,MAT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
2477     *subMat = B;
2478   } else {
2479     ierr = MatCopy_SeqAIJ(mat,*subMat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2480   }
2481   PetscFunctionReturn(0);
2482 }
2483 
2484 PetscErrorCode MatILUFactor_SeqAIJ(Mat inA,IS row,IS col,const MatFactorInfo *info)
2485 {
2486   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)inA->data;
2487   PetscErrorCode ierr;
2488   Mat            outA;
2489   PetscBool      row_identity,col_identity;
2490 
2491   PetscFunctionBegin;
2492   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels=0 supported for in-place ilu");
2493 
2494   ierr = ISIdentity(row,&row_identity);CHKERRQ(ierr);
2495   ierr = ISIdentity(col,&col_identity);CHKERRQ(ierr);
2496 
2497   outA             = inA;
2498   outA->factortype = MAT_FACTOR_LU;
2499   ierr = PetscFree(inA->solvertype);CHKERRQ(ierr);
2500   ierr = PetscStrallocpy(MATSOLVERPETSC,&inA->solvertype);CHKERRQ(ierr);
2501 
2502   ierr = PetscObjectReference((PetscObject)row);CHKERRQ(ierr);
2503   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
2504 
2505   a->row = row;
2506 
2507   ierr = PetscObjectReference((PetscObject)col);CHKERRQ(ierr);
2508   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
2509 
2510   a->col = col;
2511 
2512   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
2513   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
2514   ierr = ISInvertPermutation(col,PETSC_DECIDE,&a->icol);CHKERRQ(ierr);
2515   ierr = PetscLogObjectParent((PetscObject)inA,(PetscObject)a->icol);CHKERRQ(ierr);
2516 
2517   if (!a->solve_work) { /* this matrix may have been factored before */
2518     ierr = PetscMalloc1(inA->rmap->n+1,&a->solve_work);CHKERRQ(ierr);
2519     ierr = PetscLogObjectMemory((PetscObject)inA, (inA->rmap->n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2520   }
2521 
2522   ierr = MatMarkDiagonal_SeqAIJ(inA);CHKERRQ(ierr);
2523   if (row_identity && col_identity) {
2524     ierr = MatLUFactorNumeric_SeqAIJ_inplace(outA,inA,info);CHKERRQ(ierr);
2525   } else {
2526     ierr = MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA,inA,info);CHKERRQ(ierr);
2527   }
2528   PetscFunctionReturn(0);
2529 }
2530 
2531 PetscErrorCode MatScale_SeqAIJ(Mat inA,PetscScalar alpha)
2532 {
2533   Mat_SeqAIJ     *a     = (Mat_SeqAIJ*)inA->data;
2534   PetscScalar    oalpha = alpha;
2535   PetscErrorCode ierr;
2536   PetscBLASInt   one = 1,bnz;
2537 
2538   PetscFunctionBegin;
2539   ierr = PetscBLASIntCast(a->nz,&bnz);CHKERRQ(ierr);
2540   PetscStackCallBLAS("BLASscal",BLASscal_(&bnz,&oalpha,a->a,&one));
2541   ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2542   ierr = MatSeqAIJInvalidateDiagonal(inA);CHKERRQ(ierr);
2543   PetscFunctionReturn(0);
2544 }
2545 
2546 PetscErrorCode MatDestroySubMatrix_Private(Mat_SubSppt *submatj)
2547 {
2548   PetscErrorCode ierr;
2549   PetscInt       i;
2550 
2551   PetscFunctionBegin;
2552   if (!submatj->id) { /* delete data that are linked only to submats[id=0] */
2553     ierr = PetscFree4(submatj->sbuf1,submatj->ptr,submatj->tmp,submatj->ctr);CHKERRQ(ierr);
2554 
2555     for (i=0; i<submatj->nrqr; ++i) {
2556       ierr = PetscFree(submatj->sbuf2[i]);CHKERRQ(ierr);
2557     }
2558     ierr = PetscFree3(submatj->sbuf2,submatj->req_size,submatj->req_source1);CHKERRQ(ierr);
2559 
2560     if (submatj->rbuf1) {
2561       ierr = PetscFree(submatj->rbuf1[0]);CHKERRQ(ierr);
2562       ierr = PetscFree(submatj->rbuf1);CHKERRQ(ierr);
2563     }
2564 
2565     for (i=0; i<submatj->nrqs; ++i) {
2566       ierr = PetscFree(submatj->rbuf3[i]);CHKERRQ(ierr);
2567     }
2568     ierr = PetscFree3(submatj->req_source2,submatj->rbuf2,submatj->rbuf3);CHKERRQ(ierr);
2569     ierr = PetscFree(submatj->pa);CHKERRQ(ierr);
2570   }
2571 
2572 #if defined(PETSC_USE_CTABLE)
2573   ierr = PetscTableDestroy((PetscTable*)&submatj->rmap);CHKERRQ(ierr);
2574   if (submatj->cmap_loc) {ierr = PetscFree(submatj->cmap_loc);CHKERRQ(ierr);}
2575   ierr = PetscFree(submatj->rmap_loc);CHKERRQ(ierr);
2576 #else
2577   ierr = PetscFree(submatj->rmap);CHKERRQ(ierr);
2578 #endif
2579 
2580   if (!submatj->allcolumns) {
2581 #if defined(PETSC_USE_CTABLE)
2582     ierr = PetscTableDestroy((PetscTable*)&submatj->cmap);CHKERRQ(ierr);
2583 #else
2584     ierr = PetscFree(submatj->cmap);CHKERRQ(ierr);
2585 #endif
2586   }
2587   ierr = PetscFree(submatj->row2proc);CHKERRQ(ierr);
2588 
2589   ierr = PetscFree(submatj);CHKERRQ(ierr);
2590   PetscFunctionReturn(0);
2591 }
2592 
2593 PetscErrorCode MatDestroySubMatrix_SeqAIJ(Mat C)
2594 {
2595   PetscErrorCode ierr;
2596   Mat_SeqAIJ     *c = (Mat_SeqAIJ*)C->data;
2597   Mat_SubSppt    *submatj = c->submatis1;
2598 
2599   PetscFunctionBegin;
2600   ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
2601   ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
2602   PetscFunctionReturn(0);
2603 }
2604 
2605 PetscErrorCode MatDestroySubMatrices_SeqAIJ(PetscInt n,Mat *mat[])
2606 {
2607   PetscErrorCode ierr;
2608   PetscInt       i;
2609   Mat            C;
2610   Mat_SeqAIJ     *c;
2611   Mat_SubSppt    *submatj;
2612 
2613   PetscFunctionBegin;
2614   for (i=0; i<n; i++) {
2615     C       = (*mat)[i];
2616     c       = (Mat_SeqAIJ*)C->data;
2617     submatj = c->submatis1;
2618     if (submatj) {
2619       if (--((PetscObject)C)->refct <= 0) {
2620         ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
2621         ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
2622         ierr = PetscFree(C->defaultvectype);CHKERRQ(ierr);
2623         ierr = PetscLayoutDestroy(&C->rmap);CHKERRQ(ierr);
2624         ierr = PetscLayoutDestroy(&C->cmap);CHKERRQ(ierr);
2625         ierr = PetscHeaderDestroy(&C);CHKERRQ(ierr);
2626       }
2627     } else {
2628       ierr = MatDestroy(&C);CHKERRQ(ierr);
2629     }
2630   }
2631 
2632   ierr = PetscFree(*mat);CHKERRQ(ierr);
2633   PetscFunctionReturn(0);
2634 }
2635 
2636 PetscErrorCode MatCreateSubMatrices_SeqAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
2637 {
2638   PetscErrorCode ierr;
2639   PetscInt       i;
2640 
2641   PetscFunctionBegin;
2642   if (scall == MAT_INITIAL_MATRIX) {
2643     ierr = PetscCalloc1(n+1,B);CHKERRQ(ierr);
2644   }
2645 
2646   for (i=0; i<n; i++) {
2647     ierr = MatCreateSubMatrix_SeqAIJ(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]);CHKERRQ(ierr);
2648   }
2649   PetscFunctionReturn(0);
2650 }
2651 
2652 PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
2653 {
2654   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2655   PetscErrorCode ierr;
2656   PetscInt       row,i,j,k,l,m,n,*nidx,isz,val;
2657   const PetscInt *idx;
2658   PetscInt       start,end,*ai,*aj;
2659   PetscBT        table;
2660 
2661   PetscFunctionBegin;
2662   m  = A->rmap->n;
2663   ai = a->i;
2664   aj = a->j;
2665 
2666   if (ov < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"illegal negative overlap value used");
2667 
2668   ierr = PetscMalloc1(m+1,&nidx);CHKERRQ(ierr);
2669   ierr = PetscBTCreate(m,&table);CHKERRQ(ierr);
2670 
2671   for (i=0; i<is_max; i++) {
2672     /* Initialize the two local arrays */
2673     isz  = 0;
2674     ierr = PetscBTMemzero(m,table);CHKERRQ(ierr);
2675 
2676     /* Extract the indices, assume there can be duplicate entries */
2677     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
2678     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
2679 
2680     /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2681     for (j=0; j<n; ++j) {
2682       if (!PetscBTLookupSet(table,idx[j])) nidx[isz++] = idx[j];
2683     }
2684     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
2685     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
2686 
2687     k = 0;
2688     for (j=0; j<ov; j++) { /* for each overlap */
2689       n = isz;
2690       for (; k<n; k++) { /* do only those rows in nidx[k], which are not done yet */
2691         row   = nidx[k];
2692         start = ai[row];
2693         end   = ai[row+1];
2694         for (l = start; l<end; l++) {
2695           val = aj[l];
2696           if (!PetscBTLookupSet(table,val)) nidx[isz++] = val;
2697         }
2698       }
2699     }
2700     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz,nidx,PETSC_COPY_VALUES,(is+i));CHKERRQ(ierr);
2701   }
2702   ierr = PetscBTDestroy(&table);CHKERRQ(ierr);
2703   ierr = PetscFree(nidx);CHKERRQ(ierr);
2704   PetscFunctionReturn(0);
2705 }
2706 
2707 /* -------------------------------------------------------------- */
2708 PetscErrorCode MatPermute_SeqAIJ(Mat A,IS rowp,IS colp,Mat *B)
2709 {
2710   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2711   PetscErrorCode ierr;
2712   PetscInt       i,nz = 0,m = A->rmap->n,n = A->cmap->n;
2713   const PetscInt *row,*col;
2714   PetscInt       *cnew,j,*lens;
2715   IS             icolp,irowp;
2716   PetscInt       *cwork = NULL;
2717   PetscScalar    *vwork = NULL;
2718 
2719   PetscFunctionBegin;
2720   ierr = ISInvertPermutation(rowp,PETSC_DECIDE,&irowp);CHKERRQ(ierr);
2721   ierr = ISGetIndices(irowp,&row);CHKERRQ(ierr);
2722   ierr = ISInvertPermutation(colp,PETSC_DECIDE,&icolp);CHKERRQ(ierr);
2723   ierr = ISGetIndices(icolp,&col);CHKERRQ(ierr);
2724 
2725   /* determine lengths of permuted rows */
2726   ierr = PetscMalloc1(m+1,&lens);CHKERRQ(ierr);
2727   for (i=0; i<m; i++) lens[row[i]] = a->i[i+1] - a->i[i];
2728   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
2729   ierr = MatSetSizes(*B,m,n,m,n);CHKERRQ(ierr);
2730   ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
2731   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2732   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*B,0,lens);CHKERRQ(ierr);
2733   ierr = PetscFree(lens);CHKERRQ(ierr);
2734 
2735   ierr = PetscMalloc1(n,&cnew);CHKERRQ(ierr);
2736   for (i=0; i<m; i++) {
2737     ierr = MatGetRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2738     for (j=0; j<nz; j++) cnew[j] = col[cwork[j]];
2739     ierr = MatSetValues_SeqAIJ(*B,1,&row[i],nz,cnew,vwork,INSERT_VALUES);CHKERRQ(ierr);
2740     ierr = MatRestoreRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2741   }
2742   ierr = PetscFree(cnew);CHKERRQ(ierr);
2743 
2744   (*B)->assembled = PETSC_FALSE;
2745 
2746   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2747   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2748   ierr = ISRestoreIndices(irowp,&row);CHKERRQ(ierr);
2749   ierr = ISRestoreIndices(icolp,&col);CHKERRQ(ierr);
2750   ierr = ISDestroy(&irowp);CHKERRQ(ierr);
2751   ierr = ISDestroy(&icolp);CHKERRQ(ierr);
2752   PetscFunctionReturn(0);
2753 }
2754 
2755 PetscErrorCode MatCopy_SeqAIJ(Mat A,Mat B,MatStructure str)
2756 {
2757   PetscErrorCode ierr;
2758 
2759   PetscFunctionBegin;
2760   /* If the two matrices have the same copy implementation, use fast copy. */
2761   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
2762     Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2763     Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data;
2764 
2765     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");
2766     ierr = PetscMemcpy(b->a,a->a,(a->i[A->rmap->n])*sizeof(PetscScalar));CHKERRQ(ierr);
2767     ierr = PetscObjectStateIncrease((PetscObject)B);CHKERRQ(ierr);
2768   } else {
2769     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2770   }
2771   PetscFunctionReturn(0);
2772 }
2773 
2774 PetscErrorCode MatSetUp_SeqAIJ(Mat A)
2775 {
2776   PetscErrorCode ierr;
2777 
2778   PetscFunctionBegin;
2779   ierr =  MatSeqAIJSetPreallocation_SeqAIJ(A,PETSC_DEFAULT,0);CHKERRQ(ierr);
2780   PetscFunctionReturn(0);
2781 }
2782 
2783 PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A,PetscScalar *array[])
2784 {
2785   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2786 
2787   PetscFunctionBegin;
2788   *array = a->a;
2789   PetscFunctionReturn(0);
2790 }
2791 
2792 PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A,PetscScalar *array[])
2793 {
2794   PetscFunctionBegin;
2795   PetscFunctionReturn(0);
2796 }
2797 
2798 /*
2799    Computes the number of nonzeros per row needed for preallocation when X and Y
2800    have different nonzero structure.
2801 */
2802 PetscErrorCode MatAXPYGetPreallocation_SeqX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *yi,const PetscInt *yj,PetscInt *nnz)
2803 {
2804   PetscInt       i,j,k,nzx,nzy;
2805 
2806   PetscFunctionBegin;
2807   /* Set the number of nonzeros in the new matrix */
2808   for (i=0; i<m; i++) {
2809     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2810     nzx = xi[i+1] - xi[i];
2811     nzy = yi[i+1] - yi[i];
2812     nnz[i] = 0;
2813     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2814       for (; k<nzy && yjj[k]<xjj[j]; k++) nnz[i]++; /* Catch up to X */
2815       if (k<nzy && yjj[k]==xjj[j]) k++;             /* Skip duplicate */
2816       nnz[i]++;
2817     }
2818     for (; k<nzy; k++) nnz[i]++;
2819   }
2820   PetscFunctionReturn(0);
2821 }
2822 
2823 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
2824 {
2825   PetscInt       m = Y->rmap->N;
2826   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2827   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2828   PetscErrorCode ierr;
2829 
2830   PetscFunctionBegin;
2831   /* Set the number of nonzeros in the new matrix */
2832   ierr = MatAXPYGetPreallocation_SeqX_private(m,x->i,x->j,y->i,y->j,nnz);CHKERRQ(ierr);
2833   PetscFunctionReturn(0);
2834 }
2835 
2836 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2837 {
2838   PetscErrorCode ierr;
2839   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
2840   PetscBLASInt   one=1,bnz;
2841 
2842   PetscFunctionBegin;
2843   ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2844   if (str == SAME_NONZERO_PATTERN) {
2845     PetscScalar alpha = a;
2846     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2847     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
2848     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2849   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2850     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2851   } else {
2852     Mat      B;
2853     PetscInt *nnz;
2854     ierr = PetscMalloc1(Y->rmap->N,&nnz);CHKERRQ(ierr);
2855     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2856     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2857     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2858     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2859     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
2860     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
2861     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
2862     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2863     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2864     ierr = PetscFree(nnz);CHKERRQ(ierr);
2865   }
2866   PetscFunctionReturn(0);
2867 }
2868 
2869 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
2870 {
2871 #if defined(PETSC_USE_COMPLEX)
2872   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
2873   PetscInt    i,nz;
2874   PetscScalar *a;
2875 
2876   PetscFunctionBegin;
2877   nz = aij->nz;
2878   a  = aij->a;
2879   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
2880 #else
2881   PetscFunctionBegin;
2882 #endif
2883   PetscFunctionReturn(0);
2884 }
2885 
2886 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2887 {
2888   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2889   PetscErrorCode ierr;
2890   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2891   PetscReal      atmp;
2892   PetscScalar    *x;
2893   MatScalar      *aa;
2894 
2895   PetscFunctionBegin;
2896   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2897   aa = a->a;
2898   ai = a->i;
2899   aj = a->j;
2900 
2901   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2902   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2903   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2904   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2905   for (i=0; i<m; i++) {
2906     ncols = ai[1] - ai[0]; ai++;
2907     x[i]  = 0.0;
2908     for (j=0; j<ncols; j++) {
2909       atmp = PetscAbsScalar(*aa);
2910       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
2911       aa++; aj++;
2912     }
2913   }
2914   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2915   PetscFunctionReturn(0);
2916 }
2917 
2918 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2919 {
2920   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2921   PetscErrorCode ierr;
2922   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2923   PetscScalar    *x;
2924   MatScalar      *aa;
2925 
2926   PetscFunctionBegin;
2927   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2928   aa = a->a;
2929   ai = a->i;
2930   aj = a->j;
2931 
2932   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2933   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2934   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2935   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2936   for (i=0; i<m; i++) {
2937     ncols = ai[1] - ai[0]; ai++;
2938     if (ncols == A->cmap->n) { /* row is dense */
2939       x[i] = *aa; if (idx) idx[i] = 0;
2940     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
2941       x[i] = 0.0;
2942       if (idx) {
2943         idx[i] = 0; /* in case ncols is zero */
2944         for (j=0;j<ncols;j++) { /* find first implicit 0.0 in the row */
2945           if (aj[j] > j) {
2946             idx[i] = j;
2947             break;
2948           }
2949         }
2950       }
2951     }
2952     for (j=0; j<ncols; j++) {
2953       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
2954       aa++; aj++;
2955     }
2956   }
2957   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2958   PetscFunctionReturn(0);
2959 }
2960 
2961 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2962 {
2963   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2964   PetscErrorCode ierr;
2965   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2966   PetscReal      atmp;
2967   PetscScalar    *x;
2968   MatScalar      *aa;
2969 
2970   PetscFunctionBegin;
2971   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2972   aa = a->a;
2973   ai = a->i;
2974   aj = a->j;
2975 
2976   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2977   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2978   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2979   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);
2980   for (i=0; i<m; i++) {
2981     ncols = ai[1] - ai[0]; ai++;
2982     if (ncols) {
2983       /* Get first nonzero */
2984       for (j = 0; j < ncols; j++) {
2985         atmp = PetscAbsScalar(aa[j]);
2986         if (atmp > 1.0e-12) {
2987           x[i] = atmp;
2988           if (idx) idx[i] = aj[j];
2989           break;
2990         }
2991       }
2992       if (j == ncols) {x[i] = PetscAbsScalar(*aa); if (idx) idx[i] = *aj;}
2993     } else {
2994       x[i] = 0.0; if (idx) idx[i] = 0;
2995     }
2996     for (j = 0; j < ncols; j++) {
2997       atmp = PetscAbsScalar(*aa);
2998       if (atmp > 1.0e-12 && PetscAbsScalar(x[i]) > atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
2999       aa++; aj++;
3000     }
3001   }
3002   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3003   PetscFunctionReturn(0);
3004 }
3005 
3006 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3007 {
3008   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
3009   PetscErrorCode  ierr;
3010   PetscInt        i,j,m = A->rmap->n,ncols,n;
3011   const PetscInt  *ai,*aj;
3012   PetscScalar     *x;
3013   const MatScalar *aa;
3014 
3015   PetscFunctionBegin;
3016   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3017   aa = a->a;
3018   ai = a->i;
3019   aj = a->j;
3020 
3021   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3022   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3023   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3024   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3025   for (i=0; i<m; i++) {
3026     ncols = ai[1] - ai[0]; ai++;
3027     if (ncols == A->cmap->n) { /* row is dense */
3028       x[i] = *aa; if (idx) idx[i] = 0;
3029     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3030       x[i] = 0.0;
3031       if (idx) {   /* find first implicit 0.0 in the row */
3032         idx[i] = 0; /* in case ncols is zero */
3033         for (j=0; j<ncols; j++) {
3034           if (aj[j] > j) {
3035             idx[i] = j;
3036             break;
3037           }
3038         }
3039       }
3040     }
3041     for (j=0; j<ncols; j++) {
3042       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3043       aa++; aj++;
3044     }
3045   }
3046   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3047   PetscFunctionReturn(0);
3048 }
3049 
3050 PetscErrorCode MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3051 {
3052   Mat_SeqAIJ      *a = (Mat_SeqAIJ*) A->data;
3053   PetscErrorCode  ierr;
3054   PetscInt        i,bs = PetscAbs(A->rmap->bs),mbs = A->rmap->n/bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3055   MatScalar       *diag,work[25],*v_work;
3056   const PetscReal shift = 0.0;
3057   PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;
3058 
3059   PetscFunctionBegin;
3060   allowzeropivot = PetscNot(A->erroriffailure);
3061   if (a->ibdiagvalid) {
3062     if (values) *values = a->ibdiag;
3063     PetscFunctionReturn(0);
3064   }
3065   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3066   if (!a->ibdiag) {
3067     ierr = PetscMalloc1(bs2*mbs,&a->ibdiag);CHKERRQ(ierr);
3068     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3069   }
3070   diag = a->ibdiag;
3071   if (values) *values = a->ibdiag;
3072   /* factor and invert each block */
3073   switch (bs) {
3074   case 1:
3075     for (i=0; i<mbs; i++) {
3076       ierr = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3077       if (PetscAbsScalar(diag[i] + shift) < PETSC_MACHINE_EPSILON) {
3078         if (allowzeropivot) {
3079           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3080           A->factorerror_zeropivot_value = PetscAbsScalar(diag[i]);
3081           A->factorerror_zeropivot_row   = i;
3082           ierr = PetscInfo3(A,"Zero pivot, row %D pivot %g tolerance %g\n",i,(double)PetscAbsScalar(diag[i]),(double)PETSC_MACHINE_EPSILON);CHKERRQ(ierr);
3083         } 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);
3084       }
3085       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3086     }
3087     break;
3088   case 2:
3089     for (i=0; i<mbs; i++) {
3090       ij[0] = 2*i; ij[1] = 2*i + 1;
3091       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3092       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3093       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3094       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
3095       diag += 4;
3096     }
3097     break;
3098   case 3:
3099     for (i=0; i<mbs; i++) {
3100       ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
3101       ierr  = MatGetValues(A,3,ij,3,ij,diag);CHKERRQ(ierr);
3102       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3103       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3104       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3105       diag += 9;
3106     }
3107     break;
3108   case 4:
3109     for (i=0; i<mbs; i++) {
3110       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3111       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3112       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3113       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3114       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3115       diag += 16;
3116     }
3117     break;
3118   case 5:
3119     for (i=0; i<mbs; i++) {
3120       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3121       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3122       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3123       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3124       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3125       diag += 25;
3126     }
3127     break;
3128   case 6:
3129     for (i=0; i<mbs; i++) {
3130       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;
3131       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3132       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3133       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3134       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3135       diag += 36;
3136     }
3137     break;
3138   case 7:
3139     for (i=0; i<mbs; i++) {
3140       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;
3141       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3142       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3143       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3144       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3145       diag += 49;
3146     }
3147     break;
3148   default:
3149     ierr = PetscMalloc3(bs,&v_work,bs,&v_pivots,bs,&IJ);CHKERRQ(ierr);
3150     for (i=0; i<mbs; i++) {
3151       for (j=0; j<bs; j++) {
3152         IJ[j] = bs*i + j;
3153       }
3154       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3155       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3156       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3157       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3158       diag += bs2;
3159     }
3160     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3161   }
3162   a->ibdiagvalid = PETSC_TRUE;
3163   PetscFunctionReturn(0);
3164 }
3165 
3166 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3167 {
3168   PetscErrorCode ierr;
3169   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3170   PetscScalar    a;
3171   PetscInt       m,n,i,j,col;
3172 
3173   PetscFunctionBegin;
3174   if (!x->assembled) {
3175     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3176     for (i=0; i<m; i++) {
3177       for (j=0; j<aij->imax[i]; j++) {
3178         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3179         col  = (PetscInt)(n*PetscRealPart(a));
3180         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3181       }
3182     }
3183   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet coded");
3184   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3185   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3186   PetscFunctionReturn(0);
3187 }
3188 
3189 PetscErrorCode MatShift_SeqAIJ(Mat Y,PetscScalar a)
3190 {
3191   PetscErrorCode ierr;
3192   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)Y->data;
3193 
3194   PetscFunctionBegin;
3195   if (!Y->preallocated || !aij->nz) {
3196     ierr = MatSeqAIJSetPreallocation(Y,1,NULL);CHKERRQ(ierr);
3197   }
3198   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
3199   PetscFunctionReturn(0);
3200 }
3201 
3202 /* -------------------------------------------------------------------*/
3203 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3204                                         MatGetRow_SeqAIJ,
3205                                         MatRestoreRow_SeqAIJ,
3206                                         MatMult_SeqAIJ,
3207                                 /*  4*/ MatMultAdd_SeqAIJ,
3208                                         MatMultTranspose_SeqAIJ,
3209                                         MatMultTransposeAdd_SeqAIJ,
3210                                         0,
3211                                         0,
3212                                         0,
3213                                 /* 10*/ 0,
3214                                         MatLUFactor_SeqAIJ,
3215                                         0,
3216                                         MatSOR_SeqAIJ,
3217                                         MatTranspose_SeqAIJ_FAST,
3218                                 /*1 5*/ MatGetInfo_SeqAIJ,
3219                                         MatEqual_SeqAIJ,
3220                                         MatGetDiagonal_SeqAIJ,
3221                                         MatDiagonalScale_SeqAIJ,
3222                                         MatNorm_SeqAIJ,
3223                                 /* 20*/ 0,
3224                                         MatAssemblyEnd_SeqAIJ,
3225                                         MatSetOption_SeqAIJ,
3226                                         MatZeroEntries_SeqAIJ,
3227                                 /* 24*/ MatZeroRows_SeqAIJ,
3228                                         0,
3229                                         0,
3230                                         0,
3231                                         0,
3232                                 /* 29*/ MatSetUp_SeqAIJ,
3233                                         0,
3234                                         0,
3235                                         0,
3236                                         0,
3237                                 /* 34*/ MatDuplicate_SeqAIJ,
3238                                         0,
3239                                         0,
3240                                         MatILUFactor_SeqAIJ,
3241                                         0,
3242                                 /* 39*/ MatAXPY_SeqAIJ,
3243                                         MatCreateSubMatrices_SeqAIJ,
3244                                         MatIncreaseOverlap_SeqAIJ,
3245                                         MatGetValues_SeqAIJ,
3246                                         MatCopy_SeqAIJ,
3247                                 /* 44*/ MatGetRowMax_SeqAIJ,
3248                                         MatScale_SeqAIJ,
3249                                         MatShift_SeqAIJ,
3250                                         MatDiagonalSet_SeqAIJ,
3251                                         MatZeroRowsColumns_SeqAIJ,
3252                                 /* 49*/ MatSetRandom_SeqAIJ,
3253                                         MatGetRowIJ_SeqAIJ,
3254                                         MatRestoreRowIJ_SeqAIJ,
3255                                         MatGetColumnIJ_SeqAIJ,
3256                                         MatRestoreColumnIJ_SeqAIJ,
3257                                 /* 54*/ MatFDColoringCreate_SeqXAIJ,
3258                                         0,
3259                                         0,
3260                                         MatPermute_SeqAIJ,
3261                                         0,
3262                                 /* 59*/ 0,
3263                                         MatDestroy_SeqAIJ,
3264                                         MatView_SeqAIJ,
3265                                         0,
3266                                         MatMatMatMult_SeqAIJ_SeqAIJ_SeqAIJ,
3267                                 /* 64*/ MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ,
3268                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3269                                         0,
3270                                         0,
3271                                         0,
3272                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3273                                         MatGetRowMinAbs_SeqAIJ,
3274                                         0,
3275                                         0,
3276                                         0,
3277                                 /* 74*/ 0,
3278                                         MatFDColoringApply_AIJ,
3279                                         0,
3280                                         0,
3281                                         0,
3282                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3283                                         0,
3284                                         0,
3285                                         0,
3286                                         MatLoad_SeqAIJ,
3287                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3288                                         MatIsHermitian_SeqAIJ,
3289                                         0,
3290                                         0,
3291                                         0,
3292                                 /* 89*/ MatMatMult_SeqAIJ_SeqAIJ,
3293                                         MatMatMultSymbolic_SeqAIJ_SeqAIJ,
3294                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3295                                         MatPtAP_SeqAIJ_SeqAIJ,
3296                                         MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy,
3297                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy,
3298                                         MatMatTransposeMult_SeqAIJ_SeqAIJ,
3299                                         MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ,
3300                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3301                                         0,
3302                                 /* 99*/ 0,
3303                                         0,
3304                                         0,
3305                                         MatConjugate_SeqAIJ,
3306                                         0,
3307                                 /*104*/ MatSetValuesRow_SeqAIJ,
3308                                         MatRealPart_SeqAIJ,
3309                                         MatImaginaryPart_SeqAIJ,
3310                                         0,
3311                                         0,
3312                                 /*109*/ MatMatSolve_SeqAIJ,
3313                                         0,
3314                                         MatGetRowMin_SeqAIJ,
3315                                         0,
3316                                         MatMissingDiagonal_SeqAIJ,
3317                                 /*114*/ 0,
3318                                         0,
3319                                         0,
3320                                         0,
3321                                         0,
3322                                 /*119*/ 0,
3323                                         0,
3324                                         0,
3325                                         0,
3326                                         MatGetMultiProcBlock_SeqAIJ,
3327                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3328                                         MatGetColumnNorms_SeqAIJ,
3329                                         MatInvertBlockDiagonal_SeqAIJ,
3330                                         MatInvertVariableBlockDiagonal_SeqAIJ,
3331                                         0,
3332                                 /*129*/ 0,
3333                                         MatTransposeMatMult_SeqAIJ_SeqAIJ,
3334                                         MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ,
3335                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3336                                         MatTransposeColoringCreate_SeqAIJ,
3337                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3338                                         MatTransColoringApplyDenToSp_SeqAIJ,
3339                                         MatRARt_SeqAIJ_SeqAIJ,
3340                                         MatRARtSymbolic_SeqAIJ_SeqAIJ,
3341                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3342                                  /*139*/0,
3343                                         0,
3344                                         0,
3345                                         MatFDColoringSetUp_SeqXAIJ,
3346                                         MatFindOffBlockDiagonalEntries_SeqAIJ,
3347                                  /*144*/MatCreateMPIMatConcatenateSeqMat_SeqAIJ,
3348                                         MatDestroySubMatrices_SeqAIJ
3349 };
3350 
3351 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3352 {
3353   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3354   PetscInt   i,nz,n;
3355 
3356   PetscFunctionBegin;
3357   nz = aij->maxnz;
3358   n  = mat->rmap->n;
3359   for (i=0; i<nz; i++) {
3360     aij->j[i] = indices[i];
3361   }
3362   aij->nz = nz;
3363   for (i=0; i<n; i++) {
3364     aij->ilen[i] = aij->imax[i];
3365   }
3366   PetscFunctionReturn(0);
3367 }
3368 
3369 /*@
3370     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3371        in the matrix.
3372 
3373   Input Parameters:
3374 +  mat - the SeqAIJ matrix
3375 -  indices - the column indices
3376 
3377   Level: advanced
3378 
3379   Notes:
3380     This can be called if you have precomputed the nonzero structure of the
3381   matrix and want to provide it to the matrix object to improve the performance
3382   of the MatSetValues() operation.
3383 
3384     You MUST have set the correct numbers of nonzeros per row in the call to
3385   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3386 
3387     MUST be called before any calls to MatSetValues();
3388 
3389     The indices should start with zero, not one.
3390 
3391 @*/
3392 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3393 {
3394   PetscErrorCode ierr;
3395 
3396   PetscFunctionBegin;
3397   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3398   PetscValidPointer(indices,2);
3399   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3400   PetscFunctionReturn(0);
3401 }
3402 
3403 /* ----------------------------------------------------------------------------------------*/
3404 
3405 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3406 {
3407   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3408   PetscErrorCode ierr;
3409   size_t         nz = aij->i[mat->rmap->n];
3410 
3411   PetscFunctionBegin;
3412   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3413 
3414   /* allocate space for values if not already there */
3415   if (!aij->saved_values) {
3416     ierr = PetscMalloc1(nz+1,&aij->saved_values);CHKERRQ(ierr);
3417     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3418   }
3419 
3420   /* copy values over */
3421   ierr = PetscMemcpy(aij->saved_values,aij->a,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3422   PetscFunctionReturn(0);
3423 }
3424 
3425 /*@
3426     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3427        example, reuse of the linear part of a Jacobian, while recomputing the
3428        nonlinear portion.
3429 
3430    Collect on Mat
3431 
3432   Input Parameters:
3433 .  mat - the matrix (currently only AIJ matrices support this option)
3434 
3435   Level: advanced
3436 
3437   Common Usage, with SNESSolve():
3438 $    Create Jacobian matrix
3439 $    Set linear terms into matrix
3440 $    Apply boundary conditions to matrix, at this time matrix must have
3441 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3442 $      boundary conditions again will not change the nonzero structure
3443 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3444 $    ierr = MatStoreValues(mat);
3445 $    Call SNESSetJacobian() with matrix
3446 $    In your Jacobian routine
3447 $      ierr = MatRetrieveValues(mat);
3448 $      Set nonlinear terms in matrix
3449 
3450   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3451 $    // build linear portion of Jacobian
3452 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3453 $    ierr = MatStoreValues(mat);
3454 $    loop over nonlinear iterations
3455 $       ierr = MatRetrieveValues(mat);
3456 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3457 $       // call MatAssemblyBegin/End() on matrix
3458 $       Solve linear system with Jacobian
3459 $    endloop
3460 
3461   Notes:
3462     Matrix must already be assemblied before calling this routine
3463     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3464     calling this routine.
3465 
3466     When this is called multiple times it overwrites the previous set of stored values
3467     and does not allocated additional space.
3468 
3469 .seealso: MatRetrieveValues()
3470 
3471 @*/
3472 PetscErrorCode  MatStoreValues(Mat mat)
3473 {
3474   PetscErrorCode ierr;
3475 
3476   PetscFunctionBegin;
3477   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3478   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3479   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3480   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3481   PetscFunctionReturn(0);
3482 }
3483 
3484 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3485 {
3486   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3487   PetscErrorCode ierr;
3488   PetscInt       nz = aij->i[mat->rmap->n];
3489 
3490   PetscFunctionBegin;
3491   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3492   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3493   /* copy values over */
3494   ierr = PetscMemcpy(aij->a,aij->saved_values,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3495   PetscFunctionReturn(0);
3496 }
3497 
3498 /*@
3499     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3500        example, reuse of the linear part of a Jacobian, while recomputing the
3501        nonlinear portion.
3502 
3503    Collect on Mat
3504 
3505   Input Parameters:
3506 .  mat - the matrix (currently only AIJ matrices support this option)
3507 
3508   Level: advanced
3509 
3510 .seealso: MatStoreValues()
3511 
3512 @*/
3513 PetscErrorCode  MatRetrieveValues(Mat mat)
3514 {
3515   PetscErrorCode ierr;
3516 
3517   PetscFunctionBegin;
3518   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3519   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3520   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3521   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3522   PetscFunctionReturn(0);
3523 }
3524 
3525 
3526 /* --------------------------------------------------------------------------------*/
3527 /*@C
3528    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3529    (the default parallel PETSc format).  For good matrix assembly performance
3530    the user should preallocate the matrix storage by setting the parameter nz
3531    (or the array nnz).  By setting these parameters accurately, performance
3532    during matrix assembly can be increased by more than a factor of 50.
3533 
3534    Collective on MPI_Comm
3535 
3536    Input Parameters:
3537 +  comm - MPI communicator, set to PETSC_COMM_SELF
3538 .  m - number of rows
3539 .  n - number of columns
3540 .  nz - number of nonzeros per row (same for all rows)
3541 -  nnz - array containing the number of nonzeros in the various rows
3542          (possibly different for each row) or NULL
3543 
3544    Output Parameter:
3545 .  A - the matrix
3546 
3547    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3548    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3549    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3550 
3551    Notes:
3552    If nnz is given then nz is ignored
3553 
3554    The AIJ format (also called the Yale sparse matrix format or
3555    compressed row storage), is fully compatible with standard Fortran 77
3556    storage.  That is, the stored row and column indices can begin at
3557    either one (as in Fortran) or zero.  See the users' manual for details.
3558 
3559    Specify the preallocated storage with either nz or nnz (not both).
3560    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3561    allocation.  For large problems you MUST preallocate memory or you
3562    will get TERRIBLE performance, see the users' manual chapter on matrices.
3563 
3564    By default, this format uses inodes (identical nodes) when possible, to
3565    improve numerical efficiency of matrix-vector products and solves. We
3566    search for consecutive rows with the same nonzero structure, thereby
3567    reusing matrix information to achieve increased efficiency.
3568 
3569    Options Database Keys:
3570 +  -mat_no_inode  - Do not use inodes
3571 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3572 
3573    Level: intermediate
3574 
3575 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3576 
3577 @*/
3578 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3579 {
3580   PetscErrorCode ierr;
3581 
3582   PetscFunctionBegin;
3583   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3584   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3585   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3586   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3587   PetscFunctionReturn(0);
3588 }
3589 
3590 /*@C
3591    MatSeqAIJSetPreallocation - For good matrix assembly performance
3592    the user should preallocate the matrix storage by setting the parameter nz
3593    (or the array nnz).  By setting these parameters accurately, performance
3594    during matrix assembly can be increased by more than a factor of 50.
3595 
3596    Collective on MPI_Comm
3597 
3598    Input Parameters:
3599 +  B - The matrix
3600 .  nz - number of nonzeros per row (same for all rows)
3601 -  nnz - array containing the number of nonzeros in the various rows
3602          (possibly different for each row) or NULL
3603 
3604    Notes:
3605      If nnz is given then nz is ignored
3606 
3607     The AIJ format (also called the Yale sparse matrix format or
3608    compressed row storage), is fully compatible with standard Fortran 77
3609    storage.  That is, the stored row and column indices can begin at
3610    either one (as in Fortran) or zero.  See the users' manual for details.
3611 
3612    Specify the preallocated storage with either nz or nnz (not both).
3613    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3614    allocation.  For large problems you MUST preallocate memory or you
3615    will get TERRIBLE performance, see the users' manual chapter on matrices.
3616 
3617    You can call MatGetInfo() to get information on how effective the preallocation was;
3618    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3619    You can also run with the option -info and look for messages with the string
3620    malloc in them to see if additional memory allocation was needed.
3621 
3622    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3623    entries or columns indices
3624 
3625    By default, this format uses inodes (identical nodes) when possible, to
3626    improve numerical efficiency of matrix-vector products and solves. We
3627    search for consecutive rows with the same nonzero structure, thereby
3628    reusing matrix information to achieve increased efficiency.
3629 
3630    Options Database Keys:
3631 +  -mat_no_inode  - Do not use inodes
3632 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3633 
3634    Level: intermediate
3635 
3636 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatGetInfo()
3637 
3638 @*/
3639 PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
3640 {
3641   PetscErrorCode ierr;
3642 
3643   PetscFunctionBegin;
3644   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3645   PetscValidType(B,1);
3646   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));CHKERRQ(ierr);
3647   PetscFunctionReturn(0);
3648 }
3649 
3650 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3651 {
3652   Mat_SeqAIJ     *b;
3653   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3654   PetscErrorCode ierr;
3655   PetscInt       i;
3656 
3657   PetscFunctionBegin;
3658   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3659   if (nz == MAT_SKIP_ALLOCATION) {
3660     skipallocation = PETSC_TRUE;
3661     nz             = 0;
3662   }
3663   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3664   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3665 
3666   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3667   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %D",nz);
3668   if (nnz) {
3669     for (i=0; i<B->rmap->n; i++) {
3670       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]);
3671       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);
3672     }
3673   }
3674 
3675   B->preallocated = PETSC_TRUE;
3676 
3677   b = (Mat_SeqAIJ*)B->data;
3678 
3679   if (!skipallocation) {
3680     if (!b->imax) {
3681       ierr = PetscMalloc2(B->rmap->n,&b->imax,B->rmap->n,&b->ilen);CHKERRQ(ierr);
3682       ierr = PetscLogObjectMemory((PetscObject)B,2*B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3683     }
3684     if (!b->ipre) {
3685       ierr = PetscMalloc1(B->rmap->n,&b->ipre);CHKERRQ(ierr);
3686       ierr = PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3687     }
3688     if (!nnz) {
3689       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3690       else if (nz < 0) nz = 1;
3691       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
3692       nz = nz*B->rmap->n;
3693     } else {
3694       nz = 0;
3695       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz += nnz[i];}
3696     }
3697     /* b->ilen will count nonzeros in each row so far. */
3698     for (i=0; i<B->rmap->n; i++) b->ilen[i] = 0;
3699 
3700     /* allocate the matrix space */
3701     /* FIXME: should B's old memory be unlogged? */
3702     ierr = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
3703     if (B->structure_only) {
3704       ierr = PetscMalloc1(nz,&b->j);CHKERRQ(ierr);
3705       ierr = PetscMalloc1(B->rmap->n+1,&b->i);CHKERRQ(ierr);
3706       ierr = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*sizeof(PetscInt));CHKERRQ(ierr);
3707     } else {
3708       ierr = PetscMalloc3(nz,&b->a,nz,&b->j,B->rmap->n+1,&b->i);CHKERRQ(ierr);
3709       ierr = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
3710     }
3711     b->i[0] = 0;
3712     for (i=1; i<B->rmap->n+1; i++) {
3713       b->i[i] = b->i[i-1] + b->imax[i-1];
3714     }
3715     if (B->structure_only) {
3716       b->singlemalloc = PETSC_FALSE;
3717       b->free_a       = PETSC_FALSE;
3718     } else {
3719       b->singlemalloc = PETSC_TRUE;
3720       b->free_a       = PETSC_TRUE;
3721     }
3722     b->free_ij      = PETSC_TRUE;
3723   } else {
3724     b->free_a  = PETSC_FALSE;
3725     b->free_ij = PETSC_FALSE;
3726   }
3727 
3728   if (b->ipre && nnz != b->ipre  && b->imax) {
3729     /* reserve user-requested sparsity */
3730     ierr = PetscMemcpy(b->ipre,b->imax,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3731   }
3732 
3733 
3734   b->nz               = 0;
3735   b->maxnz            = nz;
3736   B->info.nz_unneeded = (double)b->maxnz;
3737   if (realalloc) {
3738     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3739   }
3740   B->was_assembled = PETSC_FALSE;
3741   B->assembled     = PETSC_FALSE;
3742   PetscFunctionReturn(0);
3743 }
3744 
3745 
3746 PetscErrorCode MatResetPreallocation_SeqAIJ(Mat A)
3747 {
3748   Mat_SeqAIJ     *a;
3749   PetscInt       i;
3750   PetscErrorCode ierr;
3751 
3752   PetscFunctionBegin;
3753   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
3754   a = (Mat_SeqAIJ*)A->data;
3755   /* if no saved info, we error out */
3756   if (!a->ipre) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_NULL,"No saved preallocation info \n");
3757 
3758   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");
3759 
3760   ierr = PetscMemcpy(a->imax,a->ipre,A->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3761   ierr = PetscMemzero(a->ilen,A->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3762   a->i[0] = 0;
3763   for (i=1; i<A->rmap->n+1; i++) {
3764     a->i[i] = a->i[i-1] + a->imax[i-1];
3765   }
3766   A->preallocated     = PETSC_TRUE;
3767   a->nz               = 0;
3768   a->maxnz            = a->i[A->rmap->n];
3769   A->info.nz_unneeded = (double)a->maxnz;
3770   A->was_assembled    = PETSC_FALSE;
3771   A->assembled        = PETSC_FALSE;
3772   PetscFunctionReturn(0);
3773 }
3774 
3775 /*@
3776    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
3777 
3778    Input Parameters:
3779 +  B - the matrix
3780 .  i - the indices into j for the start of each row (starts with zero)
3781 .  j - the column indices for each row (starts with zero) these must be sorted for each row
3782 -  v - optional values in the matrix
3783 
3784    Level: developer
3785 
3786    The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
3787 
3788 .keywords: matrix, aij, compressed row, sparse, sequential
3789 
3790 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), MATSEQAIJ
3791 @*/
3792 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
3793 {
3794   PetscErrorCode ierr;
3795 
3796   PetscFunctionBegin;
3797   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3798   PetscValidType(B,1);
3799   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3800   PetscFunctionReturn(0);
3801 }
3802 
3803 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3804 {
3805   PetscInt       i;
3806   PetscInt       m,n;
3807   PetscInt       nz;
3808   PetscInt       *nnz, nz_max = 0;
3809   PetscScalar    *values;
3810   PetscErrorCode ierr;
3811 
3812   PetscFunctionBegin;
3813   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
3814 
3815   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3816   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3817 
3818   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
3819   ierr = PetscMalloc1(m+1, &nnz);CHKERRQ(ierr);
3820   for (i = 0; i < m; i++) {
3821     nz     = Ii[i+1]- Ii[i];
3822     nz_max = PetscMax(nz_max, nz);
3823     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
3824     nnz[i] = nz;
3825   }
3826   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
3827   ierr = PetscFree(nnz);CHKERRQ(ierr);
3828 
3829   if (v) {
3830     values = (PetscScalar*) v;
3831   } else {
3832     ierr = PetscCalloc1(nz_max, &values);CHKERRQ(ierr);
3833   }
3834 
3835   for (i = 0; i < m; i++) {
3836     nz   = Ii[i+1] - Ii[i];
3837     ierr = MatSetValues_SeqAIJ(B, 1, &i, nz, J+Ii[i], values + (v ? Ii[i] : 0), INSERT_VALUES);CHKERRQ(ierr);
3838   }
3839 
3840   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3841   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3842 
3843   if (!v) {
3844     ierr = PetscFree(values);CHKERRQ(ierr);
3845   }
3846   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3847   PetscFunctionReturn(0);
3848 }
3849 
3850 #include <../src/mat/impls/dense/seq/dense.h>
3851 #include <petsc/private/kernels/petscaxpy.h>
3852 
3853 /*
3854     Computes (B'*A')' since computing B*A directly is untenable
3855 
3856                n                       p                          p
3857         (              )       (              )         (                  )
3858       m (      A       )  *  n (       B      )   =   m (         C        )
3859         (              )       (              )         (                  )
3860 
3861 */
3862 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
3863 {
3864   PetscErrorCode    ierr;
3865   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
3866   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
3867   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
3868   PetscInt          i,n,m,q,p;
3869   const PetscInt    *ii,*idx;
3870   const PetscScalar *b,*a,*a_q;
3871   PetscScalar       *c,*c_q;
3872 
3873   PetscFunctionBegin;
3874   m    = A->rmap->n;
3875   n    = A->cmap->n;
3876   p    = B->cmap->n;
3877   a    = sub_a->v;
3878   b    = sub_b->a;
3879   c    = sub_c->v;
3880   ierr = PetscMemzero(c,m*p*sizeof(PetscScalar));CHKERRQ(ierr);
3881 
3882   ii  = sub_b->i;
3883   idx = sub_b->j;
3884   for (i=0; i<n; i++) {
3885     q = ii[i+1] - ii[i];
3886     while (q-->0) {
3887       c_q = c + m*(*idx);
3888       a_q = a + m*i;
3889       PetscKernelAXPY(c_q,*b,a_q,m);
3890       idx++;
3891       b++;
3892     }
3893   }
3894   PetscFunctionReturn(0);
3895 }
3896 
3897 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
3898 {
3899   PetscErrorCode ierr;
3900   PetscInt       m=A->rmap->n,n=B->cmap->n;
3901   Mat            Cmat;
3902 
3903   PetscFunctionBegin;
3904   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);
3905   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
3906   ierr = MatSetSizes(Cmat,m,n,m,n);CHKERRQ(ierr);
3907   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
3908   ierr = MatSetType(Cmat,MATSEQDENSE);CHKERRQ(ierr);
3909   ierr = MatSeqDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
3910 
3911   Cmat->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
3912 
3913   *C = Cmat;
3914   PetscFunctionReturn(0);
3915 }
3916 
3917 /* ----------------------------------------------------------------*/
3918 PETSC_INTERN PetscErrorCode MatMatMult_SeqDense_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
3919 {
3920   PetscErrorCode ierr;
3921 
3922   PetscFunctionBegin;
3923   if (scall == MAT_INITIAL_MATRIX) {
3924     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
3925     ierr = MatMatMultSymbolic_SeqDense_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
3926     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
3927   }
3928   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
3929   ierr = MatMatMultNumeric_SeqDense_SeqAIJ(A,B,*C);CHKERRQ(ierr);
3930   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
3931   PetscFunctionReturn(0);
3932 }
3933 
3934 
3935 /*MC
3936    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
3937    based on compressed sparse row format.
3938 
3939    Options Database Keys:
3940 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
3941 
3942   Level: beginner
3943 
3944 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
3945 M*/
3946 
3947 /*MC
3948    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
3949 
3950    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
3951    and MATMPIAIJ otherwise.  As a result, for single process communicators,
3952   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
3953   for communicators controlling multiple processes.  It is recommended that you call both of
3954   the above preallocation routines for simplicity.
3955 
3956    Options Database Keys:
3957 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
3958 
3959   Developer Notes:
3960     Subclasses include MATAIJCUSPARSE, MATAIJPERM, MATAIJSELL, MATAIJMKL, MATAIJCRL, and also automatically switches over to use inodes when
3961    enough exist.
3962 
3963   Level: beginner
3964 
3965 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
3966 M*/
3967 
3968 /*MC
3969    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
3970 
3971    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
3972    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
3973    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
3974   for communicators controlling multiple processes.  It is recommended that you call both of
3975   the above preallocation routines for simplicity.
3976 
3977    Options Database Keys:
3978 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
3979 
3980   Level: beginner
3981 
3982 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
3983 M*/
3984 
3985 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
3986 #if defined(PETSC_HAVE_ELEMENTAL)
3987 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
3988 #endif
3989 #if defined(PETSC_HAVE_HYPRE)
3990 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat A,MatType,MatReuse,Mat*);
3991 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
3992 #endif
3993 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqDense(Mat,MatType,MatReuse,Mat*);
3994 
3995 #if defined(PETSC_HAVE_MATLAB_ENGINE)
3996 PETSC_EXTERN PetscErrorCode  MatlabEnginePut_SeqAIJ(PetscObject,void*);
3997 PETSC_EXTERN PetscErrorCode  MatlabEngineGet_SeqAIJ(PetscObject,void*);
3998 #endif
3999 
4000 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqSELL(Mat,MatType,MatReuse,Mat*);
4001 PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat,MatType,MatReuse,Mat*);
4002 PETSC_INTERN PetscErrorCode MatPtAP_IS_XAIJ(Mat,Mat,MatReuse,PetscReal,Mat*);
4003 
4004 /*@C
4005    MatSeqAIJGetArray - gives access to the array where the data for a MATSEQAIJ matrix is stored
4006 
4007    Not Collective
4008 
4009    Input Parameter:
4010 .  mat - a MATSEQAIJ matrix
4011 
4012    Output Parameter:
4013 .   array - pointer to the data
4014 
4015    Level: intermediate
4016 
4017 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4018 @*/
4019 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4020 {
4021   PetscErrorCode ierr;
4022 
4023   PetscFunctionBegin;
4024   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4025   PetscFunctionReturn(0);
4026 }
4027 
4028 /*@C
4029    MatSeqAIJGetMaxRowNonzeros - returns the maximum number of nonzeros in any row
4030 
4031    Not Collective
4032 
4033    Input Parameter:
4034 .  mat - a MATSEQAIJ matrix
4035 
4036    Output Parameter:
4037 .   nz - the maximum number of nonzeros in any row
4038 
4039    Level: intermediate
4040 
4041 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4042 @*/
4043 PetscErrorCode  MatSeqAIJGetMaxRowNonzeros(Mat A,PetscInt *nz)
4044 {
4045   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
4046 
4047   PetscFunctionBegin;
4048   *nz = aij->rmax;
4049   PetscFunctionReturn(0);
4050 }
4051 
4052 /*@C
4053    MatSeqAIJRestoreArray - returns access to the array where the data for a MATSEQAIJ matrix is stored obtained by MatSeqAIJGetArray()
4054 
4055    Not Collective
4056 
4057    Input Parameters:
4058 .  mat - a MATSEQAIJ matrix
4059 .  array - pointer to the data
4060 
4061    Level: intermediate
4062 
4063 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4064 @*/
4065 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4066 {
4067   PetscErrorCode ierr;
4068 
4069   PetscFunctionBegin;
4070   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4071   PetscFunctionReturn(0);
4072 }
4073 
4074 #if defined(PETSC_HAVE_CUDA)
4075 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat);
4076 #endif
4077 
4078 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4079 {
4080   Mat_SeqAIJ     *b;
4081   PetscErrorCode ierr;
4082   PetscMPIInt    size;
4083 
4084   PetscFunctionBegin;
4085   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4086   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4087 
4088   ierr = PetscNewLog(B,&b);CHKERRQ(ierr);
4089 
4090   B->data = (void*)b;
4091 
4092   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4093 
4094   b->row                = 0;
4095   b->col                = 0;
4096   b->icol               = 0;
4097   b->reallocs           = 0;
4098   b->ignorezeroentries  = PETSC_FALSE;
4099   b->roworiented        = PETSC_TRUE;
4100   b->nonew              = 0;
4101   b->diag               = 0;
4102   b->solve_work         = 0;
4103   B->spptr              = 0;
4104   b->saved_values       = 0;
4105   b->idiag              = 0;
4106   b->mdiag              = 0;
4107   b->ssor_work          = 0;
4108   b->omega              = 1.0;
4109   b->fshift             = 0.0;
4110   b->idiagvalid         = PETSC_FALSE;
4111   b->ibdiagvalid        = PETSC_FALSE;
4112   b->keepnonzeropattern = PETSC_FALSE;
4113 
4114   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4115   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4116   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4117 
4118 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4119   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4120   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4121 #endif
4122 
4123   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4124   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4125   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4126   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4127   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4128   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4129   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijsell_C",MatConvert_SeqAIJ_SeqAIJSELL);CHKERRQ(ierr);
4130 #if defined(PETSC_HAVE_MKL_SPARSE)
4131   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijmkl_C",MatConvert_SeqAIJ_SeqAIJMKL);CHKERRQ(ierr);
4132 #endif
4133 #if defined(PETSC_HAVE_CUDA)
4134   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcusparse_C",MatConvert_SeqAIJ_SeqAIJCUSPARSE);CHKERRQ(ierr);
4135 #endif
4136   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4137 #if defined(PETSC_HAVE_ELEMENTAL)
4138   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_elemental_C",MatConvert_SeqAIJ_Elemental);CHKERRQ(ierr);
4139 #endif
4140 #if defined(PETSC_HAVE_HYPRE)
4141   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
4142   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_seqaij_seqaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
4143 #endif
4144   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqdense_C",MatConvert_SeqAIJ_SeqDense);CHKERRQ(ierr);
4145   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsell_C",MatConvert_SeqAIJ_SeqSELL);CHKERRQ(ierr);
4146   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_is_C",MatConvert_XAIJ_IS);CHKERRQ(ierr);
4147   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4148   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4149   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4150   ierr = PetscObjectComposeFunction((PetscObject)B,"MatResetPreallocation_C",MatResetPreallocation_SeqAIJ);CHKERRQ(ierr);
4151   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4152   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4153   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaij_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
4154   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaij_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
4155   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaij_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
4156   ierr = PetscObjectComposeFunction((PetscObject)B,"MatPtAP_is_seqaij_C",MatPtAP_IS_XAIJ);CHKERRQ(ierr);
4157   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4158   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4159   ierr = MatSeqAIJSetTypeFromOptions(B);CHKERRQ(ierr);  /* this allows changing the matrix subtype to say MATSEQAIJPERM */
4160   PetscFunctionReturn(0);
4161 }
4162 
4163 /*
4164     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4165 */
4166 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4167 {
4168   Mat_SeqAIJ     *c,*a = (Mat_SeqAIJ*)A->data;
4169   PetscErrorCode ierr;
4170   PetscInt       i,m = A->rmap->n;
4171 
4172   PetscFunctionBegin;
4173   c = (Mat_SeqAIJ*)C->data;
4174 
4175   C->factortype = A->factortype;
4176   c->row        = 0;
4177   c->col        = 0;
4178   c->icol       = 0;
4179   c->reallocs   = 0;
4180 
4181   C->assembled = PETSC_TRUE;
4182 
4183   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4184   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4185 
4186   ierr = PetscMalloc2(m,&c->imax,m,&c->ilen);CHKERRQ(ierr);
4187   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4188   for (i=0; i<m; i++) {
4189     c->imax[i] = a->imax[i];
4190     c->ilen[i] = a->ilen[i];
4191   }
4192 
4193   /* allocate the matrix space */
4194   if (mallocmatspace) {
4195     ierr = PetscMalloc3(a->i[m],&c->a,a->i[m],&c->j,m+1,&c->i);CHKERRQ(ierr);
4196     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4197 
4198     c->singlemalloc = PETSC_TRUE;
4199 
4200     ierr = PetscMemcpy(c->i,a->i,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4201     if (m > 0) {
4202       ierr = PetscMemcpy(c->j,a->j,(a->i[m])*sizeof(PetscInt));CHKERRQ(ierr);
4203       if (cpvalues == MAT_COPY_VALUES) {
4204         ierr = PetscMemcpy(c->a,a->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4205       } else {
4206         ierr = PetscMemzero(c->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4207       }
4208     }
4209   }
4210 
4211   c->ignorezeroentries = a->ignorezeroentries;
4212   c->roworiented       = a->roworiented;
4213   c->nonew             = a->nonew;
4214   if (a->diag) {
4215     ierr = PetscMalloc1(m+1,&c->diag);CHKERRQ(ierr);
4216     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4217     for (i=0; i<m; i++) {
4218       c->diag[i] = a->diag[i];
4219     }
4220   } else c->diag = 0;
4221 
4222   c->solve_work         = 0;
4223   c->saved_values       = 0;
4224   c->idiag              = 0;
4225   c->ssor_work          = 0;
4226   c->keepnonzeropattern = a->keepnonzeropattern;
4227   c->free_a             = PETSC_TRUE;
4228   c->free_ij            = PETSC_TRUE;
4229 
4230   c->rmax         = a->rmax;
4231   c->nz           = a->nz;
4232   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4233   C->preallocated = PETSC_TRUE;
4234 
4235   c->compressedrow.use   = a->compressedrow.use;
4236   c->compressedrow.nrows = a->compressedrow.nrows;
4237   if (a->compressedrow.use) {
4238     i    = a->compressedrow.nrows;
4239     ierr = PetscMalloc2(i+1,&c->compressedrow.i,i,&c->compressedrow.rindex);CHKERRQ(ierr);
4240     ierr = PetscMemcpy(c->compressedrow.i,a->compressedrow.i,(i+1)*sizeof(PetscInt));CHKERRQ(ierr);
4241     ierr = PetscMemcpy(c->compressedrow.rindex,a->compressedrow.rindex,i*sizeof(PetscInt));CHKERRQ(ierr);
4242   } else {
4243     c->compressedrow.use    = PETSC_FALSE;
4244     c->compressedrow.i      = NULL;
4245     c->compressedrow.rindex = NULL;
4246   }
4247   c->nonzerorowcnt = a->nonzerorowcnt;
4248   C->nonzerostate  = A->nonzerostate;
4249 
4250   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4251   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4252   PetscFunctionReturn(0);
4253 }
4254 
4255 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4256 {
4257   PetscErrorCode ierr;
4258 
4259   PetscFunctionBegin;
4260   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4261   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4262   if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) {
4263     ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
4264   }
4265   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4266   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4267   PetscFunctionReturn(0);
4268 }
4269 
4270 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4271 {
4272   PetscBool      isbinary, ishdf5;
4273   PetscErrorCode ierr;
4274 
4275   PetscFunctionBegin;
4276   PetscValidHeaderSpecific(newMat,MAT_CLASSID,1);
4277   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
4278   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
4279   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,  &ishdf5);CHKERRQ(ierr);
4280   if (isbinary) {
4281     ierr = MatLoad_SeqAIJ_Binary(newMat,viewer);CHKERRQ(ierr);
4282   } else if (ishdf5) {
4283 #if defined(PETSC_HAVE_HDF5)
4284     ierr = MatLoad_AIJ_HDF5(newMat,viewer);CHKERRQ(ierr);
4285 #else
4286     SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
4287 #endif
4288   } else {
4289     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);
4290   }
4291   PetscFunctionReturn(0);
4292 }
4293 
4294 PetscErrorCode MatLoad_SeqAIJ_Binary(Mat newMat, PetscViewer viewer)
4295 {
4296   Mat_SeqAIJ     *a;
4297   PetscErrorCode ierr;
4298   PetscInt       i,sum,nz,header[4],*rowlengths = 0,M,N,rows,cols;
4299   int            fd;
4300   PetscMPIInt    size;
4301   MPI_Comm       comm;
4302   PetscInt       bs = newMat->rmap->bs;
4303 
4304   PetscFunctionBegin;
4305   /* force binary viewer to load .info file if it has not yet done so */
4306   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
4307   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
4308   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4309   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"view must have one processor");
4310 
4311   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
4312   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
4313   ierr = PetscOptionsEnd();CHKERRQ(ierr);
4314   if (bs < 0) bs = 1;
4315   ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);
4316 
4317   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
4318   ierr = PetscBinaryRead(fd,header,4,PETSC_INT);CHKERRQ(ierr);
4319   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
4320   M = header[1]; N = header[2]; nz = header[3];
4321 
4322   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
4323 
4324   /* read in row lengths */
4325   ierr = PetscMalloc1(M,&rowlengths);CHKERRQ(ierr);
4326   ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
4327 
4328   /* check if sum of rowlengths is same as nz */
4329   for (i=0,sum=0; i< M; i++) sum +=rowlengths[i];
4330   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);
4331 
4332   /* set global size if not set already*/
4333   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) {
4334     ierr = MatSetSizes(newMat,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
4335   } else {
4336     /* if sizes and type are already set, check if the matrix  global sizes are correct */
4337     ierr = MatGetSize(newMat,&rows,&cols);CHKERRQ(ierr);
4338     if (rows < 0 && cols < 0) { /* user might provide local size instead of global size */
4339       ierr = MatGetLocalSize(newMat,&rows,&cols);CHKERRQ(ierr);
4340     }
4341     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);
4342   }
4343   ierr = MatSeqAIJSetPreallocation_SeqAIJ(newMat,0,rowlengths);CHKERRQ(ierr);
4344   a    = (Mat_SeqAIJ*)newMat->data;
4345 
4346   ierr = PetscBinaryRead(fd,a->j,nz,PETSC_INT);CHKERRQ(ierr);
4347 
4348   /* read in nonzero values */
4349   ierr = PetscBinaryRead(fd,a->a,nz,PETSC_SCALAR);CHKERRQ(ierr);
4350 
4351   /* set matrix "i" values */
4352   a->i[0] = 0;
4353   for (i=1; i<= M; i++) {
4354     a->i[i]      = a->i[i-1] + rowlengths[i-1];
4355     a->ilen[i-1] = rowlengths[i-1];
4356   }
4357   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
4358 
4359   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4360   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4361   PetscFunctionReturn(0);
4362 }
4363 
4364 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4365 {
4366   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4367   PetscErrorCode ierr;
4368 #if defined(PETSC_USE_COMPLEX)
4369   PetscInt k;
4370 #endif
4371 
4372   PetscFunctionBegin;
4373   /* If the  matrix dimensions are not equal,or no of nonzeros */
4374   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4375     *flg = PETSC_FALSE;
4376     PetscFunctionReturn(0);
4377   }
4378 
4379   /* if the a->i are the same */
4380   ierr = PetscMemcmp(a->i,b->i,(A->rmap->n+1)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4381   if (!*flg) PetscFunctionReturn(0);
4382 
4383   /* if a->j are the same */
4384   ierr = PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4385   if (!*flg) PetscFunctionReturn(0);
4386 
4387   /* if a->a are the same */
4388 #if defined(PETSC_USE_COMPLEX)
4389   for (k=0; k<a->nz; k++) {
4390     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4391       *flg = PETSC_FALSE;
4392       PetscFunctionReturn(0);
4393     }
4394   }
4395 #else
4396   ierr = PetscMemcmp(a->a,b->a,(a->nz)*sizeof(PetscScalar),flg);CHKERRQ(ierr);
4397 #endif
4398   PetscFunctionReturn(0);
4399 }
4400 
4401 /*@
4402      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4403               provided by the user.
4404 
4405       Collective on MPI_Comm
4406 
4407    Input Parameters:
4408 +   comm - must be an MPI communicator of size 1
4409 .   m - number of rows
4410 .   n - number of columns
4411 .   i - row indices; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
4412 .   j - column indices
4413 -   a - matrix values
4414 
4415    Output Parameter:
4416 .   mat - the matrix
4417 
4418    Level: intermediate
4419 
4420    Notes:
4421        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4422     once the matrix is destroyed and not before
4423 
4424        You cannot set new nonzero locations into this matrix, that will generate an error.
4425 
4426        The i and j indices are 0 based
4427 
4428        The format which is used for the sparse matrix input, is equivalent to a
4429     row-major ordering.. i.e for the following matrix, the input data expected is
4430     as shown
4431 
4432 $        1 0 0
4433 $        2 0 3
4434 $        4 5 6
4435 $
4436 $        i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4437 $        j =  {0,0,2,0,1,2}  [size = 6]; values must be sorted for each row
4438 $        v =  {1,2,3,4,5,6}  [size = 6]
4439 
4440 
4441 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4442 
4443 @*/
4444 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat)
4445 {
4446   PetscErrorCode ierr;
4447   PetscInt       ii;
4448   Mat_SeqAIJ     *aij;
4449 #if defined(PETSC_USE_DEBUG)
4450   PetscInt jj;
4451 #endif
4452 
4453   PetscFunctionBegin;
4454   if (m > 0 && i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4455   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4456   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4457   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4458   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4459   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,0);CHKERRQ(ierr);
4460   aij  = (Mat_SeqAIJ*)(*mat)->data;
4461   ierr = PetscMalloc2(m,&aij->imax,m,&aij->ilen);CHKERRQ(ierr);
4462 
4463   aij->i            = i;
4464   aij->j            = j;
4465   aij->a            = a;
4466   aij->singlemalloc = PETSC_FALSE;
4467   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4468   aij->free_a       = PETSC_FALSE;
4469   aij->free_ij      = PETSC_FALSE;
4470 
4471   for (ii=0; ii<m; ii++) {
4472     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4473 #if defined(PETSC_USE_DEBUG)
4474     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]);
4475     for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4476       if (j[jj] < j[jj-1]) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column entry number %D (actual colum %D) in row %D is not sorted",jj-i[ii],j[jj],ii);
4477       if (j[jj] == j[jj-1]) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column entry number %D (actual colum %D) in row %D is identical to previous entry",jj-i[ii],j[jj],ii);
4478     }
4479 #endif
4480   }
4481 #if defined(PETSC_USE_DEBUG)
4482   for (ii=0; ii<aij->i[m]; ii++) {
4483     if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %D index = %D",ii,j[ii]);
4484     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]);
4485   }
4486 #endif
4487 
4488   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4489   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4490   PetscFunctionReturn(0);
4491 }
4492 /*@C
4493      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4494               provided by the user.
4495 
4496       Collective on MPI_Comm
4497 
4498    Input Parameters:
4499 +   comm - must be an MPI communicator of size 1
4500 .   m   - number of rows
4501 .   n   - number of columns
4502 .   i   - row indices
4503 .   j   - column indices
4504 .   a   - matrix values
4505 .   nz  - number of nonzeros
4506 -   idx - 0 or 1 based
4507 
4508    Output Parameter:
4509 .   mat - the matrix
4510 
4511    Level: intermediate
4512 
4513    Notes:
4514        The i and j indices are 0 based
4515 
4516        The format which is used for the sparse matrix input, is equivalent to a
4517     row-major ordering.. i.e for the following matrix, the input data expected is
4518     as shown:
4519 
4520         1 0 0
4521         2 0 3
4522         4 5 6
4523 
4524         i =  {0,1,1,2,2,2}
4525         j =  {0,0,2,0,1,2}
4526         v =  {1,2,3,4,5,6}
4527 
4528 
4529 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4530 
4531 @*/
4532 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat,PetscInt nz,PetscBool idx)
4533 {
4534   PetscErrorCode ierr;
4535   PetscInt       ii, *nnz, one = 1,row,col;
4536 
4537 
4538   PetscFunctionBegin;
4539   ierr = PetscCalloc1(m,&nnz);CHKERRQ(ierr);
4540   for (ii = 0; ii < nz; ii++) {
4541     nnz[i[ii] - !!idx] += 1;
4542   }
4543   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4544   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4545   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4546   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4547   for (ii = 0; ii < nz; ii++) {
4548     if (idx) {
4549       row = i[ii] - 1;
4550       col = j[ii] - 1;
4551     } else {
4552       row = i[ii];
4553       col = j[ii];
4554     }
4555     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4556   }
4557   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4558   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4559   ierr = PetscFree(nnz);CHKERRQ(ierr);
4560   PetscFunctionReturn(0);
4561 }
4562 
4563 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4564 {
4565   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4566   PetscErrorCode ierr;
4567 
4568   PetscFunctionBegin;
4569   a->idiagvalid  = PETSC_FALSE;
4570   a->ibdiagvalid = PETSC_FALSE;
4571 
4572   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4573   PetscFunctionReturn(0);
4574 }
4575 
4576 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4577 {
4578   PetscErrorCode ierr;
4579   PetscMPIInt    size;
4580 
4581   PetscFunctionBegin;
4582   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4583   if (size == 1) {
4584     if (scall == MAT_INITIAL_MATRIX) {
4585       ierr = MatDuplicate(inmat,MAT_COPY_VALUES,outmat);CHKERRQ(ierr);
4586     } else {
4587       ierr = MatCopy(inmat,*outmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4588     }
4589   } else {
4590     ierr = MatCreateMPIMatConcatenateSeqMat_MPIAIJ(comm,inmat,n,scall,outmat);CHKERRQ(ierr);
4591   }
4592   PetscFunctionReturn(0);
4593 }
4594 
4595 /*
4596  Permute A into C's *local* index space using rowemb,colemb.
4597  The embedding are supposed to be injections and the above implies that the range of rowemb is a subset
4598  of [0,m), colemb is in [0,n).
4599  If pattern == DIFFERENT_NONZERO_PATTERN, C is preallocated according to A.
4600  */
4601 PetscErrorCode MatSetSeqMat_SeqAIJ(Mat C,IS rowemb,IS colemb,MatStructure pattern,Mat B)
4602 {
4603   /* If making this function public, change the error returned in this function away from _PLIB. */
4604   PetscErrorCode ierr;
4605   Mat_SeqAIJ     *Baij;
4606   PetscBool      seqaij;
4607   PetscInt       m,n,*nz,i,j,count;
4608   PetscScalar    v;
4609   const PetscInt *rowindices,*colindices;
4610 
4611   PetscFunctionBegin;
4612   if (!B) PetscFunctionReturn(0);
4613   /* Check to make sure the target matrix (and embeddings) are compatible with C and each other. */
4614   ierr = PetscObjectBaseTypeCompare((PetscObject)B,MATSEQAIJ,&seqaij);CHKERRQ(ierr);
4615   if (!seqaij) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is of wrong type");
4616   if (rowemb) {
4617     ierr = ISGetLocalSize(rowemb,&m);CHKERRQ(ierr);
4618     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);
4619   } else {
4620     if (C->rmap->n != B->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is row-incompatible with the target matrix");
4621   }
4622   if (colemb) {
4623     ierr = ISGetLocalSize(colemb,&n);CHKERRQ(ierr);
4624     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);
4625   } else {
4626     if (C->cmap->n != B->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is col-incompatible with the target matrix");
4627   }
4628 
4629   Baij = (Mat_SeqAIJ*)(B->data);
4630   if (pattern == DIFFERENT_NONZERO_PATTERN) {
4631     ierr = PetscMalloc1(B->rmap->n,&nz);CHKERRQ(ierr);
4632     for (i=0; i<B->rmap->n; i++) {
4633       nz[i] = Baij->i[i+1] - Baij->i[i];
4634     }
4635     ierr = MatSeqAIJSetPreallocation(C,0,nz);CHKERRQ(ierr);
4636     ierr = PetscFree(nz);CHKERRQ(ierr);
4637   }
4638   if (pattern == SUBSET_NONZERO_PATTERN) {
4639     ierr = MatZeroEntries(C);CHKERRQ(ierr);
4640   }
4641   count = 0;
4642   rowindices = NULL;
4643   colindices = NULL;
4644   if (rowemb) {
4645     ierr = ISGetIndices(rowemb,&rowindices);CHKERRQ(ierr);
4646   }
4647   if (colemb) {
4648     ierr = ISGetIndices(colemb,&colindices);CHKERRQ(ierr);
4649   }
4650   for (i=0; i<B->rmap->n; i++) {
4651     PetscInt row;
4652     row = i;
4653     if (rowindices) row = rowindices[i];
4654     for (j=Baij->i[i]; j<Baij->i[i+1]; j++) {
4655       PetscInt col;
4656       col  = Baij->j[count];
4657       if (colindices) col = colindices[col];
4658       v    = Baij->a[count];
4659       ierr = MatSetValues(C,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
4660       ++count;
4661     }
4662   }
4663   /* FIXME: set C's nonzerostate correctly. */
4664   /* Assembly for C is necessary. */
4665   C->preallocated = PETSC_TRUE;
4666   C->assembled     = PETSC_TRUE;
4667   C->was_assembled = PETSC_FALSE;
4668   PetscFunctionReturn(0);
4669 }
4670 
4671 PetscFunctionList MatSeqAIJList = NULL;
4672 
4673 /*@C
4674    MatSeqAIJSetType - Converts a MATSEQAIJ matrix to a subtype
4675 
4676    Collective on Mat
4677 
4678    Input Parameters:
4679 +  mat      - the matrix object
4680 -  matype   - matrix type
4681 
4682    Options Database Key:
4683 .  -mat_seqai_type  <method> - for example seqaijcrl
4684 
4685 
4686   Level: intermediate
4687 
4688 .keywords: Mat, MatType, set, method
4689 
4690 .seealso: PCSetType(), VecSetType(), MatCreate(), MatType, Mat
4691 @*/
4692 PetscErrorCode  MatSeqAIJSetType(Mat mat, MatType matype)
4693 {
4694   PetscErrorCode ierr,(*r)(Mat,MatType,MatReuse,Mat*);
4695   PetscBool      sametype;
4696 
4697   PetscFunctionBegin;
4698   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
4699   ierr = PetscObjectTypeCompare((PetscObject)mat,matype,&sametype);CHKERRQ(ierr);
4700   if (sametype) PetscFunctionReturn(0);
4701 
4702   ierr =  PetscFunctionListFind(MatSeqAIJList,matype,&r);CHKERRQ(ierr);
4703   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown Mat type given: %s",matype);
4704   ierr = (*r)(mat,matype,MAT_INPLACE_MATRIX,&mat);CHKERRQ(ierr);
4705   PetscFunctionReturn(0);
4706 }
4707 
4708 
4709 /*@C
4710   MatSeqAIJRegister -  - Adds a new sub-matrix type for sequential AIJ matrices
4711 
4712    Not Collective
4713 
4714    Input Parameters:
4715 +  name - name of a new user-defined matrix type, for example MATSEQAIJCRL
4716 -  function - routine to convert to subtype
4717 
4718    Notes:
4719    MatSeqAIJRegister() may be called multiple times to add several user-defined solvers.
4720 
4721 
4722    Then, your matrix can be chosen with the procedural interface at runtime via the option
4723 $     -mat_seqaij_type my_mat
4724 
4725    Level: advanced
4726 
4727 .keywords: Mat, register
4728 
4729 .seealso: MatSeqAIJRegisterAll()
4730 
4731 
4732   Level: advanced
4733 @*/
4734 PetscErrorCode  MatSeqAIJRegister(const char sname[],PetscErrorCode (*function)(Mat,MatType,MatReuse,Mat *))
4735 {
4736   PetscErrorCode ierr;
4737 
4738   PetscFunctionBegin;
4739   ierr = MatInitializePackage();CHKERRQ(ierr);
4740   ierr = PetscFunctionListAdd(&MatSeqAIJList,sname,function);CHKERRQ(ierr);
4741   PetscFunctionReturn(0);
4742 }
4743 
4744 PetscBool MatSeqAIJRegisterAllCalled = PETSC_FALSE;
4745 
4746 /*@C
4747   MatSeqAIJRegisterAll - Registers all of the matrix subtypes of SeqAIJ
4748 
4749   Not Collective
4750 
4751   Level: advanced
4752 
4753   Developers Note: CUSP and CUSPARSE do not yet support the  MatConvert_SeqAIJ..() paradigm and thus cannot be registered here
4754 
4755 .keywords: KSP, register, all
4756 
4757 .seealso:  MatRegisterAll(), MatSeqAIJRegister()
4758 @*/
4759 PetscErrorCode  MatSeqAIJRegisterAll(void)
4760 {
4761   PetscErrorCode ierr;
4762 
4763   PetscFunctionBegin;
4764   if (MatSeqAIJRegisterAllCalled) PetscFunctionReturn(0);
4765   MatSeqAIJRegisterAllCalled = PETSC_TRUE;
4766 
4767   ierr = MatSeqAIJRegister(MATSEQAIJCRL,      MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4768   ierr = MatSeqAIJRegister(MATSEQAIJPERM,     MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4769   ierr = MatSeqAIJRegister(MATSEQAIJSELL,     MatConvert_SeqAIJ_SeqAIJSELL);CHKERRQ(ierr);
4770 #if defined(PETSC_HAVE_MKL_SPARSE)
4771   ierr = MatSeqAIJRegister(MATSEQAIJMKL,      MatConvert_SeqAIJ_SeqAIJMKL);CHKERRQ(ierr);
4772 #endif
4773 #if defined(PETSC_HAVE_VIENNACL) && defined(PETSC_HAVE_VIENNACL_NO_CUDA)
4774   ierr = MatSeqAIJRegister(MATMPIAIJVIENNACL, MatConvert_SeqAIJ_SeqAIJViennaCL);CHKERRQ(ierr);
4775 #endif
4776   PetscFunctionReturn(0);
4777 }
4778 
4779 /*
4780     Special version for direct calls from Fortran
4781 */
4782 #include <petsc/private/fortranimpl.h>
4783 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4784 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
4785 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4786 #define matsetvaluesseqaij_ matsetvaluesseqaij
4787 #endif
4788 
4789 /* Change these macros so can be used in void function */
4790 #undef CHKERRQ
4791 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
4792 #undef SETERRQ2
4793 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4794 #undef SETERRQ3
4795 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4796 
4797 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)
4798 {
4799   Mat            A  = *AA;
4800   PetscInt       m  = *mm, n = *nn;
4801   InsertMode     is = *isis;
4802   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4803   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
4804   PetscInt       *imax,*ai,*ailen;
4805   PetscErrorCode ierr;
4806   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
4807   MatScalar      *ap,value,*aa;
4808   PetscBool      ignorezeroentries = a->ignorezeroentries;
4809   PetscBool      roworiented       = a->roworiented;
4810 
4811   PetscFunctionBegin;
4812   MatCheckPreallocated(A,1);
4813   imax  = a->imax;
4814   ai    = a->i;
4815   ailen = a->ilen;
4816   aj    = a->j;
4817   aa    = a->a;
4818 
4819   for (k=0; k<m; k++) { /* loop over added rows */
4820     row = im[k];
4821     if (row < 0) continue;
4822 #if defined(PETSC_USE_DEBUG)
4823     if (row >= A->rmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
4824 #endif
4825     rp   = aj + ai[row]; ap = aa + ai[row];
4826     rmax = imax[row]; nrow = ailen[row];
4827     low  = 0;
4828     high = nrow;
4829     for (l=0; l<n; l++) { /* loop over added columns */
4830       if (in[l] < 0) continue;
4831 #if defined(PETSC_USE_DEBUG)
4832       if (in[l] >= A->cmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
4833 #endif
4834       col = in[l];
4835       if (roworiented) value = v[l + k*n];
4836       else value = v[k + l*m];
4837 
4838       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
4839 
4840       if (col <= lastcol) low = 0;
4841       else high = nrow;
4842       lastcol = col;
4843       while (high-low > 5) {
4844         t = (low+high)/2;
4845         if (rp[t] > col) high = t;
4846         else             low  = t;
4847       }
4848       for (i=low; i<high; i++) {
4849         if (rp[i] > col) break;
4850         if (rp[i] == col) {
4851           if (is == ADD_VALUES) ap[i] += value;
4852           else                  ap[i] = value;
4853           goto noinsert;
4854         }
4855       }
4856       if (value == 0.0 && ignorezeroentries) goto noinsert;
4857       if (nonew == 1) goto noinsert;
4858       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
4859       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
4860       N = nrow++ - 1; a->nz++; high++;
4861       /* shift up all the later entries in this row */
4862       for (ii=N; ii>=i; ii--) {
4863         rp[ii+1] = rp[ii];
4864         ap[ii+1] = ap[ii];
4865       }
4866       rp[i] = col;
4867       ap[i] = value;
4868       A->nonzerostate++;
4869 noinsert:;
4870       low = i + 1;
4871     }
4872     ailen[row] = nrow;
4873   }
4874   PetscFunctionReturnVoid();
4875 }
4876