xref: /petsc/src/mat/impls/aij/seq/aij.c (revision 26ba9691fcf2c44e68190ae4e578693e6edee08e)
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 #if defined(PETSC_THREADCOMM_ACTIVE)
13 #include <petscthreadcomm.h>
14 #endif
15 
16 #undef __FUNCT__
17 #define __FUNCT__ "MatGetColumnNorms_SeqAIJ"
18 PetscErrorCode MatGetColumnNorms_SeqAIJ(Mat A,NormType type,PetscReal *norms)
19 {
20   PetscErrorCode ierr;
21   PetscInt       i,m,n;
22   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
23 
24   PetscFunctionBegin;
25   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
26   ierr = PetscMemzero(norms,n*sizeof(PetscReal));CHKERRQ(ierr);
27   if (type == NORM_2) {
28     for (i=0; i<aij->i[m]; i++) {
29       norms[aij->j[i]] += PetscAbsScalar(aij->a[i]*aij->a[i]);
30     }
31   } else if (type == NORM_1) {
32     for (i=0; i<aij->i[m]; i++) {
33       norms[aij->j[i]] += PetscAbsScalar(aij->a[i]);
34     }
35   } else if (type == NORM_INFINITY) {
36     for (i=0; i<aij->i[m]; i++) {
37       norms[aij->j[i]] = PetscMax(PetscAbsScalar(aij->a[i]),norms[aij->j[i]]);
38     }
39   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unknown NormType");
40 
41   if (type == NORM_2) {
42     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
43   }
44   PetscFunctionReturn(0);
45 }
46 
47 #undef __FUNCT__
48 #define __FUNCT__ "MatFindOffBlockDiagonalEntries_SeqAIJ"
49 PetscErrorCode MatFindOffBlockDiagonalEntries_SeqAIJ(Mat A,IS *is)
50 {
51   Mat_SeqAIJ      *a  = (Mat_SeqAIJ*)A->data;
52   PetscInt        i,m=A->rmap->n,cnt = 0, bs = A->rmap->bs;
53   const PetscInt  *jj = a->j,*ii = a->i;
54   PetscInt        *rows;
55   PetscErrorCode  ierr;
56 
57   PetscFunctionBegin;
58   for (i=0; i<m; i++) {
59     if ((ii[i] != ii[i+1]) && ((jj[ii[i]] < bs*(i/bs)) || (jj[ii[i+1]-1] > bs*((i+bs)/bs)-1))) {
60       cnt++;
61     }
62   }
63   ierr = PetscMalloc1(cnt,&rows);CHKERRQ(ierr);
64   cnt  = 0;
65   for (i=0; i<m; i++) {
66     if ((ii[i] != ii[i+1]) && ((jj[ii[i]] < bs*(i/bs)) || (jj[ii[i+1]-1] > bs*((i+bs)/bs)-1))) {
67       rows[cnt] = i;
68       cnt++;
69     }
70   }
71   ierr = ISCreateGeneral(PETSC_COMM_SELF,cnt,rows,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
72   PetscFunctionReturn(0);
73 }
74 
75 #undef __FUNCT__
76 #define __FUNCT__ "MatFindZeroDiagonals_SeqAIJ_Private"
77 PetscErrorCode MatFindZeroDiagonals_SeqAIJ_Private(Mat A,PetscInt *nrows,PetscInt **zrows)
78 {
79   Mat_SeqAIJ      *a  = (Mat_SeqAIJ*)A->data;
80   const MatScalar *aa = a->a;
81   PetscInt        i,m=A->rmap->n,cnt = 0;
82   const PetscInt  *jj = a->j,*diag;
83   PetscInt        *rows;
84   PetscErrorCode  ierr;
85 
86   PetscFunctionBegin;
87   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
88   diag = a->diag;
89   for (i=0; i<m; i++) {
90     if ((jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) {
91       cnt++;
92     }
93   }
94   ierr = PetscMalloc1(cnt,&rows);CHKERRQ(ierr);
95   cnt  = 0;
96   for (i=0; i<m; i++) {
97     if ((jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) {
98       rows[cnt++] = i;
99     }
100   }
101   *nrows = cnt;
102   *zrows = rows;
103   PetscFunctionReturn(0);
104 }
105 
106 #undef __FUNCT__
107 #define __FUNCT__ "MatFindZeroDiagonals_SeqAIJ"
108 PetscErrorCode MatFindZeroDiagonals_SeqAIJ(Mat A,IS *zrows)
109 {
110   PetscInt       nrows,*rows;
111   PetscErrorCode ierr;
112 
113   PetscFunctionBegin;
114   *zrows = NULL;
115   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(A,&nrows,&rows);CHKERRQ(ierr);
116   ierr   = ISCreateGeneral(PetscObjectComm((PetscObject)A),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
117   PetscFunctionReturn(0);
118 }
119 
120 #undef __FUNCT__
121 #define __FUNCT__ "MatFindNonzeroRows_SeqAIJ"
122 PetscErrorCode MatFindNonzeroRows_SeqAIJ(Mat A,IS *keptrows)
123 {
124   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
125   const MatScalar *aa;
126   PetscInt        m=A->rmap->n,cnt = 0;
127   const PetscInt  *ii;
128   PetscInt        n,i,j,*rows;
129   PetscErrorCode  ierr;
130 
131   PetscFunctionBegin;
132   *keptrows = 0;
133   ii        = a->i;
134   for (i=0; i<m; i++) {
135     n = ii[i+1] - ii[i];
136     if (!n) {
137       cnt++;
138       goto ok1;
139     }
140     aa = a->a + ii[i];
141     for (j=0; j<n; j++) {
142       if (aa[j] != 0.0) goto ok1;
143     }
144     cnt++;
145 ok1:;
146   }
147   if (!cnt) PetscFunctionReturn(0);
148   ierr = PetscMalloc1((A->rmap->n-cnt),&rows);CHKERRQ(ierr);
149   cnt  = 0;
150   for (i=0; i<m; i++) {
151     n = ii[i+1] - ii[i];
152     if (!n) continue;
153     aa = a->a + ii[i];
154     for (j=0; j<n; j++) {
155       if (aa[j] != 0.0) {
156         rows[cnt++] = i;
157         break;
158       }
159     }
160   }
161   ierr = ISCreateGeneral(PETSC_COMM_SELF,cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
162   PetscFunctionReturn(0);
163 }
164 
165 #undef __FUNCT__
166 #define __FUNCT__ "MatDiagonalSet_SeqAIJ"
167 PetscErrorCode  MatDiagonalSet_SeqAIJ(Mat Y,Vec D,InsertMode is)
168 {
169   PetscErrorCode ierr;
170   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) Y->data;
171   PetscInt       i,*diag, m = Y->rmap->n;
172   MatScalar      *aa = aij->a;
173   PetscScalar    *v;
174   PetscBool      missing;
175 
176   PetscFunctionBegin;
177   if (Y->assembled) {
178     ierr = MatMissingDiagonal_SeqAIJ(Y,&missing,NULL);CHKERRQ(ierr);
179     if (!missing) {
180       diag = aij->diag;
181       ierr = VecGetArray(D,&v);CHKERRQ(ierr);
182       if (is == INSERT_VALUES) {
183         for (i=0; i<m; i++) {
184           aa[diag[i]] = v[i];
185         }
186       } else {
187         for (i=0; i<m; i++) {
188           aa[diag[i]] += v[i];
189         }
190       }
191       ierr = VecRestoreArray(D,&v);CHKERRQ(ierr);
192       PetscFunctionReturn(0);
193     }
194     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
195   }
196   ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
197   PetscFunctionReturn(0);
198 }
199 
200 #undef __FUNCT__
201 #define __FUNCT__ "MatGetRowIJ_SeqAIJ"
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,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 #undef __FUNCT__
235 #define __FUNCT__ "MatRestoreRowIJ_SeqAIJ"
236 PetscErrorCode MatRestoreRowIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
237 {
238   PetscErrorCode ierr;
239 
240   PetscFunctionBegin;
241   if (!ia) PetscFunctionReturn(0);
242   if ((symmetric && !A->structurally_symmetric) || oshift == 1) {
243     ierr = PetscFree(*ia);CHKERRQ(ierr);
244     if (ja) {ierr = PetscFree(*ja);CHKERRQ(ierr);}
245   }
246   PetscFunctionReturn(0);
247 }
248 
249 #undef __FUNCT__
250 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ"
251 PetscErrorCode MatGetColumnIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
252 {
253   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
254   PetscErrorCode ierr;
255   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
256   PetscInt       nz = a->i[m],row,*jj,mr,col;
257 
258   PetscFunctionBegin;
259   *nn = n;
260   if (!ia) PetscFunctionReturn(0);
261   if (symmetric) {
262     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
263   } else {
264     ierr = PetscCalloc1(n+1,&collengths);CHKERRQ(ierr);
265     ierr = PetscMalloc1((n+1),&cia);CHKERRQ(ierr);
266     ierr = PetscMalloc1((nz+1),&cja);CHKERRQ(ierr);
267     jj   = a->j;
268     for (i=0; i<nz; i++) {
269       collengths[jj[i]]++;
270     }
271     cia[0] = oshift;
272     for (i=0; i<n; i++) {
273       cia[i+1] = cia[i] + collengths[i];
274     }
275     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
276     jj   = a->j;
277     for (row=0; row<m; row++) {
278       mr = a->i[row+1] - a->i[row];
279       for (i=0; i<mr; i++) {
280         col = *jj++;
281 
282         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
283       }
284     }
285     ierr = PetscFree(collengths);CHKERRQ(ierr);
286     *ia  = cia; *ja = cja;
287   }
288   PetscFunctionReturn(0);
289 }
290 
291 #undef __FUNCT__
292 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ"
293 PetscErrorCode MatRestoreColumnIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
294 {
295   PetscErrorCode ierr;
296 
297   PetscFunctionBegin;
298   if (!ia) PetscFunctionReturn(0);
299 
300   ierr = PetscFree(*ia);CHKERRQ(ierr);
301   ierr = PetscFree(*ja);CHKERRQ(ierr);
302   PetscFunctionReturn(0);
303 }
304 
305 /*
306  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
307  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
308  spidx[], index of a->a, to be used in MatTransposeColoringCreate_SeqAIJ() and MatFDColoringCreate_SeqXAIJ()
309 */
310 #undef __FUNCT__
311 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
312 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
313 {
314   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
315   PetscErrorCode ierr;
316   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
317   PetscInt       nz = a->i[m],row,*jj,mr,col;
318   PetscInt       *cspidx;
319 
320   PetscFunctionBegin;
321   *nn = n;
322   if (!ia) PetscFunctionReturn(0);
323 
324   ierr = PetscCalloc1(n+1,&collengths);CHKERRQ(ierr);
325   ierr = PetscMalloc1((n+1),&cia);CHKERRQ(ierr);
326   ierr = PetscMalloc1((nz+1),&cja);CHKERRQ(ierr);
327   ierr = PetscMalloc1((nz+1),&cspidx);CHKERRQ(ierr);
328   jj   = a->j;
329   for (i=0; i<nz; i++) {
330     collengths[jj[i]]++;
331   }
332   cia[0] = oshift;
333   for (i=0; i<n; i++) {
334     cia[i+1] = cia[i] + collengths[i];
335   }
336   ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
337   jj   = a->j;
338   for (row=0; row<m; row++) {
339     mr = a->i[row+1] - a->i[row];
340     for (i=0; i<mr; i++) {
341       col = *jj++;
342       cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
343       cja[cia[col] + collengths[col]++ - oshift]  = row + oshift;
344     }
345   }
346   ierr   = PetscFree(collengths);CHKERRQ(ierr);
347   *ia    = cia; *ja = cja;
348   *spidx = cspidx;
349   PetscFunctionReturn(0);
350 }
351 
352 #undef __FUNCT__
353 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
354 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
355 {
356   PetscErrorCode ierr;
357 
358   PetscFunctionBegin;
359   ierr = MatRestoreColumnIJ_SeqAIJ(A,oshift,symmetric,inodecompressed,n,ia,ja,done);CHKERRQ(ierr);
360   ierr = PetscFree(*spidx);CHKERRQ(ierr);
361   PetscFunctionReturn(0);
362 }
363 
364 #undef __FUNCT__
365 #define __FUNCT__ "MatSetValuesRow_SeqAIJ"
366 PetscErrorCode MatSetValuesRow_SeqAIJ(Mat A,PetscInt row,const PetscScalar v[])
367 {
368   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
369   PetscInt       *ai = a->i;
370   PetscErrorCode ierr;
371 
372   PetscFunctionBegin;
373   ierr = PetscMemcpy(a->a+ai[row],v,(ai[row+1]-ai[row])*sizeof(PetscScalar));CHKERRQ(ierr);
374   PetscFunctionReturn(0);
375 }
376 
377 /*
378     MatSeqAIJSetValuesLocalFast - An optimized version of MatSetValuesLocal() for SeqAIJ matrices with several assumptions
379 
380       -   a single row of values is set with each call
381       -   no row or column indices are negative or (in error) larger than the number of rows or columns
382       -   the values are always added to the matrix, not set
383       -   no new locations are introduced in the nonzero structure of the matrix
384 
385      This does NOT assume the global column indices are sorted
386 
387 */
388 
389 #include <petsc-private/isimpl.h>
390 #undef __FUNCT__
391 #define __FUNCT__ "MatSeqAIJSetValuesLocalFast"
392 PetscErrorCode MatSeqAIJSetValuesLocalFast(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
393 {
394   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
395   PetscInt       low,high,t,row,nrow,i,col,l;
396   const PetscInt *rp,*ai = a->i,*ailen = a->ilen,*aj = a->j;
397   PetscInt       lastcol = -1;
398   MatScalar      *ap,value,*aa = a->a;
399   const PetscInt *ridx = A->rmap->mapping->indices,*cidx = A->cmap->mapping->indices;
400 
401   row = ridx[im[0]];
402   rp   = aj + ai[row];
403   ap = aa + ai[row];
404   nrow = ailen[row];
405   low  = 0;
406   high = nrow;
407   for (l=0; l<n; l++) { /* loop over added columns */
408     col = cidx[in[l]];
409     value = v[l];
410 
411     if (col <= lastcol) low = 0;
412     else high = nrow;
413     lastcol = col;
414     while (high-low > 5) {
415       t = (low+high)/2;
416       if (rp[t] > col) high = t;
417       else low = t;
418     }
419     for (i=low; i<high; i++) {
420       if (rp[i] == col) {
421         ap[i] += value;
422         low = i + 1;
423         break;
424       }
425     }
426   }
427   return 0;
428 }
429 
430 #undef __FUNCT__
431 #define __FUNCT__ "MatSetValues_SeqAIJ"
432 PetscErrorCode MatSetValues_SeqAIJ(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
433 {
434   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
435   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
436   PetscInt       *imax = a->imax,*ai = a->i,*ailen = a->ilen;
437   PetscErrorCode ierr;
438   PetscInt       *aj = a->j,nonew = a->nonew,lastcol = -1;
439   MatScalar      *ap,value,*aa = a->a;
440   PetscBool      ignorezeroentries = a->ignorezeroentries;
441   PetscBool      roworiented       = a->roworiented;
442 
443   PetscFunctionBegin;
444   for (k=0; k<m; k++) { /* loop over added rows */
445     row = im[k];
446     if (row < 0) continue;
447 #if defined(PETSC_USE_DEBUG)
448     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);
449 #endif
450     rp   = aj + ai[row]; ap = aa + ai[row];
451     rmax = imax[row]; nrow = ailen[row];
452     low  = 0;
453     high = nrow;
454     for (l=0; l<n; l++) { /* loop over added columns */
455       if (in[l] < 0) continue;
456 #if defined(PETSC_USE_DEBUG)
457       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);
458 #endif
459       col = in[l];
460       if (roworiented) {
461         value = v[l + k*n];
462       } else {
463         value = v[k + l*m];
464       }
465       if ((value == 0.0 && ignorezeroentries) && (is == ADD_VALUES)) continue;
466 
467       if (col <= lastcol) low = 0;
468       else high = nrow;
469       lastcol = col;
470       while (high-low > 5) {
471         t = (low+high)/2;
472         if (rp[t] > col) high = t;
473         else low = t;
474       }
475       for (i=low; i<high; i++) {
476         if (rp[i] > col) break;
477         if (rp[i] == col) {
478           if (is == ADD_VALUES) ap[i] += value;
479           else ap[i] = value;
480           low = i + 1;
481           goto noinsert;
482         }
483       }
484       if (value == 0.0 && ignorezeroentries) goto noinsert;
485       if (nonew == 1) goto noinsert;
486       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at (%D,%D) in the matrix",row,col);
487       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
488       N = nrow++ - 1; a->nz++; high++;
489       /* shift up all the later entries in this row */
490       for (ii=N; ii>=i; ii--) {
491         rp[ii+1] = rp[ii];
492         ap[ii+1] = ap[ii];
493       }
494       rp[i] = col;
495       ap[i] = value;
496       low   = i + 1;
497       A->nonzerostate++;
498 noinsert:;
499     }
500     ailen[row] = nrow;
501   }
502   PetscFunctionReturn(0);
503 }
504 
505 
506 #undef __FUNCT__
507 #define __FUNCT__ "MatGetValues_SeqAIJ"
508 PetscErrorCode MatGetValues_SeqAIJ(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],PetscScalar v[])
509 {
510   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
511   PetscInt   *rp,k,low,high,t,row,nrow,i,col,l,*aj = a->j;
512   PetscInt   *ai = a->i,*ailen = a->ilen;
513   MatScalar  *ap,*aa = a->a;
514 
515   PetscFunctionBegin;
516   for (k=0; k<m; k++) { /* loop over rows */
517     row = im[k];
518     if (row < 0) {v += n; continue;} /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",row); */
519     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);
520     rp   = aj + ai[row]; ap = aa + ai[row];
521     nrow = ailen[row];
522     for (l=0; l<n; l++) { /* loop over columns */
523       if (in[l] < 0) {v++; continue;} /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",in[l]); */
524       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);
525       col  = in[l];
526       high = nrow; low = 0; /* assume unsorted */
527       while (high-low > 5) {
528         t = (low+high)/2;
529         if (rp[t] > col) high = t;
530         else low = t;
531       }
532       for (i=low; i<high; i++) {
533         if (rp[i] > col) break;
534         if (rp[i] == col) {
535           *v++ = ap[i];
536           goto finished;
537         }
538       }
539       *v++ = 0.0;
540 finished:;
541     }
542   }
543   PetscFunctionReturn(0);
544 }
545 
546 
547 #undef __FUNCT__
548 #define __FUNCT__ "MatView_SeqAIJ_Binary"
549 PetscErrorCode MatView_SeqAIJ_Binary(Mat A,PetscViewer viewer)
550 {
551   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
552   PetscErrorCode ierr;
553   PetscInt       i,*col_lens;
554   int            fd;
555   FILE           *file;
556 
557   PetscFunctionBegin;
558   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
559   ierr = PetscMalloc1((4+A->rmap->n),&col_lens);CHKERRQ(ierr);
560 
561   col_lens[0] = MAT_FILE_CLASSID;
562   col_lens[1] = A->rmap->n;
563   col_lens[2] = A->cmap->n;
564   col_lens[3] = a->nz;
565 
566   /* store lengths of each row and write (including header) to file */
567   for (i=0; i<A->rmap->n; i++) {
568     col_lens[4+i] = a->i[i+1] - a->i[i];
569   }
570   ierr = PetscBinaryWrite(fd,col_lens,4+A->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
571   ierr = PetscFree(col_lens);CHKERRQ(ierr);
572 
573   /* store column indices (zero start index) */
574   ierr = PetscBinaryWrite(fd,a->j,a->nz,PETSC_INT,PETSC_FALSE);CHKERRQ(ierr);
575 
576   /* store nonzero values */
577   ierr = PetscBinaryWrite(fd,a->a,a->nz,PETSC_SCALAR,PETSC_FALSE);CHKERRQ(ierr);
578 
579   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
580   if (file) {
581     fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(A->rmap->bs));
582   }
583   PetscFunctionReturn(0);
584 }
585 
586 extern PetscErrorCode MatSeqAIJFactorInfo_Matlab(Mat,PetscViewer);
587 
588 #undef __FUNCT__
589 #define __FUNCT__ "MatView_SeqAIJ_ASCII"
590 PetscErrorCode MatView_SeqAIJ_ASCII(Mat A,PetscViewer viewer)
591 {
592   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
593   PetscErrorCode    ierr;
594   PetscInt          i,j,m = A->rmap->n;
595   const char        *name;
596   PetscViewerFormat format;
597 
598   PetscFunctionBegin;
599   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
600   if (format == PETSC_VIEWER_ASCII_MATLAB) {
601     PetscInt nofinalvalue = 0;
602     if (m && ((a->i[m] == a->i[m-1]) || (a->j[a->nz-1] != A->cmap->n-1))) {
603       /* Need a dummy value to ensure the dimension of the matrix. */
604       nofinalvalue = 1;
605     }
606     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
607     ierr = PetscViewerASCIIPrintf(viewer,"%% Size = %D %D \n",m,A->cmap->n);CHKERRQ(ierr);
608     ierr = PetscViewerASCIIPrintf(viewer,"%% Nonzeros = %D \n",a->nz);CHKERRQ(ierr);
609 #if defined(PETSC_USE_COMPLEX)
610     ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,4);\n",a->nz+nofinalvalue);CHKERRQ(ierr);
611 #else
612     ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",a->nz+nofinalvalue);CHKERRQ(ierr);
613 #endif
614     ierr = PetscViewerASCIIPrintf(viewer,"zzz = [\n");CHKERRQ(ierr);
615 
616     for (i=0; i<m; i++) {
617       for (j=a->i[i]; j<a->i[i+1]; j++) {
618 #if defined(PETSC_USE_COMPLEX)
619         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);
620 #else
621         ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,a->j[j]+1,(double)a->a[j]);CHKERRQ(ierr);
622 #endif
623       }
624     }
625     if (nofinalvalue) {
626 #if defined(PETSC_USE_COMPLEX)
627       ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e %18.16e\n",m,A->cmap->n,0.,0.);CHKERRQ(ierr);
628 #else
629       ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",m,A->cmap->n,0.0);CHKERRQ(ierr);
630 #endif
631     }
632     ierr = PetscObjectGetName((PetscObject)A,&name);CHKERRQ(ierr);
633     ierr = PetscViewerASCIIPrintf(viewer,"];\n %s = spconvert(zzz);\n",name);CHKERRQ(ierr);
634     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
635   } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO || format == PETSC_VIEWER_ASCII_INFO) {
636     PetscFunctionReturn(0);
637   } else if (format == PETSC_VIEWER_ASCII_COMMON) {
638     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
639     for (i=0; i<m; i++) {
640       ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
641       for (j=a->i[i]; j<a->i[i+1]; j++) {
642 #if defined(PETSC_USE_COMPLEX)
643         if (PetscImaginaryPart(a->a[j]) > 0.0 && PetscRealPart(a->a[j]) != 0.0) {
644           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
645         } else if (PetscImaginaryPart(a->a[j]) < 0.0 && PetscRealPart(a->a[j]) != 0.0) {
646           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
647         } else if (PetscRealPart(a->a[j]) != 0.0) {
648           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
649         }
650 #else
651         if (a->a[j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);}
652 #endif
653       }
654       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
655     }
656     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
657   } else if (format == PETSC_VIEWER_ASCII_SYMMODU) {
658     PetscInt nzd=0,fshift=1,*sptr;
659     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
660     ierr = PetscMalloc1((m+1),&sptr);CHKERRQ(ierr);
661     for (i=0; i<m; i++) {
662       sptr[i] = nzd+1;
663       for (j=a->i[i]; j<a->i[i+1]; j++) {
664         if (a->j[j] >= i) {
665 #if defined(PETSC_USE_COMPLEX)
666           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) nzd++;
667 #else
668           if (a->a[j] != 0.0) nzd++;
669 #endif
670         }
671       }
672     }
673     sptr[m] = nzd+1;
674     ierr    = PetscViewerASCIIPrintf(viewer," %D %D\n\n",m,nzd);CHKERRQ(ierr);
675     for (i=0; i<m+1; i+=6) {
676       if (i+4<m) {
677         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);
678       } else if (i+3<m) {
679         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);
680       } else if (i+2<m) {
681         ierr = PetscViewerASCIIPrintf(viewer," %D %D %D %D\n",sptr[i],sptr[i+1],sptr[i+2],sptr[i+3]);CHKERRQ(ierr);
682       } else if (i+1<m) {
683         ierr = PetscViewerASCIIPrintf(viewer," %D %D %D\n",sptr[i],sptr[i+1],sptr[i+2]);CHKERRQ(ierr);
684       } else if (i<m) {
685         ierr = PetscViewerASCIIPrintf(viewer," %D %D\n",sptr[i],sptr[i+1]);CHKERRQ(ierr);
686       } else {
687         ierr = PetscViewerASCIIPrintf(viewer," %D\n",sptr[i]);CHKERRQ(ierr);
688       }
689     }
690     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
691     ierr = PetscFree(sptr);CHKERRQ(ierr);
692     for (i=0; i<m; i++) {
693       for (j=a->i[i]; j<a->i[i+1]; j++) {
694         if (a->j[j] >= i) {ierr = PetscViewerASCIIPrintf(viewer," %D ",a->j[j]+fshift);CHKERRQ(ierr);}
695       }
696       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
697     }
698     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
699     for (i=0; i<m; i++) {
700       for (j=a->i[i]; j<a->i[i+1]; j++) {
701         if (a->j[j] >= i) {
702 #if defined(PETSC_USE_COMPLEX)
703           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) {
704             ierr = PetscViewerASCIIPrintf(viewer," %18.16e %18.16e ",(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
705           }
706 #else
707           if (a->a[j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," %18.16e ",(double)a->a[j]);CHKERRQ(ierr);}
708 #endif
709         }
710       }
711       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
712     }
713     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
714   } else if (format == PETSC_VIEWER_ASCII_DENSE) {
715     PetscInt    cnt = 0,jcnt;
716     PetscScalar value;
717 #if defined(PETSC_USE_COMPLEX)
718     PetscBool   realonly = PETSC_TRUE;
719 
720     for (i=0; i<a->i[m]; i++) {
721       if (PetscImaginaryPart(a->a[i]) != 0.0) {
722         realonly = PETSC_FALSE;
723         break;
724       }
725     }
726 #endif
727 
728     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
729     for (i=0; i<m; i++) {
730       jcnt = 0;
731       for (j=0; j<A->cmap->n; j++) {
732         if (jcnt < a->i[i+1]-a->i[i] && j == a->j[cnt]) {
733           value = a->a[cnt++];
734           jcnt++;
735         } else {
736           value = 0.0;
737         }
738 #if defined(PETSC_USE_COMPLEX)
739         if (realonly) {
740           ierr = PetscViewerASCIIPrintf(viewer," %7.5e ",(double)PetscRealPart(value));CHKERRQ(ierr);
741         } else {
742           ierr = PetscViewerASCIIPrintf(viewer," %7.5e+%7.5e i ",(double)PetscRealPart(value),(double)PetscImaginaryPart(value));CHKERRQ(ierr);
743         }
744 #else
745         ierr = PetscViewerASCIIPrintf(viewer," %7.5e ",(double)value);CHKERRQ(ierr);
746 #endif
747       }
748       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
749     }
750     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
751   } else if (format == PETSC_VIEWER_ASCII_MATRIXMARKET) {
752     PetscInt fshift=1;
753     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
754 #if defined(PETSC_USE_COMPLEX)
755     ierr = PetscViewerASCIIPrintf(viewer,"%%matrix complex general\n");CHKERRQ(ierr);
756 #else
757     ierr = PetscViewerASCIIPrintf(viewer,"%%matrix real general\n");CHKERRQ(ierr);
758 #endif
759     ierr = PetscViewerASCIIPrintf(viewer,"%D %D %D\n", m, A->cmap->n, a->nz);CHKERRQ(ierr);
760     for (i=0; i<m; i++) {
761       for (j=a->i[i]; j<a->i[i+1]; j++) {
762 #if defined(PETSC_USE_COMPLEX)
763         if (PetscImaginaryPart(a->a[j]) > 0.0) {
764           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);
765         } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
766           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);
767         } else {
768           ierr = PetscViewerASCIIPrintf(viewer,"%D %D, %g\n", i+fshift,a->j[j]+fshift,(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
769         }
770 #else
771         ierr = PetscViewerASCIIPrintf(viewer,"%D %D %g\n", i+fshift, a->j[j]+fshift, (double)a->a[j]);CHKERRQ(ierr);
772 #endif
773       }
774     }
775     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
776   } else {
777     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
778     if (A->factortype) {
779       for (i=0; i<m; i++) {
780         ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
781         /* L part */
782         for (j=a->i[i]; j<a->i[i+1]; j++) {
783 #if defined(PETSC_USE_COMPLEX)
784           if (PetscImaginaryPart(a->a[j]) > 0.0) {
785             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
786           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
787             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)(-PetscImaginaryPart(a->a[j])));CHKERRQ(ierr);
788           } else {
789             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
790           }
791 #else
792           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);
793 #endif
794         }
795         /* diagonal */
796         j = a->diag[i];
797 #if defined(PETSC_USE_COMPLEX)
798         if (PetscImaginaryPart(a->a[j]) > 0.0) {
799           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);
800         } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
801           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);
802         } else {
803           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(1.0/a->a[j]));CHKERRQ(ierr);
804         }
805 #else
806         ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)(1.0/a->a[j]));CHKERRQ(ierr);
807 #endif
808 
809         /* U part */
810         for (j=a->diag[i+1]+1; j<a->diag[i]; j++) {
811 #if defined(PETSC_USE_COMPLEX)
812           if (PetscImaginaryPart(a->a[j]) > 0.0) {
813             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
814           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
815             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)(-PetscImaginaryPart(a->a[j])));CHKERRQ(ierr);
816           } else {
817             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
818           }
819 #else
820           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);
821 #endif
822         }
823         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
824       }
825     } else {
826       for (i=0; i<m; i++) {
827         ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
828         for (j=a->i[i]; j<a->i[i+1]; j++) {
829 #if defined(PETSC_USE_COMPLEX)
830           if (PetscImaginaryPart(a->a[j]) > 0.0) {
831             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
832           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
833             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
834           } else {
835             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
836           }
837 #else
838           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);
839 #endif
840         }
841         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
842       }
843     }
844     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
845   }
846   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
847   PetscFunctionReturn(0);
848 }
849 
850 #include <petscdraw.h>
851 #undef __FUNCT__
852 #define __FUNCT__ "MatView_SeqAIJ_Draw_Zoom"
853 PetscErrorCode MatView_SeqAIJ_Draw_Zoom(PetscDraw draw,void *Aa)
854 {
855   Mat               A  = (Mat) Aa;
856   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
857   PetscErrorCode    ierr;
858   PetscInt          i,j,m = A->rmap->n,color;
859   PetscReal         xl,yl,xr,yr,x_l,x_r,y_l,y_r,maxv = 0.0;
860   PetscViewer       viewer;
861   PetscViewerFormat format;
862 
863   PetscFunctionBegin;
864   ierr = PetscObjectQuery((PetscObject)A,"Zoomviewer",(PetscObject*)&viewer);CHKERRQ(ierr);
865   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
866 
867   ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
868   /* loop over matrix elements drawing boxes */
869 
870   if (format != PETSC_VIEWER_DRAW_CONTOUR) {
871     /* Blue for negative, Cyan for zero and  Red for positive */
872     color = PETSC_DRAW_BLUE;
873     for (i=0; i<m; i++) {
874       y_l = m - i - 1.0; y_r = y_l + 1.0;
875       for (j=a->i[i]; j<a->i[i+1]; j++) {
876         x_l = a->j[j]; x_r = x_l + 1.0;
877         if (PetscRealPart(a->a[j]) >=  0.) continue;
878         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
879       }
880     }
881     color = PETSC_DRAW_CYAN;
882     for (i=0; i<m; i++) {
883       y_l = m - i - 1.0; y_r = y_l + 1.0;
884       for (j=a->i[i]; j<a->i[i+1]; j++) {
885         x_l = a->j[j]; x_r = x_l + 1.0;
886         if (a->a[j] !=  0.) continue;
887         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
888       }
889     }
890     color = PETSC_DRAW_RED;
891     for (i=0; i<m; i++) {
892       y_l = m - i - 1.0; y_r = y_l + 1.0;
893       for (j=a->i[i]; j<a->i[i+1]; j++) {
894         x_l = a->j[j]; x_r = x_l + 1.0;
895         if (PetscRealPart(a->a[j]) <=  0.) continue;
896         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
897       }
898     }
899   } else {
900     /* use contour shading to indicate magnitude of values */
901     /* first determine max of all nonzero values */
902     PetscInt  nz = a->nz,count;
903     PetscDraw popup;
904     PetscReal scale;
905 
906     for (i=0; i<nz; i++) {
907       if (PetscAbsScalar(a->a[i]) > maxv) maxv = PetscAbsScalar(a->a[i]);
908     }
909     scale = (245.0 - PETSC_DRAW_BASIC_COLORS)/maxv;
910     ierr  = PetscDrawGetPopup(draw,&popup);CHKERRQ(ierr);
911     if (popup) {
912       ierr = PetscDrawScalePopup(popup,0.0,maxv);CHKERRQ(ierr);
913     }
914     count = 0;
915     for (i=0; i<m; i++) {
916       y_l = m - i - 1.0; y_r = y_l + 1.0;
917       for (j=a->i[i]; j<a->i[i+1]; j++) {
918         x_l   = a->j[j]; x_r = x_l + 1.0;
919         color = PETSC_DRAW_BASIC_COLORS + (PetscInt)(scale*PetscAbsScalar(a->a[count]));
920         ierr  = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
921         count++;
922       }
923     }
924   }
925   PetscFunctionReturn(0);
926 }
927 
928 #include <petscdraw.h>
929 #undef __FUNCT__
930 #define __FUNCT__ "MatView_SeqAIJ_Draw"
931 PetscErrorCode MatView_SeqAIJ_Draw(Mat A,PetscViewer viewer)
932 {
933   PetscErrorCode ierr;
934   PetscDraw      draw;
935   PetscReal      xr,yr,xl,yl,h,w;
936   PetscBool      isnull;
937 
938   PetscFunctionBegin;
939   ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
940   ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
941   if (isnull) PetscFunctionReturn(0);
942 
943   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",(PetscObject)viewer);CHKERRQ(ierr);
944   xr   = A->cmap->n; yr = A->rmap->n; h = yr/10.0; w = xr/10.0;
945   xr  += w;    yr += h;  xl = -w;     yl = -h;
946   ierr = PetscDrawSetCoordinates(draw,xl,yl,xr,yr);CHKERRQ(ierr);
947   ierr = PetscDrawZoom(draw,MatView_SeqAIJ_Draw_Zoom,A);CHKERRQ(ierr);
948   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",NULL);CHKERRQ(ierr);
949   PetscFunctionReturn(0);
950 }
951 
952 #undef __FUNCT__
953 #define __FUNCT__ "MatView_SeqAIJ"
954 PetscErrorCode MatView_SeqAIJ(Mat A,PetscViewer viewer)
955 {
956   PetscErrorCode ierr;
957   PetscBool      iascii,isbinary,isdraw;
958 
959   PetscFunctionBegin;
960   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
961   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
962   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
963   if (iascii) {
964     ierr = MatView_SeqAIJ_ASCII(A,viewer);CHKERRQ(ierr);
965   } else if (isbinary) {
966     ierr = MatView_SeqAIJ_Binary(A,viewer);CHKERRQ(ierr);
967   } else if (isdraw) {
968     ierr = MatView_SeqAIJ_Draw(A,viewer);CHKERRQ(ierr);
969   }
970   ierr = MatView_SeqAIJ_Inode(A,viewer);CHKERRQ(ierr);
971   PetscFunctionReturn(0);
972 }
973 
974 #undef __FUNCT__
975 #define __FUNCT__ "MatAssemblyEnd_SeqAIJ"
976 PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat A,MatAssemblyType mode)
977 {
978   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
979   PetscErrorCode ierr;
980   PetscInt       fshift = 0,i,j,*ai = a->i,*aj = a->j,*imax = a->imax;
981   PetscInt       m      = A->rmap->n,*ip,N,*ailen = a->ilen,rmax = 0;
982   MatScalar      *aa    = a->a,*ap;
983   PetscReal      ratio  = 0.6;
984 
985   PetscFunctionBegin;
986   if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(0);
987 
988   if (m) rmax = ailen[0]; /* determine row with most nonzeros */
989   for (i=1; i<m; i++) {
990     /* move each row back by the amount of empty slots (fshift) before it*/
991     fshift += imax[i-1] - ailen[i-1];
992     rmax    = PetscMax(rmax,ailen[i]);
993     if (fshift) {
994       ip = aj + ai[i];
995       ap = aa + ai[i];
996       N  = ailen[i];
997       for (j=0; j<N; j++) {
998         ip[j-fshift] = ip[j];
999         ap[j-fshift] = ap[j];
1000       }
1001     }
1002     ai[i] = ai[i-1] + ailen[i-1];
1003   }
1004   if (m) {
1005     fshift += imax[m-1] - ailen[m-1];
1006     ai[m]   = ai[m-1] + ailen[m-1];
1007   }
1008 
1009   /* reset ilen and imax for each row */
1010   a->nonzerorowcnt = 0;
1011   for (i=0; i<m; i++) {
1012     ailen[i] = imax[i] = ai[i+1] - ai[i];
1013     a->nonzerorowcnt += ((ai[i+1] - ai[i]) > 0);
1014   }
1015   a->nz = ai[m];
1016   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);
1017 
1018   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1019   ierr = PetscInfo4(A,"Matrix size: %D X %D; storage space: %D unneeded,%D used\n",m,A->cmap->n,fshift,a->nz);CHKERRQ(ierr);
1020   ierr = PetscInfo1(A,"Number of mallocs during MatSetValues() is %D\n",a->reallocs);CHKERRQ(ierr);
1021   ierr = PetscInfo1(A,"Maximum nonzeros in any row is %D\n",rmax);CHKERRQ(ierr);
1022 
1023   A->info.mallocs    += a->reallocs;
1024   a->reallocs         = 0;
1025   A->info.nz_unneeded = (PetscReal)fshift;
1026   a->rmax             = rmax;
1027 
1028   ierr = MatCheckCompressedRow(A,a->nonzerorowcnt,&a->compressedrow,a->i,m,ratio);CHKERRQ(ierr);
1029   ierr = MatAssemblyEnd_SeqAIJ_Inode(A,mode);CHKERRQ(ierr);
1030   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1031   PetscFunctionReturn(0);
1032 }
1033 
1034 #undef __FUNCT__
1035 #define __FUNCT__ "MatRealPart_SeqAIJ"
1036 PetscErrorCode MatRealPart_SeqAIJ(Mat A)
1037 {
1038   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1039   PetscInt       i,nz = a->nz;
1040   MatScalar      *aa = a->a;
1041   PetscErrorCode ierr;
1042 
1043   PetscFunctionBegin;
1044   for (i=0; i<nz; i++) aa[i] = PetscRealPart(aa[i]);
1045   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1046   PetscFunctionReturn(0);
1047 }
1048 
1049 #undef __FUNCT__
1050 #define __FUNCT__ "MatImaginaryPart_SeqAIJ"
1051 PetscErrorCode MatImaginaryPart_SeqAIJ(Mat A)
1052 {
1053   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1054   PetscInt       i,nz = a->nz;
1055   MatScalar      *aa = a->a;
1056   PetscErrorCode ierr;
1057 
1058   PetscFunctionBegin;
1059   for (i=0; i<nz; i++) aa[i] = PetscImaginaryPart(aa[i]);
1060   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1061   PetscFunctionReturn(0);
1062 }
1063 
1064 #if defined(PETSC_THREADCOMM_ACTIVE)
1065 PetscErrorCode MatZeroEntries_SeqAIJ_Kernel(PetscInt thread_id,Mat A)
1066 {
1067   PetscErrorCode ierr;
1068   PetscInt       *trstarts=A->rmap->trstarts;
1069   PetscInt       n,start,end;
1070   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1071 
1072   start = trstarts[thread_id];
1073   end   = trstarts[thread_id+1];
1074   n     = a->i[end] - a->i[start];
1075   ierr  = PetscMemzero(a->a+a->i[start],n*sizeof(PetscScalar));CHKERRQ(ierr);
1076   return 0;
1077 }
1078 
1079 #undef __FUNCT__
1080 #define __FUNCT__ "MatZeroEntries_SeqAIJ"
1081 PetscErrorCode MatZeroEntries_SeqAIJ(Mat A)
1082 {
1083   PetscErrorCode ierr;
1084 
1085   PetscFunctionBegin;
1086   ierr = PetscThreadCommRunKernel(PetscObjectComm((PetscObject)A),(PetscThreadKernel)MatZeroEntries_SeqAIJ_Kernel,1,A);CHKERRQ(ierr);
1087   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1088   PetscFunctionReturn(0);
1089 }
1090 #else
1091 #undef __FUNCT__
1092 #define __FUNCT__ "MatZeroEntries_SeqAIJ"
1093 PetscErrorCode MatZeroEntries_SeqAIJ(Mat A)
1094 {
1095   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1096   PetscErrorCode ierr;
1097 
1098   PetscFunctionBegin;
1099   ierr = PetscMemzero(a->a,(a->i[A->rmap->n])*sizeof(PetscScalar));CHKERRQ(ierr);
1100   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1101   PetscFunctionReturn(0);
1102 }
1103 #endif
1104 
1105 extern PetscErrorCode MatDestroy_Redundant(Mat_Redundant **);
1106 
1107 #undef __FUNCT__
1108 #define __FUNCT__ "MatDestroy_SeqAIJ"
1109 PetscErrorCode MatDestroy_SeqAIJ(Mat A)
1110 {
1111   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1112   PetscErrorCode ierr;
1113 
1114   PetscFunctionBegin;
1115 #if defined(PETSC_USE_LOG)
1116   PetscLogObjectState((PetscObject)A,"Rows=%D, Cols=%D, NZ=%D",A->rmap->n,A->cmap->n,a->nz);
1117 #endif
1118   ierr = MatDestroy_Redundant(&a->redundant);CHKERRQ(ierr);
1119   ierr = MatSeqXAIJFreeAIJ(A,&a->a,&a->j,&a->i);CHKERRQ(ierr);
1120   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
1121   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
1122   ierr = PetscFree(a->diag);CHKERRQ(ierr);
1123   ierr = PetscFree(a->ibdiag);CHKERRQ(ierr);
1124   ierr = PetscFree2(a->imax,a->ilen);CHKERRQ(ierr);
1125   ierr = PetscFree3(a->idiag,a->mdiag,a->ssor_work);CHKERRQ(ierr);
1126   ierr = PetscFree(a->solve_work);CHKERRQ(ierr);
1127   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
1128   ierr = PetscFree(a->saved_values);CHKERRQ(ierr);
1129   ierr = ISColoringDestroy(&a->coloring);CHKERRQ(ierr);
1130   ierr = PetscFree(a->xtoy);CHKERRQ(ierr);
1131   ierr = MatDestroy(&a->XtoY);CHKERRQ(ierr);
1132   ierr = PetscFree2(a->compressedrow.i,a->compressedrow.rindex);CHKERRQ(ierr);
1133   ierr = PetscFree(a->matmult_abdense);CHKERRQ(ierr);
1134 
1135   ierr = MatDestroy_SeqAIJ_Inode(A);CHKERRQ(ierr);
1136   ierr = PetscFree(A->data);CHKERRQ(ierr);
1137 
1138   ierr = PetscObjectChangeTypeName((PetscObject)A,0);CHKERRQ(ierr);
1139   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetColumnIndices_C",NULL);CHKERRQ(ierr);
1140   ierr = PetscObjectComposeFunction((PetscObject)A,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1141   ierr = PetscObjectComposeFunction((PetscObject)A,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1142   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqsbaij_C",NULL);CHKERRQ(ierr);
1143   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqbaij_C",NULL);CHKERRQ(ierr);
1144   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqaijperm_C",NULL);CHKERRQ(ierr);
1145   ierr = PetscObjectComposeFunction((PetscObject)A,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1146   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1147   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1148   ierr = PetscObjectComposeFunction((PetscObject)A,"MatReorderForNonzeroDiagonal_C",NULL);CHKERRQ(ierr);
1149   PetscFunctionReturn(0);
1150 }
1151 
1152 #undef __FUNCT__
1153 #define __FUNCT__ "MatSetOption_SeqAIJ"
1154 PetscErrorCode MatSetOption_SeqAIJ(Mat A,MatOption op,PetscBool flg)
1155 {
1156   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1157   PetscErrorCode ierr;
1158 
1159   PetscFunctionBegin;
1160   switch (op) {
1161   case MAT_ROW_ORIENTED:
1162     a->roworiented = flg;
1163     break;
1164   case MAT_KEEP_NONZERO_PATTERN:
1165     a->keepnonzeropattern = flg;
1166     break;
1167   case MAT_NEW_NONZERO_LOCATIONS:
1168     a->nonew = (flg ? 0 : 1);
1169     break;
1170   case MAT_NEW_NONZERO_LOCATION_ERR:
1171     a->nonew = (flg ? -1 : 0);
1172     break;
1173   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1174     a->nonew = (flg ? -2 : 0);
1175     break;
1176   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1177     a->nounused = (flg ? -1 : 0);
1178     break;
1179   case MAT_IGNORE_ZERO_ENTRIES:
1180     a->ignorezeroentries = flg;
1181     break;
1182   case MAT_SPD:
1183   case MAT_SYMMETRIC:
1184   case MAT_STRUCTURALLY_SYMMETRIC:
1185   case MAT_HERMITIAN:
1186   case MAT_SYMMETRY_ETERNAL:
1187     /* These options are handled directly by MatSetOption() */
1188     break;
1189   case MAT_NEW_DIAGONALS:
1190   case MAT_IGNORE_OFF_PROC_ENTRIES:
1191   case MAT_USE_HASH_TABLE:
1192     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1193     break;
1194   case MAT_USE_INODES:
1195     /* Not an error because MatSetOption_SeqAIJ_Inode handles this one */
1196     break;
1197   default:
1198     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1199   }
1200   ierr = MatSetOption_SeqAIJ_Inode(A,op,flg);CHKERRQ(ierr);
1201   PetscFunctionReturn(0);
1202 }
1203 
1204 #undef __FUNCT__
1205 #define __FUNCT__ "MatGetDiagonal_SeqAIJ"
1206 PetscErrorCode MatGetDiagonal_SeqAIJ(Mat A,Vec v)
1207 {
1208   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1209   PetscErrorCode ierr;
1210   PetscInt       i,j,n,*ai=a->i,*aj=a->j,nz;
1211   PetscScalar    *aa=a->a,*x,zero=0.0;
1212 
1213   PetscFunctionBegin;
1214   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
1215   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
1216 
1217   if (A->factortype == MAT_FACTOR_ILU || A->factortype == MAT_FACTOR_LU) {
1218     PetscInt *diag=a->diag;
1219     ierr = VecGetArray(v,&x);CHKERRQ(ierr);
1220     for (i=0; i<n; i++) x[i] = 1.0/aa[diag[i]];
1221     ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1222     PetscFunctionReturn(0);
1223   }
1224 
1225   ierr = VecSet(v,zero);CHKERRQ(ierr);
1226   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
1227   for (i=0; i<n; i++) {
1228     nz = ai[i+1] - ai[i];
1229     if (!nz) x[i] = 0.0;
1230     for (j=ai[i]; j<ai[i+1]; j++) {
1231       if (aj[j] == i) {
1232         x[i] = aa[j];
1233         break;
1234       }
1235     }
1236   }
1237   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1238   PetscFunctionReturn(0);
1239 }
1240 
1241 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1242 #undef __FUNCT__
1243 #define __FUNCT__ "MatMultTransposeAdd_SeqAIJ"
1244 PetscErrorCode MatMultTransposeAdd_SeqAIJ(Mat A,Vec xx,Vec zz,Vec yy)
1245 {
1246   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1247   PetscScalar    *x,*y;
1248   PetscErrorCode ierr;
1249   PetscInt       m = A->rmap->n;
1250 #if !defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1251   MatScalar         *v;
1252   PetscScalar       alpha;
1253   PetscInt          n,i,j,*idx,*ii,*ridx=NULL;
1254   Mat_CompressedRow cprow    = a->compressedrow;
1255   PetscBool         usecprow = cprow.use;
1256 #endif
1257 
1258   PetscFunctionBegin;
1259   if (zz != yy) {ierr = VecCopy(zz,yy);CHKERRQ(ierr);}
1260   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1261   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1262 
1263 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1264   fortranmulttransposeaddaij_(&m,x,a->i,a->j,a->a,y);
1265 #else
1266   if (usecprow) {
1267     m    = cprow.nrows;
1268     ii   = cprow.i;
1269     ridx = cprow.rindex;
1270   } else {
1271     ii = a->i;
1272   }
1273   for (i=0; i<m; i++) {
1274     idx = a->j + ii[i];
1275     v   = a->a + ii[i];
1276     n   = ii[i+1] - ii[i];
1277     if (usecprow) {
1278       alpha = x[ridx[i]];
1279     } else {
1280       alpha = x[i];
1281     }
1282     for (j=0; j<n; j++) y[idx[j]] += alpha*v[j];
1283   }
1284 #endif
1285   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1286   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1287   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1288   PetscFunctionReturn(0);
1289 }
1290 
1291 #undef __FUNCT__
1292 #define __FUNCT__ "MatMultTranspose_SeqAIJ"
1293 PetscErrorCode MatMultTranspose_SeqAIJ(Mat A,Vec xx,Vec yy)
1294 {
1295   PetscErrorCode ierr;
1296 
1297   PetscFunctionBegin;
1298   ierr = VecSet(yy,0.0);CHKERRQ(ierr);
1299   ierr = MatMultTransposeAdd_SeqAIJ(A,xx,yy,yy);CHKERRQ(ierr);
1300   PetscFunctionReturn(0);
1301 }
1302 
1303 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1304 #if defined(PETSC_THREADCOMM_ACTIVE)
1305 PetscErrorCode MatMult_SeqAIJ_Kernel(PetscInt thread_id,Mat A,Vec xx,Vec yy)
1306 {
1307   PetscErrorCode    ierr;
1308   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1309   PetscScalar       *y;
1310   const PetscScalar *x;
1311   const MatScalar   *aa;
1312   PetscInt          *trstarts=A->rmap->trstarts;
1313   PetscInt          n,start,end,i;
1314   const PetscInt    *aj,*ai;
1315   PetscScalar       sum;
1316 
1317   ierr  = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1318   ierr  = VecGetArray(yy,&y);CHKERRQ(ierr);
1319   start = trstarts[thread_id];
1320   end   = trstarts[thread_id+1];
1321   aj    = a->j;
1322   aa    = a->a;
1323   ai    = a->i;
1324   for (i=start; i<end; i++) {
1325     n   = ai[i+1] - ai[i];
1326     aj  = a->j + ai[i];
1327     aa  = a->a + ai[i];
1328     sum = 0.0;
1329     PetscSparseDensePlusDot(sum,x,aa,aj,n);
1330     y[i] = sum;
1331   }
1332   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1333   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1334   return 0;
1335 }
1336 
1337 #undef __FUNCT__
1338 #define __FUNCT__ "MatMult_SeqAIJ"
1339 PetscErrorCode MatMult_SeqAIJ(Mat A,Vec xx,Vec yy)
1340 {
1341   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1342   PetscScalar       *y;
1343   const PetscScalar *x;
1344   const MatScalar   *aa;
1345   PetscErrorCode    ierr;
1346   PetscInt          m=A->rmap->n;
1347   const PetscInt    *aj,*ii,*ridx=NULL;
1348   PetscInt          n,i;
1349   PetscScalar       sum;
1350   PetscBool         usecprow=a->compressedrow.use;
1351 
1352 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1353 #pragma disjoint(*x,*y,*aa)
1354 #endif
1355 
1356   PetscFunctionBegin;
1357   aj = a->j;
1358   aa = a->a;
1359   ii = a->i;
1360   if (usecprow) { /* use compressed row format */
1361     ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1362     ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1363     ierr = PetscMemzero(y,m*sizeof(PetscScalar));CHKERRQ(ierr);
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       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1373       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1374       y[*ridx++] = sum;
1375     }
1376     ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1377     ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1378   } else { /* do not use compressed row format */
1379 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJ)
1380     fortranmultaij_(&m,x,ii,aj,aa,y);
1381 #else
1382     ierr = PetscThreadCommRunKernel(PetscObjectComm((PetscObject)A),(PetscThreadKernel)MatMult_SeqAIJ_Kernel,3,A,xx,yy);CHKERRQ(ierr);
1383 #endif
1384   }
1385   ierr = PetscLogFlops(2.0*a->nz - a->nonzerorowcnt);CHKERRQ(ierr);
1386   PetscFunctionReturn(0);
1387 }
1388 #else
1389 #undef __FUNCT__
1390 #define __FUNCT__ "MatMult_SeqAIJ"
1391 PetscErrorCode MatMult_SeqAIJ(Mat A,Vec xx,Vec yy)
1392 {
1393   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1394   PetscScalar       *y;
1395   const PetscScalar *x;
1396   const MatScalar   *aa;
1397   PetscErrorCode    ierr;
1398   PetscInt          m=A->rmap->n;
1399   const PetscInt    *aj,*ii,*ridx=NULL;
1400   PetscInt          n,i;
1401   PetscScalar       sum;
1402   PetscBool         usecprow=a->compressedrow.use;
1403 
1404 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1405 #pragma disjoint(*x,*y,*aa)
1406 #endif
1407 
1408   PetscFunctionBegin;
1409   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1410   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1411   aj   = a->j;
1412   aa   = a->a;
1413   ii   = a->i;
1414   if (usecprow) { /* use compressed row format */
1415     ierr = PetscMemzero(y,m*sizeof(PetscScalar));CHKERRQ(ierr);
1416     m    = a->compressedrow.nrows;
1417     ii   = a->compressedrow.i;
1418     ridx = a->compressedrow.rindex;
1419     for (i=0; i<m; i++) {
1420       n           = ii[i+1] - ii[i];
1421       aj          = a->j + ii[i];
1422       aa          = a->a + ii[i];
1423       sum         = 0.0;
1424       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1425       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1426       y[*ridx++] = sum;
1427     }
1428   } else { /* do not use compressed row format */
1429 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJ)
1430     fortranmultaij_(&m,x,ii,aj,aa,y);
1431 #else
1432 #if defined(PETSC_THREADCOMM_ACTIVE)
1433     ierr = PetscThreadCommRunKernel(PetscObjectComm((PetscObject)A),(PetscThreadKernel)MatMult_SeqAIJ_Kernel,3,A,xx,yy);CHKERRQ(ierr);
1434 #else
1435     for (i=0; i<m; i++) {
1436       n           = ii[i+1] - ii[i];
1437       aj          = a->j + ii[i];
1438       aa          = a->a + ii[i];
1439       sum         = 0.0;
1440       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1441       y[i] = sum;
1442     }
1443 #endif
1444 #endif
1445   }
1446   ierr = PetscLogFlops(2.0*a->nz - a->nonzerorowcnt);CHKERRQ(ierr);
1447   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1448   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1449   PetscFunctionReturn(0);
1450 }
1451 #endif
1452 
1453 #undef __FUNCT__
1454 #define __FUNCT__ "MatMultMax_SeqAIJ"
1455 PetscErrorCode MatMultMax_SeqAIJ(Mat A,Vec xx,Vec yy)
1456 {
1457   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1458   PetscScalar       *y;
1459   const PetscScalar *x;
1460   const MatScalar   *aa;
1461   PetscErrorCode    ierr;
1462   PetscInt          m=A->rmap->n;
1463   const PetscInt    *aj,*ii,*ridx=NULL;
1464   PetscInt          n,i,nonzerorow=0;
1465   PetscScalar       sum;
1466   PetscBool         usecprow=a->compressedrow.use;
1467 
1468 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1469 #pragma disjoint(*x,*y,*aa)
1470 #endif
1471 
1472   PetscFunctionBegin;
1473   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1474   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1475   aj   = a->j;
1476   aa   = a->a;
1477   ii   = a->i;
1478   if (usecprow) { /* use compressed row format */
1479     m    = a->compressedrow.nrows;
1480     ii   = a->compressedrow.i;
1481     ridx = a->compressedrow.rindex;
1482     for (i=0; i<m; i++) {
1483       n           = ii[i+1] - ii[i];
1484       aj          = a->j + ii[i];
1485       aa          = a->a + ii[i];
1486       sum         = 0.0;
1487       nonzerorow += (n>0);
1488       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1489       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1490       y[*ridx++] = sum;
1491     }
1492   } else { /* do not use compressed row format */
1493     for (i=0; i<m; i++) {
1494       n           = ii[i+1] - ii[i];
1495       aj          = a->j + ii[i];
1496       aa          = a->a + ii[i];
1497       sum         = 0.0;
1498       nonzerorow += (n>0);
1499       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1500       y[i] = sum;
1501     }
1502   }
1503   ierr = PetscLogFlops(2.0*a->nz - nonzerorow);CHKERRQ(ierr);
1504   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1505   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1506   PetscFunctionReturn(0);
1507 }
1508 
1509 #undef __FUNCT__
1510 #define __FUNCT__ "MatMultAddMax_SeqAIJ"
1511 PetscErrorCode MatMultAddMax_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1512 {
1513   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1514   PetscScalar       *y,*z;
1515   const PetscScalar *x;
1516   const MatScalar   *aa;
1517   PetscErrorCode    ierr;
1518   PetscInt          m = A->rmap->n,*aj,*ii;
1519   PetscInt          n,i,*ridx=NULL;
1520   PetscScalar       sum;
1521   PetscBool         usecprow=a->compressedrow.use;
1522 
1523   PetscFunctionBegin;
1524   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1525   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1526   if (zz != yy) {
1527     ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
1528   } else {
1529     z = y;
1530   }
1531 
1532   aj = a->j;
1533   aa = a->a;
1534   ii = a->i;
1535   if (usecprow) { /* use compressed row format */
1536     if (zz != yy) {
1537       ierr = PetscMemcpy(z,y,m*sizeof(PetscScalar));CHKERRQ(ierr);
1538     }
1539     m    = a->compressedrow.nrows;
1540     ii   = a->compressedrow.i;
1541     ridx = a->compressedrow.rindex;
1542     for (i=0; i<m; i++) {
1543       n   = ii[i+1] - ii[i];
1544       aj  = a->j + ii[i];
1545       aa  = a->a + ii[i];
1546       sum = y[*ridx];
1547       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1548       z[*ridx++] = sum;
1549     }
1550   } else { /* do not use compressed row format */
1551     for (i=0; i<m; i++) {
1552       n   = ii[i+1] - ii[i];
1553       aj  = a->j + ii[i];
1554       aa  = a->a + ii[i];
1555       sum = y[i];
1556       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1557       z[i] = sum;
1558     }
1559   }
1560   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1561   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1562   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1563   if (zz != yy) {
1564     ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
1565   }
1566   PetscFunctionReturn(0);
1567 }
1568 
1569 #include <../src/mat/impls/aij/seq/ftn-kernels/fmultadd.h>
1570 #undef __FUNCT__
1571 #define __FUNCT__ "MatMultAdd_SeqAIJ"
1572 PetscErrorCode MatMultAdd_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1573 {
1574   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1575   PetscScalar       *y,*z;
1576   const PetscScalar *x;
1577   const MatScalar   *aa;
1578   PetscErrorCode    ierr;
1579   PetscInt          m = A->rmap->n,*aj,*ii;
1580   PetscInt          n,i,*ridx=NULL;
1581   PetscScalar       sum;
1582   PetscBool         usecprow=a->compressedrow.use;
1583 
1584   PetscFunctionBegin;
1585   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1586   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1587   if (zz != yy) {
1588     ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
1589   } else {
1590     z = y;
1591   }
1592 
1593   aj = a->j;
1594   aa = a->a;
1595   ii = a->i;
1596   if (usecprow) { /* use compressed row format */
1597     if (zz != yy) {
1598       ierr = PetscMemcpy(z,y,m*sizeof(PetscScalar));CHKERRQ(ierr);
1599     }
1600     m    = a->compressedrow.nrows;
1601     ii   = a->compressedrow.i;
1602     ridx = a->compressedrow.rindex;
1603     for (i=0; i<m; i++) {
1604       n   = ii[i+1] - ii[i];
1605       aj  = a->j + ii[i];
1606       aa  = a->a + ii[i];
1607       sum = y[*ridx];
1608       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1609       z[*ridx++] = sum;
1610     }
1611   } else { /* do not use compressed row format */
1612 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJ)
1613     fortranmultaddaij_(&m,x,ii,aj,aa,y,z);
1614 #else
1615     for (i=0; i<m; i++) {
1616       n   = ii[i+1] - ii[i];
1617       aj  = a->j + ii[i];
1618       aa  = a->a + ii[i];
1619       sum = y[i];
1620       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1621       z[i] = sum;
1622     }
1623 #endif
1624   }
1625   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1626   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1627   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1628   if (zz != yy) {
1629     ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
1630   }
1631 #if defined(PETSC_HAVE_CUSP)
1632   /*
1633   ierr = VecView(xx,0);CHKERRQ(ierr);
1634   ierr = VecView(zz,0);CHKERRQ(ierr);
1635   ierr = MatView(A,0);CHKERRQ(ierr);
1636   */
1637 #endif
1638   PetscFunctionReturn(0);
1639 }
1640 
1641 /*
1642      Adds diagonal pointers to sparse matrix structure.
1643 */
1644 #undef __FUNCT__
1645 #define __FUNCT__ "MatMarkDiagonal_SeqAIJ"
1646 PetscErrorCode MatMarkDiagonal_SeqAIJ(Mat A)
1647 {
1648   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1649   PetscErrorCode ierr;
1650   PetscInt       i,j,m = A->rmap->n;
1651 
1652   PetscFunctionBegin;
1653   if (!a->diag) {
1654     ierr = PetscMalloc1(m,&a->diag);CHKERRQ(ierr);
1655     ierr = PetscLogObjectMemory((PetscObject)A, m*sizeof(PetscInt));CHKERRQ(ierr);
1656   }
1657   for (i=0; i<A->rmap->n; i++) {
1658     a->diag[i] = a->i[i+1];
1659     for (j=a->i[i]; j<a->i[i+1]; j++) {
1660       if (a->j[j] == i) {
1661         a->diag[i] = j;
1662         break;
1663       }
1664     }
1665   }
1666   PetscFunctionReturn(0);
1667 }
1668 
1669 /*
1670      Checks for missing diagonals
1671 */
1672 #undef __FUNCT__
1673 #define __FUNCT__ "MatMissingDiagonal_SeqAIJ"
1674 PetscErrorCode MatMissingDiagonal_SeqAIJ(Mat A,PetscBool  *missing,PetscInt *d)
1675 {
1676   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1677   PetscInt   *diag,*ii = a->i,i;
1678 
1679   PetscFunctionBegin;
1680   *missing = PETSC_FALSE;
1681   if (A->rmap->n > 0 && !ii) {
1682     *missing = PETSC_TRUE;
1683     if (d) *d = 0;
1684     PetscInfo(A,"Matrix has no entries therefore is missing diagonal");
1685   } else {
1686     diag = a->diag;
1687     for (i=0; i<A->rmap->n; i++) {
1688       if (diag[i] >= ii[i+1]) {
1689         *missing = PETSC_TRUE;
1690         if (d) *d = i;
1691         PetscInfo1(A,"Matrix is missing diagonal number %D",i);
1692         break;
1693       }
1694     }
1695   }
1696   PetscFunctionReturn(0);
1697 }
1698 
1699 #undef __FUNCT__
1700 #define __FUNCT__ "MatInvertDiagonal_SeqAIJ"
1701 PetscErrorCode  MatInvertDiagonal_SeqAIJ(Mat A,PetscScalar omega,PetscScalar fshift)
1702 {
1703   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
1704   PetscErrorCode ierr;
1705   PetscInt       i,*diag,m = A->rmap->n;
1706   MatScalar      *v = a->a;
1707   PetscScalar    *idiag,*mdiag;
1708 
1709   PetscFunctionBegin;
1710   if (a->idiagvalid) PetscFunctionReturn(0);
1711   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1712   diag = a->diag;
1713   if (!a->idiag) {
1714     ierr = PetscMalloc3(m,&a->idiag,m,&a->mdiag,m,&a->ssor_work);CHKERRQ(ierr);
1715     ierr = PetscLogObjectMemory((PetscObject)A, 3*m*sizeof(PetscScalar));CHKERRQ(ierr);
1716     v    = a->a;
1717   }
1718   mdiag = a->mdiag;
1719   idiag = a->idiag;
1720 
1721   if (omega == 1.0 && !PetscAbsScalar(fshift)) {
1722     for (i=0; i<m; i++) {
1723       mdiag[i] = v[diag[i]];
1724       if (!PetscAbsScalar(mdiag[i])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Zero diagonal on row %D",i);
1725       idiag[i] = 1.0/v[diag[i]];
1726     }
1727     ierr = PetscLogFlops(m);CHKERRQ(ierr);
1728   } else {
1729     for (i=0; i<m; i++) {
1730       mdiag[i] = v[diag[i]];
1731       idiag[i] = omega/(fshift + v[diag[i]]);
1732     }
1733     ierr = PetscLogFlops(2.0*m);CHKERRQ(ierr);
1734   }
1735   a->idiagvalid = PETSC_TRUE;
1736   PetscFunctionReturn(0);
1737 }
1738 
1739 #include <../src/mat/impls/aij/seq/ftn-kernels/frelax.h>
1740 #undef __FUNCT__
1741 #define __FUNCT__ "MatSOR_SeqAIJ"
1742 PetscErrorCode MatSOR_SeqAIJ(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1743 {
1744   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1745   PetscScalar       *x,d,sum,*t,scale;
1746   const MatScalar   *v = a->a,*idiag=0,*mdiag;
1747   const PetscScalar *b, *bs,*xb, *ts;
1748   PetscErrorCode    ierr;
1749   PetscInt          n = A->cmap->n,m = A->rmap->n,i;
1750   const PetscInt    *idx,*diag;
1751 
1752   PetscFunctionBegin;
1753   its = its*lits;
1754 
1755   if (fshift != a->fshift || omega != a->omega) a->idiagvalid = PETSC_FALSE; /* must recompute idiag[] */
1756   if (!a->idiagvalid) {ierr = MatInvertDiagonal_SeqAIJ(A,omega,fshift);CHKERRQ(ierr);}
1757   a->fshift = fshift;
1758   a->omega  = omega;
1759 
1760   diag  = a->diag;
1761   t     = a->ssor_work;
1762   idiag = a->idiag;
1763   mdiag = a->mdiag;
1764 
1765   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1766   ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
1767   /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
1768   if (flag == SOR_APPLY_UPPER) {
1769     /* apply (U + D/omega) to the vector */
1770     bs = b;
1771     for (i=0; i<m; i++) {
1772       d   = fshift + mdiag[i];
1773       n   = a->i[i+1] - diag[i] - 1;
1774       idx = a->j + diag[i] + 1;
1775       v   = a->a + diag[i] + 1;
1776       sum = b[i]*d/omega;
1777       PetscSparseDensePlusDot(sum,bs,v,idx,n);
1778       x[i] = sum;
1779     }
1780     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1781     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1782     ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1783     PetscFunctionReturn(0);
1784   }
1785 
1786   if (flag == SOR_APPLY_LOWER) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SOR_APPLY_LOWER is not implemented");
1787   else if (flag & SOR_EISENSTAT) {
1788     /* Let  A = L + U + D; where L is lower trianglar,
1789     U is upper triangular, E = D/omega; This routine applies
1790 
1791             (L + E)^{-1} A (U + E)^{-1}
1792 
1793     to a vector efficiently using Eisenstat's trick.
1794     */
1795     scale = (2.0/omega) - 1.0;
1796 
1797     /*  x = (E + U)^{-1} b */
1798     for (i=m-1; i>=0; i--) {
1799       n   = a->i[i+1] - diag[i] - 1;
1800       idx = a->j + diag[i] + 1;
1801       v   = a->a + diag[i] + 1;
1802       sum = b[i];
1803       PetscSparseDenseMinusDot(sum,x,v,idx,n);
1804       x[i] = sum*idiag[i];
1805     }
1806 
1807     /*  t = b - (2*E - D)x */
1808     v = a->a;
1809     for (i=0; i<m; i++) t[i] = b[i] - scale*(v[*diag++])*x[i];
1810 
1811     /*  t = (E + L)^{-1}t */
1812     ts   = t;
1813     diag = a->diag;
1814     for (i=0; i<m; i++) {
1815       n   = diag[i] - a->i[i];
1816       idx = a->j + a->i[i];
1817       v   = a->a + a->i[i];
1818       sum = t[i];
1819       PetscSparseDenseMinusDot(sum,ts,v,idx,n);
1820       t[i] = sum*idiag[i];
1821       /*  x = x + t */
1822       x[i] += t[i];
1823     }
1824 
1825     ierr = PetscLogFlops(6.0*m-1 + 2.0*a->nz);CHKERRQ(ierr);
1826     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1827     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1828     PetscFunctionReturn(0);
1829   }
1830   if (flag & SOR_ZERO_INITIAL_GUESS) {
1831     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1832       for (i=0; i<m; i++) {
1833         n   = diag[i] - a->i[i];
1834         idx = a->j + a->i[i];
1835         v   = a->a + a->i[i];
1836         sum = b[i];
1837         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1838         t[i] = sum;
1839         x[i] = sum*idiag[i];
1840       }
1841       xb   = t;
1842       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1843     } else xb = b;
1844     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1845       for (i=m-1; i>=0; i--) {
1846         n   = a->i[i+1] - diag[i] - 1;
1847         idx = a->j + diag[i] + 1;
1848         v   = a->a + diag[i] + 1;
1849         sum = xb[i];
1850         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1851         if (xb == b) {
1852           x[i] = sum*idiag[i];
1853         } else {
1854           x[i] = (1-omega)*x[i] + sum*idiag[i];  /* omega in idiag */
1855         }
1856       }
1857       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
1858     }
1859     its--;
1860   }
1861   while (its--) {
1862     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1863       for (i=0; i<m; i++) {
1864         /* lower */
1865         n   = diag[i] - a->i[i];
1866         idx = a->j + a->i[i];
1867         v   = a->a + a->i[i];
1868         sum = b[i];
1869         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1870         t[i] = sum;             /* save application of the lower-triangular part */
1871         /* upper */
1872         n   = a->i[i+1] - diag[i] - 1;
1873         idx = a->j + diag[i] + 1;
1874         v   = a->a + diag[i] + 1;
1875         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1876         x[i] = (1. - omega)*x[i] + sum*idiag[i]; /* omega in idiag */
1877       }
1878       xb   = t;
1879       ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1880     } else xb = b;
1881     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1882       for (i=m-1; i>=0; i--) {
1883         sum = xb[i];
1884         if (xb == b) {
1885           /* whole matrix (no checkpointing available) */
1886           n   = a->i[i+1] - a->i[i];
1887           idx = a->j + a->i[i];
1888           v   = a->a + a->i[i];
1889           PetscSparseDenseMinusDot(sum,x,v,idx,n);
1890           x[i] = (1. - omega)*x[i] + (sum + mdiag[i]*x[i])*idiag[i];
1891         } else { /* lower-triangular part has been saved, so only apply upper-triangular */
1892           n   = a->i[i+1] - diag[i] - 1;
1893           idx = a->j + diag[i] + 1;
1894           v   = a->a + diag[i] + 1;
1895           PetscSparseDenseMinusDot(sum,x,v,idx,n);
1896           x[i] = (1. - omega)*x[i] + sum*idiag[i];  /* omega in idiag */
1897         }
1898       }
1899       if (xb == b) {
1900         ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1901       } else {
1902         ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
1903       }
1904     }
1905   }
1906   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1907   ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1908   PetscFunctionReturn(0);
1909 }
1910 
1911 
1912 #undef __FUNCT__
1913 #define __FUNCT__ "MatGetInfo_SeqAIJ"
1914 PetscErrorCode MatGetInfo_SeqAIJ(Mat A,MatInfoType flag,MatInfo *info)
1915 {
1916   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1917 
1918   PetscFunctionBegin;
1919   info->block_size   = 1.0;
1920   info->nz_allocated = (double)a->maxnz;
1921   info->nz_used      = (double)a->nz;
1922   info->nz_unneeded  = (double)(a->maxnz - a->nz);
1923   info->assemblies   = (double)A->num_ass;
1924   info->mallocs      = (double)A->info.mallocs;
1925   info->memory       = ((PetscObject)A)->mem;
1926   if (A->factortype) {
1927     info->fill_ratio_given  = A->info.fill_ratio_given;
1928     info->fill_ratio_needed = A->info.fill_ratio_needed;
1929     info->factor_mallocs    = A->info.factor_mallocs;
1930   } else {
1931     info->fill_ratio_given  = 0;
1932     info->fill_ratio_needed = 0;
1933     info->factor_mallocs    = 0;
1934   }
1935   PetscFunctionReturn(0);
1936 }
1937 
1938 #undef __FUNCT__
1939 #define __FUNCT__ "MatZeroRows_SeqAIJ"
1940 PetscErrorCode MatZeroRows_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
1941 {
1942   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1943   PetscInt          i,m = A->rmap->n - 1,d = 0;
1944   PetscErrorCode    ierr;
1945   const PetscScalar *xx;
1946   PetscScalar       *bb;
1947   PetscBool         missing;
1948 
1949   PetscFunctionBegin;
1950   if (x && b) {
1951     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
1952     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
1953     for (i=0; i<N; i++) {
1954       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1955       bb[rows[i]] = diag*xx[rows[i]];
1956     }
1957     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
1958     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
1959   }
1960 
1961   if (a->keepnonzeropattern) {
1962     for (i=0; i<N; i++) {
1963       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1964       ierr = PetscMemzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]*sizeof(PetscScalar));CHKERRQ(ierr);
1965     }
1966     if (diag != 0.0) {
1967       ierr = MatMissingDiagonal_SeqAIJ(A,&missing,&d);CHKERRQ(ierr);
1968       if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in row %D",d);
1969       for (i=0; i<N; i++) {
1970         a->a[a->diag[rows[i]]] = diag;
1971       }
1972     }
1973   } else {
1974     if (diag != 0.0) {
1975       for (i=0; i<N; i++) {
1976         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1977         if (a->ilen[rows[i]] > 0) {
1978           a->ilen[rows[i]]    = 1;
1979           a->a[a->i[rows[i]]] = diag;
1980           a->j[a->i[rows[i]]] = rows[i];
1981         } else { /* in case row was completely empty */
1982           ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES);CHKERRQ(ierr);
1983         }
1984       }
1985     } else {
1986       for (i=0; i<N; i++) {
1987         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1988         a->ilen[rows[i]] = 0;
1989       }
1990     }
1991     A->nonzerostate++;
1992   }
1993   ierr = MatAssemblyEnd_SeqAIJ(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1994   PetscFunctionReturn(0);
1995 }
1996 
1997 #undef __FUNCT__
1998 #define __FUNCT__ "MatZeroRowsColumns_SeqAIJ"
1999 PetscErrorCode MatZeroRowsColumns_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
2000 {
2001   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2002   PetscInt          i,j,m = A->rmap->n - 1,d = 0;
2003   PetscErrorCode    ierr;
2004   PetscBool         missing,*zeroed,vecs = PETSC_FALSE;
2005   const PetscScalar *xx;
2006   PetscScalar       *bb;
2007 
2008   PetscFunctionBegin;
2009   if (x && b) {
2010     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
2011     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
2012     vecs = PETSC_TRUE;
2013   }
2014   ierr = PetscCalloc1(A->rmap->n,&zeroed);CHKERRQ(ierr);
2015   for (i=0; i<N; i++) {
2016     if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2017     ierr = PetscMemzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]*sizeof(PetscScalar));CHKERRQ(ierr);
2018 
2019     zeroed[rows[i]] = PETSC_TRUE;
2020   }
2021   for (i=0; i<A->rmap->n; i++) {
2022     if (!zeroed[i]) {
2023       for (j=a->i[i]; j<a->i[i+1]; j++) {
2024         if (zeroed[a->j[j]]) {
2025           if (vecs) bb[i] -= a->a[j]*xx[a->j[j]];
2026           a->a[j] = 0.0;
2027         }
2028       }
2029     } else if (vecs) bb[i] = diag*xx[i];
2030   }
2031   if (x && b) {
2032     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
2033     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
2034   }
2035   ierr = PetscFree(zeroed);CHKERRQ(ierr);
2036   if (diag != 0.0) {
2037     ierr = MatMissingDiagonal_SeqAIJ(A,&missing,&d);CHKERRQ(ierr);
2038     if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in row %D",d);
2039     for (i=0; i<N; i++) {
2040       a->a[a->diag[rows[i]]] = diag;
2041     }
2042   }
2043   ierr = MatAssemblyEnd_SeqAIJ(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2044   PetscFunctionReturn(0);
2045 }
2046 
2047 #undef __FUNCT__
2048 #define __FUNCT__ "MatGetRow_SeqAIJ"
2049 PetscErrorCode MatGetRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
2050 {
2051   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2052   PetscInt   *itmp;
2053 
2054   PetscFunctionBegin;
2055   if (row < 0 || row >= A->rmap->n) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range",row);
2056 
2057   *nz = a->i[row+1] - a->i[row];
2058   if (v) *v = a->a + a->i[row];
2059   if (idx) {
2060     itmp = a->j + a->i[row];
2061     if (*nz) *idx = itmp;
2062     else *idx = 0;
2063   }
2064   PetscFunctionReturn(0);
2065 }
2066 
2067 /* remove this function? */
2068 #undef __FUNCT__
2069 #define __FUNCT__ "MatRestoreRow_SeqAIJ"
2070 PetscErrorCode MatRestoreRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
2071 {
2072   PetscFunctionBegin;
2073   PetscFunctionReturn(0);
2074 }
2075 
2076 #undef __FUNCT__
2077 #define __FUNCT__ "MatNorm_SeqAIJ"
2078 PetscErrorCode MatNorm_SeqAIJ(Mat A,NormType type,PetscReal *nrm)
2079 {
2080   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
2081   MatScalar      *v  = a->a;
2082   PetscReal      sum = 0.0;
2083   PetscErrorCode ierr;
2084   PetscInt       i,j;
2085 
2086   PetscFunctionBegin;
2087   if (type == NORM_FROBENIUS) {
2088     for (i=0; i<a->nz; i++) {
2089       sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
2090     }
2091     *nrm = PetscSqrtReal(sum);
2092   } else if (type == NORM_1) {
2093     PetscReal *tmp;
2094     PetscInt  *jj = a->j;
2095     ierr = PetscCalloc1(A->cmap->n+1,&tmp);CHKERRQ(ierr);
2096     *nrm = 0.0;
2097     for (j=0; j<a->nz; j++) {
2098       tmp[*jj++] += PetscAbsScalar(*v);  v++;
2099     }
2100     for (j=0; j<A->cmap->n; j++) {
2101       if (tmp[j] > *nrm) *nrm = tmp[j];
2102     }
2103     ierr = PetscFree(tmp);CHKERRQ(ierr);
2104   } else if (type == NORM_INFINITY) {
2105     *nrm = 0.0;
2106     for (j=0; j<A->rmap->n; j++) {
2107       v   = a->a + a->i[j];
2108       sum = 0.0;
2109       for (i=0; i<a->i[j+1]-a->i[j]; i++) {
2110         sum += PetscAbsScalar(*v); v++;
2111       }
2112       if (sum > *nrm) *nrm = sum;
2113     }
2114   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for two norm");
2115   PetscFunctionReturn(0);
2116 }
2117 
2118 /* Merged from MatGetSymbolicTranspose_SeqAIJ() - replace MatGetSymbolicTranspose_SeqAIJ()? */
2119 #undef __FUNCT__
2120 #define __FUNCT__ "MatTransposeSymbolic_SeqAIJ"
2121 PetscErrorCode MatTransposeSymbolic_SeqAIJ(Mat A,Mat *B)
2122 {
2123   PetscErrorCode ierr;
2124   PetscInt       i,j,anzj;
2125   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b;
2126   PetscInt       an=A->cmap->N,am=A->rmap->N;
2127   PetscInt       *ati,*atj,*atfill,*ai=a->i,*aj=a->j;
2128 
2129   PetscFunctionBegin;
2130   /* Allocate space for symbolic transpose info and work array */
2131   ierr = PetscCalloc1((an+1),&ati);CHKERRQ(ierr);
2132   ierr = PetscMalloc1(ai[am],&atj);CHKERRQ(ierr);
2133   ierr = PetscMalloc1(an,&atfill);CHKERRQ(ierr);
2134 
2135   /* Walk through aj and count ## of non-zeros in each row of A^T. */
2136   /* Note: offset by 1 for fast conversion into csr format. */
2137   for (i=0;i<ai[am];i++) ati[aj[i]+1] += 1;
2138   /* Form ati for csr format of A^T. */
2139   for (i=0;i<an;i++) ati[i+1] += ati[i];
2140 
2141   /* Copy ati into atfill so we have locations of the next free space in atj */
2142   ierr = PetscMemcpy(atfill,ati,an*sizeof(PetscInt));CHKERRQ(ierr);
2143 
2144   /* Walk through A row-wise and mark nonzero entries of A^T. */
2145   for (i=0;i<am;i++) {
2146     anzj = ai[i+1] - ai[i];
2147     for (j=0;j<anzj;j++) {
2148       atj[atfill[*aj]] = i;
2149       atfill[*aj++]   += 1;
2150     }
2151   }
2152 
2153   /* Clean up temporary space and complete requests. */
2154   ierr = PetscFree(atfill);CHKERRQ(ierr);
2155   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),an,am,ati,atj,NULL,B);CHKERRQ(ierr);
2156   ierr = MatSetBlockSizes(*B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2157 
2158   b          = (Mat_SeqAIJ*)((*B)->data);
2159   b->free_a  = PETSC_FALSE;
2160   b->free_ij = PETSC_TRUE;
2161   b->nonew   = 0;
2162   PetscFunctionReturn(0);
2163 }
2164 
2165 #undef __FUNCT__
2166 #define __FUNCT__ "MatTranspose_SeqAIJ"
2167 PetscErrorCode MatTranspose_SeqAIJ(Mat A,MatReuse reuse,Mat *B)
2168 {
2169   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2170   Mat            C;
2171   PetscErrorCode ierr;
2172   PetscInt       i,*aj = a->j,*ai = a->i,m = A->rmap->n,len,*col;
2173   MatScalar      *array = a->a;
2174 
2175   PetscFunctionBegin;
2176   if (reuse == MAT_REUSE_MATRIX && A == *B && m != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
2177 
2178   if (reuse == MAT_INITIAL_MATRIX || *B == A) {
2179     ierr = PetscCalloc1((1+A->cmap->n),&col);CHKERRQ(ierr);
2180 
2181     for (i=0; i<ai[m]; i++) col[aj[i]] += 1;
2182     ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2183     ierr = MatSetSizes(C,A->cmap->n,m,A->cmap->n,m);CHKERRQ(ierr);
2184     ierr = MatSetBlockSizes(C,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2185     ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2186     ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,col);CHKERRQ(ierr);
2187     ierr = PetscFree(col);CHKERRQ(ierr);
2188   } else {
2189     C = *B;
2190   }
2191 
2192   for (i=0; i<m; i++) {
2193     len    = ai[i+1]-ai[i];
2194     ierr   = MatSetValues_SeqAIJ(C,len,aj,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2195     array += len;
2196     aj    += len;
2197   }
2198   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2199   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2200 
2201   if (reuse == MAT_INITIAL_MATRIX || *B != A) {
2202     *B = C;
2203   } else {
2204     ierr = MatHeaderMerge(A,C);CHKERRQ(ierr);
2205   }
2206   PetscFunctionReturn(0);
2207 }
2208 
2209 #undef __FUNCT__
2210 #define __FUNCT__ "MatIsTranspose_SeqAIJ"
2211 PetscErrorCode  MatIsTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2212 {
2213   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) A->data;
2214   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2215   MatScalar      *va,*vb;
2216   PetscErrorCode ierr;
2217   PetscInt       ma,na,mb,nb, i;
2218 
2219   PetscFunctionBegin;
2220   bij = (Mat_SeqAIJ*) B->data;
2221 
2222   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2223   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2224   if (ma!=nb || na!=mb) {
2225     *f = PETSC_FALSE;
2226     PetscFunctionReturn(0);
2227   }
2228   aii  = aij->i; bii = bij->i;
2229   adx  = aij->j; bdx = bij->j;
2230   va   = aij->a; vb = bij->a;
2231   ierr = PetscMalloc1(ma,&aptr);CHKERRQ(ierr);
2232   ierr = PetscMalloc1(mb,&bptr);CHKERRQ(ierr);
2233   for (i=0; i<ma; i++) aptr[i] = aii[i];
2234   for (i=0; i<mb; i++) bptr[i] = bii[i];
2235 
2236   *f = PETSC_TRUE;
2237   for (i=0; i<ma; i++) {
2238     while (aptr[i]<aii[i+1]) {
2239       PetscInt    idc,idr;
2240       PetscScalar vc,vr;
2241       /* column/row index/value */
2242       idc = adx[aptr[i]];
2243       idr = bdx[bptr[idc]];
2244       vc  = va[aptr[i]];
2245       vr  = vb[bptr[idc]];
2246       if (i!=idr || PetscAbsScalar(vc-vr) > tol) {
2247         *f = PETSC_FALSE;
2248         goto done;
2249       } else {
2250         aptr[i]++;
2251         if (B || i!=idc) bptr[idc]++;
2252       }
2253     }
2254   }
2255 done:
2256   ierr = PetscFree(aptr);CHKERRQ(ierr);
2257   ierr = PetscFree(bptr);CHKERRQ(ierr);
2258   PetscFunctionReturn(0);
2259 }
2260 
2261 #undef __FUNCT__
2262 #define __FUNCT__ "MatIsHermitianTranspose_SeqAIJ"
2263 PetscErrorCode  MatIsHermitianTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2264 {
2265   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) A->data;
2266   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2267   MatScalar      *va,*vb;
2268   PetscErrorCode ierr;
2269   PetscInt       ma,na,mb,nb, i;
2270 
2271   PetscFunctionBegin;
2272   bij = (Mat_SeqAIJ*) B->data;
2273 
2274   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2275   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2276   if (ma!=nb || na!=mb) {
2277     *f = PETSC_FALSE;
2278     PetscFunctionReturn(0);
2279   }
2280   aii  = aij->i; bii = bij->i;
2281   adx  = aij->j; bdx = bij->j;
2282   va   = aij->a; vb = bij->a;
2283   ierr = PetscMalloc1(ma,&aptr);CHKERRQ(ierr);
2284   ierr = PetscMalloc1(mb,&bptr);CHKERRQ(ierr);
2285   for (i=0; i<ma; i++) aptr[i] = aii[i];
2286   for (i=0; i<mb; i++) bptr[i] = bii[i];
2287 
2288   *f = PETSC_TRUE;
2289   for (i=0; i<ma; i++) {
2290     while (aptr[i]<aii[i+1]) {
2291       PetscInt    idc,idr;
2292       PetscScalar vc,vr;
2293       /* column/row index/value */
2294       idc = adx[aptr[i]];
2295       idr = bdx[bptr[idc]];
2296       vc  = va[aptr[i]];
2297       vr  = vb[bptr[idc]];
2298       if (i!=idr || PetscAbsScalar(vc-PetscConj(vr)) > tol) {
2299         *f = PETSC_FALSE;
2300         goto done;
2301       } else {
2302         aptr[i]++;
2303         if (B || i!=idc) bptr[idc]++;
2304       }
2305     }
2306   }
2307 done:
2308   ierr = PetscFree(aptr);CHKERRQ(ierr);
2309   ierr = PetscFree(bptr);CHKERRQ(ierr);
2310   PetscFunctionReturn(0);
2311 }
2312 
2313 #undef __FUNCT__
2314 #define __FUNCT__ "MatIsSymmetric_SeqAIJ"
2315 PetscErrorCode MatIsSymmetric_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2316 {
2317   PetscErrorCode ierr;
2318 
2319   PetscFunctionBegin;
2320   ierr = MatIsTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2321   PetscFunctionReturn(0);
2322 }
2323 
2324 #undef __FUNCT__
2325 #define __FUNCT__ "MatIsHermitian_SeqAIJ"
2326 PetscErrorCode MatIsHermitian_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2327 {
2328   PetscErrorCode ierr;
2329 
2330   PetscFunctionBegin;
2331   ierr = MatIsHermitianTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2332   PetscFunctionReturn(0);
2333 }
2334 
2335 #undef __FUNCT__
2336 #define __FUNCT__ "MatDiagonalScale_SeqAIJ"
2337 PetscErrorCode MatDiagonalScale_SeqAIJ(Mat A,Vec ll,Vec rr)
2338 {
2339   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2340   PetscScalar    *l,*r,x;
2341   MatScalar      *v;
2342   PetscErrorCode ierr;
2343   PetscInt       i,j,m = A->rmap->n,n = A->cmap->n,M,nz = a->nz,*jj;
2344 
2345   PetscFunctionBegin;
2346   if (ll) {
2347     /* The local size is used so that VecMPI can be passed to this routine
2348        by MatDiagonalScale_MPIAIJ */
2349     ierr = VecGetLocalSize(ll,&m);CHKERRQ(ierr);
2350     if (m != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
2351     ierr = VecGetArray(ll,&l);CHKERRQ(ierr);
2352     v    = a->a;
2353     for (i=0; i<m; i++) {
2354       x = l[i];
2355       M = a->i[i+1] - a->i[i];
2356       for (j=0; j<M; j++) (*v++) *= x;
2357     }
2358     ierr = VecRestoreArray(ll,&l);CHKERRQ(ierr);
2359     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2360   }
2361   if (rr) {
2362     ierr = VecGetLocalSize(rr,&n);CHKERRQ(ierr);
2363     if (n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vector wrong length");
2364     ierr = VecGetArray(rr,&r);CHKERRQ(ierr);
2365     v    = a->a; jj = a->j;
2366     for (i=0; i<nz; i++) (*v++) *= r[*jj++];
2367     ierr = VecRestoreArray(rr,&r);CHKERRQ(ierr);
2368     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2369   }
2370   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
2371   PetscFunctionReturn(0);
2372 }
2373 
2374 #undef __FUNCT__
2375 #define __FUNCT__ "MatGetSubMatrix_SeqAIJ"
2376 PetscErrorCode MatGetSubMatrix_SeqAIJ(Mat A,IS isrow,IS iscol,PetscInt csize,MatReuse scall,Mat *B)
2377 {
2378   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*c;
2379   PetscErrorCode ierr;
2380   PetscInt       *smap,i,k,kstart,kend,oldcols = A->cmap->n,*lens;
2381   PetscInt       row,mat_i,*mat_j,tcol,first,step,*mat_ilen,sum,lensi;
2382   const PetscInt *irow,*icol;
2383   PetscInt       nrows,ncols;
2384   PetscInt       *starts,*j_new,*i_new,*aj = a->j,*ai = a->i,ii,*ailen = a->ilen;
2385   MatScalar      *a_new,*mat_a;
2386   Mat            C;
2387   PetscBool      stride,sorted;
2388 
2389   PetscFunctionBegin;
2390   ierr = ISSorted(isrow,&sorted);CHKERRQ(ierr);
2391   if (!sorted) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"ISrow is not sorted");
2392   ierr = ISSorted(iscol,&sorted);CHKERRQ(ierr);
2393   if (!sorted) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"IScol is not sorted");
2394 
2395   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
2396   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
2397   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
2398 
2399   ierr = ISStrideGetInfo(iscol,&first,&step);CHKERRQ(ierr);
2400   ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&stride);CHKERRQ(ierr);
2401   if (stride && step == 1) {
2402     /* special case of contiguous rows */
2403     ierr = PetscMalloc2(nrows,&lens,nrows,&starts);CHKERRQ(ierr);
2404     /* loop over new rows determining lens and starting points */
2405     for (i=0; i<nrows; i++) {
2406       kstart = ai[irow[i]];
2407       kend   = kstart + ailen[irow[i]];
2408       for (k=kstart; k<kend; k++) {
2409         if (aj[k] >= first) {
2410           starts[i] = k;
2411           break;
2412         }
2413       }
2414       sum = 0;
2415       while (k < kend) {
2416         if (aj[k++] >= first+ncols) break;
2417         sum++;
2418       }
2419       lens[i] = sum;
2420     }
2421     /* create submatrix */
2422     if (scall == MAT_REUSE_MATRIX) {
2423       PetscInt n_cols,n_rows;
2424       ierr = MatGetSize(*B,&n_rows,&n_cols);CHKERRQ(ierr);
2425       if (n_rows != nrows || n_cols != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
2426       ierr = MatZeroEntries(*B);CHKERRQ(ierr);
2427       C    = *B;
2428     } else {
2429       PetscInt rbs,cbs;
2430       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2431       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2432       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2433       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2434       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2435       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2436       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2437     }
2438     c = (Mat_SeqAIJ*)C->data;
2439 
2440     /* loop over rows inserting into submatrix */
2441     a_new = c->a;
2442     j_new = c->j;
2443     i_new = c->i;
2444 
2445     for (i=0; i<nrows; i++) {
2446       ii    = starts[i];
2447       lensi = lens[i];
2448       for (k=0; k<lensi; k++) {
2449         *j_new++ = aj[ii+k] - first;
2450       }
2451       ierr       = PetscMemcpy(a_new,a->a + starts[i],lensi*sizeof(PetscScalar));CHKERRQ(ierr);
2452       a_new     += lensi;
2453       i_new[i+1] = i_new[i] + lensi;
2454       c->ilen[i] = lensi;
2455     }
2456     ierr = PetscFree2(lens,starts);CHKERRQ(ierr);
2457   } else {
2458     ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
2459     ierr = PetscCalloc1(oldcols,&smap);CHKERRQ(ierr);
2460     ierr = PetscMalloc1((1+nrows),&lens);CHKERRQ(ierr);
2461     for (i=0; i<ncols; i++) {
2462 #if defined(PETSC_USE_DEBUG)
2463       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);
2464 #endif
2465       smap[icol[i]] = i+1;
2466     }
2467 
2468     /* determine lens of each row */
2469     for (i=0; i<nrows; i++) {
2470       kstart  = ai[irow[i]];
2471       kend    = kstart + a->ilen[irow[i]];
2472       lens[i] = 0;
2473       for (k=kstart; k<kend; k++) {
2474         if (smap[aj[k]]) {
2475           lens[i]++;
2476         }
2477       }
2478     }
2479     /* Create and fill new matrix */
2480     if (scall == MAT_REUSE_MATRIX) {
2481       PetscBool equal;
2482 
2483       c = (Mat_SeqAIJ*)((*B)->data);
2484       if ((*B)->rmap->n  != nrows || (*B)->cmap->n != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
2485       ierr = PetscMemcmp(c->ilen,lens,(*B)->rmap->n*sizeof(PetscInt),&equal);CHKERRQ(ierr);
2486       if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
2487       ierr = PetscMemzero(c->ilen,(*B)->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
2488       C    = *B;
2489     } else {
2490       PetscInt rbs,cbs;
2491       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2492       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2493       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2494       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2495       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2496       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2497       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2498     }
2499     c = (Mat_SeqAIJ*)(C->data);
2500     for (i=0; i<nrows; i++) {
2501       row      = irow[i];
2502       kstart   = ai[row];
2503       kend     = kstart + a->ilen[row];
2504       mat_i    = c->i[i];
2505       mat_j    = c->j + mat_i;
2506       mat_a    = c->a + mat_i;
2507       mat_ilen = c->ilen + i;
2508       for (k=kstart; k<kend; k++) {
2509         if ((tcol=smap[a->j[k]])) {
2510           *mat_j++ = tcol - 1;
2511           *mat_a++ = a->a[k];
2512           (*mat_ilen)++;
2513 
2514         }
2515       }
2516     }
2517     /* Free work space */
2518     ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
2519     ierr = PetscFree(smap);CHKERRQ(ierr);
2520     ierr = PetscFree(lens);CHKERRQ(ierr);
2521   }
2522   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2523   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2524 
2525   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
2526   *B   = C;
2527   PetscFunctionReturn(0);
2528 }
2529 
2530 #undef __FUNCT__
2531 #define __FUNCT__ "MatGetMultiProcBlock_SeqAIJ"
2532 PetscErrorCode  MatGetMultiProcBlock_SeqAIJ(Mat mat,MPI_Comm subComm,MatReuse scall,Mat *subMat)
2533 {
2534   PetscErrorCode ierr;
2535   Mat            B;
2536 
2537   PetscFunctionBegin;
2538   if (scall == MAT_INITIAL_MATRIX) {
2539     ierr    = MatCreate(subComm,&B);CHKERRQ(ierr);
2540     ierr    = MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->n,mat->cmap->n);CHKERRQ(ierr);
2541     ierr    = MatSetBlockSizesFromMats(B,mat,mat);CHKERRQ(ierr);
2542     ierr    = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
2543     ierr    = MatDuplicateNoCreate_SeqAIJ(B,mat,MAT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
2544     *subMat = B;
2545   } else {
2546     ierr = MatCopy_SeqAIJ(mat,*subMat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2547   }
2548   PetscFunctionReturn(0);
2549 }
2550 
2551 #undef __FUNCT__
2552 #define __FUNCT__ "MatILUFactor_SeqAIJ"
2553 PetscErrorCode MatILUFactor_SeqAIJ(Mat inA,IS row,IS col,const MatFactorInfo *info)
2554 {
2555   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)inA->data;
2556   PetscErrorCode ierr;
2557   Mat            outA;
2558   PetscBool      row_identity,col_identity;
2559 
2560   PetscFunctionBegin;
2561   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels=0 supported for in-place ilu");
2562 
2563   ierr = ISIdentity(row,&row_identity);CHKERRQ(ierr);
2564   ierr = ISIdentity(col,&col_identity);CHKERRQ(ierr);
2565 
2566   outA             = inA;
2567   outA->factortype = MAT_FACTOR_LU;
2568 
2569   ierr = PetscObjectReference((PetscObject)row);CHKERRQ(ierr);
2570   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
2571 
2572   a->row = row;
2573 
2574   ierr = PetscObjectReference((PetscObject)col);CHKERRQ(ierr);
2575   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
2576 
2577   a->col = col;
2578 
2579   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
2580   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
2581   ierr = ISInvertPermutation(col,PETSC_DECIDE,&a->icol);CHKERRQ(ierr);
2582   ierr = PetscLogObjectParent((PetscObject)inA,(PetscObject)a->icol);CHKERRQ(ierr);
2583 
2584   if (!a->solve_work) { /* this matrix may have been factored before */
2585     ierr = PetscMalloc1((inA->rmap->n+1),&a->solve_work);CHKERRQ(ierr);
2586     ierr = PetscLogObjectMemory((PetscObject)inA, (inA->rmap->n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2587   }
2588 
2589   ierr = MatMarkDiagonal_SeqAIJ(inA);CHKERRQ(ierr);
2590   if (row_identity && col_identity) {
2591     ierr = MatLUFactorNumeric_SeqAIJ_inplace(outA,inA,info);CHKERRQ(ierr);
2592   } else {
2593     ierr = MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA,inA,info);CHKERRQ(ierr);
2594   }
2595   PetscFunctionReturn(0);
2596 }
2597 
2598 #undef __FUNCT__
2599 #define __FUNCT__ "MatScale_SeqAIJ"
2600 PetscErrorCode MatScale_SeqAIJ(Mat inA,PetscScalar alpha)
2601 {
2602   Mat_SeqAIJ     *a     = (Mat_SeqAIJ*)inA->data;
2603   PetscScalar    oalpha = alpha;
2604   PetscErrorCode ierr;
2605   PetscBLASInt   one = 1,bnz;
2606 
2607   PetscFunctionBegin;
2608   ierr = PetscBLASIntCast(a->nz,&bnz);CHKERRQ(ierr);
2609   PetscStackCallBLAS("BLASscal",BLASscal_(&bnz,&oalpha,a->a,&one));
2610   ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2611   ierr = MatSeqAIJInvalidateDiagonal(inA);CHKERRQ(ierr);
2612   PetscFunctionReturn(0);
2613 }
2614 
2615 #undef __FUNCT__
2616 #define __FUNCT__ "MatGetSubMatrices_SeqAIJ"
2617 PetscErrorCode MatGetSubMatrices_SeqAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
2618 {
2619   PetscErrorCode ierr;
2620   PetscInt       i;
2621 
2622   PetscFunctionBegin;
2623   if (scall == MAT_INITIAL_MATRIX) {
2624     ierr = PetscMalloc1((n+1),B);CHKERRQ(ierr);
2625   }
2626 
2627   for (i=0; i<n; i++) {
2628     ierr = MatGetSubMatrix_SeqAIJ(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]);CHKERRQ(ierr);
2629   }
2630   PetscFunctionReturn(0);
2631 }
2632 
2633 #undef __FUNCT__
2634 #define __FUNCT__ "MatIncreaseOverlap_SeqAIJ"
2635 PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
2636 {
2637   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2638   PetscErrorCode ierr;
2639   PetscInt       row,i,j,k,l,m,n,*nidx,isz,val;
2640   const PetscInt *idx;
2641   PetscInt       start,end,*ai,*aj;
2642   PetscBT        table;
2643 
2644   PetscFunctionBegin;
2645   m  = A->rmap->n;
2646   ai = a->i;
2647   aj = a->j;
2648 
2649   if (ov < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"illegal negative overlap value used");
2650 
2651   ierr = PetscMalloc1((m+1),&nidx);CHKERRQ(ierr);
2652   ierr = PetscBTCreate(m,&table);CHKERRQ(ierr);
2653 
2654   for (i=0; i<is_max; i++) {
2655     /* Initialize the two local arrays */
2656     isz  = 0;
2657     ierr = PetscBTMemzero(m,table);CHKERRQ(ierr);
2658 
2659     /* Extract the indices, assume there can be duplicate entries */
2660     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
2661     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
2662 
2663     /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2664     for (j=0; j<n; ++j) {
2665       if (!PetscBTLookupSet(table,idx[j])) nidx[isz++] = idx[j];
2666     }
2667     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
2668     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
2669 
2670     k = 0;
2671     for (j=0; j<ov; j++) { /* for each overlap */
2672       n = isz;
2673       for (; k<n; k++) { /* do only those rows in nidx[k], which are not done yet */
2674         row   = nidx[k];
2675         start = ai[row];
2676         end   = ai[row+1];
2677         for (l = start; l<end; l++) {
2678           val = aj[l];
2679           if (!PetscBTLookupSet(table,val)) nidx[isz++] = val;
2680         }
2681       }
2682     }
2683     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz,nidx,PETSC_COPY_VALUES,(is+i));CHKERRQ(ierr);
2684   }
2685   ierr = PetscBTDestroy(&table);CHKERRQ(ierr);
2686   ierr = PetscFree(nidx);CHKERRQ(ierr);
2687   PetscFunctionReturn(0);
2688 }
2689 
2690 /* -------------------------------------------------------------- */
2691 #undef __FUNCT__
2692 #define __FUNCT__ "MatPermute_SeqAIJ"
2693 PetscErrorCode MatPermute_SeqAIJ(Mat A,IS rowp,IS colp,Mat *B)
2694 {
2695   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2696   PetscErrorCode ierr;
2697   PetscInt       i,nz = 0,m = A->rmap->n,n = A->cmap->n;
2698   const PetscInt *row,*col;
2699   PetscInt       *cnew,j,*lens;
2700   IS             icolp,irowp;
2701   PetscInt       *cwork = NULL;
2702   PetscScalar    *vwork = NULL;
2703 
2704   PetscFunctionBegin;
2705   ierr = ISInvertPermutation(rowp,PETSC_DECIDE,&irowp);CHKERRQ(ierr);
2706   ierr = ISGetIndices(irowp,&row);CHKERRQ(ierr);
2707   ierr = ISInvertPermutation(colp,PETSC_DECIDE,&icolp);CHKERRQ(ierr);
2708   ierr = ISGetIndices(icolp,&col);CHKERRQ(ierr);
2709 
2710   /* determine lengths of permuted rows */
2711   ierr = PetscMalloc1((m+1),&lens);CHKERRQ(ierr);
2712   for (i=0; i<m; i++) lens[row[i]] = a->i[i+1] - a->i[i];
2713   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
2714   ierr = MatSetSizes(*B,m,n,m,n);CHKERRQ(ierr);
2715   ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
2716   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2717   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*B,0,lens);CHKERRQ(ierr);
2718   ierr = PetscFree(lens);CHKERRQ(ierr);
2719 
2720   ierr = PetscMalloc1(n,&cnew);CHKERRQ(ierr);
2721   for (i=0; i<m; i++) {
2722     ierr = MatGetRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2723     for (j=0; j<nz; j++) cnew[j] = col[cwork[j]];
2724     ierr = MatSetValues_SeqAIJ(*B,1,&row[i],nz,cnew,vwork,INSERT_VALUES);CHKERRQ(ierr);
2725     ierr = MatRestoreRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2726   }
2727   ierr = PetscFree(cnew);CHKERRQ(ierr);
2728 
2729   (*B)->assembled = PETSC_FALSE;
2730 
2731   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2732   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2733   ierr = ISRestoreIndices(irowp,&row);CHKERRQ(ierr);
2734   ierr = ISRestoreIndices(icolp,&col);CHKERRQ(ierr);
2735   ierr = ISDestroy(&irowp);CHKERRQ(ierr);
2736   ierr = ISDestroy(&icolp);CHKERRQ(ierr);
2737   PetscFunctionReturn(0);
2738 }
2739 
2740 #undef __FUNCT__
2741 #define __FUNCT__ "MatCopy_SeqAIJ"
2742 PetscErrorCode MatCopy_SeqAIJ(Mat A,Mat B,MatStructure str)
2743 {
2744   PetscErrorCode ierr;
2745 
2746   PetscFunctionBegin;
2747   /* If the two matrices have the same copy implementation, use fast copy. */
2748   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
2749     Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2750     Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data;
2751 
2752     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");
2753     ierr = PetscMemcpy(b->a,a->a,(a->i[A->rmap->n])*sizeof(PetscScalar));CHKERRQ(ierr);
2754   } else {
2755     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2756   }
2757   PetscFunctionReturn(0);
2758 }
2759 
2760 #undef __FUNCT__
2761 #define __FUNCT__ "MatSetUp_SeqAIJ"
2762 PetscErrorCode MatSetUp_SeqAIJ(Mat A)
2763 {
2764   PetscErrorCode ierr;
2765 
2766   PetscFunctionBegin;
2767   ierr =  MatSeqAIJSetPreallocation_SeqAIJ(A,PETSC_DEFAULT,0);CHKERRQ(ierr);
2768   PetscFunctionReturn(0);
2769 }
2770 
2771 #undef __FUNCT__
2772 #define __FUNCT__ "MatSeqAIJGetArray_SeqAIJ"
2773 PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A,PetscScalar *array[])
2774 {
2775   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2776 
2777   PetscFunctionBegin;
2778   *array = a->a;
2779   PetscFunctionReturn(0);
2780 }
2781 
2782 #undef __FUNCT__
2783 #define __FUNCT__ "MatSeqAIJRestoreArray_SeqAIJ"
2784 PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A,PetscScalar *array[])
2785 {
2786   PetscFunctionBegin;
2787   PetscFunctionReturn(0);
2788 }
2789 
2790 /*
2791    Computes the number of nonzeros per row needed for preallocation when X and Y
2792    have different nonzero structure.
2793 */
2794 #undef __FUNCT__
2795 #define __FUNCT__ "MatAXPYGetPreallocation_SeqAIJ"
2796 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
2797 {
2798   PetscInt       i,m=Y->rmap->N;
2799   Mat_SeqAIJ     *x  = (Mat_SeqAIJ*)X->data;
2800   Mat_SeqAIJ     *y  = (Mat_SeqAIJ*)Y->data;
2801   const PetscInt *xi = x->i,*yi = y->i;
2802 
2803   PetscFunctionBegin;
2804   /* Set the number of nonzeros in the new matrix */
2805   for (i=0; i<m; i++) {
2806     PetscInt       j,k,nzx = xi[i+1] - xi[i],nzy = yi[i+1] - yi[i];
2807     const PetscInt *xj = x->j+xi[i],*yj = y->j+yi[i];
2808     nnz[i] = 0;
2809     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2810       for (; k<nzy && yj[k]<xj[j]; k++) nnz[i]++; /* Catch up to X */
2811       if (k<nzy && yj[k]==xj[j]) k++;             /* Skip duplicate */
2812       nnz[i]++;
2813     }
2814     for (; k<nzy; k++) nnz[i]++;
2815   }
2816   PetscFunctionReturn(0);
2817 }
2818 
2819 #undef __FUNCT__
2820 #define __FUNCT__ "MatAXPY_SeqAIJ"
2821 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2822 {
2823   PetscErrorCode ierr;
2824   PetscInt       i;
2825   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
2826   PetscBLASInt   one=1,bnz;
2827 
2828   PetscFunctionBegin;
2829   ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2830   if (str == SAME_NONZERO_PATTERN) {
2831     PetscScalar alpha = a;
2832     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2833     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
2834     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2835   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2836     if (y->xtoy && y->XtoY != X) {
2837       ierr = PetscFree(y->xtoy);CHKERRQ(ierr);
2838       ierr = MatDestroy(&y->XtoY);CHKERRQ(ierr);
2839     }
2840     if (!y->xtoy) { /* get xtoy */
2841       ierr    = MatAXPYGetxtoy_Private(X->rmap->n,x->i,x->j,NULL, y->i,y->j,NULL, &y->xtoy);CHKERRQ(ierr);
2842       y->XtoY = X;
2843       ierr    = PetscObjectReference((PetscObject)X);CHKERRQ(ierr);
2844     }
2845     for (i=0; i<x->nz; i++) y->a[y->xtoy[i]] += a*(x->a[i]);
2846     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2847     ierr = PetscInfo3(Y,"ratio of nnz(X)/nnz(Y): %D/%D = %g\n",x->nz,y->nz,(double)((PetscReal)(x->nz)/(y->nz+1)));CHKERRQ(ierr);
2848   } else {
2849     Mat      B;
2850     PetscInt *nnz;
2851     ierr = PetscMalloc1(Y->rmap->N,&nnz);CHKERRQ(ierr);
2852     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2853     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2854     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2855     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2856     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
2857     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
2858     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
2859     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2860     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
2861     ierr = PetscFree(nnz);CHKERRQ(ierr);
2862   }
2863   PetscFunctionReturn(0);
2864 }
2865 
2866 #undef __FUNCT__
2867 #define __FUNCT__ "MatConjugate_SeqAIJ"
2868 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
2869 {
2870 #if defined(PETSC_USE_COMPLEX)
2871   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
2872   PetscInt    i,nz;
2873   PetscScalar *a;
2874 
2875   PetscFunctionBegin;
2876   nz = aij->nz;
2877   a  = aij->a;
2878   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
2879 #else
2880   PetscFunctionBegin;
2881 #endif
2882   PetscFunctionReturn(0);
2883 }
2884 
2885 #undef __FUNCT__
2886 #define __FUNCT__ "MatGetRowMaxAbs_SeqAIJ"
2887 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2888 {
2889   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2890   PetscErrorCode ierr;
2891   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2892   PetscReal      atmp;
2893   PetscScalar    *x;
2894   MatScalar      *aa;
2895 
2896   PetscFunctionBegin;
2897   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2898   aa = a->a;
2899   ai = a->i;
2900   aj = a->j;
2901 
2902   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2903   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2904   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2905   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2906   for (i=0; i<m; i++) {
2907     ncols = ai[1] - ai[0]; ai++;
2908     x[i]  = 0.0;
2909     for (j=0; j<ncols; j++) {
2910       atmp = PetscAbsScalar(*aa);
2911       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
2912       aa++; aj++;
2913     }
2914   }
2915   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2916   PetscFunctionReturn(0);
2917 }
2918 
2919 #undef __FUNCT__
2920 #define __FUNCT__ "MatGetRowMax_SeqAIJ"
2921 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2922 {
2923   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2924   PetscErrorCode ierr;
2925   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2926   PetscScalar    *x;
2927   MatScalar      *aa;
2928 
2929   PetscFunctionBegin;
2930   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2931   aa = a->a;
2932   ai = a->i;
2933   aj = a->j;
2934 
2935   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2936   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2937   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2938   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2939   for (i=0; i<m; i++) {
2940     ncols = ai[1] - ai[0]; ai++;
2941     if (ncols == A->cmap->n) { /* row is dense */
2942       x[i] = *aa; if (idx) idx[i] = 0;
2943     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
2944       x[i] = 0.0;
2945       if (idx) {
2946         idx[i] = 0; /* in case ncols is zero */
2947         for (j=0;j<ncols;j++) { /* find first implicit 0.0 in the row */
2948           if (aj[j] > j) {
2949             idx[i] = j;
2950             break;
2951           }
2952         }
2953       }
2954     }
2955     for (j=0; j<ncols; j++) {
2956       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
2957       aa++; aj++;
2958     }
2959   }
2960   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2961   PetscFunctionReturn(0);
2962 }
2963 
2964 #undef __FUNCT__
2965 #define __FUNCT__ "MatGetRowMinAbs_SeqAIJ"
2966 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2967 {
2968   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2969   PetscErrorCode ierr;
2970   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2971   PetscReal      atmp;
2972   PetscScalar    *x;
2973   MatScalar      *aa;
2974 
2975   PetscFunctionBegin;
2976   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2977   aa = a->a;
2978   ai = a->i;
2979   aj = a->j;
2980 
2981   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2982   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2983   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2984   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);
2985   for (i=0; i<m; i++) {
2986     ncols = ai[1] - ai[0]; ai++;
2987     if (ncols) {
2988       /* Get first nonzero */
2989       for (j = 0; j < ncols; j++) {
2990         atmp = PetscAbsScalar(aa[j]);
2991         if (atmp > 1.0e-12) {
2992           x[i] = atmp;
2993           if (idx) idx[i] = aj[j];
2994           break;
2995         }
2996       }
2997       if (j == ncols) {x[i] = PetscAbsScalar(*aa); if (idx) idx[i] = *aj;}
2998     } else {
2999       x[i] = 0.0; if (idx) idx[i] = 0;
3000     }
3001     for (j = 0; j < ncols; j++) {
3002       atmp = PetscAbsScalar(*aa);
3003       if (atmp > 1.0e-12 && PetscAbsScalar(x[i]) > atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3004       aa++; aj++;
3005     }
3006   }
3007   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3008   PetscFunctionReturn(0);
3009 }
3010 
3011 #undef __FUNCT__
3012 #define __FUNCT__ "MatGetRowMin_SeqAIJ"
3013 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3014 {
3015   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3016   PetscErrorCode ierr;
3017   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3018   PetscScalar    *x;
3019   MatScalar      *aa;
3020 
3021   PetscFunctionBegin;
3022   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3023   aa = a->a;
3024   ai = a->i;
3025   aj = a->j;
3026 
3027   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3028   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3029   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3030   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3031   for (i=0; i<m; i++) {
3032     ncols = ai[1] - ai[0]; ai++;
3033     if (ncols == A->cmap->n) { /* row is dense */
3034       x[i] = *aa; if (idx) idx[i] = 0;
3035     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3036       x[i] = 0.0;
3037       if (idx) {   /* find first implicit 0.0 in the row */
3038         idx[i] = 0; /* in case ncols is zero */
3039         for (j=0; j<ncols; j++) {
3040           if (aj[j] > j) {
3041             idx[i] = j;
3042             break;
3043           }
3044         }
3045       }
3046     }
3047     for (j=0; j<ncols; j++) {
3048       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3049       aa++; aj++;
3050     }
3051   }
3052   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3053   PetscFunctionReturn(0);
3054 }
3055 
3056 #include <petscblaslapack.h>
3057 #include <petsc-private/kernels/blockinvert.h>
3058 
3059 #undef __FUNCT__
3060 #define __FUNCT__ "MatInvertBlockDiagonal_SeqAIJ"
3061 PetscErrorCode  MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3062 {
3063   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
3064   PetscErrorCode ierr;
3065   PetscInt       i,bs = PetscAbs(A->rmap->bs),mbs = A->rmap->n/bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3066   MatScalar      *diag,work[25],*v_work;
3067   PetscReal      shift = 0.0;
3068 
3069   PetscFunctionBegin;
3070   if (a->ibdiagvalid) {
3071     if (values) *values = a->ibdiag;
3072     PetscFunctionReturn(0);
3073   }
3074   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3075   if (!a->ibdiag) {
3076     ierr = PetscMalloc1(bs2*mbs,&a->ibdiag);CHKERRQ(ierr);
3077     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3078   }
3079   diag = a->ibdiag;
3080   if (values) *values = a->ibdiag;
3081   /* factor and invert each block */
3082   switch (bs) {
3083   case 1:
3084     for (i=0; i<mbs; i++) {
3085       ierr    = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3086       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3087     }
3088     break;
3089   case 2:
3090     for (i=0; i<mbs; i++) {
3091       ij[0] = 2*i; ij[1] = 2*i + 1;
3092       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3093       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift);CHKERRQ(ierr);
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);CHKERRQ(ierr);
3103       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3104       diag += 9;
3105     }
3106     break;
3107   case 4:
3108     for (i=0; i<mbs; i++) {
3109       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3110       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3111       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift);CHKERRQ(ierr);
3112       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3113       diag += 16;
3114     }
3115     break;
3116   case 5:
3117     for (i=0; i<mbs; i++) {
3118       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3119       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3120       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift);CHKERRQ(ierr);
3121       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3122       diag += 25;
3123     }
3124     break;
3125   case 6:
3126     for (i=0; i<mbs; i++) {
3127       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;
3128       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3129       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift);CHKERRQ(ierr);
3130       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3131       diag += 36;
3132     }
3133     break;
3134   case 7:
3135     for (i=0; i<mbs; i++) {
3136       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;
3137       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3138       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift);CHKERRQ(ierr);
3139       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3140       diag += 49;
3141     }
3142     break;
3143   default:
3144     ierr = PetscMalloc3(bs,&v_work,bs,&v_pivots,bs,&IJ);CHKERRQ(ierr);
3145     for (i=0; i<mbs; i++) {
3146       for (j=0; j<bs; j++) {
3147         IJ[j] = bs*i + j;
3148       }
3149       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3150       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work);CHKERRQ(ierr);
3151       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3152       diag += bs2;
3153     }
3154     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3155   }
3156   a->ibdiagvalid = PETSC_TRUE;
3157   PetscFunctionReturn(0);
3158 }
3159 
3160 #undef __FUNCT__
3161 #define __FUNCT__ "MatSetRandom_SeqAIJ"
3162 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3163 {
3164   PetscErrorCode ierr;
3165   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3166   PetscScalar    a;
3167   PetscInt       m,n,i,j,col;
3168 
3169   PetscFunctionBegin;
3170   if (!x->assembled) {
3171     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3172     for (i=0; i<m; i++) {
3173       for (j=0; j<aij->imax[i]; j++) {
3174         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3175         col  = (PetscInt)(n*PetscRealPart(a));
3176         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3177       }
3178     }
3179   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet coded");
3180   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3181   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3182   PetscFunctionReturn(0);
3183 }
3184 
3185 /* -------------------------------------------------------------------*/
3186 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3187                                         MatGetRow_SeqAIJ,
3188                                         MatRestoreRow_SeqAIJ,
3189                                         MatMult_SeqAIJ,
3190                                 /*  4*/ MatMultAdd_SeqAIJ,
3191                                         MatMultTranspose_SeqAIJ,
3192                                         MatMultTransposeAdd_SeqAIJ,
3193                                         0,
3194                                         0,
3195                                         0,
3196                                 /* 10*/ 0,
3197                                         MatLUFactor_SeqAIJ,
3198                                         0,
3199                                         MatSOR_SeqAIJ,
3200                                         MatTranspose_SeqAIJ,
3201                                 /*1 5*/ MatGetInfo_SeqAIJ,
3202                                         MatEqual_SeqAIJ,
3203                                         MatGetDiagonal_SeqAIJ,
3204                                         MatDiagonalScale_SeqAIJ,
3205                                         MatNorm_SeqAIJ,
3206                                 /* 20*/ 0,
3207                                         MatAssemblyEnd_SeqAIJ,
3208                                         MatSetOption_SeqAIJ,
3209                                         MatZeroEntries_SeqAIJ,
3210                                 /* 24*/ MatZeroRows_SeqAIJ,
3211                                         0,
3212                                         0,
3213                                         0,
3214                                         0,
3215                                 /* 29*/ MatSetUp_SeqAIJ,
3216                                         0,
3217                                         0,
3218                                         0,
3219                                         0,
3220                                 /* 34*/ MatDuplicate_SeqAIJ,
3221                                         0,
3222                                         0,
3223                                         MatILUFactor_SeqAIJ,
3224                                         0,
3225                                 /* 39*/ MatAXPY_SeqAIJ,
3226                                         MatGetSubMatrices_SeqAIJ,
3227                                         MatIncreaseOverlap_SeqAIJ,
3228                                         MatGetValues_SeqAIJ,
3229                                         MatCopy_SeqAIJ,
3230                                 /* 44*/ MatGetRowMax_SeqAIJ,
3231                                         MatScale_SeqAIJ,
3232                                         0,
3233                                         MatDiagonalSet_SeqAIJ,
3234                                         MatZeroRowsColumns_SeqAIJ,
3235                                 /* 49*/ MatSetRandom_SeqAIJ,
3236                                         MatGetRowIJ_SeqAIJ,
3237                                         MatRestoreRowIJ_SeqAIJ,
3238                                         MatGetColumnIJ_SeqAIJ,
3239                                         MatRestoreColumnIJ_SeqAIJ,
3240                                 /* 54*/ MatFDColoringCreate_SeqXAIJ,
3241                                         0,
3242                                         0,
3243                                         MatPermute_SeqAIJ,
3244                                         0,
3245                                 /* 59*/ 0,
3246                                         MatDestroy_SeqAIJ,
3247                                         MatView_SeqAIJ,
3248                                         0,
3249                                         MatMatMatMult_SeqAIJ_SeqAIJ_SeqAIJ,
3250                                 /* 64*/ MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ,
3251                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3252                                         0,
3253                                         0,
3254                                         0,
3255                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3256                                         MatGetRowMinAbs_SeqAIJ,
3257                                         0,
3258                                         MatSetColoring_SeqAIJ,
3259                                         0,
3260                                 /* 74*/ MatSetValuesAdifor_SeqAIJ,
3261                                         MatFDColoringApply_AIJ,
3262                                         0,
3263                                         0,
3264                                         0,
3265                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3266                                         0,
3267                                         0,
3268                                         0,
3269                                         MatLoad_SeqAIJ,
3270                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3271                                         MatIsHermitian_SeqAIJ,
3272                                         0,
3273                                         0,
3274                                         0,
3275                                 /* 89*/ MatMatMult_SeqAIJ_SeqAIJ,
3276                                         MatMatMultSymbolic_SeqAIJ_SeqAIJ,
3277                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3278                                         MatPtAP_SeqAIJ_SeqAIJ,
3279                                         MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy,
3280                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ,
3281                                         MatMatTransposeMult_SeqAIJ_SeqAIJ,
3282                                         MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ,
3283                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3284                                         0,
3285                                 /* 99*/ 0,
3286                                         0,
3287                                         0,
3288                                         MatConjugate_SeqAIJ,
3289                                         0,
3290                                 /*104*/ MatSetValuesRow_SeqAIJ,
3291                                         MatRealPart_SeqAIJ,
3292                                         MatImaginaryPart_SeqAIJ,
3293                                         0,
3294                                         0,
3295                                 /*109*/ MatMatSolve_SeqAIJ,
3296                                         0,
3297                                         MatGetRowMin_SeqAIJ,
3298                                         0,
3299                                         MatMissingDiagonal_SeqAIJ,
3300                                 /*114*/ 0,
3301                                         0,
3302                                         0,
3303                                         0,
3304                                         0,
3305                                 /*119*/ 0,
3306                                         0,
3307                                         0,
3308                                         0,
3309                                         MatGetMultiProcBlock_SeqAIJ,
3310                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3311                                         MatGetColumnNorms_SeqAIJ,
3312                                         MatInvertBlockDiagonal_SeqAIJ,
3313                                         0,
3314                                         0,
3315                                 /*129*/ 0,
3316                                         MatTransposeMatMult_SeqAIJ_SeqAIJ,
3317                                         MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ,
3318                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3319                                         MatTransposeColoringCreate_SeqAIJ,
3320                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3321                                         MatTransColoringApplyDenToSp_SeqAIJ,
3322                                         MatRARt_SeqAIJ_SeqAIJ,
3323                                         MatRARtSymbolic_SeqAIJ_SeqAIJ,
3324                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3325                                  /*139*/0,
3326                                         0,
3327                                         0,
3328                                         MatFDColoringSetUp_SeqXAIJ,
3329                                         MatFindOffBlockDiagonalEntries_SeqAIJ
3330 };
3331 
3332 #undef __FUNCT__
3333 #define __FUNCT__ "MatSeqAIJSetColumnIndices_SeqAIJ"
3334 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3335 {
3336   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3337   PetscInt   i,nz,n;
3338 
3339   PetscFunctionBegin;
3340   nz = aij->maxnz;
3341   n  = mat->rmap->n;
3342   for (i=0; i<nz; i++) {
3343     aij->j[i] = indices[i];
3344   }
3345   aij->nz = nz;
3346   for (i=0; i<n; i++) {
3347     aij->ilen[i] = aij->imax[i];
3348   }
3349   PetscFunctionReturn(0);
3350 }
3351 
3352 #undef __FUNCT__
3353 #define __FUNCT__ "MatSeqAIJSetColumnIndices"
3354 /*@
3355     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3356        in the matrix.
3357 
3358   Input Parameters:
3359 +  mat - the SeqAIJ matrix
3360 -  indices - the column indices
3361 
3362   Level: advanced
3363 
3364   Notes:
3365     This can be called if you have precomputed the nonzero structure of the
3366   matrix and want to provide it to the matrix object to improve the performance
3367   of the MatSetValues() operation.
3368 
3369     You MUST have set the correct numbers of nonzeros per row in the call to
3370   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3371 
3372     MUST be called before any calls to MatSetValues();
3373 
3374     The indices should start with zero, not one.
3375 
3376 @*/
3377 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3378 {
3379   PetscErrorCode ierr;
3380 
3381   PetscFunctionBegin;
3382   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3383   PetscValidPointer(indices,2);
3384   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3385   PetscFunctionReturn(0);
3386 }
3387 
3388 /* ----------------------------------------------------------------------------------------*/
3389 
3390 #undef __FUNCT__
3391 #define __FUNCT__ "MatStoreValues_SeqAIJ"
3392 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3393 {
3394   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3395   PetscErrorCode ierr;
3396   size_t         nz = aij->i[mat->rmap->n];
3397 
3398   PetscFunctionBegin;
3399   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3400 
3401   /* allocate space for values if not already there */
3402   if (!aij->saved_values) {
3403     ierr = PetscMalloc1((nz+1),&aij->saved_values);CHKERRQ(ierr);
3404     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3405   }
3406 
3407   /* copy values over */
3408   ierr = PetscMemcpy(aij->saved_values,aij->a,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3409   PetscFunctionReturn(0);
3410 }
3411 
3412 #undef __FUNCT__
3413 #define __FUNCT__ "MatStoreValues"
3414 /*@
3415     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3416        example, reuse of the linear part of a Jacobian, while recomputing the
3417        nonlinear portion.
3418 
3419    Collect on Mat
3420 
3421   Input Parameters:
3422 .  mat - the matrix (currently only AIJ matrices support this option)
3423 
3424   Level: advanced
3425 
3426   Common Usage, with SNESSolve():
3427 $    Create Jacobian matrix
3428 $    Set linear terms into matrix
3429 $    Apply boundary conditions to matrix, at this time matrix must have
3430 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3431 $      boundary conditions again will not change the nonzero structure
3432 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3433 $    ierr = MatStoreValues(mat);
3434 $    Call SNESSetJacobian() with matrix
3435 $    In your Jacobian routine
3436 $      ierr = MatRetrieveValues(mat);
3437 $      Set nonlinear terms in matrix
3438 
3439   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3440 $    // build linear portion of Jacobian
3441 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3442 $    ierr = MatStoreValues(mat);
3443 $    loop over nonlinear iterations
3444 $       ierr = MatRetrieveValues(mat);
3445 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3446 $       // call MatAssemblyBegin/End() on matrix
3447 $       Solve linear system with Jacobian
3448 $    endloop
3449 
3450   Notes:
3451     Matrix must already be assemblied before calling this routine
3452     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3453     calling this routine.
3454 
3455     When this is called multiple times it overwrites the previous set of stored values
3456     and does not allocated additional space.
3457 
3458 .seealso: MatRetrieveValues()
3459 
3460 @*/
3461 PetscErrorCode  MatStoreValues(Mat mat)
3462 {
3463   PetscErrorCode ierr;
3464 
3465   PetscFunctionBegin;
3466   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3467   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3468   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3469   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3470   PetscFunctionReturn(0);
3471 }
3472 
3473 #undef __FUNCT__
3474 #define __FUNCT__ "MatRetrieveValues_SeqAIJ"
3475 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3476 {
3477   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3478   PetscErrorCode ierr;
3479   PetscInt       nz = aij->i[mat->rmap->n];
3480 
3481   PetscFunctionBegin;
3482   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3483   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3484   /* copy values over */
3485   ierr = PetscMemcpy(aij->a,aij->saved_values,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3486   PetscFunctionReturn(0);
3487 }
3488 
3489 #undef __FUNCT__
3490 #define __FUNCT__ "MatRetrieveValues"
3491 /*@
3492     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3493        example, reuse of the linear part of a Jacobian, while recomputing the
3494        nonlinear portion.
3495 
3496    Collect on Mat
3497 
3498   Input Parameters:
3499 .  mat - the matrix (currently on AIJ matrices support this option)
3500 
3501   Level: advanced
3502 
3503 .seealso: MatStoreValues()
3504 
3505 @*/
3506 PetscErrorCode  MatRetrieveValues(Mat mat)
3507 {
3508   PetscErrorCode ierr;
3509 
3510   PetscFunctionBegin;
3511   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3512   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3513   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3514   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3515   PetscFunctionReturn(0);
3516 }
3517 
3518 
3519 /* --------------------------------------------------------------------------------*/
3520 #undef __FUNCT__
3521 #define __FUNCT__ "MatCreateSeqAIJ"
3522 /*@C
3523    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3524    (the default parallel PETSc format).  For good matrix assembly performance
3525    the user should preallocate the matrix storage by setting the parameter nz
3526    (or the array nnz).  By setting these parameters accurately, performance
3527    during matrix assembly can be increased by more than a factor of 50.
3528 
3529    Collective on MPI_Comm
3530 
3531    Input Parameters:
3532 +  comm - MPI communicator, set to PETSC_COMM_SELF
3533 .  m - number of rows
3534 .  n - number of columns
3535 .  nz - number of nonzeros per row (same for all rows)
3536 -  nnz - array containing the number of nonzeros in the various rows
3537          (possibly different for each row) or NULL
3538 
3539    Output Parameter:
3540 .  A - the matrix
3541 
3542    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3543    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3544    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3545 
3546    Notes:
3547    If nnz is given then nz is ignored
3548 
3549    The AIJ format (also called the Yale sparse matrix format or
3550    compressed row storage), is fully compatible with standard Fortran 77
3551    storage.  That is, the stored row and column indices can begin at
3552    either one (as in Fortran) or zero.  See the users' manual for details.
3553 
3554    Specify the preallocated storage with either nz or nnz (not both).
3555    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3556    allocation.  For large problems you MUST preallocate memory or you
3557    will get TERRIBLE performance, see the users' manual chapter on matrices.
3558 
3559    By default, this format uses inodes (identical nodes) when possible, to
3560    improve numerical efficiency of matrix-vector products and solves. We
3561    search for consecutive rows with the same nonzero structure, thereby
3562    reusing matrix information to achieve increased efficiency.
3563 
3564    Options Database Keys:
3565 +  -mat_no_inode  - Do not use inodes
3566 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3567 
3568    Level: intermediate
3569 
3570 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3571 
3572 @*/
3573 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3574 {
3575   PetscErrorCode ierr;
3576 
3577   PetscFunctionBegin;
3578   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3579   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3580   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3581   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3582   PetscFunctionReturn(0);
3583 }
3584 
3585 #undef __FUNCT__
3586 #define __FUNCT__ "MatSeqAIJSetPreallocation"
3587 /*@C
3588    MatSeqAIJSetPreallocation - For good matrix assembly performance
3589    the user should preallocate the matrix storage by setting the parameter nz
3590    (or the array nnz).  By setting these parameters accurately, performance
3591    during matrix assembly can be increased by more than a factor of 50.
3592 
3593    Collective on MPI_Comm
3594 
3595    Input Parameters:
3596 +  B - The matrix-free
3597 .  nz - number of nonzeros per row (same for all rows)
3598 -  nnz - array containing the number of nonzeros in the various rows
3599          (possibly different for each row) or NULL
3600 
3601    Notes:
3602      If nnz is given then nz is ignored
3603 
3604     The AIJ format (also called the Yale sparse matrix format or
3605    compressed row storage), is fully compatible with standard Fortran 77
3606    storage.  That is, the stored row and column indices can begin at
3607    either one (as in Fortran) or zero.  See the users' manual for details.
3608 
3609    Specify the preallocated storage with either nz or nnz (not both).
3610    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3611    allocation.  For large problems you MUST preallocate memory or you
3612    will get TERRIBLE performance, see the users' manual chapter on matrices.
3613 
3614    You can call MatGetInfo() to get information on how effective the preallocation was;
3615    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3616    You can also run with the option -info and look for messages with the string
3617    malloc in them to see if additional memory allocation was needed.
3618 
3619    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3620    entries or columns indices
3621 
3622    By default, this format uses inodes (identical nodes) when possible, to
3623    improve numerical efficiency of matrix-vector products and solves. We
3624    search for consecutive rows with the same nonzero structure, thereby
3625    reusing matrix information to achieve increased efficiency.
3626 
3627    Options Database Keys:
3628 +  -mat_no_inode  - Do not use inodes
3629 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3630 -  -mat_aij_oneindex - Internally use indexing starting at 1
3631         rather than 0.  Note that when calling MatSetValues(),
3632         the user still MUST index entries starting at 0!
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 #undef __FUNCT__
3651 #define __FUNCT__ "MatSeqAIJSetPreallocation_SeqAIJ"
3652 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3653 {
3654   Mat_SeqAIJ     *b;
3655   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3656   PetscErrorCode ierr;
3657   PetscInt       i;
3658 
3659   PetscFunctionBegin;
3660   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3661   if (nz == MAT_SKIP_ALLOCATION) {
3662     skipallocation = PETSC_TRUE;
3663     nz             = 0;
3664   }
3665 
3666   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3667   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3668 
3669   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3670   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %D",nz);
3671   if (nnz) {
3672     for (i=0; i<B->rmap->n; i++) {
3673       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]);
3674       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);
3675     }
3676   }
3677 
3678   B->preallocated = PETSC_TRUE;
3679 
3680   b = (Mat_SeqAIJ*)B->data;
3681 
3682   if (!skipallocation) {
3683     if (!b->imax) {
3684       ierr = PetscMalloc2(B->rmap->n,&b->imax,B->rmap->n,&b->ilen);CHKERRQ(ierr);
3685       ierr = PetscLogObjectMemory((PetscObject)B,2*B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3686     }
3687     if (!nnz) {
3688       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3689       else if (nz < 0) nz = 1;
3690       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
3691       nz = nz*B->rmap->n;
3692     } else {
3693       nz = 0;
3694       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz += nnz[i];}
3695     }
3696     /* b->ilen will count nonzeros in each row so far. */
3697     for (i=0; i<B->rmap->n; i++) b->ilen[i] = 0;
3698 
3699     /* allocate the matrix space */
3700     ierr    = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
3701     ierr    = PetscMalloc3(nz,&b->a,nz,&b->j,B->rmap->n+1,&b->i);CHKERRQ(ierr);
3702     ierr    = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
3703     b->i[0] = 0;
3704     for (i=1; i<B->rmap->n+1; i++) {
3705       b->i[i] = b->i[i-1] + b->imax[i-1];
3706     }
3707     b->singlemalloc = PETSC_TRUE;
3708     b->free_a       = PETSC_TRUE;
3709     b->free_ij      = PETSC_TRUE;
3710 #if defined(PETSC_THREADCOMM_ACTIVE)
3711     ierr = MatZeroEntries_SeqAIJ(B);CHKERRQ(ierr);
3712 #endif
3713   } else {
3714     b->free_a  = PETSC_FALSE;
3715     b->free_ij = PETSC_FALSE;
3716   }
3717 
3718   b->nz               = 0;
3719   b->maxnz            = nz;
3720   B->info.nz_unneeded = (double)b->maxnz;
3721   if (realalloc) {
3722     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3723   }
3724   PetscFunctionReturn(0);
3725 }
3726 
3727 #undef  __FUNCT__
3728 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR"
3729 /*@
3730    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
3731 
3732    Input Parameters:
3733 +  B - the matrix
3734 .  i - the indices into j for the start of each row (starts with zero)
3735 .  j - the column indices for each row (starts with zero) these must be sorted for each row
3736 -  v - optional values in the matrix
3737 
3738    Level: developer
3739 
3740    The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
3741 
3742 .keywords: matrix, aij, compressed row, sparse, sequential
3743 
3744 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), SeqAIJ
3745 @*/
3746 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
3747 {
3748   PetscErrorCode ierr;
3749 
3750   PetscFunctionBegin;
3751   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3752   PetscValidType(B,1);
3753   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3754   PetscFunctionReturn(0);
3755 }
3756 
3757 #undef  __FUNCT__
3758 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR_SeqAIJ"
3759 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3760 {
3761   PetscInt       i;
3762   PetscInt       m,n;
3763   PetscInt       nz;
3764   PetscInt       *nnz, nz_max = 0;
3765   PetscScalar    *values;
3766   PetscErrorCode ierr;
3767 
3768   PetscFunctionBegin;
3769   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
3770 
3771   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3772   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3773 
3774   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
3775   ierr = PetscMalloc1((m+1), &nnz);CHKERRQ(ierr);
3776   for (i = 0; i < m; i++) {
3777     nz     = Ii[i+1]- Ii[i];
3778     nz_max = PetscMax(nz_max, nz);
3779     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
3780     nnz[i] = nz;
3781   }
3782   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
3783   ierr = PetscFree(nnz);CHKERRQ(ierr);
3784 
3785   if (v) {
3786     values = (PetscScalar*) v;
3787   } else {
3788     ierr = PetscCalloc1(nz_max, &values);CHKERRQ(ierr);
3789   }
3790 
3791   for (i = 0; i < m; i++) {
3792     nz   = Ii[i+1] - Ii[i];
3793     ierr = MatSetValues_SeqAIJ(B, 1, &i, nz, J+Ii[i], values + (v ? Ii[i] : 0), INSERT_VALUES);CHKERRQ(ierr);
3794   }
3795 
3796   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3797   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3798 
3799   if (!v) {
3800     ierr = PetscFree(values);CHKERRQ(ierr);
3801   }
3802   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3803   PetscFunctionReturn(0);
3804 }
3805 
3806 #include <../src/mat/impls/dense/seq/dense.h>
3807 #include <petsc-private/kernels/petscaxpy.h>
3808 
3809 #undef __FUNCT__
3810 #define __FUNCT__ "MatMatMultNumeric_SeqDense_SeqAIJ"
3811 /*
3812     Computes (B'*A')' since computing B*A directly is untenable
3813 
3814                n                       p                          p
3815         (              )       (              )         (                  )
3816       m (      A       )  *  n (       B      )   =   m (         C        )
3817         (              )       (              )         (                  )
3818 
3819 */
3820 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
3821 {
3822   PetscErrorCode    ierr;
3823   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
3824   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
3825   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
3826   PetscInt          i,n,m,q,p;
3827   const PetscInt    *ii,*idx;
3828   const PetscScalar *b,*a,*a_q;
3829   PetscScalar       *c,*c_q;
3830 
3831   PetscFunctionBegin;
3832   m    = A->rmap->n;
3833   n    = A->cmap->n;
3834   p    = B->cmap->n;
3835   a    = sub_a->v;
3836   b    = sub_b->a;
3837   c    = sub_c->v;
3838   ierr = PetscMemzero(c,m*p*sizeof(PetscScalar));CHKERRQ(ierr);
3839 
3840   ii  = sub_b->i;
3841   idx = sub_b->j;
3842   for (i=0; i<n; i++) {
3843     q = ii[i+1] - ii[i];
3844     while (q-->0) {
3845       c_q = c + m*(*idx);
3846       a_q = a + m*i;
3847       PetscKernelAXPY(c_q,*b,a_q,m);
3848       idx++;
3849       b++;
3850     }
3851   }
3852   PetscFunctionReturn(0);
3853 }
3854 
3855 #undef __FUNCT__
3856 #define __FUNCT__ "MatMatMultSymbolic_SeqDense_SeqAIJ"
3857 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
3858 {
3859   PetscErrorCode ierr;
3860   PetscInt       m=A->rmap->n,n=B->cmap->n;
3861   Mat            Cmat;
3862 
3863   PetscFunctionBegin;
3864   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);
3865   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
3866   ierr = MatSetSizes(Cmat,m,n,m,n);CHKERRQ(ierr);
3867   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
3868   ierr = MatSetType(Cmat,MATSEQDENSE);CHKERRQ(ierr);
3869   ierr = MatSeqDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
3870 
3871   Cmat->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
3872 
3873   *C = Cmat;
3874   PetscFunctionReturn(0);
3875 }
3876 
3877 /* ----------------------------------------------------------------*/
3878 #undef __FUNCT__
3879 #define __FUNCT__ "MatMatMult_SeqDense_SeqAIJ"
3880 PetscErrorCode MatMatMult_SeqDense_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
3881 {
3882   PetscErrorCode ierr;
3883 
3884   PetscFunctionBegin;
3885   if (scall == MAT_INITIAL_MATRIX) {
3886     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
3887     ierr = MatMatMultSymbolic_SeqDense_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
3888     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
3889   }
3890   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
3891   ierr = MatMatMultNumeric_SeqDense_SeqAIJ(A,B,*C);CHKERRQ(ierr);
3892   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
3893   PetscFunctionReturn(0);
3894 }
3895 
3896 
3897 /*MC
3898    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
3899    based on compressed sparse row format.
3900 
3901    Options Database Keys:
3902 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
3903 
3904   Level: beginner
3905 
3906 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
3907 M*/
3908 
3909 /*MC
3910    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
3911 
3912    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
3913    and MATMPIAIJ otherwise.  As a result, for single process communicators,
3914   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
3915   for communicators controlling multiple processes.  It is recommended that you call both of
3916   the above preallocation routines for simplicity.
3917 
3918    Options Database Keys:
3919 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
3920 
3921   Developer Notes: Subclasses include MATAIJCUSP, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
3922    enough exist.
3923 
3924   Level: beginner
3925 
3926 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
3927 M*/
3928 
3929 /*MC
3930    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
3931 
3932    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
3933    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
3934    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
3935   for communicators controlling multiple processes.  It is recommended that you call both of
3936   the above preallocation routines for simplicity.
3937 
3938    Options Database Keys:
3939 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
3940 
3941   Level: beginner
3942 
3943 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
3944 M*/
3945 
3946 #if defined(PETSC_HAVE_PASTIX)
3947 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_pastix(Mat,MatFactorType,Mat*);
3948 #endif
3949 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
3950 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_essl(Mat,MatFactorType,Mat*);
3951 #endif
3952 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
3953 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_petsc(Mat,MatFactorType,Mat*);
3954 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_bas(Mat,MatFactorType,Mat*);
3955 extern PetscErrorCode  MatGetFactorAvailable_seqaij_petsc(Mat,MatFactorType,PetscBool*);
3956 #if defined(PETSC_HAVE_MUMPS)
3957 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mumps(Mat,MatFactorType,Mat*);
3958 #endif
3959 #if defined(PETSC_HAVE_SUPERLU)
3960 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu(Mat,MatFactorType,Mat*);
3961 #endif
3962 #if defined(PETSC_HAVE_MKL_PARDISO)
3963 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mkl_pardiso(Mat,MatFactorType,Mat*);
3964 #endif
3965 #if defined(PETSC_HAVE_SUPERLU_DIST)
3966 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu_dist(Mat,MatFactorType,Mat*);
3967 #endif
3968 #if defined(PETSC_HAVE_SUITESPARSE)
3969 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_umfpack(Mat,MatFactorType,Mat*);
3970 #endif
3971 #if defined(PETSC_HAVE_SUITESPARSE)
3972 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_cholmod(Mat,MatFactorType,Mat*);
3973 #endif
3974 #if defined(PETSC_HAVE_SUITESPARSE)
3975 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_klu(Mat,MatFactorType,Mat*);
3976 #endif
3977 #if defined(PETSC_HAVE_LUSOL)
3978 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_lusol(Mat,MatFactorType,Mat*);
3979 #endif
3980 #if defined(PETSC_HAVE_MATLAB_ENGINE)
3981 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_matlab(Mat,MatFactorType,Mat*);
3982 extern PetscErrorCode  MatlabEnginePut_SeqAIJ(PetscObject,void*);
3983 extern PetscErrorCode  MatlabEngineGet_SeqAIJ(PetscObject,void*);
3984 #endif
3985 #if defined(PETSC_HAVE_CLIQUE)
3986 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_clique(Mat,MatFactorType,Mat*);
3987 #endif
3988 
3989 
3990 #undef __FUNCT__
3991 #define __FUNCT__ "MatSeqAIJGetArray"
3992 /*@C
3993    MatSeqAIJGetArray - gives access to the array where the data for a SeqSeqAIJ matrix is stored
3994 
3995    Not Collective
3996 
3997    Input Parameter:
3998 .  mat - a MATSEQDENSE matrix
3999 
4000    Output Parameter:
4001 .   array - pointer to the data
4002 
4003    Level: intermediate
4004 
4005 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4006 @*/
4007 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4008 {
4009   PetscErrorCode ierr;
4010 
4011   PetscFunctionBegin;
4012   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4013   PetscFunctionReturn(0);
4014 }
4015 
4016 #undef __FUNCT__
4017 #define __FUNCT__ "MatSeqAIJRestoreArray"
4018 /*@C
4019    MatSeqAIJRestoreArray - returns access to the array where the data for a SeqSeqAIJ matrix is stored obtained by MatSeqAIJGetArray()
4020 
4021    Not Collective
4022 
4023    Input Parameters:
4024 .  mat - a MATSEQDENSE matrix
4025 .  array - pointer to the data
4026 
4027    Level: intermediate
4028 
4029 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4030 @*/
4031 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4032 {
4033   PetscErrorCode ierr;
4034 
4035   PetscFunctionBegin;
4036   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4037   PetscFunctionReturn(0);
4038 }
4039 
4040 #undef __FUNCT__
4041 #define __FUNCT__ "MatCreate_SeqAIJ"
4042 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4043 {
4044   Mat_SeqAIJ     *b;
4045   PetscErrorCode ierr;
4046   PetscMPIInt    size;
4047 
4048   PetscFunctionBegin;
4049   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4050   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4051 
4052   ierr = PetscNewLog(B,&b);CHKERRQ(ierr);
4053 
4054   B->data = (void*)b;
4055 
4056   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4057 
4058   b->row                = 0;
4059   b->col                = 0;
4060   b->icol               = 0;
4061   b->reallocs           = 0;
4062   b->ignorezeroentries  = PETSC_FALSE;
4063   b->roworiented        = PETSC_TRUE;
4064   b->nonew              = 0;
4065   b->diag               = 0;
4066   b->solve_work         = 0;
4067   B->spptr              = 0;
4068   b->saved_values       = 0;
4069   b->idiag              = 0;
4070   b->mdiag              = 0;
4071   b->ssor_work          = 0;
4072   b->omega              = 1.0;
4073   b->fshift             = 0.0;
4074   b->idiagvalid         = PETSC_FALSE;
4075   b->ibdiagvalid        = PETSC_FALSE;
4076   b->keepnonzeropattern = PETSC_FALSE;
4077   b->xtoy               = 0;
4078   b->XtoY               = 0;
4079 
4080   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4081   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4082   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4083 
4084 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4085   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_matlab_C",MatGetFactor_seqaij_matlab);CHKERRQ(ierr);
4086   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4087   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4088 #endif
4089 #if defined(PETSC_HAVE_PASTIX)
4090   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_pastix_C",MatGetFactor_seqaij_pastix);CHKERRQ(ierr);
4091 #endif
4092 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
4093   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_essl_C",MatGetFactor_seqaij_essl);CHKERRQ(ierr);
4094 #endif
4095 #if defined(PETSC_HAVE_SUPERLU)
4096   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_C",MatGetFactor_seqaij_superlu);CHKERRQ(ierr);
4097 #endif
4098 #if defined(PETSC_HAVE_MKL_PARDISO)
4099   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mkl_pardiso_C",MatGetFactor_aij_mkl_pardiso);CHKERRQ(ierr);
4100 #endif
4101 #if defined(PETSC_HAVE_SUPERLU_DIST)
4102   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_dist_C",MatGetFactor_seqaij_superlu_dist);CHKERRQ(ierr);
4103 #endif
4104 #if defined(PETSC_HAVE_MUMPS)
4105   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mumps_C",MatGetFactor_aij_mumps);CHKERRQ(ierr);
4106 #endif
4107 #if defined(PETSC_HAVE_SUITESPARSE)
4108   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_umfpack_C",MatGetFactor_seqaij_umfpack);CHKERRQ(ierr);
4109 #endif
4110 #if defined(PETSC_HAVE_SUITESPARSE)
4111   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_cholmod_C",MatGetFactor_seqaij_cholmod);CHKERRQ(ierr);
4112 #endif
4113 #if defined(PETSC_HAVE_SUITESPARSE)
4114   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_klu_C",MatGetFactor_seqaij_klu);CHKERRQ(ierr);
4115 #endif
4116 #if defined(PETSC_HAVE_LUSOL)
4117   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_lusol_C",MatGetFactor_seqaij_lusol);CHKERRQ(ierr);
4118 #endif
4119 #if defined(PETSC_HAVE_CLIQUE)
4120   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_clique_C",MatGetFactor_aij_clique);CHKERRQ(ierr);
4121 #endif
4122 
4123   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_petsc_C",MatGetFactor_seqaij_petsc);CHKERRQ(ierr);
4124   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactorAvailable_petsc_C",MatGetFactorAvailable_seqaij_petsc);CHKERRQ(ierr);
4125   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_bas_C",MatGetFactor_seqaij_bas);CHKERRQ(ierr);
4126   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4127   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4128   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4129   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4130   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4131   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4132   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4133   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4134   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4135   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4136   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4137   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4138   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaij_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
4139   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaij_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
4140   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaij_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
4141   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4142   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4143   PetscFunctionReturn(0);
4144 }
4145 
4146 #undef __FUNCT__
4147 #define __FUNCT__ "MatDuplicateNoCreate_SeqAIJ"
4148 /*
4149     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4150 */
4151 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4152 {
4153   Mat_SeqAIJ     *c,*a = (Mat_SeqAIJ*)A->data;
4154   PetscErrorCode ierr;
4155   PetscInt       i,m = A->rmap->n;
4156 
4157   PetscFunctionBegin;
4158   c = (Mat_SeqAIJ*)C->data;
4159 
4160   C->factortype = A->factortype;
4161   c->row        = 0;
4162   c->col        = 0;
4163   c->icol       = 0;
4164   c->reallocs   = 0;
4165 
4166   C->assembled = PETSC_TRUE;
4167 
4168   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4169   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4170 
4171   ierr = PetscMalloc2(m,&c->imax,m,&c->ilen);CHKERRQ(ierr);
4172   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4173   for (i=0; i<m; i++) {
4174     c->imax[i] = a->imax[i];
4175     c->ilen[i] = a->ilen[i];
4176   }
4177 
4178   /* allocate the matrix space */
4179   if (mallocmatspace) {
4180     ierr = PetscMalloc3(a->i[m],&c->a,a->i[m],&c->j,m+1,&c->i);CHKERRQ(ierr);
4181     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4182 
4183     c->singlemalloc = PETSC_TRUE;
4184 
4185     ierr = PetscMemcpy(c->i,a->i,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4186     if (m > 0) {
4187       ierr = PetscMemcpy(c->j,a->j,(a->i[m])*sizeof(PetscInt));CHKERRQ(ierr);
4188       if (cpvalues == MAT_COPY_VALUES) {
4189         ierr = PetscMemcpy(c->a,a->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4190       } else {
4191         ierr = PetscMemzero(c->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4192       }
4193     }
4194   }
4195 
4196   c->ignorezeroentries = a->ignorezeroentries;
4197   c->roworiented       = a->roworiented;
4198   c->nonew             = a->nonew;
4199   if (a->diag) {
4200     ierr = PetscMalloc1((m+1),&c->diag);CHKERRQ(ierr);
4201     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4202     for (i=0; i<m; i++) {
4203       c->diag[i] = a->diag[i];
4204     }
4205   } else c->diag = 0;
4206 
4207   c->solve_work         = 0;
4208   c->saved_values       = 0;
4209   c->idiag              = 0;
4210   c->ssor_work          = 0;
4211   c->keepnonzeropattern = a->keepnonzeropattern;
4212   c->free_a             = PETSC_TRUE;
4213   c->free_ij            = PETSC_TRUE;
4214   c->xtoy               = 0;
4215   c->XtoY               = 0;
4216 
4217   c->rmax         = a->rmax;
4218   c->nz           = a->nz;
4219   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4220   C->preallocated = PETSC_TRUE;
4221 
4222   c->compressedrow.use   = a->compressedrow.use;
4223   c->compressedrow.nrows = a->compressedrow.nrows;
4224   if (a->compressedrow.use) {
4225     i    = a->compressedrow.nrows;
4226     ierr = PetscMalloc2(i+1,&c->compressedrow.i,i,&c->compressedrow.rindex);CHKERRQ(ierr);
4227     ierr = PetscMemcpy(c->compressedrow.i,a->compressedrow.i,(i+1)*sizeof(PetscInt));CHKERRQ(ierr);
4228     ierr = PetscMemcpy(c->compressedrow.rindex,a->compressedrow.rindex,i*sizeof(PetscInt));CHKERRQ(ierr);
4229   } else {
4230     c->compressedrow.use    = PETSC_FALSE;
4231     c->compressedrow.i      = NULL;
4232     c->compressedrow.rindex = NULL;
4233   }
4234   C->nonzerostate = A->nonzerostate;
4235 
4236   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4237   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4238   PetscFunctionReturn(0);
4239 }
4240 
4241 #undef __FUNCT__
4242 #define __FUNCT__ "MatDuplicate_SeqAIJ"
4243 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4244 {
4245   PetscErrorCode ierr;
4246 
4247   PetscFunctionBegin;
4248   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4249   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4250   if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) {
4251     ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
4252   }
4253   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4254   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4255   PetscFunctionReturn(0);
4256 }
4257 
4258 #undef __FUNCT__
4259 #define __FUNCT__ "MatLoad_SeqAIJ"
4260 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4261 {
4262   Mat_SeqAIJ     *a;
4263   PetscErrorCode ierr;
4264   PetscInt       i,sum,nz,header[4],*rowlengths = 0,M,N,rows,cols;
4265   int            fd;
4266   PetscMPIInt    size;
4267   MPI_Comm       comm;
4268   PetscInt       bs = 1;
4269 
4270   PetscFunctionBegin;
4271   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
4272   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4273   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"view must have one processor");
4274 
4275   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
4276   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
4277   ierr = PetscOptionsEnd();CHKERRQ(ierr);
4278   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
4279 
4280   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
4281   ierr = PetscBinaryRead(fd,header,4,PETSC_INT);CHKERRQ(ierr);
4282   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
4283   M = header[1]; N = header[2]; nz = header[3];
4284 
4285   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
4286 
4287   /* read in row lengths */
4288   ierr = PetscMalloc1(M,&rowlengths);CHKERRQ(ierr);
4289   ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
4290 
4291   /* check if sum of rowlengths is same as nz */
4292   for (i=0,sum=0; i< M; i++) sum +=rowlengths[i];
4293   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);
4294 
4295   /* set global size if not set already*/
4296   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) {
4297     ierr = MatSetSizes(newMat,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
4298   } else {
4299     /* if sizes and type are already set, check if the vector global sizes are correct */
4300     ierr = MatGetSize(newMat,&rows,&cols);CHKERRQ(ierr);
4301     if (rows < 0 && cols < 0) { /* user might provide local size instead of global size */
4302       ierr = MatGetLocalSize(newMat,&rows,&cols);CHKERRQ(ierr);
4303     }
4304     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);
4305   }
4306   ierr = MatSeqAIJSetPreallocation_SeqAIJ(newMat,0,rowlengths);CHKERRQ(ierr);
4307   a    = (Mat_SeqAIJ*)newMat->data;
4308 
4309   ierr = PetscBinaryRead(fd,a->j,nz,PETSC_INT);CHKERRQ(ierr);
4310 
4311   /* read in nonzero values */
4312   ierr = PetscBinaryRead(fd,a->a,nz,PETSC_SCALAR);CHKERRQ(ierr);
4313 
4314   /* set matrix "i" values */
4315   a->i[0] = 0;
4316   for (i=1; i<= M; i++) {
4317     a->i[i]      = a->i[i-1] + rowlengths[i-1];
4318     a->ilen[i-1] = rowlengths[i-1];
4319   }
4320   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
4321 
4322   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4323   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4324   PetscFunctionReturn(0);
4325 }
4326 
4327 #undef __FUNCT__
4328 #define __FUNCT__ "MatEqual_SeqAIJ"
4329 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4330 {
4331   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4332   PetscErrorCode ierr;
4333 #if defined(PETSC_USE_COMPLEX)
4334   PetscInt k;
4335 #endif
4336 
4337   PetscFunctionBegin;
4338   /* If the  matrix dimensions are not equal,or no of nonzeros */
4339   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4340     *flg = PETSC_FALSE;
4341     PetscFunctionReturn(0);
4342   }
4343 
4344   /* if the a->i are the same */
4345   ierr = PetscMemcmp(a->i,b->i,(A->rmap->n+1)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4346   if (!*flg) PetscFunctionReturn(0);
4347 
4348   /* if a->j are the same */
4349   ierr = PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4350   if (!*flg) PetscFunctionReturn(0);
4351 
4352   /* if a->a are the same */
4353 #if defined(PETSC_USE_COMPLEX)
4354   for (k=0; k<a->nz; k++) {
4355     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4356       *flg = PETSC_FALSE;
4357       PetscFunctionReturn(0);
4358     }
4359   }
4360 #else
4361   ierr = PetscMemcmp(a->a,b->a,(a->nz)*sizeof(PetscScalar),flg);CHKERRQ(ierr);
4362 #endif
4363   PetscFunctionReturn(0);
4364 }
4365 
4366 #undef __FUNCT__
4367 #define __FUNCT__ "MatCreateSeqAIJWithArrays"
4368 /*@
4369      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4370               provided by the user.
4371 
4372       Collective on MPI_Comm
4373 
4374    Input Parameters:
4375 +   comm - must be an MPI communicator of size 1
4376 .   m - number of rows
4377 .   n - number of columns
4378 .   i - row indices
4379 .   j - column indices
4380 -   a - matrix values
4381 
4382    Output Parameter:
4383 .   mat - the matrix
4384 
4385    Level: intermediate
4386 
4387    Notes:
4388        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4389     once the matrix is destroyed and not before
4390 
4391        You cannot set new nonzero locations into this matrix, that will generate an error.
4392 
4393        The i and j indices are 0 based
4394 
4395        The format which is used for the sparse matrix input, is equivalent to a
4396     row-major ordering.. i.e for the following matrix, the input data expected is
4397     as shown:
4398 
4399         1 0 0
4400         2 0 3
4401         4 5 6
4402 
4403         i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4404         j =  {0,0,2,0,1,2}  [size = nz = 6]; values must be sorted for each row
4405         v =  {1,2,3,4,5,6}  [size = nz = 6]
4406 
4407 
4408 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4409 
4410 @*/
4411 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat)
4412 {
4413   PetscErrorCode ierr;
4414   PetscInt       ii;
4415   Mat_SeqAIJ     *aij;
4416 #if defined(PETSC_USE_DEBUG)
4417   PetscInt jj;
4418 #endif
4419 
4420   PetscFunctionBegin;
4421   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4422   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4423   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4424   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4425   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4426   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,0);CHKERRQ(ierr);
4427   aij  = (Mat_SeqAIJ*)(*mat)->data;
4428   ierr = PetscMalloc2(m,&aij->imax,m,&aij->ilen);CHKERRQ(ierr);
4429 
4430   aij->i            = i;
4431   aij->j            = j;
4432   aij->a            = a;
4433   aij->singlemalloc = PETSC_FALSE;
4434   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4435   aij->free_a       = PETSC_FALSE;
4436   aij->free_ij      = PETSC_FALSE;
4437 
4438   for (ii=0; ii<m; ii++) {
4439     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4440 #if defined(PETSC_USE_DEBUG)
4441     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]);
4442     for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4443       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);
4444       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);
4445     }
4446 #endif
4447   }
4448 #if defined(PETSC_USE_DEBUG)
4449   for (ii=0; ii<aij->i[m]; ii++) {
4450     if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %D index = %D",ii,j[ii]);
4451     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]);
4452   }
4453 #endif
4454 
4455   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4456   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4457   PetscFunctionReturn(0);
4458 }
4459 #undef __FUNCT__
4460 #define __FUNCT__ "MatCreateSeqAIJFromTriple"
4461 /*@C
4462      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4463               provided by the user.
4464 
4465       Collective on MPI_Comm
4466 
4467    Input Parameters:
4468 +   comm - must be an MPI communicator of size 1
4469 .   m   - number of rows
4470 .   n   - number of columns
4471 .   i   - row indices
4472 .   j   - column indices
4473 .   a   - matrix values
4474 .   nz  - number of nonzeros
4475 -   idx - 0 or 1 based
4476 
4477    Output Parameter:
4478 .   mat - the matrix
4479 
4480    Level: intermediate
4481 
4482    Notes:
4483        The i and j indices are 0 based
4484 
4485        The format which is used for the sparse matrix input, is equivalent to a
4486     row-major ordering.. i.e for the following matrix, the input data expected is
4487     as shown:
4488 
4489         1 0 0
4490         2 0 3
4491         4 5 6
4492 
4493         i =  {0,1,1,2,2,2}
4494         j =  {0,0,2,0,1,2}
4495         v =  {1,2,3,4,5,6}
4496 
4497 
4498 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4499 
4500 @*/
4501 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat,PetscInt nz,PetscBool idx)
4502 {
4503   PetscErrorCode ierr;
4504   PetscInt       ii, *nnz, one = 1,row,col;
4505 
4506 
4507   PetscFunctionBegin;
4508   ierr = PetscCalloc1(m,&nnz);CHKERRQ(ierr);
4509   for (ii = 0; ii < nz; ii++) {
4510     nnz[i[ii] - !!idx] += 1;
4511   }
4512   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4513   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4514   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4515   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4516   for (ii = 0; ii < nz; ii++) {
4517     if (idx) {
4518       row = i[ii] - 1;
4519       col = j[ii] - 1;
4520     } else {
4521       row = i[ii];
4522       col = j[ii];
4523     }
4524     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4525   }
4526   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4527   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4528   ierr = PetscFree(nnz);CHKERRQ(ierr);
4529   PetscFunctionReturn(0);
4530 }
4531 
4532 #undef __FUNCT__
4533 #define __FUNCT__ "MatSetColoring_SeqAIJ"
4534 PetscErrorCode MatSetColoring_SeqAIJ(Mat A,ISColoring coloring)
4535 {
4536   PetscErrorCode ierr;
4537   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4538 
4539   PetscFunctionBegin;
4540   if (coloring->ctype == IS_COLORING_GLOBAL) {
4541     ierr        = ISColoringReference(coloring);CHKERRQ(ierr);
4542     a->coloring = coloring;
4543   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
4544     PetscInt        i,*larray;
4545     ISColoring      ocoloring;
4546     ISColoringValue *colors;
4547 
4548     /* set coloring for diagonal portion */
4549     ierr = PetscMalloc1(A->cmap->n,&larray);CHKERRQ(ierr);
4550     for (i=0; i<A->cmap->n; i++) larray[i] = i;
4551     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
4552     ierr = PetscMalloc1(A->cmap->n,&colors);CHKERRQ(ierr);
4553     for (i=0; i<A->cmap->n; i++) colors[i] = coloring->colors[larray[i]];
4554     ierr        = PetscFree(larray);CHKERRQ(ierr);
4555     ierr        = ISColoringCreate(PETSC_COMM_SELF,coloring->n,A->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4556     a->coloring = ocoloring;
4557   }
4558   PetscFunctionReturn(0);
4559 }
4560 
4561 #undef __FUNCT__
4562 #define __FUNCT__ "MatSetValuesAdifor_SeqAIJ"
4563 PetscErrorCode MatSetValuesAdifor_SeqAIJ(Mat A,PetscInt nl,void *advalues)
4564 {
4565   Mat_SeqAIJ      *a      = (Mat_SeqAIJ*)A->data;
4566   PetscInt        m       = A->rmap->n,*ii = a->i,*jj = a->j,nz,i,j;
4567   MatScalar       *v      = a->a;
4568   PetscScalar     *values = (PetscScalar*)advalues;
4569   ISColoringValue *color;
4570 
4571   PetscFunctionBegin;
4572   if (!a->coloring) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Coloring not set for matrix");
4573   color = a->coloring->colors;
4574   /* loop over rows */
4575   for (i=0; i<m; i++) {
4576     nz = ii[i+1] - ii[i];
4577     /* loop over columns putting computed value into matrix */
4578     for (j=0; j<nz; j++) *v++ = values[color[*jj++]];
4579     values += nl; /* jump to next row of derivatives */
4580   }
4581   PetscFunctionReturn(0);
4582 }
4583 
4584 #undef __FUNCT__
4585 #define __FUNCT__ "MatSeqAIJInvalidateDiagonal"
4586 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4587 {
4588   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4589   PetscErrorCode ierr;
4590 
4591   PetscFunctionBegin;
4592   a->idiagvalid  = PETSC_FALSE;
4593   a->ibdiagvalid = PETSC_FALSE;
4594 
4595   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4596   PetscFunctionReturn(0);
4597 }
4598 
4599 /*
4600     Special version for direct calls from Fortran
4601 */
4602 #include <petsc-private/fortranimpl.h>
4603 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4604 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
4605 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4606 #define matsetvaluesseqaij_ matsetvaluesseqaij
4607 #endif
4608 
4609 /* Change these macros so can be used in void function */
4610 #undef CHKERRQ
4611 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
4612 #undef SETERRQ2
4613 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4614 #undef SETERRQ3
4615 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4616 
4617 #undef __FUNCT__
4618 #define __FUNCT__ "matsetvaluesseqaij_"
4619 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)
4620 {
4621   Mat            A  = *AA;
4622   PetscInt       m  = *mm, n = *nn;
4623   InsertMode     is = *isis;
4624   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4625   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
4626   PetscInt       *imax,*ai,*ailen;
4627   PetscErrorCode ierr;
4628   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
4629   MatScalar      *ap,value,*aa;
4630   PetscBool      ignorezeroentries = a->ignorezeroentries;
4631   PetscBool      roworiented       = a->roworiented;
4632 
4633   PetscFunctionBegin;
4634   MatCheckPreallocated(A,1);
4635   imax  = a->imax;
4636   ai    = a->i;
4637   ailen = a->ilen;
4638   aj    = a->j;
4639   aa    = a->a;
4640 
4641   for (k=0; k<m; k++) { /* loop over added rows */
4642     row = im[k];
4643     if (row < 0) continue;
4644 #if defined(PETSC_USE_DEBUG)
4645     if (row >= A->rmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
4646 #endif
4647     rp   = aj + ai[row]; ap = aa + ai[row];
4648     rmax = imax[row]; nrow = ailen[row];
4649     low  = 0;
4650     high = nrow;
4651     for (l=0; l<n; l++) { /* loop over added columns */
4652       if (in[l] < 0) continue;
4653 #if defined(PETSC_USE_DEBUG)
4654       if (in[l] >= A->cmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
4655 #endif
4656       col = in[l];
4657       if (roworiented) value = v[l + k*n];
4658       else value = v[k + l*m];
4659 
4660       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
4661 
4662       if (col <= lastcol) low = 0;
4663       else high = nrow;
4664       lastcol = col;
4665       while (high-low > 5) {
4666         t = (low+high)/2;
4667         if (rp[t] > col) high = t;
4668         else             low  = t;
4669       }
4670       for (i=low; i<high; i++) {
4671         if (rp[i] > col) break;
4672         if (rp[i] == col) {
4673           if (is == ADD_VALUES) ap[i] += value;
4674           else                  ap[i] = value;
4675           goto noinsert;
4676         }
4677       }
4678       if (value == 0.0 && ignorezeroentries) goto noinsert;
4679       if (nonew == 1) goto noinsert;
4680       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
4681       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
4682       N = nrow++ - 1; a->nz++; high++;
4683       /* shift up all the later entries in this row */
4684       for (ii=N; ii>=i; ii--) {
4685         rp[ii+1] = rp[ii];
4686         ap[ii+1] = ap[ii];
4687       }
4688       rp[i] = col;
4689       ap[i] = value;
4690       A->nonzerostate++;
4691 noinsert:;
4692       low = i + 1;
4693     }
4694     ailen[row] = nrow;
4695   }
4696   PetscFunctionReturnVoid();
4697 }
4698 
4699 
4700