xref: /petsc/src/mat/impls/aij/seq/aij.c (revision 4cefc2ff75e4fd40cdd0827272dcde5d684e9831)
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 = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&stride);CHKERRQ(ierr);
2400   if (stride) {
2401     ierr = ISStrideGetInfo(iscol,&first,&step);CHKERRQ(ierr);
2402   } else {
2403     first = 0;
2404     step  = 0;
2405   }
2406   if (stride && step == 1) {
2407     /* special case of contiguous rows */
2408     ierr = PetscMalloc2(nrows,&lens,nrows,&starts);CHKERRQ(ierr);
2409     /* loop over new rows determining lens and starting points */
2410     for (i=0; i<nrows; i++) {
2411       kstart = ai[irow[i]];
2412       kend   = kstart + ailen[irow[i]];
2413       starts[i] = kstart;
2414       for (k=kstart; k<kend; k++) {
2415         if (aj[k] >= first) {
2416           starts[i] = k;
2417           break;
2418         }
2419       }
2420       sum = 0;
2421       while (k < kend) {
2422         if (aj[k++] >= first+ncols) break;
2423         sum++;
2424       }
2425       lens[i] = sum;
2426     }
2427     /* create submatrix */
2428     if (scall == MAT_REUSE_MATRIX) {
2429       PetscInt n_cols,n_rows;
2430       ierr = MatGetSize(*B,&n_rows,&n_cols);CHKERRQ(ierr);
2431       if (n_rows != nrows || n_cols != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
2432       ierr = MatZeroEntries(*B);CHKERRQ(ierr);
2433       C    = *B;
2434     } else {
2435       PetscInt rbs,cbs;
2436       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2437       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2438       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2439       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2440       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2441       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2442       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2443     }
2444     c = (Mat_SeqAIJ*)C->data;
2445 
2446     /* loop over rows inserting into submatrix */
2447     a_new = c->a;
2448     j_new = c->j;
2449     i_new = c->i;
2450 
2451     for (i=0; i<nrows; i++) {
2452       ii    = starts[i];
2453       lensi = lens[i];
2454       for (k=0; k<lensi; k++) {
2455         *j_new++ = aj[ii+k] - first;
2456       }
2457       ierr       = PetscMemcpy(a_new,a->a + starts[i],lensi*sizeof(PetscScalar));CHKERRQ(ierr);
2458       a_new     += lensi;
2459       i_new[i+1] = i_new[i] + lensi;
2460       c->ilen[i] = lensi;
2461     }
2462     ierr = PetscFree2(lens,starts);CHKERRQ(ierr);
2463   } else {
2464     ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
2465     ierr = PetscCalloc1(oldcols,&smap);CHKERRQ(ierr);
2466     ierr = PetscMalloc1((1+nrows),&lens);CHKERRQ(ierr);
2467     for (i=0; i<ncols; i++) {
2468 #if defined(PETSC_USE_DEBUG)
2469       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);
2470 #endif
2471       smap[icol[i]] = i+1;
2472     }
2473 
2474     /* determine lens of each row */
2475     for (i=0; i<nrows; i++) {
2476       kstart  = ai[irow[i]];
2477       kend    = kstart + a->ilen[irow[i]];
2478       lens[i] = 0;
2479       for (k=kstart; k<kend; k++) {
2480         if (smap[aj[k]]) {
2481           lens[i]++;
2482         }
2483       }
2484     }
2485     /* Create and fill new matrix */
2486     if (scall == MAT_REUSE_MATRIX) {
2487       PetscBool equal;
2488 
2489       c = (Mat_SeqAIJ*)((*B)->data);
2490       if ((*B)->rmap->n  != nrows || (*B)->cmap->n != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
2491       ierr = PetscMemcmp(c->ilen,lens,(*B)->rmap->n*sizeof(PetscInt),&equal);CHKERRQ(ierr);
2492       if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
2493       ierr = PetscMemzero(c->ilen,(*B)->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
2494       C    = *B;
2495     } else {
2496       PetscInt rbs,cbs;
2497       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2498       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2499       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2500       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2501       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2502       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2503       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2504     }
2505     c = (Mat_SeqAIJ*)(C->data);
2506     for (i=0; i<nrows; i++) {
2507       row      = irow[i];
2508       kstart   = ai[row];
2509       kend     = kstart + a->ilen[row];
2510       mat_i    = c->i[i];
2511       mat_j    = c->j + mat_i;
2512       mat_a    = c->a + mat_i;
2513       mat_ilen = c->ilen + i;
2514       for (k=kstart; k<kend; k++) {
2515         if ((tcol=smap[a->j[k]])) {
2516           *mat_j++ = tcol - 1;
2517           *mat_a++ = a->a[k];
2518           (*mat_ilen)++;
2519 
2520         }
2521       }
2522     }
2523     /* Free work space */
2524     ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
2525     ierr = PetscFree(smap);CHKERRQ(ierr);
2526     ierr = PetscFree(lens);CHKERRQ(ierr);
2527   }
2528   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2529   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2530 
2531   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
2532   *B   = C;
2533   PetscFunctionReturn(0);
2534 }
2535 
2536 #undef __FUNCT__
2537 #define __FUNCT__ "MatGetMultiProcBlock_SeqAIJ"
2538 PetscErrorCode  MatGetMultiProcBlock_SeqAIJ(Mat mat,MPI_Comm subComm,MatReuse scall,Mat *subMat)
2539 {
2540   PetscErrorCode ierr;
2541   Mat            B;
2542 
2543   PetscFunctionBegin;
2544   if (scall == MAT_INITIAL_MATRIX) {
2545     ierr    = MatCreate(subComm,&B);CHKERRQ(ierr);
2546     ierr    = MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->n,mat->cmap->n);CHKERRQ(ierr);
2547     ierr    = MatSetBlockSizesFromMats(B,mat,mat);CHKERRQ(ierr);
2548     ierr    = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
2549     ierr    = MatDuplicateNoCreate_SeqAIJ(B,mat,MAT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
2550     *subMat = B;
2551   } else {
2552     ierr = MatCopy_SeqAIJ(mat,*subMat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2553   }
2554   PetscFunctionReturn(0);
2555 }
2556 
2557 #undef __FUNCT__
2558 #define __FUNCT__ "MatILUFactor_SeqAIJ"
2559 PetscErrorCode MatILUFactor_SeqAIJ(Mat inA,IS row,IS col,const MatFactorInfo *info)
2560 {
2561   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)inA->data;
2562   PetscErrorCode ierr;
2563   Mat            outA;
2564   PetscBool      row_identity,col_identity;
2565 
2566   PetscFunctionBegin;
2567   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels=0 supported for in-place ilu");
2568 
2569   ierr = ISIdentity(row,&row_identity);CHKERRQ(ierr);
2570   ierr = ISIdentity(col,&col_identity);CHKERRQ(ierr);
2571 
2572   outA             = inA;
2573   outA->factortype = MAT_FACTOR_LU;
2574 
2575   ierr = PetscObjectReference((PetscObject)row);CHKERRQ(ierr);
2576   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
2577 
2578   a->row = row;
2579 
2580   ierr = PetscObjectReference((PetscObject)col);CHKERRQ(ierr);
2581   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
2582 
2583   a->col = col;
2584 
2585   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
2586   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
2587   ierr = ISInvertPermutation(col,PETSC_DECIDE,&a->icol);CHKERRQ(ierr);
2588   ierr = PetscLogObjectParent((PetscObject)inA,(PetscObject)a->icol);CHKERRQ(ierr);
2589 
2590   if (!a->solve_work) { /* this matrix may have been factored before */
2591     ierr = PetscMalloc1((inA->rmap->n+1),&a->solve_work);CHKERRQ(ierr);
2592     ierr = PetscLogObjectMemory((PetscObject)inA, (inA->rmap->n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2593   }
2594 
2595   ierr = MatMarkDiagonal_SeqAIJ(inA);CHKERRQ(ierr);
2596   if (row_identity && col_identity) {
2597     ierr = MatLUFactorNumeric_SeqAIJ_inplace(outA,inA,info);CHKERRQ(ierr);
2598   } else {
2599     ierr = MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA,inA,info);CHKERRQ(ierr);
2600   }
2601   PetscFunctionReturn(0);
2602 }
2603 
2604 #undef __FUNCT__
2605 #define __FUNCT__ "MatScale_SeqAIJ"
2606 PetscErrorCode MatScale_SeqAIJ(Mat inA,PetscScalar alpha)
2607 {
2608   Mat_SeqAIJ     *a     = (Mat_SeqAIJ*)inA->data;
2609   PetscScalar    oalpha = alpha;
2610   PetscErrorCode ierr;
2611   PetscBLASInt   one = 1,bnz;
2612 
2613   PetscFunctionBegin;
2614   ierr = PetscBLASIntCast(a->nz,&bnz);CHKERRQ(ierr);
2615   PetscStackCallBLAS("BLASscal",BLASscal_(&bnz,&oalpha,a->a,&one));
2616   ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2617   ierr = MatSeqAIJInvalidateDiagonal(inA);CHKERRQ(ierr);
2618   PetscFunctionReturn(0);
2619 }
2620 
2621 #undef __FUNCT__
2622 #define __FUNCT__ "MatGetSubMatrices_SeqAIJ"
2623 PetscErrorCode MatGetSubMatrices_SeqAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
2624 {
2625   PetscErrorCode ierr;
2626   PetscInt       i;
2627 
2628   PetscFunctionBegin;
2629   if (scall == MAT_INITIAL_MATRIX) {
2630     ierr = PetscMalloc1((n+1),B);CHKERRQ(ierr);
2631   }
2632 
2633   for (i=0; i<n; i++) {
2634     ierr = MatGetSubMatrix_SeqAIJ(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]);CHKERRQ(ierr);
2635   }
2636   PetscFunctionReturn(0);
2637 }
2638 
2639 #undef __FUNCT__
2640 #define __FUNCT__ "MatIncreaseOverlap_SeqAIJ"
2641 PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
2642 {
2643   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2644   PetscErrorCode ierr;
2645   PetscInt       row,i,j,k,l,m,n,*nidx,isz,val;
2646   const PetscInt *idx;
2647   PetscInt       start,end,*ai,*aj;
2648   PetscBT        table;
2649 
2650   PetscFunctionBegin;
2651   m  = A->rmap->n;
2652   ai = a->i;
2653   aj = a->j;
2654 
2655   if (ov < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"illegal negative overlap value used");
2656 
2657   ierr = PetscMalloc1((m+1),&nidx);CHKERRQ(ierr);
2658   ierr = PetscBTCreate(m,&table);CHKERRQ(ierr);
2659 
2660   for (i=0; i<is_max; i++) {
2661     /* Initialize the two local arrays */
2662     isz  = 0;
2663     ierr = PetscBTMemzero(m,table);CHKERRQ(ierr);
2664 
2665     /* Extract the indices, assume there can be duplicate entries */
2666     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
2667     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
2668 
2669     /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2670     for (j=0; j<n; ++j) {
2671       if (!PetscBTLookupSet(table,idx[j])) nidx[isz++] = idx[j];
2672     }
2673     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
2674     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
2675 
2676     k = 0;
2677     for (j=0; j<ov; j++) { /* for each overlap */
2678       n = isz;
2679       for (; k<n; k++) { /* do only those rows in nidx[k], which are not done yet */
2680         row   = nidx[k];
2681         start = ai[row];
2682         end   = ai[row+1];
2683         for (l = start; l<end; l++) {
2684           val = aj[l];
2685           if (!PetscBTLookupSet(table,val)) nidx[isz++] = val;
2686         }
2687       }
2688     }
2689     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz,nidx,PETSC_COPY_VALUES,(is+i));CHKERRQ(ierr);
2690   }
2691   ierr = PetscBTDestroy(&table);CHKERRQ(ierr);
2692   ierr = PetscFree(nidx);CHKERRQ(ierr);
2693   PetscFunctionReturn(0);
2694 }
2695 
2696 /* -------------------------------------------------------------- */
2697 #undef __FUNCT__
2698 #define __FUNCT__ "MatPermute_SeqAIJ"
2699 PetscErrorCode MatPermute_SeqAIJ(Mat A,IS rowp,IS colp,Mat *B)
2700 {
2701   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2702   PetscErrorCode ierr;
2703   PetscInt       i,nz = 0,m = A->rmap->n,n = A->cmap->n;
2704   const PetscInt *row,*col;
2705   PetscInt       *cnew,j,*lens;
2706   IS             icolp,irowp;
2707   PetscInt       *cwork = NULL;
2708   PetscScalar    *vwork = NULL;
2709 
2710   PetscFunctionBegin;
2711   ierr = ISInvertPermutation(rowp,PETSC_DECIDE,&irowp);CHKERRQ(ierr);
2712   ierr = ISGetIndices(irowp,&row);CHKERRQ(ierr);
2713   ierr = ISInvertPermutation(colp,PETSC_DECIDE,&icolp);CHKERRQ(ierr);
2714   ierr = ISGetIndices(icolp,&col);CHKERRQ(ierr);
2715 
2716   /* determine lengths of permuted rows */
2717   ierr = PetscMalloc1((m+1),&lens);CHKERRQ(ierr);
2718   for (i=0; i<m; i++) lens[row[i]] = a->i[i+1] - a->i[i];
2719   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
2720   ierr = MatSetSizes(*B,m,n,m,n);CHKERRQ(ierr);
2721   ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
2722   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2723   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*B,0,lens);CHKERRQ(ierr);
2724   ierr = PetscFree(lens);CHKERRQ(ierr);
2725 
2726   ierr = PetscMalloc1(n,&cnew);CHKERRQ(ierr);
2727   for (i=0; i<m; i++) {
2728     ierr = MatGetRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2729     for (j=0; j<nz; j++) cnew[j] = col[cwork[j]];
2730     ierr = MatSetValues_SeqAIJ(*B,1,&row[i],nz,cnew,vwork,INSERT_VALUES);CHKERRQ(ierr);
2731     ierr = MatRestoreRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2732   }
2733   ierr = PetscFree(cnew);CHKERRQ(ierr);
2734 
2735   (*B)->assembled = PETSC_FALSE;
2736 
2737   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2738   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2739   ierr = ISRestoreIndices(irowp,&row);CHKERRQ(ierr);
2740   ierr = ISRestoreIndices(icolp,&col);CHKERRQ(ierr);
2741   ierr = ISDestroy(&irowp);CHKERRQ(ierr);
2742   ierr = ISDestroy(&icolp);CHKERRQ(ierr);
2743   PetscFunctionReturn(0);
2744 }
2745 
2746 #undef __FUNCT__
2747 #define __FUNCT__ "MatCopy_SeqAIJ"
2748 PetscErrorCode MatCopy_SeqAIJ(Mat A,Mat B,MatStructure str)
2749 {
2750   PetscErrorCode ierr;
2751 
2752   PetscFunctionBegin;
2753   /* If the two matrices have the same copy implementation, use fast copy. */
2754   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
2755     Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2756     Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data;
2757 
2758     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");
2759     ierr = PetscMemcpy(b->a,a->a,(a->i[A->rmap->n])*sizeof(PetscScalar));CHKERRQ(ierr);
2760   } else {
2761     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2762   }
2763   PetscFunctionReturn(0);
2764 }
2765 
2766 #undef __FUNCT__
2767 #define __FUNCT__ "MatSetUp_SeqAIJ"
2768 PetscErrorCode MatSetUp_SeqAIJ(Mat A)
2769 {
2770   PetscErrorCode ierr;
2771 
2772   PetscFunctionBegin;
2773   ierr =  MatSeqAIJSetPreallocation_SeqAIJ(A,PETSC_DEFAULT,0);CHKERRQ(ierr);
2774   PetscFunctionReturn(0);
2775 }
2776 
2777 #undef __FUNCT__
2778 #define __FUNCT__ "MatSeqAIJGetArray_SeqAIJ"
2779 PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A,PetscScalar *array[])
2780 {
2781   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2782 
2783   PetscFunctionBegin;
2784   *array = a->a;
2785   PetscFunctionReturn(0);
2786 }
2787 
2788 #undef __FUNCT__
2789 #define __FUNCT__ "MatSeqAIJRestoreArray_SeqAIJ"
2790 PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A,PetscScalar *array[])
2791 {
2792   PetscFunctionBegin;
2793   PetscFunctionReturn(0);
2794 }
2795 
2796 /*
2797    Computes the number of nonzeros per row needed for preallocation when X and Y
2798    have different nonzero structure.
2799 */
2800 #undef __FUNCT__
2801 #define __FUNCT__ "MatAXPYGetPreallocation_SeqX_private"
2802 PetscErrorCode MatAXPYGetPreallocation_SeqX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *yi,const PetscInt *yj,PetscInt *nnz)
2803 {
2804   PetscInt       i,j,k,nzx,nzy;
2805 
2806   PetscFunctionBegin;
2807   /* Set the number of nonzeros in the new matrix */
2808   for (i=0; i<m; i++) {
2809     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2810     nzx = xi[i+1] - xi[i];
2811     nzy = yi[i+1] - yi[i];
2812     nnz[i] = 0;
2813     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2814       for (; k<nzy && yjj[k]<xjj[j]; k++) nnz[i]++; /* Catch up to X */
2815       if (k<nzy && yjj[k]==xjj[j]) k++;             /* Skip duplicate */
2816       nnz[i]++;
2817     }
2818     for (; k<nzy; k++) nnz[i]++;
2819   }
2820   PetscFunctionReturn(0);
2821 }
2822 
2823 #undef __FUNCT__
2824 #define __FUNCT__ "MatAXPYGetPreallocation_SeqAIJ"
2825 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
2826 {
2827   PetscInt       m = Y->rmap->N;
2828   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2829   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2830   PetscErrorCode ierr;
2831 
2832   PetscFunctionBegin;
2833   /* Set the number of nonzeros in the new matrix */
2834   ierr = MatAXPYGetPreallocation_SeqX_private(m,x->i,x->j,y->i,y->j,nnz);CHKERRQ(ierr);
2835   PetscFunctionReturn(0);
2836 }
2837 
2838 #undef __FUNCT__
2839 #define __FUNCT__ "MatAXPY_SeqAIJ"
2840 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2841 {
2842   PetscErrorCode ierr;
2843   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
2844   PetscBLASInt   one=1,bnz;
2845 
2846   PetscFunctionBegin;
2847   ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2848   if (str == SAME_NONZERO_PATTERN) {
2849     PetscScalar alpha = a;
2850     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2851     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
2852     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2853   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2854     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2855   } else {
2856     Mat      B;
2857     PetscInt *nnz;
2858     ierr = PetscMalloc1(Y->rmap->N,&nnz);CHKERRQ(ierr);
2859     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2860     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2861     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2862     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2863     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
2864     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
2865     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
2866     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2867     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
2868     ierr = PetscFree(nnz);CHKERRQ(ierr);
2869   }
2870   PetscFunctionReturn(0);
2871 }
2872 
2873 #undef __FUNCT__
2874 #define __FUNCT__ "MatConjugate_SeqAIJ"
2875 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
2876 {
2877 #if defined(PETSC_USE_COMPLEX)
2878   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
2879   PetscInt    i,nz;
2880   PetscScalar *a;
2881 
2882   PetscFunctionBegin;
2883   nz = aij->nz;
2884   a  = aij->a;
2885   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
2886 #else
2887   PetscFunctionBegin;
2888 #endif
2889   PetscFunctionReturn(0);
2890 }
2891 
2892 #undef __FUNCT__
2893 #define __FUNCT__ "MatGetRowMaxAbs_SeqAIJ"
2894 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2895 {
2896   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2897   PetscErrorCode ierr;
2898   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2899   PetscReal      atmp;
2900   PetscScalar    *x;
2901   MatScalar      *aa;
2902 
2903   PetscFunctionBegin;
2904   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2905   aa = a->a;
2906   ai = a->i;
2907   aj = a->j;
2908 
2909   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2910   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2911   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2912   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2913   for (i=0; i<m; i++) {
2914     ncols = ai[1] - ai[0]; ai++;
2915     x[i]  = 0.0;
2916     for (j=0; j<ncols; j++) {
2917       atmp = PetscAbsScalar(*aa);
2918       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
2919       aa++; aj++;
2920     }
2921   }
2922   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2923   PetscFunctionReturn(0);
2924 }
2925 
2926 #undef __FUNCT__
2927 #define __FUNCT__ "MatGetRowMax_SeqAIJ"
2928 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2929 {
2930   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2931   PetscErrorCode ierr;
2932   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2933   PetscScalar    *x;
2934   MatScalar      *aa;
2935 
2936   PetscFunctionBegin;
2937   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2938   aa = a->a;
2939   ai = a->i;
2940   aj = a->j;
2941 
2942   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2943   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2944   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2945   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2946   for (i=0; i<m; i++) {
2947     ncols = ai[1] - ai[0]; ai++;
2948     if (ncols == A->cmap->n) { /* row is dense */
2949       x[i] = *aa; if (idx) idx[i] = 0;
2950     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
2951       x[i] = 0.0;
2952       if (idx) {
2953         idx[i] = 0; /* in case ncols is zero */
2954         for (j=0;j<ncols;j++) { /* find first implicit 0.0 in the row */
2955           if (aj[j] > j) {
2956             idx[i] = j;
2957             break;
2958           }
2959         }
2960       }
2961     }
2962     for (j=0; j<ncols; j++) {
2963       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
2964       aa++; aj++;
2965     }
2966   }
2967   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2968   PetscFunctionReturn(0);
2969 }
2970 
2971 #undef __FUNCT__
2972 #define __FUNCT__ "MatGetRowMinAbs_SeqAIJ"
2973 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2974 {
2975   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2976   PetscErrorCode ierr;
2977   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2978   PetscReal      atmp;
2979   PetscScalar    *x;
2980   MatScalar      *aa;
2981 
2982   PetscFunctionBegin;
2983   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2984   aa = a->a;
2985   ai = a->i;
2986   aj = a->j;
2987 
2988   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2989   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2990   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2991   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);
2992   for (i=0; i<m; i++) {
2993     ncols = ai[1] - ai[0]; ai++;
2994     if (ncols) {
2995       /* Get first nonzero */
2996       for (j = 0; j < ncols; j++) {
2997         atmp = PetscAbsScalar(aa[j]);
2998         if (atmp > 1.0e-12) {
2999           x[i] = atmp;
3000           if (idx) idx[i] = aj[j];
3001           break;
3002         }
3003       }
3004       if (j == ncols) {x[i] = PetscAbsScalar(*aa); if (idx) idx[i] = *aj;}
3005     } else {
3006       x[i] = 0.0; if (idx) idx[i] = 0;
3007     }
3008     for (j = 0; j < ncols; j++) {
3009       atmp = PetscAbsScalar(*aa);
3010       if (atmp > 1.0e-12 && PetscAbsScalar(x[i]) > atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3011       aa++; aj++;
3012     }
3013   }
3014   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3015   PetscFunctionReturn(0);
3016 }
3017 
3018 #undef __FUNCT__
3019 #define __FUNCT__ "MatGetRowMin_SeqAIJ"
3020 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3021 {
3022   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3023   PetscErrorCode ierr;
3024   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3025   PetscScalar    *x;
3026   MatScalar      *aa;
3027 
3028   PetscFunctionBegin;
3029   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3030   aa = a->a;
3031   ai = a->i;
3032   aj = a->j;
3033 
3034   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3035   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3036   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3037   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3038   for (i=0; i<m; i++) {
3039     ncols = ai[1] - ai[0]; ai++;
3040     if (ncols == A->cmap->n) { /* row is dense */
3041       x[i] = *aa; if (idx) idx[i] = 0;
3042     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3043       x[i] = 0.0;
3044       if (idx) {   /* find first implicit 0.0 in the row */
3045         idx[i] = 0; /* in case ncols is zero */
3046         for (j=0; j<ncols; j++) {
3047           if (aj[j] > j) {
3048             idx[i] = j;
3049             break;
3050           }
3051         }
3052       }
3053     }
3054     for (j=0; j<ncols; j++) {
3055       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3056       aa++; aj++;
3057     }
3058   }
3059   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3060   PetscFunctionReturn(0);
3061 }
3062 
3063 #include <petscblaslapack.h>
3064 #include <petsc-private/kernels/blockinvert.h>
3065 
3066 #undef __FUNCT__
3067 #define __FUNCT__ "MatInvertBlockDiagonal_SeqAIJ"
3068 PetscErrorCode  MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3069 {
3070   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
3071   PetscErrorCode ierr;
3072   PetscInt       i,bs = PetscAbs(A->rmap->bs),mbs = A->rmap->n/bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3073   MatScalar      *diag,work[25],*v_work;
3074   PetscReal      shift = 0.0;
3075 
3076   PetscFunctionBegin;
3077   if (a->ibdiagvalid) {
3078     if (values) *values = a->ibdiag;
3079     PetscFunctionReturn(0);
3080   }
3081   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3082   if (!a->ibdiag) {
3083     ierr = PetscMalloc1(bs2*mbs,&a->ibdiag);CHKERRQ(ierr);
3084     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3085   }
3086   diag = a->ibdiag;
3087   if (values) *values = a->ibdiag;
3088   /* factor and invert each block */
3089   switch (bs) {
3090   case 1:
3091     for (i=0; i<mbs; i++) {
3092       ierr    = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3093       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3094     }
3095     break;
3096   case 2:
3097     for (i=0; i<mbs; i++) {
3098       ij[0] = 2*i; ij[1] = 2*i + 1;
3099       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3100       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift);CHKERRQ(ierr);
3101       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
3102       diag += 4;
3103     }
3104     break;
3105   case 3:
3106     for (i=0; i<mbs; i++) {
3107       ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
3108       ierr  = MatGetValues(A,3,ij,3,ij,diag);CHKERRQ(ierr);
3109       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr);
3110       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3111       diag += 9;
3112     }
3113     break;
3114   case 4:
3115     for (i=0; i<mbs; i++) {
3116       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3117       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3118       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift);CHKERRQ(ierr);
3119       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3120       diag += 16;
3121     }
3122     break;
3123   case 5:
3124     for (i=0; i<mbs; i++) {
3125       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3126       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3127       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift);CHKERRQ(ierr);
3128       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3129       diag += 25;
3130     }
3131     break;
3132   case 6:
3133     for (i=0; i<mbs; i++) {
3134       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;
3135       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3136       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift);CHKERRQ(ierr);
3137       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3138       diag += 36;
3139     }
3140     break;
3141   case 7:
3142     for (i=0; i<mbs; i++) {
3143       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;
3144       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3145       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift);CHKERRQ(ierr);
3146       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3147       diag += 49;
3148     }
3149     break;
3150   default:
3151     ierr = PetscMalloc3(bs,&v_work,bs,&v_pivots,bs,&IJ);CHKERRQ(ierr);
3152     for (i=0; i<mbs; i++) {
3153       for (j=0; j<bs; j++) {
3154         IJ[j] = bs*i + j;
3155       }
3156       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3157       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work);CHKERRQ(ierr);
3158       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3159       diag += bs2;
3160     }
3161     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3162   }
3163   a->ibdiagvalid = PETSC_TRUE;
3164   PetscFunctionReturn(0);
3165 }
3166 
3167 #undef __FUNCT__
3168 #define __FUNCT__ "MatSetRandom_SeqAIJ"
3169 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3170 {
3171   PetscErrorCode ierr;
3172   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3173   PetscScalar    a;
3174   PetscInt       m,n,i,j,col;
3175 
3176   PetscFunctionBegin;
3177   if (!x->assembled) {
3178     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3179     for (i=0; i<m; i++) {
3180       for (j=0; j<aij->imax[i]; j++) {
3181         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3182         col  = (PetscInt)(n*PetscRealPart(a));
3183         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3184       }
3185     }
3186   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet coded");
3187   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3188   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3189   PetscFunctionReturn(0);
3190 }
3191 
3192 /* -------------------------------------------------------------------*/
3193 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3194                                         MatGetRow_SeqAIJ,
3195                                         MatRestoreRow_SeqAIJ,
3196                                         MatMult_SeqAIJ,
3197                                 /*  4*/ MatMultAdd_SeqAIJ,
3198                                         MatMultTranspose_SeqAIJ,
3199                                         MatMultTransposeAdd_SeqAIJ,
3200                                         0,
3201                                         0,
3202                                         0,
3203                                 /* 10*/ 0,
3204                                         MatLUFactor_SeqAIJ,
3205                                         0,
3206                                         MatSOR_SeqAIJ,
3207                                         MatTranspose_SeqAIJ,
3208                                 /*1 5*/ MatGetInfo_SeqAIJ,
3209                                         MatEqual_SeqAIJ,
3210                                         MatGetDiagonal_SeqAIJ,
3211                                         MatDiagonalScale_SeqAIJ,
3212                                         MatNorm_SeqAIJ,
3213                                 /* 20*/ 0,
3214                                         MatAssemblyEnd_SeqAIJ,
3215                                         MatSetOption_SeqAIJ,
3216                                         MatZeroEntries_SeqAIJ,
3217                                 /* 24*/ MatZeroRows_SeqAIJ,
3218                                         0,
3219                                         0,
3220                                         0,
3221                                         0,
3222                                 /* 29*/ MatSetUp_SeqAIJ,
3223                                         0,
3224                                         0,
3225                                         0,
3226                                         0,
3227                                 /* 34*/ MatDuplicate_SeqAIJ,
3228                                         0,
3229                                         0,
3230                                         MatILUFactor_SeqAIJ,
3231                                         0,
3232                                 /* 39*/ MatAXPY_SeqAIJ,
3233                                         MatGetSubMatrices_SeqAIJ,
3234                                         MatIncreaseOverlap_SeqAIJ,
3235                                         MatGetValues_SeqAIJ,
3236                                         MatCopy_SeqAIJ,
3237                                 /* 44*/ MatGetRowMax_SeqAIJ,
3238                                         MatScale_SeqAIJ,
3239                                         0,
3240                                         MatDiagonalSet_SeqAIJ,
3241                                         MatZeroRowsColumns_SeqAIJ,
3242                                 /* 49*/ MatSetRandom_SeqAIJ,
3243                                         MatGetRowIJ_SeqAIJ,
3244                                         MatRestoreRowIJ_SeqAIJ,
3245                                         MatGetColumnIJ_SeqAIJ,
3246                                         MatRestoreColumnIJ_SeqAIJ,
3247                                 /* 54*/ MatFDColoringCreate_SeqXAIJ,
3248                                         0,
3249                                         0,
3250                                         MatPermute_SeqAIJ,
3251                                         0,
3252                                 /* 59*/ 0,
3253                                         MatDestroy_SeqAIJ,
3254                                         MatView_SeqAIJ,
3255                                         0,
3256                                         MatMatMatMult_SeqAIJ_SeqAIJ_SeqAIJ,
3257                                 /* 64*/ MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ,
3258                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3259                                         0,
3260                                         0,
3261                                         0,
3262                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3263                                         MatGetRowMinAbs_SeqAIJ,
3264                                         0,
3265                                         MatSetColoring_SeqAIJ,
3266                                         0,
3267                                 /* 74*/ MatSetValuesAdifor_SeqAIJ,
3268                                         MatFDColoringApply_AIJ,
3269                                         0,
3270                                         0,
3271                                         0,
3272                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3273                                         0,
3274                                         0,
3275                                         0,
3276                                         MatLoad_SeqAIJ,
3277                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3278                                         MatIsHermitian_SeqAIJ,
3279                                         0,
3280                                         0,
3281                                         0,
3282                                 /* 89*/ MatMatMult_SeqAIJ_SeqAIJ,
3283                                         MatMatMultSymbolic_SeqAIJ_SeqAIJ,
3284                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3285                                         MatPtAP_SeqAIJ_SeqAIJ,
3286                                         MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy,
3287                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ,
3288                                         MatMatTransposeMult_SeqAIJ_SeqAIJ,
3289                                         MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ,
3290                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3291                                         0,
3292                                 /* 99*/ 0,
3293                                         0,
3294                                         0,
3295                                         MatConjugate_SeqAIJ,
3296                                         0,
3297                                 /*104*/ MatSetValuesRow_SeqAIJ,
3298                                         MatRealPart_SeqAIJ,
3299                                         MatImaginaryPart_SeqAIJ,
3300                                         0,
3301                                         0,
3302                                 /*109*/ MatMatSolve_SeqAIJ,
3303                                         0,
3304                                         MatGetRowMin_SeqAIJ,
3305                                         0,
3306                                         MatMissingDiagonal_SeqAIJ,
3307                                 /*114*/ 0,
3308                                         0,
3309                                         0,
3310                                         0,
3311                                         0,
3312                                 /*119*/ 0,
3313                                         0,
3314                                         0,
3315                                         0,
3316                                         MatGetMultiProcBlock_SeqAIJ,
3317                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3318                                         MatGetColumnNorms_SeqAIJ,
3319                                         MatInvertBlockDiagonal_SeqAIJ,
3320                                         0,
3321                                         0,
3322                                 /*129*/ 0,
3323                                         MatTransposeMatMult_SeqAIJ_SeqAIJ,
3324                                         MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ,
3325                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3326                                         MatTransposeColoringCreate_SeqAIJ,
3327                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3328                                         MatTransColoringApplyDenToSp_SeqAIJ,
3329                                         MatRARt_SeqAIJ_SeqAIJ,
3330                                         MatRARtSymbolic_SeqAIJ_SeqAIJ,
3331                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3332                                  /*139*/0,
3333                                         0,
3334                                         0,
3335                                         MatFDColoringSetUp_SeqXAIJ,
3336                                         MatFindOffBlockDiagonalEntries_SeqAIJ
3337 };
3338 
3339 #undef __FUNCT__
3340 #define __FUNCT__ "MatSeqAIJSetColumnIndices_SeqAIJ"
3341 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3342 {
3343   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3344   PetscInt   i,nz,n;
3345 
3346   PetscFunctionBegin;
3347   nz = aij->maxnz;
3348   n  = mat->rmap->n;
3349   for (i=0; i<nz; i++) {
3350     aij->j[i] = indices[i];
3351   }
3352   aij->nz = nz;
3353   for (i=0; i<n; i++) {
3354     aij->ilen[i] = aij->imax[i];
3355   }
3356   PetscFunctionReturn(0);
3357 }
3358 
3359 #undef __FUNCT__
3360 #define __FUNCT__ "MatSeqAIJSetColumnIndices"
3361 /*@
3362     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3363        in the matrix.
3364 
3365   Input Parameters:
3366 +  mat - the SeqAIJ matrix
3367 -  indices - the column indices
3368 
3369   Level: advanced
3370 
3371   Notes:
3372     This can be called if you have precomputed the nonzero structure of the
3373   matrix and want to provide it to the matrix object to improve the performance
3374   of the MatSetValues() operation.
3375 
3376     You MUST have set the correct numbers of nonzeros per row in the call to
3377   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3378 
3379     MUST be called before any calls to MatSetValues();
3380 
3381     The indices should start with zero, not one.
3382 
3383 @*/
3384 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3385 {
3386   PetscErrorCode ierr;
3387 
3388   PetscFunctionBegin;
3389   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3390   PetscValidPointer(indices,2);
3391   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3392   PetscFunctionReturn(0);
3393 }
3394 
3395 /* ----------------------------------------------------------------------------------------*/
3396 
3397 #undef __FUNCT__
3398 #define __FUNCT__ "MatStoreValues_SeqAIJ"
3399 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3400 {
3401   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3402   PetscErrorCode ierr;
3403   size_t         nz = aij->i[mat->rmap->n];
3404 
3405   PetscFunctionBegin;
3406   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3407 
3408   /* allocate space for values if not already there */
3409   if (!aij->saved_values) {
3410     ierr = PetscMalloc1((nz+1),&aij->saved_values);CHKERRQ(ierr);
3411     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3412   }
3413 
3414   /* copy values over */
3415   ierr = PetscMemcpy(aij->saved_values,aij->a,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3416   PetscFunctionReturn(0);
3417 }
3418 
3419 #undef __FUNCT__
3420 #define __FUNCT__ "MatStoreValues"
3421 /*@
3422     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3423        example, reuse of the linear part of a Jacobian, while recomputing the
3424        nonlinear portion.
3425 
3426    Collect on Mat
3427 
3428   Input Parameters:
3429 .  mat - the matrix (currently only AIJ matrices support this option)
3430 
3431   Level: advanced
3432 
3433   Common Usage, with SNESSolve():
3434 $    Create Jacobian matrix
3435 $    Set linear terms into matrix
3436 $    Apply boundary conditions to matrix, at this time matrix must have
3437 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3438 $      boundary conditions again will not change the nonzero structure
3439 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3440 $    ierr = MatStoreValues(mat);
3441 $    Call SNESSetJacobian() with matrix
3442 $    In your Jacobian routine
3443 $      ierr = MatRetrieveValues(mat);
3444 $      Set nonlinear terms in matrix
3445 
3446   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3447 $    // build linear portion of Jacobian
3448 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3449 $    ierr = MatStoreValues(mat);
3450 $    loop over nonlinear iterations
3451 $       ierr = MatRetrieveValues(mat);
3452 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3453 $       // call MatAssemblyBegin/End() on matrix
3454 $       Solve linear system with Jacobian
3455 $    endloop
3456 
3457   Notes:
3458     Matrix must already be assemblied before calling this routine
3459     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3460     calling this routine.
3461 
3462     When this is called multiple times it overwrites the previous set of stored values
3463     and does not allocated additional space.
3464 
3465 .seealso: MatRetrieveValues()
3466 
3467 @*/
3468 PetscErrorCode  MatStoreValues(Mat mat)
3469 {
3470   PetscErrorCode ierr;
3471 
3472   PetscFunctionBegin;
3473   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3474   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3475   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3476   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3477   PetscFunctionReturn(0);
3478 }
3479 
3480 #undef __FUNCT__
3481 #define __FUNCT__ "MatRetrieveValues_SeqAIJ"
3482 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3483 {
3484   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3485   PetscErrorCode ierr;
3486   PetscInt       nz = aij->i[mat->rmap->n];
3487 
3488   PetscFunctionBegin;
3489   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3490   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3491   /* copy values over */
3492   ierr = PetscMemcpy(aij->a,aij->saved_values,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3493   PetscFunctionReturn(0);
3494 }
3495 
3496 #undef __FUNCT__
3497 #define __FUNCT__ "MatRetrieveValues"
3498 /*@
3499     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3500        example, reuse of the linear part of a Jacobian, while recomputing the
3501        nonlinear portion.
3502 
3503    Collect on Mat
3504 
3505   Input Parameters:
3506 .  mat - the matrix (currently on AIJ matrices support this option)
3507 
3508   Level: advanced
3509 
3510 .seealso: MatStoreValues()
3511 
3512 @*/
3513 PetscErrorCode  MatRetrieveValues(Mat mat)
3514 {
3515   PetscErrorCode ierr;
3516 
3517   PetscFunctionBegin;
3518   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3519   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3520   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3521   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3522   PetscFunctionReturn(0);
3523 }
3524 
3525 
3526 /* --------------------------------------------------------------------------------*/
3527 #undef __FUNCT__
3528 #define __FUNCT__ "MatCreateSeqAIJ"
3529 /*@C
3530    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3531    (the default parallel PETSc format).  For good matrix assembly performance
3532    the user should preallocate the matrix storage by setting the parameter nz
3533    (or the array nnz).  By setting these parameters accurately, performance
3534    during matrix assembly can be increased by more than a factor of 50.
3535 
3536    Collective on MPI_Comm
3537 
3538    Input Parameters:
3539 +  comm - MPI communicator, set to PETSC_COMM_SELF
3540 .  m - number of rows
3541 .  n - number of columns
3542 .  nz - number of nonzeros per row (same for all rows)
3543 -  nnz - array containing the number of nonzeros in the various rows
3544          (possibly different for each row) or NULL
3545 
3546    Output Parameter:
3547 .  A - the matrix
3548 
3549    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3550    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3551    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3552 
3553    Notes:
3554    If nnz is given then nz is ignored
3555 
3556    The AIJ format (also called the Yale sparse matrix format or
3557    compressed row storage), is fully compatible with standard Fortran 77
3558    storage.  That is, the stored row and column indices can begin at
3559    either one (as in Fortran) or zero.  See the users' manual for details.
3560 
3561    Specify the preallocated storage with either nz or nnz (not both).
3562    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3563    allocation.  For large problems you MUST preallocate memory or you
3564    will get TERRIBLE performance, see the users' manual chapter on matrices.
3565 
3566    By default, this format uses inodes (identical nodes) when possible, to
3567    improve numerical efficiency of matrix-vector products and solves. We
3568    search for consecutive rows with the same nonzero structure, thereby
3569    reusing matrix information to achieve increased efficiency.
3570 
3571    Options Database Keys:
3572 +  -mat_no_inode  - Do not use inodes
3573 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3574 
3575    Level: intermediate
3576 
3577 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3578 
3579 @*/
3580 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3581 {
3582   PetscErrorCode ierr;
3583 
3584   PetscFunctionBegin;
3585   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3586   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3587   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3588   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3589   PetscFunctionReturn(0);
3590 }
3591 
3592 #undef __FUNCT__
3593 #define __FUNCT__ "MatSeqAIJSetPreallocation"
3594 /*@C
3595    MatSeqAIJSetPreallocation - For good matrix assembly performance
3596    the user should preallocate the matrix storage by setting the parameter nz
3597    (or the array nnz).  By setting these parameters accurately, performance
3598    during matrix assembly can be increased by more than a factor of 50.
3599 
3600    Collective on MPI_Comm
3601 
3602    Input Parameters:
3603 +  B - The matrix
3604 .  nz - number of nonzeros per row (same for all rows)
3605 -  nnz - array containing the number of nonzeros in the various rows
3606          (possibly different for each row) or NULL
3607 
3608    Notes:
3609      If nnz is given then nz is ignored
3610 
3611     The AIJ format (also called the Yale sparse matrix format or
3612    compressed row storage), is fully compatible with standard Fortran 77
3613    storage.  That is, the stored row and column indices can begin at
3614    either one (as in Fortran) or zero.  See the users' manual for details.
3615 
3616    Specify the preallocated storage with either nz or nnz (not both).
3617    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3618    allocation.  For large problems you MUST preallocate memory or you
3619    will get TERRIBLE performance, see the users' manual chapter on matrices.
3620 
3621    You can call MatGetInfo() to get information on how effective the preallocation was;
3622    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3623    You can also run with the option -info and look for messages with the string
3624    malloc in them to see if additional memory allocation was needed.
3625 
3626    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3627    entries or columns indices
3628 
3629    By default, this format uses inodes (identical nodes) when possible, to
3630    improve numerical efficiency of matrix-vector products and solves. We
3631    search for consecutive rows with the same nonzero structure, thereby
3632    reusing matrix information to achieve increased efficiency.
3633 
3634    Options Database Keys:
3635 +  -mat_no_inode  - Do not use inodes
3636 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3637 -  -mat_aij_oneindex - Internally use indexing starting at 1
3638         rather than 0.  Note that when calling MatSetValues(),
3639         the user still MUST index entries starting at 0!
3640 
3641    Level: intermediate
3642 
3643 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatGetInfo()
3644 
3645 @*/
3646 PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
3647 {
3648   PetscErrorCode ierr;
3649 
3650   PetscFunctionBegin;
3651   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3652   PetscValidType(B,1);
3653   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));CHKERRQ(ierr);
3654   PetscFunctionReturn(0);
3655 }
3656 
3657 #undef __FUNCT__
3658 #define __FUNCT__ "MatSeqAIJSetPreallocation_SeqAIJ"
3659 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3660 {
3661   Mat_SeqAIJ     *b;
3662   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3663   PetscErrorCode ierr;
3664   PetscInt       i;
3665 
3666   PetscFunctionBegin;
3667   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3668   if (nz == MAT_SKIP_ALLOCATION) {
3669     skipallocation = PETSC_TRUE;
3670     nz             = 0;
3671   }
3672 
3673   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3674   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3675 
3676   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3677   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %D",nz);
3678   if (nnz) {
3679     for (i=0; i<B->rmap->n; i++) {
3680       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]);
3681       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);
3682     }
3683   }
3684 
3685   B->preallocated = PETSC_TRUE;
3686 
3687   b = (Mat_SeqAIJ*)B->data;
3688 
3689   if (!skipallocation) {
3690     if (!b->imax) {
3691       ierr = PetscMalloc2(B->rmap->n,&b->imax,B->rmap->n,&b->ilen);CHKERRQ(ierr);
3692       ierr = PetscLogObjectMemory((PetscObject)B,2*B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3693     }
3694     if (!nnz) {
3695       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3696       else if (nz < 0) nz = 1;
3697       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
3698       nz = nz*B->rmap->n;
3699     } else {
3700       nz = 0;
3701       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz += nnz[i];}
3702     }
3703     /* b->ilen will count nonzeros in each row so far. */
3704     for (i=0; i<B->rmap->n; i++) b->ilen[i] = 0;
3705 
3706     /* allocate the matrix space */
3707     ierr    = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
3708     ierr    = PetscMalloc3(nz,&b->a,nz,&b->j,B->rmap->n+1,&b->i);CHKERRQ(ierr);
3709     ierr    = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
3710     b->i[0] = 0;
3711     for (i=1; i<B->rmap->n+1; i++) {
3712       b->i[i] = b->i[i-1] + b->imax[i-1];
3713     }
3714     b->singlemalloc = PETSC_TRUE;
3715     b->free_a       = PETSC_TRUE;
3716     b->free_ij      = PETSC_TRUE;
3717 #if defined(PETSC_THREADCOMM_ACTIVE)
3718     ierr = MatZeroEntries_SeqAIJ(B);CHKERRQ(ierr);
3719 #endif
3720   } else {
3721     b->free_a  = PETSC_FALSE;
3722     b->free_ij = PETSC_FALSE;
3723   }
3724 
3725   b->nz               = 0;
3726   b->maxnz            = nz;
3727   B->info.nz_unneeded = (double)b->maxnz;
3728   if (realalloc) {
3729     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3730   }
3731   PetscFunctionReturn(0);
3732 }
3733 
3734 #undef  __FUNCT__
3735 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR"
3736 /*@
3737    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
3738 
3739    Input Parameters:
3740 +  B - the matrix
3741 .  i - the indices into j for the start of each row (starts with zero)
3742 .  j - the column indices for each row (starts with zero) these must be sorted for each row
3743 -  v - optional values in the matrix
3744 
3745    Level: developer
3746 
3747    The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
3748 
3749 .keywords: matrix, aij, compressed row, sparse, sequential
3750 
3751 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), SeqAIJ
3752 @*/
3753 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
3754 {
3755   PetscErrorCode ierr;
3756 
3757   PetscFunctionBegin;
3758   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3759   PetscValidType(B,1);
3760   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3761   PetscFunctionReturn(0);
3762 }
3763 
3764 #undef  __FUNCT__
3765 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR_SeqAIJ"
3766 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3767 {
3768   PetscInt       i;
3769   PetscInt       m,n;
3770   PetscInt       nz;
3771   PetscInt       *nnz, nz_max = 0;
3772   PetscScalar    *values;
3773   PetscErrorCode ierr;
3774 
3775   PetscFunctionBegin;
3776   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
3777 
3778   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3779   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3780 
3781   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
3782   ierr = PetscMalloc1((m+1), &nnz);CHKERRQ(ierr);
3783   for (i = 0; i < m; i++) {
3784     nz     = Ii[i+1]- Ii[i];
3785     nz_max = PetscMax(nz_max, nz);
3786     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
3787     nnz[i] = nz;
3788   }
3789   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
3790   ierr = PetscFree(nnz);CHKERRQ(ierr);
3791 
3792   if (v) {
3793     values = (PetscScalar*) v;
3794   } else {
3795     ierr = PetscCalloc1(nz_max, &values);CHKERRQ(ierr);
3796   }
3797 
3798   for (i = 0; i < m; i++) {
3799     nz   = Ii[i+1] - Ii[i];
3800     ierr = MatSetValues_SeqAIJ(B, 1, &i, nz, J+Ii[i], values + (v ? Ii[i] : 0), INSERT_VALUES);CHKERRQ(ierr);
3801   }
3802 
3803   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3804   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3805 
3806   if (!v) {
3807     ierr = PetscFree(values);CHKERRQ(ierr);
3808   }
3809   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3810   PetscFunctionReturn(0);
3811 }
3812 
3813 #include <../src/mat/impls/dense/seq/dense.h>
3814 #include <petsc-private/kernels/petscaxpy.h>
3815 
3816 #undef __FUNCT__
3817 #define __FUNCT__ "MatMatMultNumeric_SeqDense_SeqAIJ"
3818 /*
3819     Computes (B'*A')' since computing B*A directly is untenable
3820 
3821                n                       p                          p
3822         (              )       (              )         (                  )
3823       m (      A       )  *  n (       B      )   =   m (         C        )
3824         (              )       (              )         (                  )
3825 
3826 */
3827 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
3828 {
3829   PetscErrorCode    ierr;
3830   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
3831   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
3832   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
3833   PetscInt          i,n,m,q,p;
3834   const PetscInt    *ii,*idx;
3835   const PetscScalar *b,*a,*a_q;
3836   PetscScalar       *c,*c_q;
3837 
3838   PetscFunctionBegin;
3839   m    = A->rmap->n;
3840   n    = A->cmap->n;
3841   p    = B->cmap->n;
3842   a    = sub_a->v;
3843   b    = sub_b->a;
3844   c    = sub_c->v;
3845   ierr = PetscMemzero(c,m*p*sizeof(PetscScalar));CHKERRQ(ierr);
3846 
3847   ii  = sub_b->i;
3848   idx = sub_b->j;
3849   for (i=0; i<n; i++) {
3850     q = ii[i+1] - ii[i];
3851     while (q-->0) {
3852       c_q = c + m*(*idx);
3853       a_q = a + m*i;
3854       PetscKernelAXPY(c_q,*b,a_q,m);
3855       idx++;
3856       b++;
3857     }
3858   }
3859   PetscFunctionReturn(0);
3860 }
3861 
3862 #undef __FUNCT__
3863 #define __FUNCT__ "MatMatMultSymbolic_SeqDense_SeqAIJ"
3864 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
3865 {
3866   PetscErrorCode ierr;
3867   PetscInt       m=A->rmap->n,n=B->cmap->n;
3868   Mat            Cmat;
3869 
3870   PetscFunctionBegin;
3871   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);
3872   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
3873   ierr = MatSetSizes(Cmat,m,n,m,n);CHKERRQ(ierr);
3874   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
3875   ierr = MatSetType(Cmat,MATSEQDENSE);CHKERRQ(ierr);
3876   ierr = MatSeqDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
3877 
3878   Cmat->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
3879 
3880   *C = Cmat;
3881   PetscFunctionReturn(0);
3882 }
3883 
3884 /* ----------------------------------------------------------------*/
3885 #undef __FUNCT__
3886 #define __FUNCT__ "MatMatMult_SeqDense_SeqAIJ"
3887 PetscErrorCode MatMatMult_SeqDense_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
3888 {
3889   PetscErrorCode ierr;
3890 
3891   PetscFunctionBegin;
3892   if (scall == MAT_INITIAL_MATRIX) {
3893     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
3894     ierr = MatMatMultSymbolic_SeqDense_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
3895     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
3896   }
3897   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
3898   ierr = MatMatMultNumeric_SeqDense_SeqAIJ(A,B,*C);CHKERRQ(ierr);
3899   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
3900   PetscFunctionReturn(0);
3901 }
3902 
3903 
3904 /*MC
3905    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
3906    based on compressed sparse row format.
3907 
3908    Options Database Keys:
3909 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
3910 
3911   Level: beginner
3912 
3913 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
3914 M*/
3915 
3916 /*MC
3917    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
3918 
3919    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
3920    and MATMPIAIJ otherwise.  As a result, for single process communicators,
3921   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
3922   for communicators controlling multiple processes.  It is recommended that you call both of
3923   the above preallocation routines for simplicity.
3924 
3925    Options Database Keys:
3926 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
3927 
3928   Developer Notes: Subclasses include MATAIJCUSP, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
3929    enough exist.
3930 
3931   Level: beginner
3932 
3933 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
3934 M*/
3935 
3936 /*MC
3937    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
3938 
3939    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
3940    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
3941    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
3942   for communicators controlling multiple processes.  It is recommended that you call both of
3943   the above preallocation routines for simplicity.
3944 
3945    Options Database Keys:
3946 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
3947 
3948   Level: beginner
3949 
3950 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
3951 M*/
3952 
3953 #if defined(PETSC_HAVE_PASTIX)
3954 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_pastix(Mat,MatFactorType,Mat*);
3955 #endif
3956 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
3957 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_essl(Mat,MatFactorType,Mat*);
3958 #endif
3959 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
3960 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_petsc(Mat,MatFactorType,Mat*);
3961 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_bas(Mat,MatFactorType,Mat*);
3962 extern PetscErrorCode  MatGetFactorAvailable_seqaij_petsc(Mat,MatFactorType,PetscBool*);
3963 #if defined(PETSC_HAVE_MUMPS)
3964 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mumps(Mat,MatFactorType,Mat*);
3965 #endif
3966 #if defined(PETSC_HAVE_SUPERLU)
3967 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu(Mat,MatFactorType,Mat*);
3968 #endif
3969 #if defined(PETSC_HAVE_MKL_PARDISO)
3970 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mkl_pardiso(Mat,MatFactorType,Mat*);
3971 #endif
3972 #if defined(PETSC_HAVE_SUPERLU_DIST)
3973 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu_dist(Mat,MatFactorType,Mat*);
3974 #endif
3975 #if defined(PETSC_HAVE_SUITESPARSE)
3976 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_umfpack(Mat,MatFactorType,Mat*);
3977 #endif
3978 #if defined(PETSC_HAVE_SUITESPARSE)
3979 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_cholmod(Mat,MatFactorType,Mat*);
3980 #endif
3981 #if defined(PETSC_HAVE_SUITESPARSE)
3982 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_klu(Mat,MatFactorType,Mat*);
3983 #endif
3984 #if defined(PETSC_HAVE_LUSOL)
3985 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_lusol(Mat,MatFactorType,Mat*);
3986 #endif
3987 #if defined(PETSC_HAVE_MATLAB_ENGINE)
3988 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_matlab(Mat,MatFactorType,Mat*);
3989 extern PetscErrorCode  MatlabEnginePut_SeqAIJ(PetscObject,void*);
3990 extern PetscErrorCode  MatlabEngineGet_SeqAIJ(PetscObject,void*);
3991 #endif
3992 #if defined(PETSC_HAVE_CLIQUE)
3993 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_clique(Mat,MatFactorType,Mat*);
3994 #endif
3995 
3996 
3997 #undef __FUNCT__
3998 #define __FUNCT__ "MatSeqAIJGetArray"
3999 /*@C
4000    MatSeqAIJGetArray - gives access to the array where the data for a SeqSeqAIJ matrix is stored
4001 
4002    Not Collective
4003 
4004    Input Parameter:
4005 .  mat - a MATSEQAIJ matrix
4006 
4007    Output Parameter:
4008 .   array - pointer to the data
4009 
4010    Level: intermediate
4011 
4012 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4013 @*/
4014 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4015 {
4016   PetscErrorCode ierr;
4017 
4018   PetscFunctionBegin;
4019   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4020   PetscFunctionReturn(0);
4021 }
4022 
4023 #undef __FUNCT__
4024 #define __FUNCT__ "MatSeqAIJGetMaxRowNonzeros"
4025 /*@C
4026    MatSeqAIJGetMaxRowNonzeros - returns the maximum number of nonzeros in any row
4027 
4028    Not Collective
4029 
4030    Input Parameter:
4031 .  mat - a MATSEQAIJ matrix
4032 
4033    Output Parameter:
4034 .   nz - the maximum number of nonzeros in any row
4035 
4036    Level: intermediate
4037 
4038 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4039 @*/
4040 PetscErrorCode  MatSeqAIJGetMaxRowNonzeros(Mat A,PetscInt *nz)
4041 {
4042   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
4043 
4044   PetscFunctionBegin;
4045   *nz = aij->rmax;
4046   PetscFunctionReturn(0);
4047 }
4048 
4049 #undef __FUNCT__
4050 #define __FUNCT__ "MatSeqAIJRestoreArray"
4051 /*@C
4052    MatSeqAIJRestoreArray - returns access to the array where the data for a MATSEQAIJ matrix is stored obtained by MatSeqAIJGetArray()
4053 
4054    Not Collective
4055 
4056    Input Parameters:
4057 .  mat - a MATSEQAIJ matrix
4058 .  array - pointer to the data
4059 
4060    Level: intermediate
4061 
4062 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4063 @*/
4064 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4065 {
4066   PetscErrorCode ierr;
4067 
4068   PetscFunctionBegin;
4069   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4070   PetscFunctionReturn(0);
4071 }
4072 
4073 #undef __FUNCT__
4074 #define __FUNCT__ "MatCreate_SeqAIJ"
4075 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4076 {
4077   Mat_SeqAIJ     *b;
4078   PetscErrorCode ierr;
4079   PetscMPIInt    size;
4080 
4081   PetscFunctionBegin;
4082   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4083   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4084 
4085   ierr = PetscNewLog(B,&b);CHKERRQ(ierr);
4086 
4087   B->data = (void*)b;
4088 
4089   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4090 
4091   b->row                = 0;
4092   b->col                = 0;
4093   b->icol               = 0;
4094   b->reallocs           = 0;
4095   b->ignorezeroentries  = PETSC_FALSE;
4096   b->roworiented        = PETSC_TRUE;
4097   b->nonew              = 0;
4098   b->diag               = 0;
4099   b->solve_work         = 0;
4100   B->spptr              = 0;
4101   b->saved_values       = 0;
4102   b->idiag              = 0;
4103   b->mdiag              = 0;
4104   b->ssor_work          = 0;
4105   b->omega              = 1.0;
4106   b->fshift             = 0.0;
4107   b->idiagvalid         = PETSC_FALSE;
4108   b->ibdiagvalid        = PETSC_FALSE;
4109   b->keepnonzeropattern = PETSC_FALSE;
4110   b->xtoy               = 0;
4111   b->XtoY               = 0;
4112 
4113   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4114   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4115   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4116 
4117 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4118   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_matlab_C",MatGetFactor_seqaij_matlab);CHKERRQ(ierr);
4119   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4120   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4121 #endif
4122 #if defined(PETSC_HAVE_PASTIX)
4123   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_pastix_C",MatGetFactor_seqaij_pastix);CHKERRQ(ierr);
4124 #endif
4125 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
4126   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_essl_C",MatGetFactor_seqaij_essl);CHKERRQ(ierr);
4127 #endif
4128 #if defined(PETSC_HAVE_SUPERLU)
4129   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_C",MatGetFactor_seqaij_superlu);CHKERRQ(ierr);
4130 #endif
4131 #if defined(PETSC_HAVE_MKL_PARDISO)
4132   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mkl_pardiso_C",MatGetFactor_aij_mkl_pardiso);CHKERRQ(ierr);
4133 #endif
4134 #if defined(PETSC_HAVE_SUPERLU_DIST)
4135   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_dist_C",MatGetFactor_seqaij_superlu_dist);CHKERRQ(ierr);
4136 #endif
4137 #if defined(PETSC_HAVE_MUMPS)
4138   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mumps_C",MatGetFactor_aij_mumps);CHKERRQ(ierr);
4139 #endif
4140 #if defined(PETSC_HAVE_SUITESPARSE)
4141   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_umfpack_C",MatGetFactor_seqaij_umfpack);CHKERRQ(ierr);
4142 #endif
4143 #if defined(PETSC_HAVE_SUITESPARSE)
4144   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_cholmod_C",MatGetFactor_seqaij_cholmod);CHKERRQ(ierr);
4145 #endif
4146 #if defined(PETSC_HAVE_SUITESPARSE)
4147   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_klu_C",MatGetFactor_seqaij_klu);CHKERRQ(ierr);
4148 #endif
4149 #if defined(PETSC_HAVE_LUSOL)
4150   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_lusol_C",MatGetFactor_seqaij_lusol);CHKERRQ(ierr);
4151 #endif
4152 #if defined(PETSC_HAVE_CLIQUE)
4153   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_clique_C",MatGetFactor_aij_clique);CHKERRQ(ierr);
4154 #endif
4155 
4156   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_petsc_C",MatGetFactor_seqaij_petsc);CHKERRQ(ierr);
4157   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactorAvailable_petsc_C",MatGetFactorAvailable_seqaij_petsc);CHKERRQ(ierr);
4158   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_bas_C",MatGetFactor_seqaij_bas);CHKERRQ(ierr);
4159   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4160   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4161   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4162   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4163   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4164   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4165   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4166   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4167   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4168   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4169   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4170   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4171   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaij_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
4172   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaij_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
4173   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaij_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
4174   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4175   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4176   PetscFunctionReturn(0);
4177 }
4178 
4179 #undef __FUNCT__
4180 #define __FUNCT__ "MatDuplicateNoCreate_SeqAIJ"
4181 /*
4182     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4183 */
4184 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4185 {
4186   Mat_SeqAIJ     *c,*a = (Mat_SeqAIJ*)A->data;
4187   PetscErrorCode ierr;
4188   PetscInt       i,m = A->rmap->n;
4189 
4190   PetscFunctionBegin;
4191   c = (Mat_SeqAIJ*)C->data;
4192 
4193   C->factortype = A->factortype;
4194   c->row        = 0;
4195   c->col        = 0;
4196   c->icol       = 0;
4197   c->reallocs   = 0;
4198 
4199   C->assembled = PETSC_TRUE;
4200 
4201   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4202   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4203 
4204   ierr = PetscMalloc2(m,&c->imax,m,&c->ilen);CHKERRQ(ierr);
4205   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4206   for (i=0; i<m; i++) {
4207     c->imax[i] = a->imax[i];
4208     c->ilen[i] = a->ilen[i];
4209   }
4210 
4211   /* allocate the matrix space */
4212   if (mallocmatspace) {
4213     ierr = PetscMalloc3(a->i[m],&c->a,a->i[m],&c->j,m+1,&c->i);CHKERRQ(ierr);
4214     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4215 
4216     c->singlemalloc = PETSC_TRUE;
4217 
4218     ierr = PetscMemcpy(c->i,a->i,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4219     if (m > 0) {
4220       ierr = PetscMemcpy(c->j,a->j,(a->i[m])*sizeof(PetscInt));CHKERRQ(ierr);
4221       if (cpvalues == MAT_COPY_VALUES) {
4222         ierr = PetscMemcpy(c->a,a->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4223       } else {
4224         ierr = PetscMemzero(c->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4225       }
4226     }
4227   }
4228 
4229   c->ignorezeroentries = a->ignorezeroentries;
4230   c->roworiented       = a->roworiented;
4231   c->nonew             = a->nonew;
4232   if (a->diag) {
4233     ierr = PetscMalloc1((m+1),&c->diag);CHKERRQ(ierr);
4234     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4235     for (i=0; i<m; i++) {
4236       c->diag[i] = a->diag[i];
4237     }
4238   } else c->diag = 0;
4239 
4240   c->solve_work         = 0;
4241   c->saved_values       = 0;
4242   c->idiag              = 0;
4243   c->ssor_work          = 0;
4244   c->keepnonzeropattern = a->keepnonzeropattern;
4245   c->free_a             = PETSC_TRUE;
4246   c->free_ij            = PETSC_TRUE;
4247   c->xtoy               = 0;
4248   c->XtoY               = 0;
4249 
4250   c->rmax         = a->rmax;
4251   c->nz           = a->nz;
4252   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4253   C->preallocated = PETSC_TRUE;
4254 
4255   c->compressedrow.use   = a->compressedrow.use;
4256   c->compressedrow.nrows = a->compressedrow.nrows;
4257   if (a->compressedrow.use) {
4258     i    = a->compressedrow.nrows;
4259     ierr = PetscMalloc2(i+1,&c->compressedrow.i,i,&c->compressedrow.rindex);CHKERRQ(ierr);
4260     ierr = PetscMemcpy(c->compressedrow.i,a->compressedrow.i,(i+1)*sizeof(PetscInt));CHKERRQ(ierr);
4261     ierr = PetscMemcpy(c->compressedrow.rindex,a->compressedrow.rindex,i*sizeof(PetscInt));CHKERRQ(ierr);
4262   } else {
4263     c->compressedrow.use    = PETSC_FALSE;
4264     c->compressedrow.i      = NULL;
4265     c->compressedrow.rindex = NULL;
4266   }
4267   C->nonzerostate = A->nonzerostate;
4268 
4269   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4270   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4271   PetscFunctionReturn(0);
4272 }
4273 
4274 #undef __FUNCT__
4275 #define __FUNCT__ "MatDuplicate_SeqAIJ"
4276 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4277 {
4278   PetscErrorCode ierr;
4279 
4280   PetscFunctionBegin;
4281   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4282   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4283   if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) {
4284     ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
4285   }
4286   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4287   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4288   PetscFunctionReturn(0);
4289 }
4290 
4291 #undef __FUNCT__
4292 #define __FUNCT__ "MatLoad_SeqAIJ"
4293 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4294 {
4295   Mat_SeqAIJ     *a;
4296   PetscErrorCode ierr;
4297   PetscInt       i,sum,nz,header[4],*rowlengths = 0,M,N,rows,cols;
4298   int            fd;
4299   PetscMPIInt    size;
4300   MPI_Comm       comm;
4301   PetscInt       bs = newMat->rmap->bs;
4302 
4303   PetscFunctionBegin;
4304   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
4305   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4306   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"view must have one processor");
4307 
4308   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
4309   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
4310   ierr = PetscOptionsEnd();CHKERRQ(ierr);
4311   if (bs < 0) bs = 1;
4312   ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);
4313 
4314   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
4315   ierr = PetscBinaryRead(fd,header,4,PETSC_INT);CHKERRQ(ierr);
4316   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
4317   M = header[1]; N = header[2]; nz = header[3];
4318 
4319   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
4320 
4321   /* read in row lengths */
4322   ierr = PetscMalloc1(M,&rowlengths);CHKERRQ(ierr);
4323   ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
4324 
4325   /* check if sum of rowlengths is same as nz */
4326   for (i=0,sum=0; i< M; i++) sum +=rowlengths[i];
4327   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);
4328 
4329   /* set global size if not set already*/
4330   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) {
4331     ierr = MatSetSizes(newMat,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
4332   } else {
4333     /* if sizes and type are already set, check if the vector global sizes are correct */
4334     ierr = MatGetSize(newMat,&rows,&cols);CHKERRQ(ierr);
4335     if (rows < 0 && cols < 0) { /* user might provide local size instead of global size */
4336       ierr = MatGetLocalSize(newMat,&rows,&cols);CHKERRQ(ierr);
4337     }
4338     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);
4339   }
4340   ierr = MatSeqAIJSetPreallocation_SeqAIJ(newMat,0,rowlengths);CHKERRQ(ierr);
4341   a    = (Mat_SeqAIJ*)newMat->data;
4342 
4343   ierr = PetscBinaryRead(fd,a->j,nz,PETSC_INT);CHKERRQ(ierr);
4344 
4345   /* read in nonzero values */
4346   ierr = PetscBinaryRead(fd,a->a,nz,PETSC_SCALAR);CHKERRQ(ierr);
4347 
4348   /* set matrix "i" values */
4349   a->i[0] = 0;
4350   for (i=1; i<= M; i++) {
4351     a->i[i]      = a->i[i-1] + rowlengths[i-1];
4352     a->ilen[i-1] = rowlengths[i-1];
4353   }
4354   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
4355 
4356   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4357   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4358   PetscFunctionReturn(0);
4359 }
4360 
4361 #undef __FUNCT__
4362 #define __FUNCT__ "MatEqual_SeqAIJ"
4363 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4364 {
4365   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4366   PetscErrorCode ierr;
4367 #if defined(PETSC_USE_COMPLEX)
4368   PetscInt k;
4369 #endif
4370 
4371   PetscFunctionBegin;
4372   /* If the  matrix dimensions are not equal,or no of nonzeros */
4373   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4374     *flg = PETSC_FALSE;
4375     PetscFunctionReturn(0);
4376   }
4377 
4378   /* if the a->i are the same */
4379   ierr = PetscMemcmp(a->i,b->i,(A->rmap->n+1)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4380   if (!*flg) PetscFunctionReturn(0);
4381 
4382   /* if a->j are the same */
4383   ierr = PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4384   if (!*flg) PetscFunctionReturn(0);
4385 
4386   /* if a->a are the same */
4387 #if defined(PETSC_USE_COMPLEX)
4388   for (k=0; k<a->nz; k++) {
4389     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4390       *flg = PETSC_FALSE;
4391       PetscFunctionReturn(0);
4392     }
4393   }
4394 #else
4395   ierr = PetscMemcmp(a->a,b->a,(a->nz)*sizeof(PetscScalar),flg);CHKERRQ(ierr);
4396 #endif
4397   PetscFunctionReturn(0);
4398 }
4399 
4400 #undef __FUNCT__
4401 #define __FUNCT__ "MatCreateSeqAIJWithArrays"
4402 /*@
4403      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4404               provided by the user.
4405 
4406       Collective on MPI_Comm
4407 
4408    Input Parameters:
4409 +   comm - must be an MPI communicator of size 1
4410 .   m - number of rows
4411 .   n - number of columns
4412 .   i - row indices
4413 .   j - column indices
4414 -   a - matrix values
4415 
4416    Output Parameter:
4417 .   mat - the matrix
4418 
4419    Level: intermediate
4420 
4421    Notes:
4422        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4423     once the matrix is destroyed and not before
4424 
4425        You cannot set new nonzero locations into this matrix, that will generate an error.
4426 
4427        The i and j indices are 0 based
4428 
4429        The format which is used for the sparse matrix input, is equivalent to a
4430     row-major ordering.. i.e for the following matrix, the input data expected is
4431     as shown:
4432 
4433         1 0 0
4434         2 0 3
4435         4 5 6
4436 
4437         i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4438         j =  {0,0,2,0,1,2}  [size = nz = 6]; values must be sorted for each row
4439         v =  {1,2,3,4,5,6}  [size = nz = 6]
4440 
4441 
4442 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4443 
4444 @*/
4445 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat)
4446 {
4447   PetscErrorCode ierr;
4448   PetscInt       ii;
4449   Mat_SeqAIJ     *aij;
4450 #if defined(PETSC_USE_DEBUG)
4451   PetscInt jj;
4452 #endif
4453 
4454   PetscFunctionBegin;
4455   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4456   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4457   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4458   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4459   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4460   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,0);CHKERRQ(ierr);
4461   aij  = (Mat_SeqAIJ*)(*mat)->data;
4462   ierr = PetscMalloc2(m,&aij->imax,m,&aij->ilen);CHKERRQ(ierr);
4463 
4464   aij->i            = i;
4465   aij->j            = j;
4466   aij->a            = a;
4467   aij->singlemalloc = PETSC_FALSE;
4468   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4469   aij->free_a       = PETSC_FALSE;
4470   aij->free_ij      = PETSC_FALSE;
4471 
4472   for (ii=0; ii<m; ii++) {
4473     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4474 #if defined(PETSC_USE_DEBUG)
4475     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]);
4476     for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4477       if (j[jj] < j[jj-1]) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column entry number %D (actual colum %D) in row %D is not sorted",jj-i[ii],j[jj],ii);
4478       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);
4479     }
4480 #endif
4481   }
4482 #if defined(PETSC_USE_DEBUG)
4483   for (ii=0; ii<aij->i[m]; ii++) {
4484     if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %D index = %D",ii,j[ii]);
4485     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]);
4486   }
4487 #endif
4488 
4489   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4490   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4491   PetscFunctionReturn(0);
4492 }
4493 #undef __FUNCT__
4494 #define __FUNCT__ "MatCreateSeqAIJFromTriple"
4495 /*@C
4496      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4497               provided by the user.
4498 
4499       Collective on MPI_Comm
4500 
4501    Input Parameters:
4502 +   comm - must be an MPI communicator of size 1
4503 .   m   - number of rows
4504 .   n   - number of columns
4505 .   i   - row indices
4506 .   j   - column indices
4507 .   a   - matrix values
4508 .   nz  - number of nonzeros
4509 -   idx - 0 or 1 based
4510 
4511    Output Parameter:
4512 .   mat - the matrix
4513 
4514    Level: intermediate
4515 
4516    Notes:
4517        The i and j indices are 0 based
4518 
4519        The format which is used for the sparse matrix input, is equivalent to a
4520     row-major ordering.. i.e for the following matrix, the input data expected is
4521     as shown:
4522 
4523         1 0 0
4524         2 0 3
4525         4 5 6
4526 
4527         i =  {0,1,1,2,2,2}
4528         j =  {0,0,2,0,1,2}
4529         v =  {1,2,3,4,5,6}
4530 
4531 
4532 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4533 
4534 @*/
4535 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat,PetscInt nz,PetscBool idx)
4536 {
4537   PetscErrorCode ierr;
4538   PetscInt       ii, *nnz, one = 1,row,col;
4539 
4540 
4541   PetscFunctionBegin;
4542   ierr = PetscCalloc1(m,&nnz);CHKERRQ(ierr);
4543   for (ii = 0; ii < nz; ii++) {
4544     nnz[i[ii] - !!idx] += 1;
4545   }
4546   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4547   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4548   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4549   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4550   for (ii = 0; ii < nz; ii++) {
4551     if (idx) {
4552       row = i[ii] - 1;
4553       col = j[ii] - 1;
4554     } else {
4555       row = i[ii];
4556       col = j[ii];
4557     }
4558     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4559   }
4560   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4561   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4562   ierr = PetscFree(nnz);CHKERRQ(ierr);
4563   PetscFunctionReturn(0);
4564 }
4565 
4566 #undef __FUNCT__
4567 #define __FUNCT__ "MatSetColoring_SeqAIJ"
4568 PetscErrorCode MatSetColoring_SeqAIJ(Mat A,ISColoring coloring)
4569 {
4570   PetscErrorCode ierr;
4571   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4572 
4573   PetscFunctionBegin;
4574   if (coloring->ctype == IS_COLORING_GLOBAL) {
4575     ierr        = ISColoringReference(coloring);CHKERRQ(ierr);
4576     a->coloring = coloring;
4577   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
4578     PetscInt        i,*larray;
4579     ISColoring      ocoloring;
4580     ISColoringValue *colors;
4581 
4582     /* set coloring for diagonal portion */
4583     ierr = PetscMalloc1(A->cmap->n,&larray);CHKERRQ(ierr);
4584     for (i=0; i<A->cmap->n; i++) larray[i] = i;
4585     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
4586     ierr = PetscMalloc1(A->cmap->n,&colors);CHKERRQ(ierr);
4587     for (i=0; i<A->cmap->n; i++) colors[i] = coloring->colors[larray[i]];
4588     ierr        = PetscFree(larray);CHKERRQ(ierr);
4589     ierr        = ISColoringCreate(PETSC_COMM_SELF,coloring->n,A->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4590     a->coloring = ocoloring;
4591   }
4592   PetscFunctionReturn(0);
4593 }
4594 
4595 #undef __FUNCT__
4596 #define __FUNCT__ "MatSetValuesAdifor_SeqAIJ"
4597 PetscErrorCode MatSetValuesAdifor_SeqAIJ(Mat A,PetscInt nl,void *advalues)
4598 {
4599   Mat_SeqAIJ      *a      = (Mat_SeqAIJ*)A->data;
4600   PetscInt        m       = A->rmap->n,*ii = a->i,*jj = a->j,nz,i,j;
4601   MatScalar       *v      = a->a;
4602   PetscScalar     *values = (PetscScalar*)advalues;
4603   ISColoringValue *color;
4604 
4605   PetscFunctionBegin;
4606   if (!a->coloring) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Coloring not set for matrix");
4607   color = a->coloring->colors;
4608   /* loop over rows */
4609   for (i=0; i<m; i++) {
4610     nz = ii[i+1] - ii[i];
4611     /* loop over columns putting computed value into matrix */
4612     for (j=0; j<nz; j++) *v++ = values[color[*jj++]];
4613     values += nl; /* jump to next row of derivatives */
4614   }
4615   PetscFunctionReturn(0);
4616 }
4617 
4618 #undef __FUNCT__
4619 #define __FUNCT__ "MatSeqAIJInvalidateDiagonal"
4620 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4621 {
4622   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4623   PetscErrorCode ierr;
4624 
4625   PetscFunctionBegin;
4626   a->idiagvalid  = PETSC_FALSE;
4627   a->ibdiagvalid = PETSC_FALSE;
4628 
4629   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4630   PetscFunctionReturn(0);
4631 }
4632 
4633 /*
4634     Special version for direct calls from Fortran
4635 */
4636 #include <petsc-private/fortranimpl.h>
4637 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4638 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
4639 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4640 #define matsetvaluesseqaij_ matsetvaluesseqaij
4641 #endif
4642 
4643 /* Change these macros so can be used in void function */
4644 #undef CHKERRQ
4645 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
4646 #undef SETERRQ2
4647 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4648 #undef SETERRQ3
4649 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4650 
4651 #undef __FUNCT__
4652 #define __FUNCT__ "matsetvaluesseqaij_"
4653 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)
4654 {
4655   Mat            A  = *AA;
4656   PetscInt       m  = *mm, n = *nn;
4657   InsertMode     is = *isis;
4658   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4659   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
4660   PetscInt       *imax,*ai,*ailen;
4661   PetscErrorCode ierr;
4662   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
4663   MatScalar      *ap,value,*aa;
4664   PetscBool      ignorezeroentries = a->ignorezeroentries;
4665   PetscBool      roworiented       = a->roworiented;
4666 
4667   PetscFunctionBegin;
4668   MatCheckPreallocated(A,1);
4669   imax  = a->imax;
4670   ai    = a->i;
4671   ailen = a->ilen;
4672   aj    = a->j;
4673   aa    = a->a;
4674 
4675   for (k=0; k<m; k++) { /* loop over added rows */
4676     row = im[k];
4677     if (row < 0) continue;
4678 #if defined(PETSC_USE_DEBUG)
4679     if (row >= A->rmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
4680 #endif
4681     rp   = aj + ai[row]; ap = aa + ai[row];
4682     rmax = imax[row]; nrow = ailen[row];
4683     low  = 0;
4684     high = nrow;
4685     for (l=0; l<n; l++) { /* loop over added columns */
4686       if (in[l] < 0) continue;
4687 #if defined(PETSC_USE_DEBUG)
4688       if (in[l] >= A->cmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
4689 #endif
4690       col = in[l];
4691       if (roworiented) value = v[l + k*n];
4692       else value = v[k + l*m];
4693 
4694       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
4695 
4696       if (col <= lastcol) low = 0;
4697       else high = nrow;
4698       lastcol = col;
4699       while (high-low > 5) {
4700         t = (low+high)/2;
4701         if (rp[t] > col) high = t;
4702         else             low  = t;
4703       }
4704       for (i=low; i<high; i++) {
4705         if (rp[i] > col) break;
4706         if (rp[i] == col) {
4707           if (is == ADD_VALUES) ap[i] += value;
4708           else                  ap[i] = value;
4709           goto noinsert;
4710         }
4711       }
4712       if (value == 0.0 && ignorezeroentries) goto noinsert;
4713       if (nonew == 1) goto noinsert;
4714       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
4715       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
4716       N = nrow++ - 1; a->nz++; high++;
4717       /* shift up all the later entries in this row */
4718       for (ii=N; ii>=i; ii--) {
4719         rp[ii+1] = rp[ii];
4720         ap[ii+1] = ap[ii];
4721       }
4722       rp[i] = col;
4723       ap[i] = value;
4724       A->nonzerostate++;
4725 noinsert:;
4726       low = i + 1;
4727     }
4728     ailen[row] = nrow;
4729   }
4730   PetscFunctionReturnVoid();
4731 }
4732 
4733 
4734