xref: /petsc/src/mat/impls/aij/seq/aij.c (revision bbd3f3368baff017a6ea7962313571cf23b2b4ec)
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       for (k=kstart; k<kend; k++) {
2414         if (aj[k] >= first) {
2415           starts[i] = k;
2416           break;
2417         }
2418       }
2419       sum = 0;
2420       while (k < kend) {
2421         if (aj[k++] >= first+ncols) break;
2422         sum++;
2423       }
2424       lens[i] = sum;
2425     }
2426     /* create submatrix */
2427     if (scall == MAT_REUSE_MATRIX) {
2428       PetscInt n_cols,n_rows;
2429       ierr = MatGetSize(*B,&n_rows,&n_cols);CHKERRQ(ierr);
2430       if (n_rows != nrows || n_cols != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
2431       ierr = MatZeroEntries(*B);CHKERRQ(ierr);
2432       C    = *B;
2433     } else {
2434       PetscInt rbs,cbs;
2435       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2436       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2437       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2438       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2439       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2440       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2441       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2442     }
2443     c = (Mat_SeqAIJ*)C->data;
2444 
2445     /* loop over rows inserting into submatrix */
2446     a_new = c->a;
2447     j_new = c->j;
2448     i_new = c->i;
2449 
2450     for (i=0; i<nrows; i++) {
2451       ii    = starts[i];
2452       lensi = lens[i];
2453       for (k=0; k<lensi; k++) {
2454         *j_new++ = aj[ii+k] - first;
2455       }
2456       ierr       = PetscMemcpy(a_new,a->a + starts[i],lensi*sizeof(PetscScalar));CHKERRQ(ierr);
2457       a_new     += lensi;
2458       i_new[i+1] = i_new[i] + lensi;
2459       c->ilen[i] = lensi;
2460     }
2461     ierr = PetscFree2(lens,starts);CHKERRQ(ierr);
2462   } else {
2463     ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
2464     ierr = PetscCalloc1(oldcols,&smap);CHKERRQ(ierr);
2465     ierr = PetscMalloc1((1+nrows),&lens);CHKERRQ(ierr);
2466     for (i=0; i<ncols; i++) {
2467 #if defined(PETSC_USE_DEBUG)
2468       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);
2469 #endif
2470       smap[icol[i]] = i+1;
2471     }
2472 
2473     /* determine lens of each row */
2474     for (i=0; i<nrows; i++) {
2475       kstart  = ai[irow[i]];
2476       kend    = kstart + a->ilen[irow[i]];
2477       lens[i] = 0;
2478       for (k=kstart; k<kend; k++) {
2479         if (smap[aj[k]]) {
2480           lens[i]++;
2481         }
2482       }
2483     }
2484     /* Create and fill new matrix */
2485     if (scall == MAT_REUSE_MATRIX) {
2486       PetscBool equal;
2487 
2488       c = (Mat_SeqAIJ*)((*B)->data);
2489       if ((*B)->rmap->n  != nrows || (*B)->cmap->n != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
2490       ierr = PetscMemcmp(c->ilen,lens,(*B)->rmap->n*sizeof(PetscInt),&equal);CHKERRQ(ierr);
2491       if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
2492       ierr = PetscMemzero(c->ilen,(*B)->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
2493       C    = *B;
2494     } else {
2495       PetscInt rbs,cbs;
2496       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2497       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2498       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2499       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2500       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2501       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2502       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2503     }
2504     c = (Mat_SeqAIJ*)(C->data);
2505     for (i=0; i<nrows; i++) {
2506       row      = irow[i];
2507       kstart   = ai[row];
2508       kend     = kstart + a->ilen[row];
2509       mat_i    = c->i[i];
2510       mat_j    = c->j + mat_i;
2511       mat_a    = c->a + mat_i;
2512       mat_ilen = c->ilen + i;
2513       for (k=kstart; k<kend; k++) {
2514         if ((tcol=smap[a->j[k]])) {
2515           *mat_j++ = tcol - 1;
2516           *mat_a++ = a->a[k];
2517           (*mat_ilen)++;
2518 
2519         }
2520       }
2521     }
2522     /* Free work space */
2523     ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
2524     ierr = PetscFree(smap);CHKERRQ(ierr);
2525     ierr = PetscFree(lens);CHKERRQ(ierr);
2526   }
2527   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2528   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2529 
2530   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
2531   *B   = C;
2532   PetscFunctionReturn(0);
2533 }
2534 
2535 #undef __FUNCT__
2536 #define __FUNCT__ "MatGetMultiProcBlock_SeqAIJ"
2537 PetscErrorCode  MatGetMultiProcBlock_SeqAIJ(Mat mat,MPI_Comm subComm,MatReuse scall,Mat *subMat)
2538 {
2539   PetscErrorCode ierr;
2540   Mat            B;
2541 
2542   PetscFunctionBegin;
2543   if (scall == MAT_INITIAL_MATRIX) {
2544     ierr    = MatCreate(subComm,&B);CHKERRQ(ierr);
2545     ierr    = MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->n,mat->cmap->n);CHKERRQ(ierr);
2546     ierr    = MatSetBlockSizesFromMats(B,mat,mat);CHKERRQ(ierr);
2547     ierr    = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
2548     ierr    = MatDuplicateNoCreate_SeqAIJ(B,mat,MAT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
2549     *subMat = B;
2550   } else {
2551     ierr = MatCopy_SeqAIJ(mat,*subMat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2552   }
2553   PetscFunctionReturn(0);
2554 }
2555 
2556 #undef __FUNCT__
2557 #define __FUNCT__ "MatILUFactor_SeqAIJ"
2558 PetscErrorCode MatILUFactor_SeqAIJ(Mat inA,IS row,IS col,const MatFactorInfo *info)
2559 {
2560   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)inA->data;
2561   PetscErrorCode ierr;
2562   Mat            outA;
2563   PetscBool      row_identity,col_identity;
2564 
2565   PetscFunctionBegin;
2566   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels=0 supported for in-place ilu");
2567 
2568   ierr = ISIdentity(row,&row_identity);CHKERRQ(ierr);
2569   ierr = ISIdentity(col,&col_identity);CHKERRQ(ierr);
2570 
2571   outA             = inA;
2572   outA->factortype = MAT_FACTOR_LU;
2573 
2574   ierr = PetscObjectReference((PetscObject)row);CHKERRQ(ierr);
2575   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
2576 
2577   a->row = row;
2578 
2579   ierr = PetscObjectReference((PetscObject)col);CHKERRQ(ierr);
2580   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
2581 
2582   a->col = col;
2583 
2584   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
2585   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
2586   ierr = ISInvertPermutation(col,PETSC_DECIDE,&a->icol);CHKERRQ(ierr);
2587   ierr = PetscLogObjectParent((PetscObject)inA,(PetscObject)a->icol);CHKERRQ(ierr);
2588 
2589   if (!a->solve_work) { /* this matrix may have been factored before */
2590     ierr = PetscMalloc1((inA->rmap->n+1),&a->solve_work);CHKERRQ(ierr);
2591     ierr = PetscLogObjectMemory((PetscObject)inA, (inA->rmap->n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2592   }
2593 
2594   ierr = MatMarkDiagonal_SeqAIJ(inA);CHKERRQ(ierr);
2595   if (row_identity && col_identity) {
2596     ierr = MatLUFactorNumeric_SeqAIJ_inplace(outA,inA,info);CHKERRQ(ierr);
2597   } else {
2598     ierr = MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA,inA,info);CHKERRQ(ierr);
2599   }
2600   PetscFunctionReturn(0);
2601 }
2602 
2603 #undef __FUNCT__
2604 #define __FUNCT__ "MatScale_SeqAIJ"
2605 PetscErrorCode MatScale_SeqAIJ(Mat inA,PetscScalar alpha)
2606 {
2607   Mat_SeqAIJ     *a     = (Mat_SeqAIJ*)inA->data;
2608   PetscScalar    oalpha = alpha;
2609   PetscErrorCode ierr;
2610   PetscBLASInt   one = 1,bnz;
2611 
2612   PetscFunctionBegin;
2613   ierr = PetscBLASIntCast(a->nz,&bnz);CHKERRQ(ierr);
2614   PetscStackCallBLAS("BLASscal",BLASscal_(&bnz,&oalpha,a->a,&one));
2615   ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2616   ierr = MatSeqAIJInvalidateDiagonal(inA);CHKERRQ(ierr);
2617   PetscFunctionReturn(0);
2618 }
2619 
2620 #undef __FUNCT__
2621 #define __FUNCT__ "MatGetSubMatrices_SeqAIJ"
2622 PetscErrorCode MatGetSubMatrices_SeqAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
2623 {
2624   PetscErrorCode ierr;
2625   PetscInt       i;
2626 
2627   PetscFunctionBegin;
2628   if (scall == MAT_INITIAL_MATRIX) {
2629     ierr = PetscMalloc1((n+1),B);CHKERRQ(ierr);
2630   }
2631 
2632   for (i=0; i<n; i++) {
2633     ierr = MatGetSubMatrix_SeqAIJ(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]);CHKERRQ(ierr);
2634   }
2635   PetscFunctionReturn(0);
2636 }
2637 
2638 #undef __FUNCT__
2639 #define __FUNCT__ "MatIncreaseOverlap_SeqAIJ"
2640 PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
2641 {
2642   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2643   PetscErrorCode ierr;
2644   PetscInt       row,i,j,k,l,m,n,*nidx,isz,val;
2645   const PetscInt *idx;
2646   PetscInt       start,end,*ai,*aj;
2647   PetscBT        table;
2648 
2649   PetscFunctionBegin;
2650   m  = A->rmap->n;
2651   ai = a->i;
2652   aj = a->j;
2653 
2654   if (ov < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"illegal negative overlap value used");
2655 
2656   ierr = PetscMalloc1((m+1),&nidx);CHKERRQ(ierr);
2657   ierr = PetscBTCreate(m,&table);CHKERRQ(ierr);
2658 
2659   for (i=0; i<is_max; i++) {
2660     /* Initialize the two local arrays */
2661     isz  = 0;
2662     ierr = PetscBTMemzero(m,table);CHKERRQ(ierr);
2663 
2664     /* Extract the indices, assume there can be duplicate entries */
2665     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
2666     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
2667 
2668     /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2669     for (j=0; j<n; ++j) {
2670       if (!PetscBTLookupSet(table,idx[j])) nidx[isz++] = idx[j];
2671     }
2672     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
2673     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
2674 
2675     k = 0;
2676     for (j=0; j<ov; j++) { /* for each overlap */
2677       n = isz;
2678       for (; k<n; k++) { /* do only those rows in nidx[k], which are not done yet */
2679         row   = nidx[k];
2680         start = ai[row];
2681         end   = ai[row+1];
2682         for (l = start; l<end; l++) {
2683           val = aj[l];
2684           if (!PetscBTLookupSet(table,val)) nidx[isz++] = val;
2685         }
2686       }
2687     }
2688     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz,nidx,PETSC_COPY_VALUES,(is+i));CHKERRQ(ierr);
2689   }
2690   ierr = PetscBTDestroy(&table);CHKERRQ(ierr);
2691   ierr = PetscFree(nidx);CHKERRQ(ierr);
2692   PetscFunctionReturn(0);
2693 }
2694 
2695 /* -------------------------------------------------------------- */
2696 #undef __FUNCT__
2697 #define __FUNCT__ "MatPermute_SeqAIJ"
2698 PetscErrorCode MatPermute_SeqAIJ(Mat A,IS rowp,IS colp,Mat *B)
2699 {
2700   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2701   PetscErrorCode ierr;
2702   PetscInt       i,nz = 0,m = A->rmap->n,n = A->cmap->n;
2703   const PetscInt *row,*col;
2704   PetscInt       *cnew,j,*lens;
2705   IS             icolp,irowp;
2706   PetscInt       *cwork = NULL;
2707   PetscScalar    *vwork = NULL;
2708 
2709   PetscFunctionBegin;
2710   ierr = ISInvertPermutation(rowp,PETSC_DECIDE,&irowp);CHKERRQ(ierr);
2711   ierr = ISGetIndices(irowp,&row);CHKERRQ(ierr);
2712   ierr = ISInvertPermutation(colp,PETSC_DECIDE,&icolp);CHKERRQ(ierr);
2713   ierr = ISGetIndices(icolp,&col);CHKERRQ(ierr);
2714 
2715   /* determine lengths of permuted rows */
2716   ierr = PetscMalloc1((m+1),&lens);CHKERRQ(ierr);
2717   for (i=0; i<m; i++) lens[row[i]] = a->i[i+1] - a->i[i];
2718   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
2719   ierr = MatSetSizes(*B,m,n,m,n);CHKERRQ(ierr);
2720   ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
2721   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2722   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*B,0,lens);CHKERRQ(ierr);
2723   ierr = PetscFree(lens);CHKERRQ(ierr);
2724 
2725   ierr = PetscMalloc1(n,&cnew);CHKERRQ(ierr);
2726   for (i=0; i<m; i++) {
2727     ierr = MatGetRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2728     for (j=0; j<nz; j++) cnew[j] = col[cwork[j]];
2729     ierr = MatSetValues_SeqAIJ(*B,1,&row[i],nz,cnew,vwork,INSERT_VALUES);CHKERRQ(ierr);
2730     ierr = MatRestoreRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2731   }
2732   ierr = PetscFree(cnew);CHKERRQ(ierr);
2733 
2734   (*B)->assembled = PETSC_FALSE;
2735 
2736   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2737   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2738   ierr = ISRestoreIndices(irowp,&row);CHKERRQ(ierr);
2739   ierr = ISRestoreIndices(icolp,&col);CHKERRQ(ierr);
2740   ierr = ISDestroy(&irowp);CHKERRQ(ierr);
2741   ierr = ISDestroy(&icolp);CHKERRQ(ierr);
2742   PetscFunctionReturn(0);
2743 }
2744 
2745 #undef __FUNCT__
2746 #define __FUNCT__ "MatCopy_SeqAIJ"
2747 PetscErrorCode MatCopy_SeqAIJ(Mat A,Mat B,MatStructure str)
2748 {
2749   PetscErrorCode ierr;
2750 
2751   PetscFunctionBegin;
2752   /* If the two matrices have the same copy implementation, use fast copy. */
2753   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
2754     Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2755     Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data;
2756 
2757     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");
2758     ierr = PetscMemcpy(b->a,a->a,(a->i[A->rmap->n])*sizeof(PetscScalar));CHKERRQ(ierr);
2759   } else {
2760     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2761   }
2762   PetscFunctionReturn(0);
2763 }
2764 
2765 #undef __FUNCT__
2766 #define __FUNCT__ "MatSetUp_SeqAIJ"
2767 PetscErrorCode MatSetUp_SeqAIJ(Mat A)
2768 {
2769   PetscErrorCode ierr;
2770 
2771   PetscFunctionBegin;
2772   ierr =  MatSeqAIJSetPreallocation_SeqAIJ(A,PETSC_DEFAULT,0);CHKERRQ(ierr);
2773   PetscFunctionReturn(0);
2774 }
2775 
2776 #undef __FUNCT__
2777 #define __FUNCT__ "MatSeqAIJGetArray_SeqAIJ"
2778 PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A,PetscScalar *array[])
2779 {
2780   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2781 
2782   PetscFunctionBegin;
2783   *array = a->a;
2784   PetscFunctionReturn(0);
2785 }
2786 
2787 #undef __FUNCT__
2788 #define __FUNCT__ "MatSeqAIJRestoreArray_SeqAIJ"
2789 PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A,PetscScalar *array[])
2790 {
2791   PetscFunctionBegin;
2792   PetscFunctionReturn(0);
2793 }
2794 
2795 /*
2796    Computes the number of nonzeros per row needed for preallocation when X and Y
2797    have different nonzero structure.
2798 */
2799 #undef __FUNCT__
2800 #define __FUNCT__ "MatAXPYGetPreallocation_SeqAIJ"
2801 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
2802 {
2803   PetscInt       i,m=Y->rmap->N;
2804   Mat_SeqAIJ     *x  = (Mat_SeqAIJ*)X->data;
2805   Mat_SeqAIJ     *y  = (Mat_SeqAIJ*)Y->data;
2806   const PetscInt *xi = x->i,*yi = y->i;
2807 
2808   PetscFunctionBegin;
2809   /* Set the number of nonzeros in the new matrix */
2810   for (i=0; i<m; i++) {
2811     PetscInt       j,k,nzx = xi[i+1] - xi[i],nzy = yi[i+1] - yi[i];
2812     const PetscInt *xj = x->j+xi[i],*yj = y->j+yi[i];
2813     nnz[i] = 0;
2814     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2815       for (; k<nzy && yj[k]<xj[j]; k++) nnz[i]++; /* Catch up to X */
2816       if (k<nzy && yj[k]==xj[j]) k++;             /* Skip duplicate */
2817       nnz[i]++;
2818     }
2819     for (; k<nzy; k++) nnz[i]++;
2820   }
2821   PetscFunctionReturn(0);
2822 }
2823 
2824 #undef __FUNCT__
2825 #define __FUNCT__ "MatAXPY_SeqAIJ"
2826 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2827 {
2828   PetscErrorCode ierr;
2829   PetscInt       i;
2830   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
2831   PetscBLASInt   one=1,bnz;
2832 
2833   PetscFunctionBegin;
2834   ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2835   if (str == SAME_NONZERO_PATTERN) {
2836     PetscScalar alpha = a;
2837     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2838     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
2839     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2840   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2841     if (y->xtoy && y->XtoY != X) {
2842       ierr = PetscFree(y->xtoy);CHKERRQ(ierr);
2843       ierr = MatDestroy(&y->XtoY);CHKERRQ(ierr);
2844     }
2845     if (!y->xtoy) { /* get xtoy */
2846       ierr    = MatAXPYGetxtoy_Private(X->rmap->n,x->i,x->j,NULL, y->i,y->j,NULL, &y->xtoy);CHKERRQ(ierr);
2847       y->XtoY = X;
2848       ierr    = PetscObjectReference((PetscObject)X);CHKERRQ(ierr);
2849     }
2850     for (i=0; i<x->nz; i++) y->a[y->xtoy[i]] += a*(x->a[i]);
2851     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2852     ierr = PetscInfo3(Y,"ratio of nnz(X)/nnz(Y): %D/%D = %g\n",x->nz,y->nz,(double)((PetscReal)(x->nz)/(y->nz+1)));CHKERRQ(ierr);
2853   } else {
2854     Mat      B;
2855     PetscInt *nnz;
2856     ierr = PetscMalloc1(Y->rmap->N,&nnz);CHKERRQ(ierr);
2857     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2858     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2859     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2860     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2861     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
2862     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
2863     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
2864     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2865     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
2866     ierr = PetscFree(nnz);CHKERRQ(ierr);
2867   }
2868   PetscFunctionReturn(0);
2869 }
2870 
2871 #undef __FUNCT__
2872 #define __FUNCT__ "MatConjugate_SeqAIJ"
2873 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
2874 {
2875 #if defined(PETSC_USE_COMPLEX)
2876   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
2877   PetscInt    i,nz;
2878   PetscScalar *a;
2879 
2880   PetscFunctionBegin;
2881   nz = aij->nz;
2882   a  = aij->a;
2883   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
2884 #else
2885   PetscFunctionBegin;
2886 #endif
2887   PetscFunctionReturn(0);
2888 }
2889 
2890 #undef __FUNCT__
2891 #define __FUNCT__ "MatGetRowMaxAbs_SeqAIJ"
2892 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2893 {
2894   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2895   PetscErrorCode ierr;
2896   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2897   PetscReal      atmp;
2898   PetscScalar    *x;
2899   MatScalar      *aa;
2900 
2901   PetscFunctionBegin;
2902   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2903   aa = a->a;
2904   ai = a->i;
2905   aj = a->j;
2906 
2907   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2908   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2909   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2910   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2911   for (i=0; i<m; i++) {
2912     ncols = ai[1] - ai[0]; ai++;
2913     x[i]  = 0.0;
2914     for (j=0; j<ncols; j++) {
2915       atmp = PetscAbsScalar(*aa);
2916       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
2917       aa++; aj++;
2918     }
2919   }
2920   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2921   PetscFunctionReturn(0);
2922 }
2923 
2924 #undef __FUNCT__
2925 #define __FUNCT__ "MatGetRowMax_SeqAIJ"
2926 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2927 {
2928   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2929   PetscErrorCode ierr;
2930   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2931   PetscScalar    *x;
2932   MatScalar      *aa;
2933 
2934   PetscFunctionBegin;
2935   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2936   aa = a->a;
2937   ai = a->i;
2938   aj = a->j;
2939 
2940   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2941   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2942   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2943   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2944   for (i=0; i<m; i++) {
2945     ncols = ai[1] - ai[0]; ai++;
2946     if (ncols == A->cmap->n) { /* row is dense */
2947       x[i] = *aa; if (idx) idx[i] = 0;
2948     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
2949       x[i] = 0.0;
2950       if (idx) {
2951         idx[i] = 0; /* in case ncols is zero */
2952         for (j=0;j<ncols;j++) { /* find first implicit 0.0 in the row */
2953           if (aj[j] > j) {
2954             idx[i] = j;
2955             break;
2956           }
2957         }
2958       }
2959     }
2960     for (j=0; j<ncols; j++) {
2961       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
2962       aa++; aj++;
2963     }
2964   }
2965   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2966   PetscFunctionReturn(0);
2967 }
2968 
2969 #undef __FUNCT__
2970 #define __FUNCT__ "MatGetRowMinAbs_SeqAIJ"
2971 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2972 {
2973   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2974   PetscErrorCode ierr;
2975   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2976   PetscReal      atmp;
2977   PetscScalar    *x;
2978   MatScalar      *aa;
2979 
2980   PetscFunctionBegin;
2981   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2982   aa = a->a;
2983   ai = a->i;
2984   aj = a->j;
2985 
2986   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2987   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2988   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2989   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);
2990   for (i=0; i<m; i++) {
2991     ncols = ai[1] - ai[0]; ai++;
2992     if (ncols) {
2993       /* Get first nonzero */
2994       for (j = 0; j < ncols; j++) {
2995         atmp = PetscAbsScalar(aa[j]);
2996         if (atmp > 1.0e-12) {
2997           x[i] = atmp;
2998           if (idx) idx[i] = aj[j];
2999           break;
3000         }
3001       }
3002       if (j == ncols) {x[i] = PetscAbsScalar(*aa); if (idx) idx[i] = *aj;}
3003     } else {
3004       x[i] = 0.0; if (idx) idx[i] = 0;
3005     }
3006     for (j = 0; j < ncols; j++) {
3007       atmp = PetscAbsScalar(*aa);
3008       if (atmp > 1.0e-12 && PetscAbsScalar(x[i]) > atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3009       aa++; aj++;
3010     }
3011   }
3012   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3013   PetscFunctionReturn(0);
3014 }
3015 
3016 #undef __FUNCT__
3017 #define __FUNCT__ "MatGetRowMin_SeqAIJ"
3018 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3019 {
3020   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3021   PetscErrorCode ierr;
3022   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3023   PetscScalar    *x;
3024   MatScalar      *aa;
3025 
3026   PetscFunctionBegin;
3027   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3028   aa = a->a;
3029   ai = a->i;
3030   aj = a->j;
3031 
3032   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3033   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3034   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3035   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3036   for (i=0; i<m; i++) {
3037     ncols = ai[1] - ai[0]; ai++;
3038     if (ncols == A->cmap->n) { /* row is dense */
3039       x[i] = *aa; if (idx) idx[i] = 0;
3040     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3041       x[i] = 0.0;
3042       if (idx) {   /* find first implicit 0.0 in the row */
3043         idx[i] = 0; /* in case ncols is zero */
3044         for (j=0; j<ncols; j++) {
3045           if (aj[j] > j) {
3046             idx[i] = j;
3047             break;
3048           }
3049         }
3050       }
3051     }
3052     for (j=0; j<ncols; j++) {
3053       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3054       aa++; aj++;
3055     }
3056   }
3057   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3058   PetscFunctionReturn(0);
3059 }
3060 
3061 #include <petscblaslapack.h>
3062 #include <petsc-private/kernels/blockinvert.h>
3063 
3064 #undef __FUNCT__
3065 #define __FUNCT__ "MatInvertBlockDiagonal_SeqAIJ"
3066 PetscErrorCode  MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3067 {
3068   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
3069   PetscErrorCode ierr;
3070   PetscInt       i,bs = PetscAbs(A->rmap->bs),mbs = A->rmap->n/bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3071   MatScalar      *diag,work[25],*v_work;
3072   PetscReal      shift = 0.0;
3073 
3074   PetscFunctionBegin;
3075   if (a->ibdiagvalid) {
3076     if (values) *values = a->ibdiag;
3077     PetscFunctionReturn(0);
3078   }
3079   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3080   if (!a->ibdiag) {
3081     ierr = PetscMalloc1(bs2*mbs,&a->ibdiag);CHKERRQ(ierr);
3082     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3083   }
3084   diag = a->ibdiag;
3085   if (values) *values = a->ibdiag;
3086   /* factor and invert each block */
3087   switch (bs) {
3088   case 1:
3089     for (i=0; i<mbs; i++) {
3090       ierr    = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3091       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3092     }
3093     break;
3094   case 2:
3095     for (i=0; i<mbs; i++) {
3096       ij[0] = 2*i; ij[1] = 2*i + 1;
3097       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3098       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift);CHKERRQ(ierr);
3099       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
3100       diag += 4;
3101     }
3102     break;
3103   case 3:
3104     for (i=0; i<mbs; i++) {
3105       ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
3106       ierr  = MatGetValues(A,3,ij,3,ij,diag);CHKERRQ(ierr);
3107       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr);
3108       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3109       diag += 9;
3110     }
3111     break;
3112   case 4:
3113     for (i=0; i<mbs; i++) {
3114       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3115       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3116       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift);CHKERRQ(ierr);
3117       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3118       diag += 16;
3119     }
3120     break;
3121   case 5:
3122     for (i=0; i<mbs; i++) {
3123       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3124       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3125       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift);CHKERRQ(ierr);
3126       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3127       diag += 25;
3128     }
3129     break;
3130   case 6:
3131     for (i=0; i<mbs; i++) {
3132       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;
3133       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3134       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift);CHKERRQ(ierr);
3135       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3136       diag += 36;
3137     }
3138     break;
3139   case 7:
3140     for (i=0; i<mbs; i++) {
3141       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;
3142       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3143       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift);CHKERRQ(ierr);
3144       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3145       diag += 49;
3146     }
3147     break;
3148   default:
3149     ierr = PetscMalloc3(bs,&v_work,bs,&v_pivots,bs,&IJ);CHKERRQ(ierr);
3150     for (i=0; i<mbs; i++) {
3151       for (j=0; j<bs; j++) {
3152         IJ[j] = bs*i + j;
3153       }
3154       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3155       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work);CHKERRQ(ierr);
3156       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3157       diag += bs2;
3158     }
3159     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3160   }
3161   a->ibdiagvalid = PETSC_TRUE;
3162   PetscFunctionReturn(0);
3163 }
3164 
3165 #undef __FUNCT__
3166 #define __FUNCT__ "MatSetRandom_SeqAIJ"
3167 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3168 {
3169   PetscErrorCode ierr;
3170   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3171   PetscScalar    a;
3172   PetscInt       m,n,i,j,col;
3173 
3174   PetscFunctionBegin;
3175   if (!x->assembled) {
3176     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3177     for (i=0; i<m; i++) {
3178       for (j=0; j<aij->imax[i]; j++) {
3179         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3180         col  = (PetscInt)(n*PetscRealPart(a));
3181         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3182       }
3183     }
3184   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet coded");
3185   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3186   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3187   PetscFunctionReturn(0);
3188 }
3189 
3190 /* -------------------------------------------------------------------*/
3191 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3192                                         MatGetRow_SeqAIJ,
3193                                         MatRestoreRow_SeqAIJ,
3194                                         MatMult_SeqAIJ,
3195                                 /*  4*/ MatMultAdd_SeqAIJ,
3196                                         MatMultTranspose_SeqAIJ,
3197                                         MatMultTransposeAdd_SeqAIJ,
3198                                         0,
3199                                         0,
3200                                         0,
3201                                 /* 10*/ 0,
3202                                         MatLUFactor_SeqAIJ,
3203                                         0,
3204                                         MatSOR_SeqAIJ,
3205                                         MatTranspose_SeqAIJ,
3206                                 /*1 5*/ MatGetInfo_SeqAIJ,
3207                                         MatEqual_SeqAIJ,
3208                                         MatGetDiagonal_SeqAIJ,
3209                                         MatDiagonalScale_SeqAIJ,
3210                                         MatNorm_SeqAIJ,
3211                                 /* 20*/ 0,
3212                                         MatAssemblyEnd_SeqAIJ,
3213                                         MatSetOption_SeqAIJ,
3214                                         MatZeroEntries_SeqAIJ,
3215                                 /* 24*/ MatZeroRows_SeqAIJ,
3216                                         0,
3217                                         0,
3218                                         0,
3219                                         0,
3220                                 /* 29*/ MatSetUp_SeqAIJ,
3221                                         0,
3222                                         0,
3223                                         0,
3224                                         0,
3225                                 /* 34*/ MatDuplicate_SeqAIJ,
3226                                         0,
3227                                         0,
3228                                         MatILUFactor_SeqAIJ,
3229                                         0,
3230                                 /* 39*/ MatAXPY_SeqAIJ,
3231                                         MatGetSubMatrices_SeqAIJ,
3232                                         MatIncreaseOverlap_SeqAIJ,
3233                                         MatGetValues_SeqAIJ,
3234                                         MatCopy_SeqAIJ,
3235                                 /* 44*/ MatGetRowMax_SeqAIJ,
3236                                         MatScale_SeqAIJ,
3237                                         0,
3238                                         MatDiagonalSet_SeqAIJ,
3239                                         MatZeroRowsColumns_SeqAIJ,
3240                                 /* 49*/ MatSetRandom_SeqAIJ,
3241                                         MatGetRowIJ_SeqAIJ,
3242                                         MatRestoreRowIJ_SeqAIJ,
3243                                         MatGetColumnIJ_SeqAIJ,
3244                                         MatRestoreColumnIJ_SeqAIJ,
3245                                 /* 54*/ MatFDColoringCreate_SeqXAIJ,
3246                                         0,
3247                                         0,
3248                                         MatPermute_SeqAIJ,
3249                                         0,
3250                                 /* 59*/ 0,
3251                                         MatDestroy_SeqAIJ,
3252                                         MatView_SeqAIJ,
3253                                         0,
3254                                         MatMatMatMult_SeqAIJ_SeqAIJ_SeqAIJ,
3255                                 /* 64*/ MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ,
3256                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3257                                         0,
3258                                         0,
3259                                         0,
3260                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3261                                         MatGetRowMinAbs_SeqAIJ,
3262                                         0,
3263                                         MatSetColoring_SeqAIJ,
3264                                         0,
3265                                 /* 74*/ MatSetValuesAdifor_SeqAIJ,
3266                                         MatFDColoringApply_AIJ,
3267                                         0,
3268                                         0,
3269                                         0,
3270                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3271                                         0,
3272                                         0,
3273                                         0,
3274                                         MatLoad_SeqAIJ,
3275                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3276                                         MatIsHermitian_SeqAIJ,
3277                                         0,
3278                                         0,
3279                                         0,
3280                                 /* 89*/ MatMatMult_SeqAIJ_SeqAIJ,
3281                                         MatMatMultSymbolic_SeqAIJ_SeqAIJ,
3282                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3283                                         MatPtAP_SeqAIJ_SeqAIJ,
3284                                         MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy,
3285                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ,
3286                                         MatMatTransposeMult_SeqAIJ_SeqAIJ,
3287                                         MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ,
3288                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3289                                         0,
3290                                 /* 99*/ 0,
3291                                         0,
3292                                         0,
3293                                         MatConjugate_SeqAIJ,
3294                                         0,
3295                                 /*104*/ MatSetValuesRow_SeqAIJ,
3296                                         MatRealPart_SeqAIJ,
3297                                         MatImaginaryPart_SeqAIJ,
3298                                         0,
3299                                         0,
3300                                 /*109*/ MatMatSolve_SeqAIJ,
3301                                         0,
3302                                         MatGetRowMin_SeqAIJ,
3303                                         0,
3304                                         MatMissingDiagonal_SeqAIJ,
3305                                 /*114*/ 0,
3306                                         0,
3307                                         0,
3308                                         0,
3309                                         0,
3310                                 /*119*/ 0,
3311                                         0,
3312                                         0,
3313                                         0,
3314                                         MatGetMultiProcBlock_SeqAIJ,
3315                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3316                                         MatGetColumnNorms_SeqAIJ,
3317                                         MatInvertBlockDiagonal_SeqAIJ,
3318                                         0,
3319                                         0,
3320                                 /*129*/ 0,
3321                                         MatTransposeMatMult_SeqAIJ_SeqAIJ,
3322                                         MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ,
3323                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3324                                         MatTransposeColoringCreate_SeqAIJ,
3325                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3326                                         MatTransColoringApplyDenToSp_SeqAIJ,
3327                                         MatRARt_SeqAIJ_SeqAIJ,
3328                                         MatRARtSymbolic_SeqAIJ_SeqAIJ,
3329                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3330                                  /*139*/0,
3331                                         0,
3332                                         0,
3333                                         MatFDColoringSetUp_SeqXAIJ,
3334                                         MatFindOffBlockDiagonalEntries_SeqAIJ
3335 };
3336 
3337 #undef __FUNCT__
3338 #define __FUNCT__ "MatSeqAIJSetColumnIndices_SeqAIJ"
3339 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3340 {
3341   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3342   PetscInt   i,nz,n;
3343 
3344   PetscFunctionBegin;
3345   nz = aij->maxnz;
3346   n  = mat->rmap->n;
3347   for (i=0; i<nz; i++) {
3348     aij->j[i] = indices[i];
3349   }
3350   aij->nz = nz;
3351   for (i=0; i<n; i++) {
3352     aij->ilen[i] = aij->imax[i];
3353   }
3354   PetscFunctionReturn(0);
3355 }
3356 
3357 #undef __FUNCT__
3358 #define __FUNCT__ "MatSeqAIJSetColumnIndices"
3359 /*@
3360     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3361        in the matrix.
3362 
3363   Input Parameters:
3364 +  mat - the SeqAIJ matrix
3365 -  indices - the column indices
3366 
3367   Level: advanced
3368 
3369   Notes:
3370     This can be called if you have precomputed the nonzero structure of the
3371   matrix and want to provide it to the matrix object to improve the performance
3372   of the MatSetValues() operation.
3373 
3374     You MUST have set the correct numbers of nonzeros per row in the call to
3375   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3376 
3377     MUST be called before any calls to MatSetValues();
3378 
3379     The indices should start with zero, not one.
3380 
3381 @*/
3382 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3383 {
3384   PetscErrorCode ierr;
3385 
3386   PetscFunctionBegin;
3387   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3388   PetscValidPointer(indices,2);
3389   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3390   PetscFunctionReturn(0);
3391 }
3392 
3393 /* ----------------------------------------------------------------------------------------*/
3394 
3395 #undef __FUNCT__
3396 #define __FUNCT__ "MatStoreValues_SeqAIJ"
3397 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3398 {
3399   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3400   PetscErrorCode ierr;
3401   size_t         nz = aij->i[mat->rmap->n];
3402 
3403   PetscFunctionBegin;
3404   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3405 
3406   /* allocate space for values if not already there */
3407   if (!aij->saved_values) {
3408     ierr = PetscMalloc1((nz+1),&aij->saved_values);CHKERRQ(ierr);
3409     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3410   }
3411 
3412   /* copy values over */
3413   ierr = PetscMemcpy(aij->saved_values,aij->a,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3414   PetscFunctionReturn(0);
3415 }
3416 
3417 #undef __FUNCT__
3418 #define __FUNCT__ "MatStoreValues"
3419 /*@
3420     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3421        example, reuse of the linear part of a Jacobian, while recomputing the
3422        nonlinear portion.
3423 
3424    Collect on Mat
3425 
3426   Input Parameters:
3427 .  mat - the matrix (currently only AIJ matrices support this option)
3428 
3429   Level: advanced
3430 
3431   Common Usage, with SNESSolve():
3432 $    Create Jacobian matrix
3433 $    Set linear terms into matrix
3434 $    Apply boundary conditions to matrix, at this time matrix must have
3435 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3436 $      boundary conditions again will not change the nonzero structure
3437 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3438 $    ierr = MatStoreValues(mat);
3439 $    Call SNESSetJacobian() with matrix
3440 $    In your Jacobian routine
3441 $      ierr = MatRetrieveValues(mat);
3442 $      Set nonlinear terms in matrix
3443 
3444   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3445 $    // build linear portion of Jacobian
3446 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3447 $    ierr = MatStoreValues(mat);
3448 $    loop over nonlinear iterations
3449 $       ierr = MatRetrieveValues(mat);
3450 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3451 $       // call MatAssemblyBegin/End() on matrix
3452 $       Solve linear system with Jacobian
3453 $    endloop
3454 
3455   Notes:
3456     Matrix must already be assemblied before calling this routine
3457     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3458     calling this routine.
3459 
3460     When this is called multiple times it overwrites the previous set of stored values
3461     and does not allocated additional space.
3462 
3463 .seealso: MatRetrieveValues()
3464 
3465 @*/
3466 PetscErrorCode  MatStoreValues(Mat mat)
3467 {
3468   PetscErrorCode ierr;
3469 
3470   PetscFunctionBegin;
3471   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3472   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3473   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3474   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3475   PetscFunctionReturn(0);
3476 }
3477 
3478 #undef __FUNCT__
3479 #define __FUNCT__ "MatRetrieveValues_SeqAIJ"
3480 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3481 {
3482   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3483   PetscErrorCode ierr;
3484   PetscInt       nz = aij->i[mat->rmap->n];
3485 
3486   PetscFunctionBegin;
3487   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3488   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3489   /* copy values over */
3490   ierr = PetscMemcpy(aij->a,aij->saved_values,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3491   PetscFunctionReturn(0);
3492 }
3493 
3494 #undef __FUNCT__
3495 #define __FUNCT__ "MatRetrieveValues"
3496 /*@
3497     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3498        example, reuse of the linear part of a Jacobian, while recomputing the
3499        nonlinear portion.
3500 
3501    Collect on Mat
3502 
3503   Input Parameters:
3504 .  mat - the matrix (currently on AIJ matrices support this option)
3505 
3506   Level: advanced
3507 
3508 .seealso: MatStoreValues()
3509 
3510 @*/
3511 PetscErrorCode  MatRetrieveValues(Mat mat)
3512 {
3513   PetscErrorCode ierr;
3514 
3515   PetscFunctionBegin;
3516   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3517   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3518   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3519   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3520   PetscFunctionReturn(0);
3521 }
3522 
3523 
3524 /* --------------------------------------------------------------------------------*/
3525 #undef __FUNCT__
3526 #define __FUNCT__ "MatCreateSeqAIJ"
3527 /*@C
3528    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3529    (the default parallel PETSc format).  For good matrix assembly performance
3530    the user should preallocate the matrix storage by setting the parameter nz
3531    (or the array nnz).  By setting these parameters accurately, performance
3532    during matrix assembly can be increased by more than a factor of 50.
3533 
3534    Collective on MPI_Comm
3535 
3536    Input Parameters:
3537 +  comm - MPI communicator, set to PETSC_COMM_SELF
3538 .  m - number of rows
3539 .  n - number of columns
3540 .  nz - number of nonzeros per row (same for all rows)
3541 -  nnz - array containing the number of nonzeros in the various rows
3542          (possibly different for each row) or NULL
3543 
3544    Output Parameter:
3545 .  A - the matrix
3546 
3547    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3548    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3549    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3550 
3551    Notes:
3552    If nnz is given then nz is ignored
3553 
3554    The AIJ format (also called the Yale sparse matrix format or
3555    compressed row storage), is fully compatible with standard Fortran 77
3556    storage.  That is, the stored row and column indices can begin at
3557    either one (as in Fortran) or zero.  See the users' manual for details.
3558 
3559    Specify the preallocated storage with either nz or nnz (not both).
3560    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3561    allocation.  For large problems you MUST preallocate memory or you
3562    will get TERRIBLE performance, see the users' manual chapter on matrices.
3563 
3564    By default, this format uses inodes (identical nodes) when possible, to
3565    improve numerical efficiency of matrix-vector products and solves. We
3566    search for consecutive rows with the same nonzero structure, thereby
3567    reusing matrix information to achieve increased efficiency.
3568 
3569    Options Database Keys:
3570 +  -mat_no_inode  - Do not use inodes
3571 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3572 
3573    Level: intermediate
3574 
3575 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3576 
3577 @*/
3578 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3579 {
3580   PetscErrorCode ierr;
3581 
3582   PetscFunctionBegin;
3583   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3584   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3585   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3586   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3587   PetscFunctionReturn(0);
3588 }
3589 
3590 #undef __FUNCT__
3591 #define __FUNCT__ "MatSeqAIJSetPreallocation"
3592 /*@C
3593    MatSeqAIJSetPreallocation - For good matrix assembly performance
3594    the user should preallocate the matrix storage by setting the parameter nz
3595    (or the array nnz).  By setting these parameters accurately, performance
3596    during matrix assembly can be increased by more than a factor of 50.
3597 
3598    Collective on MPI_Comm
3599 
3600    Input Parameters:
3601 +  B - The matrix
3602 .  nz - number of nonzeros per row (same for all rows)
3603 -  nnz - array containing the number of nonzeros in the various rows
3604          (possibly different for each row) or NULL
3605 
3606    Notes:
3607      If nnz is given then nz is ignored
3608 
3609     The AIJ format (also called the Yale sparse matrix format or
3610    compressed row storage), is fully compatible with standard Fortran 77
3611    storage.  That is, the stored row and column indices can begin at
3612    either one (as in Fortran) or zero.  See the users' manual for details.
3613 
3614    Specify the preallocated storage with either nz or nnz (not both).
3615    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3616    allocation.  For large problems you MUST preallocate memory or you
3617    will get TERRIBLE performance, see the users' manual chapter on matrices.
3618 
3619    You can call MatGetInfo() to get information on how effective the preallocation was;
3620    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3621    You can also run with the option -info and look for messages with the string
3622    malloc in them to see if additional memory allocation was needed.
3623 
3624    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3625    entries or columns indices
3626 
3627    By default, this format uses inodes (identical nodes) when possible, to
3628    improve numerical efficiency of matrix-vector products and solves. We
3629    search for consecutive rows with the same nonzero structure, thereby
3630    reusing matrix information to achieve increased efficiency.
3631 
3632    Options Database Keys:
3633 +  -mat_no_inode  - Do not use inodes
3634 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3635 -  -mat_aij_oneindex - Internally use indexing starting at 1
3636         rather than 0.  Note that when calling MatSetValues(),
3637         the user still MUST index entries starting at 0!
3638 
3639    Level: intermediate
3640 
3641 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatGetInfo()
3642 
3643 @*/
3644 PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
3645 {
3646   PetscErrorCode ierr;
3647 
3648   PetscFunctionBegin;
3649   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3650   PetscValidType(B,1);
3651   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));CHKERRQ(ierr);
3652   PetscFunctionReturn(0);
3653 }
3654 
3655 #undef __FUNCT__
3656 #define __FUNCT__ "MatSeqAIJSetPreallocation_SeqAIJ"
3657 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3658 {
3659   Mat_SeqAIJ     *b;
3660   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3661   PetscErrorCode ierr;
3662   PetscInt       i;
3663 
3664   PetscFunctionBegin;
3665   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3666   if (nz == MAT_SKIP_ALLOCATION) {
3667     skipallocation = PETSC_TRUE;
3668     nz             = 0;
3669   }
3670 
3671   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3672   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3673 
3674   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3675   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %D",nz);
3676   if (nnz) {
3677     for (i=0; i<B->rmap->n; i++) {
3678       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]);
3679       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);
3680     }
3681   }
3682 
3683   B->preallocated = PETSC_TRUE;
3684 
3685   b = (Mat_SeqAIJ*)B->data;
3686 
3687   if (!skipallocation) {
3688     if (!b->imax) {
3689       ierr = PetscMalloc2(B->rmap->n,&b->imax,B->rmap->n,&b->ilen);CHKERRQ(ierr);
3690       ierr = PetscLogObjectMemory((PetscObject)B,2*B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3691     }
3692     if (!nnz) {
3693       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3694       else if (nz < 0) nz = 1;
3695       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
3696       nz = nz*B->rmap->n;
3697     } else {
3698       nz = 0;
3699       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz += nnz[i];}
3700     }
3701     /* b->ilen will count nonzeros in each row so far. */
3702     for (i=0; i<B->rmap->n; i++) b->ilen[i] = 0;
3703 
3704     /* allocate the matrix space */
3705     ierr    = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
3706     ierr    = PetscMalloc3(nz,&b->a,nz,&b->j,B->rmap->n+1,&b->i);CHKERRQ(ierr);
3707     ierr    = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
3708     b->i[0] = 0;
3709     for (i=1; i<B->rmap->n+1; i++) {
3710       b->i[i] = b->i[i-1] + b->imax[i-1];
3711     }
3712     b->singlemalloc = PETSC_TRUE;
3713     b->free_a       = PETSC_TRUE;
3714     b->free_ij      = PETSC_TRUE;
3715 #if defined(PETSC_THREADCOMM_ACTIVE)
3716     ierr = MatZeroEntries_SeqAIJ(B);CHKERRQ(ierr);
3717 #endif
3718   } else {
3719     b->free_a  = PETSC_FALSE;
3720     b->free_ij = PETSC_FALSE;
3721   }
3722 
3723   b->nz               = 0;
3724   b->maxnz            = nz;
3725   B->info.nz_unneeded = (double)b->maxnz;
3726   if (realalloc) {
3727     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3728   }
3729   PetscFunctionReturn(0);
3730 }
3731 
3732 #undef  __FUNCT__
3733 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR"
3734 /*@
3735    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
3736 
3737    Input Parameters:
3738 +  B - the matrix
3739 .  i - the indices into j for the start of each row (starts with zero)
3740 .  j - the column indices for each row (starts with zero) these must be sorted for each row
3741 -  v - optional values in the matrix
3742 
3743    Level: developer
3744 
3745    The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
3746 
3747 .keywords: matrix, aij, compressed row, sparse, sequential
3748 
3749 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), SeqAIJ
3750 @*/
3751 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
3752 {
3753   PetscErrorCode ierr;
3754 
3755   PetscFunctionBegin;
3756   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3757   PetscValidType(B,1);
3758   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3759   PetscFunctionReturn(0);
3760 }
3761 
3762 #undef  __FUNCT__
3763 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR_SeqAIJ"
3764 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3765 {
3766   PetscInt       i;
3767   PetscInt       m,n;
3768   PetscInt       nz;
3769   PetscInt       *nnz, nz_max = 0;
3770   PetscScalar    *values;
3771   PetscErrorCode ierr;
3772 
3773   PetscFunctionBegin;
3774   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
3775 
3776   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3777   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3778 
3779   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
3780   ierr = PetscMalloc1((m+1), &nnz);CHKERRQ(ierr);
3781   for (i = 0; i < m; i++) {
3782     nz     = Ii[i+1]- Ii[i];
3783     nz_max = PetscMax(nz_max, nz);
3784     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
3785     nnz[i] = nz;
3786   }
3787   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
3788   ierr = PetscFree(nnz);CHKERRQ(ierr);
3789 
3790   if (v) {
3791     values = (PetscScalar*) v;
3792   } else {
3793     ierr = PetscCalloc1(nz_max, &values);CHKERRQ(ierr);
3794   }
3795 
3796   for (i = 0; i < m; i++) {
3797     nz   = Ii[i+1] - Ii[i];
3798     ierr = MatSetValues_SeqAIJ(B, 1, &i, nz, J+Ii[i], values + (v ? Ii[i] : 0), INSERT_VALUES);CHKERRQ(ierr);
3799   }
3800 
3801   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3802   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3803 
3804   if (!v) {
3805     ierr = PetscFree(values);CHKERRQ(ierr);
3806   }
3807   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3808   PetscFunctionReturn(0);
3809 }
3810 
3811 #include <../src/mat/impls/dense/seq/dense.h>
3812 #include <petsc-private/kernels/petscaxpy.h>
3813 
3814 #undef __FUNCT__
3815 #define __FUNCT__ "MatMatMultNumeric_SeqDense_SeqAIJ"
3816 /*
3817     Computes (B'*A')' since computing B*A directly is untenable
3818 
3819                n                       p                          p
3820         (              )       (              )         (                  )
3821       m (      A       )  *  n (       B      )   =   m (         C        )
3822         (              )       (              )         (                  )
3823 
3824 */
3825 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
3826 {
3827   PetscErrorCode    ierr;
3828   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
3829   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
3830   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
3831   PetscInt          i,n,m,q,p;
3832   const PetscInt    *ii,*idx;
3833   const PetscScalar *b,*a,*a_q;
3834   PetscScalar       *c,*c_q;
3835 
3836   PetscFunctionBegin;
3837   m    = A->rmap->n;
3838   n    = A->cmap->n;
3839   p    = B->cmap->n;
3840   a    = sub_a->v;
3841   b    = sub_b->a;
3842   c    = sub_c->v;
3843   ierr = PetscMemzero(c,m*p*sizeof(PetscScalar));CHKERRQ(ierr);
3844 
3845   ii  = sub_b->i;
3846   idx = sub_b->j;
3847   for (i=0; i<n; i++) {
3848     q = ii[i+1] - ii[i];
3849     while (q-->0) {
3850       c_q = c + m*(*idx);
3851       a_q = a + m*i;
3852       PetscKernelAXPY(c_q,*b,a_q,m);
3853       idx++;
3854       b++;
3855     }
3856   }
3857   PetscFunctionReturn(0);
3858 }
3859 
3860 #undef __FUNCT__
3861 #define __FUNCT__ "MatMatMultSymbolic_SeqDense_SeqAIJ"
3862 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
3863 {
3864   PetscErrorCode ierr;
3865   PetscInt       m=A->rmap->n,n=B->cmap->n;
3866   Mat            Cmat;
3867 
3868   PetscFunctionBegin;
3869   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);
3870   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
3871   ierr = MatSetSizes(Cmat,m,n,m,n);CHKERRQ(ierr);
3872   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
3873   ierr = MatSetType(Cmat,MATSEQDENSE);CHKERRQ(ierr);
3874   ierr = MatSeqDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
3875 
3876   Cmat->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
3877 
3878   *C = Cmat;
3879   PetscFunctionReturn(0);
3880 }
3881 
3882 /* ----------------------------------------------------------------*/
3883 #undef __FUNCT__
3884 #define __FUNCT__ "MatMatMult_SeqDense_SeqAIJ"
3885 PetscErrorCode MatMatMult_SeqDense_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
3886 {
3887   PetscErrorCode ierr;
3888 
3889   PetscFunctionBegin;
3890   if (scall == MAT_INITIAL_MATRIX) {
3891     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
3892     ierr = MatMatMultSymbolic_SeqDense_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
3893     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
3894   }
3895   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
3896   ierr = MatMatMultNumeric_SeqDense_SeqAIJ(A,B,*C);CHKERRQ(ierr);
3897   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
3898   PetscFunctionReturn(0);
3899 }
3900 
3901 
3902 /*MC
3903    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
3904    based on compressed sparse row format.
3905 
3906    Options Database Keys:
3907 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
3908 
3909   Level: beginner
3910 
3911 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
3912 M*/
3913 
3914 /*MC
3915    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
3916 
3917    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
3918    and MATMPIAIJ otherwise.  As a result, for single process communicators,
3919   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
3920   for communicators controlling multiple processes.  It is recommended that you call both of
3921   the above preallocation routines for simplicity.
3922 
3923    Options Database Keys:
3924 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
3925 
3926   Developer Notes: Subclasses include MATAIJCUSP, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
3927    enough exist.
3928 
3929   Level: beginner
3930 
3931 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
3932 M*/
3933 
3934 /*MC
3935    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
3936 
3937    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
3938    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
3939    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
3940   for communicators controlling multiple processes.  It is recommended that you call both of
3941   the above preallocation routines for simplicity.
3942 
3943    Options Database Keys:
3944 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
3945 
3946   Level: beginner
3947 
3948 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
3949 M*/
3950 
3951 #if defined(PETSC_HAVE_PASTIX)
3952 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_pastix(Mat,MatFactorType,Mat*);
3953 #endif
3954 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
3955 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_essl(Mat,MatFactorType,Mat*);
3956 #endif
3957 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
3958 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_petsc(Mat,MatFactorType,Mat*);
3959 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_bas(Mat,MatFactorType,Mat*);
3960 extern PetscErrorCode  MatGetFactorAvailable_seqaij_petsc(Mat,MatFactorType,PetscBool*);
3961 #if defined(PETSC_HAVE_MUMPS)
3962 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mumps(Mat,MatFactorType,Mat*);
3963 #endif
3964 #if defined(PETSC_HAVE_SUPERLU)
3965 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu(Mat,MatFactorType,Mat*);
3966 #endif
3967 #if defined(PETSC_HAVE_MKL_PARDISO)
3968 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mkl_pardiso(Mat,MatFactorType,Mat*);
3969 #endif
3970 #if defined(PETSC_HAVE_SUPERLU_DIST)
3971 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu_dist(Mat,MatFactorType,Mat*);
3972 #endif
3973 #if defined(PETSC_HAVE_SUITESPARSE)
3974 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_umfpack(Mat,MatFactorType,Mat*);
3975 #endif
3976 #if defined(PETSC_HAVE_SUITESPARSE)
3977 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_cholmod(Mat,MatFactorType,Mat*);
3978 #endif
3979 #if defined(PETSC_HAVE_SUITESPARSE)
3980 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_klu(Mat,MatFactorType,Mat*);
3981 #endif
3982 #if defined(PETSC_HAVE_LUSOL)
3983 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_lusol(Mat,MatFactorType,Mat*);
3984 #endif
3985 #if defined(PETSC_HAVE_MATLAB_ENGINE)
3986 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_matlab(Mat,MatFactorType,Mat*);
3987 extern PetscErrorCode  MatlabEnginePut_SeqAIJ(PetscObject,void*);
3988 extern PetscErrorCode  MatlabEngineGet_SeqAIJ(PetscObject,void*);
3989 #endif
3990 #if defined(PETSC_HAVE_CLIQUE)
3991 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_clique(Mat,MatFactorType,Mat*);
3992 #endif
3993 
3994 
3995 #undef __FUNCT__
3996 #define __FUNCT__ "MatSeqAIJGetArray"
3997 /*@C
3998    MatSeqAIJGetArray - gives access to the array where the data for a SeqSeqAIJ matrix is stored
3999 
4000    Not Collective
4001 
4002    Input Parameter:
4003 .  mat - a MATSEQDENSE matrix
4004 
4005    Output Parameter:
4006 .   array - pointer to the data
4007 
4008    Level: intermediate
4009 
4010 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4011 @*/
4012 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4013 {
4014   PetscErrorCode ierr;
4015 
4016   PetscFunctionBegin;
4017   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4018   PetscFunctionReturn(0);
4019 }
4020 
4021 #undef __FUNCT__
4022 #define __FUNCT__ "MatSeqAIJGetMaxRowNonzeros"
4023 /*@C
4024    MatSeqAIJGetMaxRowNonzeros - returns the maximum number of nonzeros in any row
4025 
4026    Not Collective
4027 
4028    Input Parameter:
4029 .  mat - a MATSEQDENSE matrix
4030 
4031    Output Parameter:
4032 .   nz - the maximum number of nonzeros in any row
4033 
4034    Level: intermediate
4035 
4036 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4037 @*/
4038 PetscErrorCode  MatSeqAIJGetMaxRowNonzeros(Mat A,PetscInt *nz)
4039 {
4040   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
4041 
4042   PetscFunctionBegin;
4043   *nz = aij->rmax;
4044   PetscFunctionReturn(0);
4045 }
4046 
4047 #undef __FUNCT__
4048 #define __FUNCT__ "MatSeqAIJRestoreArray"
4049 /*@C
4050    MatSeqAIJRestoreArray - returns access to the array where the data for a SeqSeqAIJ matrix is stored obtained by MatSeqAIJGetArray()
4051 
4052    Not Collective
4053 
4054    Input Parameters:
4055 .  mat - a MATSEQDENSE matrix
4056 .  array - pointer to the data
4057 
4058    Level: intermediate
4059 
4060 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4061 @*/
4062 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4063 {
4064   PetscErrorCode ierr;
4065 
4066   PetscFunctionBegin;
4067   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4068   PetscFunctionReturn(0);
4069 }
4070 
4071 #undef __FUNCT__
4072 #define __FUNCT__ "MatCreate_SeqAIJ"
4073 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4074 {
4075   Mat_SeqAIJ     *b;
4076   PetscErrorCode ierr;
4077   PetscMPIInt    size;
4078 
4079   PetscFunctionBegin;
4080   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4081   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4082 
4083   ierr = PetscNewLog(B,&b);CHKERRQ(ierr);
4084 
4085   B->data = (void*)b;
4086 
4087   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4088 
4089   b->row                = 0;
4090   b->col                = 0;
4091   b->icol               = 0;
4092   b->reallocs           = 0;
4093   b->ignorezeroentries  = PETSC_FALSE;
4094   b->roworiented        = PETSC_TRUE;
4095   b->nonew              = 0;
4096   b->diag               = 0;
4097   b->solve_work         = 0;
4098   B->spptr              = 0;
4099   b->saved_values       = 0;
4100   b->idiag              = 0;
4101   b->mdiag              = 0;
4102   b->ssor_work          = 0;
4103   b->omega              = 1.0;
4104   b->fshift             = 0.0;
4105   b->idiagvalid         = PETSC_FALSE;
4106   b->ibdiagvalid        = PETSC_FALSE;
4107   b->keepnonzeropattern = PETSC_FALSE;
4108   b->xtoy               = 0;
4109   b->XtoY               = 0;
4110 
4111   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4112   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4113   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4114 
4115 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4116   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_matlab_C",MatGetFactor_seqaij_matlab);CHKERRQ(ierr);
4117   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4118   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4119 #endif
4120 #if defined(PETSC_HAVE_PASTIX)
4121   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_pastix_C",MatGetFactor_seqaij_pastix);CHKERRQ(ierr);
4122 #endif
4123 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
4124   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_essl_C",MatGetFactor_seqaij_essl);CHKERRQ(ierr);
4125 #endif
4126 #if defined(PETSC_HAVE_SUPERLU)
4127   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_C",MatGetFactor_seqaij_superlu);CHKERRQ(ierr);
4128 #endif
4129 #if defined(PETSC_HAVE_MKL_PARDISO)
4130   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mkl_pardiso_C",MatGetFactor_aij_mkl_pardiso);CHKERRQ(ierr);
4131 #endif
4132 #if defined(PETSC_HAVE_SUPERLU_DIST)
4133   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_dist_C",MatGetFactor_seqaij_superlu_dist);CHKERRQ(ierr);
4134 #endif
4135 #if defined(PETSC_HAVE_MUMPS)
4136   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mumps_C",MatGetFactor_aij_mumps);CHKERRQ(ierr);
4137 #endif
4138 #if defined(PETSC_HAVE_SUITESPARSE)
4139   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_umfpack_C",MatGetFactor_seqaij_umfpack);CHKERRQ(ierr);
4140 #endif
4141 #if defined(PETSC_HAVE_SUITESPARSE)
4142   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_cholmod_C",MatGetFactor_seqaij_cholmod);CHKERRQ(ierr);
4143 #endif
4144 #if defined(PETSC_HAVE_SUITESPARSE)
4145   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_klu_C",MatGetFactor_seqaij_klu);CHKERRQ(ierr);
4146 #endif
4147 #if defined(PETSC_HAVE_LUSOL)
4148   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_lusol_C",MatGetFactor_seqaij_lusol);CHKERRQ(ierr);
4149 #endif
4150 #if defined(PETSC_HAVE_CLIQUE)
4151   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_clique_C",MatGetFactor_aij_clique);CHKERRQ(ierr);
4152 #endif
4153 
4154   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_petsc_C",MatGetFactor_seqaij_petsc);CHKERRQ(ierr);
4155   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactorAvailable_petsc_C",MatGetFactorAvailable_seqaij_petsc);CHKERRQ(ierr);
4156   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_bas_C",MatGetFactor_seqaij_bas);CHKERRQ(ierr);
4157   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4158   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4159   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4160   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4161   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4162   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4163   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4164   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4165   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4166   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4167   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4168   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4169   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaij_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
4170   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaij_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
4171   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaij_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
4172   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4173   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4174   PetscFunctionReturn(0);
4175 }
4176 
4177 #undef __FUNCT__
4178 #define __FUNCT__ "MatDuplicateNoCreate_SeqAIJ"
4179 /*
4180     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4181 */
4182 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4183 {
4184   Mat_SeqAIJ     *c,*a = (Mat_SeqAIJ*)A->data;
4185   PetscErrorCode ierr;
4186   PetscInt       i,m = A->rmap->n;
4187 
4188   PetscFunctionBegin;
4189   c = (Mat_SeqAIJ*)C->data;
4190 
4191   C->factortype = A->factortype;
4192   c->row        = 0;
4193   c->col        = 0;
4194   c->icol       = 0;
4195   c->reallocs   = 0;
4196 
4197   C->assembled = PETSC_TRUE;
4198 
4199   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4200   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4201 
4202   ierr = PetscMalloc2(m,&c->imax,m,&c->ilen);CHKERRQ(ierr);
4203   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4204   for (i=0; i<m; i++) {
4205     c->imax[i] = a->imax[i];
4206     c->ilen[i] = a->ilen[i];
4207   }
4208 
4209   /* allocate the matrix space */
4210   if (mallocmatspace) {
4211     ierr = PetscMalloc3(a->i[m],&c->a,a->i[m],&c->j,m+1,&c->i);CHKERRQ(ierr);
4212     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4213 
4214     c->singlemalloc = PETSC_TRUE;
4215 
4216     ierr = PetscMemcpy(c->i,a->i,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4217     if (m > 0) {
4218       ierr = PetscMemcpy(c->j,a->j,(a->i[m])*sizeof(PetscInt));CHKERRQ(ierr);
4219       if (cpvalues == MAT_COPY_VALUES) {
4220         ierr = PetscMemcpy(c->a,a->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4221       } else {
4222         ierr = PetscMemzero(c->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4223       }
4224     }
4225   }
4226 
4227   c->ignorezeroentries = a->ignorezeroentries;
4228   c->roworiented       = a->roworiented;
4229   c->nonew             = a->nonew;
4230   if (a->diag) {
4231     ierr = PetscMalloc1((m+1),&c->diag);CHKERRQ(ierr);
4232     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4233     for (i=0; i<m; i++) {
4234       c->diag[i] = a->diag[i];
4235     }
4236   } else c->diag = 0;
4237 
4238   c->solve_work         = 0;
4239   c->saved_values       = 0;
4240   c->idiag              = 0;
4241   c->ssor_work          = 0;
4242   c->keepnonzeropattern = a->keepnonzeropattern;
4243   c->free_a             = PETSC_TRUE;
4244   c->free_ij            = PETSC_TRUE;
4245   c->xtoy               = 0;
4246   c->XtoY               = 0;
4247 
4248   c->rmax         = a->rmax;
4249   c->nz           = a->nz;
4250   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4251   C->preallocated = PETSC_TRUE;
4252 
4253   c->compressedrow.use   = a->compressedrow.use;
4254   c->compressedrow.nrows = a->compressedrow.nrows;
4255   if (a->compressedrow.use) {
4256     i    = a->compressedrow.nrows;
4257     ierr = PetscMalloc2(i+1,&c->compressedrow.i,i,&c->compressedrow.rindex);CHKERRQ(ierr);
4258     ierr = PetscMemcpy(c->compressedrow.i,a->compressedrow.i,(i+1)*sizeof(PetscInt));CHKERRQ(ierr);
4259     ierr = PetscMemcpy(c->compressedrow.rindex,a->compressedrow.rindex,i*sizeof(PetscInt));CHKERRQ(ierr);
4260   } else {
4261     c->compressedrow.use    = PETSC_FALSE;
4262     c->compressedrow.i      = NULL;
4263     c->compressedrow.rindex = NULL;
4264   }
4265   C->nonzerostate = A->nonzerostate;
4266 
4267   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4268   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4269   PetscFunctionReturn(0);
4270 }
4271 
4272 #undef __FUNCT__
4273 #define __FUNCT__ "MatDuplicate_SeqAIJ"
4274 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4275 {
4276   PetscErrorCode ierr;
4277 
4278   PetscFunctionBegin;
4279   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4280   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4281   if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) {
4282     ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
4283   }
4284   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4285   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4286   PetscFunctionReturn(0);
4287 }
4288 
4289 #undef __FUNCT__
4290 #define __FUNCT__ "MatLoad_SeqAIJ"
4291 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4292 {
4293   Mat_SeqAIJ     *a;
4294   PetscErrorCode ierr;
4295   PetscInt       i,sum,nz,header[4],*rowlengths = 0,M,N,rows,cols;
4296   int            fd;
4297   PetscMPIInt    size;
4298   MPI_Comm       comm;
4299   PetscInt       bs = 1;
4300 
4301   PetscFunctionBegin;
4302   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
4303   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4304   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"view must have one processor");
4305 
4306   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
4307   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
4308   ierr = PetscOptionsEnd();CHKERRQ(ierr);
4309   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
4310 
4311   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
4312   ierr = PetscBinaryRead(fd,header,4,PETSC_INT);CHKERRQ(ierr);
4313   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
4314   M = header[1]; N = header[2]; nz = header[3];
4315 
4316   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
4317 
4318   /* read in row lengths */
4319   ierr = PetscMalloc1(M,&rowlengths);CHKERRQ(ierr);
4320   ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
4321 
4322   /* check if sum of rowlengths is same as nz */
4323   for (i=0,sum=0; i< M; i++) sum +=rowlengths[i];
4324   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);
4325 
4326   /* set global size if not set already*/
4327   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) {
4328     ierr = MatSetSizes(newMat,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
4329   } else {
4330     /* if sizes and type are already set, check if the vector global sizes are correct */
4331     ierr = MatGetSize(newMat,&rows,&cols);CHKERRQ(ierr);
4332     if (rows < 0 && cols < 0) { /* user might provide local size instead of global size */
4333       ierr = MatGetLocalSize(newMat,&rows,&cols);CHKERRQ(ierr);
4334     }
4335     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);
4336   }
4337   ierr = MatSeqAIJSetPreallocation_SeqAIJ(newMat,0,rowlengths);CHKERRQ(ierr);
4338   a    = (Mat_SeqAIJ*)newMat->data;
4339 
4340   ierr = PetscBinaryRead(fd,a->j,nz,PETSC_INT);CHKERRQ(ierr);
4341 
4342   /* read in nonzero values */
4343   ierr = PetscBinaryRead(fd,a->a,nz,PETSC_SCALAR);CHKERRQ(ierr);
4344 
4345   /* set matrix "i" values */
4346   a->i[0] = 0;
4347   for (i=1; i<= M; i++) {
4348     a->i[i]      = a->i[i-1] + rowlengths[i-1];
4349     a->ilen[i-1] = rowlengths[i-1];
4350   }
4351   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
4352 
4353   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4354   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4355   PetscFunctionReturn(0);
4356 }
4357 
4358 #undef __FUNCT__
4359 #define __FUNCT__ "MatEqual_SeqAIJ"
4360 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4361 {
4362   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4363   PetscErrorCode ierr;
4364 #if defined(PETSC_USE_COMPLEX)
4365   PetscInt k;
4366 #endif
4367 
4368   PetscFunctionBegin;
4369   /* If the  matrix dimensions are not equal,or no of nonzeros */
4370   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4371     *flg = PETSC_FALSE;
4372     PetscFunctionReturn(0);
4373   }
4374 
4375   /* if the a->i are the same */
4376   ierr = PetscMemcmp(a->i,b->i,(A->rmap->n+1)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4377   if (!*flg) PetscFunctionReturn(0);
4378 
4379   /* if a->j are the same */
4380   ierr = PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4381   if (!*flg) PetscFunctionReturn(0);
4382 
4383   /* if a->a are the same */
4384 #if defined(PETSC_USE_COMPLEX)
4385   for (k=0; k<a->nz; k++) {
4386     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4387       *flg = PETSC_FALSE;
4388       PetscFunctionReturn(0);
4389     }
4390   }
4391 #else
4392   ierr = PetscMemcmp(a->a,b->a,(a->nz)*sizeof(PetscScalar),flg);CHKERRQ(ierr);
4393 #endif
4394   PetscFunctionReturn(0);
4395 }
4396 
4397 #undef __FUNCT__
4398 #define __FUNCT__ "MatCreateSeqAIJWithArrays"
4399 /*@
4400      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4401               provided by the user.
4402 
4403       Collective on MPI_Comm
4404 
4405    Input Parameters:
4406 +   comm - must be an MPI communicator of size 1
4407 .   m - number of rows
4408 .   n - number of columns
4409 .   i - row indices
4410 .   j - column indices
4411 -   a - matrix values
4412 
4413    Output Parameter:
4414 .   mat - the matrix
4415 
4416    Level: intermediate
4417 
4418    Notes:
4419        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4420     once the matrix is destroyed and not before
4421 
4422        You cannot set new nonzero locations into this matrix, that will generate an error.
4423 
4424        The i and j indices are 0 based
4425 
4426        The format which is used for the sparse matrix input, is equivalent to a
4427     row-major ordering.. i.e for the following matrix, the input data expected is
4428     as shown:
4429 
4430         1 0 0
4431         2 0 3
4432         4 5 6
4433 
4434         i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4435         j =  {0,0,2,0,1,2}  [size = nz = 6]; values must be sorted for each row
4436         v =  {1,2,3,4,5,6}  [size = nz = 6]
4437 
4438 
4439 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4440 
4441 @*/
4442 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat)
4443 {
4444   PetscErrorCode ierr;
4445   PetscInt       ii;
4446   Mat_SeqAIJ     *aij;
4447 #if defined(PETSC_USE_DEBUG)
4448   PetscInt jj;
4449 #endif
4450 
4451   PetscFunctionBegin;
4452   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4453   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4454   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4455   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4456   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4457   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,0);CHKERRQ(ierr);
4458   aij  = (Mat_SeqAIJ*)(*mat)->data;
4459   ierr = PetscMalloc2(m,&aij->imax,m,&aij->ilen);CHKERRQ(ierr);
4460 
4461   aij->i            = i;
4462   aij->j            = j;
4463   aij->a            = a;
4464   aij->singlemalloc = PETSC_FALSE;
4465   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4466   aij->free_a       = PETSC_FALSE;
4467   aij->free_ij      = PETSC_FALSE;
4468 
4469   for (ii=0; ii<m; ii++) {
4470     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4471 #if defined(PETSC_USE_DEBUG)
4472     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]);
4473     for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4474       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);
4475       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);
4476     }
4477 #endif
4478   }
4479 #if defined(PETSC_USE_DEBUG)
4480   for (ii=0; ii<aij->i[m]; ii++) {
4481     if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %D index = %D",ii,j[ii]);
4482     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]);
4483   }
4484 #endif
4485 
4486   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4487   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4488   PetscFunctionReturn(0);
4489 }
4490 #undef __FUNCT__
4491 #define __FUNCT__ "MatCreateSeqAIJFromTriple"
4492 /*@C
4493      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4494               provided by the user.
4495 
4496       Collective on MPI_Comm
4497 
4498    Input Parameters:
4499 +   comm - must be an MPI communicator of size 1
4500 .   m   - number of rows
4501 .   n   - number of columns
4502 .   i   - row indices
4503 .   j   - column indices
4504 .   a   - matrix values
4505 .   nz  - number of nonzeros
4506 -   idx - 0 or 1 based
4507 
4508    Output Parameter:
4509 .   mat - the matrix
4510 
4511    Level: intermediate
4512 
4513    Notes:
4514        The i and j indices are 0 based
4515 
4516        The format which is used for the sparse matrix input, is equivalent to a
4517     row-major ordering.. i.e for the following matrix, the input data expected is
4518     as shown:
4519 
4520         1 0 0
4521         2 0 3
4522         4 5 6
4523 
4524         i =  {0,1,1,2,2,2}
4525         j =  {0,0,2,0,1,2}
4526         v =  {1,2,3,4,5,6}
4527 
4528 
4529 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4530 
4531 @*/
4532 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat,PetscInt nz,PetscBool idx)
4533 {
4534   PetscErrorCode ierr;
4535   PetscInt       ii, *nnz, one = 1,row,col;
4536 
4537 
4538   PetscFunctionBegin;
4539   ierr = PetscCalloc1(m,&nnz);CHKERRQ(ierr);
4540   for (ii = 0; ii < nz; ii++) {
4541     nnz[i[ii] - !!idx] += 1;
4542   }
4543   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4544   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4545   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4546   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4547   for (ii = 0; ii < nz; ii++) {
4548     if (idx) {
4549       row = i[ii] - 1;
4550       col = j[ii] - 1;
4551     } else {
4552       row = i[ii];
4553       col = j[ii];
4554     }
4555     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4556   }
4557   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4558   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4559   ierr = PetscFree(nnz);CHKERRQ(ierr);
4560   PetscFunctionReturn(0);
4561 }
4562 
4563 #undef __FUNCT__
4564 #define __FUNCT__ "MatSetColoring_SeqAIJ"
4565 PetscErrorCode MatSetColoring_SeqAIJ(Mat A,ISColoring coloring)
4566 {
4567   PetscErrorCode ierr;
4568   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4569 
4570   PetscFunctionBegin;
4571   if (coloring->ctype == IS_COLORING_GLOBAL) {
4572     ierr        = ISColoringReference(coloring);CHKERRQ(ierr);
4573     a->coloring = coloring;
4574   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
4575     PetscInt        i,*larray;
4576     ISColoring      ocoloring;
4577     ISColoringValue *colors;
4578 
4579     /* set coloring for diagonal portion */
4580     ierr = PetscMalloc1(A->cmap->n,&larray);CHKERRQ(ierr);
4581     for (i=0; i<A->cmap->n; i++) larray[i] = i;
4582     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
4583     ierr = PetscMalloc1(A->cmap->n,&colors);CHKERRQ(ierr);
4584     for (i=0; i<A->cmap->n; i++) colors[i] = coloring->colors[larray[i]];
4585     ierr        = PetscFree(larray);CHKERRQ(ierr);
4586     ierr        = ISColoringCreate(PETSC_COMM_SELF,coloring->n,A->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4587     a->coloring = ocoloring;
4588   }
4589   PetscFunctionReturn(0);
4590 }
4591 
4592 #undef __FUNCT__
4593 #define __FUNCT__ "MatSetValuesAdifor_SeqAIJ"
4594 PetscErrorCode MatSetValuesAdifor_SeqAIJ(Mat A,PetscInt nl,void *advalues)
4595 {
4596   Mat_SeqAIJ      *a      = (Mat_SeqAIJ*)A->data;
4597   PetscInt        m       = A->rmap->n,*ii = a->i,*jj = a->j,nz,i,j;
4598   MatScalar       *v      = a->a;
4599   PetscScalar     *values = (PetscScalar*)advalues;
4600   ISColoringValue *color;
4601 
4602   PetscFunctionBegin;
4603   if (!a->coloring) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Coloring not set for matrix");
4604   color = a->coloring->colors;
4605   /* loop over rows */
4606   for (i=0; i<m; i++) {
4607     nz = ii[i+1] - ii[i];
4608     /* loop over columns putting computed value into matrix */
4609     for (j=0; j<nz; j++) *v++ = values[color[*jj++]];
4610     values += nl; /* jump to next row of derivatives */
4611   }
4612   PetscFunctionReturn(0);
4613 }
4614 
4615 #undef __FUNCT__
4616 #define __FUNCT__ "MatSeqAIJInvalidateDiagonal"
4617 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4618 {
4619   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4620   PetscErrorCode ierr;
4621 
4622   PetscFunctionBegin;
4623   a->idiagvalid  = PETSC_FALSE;
4624   a->ibdiagvalid = PETSC_FALSE;
4625 
4626   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4627   PetscFunctionReturn(0);
4628 }
4629 
4630 /*
4631     Special version for direct calls from Fortran
4632 */
4633 #include <petsc-private/fortranimpl.h>
4634 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4635 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
4636 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4637 #define matsetvaluesseqaij_ matsetvaluesseqaij
4638 #endif
4639 
4640 /* Change these macros so can be used in void function */
4641 #undef CHKERRQ
4642 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
4643 #undef SETERRQ2
4644 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4645 #undef SETERRQ3
4646 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4647 
4648 #undef __FUNCT__
4649 #define __FUNCT__ "matsetvaluesseqaij_"
4650 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)
4651 {
4652   Mat            A  = *AA;
4653   PetscInt       m  = *mm, n = *nn;
4654   InsertMode     is = *isis;
4655   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4656   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
4657   PetscInt       *imax,*ai,*ailen;
4658   PetscErrorCode ierr;
4659   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
4660   MatScalar      *ap,value,*aa;
4661   PetscBool      ignorezeroentries = a->ignorezeroentries;
4662   PetscBool      roworiented       = a->roworiented;
4663 
4664   PetscFunctionBegin;
4665   MatCheckPreallocated(A,1);
4666   imax  = a->imax;
4667   ai    = a->i;
4668   ailen = a->ilen;
4669   aj    = a->j;
4670   aa    = a->a;
4671 
4672   for (k=0; k<m; k++) { /* loop over added rows */
4673     row = im[k];
4674     if (row < 0) continue;
4675 #if defined(PETSC_USE_DEBUG)
4676     if (row >= A->rmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
4677 #endif
4678     rp   = aj + ai[row]; ap = aa + ai[row];
4679     rmax = imax[row]; nrow = ailen[row];
4680     low  = 0;
4681     high = nrow;
4682     for (l=0; l<n; l++) { /* loop over added columns */
4683       if (in[l] < 0) continue;
4684 #if defined(PETSC_USE_DEBUG)
4685       if (in[l] >= A->cmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
4686 #endif
4687       col = in[l];
4688       if (roworiented) value = v[l + k*n];
4689       else value = v[k + l*m];
4690 
4691       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
4692 
4693       if (col <= lastcol) low = 0;
4694       else high = nrow;
4695       lastcol = col;
4696       while (high-low > 5) {
4697         t = (low+high)/2;
4698         if (rp[t] > col) high = t;
4699         else             low  = t;
4700       }
4701       for (i=low; i<high; i++) {
4702         if (rp[i] > col) break;
4703         if (rp[i] == col) {
4704           if (is == ADD_VALUES) ap[i] += value;
4705           else                  ap[i] = value;
4706           goto noinsert;
4707         }
4708       }
4709       if (value == 0.0 && ignorezeroentries) goto noinsert;
4710       if (nonew == 1) goto noinsert;
4711       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
4712       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
4713       N = nrow++ - 1; a->nz++; high++;
4714       /* shift up all the later entries in this row */
4715       for (ii=N; ii>=i; ii--) {
4716         rp[ii+1] = rp[ii];
4717         ap[ii+1] = ap[ii];
4718       }
4719       rp[i] = col;
4720       ap[i] = value;
4721       A->nonzerostate++;
4722 noinsert:;
4723       low = i + 1;
4724     }
4725     ailen[row] = nrow;
4726   }
4727   PetscFunctionReturnVoid();
4728 }
4729 
4730 
4731