xref: /petsc/src/mat/impls/aij/seq/aij.c (revision 5276853724e192b300785f6f0437575a70c6dcbb)
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 #include <petsctime.h>
2825 #undef __FUNCT__
2826 #define __FUNCT__ "MatAXPY_SeqAIJ"
2827 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2828 {
2829   PetscErrorCode ierr;
2830   PetscInt       i;
2831   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
2832   PetscBLASInt   one=1,bnz;
2833 
2834   PetscFunctionBegin;
2835   ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2836   if (str == SAME_NONZERO_PATTERN) {
2837     PetscScalar alpha = a;
2838     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2839     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
2840     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2841   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2842     if (y->xtoy && y->XtoY != X) {
2843       ierr = PetscFree(y->xtoy);CHKERRQ(ierr);
2844       ierr = MatDestroy(&y->XtoY);CHKERRQ(ierr);
2845     }
2846     if (!y->xtoy) { /* get xtoy */
2847       ierr    = MatAXPYGetxtoy_Private(X->rmap->n,x->i,x->j,NULL, y->i,y->j,NULL, &y->xtoy);CHKERRQ(ierr);
2848       y->XtoY = X;
2849       ierr    = PetscObjectReference((PetscObject)X);CHKERRQ(ierr);
2850     }
2851     for (i=0; i<x->nz; i++) y->a[y->xtoy[i]] += a*(x->a[i]);
2852     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2853     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);
2854   } else {
2855     Mat      B;
2856     PetscInt *nnz;
2857     ierr = PetscMalloc1(Y->rmap->N,&nnz);CHKERRQ(ierr);
2858     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2859     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2860     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2861     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2862     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
2863     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
2864     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
2865 
2866     PetscLogDouble t0,t1;
2867     ierr = PetscTime(&t0);CHKERRQ(ierr);
2868     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2869     ierr = PetscTime(&t1);CHKERRQ(ierr);
2870     printf("Time for aij MatAXPY_BasicWithPreallocation: %g\n",t1-t0);
2871 
2872     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
2873     ierr = PetscFree(nnz);CHKERRQ(ierr);
2874   }
2875   PetscFunctionReturn(0);
2876 }
2877 
2878 #undef __FUNCT__
2879 #define __FUNCT__ "MatConjugate_SeqAIJ"
2880 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
2881 {
2882 #if defined(PETSC_USE_COMPLEX)
2883   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
2884   PetscInt    i,nz;
2885   PetscScalar *a;
2886 
2887   PetscFunctionBegin;
2888   nz = aij->nz;
2889   a  = aij->a;
2890   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
2891 #else
2892   PetscFunctionBegin;
2893 #endif
2894   PetscFunctionReturn(0);
2895 }
2896 
2897 #undef __FUNCT__
2898 #define __FUNCT__ "MatGetRowMaxAbs_SeqAIJ"
2899 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2900 {
2901   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2902   PetscErrorCode ierr;
2903   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2904   PetscReal      atmp;
2905   PetscScalar    *x;
2906   MatScalar      *aa;
2907 
2908   PetscFunctionBegin;
2909   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2910   aa = a->a;
2911   ai = a->i;
2912   aj = a->j;
2913 
2914   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2915   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2916   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2917   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2918   for (i=0; i<m; i++) {
2919     ncols = ai[1] - ai[0]; ai++;
2920     x[i]  = 0.0;
2921     for (j=0; j<ncols; j++) {
2922       atmp = PetscAbsScalar(*aa);
2923       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
2924       aa++; aj++;
2925     }
2926   }
2927   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2928   PetscFunctionReturn(0);
2929 }
2930 
2931 #undef __FUNCT__
2932 #define __FUNCT__ "MatGetRowMax_SeqAIJ"
2933 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2934 {
2935   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2936   PetscErrorCode ierr;
2937   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2938   PetscScalar    *x;
2939   MatScalar      *aa;
2940 
2941   PetscFunctionBegin;
2942   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2943   aa = a->a;
2944   ai = a->i;
2945   aj = a->j;
2946 
2947   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2948   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2949   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2950   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
2951   for (i=0; i<m; i++) {
2952     ncols = ai[1] - ai[0]; ai++;
2953     if (ncols == A->cmap->n) { /* row is dense */
2954       x[i] = *aa; if (idx) idx[i] = 0;
2955     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
2956       x[i] = 0.0;
2957       if (idx) {
2958         idx[i] = 0; /* in case ncols is zero */
2959         for (j=0;j<ncols;j++) { /* find first implicit 0.0 in the row */
2960           if (aj[j] > j) {
2961             idx[i] = j;
2962             break;
2963           }
2964         }
2965       }
2966     }
2967     for (j=0; j<ncols; j++) {
2968       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
2969       aa++; aj++;
2970     }
2971   }
2972   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
2973   PetscFunctionReturn(0);
2974 }
2975 
2976 #undef __FUNCT__
2977 #define __FUNCT__ "MatGetRowMinAbs_SeqAIJ"
2978 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
2979 {
2980   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2981   PetscErrorCode ierr;
2982   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
2983   PetscReal      atmp;
2984   PetscScalar    *x;
2985   MatScalar      *aa;
2986 
2987   PetscFunctionBegin;
2988   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2989   aa = a->a;
2990   ai = a->i;
2991   aj = a->j;
2992 
2993   ierr = VecSet(v,0.0);CHKERRQ(ierr);
2994   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
2995   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
2996   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);
2997   for (i=0; i<m; i++) {
2998     ncols = ai[1] - ai[0]; ai++;
2999     if (ncols) {
3000       /* Get first nonzero */
3001       for (j = 0; j < ncols; j++) {
3002         atmp = PetscAbsScalar(aa[j]);
3003         if (atmp > 1.0e-12) {
3004           x[i] = atmp;
3005           if (idx) idx[i] = aj[j];
3006           break;
3007         }
3008       }
3009       if (j == ncols) {x[i] = PetscAbsScalar(*aa); if (idx) idx[i] = *aj;}
3010     } else {
3011       x[i] = 0.0; if (idx) idx[i] = 0;
3012     }
3013     for (j = 0; j < ncols; j++) {
3014       atmp = PetscAbsScalar(*aa);
3015       if (atmp > 1.0e-12 && PetscAbsScalar(x[i]) > atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3016       aa++; aj++;
3017     }
3018   }
3019   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3020   PetscFunctionReturn(0);
3021 }
3022 
3023 #undef __FUNCT__
3024 #define __FUNCT__ "MatGetRowMin_SeqAIJ"
3025 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3026 {
3027   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3028   PetscErrorCode ierr;
3029   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3030   PetscScalar    *x;
3031   MatScalar      *aa;
3032 
3033   PetscFunctionBegin;
3034   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3035   aa = a->a;
3036   ai = a->i;
3037   aj = a->j;
3038 
3039   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3040   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3041   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3042   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3043   for (i=0; i<m; i++) {
3044     ncols = ai[1] - ai[0]; ai++;
3045     if (ncols == A->cmap->n) { /* row is dense */
3046       x[i] = *aa; if (idx) idx[i] = 0;
3047     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3048       x[i] = 0.0;
3049       if (idx) {   /* find first implicit 0.0 in the row */
3050         idx[i] = 0; /* in case ncols is zero */
3051         for (j=0; j<ncols; j++) {
3052           if (aj[j] > j) {
3053             idx[i] = j;
3054             break;
3055           }
3056         }
3057       }
3058     }
3059     for (j=0; j<ncols; j++) {
3060       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3061       aa++; aj++;
3062     }
3063   }
3064   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3065   PetscFunctionReturn(0);
3066 }
3067 
3068 #include <petscblaslapack.h>
3069 #include <petsc-private/kernels/blockinvert.h>
3070 
3071 #undef __FUNCT__
3072 #define __FUNCT__ "MatInvertBlockDiagonal_SeqAIJ"
3073 PetscErrorCode  MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3074 {
3075   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
3076   PetscErrorCode ierr;
3077   PetscInt       i,bs = PetscAbs(A->rmap->bs),mbs = A->rmap->n/bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3078   MatScalar      *diag,work[25],*v_work;
3079   PetscReal      shift = 0.0;
3080 
3081   PetscFunctionBegin;
3082   if (a->ibdiagvalid) {
3083     if (values) *values = a->ibdiag;
3084     PetscFunctionReturn(0);
3085   }
3086   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3087   if (!a->ibdiag) {
3088     ierr = PetscMalloc1(bs2*mbs,&a->ibdiag);CHKERRQ(ierr);
3089     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3090   }
3091   diag = a->ibdiag;
3092   if (values) *values = a->ibdiag;
3093   /* factor and invert each block */
3094   switch (bs) {
3095   case 1:
3096     for (i=0; i<mbs; i++) {
3097       ierr    = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3098       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3099     }
3100     break;
3101   case 2:
3102     for (i=0; i<mbs; i++) {
3103       ij[0] = 2*i; ij[1] = 2*i + 1;
3104       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3105       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift);CHKERRQ(ierr);
3106       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
3107       diag += 4;
3108     }
3109     break;
3110   case 3:
3111     for (i=0; i<mbs; i++) {
3112       ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
3113       ierr  = MatGetValues(A,3,ij,3,ij,diag);CHKERRQ(ierr);
3114       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr);
3115       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3116       diag += 9;
3117     }
3118     break;
3119   case 4:
3120     for (i=0; i<mbs; i++) {
3121       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3122       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3123       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift);CHKERRQ(ierr);
3124       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3125       diag += 16;
3126     }
3127     break;
3128   case 5:
3129     for (i=0; i<mbs; i++) {
3130       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3131       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3132       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift);CHKERRQ(ierr);
3133       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3134       diag += 25;
3135     }
3136     break;
3137   case 6:
3138     for (i=0; i<mbs; i++) {
3139       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;
3140       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3141       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift);CHKERRQ(ierr);
3142       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3143       diag += 36;
3144     }
3145     break;
3146   case 7:
3147     for (i=0; i<mbs; i++) {
3148       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;
3149       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3150       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift);CHKERRQ(ierr);
3151       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3152       diag += 49;
3153     }
3154     break;
3155   default:
3156     ierr = PetscMalloc3(bs,&v_work,bs,&v_pivots,bs,&IJ);CHKERRQ(ierr);
3157     for (i=0; i<mbs; i++) {
3158       for (j=0; j<bs; j++) {
3159         IJ[j] = bs*i + j;
3160       }
3161       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3162       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work);CHKERRQ(ierr);
3163       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3164       diag += bs2;
3165     }
3166     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3167   }
3168   a->ibdiagvalid = PETSC_TRUE;
3169   PetscFunctionReturn(0);
3170 }
3171 
3172 #undef __FUNCT__
3173 #define __FUNCT__ "MatSetRandom_SeqAIJ"
3174 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3175 {
3176   PetscErrorCode ierr;
3177   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3178   PetscScalar    a;
3179   PetscInt       m,n,i,j,col;
3180 
3181   PetscFunctionBegin;
3182   if (!x->assembled) {
3183     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3184     for (i=0; i<m; i++) {
3185       for (j=0; j<aij->imax[i]; j++) {
3186         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3187         col  = (PetscInt)(n*PetscRealPart(a));
3188         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3189       }
3190     }
3191   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet coded");
3192   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3193   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3194   PetscFunctionReturn(0);
3195 }
3196 
3197 /* -------------------------------------------------------------------*/
3198 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3199                                         MatGetRow_SeqAIJ,
3200                                         MatRestoreRow_SeqAIJ,
3201                                         MatMult_SeqAIJ,
3202                                 /*  4*/ MatMultAdd_SeqAIJ,
3203                                         MatMultTranspose_SeqAIJ,
3204                                         MatMultTransposeAdd_SeqAIJ,
3205                                         0,
3206                                         0,
3207                                         0,
3208                                 /* 10*/ 0,
3209                                         MatLUFactor_SeqAIJ,
3210                                         0,
3211                                         MatSOR_SeqAIJ,
3212                                         MatTranspose_SeqAIJ,
3213                                 /*1 5*/ MatGetInfo_SeqAIJ,
3214                                         MatEqual_SeqAIJ,
3215                                         MatGetDiagonal_SeqAIJ,
3216                                         MatDiagonalScale_SeqAIJ,
3217                                         MatNorm_SeqAIJ,
3218                                 /* 20*/ 0,
3219                                         MatAssemblyEnd_SeqAIJ,
3220                                         MatSetOption_SeqAIJ,
3221                                         MatZeroEntries_SeqAIJ,
3222                                 /* 24*/ MatZeroRows_SeqAIJ,
3223                                         0,
3224                                         0,
3225                                         0,
3226                                         0,
3227                                 /* 29*/ MatSetUp_SeqAIJ,
3228                                         0,
3229                                         0,
3230                                         0,
3231                                         0,
3232                                 /* 34*/ MatDuplicate_SeqAIJ,
3233                                         0,
3234                                         0,
3235                                         MatILUFactor_SeqAIJ,
3236                                         0,
3237                                 /* 39*/ MatAXPY_SeqAIJ,
3238                                         MatGetSubMatrices_SeqAIJ,
3239                                         MatIncreaseOverlap_SeqAIJ,
3240                                         MatGetValues_SeqAIJ,
3241                                         MatCopy_SeqAIJ,
3242                                 /* 44*/ MatGetRowMax_SeqAIJ,
3243                                         MatScale_SeqAIJ,
3244                                         0,
3245                                         MatDiagonalSet_SeqAIJ,
3246                                         MatZeroRowsColumns_SeqAIJ,
3247                                 /* 49*/ MatSetRandom_SeqAIJ,
3248                                         MatGetRowIJ_SeqAIJ,
3249                                         MatRestoreRowIJ_SeqAIJ,
3250                                         MatGetColumnIJ_SeqAIJ,
3251                                         MatRestoreColumnIJ_SeqAIJ,
3252                                 /* 54*/ MatFDColoringCreate_SeqXAIJ,
3253                                         0,
3254                                         0,
3255                                         MatPermute_SeqAIJ,
3256                                         0,
3257                                 /* 59*/ 0,
3258                                         MatDestroy_SeqAIJ,
3259                                         MatView_SeqAIJ,
3260                                         0,
3261                                         MatMatMatMult_SeqAIJ_SeqAIJ_SeqAIJ,
3262                                 /* 64*/ MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ,
3263                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3264                                         0,
3265                                         0,
3266                                         0,
3267                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3268                                         MatGetRowMinAbs_SeqAIJ,
3269                                         0,
3270                                         MatSetColoring_SeqAIJ,
3271                                         0,
3272                                 /* 74*/ MatSetValuesAdifor_SeqAIJ,
3273                                         MatFDColoringApply_AIJ,
3274                                         0,
3275                                         0,
3276                                         0,
3277                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3278                                         0,
3279                                         0,
3280                                         0,
3281                                         MatLoad_SeqAIJ,
3282                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3283                                         MatIsHermitian_SeqAIJ,
3284                                         0,
3285                                         0,
3286                                         0,
3287                                 /* 89*/ MatMatMult_SeqAIJ_SeqAIJ,
3288                                         MatMatMultSymbolic_SeqAIJ_SeqAIJ,
3289                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3290                                         MatPtAP_SeqAIJ_SeqAIJ,
3291                                         MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy,
3292                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ,
3293                                         MatMatTransposeMult_SeqAIJ_SeqAIJ,
3294                                         MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ,
3295                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3296                                         0,
3297                                 /* 99*/ 0,
3298                                         0,
3299                                         0,
3300                                         MatConjugate_SeqAIJ,
3301                                         0,
3302                                 /*104*/ MatSetValuesRow_SeqAIJ,
3303                                         MatRealPart_SeqAIJ,
3304                                         MatImaginaryPart_SeqAIJ,
3305                                         0,
3306                                         0,
3307                                 /*109*/ MatMatSolve_SeqAIJ,
3308                                         0,
3309                                         MatGetRowMin_SeqAIJ,
3310                                         0,
3311                                         MatMissingDiagonal_SeqAIJ,
3312                                 /*114*/ 0,
3313                                         0,
3314                                         0,
3315                                         0,
3316                                         0,
3317                                 /*119*/ 0,
3318                                         0,
3319                                         0,
3320                                         0,
3321                                         MatGetMultiProcBlock_SeqAIJ,
3322                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3323                                         MatGetColumnNorms_SeqAIJ,
3324                                         MatInvertBlockDiagonal_SeqAIJ,
3325                                         0,
3326                                         0,
3327                                 /*129*/ 0,
3328                                         MatTransposeMatMult_SeqAIJ_SeqAIJ,
3329                                         MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ,
3330                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3331                                         MatTransposeColoringCreate_SeqAIJ,
3332                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3333                                         MatTransColoringApplyDenToSp_SeqAIJ,
3334                                         MatRARt_SeqAIJ_SeqAIJ,
3335                                         MatRARtSymbolic_SeqAIJ_SeqAIJ,
3336                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3337                                  /*139*/0,
3338                                         0,
3339                                         0,
3340                                         MatFDColoringSetUp_SeqXAIJ,
3341                                         MatFindOffBlockDiagonalEntries_SeqAIJ
3342 };
3343 
3344 #undef __FUNCT__
3345 #define __FUNCT__ "MatSeqAIJSetColumnIndices_SeqAIJ"
3346 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3347 {
3348   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3349   PetscInt   i,nz,n;
3350 
3351   PetscFunctionBegin;
3352   nz = aij->maxnz;
3353   n  = mat->rmap->n;
3354   for (i=0; i<nz; i++) {
3355     aij->j[i] = indices[i];
3356   }
3357   aij->nz = nz;
3358   for (i=0; i<n; i++) {
3359     aij->ilen[i] = aij->imax[i];
3360   }
3361   PetscFunctionReturn(0);
3362 }
3363 
3364 #undef __FUNCT__
3365 #define __FUNCT__ "MatSeqAIJSetColumnIndices"
3366 /*@
3367     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3368        in the matrix.
3369 
3370   Input Parameters:
3371 +  mat - the SeqAIJ matrix
3372 -  indices - the column indices
3373 
3374   Level: advanced
3375 
3376   Notes:
3377     This can be called if you have precomputed the nonzero structure of the
3378   matrix and want to provide it to the matrix object to improve the performance
3379   of the MatSetValues() operation.
3380 
3381     You MUST have set the correct numbers of nonzeros per row in the call to
3382   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3383 
3384     MUST be called before any calls to MatSetValues();
3385 
3386     The indices should start with zero, not one.
3387 
3388 @*/
3389 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3390 {
3391   PetscErrorCode ierr;
3392 
3393   PetscFunctionBegin;
3394   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3395   PetscValidPointer(indices,2);
3396   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3397   PetscFunctionReturn(0);
3398 }
3399 
3400 /* ----------------------------------------------------------------------------------------*/
3401 
3402 #undef __FUNCT__
3403 #define __FUNCT__ "MatStoreValues_SeqAIJ"
3404 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3405 {
3406   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3407   PetscErrorCode ierr;
3408   size_t         nz = aij->i[mat->rmap->n];
3409 
3410   PetscFunctionBegin;
3411   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3412 
3413   /* allocate space for values if not already there */
3414   if (!aij->saved_values) {
3415     ierr = PetscMalloc1((nz+1),&aij->saved_values);CHKERRQ(ierr);
3416     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3417   }
3418 
3419   /* copy values over */
3420   ierr = PetscMemcpy(aij->saved_values,aij->a,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3421   PetscFunctionReturn(0);
3422 }
3423 
3424 #undef __FUNCT__
3425 #define __FUNCT__ "MatStoreValues"
3426 /*@
3427     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3428        example, reuse of the linear part of a Jacobian, while recomputing the
3429        nonlinear portion.
3430 
3431    Collect on Mat
3432 
3433   Input Parameters:
3434 .  mat - the matrix (currently only AIJ matrices support this option)
3435 
3436   Level: advanced
3437 
3438   Common Usage, with SNESSolve():
3439 $    Create Jacobian matrix
3440 $    Set linear terms into matrix
3441 $    Apply boundary conditions to matrix, at this time matrix must have
3442 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3443 $      boundary conditions again will not change the nonzero structure
3444 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3445 $    ierr = MatStoreValues(mat);
3446 $    Call SNESSetJacobian() with matrix
3447 $    In your Jacobian routine
3448 $      ierr = MatRetrieveValues(mat);
3449 $      Set nonlinear terms in matrix
3450 
3451   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3452 $    // build linear portion of Jacobian
3453 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3454 $    ierr = MatStoreValues(mat);
3455 $    loop over nonlinear iterations
3456 $       ierr = MatRetrieveValues(mat);
3457 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3458 $       // call MatAssemblyBegin/End() on matrix
3459 $       Solve linear system with Jacobian
3460 $    endloop
3461 
3462   Notes:
3463     Matrix must already be assemblied before calling this routine
3464     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3465     calling this routine.
3466 
3467     When this is called multiple times it overwrites the previous set of stored values
3468     and does not allocated additional space.
3469 
3470 .seealso: MatRetrieveValues()
3471 
3472 @*/
3473 PetscErrorCode  MatStoreValues(Mat mat)
3474 {
3475   PetscErrorCode ierr;
3476 
3477   PetscFunctionBegin;
3478   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3479   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3480   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3481   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3482   PetscFunctionReturn(0);
3483 }
3484 
3485 #undef __FUNCT__
3486 #define __FUNCT__ "MatRetrieveValues_SeqAIJ"
3487 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3488 {
3489   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3490   PetscErrorCode ierr;
3491   PetscInt       nz = aij->i[mat->rmap->n];
3492 
3493   PetscFunctionBegin;
3494   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3495   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3496   /* copy values over */
3497   ierr = PetscMemcpy(aij->a,aij->saved_values,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3498   PetscFunctionReturn(0);
3499 }
3500 
3501 #undef __FUNCT__
3502 #define __FUNCT__ "MatRetrieveValues"
3503 /*@
3504     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3505        example, reuse of the linear part of a Jacobian, while recomputing the
3506        nonlinear portion.
3507 
3508    Collect on Mat
3509 
3510   Input Parameters:
3511 .  mat - the matrix (currently on AIJ matrices support this option)
3512 
3513   Level: advanced
3514 
3515 .seealso: MatStoreValues()
3516 
3517 @*/
3518 PetscErrorCode  MatRetrieveValues(Mat mat)
3519 {
3520   PetscErrorCode ierr;
3521 
3522   PetscFunctionBegin;
3523   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3524   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3525   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3526   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3527   PetscFunctionReturn(0);
3528 }
3529 
3530 
3531 /* --------------------------------------------------------------------------------*/
3532 #undef __FUNCT__
3533 #define __FUNCT__ "MatCreateSeqAIJ"
3534 /*@C
3535    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3536    (the default parallel PETSc format).  For good matrix assembly performance
3537    the user should preallocate the matrix storage by setting the parameter nz
3538    (or the array nnz).  By setting these parameters accurately, performance
3539    during matrix assembly can be increased by more than a factor of 50.
3540 
3541    Collective on MPI_Comm
3542 
3543    Input Parameters:
3544 +  comm - MPI communicator, set to PETSC_COMM_SELF
3545 .  m - number of rows
3546 .  n - number of columns
3547 .  nz - number of nonzeros per row (same for all rows)
3548 -  nnz - array containing the number of nonzeros in the various rows
3549          (possibly different for each row) or NULL
3550 
3551    Output Parameter:
3552 .  A - the matrix
3553 
3554    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3555    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3556    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3557 
3558    Notes:
3559    If nnz is given then nz is ignored
3560 
3561    The AIJ format (also called the Yale sparse matrix format or
3562    compressed row storage), is fully compatible with standard Fortran 77
3563    storage.  That is, the stored row and column indices can begin at
3564    either one (as in Fortran) or zero.  See the users' manual for details.
3565 
3566    Specify the preallocated storage with either nz or nnz (not both).
3567    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3568    allocation.  For large problems you MUST preallocate memory or you
3569    will get TERRIBLE performance, see the users' manual chapter on matrices.
3570 
3571    By default, this format uses inodes (identical nodes) when possible, to
3572    improve numerical efficiency of matrix-vector products and solves. We
3573    search for consecutive rows with the same nonzero structure, thereby
3574    reusing matrix information to achieve increased efficiency.
3575 
3576    Options Database Keys:
3577 +  -mat_no_inode  - Do not use inodes
3578 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3579 
3580    Level: intermediate
3581 
3582 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3583 
3584 @*/
3585 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3586 {
3587   PetscErrorCode ierr;
3588 
3589   PetscFunctionBegin;
3590   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3591   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3592   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3593   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3594   PetscFunctionReturn(0);
3595 }
3596 
3597 #undef __FUNCT__
3598 #define __FUNCT__ "MatSeqAIJSetPreallocation"
3599 /*@C
3600    MatSeqAIJSetPreallocation - For good matrix assembly performance
3601    the user should preallocate the matrix storage by setting the parameter nz
3602    (or the array nnz).  By setting these parameters accurately, performance
3603    during matrix assembly can be increased by more than a factor of 50.
3604 
3605    Collective on MPI_Comm
3606 
3607    Input Parameters:
3608 +  B - The matrix
3609 .  nz - number of nonzeros per row (same for all rows)
3610 -  nnz - array containing the number of nonzeros in the various rows
3611          (possibly different for each row) or NULL
3612 
3613    Notes:
3614      If nnz is given then nz is ignored
3615 
3616     The AIJ format (also called the Yale sparse matrix format or
3617    compressed row storage), is fully compatible with standard Fortran 77
3618    storage.  That is, the stored row and column indices can begin at
3619    either one (as in Fortran) or zero.  See the users' manual for details.
3620 
3621    Specify the preallocated storage with either nz or nnz (not both).
3622    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3623    allocation.  For large problems you MUST preallocate memory or you
3624    will get TERRIBLE performance, see the users' manual chapter on matrices.
3625 
3626    You can call MatGetInfo() to get information on how effective the preallocation was;
3627    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3628    You can also run with the option -info and look for messages with the string
3629    malloc in them to see if additional memory allocation was needed.
3630 
3631    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3632    entries or columns indices
3633 
3634    By default, this format uses inodes (identical nodes) when possible, to
3635    improve numerical efficiency of matrix-vector products and solves. We
3636    search for consecutive rows with the same nonzero structure, thereby
3637    reusing matrix information to achieve increased efficiency.
3638 
3639    Options Database Keys:
3640 +  -mat_no_inode  - Do not use inodes
3641 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3642 -  -mat_aij_oneindex - Internally use indexing starting at 1
3643         rather than 0.  Note that when calling MatSetValues(),
3644         the user still MUST index entries starting at 0!
3645 
3646    Level: intermediate
3647 
3648 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatGetInfo()
3649 
3650 @*/
3651 PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
3652 {
3653   PetscErrorCode ierr;
3654 
3655   PetscFunctionBegin;
3656   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3657   PetscValidType(B,1);
3658   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));CHKERRQ(ierr);
3659   PetscFunctionReturn(0);
3660 }
3661 
3662 #undef __FUNCT__
3663 #define __FUNCT__ "MatSeqAIJSetPreallocation_SeqAIJ"
3664 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3665 {
3666   Mat_SeqAIJ     *b;
3667   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3668   PetscErrorCode ierr;
3669   PetscInt       i;
3670 
3671   PetscFunctionBegin;
3672   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3673   if (nz == MAT_SKIP_ALLOCATION) {
3674     skipallocation = PETSC_TRUE;
3675     nz             = 0;
3676   }
3677 
3678   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3679   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3680 
3681   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3682   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %D",nz);
3683   if (nnz) {
3684     for (i=0; i<B->rmap->n; i++) {
3685       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]);
3686       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);
3687     }
3688   }
3689 
3690   B->preallocated = PETSC_TRUE;
3691 
3692   b = (Mat_SeqAIJ*)B->data;
3693 
3694   if (!skipallocation) {
3695     if (!b->imax) {
3696       ierr = PetscMalloc2(B->rmap->n,&b->imax,B->rmap->n,&b->ilen);CHKERRQ(ierr);
3697       ierr = PetscLogObjectMemory((PetscObject)B,2*B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3698     }
3699     if (!nnz) {
3700       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3701       else if (nz < 0) nz = 1;
3702       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
3703       nz = nz*B->rmap->n;
3704     } else {
3705       nz = 0;
3706       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz += nnz[i];}
3707     }
3708     /* b->ilen will count nonzeros in each row so far. */
3709     for (i=0; i<B->rmap->n; i++) b->ilen[i] = 0;
3710 
3711     /* allocate the matrix space */
3712     ierr    = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
3713     ierr    = PetscMalloc3(nz,&b->a,nz,&b->j,B->rmap->n+1,&b->i);CHKERRQ(ierr);
3714     ierr    = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
3715     b->i[0] = 0;
3716     for (i=1; i<B->rmap->n+1; i++) {
3717       b->i[i] = b->i[i-1] + b->imax[i-1];
3718     }
3719     b->singlemalloc = PETSC_TRUE;
3720     b->free_a       = PETSC_TRUE;
3721     b->free_ij      = PETSC_TRUE;
3722 #if defined(PETSC_THREADCOMM_ACTIVE)
3723     ierr = MatZeroEntries_SeqAIJ(B);CHKERRQ(ierr);
3724 #endif
3725   } else {
3726     b->free_a  = PETSC_FALSE;
3727     b->free_ij = PETSC_FALSE;
3728   }
3729 
3730   b->nz               = 0;
3731   b->maxnz            = nz;
3732   B->info.nz_unneeded = (double)b->maxnz;
3733   if (realalloc) {
3734     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3735   }
3736   PetscFunctionReturn(0);
3737 }
3738 
3739 #undef  __FUNCT__
3740 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR"
3741 /*@
3742    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
3743 
3744    Input Parameters:
3745 +  B - the matrix
3746 .  i - the indices into j for the start of each row (starts with zero)
3747 .  j - the column indices for each row (starts with zero) these must be sorted for each row
3748 -  v - optional values in the matrix
3749 
3750    Level: developer
3751 
3752    The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
3753 
3754 .keywords: matrix, aij, compressed row, sparse, sequential
3755 
3756 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), SeqAIJ
3757 @*/
3758 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
3759 {
3760   PetscErrorCode ierr;
3761 
3762   PetscFunctionBegin;
3763   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3764   PetscValidType(B,1);
3765   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3766   PetscFunctionReturn(0);
3767 }
3768 
3769 #undef  __FUNCT__
3770 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR_SeqAIJ"
3771 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3772 {
3773   PetscInt       i;
3774   PetscInt       m,n;
3775   PetscInt       nz;
3776   PetscInt       *nnz, nz_max = 0;
3777   PetscScalar    *values;
3778   PetscErrorCode ierr;
3779 
3780   PetscFunctionBegin;
3781   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
3782 
3783   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3784   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3785 
3786   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
3787   ierr = PetscMalloc1((m+1), &nnz);CHKERRQ(ierr);
3788   for (i = 0; i < m; i++) {
3789     nz     = Ii[i+1]- Ii[i];
3790     nz_max = PetscMax(nz_max, nz);
3791     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
3792     nnz[i] = nz;
3793   }
3794   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
3795   ierr = PetscFree(nnz);CHKERRQ(ierr);
3796 
3797   if (v) {
3798     values = (PetscScalar*) v;
3799   } else {
3800     ierr = PetscCalloc1(nz_max, &values);CHKERRQ(ierr);
3801   }
3802 
3803   for (i = 0; i < m; i++) {
3804     nz   = Ii[i+1] - Ii[i];
3805     ierr = MatSetValues_SeqAIJ(B, 1, &i, nz, J+Ii[i], values + (v ? Ii[i] : 0), INSERT_VALUES);CHKERRQ(ierr);
3806   }
3807 
3808   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3809   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3810 
3811   if (!v) {
3812     ierr = PetscFree(values);CHKERRQ(ierr);
3813   }
3814   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3815   PetscFunctionReturn(0);
3816 }
3817 
3818 #include <../src/mat/impls/dense/seq/dense.h>
3819 #include <petsc-private/kernels/petscaxpy.h>
3820 
3821 #undef __FUNCT__
3822 #define __FUNCT__ "MatMatMultNumeric_SeqDense_SeqAIJ"
3823 /*
3824     Computes (B'*A')' since computing B*A directly is untenable
3825 
3826                n                       p                          p
3827         (              )       (              )         (                  )
3828       m (      A       )  *  n (       B      )   =   m (         C        )
3829         (              )       (              )         (                  )
3830 
3831 */
3832 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
3833 {
3834   PetscErrorCode    ierr;
3835   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
3836   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
3837   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
3838   PetscInt          i,n,m,q,p;
3839   const PetscInt    *ii,*idx;
3840   const PetscScalar *b,*a,*a_q;
3841   PetscScalar       *c,*c_q;
3842 
3843   PetscFunctionBegin;
3844   m    = A->rmap->n;
3845   n    = A->cmap->n;
3846   p    = B->cmap->n;
3847   a    = sub_a->v;
3848   b    = sub_b->a;
3849   c    = sub_c->v;
3850   ierr = PetscMemzero(c,m*p*sizeof(PetscScalar));CHKERRQ(ierr);
3851 
3852   ii  = sub_b->i;
3853   idx = sub_b->j;
3854   for (i=0; i<n; i++) {
3855     q = ii[i+1] - ii[i];
3856     while (q-->0) {
3857       c_q = c + m*(*idx);
3858       a_q = a + m*i;
3859       PetscKernelAXPY(c_q,*b,a_q,m);
3860       idx++;
3861       b++;
3862     }
3863   }
3864   PetscFunctionReturn(0);
3865 }
3866 
3867 #undef __FUNCT__
3868 #define __FUNCT__ "MatMatMultSymbolic_SeqDense_SeqAIJ"
3869 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
3870 {
3871   PetscErrorCode ierr;
3872   PetscInt       m=A->rmap->n,n=B->cmap->n;
3873   Mat            Cmat;
3874 
3875   PetscFunctionBegin;
3876   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);
3877   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
3878   ierr = MatSetSizes(Cmat,m,n,m,n);CHKERRQ(ierr);
3879   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
3880   ierr = MatSetType(Cmat,MATSEQDENSE);CHKERRQ(ierr);
3881   ierr = MatSeqDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
3882 
3883   Cmat->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
3884 
3885   *C = Cmat;
3886   PetscFunctionReturn(0);
3887 }
3888 
3889 /* ----------------------------------------------------------------*/
3890 #undef __FUNCT__
3891 #define __FUNCT__ "MatMatMult_SeqDense_SeqAIJ"
3892 PetscErrorCode MatMatMult_SeqDense_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
3893 {
3894   PetscErrorCode ierr;
3895 
3896   PetscFunctionBegin;
3897   if (scall == MAT_INITIAL_MATRIX) {
3898     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
3899     ierr = MatMatMultSymbolic_SeqDense_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
3900     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
3901   }
3902   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
3903   ierr = MatMatMultNumeric_SeqDense_SeqAIJ(A,B,*C);CHKERRQ(ierr);
3904   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
3905   PetscFunctionReturn(0);
3906 }
3907 
3908 
3909 /*MC
3910    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
3911    based on compressed sparse row format.
3912 
3913    Options Database Keys:
3914 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
3915 
3916   Level: beginner
3917 
3918 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
3919 M*/
3920 
3921 /*MC
3922    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
3923 
3924    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
3925    and MATMPIAIJ otherwise.  As a result, for single process communicators,
3926   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
3927   for communicators controlling multiple processes.  It is recommended that you call both of
3928   the above preallocation routines for simplicity.
3929 
3930    Options Database Keys:
3931 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
3932 
3933   Developer Notes: Subclasses include MATAIJCUSP, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
3934    enough exist.
3935 
3936   Level: beginner
3937 
3938 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
3939 M*/
3940 
3941 /*MC
3942    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
3943 
3944    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
3945    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
3946    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
3947   for communicators controlling multiple processes.  It is recommended that you call both of
3948   the above preallocation routines for simplicity.
3949 
3950    Options Database Keys:
3951 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
3952 
3953   Level: beginner
3954 
3955 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
3956 M*/
3957 
3958 #if defined(PETSC_HAVE_PASTIX)
3959 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_pastix(Mat,MatFactorType,Mat*);
3960 #endif
3961 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
3962 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_essl(Mat,MatFactorType,Mat*);
3963 #endif
3964 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
3965 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_petsc(Mat,MatFactorType,Mat*);
3966 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_bas(Mat,MatFactorType,Mat*);
3967 extern PetscErrorCode  MatGetFactorAvailable_seqaij_petsc(Mat,MatFactorType,PetscBool*);
3968 #if defined(PETSC_HAVE_MUMPS)
3969 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mumps(Mat,MatFactorType,Mat*);
3970 #endif
3971 #if defined(PETSC_HAVE_SUPERLU)
3972 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu(Mat,MatFactorType,Mat*);
3973 #endif
3974 #if defined(PETSC_HAVE_MKL_PARDISO)
3975 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mkl_pardiso(Mat,MatFactorType,Mat*);
3976 #endif
3977 #if defined(PETSC_HAVE_SUPERLU_DIST)
3978 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu_dist(Mat,MatFactorType,Mat*);
3979 #endif
3980 #if defined(PETSC_HAVE_SUITESPARSE)
3981 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_umfpack(Mat,MatFactorType,Mat*);
3982 #endif
3983 #if defined(PETSC_HAVE_SUITESPARSE)
3984 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_cholmod(Mat,MatFactorType,Mat*);
3985 #endif
3986 #if defined(PETSC_HAVE_SUITESPARSE)
3987 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_klu(Mat,MatFactorType,Mat*);
3988 #endif
3989 #if defined(PETSC_HAVE_LUSOL)
3990 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_lusol(Mat,MatFactorType,Mat*);
3991 #endif
3992 #if defined(PETSC_HAVE_MATLAB_ENGINE)
3993 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_matlab(Mat,MatFactorType,Mat*);
3994 extern PetscErrorCode  MatlabEnginePut_SeqAIJ(PetscObject,void*);
3995 extern PetscErrorCode  MatlabEngineGet_SeqAIJ(PetscObject,void*);
3996 #endif
3997 #if defined(PETSC_HAVE_CLIQUE)
3998 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_clique(Mat,MatFactorType,Mat*);
3999 #endif
4000 
4001 
4002 #undef __FUNCT__
4003 #define __FUNCT__ "MatSeqAIJGetArray"
4004 /*@C
4005    MatSeqAIJGetArray - gives access to the array where the data for a SeqSeqAIJ matrix is stored
4006 
4007    Not Collective
4008 
4009    Input Parameter:
4010 .  mat - a MATSEQDENSE matrix
4011 
4012    Output Parameter:
4013 .   array - pointer to the data
4014 
4015    Level: intermediate
4016 
4017 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4018 @*/
4019 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4020 {
4021   PetscErrorCode ierr;
4022 
4023   PetscFunctionBegin;
4024   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4025   PetscFunctionReturn(0);
4026 }
4027 
4028 #undef __FUNCT__
4029 #define __FUNCT__ "MatSeqAIJGetMaxRowNonzeros"
4030 /*@C
4031    MatSeqAIJGetMaxRowNonzeros - returns the maximum number of nonzeros in any row
4032 
4033    Not Collective
4034 
4035    Input Parameter:
4036 .  mat - a MATSEQDENSE matrix
4037 
4038    Output Parameter:
4039 .   nz - the maximum number of nonzeros in any row
4040 
4041    Level: intermediate
4042 
4043 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4044 @*/
4045 PetscErrorCode  MatSeqAIJGetMaxRowNonzeros(Mat A,PetscInt *nz)
4046 {
4047   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
4048 
4049   PetscFunctionBegin;
4050   *nz = aij->rmax;
4051   PetscFunctionReturn(0);
4052 }
4053 
4054 #undef __FUNCT__
4055 #define __FUNCT__ "MatSeqAIJRestoreArray"
4056 /*@C
4057    MatSeqAIJRestoreArray - returns access to the array where the data for a SeqSeqAIJ matrix is stored obtained by MatSeqAIJGetArray()
4058 
4059    Not Collective
4060 
4061    Input Parameters:
4062 .  mat - a MATSEQDENSE matrix
4063 .  array - pointer to the data
4064 
4065    Level: intermediate
4066 
4067 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4068 @*/
4069 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4070 {
4071   PetscErrorCode ierr;
4072 
4073   PetscFunctionBegin;
4074   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4075   PetscFunctionReturn(0);
4076 }
4077 
4078 #undef __FUNCT__
4079 #define __FUNCT__ "MatCreate_SeqAIJ"
4080 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4081 {
4082   Mat_SeqAIJ     *b;
4083   PetscErrorCode ierr;
4084   PetscMPIInt    size;
4085 
4086   PetscFunctionBegin;
4087   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4088   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4089 
4090   ierr = PetscNewLog(B,&b);CHKERRQ(ierr);
4091 
4092   B->data = (void*)b;
4093 
4094   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4095 
4096   b->row                = 0;
4097   b->col                = 0;
4098   b->icol               = 0;
4099   b->reallocs           = 0;
4100   b->ignorezeroentries  = PETSC_FALSE;
4101   b->roworiented        = PETSC_TRUE;
4102   b->nonew              = 0;
4103   b->diag               = 0;
4104   b->solve_work         = 0;
4105   B->spptr              = 0;
4106   b->saved_values       = 0;
4107   b->idiag              = 0;
4108   b->mdiag              = 0;
4109   b->ssor_work          = 0;
4110   b->omega              = 1.0;
4111   b->fshift             = 0.0;
4112   b->idiagvalid         = PETSC_FALSE;
4113   b->ibdiagvalid        = PETSC_FALSE;
4114   b->keepnonzeropattern = PETSC_FALSE;
4115   b->xtoy               = 0;
4116   b->XtoY               = 0;
4117 
4118   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4119   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4120   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4121 
4122 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4123   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_matlab_C",MatGetFactor_seqaij_matlab);CHKERRQ(ierr);
4124   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4125   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4126 #endif
4127 #if defined(PETSC_HAVE_PASTIX)
4128   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_pastix_C",MatGetFactor_seqaij_pastix);CHKERRQ(ierr);
4129 #endif
4130 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
4131   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_essl_C",MatGetFactor_seqaij_essl);CHKERRQ(ierr);
4132 #endif
4133 #if defined(PETSC_HAVE_SUPERLU)
4134   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_C",MatGetFactor_seqaij_superlu);CHKERRQ(ierr);
4135 #endif
4136 #if defined(PETSC_HAVE_MKL_PARDISO)
4137   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mkl_pardiso_C",MatGetFactor_aij_mkl_pardiso);CHKERRQ(ierr);
4138 #endif
4139 #if defined(PETSC_HAVE_SUPERLU_DIST)
4140   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_dist_C",MatGetFactor_seqaij_superlu_dist);CHKERRQ(ierr);
4141 #endif
4142 #if defined(PETSC_HAVE_MUMPS)
4143   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mumps_C",MatGetFactor_aij_mumps);CHKERRQ(ierr);
4144 #endif
4145 #if defined(PETSC_HAVE_SUITESPARSE)
4146   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_umfpack_C",MatGetFactor_seqaij_umfpack);CHKERRQ(ierr);
4147 #endif
4148 #if defined(PETSC_HAVE_SUITESPARSE)
4149   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_cholmod_C",MatGetFactor_seqaij_cholmod);CHKERRQ(ierr);
4150 #endif
4151 #if defined(PETSC_HAVE_SUITESPARSE)
4152   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_klu_C",MatGetFactor_seqaij_klu);CHKERRQ(ierr);
4153 #endif
4154 #if defined(PETSC_HAVE_LUSOL)
4155   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_lusol_C",MatGetFactor_seqaij_lusol);CHKERRQ(ierr);
4156 #endif
4157 #if defined(PETSC_HAVE_CLIQUE)
4158   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_clique_C",MatGetFactor_aij_clique);CHKERRQ(ierr);
4159 #endif
4160 
4161   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_petsc_C",MatGetFactor_seqaij_petsc);CHKERRQ(ierr);
4162   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactorAvailable_petsc_C",MatGetFactorAvailable_seqaij_petsc);CHKERRQ(ierr);
4163   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_bas_C",MatGetFactor_seqaij_bas);CHKERRQ(ierr);
4164   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4165   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4166   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4167   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4168   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4169   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4170   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4171   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4172   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4173   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4174   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4175   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4176   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaij_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
4177   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaij_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
4178   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaij_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
4179   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4180   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4181   PetscFunctionReturn(0);
4182 }
4183 
4184 #undef __FUNCT__
4185 #define __FUNCT__ "MatDuplicateNoCreate_SeqAIJ"
4186 /*
4187     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4188 */
4189 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4190 {
4191   Mat_SeqAIJ     *c,*a = (Mat_SeqAIJ*)A->data;
4192   PetscErrorCode ierr;
4193   PetscInt       i,m = A->rmap->n;
4194 
4195   PetscFunctionBegin;
4196   c = (Mat_SeqAIJ*)C->data;
4197 
4198   C->factortype = A->factortype;
4199   c->row        = 0;
4200   c->col        = 0;
4201   c->icol       = 0;
4202   c->reallocs   = 0;
4203 
4204   C->assembled = PETSC_TRUE;
4205 
4206   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4207   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4208 
4209   ierr = PetscMalloc2(m,&c->imax,m,&c->ilen);CHKERRQ(ierr);
4210   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4211   for (i=0; i<m; i++) {
4212     c->imax[i] = a->imax[i];
4213     c->ilen[i] = a->ilen[i];
4214   }
4215 
4216   /* allocate the matrix space */
4217   if (mallocmatspace) {
4218     ierr = PetscMalloc3(a->i[m],&c->a,a->i[m],&c->j,m+1,&c->i);CHKERRQ(ierr);
4219     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4220 
4221     c->singlemalloc = PETSC_TRUE;
4222 
4223     ierr = PetscMemcpy(c->i,a->i,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4224     if (m > 0) {
4225       ierr = PetscMemcpy(c->j,a->j,(a->i[m])*sizeof(PetscInt));CHKERRQ(ierr);
4226       if (cpvalues == MAT_COPY_VALUES) {
4227         ierr = PetscMemcpy(c->a,a->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4228       } else {
4229         ierr = PetscMemzero(c->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4230       }
4231     }
4232   }
4233 
4234   c->ignorezeroentries = a->ignorezeroentries;
4235   c->roworiented       = a->roworiented;
4236   c->nonew             = a->nonew;
4237   if (a->diag) {
4238     ierr = PetscMalloc1((m+1),&c->diag);CHKERRQ(ierr);
4239     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4240     for (i=0; i<m; i++) {
4241       c->diag[i] = a->diag[i];
4242     }
4243   } else c->diag = 0;
4244 
4245   c->solve_work         = 0;
4246   c->saved_values       = 0;
4247   c->idiag              = 0;
4248   c->ssor_work          = 0;
4249   c->keepnonzeropattern = a->keepnonzeropattern;
4250   c->free_a             = PETSC_TRUE;
4251   c->free_ij            = PETSC_TRUE;
4252   c->xtoy               = 0;
4253   c->XtoY               = 0;
4254 
4255   c->rmax         = a->rmax;
4256   c->nz           = a->nz;
4257   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4258   C->preallocated = PETSC_TRUE;
4259 
4260   c->compressedrow.use   = a->compressedrow.use;
4261   c->compressedrow.nrows = a->compressedrow.nrows;
4262   if (a->compressedrow.use) {
4263     i    = a->compressedrow.nrows;
4264     ierr = PetscMalloc2(i+1,&c->compressedrow.i,i,&c->compressedrow.rindex);CHKERRQ(ierr);
4265     ierr = PetscMemcpy(c->compressedrow.i,a->compressedrow.i,(i+1)*sizeof(PetscInt));CHKERRQ(ierr);
4266     ierr = PetscMemcpy(c->compressedrow.rindex,a->compressedrow.rindex,i*sizeof(PetscInt));CHKERRQ(ierr);
4267   } else {
4268     c->compressedrow.use    = PETSC_FALSE;
4269     c->compressedrow.i      = NULL;
4270     c->compressedrow.rindex = NULL;
4271   }
4272   C->nonzerostate = A->nonzerostate;
4273 
4274   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4275   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4276   PetscFunctionReturn(0);
4277 }
4278 
4279 #undef __FUNCT__
4280 #define __FUNCT__ "MatDuplicate_SeqAIJ"
4281 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4282 {
4283   PetscErrorCode ierr;
4284 
4285   PetscFunctionBegin;
4286   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4287   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4288   if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) {
4289     ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
4290   }
4291   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4292   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4293   PetscFunctionReturn(0);
4294 }
4295 
4296 #undef __FUNCT__
4297 #define __FUNCT__ "MatLoad_SeqAIJ"
4298 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4299 {
4300   Mat_SeqAIJ     *a;
4301   PetscErrorCode ierr;
4302   PetscInt       i,sum,nz,header[4],*rowlengths = 0,M,N,rows,cols;
4303   int            fd;
4304   PetscMPIInt    size;
4305   MPI_Comm       comm;
4306   PetscInt       bs = 1;
4307 
4308   PetscFunctionBegin;
4309   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
4310   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4311   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"view must have one processor");
4312 
4313   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
4314   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
4315   ierr = PetscOptionsEnd();CHKERRQ(ierr);
4316   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
4317 
4318   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
4319   ierr = PetscBinaryRead(fd,header,4,PETSC_INT);CHKERRQ(ierr);
4320   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
4321   M = header[1]; N = header[2]; nz = header[3];
4322 
4323   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
4324 
4325   /* read in row lengths */
4326   ierr = PetscMalloc1(M,&rowlengths);CHKERRQ(ierr);
4327   ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
4328 
4329   /* check if sum of rowlengths is same as nz */
4330   for (i=0,sum=0; i< M; i++) sum +=rowlengths[i];
4331   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);
4332 
4333   /* set global size if not set already*/
4334   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) {
4335     ierr = MatSetSizes(newMat,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
4336   } else {
4337     /* if sizes and type are already set, check if the vector global sizes are correct */
4338     ierr = MatGetSize(newMat,&rows,&cols);CHKERRQ(ierr);
4339     if (rows < 0 && cols < 0) { /* user might provide local size instead of global size */
4340       ierr = MatGetLocalSize(newMat,&rows,&cols);CHKERRQ(ierr);
4341     }
4342     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);
4343   }
4344   ierr = MatSeqAIJSetPreallocation_SeqAIJ(newMat,0,rowlengths);CHKERRQ(ierr);
4345   a    = (Mat_SeqAIJ*)newMat->data;
4346 
4347   ierr = PetscBinaryRead(fd,a->j,nz,PETSC_INT);CHKERRQ(ierr);
4348 
4349   /* read in nonzero values */
4350   ierr = PetscBinaryRead(fd,a->a,nz,PETSC_SCALAR);CHKERRQ(ierr);
4351 
4352   /* set matrix "i" values */
4353   a->i[0] = 0;
4354   for (i=1; i<= M; i++) {
4355     a->i[i]      = a->i[i-1] + rowlengths[i-1];
4356     a->ilen[i-1] = rowlengths[i-1];
4357   }
4358   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
4359 
4360   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4361   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4362   PetscFunctionReturn(0);
4363 }
4364 
4365 #undef __FUNCT__
4366 #define __FUNCT__ "MatEqual_SeqAIJ"
4367 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4368 {
4369   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4370   PetscErrorCode ierr;
4371 #if defined(PETSC_USE_COMPLEX)
4372   PetscInt k;
4373 #endif
4374 
4375   PetscFunctionBegin;
4376   /* If the  matrix dimensions are not equal,or no of nonzeros */
4377   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4378     *flg = PETSC_FALSE;
4379     PetscFunctionReturn(0);
4380   }
4381 
4382   /* if the a->i are the same */
4383   ierr = PetscMemcmp(a->i,b->i,(A->rmap->n+1)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4384   if (!*flg) PetscFunctionReturn(0);
4385 
4386   /* if a->j are the same */
4387   ierr = PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4388   if (!*flg) PetscFunctionReturn(0);
4389 
4390   /* if a->a are the same */
4391 #if defined(PETSC_USE_COMPLEX)
4392   for (k=0; k<a->nz; k++) {
4393     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4394       *flg = PETSC_FALSE;
4395       PetscFunctionReturn(0);
4396     }
4397   }
4398 #else
4399   ierr = PetscMemcmp(a->a,b->a,(a->nz)*sizeof(PetscScalar),flg);CHKERRQ(ierr);
4400 #endif
4401   PetscFunctionReturn(0);
4402 }
4403 
4404 #undef __FUNCT__
4405 #define __FUNCT__ "MatCreateSeqAIJWithArrays"
4406 /*@
4407      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4408               provided by the user.
4409 
4410       Collective on MPI_Comm
4411 
4412    Input Parameters:
4413 +   comm - must be an MPI communicator of size 1
4414 .   m - number of rows
4415 .   n - number of columns
4416 .   i - row indices
4417 .   j - column indices
4418 -   a - matrix values
4419 
4420    Output Parameter:
4421 .   mat - the matrix
4422 
4423    Level: intermediate
4424 
4425    Notes:
4426        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4427     once the matrix is destroyed and not before
4428 
4429        You cannot set new nonzero locations into this matrix, that will generate an error.
4430 
4431        The i and j indices are 0 based
4432 
4433        The format which is used for the sparse matrix input, is equivalent to a
4434     row-major ordering.. i.e for the following matrix, the input data expected is
4435     as shown:
4436 
4437         1 0 0
4438         2 0 3
4439         4 5 6
4440 
4441         i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4442         j =  {0,0,2,0,1,2}  [size = nz = 6]; values must be sorted for each row
4443         v =  {1,2,3,4,5,6}  [size = nz = 6]
4444 
4445 
4446 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4447 
4448 @*/
4449 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat)
4450 {
4451   PetscErrorCode ierr;
4452   PetscInt       ii;
4453   Mat_SeqAIJ     *aij;
4454 #if defined(PETSC_USE_DEBUG)
4455   PetscInt jj;
4456 #endif
4457 
4458   PetscFunctionBegin;
4459   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4460   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4461   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4462   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4463   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4464   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,0);CHKERRQ(ierr);
4465   aij  = (Mat_SeqAIJ*)(*mat)->data;
4466   ierr = PetscMalloc2(m,&aij->imax,m,&aij->ilen);CHKERRQ(ierr);
4467 
4468   aij->i            = i;
4469   aij->j            = j;
4470   aij->a            = a;
4471   aij->singlemalloc = PETSC_FALSE;
4472   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4473   aij->free_a       = PETSC_FALSE;
4474   aij->free_ij      = PETSC_FALSE;
4475 
4476   for (ii=0; ii<m; ii++) {
4477     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4478 #if defined(PETSC_USE_DEBUG)
4479     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]);
4480     for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4481       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);
4482       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);
4483     }
4484 #endif
4485   }
4486 #if defined(PETSC_USE_DEBUG)
4487   for (ii=0; ii<aij->i[m]; ii++) {
4488     if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %D index = %D",ii,j[ii]);
4489     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]);
4490   }
4491 #endif
4492 
4493   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4494   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4495   PetscFunctionReturn(0);
4496 }
4497 #undef __FUNCT__
4498 #define __FUNCT__ "MatCreateSeqAIJFromTriple"
4499 /*@C
4500      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4501               provided by the user.
4502 
4503       Collective on MPI_Comm
4504 
4505    Input Parameters:
4506 +   comm - must be an MPI communicator of size 1
4507 .   m   - number of rows
4508 .   n   - number of columns
4509 .   i   - row indices
4510 .   j   - column indices
4511 .   a   - matrix values
4512 .   nz  - number of nonzeros
4513 -   idx - 0 or 1 based
4514 
4515    Output Parameter:
4516 .   mat - the matrix
4517 
4518    Level: intermediate
4519 
4520    Notes:
4521        The i and j indices are 0 based
4522 
4523        The format which is used for the sparse matrix input, is equivalent to a
4524     row-major ordering.. i.e for the following matrix, the input data expected is
4525     as shown:
4526 
4527         1 0 0
4528         2 0 3
4529         4 5 6
4530 
4531         i =  {0,1,1,2,2,2}
4532         j =  {0,0,2,0,1,2}
4533         v =  {1,2,3,4,5,6}
4534 
4535 
4536 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4537 
4538 @*/
4539 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat,PetscInt nz,PetscBool idx)
4540 {
4541   PetscErrorCode ierr;
4542   PetscInt       ii, *nnz, one = 1,row,col;
4543 
4544 
4545   PetscFunctionBegin;
4546   ierr = PetscCalloc1(m,&nnz);CHKERRQ(ierr);
4547   for (ii = 0; ii < nz; ii++) {
4548     nnz[i[ii] - !!idx] += 1;
4549   }
4550   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4551   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4552   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4553   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4554   for (ii = 0; ii < nz; ii++) {
4555     if (idx) {
4556       row = i[ii] - 1;
4557       col = j[ii] - 1;
4558     } else {
4559       row = i[ii];
4560       col = j[ii];
4561     }
4562     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4563   }
4564   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4565   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4566   ierr = PetscFree(nnz);CHKERRQ(ierr);
4567   PetscFunctionReturn(0);
4568 }
4569 
4570 #undef __FUNCT__
4571 #define __FUNCT__ "MatSetColoring_SeqAIJ"
4572 PetscErrorCode MatSetColoring_SeqAIJ(Mat A,ISColoring coloring)
4573 {
4574   PetscErrorCode ierr;
4575   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4576 
4577   PetscFunctionBegin;
4578   if (coloring->ctype == IS_COLORING_GLOBAL) {
4579     ierr        = ISColoringReference(coloring);CHKERRQ(ierr);
4580     a->coloring = coloring;
4581   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
4582     PetscInt        i,*larray;
4583     ISColoring      ocoloring;
4584     ISColoringValue *colors;
4585 
4586     /* set coloring for diagonal portion */
4587     ierr = PetscMalloc1(A->cmap->n,&larray);CHKERRQ(ierr);
4588     for (i=0; i<A->cmap->n; i++) larray[i] = i;
4589     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
4590     ierr = PetscMalloc1(A->cmap->n,&colors);CHKERRQ(ierr);
4591     for (i=0; i<A->cmap->n; i++) colors[i] = coloring->colors[larray[i]];
4592     ierr        = PetscFree(larray);CHKERRQ(ierr);
4593     ierr        = ISColoringCreate(PETSC_COMM_SELF,coloring->n,A->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4594     a->coloring = ocoloring;
4595   }
4596   PetscFunctionReturn(0);
4597 }
4598 
4599 #undef __FUNCT__
4600 #define __FUNCT__ "MatSetValuesAdifor_SeqAIJ"
4601 PetscErrorCode MatSetValuesAdifor_SeqAIJ(Mat A,PetscInt nl,void *advalues)
4602 {
4603   Mat_SeqAIJ      *a      = (Mat_SeqAIJ*)A->data;
4604   PetscInt        m       = A->rmap->n,*ii = a->i,*jj = a->j,nz,i,j;
4605   MatScalar       *v      = a->a;
4606   PetscScalar     *values = (PetscScalar*)advalues;
4607   ISColoringValue *color;
4608 
4609   PetscFunctionBegin;
4610   if (!a->coloring) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Coloring not set for matrix");
4611   color = a->coloring->colors;
4612   /* loop over rows */
4613   for (i=0; i<m; i++) {
4614     nz = ii[i+1] - ii[i];
4615     /* loop over columns putting computed value into matrix */
4616     for (j=0; j<nz; j++) *v++ = values[color[*jj++]];
4617     values += nl; /* jump to next row of derivatives */
4618   }
4619   PetscFunctionReturn(0);
4620 }
4621 
4622 #undef __FUNCT__
4623 #define __FUNCT__ "MatSeqAIJInvalidateDiagonal"
4624 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4625 {
4626   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4627   PetscErrorCode ierr;
4628 
4629   PetscFunctionBegin;
4630   a->idiagvalid  = PETSC_FALSE;
4631   a->ibdiagvalid = PETSC_FALSE;
4632 
4633   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4634   PetscFunctionReturn(0);
4635 }
4636 
4637 /*
4638     Special version for direct calls from Fortran
4639 */
4640 #include <petsc-private/fortranimpl.h>
4641 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4642 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
4643 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4644 #define matsetvaluesseqaij_ matsetvaluesseqaij
4645 #endif
4646 
4647 /* Change these macros so can be used in void function */
4648 #undef CHKERRQ
4649 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
4650 #undef SETERRQ2
4651 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4652 #undef SETERRQ3
4653 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4654 
4655 #undef __FUNCT__
4656 #define __FUNCT__ "matsetvaluesseqaij_"
4657 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)
4658 {
4659   Mat            A  = *AA;
4660   PetscInt       m  = *mm, n = *nn;
4661   InsertMode     is = *isis;
4662   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4663   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
4664   PetscInt       *imax,*ai,*ailen;
4665   PetscErrorCode ierr;
4666   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
4667   MatScalar      *ap,value,*aa;
4668   PetscBool      ignorezeroentries = a->ignorezeroentries;
4669   PetscBool      roworiented       = a->roworiented;
4670 
4671   PetscFunctionBegin;
4672   MatCheckPreallocated(A,1);
4673   imax  = a->imax;
4674   ai    = a->i;
4675   ailen = a->ilen;
4676   aj    = a->j;
4677   aa    = a->a;
4678 
4679   for (k=0; k<m; k++) { /* loop over added rows */
4680     row = im[k];
4681     if (row < 0) continue;
4682 #if defined(PETSC_USE_DEBUG)
4683     if (row >= A->rmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
4684 #endif
4685     rp   = aj + ai[row]; ap = aa + ai[row];
4686     rmax = imax[row]; nrow = ailen[row];
4687     low  = 0;
4688     high = nrow;
4689     for (l=0; l<n; l++) { /* loop over added columns */
4690       if (in[l] < 0) continue;
4691 #if defined(PETSC_USE_DEBUG)
4692       if (in[l] >= A->cmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
4693 #endif
4694       col = in[l];
4695       if (roworiented) value = v[l + k*n];
4696       else value = v[k + l*m];
4697 
4698       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
4699 
4700       if (col <= lastcol) low = 0;
4701       else high = nrow;
4702       lastcol = col;
4703       while (high-low > 5) {
4704         t = (low+high)/2;
4705         if (rp[t] > col) high = t;
4706         else             low  = t;
4707       }
4708       for (i=low; i<high; i++) {
4709         if (rp[i] > col) break;
4710         if (rp[i] == col) {
4711           if (is == ADD_VALUES) ap[i] += value;
4712           else                  ap[i] = value;
4713           goto noinsert;
4714         }
4715       }
4716       if (value == 0.0 && ignorezeroentries) goto noinsert;
4717       if (nonew == 1) goto noinsert;
4718       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
4719       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
4720       N = nrow++ - 1; a->nz++; high++;
4721       /* shift up all the later entries in this row */
4722       for (ii=N; ii>=i; ii--) {
4723         rp[ii+1] = rp[ii];
4724         ap[ii+1] = ap[ii];
4725       }
4726       rp[i] = col;
4727       ap[i] = value;
4728       A->nonzerostate++;
4729 noinsert:;
4730       low = i + 1;
4731     }
4732     ailen[row] = nrow;
4733   }
4734   PetscFunctionReturnVoid();
4735 }
4736 
4737 
4738