xref: /petsc/src/mat/impls/aij/seq/aij.c (revision efbe7e8a80d07327753dbe0b33efee01e046af3f)
1 /*
2     Defines the basic matrix operations for the AIJ (compressed row)
3   matrix storage format.
4 */
5 
6 
7 #include <../src/mat/impls/aij/seq/aij.h>          /*I "petscmat.h" I*/
8 #include <petscblaslapack.h>
9 #include <petscbt.h>
10 #include <petsc/private/kernels/blocktranspose.h>
11 
12 PetscErrorCode MatSeqAIJSetTypeFromOptions(Mat A)
13 {
14   PetscErrorCode       ierr;
15   PetscBool            flg;
16   char                 type[256];
17 
18   PetscFunctionBegin;
19   ierr = PetscObjectOptionsBegin((PetscObject)A);
20   ierr = PetscOptionsFList("-mat_seqaij_type","Matrix SeqAIJ type","MatSeqAIJSetType",MatSeqAIJList,"seqaij",type,256,&flg);CHKERRQ(ierr);
21   if (flg) {
22     ierr = MatSeqAIJSetType(A,type);CHKERRQ(ierr);
23   }
24   ierr = PetscOptionsEnd();CHKERRQ(ierr);
25   PetscFunctionReturn(0);
26 }
27 
28 PetscErrorCode MatGetColumnNorms_SeqAIJ(Mat A,NormType type,PetscReal *norms)
29 {
30   PetscErrorCode ierr;
31   PetscInt       i,m,n;
32   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
33 
34   PetscFunctionBegin;
35   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
36   ierr = PetscArrayzero(norms,n);CHKERRQ(ierr);
37   if (type == NORM_2) {
38     for (i=0; i<aij->i[m]; i++) {
39       norms[aij->j[i]] += PetscAbsScalar(aij->a[i]*aij->a[i]);
40     }
41   } else if (type == NORM_1) {
42     for (i=0; i<aij->i[m]; i++) {
43       norms[aij->j[i]] += PetscAbsScalar(aij->a[i]);
44     }
45   } else if (type == NORM_INFINITY) {
46     for (i=0; i<aij->i[m]; i++) {
47       norms[aij->j[i]] = PetscMax(PetscAbsScalar(aij->a[i]),norms[aij->j[i]]);
48     }
49   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unknown NormType");
50 
51   if (type == NORM_2) {
52     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
53   }
54   PetscFunctionReturn(0);
55 }
56 
57 PetscErrorCode MatFindOffBlockDiagonalEntries_SeqAIJ(Mat A,IS *is)
58 {
59   Mat_SeqAIJ      *a  = (Mat_SeqAIJ*)A->data;
60   PetscInt        i,m=A->rmap->n,cnt = 0, bs = A->rmap->bs;
61   const PetscInt  *jj = a->j,*ii = a->i;
62   PetscInt        *rows;
63   PetscErrorCode  ierr;
64 
65   PetscFunctionBegin;
66   for (i=0; i<m; i++) {
67     if ((ii[i] != ii[i+1]) && ((jj[ii[i]] < bs*(i/bs)) || (jj[ii[i+1]-1] > bs*((i+bs)/bs)-1))) {
68       cnt++;
69     }
70   }
71   ierr = PetscMalloc1(cnt,&rows);CHKERRQ(ierr);
72   cnt  = 0;
73   for (i=0; i<m; i++) {
74     if ((ii[i] != ii[i+1]) && ((jj[ii[i]] < bs*(i/bs)) || (jj[ii[i+1]-1] > bs*((i+bs)/bs)-1))) {
75       rows[cnt] = i;
76       cnt++;
77     }
78   }
79   ierr = ISCreateGeneral(PETSC_COMM_SELF,cnt,rows,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
80   PetscFunctionReturn(0);
81 }
82 
83 PetscErrorCode MatFindZeroDiagonals_SeqAIJ_Private(Mat A,PetscInt *nrows,PetscInt **zrows)
84 {
85   Mat_SeqAIJ      *a  = (Mat_SeqAIJ*)A->data;
86   const MatScalar *aa = a->a;
87   PetscInt        i,m=A->rmap->n,cnt = 0;
88   const PetscInt  *ii = a->i,*jj = a->j,*diag;
89   PetscInt        *rows;
90   PetscErrorCode  ierr;
91 
92   PetscFunctionBegin;
93   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
94   diag = a->diag;
95   for (i=0; i<m; i++) {
96     if ((diag[i] >= ii[i+1]) || (jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) {
97       cnt++;
98     }
99   }
100   ierr = PetscMalloc1(cnt,&rows);CHKERRQ(ierr);
101   cnt  = 0;
102   for (i=0; i<m; i++) {
103     if ((diag[i] >= ii[i+1]) || (jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) {
104       rows[cnt++] = i;
105     }
106   }
107   *nrows = cnt;
108   *zrows = rows;
109   PetscFunctionReturn(0);
110 }
111 
112 PetscErrorCode MatFindZeroDiagonals_SeqAIJ(Mat A,IS *zrows)
113 {
114   PetscInt       nrows,*rows;
115   PetscErrorCode ierr;
116 
117   PetscFunctionBegin;
118   *zrows = NULL;
119   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(A,&nrows,&rows);CHKERRQ(ierr);
120   ierr   = ISCreateGeneral(PetscObjectComm((PetscObject)A),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
121   PetscFunctionReturn(0);
122 }
123 
124 PetscErrorCode MatFindNonzeroRows_SeqAIJ(Mat A,IS *keptrows)
125 {
126   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
127   const MatScalar *aa;
128   PetscInt        m=A->rmap->n,cnt = 0;
129   const PetscInt  *ii;
130   PetscInt        n,i,j,*rows;
131   PetscErrorCode  ierr;
132 
133   PetscFunctionBegin;
134   *keptrows = NULL;
135   ii        = a->i;
136   for (i=0; i<m; i++) {
137     n = ii[i+1] - ii[i];
138     if (!n) {
139       cnt++;
140       goto ok1;
141     }
142     aa = a->a + ii[i];
143     for (j=0; j<n; j++) {
144       if (aa[j] != 0.0) goto ok1;
145     }
146     cnt++;
147 ok1:;
148   }
149   if (!cnt) PetscFunctionReturn(0);
150   ierr = PetscMalloc1(A->rmap->n-cnt,&rows);CHKERRQ(ierr);
151   cnt  = 0;
152   for (i=0; i<m; i++) {
153     n = ii[i+1] - ii[i];
154     if (!n) continue;
155     aa = a->a + ii[i];
156     for (j=0; j<n; j++) {
157       if (aa[j] != 0.0) {
158         rows[cnt++] = i;
159         break;
160       }
161     }
162   }
163   ierr = ISCreateGeneral(PETSC_COMM_SELF,cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
164   PetscFunctionReturn(0);
165 }
166 
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,m = Y->rmap->n;
172   const PetscInt    *diag;
173   MatScalar         *aa = aij->a;
174   const PetscScalar *v;
175   PetscBool         missing;
176 #if defined(PETSC_HAVE_DEVICE)
177   PetscBool         inserted = PETSC_FALSE;
178 #endif
179 
180   PetscFunctionBegin;
181   if (Y->assembled) {
182     ierr = MatMissingDiagonal_SeqAIJ(Y,&missing,NULL);CHKERRQ(ierr);
183     if (!missing) {
184       diag = aij->diag;
185       ierr = VecGetArrayRead(D,&v);CHKERRQ(ierr);
186       if (is == INSERT_VALUES) {
187 #if defined(PETSC_HAVE_DEVICE)
188         inserted = PETSC_TRUE;
189 #endif
190         for (i=0; i<m; i++) {
191           aa[diag[i]] = v[i];
192         }
193       } else {
194         for (i=0; i<m; i++) {
195 #if defined(PETSC_HAVE_DEVICE)
196           if (v[i] != 0.0) inserted = PETSC_TRUE;
197 #endif
198           aa[diag[i]] += v[i];
199         }
200       }
201 #if defined(PETSC_HAVE_DEVICE)
202       if (inserted) Y->offloadmask = PETSC_OFFLOAD_CPU;
203 #endif
204       ierr = VecRestoreArrayRead(D,&v);CHKERRQ(ierr);
205       PetscFunctionReturn(0);
206     }
207     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
208   }
209   ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
210   PetscFunctionReturn(0);
211 }
212 
213 PetscErrorCode MatGetRowIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *m,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
214 {
215   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
216   PetscErrorCode ierr;
217   PetscInt       i,ishift;
218 
219   PetscFunctionBegin;
220   *m = A->rmap->n;
221   if (!ia) PetscFunctionReturn(0);
222   ishift = 0;
223   if (symmetric && !A->structurally_symmetric) {
224     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,PETSC_TRUE,ishift,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
225   } else if (oshift == 1) {
226     PetscInt *tia;
227     PetscInt nz = a->i[A->rmap->n];
228     /* malloc space and  add 1 to i and j indices */
229     ierr = PetscMalloc1(A->rmap->n+1,&tia);CHKERRQ(ierr);
230     for (i=0; i<A->rmap->n+1; i++) tia[i] = a->i[i] + 1;
231     *ia = tia;
232     if (ja) {
233       PetscInt *tja;
234       ierr = PetscMalloc1(nz+1,&tja);CHKERRQ(ierr);
235       for (i=0; i<nz; i++) tja[i] = a->j[i] + 1;
236       *ja = tja;
237     }
238   } else {
239     *ia = a->i;
240     if (ja) *ja = a->j;
241   }
242   PetscFunctionReturn(0);
243 }
244 
245 PetscErrorCode MatRestoreRowIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
246 {
247   PetscErrorCode ierr;
248 
249   PetscFunctionBegin;
250   if (!ia) PetscFunctionReturn(0);
251   if ((symmetric && !A->structurally_symmetric) || oshift == 1) {
252     ierr = PetscFree(*ia);CHKERRQ(ierr);
253     if (ja) {ierr = PetscFree(*ja);CHKERRQ(ierr);}
254   }
255   PetscFunctionReturn(0);
256 }
257 
258 PetscErrorCode MatGetColumnIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
259 {
260   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
261   PetscErrorCode ierr;
262   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
263   PetscInt       nz = a->i[m],row,*jj,mr,col;
264 
265   PetscFunctionBegin;
266   *nn = n;
267   if (!ia) PetscFunctionReturn(0);
268   if (symmetric) {
269     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,PETSC_TRUE,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
270   } else {
271     ierr = PetscCalloc1(n,&collengths);CHKERRQ(ierr);
272     ierr = PetscMalloc1(n+1,&cia);CHKERRQ(ierr);
273     ierr = PetscMalloc1(nz,&cja);CHKERRQ(ierr);
274     jj   = a->j;
275     for (i=0; i<nz; i++) {
276       collengths[jj[i]]++;
277     }
278     cia[0] = oshift;
279     for (i=0; i<n; i++) {
280       cia[i+1] = cia[i] + collengths[i];
281     }
282     ierr = PetscArrayzero(collengths,n);CHKERRQ(ierr);
283     jj   = a->j;
284     for (row=0; row<m; row++) {
285       mr = a->i[row+1] - a->i[row];
286       for (i=0; i<mr; i++) {
287         col = *jj++;
288 
289         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
290       }
291     }
292     ierr = PetscFree(collengths);CHKERRQ(ierr);
293     *ia  = cia; *ja = cja;
294   }
295   PetscFunctionReturn(0);
296 }
297 
298 PetscErrorCode MatRestoreColumnIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
299 {
300   PetscErrorCode ierr;
301 
302   PetscFunctionBegin;
303   if (!ia) PetscFunctionReturn(0);
304 
305   ierr = PetscFree(*ia);CHKERRQ(ierr);
306   ierr = PetscFree(*ja);CHKERRQ(ierr);
307   PetscFunctionReturn(0);
308 }
309 
310 /*
311  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
312  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
313  spidx[], index of a->a, to be used in MatTransposeColoringCreate_SeqAIJ() and MatFDColoringCreate_SeqXAIJ()
314 */
315 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
316 {
317   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
318   PetscErrorCode ierr;
319   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
320   PetscInt       nz = a->i[m],row,mr,col,tmp;
321   PetscInt       *cspidx;
322   const PetscInt *jj;
323 
324   PetscFunctionBegin;
325   *nn = n;
326   if (!ia) PetscFunctionReturn(0);
327 
328   ierr = PetscCalloc1(n,&collengths);CHKERRQ(ierr);
329   ierr = PetscMalloc1(n+1,&cia);CHKERRQ(ierr);
330   ierr = PetscMalloc1(nz,&cja);CHKERRQ(ierr);
331   ierr = PetscMalloc1(nz,&cspidx);CHKERRQ(ierr);
332   jj   = a->j;
333   for (i=0; i<nz; i++) {
334     collengths[jj[i]]++;
335   }
336   cia[0] = oshift;
337   for (i=0; i<n; i++) {
338     cia[i+1] = cia[i] + collengths[i];
339   }
340   ierr = PetscArrayzero(collengths,n);CHKERRQ(ierr);
341   jj   = a->j;
342   for (row=0; row<m; row++) {
343     mr = a->i[row+1] - a->i[row];
344     for (i=0; i<mr; i++) {
345       col         = *jj++;
346       tmp         = cia[col] + collengths[col]++ - oshift;
347       cspidx[tmp] = a->i[row] + i; /* index of a->j */
348       cja[tmp]    = row + oshift;
349     }
350   }
351   ierr   = PetscFree(collengths);CHKERRQ(ierr);
352   *ia    = cia;
353   *ja    = cja;
354   *spidx = cspidx;
355   PetscFunctionReturn(0);
356 }
357 
358 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
359 {
360   PetscErrorCode ierr;
361 
362   PetscFunctionBegin;
363   ierr = MatRestoreColumnIJ_SeqAIJ(A,oshift,symmetric,inodecompressed,n,ia,ja,done);CHKERRQ(ierr);
364   ierr = PetscFree(*spidx);CHKERRQ(ierr);
365   PetscFunctionReturn(0);
366 }
367 
368 PetscErrorCode MatSetValuesRow_SeqAIJ(Mat A,PetscInt row,const PetscScalar v[])
369 {
370   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
371   PetscInt       *ai = a->i;
372   PetscErrorCode ierr;
373 
374   PetscFunctionBegin;
375   ierr = PetscArraycpy(a->a+ai[row],v,ai[row+1]-ai[row]);CHKERRQ(ierr);
376 #if defined(PETSC_HAVE_DEVICE)
377   if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED && ai[row+1]-ai[row]) A->offloadmask = PETSC_OFFLOAD_CPU;
378 #endif
379   PetscFunctionReturn(0);
380 }
381 
382 /*
383     MatSeqAIJSetValuesLocalFast - An optimized version of MatSetValuesLocal() for SeqAIJ matrices with several assumptions
384 
385       -   a single row of values is set with each call
386       -   no row or column indices are negative or (in error) larger than the number of rows or columns
387       -   the values are always added to the matrix, not set
388       -   no new locations are introduced in the nonzero structure of the matrix
389 
390      This does NOT assume the global column indices are sorted
391 
392 */
393 
394 #include <petsc/private/isimpl.h>
395 PetscErrorCode MatSeqAIJSetValuesLocalFast(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
396 {
397   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
398   PetscInt       low,high,t,row,nrow,i,col,l;
399   const PetscInt *rp,*ai = a->i,*ailen = a->ilen,*aj = a->j;
400   PetscInt       lastcol = -1;
401   MatScalar      *ap,value,*aa = a->a;
402   const PetscInt *ridx = A->rmap->mapping->indices,*cidx = A->cmap->mapping->indices;
403 
404   row  = ridx[im[0]];
405   rp   = aj + ai[row];
406   ap   = aa + ai[row];
407   nrow = ailen[row];
408   low  = 0;
409   high = nrow;
410   for (l=0; l<n; l++) { /* loop over added columns */
411     col = cidx[in[l]];
412     value = v[l];
413 
414     if (col <= lastcol) low = 0;
415     else high = nrow;
416     lastcol = col;
417     while (high-low > 5) {
418       t = (low+high)/2;
419       if (rp[t] > col) high = t;
420       else low = t;
421     }
422     for (i=low; i<high; i++) {
423       if (rp[i] == col) {
424         ap[i] += value;
425         low = i + 1;
426         break;
427       }
428     }
429   }
430 #if defined(PETSC_HAVE_DEVICE)
431   if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED && m && n) A->offloadmask = PETSC_OFFLOAD_CPU;
432 #endif
433   return 0;
434 }
435 
436 PetscErrorCode MatSetValues_SeqAIJ(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
437 {
438   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
439   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
440   PetscInt       *imax = a->imax,*ai = a->i,*ailen = a->ilen;
441   PetscErrorCode ierr;
442   PetscInt       *aj = a->j,nonew = a->nonew,lastcol = -1;
443   MatScalar      *ap=NULL,value=0.0,*aa = a->a;
444   PetscBool      ignorezeroentries = a->ignorezeroentries;
445   PetscBool      roworiented       = a->roworiented;
446 #if defined(PETSC_HAVE_DEVICE)
447   PetscBool      inserted          = PETSC_FALSE;
448 #endif
449 
450   PetscFunctionBegin;
451   for (k=0; k<m; k++) { /* loop over added rows */
452     row = im[k];
453     if (row < 0) continue;
454     if (PetscUnlikelyDebug(row >= A->rmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",row,A->rmap->n-1);
455     rp   = aj + ai[row];
456     if (!A->structure_only) ap = aa + ai[row];
457     rmax = imax[row]; nrow = ailen[row];
458     low  = 0;
459     high = nrow;
460     for (l=0; l<n; l++) { /* loop over added columns */
461       if (in[l] < 0) continue;
462       if (PetscUnlikelyDebug(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);
463       col = in[l];
464       if (v && !A->structure_only) value = roworiented ? v[l + k*n] : v[k + l*m];
465       if (!A->structure_only && value == 0.0 && ignorezeroentries && is == ADD_VALUES && row != col) 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 (!A->structure_only) {
479             if (is == ADD_VALUES) {
480               ap[i] += value;
481               (void)PetscLogFlops(1.0);
482             }
483             else ap[i] = value;
484 #if defined(PETSC_HAVE_DEVICE)
485             inserted = PETSC_TRUE;
486 #endif
487           }
488           low = i + 1;
489           goto noinsert;
490         }
491       }
492       if (value == 0.0 && ignorezeroentries && row != col) goto noinsert;
493       if (nonew == 1) goto noinsert;
494       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at (%D,%D) in the matrix",row,col);
495       if (A->structure_only) {
496         MatSeqXAIJReallocateAIJ_structure_only(A,A->rmap->n,1,nrow,row,col,rmax,ai,aj,rp,imax,nonew,MatScalar);
497       } else {
498         MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
499       }
500       N = nrow++ - 1; a->nz++; high++;
501       /* shift up all the later entries in this row */
502       ierr  = PetscArraymove(rp+i+1,rp+i,N-i+1);CHKERRQ(ierr);
503       rp[i] = col;
504       if (!A->structure_only){
505         ierr  = PetscArraymove(ap+i+1,ap+i,N-i+1);CHKERRQ(ierr);
506         ap[i] = value;
507       }
508       low = i + 1;
509       A->nonzerostate++;
510 #if defined(PETSC_HAVE_DEVICE)
511       inserted = PETSC_TRUE;
512 #endif
513 noinsert:;
514     }
515     ailen[row] = nrow;
516   }
517 #if defined(PETSC_HAVE_DEVICE)
518   if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED && inserted) A->offloadmask = PETSC_OFFLOAD_CPU;
519 #endif
520   PetscFunctionReturn(0);
521 }
522 
523 
524 PetscErrorCode MatSetValues_SeqAIJ_SortedFullNoPreallocation(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
525 {
526   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
527   PetscInt       *rp,k,row;
528   PetscInt       *ai = a->i;
529   PetscErrorCode ierr;
530   PetscInt       *aj = a->j;
531   MatScalar      *aa = a->a,*ap;
532 
533   PetscFunctionBegin;
534   if (A->was_assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot call on assembled matrix.");
535   if (m*n+a->nz > a->maxnz) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of entries in matrix will be larger than maximum nonzeros allocated for %D in MatSeqAIJSetTotalPreallocation()",a->maxnz);
536   for (k=0; k<m; k++) { /* loop over added rows */
537     row  = im[k];
538     rp   = aj + ai[row];
539     ap   = aa + ai[row];
540 
541     ierr = PetscMemcpy(rp,in,n*sizeof(PetscInt));CHKERRQ(ierr);
542     if (!A->structure_only) {
543       if (v) {
544         ierr = PetscMemcpy(ap,v,n*sizeof(PetscScalar));CHKERRQ(ierr);
545         v   += n;
546       } else {
547         ierr = PetscMemzero(ap,n*sizeof(PetscScalar));CHKERRQ(ierr);
548       }
549     }
550     a->ilen[row] = n;
551     a->imax[row] = n;
552     a->i[row+1]  = a->i[row]+n;
553     a->nz       += n;
554   }
555 #if defined(PETSC_HAVE_DEVICE)
556   if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED && m && n) A->offloadmask = PETSC_OFFLOAD_CPU;
557 #endif
558   PetscFunctionReturn(0);
559 }
560 
561 /*@
562     MatSeqAIJSetTotalPreallocation - Sets an upper bound on the total number of expected nonzeros in the matrix.
563 
564   Input Parameters:
565 +  A - the SeqAIJ matrix
566 -  nztotal - bound on the number of nonzeros
567 
568   Level: advanced
569 
570   Notes:
571     This can be called if you will be provided the matrix row by row (from row zero) with sorted column indices for each row.
572     Simply call MatSetValues() after this call to provide the matrix entries in the usual manner. This matrix may be used
573     as always with multiple matrix assemblies.
574 
575 .seealso: MatSetOption(), MAT_SORTED_FULL, MatSetValues(), MatSeqAIJSetPreallocation()
576 @*/
577 
578 PetscErrorCode MatSeqAIJSetTotalPreallocation(Mat A,PetscInt nztotal)
579 {
580   PetscErrorCode ierr;
581   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
582 
583   PetscFunctionBegin;
584   ierr = PetscLayoutSetUp(A->rmap);CHKERRQ(ierr);
585   ierr = PetscLayoutSetUp(A->cmap);CHKERRQ(ierr);
586   a->maxnz  = nztotal;
587   if (!a->imax) {
588     ierr = PetscMalloc1(A->rmap->n,&a->imax);CHKERRQ(ierr);
589     ierr = PetscLogObjectMemory((PetscObject)A,A->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
590   }
591   if (!a->ilen) {
592     ierr = PetscMalloc1(A->rmap->n,&a->ilen);CHKERRQ(ierr);
593     ierr = PetscLogObjectMemory((PetscObject)A,A->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
594   } else {
595     ierr = PetscMemzero(a->ilen,A->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
596   }
597 
598   /* allocate the matrix space */
599   if (A->structure_only) {
600     ierr = PetscMalloc1(nztotal,&a->j);CHKERRQ(ierr);
601     ierr = PetscMalloc1(A->rmap->n+1,&a->i);CHKERRQ(ierr);
602     ierr = PetscLogObjectMemory((PetscObject)A,(A->rmap->n+1)*sizeof(PetscInt)+nztotal*sizeof(PetscInt));CHKERRQ(ierr);
603   } else {
604     ierr = PetscMalloc3(nztotal,&a->a,nztotal,&a->j,A->rmap->n+1,&a->i);CHKERRQ(ierr);
605     ierr = PetscLogObjectMemory((PetscObject)A,(A->rmap->n+1)*sizeof(PetscInt)+nztotal*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
606   }
607   a->i[0] = 0;
608   if (A->structure_only) {
609     a->singlemalloc = PETSC_FALSE;
610     a->free_a       = PETSC_FALSE;
611   } else {
612     a->singlemalloc = PETSC_TRUE;
613     a->free_a       = PETSC_TRUE;
614   }
615   a->free_ij         = PETSC_TRUE;
616   A->ops->setvalues = MatSetValues_SeqAIJ_SortedFullNoPreallocation;
617   A->preallocated   = PETSC_TRUE;
618   PetscFunctionReturn(0);
619 }
620 
621 PetscErrorCode MatSetValues_SeqAIJ_SortedFull(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
622 {
623   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
624   PetscInt       *rp,k,row;
625   PetscInt       *ai = a->i,*ailen = a->ilen;
626   PetscErrorCode ierr;
627   PetscInt       *aj = a->j;
628   MatScalar      *aa = a->a,*ap;
629 
630   PetscFunctionBegin;
631   for (k=0; k<m; k++) { /* loop over added rows */
632     row  = im[k];
633     if (PetscUnlikelyDebug(n > a->imax[row])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Preallocation for row %D does not match number of columns provided",n);
634     rp   = aj + ai[row];
635     ap   = aa + ai[row];
636     if (!A->was_assembled) {
637       ierr = PetscMemcpy(rp,in,n*sizeof(PetscInt));CHKERRQ(ierr);
638     }
639     if (!A->structure_only) {
640       if (v) {
641         ierr = PetscMemcpy(ap,v,n*sizeof(PetscScalar));CHKERRQ(ierr);
642         v   += n;
643       } else {
644         ierr = PetscMemzero(ap,n*sizeof(PetscScalar));CHKERRQ(ierr);
645       }
646     }
647     ailen[row] = n;
648     a->nz      += n;
649   }
650 #if defined(PETSC_HAVE_DEVICE)
651   if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED && m && n) A->offloadmask = PETSC_OFFLOAD_CPU;
652 #endif
653   PetscFunctionReturn(0);
654 }
655 
656 
657 PetscErrorCode MatGetValues_SeqAIJ(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],PetscScalar v[])
658 {
659   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
660   PetscInt   *rp,k,low,high,t,row,nrow,i,col,l,*aj = a->j;
661   PetscInt   *ai = a->i,*ailen = a->ilen;
662   MatScalar  *ap,*aa = a->a;
663 
664   PetscFunctionBegin;
665   for (k=0; k<m; k++) { /* loop over rows */
666     row = im[k];
667     if (row < 0) {v += n; continue;} /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",row); */
668     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);
669     rp   = aj + ai[row]; ap = aa + ai[row];
670     nrow = ailen[row];
671     for (l=0; l<n; l++) { /* loop over columns */
672       if (in[l] < 0) {v++; continue;} /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",in[l]); */
673       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);
674       col  = in[l];
675       high = nrow; low = 0; /* assume unsorted */
676       while (high-low > 5) {
677         t = (low+high)/2;
678         if (rp[t] > col) high = t;
679         else low = t;
680       }
681       for (i=low; i<high; i++) {
682         if (rp[i] > col) break;
683         if (rp[i] == col) {
684           *v++ = ap[i];
685           goto finished;
686         }
687       }
688       *v++ = 0.0;
689 finished:;
690     }
691   }
692   PetscFunctionReturn(0);
693 }
694 
695 PetscErrorCode MatView_SeqAIJ_Binary(Mat mat,PetscViewer viewer)
696 {
697   Mat_SeqAIJ     *A = (Mat_SeqAIJ*)mat->data;
698   PetscInt       header[4],M,N,m,nz,i;
699   PetscInt       *rowlens;
700   PetscErrorCode ierr;
701 
702   PetscFunctionBegin;
703   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
704 
705   M  = mat->rmap->N;
706   N  = mat->cmap->N;
707   m  = mat->rmap->n;
708   nz = A->nz;
709 
710   /* write matrix header */
711   header[0] = MAT_FILE_CLASSID;
712   header[1] = M; header[2] = N; header[3] = nz;
713   ierr = PetscViewerBinaryWrite(viewer,header,4,PETSC_INT);CHKERRQ(ierr);
714 
715   /* fill in and store row lengths */
716   ierr = PetscMalloc1(m,&rowlens);CHKERRQ(ierr);
717   for (i=0; i<m; i++) rowlens[i] = A->i[i+1] - A->i[i];
718   ierr = PetscViewerBinaryWrite(viewer,rowlens,m,PETSC_INT);CHKERRQ(ierr);
719   ierr = PetscFree(rowlens);CHKERRQ(ierr);
720   /* store column indices */
721   ierr = PetscViewerBinaryWrite(viewer,A->j,nz,PETSC_INT);CHKERRQ(ierr);
722   /* store nonzero values */
723   ierr = PetscViewerBinaryWrite(viewer,A->a,nz,PETSC_SCALAR);CHKERRQ(ierr);
724 
725   /* write block size option to the viewer's .info file */
726   ierr = MatView_Binary_BlockSizes(mat,viewer);CHKERRQ(ierr);
727   PetscFunctionReturn(0);
728 }
729 
730 static PetscErrorCode MatView_SeqAIJ_ASCII_structonly(Mat A,PetscViewer viewer)
731 {
732   PetscErrorCode ierr;
733   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
734   PetscInt       i,k,m=A->rmap->N;
735 
736   PetscFunctionBegin;
737   ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
738   for (i=0; i<m; i++) {
739     ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
740     for (k=a->i[i]; k<a->i[i+1]; k++) {
741       ierr = PetscViewerASCIIPrintf(viewer," (%D) ",a->j[k]);CHKERRQ(ierr);
742     }
743     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
744   }
745   ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
746   PetscFunctionReturn(0);
747 }
748 
749 extern PetscErrorCode MatSeqAIJFactorInfo_Matlab(Mat,PetscViewer);
750 
751 PetscErrorCode MatView_SeqAIJ_ASCII(Mat A,PetscViewer viewer)
752 {
753   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
754   PetscErrorCode    ierr;
755   PetscInt          i,j,m = A->rmap->n;
756   const char        *name;
757   PetscViewerFormat format;
758 
759   PetscFunctionBegin;
760   if (A->structure_only) {
761     ierr = MatView_SeqAIJ_ASCII_structonly(A,viewer);CHKERRQ(ierr);
762     PetscFunctionReturn(0);
763   }
764 
765   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
766   if (format == PETSC_VIEWER_ASCII_MATLAB) {
767     PetscInt nofinalvalue = 0;
768     if (m && ((a->i[m] == a->i[m-1]) || (a->j[a->nz-1] != A->cmap->n-1))) {
769       /* Need a dummy value to ensure the dimension of the matrix. */
770       nofinalvalue = 1;
771     }
772     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
773     ierr = PetscViewerASCIIPrintf(viewer,"%% Size = %D %D \n",m,A->cmap->n);CHKERRQ(ierr);
774     ierr = PetscViewerASCIIPrintf(viewer,"%% Nonzeros = %D \n",a->nz);CHKERRQ(ierr);
775 #if defined(PETSC_USE_COMPLEX)
776     ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,4);\n",a->nz+nofinalvalue);CHKERRQ(ierr);
777 #else
778     ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",a->nz+nofinalvalue);CHKERRQ(ierr);
779 #endif
780     ierr = PetscViewerASCIIPrintf(viewer,"zzz = [\n");CHKERRQ(ierr);
781 
782     for (i=0; i<m; i++) {
783       for (j=a->i[i]; j<a->i[i+1]; j++) {
784 #if defined(PETSC_USE_COMPLEX)
785         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);
786 #else
787         ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,a->j[j]+1,(double)a->a[j]);CHKERRQ(ierr);
788 #endif
789       }
790     }
791     if (nofinalvalue) {
792 #if defined(PETSC_USE_COMPLEX)
793       ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e %18.16e\n",m,A->cmap->n,0.,0.);CHKERRQ(ierr);
794 #else
795       ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",m,A->cmap->n,0.0);CHKERRQ(ierr);
796 #endif
797     }
798     ierr = PetscObjectGetName((PetscObject)A,&name);CHKERRQ(ierr);
799     ierr = PetscViewerASCIIPrintf(viewer,"];\n %s = spconvert(zzz);\n",name);CHKERRQ(ierr);
800     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
801   } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO || format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
802     PetscFunctionReturn(0);
803   } else if (format == PETSC_VIEWER_ASCII_COMMON) {
804     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
805     for (i=0; i<m; i++) {
806       ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
807       for (j=a->i[i]; j<a->i[i+1]; j++) {
808 #if defined(PETSC_USE_COMPLEX)
809         if (PetscImaginaryPart(a->a[j]) > 0.0 && PetscRealPart(a->a[j]) != 0.0) {
810           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
811         } else if (PetscImaginaryPart(a->a[j]) < 0.0 && PetscRealPart(a->a[j]) != 0.0) {
812           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
813         } else if (PetscRealPart(a->a[j]) != 0.0) {
814           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
815         }
816 #else
817         if (a->a[j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);}
818 #endif
819       }
820       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
821     }
822     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
823   } else if (format == PETSC_VIEWER_ASCII_SYMMODU) {
824     PetscInt nzd=0,fshift=1,*sptr;
825     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
826     ierr = PetscMalloc1(m+1,&sptr);CHKERRQ(ierr);
827     for (i=0; i<m; i++) {
828       sptr[i] = nzd+1;
829       for (j=a->i[i]; j<a->i[i+1]; j++) {
830         if (a->j[j] >= i) {
831 #if defined(PETSC_USE_COMPLEX)
832           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) nzd++;
833 #else
834           if (a->a[j] != 0.0) nzd++;
835 #endif
836         }
837       }
838     }
839     sptr[m] = nzd+1;
840     ierr    = PetscViewerASCIIPrintf(viewer," %D %D\n\n",m,nzd);CHKERRQ(ierr);
841     for (i=0; i<m+1; i+=6) {
842       if (i+4<m) {
843         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);
844       } else if (i+3<m) {
845         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);
846       } else if (i+2<m) {
847         ierr = PetscViewerASCIIPrintf(viewer," %D %D %D %D\n",sptr[i],sptr[i+1],sptr[i+2],sptr[i+3]);CHKERRQ(ierr);
848       } else if (i+1<m) {
849         ierr = PetscViewerASCIIPrintf(viewer," %D %D %D\n",sptr[i],sptr[i+1],sptr[i+2]);CHKERRQ(ierr);
850       } else if (i<m) {
851         ierr = PetscViewerASCIIPrintf(viewer," %D %D\n",sptr[i],sptr[i+1]);CHKERRQ(ierr);
852       } else {
853         ierr = PetscViewerASCIIPrintf(viewer," %D\n",sptr[i]);CHKERRQ(ierr);
854       }
855     }
856     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
857     ierr = PetscFree(sptr);CHKERRQ(ierr);
858     for (i=0; i<m; i++) {
859       for (j=a->i[i]; j<a->i[i+1]; j++) {
860         if (a->j[j] >= i) {ierr = PetscViewerASCIIPrintf(viewer," %D ",a->j[j]+fshift);CHKERRQ(ierr);}
861       }
862       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
863     }
864     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
865     for (i=0; i<m; i++) {
866       for (j=a->i[i]; j<a->i[i+1]; j++) {
867         if (a->j[j] >= i) {
868 #if defined(PETSC_USE_COMPLEX)
869           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) {
870             ierr = PetscViewerASCIIPrintf(viewer," %18.16e %18.16e ",(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
871           }
872 #else
873           if (a->a[j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," %18.16e ",(double)a->a[j]);CHKERRQ(ierr);}
874 #endif
875         }
876       }
877       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
878     }
879     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
880   } else if (format == PETSC_VIEWER_ASCII_DENSE) {
881     PetscInt    cnt = 0,jcnt;
882     PetscScalar value;
883 #if defined(PETSC_USE_COMPLEX)
884     PetscBool   realonly = PETSC_TRUE;
885 
886     for (i=0; i<a->i[m]; i++) {
887       if (PetscImaginaryPart(a->a[i]) != 0.0) {
888         realonly = PETSC_FALSE;
889         break;
890       }
891     }
892 #endif
893 
894     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
895     for (i=0; i<m; i++) {
896       jcnt = 0;
897       for (j=0; j<A->cmap->n; j++) {
898         if (jcnt < a->i[i+1]-a->i[i] && j == a->j[cnt]) {
899           value = a->a[cnt++];
900           jcnt++;
901         } else {
902           value = 0.0;
903         }
904 #if defined(PETSC_USE_COMPLEX)
905         if (realonly) {
906           ierr = PetscViewerASCIIPrintf(viewer," %7.5e ",(double)PetscRealPart(value));CHKERRQ(ierr);
907         } else {
908           ierr = PetscViewerASCIIPrintf(viewer," %7.5e+%7.5e i ",(double)PetscRealPart(value),(double)PetscImaginaryPart(value));CHKERRQ(ierr);
909         }
910 #else
911         ierr = PetscViewerASCIIPrintf(viewer," %7.5e ",(double)value);CHKERRQ(ierr);
912 #endif
913       }
914       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
915     }
916     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
917   } else if (format == PETSC_VIEWER_ASCII_MATRIXMARKET) {
918     PetscInt fshift=1;
919     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
920 #if defined(PETSC_USE_COMPLEX)
921     ierr = PetscViewerASCIIPrintf(viewer,"%%%%MatrixMarket matrix coordinate complex general\n");CHKERRQ(ierr);
922 #else
923     ierr = PetscViewerASCIIPrintf(viewer,"%%%%MatrixMarket matrix coordinate real general\n");CHKERRQ(ierr);
924 #endif
925     ierr = PetscViewerASCIIPrintf(viewer,"%D %D %D\n", m, A->cmap->n, a->nz);CHKERRQ(ierr);
926     for (i=0; i<m; i++) {
927       for (j=a->i[i]; j<a->i[i+1]; j++) {
928 #if defined(PETSC_USE_COMPLEX)
929         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);
930 #else
931         ierr = PetscViewerASCIIPrintf(viewer,"%D %D %g\n", i+fshift, a->j[j]+fshift, (double)a->a[j]);CHKERRQ(ierr);
932 #endif
933       }
934     }
935     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
936   } else {
937     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
938     if (A->factortype) {
939       for (i=0; i<m; i++) {
940         ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
941         /* L part */
942         for (j=a->i[i]; j<a->i[i+1]; j++) {
943 #if defined(PETSC_USE_COMPLEX)
944           if (PetscImaginaryPart(a->a[j]) > 0.0) {
945             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
946           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
947             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)(-PetscImaginaryPart(a->a[j])));CHKERRQ(ierr);
948           } else {
949             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
950           }
951 #else
952           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);
953 #endif
954         }
955         /* diagonal */
956         j = a->diag[i];
957 #if defined(PETSC_USE_COMPLEX)
958         if (PetscImaginaryPart(a->a[j]) > 0.0) {
959           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);
960         } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
961           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);
962         } else {
963           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(1.0/a->a[j]));CHKERRQ(ierr);
964         }
965 #else
966         ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)(1.0/a->a[j]));CHKERRQ(ierr);
967 #endif
968 
969         /* U part */
970         for (j=a->diag[i+1]+1; j<a->diag[i]; j++) {
971 #if defined(PETSC_USE_COMPLEX)
972           if (PetscImaginaryPart(a->a[j]) > 0.0) {
973             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
974           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
975             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)(-PetscImaginaryPart(a->a[j])));CHKERRQ(ierr);
976           } else {
977             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
978           }
979 #else
980           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);
981 #endif
982         }
983         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
984       }
985     } else {
986       for (i=0; i<m; i++) {
987         ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
988         for (j=a->i[i]; j<a->i[i+1]; j++) {
989 #if defined(PETSC_USE_COMPLEX)
990           if (PetscImaginaryPart(a->a[j]) > 0.0) {
991             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
992           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
993             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j],(double)PetscRealPart(a->a[j]),(double)-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
994           } else {
995             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)PetscRealPart(a->a[j]));CHKERRQ(ierr);
996           }
997 #else
998           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j],(double)a->a[j]);CHKERRQ(ierr);
999 #endif
1000         }
1001         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
1002       }
1003     }
1004     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
1005   }
1006   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1007   PetscFunctionReturn(0);
1008 }
1009 
1010 #include <petscdraw.h>
1011 PetscErrorCode MatView_SeqAIJ_Draw_Zoom(PetscDraw draw,void *Aa)
1012 {
1013   Mat               A  = (Mat) Aa;
1014   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1015   PetscErrorCode    ierr;
1016   PetscInt          i,j,m = A->rmap->n;
1017   int               color;
1018   PetscReal         xl,yl,xr,yr,x_l,x_r,y_l,y_r;
1019   PetscViewer       viewer;
1020   PetscViewerFormat format;
1021 
1022   PetscFunctionBegin;
1023   ierr = PetscObjectQuery((PetscObject)A,"Zoomviewer",(PetscObject*)&viewer);CHKERRQ(ierr);
1024   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1025   ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
1026 
1027   /* loop over matrix elements drawing boxes */
1028 
1029   if (format != PETSC_VIEWER_DRAW_CONTOUR) {
1030     ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
1031     /* Blue for negative, Cyan for zero and  Red for positive */
1032     color = PETSC_DRAW_BLUE;
1033     for (i=0; i<m; i++) {
1034       y_l = m - i - 1.0; y_r = y_l + 1.0;
1035       for (j=a->i[i]; j<a->i[i+1]; j++) {
1036         x_l = a->j[j]; x_r = x_l + 1.0;
1037         if (PetscRealPart(a->a[j]) >=  0.) continue;
1038         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
1039       }
1040     }
1041     color = PETSC_DRAW_CYAN;
1042     for (i=0; i<m; i++) {
1043       y_l = m - i - 1.0; y_r = y_l + 1.0;
1044       for (j=a->i[i]; j<a->i[i+1]; j++) {
1045         x_l = a->j[j]; x_r = x_l + 1.0;
1046         if (a->a[j] !=  0.) continue;
1047         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
1048       }
1049     }
1050     color = PETSC_DRAW_RED;
1051     for (i=0; i<m; i++) {
1052       y_l = m - i - 1.0; y_r = y_l + 1.0;
1053       for (j=a->i[i]; j<a->i[i+1]; j++) {
1054         x_l = a->j[j]; x_r = x_l + 1.0;
1055         if (PetscRealPart(a->a[j]) <=  0.) continue;
1056         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
1057       }
1058     }
1059     ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
1060   } else {
1061     /* use contour shading to indicate magnitude of values */
1062     /* first determine max of all nonzero values */
1063     PetscReal minv = 0.0, maxv = 0.0;
1064     PetscInt  nz = a->nz, count = 0;
1065     PetscDraw popup;
1066 
1067     for (i=0; i<nz; i++) {
1068       if (PetscAbsScalar(a->a[i]) > maxv) maxv = PetscAbsScalar(a->a[i]);
1069     }
1070     if (minv >= maxv) maxv = minv + PETSC_SMALL;
1071     ierr = PetscDrawGetPopup(draw,&popup);CHKERRQ(ierr);
1072     ierr = PetscDrawScalePopup(popup,minv,maxv);CHKERRQ(ierr);
1073 
1074     ierr = PetscDrawCollectiveBegin(draw);CHKERRQ(ierr);
1075     for (i=0; i<m; i++) {
1076       y_l = m - i - 1.0;
1077       y_r = y_l + 1.0;
1078       for (j=a->i[i]; j<a->i[i+1]; j++) {
1079         x_l = a->j[j];
1080         x_r = x_l + 1.0;
1081         color = PetscDrawRealToColor(PetscAbsScalar(a->a[count]),minv,maxv);
1082         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
1083         count++;
1084       }
1085     }
1086     ierr = PetscDrawCollectiveEnd(draw);CHKERRQ(ierr);
1087   }
1088   PetscFunctionReturn(0);
1089 }
1090 
1091 #include <petscdraw.h>
1092 PetscErrorCode MatView_SeqAIJ_Draw(Mat A,PetscViewer viewer)
1093 {
1094   PetscErrorCode ierr;
1095   PetscDraw      draw;
1096   PetscReal      xr,yr,xl,yl,h,w;
1097   PetscBool      isnull;
1098 
1099   PetscFunctionBegin;
1100   ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1101   ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
1102   if (isnull) PetscFunctionReturn(0);
1103 
1104   xr   = A->cmap->n; yr  = A->rmap->n; h = yr/10.0; w = xr/10.0;
1105   xr  += w;          yr += h;         xl = -w;     yl = -h;
1106   ierr = PetscDrawSetCoordinates(draw,xl,yl,xr,yr);CHKERRQ(ierr);
1107   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",(PetscObject)viewer);CHKERRQ(ierr);
1108   ierr = PetscDrawZoom(draw,MatView_SeqAIJ_Draw_Zoom,A);CHKERRQ(ierr);
1109   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",NULL);CHKERRQ(ierr);
1110   ierr = PetscDrawSave(draw);CHKERRQ(ierr);
1111   PetscFunctionReturn(0);
1112 }
1113 
1114 PetscErrorCode MatView_SeqAIJ(Mat A,PetscViewer viewer)
1115 {
1116   PetscErrorCode ierr;
1117   PetscBool      iascii,isbinary,isdraw;
1118 
1119   PetscFunctionBegin;
1120   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1121   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1122   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1123   if (iascii) {
1124     ierr = MatView_SeqAIJ_ASCII(A,viewer);CHKERRQ(ierr);
1125   } else if (isbinary) {
1126     ierr = MatView_SeqAIJ_Binary(A,viewer);CHKERRQ(ierr);
1127   } else if (isdraw) {
1128     ierr = MatView_SeqAIJ_Draw(A,viewer);CHKERRQ(ierr);
1129   }
1130   ierr = MatView_SeqAIJ_Inode(A,viewer);CHKERRQ(ierr);
1131   PetscFunctionReturn(0);
1132 }
1133 
1134 PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat A,MatAssemblyType mode)
1135 {
1136   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1137   PetscErrorCode ierr;
1138   PetscInt       fshift = 0,i,*ai = a->i,*aj = a->j,*imax = a->imax;
1139   PetscInt       m      = A->rmap->n,*ip,N,*ailen = a->ilen,rmax = 0;
1140   MatScalar      *aa    = a->a,*ap;
1141   PetscReal      ratio  = 0.6;
1142 
1143   PetscFunctionBegin;
1144   if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(0);
1145   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1146   if (A->was_assembled && A->ass_nonzerostate == A->nonzerostate) PetscFunctionReturn(0);
1147 
1148   if (m) rmax = ailen[0]; /* determine row with most nonzeros */
1149   for (i=1; i<m; i++) {
1150     /* move each row back by the amount of empty slots (fshift) before it*/
1151     fshift += imax[i-1] - ailen[i-1];
1152     rmax    = PetscMax(rmax,ailen[i]);
1153     if (fshift) {
1154       ip = aj + ai[i];
1155       ap = aa + ai[i];
1156       N  = ailen[i];
1157       ierr = PetscArraymove(ip-fshift,ip,N);CHKERRQ(ierr);
1158       if (!A->structure_only) {
1159         ierr = PetscArraymove(ap-fshift,ap,N);CHKERRQ(ierr);
1160       }
1161     }
1162     ai[i] = ai[i-1] + ailen[i-1];
1163   }
1164   if (m) {
1165     fshift += imax[m-1] - ailen[m-1];
1166     ai[m]   = ai[m-1] + ailen[m-1];
1167   }
1168 
1169   /* reset ilen and imax for each row */
1170   a->nonzerorowcnt = 0;
1171   if (A->structure_only) {
1172     ierr = PetscFree(a->imax);CHKERRQ(ierr);
1173     ierr = PetscFree(a->ilen);CHKERRQ(ierr);
1174   } else { /* !A->structure_only */
1175     for (i=0; i<m; i++) {
1176       ailen[i] = imax[i] = ai[i+1] - ai[i];
1177       a->nonzerorowcnt += ((ai[i+1] - ai[i]) > 0);
1178     }
1179   }
1180   a->nz = ai[m];
1181   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);
1182 
1183   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1184   ierr = PetscInfo4(A,"Matrix size: %D X %D; storage space: %D unneeded,%D used\n",m,A->cmap->n,fshift,a->nz);CHKERRQ(ierr);
1185   ierr = PetscInfo1(A,"Number of mallocs during MatSetValues() is %D\n",a->reallocs);CHKERRQ(ierr);
1186   ierr = PetscInfo1(A,"Maximum nonzeros in any row is %D\n",rmax);CHKERRQ(ierr);
1187 
1188   A->info.mallocs    += a->reallocs;
1189   a->reallocs         = 0;
1190   A->info.nz_unneeded = (PetscReal)fshift;
1191   a->rmax             = rmax;
1192 
1193   if (!A->structure_only) {
1194     ierr = MatCheckCompressedRow(A,a->nonzerorowcnt,&a->compressedrow,a->i,m,ratio);CHKERRQ(ierr);
1195   }
1196   ierr = MatAssemblyEnd_SeqAIJ_Inode(A,mode);CHKERRQ(ierr);
1197   PetscFunctionReturn(0);
1198 }
1199 
1200 PetscErrorCode MatRealPart_SeqAIJ(Mat A)
1201 {
1202   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1203   PetscInt       i,nz = a->nz;
1204   MatScalar      *aa = a->a;
1205   PetscErrorCode ierr;
1206 
1207   PetscFunctionBegin;
1208   for (i=0; i<nz; i++) aa[i] = PetscRealPart(aa[i]);
1209   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1210 #if defined(PETSC_HAVE_DEVICE)
1211   if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) A->offloadmask = PETSC_OFFLOAD_CPU;
1212 #endif
1213   PetscFunctionReturn(0);
1214 }
1215 
1216 PetscErrorCode MatImaginaryPart_SeqAIJ(Mat A)
1217 {
1218   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1219   PetscInt       i,nz = a->nz;
1220   MatScalar      *aa = a->a;
1221   PetscErrorCode ierr;
1222 
1223   PetscFunctionBegin;
1224   for (i=0; i<nz; i++) aa[i] = PetscImaginaryPart(aa[i]);
1225   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1226 #if defined(PETSC_HAVE_DEVICE)
1227   if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) A->offloadmask = PETSC_OFFLOAD_CPU;
1228 #endif
1229   PetscFunctionReturn(0);
1230 }
1231 
1232 PetscErrorCode MatZeroEntries_SeqAIJ(Mat A)
1233 {
1234   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1235   PetscErrorCode ierr;
1236 
1237   PetscFunctionBegin;
1238   ierr = PetscArrayzero(a->a,a->i[A->rmap->n]);CHKERRQ(ierr);
1239   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1240 #if defined(PETSC_HAVE_DEVICE)
1241   if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) A->offloadmask = PETSC_OFFLOAD_CPU;
1242 #endif
1243   PetscFunctionReturn(0);
1244 }
1245 
1246 PetscErrorCode MatDestroy_SeqAIJ(Mat A)
1247 {
1248   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1249   PetscErrorCode ierr;
1250 
1251   PetscFunctionBegin;
1252 #if defined(PETSC_USE_LOG)
1253   PetscLogObjectState((PetscObject)A,"Rows=%D, Cols=%D, NZ=%D",A->rmap->n,A->cmap->n,a->nz);
1254 #endif
1255   ierr = MatSeqXAIJFreeAIJ(A,&a->a,&a->j,&a->i);CHKERRQ(ierr);
1256   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
1257   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
1258   ierr = PetscFree(a->diag);CHKERRQ(ierr);
1259   ierr = PetscFree(a->ibdiag);CHKERRQ(ierr);
1260   ierr = PetscFree(a->imax);CHKERRQ(ierr);
1261   ierr = PetscFree(a->ilen);CHKERRQ(ierr);
1262   ierr = PetscFree(a->ipre);CHKERRQ(ierr);
1263   ierr = PetscFree3(a->idiag,a->mdiag,a->ssor_work);CHKERRQ(ierr);
1264   ierr = PetscFree(a->solve_work);CHKERRQ(ierr);
1265   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
1266   ierr = PetscFree(a->saved_values);CHKERRQ(ierr);
1267   ierr = PetscFree2(a->compressedrow.i,a->compressedrow.rindex);CHKERRQ(ierr);
1268 
1269   ierr = MatDestroy_SeqAIJ_Inode(A);CHKERRQ(ierr);
1270   ierr = PetscFree(A->data);CHKERRQ(ierr);
1271 
1272   /* MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted may allocate this.
1273      That function is so heavily used (sometimes in an hidden way through multnumeric function pointers)
1274      that is hard to properly add this data to the MatProduct data. We free it here to avoid
1275      users reusing the matrix object with different data to incur in obscure segmentation faults
1276      due to different matrix sizes */
1277   ierr = PetscObjectCompose((PetscObject)A,"__PETSc__ab_dense",NULL);CHKERRQ(ierr);
1278 
1279   ierr = PetscObjectChangeTypeName((PetscObject)A,NULL);CHKERRQ(ierr);
1280   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetColumnIndices_C",NULL);CHKERRQ(ierr);
1281   ierr = PetscObjectComposeFunction((PetscObject)A,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1282   ierr = PetscObjectComposeFunction((PetscObject)A,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1283   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqsbaij_C",NULL);CHKERRQ(ierr);
1284   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqbaij_C",NULL);CHKERRQ(ierr);
1285   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqaijperm_C",NULL);CHKERRQ(ierr);
1286 
1287 #if defined(PETSC_HAVE_CUDA)
1288   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqaijcusparse_C",NULL);CHKERRQ(ierr);
1289   ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqaijcusparse_seqaij_C",NULL);CHKERRQ(ierr);
1290 #endif
1291   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqaijcrl_C",NULL);CHKERRQ(ierr);
1292 #if defined(PETSC_HAVE_ELEMENTAL)
1293   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_elemental_C",NULL);CHKERRQ(ierr);
1294 #endif
1295 #if defined(PETSC_HAVE_SCALAPACK)
1296   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_scalapack_C",NULL);CHKERRQ(ierr);
1297 #endif
1298 #if defined(PETSC_HAVE_HYPRE)
1299   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_hypre_C",NULL);CHKERRQ(ierr);
1300   ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_transpose_seqaij_seqaij_C",NULL);CHKERRQ(ierr);
1301 #endif
1302   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqdense_C",NULL);CHKERRQ(ierr);
1303   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqsell_C",NULL);CHKERRQ(ierr);
1304   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_is_C",NULL);CHKERRQ(ierr);
1305   ierr = PetscObjectComposeFunction((PetscObject)A,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1306   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1307   ierr = PetscObjectComposeFunction((PetscObject)A,"MatResetPreallocation_C",NULL);CHKERRQ(ierr);
1308   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1309   ierr = PetscObjectComposeFunction((PetscObject)A,"MatReorderForNonzeroDiagonal_C",NULL);CHKERRQ(ierr);
1310   ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_is_seqaij_C",NULL);CHKERRQ(ierr);
1311   ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqdense_seqaij_C",NULL);CHKERRQ(ierr);
1312   ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqaij_seqaij_C",NULL);CHKERRQ(ierr);
1313   PetscFunctionReturn(0);
1314 }
1315 
1316 PetscErrorCode MatSetOption_SeqAIJ(Mat A,MatOption op,PetscBool flg)
1317 {
1318   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1319   PetscErrorCode ierr;
1320 
1321   PetscFunctionBegin;
1322   switch (op) {
1323   case MAT_ROW_ORIENTED:
1324     a->roworiented = flg;
1325     break;
1326   case MAT_KEEP_NONZERO_PATTERN:
1327     a->keepnonzeropattern = flg;
1328     break;
1329   case MAT_NEW_NONZERO_LOCATIONS:
1330     a->nonew = (flg ? 0 : 1);
1331     break;
1332   case MAT_NEW_NONZERO_LOCATION_ERR:
1333     a->nonew = (flg ? -1 : 0);
1334     break;
1335   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1336     a->nonew = (flg ? -2 : 0);
1337     break;
1338   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1339     a->nounused = (flg ? -1 : 0);
1340     break;
1341   case MAT_IGNORE_ZERO_ENTRIES:
1342     a->ignorezeroentries = flg;
1343     break;
1344   case MAT_SPD:
1345   case MAT_SYMMETRIC:
1346   case MAT_STRUCTURALLY_SYMMETRIC:
1347   case MAT_HERMITIAN:
1348   case MAT_SYMMETRY_ETERNAL:
1349   case MAT_STRUCTURE_ONLY:
1350     /* These options are handled directly by MatSetOption() */
1351     break;
1352   case MAT_NEW_DIAGONALS:
1353   case MAT_IGNORE_OFF_PROC_ENTRIES:
1354   case MAT_USE_HASH_TABLE:
1355     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1356     break;
1357   case MAT_USE_INODES:
1358     /* Not an error because MatSetOption_SeqAIJ_Inode handles this one */
1359     break;
1360   case MAT_SUBMAT_SINGLEIS:
1361     A->submat_singleis = flg;
1362     break;
1363   case MAT_SORTED_FULL:
1364     if (flg) A->ops->setvalues = MatSetValues_SeqAIJ_SortedFull;
1365     else     A->ops->setvalues = MatSetValues_SeqAIJ;
1366     break;
1367   default:
1368     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1369   }
1370   ierr = MatSetOption_SeqAIJ_Inode(A,op,flg);CHKERRQ(ierr);
1371   PetscFunctionReturn(0);
1372 }
1373 
1374 PetscErrorCode MatGetDiagonal_SeqAIJ(Mat A,Vec v)
1375 {
1376   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1377   PetscErrorCode ierr;
1378   PetscInt       i,j,n,*ai=a->i,*aj=a->j;
1379   PetscScalar    *aa=a->a,*x;
1380 
1381   PetscFunctionBegin;
1382   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
1383   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
1384 
1385   if (A->factortype == MAT_FACTOR_ILU || A->factortype == MAT_FACTOR_LU) {
1386     PetscInt *diag=a->diag;
1387     ierr = VecGetArrayWrite(v,&x);CHKERRQ(ierr);
1388     for (i=0; i<n; i++) x[i] = 1.0/aa[diag[i]];
1389     ierr = VecRestoreArrayWrite(v,&x);CHKERRQ(ierr);
1390     PetscFunctionReturn(0);
1391   }
1392 
1393   ierr = VecGetArrayWrite(v,&x);CHKERRQ(ierr);
1394   for (i=0; i<n; i++) {
1395     x[i] = 0.0;
1396     for (j=ai[i]; j<ai[i+1]; j++) {
1397       if (aj[j] == i) {
1398         x[i] = aa[j];
1399         break;
1400       }
1401     }
1402   }
1403   ierr = VecRestoreArrayWrite(v,&x);CHKERRQ(ierr);
1404   PetscFunctionReturn(0);
1405 }
1406 
1407 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1408 PetscErrorCode MatMultTransposeAdd_SeqAIJ(Mat A,Vec xx,Vec zz,Vec yy)
1409 {
1410   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1411   PetscScalar       *y;
1412   const PetscScalar *x;
1413   PetscErrorCode    ierr;
1414   PetscInt          m = A->rmap->n;
1415 #if !defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1416   const MatScalar   *v;
1417   PetscScalar       alpha;
1418   PetscInt          n,i,j;
1419   const PetscInt    *idx,*ii,*ridx=NULL;
1420   Mat_CompressedRow cprow    = a->compressedrow;
1421   PetscBool         usecprow = cprow.use;
1422 #endif
1423 
1424   PetscFunctionBegin;
1425   if (zz != yy) {ierr = VecCopy(zz,yy);CHKERRQ(ierr);}
1426   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1427   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1428 
1429 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1430   fortranmulttransposeaddaij_(&m,x,a->i,a->j,a->a,y);
1431 #else
1432   if (usecprow) {
1433     m    = cprow.nrows;
1434     ii   = cprow.i;
1435     ridx = cprow.rindex;
1436   } else {
1437     ii = a->i;
1438   }
1439   for (i=0; i<m; i++) {
1440     idx = a->j + ii[i];
1441     v   = a->a + ii[i];
1442     n   = ii[i+1] - ii[i];
1443     if (usecprow) {
1444       alpha = x[ridx[i]];
1445     } else {
1446       alpha = x[i];
1447     }
1448     for (j=0; j<n; j++) y[idx[j]] += alpha*v[j];
1449   }
1450 #endif
1451   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1452   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1453   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1454   PetscFunctionReturn(0);
1455 }
1456 
1457 PetscErrorCode MatMultTranspose_SeqAIJ(Mat A,Vec xx,Vec yy)
1458 {
1459   PetscErrorCode ierr;
1460 
1461   PetscFunctionBegin;
1462   ierr = VecSet(yy,0.0);CHKERRQ(ierr);
1463   ierr = MatMultTransposeAdd_SeqAIJ(A,xx,yy,yy);CHKERRQ(ierr);
1464   PetscFunctionReturn(0);
1465 }
1466 
1467 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1468 
1469 PetscErrorCode MatMult_SeqAIJ(Mat A,Vec xx,Vec yy)
1470 {
1471   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1472   PetscScalar       *y;
1473   const PetscScalar *x;
1474   const MatScalar   *aa;
1475   PetscErrorCode    ierr;
1476   PetscInt          m=A->rmap->n;
1477   const PetscInt    *aj,*ii,*ridx=NULL;
1478   PetscInt          n,i;
1479   PetscScalar       sum;
1480   PetscBool         usecprow=a->compressedrow.use;
1481 
1482 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1483 #pragma disjoint(*x,*y,*aa)
1484 #endif
1485 
1486   PetscFunctionBegin;
1487   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1488   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1489   ii   = a->i;
1490   if (usecprow) { /* use compressed row format */
1491     ierr = PetscArrayzero(y,m);CHKERRQ(ierr);
1492     m    = a->compressedrow.nrows;
1493     ii   = a->compressedrow.i;
1494     ridx = a->compressedrow.rindex;
1495     for (i=0; i<m; i++) {
1496       n           = ii[i+1] - ii[i];
1497       aj          = a->j + ii[i];
1498       aa          = a->a + ii[i];
1499       sum         = 0.0;
1500       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1501       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1502       y[*ridx++] = sum;
1503     }
1504   } else { /* do not use compressed row format */
1505 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJ)
1506     aj   = a->j;
1507     aa   = a->a;
1508     fortranmultaij_(&m,x,ii,aj,aa,y);
1509 #else
1510     for (i=0; i<m; i++) {
1511       n           = ii[i+1] - ii[i];
1512       aj          = a->j + ii[i];
1513       aa          = a->a + ii[i];
1514       sum         = 0.0;
1515       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1516       y[i] = sum;
1517     }
1518 #endif
1519   }
1520   ierr = PetscLogFlops(2.0*a->nz - a->nonzerorowcnt);CHKERRQ(ierr);
1521   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1522   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1523   PetscFunctionReturn(0);
1524 }
1525 
1526 PetscErrorCode MatMultMax_SeqAIJ(Mat A,Vec xx,Vec yy)
1527 {
1528   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1529   PetscScalar       *y;
1530   const PetscScalar *x;
1531   const MatScalar   *aa;
1532   PetscErrorCode    ierr;
1533   PetscInt          m=A->rmap->n;
1534   const PetscInt    *aj,*ii,*ridx=NULL;
1535   PetscInt          n,i,nonzerorow=0;
1536   PetscScalar       sum;
1537   PetscBool         usecprow=a->compressedrow.use;
1538 
1539 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1540 #pragma disjoint(*x,*y,*aa)
1541 #endif
1542 
1543   PetscFunctionBegin;
1544   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1545   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1546   if (usecprow) { /* use compressed row format */
1547     m    = a->compressedrow.nrows;
1548     ii   = a->compressedrow.i;
1549     ridx = a->compressedrow.rindex;
1550     for (i=0; i<m; i++) {
1551       n           = ii[i+1] - ii[i];
1552       aj          = a->j + ii[i];
1553       aa          = a->a + ii[i];
1554       sum         = 0.0;
1555       nonzerorow += (n>0);
1556       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1557       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1558       y[*ridx++] = sum;
1559     }
1560   } else { /* do not use compressed row format */
1561     ii = a->i;
1562     for (i=0; i<m; i++) {
1563       n           = ii[i+1] - ii[i];
1564       aj          = a->j + ii[i];
1565       aa          = a->a + ii[i];
1566       sum         = 0.0;
1567       nonzerorow += (n>0);
1568       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1569       y[i] = sum;
1570     }
1571   }
1572   ierr = PetscLogFlops(2.0*a->nz - nonzerorow);CHKERRQ(ierr);
1573   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1574   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1575   PetscFunctionReturn(0);
1576 }
1577 
1578 PetscErrorCode MatMultAddMax_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1579 {
1580   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1581   PetscScalar       *y,*z;
1582   const PetscScalar *x;
1583   const MatScalar   *aa;
1584   PetscErrorCode    ierr;
1585   PetscInt          m = A->rmap->n,*aj,*ii;
1586   PetscInt          n,i,*ridx=NULL;
1587   PetscScalar       sum;
1588   PetscBool         usecprow=a->compressedrow.use;
1589 
1590   PetscFunctionBegin;
1591   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1592   ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1593   if (usecprow) { /* use compressed row format */
1594     if (zz != yy) {
1595       ierr = PetscArraycpy(z,y,m);CHKERRQ(ierr);
1596     }
1597     m    = a->compressedrow.nrows;
1598     ii   = a->compressedrow.i;
1599     ridx = a->compressedrow.rindex;
1600     for (i=0; i<m; i++) {
1601       n   = ii[i+1] - ii[i];
1602       aj  = a->j + ii[i];
1603       aa  = a->a + ii[i];
1604       sum = y[*ridx];
1605       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1606       z[*ridx++] = sum;
1607     }
1608   } else { /* do not use compressed row format */
1609     ii = a->i;
1610     for (i=0; i<m; i++) {
1611       n   = ii[i+1] - ii[i];
1612       aj  = a->j + ii[i];
1613       aa  = a->a + ii[i];
1614       sum = y[i];
1615       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1616       z[i] = sum;
1617     }
1618   }
1619   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1620   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1621   ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1622   PetscFunctionReturn(0);
1623 }
1624 
1625 #include <../src/mat/impls/aij/seq/ftn-kernels/fmultadd.h>
1626 PetscErrorCode MatMultAdd_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1627 {
1628   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1629   PetscScalar       *y,*z;
1630   const PetscScalar *x;
1631   const MatScalar   *aa;
1632   PetscErrorCode    ierr;
1633   const PetscInt    *aj,*ii,*ridx=NULL;
1634   PetscInt          m = A->rmap->n,n,i;
1635   PetscScalar       sum;
1636   PetscBool         usecprow=a->compressedrow.use;
1637 
1638   PetscFunctionBegin;
1639   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1640   ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1641   if (usecprow) { /* use compressed row format */
1642     if (zz != yy) {
1643       ierr = PetscArraycpy(z,y,m);CHKERRQ(ierr);
1644     }
1645     m    = a->compressedrow.nrows;
1646     ii   = a->compressedrow.i;
1647     ridx = a->compressedrow.rindex;
1648     for (i=0; i<m; i++) {
1649       n   = ii[i+1] - ii[i];
1650       aj  = a->j + ii[i];
1651       aa  = a->a + ii[i];
1652       sum = y[*ridx];
1653       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1654       z[*ridx++] = sum;
1655     }
1656   } else { /* do not use compressed row format */
1657     ii = a->i;
1658 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJ)
1659     aj = a->j;
1660     aa = a->a;
1661     fortranmultaddaij_(&m,x,ii,aj,aa,y,z);
1662 #else
1663     for (i=0; i<m; i++) {
1664       n   = ii[i+1] - ii[i];
1665       aj  = a->j + ii[i];
1666       aa  = a->a + ii[i];
1667       sum = y[i];
1668       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1669       z[i] = sum;
1670     }
1671 #endif
1672   }
1673   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1674   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1675   ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
1676   PetscFunctionReturn(0);
1677 }
1678 
1679 /*
1680      Adds diagonal pointers to sparse matrix structure.
1681 */
1682 PetscErrorCode MatMarkDiagonal_SeqAIJ(Mat A)
1683 {
1684   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1685   PetscErrorCode ierr;
1686   PetscInt       i,j,m = A->rmap->n;
1687 
1688   PetscFunctionBegin;
1689   if (!a->diag) {
1690     ierr = PetscMalloc1(m,&a->diag);CHKERRQ(ierr);
1691     ierr = PetscLogObjectMemory((PetscObject)A, m*sizeof(PetscInt));CHKERRQ(ierr);
1692   }
1693   for (i=0; i<A->rmap->n; i++) {
1694     a->diag[i] = a->i[i+1];
1695     for (j=a->i[i]; j<a->i[i+1]; j++) {
1696       if (a->j[j] == i) {
1697         a->diag[i] = j;
1698         break;
1699       }
1700     }
1701   }
1702   PetscFunctionReturn(0);
1703 }
1704 
1705 PetscErrorCode MatShift_SeqAIJ(Mat A,PetscScalar v)
1706 {
1707   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1708   const PetscInt    *diag = (const PetscInt*)a->diag;
1709   const PetscInt    *ii = (const PetscInt*) a->i;
1710   PetscInt          i,*mdiag = NULL;
1711   PetscErrorCode    ierr;
1712   PetscInt          cnt = 0; /* how many diagonals are missing */
1713 
1714   PetscFunctionBegin;
1715   if (!A->preallocated || !a->nz) {
1716     ierr = MatSeqAIJSetPreallocation(A,1,NULL);CHKERRQ(ierr);
1717     ierr = MatShift_Basic(A,v);CHKERRQ(ierr);
1718     PetscFunctionReturn(0);
1719   }
1720 
1721   if (a->diagonaldense) {
1722     cnt = 0;
1723   } else {
1724     ierr = PetscCalloc1(A->rmap->n,&mdiag);CHKERRQ(ierr);
1725     for (i=0; i<A->rmap->n; i++) {
1726       if (diag[i] >= ii[i+1]) {
1727         cnt++;
1728         mdiag[i] = 1;
1729       }
1730     }
1731   }
1732   if (!cnt) {
1733     ierr = MatShift_Basic(A,v);CHKERRQ(ierr);
1734   } else {
1735     PetscScalar *olda = a->a;  /* preserve pointers to current matrix nonzeros structure and values */
1736     PetscInt    *oldj = a->j, *oldi = a->i;
1737     PetscBool   singlemalloc = a->singlemalloc,free_a = a->free_a,free_ij = a->free_ij;
1738 
1739     a->a = NULL;
1740     a->j = NULL;
1741     a->i = NULL;
1742     /* increase the values in imax for each row where a diagonal is being inserted then reallocate the matrix data structures */
1743     for (i=0; i<A->rmap->n; i++) {
1744       a->imax[i] += mdiag[i];
1745       a->imax[i] = PetscMin(a->imax[i],A->cmap->n);
1746     }
1747     ierr = MatSeqAIJSetPreallocation_SeqAIJ(A,0,a->imax);CHKERRQ(ierr);
1748 
1749     /* copy old values into new matrix data structure */
1750     for (i=0; i<A->rmap->n; i++) {
1751       ierr = MatSetValues(A,1,&i,a->imax[i] - mdiag[i],&oldj[oldi[i]],&olda[oldi[i]],ADD_VALUES);CHKERRQ(ierr);
1752       if (i < A->cmap->n) {
1753         ierr = MatSetValue(A,i,i,v,ADD_VALUES);CHKERRQ(ierr);
1754       }
1755     }
1756     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1757     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1758     if (singlemalloc) {
1759       ierr = PetscFree3(olda,oldj,oldi);CHKERRQ(ierr);
1760     } else {
1761       if (free_a)  {ierr = PetscFree(olda);CHKERRQ(ierr);}
1762       if (free_ij) {ierr = PetscFree(oldj);CHKERRQ(ierr);}
1763       if (free_ij) {ierr = PetscFree(oldi);CHKERRQ(ierr);}
1764     }
1765   }
1766   ierr = PetscFree(mdiag);CHKERRQ(ierr);
1767   a->diagonaldense = PETSC_TRUE;
1768   PetscFunctionReturn(0);
1769 }
1770 
1771 /*
1772      Checks for missing diagonals
1773 */
1774 PetscErrorCode MatMissingDiagonal_SeqAIJ(Mat A,PetscBool  *missing,PetscInt *d)
1775 {
1776   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1777   PetscInt       *diag,*ii = a->i,i;
1778   PetscErrorCode ierr;
1779 
1780   PetscFunctionBegin;
1781   *missing = PETSC_FALSE;
1782   if (A->rmap->n > 0 && !ii) {
1783     *missing = PETSC_TRUE;
1784     if (d) *d = 0;
1785     ierr = PetscInfo(A,"Matrix has no entries therefore is missing diagonal\n");CHKERRQ(ierr);
1786   } else {
1787     PetscInt n;
1788     n = PetscMin(A->rmap->n, A->cmap->n);
1789     diag = a->diag;
1790     for (i=0; i<n; i++) {
1791       if (diag[i] >= ii[i+1]) {
1792         *missing = PETSC_TRUE;
1793         if (d) *d = i;
1794         ierr = PetscInfo1(A,"Matrix is missing diagonal number %D\n",i);CHKERRQ(ierr);
1795         break;
1796       }
1797     }
1798   }
1799   PetscFunctionReturn(0);
1800 }
1801 
1802 #include <petscblaslapack.h>
1803 #include <petsc/private/kernels/blockinvert.h>
1804 
1805 /*
1806     Note that values is allocated externally by the PC and then passed into this routine
1807 */
1808 PetscErrorCode MatInvertVariableBlockDiagonal_SeqAIJ(Mat A,PetscInt nblocks,const PetscInt *bsizes,PetscScalar *diag)
1809 {
1810   PetscErrorCode  ierr;
1811   PetscInt        n = A->rmap->n, i, ncnt = 0, *indx,j,bsizemax = 0,*v_pivots;
1812   PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;
1813   const PetscReal shift = 0.0;
1814   PetscInt        ipvt[5];
1815   PetscScalar     work[25],*v_work;
1816 
1817   PetscFunctionBegin;
1818   allowzeropivot = PetscNot(A->erroriffailure);
1819   for (i=0; i<nblocks; i++) ncnt += bsizes[i];
1820   if (ncnt != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Total blocksizes %D doesn't match number matrix rows %D",ncnt,n);
1821   for (i=0; i<nblocks; i++) {
1822     bsizemax = PetscMax(bsizemax,bsizes[i]);
1823   }
1824   ierr = PetscMalloc1(bsizemax,&indx);CHKERRQ(ierr);
1825   if (bsizemax > 7) {
1826     ierr = PetscMalloc2(bsizemax,&v_work,bsizemax,&v_pivots);CHKERRQ(ierr);
1827   }
1828   ncnt = 0;
1829   for (i=0; i<nblocks; i++) {
1830     for (j=0; j<bsizes[i]; j++) indx[j] = ncnt+j;
1831     ierr    = MatGetValues(A,bsizes[i],indx,bsizes[i],indx,diag);CHKERRQ(ierr);
1832     switch (bsizes[i]) {
1833     case 1:
1834       *diag = 1.0/(*diag);
1835       break;
1836     case 2:
1837       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1838       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1839       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
1840       break;
1841     case 3:
1842       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1843       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1844       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
1845       break;
1846     case 4:
1847       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1848       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1849       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
1850       break;
1851     case 5:
1852       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1853       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1854       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
1855       break;
1856     case 6:
1857       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1858       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1859       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
1860       break;
1861     case 7:
1862       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1863       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1864       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
1865       break;
1866     default:
1867       ierr  = PetscKernel_A_gets_inverse_A(bsizes[i],diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
1868       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1869       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bsizes[i]);CHKERRQ(ierr);
1870     }
1871     ncnt   += bsizes[i];
1872     diag += bsizes[i]*bsizes[i];
1873   }
1874   if (bsizemax > 7) {
1875     ierr = PetscFree2(v_work,v_pivots);CHKERRQ(ierr);
1876   }
1877   ierr = PetscFree(indx);CHKERRQ(ierr);
1878   PetscFunctionReturn(0);
1879 }
1880 
1881 /*
1882    Negative shift indicates do not generate an error if there is a zero diagonal, just invert it anyways
1883 */
1884 PetscErrorCode  MatInvertDiagonal_SeqAIJ(Mat A,PetscScalar omega,PetscScalar fshift)
1885 {
1886   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
1887   PetscErrorCode ierr;
1888   PetscInt       i,*diag,m = A->rmap->n;
1889   MatScalar      *v = a->a;
1890   PetscScalar    *idiag,*mdiag;
1891 
1892   PetscFunctionBegin;
1893   if (a->idiagvalid) PetscFunctionReturn(0);
1894   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1895   diag = a->diag;
1896   if (!a->idiag) {
1897     ierr = PetscMalloc3(m,&a->idiag,m,&a->mdiag,m,&a->ssor_work);CHKERRQ(ierr);
1898     ierr = PetscLogObjectMemory((PetscObject)A, 3*m*sizeof(PetscScalar));CHKERRQ(ierr);
1899     v    = a->a;
1900   }
1901   mdiag = a->mdiag;
1902   idiag = a->idiag;
1903 
1904   if (omega == 1.0 && PetscRealPart(fshift) <= 0.0) {
1905     for (i=0; i<m; i++) {
1906       mdiag[i] = v[diag[i]];
1907       if (!PetscAbsScalar(mdiag[i])) { /* zero diagonal */
1908         if (PetscRealPart(fshift)) {
1909           ierr = PetscInfo1(A,"Zero diagonal on row %D\n",i);CHKERRQ(ierr);
1910           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
1911           A->factorerror_zeropivot_value = 0.0;
1912           A->factorerror_zeropivot_row   = i;
1913         } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Zero diagonal on row %D",i);
1914       }
1915       idiag[i] = 1.0/v[diag[i]];
1916     }
1917     ierr = PetscLogFlops(m);CHKERRQ(ierr);
1918   } else {
1919     for (i=0; i<m; i++) {
1920       mdiag[i] = v[diag[i]];
1921       idiag[i] = omega/(fshift + v[diag[i]]);
1922     }
1923     ierr = PetscLogFlops(2.0*m);CHKERRQ(ierr);
1924   }
1925   a->idiagvalid = PETSC_TRUE;
1926   PetscFunctionReturn(0);
1927 }
1928 
1929 #include <../src/mat/impls/aij/seq/ftn-kernels/frelax.h>
1930 PetscErrorCode MatSOR_SeqAIJ(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1931 {
1932   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1933   PetscScalar       *x,d,sum,*t,scale;
1934   const MatScalar   *v,*idiag=NULL,*mdiag;
1935   const PetscScalar *b, *bs,*xb, *ts;
1936   PetscErrorCode    ierr;
1937   PetscInt          n,m = A->rmap->n,i;
1938   const PetscInt    *idx,*diag;
1939 
1940   PetscFunctionBegin;
1941   its = its*lits;
1942 
1943   if (fshift != a->fshift || omega != a->omega) a->idiagvalid = PETSC_FALSE; /* must recompute idiag[] */
1944   if (!a->idiagvalid) {ierr = MatInvertDiagonal_SeqAIJ(A,omega,fshift);CHKERRQ(ierr);}
1945   a->fshift = fshift;
1946   a->omega  = omega;
1947 
1948   diag  = a->diag;
1949   t     = a->ssor_work;
1950   idiag = a->idiag;
1951   mdiag = a->mdiag;
1952 
1953   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1954   ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
1955   /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
1956   if (flag == SOR_APPLY_UPPER) {
1957     /* apply (U + D/omega) to the vector */
1958     bs = b;
1959     for (i=0; i<m; i++) {
1960       d   = fshift + mdiag[i];
1961       n   = a->i[i+1] - diag[i] - 1;
1962       idx = a->j + diag[i] + 1;
1963       v   = a->a + diag[i] + 1;
1964       sum = b[i]*d/omega;
1965       PetscSparseDensePlusDot(sum,bs,v,idx,n);
1966       x[i] = sum;
1967     }
1968     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1969     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1970     ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1971     PetscFunctionReturn(0);
1972   }
1973 
1974   if (flag == SOR_APPLY_LOWER) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SOR_APPLY_LOWER is not implemented");
1975   else if (flag & SOR_EISENSTAT) {
1976     /* Let  A = L + U + D; where L is lower triangular,
1977     U is upper triangular, E = D/omega; This routine applies
1978 
1979             (L + E)^{-1} A (U + E)^{-1}
1980 
1981     to a vector efficiently using Eisenstat's trick.
1982     */
1983     scale = (2.0/omega) - 1.0;
1984 
1985     /*  x = (E + U)^{-1} b */
1986     for (i=m-1; i>=0; i--) {
1987       n   = a->i[i+1] - diag[i] - 1;
1988       idx = a->j + diag[i] + 1;
1989       v   = a->a + diag[i] + 1;
1990       sum = b[i];
1991       PetscSparseDenseMinusDot(sum,x,v,idx,n);
1992       x[i] = sum*idiag[i];
1993     }
1994 
1995     /*  t = b - (2*E - D)x */
1996     v = a->a;
1997     for (i=0; i<m; i++) t[i] = b[i] - scale*(v[*diag++])*x[i];
1998 
1999     /*  t = (E + L)^{-1}t */
2000     ts   = t;
2001     diag = a->diag;
2002     for (i=0; i<m; i++) {
2003       n   = diag[i] - a->i[i];
2004       idx = a->j + a->i[i];
2005       v   = a->a + a->i[i];
2006       sum = t[i];
2007       PetscSparseDenseMinusDot(sum,ts,v,idx,n);
2008       t[i] = sum*idiag[i];
2009       /*  x = x + t */
2010       x[i] += t[i];
2011     }
2012 
2013     ierr = PetscLogFlops(6.0*m-1 + 2.0*a->nz);CHKERRQ(ierr);
2014     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2015     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
2016     PetscFunctionReturn(0);
2017   }
2018   if (flag & SOR_ZERO_INITIAL_GUESS) {
2019     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
2020       for (i=0; i<m; i++) {
2021         n   = diag[i] - a->i[i];
2022         idx = a->j + a->i[i];
2023         v   = a->a + a->i[i];
2024         sum = b[i];
2025         PetscSparseDenseMinusDot(sum,x,v,idx,n);
2026         t[i] = sum;
2027         x[i] = sum*idiag[i];
2028       }
2029       xb   = t;
2030       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2031     } else xb = b;
2032     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
2033       for (i=m-1; i>=0; i--) {
2034         n   = a->i[i+1] - diag[i] - 1;
2035         idx = a->j + diag[i] + 1;
2036         v   = a->a + diag[i] + 1;
2037         sum = xb[i];
2038         PetscSparseDenseMinusDot(sum,x,v,idx,n);
2039         if (xb == b) {
2040           x[i] = sum*idiag[i];
2041         } else {
2042           x[i] = (1-omega)*x[i] + sum*idiag[i];  /* omega in idiag */
2043         }
2044       }
2045       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
2046     }
2047     its--;
2048   }
2049   while (its--) {
2050     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
2051       for (i=0; i<m; i++) {
2052         /* lower */
2053         n   = diag[i] - a->i[i];
2054         idx = a->j + a->i[i];
2055         v   = a->a + a->i[i];
2056         sum = b[i];
2057         PetscSparseDenseMinusDot(sum,x,v,idx,n);
2058         t[i] = sum;             /* save application of the lower-triangular part */
2059         /* upper */
2060         n   = a->i[i+1] - diag[i] - 1;
2061         idx = a->j + diag[i] + 1;
2062         v   = a->a + diag[i] + 1;
2063         PetscSparseDenseMinusDot(sum,x,v,idx,n);
2064         x[i] = (1. - omega)*x[i] + sum*idiag[i]; /* omega in idiag */
2065       }
2066       xb   = t;
2067       ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
2068     } else xb = b;
2069     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
2070       for (i=m-1; i>=0; i--) {
2071         sum = xb[i];
2072         if (xb == b) {
2073           /* whole matrix (no checkpointing available) */
2074           n   = a->i[i+1] - a->i[i];
2075           idx = a->j + a->i[i];
2076           v   = a->a + a->i[i];
2077           PetscSparseDenseMinusDot(sum,x,v,idx,n);
2078           x[i] = (1. - omega)*x[i] + (sum + mdiag[i]*x[i])*idiag[i];
2079         } else { /* lower-triangular part has been saved, so only apply upper-triangular */
2080           n   = a->i[i+1] - diag[i] - 1;
2081           idx = a->j + diag[i] + 1;
2082           v   = a->a + diag[i] + 1;
2083           PetscSparseDenseMinusDot(sum,x,v,idx,n);
2084           x[i] = (1. - omega)*x[i] + sum*idiag[i];  /* omega in idiag */
2085         }
2086       }
2087       if (xb == b) {
2088         ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
2089       } else {
2090         ierr = PetscLogFlops(a->nz);CHKERRQ(ierr); /* assumes 1/2 in upper */
2091       }
2092     }
2093   }
2094   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2095   ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
2096   PetscFunctionReturn(0);
2097 }
2098 
2099 
2100 PetscErrorCode MatGetInfo_SeqAIJ(Mat A,MatInfoType flag,MatInfo *info)
2101 {
2102   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2103 
2104   PetscFunctionBegin;
2105   info->block_size   = 1.0;
2106   info->nz_allocated = a->maxnz;
2107   info->nz_used      = a->nz;
2108   info->nz_unneeded  = (a->maxnz - a->nz);
2109   info->assemblies   = A->num_ass;
2110   info->mallocs      = A->info.mallocs;
2111   info->memory       = ((PetscObject)A)->mem;
2112   if (A->factortype) {
2113     info->fill_ratio_given  = A->info.fill_ratio_given;
2114     info->fill_ratio_needed = A->info.fill_ratio_needed;
2115     info->factor_mallocs    = A->info.factor_mallocs;
2116   } else {
2117     info->fill_ratio_given  = 0;
2118     info->fill_ratio_needed = 0;
2119     info->factor_mallocs    = 0;
2120   }
2121   PetscFunctionReturn(0);
2122 }
2123 
2124 PetscErrorCode MatZeroRows_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
2125 {
2126   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2127   PetscInt          i,m = A->rmap->n - 1;
2128   PetscErrorCode    ierr;
2129   const PetscScalar *xx;
2130   PetscScalar       *bb;
2131   PetscInt          d = 0;
2132 
2133   PetscFunctionBegin;
2134   if (x && b) {
2135     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
2136     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
2137     for (i=0; i<N; i++) {
2138       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2139       if (rows[i] >= A->cmap->n) continue;
2140       bb[rows[i]] = diag*xx[rows[i]];
2141     }
2142     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
2143     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
2144   }
2145 
2146   if (a->keepnonzeropattern) {
2147     for (i=0; i<N; i++) {
2148       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2149       ierr = PetscArrayzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]);CHKERRQ(ierr);
2150     }
2151     if (diag != 0.0) {
2152       for (i=0; i<N; i++) {
2153         d = rows[i];
2154         if (rows[i] >= A->cmap->n) continue;
2155         if (a->diag[d] >= a->i[d+1]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in the zeroed row %D",d);
2156       }
2157       for (i=0; i<N; i++) {
2158         if (rows[i] >= A->cmap->n) continue;
2159         a->a[a->diag[rows[i]]] = diag;
2160       }
2161     }
2162   } else {
2163     if (diag != 0.0) {
2164       for (i=0; i<N; i++) {
2165         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2166         if (a->ilen[rows[i]] > 0) {
2167           if (rows[i] >= A->cmap->n) {
2168             a->ilen[rows[i]] = 0;
2169           } else {
2170             a->ilen[rows[i]]    = 1;
2171             a->a[a->i[rows[i]]] = diag;
2172             a->j[a->i[rows[i]]] = rows[i];
2173           }
2174         } else if (rows[i] < A->cmap->n) { /* in case row was completely empty */
2175           ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES);CHKERRQ(ierr);
2176         }
2177       }
2178     } else {
2179       for (i=0; i<N; i++) {
2180         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2181         a->ilen[rows[i]] = 0;
2182       }
2183     }
2184     A->nonzerostate++;
2185   }
2186 #if defined(PETSC_HAVE_DEVICE)
2187   if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) A->offloadmask = PETSC_OFFLOAD_CPU;
2188 #endif
2189   ierr = (*A->ops->assemblyend)(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2190   PetscFunctionReturn(0);
2191 }
2192 
2193 PetscErrorCode MatZeroRowsColumns_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
2194 {
2195   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2196   PetscInt          i,j,m = A->rmap->n - 1,d = 0;
2197   PetscErrorCode    ierr;
2198   PetscBool         missing,*zeroed,vecs = PETSC_FALSE;
2199   const PetscScalar *xx;
2200   PetscScalar       *bb;
2201 
2202   PetscFunctionBegin;
2203   if (x && b) {
2204     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
2205     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
2206     vecs = PETSC_TRUE;
2207   }
2208   ierr = PetscCalloc1(A->rmap->n,&zeroed);CHKERRQ(ierr);
2209   for (i=0; i<N; i++) {
2210     if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
2211     ierr = PetscArrayzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]);CHKERRQ(ierr);
2212 
2213     zeroed[rows[i]] = PETSC_TRUE;
2214   }
2215   for (i=0; i<A->rmap->n; i++) {
2216     if (!zeroed[i]) {
2217       for (j=a->i[i]; j<a->i[i+1]; j++) {
2218         if (a->j[j] < A->rmap->n && zeroed[a->j[j]]) {
2219           if (vecs) bb[i] -= a->a[j]*xx[a->j[j]];
2220           a->a[j] = 0.0;
2221         }
2222       }
2223     } else if (vecs && i < A->cmap->N) bb[i] = diag*xx[i];
2224   }
2225   if (x && b) {
2226     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
2227     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
2228   }
2229   ierr = PetscFree(zeroed);CHKERRQ(ierr);
2230   if (diag != 0.0) {
2231     ierr = MatMissingDiagonal_SeqAIJ(A,&missing,&d);CHKERRQ(ierr);
2232     if (missing) {
2233       for (i=0; i<N; i++) {
2234         if (rows[i] >= A->cmap->N) continue;
2235         if (a->nonew && rows[i] >= d) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in row %D (%D)",d,rows[i]);
2236         ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES);CHKERRQ(ierr);
2237       }
2238     } else {
2239       for (i=0; i<N; i++) {
2240         a->a[a->diag[rows[i]]] = diag;
2241       }
2242     }
2243   }
2244 #if defined(PETSC_HAVE_DEVICE)
2245   if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) A->offloadmask = PETSC_OFFLOAD_CPU;
2246 #endif
2247   ierr = (*A->ops->assemblyend)(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2248   PetscFunctionReturn(0);
2249 }
2250 
2251 PetscErrorCode MatGetRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
2252 {
2253   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2254   PetscInt   *itmp;
2255 
2256   PetscFunctionBegin;
2257   if (row < 0 || row >= A->rmap->n) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range",row);
2258 
2259   *nz = a->i[row+1] - a->i[row];
2260   if (v) *v = a->a + a->i[row];
2261   if (idx) {
2262     itmp = a->j + a->i[row];
2263     if (*nz) *idx = itmp;
2264     else *idx = NULL;
2265   }
2266   PetscFunctionReturn(0);
2267 }
2268 
2269 /* remove this function? */
2270 PetscErrorCode MatRestoreRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
2271 {
2272   PetscFunctionBegin;
2273   PetscFunctionReturn(0);
2274 }
2275 
2276 PetscErrorCode MatNorm_SeqAIJ(Mat A,NormType type,PetscReal *nrm)
2277 {
2278   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
2279   MatScalar      *v  = a->a;
2280   PetscReal      sum = 0.0;
2281   PetscErrorCode ierr;
2282   PetscInt       i,j;
2283 
2284   PetscFunctionBegin;
2285   if (type == NORM_FROBENIUS) {
2286 #if defined(PETSC_USE_REAL___FP16)
2287     PetscBLASInt one = 1,nz = a->nz;
2288     *nrm = BLASnrm2_(&nz,v,&one);
2289 #else
2290     for (i=0; i<a->nz; i++) {
2291       sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
2292     }
2293     *nrm = PetscSqrtReal(sum);
2294 #endif
2295     ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
2296   } else if (type == NORM_1) {
2297     PetscReal *tmp;
2298     PetscInt  *jj = a->j;
2299     ierr = PetscCalloc1(A->cmap->n+1,&tmp);CHKERRQ(ierr);
2300     *nrm = 0.0;
2301     for (j=0; j<a->nz; j++) {
2302       tmp[*jj++] += PetscAbsScalar(*v);  v++;
2303     }
2304     for (j=0; j<A->cmap->n; j++) {
2305       if (tmp[j] > *nrm) *nrm = tmp[j];
2306     }
2307     ierr = PetscFree(tmp);CHKERRQ(ierr);
2308     ierr = PetscLogFlops(PetscMax(a->nz-1,0));CHKERRQ(ierr);
2309   } else if (type == NORM_INFINITY) {
2310     *nrm = 0.0;
2311     for (j=0; j<A->rmap->n; j++) {
2312       v   = a->a + a->i[j];
2313       sum = 0.0;
2314       for (i=0; i<a->i[j+1]-a->i[j]; i++) {
2315         sum += PetscAbsScalar(*v); v++;
2316       }
2317       if (sum > *nrm) *nrm = sum;
2318     }
2319     ierr = PetscLogFlops(PetscMax(a->nz-1,0));CHKERRQ(ierr);
2320   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for two norm");
2321   PetscFunctionReturn(0);
2322 }
2323 
2324 /* Merged from MatGetSymbolicTranspose_SeqAIJ() - replace MatGetSymbolicTranspose_SeqAIJ()? */
2325 PetscErrorCode MatTransposeSymbolic_SeqAIJ(Mat A,Mat *B)
2326 {
2327   PetscErrorCode ierr;
2328   PetscInt       i,j,anzj;
2329   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b;
2330   PetscInt       an=A->cmap->N,am=A->rmap->N;
2331   PetscInt       *ati,*atj,*atfill,*ai=a->i,*aj=a->j;
2332 
2333   PetscFunctionBegin;
2334   /* Allocate space for symbolic transpose info and work array */
2335   ierr = PetscCalloc1(an+1,&ati);CHKERRQ(ierr);
2336   ierr = PetscMalloc1(ai[am],&atj);CHKERRQ(ierr);
2337   ierr = PetscMalloc1(an,&atfill);CHKERRQ(ierr);
2338 
2339   /* Walk through aj and count ## of non-zeros in each row of A^T. */
2340   /* Note: offset by 1 for fast conversion into csr format. */
2341   for (i=0;i<ai[am];i++) ati[aj[i]+1] += 1;
2342   /* Form ati for csr format of A^T. */
2343   for (i=0;i<an;i++) ati[i+1] += ati[i];
2344 
2345   /* Copy ati into atfill so we have locations of the next free space in atj */
2346   ierr = PetscArraycpy(atfill,ati,an);CHKERRQ(ierr);
2347 
2348   /* Walk through A row-wise and mark nonzero entries of A^T. */
2349   for (i=0;i<am;i++) {
2350     anzj = ai[i+1] - ai[i];
2351     for (j=0;j<anzj;j++) {
2352       atj[atfill[*aj]] = i;
2353       atfill[*aj++]   += 1;
2354     }
2355   }
2356 
2357   /* Clean up temporary space and complete requests. */
2358   ierr = PetscFree(atfill);CHKERRQ(ierr);
2359   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),an,am,ati,atj,NULL,B);CHKERRQ(ierr);
2360   ierr = MatSetBlockSizes(*B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
2361   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2362 
2363   b          = (Mat_SeqAIJ*)((*B)->data);
2364   b->free_a  = PETSC_FALSE;
2365   b->free_ij = PETSC_TRUE;
2366   b->nonew   = 0;
2367   PetscFunctionReturn(0);
2368 }
2369 
2370 PetscErrorCode  MatIsTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2371 {
2372   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) B->data;
2373   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2374   MatScalar      *va,*vb;
2375   PetscErrorCode ierr;
2376   PetscInt       ma,na,mb,nb, i;
2377 
2378   PetscFunctionBegin;
2379   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2380   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2381   if (ma!=nb || na!=mb) {
2382     *f = PETSC_FALSE;
2383     PetscFunctionReturn(0);
2384   }
2385   aii  = aij->i; bii = bij->i;
2386   adx  = aij->j; bdx = bij->j;
2387   va   = aij->a; vb = bij->a;
2388   ierr = PetscMalloc1(ma,&aptr);CHKERRQ(ierr);
2389   ierr = PetscMalloc1(mb,&bptr);CHKERRQ(ierr);
2390   for (i=0; i<ma; i++) aptr[i] = aii[i];
2391   for (i=0; i<mb; i++) bptr[i] = bii[i];
2392 
2393   *f = PETSC_TRUE;
2394   for (i=0; i<ma; i++) {
2395     while (aptr[i]<aii[i+1]) {
2396       PetscInt    idc,idr;
2397       PetscScalar vc,vr;
2398       /* column/row index/value */
2399       idc = adx[aptr[i]];
2400       idr = bdx[bptr[idc]];
2401       vc  = va[aptr[i]];
2402       vr  = vb[bptr[idc]];
2403       if (i!=idr || PetscAbsScalar(vc-vr) > tol) {
2404         *f = PETSC_FALSE;
2405         goto done;
2406       } else {
2407         aptr[i]++;
2408         if (B || i!=idc) bptr[idc]++;
2409       }
2410     }
2411   }
2412 done:
2413   ierr = PetscFree(aptr);CHKERRQ(ierr);
2414   ierr = PetscFree(bptr);CHKERRQ(ierr);
2415   PetscFunctionReturn(0);
2416 }
2417 
2418 PetscErrorCode  MatIsHermitianTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2419 {
2420   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) B->data;
2421   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2422   MatScalar      *va,*vb;
2423   PetscErrorCode ierr;
2424   PetscInt       ma,na,mb,nb, i;
2425 
2426   PetscFunctionBegin;
2427   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2428   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2429   if (ma!=nb || na!=mb) {
2430     *f = PETSC_FALSE;
2431     PetscFunctionReturn(0);
2432   }
2433   aii  = aij->i; bii = bij->i;
2434   adx  = aij->j; bdx = bij->j;
2435   va   = aij->a; vb = bij->a;
2436   ierr = PetscMalloc1(ma,&aptr);CHKERRQ(ierr);
2437   ierr = PetscMalloc1(mb,&bptr);CHKERRQ(ierr);
2438   for (i=0; i<ma; i++) aptr[i] = aii[i];
2439   for (i=0; i<mb; i++) bptr[i] = bii[i];
2440 
2441   *f = PETSC_TRUE;
2442   for (i=0; i<ma; i++) {
2443     while (aptr[i]<aii[i+1]) {
2444       PetscInt    idc,idr;
2445       PetscScalar vc,vr;
2446       /* column/row index/value */
2447       idc = adx[aptr[i]];
2448       idr = bdx[bptr[idc]];
2449       vc  = va[aptr[i]];
2450       vr  = vb[bptr[idc]];
2451       if (i!=idr || PetscAbsScalar(vc-PetscConj(vr)) > tol) {
2452         *f = PETSC_FALSE;
2453         goto done;
2454       } else {
2455         aptr[i]++;
2456         if (B || i!=idc) bptr[idc]++;
2457       }
2458     }
2459   }
2460 done:
2461   ierr = PetscFree(aptr);CHKERRQ(ierr);
2462   ierr = PetscFree(bptr);CHKERRQ(ierr);
2463   PetscFunctionReturn(0);
2464 }
2465 
2466 PetscErrorCode MatIsSymmetric_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2467 {
2468   PetscErrorCode ierr;
2469 
2470   PetscFunctionBegin;
2471   ierr = MatIsTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2472   PetscFunctionReturn(0);
2473 }
2474 
2475 PetscErrorCode MatIsHermitian_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2476 {
2477   PetscErrorCode ierr;
2478 
2479   PetscFunctionBegin;
2480   ierr = MatIsHermitianTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2481   PetscFunctionReturn(0);
2482 }
2483 
2484 PetscErrorCode MatDiagonalScale_SeqAIJ(Mat A,Vec ll,Vec rr)
2485 {
2486   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
2487   const PetscScalar *l,*r;
2488   PetscScalar       x;
2489   MatScalar         *v;
2490   PetscErrorCode    ierr;
2491   PetscInt          i,j,m = A->rmap->n,n = A->cmap->n,M,nz = a->nz;
2492   const PetscInt    *jj;
2493 
2494   PetscFunctionBegin;
2495   if (ll) {
2496     /* The local size is used so that VecMPI can be passed to this routine
2497        by MatDiagonalScale_MPIAIJ */
2498     ierr = VecGetLocalSize(ll,&m);CHKERRQ(ierr);
2499     if (m != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
2500     ierr = VecGetArrayRead(ll,&l);CHKERRQ(ierr);
2501     v    = a->a;
2502     for (i=0; i<m; i++) {
2503       x = l[i];
2504       M = a->i[i+1] - a->i[i];
2505       for (j=0; j<M; j++) (*v++) *= x;
2506     }
2507     ierr = VecRestoreArrayRead(ll,&l);CHKERRQ(ierr);
2508     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2509   }
2510   if (rr) {
2511     ierr = VecGetLocalSize(rr,&n);CHKERRQ(ierr);
2512     if (n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vector wrong length");
2513     ierr = VecGetArrayRead(rr,&r);CHKERRQ(ierr);
2514     v    = a->a; jj = a->j;
2515     for (i=0; i<nz; i++) (*v++) *= r[*jj++];
2516     ierr = VecRestoreArrayRead(rr,&r);CHKERRQ(ierr);
2517     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2518   }
2519   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
2520 #if defined(PETSC_HAVE_DEVICE)
2521   if (A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) A->offloadmask = PETSC_OFFLOAD_CPU;
2522 #endif
2523   PetscFunctionReturn(0);
2524 }
2525 
2526 PetscErrorCode MatCreateSubMatrix_SeqAIJ(Mat A,IS isrow,IS iscol,PetscInt csize,MatReuse scall,Mat *B)
2527 {
2528   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*c;
2529   PetscErrorCode ierr;
2530   PetscInt       *smap,i,k,kstart,kend,oldcols = A->cmap->n,*lens;
2531   PetscInt       row,mat_i,*mat_j,tcol,first,step,*mat_ilen,sum,lensi;
2532   const PetscInt *irow,*icol;
2533   PetscInt       nrows,ncols;
2534   PetscInt       *starts,*j_new,*i_new,*aj = a->j,*ai = a->i,ii,*ailen = a->ilen;
2535   MatScalar      *a_new,*mat_a;
2536   Mat            C;
2537   PetscBool      stride;
2538 
2539   PetscFunctionBegin;
2540 
2541   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
2542   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
2543   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
2544 
2545   ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&stride);CHKERRQ(ierr);
2546   if (stride) {
2547     ierr = ISStrideGetInfo(iscol,&first,&step);CHKERRQ(ierr);
2548   } else {
2549     first = 0;
2550     step  = 0;
2551   }
2552   if (stride && step == 1) {
2553     /* special case of contiguous rows */
2554     ierr = PetscMalloc2(nrows,&lens,nrows,&starts);CHKERRQ(ierr);
2555     /* loop over new rows determining lens and starting points */
2556     for (i=0; i<nrows; i++) {
2557       kstart = ai[irow[i]];
2558       kend   = kstart + ailen[irow[i]];
2559       starts[i] = kstart;
2560       for (k=kstart; k<kend; k++) {
2561         if (aj[k] >= first) {
2562           starts[i] = k;
2563           break;
2564         }
2565       }
2566       sum = 0;
2567       while (k < kend) {
2568         if (aj[k++] >= first+ncols) break;
2569         sum++;
2570       }
2571       lens[i] = sum;
2572     }
2573     /* create submatrix */
2574     if (scall == MAT_REUSE_MATRIX) {
2575       PetscInt n_cols,n_rows;
2576       ierr = MatGetSize(*B,&n_rows,&n_cols);CHKERRQ(ierr);
2577       if (n_rows != nrows || n_cols != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
2578       ierr = MatZeroEntries(*B);CHKERRQ(ierr);
2579       C    = *B;
2580     } else {
2581       PetscInt rbs,cbs;
2582       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2583       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2584       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2585       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2586       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2587       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2588       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2589     }
2590     c = (Mat_SeqAIJ*)C->data;
2591 
2592     /* loop over rows inserting into submatrix */
2593     a_new = c->a;
2594     j_new = c->j;
2595     i_new = c->i;
2596 
2597     for (i=0; i<nrows; i++) {
2598       ii    = starts[i];
2599       lensi = lens[i];
2600       for (k=0; k<lensi; k++) {
2601         *j_new++ = aj[ii+k] - first;
2602       }
2603       ierr       = PetscArraycpy(a_new,a->a + starts[i],lensi);CHKERRQ(ierr);
2604       a_new     += lensi;
2605       i_new[i+1] = i_new[i] + lensi;
2606       c->ilen[i] = lensi;
2607     }
2608     ierr = PetscFree2(lens,starts);CHKERRQ(ierr);
2609   } else {
2610     ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
2611     ierr = PetscCalloc1(oldcols,&smap);CHKERRQ(ierr);
2612     ierr = PetscMalloc1(1+nrows,&lens);CHKERRQ(ierr);
2613     for (i=0; i<ncols; i++) {
2614       if (PetscUnlikelyDebug(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);
2615       smap[icol[i]] = i+1;
2616     }
2617 
2618     /* determine lens of each row */
2619     for (i=0; i<nrows; i++) {
2620       kstart  = ai[irow[i]];
2621       kend    = kstart + a->ilen[irow[i]];
2622       lens[i] = 0;
2623       for (k=kstart; k<kend; k++) {
2624         if (smap[aj[k]]) {
2625           lens[i]++;
2626         }
2627       }
2628     }
2629     /* Create and fill new matrix */
2630     if (scall == MAT_REUSE_MATRIX) {
2631       PetscBool equal;
2632 
2633       c = (Mat_SeqAIJ*)((*B)->data);
2634       if ((*B)->rmap->n  != nrows || (*B)->cmap->n != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
2635       ierr = PetscArraycmp(c->ilen,lens,(*B)->rmap->n,&equal);CHKERRQ(ierr);
2636       if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
2637       ierr = PetscArrayzero(c->ilen,(*B)->rmap->n);CHKERRQ(ierr);
2638       C    = *B;
2639     } else {
2640       PetscInt rbs,cbs;
2641       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2642       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2643       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2644       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2645       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2646       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2647       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2648     }
2649     c = (Mat_SeqAIJ*)(C->data);
2650     for (i=0; i<nrows; i++) {
2651       row      = irow[i];
2652       kstart   = ai[row];
2653       kend     = kstart + a->ilen[row];
2654       mat_i    = c->i[i];
2655       mat_j    = c->j + mat_i;
2656       mat_a    = c->a + mat_i;
2657       mat_ilen = c->ilen + i;
2658       for (k=kstart; k<kend; k++) {
2659         if ((tcol=smap[a->j[k]])) {
2660           *mat_j++ = tcol - 1;
2661           *mat_a++ = a->a[k];
2662           (*mat_ilen)++;
2663 
2664         }
2665       }
2666     }
2667     /* Free work space */
2668     ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
2669     ierr = PetscFree(smap);CHKERRQ(ierr);
2670     ierr = PetscFree(lens);CHKERRQ(ierr);
2671     /* sort */
2672     for (i = 0; i < nrows; i++) {
2673       PetscInt ilen;
2674 
2675       mat_i = c->i[i];
2676       mat_j = c->j + mat_i;
2677       mat_a = c->a + mat_i;
2678       ilen  = c->ilen[i];
2679       ierr  = PetscSortIntWithScalarArray(ilen,mat_j,mat_a);CHKERRQ(ierr);
2680     }
2681   }
2682 #if defined(PETSC_HAVE_DEVICE)
2683   ierr = MatBindToCPU(C,A->boundtocpu);CHKERRQ(ierr);
2684 #endif
2685   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2686   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2687 
2688   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
2689   *B   = C;
2690   PetscFunctionReturn(0);
2691 }
2692 
2693 PetscErrorCode  MatGetMultiProcBlock_SeqAIJ(Mat mat,MPI_Comm subComm,MatReuse scall,Mat *subMat)
2694 {
2695   PetscErrorCode ierr;
2696   Mat            B;
2697 
2698   PetscFunctionBegin;
2699   if (scall == MAT_INITIAL_MATRIX) {
2700     ierr    = MatCreate(subComm,&B);CHKERRQ(ierr);
2701     ierr    = MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->n,mat->cmap->n);CHKERRQ(ierr);
2702     ierr    = MatSetBlockSizesFromMats(B,mat,mat);CHKERRQ(ierr);
2703     ierr    = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
2704     ierr    = MatDuplicateNoCreate_SeqAIJ(B,mat,MAT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
2705     *subMat = B;
2706   } else {
2707     ierr = MatCopy_SeqAIJ(mat,*subMat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2708   }
2709   PetscFunctionReturn(0);
2710 }
2711 
2712 PetscErrorCode MatILUFactor_SeqAIJ(Mat inA,IS row,IS col,const MatFactorInfo *info)
2713 {
2714   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)inA->data;
2715   PetscErrorCode ierr;
2716   Mat            outA;
2717   PetscBool      row_identity,col_identity;
2718 
2719   PetscFunctionBegin;
2720   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels=0 supported for in-place ilu");
2721 
2722   ierr = ISIdentity(row,&row_identity);CHKERRQ(ierr);
2723   ierr = ISIdentity(col,&col_identity);CHKERRQ(ierr);
2724 
2725   outA             = inA;
2726   outA->factortype = MAT_FACTOR_LU;
2727   ierr = PetscFree(inA->solvertype);CHKERRQ(ierr);
2728   ierr = PetscStrallocpy(MATSOLVERPETSC,&inA->solvertype);CHKERRQ(ierr);
2729 
2730   ierr = PetscObjectReference((PetscObject)row);CHKERRQ(ierr);
2731   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
2732 
2733   a->row = row;
2734 
2735   ierr = PetscObjectReference((PetscObject)col);CHKERRQ(ierr);
2736   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
2737 
2738   a->col = col;
2739 
2740   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
2741   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
2742   ierr = ISInvertPermutation(col,PETSC_DECIDE,&a->icol);CHKERRQ(ierr);
2743   ierr = PetscLogObjectParent((PetscObject)inA,(PetscObject)a->icol);CHKERRQ(ierr);
2744 
2745   if (!a->solve_work) { /* this matrix may have been factored before */
2746     ierr = PetscMalloc1(inA->rmap->n+1,&a->solve_work);CHKERRQ(ierr);
2747     ierr = PetscLogObjectMemory((PetscObject)inA, (inA->rmap->n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2748   }
2749 
2750   ierr = MatMarkDiagonal_SeqAIJ(inA);CHKERRQ(ierr);
2751   if (row_identity && col_identity) {
2752     ierr = MatLUFactorNumeric_SeqAIJ_inplace(outA,inA,info);CHKERRQ(ierr);
2753   } else {
2754     ierr = MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA,inA,info);CHKERRQ(ierr);
2755   }
2756   PetscFunctionReturn(0);
2757 }
2758 
2759 PetscErrorCode MatScale_SeqAIJ(Mat inA,PetscScalar alpha)
2760 {
2761   Mat_SeqAIJ     *a     = (Mat_SeqAIJ*)inA->data;
2762   PetscScalar    oalpha = alpha;
2763   PetscErrorCode ierr;
2764   PetscBLASInt   one = 1,bnz;
2765 
2766   PetscFunctionBegin;
2767   ierr = PetscBLASIntCast(a->nz,&bnz);CHKERRQ(ierr);
2768   PetscStackCallBLAS("BLASscal",BLASscal_(&bnz,&oalpha,a->a,&one));
2769   ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2770   ierr = MatSeqAIJInvalidateDiagonal(inA);CHKERRQ(ierr);
2771 #if defined(PETSC_HAVE_DEVICE)
2772   if (inA->offloadmask != PETSC_OFFLOAD_UNALLOCATED) inA->offloadmask = PETSC_OFFLOAD_CPU;
2773 #endif
2774   PetscFunctionReturn(0);
2775 }
2776 
2777 PetscErrorCode MatDestroySubMatrix_Private(Mat_SubSppt *submatj)
2778 {
2779   PetscErrorCode ierr;
2780   PetscInt       i;
2781 
2782   PetscFunctionBegin;
2783   if (!submatj->id) { /* delete data that are linked only to submats[id=0] */
2784     ierr = PetscFree4(submatj->sbuf1,submatj->ptr,submatj->tmp,submatj->ctr);CHKERRQ(ierr);
2785 
2786     for (i=0; i<submatj->nrqr; ++i) {
2787       ierr = PetscFree(submatj->sbuf2[i]);CHKERRQ(ierr);
2788     }
2789     ierr = PetscFree3(submatj->sbuf2,submatj->req_size,submatj->req_source1);CHKERRQ(ierr);
2790 
2791     if (submatj->rbuf1) {
2792       ierr = PetscFree(submatj->rbuf1[0]);CHKERRQ(ierr);
2793       ierr = PetscFree(submatj->rbuf1);CHKERRQ(ierr);
2794     }
2795 
2796     for (i=0; i<submatj->nrqs; ++i) {
2797       ierr = PetscFree(submatj->rbuf3[i]);CHKERRQ(ierr);
2798     }
2799     ierr = PetscFree3(submatj->req_source2,submatj->rbuf2,submatj->rbuf3);CHKERRQ(ierr);
2800     ierr = PetscFree(submatj->pa);CHKERRQ(ierr);
2801   }
2802 
2803 #if defined(PETSC_USE_CTABLE)
2804   ierr = PetscTableDestroy((PetscTable*)&submatj->rmap);CHKERRQ(ierr);
2805   if (submatj->cmap_loc) {ierr = PetscFree(submatj->cmap_loc);CHKERRQ(ierr);}
2806   ierr = PetscFree(submatj->rmap_loc);CHKERRQ(ierr);
2807 #else
2808   ierr = PetscFree(submatj->rmap);CHKERRQ(ierr);
2809 #endif
2810 
2811   if (!submatj->allcolumns) {
2812 #if defined(PETSC_USE_CTABLE)
2813     ierr = PetscTableDestroy((PetscTable*)&submatj->cmap);CHKERRQ(ierr);
2814 #else
2815     ierr = PetscFree(submatj->cmap);CHKERRQ(ierr);
2816 #endif
2817   }
2818   ierr = PetscFree(submatj->row2proc);CHKERRQ(ierr);
2819 
2820   ierr = PetscFree(submatj);CHKERRQ(ierr);
2821   PetscFunctionReturn(0);
2822 }
2823 
2824 PetscErrorCode MatDestroySubMatrix_SeqAIJ(Mat C)
2825 {
2826   PetscErrorCode ierr;
2827   Mat_SeqAIJ     *c = (Mat_SeqAIJ*)C->data;
2828   Mat_SubSppt    *submatj = c->submatis1;
2829 
2830   PetscFunctionBegin;
2831   ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
2832   ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
2833   PetscFunctionReturn(0);
2834 }
2835 
2836 PetscErrorCode MatDestroySubMatrices_SeqAIJ(PetscInt n,Mat *mat[])
2837 {
2838   PetscErrorCode ierr;
2839   PetscInt       i;
2840   Mat            C;
2841   Mat_SeqAIJ     *c;
2842   Mat_SubSppt    *submatj;
2843 
2844   PetscFunctionBegin;
2845   for (i=0; i<n; i++) {
2846     C       = (*mat)[i];
2847     c       = (Mat_SeqAIJ*)C->data;
2848     submatj = c->submatis1;
2849     if (submatj) {
2850       if (--((PetscObject)C)->refct <= 0) {
2851         ierr = (*submatj->destroy)(C);CHKERRQ(ierr);
2852         ierr = MatDestroySubMatrix_Private(submatj);CHKERRQ(ierr);
2853         ierr = PetscFree(C->defaultvectype);CHKERRQ(ierr);
2854         ierr = PetscLayoutDestroy(&C->rmap);CHKERRQ(ierr);
2855         ierr = PetscLayoutDestroy(&C->cmap);CHKERRQ(ierr);
2856         ierr = PetscHeaderDestroy(&C);CHKERRQ(ierr);
2857       }
2858     } else {
2859       ierr = MatDestroy(&C);CHKERRQ(ierr);
2860     }
2861   }
2862 
2863   /* Destroy Dummy submatrices created for reuse */
2864   ierr = MatDestroySubMatrices_Dummy(n,mat);CHKERRQ(ierr);
2865 
2866   ierr = PetscFree(*mat);CHKERRQ(ierr);
2867   PetscFunctionReturn(0);
2868 }
2869 
2870 PetscErrorCode MatCreateSubMatrices_SeqAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
2871 {
2872   PetscErrorCode ierr;
2873   PetscInt       i;
2874 
2875   PetscFunctionBegin;
2876   if (scall == MAT_INITIAL_MATRIX) {
2877     ierr = PetscCalloc1(n+1,B);CHKERRQ(ierr);
2878   }
2879 
2880   for (i=0; i<n; i++) {
2881     ierr = MatCreateSubMatrix_SeqAIJ(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]);CHKERRQ(ierr);
2882   }
2883   PetscFunctionReturn(0);
2884 }
2885 
2886 PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
2887 {
2888   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2889   PetscErrorCode ierr;
2890   PetscInt       row,i,j,k,l,m,n,*nidx,isz,val;
2891   const PetscInt *idx;
2892   PetscInt       start,end,*ai,*aj;
2893   PetscBT        table;
2894 
2895   PetscFunctionBegin;
2896   m  = A->rmap->n;
2897   ai = a->i;
2898   aj = a->j;
2899 
2900   if (ov < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"illegal negative overlap value used");
2901 
2902   ierr = PetscMalloc1(m+1,&nidx);CHKERRQ(ierr);
2903   ierr = PetscBTCreate(m,&table);CHKERRQ(ierr);
2904 
2905   for (i=0; i<is_max; i++) {
2906     /* Initialize the two local arrays */
2907     isz  = 0;
2908     ierr = PetscBTMemzero(m,table);CHKERRQ(ierr);
2909 
2910     /* Extract the indices, assume there can be duplicate entries */
2911     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
2912     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
2913 
2914     /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2915     for (j=0; j<n; ++j) {
2916       if (!PetscBTLookupSet(table,idx[j])) nidx[isz++] = idx[j];
2917     }
2918     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
2919     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
2920 
2921     k = 0;
2922     for (j=0; j<ov; j++) { /* for each overlap */
2923       n = isz;
2924       for (; k<n; k++) { /* do only those rows in nidx[k], which are not done yet */
2925         row   = nidx[k];
2926         start = ai[row];
2927         end   = ai[row+1];
2928         for (l = start; l<end; l++) {
2929           val = aj[l];
2930           if (!PetscBTLookupSet(table,val)) nidx[isz++] = val;
2931         }
2932       }
2933     }
2934     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz,nidx,PETSC_COPY_VALUES,(is+i));CHKERRQ(ierr);
2935   }
2936   ierr = PetscBTDestroy(&table);CHKERRQ(ierr);
2937   ierr = PetscFree(nidx);CHKERRQ(ierr);
2938   PetscFunctionReturn(0);
2939 }
2940 
2941 /* -------------------------------------------------------------- */
2942 PetscErrorCode MatPermute_SeqAIJ(Mat A,IS rowp,IS colp,Mat *B)
2943 {
2944   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2945   PetscErrorCode ierr;
2946   PetscInt       i,nz = 0,m = A->rmap->n,n = A->cmap->n;
2947   const PetscInt *row,*col;
2948   PetscInt       *cnew,j,*lens;
2949   IS             icolp,irowp;
2950   PetscInt       *cwork = NULL;
2951   PetscScalar    *vwork = NULL;
2952 
2953   PetscFunctionBegin;
2954   ierr = ISInvertPermutation(rowp,PETSC_DECIDE,&irowp);CHKERRQ(ierr);
2955   ierr = ISGetIndices(irowp,&row);CHKERRQ(ierr);
2956   ierr = ISInvertPermutation(colp,PETSC_DECIDE,&icolp);CHKERRQ(ierr);
2957   ierr = ISGetIndices(icolp,&col);CHKERRQ(ierr);
2958 
2959   /* determine lengths of permuted rows */
2960   ierr = PetscMalloc1(m+1,&lens);CHKERRQ(ierr);
2961   for (i=0; i<m; i++) lens[row[i]] = a->i[i+1] - a->i[i];
2962   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
2963   ierr = MatSetSizes(*B,m,n,m,n);CHKERRQ(ierr);
2964   ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
2965   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2966   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*B,0,lens);CHKERRQ(ierr);
2967   ierr = PetscFree(lens);CHKERRQ(ierr);
2968 
2969   ierr = PetscMalloc1(n,&cnew);CHKERRQ(ierr);
2970   for (i=0; i<m; i++) {
2971     ierr = MatGetRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2972     for (j=0; j<nz; j++) cnew[j] = col[cwork[j]];
2973     ierr = MatSetValues_SeqAIJ(*B,1,&row[i],nz,cnew,vwork,INSERT_VALUES);CHKERRQ(ierr);
2974     ierr = MatRestoreRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2975   }
2976   ierr = PetscFree(cnew);CHKERRQ(ierr);
2977 
2978   (*B)->assembled = PETSC_FALSE;
2979 
2980 #if defined(PETSC_HAVE_DEVICE)
2981   ierr = MatBindToCPU(*B,A->boundtocpu);CHKERRQ(ierr);
2982 #endif
2983   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2984   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2985   ierr = ISRestoreIndices(irowp,&row);CHKERRQ(ierr);
2986   ierr = ISRestoreIndices(icolp,&col);CHKERRQ(ierr);
2987   ierr = ISDestroy(&irowp);CHKERRQ(ierr);
2988   ierr = ISDestroy(&icolp);CHKERRQ(ierr);
2989   if (rowp == colp) {
2990     if (A->symmetric) {
2991       ierr = MatSetOption(*B,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
2992     }
2993     if (A->hermitian) {
2994       ierr = MatSetOption(*B,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
2995     }
2996   }
2997   PetscFunctionReturn(0);
2998 }
2999 
3000 PetscErrorCode MatCopy_SeqAIJ(Mat A,Mat B,MatStructure str)
3001 {
3002   PetscErrorCode ierr;
3003 
3004   PetscFunctionBegin;
3005   /* If the two matrices have the same copy implementation, use fast copy. */
3006   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
3007     Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
3008     Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data;
3009 
3010     if (a->i[A->rmap->n] != b->i[B->rmap->n]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Number of nonzeros in two matrices are different %D != %D",a->i[A->rmap->n],b->i[B->rmap->n]);
3011     ierr = PetscArraycpy(b->a,a->a,a->i[A->rmap->n]);CHKERRQ(ierr);
3012     ierr = PetscObjectStateIncrease((PetscObject)B);CHKERRQ(ierr);
3013   } else {
3014     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
3015   }
3016   PetscFunctionReturn(0);
3017 }
3018 
3019 PetscErrorCode MatSetUp_SeqAIJ(Mat A)
3020 {
3021   PetscErrorCode ierr;
3022 
3023   PetscFunctionBegin;
3024   ierr = MatSeqAIJSetPreallocation_SeqAIJ(A,PETSC_DEFAULT,NULL);CHKERRQ(ierr);
3025   PetscFunctionReturn(0);
3026 }
3027 
3028 PETSC_INTERN PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A,PetscScalar *array[])
3029 {
3030   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
3031 
3032   PetscFunctionBegin;
3033   *array = a->a;
3034   PetscFunctionReturn(0);
3035 }
3036 
3037 PETSC_INTERN PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A,PetscScalar *array[])
3038 {
3039   PetscFunctionBegin;
3040   *array = NULL;
3041   PetscFunctionReturn(0);
3042 }
3043 
3044 /*
3045    Computes the number of nonzeros per row needed for preallocation when X and Y
3046    have different nonzero structure.
3047 */
3048 PetscErrorCode MatAXPYGetPreallocation_SeqX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *yi,const PetscInt *yj,PetscInt *nnz)
3049 {
3050   PetscInt       i,j,k,nzx,nzy;
3051 
3052   PetscFunctionBegin;
3053   /* Set the number of nonzeros in the new matrix */
3054   for (i=0; i<m; i++) {
3055     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
3056     nzx = xi[i+1] - xi[i];
3057     nzy = yi[i+1] - yi[i];
3058     nnz[i] = 0;
3059     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
3060       for (; k<nzy && yjj[k]<xjj[j]; k++) nnz[i]++; /* Catch up to X */
3061       if (k<nzy && yjj[k]==xjj[j]) k++;             /* Skip duplicate */
3062       nnz[i]++;
3063     }
3064     for (; k<nzy; k++) nnz[i]++;
3065   }
3066   PetscFunctionReturn(0);
3067 }
3068 
3069 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
3070 {
3071   PetscInt       m = Y->rmap->N;
3072   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
3073   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
3074   PetscErrorCode ierr;
3075 
3076   PetscFunctionBegin;
3077   /* Set the number of nonzeros in the new matrix */
3078   ierr = MatAXPYGetPreallocation_SeqX_private(m,x->i,x->j,y->i,y->j,nnz);CHKERRQ(ierr);
3079   PetscFunctionReturn(0);
3080 }
3081 
3082 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
3083 {
3084   PetscErrorCode ierr;
3085   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
3086 
3087   PetscFunctionBegin;
3088   if (str == DIFFERENT_NONZERO_PATTERN) {
3089     if (x->nz == y->nz) {
3090       PetscBool e;
3091       ierr = PetscArraycmp(x->i,y->i,Y->rmap->n+1,&e);CHKERRQ(ierr);
3092       if (e) {
3093         ierr = PetscArraycmp(x->j,y->j,y->nz,&e);CHKERRQ(ierr);
3094         if (e) {
3095           str = SAME_NONZERO_PATTERN;
3096         }
3097       }
3098     }
3099   }
3100   if (str == SAME_NONZERO_PATTERN) {
3101     PetscScalar  alpha = a;
3102     PetscBLASInt one = 1,bnz;
3103 
3104     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
3105     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
3106     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
3107     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
3108     /* the MatAXPY_Basic* subroutines calls MatAssembly, so the matrix on the GPU will be updated */
3109 #if defined(PETSC_HAVE_DEVICE)
3110     if (Y->offloadmask != PETSC_OFFLOAD_UNALLOCATED) {
3111       Y->offloadmask = PETSC_OFFLOAD_CPU;
3112     }
3113 #endif
3114   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
3115     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
3116   } else {
3117     Mat      B;
3118     PetscInt *nnz;
3119     ierr = PetscMalloc1(Y->rmap->N,&nnz);CHKERRQ(ierr);
3120     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
3121     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
3122     ierr = MatSetLayouts(B,Y->rmap,Y->cmap);CHKERRQ(ierr);
3123     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
3124     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
3125     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
3126     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
3127     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
3128     ierr = PetscFree(nnz);CHKERRQ(ierr);
3129   }
3130   PetscFunctionReturn(0);
3131 }
3132 
3133 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
3134 {
3135 #if defined(PETSC_USE_COMPLEX)
3136   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
3137   PetscInt    i,nz;
3138   PetscScalar *a;
3139 
3140   PetscFunctionBegin;
3141   nz = aij->nz;
3142   a  = aij->a;
3143   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
3144 #if defined(PETSC_HAVE_DEVICE)
3145   if (mat->offloadmask != PETSC_OFFLOAD_UNALLOCATED) mat->offloadmask = PETSC_OFFLOAD_CPU;
3146 #endif
3147 #else
3148   PetscFunctionBegin;
3149 #endif
3150   PetscFunctionReturn(0);
3151 }
3152 
3153 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3154 {
3155   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3156   PetscErrorCode ierr;
3157   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3158   PetscReal      atmp;
3159   PetscScalar    *x;
3160   MatScalar      *aa;
3161 
3162   PetscFunctionBegin;
3163   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3164   aa = a->a;
3165   ai = a->i;
3166   aj = a->j;
3167 
3168   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3169   ierr = VecGetArrayWrite(v,&x);CHKERRQ(ierr);
3170   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3171   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3172   for (i=0; i<m; i++) {
3173     ncols = ai[1] - ai[0]; ai++;
3174     for (j=0; j<ncols; j++) {
3175       atmp = PetscAbsScalar(*aa);
3176       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3177       aa++; aj++;
3178     }
3179   }
3180   ierr = VecRestoreArrayWrite(v,&x);CHKERRQ(ierr);
3181   PetscFunctionReturn(0);
3182 }
3183 
3184 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3185 {
3186   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3187   PetscErrorCode ierr;
3188   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3189   PetscScalar    *x;
3190   MatScalar      *aa;
3191 
3192   PetscFunctionBegin;
3193   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3194   aa = a->a;
3195   ai = a->i;
3196   aj = a->j;
3197 
3198   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3199   ierr = VecGetArrayWrite(v,&x);CHKERRQ(ierr);
3200   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3201   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3202   for (i=0; i<m; i++) {
3203     ncols = ai[1] - ai[0]; ai++;
3204     if (ncols == A->cmap->n) { /* row is dense */
3205       x[i] = *aa; if (idx) idx[i] = 0;
3206     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
3207       x[i] = 0.0;
3208       if (idx) {
3209         for (j=0; j<ncols; j++) { /* find first implicit 0.0 in the row */
3210           if (aj[j] > j) {
3211             idx[i] = j;
3212             break;
3213           }
3214         }
3215         /* in case first implicit 0.0 in the row occurs at ncols-th column */
3216         if (j==ncols && j < A->cmap->n) idx[i] = j;
3217       }
3218     }
3219     for (j=0; j<ncols; j++) {
3220       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3221       aa++; aj++;
3222     }
3223   }
3224   ierr = VecRestoreArrayWrite(v,&x);CHKERRQ(ierr);
3225   PetscFunctionReturn(0);
3226 }
3227 
3228 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3229 {
3230   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3231   PetscErrorCode ierr;
3232   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3233   PetscScalar    *x,*aa;
3234 
3235   PetscFunctionBegin;
3236   aa = a->a;
3237   ai = a->i;
3238   aj = a->j;
3239 
3240   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3241   ierr = VecGetArrayWrite(v,&x);CHKERRQ(ierr);
3242   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3243   if (n != m) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector, %D vs. %D rows", m, n);
3244   for (i=0; i<m; i++) {
3245     ncols = ai[1] - ai[0]; ai++;
3246     if (ncols == A->cmap->n) { /* row is dense */
3247       x[i] = *aa; if (idx) idx[i] = 0;
3248     } else {  /* row is sparse so already KNOW minimum is 0.0 or higher */
3249       x[i] = 0.0;
3250       if (idx) {   /* find first implicit 0.0 in the row */
3251         for (j=0; j<ncols; j++) {
3252           if (aj[j] > j) {
3253             idx[i] = j;
3254             break;
3255           }
3256         }
3257         /* in case first implicit 0.0 in the row occurs at ncols-th column */
3258         if (j==ncols && j < A->cmap->n) idx[i] = j;
3259       }
3260     }
3261     for (j=0; j<ncols; j++) {
3262       if (PetscAbsScalar(x[i]) > PetscAbsScalar(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3263       aa++; aj++;
3264     }
3265   }
3266   ierr = VecRestoreArrayWrite(v,&x);CHKERRQ(ierr);
3267   PetscFunctionReturn(0);
3268 }
3269 
3270 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3271 {
3272   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
3273   PetscErrorCode  ierr;
3274   PetscInt        i,j,m = A->rmap->n,ncols,n;
3275   const PetscInt  *ai,*aj;
3276   PetscScalar     *x;
3277   const MatScalar *aa;
3278 
3279   PetscFunctionBegin;
3280   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3281   aa = a->a;
3282   ai = a->i;
3283   aj = a->j;
3284 
3285   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3286   ierr = VecGetArrayWrite(v,&x);CHKERRQ(ierr);
3287   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3288   if (n != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3289   for (i=0; i<m; i++) {
3290     ncols = ai[1] - ai[0]; ai++;
3291     if (ncols == A->cmap->n) { /* row is dense */
3292       x[i] = *aa; if (idx) idx[i] = 0;
3293     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3294       x[i] = 0.0;
3295       if (idx) {   /* find first implicit 0.0 in the row */
3296         for (j=0; j<ncols; j++) {
3297           if (aj[j] > j) {
3298             idx[i] = j;
3299             break;
3300           }
3301         }
3302         /* in case first implicit 0.0 in the row occurs at ncols-th column */
3303         if (j==ncols && j < A->cmap->n) idx[i] = j;
3304       }
3305     }
3306     for (j=0; j<ncols; j++) {
3307       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3308       aa++; aj++;
3309     }
3310   }
3311   ierr = VecRestoreArrayWrite(v,&x);CHKERRQ(ierr);
3312   PetscFunctionReturn(0);
3313 }
3314 
3315 PetscErrorCode MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3316 {
3317   Mat_SeqAIJ      *a = (Mat_SeqAIJ*) A->data;
3318   PetscErrorCode  ierr;
3319   PetscInt        i,bs = PetscAbs(A->rmap->bs),mbs = A->rmap->n/bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3320   MatScalar       *diag,work[25],*v_work;
3321   const PetscReal shift = 0.0;
3322   PetscBool       allowzeropivot,zeropivotdetected=PETSC_FALSE;
3323 
3324   PetscFunctionBegin;
3325   allowzeropivot = PetscNot(A->erroriffailure);
3326   if (a->ibdiagvalid) {
3327     if (values) *values = a->ibdiag;
3328     PetscFunctionReturn(0);
3329   }
3330   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3331   if (!a->ibdiag) {
3332     ierr = PetscMalloc1(bs2*mbs,&a->ibdiag);CHKERRQ(ierr);
3333     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3334   }
3335   diag = a->ibdiag;
3336   if (values) *values = a->ibdiag;
3337   /* factor and invert each block */
3338   switch (bs) {
3339   case 1:
3340     for (i=0; i<mbs; i++) {
3341       ierr = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3342       if (PetscAbsScalar(diag[i] + shift) < PETSC_MACHINE_EPSILON) {
3343         if (allowzeropivot) {
3344           A->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3345           A->factorerror_zeropivot_value = PetscAbsScalar(diag[i]);
3346           A->factorerror_zeropivot_row   = i;
3347           ierr = PetscInfo3(A,"Zero pivot, row %D pivot %g tolerance %g\n",i,(double)PetscAbsScalar(diag[i]),(double)PETSC_MACHINE_EPSILON);CHKERRQ(ierr);
3348         } else SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot, row %D pivot %g tolerance %g",i,(double)PetscAbsScalar(diag[i]),(double)PETSC_MACHINE_EPSILON);
3349       }
3350       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3351     }
3352     break;
3353   case 2:
3354     for (i=0; i<mbs; i++) {
3355       ij[0] = 2*i; ij[1] = 2*i + 1;
3356       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3357       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3358       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3359       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
3360       diag += 4;
3361     }
3362     break;
3363   case 3:
3364     for (i=0; i<mbs; i++) {
3365       ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
3366       ierr  = MatGetValues(A,3,ij,3,ij,diag);CHKERRQ(ierr);
3367       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3368       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3369       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3370       diag += 9;
3371     }
3372     break;
3373   case 4:
3374     for (i=0; i<mbs; i++) {
3375       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3376       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3377       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3378       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3379       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3380       diag += 16;
3381     }
3382     break;
3383   case 5:
3384     for (i=0; i<mbs; i++) {
3385       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3386       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3387       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3388       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3389       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3390       diag += 25;
3391     }
3392     break;
3393   case 6:
3394     for (i=0; i<mbs; i++) {
3395       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;
3396       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3397       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3398       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3399       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3400       diag += 36;
3401     }
3402     break;
3403   case 7:
3404     for (i=0; i<mbs; i++) {
3405       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;
3406       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3407       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3408       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3409       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3410       diag += 49;
3411     }
3412     break;
3413   default:
3414     ierr = PetscMalloc3(bs,&v_work,bs,&v_pivots,bs,&IJ);CHKERRQ(ierr);
3415     for (i=0; i<mbs; i++) {
3416       for (j=0; j<bs; j++) {
3417         IJ[j] = bs*i + j;
3418       }
3419       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3420       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
3421       if (zeropivotdetected) A->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
3422       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3423       diag += bs2;
3424     }
3425     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3426   }
3427   a->ibdiagvalid = PETSC_TRUE;
3428   PetscFunctionReturn(0);
3429 }
3430 
3431 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3432 {
3433   PetscErrorCode ierr;
3434   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3435   PetscScalar    a;
3436   PetscInt       m,n,i,j,col;
3437 
3438   PetscFunctionBegin;
3439   if (!x->assembled) {
3440     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3441     for (i=0; i<m; i++) {
3442       for (j=0; j<aij->imax[i]; j++) {
3443         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3444         col  = (PetscInt)(n*PetscRealPart(a));
3445         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3446       }
3447     }
3448   } else {
3449     for (i=0; i<aij->nz; i++) {ierr = PetscRandomGetValue(rctx,aij->a+i);CHKERRQ(ierr);}
3450   }
3451   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3452   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3453   PetscFunctionReturn(0);
3454 }
3455 
3456 /* Like MatSetRandom_SeqAIJ, but do not set values on columns in range of [low, high) */
3457 PetscErrorCode  MatSetRandomSkipColumnRange_SeqAIJ_Private(Mat x,PetscInt low,PetscInt high,PetscRandom rctx)
3458 {
3459   PetscErrorCode ierr;
3460   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3461   PetscScalar    a;
3462   PetscInt       m,n,i,j,col,nskip;
3463 
3464   PetscFunctionBegin;
3465   nskip = high - low;
3466   ierr  = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3467   n    -= nskip; /* shrink number of columns where nonzeros can be set */
3468   for (i=0; i<m; i++) {
3469     for (j=0; j<aij->imax[i]; j++) {
3470       ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3471       col  = (PetscInt)(n*PetscRealPart(a));
3472       if (col >= low) col += nskip; /* shift col rightward to skip the hole */
3473       ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3474     }
3475   }
3476   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3477   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3478   PetscFunctionReturn(0);
3479 }
3480 
3481 
3482 /* -------------------------------------------------------------------*/
3483 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3484                                         MatGetRow_SeqAIJ,
3485                                         MatRestoreRow_SeqAIJ,
3486                                         MatMult_SeqAIJ,
3487                                 /*  4*/ MatMultAdd_SeqAIJ,
3488                                         MatMultTranspose_SeqAIJ,
3489                                         MatMultTransposeAdd_SeqAIJ,
3490                                         NULL,
3491                                         NULL,
3492                                         NULL,
3493                                 /* 10*/ NULL,
3494                                         MatLUFactor_SeqAIJ,
3495                                         NULL,
3496                                         MatSOR_SeqAIJ,
3497                                         MatTranspose_SeqAIJ,
3498                                 /*1 5*/ MatGetInfo_SeqAIJ,
3499                                         MatEqual_SeqAIJ,
3500                                         MatGetDiagonal_SeqAIJ,
3501                                         MatDiagonalScale_SeqAIJ,
3502                                         MatNorm_SeqAIJ,
3503                                 /* 20*/ NULL,
3504                                         MatAssemblyEnd_SeqAIJ,
3505                                         MatSetOption_SeqAIJ,
3506                                         MatZeroEntries_SeqAIJ,
3507                                 /* 24*/ MatZeroRows_SeqAIJ,
3508                                         NULL,
3509                                         NULL,
3510                                         NULL,
3511                                         NULL,
3512                                 /* 29*/ MatSetUp_SeqAIJ,
3513                                         NULL,
3514                                         NULL,
3515                                         NULL,
3516                                         NULL,
3517                                 /* 34*/ MatDuplicate_SeqAIJ,
3518                                         NULL,
3519                                         NULL,
3520                                         MatILUFactor_SeqAIJ,
3521                                         NULL,
3522                                 /* 39*/ MatAXPY_SeqAIJ,
3523                                         MatCreateSubMatrices_SeqAIJ,
3524                                         MatIncreaseOverlap_SeqAIJ,
3525                                         MatGetValues_SeqAIJ,
3526                                         MatCopy_SeqAIJ,
3527                                 /* 44*/ MatGetRowMax_SeqAIJ,
3528                                         MatScale_SeqAIJ,
3529                                         MatShift_SeqAIJ,
3530                                         MatDiagonalSet_SeqAIJ,
3531                                         MatZeroRowsColumns_SeqAIJ,
3532                                 /* 49*/ MatSetRandom_SeqAIJ,
3533                                         MatGetRowIJ_SeqAIJ,
3534                                         MatRestoreRowIJ_SeqAIJ,
3535                                         MatGetColumnIJ_SeqAIJ,
3536                                         MatRestoreColumnIJ_SeqAIJ,
3537                                 /* 54*/ MatFDColoringCreate_SeqXAIJ,
3538                                         NULL,
3539                                         NULL,
3540                                         MatPermute_SeqAIJ,
3541                                         NULL,
3542                                 /* 59*/ NULL,
3543                                         MatDestroy_SeqAIJ,
3544                                         MatView_SeqAIJ,
3545                                         NULL,
3546                                         NULL,
3547                                 /* 64*/ NULL,
3548                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3549                                         NULL,
3550                                         NULL,
3551                                         NULL,
3552                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3553                                         MatGetRowMinAbs_SeqAIJ,
3554                                         NULL,
3555                                         NULL,
3556                                         NULL,
3557                                 /* 74*/ NULL,
3558                                         MatFDColoringApply_AIJ,
3559                                         NULL,
3560                                         NULL,
3561                                         NULL,
3562                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3563                                         NULL,
3564                                         NULL,
3565                                         NULL,
3566                                         MatLoad_SeqAIJ,
3567                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3568                                         MatIsHermitian_SeqAIJ,
3569                                         NULL,
3570                                         NULL,
3571                                         NULL,
3572                                 /* 89*/ NULL,
3573                                         NULL,
3574                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3575                                         NULL,
3576                                         NULL,
3577                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy,
3578                                         NULL,
3579                                         NULL,
3580                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3581                                         NULL,
3582                                 /* 99*/ MatProductSetFromOptions_SeqAIJ,
3583                                         NULL,
3584                                         NULL,
3585                                         MatConjugate_SeqAIJ,
3586                                         NULL,
3587                                 /*104*/ MatSetValuesRow_SeqAIJ,
3588                                         MatRealPart_SeqAIJ,
3589                                         MatImaginaryPart_SeqAIJ,
3590                                         NULL,
3591                                         NULL,
3592                                 /*109*/ MatMatSolve_SeqAIJ,
3593                                         NULL,
3594                                         MatGetRowMin_SeqAIJ,
3595                                         NULL,
3596                                         MatMissingDiagonal_SeqAIJ,
3597                                 /*114*/ NULL,
3598                                         NULL,
3599                                         NULL,
3600                                         NULL,
3601                                         NULL,
3602                                 /*119*/ NULL,
3603                                         NULL,
3604                                         NULL,
3605                                         NULL,
3606                                         MatGetMultiProcBlock_SeqAIJ,
3607                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3608                                         MatGetColumnNorms_SeqAIJ,
3609                                         MatInvertBlockDiagonal_SeqAIJ,
3610                                         MatInvertVariableBlockDiagonal_SeqAIJ,
3611                                         NULL,
3612                                 /*129*/ NULL,
3613                                         NULL,
3614                                         NULL,
3615                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3616                                         MatTransposeColoringCreate_SeqAIJ,
3617                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3618                                         MatTransColoringApplyDenToSp_SeqAIJ,
3619                                         NULL,
3620                                         NULL,
3621                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3622                                  /*139*/NULL,
3623                                         NULL,
3624                                         NULL,
3625                                         MatFDColoringSetUp_SeqXAIJ,
3626                                         MatFindOffBlockDiagonalEntries_SeqAIJ,
3627                                         MatCreateMPIMatConcatenateSeqMat_SeqAIJ,
3628                                  /*145*/MatDestroySubMatrices_SeqAIJ,
3629                                         NULL,
3630                                         NULL
3631 };
3632 
3633 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3634 {
3635   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3636   PetscInt   i,nz,n;
3637 
3638   PetscFunctionBegin;
3639   nz = aij->maxnz;
3640   n  = mat->rmap->n;
3641   for (i=0; i<nz; i++) {
3642     aij->j[i] = indices[i];
3643   }
3644   aij->nz = nz;
3645   for (i=0; i<n; i++) {
3646     aij->ilen[i] = aij->imax[i];
3647   }
3648   PetscFunctionReturn(0);
3649 }
3650 
3651 /*
3652  * When a sparse matrix has many zero columns, we should compact them out to save the space
3653  * This happens in MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable()
3654  * */
3655 PetscErrorCode  MatSeqAIJCompactOutExtraColumns_SeqAIJ(Mat mat, ISLocalToGlobalMapping *mapping)
3656 {
3657   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3658   PetscTable         gid1_lid1;
3659   PetscTablePosition tpos;
3660   PetscInt           gid,lid,i,j,ncols,ec;
3661   PetscInt           *garray;
3662   PetscErrorCode  ierr;
3663 
3664   PetscFunctionBegin;
3665   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3666   PetscValidPointer(mapping,2);
3667   /* use a table */
3668   ierr = PetscTableCreate(mat->rmap->n,mat->cmap->N+1,&gid1_lid1);CHKERRQ(ierr);
3669   ec = 0;
3670   for (i=0; i<mat->rmap->n; i++) {
3671     ncols = aij->i[i+1] - aij->i[i];
3672     for (j=0; j<ncols; j++) {
3673       PetscInt data,gid1 = aij->j[aij->i[i] + j] + 1;
3674       ierr = PetscTableFind(gid1_lid1,gid1,&data);CHKERRQ(ierr);
3675       if (!data) {
3676         /* one based table */
3677         ierr = PetscTableAdd(gid1_lid1,gid1,++ec,INSERT_VALUES);CHKERRQ(ierr);
3678       }
3679     }
3680   }
3681   /* form array of columns we need */
3682   ierr = PetscMalloc1(ec+1,&garray);CHKERRQ(ierr);
3683   ierr = PetscTableGetHeadPosition(gid1_lid1,&tpos);CHKERRQ(ierr);
3684   while (tpos) {
3685     ierr = PetscTableGetNext(gid1_lid1,&tpos,&gid,&lid);CHKERRQ(ierr);
3686     gid--;
3687     lid--;
3688     garray[lid] = gid;
3689   }
3690   ierr = PetscSortInt(ec,garray);CHKERRQ(ierr); /* sort, and rebuild */
3691   ierr = PetscTableRemoveAll(gid1_lid1);CHKERRQ(ierr);
3692   for (i=0; i<ec; i++) {
3693     ierr = PetscTableAdd(gid1_lid1,garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
3694   }
3695   /* compact out the extra columns in B */
3696   for (i=0; i<mat->rmap->n; i++) {
3697         ncols = aij->i[i+1] - aij->i[i];
3698     for (j=0; j<ncols; j++) {
3699       PetscInt gid1 = aij->j[aij->i[i] + j] + 1;
3700       ierr = PetscTableFind(gid1_lid1,gid1,&lid);CHKERRQ(ierr);
3701       lid--;
3702       aij->j[aij->i[i] + j] = lid;
3703     }
3704   }
3705   ierr = PetscLayoutDestroy(&mat->cmap);CHKERRQ(ierr);
3706   ierr = PetscLayoutCreateFromSizes(PetscObjectComm((PetscObject)mat),ec,ec,1,&mat->cmap);CHKERRQ(ierr);
3707   ierr = PetscTableDestroy(&gid1_lid1);CHKERRQ(ierr);
3708   ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,mat->cmap->bs,mat->cmap->n,garray,PETSC_OWN_POINTER,mapping);CHKERRQ(ierr);
3709   ierr = ISLocalToGlobalMappingSetType(*mapping,ISLOCALTOGLOBALMAPPINGHASH);CHKERRQ(ierr);
3710   PetscFunctionReturn(0);
3711 }
3712 
3713 /*@
3714     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3715        in the matrix.
3716 
3717   Input Parameters:
3718 +  mat - the SeqAIJ matrix
3719 -  indices - the column indices
3720 
3721   Level: advanced
3722 
3723   Notes:
3724     This can be called if you have precomputed the nonzero structure of the
3725   matrix and want to provide it to the matrix object to improve the performance
3726   of the MatSetValues() operation.
3727 
3728     You MUST have set the correct numbers of nonzeros per row in the call to
3729   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3730 
3731     MUST be called before any calls to MatSetValues();
3732 
3733     The indices should start with zero, not one.
3734 
3735 @*/
3736 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3737 {
3738   PetscErrorCode ierr;
3739 
3740   PetscFunctionBegin;
3741   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3742   PetscValidPointer(indices,2);
3743   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3744   PetscFunctionReturn(0);
3745 }
3746 
3747 /* ----------------------------------------------------------------------------------------*/
3748 
3749 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3750 {
3751   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3752   PetscErrorCode ierr;
3753   size_t         nz = aij->i[mat->rmap->n];
3754 
3755   PetscFunctionBegin;
3756   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3757 
3758   /* allocate space for values if not already there */
3759   if (!aij->saved_values) {
3760     ierr = PetscMalloc1(nz+1,&aij->saved_values);CHKERRQ(ierr);
3761     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3762   }
3763 
3764   /* copy values over */
3765   ierr = PetscArraycpy(aij->saved_values,aij->a,nz);CHKERRQ(ierr);
3766   PetscFunctionReturn(0);
3767 }
3768 
3769 /*@
3770     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3771        example, reuse of the linear part of a Jacobian, while recomputing the
3772        nonlinear portion.
3773 
3774    Collect on Mat
3775 
3776   Input Parameters:
3777 .  mat - the matrix (currently only AIJ matrices support this option)
3778 
3779   Level: advanced
3780 
3781   Common Usage, with SNESSolve():
3782 $    Create Jacobian matrix
3783 $    Set linear terms into matrix
3784 $    Apply boundary conditions to matrix, at this time matrix must have
3785 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3786 $      boundary conditions again will not change the nonzero structure
3787 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3788 $    ierr = MatStoreValues(mat);
3789 $    Call SNESSetJacobian() with matrix
3790 $    In your Jacobian routine
3791 $      ierr = MatRetrieveValues(mat);
3792 $      Set nonlinear terms in matrix
3793 
3794   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3795 $    // build linear portion of Jacobian
3796 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3797 $    ierr = MatStoreValues(mat);
3798 $    loop over nonlinear iterations
3799 $       ierr = MatRetrieveValues(mat);
3800 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3801 $       // call MatAssemblyBegin/End() on matrix
3802 $       Solve linear system with Jacobian
3803 $    endloop
3804 
3805   Notes:
3806     Matrix must already be assemblied before calling this routine
3807     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3808     calling this routine.
3809 
3810     When this is called multiple times it overwrites the previous set of stored values
3811     and does not allocated additional space.
3812 
3813 .seealso: MatRetrieveValues()
3814 
3815 @*/
3816 PetscErrorCode  MatStoreValues(Mat mat)
3817 {
3818   PetscErrorCode ierr;
3819 
3820   PetscFunctionBegin;
3821   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3822   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3823   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3824   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3825   PetscFunctionReturn(0);
3826 }
3827 
3828 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3829 {
3830   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3831   PetscErrorCode ierr;
3832   PetscInt       nz = aij->i[mat->rmap->n];
3833 
3834   PetscFunctionBegin;
3835   if (!aij->nonew) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3836   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3837   /* copy values over */
3838   ierr = PetscArraycpy(aij->a,aij->saved_values,nz);CHKERRQ(ierr);
3839   PetscFunctionReturn(0);
3840 }
3841 
3842 /*@
3843     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3844        example, reuse of the linear part of a Jacobian, while recomputing the
3845        nonlinear portion.
3846 
3847    Collect on Mat
3848 
3849   Input Parameters:
3850 .  mat - the matrix (currently only AIJ matrices support this option)
3851 
3852   Level: advanced
3853 
3854 .seealso: MatStoreValues()
3855 
3856 @*/
3857 PetscErrorCode  MatRetrieveValues(Mat mat)
3858 {
3859   PetscErrorCode ierr;
3860 
3861   PetscFunctionBegin;
3862   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3863   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3864   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3865   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3866   PetscFunctionReturn(0);
3867 }
3868 
3869 
3870 /* --------------------------------------------------------------------------------*/
3871 /*@C
3872    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3873    (the default parallel PETSc format).  For good matrix assembly performance
3874    the user should preallocate the matrix storage by setting the parameter nz
3875    (or the array nnz).  By setting these parameters accurately, performance
3876    during matrix assembly can be increased by more than a factor of 50.
3877 
3878    Collective
3879 
3880    Input Parameters:
3881 +  comm - MPI communicator, set to PETSC_COMM_SELF
3882 .  m - number of rows
3883 .  n - number of columns
3884 .  nz - number of nonzeros per row (same for all rows)
3885 -  nnz - array containing the number of nonzeros in the various rows
3886          (possibly different for each row) or NULL
3887 
3888    Output Parameter:
3889 .  A - the matrix
3890 
3891    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3892    MatXXXXSetPreallocation() paradigm instead of this routine directly.
3893    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3894 
3895    Notes:
3896    If nnz is given then nz is ignored
3897 
3898    The AIJ format (also called the Yale sparse matrix format or
3899    compressed row storage), is fully compatible with standard Fortran 77
3900    storage.  That is, the stored row and column indices can begin at
3901    either one (as in Fortran) or zero.  See the users' manual for details.
3902 
3903    Specify the preallocated storage with either nz or nnz (not both).
3904    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3905    allocation.  For large problems you MUST preallocate memory or you
3906    will get TERRIBLE performance, see the users' manual chapter on matrices.
3907 
3908    By default, this format uses inodes (identical nodes) when possible, to
3909    improve numerical efficiency of matrix-vector products and solves. We
3910    search for consecutive rows with the same nonzero structure, thereby
3911    reusing matrix information to achieve increased efficiency.
3912 
3913    Options Database Keys:
3914 +  -mat_no_inode  - Do not use inodes
3915 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3916 
3917    Level: intermediate
3918 
3919 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3920 
3921 @*/
3922 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3923 {
3924   PetscErrorCode ierr;
3925 
3926   PetscFunctionBegin;
3927   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3928   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3929   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3930   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3931   PetscFunctionReturn(0);
3932 }
3933 
3934 /*@C
3935    MatSeqAIJSetPreallocation - For good matrix assembly performance
3936    the user should preallocate the matrix storage by setting the parameter nz
3937    (or the array nnz).  By setting these parameters accurately, performance
3938    during matrix assembly can be increased by more than a factor of 50.
3939 
3940    Collective
3941 
3942    Input Parameters:
3943 +  B - The matrix
3944 .  nz - number of nonzeros per row (same for all rows)
3945 -  nnz - array containing the number of nonzeros in the various rows
3946          (possibly different for each row) or NULL
3947 
3948    Notes:
3949      If nnz is given then nz is ignored
3950 
3951     The AIJ format (also called the Yale sparse matrix format or
3952    compressed row storage), is fully compatible with standard Fortran 77
3953    storage.  That is, the stored row and column indices can begin at
3954    either one (as in Fortran) or zero.  See the users' manual for details.
3955 
3956    Specify the preallocated storage with either nz or nnz (not both).
3957    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3958    allocation.  For large problems you MUST preallocate memory or you
3959    will get TERRIBLE performance, see the users' manual chapter on matrices.
3960 
3961    You can call MatGetInfo() to get information on how effective the preallocation was;
3962    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3963    You can also run with the option -info and look for messages with the string
3964    malloc in them to see if additional memory allocation was needed.
3965 
3966    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3967    entries or columns indices
3968 
3969    By default, this format uses inodes (identical nodes) when possible, to
3970    improve numerical efficiency of matrix-vector products and solves. We
3971    search for consecutive rows with the same nonzero structure, thereby
3972    reusing matrix information to achieve increased efficiency.
3973 
3974    Options Database Keys:
3975 +  -mat_no_inode  - Do not use inodes
3976 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3977 
3978    Level: intermediate
3979 
3980 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatGetInfo(),
3981           MatSeqAIJSetTotalPreallocation()
3982 
3983 @*/
3984 PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
3985 {
3986   PetscErrorCode ierr;
3987 
3988   PetscFunctionBegin;
3989   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3990   PetscValidType(B,1);
3991   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));CHKERRQ(ierr);
3992   PetscFunctionReturn(0);
3993 }
3994 
3995 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3996 {
3997   Mat_SeqAIJ     *b;
3998   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3999   PetscErrorCode ierr;
4000   PetscInt       i;
4001 
4002   PetscFunctionBegin;
4003   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
4004   if (nz == MAT_SKIP_ALLOCATION) {
4005     skipallocation = PETSC_TRUE;
4006     nz             = 0;
4007   }
4008   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
4009   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
4010 
4011   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
4012   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %D",nz);
4013   if (PetscUnlikelyDebug(nnz)) {
4014     for (i=0; i<B->rmap->n; i++) {
4015       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]);
4016       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);
4017     }
4018   }
4019 
4020   B->preallocated = PETSC_TRUE;
4021 
4022   b = (Mat_SeqAIJ*)B->data;
4023 
4024   if (!skipallocation) {
4025     if (!b->imax) {
4026       ierr = PetscMalloc1(B->rmap->n,&b->imax);CHKERRQ(ierr);
4027       ierr = PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
4028     }
4029     if (!b->ilen) {
4030       /* b->ilen will count nonzeros in each row so far. */
4031       ierr = PetscCalloc1(B->rmap->n,&b->ilen);CHKERRQ(ierr);
4032       ierr = PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
4033     } else {
4034       ierr = PetscMemzero(b->ilen,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
4035     }
4036     if (!b->ipre) {
4037       ierr = PetscMalloc1(B->rmap->n,&b->ipre);CHKERRQ(ierr);
4038       ierr = PetscLogObjectMemory((PetscObject)B,B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
4039     }
4040     if (!nnz) {
4041       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
4042       else if (nz < 0) nz = 1;
4043       nz = PetscMin(nz,B->cmap->n);
4044       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
4045       nz = nz*B->rmap->n;
4046     } else {
4047       PetscInt64 nz64 = 0;
4048       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz64 += nnz[i];}
4049       ierr = PetscIntCast(nz64,&nz);CHKERRQ(ierr);
4050     }
4051 
4052     /* allocate the matrix space */
4053     /* FIXME: should B's old memory be unlogged? */
4054     ierr = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
4055     if (B->structure_only) {
4056       ierr = PetscMalloc1(nz,&b->j);CHKERRQ(ierr);
4057       ierr = PetscMalloc1(B->rmap->n+1,&b->i);CHKERRQ(ierr);
4058       ierr = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*sizeof(PetscInt));CHKERRQ(ierr);
4059     } else {
4060       ierr = PetscMalloc3(nz,&b->a,nz,&b->j,B->rmap->n+1,&b->i);CHKERRQ(ierr);
4061       ierr = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
4062     }
4063     b->i[0] = 0;
4064     for (i=1; i<B->rmap->n+1; i++) {
4065       b->i[i] = b->i[i-1] + b->imax[i-1];
4066     }
4067     if (B->structure_only) {
4068       b->singlemalloc = PETSC_FALSE;
4069       b->free_a       = PETSC_FALSE;
4070     } else {
4071       b->singlemalloc = PETSC_TRUE;
4072       b->free_a       = PETSC_TRUE;
4073     }
4074     b->free_ij      = PETSC_TRUE;
4075   } else {
4076     b->free_a  = PETSC_FALSE;
4077     b->free_ij = PETSC_FALSE;
4078   }
4079 
4080   if (b->ipre && nnz != b->ipre  && b->imax) {
4081     /* reserve user-requested sparsity */
4082     ierr = PetscArraycpy(b->ipre,b->imax,B->rmap->n);CHKERRQ(ierr);
4083   }
4084 
4085 
4086   b->nz               = 0;
4087   b->maxnz            = nz;
4088   B->info.nz_unneeded = (double)b->maxnz;
4089   if (realalloc) {
4090     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
4091   }
4092   B->was_assembled = PETSC_FALSE;
4093   B->assembled     = PETSC_FALSE;
4094   PetscFunctionReturn(0);
4095 }
4096 
4097 
4098 PetscErrorCode MatResetPreallocation_SeqAIJ(Mat A)
4099 {
4100   Mat_SeqAIJ     *a;
4101   PetscInt       i;
4102   PetscErrorCode ierr;
4103 
4104   PetscFunctionBegin;
4105   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
4106 
4107   /* Check local size. If zero, then return */
4108   if (!A->rmap->n) PetscFunctionReturn(0);
4109 
4110   a = (Mat_SeqAIJ*)A->data;
4111   /* if no saved info, we error out */
4112   if (!a->ipre) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"No saved preallocation info \n");
4113 
4114   if (!a->i || !a->j || !a->a || !a->imax || !a->ilen) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"Memory info is incomplete, and can not reset preallocation \n");
4115 
4116   ierr = PetscArraycpy(a->imax,a->ipre,A->rmap->n);CHKERRQ(ierr);
4117   ierr = PetscArrayzero(a->ilen,A->rmap->n);CHKERRQ(ierr);
4118   a->i[0] = 0;
4119   for (i=1; i<A->rmap->n+1; i++) {
4120     a->i[i] = a->i[i-1] + a->imax[i-1];
4121   }
4122   A->preallocated     = PETSC_TRUE;
4123   a->nz               = 0;
4124   a->maxnz            = a->i[A->rmap->n];
4125   A->info.nz_unneeded = (double)a->maxnz;
4126   A->was_assembled    = PETSC_FALSE;
4127   A->assembled        = PETSC_FALSE;
4128   PetscFunctionReturn(0);
4129 }
4130 
4131 /*@
4132    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
4133 
4134    Input Parameters:
4135 +  B - the matrix
4136 .  i - the indices into j for the start of each row (starts with zero)
4137 .  j - the column indices for each row (starts with zero) these must be sorted for each row
4138 -  v - optional values in the matrix
4139 
4140    Level: developer
4141 
4142    Notes:
4143       The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
4144 
4145       This routine may be called multiple times with different nonzero patterns (or the same nonzero pattern). The nonzero
4146       structure will be the union of all the previous nonzero structures.
4147 
4148     Developer Notes:
4149       An optimization could be added to the implementation where it checks if the i, and j are identical to the current i and j and
4150       then just copies the v values directly with PetscMemcpy().
4151 
4152       This routine could also take a PetscCopyMode argument to allow sharing the values instead of always copying them.
4153 
4154 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), MATSEQAIJ, MatResetPreallocation()
4155 @*/
4156 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
4157 {
4158   PetscErrorCode ierr;
4159 
4160   PetscFunctionBegin;
4161   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
4162   PetscValidType(B,1);
4163   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
4164   PetscFunctionReturn(0);
4165 }
4166 
4167 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
4168 {
4169   PetscInt       i;
4170   PetscInt       m,n;
4171   PetscInt       nz;
4172   PetscInt       *nnz;
4173   PetscErrorCode ierr;
4174 
4175   PetscFunctionBegin;
4176   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
4177 
4178   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
4179   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
4180 
4181   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
4182   ierr = PetscMalloc1(m+1, &nnz);CHKERRQ(ierr);
4183   for (i = 0; i < m; i++) {
4184     nz     = Ii[i+1]- Ii[i];
4185     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
4186     nnz[i] = nz;
4187   }
4188   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
4189   ierr = PetscFree(nnz);CHKERRQ(ierr);
4190 
4191   for (i = 0; i < m; i++) {
4192     ierr = MatSetValues_SeqAIJ(B, 1, &i, Ii[i+1] - Ii[i], J+Ii[i], v ? v + Ii[i] : NULL, INSERT_VALUES);CHKERRQ(ierr);
4193   }
4194 
4195   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4196   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4197 
4198   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
4199   PetscFunctionReturn(0);
4200 }
4201 
4202 #include <../src/mat/impls/dense/seq/dense.h>
4203 #include <petsc/private/kernels/petscaxpy.h>
4204 
4205 /*
4206     Computes (B'*A')' since computing B*A directly is untenable
4207 
4208                n                       p                          p
4209         [             ]       [             ]         [                 ]
4210       m [      A      ]  *  n [       B     ]   =   m [         C       ]
4211         [             ]       [             ]         [                 ]
4212 
4213 */
4214 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
4215 {
4216   PetscErrorCode    ierr;
4217   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
4218   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
4219   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
4220   PetscInt          i,j,n,m,q,p;
4221   const PetscInt    *ii,*idx;
4222   const PetscScalar *b,*a,*a_q;
4223   PetscScalar       *c,*c_q;
4224   PetscInt          clda = sub_c->lda;
4225   PetscInt          alda = sub_a->lda;
4226 
4227   PetscFunctionBegin;
4228   m    = A->rmap->n;
4229   n    = A->cmap->n;
4230   p    = B->cmap->n;
4231   a    = sub_a->v;
4232   b    = sub_b->a;
4233   c    = sub_c->v;
4234   if (clda == m) {
4235     ierr = PetscArrayzero(c,m*p);CHKERRQ(ierr);
4236   } else {
4237     for (j=0;j<p;j++)
4238       for (i=0;i<m;i++)
4239         c[j*clda + i] = 0.0;
4240   }
4241   ii  = sub_b->i;
4242   idx = sub_b->j;
4243   for (i=0; i<n; i++) {
4244     q = ii[i+1] - ii[i];
4245     while (q-->0) {
4246       c_q = c + clda*(*idx);
4247       a_q = a + alda*i;
4248       PetscKernelAXPY(c_q,*b,a_q,m);
4249       idx++;
4250       b++;
4251     }
4252   }
4253   PetscFunctionReturn(0);
4254 }
4255 
4256 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat C)
4257 {
4258   PetscErrorCode ierr;
4259   PetscInt       m=A->rmap->n,n=B->cmap->n;
4260   PetscBool      cisdense;
4261 
4262   PetscFunctionBegin;
4263   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);
4264   ierr = MatSetSizes(C,m,n,m,n);CHKERRQ(ierr);
4265   ierr = MatSetBlockSizesFromMats(C,A,B);CHKERRQ(ierr);
4266   ierr = PetscObjectTypeCompareAny((PetscObject)C,&cisdense,MATSEQDENSE,MATSEQDENSECUDA,"");CHKERRQ(ierr);
4267   if (!cisdense) {
4268     ierr = MatSetType(C,MATDENSE);CHKERRQ(ierr);
4269   }
4270   ierr = MatSetUp(C);CHKERRQ(ierr);
4271 
4272   C->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
4273   PetscFunctionReturn(0);
4274 }
4275 
4276 /* ----------------------------------------------------------------*/
4277 /*MC
4278    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
4279    based on compressed sparse row format.
4280 
4281    Options Database Keys:
4282 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
4283 
4284    Level: beginner
4285 
4286    Notes:
4287     MatSetValues() may be called for this matrix type with a NULL argument for the numerical values,
4288     in this case the values associated with the rows and columns one passes in are set to zero
4289     in the matrix
4290 
4291     MatSetOptions(,MAT_STRUCTURE_ONLY,PETSC_TRUE) may be called for this matrix type. In this no
4292     space is allocated for the nonzero entries and any entries passed with MatSetValues() are ignored
4293 
4294   Developer Notes:
4295     It would be nice if all matrix formats supported passing NULL in for the numerical values
4296 
4297 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
4298 M*/
4299 
4300 /*MC
4301    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
4302 
4303    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
4304    and MATMPIAIJ otherwise.  As a result, for single process communicators,
4305   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation() is supported
4306   for communicators controlling multiple processes.  It is recommended that you call both of
4307   the above preallocation routines for simplicity.
4308 
4309    Options Database Keys:
4310 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
4311 
4312   Developer Notes:
4313     Subclasses include MATAIJCUSPARSE, MATAIJPERM, MATAIJSELL, MATAIJMKL, MATAIJCRL, and also automatically switches over to use inodes when
4314    enough exist.
4315 
4316   Level: beginner
4317 
4318 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
4319 M*/
4320 
4321 /*MC
4322    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
4323 
4324    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
4325    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
4326    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
4327   for communicators controlling multiple processes.  It is recommended that you call both of
4328   the above preallocation routines for simplicity.
4329 
4330    Options Database Keys:
4331 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
4332 
4333   Level: beginner
4334 
4335 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
4336 M*/
4337 
4338 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
4339 #if defined(PETSC_HAVE_ELEMENTAL)
4340 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4341 #endif
4342 #if defined(PETSC_HAVE_SCALAPACK)
4343 PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat,MatType,MatReuse,Mat*);
4344 #endif
4345 #if defined(PETSC_HAVE_HYPRE)
4346 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat A,MatType,MatReuse,Mat*);
4347 #endif
4348 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqDense(Mat,MatType,MatReuse,Mat*);
4349 
4350 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqSELL(Mat,MatType,MatReuse,Mat*);
4351 PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat,MatType,MatReuse,Mat*);
4352 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_IS_XAIJ(Mat);
4353 
4354 /*@C
4355    MatSeqAIJGetArray - gives read/write access to the array where the data for a MATSEQAIJ matrix is stored
4356 
4357    Not Collective
4358 
4359    Input Parameter:
4360 .  mat - a MATSEQAIJ matrix
4361 
4362    Output Parameter:
4363 .   array - pointer to the data
4364 
4365    Level: intermediate
4366 
4367 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4368 @*/
4369 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4370 {
4371   PetscErrorCode ierr;
4372 
4373   PetscFunctionBegin;
4374   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4375   PetscFunctionReturn(0);
4376 }
4377 
4378 /*@C
4379    MatSeqAIJGetArrayRead - gives read-only access to the array where the data for a MATSEQAIJ matrix is stored
4380 
4381    Not Collective
4382 
4383    Input Parameter:
4384 .  mat - a MATSEQAIJ matrix
4385 
4386    Output Parameter:
4387 .   array - pointer to the data
4388 
4389    Level: intermediate
4390 
4391 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayRead()
4392 @*/
4393 PetscErrorCode  MatSeqAIJGetArrayRead(Mat A,const PetscScalar **array)
4394 {
4395 #if defined(PETSC_HAVE_DEVICE)
4396   PetscOffloadMask oval;
4397 #endif
4398   PetscErrorCode ierr;
4399 
4400   PetscFunctionBegin;
4401 #if defined(PETSC_HAVE_DEVICE)
4402   oval = A->offloadmask;
4403 #endif
4404   ierr = MatSeqAIJGetArray(A,(PetscScalar**)array);CHKERRQ(ierr);
4405 #if defined(PETSC_HAVE_DEVICE)
4406   if (oval == PETSC_OFFLOAD_GPU || oval == PETSC_OFFLOAD_BOTH) A->offloadmask = PETSC_OFFLOAD_BOTH;
4407 #endif
4408   PetscFunctionReturn(0);
4409 }
4410 
4411 /*@C
4412    MatSeqAIJRestoreArrayRead - restore the read-only access array obtained from MatSeqAIJGetArrayRead
4413 
4414    Not Collective
4415 
4416    Input Parameter:
4417 .  mat - a MATSEQAIJ matrix
4418 
4419    Output Parameter:
4420 .   array - pointer to the data
4421 
4422    Level: intermediate
4423 
4424 .seealso: MatSeqAIJGetArray(), MatSeqAIJGetArrayRead()
4425 @*/
4426 PetscErrorCode  MatSeqAIJRestoreArrayRead(Mat A,const PetscScalar **array)
4427 {
4428 #if defined(PETSC_HAVE_DEVICE)
4429   PetscOffloadMask oval;
4430 #endif
4431   PetscErrorCode ierr;
4432 
4433   PetscFunctionBegin;
4434 #if defined(PETSC_HAVE_DEVICE)
4435   oval = A->offloadmask;
4436 #endif
4437   ierr = MatSeqAIJRestoreArray(A,(PetscScalar**)array);CHKERRQ(ierr);
4438 #if defined(PETSC_HAVE_DEVICE)
4439   A->offloadmask = oval;
4440 #endif
4441   PetscFunctionReturn(0);
4442 }
4443 
4444 /*@C
4445    MatSeqAIJGetMaxRowNonzeros - returns the maximum number of nonzeros in any row
4446 
4447    Not Collective
4448 
4449    Input Parameter:
4450 .  mat - a MATSEQAIJ matrix
4451 
4452    Output Parameter:
4453 .   nz - the maximum number of nonzeros in any row
4454 
4455    Level: intermediate
4456 
4457 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4458 @*/
4459 PetscErrorCode  MatSeqAIJGetMaxRowNonzeros(Mat A,PetscInt *nz)
4460 {
4461   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
4462 
4463   PetscFunctionBegin;
4464   *nz = aij->rmax;
4465   PetscFunctionReturn(0);
4466 }
4467 
4468 /*@C
4469    MatSeqAIJRestoreArray - returns access to the array where the data for a MATSEQAIJ matrix is stored obtained by MatSeqAIJGetArray()
4470 
4471    Not Collective
4472 
4473    Input Parameters:
4474 +  mat - a MATSEQAIJ matrix
4475 -  array - pointer to the data
4476 
4477    Level: intermediate
4478 
4479 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4480 @*/
4481 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4482 {
4483   PetscErrorCode ierr;
4484 
4485   PetscFunctionBegin;
4486   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4487   PetscFunctionReturn(0);
4488 }
4489 
4490 #if defined(PETSC_HAVE_CUDA)
4491 PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCUSPARSE(Mat);
4492 #endif
4493 
4494 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4495 {
4496   Mat_SeqAIJ     *b;
4497   PetscErrorCode ierr;
4498   PetscMPIInt    size;
4499 
4500   PetscFunctionBegin;
4501   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4502   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4503 
4504   ierr = PetscNewLog(B,&b);CHKERRQ(ierr);
4505 
4506   B->data = (void*)b;
4507 
4508   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4509   if (B->sortedfull) B->ops->setvalues = MatSetValues_SeqAIJ_SortedFull;
4510 
4511   b->row                = NULL;
4512   b->col                = NULL;
4513   b->icol               = NULL;
4514   b->reallocs           = 0;
4515   b->ignorezeroentries  = PETSC_FALSE;
4516   b->roworiented        = PETSC_TRUE;
4517   b->nonew              = 0;
4518   b->diag               = NULL;
4519   b->solve_work         = NULL;
4520   B->spptr              = NULL;
4521   b->saved_values       = NULL;
4522   b->idiag              = NULL;
4523   b->mdiag              = NULL;
4524   b->ssor_work          = NULL;
4525   b->omega              = 1.0;
4526   b->fshift             = 0.0;
4527   b->idiagvalid         = PETSC_FALSE;
4528   b->ibdiagvalid        = PETSC_FALSE;
4529   b->keepnonzeropattern = PETSC_FALSE;
4530 
4531   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4532   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4533   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4534 
4535 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4536   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4537   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4538 #endif
4539 
4540   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4541   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4542   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4543   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4544   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4545   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4546   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijsell_C",MatConvert_SeqAIJ_SeqAIJSELL);CHKERRQ(ierr);
4547 #if defined(PETSC_HAVE_MKL_SPARSE)
4548   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijmkl_C",MatConvert_SeqAIJ_SeqAIJMKL);CHKERRQ(ierr);
4549 #endif
4550 #if defined(PETSC_HAVE_CUDA)
4551   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcusparse_C",MatConvert_SeqAIJ_SeqAIJCUSPARSE);CHKERRQ(ierr);
4552   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqaijcusparse_seqaij_C",MatProductSetFromOptions_SeqAIJ);CHKERRQ(ierr);
4553 #endif
4554   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4555 #if defined(PETSC_HAVE_ELEMENTAL)
4556   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_elemental_C",MatConvert_SeqAIJ_Elemental);CHKERRQ(ierr);
4557 #endif
4558 #if defined(PETSC_HAVE_SCALAPACK)
4559   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_scalapack_C",MatConvert_AIJ_ScaLAPACK);CHKERRQ(ierr);
4560 #endif
4561 #if defined(PETSC_HAVE_HYPRE)
4562   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
4563   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_transpose_seqaij_seqaij_C",MatProductSetFromOptions_Transpose_AIJ_AIJ);CHKERRQ(ierr);
4564 #endif
4565   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqdense_C",MatConvert_SeqAIJ_SeqDense);CHKERRQ(ierr);
4566   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsell_C",MatConvert_SeqAIJ_SeqSELL);CHKERRQ(ierr);
4567   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_is_C",MatConvert_XAIJ_IS);CHKERRQ(ierr);
4568   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4569   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4570   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4571   ierr = PetscObjectComposeFunction((PetscObject)B,"MatResetPreallocation_C",MatResetPreallocation_SeqAIJ);CHKERRQ(ierr);
4572   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4573   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4574   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_is_seqaij_C",MatProductSetFromOptions_IS_XAIJ);CHKERRQ(ierr);
4575   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqdense_seqaij_C",MatProductSetFromOptions_SeqDense_SeqAIJ);CHKERRQ(ierr);
4576   ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqaij_seqaij_C",MatProductSetFromOptions_SeqAIJ);CHKERRQ(ierr);
4577   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4578   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4579   ierr = MatSeqAIJSetTypeFromOptions(B);CHKERRQ(ierr);  /* this allows changing the matrix subtype to say MATSEQAIJPERM */
4580   PetscFunctionReturn(0);
4581 }
4582 
4583 /*
4584     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4585 */
4586 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4587 {
4588   Mat_SeqAIJ     *c = (Mat_SeqAIJ*)C->data,*a = (Mat_SeqAIJ*)A->data;
4589   PetscErrorCode ierr;
4590   PetscInt       m = A->rmap->n,i;
4591 
4592   PetscFunctionBegin;
4593   if (!A->assembled && cpvalues!=MAT_DO_NOT_COPY_VALUES) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot duplicate unassembled matrix");
4594 
4595   C->factortype = A->factortype;
4596   c->row        = NULL;
4597   c->col        = NULL;
4598   c->icol       = NULL;
4599   c->reallocs   = 0;
4600 
4601   C->assembled = PETSC_TRUE;
4602 
4603   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4604   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4605 
4606   ierr = PetscMalloc1(m,&c->imax);CHKERRQ(ierr);
4607   ierr = PetscMemcpy(c->imax,a->imax,m*sizeof(PetscInt));CHKERRQ(ierr);
4608   ierr = PetscMalloc1(m,&c->ilen);CHKERRQ(ierr);
4609   ierr = PetscMemcpy(c->ilen,a->ilen,m*sizeof(PetscInt));CHKERRQ(ierr);
4610   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4611 
4612   /* allocate the matrix space */
4613   if (mallocmatspace) {
4614     ierr = PetscMalloc3(a->i[m],&c->a,a->i[m],&c->j,m+1,&c->i);CHKERRQ(ierr);
4615     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4616 
4617     c->singlemalloc = PETSC_TRUE;
4618 
4619     ierr = PetscArraycpy(c->i,a->i,m+1);CHKERRQ(ierr);
4620     if (m > 0) {
4621       ierr = PetscArraycpy(c->j,a->j,a->i[m]);CHKERRQ(ierr);
4622       if (cpvalues == MAT_COPY_VALUES) {
4623         ierr = PetscArraycpy(c->a,a->a,a->i[m]);CHKERRQ(ierr);
4624       } else {
4625         ierr = PetscArrayzero(c->a,a->i[m]);CHKERRQ(ierr);
4626       }
4627     }
4628   }
4629 
4630   c->ignorezeroentries = a->ignorezeroentries;
4631   c->roworiented       = a->roworiented;
4632   c->nonew             = a->nonew;
4633   if (a->diag) {
4634     ierr = PetscMalloc1(m+1,&c->diag);CHKERRQ(ierr);
4635     ierr = PetscMemcpy(c->diag,a->diag,m*sizeof(PetscInt));CHKERRQ(ierr);
4636     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4637   } else c->diag = NULL;
4638 
4639   c->solve_work         = NULL;
4640   c->saved_values       = NULL;
4641   c->idiag              = NULL;
4642   c->ssor_work          = NULL;
4643   c->keepnonzeropattern = a->keepnonzeropattern;
4644   c->free_a             = PETSC_TRUE;
4645   c->free_ij            = PETSC_TRUE;
4646 
4647   c->rmax         = a->rmax;
4648   c->nz           = a->nz;
4649   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4650   C->preallocated = PETSC_TRUE;
4651 
4652   c->compressedrow.use   = a->compressedrow.use;
4653   c->compressedrow.nrows = a->compressedrow.nrows;
4654   if (a->compressedrow.use) {
4655     i    = a->compressedrow.nrows;
4656     ierr = PetscMalloc2(i+1,&c->compressedrow.i,i,&c->compressedrow.rindex);CHKERRQ(ierr);
4657     ierr = PetscArraycpy(c->compressedrow.i,a->compressedrow.i,i+1);CHKERRQ(ierr);
4658     ierr = PetscArraycpy(c->compressedrow.rindex,a->compressedrow.rindex,i);CHKERRQ(ierr);
4659   } else {
4660     c->compressedrow.use    = PETSC_FALSE;
4661     c->compressedrow.i      = NULL;
4662     c->compressedrow.rindex = NULL;
4663   }
4664   c->nonzerorowcnt = a->nonzerorowcnt;
4665   C->nonzerostate  = A->nonzerostate;
4666 
4667   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4668   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4669   PetscFunctionReturn(0);
4670 }
4671 
4672 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4673 {
4674   PetscErrorCode ierr;
4675 
4676   PetscFunctionBegin;
4677   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4678   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4679   if (!(A->rmap->n % A->rmap->bs) && !(A->cmap->n % A->cmap->bs)) {
4680     ierr = MatSetBlockSizesFromMats(*B,A,A);CHKERRQ(ierr);
4681   }
4682   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4683   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4684   PetscFunctionReturn(0);
4685 }
4686 
4687 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4688 {
4689   PetscBool      isbinary, ishdf5;
4690   PetscErrorCode ierr;
4691 
4692   PetscFunctionBegin;
4693   PetscValidHeaderSpecific(newMat,MAT_CLASSID,1);
4694   PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
4695   /* force binary viewer to load .info file if it has not yet done so */
4696   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
4697   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
4698   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,  &ishdf5);CHKERRQ(ierr);
4699   if (isbinary) {
4700     ierr = MatLoad_SeqAIJ_Binary(newMat,viewer);CHKERRQ(ierr);
4701   } else if (ishdf5) {
4702 #if defined(PETSC_HAVE_HDF5)
4703     ierr = MatLoad_AIJ_HDF5(newMat,viewer);CHKERRQ(ierr);
4704 #else
4705     SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
4706 #endif
4707   } else {
4708     SETERRQ2(PetscObjectComm((PetscObject)newMat),PETSC_ERR_SUP,"Viewer type %s not yet supported for reading %s matrices",((PetscObject)viewer)->type_name,((PetscObject)newMat)->type_name);
4709   }
4710   PetscFunctionReturn(0);
4711 }
4712 
4713 PetscErrorCode MatLoad_SeqAIJ_Binary(Mat mat, PetscViewer viewer)
4714 {
4715   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)mat->data;
4716   PetscErrorCode ierr;
4717   PetscInt       header[4],*rowlens,M,N,nz,sum,rows,cols,i;
4718 
4719   PetscFunctionBegin;
4720   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
4721 
4722   /* read in matrix header */
4723   ierr = PetscViewerBinaryRead(viewer,header,4,NULL,PETSC_INT);CHKERRQ(ierr);
4724   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Not a matrix object in file");
4725   M = header[1]; N = header[2]; nz = header[3];
4726   if (M < 0) SETERRQ1(PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Matrix row size (%D) in file is negative",M);
4727   if (N < 0) SETERRQ1(PetscObjectComm((PetscObject)viewer),PETSC_ERR_FILE_UNEXPECTED,"Matrix column size (%D) in file is negative",N);
4728   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk, cannot load as SeqAIJ");
4729 
4730   /* set block sizes from the viewer's .info file */
4731   ierr = MatLoad_Binary_BlockSizes(mat,viewer);CHKERRQ(ierr);
4732   /* set local and global sizes if not set already */
4733   if (mat->rmap->n < 0) mat->rmap->n = M;
4734   if (mat->cmap->n < 0) mat->cmap->n = N;
4735   if (mat->rmap->N < 0) mat->rmap->N = M;
4736   if (mat->cmap->N < 0) mat->cmap->N = N;
4737   ierr = PetscLayoutSetUp(mat->rmap);CHKERRQ(ierr);
4738   ierr = PetscLayoutSetUp(mat->cmap);CHKERRQ(ierr);
4739 
4740   /* check if the matrix sizes are correct */
4741   ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
4742   if (M != rows || N != cols) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Matrix in file of different sizes (%D, %D) than the input matrix (%D, %D)",M,N,rows,cols);
4743 
4744   /* read in row lengths */
4745   ierr = PetscMalloc1(M,&rowlens);CHKERRQ(ierr);
4746   ierr = PetscViewerBinaryRead(viewer,rowlens,M,NULL,PETSC_INT);CHKERRQ(ierr);
4747   /* check if sum(rowlens) is same as nz */
4748   sum = 0; for (i=0; i<M; i++) sum += rowlens[i];
4749   if (sum != nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Inconsistent matrix data in file: nonzeros = %D, sum-row-lengths = %D\n",nz,sum);
4750   /* preallocate and check sizes */
4751   ierr = MatSeqAIJSetPreallocation_SeqAIJ(mat,0,rowlens);CHKERRQ(ierr);
4752   ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
4753   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);
4754   /* store row lengths */
4755   ierr = PetscArraycpy(a->ilen,rowlens,M);CHKERRQ(ierr);
4756   ierr = PetscFree(rowlens);CHKERRQ(ierr);
4757 
4758   /* fill in "i" row pointers */
4759   a->i[0] = 0; for (i=0; i<M; i++) a->i[i+1] = a->i[i] + a->ilen[i];
4760   /* read in "j" column indices */
4761   ierr = PetscViewerBinaryRead(viewer,a->j,nz,NULL,PETSC_INT);CHKERRQ(ierr);
4762   /* read in "a" nonzero values */
4763   ierr = PetscViewerBinaryRead(viewer,a->a,nz,NULL,PETSC_SCALAR);CHKERRQ(ierr);
4764 
4765   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4766   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4767   PetscFunctionReturn(0);
4768 }
4769 
4770 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4771 {
4772   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4773   PetscErrorCode ierr;
4774 #if defined(PETSC_USE_COMPLEX)
4775   PetscInt k;
4776 #endif
4777 
4778   PetscFunctionBegin;
4779   /* If the  matrix dimensions are not equal,or no of nonzeros */
4780   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4781     *flg = PETSC_FALSE;
4782     PetscFunctionReturn(0);
4783   }
4784 
4785   /* if the a->i are the same */
4786   ierr = PetscArraycmp(a->i,b->i,A->rmap->n+1,flg);CHKERRQ(ierr);
4787   if (!*flg) PetscFunctionReturn(0);
4788 
4789   /* if a->j are the same */
4790   ierr = PetscArraycmp(a->j,b->j,a->nz,flg);CHKERRQ(ierr);
4791   if (!*flg) PetscFunctionReturn(0);
4792 
4793   /* if a->a are the same */
4794 #if defined(PETSC_USE_COMPLEX)
4795   for (k=0; k<a->nz; k++) {
4796     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4797       *flg = PETSC_FALSE;
4798       PetscFunctionReturn(0);
4799     }
4800   }
4801 #else
4802   ierr = PetscArraycmp(a->a,b->a,a->nz,flg);CHKERRQ(ierr);
4803 #endif
4804   PetscFunctionReturn(0);
4805 }
4806 
4807 /*@
4808      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4809               provided by the user.
4810 
4811       Collective
4812 
4813    Input Parameters:
4814 +   comm - must be an MPI communicator of size 1
4815 .   m - number of rows
4816 .   n - number of columns
4817 .   i - row indices; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
4818 .   j - column indices
4819 -   a - matrix values
4820 
4821    Output Parameter:
4822 .   mat - the matrix
4823 
4824    Level: intermediate
4825 
4826    Notes:
4827        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4828     once the matrix is destroyed and not before
4829 
4830        You cannot set new nonzero locations into this matrix, that will generate an error.
4831 
4832        The i and j indices are 0 based
4833 
4834        The format which is used for the sparse matrix input, is equivalent to a
4835     row-major ordering.. i.e for the following matrix, the input data expected is
4836     as shown
4837 
4838 $        1 0 0
4839 $        2 0 3
4840 $        4 5 6
4841 $
4842 $        i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4843 $        j =  {0,0,2,0,1,2}  [size = 6]; values must be sorted for each row
4844 $        v =  {1,2,3,4,5,6}  [size = 6]
4845 
4846 
4847 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4848 
4849 @*/
4850 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat)
4851 {
4852   PetscErrorCode ierr;
4853   PetscInt       ii;
4854   Mat_SeqAIJ     *aij;
4855   PetscInt jj;
4856 
4857   PetscFunctionBegin;
4858   if (m > 0 && i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4859   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4860   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4861   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4862   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4863   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr);
4864   aij  = (Mat_SeqAIJ*)(*mat)->data;
4865   ierr = PetscMalloc1(m,&aij->imax);CHKERRQ(ierr);
4866   ierr = PetscMalloc1(m,&aij->ilen);CHKERRQ(ierr);
4867 
4868   aij->i            = i;
4869   aij->j            = j;
4870   aij->a            = a;
4871   aij->singlemalloc = PETSC_FALSE;
4872   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4873   aij->free_a       = PETSC_FALSE;
4874   aij->free_ij      = PETSC_FALSE;
4875 
4876   for (ii=0; ii<m; ii++) {
4877     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4878     if (PetscDefined(USE_DEBUG)) {
4879       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]);
4880       for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4881         if (j[jj] < j[jj-1]) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column entry number %D (actual column %D) in row %D is not sorted",jj-i[ii],j[jj],ii);
4882         if (j[jj] == j[jj-1]) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column entry number %D (actual column %D) in row %D is identical to previous entry",jj-i[ii],j[jj],ii);
4883       }
4884     }
4885   }
4886   if (PetscDefined(USE_DEBUG)) {
4887     for (ii=0; ii<aij->i[m]; ii++) {
4888       if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %D index = %D",ii,j[ii]);
4889       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]);
4890     }
4891   }
4892 
4893   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4894   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4895   PetscFunctionReturn(0);
4896 }
4897 /*@C
4898      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4899               provided by the user.
4900 
4901       Collective
4902 
4903    Input Parameters:
4904 +   comm - must be an MPI communicator of size 1
4905 .   m   - number of rows
4906 .   n   - number of columns
4907 .   i   - row indices
4908 .   j   - column indices
4909 .   a   - matrix values
4910 .   nz  - number of nonzeros
4911 -   idx - 0 or 1 based
4912 
4913    Output Parameter:
4914 .   mat - the matrix
4915 
4916    Level: intermediate
4917 
4918    Notes:
4919        The i and j indices are 0 based
4920 
4921        The format which is used for the sparse matrix input, is equivalent to a
4922     row-major ordering.. i.e for the following matrix, the input data expected is
4923     as shown:
4924 
4925         1 0 0
4926         2 0 3
4927         4 5 6
4928 
4929         i =  {0,1,1,2,2,2}
4930         j =  {0,0,2,0,1,2}
4931         v =  {1,2,3,4,5,6}
4932 
4933 
4934 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4935 
4936 @*/
4937 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],Mat *mat,PetscInt nz,PetscBool idx)
4938 {
4939   PetscErrorCode ierr;
4940   PetscInt       ii, *nnz, one = 1,row,col;
4941 
4942 
4943   PetscFunctionBegin;
4944   ierr = PetscCalloc1(m,&nnz);CHKERRQ(ierr);
4945   for (ii = 0; ii < nz; ii++) {
4946     nnz[i[ii] - !!idx] += 1;
4947   }
4948   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4949   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4950   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4951   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4952   for (ii = 0; ii < nz; ii++) {
4953     if (idx) {
4954       row = i[ii] - 1;
4955       col = j[ii] - 1;
4956     } else {
4957       row = i[ii];
4958       col = j[ii];
4959     }
4960     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4961   }
4962   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4963   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4964   ierr = PetscFree(nnz);CHKERRQ(ierr);
4965   PetscFunctionReturn(0);
4966 }
4967 
4968 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4969 {
4970   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4971   PetscErrorCode ierr;
4972 
4973   PetscFunctionBegin;
4974   a->idiagvalid  = PETSC_FALSE;
4975   a->ibdiagvalid = PETSC_FALSE;
4976 
4977   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4978   PetscFunctionReturn(0);
4979 }
4980 
4981 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
4982 {
4983   PetscErrorCode ierr;
4984   PetscMPIInt    size;
4985 
4986   PetscFunctionBegin;
4987   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4988   if (size == 1) {
4989     if (scall == MAT_INITIAL_MATRIX) {
4990       ierr = MatDuplicate(inmat,MAT_COPY_VALUES,outmat);CHKERRQ(ierr);
4991     } else {
4992       ierr = MatCopy(inmat,*outmat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4993     }
4994   } else {
4995     ierr = MatCreateMPIMatConcatenateSeqMat_MPIAIJ(comm,inmat,n,scall,outmat);CHKERRQ(ierr);
4996   }
4997   PetscFunctionReturn(0);
4998 }
4999 
5000 /*
5001  Permute A into C's *local* index space using rowemb,colemb.
5002  The embedding are supposed to be injections and the above implies that the range of rowemb is a subset
5003  of [0,m), colemb is in [0,n).
5004  If pattern == DIFFERENT_NONZERO_PATTERN, C is preallocated according to A.
5005  */
5006 PetscErrorCode MatSetSeqMat_SeqAIJ(Mat C,IS rowemb,IS colemb,MatStructure pattern,Mat B)
5007 {
5008   /* If making this function public, change the error returned in this function away from _PLIB. */
5009   PetscErrorCode ierr;
5010   Mat_SeqAIJ     *Baij;
5011   PetscBool      seqaij;
5012   PetscInt       m,n,*nz,i,j,count;
5013   PetscScalar    v;
5014   const PetscInt *rowindices,*colindices;
5015 
5016   PetscFunctionBegin;
5017   if (!B) PetscFunctionReturn(0);
5018   /* Check to make sure the target matrix (and embeddings) are compatible with C and each other. */
5019   ierr = PetscObjectBaseTypeCompare((PetscObject)B,MATSEQAIJ,&seqaij);CHKERRQ(ierr);
5020   if (!seqaij) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is of wrong type");
5021   if (rowemb) {
5022     ierr = ISGetLocalSize(rowemb,&m);CHKERRQ(ierr);
5023     if (m != B->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Row IS of size %D is incompatible with matrix row size %D",m,B->rmap->n);
5024   } else {
5025     if (C->rmap->n != B->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is row-incompatible with the target matrix");
5026   }
5027   if (colemb) {
5028     ierr = ISGetLocalSize(colemb,&n);CHKERRQ(ierr);
5029     if (n != B->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Diag col IS of size %D is incompatible with input matrix col size %D",n,B->cmap->n);
5030   } else {
5031     if (C->cmap->n != B->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Input matrix is col-incompatible with the target matrix");
5032   }
5033 
5034   Baij = (Mat_SeqAIJ*)(B->data);
5035   if (pattern == DIFFERENT_NONZERO_PATTERN) {
5036     ierr = PetscMalloc1(B->rmap->n,&nz);CHKERRQ(ierr);
5037     for (i=0; i<B->rmap->n; i++) {
5038       nz[i] = Baij->i[i+1] - Baij->i[i];
5039     }
5040     ierr = MatSeqAIJSetPreallocation(C,0,nz);CHKERRQ(ierr);
5041     ierr = PetscFree(nz);CHKERRQ(ierr);
5042   }
5043   if (pattern == SUBSET_NONZERO_PATTERN) {
5044     ierr = MatZeroEntries(C);CHKERRQ(ierr);
5045   }
5046   count = 0;
5047   rowindices = NULL;
5048   colindices = NULL;
5049   if (rowemb) {
5050     ierr = ISGetIndices(rowemb,&rowindices);CHKERRQ(ierr);
5051   }
5052   if (colemb) {
5053     ierr = ISGetIndices(colemb,&colindices);CHKERRQ(ierr);
5054   }
5055   for (i=0; i<B->rmap->n; i++) {
5056     PetscInt row;
5057     row = i;
5058     if (rowindices) row = rowindices[i];
5059     for (j=Baij->i[i]; j<Baij->i[i+1]; j++) {
5060       PetscInt col;
5061       col  = Baij->j[count];
5062       if (colindices) col = colindices[col];
5063       v    = Baij->a[count];
5064       ierr = MatSetValues(C,1,&row,1,&col,&v,INSERT_VALUES);CHKERRQ(ierr);
5065       ++count;
5066     }
5067   }
5068   /* FIXME: set C's nonzerostate correctly. */
5069   /* Assembly for C is necessary. */
5070   C->preallocated = PETSC_TRUE;
5071   C->assembled     = PETSC_TRUE;
5072   C->was_assembled = PETSC_FALSE;
5073   PetscFunctionReturn(0);
5074 }
5075 
5076 PetscFunctionList MatSeqAIJList = NULL;
5077 
5078 /*@C
5079    MatSeqAIJSetType - Converts a MATSEQAIJ matrix to a subtype
5080 
5081    Collective on Mat
5082 
5083    Input Parameters:
5084 +  mat      - the matrix object
5085 -  matype   - matrix type
5086 
5087    Options Database Key:
5088 .  -mat_seqai_type  <method> - for example seqaijcrl
5089 
5090 
5091   Level: intermediate
5092 
5093 .seealso: PCSetType(), VecSetType(), MatCreate(), MatType, Mat
5094 @*/
5095 PetscErrorCode  MatSeqAIJSetType(Mat mat, MatType matype)
5096 {
5097   PetscErrorCode ierr,(*r)(Mat,MatType,MatReuse,Mat*);
5098   PetscBool      sametype;
5099 
5100   PetscFunctionBegin;
5101   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
5102   ierr = PetscObjectTypeCompare((PetscObject)mat,matype,&sametype);CHKERRQ(ierr);
5103   if (sametype) PetscFunctionReturn(0);
5104 
5105   ierr =  PetscFunctionListFind(MatSeqAIJList,matype,&r);CHKERRQ(ierr);
5106   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown Mat type given: %s",matype);
5107   ierr = (*r)(mat,matype,MAT_INPLACE_MATRIX,&mat);CHKERRQ(ierr);
5108   PetscFunctionReturn(0);
5109 }
5110 
5111 
5112 /*@C
5113   MatSeqAIJRegister -  - Adds a new sub-matrix type for sequential AIJ matrices
5114 
5115    Not Collective
5116 
5117    Input Parameters:
5118 +  name - name of a new user-defined matrix type, for example MATSEQAIJCRL
5119 -  function - routine to convert to subtype
5120 
5121    Notes:
5122    MatSeqAIJRegister() may be called multiple times to add several user-defined solvers.
5123 
5124 
5125    Then, your matrix can be chosen with the procedural interface at runtime via the option
5126 $     -mat_seqaij_type my_mat
5127 
5128    Level: advanced
5129 
5130 .seealso: MatSeqAIJRegisterAll()
5131 
5132 
5133   Level: advanced
5134 @*/
5135 PetscErrorCode  MatSeqAIJRegister(const char sname[],PetscErrorCode (*function)(Mat,MatType,MatReuse,Mat *))
5136 {
5137   PetscErrorCode ierr;
5138 
5139   PetscFunctionBegin;
5140   ierr = MatInitializePackage();CHKERRQ(ierr);
5141   ierr = PetscFunctionListAdd(&MatSeqAIJList,sname,function);CHKERRQ(ierr);
5142   PetscFunctionReturn(0);
5143 }
5144 
5145 PetscBool MatSeqAIJRegisterAllCalled = PETSC_FALSE;
5146 
5147 /*@C
5148   MatSeqAIJRegisterAll - Registers all of the matrix subtypes of SeqAIJ
5149 
5150   Not Collective
5151 
5152   Level: advanced
5153 
5154   Developers Note: CUSP and CUSPARSE do not yet support the  MatConvert_SeqAIJ..() paradigm and thus cannot be registered here
5155 
5156 .seealso:  MatRegisterAll(), MatSeqAIJRegister()
5157 @*/
5158 PetscErrorCode  MatSeqAIJRegisterAll(void)
5159 {
5160   PetscErrorCode ierr;
5161 
5162   PetscFunctionBegin;
5163   if (MatSeqAIJRegisterAllCalled) PetscFunctionReturn(0);
5164   MatSeqAIJRegisterAllCalled = PETSC_TRUE;
5165 
5166   ierr = MatSeqAIJRegister(MATSEQAIJCRL,      MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
5167   ierr = MatSeqAIJRegister(MATSEQAIJPERM,     MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
5168   ierr = MatSeqAIJRegister(MATSEQAIJSELL,     MatConvert_SeqAIJ_SeqAIJSELL);CHKERRQ(ierr);
5169 #if defined(PETSC_HAVE_MKL_SPARSE)
5170   ierr = MatSeqAIJRegister(MATSEQAIJMKL,      MatConvert_SeqAIJ_SeqAIJMKL);CHKERRQ(ierr);
5171 #endif
5172 #if defined(PETSC_HAVE_VIENNACL) && defined(PETSC_HAVE_VIENNACL_NO_CUDA)
5173   ierr = MatSeqAIJRegister(MATMPIAIJVIENNACL, MatConvert_SeqAIJ_SeqAIJViennaCL);CHKERRQ(ierr);
5174 #endif
5175   PetscFunctionReturn(0);
5176 }
5177 
5178 /*
5179     Special version for direct calls from Fortran
5180 */
5181 #include <petsc/private/fortranimpl.h>
5182 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5183 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
5184 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5185 #define matsetvaluesseqaij_ matsetvaluesseqaij
5186 #endif
5187 
5188 /* Change these macros so can be used in void function */
5189 #undef CHKERRQ
5190 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
5191 #undef SETERRQ2
5192 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5193 #undef SETERRQ3
5194 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5195 
5196 PETSC_EXTERN void matsetvaluesseqaij_(Mat *AA,PetscInt *mm,const PetscInt im[],PetscInt *nn,const PetscInt in[],const PetscScalar v[],InsertMode *isis, PetscErrorCode *_ierr)
5197 {
5198   Mat            A  = *AA;
5199   PetscInt       m  = *mm, n = *nn;
5200   InsertMode     is = *isis;
5201   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
5202   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
5203   PetscInt       *imax,*ai,*ailen;
5204   PetscErrorCode ierr;
5205   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
5206   MatScalar      *ap,value,*aa;
5207   PetscBool      ignorezeroentries = a->ignorezeroentries;
5208   PetscBool      roworiented       = a->roworiented;
5209 
5210   PetscFunctionBegin;
5211   MatCheckPreallocated(A,1);
5212   imax  = a->imax;
5213   ai    = a->i;
5214   ailen = a->ilen;
5215   aj    = a->j;
5216   aa    = a->a;
5217 
5218   for (k=0; k<m; k++) { /* loop over added rows */
5219     row = im[k];
5220     if (row < 0) continue;
5221     if (PetscUnlikelyDebug(row >= A->rmap->n)) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
5222     rp   = aj + ai[row]; ap = aa + ai[row];
5223     rmax = imax[row]; nrow = ailen[row];
5224     low  = 0;
5225     high = nrow;
5226     for (l=0; l<n; l++) { /* loop over added columns */
5227       if (in[l] < 0) continue;
5228       if (PetscUnlikelyDebug(in[l] >= A->cmap->n)) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
5229       col = in[l];
5230       if (roworiented) value = v[l + k*n];
5231       else value = v[k + l*m];
5232 
5233       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
5234 
5235       if (col <= lastcol) low = 0;
5236       else high = nrow;
5237       lastcol = col;
5238       while (high-low > 5) {
5239         t = (low+high)/2;
5240         if (rp[t] > col) high = t;
5241         else             low  = t;
5242       }
5243       for (i=low; i<high; i++) {
5244         if (rp[i] > col) break;
5245         if (rp[i] == col) {
5246           if (is == ADD_VALUES) ap[i] += value;
5247           else                  ap[i] = value;
5248           goto noinsert;
5249         }
5250       }
5251       if (value == 0.0 && ignorezeroentries) goto noinsert;
5252       if (nonew == 1) goto noinsert;
5253       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
5254       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
5255       N = nrow++ - 1; a->nz++; high++;
5256       /* shift up all the later entries in this row */
5257       for (ii=N; ii>=i; ii--) {
5258         rp[ii+1] = rp[ii];
5259         ap[ii+1] = ap[ii];
5260       }
5261       rp[i] = col;
5262       ap[i] = value;
5263       A->nonzerostate++;
5264 noinsert:;
5265       low = i + 1;
5266     }
5267     ailen[row] = nrow;
5268   }
5269   PetscFunctionReturnVoid();
5270 }
5271