xref: /petsc/src/mat/impls/aij/seq/aij.c (revision 6378f32dd8656d85e3a9cd8ab0fbf0edbabc7e18)
1 
2 /*
3     Defines the basic matrix operations for the AIJ (compressed row)
4   matrix storage format.
5 */
6 
7 
8 #include <../src/mat/impls/aij/seq/aij.h>          /*I "petscmat.h" I*/
9 #include <petscblaslapack.h>
10 #include <petscbt.h>
11 #include <petsc-private/kernels/blocktranspose.h>
12 #if defined(PETSC_THREADCOMM_ACTIVE)
13 #include <petscthreadcomm.h>
14 #endif
15 
16 #undef __FUNCT__
17 #define __FUNCT__ "MatGetColumnNorms_SeqAIJ"
18 PetscErrorCode MatGetColumnNorms_SeqAIJ(Mat A,NormType type,PetscReal *norms)
19 {
20   PetscErrorCode ierr;
21   PetscInt       i,m,n;
22   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)A->data;
23 
24   PetscFunctionBegin;
25   ierr = MatGetSize(A,&m,&n);CHKERRQ(ierr);
26   ierr = PetscMemzero(norms,n*sizeof(PetscReal));CHKERRQ(ierr);
27   if (type == NORM_2) {
28     for (i=0; i<aij->i[m]; i++) {
29       norms[aij->j[i]] += PetscAbsScalar(aij->a[i]*aij->a[i]);
30     }
31   } else if (type == NORM_1) {
32     for (i=0; i<aij->i[m]; i++) {
33       norms[aij->j[i]] += PetscAbsScalar(aij->a[i]);
34     }
35   } else if (type == NORM_INFINITY) {
36     for (i=0; i<aij->i[m]; i++) {
37       norms[aij->j[i]] = PetscMax(PetscAbsScalar(aij->a[i]),norms[aij->j[i]]);
38     }
39   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unknown NormType");
40 
41   if (type == NORM_2) {
42     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
43   }
44   PetscFunctionReturn(0);
45 }
46 
47 #undef __FUNCT__
48 #define __FUNCT__ "MatFindZeroDiagonals_SeqAIJ_Private"
49 PetscErrorCode MatFindZeroDiagonals_SeqAIJ_Private(Mat A,PetscInt *nrows,PetscInt **zrows)
50 {
51   Mat_SeqAIJ      *a  = (Mat_SeqAIJ*)A->data;
52   const MatScalar *aa = a->a;
53   PetscInt        i,m=A->rmap->n,cnt = 0;
54   const PetscInt  *jj = a->j,*diag;
55   PetscInt        *rows;
56   PetscErrorCode  ierr;
57 
58   PetscFunctionBegin;
59   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
60   diag = a->diag;
61   for (i=0; i<m; i++) {
62     if ((jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) {
63       cnt++;
64     }
65   }
66   ierr = PetscMalloc(cnt*sizeof(PetscInt),&rows);CHKERRQ(ierr);
67   cnt  = 0;
68   for (i=0; i<m; i++) {
69     if ((jj[diag[i]] != i) || (aa[diag[i]] == 0.0)) {
70       rows[cnt++] = i;
71     }
72   }
73   *nrows = cnt;
74   *zrows = rows;
75   PetscFunctionReturn(0);
76 }
77 
78 #undef __FUNCT__
79 #define __FUNCT__ "MatFindZeroDiagonals_SeqAIJ"
80 PetscErrorCode MatFindZeroDiagonals_SeqAIJ(Mat A,IS *zrows)
81 {
82   PetscInt       nrows,*rows;
83   PetscErrorCode ierr;
84 
85   PetscFunctionBegin;
86   *zrows = NULL;
87   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(A,&nrows,&rows);CHKERRQ(ierr);
88   ierr   = ISCreateGeneral(PetscObjectComm((PetscObject)A),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
89   PetscFunctionReturn(0);
90 }
91 
92 #undef __FUNCT__
93 #define __FUNCT__ "MatFindNonzeroRows_SeqAIJ"
94 PetscErrorCode MatFindNonzeroRows_SeqAIJ(Mat A,IS *keptrows)
95 {
96   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
97   const MatScalar *aa;
98   PetscInt        m=A->rmap->n,cnt = 0;
99   const PetscInt  *ii;
100   PetscInt        n,i,j,*rows;
101   PetscErrorCode  ierr;
102 
103   PetscFunctionBegin;
104   *keptrows = 0;
105   ii        = a->i;
106   for (i=0; i<m; i++) {
107     n = ii[i+1] - ii[i];
108     if (!n) {
109       cnt++;
110       goto ok1;
111     }
112     aa = a->a + ii[i];
113     for (j=0; j<n; j++) {
114       if (aa[j] != 0.0) goto ok1;
115     }
116     cnt++;
117 ok1:;
118   }
119   if (!cnt) PetscFunctionReturn(0);
120   ierr = PetscMalloc((A->rmap->n-cnt)*sizeof(PetscInt),&rows);CHKERRQ(ierr);
121   cnt  = 0;
122   for (i=0; i<m; i++) {
123     n = ii[i+1] - ii[i];
124     if (!n) continue;
125     aa = a->a + ii[i];
126     for (j=0; j<n; j++) {
127       if (aa[j] != 0.0) {
128         rows[cnt++] = i;
129         break;
130       }
131     }
132   }
133   ierr = ISCreateGeneral(PETSC_COMM_SELF,cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
134   PetscFunctionReturn(0);
135 }
136 
137 #undef __FUNCT__
138 #define __FUNCT__ "MatDiagonalSet_SeqAIJ"
139 PetscErrorCode  MatDiagonalSet_SeqAIJ(Mat Y,Vec D,InsertMode is)
140 {
141   PetscErrorCode ierr;
142   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) Y->data;
143   PetscInt       i,*diag, m = Y->rmap->n;
144   MatScalar      *aa = aij->a;
145   PetscScalar    *v;
146   PetscBool      missing;
147 
148   PetscFunctionBegin;
149   if (Y->assembled) {
150     ierr = MatMissingDiagonal_SeqAIJ(Y,&missing,NULL);CHKERRQ(ierr);
151     if (!missing) {
152       diag = aij->diag;
153       ierr = VecGetArray(D,&v);CHKERRQ(ierr);
154       if (is == INSERT_VALUES) {
155         for (i=0; i<m; i++) {
156           aa[diag[i]] = v[i];
157         }
158       } else {
159         for (i=0; i<m; i++) {
160           aa[diag[i]] += v[i];
161         }
162       }
163       ierr = VecRestoreArray(D,&v);CHKERRQ(ierr);
164       PetscFunctionReturn(0);
165     }
166     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
167   }
168   ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
169   PetscFunctionReturn(0);
170 }
171 
172 #undef __FUNCT__
173 #define __FUNCT__ "MatGetRowIJ_SeqAIJ"
174 PetscErrorCode MatGetRowIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *m,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
175 {
176   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
177   PetscErrorCode ierr;
178   PetscInt       i,ishift;
179 
180   PetscFunctionBegin;
181   *m = A->rmap->n;
182   if (!ia) PetscFunctionReturn(0);
183   ishift = 0;
184   if (symmetric && !A->structurally_symmetric) {
185     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,ishift,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
186   } else if (oshift == 1) {
187     PetscInt *tia;
188     PetscInt nz = a->i[A->rmap->n];
189     /* malloc space and  add 1 to i and j indices */
190     ierr = PetscMalloc((A->rmap->n+1)*sizeof(PetscInt),&tia);CHKERRQ(ierr);
191     for (i=0; i<A->rmap->n+1; i++) tia[i] = a->i[i] + 1;
192     *ia = tia;
193     if (ja) {
194       PetscInt *tja;
195       ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&tja);CHKERRQ(ierr);
196       for (i=0; i<nz; i++) tja[i] = a->j[i] + 1;
197       *ja = tja;
198     }
199   } else {
200     *ia = a->i;
201     if (ja) *ja = a->j;
202   }
203   PetscFunctionReturn(0);
204 }
205 
206 #undef __FUNCT__
207 #define __FUNCT__ "MatRestoreRowIJ_SeqAIJ"
208 PetscErrorCode MatRestoreRowIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
209 {
210   PetscErrorCode ierr;
211 
212   PetscFunctionBegin;
213   if (!ia) PetscFunctionReturn(0);
214   if ((symmetric && !A->structurally_symmetric) || oshift == 1) {
215     ierr = PetscFree(*ia);CHKERRQ(ierr);
216     if (ja) {ierr = PetscFree(*ja);CHKERRQ(ierr);}
217   }
218   PetscFunctionReturn(0);
219 }
220 
221 #undef __FUNCT__
222 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ"
223 PetscErrorCode MatGetColumnIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
224 {
225   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
226   PetscErrorCode ierr;
227   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
228   PetscInt       nz = a->i[m],row,*jj,mr,col;
229 
230   PetscFunctionBegin;
231   *nn = n;
232   if (!ia) PetscFunctionReturn(0);
233   if (symmetric) {
234     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
235   } else {
236     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
237     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
238     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
239     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
240     jj   = a->j;
241     for (i=0; i<nz; i++) {
242       collengths[jj[i]]++;
243     }
244     cia[0] = oshift;
245     for (i=0; i<n; i++) {
246       cia[i+1] = cia[i] + collengths[i];
247     }
248     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
249     jj   = a->j;
250     for (row=0; row<m; row++) {
251       mr = a->i[row+1] - a->i[row];
252       for (i=0; i<mr; i++) {
253         col = *jj++;
254 
255         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
256       }
257     }
258     ierr = PetscFree(collengths);CHKERRQ(ierr);
259     *ia  = cia; *ja = cja;
260   }
261   PetscFunctionReturn(0);
262 }
263 
264 #undef __FUNCT__
265 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ"
266 PetscErrorCode MatRestoreColumnIJ_SeqAIJ(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
267 {
268   PetscErrorCode ierr;
269 
270   PetscFunctionBegin;
271   if (!ia) PetscFunctionReturn(0);
272 
273   ierr = PetscFree(*ia);CHKERRQ(ierr);
274   ierr = PetscFree(*ja);CHKERRQ(ierr);
275   PetscFunctionReturn(0);
276 }
277 
278 /*
279  MatGetColumnIJ_SeqAIJ_Color() and MatRestoreColumnIJ_SeqAIJ_Color() are customized from
280  MatGetColumnIJ_SeqAIJ() and MatRestoreColumnIJ_SeqAIJ() by adding an output
281  spidx[], index of a->a, to be used in MatTransposeColoringCreate_SeqAIJ() and MatFDColoringCreate_SeqAIJ()
282 */
283 #undef __FUNCT__
284 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ_Color"
285 PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *nn,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
286 {
287   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
288   PetscErrorCode ierr;
289   PetscInt       i,*collengths,*cia,*cja,n = A->cmap->n,m = A->rmap->n;
290   PetscInt       nz = a->i[m],row,*jj,mr,col;
291   PetscInt       *cspidx;
292 
293   PetscFunctionBegin;
294   *nn = n;
295   if (!ia) PetscFunctionReturn(0);
296   if (symmetric) {
297     SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatGetColumnIJ_SeqAIJ_Color() not supported for the case symmetric");
298     ierr = MatToSymmetricIJ_SeqAIJ(A->rmap->n,a->i,a->j,0,oshift,(PetscInt**)ia,(PetscInt**)ja);CHKERRQ(ierr);
299   } else {
300     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&collengths);CHKERRQ(ierr);
301     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
302     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&cia);CHKERRQ(ierr);
303     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cja);CHKERRQ(ierr);
304     ierr = PetscMalloc((nz+1)*sizeof(PetscInt),&cspidx);CHKERRQ(ierr);
305     jj   = a->j;
306     for (i=0; i<nz; i++) {
307       collengths[jj[i]]++;
308     }
309     cia[0] = oshift;
310     for (i=0; i<n; i++) {
311       cia[i+1] = cia[i] + collengths[i];
312     }
313     ierr = PetscMemzero(collengths,n*sizeof(PetscInt));CHKERRQ(ierr);
314     jj   = a->j;
315     for (row=0; row<m; row++) {
316       mr = a->i[row+1] - a->i[row];
317       for (i=0; i<mr; i++) {
318         col = *jj++;
319 
320         cspidx[cia[col] + collengths[col] - oshift] = a->i[row] + i; /* index of a->j */
321         cja[cia[col] + collengths[col]++ - oshift]  = row + oshift;
322       }
323     }
324     ierr   = PetscFree(collengths);CHKERRQ(ierr);
325     *ia    = cia; *ja = cja;
326     *spidx = cspidx;
327   }
328   PetscFunctionReturn(0);
329 }
330 
331 #undef __FUNCT__
332 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ_Color"
333 PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat A,PetscInt oshift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscInt *spidx[],PetscBool  *done)
334 {
335   PetscErrorCode ierr;
336 
337   PetscFunctionBegin;
338   if (!ia) PetscFunctionReturn(0);
339 
340   ierr = PetscFree(*ia);CHKERRQ(ierr);
341   ierr = PetscFree(*ja);CHKERRQ(ierr);
342   ierr = PetscFree(*spidx);CHKERRQ(ierr);
343   PetscFunctionReturn(0);
344 }
345 
346 #undef __FUNCT__
347 #define __FUNCT__ "MatSetValuesRow_SeqAIJ"
348 PetscErrorCode MatSetValuesRow_SeqAIJ(Mat A,PetscInt row,const PetscScalar v[])
349 {
350   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
351   PetscInt       *ai = a->i;
352   PetscErrorCode ierr;
353 
354   PetscFunctionBegin;
355   ierr = PetscMemcpy(a->a+ai[row],v,(ai[row+1]-ai[row])*sizeof(PetscScalar));CHKERRQ(ierr);
356   PetscFunctionReturn(0);
357 }
358 
359 #undef __FUNCT__
360 #define __FUNCT__ "MatSetValues_SeqAIJ"
361 PetscErrorCode MatSetValues_SeqAIJ(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
362 {
363   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
364   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
365   PetscInt       *imax = a->imax,*ai = a->i,*ailen = a->ilen;
366   PetscErrorCode ierr;
367   PetscInt       *aj = a->j,nonew = a->nonew,lastcol = -1;
368   MatScalar      *ap,value,*aa = a->a;
369   PetscBool      ignorezeroentries = a->ignorezeroentries;
370   PetscBool      roworiented       = a->roworiented;
371 
372   PetscFunctionBegin;
373   if (v) PetscValidScalarPointer(v,6);
374   for (k=0; k<m; k++) { /* loop over added rows */
375     row = im[k];
376     if (row < 0) continue;
377 #if defined(PETSC_USE_DEBUG)
378     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);
379 #endif
380     rp   = aj + ai[row]; ap = aa + ai[row];
381     rmax = imax[row]; nrow = ailen[row];
382     low  = 0;
383     high = nrow;
384     for (l=0; l<n; l++) { /* loop over added columns */
385       if (in[l] < 0) continue;
386 #if defined(PETSC_USE_DEBUG)
387       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);
388 #endif
389       col = in[l];
390       if (v) {
391         if (roworiented) {
392           value = v[l + k*n];
393         } else {
394           value = v[k + l*m];
395         }
396       } else {
397         value = 0.;
398       }
399       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
400 
401       if (col <= lastcol) low = 0;
402       else high = nrow;
403       lastcol = col;
404       while (high-low > 5) {
405         t = (low+high)/2;
406         if (rp[t] > col) high = t;
407         else low = t;
408       }
409       for (i=low; i<high; i++) {
410         if (rp[i] > col) break;
411         if (rp[i] == col) {
412           if (is == ADD_VALUES) ap[i] += value;
413           else ap[i] = value;
414           low = i + 1;
415           goto noinsert;
416         }
417       }
418       if (value == 0.0 && ignorezeroentries) goto noinsert;
419       if (nonew == 1) goto noinsert;
420       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at (%D,%D) in the matrix",row,col);
421       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
422       N = nrow++ - 1; a->nz++; high++;
423       /* shift up all the later entries in this row */
424       for (ii=N; ii>=i; ii--) {
425         rp[ii+1] = rp[ii];
426         ap[ii+1] = ap[ii];
427       }
428       rp[i] = col;
429       ap[i] = value;
430       low   = i + 1;
431 noinsert:;
432     }
433     ailen[row] = nrow;
434   }
435   A->same_nonzero = PETSC_FALSE;
436   PetscFunctionReturn(0);
437 }
438 
439 
440 #undef __FUNCT__
441 #define __FUNCT__ "MatGetValues_SeqAIJ"
442 PetscErrorCode MatGetValues_SeqAIJ(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],PetscScalar v[])
443 {
444   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
445   PetscInt   *rp,k,low,high,t,row,nrow,i,col,l,*aj = a->j;
446   PetscInt   *ai = a->i,*ailen = a->ilen;
447   MatScalar  *ap,*aa = a->a;
448 
449   PetscFunctionBegin;
450   for (k=0; k<m; k++) { /* loop over rows */
451     row = im[k];
452     if (row < 0) {v += n; continue;} /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",row); */
453     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);
454     rp   = aj + ai[row]; ap = aa + ai[row];
455     nrow = ailen[row];
456     for (l=0; l<n; l++) { /* loop over columns */
457       if (in[l] < 0) {v++; continue;} /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",in[l]); */
458       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);
459       col  = in[l];
460       high = nrow; low = 0; /* assume unsorted */
461       while (high-low > 5) {
462         t = (low+high)/2;
463         if (rp[t] > col) high = t;
464         else low = t;
465       }
466       for (i=low; i<high; i++) {
467         if (rp[i] > col) break;
468         if (rp[i] == col) {
469           *v++ = ap[i];
470           goto finished;
471         }
472       }
473       *v++ = 0.0;
474 finished:;
475     }
476   }
477   PetscFunctionReturn(0);
478 }
479 
480 
481 #undef __FUNCT__
482 #define __FUNCT__ "MatView_SeqAIJ_Binary"
483 PetscErrorCode MatView_SeqAIJ_Binary(Mat A,PetscViewer viewer)
484 {
485   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
486   PetscErrorCode ierr;
487   PetscInt       i,*col_lens;
488   int            fd;
489   FILE           *file;
490 
491   PetscFunctionBegin;
492   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
493   ierr = PetscMalloc((4+A->rmap->n)*sizeof(PetscInt),&col_lens);CHKERRQ(ierr);
494 
495   col_lens[0] = MAT_FILE_CLASSID;
496   col_lens[1] = A->rmap->n;
497   col_lens[2] = A->cmap->n;
498   col_lens[3] = a->nz;
499 
500   /* store lengths of each row and write (including header) to file */
501   for (i=0; i<A->rmap->n; i++) {
502     col_lens[4+i] = a->i[i+1] - a->i[i];
503   }
504   ierr = PetscBinaryWrite(fd,col_lens,4+A->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
505   ierr = PetscFree(col_lens);CHKERRQ(ierr);
506 
507   /* store column indices (zero start index) */
508   ierr = PetscBinaryWrite(fd,a->j,a->nz,PETSC_INT,PETSC_FALSE);CHKERRQ(ierr);
509 
510   /* store nonzero values */
511   ierr = PetscBinaryWrite(fd,a->a,a->nz,PETSC_SCALAR,PETSC_FALSE);CHKERRQ(ierr);
512 
513   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
514   if (file) {
515     fprintf(file,"-matload_block_size %d\n",(int)A->rmap->bs);
516   }
517   PetscFunctionReturn(0);
518 }
519 
520 extern PetscErrorCode MatSeqAIJFactorInfo_Matlab(Mat,PetscViewer);
521 
522 #undef __FUNCT__
523 #define __FUNCT__ "MatView_SeqAIJ_ASCII"
524 PetscErrorCode MatView_SeqAIJ_ASCII(Mat A,PetscViewer viewer)
525 {
526   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
527   PetscErrorCode    ierr;
528   PetscInt          i,j,m = A->rmap->n,shift=0;
529   const char        *name;
530   PetscViewerFormat format;
531 
532   PetscFunctionBegin;
533   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
534   if (format == PETSC_VIEWER_ASCII_MATLAB) {
535     PetscInt nofinalvalue = 0;
536     if (m && ((a->i[m] == a->i[m-1]) || (a->j[a->nz-1] != A->cmap->n-!shift))) {
537       nofinalvalue = 1;
538     }
539     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
540     ierr = PetscViewerASCIIPrintf(viewer,"%% Size = %D %D \n",m,A->cmap->n);CHKERRQ(ierr);
541     ierr = PetscViewerASCIIPrintf(viewer,"%% Nonzeros = %D \n",a->nz);CHKERRQ(ierr);
542     ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",a->nz+nofinalvalue);CHKERRQ(ierr);
543     ierr = PetscViewerASCIIPrintf(viewer,"zzz = [\n");CHKERRQ(ierr);
544 
545     for (i=0; i<m; i++) {
546       for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
547 #if defined(PETSC_USE_COMPLEX)
548         ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e + %18.16ei \n",i+1,a->j[j]+!shift,PetscRealPart(a->a[j]),PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
549 #else
550         ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",i+1,a->j[j]+!shift,a->a[j]);CHKERRQ(ierr);
551 #endif
552       }
553     }
554     if (nofinalvalue) {
555       ierr = PetscViewerASCIIPrintf(viewer,"%D %D  %18.16e\n",m,A->cmap->n,0.0);CHKERRQ(ierr);
556     }
557     ierr = PetscObjectGetName((PetscObject)A,&name);CHKERRQ(ierr);
558     ierr = PetscViewerASCIIPrintf(viewer,"];\n %s = spconvert(zzz);\n",name);CHKERRQ(ierr);
559     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
560   } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO || format == PETSC_VIEWER_ASCII_INFO) {
561     PetscFunctionReturn(0);
562   } else if (format == PETSC_VIEWER_ASCII_COMMON) {
563     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
564     ierr = PetscObjectPrintClassNamePrefixType((PetscObject)A,viewer);CHKERRQ(ierr);
565     for (i=0; i<m; i++) {
566       ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
567       for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
568 #if defined(PETSC_USE_COMPLEX)
569         if (PetscImaginaryPart(a->a[j]) > 0.0 && PetscRealPart(a->a[j]) != 0.0) {
570           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j]+shift,PetscRealPart(a->a[j]),PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
571         } else if (PetscImaginaryPart(a->a[j]) < 0.0 && PetscRealPart(a->a[j]) != 0.0) {
572           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j]+shift,PetscRealPart(a->a[j]),-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
573         } else if (PetscRealPart(a->a[j]) != 0.0) {
574           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j]+shift,PetscRealPart(a->a[j]));CHKERRQ(ierr);
575         }
576 #else
577         if (a->a[j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j]+shift,(double)a->a[j]);CHKERRQ(ierr);}
578 #endif
579       }
580       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
581     }
582     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
583   } else if (format == PETSC_VIEWER_ASCII_SYMMODU) {
584     PetscInt nzd=0,fshift=1,*sptr;
585     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
586     ierr = PetscObjectPrintClassNamePrefixType((PetscObject)A,viewer);CHKERRQ(ierr);
587     ierr = PetscMalloc((m+1)*sizeof(PetscInt),&sptr);CHKERRQ(ierr);
588     for (i=0; i<m; i++) {
589       sptr[i] = nzd+1;
590       for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
591         if (a->j[j] >= i) {
592 #if defined(PETSC_USE_COMPLEX)
593           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) nzd++;
594 #else
595           if (a->a[j] != 0.0) nzd++;
596 #endif
597         }
598       }
599     }
600     sptr[m] = nzd+1;
601     ierr    = PetscViewerASCIIPrintf(viewer," %D %D\n\n",m,nzd);CHKERRQ(ierr);
602     for (i=0; i<m+1; i+=6) {
603       if (i+4<m) {
604         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);
605       } else if (i+3<m) {
606         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);
607       } else if (i+2<m) {
608         ierr = PetscViewerASCIIPrintf(viewer," %D %D %D %D\n",sptr[i],sptr[i+1],sptr[i+2],sptr[i+3]);CHKERRQ(ierr);
609       } else if (i+1<m) {
610         ierr = PetscViewerASCIIPrintf(viewer," %D %D %D\n",sptr[i],sptr[i+1],sptr[i+2]);CHKERRQ(ierr);
611       } else if (i<m) {
612         ierr = PetscViewerASCIIPrintf(viewer," %D %D\n",sptr[i],sptr[i+1]);CHKERRQ(ierr);
613       } else {
614         ierr = PetscViewerASCIIPrintf(viewer," %D\n",sptr[i]);CHKERRQ(ierr);
615       }
616     }
617     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
618     ierr = PetscFree(sptr);CHKERRQ(ierr);
619     for (i=0; i<m; i++) {
620       for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
621         if (a->j[j] >= i) {ierr = PetscViewerASCIIPrintf(viewer," %D ",a->j[j]+fshift);CHKERRQ(ierr);}
622       }
623       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
624     }
625     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
626     for (i=0; i<m; i++) {
627       for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
628         if (a->j[j] >= i) {
629 #if defined(PETSC_USE_COMPLEX)
630           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) {
631             ierr = PetscViewerASCIIPrintf(viewer," %18.16e %18.16e ",PetscRealPart(a->a[j]),PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
632           }
633 #else
634           if (a->a[j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," %18.16e ",a->a[j]);CHKERRQ(ierr);}
635 #endif
636         }
637       }
638       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
639     }
640     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
641   } else if (format == PETSC_VIEWER_ASCII_DENSE) {
642     PetscInt    cnt = 0,jcnt;
643     PetscScalar value;
644 
645     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
646     ierr = PetscObjectPrintClassNamePrefixType((PetscObject)A,viewer);CHKERRQ(ierr);
647     for (i=0; i<m; i++) {
648       jcnt = 0;
649       for (j=0; j<A->cmap->n; j++) {
650         if (jcnt < a->i[i+1]-a->i[i] && j == a->j[cnt]) {
651           value = a->a[cnt++];
652           jcnt++;
653         } else {
654           value = 0.0;
655         }
656 #if defined(PETSC_USE_COMPLEX)
657         ierr = PetscViewerASCIIPrintf(viewer," %7.5e+%7.5e i ",PetscRealPart(value),PetscImaginaryPart(value));CHKERRQ(ierr);
658 #else
659         ierr = PetscViewerASCIIPrintf(viewer," %7.5e ",value);CHKERRQ(ierr);
660 #endif
661       }
662       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
663     }
664     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
665   } else if (format == PETSC_VIEWER_ASCII_MATRIXMARKET) {
666     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
667     ierr = PetscObjectPrintClassNamePrefixType((PetscObject)A,viewer);CHKERRQ(ierr);
668 #if defined(PETSC_USE_COMPLEX)
669     ierr = PetscViewerASCIIPrintf(viewer,"%%matrix complex general\n");CHKERRQ(ierr);
670 #else
671     ierr = PetscViewerASCIIPrintf(viewer,"%%matrix real general\n");CHKERRQ(ierr);
672 #endif
673     ierr = PetscViewerASCIIPrintf(viewer,"%D %D %D\n", m, A->cmap->n, a->nz);CHKERRQ(ierr);
674     for (i=0; i<m; i++) {
675       for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
676 #if defined(PETSC_USE_COMPLEX)
677         if (PetscImaginaryPart(a->a[j]) > 0.0) {
678           ierr = PetscViewerASCIIPrintf(viewer,"%D %D, %g %g\n", i+shift,a->j[j]+shift,PetscRealPart(a->a[j]),PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
679         } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
680           ierr = PetscViewerASCIIPrintf(viewer,"%D %D, %g -%g\n", i+shift,a->j[j]+shift,PetscRealPart(a->a[j]),-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
681         } else {
682           ierr = PetscViewerASCIIPrintf(viewer,"%D %D, %g\n", i+shift,a->j[j]+shift,PetscRealPart(a->a[j]));CHKERRQ(ierr);
683         }
684 #else
685         ierr = PetscViewerASCIIPrintf(viewer,"%D %D %g\n", i+shift, a->j[j]+shift, (double)a->a[j]);CHKERRQ(ierr);
686 #endif
687       }
688     }
689     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
690   } else {
691     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
692     ierr = PetscObjectPrintClassNamePrefixType((PetscObject)A,viewer);CHKERRQ(ierr);
693     if (A->factortype) {
694       for (i=0; i<m; i++) {
695         ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
696         /* L part */
697         for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
698 #if defined(PETSC_USE_COMPLEX)
699           if (PetscImaginaryPart(a->a[j]) > 0.0) {
700             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j]+shift,PetscRealPart(a->a[j]),PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
701           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
702             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j]+shift,PetscRealPart(a->a[j]),-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
703           } else {
704             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j]+shift,PetscRealPart(a->a[j]));CHKERRQ(ierr);
705           }
706 #else
707           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j]+shift,(double)a->a[j]);CHKERRQ(ierr);
708 #endif
709         }
710         /* diagonal */
711         j = a->diag[i];
712 #if defined(PETSC_USE_COMPLEX)
713         if (PetscImaginaryPart(a->a[j]) > 0.0) {
714           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j]+shift,PetscRealPart(1.0/a->a[j]),PetscImaginaryPart(1.0/a->a[j]));CHKERRQ(ierr);
715         } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
716           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j]+shift,PetscRealPart(1.0/a->a[j]),-PetscImaginaryPart(1.0/a->a[j]));CHKERRQ(ierr);
717         } else {
718           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j]+shift,PetscRealPart(1.0/a->a[j]));CHKERRQ(ierr);
719         }
720 #else
721         ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j]+shift,(double)1.0/a->a[j]);CHKERRQ(ierr);
722 #endif
723 
724         /* U part */
725         for (j=a->diag[i+1]+1+shift; j<a->diag[i]+shift; j++) {
726 #if defined(PETSC_USE_COMPLEX)
727           if (PetscImaginaryPart(a->a[j]) > 0.0) {
728             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j]+shift,PetscRealPart(a->a[j]),PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
729           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
730             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j]+shift,PetscRealPart(a->a[j]),-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
731           } else {
732             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j]+shift,PetscRealPart(a->a[j]));CHKERRQ(ierr);
733           }
734 #else
735           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j]+shift,(double)a->a[j]);CHKERRQ(ierr);
736 #endif
737         }
738         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
739       }
740     } else {
741       for (i=0; i<m; i++) {
742         ierr = PetscViewerASCIIPrintf(viewer,"row %D:",i);CHKERRQ(ierr);
743         for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
744 #if defined(PETSC_USE_COMPLEX)
745           if (PetscImaginaryPart(a->a[j]) > 0.0) {
746             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g + %g i)",a->j[j]+shift,PetscRealPart(a->a[j]),PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
747           } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
748             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g - %g i)",a->j[j]+shift,PetscRealPart(a->a[j]),-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
749           } else {
750             ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j]+shift,PetscRealPart(a->a[j]));CHKERRQ(ierr);
751           }
752 #else
753           ierr = PetscViewerASCIIPrintf(viewer," (%D, %g) ",a->j[j]+shift,(double)a->a[j]);CHKERRQ(ierr);
754 #endif
755         }
756         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
757       }
758     }
759     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
760   }
761   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
762   PetscFunctionReturn(0);
763 }
764 
765 #include <petscdraw.h>
766 #undef __FUNCT__
767 #define __FUNCT__ "MatView_SeqAIJ_Draw_Zoom"
768 PetscErrorCode MatView_SeqAIJ_Draw_Zoom(PetscDraw draw,void *Aa)
769 {
770   Mat               A  = (Mat) Aa;
771   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
772   PetscErrorCode    ierr;
773   PetscInt          i,j,m = A->rmap->n,color;
774   PetscReal         xl,yl,xr,yr,x_l,x_r,y_l,y_r,maxv = 0.0;
775   PetscViewer       viewer;
776   PetscViewerFormat format;
777 
778   PetscFunctionBegin;
779   ierr = PetscObjectQuery((PetscObject)A,"Zoomviewer",(PetscObject*)&viewer);CHKERRQ(ierr);
780   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
781 
782   ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
783   /* loop over matrix elements drawing boxes */
784 
785   if (format != PETSC_VIEWER_DRAW_CONTOUR) {
786     /* Blue for negative, Cyan for zero and  Red for positive */
787     color = PETSC_DRAW_BLUE;
788     for (i=0; i<m; i++) {
789       y_l = m - i - 1.0; y_r = y_l + 1.0;
790       for (j=a->i[i]; j<a->i[i+1]; j++) {
791         x_l = a->j[j]; x_r = x_l + 1.0;
792         if (PetscRealPart(a->a[j]) >=  0.) continue;
793         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
794       }
795     }
796     color = PETSC_DRAW_CYAN;
797     for (i=0; i<m; i++) {
798       y_l = m - i - 1.0; y_r = y_l + 1.0;
799       for (j=a->i[i]; j<a->i[i+1]; j++) {
800         x_l = a->j[j]; x_r = x_l + 1.0;
801         if (a->a[j] !=  0.) continue;
802         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
803       }
804     }
805     color = PETSC_DRAW_RED;
806     for (i=0; i<m; i++) {
807       y_l = m - i - 1.0; y_r = y_l + 1.0;
808       for (j=a->i[i]; j<a->i[i+1]; j++) {
809         x_l = a->j[j]; x_r = x_l + 1.0;
810         if (PetscRealPart(a->a[j]) <=  0.) continue;
811         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
812       }
813     }
814   } else {
815     /* use contour shading to indicate magnitude of values */
816     /* first determine max of all nonzero values */
817     PetscInt  nz = a->nz,count;
818     PetscDraw popup;
819     PetscReal scale;
820 
821     for (i=0; i<nz; i++) {
822       if (PetscAbsScalar(a->a[i]) > maxv) maxv = PetscAbsScalar(a->a[i]);
823     }
824     scale = (245.0 - PETSC_DRAW_BASIC_COLORS)/maxv;
825     ierr  = PetscDrawGetPopup(draw,&popup);CHKERRQ(ierr);
826     if (popup) {
827       ierr = PetscDrawScalePopup(popup,0.0,maxv);CHKERRQ(ierr);
828     }
829     count = 0;
830     for (i=0; i<m; i++) {
831       y_l = m - i - 1.0; y_r = y_l + 1.0;
832       for (j=a->i[i]; j<a->i[i+1]; j++) {
833         x_l   = a->j[j]; x_r = x_l + 1.0;
834         color = PETSC_DRAW_BASIC_COLORS + (PetscInt)(scale*PetscAbsScalar(a->a[count]));
835         ierr  = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
836         count++;
837       }
838     }
839   }
840   PetscFunctionReturn(0);
841 }
842 
843 #include <petscdraw.h>
844 #undef __FUNCT__
845 #define __FUNCT__ "MatView_SeqAIJ_Draw"
846 PetscErrorCode MatView_SeqAIJ_Draw(Mat A,PetscViewer viewer)
847 {
848   PetscErrorCode ierr;
849   PetscDraw      draw;
850   PetscReal      xr,yr,xl,yl,h,w;
851   PetscBool      isnull;
852 
853   PetscFunctionBegin;
854   ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
855   ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
856   if (isnull) PetscFunctionReturn(0);
857 
858   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",(PetscObject)viewer);CHKERRQ(ierr);
859   xr   = A->cmap->n; yr = A->rmap->n; h = yr/10.0; w = xr/10.0;
860   xr  += w;    yr += h;  xl = -w;     yl = -h;
861   ierr = PetscDrawSetCoordinates(draw,xl,yl,xr,yr);CHKERRQ(ierr);
862   ierr = PetscDrawZoom(draw,MatView_SeqAIJ_Draw_Zoom,A);CHKERRQ(ierr);
863   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",NULL);CHKERRQ(ierr);
864   PetscFunctionReturn(0);
865 }
866 
867 #undef __FUNCT__
868 #define __FUNCT__ "MatView_SeqAIJ"
869 PetscErrorCode MatView_SeqAIJ(Mat A,PetscViewer viewer)
870 {
871   PetscErrorCode ierr;
872   PetscBool      iascii,isbinary,isdraw;
873 
874   PetscFunctionBegin;
875   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
876   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
877   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
878   if (iascii) {
879     ierr = MatView_SeqAIJ_ASCII(A,viewer);CHKERRQ(ierr);
880   } else if (isbinary) {
881     ierr = MatView_SeqAIJ_Binary(A,viewer);CHKERRQ(ierr);
882   } else if (isdraw) {
883     ierr = MatView_SeqAIJ_Draw(A,viewer);CHKERRQ(ierr);
884   }
885   ierr = MatView_SeqAIJ_Inode(A,viewer);CHKERRQ(ierr);
886   PetscFunctionReturn(0);
887 }
888 
889 #undef __FUNCT__
890 #define __FUNCT__ "MatAssemblyEnd_SeqAIJ"
891 PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat A,MatAssemblyType mode)
892 {
893   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
894   PetscErrorCode ierr;
895   PetscInt       fshift = 0,i,j,*ai = a->i,*aj = a->j,*imax = a->imax;
896   PetscInt       m      = A->rmap->n,*ip,N,*ailen = a->ilen,rmax = 0;
897   MatScalar      *aa    = a->a,*ap;
898   PetscReal      ratio  = 0.6;
899 
900   PetscFunctionBegin;
901   if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(0);
902 
903   if (m) rmax = ailen[0]; /* determine row with most nonzeros */
904   for (i=1; i<m; i++) {
905     /* move each row back by the amount of empty slots (fshift) before it*/
906     fshift += imax[i-1] - ailen[i-1];
907     rmax    = PetscMax(rmax,ailen[i]);
908     if (fshift) {
909       ip = aj + ai[i];
910       ap = aa + ai[i];
911       N  = ailen[i];
912       for (j=0; j<N; j++) {
913         ip[j-fshift] = ip[j];
914         ap[j-fshift] = ap[j];
915       }
916     }
917     ai[i] = ai[i-1] + ailen[i-1];
918   }
919   if (m) {
920     fshift += imax[m-1] - ailen[m-1];
921     ai[m]   = ai[m-1] + ailen[m-1];
922   }
923   /* reset ilen and imax for each row */
924   for (i=0; i<m; i++) {
925     ailen[i] = imax[i] = ai[i+1] - ai[i];
926   }
927   a->nz = ai[m];
928   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);
929 
930   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
931   ierr = PetscInfo4(A,"Matrix size: %D X %D; storage space: %D unneeded,%D used\n",m,A->cmap->n,fshift,a->nz);CHKERRQ(ierr);
932   ierr = PetscInfo1(A,"Number of mallocs during MatSetValues() is %D\n",a->reallocs);CHKERRQ(ierr);
933   ierr = PetscInfo1(A,"Maximum nonzeros in any row is %D\n",rmax);CHKERRQ(ierr);
934 
935   A->info.mallocs    += a->reallocs;
936   a->reallocs         = 0;
937   A->info.nz_unneeded = (double)fshift;
938   a->rmax             = rmax;
939 
940   ierr = MatCheckCompressedRow(A,&a->compressedrow,a->i,m,ratio);CHKERRQ(ierr);
941 
942   A->same_nonzero = PETSC_TRUE;
943 
944   ierr = MatAssemblyEnd_SeqAIJ_Inode(A,mode);CHKERRQ(ierr);
945 
946   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
947   PetscFunctionReturn(0);
948 }
949 
950 #undef __FUNCT__
951 #define __FUNCT__ "MatRealPart_SeqAIJ"
952 PetscErrorCode MatRealPart_SeqAIJ(Mat A)
953 {
954   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
955   PetscInt       i,nz = a->nz;
956   MatScalar      *aa = a->a;
957   PetscErrorCode ierr;
958 
959   PetscFunctionBegin;
960   for (i=0; i<nz; i++) aa[i] = PetscRealPart(aa[i]);
961   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
962   PetscFunctionReturn(0);
963 }
964 
965 #undef __FUNCT__
966 #define __FUNCT__ "MatImaginaryPart_SeqAIJ"
967 PetscErrorCode MatImaginaryPart_SeqAIJ(Mat A)
968 {
969   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
970   PetscInt       i,nz = a->nz;
971   MatScalar      *aa = a->a;
972   PetscErrorCode ierr;
973 
974   PetscFunctionBegin;
975   for (i=0; i<nz; i++) aa[i] = PetscImaginaryPart(aa[i]);
976   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
977   PetscFunctionReturn(0);
978 }
979 
980 #if defined(PETSC_THREADCOMM_ACTIVE)
981 PetscErrorCode MatZeroEntries_SeqAIJ_Kernel(PetscInt thread_id,Mat A)
982 {
983   PetscErrorCode ierr;
984   PetscInt       *trstarts=A->rmap->trstarts;
985   PetscInt       n,start,end;
986   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
987 
988   start = trstarts[thread_id];
989   end   = trstarts[thread_id+1];
990   n     = a->i[end] - a->i[start];
991   ierr  = PetscMemzero(a->a+a->i[start],n*sizeof(PetscScalar));CHKERRQ(ierr);
992   return 0;
993 }
994 
995 #undef __FUNCT__
996 #define __FUNCT__ "MatZeroEntries_SeqAIJ"
997 PetscErrorCode MatZeroEntries_SeqAIJ(Mat A)
998 {
999   PetscErrorCode ierr;
1000 
1001   PetscFunctionBegin;
1002   ierr = PetscThreadCommRunKernel(PetscObjectComm((PetscObject)A),(PetscThreadKernel)MatZeroEntries_SeqAIJ_Kernel,1,A);CHKERRQ(ierr);
1003   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1004   PetscFunctionReturn(0);
1005 }
1006 #else
1007 #undef __FUNCT__
1008 #define __FUNCT__ "MatZeroEntries_SeqAIJ"
1009 PetscErrorCode MatZeroEntries_SeqAIJ(Mat A)
1010 {
1011   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1012   PetscErrorCode ierr;
1013 
1014   PetscFunctionBegin;
1015   ierr = PetscMemzero(a->a,(a->i[A->rmap->n])*sizeof(PetscScalar));CHKERRQ(ierr);
1016   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
1017   PetscFunctionReturn(0);
1018 }
1019 #endif
1020 
1021 #undef __FUNCT__
1022 #define __FUNCT__ "MatDestroy_SeqAIJ"
1023 PetscErrorCode MatDestroy_SeqAIJ(Mat A)
1024 {
1025   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1026   PetscErrorCode ierr;
1027 
1028   PetscFunctionBegin;
1029 #if defined(PETSC_USE_LOG)
1030   PetscLogObjectState((PetscObject)A,"Rows=%D, Cols=%D, NZ=%D",A->rmap->n,A->cmap->n,a->nz);
1031 #endif
1032   ierr = MatSeqXAIJFreeAIJ(A,&a->a,&a->j,&a->i);CHKERRQ(ierr);
1033   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
1034   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
1035   ierr = PetscFree(a->diag);CHKERRQ(ierr);
1036   ierr = PetscFree(a->ibdiag);CHKERRQ(ierr);
1037   ierr = PetscFree2(a->imax,a->ilen);CHKERRQ(ierr);
1038   ierr = PetscFree3(a->idiag,a->mdiag,a->ssor_work);CHKERRQ(ierr);
1039   ierr = PetscFree(a->solve_work);CHKERRQ(ierr);
1040   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
1041   ierr = PetscFree(a->saved_values);CHKERRQ(ierr);
1042   ierr = ISColoringDestroy(&a->coloring);CHKERRQ(ierr);
1043   ierr = PetscFree(a->xtoy);CHKERRQ(ierr);
1044   ierr = MatDestroy(&a->XtoY);CHKERRQ(ierr);
1045   ierr = PetscFree2(a->compressedrow.i,a->compressedrow.rindex);CHKERRQ(ierr);
1046   ierr = PetscFree(a->matmult_abdense);CHKERRQ(ierr);
1047 
1048   ierr = MatDestroy_SeqAIJ_Inode(A);CHKERRQ(ierr);
1049   ierr = PetscFree(A->data);CHKERRQ(ierr);
1050 
1051   ierr = PetscObjectChangeTypeName((PetscObject)A,0);CHKERRQ(ierr);
1052   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetColumnIndices_C",NULL);CHKERRQ(ierr);
1053   ierr = PetscObjectComposeFunction((PetscObject)A,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1054   ierr = PetscObjectComposeFunction((PetscObject)A,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1055   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqsbaij_C",NULL);CHKERRQ(ierr);
1056   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqbaij_C",NULL);CHKERRQ(ierr);
1057   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqaij_seqaijperm_C",NULL);CHKERRQ(ierr);
1058   ierr = PetscObjectComposeFunction((PetscObject)A,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1059   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1060   ierr = PetscObjectComposeFunction((PetscObject)A,"MatSeqAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1061   ierr = PetscObjectComposeFunction((PetscObject)A,"MatReorderForNonzeroDiagonal_C",NULL);CHKERRQ(ierr);
1062   PetscFunctionReturn(0);
1063 }
1064 
1065 #undef __FUNCT__
1066 #define __FUNCT__ "MatSetOption_SeqAIJ"
1067 PetscErrorCode MatSetOption_SeqAIJ(Mat A,MatOption op,PetscBool flg)
1068 {
1069   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1070   PetscErrorCode ierr;
1071 
1072   PetscFunctionBegin;
1073   switch (op) {
1074   case MAT_ROW_ORIENTED:
1075     a->roworiented = flg;
1076     break;
1077   case MAT_KEEP_NONZERO_PATTERN:
1078     a->keepnonzeropattern = flg;
1079     break;
1080   case MAT_NEW_NONZERO_LOCATIONS:
1081     a->nonew = (flg ? 0 : 1);
1082     break;
1083   case MAT_NEW_NONZERO_LOCATION_ERR:
1084     a->nonew = (flg ? -1 : 0);
1085     break;
1086   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1087     a->nonew = (flg ? -2 : 0);
1088     break;
1089   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1090     a->nounused = (flg ? -1 : 0);
1091     break;
1092   case MAT_IGNORE_ZERO_ENTRIES:
1093     a->ignorezeroentries = flg;
1094     break;
1095   case MAT_CHECK_COMPRESSED_ROW:
1096     a->compressedrow.check = flg;
1097     break;
1098   case MAT_SPD:
1099   case MAT_SYMMETRIC:
1100   case MAT_STRUCTURALLY_SYMMETRIC:
1101   case MAT_HERMITIAN:
1102   case MAT_SYMMETRY_ETERNAL:
1103     /* These options are handled directly by MatSetOption() */
1104     break;
1105   case MAT_NEW_DIAGONALS:
1106   case MAT_IGNORE_OFF_PROC_ENTRIES:
1107   case MAT_USE_HASH_TABLE:
1108     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1109     break;
1110   case MAT_USE_INODES:
1111     /* Not an error because MatSetOption_SeqAIJ_Inode handles this one */
1112     break;
1113   default:
1114     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1115   }
1116   ierr = MatSetOption_SeqAIJ_Inode(A,op,flg);CHKERRQ(ierr);
1117   PetscFunctionReturn(0);
1118 }
1119 
1120 #undef __FUNCT__
1121 #define __FUNCT__ "MatGetDiagonal_SeqAIJ"
1122 PetscErrorCode MatGetDiagonal_SeqAIJ(Mat A,Vec v)
1123 {
1124   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1125   PetscErrorCode ierr;
1126   PetscInt       i,j,n,*ai=a->i,*aj=a->j,nz;
1127   PetscScalar    *aa=a->a,*x,zero=0.0;
1128 
1129   PetscFunctionBegin;
1130   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
1131   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
1132 
1133   if (A->factortype == MAT_FACTOR_ILU || A->factortype == MAT_FACTOR_LU) {
1134     PetscInt *diag=a->diag;
1135     ierr = VecGetArray(v,&x);CHKERRQ(ierr);
1136     for (i=0; i<n; i++) x[i] = 1.0/aa[diag[i]];
1137     ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1138     PetscFunctionReturn(0);
1139   }
1140 
1141   ierr = VecSet(v,zero);CHKERRQ(ierr);
1142   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
1143   for (i=0; i<n; i++) {
1144     nz = ai[i+1] - ai[i];
1145     if (!nz) x[i] = 0.0;
1146     for (j=ai[i]; j<ai[i+1]; j++) {
1147       if (aj[j] == i) {
1148         x[i] = aa[j];
1149         break;
1150       }
1151     }
1152   }
1153   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1154   PetscFunctionReturn(0);
1155 }
1156 
1157 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1158 #undef __FUNCT__
1159 #define __FUNCT__ "MatMultTransposeAdd_SeqAIJ"
1160 PetscErrorCode MatMultTransposeAdd_SeqAIJ(Mat A,Vec xx,Vec zz,Vec yy)
1161 {
1162   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1163   PetscScalar    *x,*y;
1164   PetscErrorCode ierr;
1165   PetscInt       m = A->rmap->n;
1166 #if !defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1167   MatScalar         *v;
1168   PetscScalar       alpha;
1169   PetscInt          n,i,j,*idx,*ii,*ridx=NULL;
1170   Mat_CompressedRow cprow    = a->compressedrow;
1171   PetscBool         usecprow = cprow.use;
1172 #endif
1173 
1174   PetscFunctionBegin;
1175   if (zz != yy) {ierr = VecCopy(zz,yy);CHKERRQ(ierr);}
1176   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1177   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1178 
1179 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
1180   fortranmulttransposeaddaij_(&m,x,a->i,a->j,a->a,y);
1181 #else
1182   if (usecprow) {
1183     m    = cprow.nrows;
1184     ii   = cprow.i;
1185     ridx = cprow.rindex;
1186   } else {
1187     ii = a->i;
1188   }
1189   for (i=0; i<m; i++) {
1190     idx = a->j + ii[i];
1191     v   = a->a + ii[i];
1192     n   = ii[i+1] - ii[i];
1193     if (usecprow) {
1194       alpha = x[ridx[i]];
1195     } else {
1196       alpha = x[i];
1197     }
1198     for (j=0; j<n; j++) y[idx[j]] += alpha*v[j];
1199   }
1200 #endif
1201   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1202   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1203   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1204   PetscFunctionReturn(0);
1205 }
1206 
1207 #undef __FUNCT__
1208 #define __FUNCT__ "MatMultTranspose_SeqAIJ"
1209 PetscErrorCode MatMultTranspose_SeqAIJ(Mat A,Vec xx,Vec yy)
1210 {
1211   PetscErrorCode ierr;
1212 
1213   PetscFunctionBegin;
1214   ierr = VecSet(yy,0.0);CHKERRQ(ierr);
1215   ierr = MatMultTransposeAdd_SeqAIJ(A,xx,yy,yy);CHKERRQ(ierr);
1216   PetscFunctionReturn(0);
1217 }
1218 
1219 #include <../src/mat/impls/aij/seq/ftn-kernels/fmult.h>
1220 #if defined(PETSC_THREADCOMM_ACTIVE)
1221 PetscErrorCode MatMult_SeqAIJ_Kernel(PetscInt thread_id,Mat A,Vec xx,Vec yy)
1222 {
1223   PetscErrorCode    ierr;
1224   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1225   PetscScalar       *y;
1226   const PetscScalar *x;
1227   const MatScalar   *aa;
1228   PetscInt          *trstarts=A->rmap->trstarts;
1229   PetscInt          n,start,end,i;
1230   const PetscInt    *aj,*ai;
1231   PetscScalar       sum;
1232 
1233   ierr  = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1234   ierr  = VecGetArray(yy,&y);CHKERRQ(ierr);
1235   start = trstarts[thread_id];
1236   end   = trstarts[thread_id+1];
1237   aj    = a->j;
1238   aa    = a->a;
1239   ai    = a->i;
1240   for (i=start; i<end; i++) {
1241     n   = ai[i+1] - ai[i];
1242     aj  = a->j + ai[i];
1243     aa  = a->a + ai[i];
1244     sum = 0.0;
1245     PetscSparseDensePlusDot(sum,x,aa,aj,n);
1246     y[i] = sum;
1247   }
1248   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1249   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1250   return 0;
1251 }
1252 
1253 #undef __FUNCT__
1254 #define __FUNCT__ "MatMult_SeqAIJ"
1255 PetscErrorCode MatMult_SeqAIJ(Mat A,Vec xx,Vec yy)
1256 {
1257   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1258   PetscScalar       *y;
1259   const PetscScalar *x;
1260   const MatScalar   *aa;
1261   PetscErrorCode    ierr;
1262   PetscInt          m=A->rmap->n;
1263   const PetscInt    *aj,*ii,*ridx=NULL;
1264   PetscInt          n,i,nonzerorow=0;
1265   PetscScalar       sum;
1266   PetscBool         usecprow=a->compressedrow.use;
1267 
1268 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1269 #pragma disjoint(*x,*y,*aa)
1270 #endif
1271 
1272   PetscFunctionBegin;
1273   aj = a->j;
1274   aa = a->a;
1275   ii = a->i;
1276   if (usecprow) { /* use compressed row format */
1277     ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1278     ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1279     m    = a->compressedrow.nrows;
1280     ii   = a->compressedrow.i;
1281     ridx = a->compressedrow.rindex;
1282     for (i=0; i<m; i++) {
1283       n           = ii[i+1] - ii[i];
1284       aj          = a->j + ii[i];
1285       aa          = a->a + ii[i];
1286       sum         = 0.0;
1287       nonzerorow += (n>0);
1288       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1289       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1290       y[*ridx++] = sum;
1291     }
1292     ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1293     ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1294   } else { /* do not use compressed row format */
1295 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJ)
1296     fortranmultaij_(&m,x,ii,aj,aa,y);
1297 #else
1298     ierr = PetscThreadCommRunKernel(PetscObjectComm((PetscObject)A),(PetscThreadKernel)MatMult_SeqAIJ_Kernel,3,A,xx,yy);CHKERRQ(ierr);
1299 #endif
1300   }
1301   ierr = PetscLogFlops(2.0*a->nz - nonzerorow);CHKERRQ(ierr);
1302   PetscFunctionReturn(0);
1303 }
1304 #else
1305 #undef __FUNCT__
1306 #define __FUNCT__ "MatMult_SeqAIJ"
1307 PetscErrorCode MatMult_SeqAIJ(Mat A,Vec xx,Vec yy)
1308 {
1309   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1310   PetscScalar       *y;
1311   const PetscScalar *x;
1312   const MatScalar   *aa;
1313   PetscErrorCode    ierr;
1314   PetscInt          m=A->rmap->n;
1315   const PetscInt    *aj,*ii,*ridx=NULL;
1316   PetscInt          n,i,nonzerorow=0;
1317   PetscScalar       sum;
1318   PetscBool         usecprow=a->compressedrow.use;
1319 
1320 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1321 #pragma disjoint(*x,*y,*aa)
1322 #endif
1323 
1324   PetscFunctionBegin;
1325   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1326   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1327   aj   = a->j;
1328   aa   = a->a;
1329   ii   = a->i;
1330   if (usecprow) { /* use compressed row format */
1331     m    = a->compressedrow.nrows;
1332     ii   = a->compressedrow.i;
1333     ridx = a->compressedrow.rindex;
1334     for (i=0; i<m; i++) {
1335       n           = ii[i+1] - ii[i];
1336       aj          = a->j + ii[i];
1337       aa          = a->a + ii[i];
1338       sum         = 0.0;
1339       nonzerorow += (n>0);
1340       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1341       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1342       y[*ridx++] = sum;
1343     }
1344   } else { /* do not use compressed row format */
1345 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJ)
1346     fortranmultaij_(&m,x,ii,aj,aa,y);
1347 #else
1348 #if defined(PETSC_THREADCOMM_ACTIVE)
1349     ierr = PetscThreadCommRunKernel(PetscObjectComm((PetscObject)A),(PetscThreadKernel)MatMult_SeqAIJ_Kernel,3,A,xx,yy);CHKERRQ(ierr);
1350 #else
1351     for (i=0; i<m; i++) {
1352       n           = ii[i+1] - ii[i];
1353       aj          = a->j + ii[i];
1354       aa          = a->a + ii[i];
1355       sum         = 0.0;
1356       nonzerorow += (n>0);
1357       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1358       y[i] = sum;
1359     }
1360 #endif
1361 #endif
1362   }
1363   ierr = PetscLogFlops(2.0*a->nz - nonzerorow);CHKERRQ(ierr);
1364   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1365   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1366   PetscFunctionReturn(0);
1367 }
1368 #endif
1369 
1370 #undef __FUNCT__
1371 #define __FUNCT__ "MatMultMax_SeqAIJ"
1372 PetscErrorCode MatMultMax_SeqAIJ(Mat A,Vec xx,Vec yy)
1373 {
1374   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1375   PetscScalar       *y;
1376   const PetscScalar *x;
1377   const MatScalar   *aa;
1378   PetscErrorCode    ierr;
1379   PetscInt          m=A->rmap->n;
1380   const PetscInt    *aj,*ii,*ridx=NULL;
1381   PetscInt          n,i,nonzerorow=0;
1382   PetscScalar       sum;
1383   PetscBool         usecprow=a->compressedrow.use;
1384 
1385 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
1386 #pragma disjoint(*x,*y,*aa)
1387 #endif
1388 
1389   PetscFunctionBegin;
1390   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1391   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1392   aj   = a->j;
1393   aa   = a->a;
1394   ii   = a->i;
1395   if (usecprow) { /* use compressed row format */
1396     m    = a->compressedrow.nrows;
1397     ii   = a->compressedrow.i;
1398     ridx = a->compressedrow.rindex;
1399     for (i=0; i<m; i++) {
1400       n           = ii[i+1] - ii[i];
1401       aj          = a->j + ii[i];
1402       aa          = a->a + ii[i];
1403       sum         = 0.0;
1404       nonzerorow += (n>0);
1405       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1406       /* for (j=0; j<n; j++) sum += (*aa++)*x[*aj++]; */
1407       y[*ridx++] = sum;
1408     }
1409   } else { /* do not use compressed row format */
1410     for (i=0; i<m; i++) {
1411       n           = ii[i+1] - ii[i];
1412       aj          = a->j + ii[i];
1413       aa          = a->a + ii[i];
1414       sum         = 0.0;
1415       nonzerorow += (n>0);
1416       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1417       y[i] = sum;
1418     }
1419   }
1420   ierr = PetscLogFlops(2.0*a->nz - nonzerorow);CHKERRQ(ierr);
1421   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1422   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1423   PetscFunctionReturn(0);
1424 }
1425 
1426 #undef __FUNCT__
1427 #define __FUNCT__ "MatMultAddMax_SeqAIJ"
1428 PetscErrorCode MatMultAddMax_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1429 {
1430   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1431   PetscScalar       *y,*z;
1432   const PetscScalar *x;
1433   const MatScalar   *aa;
1434   PetscErrorCode    ierr;
1435   PetscInt          m = A->rmap->n,*aj,*ii;
1436   PetscInt          n,i,*ridx=NULL;
1437   PetscScalar       sum;
1438   PetscBool         usecprow=a->compressedrow.use;
1439 
1440   PetscFunctionBegin;
1441   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1442   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1443   if (zz != yy) {
1444     ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
1445   } else {
1446     z = y;
1447   }
1448 
1449   aj = a->j;
1450   aa = a->a;
1451   ii = a->i;
1452   if (usecprow) { /* use compressed row format */
1453     if (zz != yy) {
1454       ierr = PetscMemcpy(z,y,m*sizeof(PetscScalar));CHKERRQ(ierr);
1455     }
1456     m    = a->compressedrow.nrows;
1457     ii   = a->compressedrow.i;
1458     ridx = a->compressedrow.rindex;
1459     for (i=0; i<m; i++) {
1460       n   = ii[i+1] - ii[i];
1461       aj  = a->j + ii[i];
1462       aa  = a->a + ii[i];
1463       sum = y[*ridx];
1464       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1465       z[*ridx++] = sum;
1466     }
1467   } else { /* do not use compressed row format */
1468     for (i=0; i<m; i++) {
1469       n   = ii[i+1] - ii[i];
1470       aj  = a->j + ii[i];
1471       aa  = a->a + ii[i];
1472       sum = y[i];
1473       PetscSparseDenseMaxDot(sum,x,aa,aj,n);
1474       z[i] = sum;
1475     }
1476   }
1477   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1478   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1479   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1480   if (zz != yy) {
1481     ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
1482   }
1483   PetscFunctionReturn(0);
1484 }
1485 
1486 #include <../src/mat/impls/aij/seq/ftn-kernels/fmultadd.h>
1487 #undef __FUNCT__
1488 #define __FUNCT__ "MatMultAdd_SeqAIJ"
1489 PetscErrorCode MatMultAdd_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1490 {
1491   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1492   PetscScalar       *y,*z;
1493   const PetscScalar *x;
1494   const MatScalar   *aa;
1495   PetscErrorCode    ierr;
1496   PetscInt          m = A->rmap->n,*aj,*ii;
1497   PetscInt          n,i,*ridx=NULL;
1498   PetscScalar       sum;
1499   PetscBool         usecprow=a->compressedrow.use;
1500 
1501   PetscFunctionBegin;
1502   ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
1503   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
1504   if (zz != yy) {
1505     ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
1506   } else {
1507     z = y;
1508   }
1509 
1510   aj = a->j;
1511   aa = a->a;
1512   ii = a->i;
1513   if (usecprow) { /* use compressed row format */
1514     if (zz != yy) {
1515       ierr = PetscMemcpy(z,y,m*sizeof(PetscScalar));CHKERRQ(ierr);
1516     }
1517     m    = a->compressedrow.nrows;
1518     ii   = a->compressedrow.i;
1519     ridx = a->compressedrow.rindex;
1520     for (i=0; i<m; i++) {
1521       n   = ii[i+1] - ii[i];
1522       aj  = a->j + ii[i];
1523       aa  = a->a + ii[i];
1524       sum = y[*ridx];
1525       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1526       z[*ridx++] = sum;
1527     }
1528   } else { /* do not use compressed row format */
1529 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJ)
1530     fortranmultaddaij_(&m,x,ii,aj,aa,y,z);
1531 #else
1532     for (i=0; i<m; i++) {
1533       n   = ii[i+1] - ii[i];
1534       aj  = a->j + ii[i];
1535       aa  = a->a + ii[i];
1536       sum = y[i];
1537       PetscSparseDensePlusDot(sum,x,aa,aj,n);
1538       z[i] = sum;
1539     }
1540 #endif
1541   }
1542   ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1543   ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
1544   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
1545   if (zz != yy) {
1546     ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
1547   }
1548 #if defined(PETSC_HAVE_CUSP)
1549   /*
1550   ierr = VecView(xx,0);CHKERRQ(ierr);
1551   ierr = VecView(zz,0);CHKERRQ(ierr);
1552   ierr = MatView(A,0);CHKERRQ(ierr);
1553   */
1554 #endif
1555   PetscFunctionReturn(0);
1556 }
1557 
1558 /*
1559      Adds diagonal pointers to sparse matrix structure.
1560 */
1561 #undef __FUNCT__
1562 #define __FUNCT__ "MatMarkDiagonal_SeqAIJ"
1563 PetscErrorCode MatMarkDiagonal_SeqAIJ(Mat A)
1564 {
1565   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
1566   PetscErrorCode ierr;
1567   PetscInt       i,j,m = A->rmap->n;
1568 
1569   PetscFunctionBegin;
1570   if (!a->diag) {
1571     ierr = PetscMalloc(m*sizeof(PetscInt),&a->diag);CHKERRQ(ierr);
1572     ierr = PetscLogObjectMemory((PetscObject)A, m*sizeof(PetscInt));CHKERRQ(ierr);
1573   }
1574   for (i=0; i<A->rmap->n; i++) {
1575     a->diag[i] = a->i[i+1];
1576     for (j=a->i[i]; j<a->i[i+1]; j++) {
1577       if (a->j[j] == i) {
1578         a->diag[i] = j;
1579         break;
1580       }
1581     }
1582   }
1583   PetscFunctionReturn(0);
1584 }
1585 
1586 /*
1587      Checks for missing diagonals
1588 */
1589 #undef __FUNCT__
1590 #define __FUNCT__ "MatMissingDiagonal_SeqAIJ"
1591 PetscErrorCode MatMissingDiagonal_SeqAIJ(Mat A,PetscBool  *missing,PetscInt *d)
1592 {
1593   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1594   PetscInt   *diag,*jj = a->j,i;
1595 
1596   PetscFunctionBegin;
1597   *missing = PETSC_FALSE;
1598   if (A->rmap->n > 0 && !jj) {
1599     *missing = PETSC_TRUE;
1600     if (d) *d = 0;
1601     PetscInfo(A,"Matrix has no entries therefore is missing diagonal");
1602   } else {
1603     diag = a->diag;
1604     for (i=0; i<A->rmap->n; i++) {
1605       if (jj[diag[i]] != i) {
1606         *missing = PETSC_TRUE;
1607         if (d) *d = i;
1608         PetscInfo1(A,"Matrix is missing diagonal number %D",i);
1609         break;
1610       }
1611     }
1612   }
1613   PetscFunctionReturn(0);
1614 }
1615 
1616 #undef __FUNCT__
1617 #define __FUNCT__ "MatInvertDiagonal_SeqAIJ"
1618 PetscErrorCode  MatInvertDiagonal_SeqAIJ(Mat A,PetscScalar omega,PetscScalar fshift)
1619 {
1620   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
1621   PetscErrorCode ierr;
1622   PetscInt       i,*diag,m = A->rmap->n;
1623   MatScalar      *v = a->a;
1624   PetscScalar    *idiag,*mdiag;
1625 
1626   PetscFunctionBegin;
1627   if (a->idiagvalid) PetscFunctionReturn(0);
1628   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1629   diag = a->diag;
1630   if (!a->idiag) {
1631     ierr = PetscMalloc3(m,PetscScalar,&a->idiag,m,PetscScalar,&a->mdiag,m,PetscScalar,&a->ssor_work);CHKERRQ(ierr);
1632     ierr = PetscLogObjectMemory((PetscObject)A, 3*m*sizeof(PetscScalar));CHKERRQ(ierr);
1633     v    = a->a;
1634   }
1635   mdiag = a->mdiag;
1636   idiag = a->idiag;
1637 
1638   if (omega == 1.0 && !PetscAbsScalar(fshift)) {
1639     for (i=0; i<m; i++) {
1640       mdiag[i] = v[diag[i]];
1641       if (!PetscAbsScalar(mdiag[i])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Zero diagonal on row %D",i);
1642       idiag[i] = 1.0/v[diag[i]];
1643     }
1644     ierr = PetscLogFlops(m);CHKERRQ(ierr);
1645   } else {
1646     for (i=0; i<m; i++) {
1647       mdiag[i] = v[diag[i]];
1648       idiag[i] = omega/(fshift + v[diag[i]]);
1649     }
1650     ierr = PetscLogFlops(2.0*m);CHKERRQ(ierr);
1651   }
1652   a->idiagvalid = PETSC_TRUE;
1653   PetscFunctionReturn(0);
1654 }
1655 
1656 #include <../src/mat/impls/aij/seq/ftn-kernels/frelax.h>
1657 #undef __FUNCT__
1658 #define __FUNCT__ "MatSOR_SeqAIJ"
1659 PetscErrorCode MatSOR_SeqAIJ(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1660 {
1661   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1662   PetscScalar       *x,d,sum,*t,scale;
1663   const MatScalar   *v = a->a,*idiag=0,*mdiag;
1664   const PetscScalar *b, *bs,*xb, *ts;
1665   PetscErrorCode    ierr;
1666   PetscInt          n = A->cmap->n,m = A->rmap->n,i;
1667   const PetscInt    *idx,*diag;
1668 
1669   PetscFunctionBegin;
1670   its = its*lits;
1671 
1672   if (fshift != a->fshift || omega != a->omega) a->idiagvalid = PETSC_FALSE; /* must recompute idiag[] */
1673   if (!a->idiagvalid) {ierr = MatInvertDiagonal_SeqAIJ(A,omega,fshift);CHKERRQ(ierr);}
1674   a->fshift = fshift;
1675   a->omega  = omega;
1676 
1677   diag  = a->diag;
1678   t     = a->ssor_work;
1679   idiag = a->idiag;
1680   mdiag = a->mdiag;
1681 
1682   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1683   ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);
1684   /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
1685   if (flag == SOR_APPLY_UPPER) {
1686     /* apply (U + D/omega) to the vector */
1687     bs = b;
1688     for (i=0; i<m; i++) {
1689       d   = fshift + mdiag[i];
1690       n   = a->i[i+1] - diag[i] - 1;
1691       idx = a->j + diag[i] + 1;
1692       v   = a->a + diag[i] + 1;
1693       sum = b[i]*d/omega;
1694       PetscSparseDensePlusDot(sum,bs,v,idx,n);
1695       x[i] = sum;
1696     }
1697     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1698     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1699     ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1700     PetscFunctionReturn(0);
1701   }
1702 
1703   if (flag == SOR_APPLY_LOWER) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SOR_APPLY_LOWER is not implemented");
1704   else if (flag & SOR_EISENSTAT) {
1705     /* Let  A = L + U + D; where L is lower trianglar,
1706     U is upper triangular, E = D/omega; This routine applies
1707 
1708             (L + E)^{-1} A (U + E)^{-1}
1709 
1710     to a vector efficiently using Eisenstat's trick.
1711     */
1712     scale = (2.0/omega) - 1.0;
1713 
1714     /*  x = (E + U)^{-1} b */
1715     for (i=m-1; i>=0; i--) {
1716       n   = a->i[i+1] - diag[i] - 1;
1717       idx = a->j + diag[i] + 1;
1718       v   = a->a + diag[i] + 1;
1719       sum = b[i];
1720       PetscSparseDenseMinusDot(sum,x,v,idx,n);
1721       x[i] = sum*idiag[i];
1722     }
1723 
1724     /*  t = b - (2*E - D)x */
1725     v = a->a;
1726     for (i=0; i<m; i++) t[i] = b[i] - scale*(v[*diag++])*x[i];
1727 
1728     /*  t = (E + L)^{-1}t */
1729     ts   = t;
1730     diag = a->diag;
1731     for (i=0; i<m; i++) {
1732       n   = diag[i] - a->i[i];
1733       idx = a->j + a->i[i];
1734       v   = a->a + a->i[i];
1735       sum = t[i];
1736       PetscSparseDenseMinusDot(sum,ts,v,idx,n);
1737       t[i] = sum*idiag[i];
1738       /*  x = x + t */
1739       x[i] += t[i];
1740     }
1741 
1742     ierr = PetscLogFlops(6.0*m-1 + 2.0*a->nz);CHKERRQ(ierr);
1743     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1744     ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1745     PetscFunctionReturn(0);
1746   }
1747   if (flag & SOR_ZERO_INITIAL_GUESS) {
1748     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1749       for (i=0; i<m; i++) {
1750         n   = diag[i] - a->i[i];
1751         idx = a->j + a->i[i];
1752         v   = a->a + a->i[i];
1753         sum = b[i];
1754         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1755         t[i] = sum;
1756         x[i] = sum*idiag[i];
1757       }
1758       xb   = t;
1759       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1760     } else xb = b;
1761     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1762       for (i=m-1; i>=0; i--) {
1763         n   = a->i[i+1] - diag[i] - 1;
1764         idx = a->j + diag[i] + 1;
1765         v   = a->a + diag[i] + 1;
1766         sum = xb[i];
1767         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1768         if (xb == b) {
1769           x[i] = sum*idiag[i];
1770         } else {
1771           x[i] = (1-omega)*x[i] + sum*idiag[i];
1772         }
1773       }
1774       ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
1775     }
1776     its--;
1777   }
1778   while (its--) {
1779     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
1780       for (i=0; i<m; i++) {
1781         n   = a->i[i+1] - a->i[i];
1782         idx = a->j + a->i[i];
1783         v   = a->a + a->i[i];
1784         sum = b[i];
1785         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1786         x[i] = (1. - omega)*x[i] + (sum + mdiag[i]*x[i])*idiag[i];
1787       }
1788       ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1789     }
1790     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
1791       for (i=m-1; i>=0; i--) {
1792         n   = a->i[i+1] - a->i[i];
1793         idx = a->j + a->i[i];
1794         v   = a->a + a->i[i];
1795         sum = b[i];
1796         PetscSparseDenseMinusDot(sum,x,v,idx,n);
1797         x[i] = (1. - omega)*x[i] + (sum + mdiag[i]*x[i])*idiag[i];
1798       }
1799       ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
1800     }
1801   }
1802   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1803   ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
1804   PetscFunctionReturn(0);
1805 }
1806 
1807 
1808 #undef __FUNCT__
1809 #define __FUNCT__ "MatGetInfo_SeqAIJ"
1810 PetscErrorCode MatGetInfo_SeqAIJ(Mat A,MatInfoType flag,MatInfo *info)
1811 {
1812   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1813 
1814   PetscFunctionBegin;
1815   info->block_size   = 1.0;
1816   info->nz_allocated = (double)a->maxnz;
1817   info->nz_used      = (double)a->nz;
1818   info->nz_unneeded  = (double)(a->maxnz - a->nz);
1819   info->assemblies   = (double)A->num_ass;
1820   info->mallocs      = (double)A->info.mallocs;
1821   info->memory       = ((PetscObject)A)->mem;
1822   if (A->factortype) {
1823     info->fill_ratio_given  = A->info.fill_ratio_given;
1824     info->fill_ratio_needed = A->info.fill_ratio_needed;
1825     info->factor_mallocs    = A->info.factor_mallocs;
1826   } else {
1827     info->fill_ratio_given  = 0;
1828     info->fill_ratio_needed = 0;
1829     info->factor_mallocs    = 0;
1830   }
1831   PetscFunctionReturn(0);
1832 }
1833 
1834 #undef __FUNCT__
1835 #define __FUNCT__ "MatZeroRows_SeqAIJ"
1836 PetscErrorCode MatZeroRows_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
1837 {
1838   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1839   PetscInt          i,m = A->rmap->n - 1,d = 0;
1840   PetscErrorCode    ierr;
1841   const PetscScalar *xx;
1842   PetscScalar       *bb;
1843   PetscBool         missing;
1844 
1845   PetscFunctionBegin;
1846   if (x && b) {
1847     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
1848     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
1849     for (i=0; i<N; i++) {
1850       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1851       bb[rows[i]] = diag*xx[rows[i]];
1852     }
1853     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
1854     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
1855   }
1856 
1857   if (a->keepnonzeropattern) {
1858     for (i=0; i<N; i++) {
1859       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1860       ierr = PetscMemzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]*sizeof(PetscScalar));CHKERRQ(ierr);
1861     }
1862     if (diag != 0.0) {
1863       ierr = MatMissingDiagonal_SeqAIJ(A,&missing,&d);CHKERRQ(ierr);
1864       if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in row %D",d);
1865       for (i=0; i<N; i++) {
1866         a->a[a->diag[rows[i]]] = diag;
1867       }
1868     }
1869     A->same_nonzero = PETSC_TRUE;
1870   } else {
1871     if (diag != 0.0) {
1872       for (i=0; i<N; i++) {
1873         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1874         if (a->ilen[rows[i]] > 0) {
1875           a->ilen[rows[i]]    = 1;
1876           a->a[a->i[rows[i]]] = diag;
1877           a->j[a->i[rows[i]]] = rows[i];
1878         } else { /* in case row was completely empty */
1879           ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],&diag,INSERT_VALUES);CHKERRQ(ierr);
1880         }
1881       }
1882     } else {
1883       for (i=0; i<N; i++) {
1884         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1885         a->ilen[rows[i]] = 0;
1886       }
1887     }
1888     A->same_nonzero = PETSC_FALSE;
1889   }
1890   ierr = MatAssemblyEnd_SeqAIJ(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1891   PetscFunctionReturn(0);
1892 }
1893 
1894 #undef __FUNCT__
1895 #define __FUNCT__ "MatZeroRowsColumns_SeqAIJ"
1896 PetscErrorCode MatZeroRowsColumns_SeqAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
1897 {
1898   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1899   PetscInt          i,j,m = A->rmap->n - 1,d = 0;
1900   PetscErrorCode    ierr;
1901   PetscBool         missing,*zeroed,vecs = PETSC_FALSE;
1902   const PetscScalar *xx;
1903   PetscScalar       *bb;
1904 
1905   PetscFunctionBegin;
1906   if (x && b) {
1907     ierr = VecGetArrayRead(x,&xx);CHKERRQ(ierr);
1908     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
1909     vecs = PETSC_TRUE;
1910   }
1911   ierr = PetscMalloc(A->rmap->n*sizeof(PetscBool),&zeroed);CHKERRQ(ierr);
1912   ierr = PetscMemzero(zeroed,A->rmap->n*sizeof(PetscBool));CHKERRQ(ierr);
1913   for (i=0; i<N; i++) {
1914     if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"row %D out of range", rows[i]);
1915     ierr = PetscMemzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]*sizeof(PetscScalar));CHKERRQ(ierr);
1916 
1917     zeroed[rows[i]] = PETSC_TRUE;
1918   }
1919   for (i=0; i<A->rmap->n; i++) {
1920     if (!zeroed[i]) {
1921       for (j=a->i[i]; j<a->i[i+1]; j++) {
1922         if (zeroed[a->j[j]]) {
1923           if (vecs) bb[i] -= a->a[j]*xx[a->j[j]];
1924           a->a[j] = 0.0;
1925         }
1926       }
1927     } else if (vecs) bb[i] = diag*xx[i];
1928   }
1929   if (x && b) {
1930     ierr = VecRestoreArrayRead(x,&xx);CHKERRQ(ierr);
1931     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
1932   }
1933   ierr = PetscFree(zeroed);CHKERRQ(ierr);
1934   if (diag != 0.0) {
1935     ierr = MatMissingDiagonal_SeqAIJ(A,&missing,&d);CHKERRQ(ierr);
1936     if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry in row %D",d);
1937     for (i=0; i<N; i++) {
1938       a->a[a->diag[rows[i]]] = diag;
1939     }
1940   }
1941   A->same_nonzero = PETSC_TRUE;
1942   ierr = MatAssemblyEnd_SeqAIJ(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1943   PetscFunctionReturn(0);
1944 }
1945 
1946 #undef __FUNCT__
1947 #define __FUNCT__ "MatGetRow_SeqAIJ"
1948 PetscErrorCode MatGetRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1949 {
1950   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1951   PetscInt   *itmp;
1952 
1953   PetscFunctionBegin;
1954   if (row < 0 || row >= A->rmap->n) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range",row);
1955 
1956   *nz = a->i[row+1] - a->i[row];
1957   if (v) *v = a->a + a->i[row];
1958   if (idx) {
1959     itmp = a->j + a->i[row];
1960     if (*nz) *idx = itmp;
1961     else *idx = 0;
1962   }
1963   PetscFunctionReturn(0);
1964 }
1965 
1966 /* remove this function? */
1967 #undef __FUNCT__
1968 #define __FUNCT__ "MatRestoreRow_SeqAIJ"
1969 PetscErrorCode MatRestoreRow_SeqAIJ(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1970 {
1971   PetscFunctionBegin;
1972   PetscFunctionReturn(0);
1973 }
1974 
1975 #undef __FUNCT__
1976 #define __FUNCT__ "MatNorm_SeqAIJ"
1977 PetscErrorCode MatNorm_SeqAIJ(Mat A,NormType type,PetscReal *nrm)
1978 {
1979   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data;
1980   MatScalar      *v  = a->a;
1981   PetscReal      sum = 0.0;
1982   PetscErrorCode ierr;
1983   PetscInt       i,j;
1984 
1985   PetscFunctionBegin;
1986   if (type == NORM_FROBENIUS) {
1987     for (i=0; i<a->nz; i++) {
1988       sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1989     }
1990     *nrm = PetscSqrtReal(sum);
1991   } else if (type == NORM_1) {
1992     PetscReal *tmp;
1993     PetscInt  *jj = a->j;
1994     ierr = PetscMalloc((A->cmap->n+1)*sizeof(PetscReal),&tmp);CHKERRQ(ierr);
1995     ierr = PetscMemzero(tmp,A->cmap->n*sizeof(PetscReal));CHKERRQ(ierr);
1996     *nrm = 0.0;
1997     for (j=0; j<a->nz; j++) {
1998       tmp[*jj++] += PetscAbsScalar(*v);  v++;
1999     }
2000     for (j=0; j<A->cmap->n; j++) {
2001       if (tmp[j] > *nrm) *nrm = tmp[j];
2002     }
2003     ierr = PetscFree(tmp);CHKERRQ(ierr);
2004   } else if (type == NORM_INFINITY) {
2005     *nrm = 0.0;
2006     for (j=0; j<A->rmap->n; j++) {
2007       v   = a->a + a->i[j];
2008       sum = 0.0;
2009       for (i=0; i<a->i[j+1]-a->i[j]; i++) {
2010         sum += PetscAbsScalar(*v); v++;
2011       }
2012       if (sum > *nrm) *nrm = sum;
2013     }
2014   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for two norm");
2015   PetscFunctionReturn(0);
2016 }
2017 
2018 /* Merged from MatGetSymbolicTranspose_SeqAIJ() - replace MatGetSymbolicTranspose_SeqAIJ()? */
2019 #undef __FUNCT__
2020 #define __FUNCT__ "MatTransposeSymbolic_SeqAIJ"
2021 PetscErrorCode MatTransposeSymbolic_SeqAIJ(Mat A,Mat *B)
2022 {
2023   PetscErrorCode ierr;
2024   PetscInt       i,j,anzj;
2025   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b;
2026   PetscInt       an=A->cmap->N,am=A->rmap->N;
2027   PetscInt       *ati,*atj,*atfill,*ai=a->i,*aj=a->j;
2028 
2029   PetscFunctionBegin;
2030   /* Allocate space for symbolic transpose info and work array */
2031   ierr = PetscMalloc((an+1)*sizeof(PetscInt),&ati);CHKERRQ(ierr);
2032   ierr = PetscMalloc(ai[am]*sizeof(PetscInt),&atj);CHKERRQ(ierr);
2033   ierr = PetscMalloc(an*sizeof(PetscInt),&atfill);CHKERRQ(ierr);
2034   ierr = PetscMemzero(ati,(an+1)*sizeof(PetscInt));CHKERRQ(ierr);
2035 
2036   /* Walk through aj and count ## of non-zeros in each row of A^T. */
2037   /* Note: offset by 1 for fast conversion into csr format. */
2038   for (i=0;i<ai[am];i++) ati[aj[i]+1] += 1;
2039   /* Form ati for csr format of A^T. */
2040   for (i=0;i<an;i++) ati[i+1] += ati[i];
2041 
2042   /* Copy ati into atfill so we have locations of the next free space in atj */
2043   ierr = PetscMemcpy(atfill,ati,an*sizeof(PetscInt));CHKERRQ(ierr);
2044 
2045   /* Walk through A row-wise and mark nonzero entries of A^T. */
2046   for (i=0;i<am;i++) {
2047     anzj = ai[i+1] - ai[i];
2048     for (j=0;j<anzj;j++) {
2049       atj[atfill[*aj]] = i;
2050       atfill[*aj++]   += 1;
2051     }
2052   }
2053 
2054   /* Clean up temporary space and complete requests. */
2055   ierr = PetscFree(atfill);CHKERRQ(ierr);
2056   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),an,am,ati,atj,NULL,B);CHKERRQ(ierr);
2057 
2058   (*B)->rmap->bs = A->cmap->bs;
2059   (*B)->cmap->bs = A->rmap->bs;
2060 
2061   b          = (Mat_SeqAIJ*)((*B)->data);
2062   b->free_a  = PETSC_FALSE;
2063   b->free_ij = PETSC_TRUE;
2064   b->nonew   = 0;
2065   PetscFunctionReturn(0);
2066 }
2067 
2068 #undef __FUNCT__
2069 #define __FUNCT__ "MatTranspose_SeqAIJ"
2070 PetscErrorCode MatTranspose_SeqAIJ(Mat A,MatReuse reuse,Mat *B)
2071 {
2072   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2073   Mat            C;
2074   PetscErrorCode ierr;
2075   PetscInt       i,*aj = a->j,*ai = a->i,m = A->rmap->n,len,*col;
2076   MatScalar      *array = a->a;
2077 
2078   PetscFunctionBegin;
2079   if (reuse == MAT_REUSE_MATRIX && A == *B && m != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
2080 
2081   if (reuse == MAT_INITIAL_MATRIX || *B == A) {
2082     ierr = PetscMalloc((1+A->cmap->n)*sizeof(PetscInt),&col);CHKERRQ(ierr);
2083     ierr = PetscMemzero(col,(1+A->cmap->n)*sizeof(PetscInt));CHKERRQ(ierr);
2084 
2085     for (i=0; i<ai[m]; i++) col[aj[i]] += 1;
2086     ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2087     ierr = MatSetSizes(C,A->cmap->n,m,A->cmap->n,m);CHKERRQ(ierr);
2088     ierr = MatSetBlockSizes(C,A->cmap->bs,A->rmap->bs);CHKERRQ(ierr);
2089     ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2090     ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,col);CHKERRQ(ierr);
2091     ierr = PetscFree(col);CHKERRQ(ierr);
2092   } else {
2093     C = *B;
2094   }
2095 
2096   for (i=0; i<m; i++) {
2097     len    = ai[i+1]-ai[i];
2098     ierr   = MatSetValues_SeqAIJ(C,len,aj,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
2099     array += len;
2100     aj    += len;
2101   }
2102   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2103   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2104 
2105   if (reuse == MAT_INITIAL_MATRIX || *B != A) {
2106     *B = C;
2107   } else {
2108     ierr = MatHeaderMerge(A,C);CHKERRQ(ierr);
2109   }
2110   PetscFunctionReturn(0);
2111 }
2112 
2113 #undef __FUNCT__
2114 #define __FUNCT__ "MatIsTranspose_SeqAIJ"
2115 PetscErrorCode  MatIsTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2116 {
2117   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) A->data;
2118   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2119   MatScalar      *va,*vb;
2120   PetscErrorCode ierr;
2121   PetscInt       ma,na,mb,nb, i;
2122 
2123   PetscFunctionBegin;
2124   bij = (Mat_SeqAIJ*) B->data;
2125 
2126   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2127   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2128   if (ma!=nb || na!=mb) {
2129     *f = PETSC_FALSE;
2130     PetscFunctionReturn(0);
2131   }
2132   aii  = aij->i; bii = bij->i;
2133   adx  = aij->j; bdx = bij->j;
2134   va   = aij->a; vb = bij->a;
2135   ierr = PetscMalloc(ma*sizeof(PetscInt),&aptr);CHKERRQ(ierr);
2136   ierr = PetscMalloc(mb*sizeof(PetscInt),&bptr);CHKERRQ(ierr);
2137   for (i=0; i<ma; i++) aptr[i] = aii[i];
2138   for (i=0; i<mb; i++) bptr[i] = bii[i];
2139 
2140   *f = PETSC_TRUE;
2141   for (i=0; i<ma; i++) {
2142     while (aptr[i]<aii[i+1]) {
2143       PetscInt    idc,idr;
2144       PetscScalar vc,vr;
2145       /* column/row index/value */
2146       idc = adx[aptr[i]];
2147       idr = bdx[bptr[idc]];
2148       vc  = va[aptr[i]];
2149       vr  = vb[bptr[idc]];
2150       if (i!=idr || PetscAbsScalar(vc-vr) > tol) {
2151         *f = PETSC_FALSE;
2152         goto done;
2153       } else {
2154         aptr[i]++;
2155         if (B || i!=idc) bptr[idc]++;
2156       }
2157     }
2158   }
2159 done:
2160   ierr = PetscFree(aptr);CHKERRQ(ierr);
2161   ierr = PetscFree(bptr);CHKERRQ(ierr);
2162   PetscFunctionReturn(0);
2163 }
2164 
2165 #undef __FUNCT__
2166 #define __FUNCT__ "MatIsHermitianTranspose_SeqAIJ"
2167 PetscErrorCode  MatIsHermitianTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscBool  *f)
2168 {
2169   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*) A->data,*bij = (Mat_SeqAIJ*) A->data;
2170   PetscInt       *adx,*bdx,*aii,*bii,*aptr,*bptr;
2171   MatScalar      *va,*vb;
2172   PetscErrorCode ierr;
2173   PetscInt       ma,na,mb,nb, i;
2174 
2175   PetscFunctionBegin;
2176   bij = (Mat_SeqAIJ*) B->data;
2177 
2178   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
2179   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
2180   if (ma!=nb || na!=mb) {
2181     *f = PETSC_FALSE;
2182     PetscFunctionReturn(0);
2183   }
2184   aii  = aij->i; bii = bij->i;
2185   adx  = aij->j; bdx = bij->j;
2186   va   = aij->a; vb = bij->a;
2187   ierr = PetscMalloc(ma*sizeof(PetscInt),&aptr);CHKERRQ(ierr);
2188   ierr = PetscMalloc(mb*sizeof(PetscInt),&bptr);CHKERRQ(ierr);
2189   for (i=0; i<ma; i++) aptr[i] = aii[i];
2190   for (i=0; i<mb; i++) bptr[i] = bii[i];
2191 
2192   *f = PETSC_TRUE;
2193   for (i=0; i<ma; i++) {
2194     while (aptr[i]<aii[i+1]) {
2195       PetscInt    idc,idr;
2196       PetscScalar vc,vr;
2197       /* column/row index/value */
2198       idc = adx[aptr[i]];
2199       idr = bdx[bptr[idc]];
2200       vc  = va[aptr[i]];
2201       vr  = vb[bptr[idc]];
2202       if (i!=idr || PetscAbsScalar(vc-PetscConj(vr)) > tol) {
2203         *f = PETSC_FALSE;
2204         goto done;
2205       } else {
2206         aptr[i]++;
2207         if (B || i!=idc) bptr[idc]++;
2208       }
2209     }
2210   }
2211 done:
2212   ierr = PetscFree(aptr);CHKERRQ(ierr);
2213   ierr = PetscFree(bptr);CHKERRQ(ierr);
2214   PetscFunctionReturn(0);
2215 }
2216 
2217 #undef __FUNCT__
2218 #define __FUNCT__ "MatIsSymmetric_SeqAIJ"
2219 PetscErrorCode MatIsSymmetric_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2220 {
2221   PetscErrorCode ierr;
2222 
2223   PetscFunctionBegin;
2224   ierr = MatIsTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2225   PetscFunctionReturn(0);
2226 }
2227 
2228 #undef __FUNCT__
2229 #define __FUNCT__ "MatIsHermitian_SeqAIJ"
2230 PetscErrorCode MatIsHermitian_SeqAIJ(Mat A,PetscReal tol,PetscBool  *f)
2231 {
2232   PetscErrorCode ierr;
2233 
2234   PetscFunctionBegin;
2235   ierr = MatIsHermitianTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
2236   PetscFunctionReturn(0);
2237 }
2238 
2239 #undef __FUNCT__
2240 #define __FUNCT__ "MatDiagonalScale_SeqAIJ"
2241 PetscErrorCode MatDiagonalScale_SeqAIJ(Mat A,Vec ll,Vec rr)
2242 {
2243   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2244   PetscScalar    *l,*r,x;
2245   MatScalar      *v;
2246   PetscErrorCode ierr;
2247   PetscInt       i,j,m = A->rmap->n,n = A->cmap->n,M,nz = a->nz,*jj;
2248 
2249   PetscFunctionBegin;
2250   if (ll) {
2251     /* The local size is used so that VecMPI can be passed to this routine
2252        by MatDiagonalScale_MPIAIJ */
2253     ierr = VecGetLocalSize(ll,&m);CHKERRQ(ierr);
2254     if (m != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
2255     ierr = VecGetArray(ll,&l);CHKERRQ(ierr);
2256     v    = a->a;
2257     for (i=0; i<m; i++) {
2258       x = l[i];
2259       M = a->i[i+1] - a->i[i];
2260       for (j=0; j<M; j++) (*v++) *= x;
2261     }
2262     ierr = VecRestoreArray(ll,&l);CHKERRQ(ierr);
2263     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2264   }
2265   if (rr) {
2266     ierr = VecGetLocalSize(rr,&n);CHKERRQ(ierr);
2267     if (n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Right scaling vector wrong length");
2268     ierr = VecGetArray(rr,&r);CHKERRQ(ierr);
2269     v    = a->a; jj = a->j;
2270     for (i=0; i<nz; i++) (*v++) *= r[*jj++];
2271     ierr = VecRestoreArray(rr,&r);CHKERRQ(ierr);
2272     ierr = PetscLogFlops(nz);CHKERRQ(ierr);
2273   }
2274   ierr = MatSeqAIJInvalidateDiagonal(A);CHKERRQ(ierr);
2275   PetscFunctionReturn(0);
2276 }
2277 
2278 #undef __FUNCT__
2279 #define __FUNCT__ "MatGetSubMatrix_SeqAIJ"
2280 PetscErrorCode MatGetSubMatrix_SeqAIJ(Mat A,IS isrow,IS iscol,PetscInt csize,MatReuse scall,Mat *B)
2281 {
2282   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*c;
2283   PetscErrorCode ierr;
2284   PetscInt       *smap,i,k,kstart,kend,oldcols = A->cmap->n,*lens;
2285   PetscInt       row,mat_i,*mat_j,tcol,first,step,*mat_ilen,sum,lensi;
2286   const PetscInt *irow,*icol;
2287   PetscInt       nrows,ncols;
2288   PetscInt       *starts,*j_new,*i_new,*aj = a->j,*ai = a->i,ii,*ailen = a->ilen;
2289   MatScalar      *a_new,*mat_a;
2290   Mat            C;
2291   PetscBool      stride,sorted;
2292 
2293   PetscFunctionBegin;
2294   ierr = ISSorted(isrow,&sorted);CHKERRQ(ierr);
2295   if (!sorted) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"ISrow is not sorted");
2296   ierr = ISSorted(iscol,&sorted);CHKERRQ(ierr);
2297   if (!sorted) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"IScol is not sorted");
2298 
2299   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
2300   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
2301   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
2302 
2303   ierr = ISStrideGetInfo(iscol,&first,&step);CHKERRQ(ierr);
2304   ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&stride);CHKERRQ(ierr);
2305   if (stride && step == 1) {
2306     /* special case of contiguous rows */
2307     ierr = PetscMalloc2(nrows,PetscInt,&lens,nrows,PetscInt,&starts);CHKERRQ(ierr);
2308     /* loop over new rows determining lens and starting points */
2309     for (i=0; i<nrows; i++) {
2310       kstart = ai[irow[i]];
2311       kend   = kstart + ailen[irow[i]];
2312       for (k=kstart; k<kend; k++) {
2313         if (aj[k] >= first) {
2314           starts[i] = k;
2315           break;
2316         }
2317       }
2318       sum = 0;
2319       while (k < kend) {
2320         if (aj[k++] >= first+ncols) break;
2321         sum++;
2322       }
2323       lens[i] = sum;
2324     }
2325     /* create submatrix */
2326     if (scall == MAT_REUSE_MATRIX) {
2327       PetscInt n_cols,n_rows;
2328       ierr = MatGetSize(*B,&n_rows,&n_cols);CHKERRQ(ierr);
2329       if (n_rows != nrows || n_cols != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
2330       ierr = MatZeroEntries(*B);CHKERRQ(ierr);
2331       C    = *B;
2332     } else {
2333       PetscInt rbs,cbs;
2334       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2335       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2336       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2337       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2338       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2339       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2340       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2341     }
2342     c = (Mat_SeqAIJ*)C->data;
2343 
2344     /* loop over rows inserting into submatrix */
2345     a_new = c->a;
2346     j_new = c->j;
2347     i_new = c->i;
2348 
2349     for (i=0; i<nrows; i++) {
2350       ii    = starts[i];
2351       lensi = lens[i];
2352       for (k=0; k<lensi; k++) {
2353         *j_new++ = aj[ii+k] - first;
2354       }
2355       ierr       = PetscMemcpy(a_new,a->a + starts[i],lensi*sizeof(PetscScalar));CHKERRQ(ierr);
2356       a_new     += lensi;
2357       i_new[i+1] = i_new[i] + lensi;
2358       c->ilen[i] = lensi;
2359     }
2360     ierr = PetscFree2(lens,starts);CHKERRQ(ierr);
2361   } else {
2362     ierr = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
2363     ierr = PetscMalloc(oldcols*sizeof(PetscInt),&smap);CHKERRQ(ierr);
2364     ierr = PetscMemzero(smap,oldcols*sizeof(PetscInt));CHKERRQ(ierr);
2365     ierr = PetscMalloc((1+nrows)*sizeof(PetscInt),&lens);CHKERRQ(ierr);
2366     for (i=0; i<ncols; i++) {
2367 #if defined(PETSC_USE_DEBUG)
2368       if (icol[i] >= oldcols) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Requesting column beyond largest column icol[%D] %D <= A->cmap->n %D",i,icol[i],oldcols);
2369 #endif
2370       smap[icol[i]] = i+1;
2371     }
2372 
2373     /* determine lens of each row */
2374     for (i=0; i<nrows; i++) {
2375       kstart  = ai[irow[i]];
2376       kend    = kstart + a->ilen[irow[i]];
2377       lens[i] = 0;
2378       for (k=kstart; k<kend; k++) {
2379         if (smap[aj[k]]) {
2380           lens[i]++;
2381         }
2382       }
2383     }
2384     /* Create and fill new matrix */
2385     if (scall == MAT_REUSE_MATRIX) {
2386       PetscBool equal;
2387 
2388       c = (Mat_SeqAIJ*)((*B)->data);
2389       if ((*B)->rmap->n  != nrows || (*B)->cmap->n != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
2390       ierr = PetscMemcmp(c->ilen,lens,(*B)->rmap->n*sizeof(PetscInt),&equal);CHKERRQ(ierr);
2391       if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
2392       ierr = PetscMemzero(c->ilen,(*B)->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
2393       C    = *B;
2394     } else {
2395       PetscInt rbs,cbs;
2396       ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
2397       ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2398       ierr = ISGetBlockSize(isrow,&rbs);CHKERRQ(ierr);
2399       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2400       ierr = MatSetBlockSizes(C,rbs,cbs);CHKERRQ(ierr);
2401       ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
2402       ierr = MatSeqAIJSetPreallocation_SeqAIJ(C,0,lens);CHKERRQ(ierr);
2403     }
2404     c = (Mat_SeqAIJ*)(C->data);
2405     for (i=0; i<nrows; i++) {
2406       row      = irow[i];
2407       kstart   = ai[row];
2408       kend     = kstart + a->ilen[row];
2409       mat_i    = c->i[i];
2410       mat_j    = c->j + mat_i;
2411       mat_a    = c->a + mat_i;
2412       mat_ilen = c->ilen + i;
2413       for (k=kstart; k<kend; k++) {
2414         if ((tcol=smap[a->j[k]])) {
2415           *mat_j++ = tcol - 1;
2416           *mat_a++ = a->a[k];
2417           (*mat_ilen)++;
2418 
2419         }
2420       }
2421     }
2422     /* Free work space */
2423     ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
2424     ierr = PetscFree(smap);CHKERRQ(ierr);
2425     ierr = PetscFree(lens);CHKERRQ(ierr);
2426   }
2427   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2428   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2429 
2430   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
2431   *B   = C;
2432   PetscFunctionReturn(0);
2433 }
2434 
2435 #undef __FUNCT__
2436 #define __FUNCT__ "MatGetMultiProcBlock_SeqAIJ"
2437 PetscErrorCode  MatGetMultiProcBlock_SeqAIJ(Mat mat,MPI_Comm subComm,MatReuse scall,Mat *subMat)
2438 {
2439   PetscErrorCode ierr;
2440   Mat            B;
2441 
2442   PetscFunctionBegin;
2443   if (scall == MAT_INITIAL_MATRIX) {
2444     ierr    = MatCreate(subComm,&B);CHKERRQ(ierr);
2445     ierr    = MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->n,mat->cmap->n);CHKERRQ(ierr);
2446     ierr    = MatSetBlockSizes(B,mat->rmap->bs,mat->cmap->bs);CHKERRQ(ierr);
2447     ierr    = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
2448     ierr    = MatDuplicateNoCreate_SeqAIJ(B,mat,MAT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
2449     *subMat = B;
2450   } else {
2451     ierr = MatCopy_SeqAIJ(mat,*subMat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
2452   }
2453   PetscFunctionReturn(0);
2454 }
2455 
2456 #undef __FUNCT__
2457 #define __FUNCT__ "MatILUFactor_SeqAIJ"
2458 PetscErrorCode MatILUFactor_SeqAIJ(Mat inA,IS row,IS col,const MatFactorInfo *info)
2459 {
2460   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)inA->data;
2461   PetscErrorCode ierr;
2462   Mat            outA;
2463   PetscBool      row_identity,col_identity;
2464 
2465   PetscFunctionBegin;
2466   if (info->levels != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only levels=0 supported for in-place ilu");
2467 
2468   ierr = ISIdentity(row,&row_identity);CHKERRQ(ierr);
2469   ierr = ISIdentity(col,&col_identity);CHKERRQ(ierr);
2470 
2471   outA             = inA;
2472   outA->factortype = MAT_FACTOR_LU;
2473 
2474   ierr = PetscObjectReference((PetscObject)row);CHKERRQ(ierr);
2475   ierr = ISDestroy(&a->row);CHKERRQ(ierr);
2476 
2477   a->row = row;
2478 
2479   ierr = PetscObjectReference((PetscObject)col);CHKERRQ(ierr);
2480   ierr = ISDestroy(&a->col);CHKERRQ(ierr);
2481 
2482   a->col = col;
2483 
2484   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
2485   ierr = ISDestroy(&a->icol);CHKERRQ(ierr);
2486   ierr = ISInvertPermutation(col,PETSC_DECIDE,&a->icol);CHKERRQ(ierr);
2487   ierr = PetscLogObjectParent((PetscObject)inA,(PetscObject)a->icol);CHKERRQ(ierr);
2488 
2489   if (!a->solve_work) { /* this matrix may have been factored before */
2490     ierr = PetscMalloc((inA->rmap->n+1)*sizeof(PetscScalar),&a->solve_work);CHKERRQ(ierr);
2491     ierr = PetscLogObjectMemory((PetscObject)inA, (inA->rmap->n+1)*sizeof(PetscScalar));CHKERRQ(ierr);
2492   }
2493 
2494   ierr = MatMarkDiagonal_SeqAIJ(inA);CHKERRQ(ierr);
2495   if (row_identity && col_identity) {
2496     ierr = MatLUFactorNumeric_SeqAIJ_inplace(outA,inA,info);CHKERRQ(ierr);
2497   } else {
2498     ierr = MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(outA,inA,info);CHKERRQ(ierr);
2499   }
2500   PetscFunctionReturn(0);
2501 }
2502 
2503 #undef __FUNCT__
2504 #define __FUNCT__ "MatScale_SeqAIJ"
2505 PetscErrorCode MatScale_SeqAIJ(Mat inA,PetscScalar alpha)
2506 {
2507   Mat_SeqAIJ     *a     = (Mat_SeqAIJ*)inA->data;
2508   PetscScalar    oalpha = alpha;
2509   PetscErrorCode ierr;
2510   PetscBLASInt   one = 1,bnz;
2511 
2512   PetscFunctionBegin;
2513   ierr = PetscBLASIntCast(a->nz,&bnz);CHKERRQ(ierr);
2514   PetscStackCallBLAS("BLASscal",BLASscal_(&bnz,&oalpha,a->a,&one));
2515   ierr = PetscLogFlops(a->nz);CHKERRQ(ierr);
2516   ierr = MatSeqAIJInvalidateDiagonal(inA);CHKERRQ(ierr);
2517   PetscFunctionReturn(0);
2518 }
2519 
2520 #undef __FUNCT__
2521 #define __FUNCT__ "MatGetSubMatrices_SeqAIJ"
2522 PetscErrorCode MatGetSubMatrices_SeqAIJ(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
2523 {
2524   PetscErrorCode ierr;
2525   PetscInt       i;
2526 
2527   PetscFunctionBegin;
2528   if (scall == MAT_INITIAL_MATRIX) {
2529     ierr = PetscMalloc((n+1)*sizeof(Mat),B);CHKERRQ(ierr);
2530   }
2531 
2532   for (i=0; i<n; i++) {
2533     ierr = MatGetSubMatrix_SeqAIJ(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]);CHKERRQ(ierr);
2534   }
2535   PetscFunctionReturn(0);
2536 }
2537 
2538 #undef __FUNCT__
2539 #define __FUNCT__ "MatIncreaseOverlap_SeqAIJ"
2540 PetscErrorCode MatIncreaseOverlap_SeqAIJ(Mat A,PetscInt is_max,IS is[],PetscInt ov)
2541 {
2542   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2543   PetscErrorCode ierr;
2544   PetscInt       row,i,j,k,l,m,n,*nidx,isz,val;
2545   const PetscInt *idx;
2546   PetscInt       start,end,*ai,*aj;
2547   PetscBT        table;
2548 
2549   PetscFunctionBegin;
2550   m  = A->rmap->n;
2551   ai = a->i;
2552   aj = a->j;
2553 
2554   if (ov < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"illegal negative overlap value used");
2555 
2556   ierr = PetscMalloc((m+1)*sizeof(PetscInt),&nidx);CHKERRQ(ierr);
2557   ierr = PetscBTCreate(m,&table);CHKERRQ(ierr);
2558 
2559   for (i=0; i<is_max; i++) {
2560     /* Initialize the two local arrays */
2561     isz  = 0;
2562     ierr = PetscBTMemzero(m,table);CHKERRQ(ierr);
2563 
2564     /* Extract the indices, assume there can be duplicate entries */
2565     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
2566     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
2567 
2568     /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
2569     for (j=0; j<n; ++j) {
2570       if (!PetscBTLookupSet(table,idx[j])) nidx[isz++] = idx[j];
2571     }
2572     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
2573     ierr = ISDestroy(&is[i]);CHKERRQ(ierr);
2574 
2575     k = 0;
2576     for (j=0; j<ov; j++) { /* for each overlap */
2577       n = isz;
2578       for (; k<n; k++) { /* do only those rows in nidx[k], which are not done yet */
2579         row   = nidx[k];
2580         start = ai[row];
2581         end   = ai[row+1];
2582         for (l = start; l<end; l++) {
2583           val = aj[l];
2584           if (!PetscBTLookupSet(table,val)) nidx[isz++] = val;
2585         }
2586       }
2587     }
2588     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz,nidx,PETSC_COPY_VALUES,(is+i));CHKERRQ(ierr);
2589   }
2590   ierr = PetscBTDestroy(&table);CHKERRQ(ierr);
2591   ierr = PetscFree(nidx);CHKERRQ(ierr);
2592   PetscFunctionReturn(0);
2593 }
2594 
2595 /* -------------------------------------------------------------- */
2596 #undef __FUNCT__
2597 #define __FUNCT__ "MatPermute_SeqAIJ"
2598 PetscErrorCode MatPermute_SeqAIJ(Mat A,IS rowp,IS colp,Mat *B)
2599 {
2600   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
2601   PetscErrorCode ierr;
2602   PetscInt       i,nz = 0,m = A->rmap->n,n = A->cmap->n;
2603   const PetscInt *row,*col;
2604   PetscInt       *cnew,j,*lens;
2605   IS             icolp,irowp;
2606   PetscInt       *cwork = NULL;
2607   PetscScalar    *vwork = NULL;
2608 
2609   PetscFunctionBegin;
2610   ierr = ISInvertPermutation(rowp,PETSC_DECIDE,&irowp);CHKERRQ(ierr);
2611   ierr = ISGetIndices(irowp,&row);CHKERRQ(ierr);
2612   ierr = ISInvertPermutation(colp,PETSC_DECIDE,&icolp);CHKERRQ(ierr);
2613   ierr = ISGetIndices(icolp,&col);CHKERRQ(ierr);
2614 
2615   /* determine lengths of permuted rows */
2616   ierr = PetscMalloc((m+1)*sizeof(PetscInt),&lens);CHKERRQ(ierr);
2617   for (i=0; i<m; i++) lens[row[i]] = a->i[i+1] - a->i[i];
2618   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
2619   ierr = MatSetSizes(*B,m,n,m,n);CHKERRQ(ierr);
2620   ierr = MatSetBlockSizes(*B,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
2621   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
2622   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*B,0,lens);CHKERRQ(ierr);
2623   ierr = PetscFree(lens);CHKERRQ(ierr);
2624 
2625   ierr = PetscMalloc(n*sizeof(PetscInt),&cnew);CHKERRQ(ierr);
2626   for (i=0; i<m; i++) {
2627     ierr = MatGetRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2628     for (j=0; j<nz; j++) cnew[j] = col[cwork[j]];
2629     ierr = MatSetValues_SeqAIJ(*B,1,&row[i],nz,cnew,vwork,INSERT_VALUES);CHKERRQ(ierr);
2630     ierr = MatRestoreRow_SeqAIJ(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
2631   }
2632   ierr = PetscFree(cnew);CHKERRQ(ierr);
2633 
2634   (*B)->assembled = PETSC_FALSE;
2635 
2636   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2637   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2638   ierr = ISRestoreIndices(irowp,&row);CHKERRQ(ierr);
2639   ierr = ISRestoreIndices(icolp,&col);CHKERRQ(ierr);
2640   ierr = ISDestroy(&irowp);CHKERRQ(ierr);
2641   ierr = ISDestroy(&icolp);CHKERRQ(ierr);
2642   PetscFunctionReturn(0);
2643 }
2644 
2645 #undef __FUNCT__
2646 #define __FUNCT__ "MatCopy_SeqAIJ"
2647 PetscErrorCode MatCopy_SeqAIJ(Mat A,Mat B,MatStructure str)
2648 {
2649   PetscErrorCode ierr;
2650 
2651   PetscFunctionBegin;
2652   /* If the two matrices have the same copy implementation, use fast copy. */
2653   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
2654     Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2655     Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data;
2656 
2657     if (a->i[A->rmap->n] != b->i[B->rmap->n]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Number of nonzeros in two matrices are different");
2658     ierr = PetscMemcpy(b->a,a->a,(a->i[A->rmap->n])*sizeof(PetscScalar));CHKERRQ(ierr);
2659   } else {
2660     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2661   }
2662   PetscFunctionReturn(0);
2663 }
2664 
2665 #undef __FUNCT__
2666 #define __FUNCT__ "MatSetUp_SeqAIJ"
2667 PetscErrorCode MatSetUp_SeqAIJ(Mat A)
2668 {
2669   PetscErrorCode ierr;
2670 
2671   PetscFunctionBegin;
2672   ierr =  MatSeqAIJSetPreallocation_SeqAIJ(A,PETSC_DEFAULT,0);CHKERRQ(ierr);
2673   PetscFunctionReturn(0);
2674 }
2675 
2676 #undef __FUNCT__
2677 #define __FUNCT__ "MatSeqAIJGetArray_SeqAIJ"
2678 PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat A,PetscScalar *array[])
2679 {
2680   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2681 
2682   PetscFunctionBegin;
2683   *array = a->a;
2684   PetscFunctionReturn(0);
2685 }
2686 
2687 #undef __FUNCT__
2688 #define __FUNCT__ "MatSeqAIJRestoreArray_SeqAIJ"
2689 PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat A,PetscScalar *array[])
2690 {
2691   PetscFunctionBegin;
2692   PetscFunctionReturn(0);
2693 }
2694 
2695 /*---------------------------------------------*/
2696 /* #define JACOBIANCOLOROPT */
2697 #if defined(JACOBIANCOLOROPT)
2698 #include <petsctime.h>
2699 #endif
2700 #undef __FUNCT__
2701 #define __FUNCT__ "MatFDColoringApply_SeqAIJ"
2702 PetscErrorCode MatFDColoringApply_SeqAIJ(Mat J,MatFDColoring coloring,Vec x1,MatStructure *flag,void *sctx)
2703 {
2704   PetscErrorCode (*f)(void*,Vec,Vec,void*) = (PetscErrorCode (*)(void*,Vec,Vec,void*))coloring->f;
2705   PetscErrorCode ierr;
2706   PetscInt       k,start,end,l,row,col,**vscaleforrow;
2707   PetscScalar    dx,*y,*xx,*w3_array;
2708   PetscScalar    *vscale_array;
2709   PetscReal      epsilon = coloring->error_rel,umin = coloring->umin,unorm;
2710   Vec            w1      = coloring->w1,w2=coloring->w2,w3;
2711   void           *fctx   = coloring->fctx;
2712   PetscBool      flg     = PETSC_FALSE;
2713   PetscInt       ctype   = coloring->ctype,N,col_start=0,col_end=0;
2714   Vec            x1_tmp;
2715   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)J->data;
2716   PetscInt       *den2sp=coloring->den2sp,*idx=den2sp;
2717   PetscScalar    *ca=csp->a;
2718 #if defined(JACOBIANCOLOROPT)
2719   PetscLogDouble t0,t1,time_setvalues=0.0;
2720 #endif
2721 
2722   PetscFunctionBegin;
2723   PetscValidHeaderSpecific(J,MAT_CLASSID,1);
2724   PetscValidHeaderSpecific(coloring,MAT_FDCOLORING_CLASSID,2);
2725   PetscValidHeaderSpecific(x1,VEC_CLASSID,3);
2726   if (!f) SETERRQ(PetscObjectComm((PetscObject)J),PETSC_ERR_ARG_WRONGSTATE,"Must call MatFDColoringSetFunction()");
2727 
2728   ierr = PetscLogEventBegin(MAT_FDColoringApply,coloring,J,x1,0);CHKERRQ(ierr);
2729   ierr = MatSetUnfactored(J);CHKERRQ(ierr);
2730   ierr = PetscOptionsGetBool(NULL,"-mat_fd_coloring_dont_rezero",&flg,NULL);CHKERRQ(ierr);
2731   if (flg) {
2732     ierr = PetscInfo(coloring,"Not calling MatZeroEntries()\n");CHKERRQ(ierr);
2733   } else {
2734     PetscBool assembled;
2735     ierr = MatAssembled(J,&assembled);CHKERRQ(ierr);
2736     if (assembled) {
2737       ierr = MatZeroEntries(J);CHKERRQ(ierr);
2738     }
2739   }
2740 
2741   x1_tmp = x1;
2742   if (!coloring->vscale) {
2743     ierr = VecDuplicate(x1_tmp,&coloring->vscale);CHKERRQ(ierr);
2744   }
2745 
2746   if (coloring->htype[0] == 'w') { /* tacky test; need to make systematic if we add other approaches to computing h*/
2747     ierr = VecNorm(x1_tmp,NORM_2,&unorm);CHKERRQ(ierr);
2748   }
2749   ierr = VecGetOwnershipRange(w1,&start,&end);CHKERRQ(ierr); /* OwnershipRange is used by ghosted x! */
2750 
2751   /* Set w1 = F(x1) */
2752   if (!coloring->fset) {
2753     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2754     ierr = (*f)(sctx,x1_tmp,w1,fctx);CHKERRQ(ierr);
2755     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2756   } else {
2757     coloring->fset = PETSC_FALSE;
2758   }
2759 
2760   if (!coloring->w3) {
2761     ierr = VecDuplicate(x1_tmp,&coloring->w3);CHKERRQ(ierr);
2762     ierr = PetscLogObjectParent((PetscObject)coloring,(PetscObject)coloring->w3);CHKERRQ(ierr);
2763   }
2764   w3 = coloring->w3;
2765 
2766   /* Compute all the local scale factors, including ghost points */
2767   ierr = VecGetLocalSize(x1_tmp,&N);CHKERRQ(ierr);
2768   ierr = VecGetArray(x1_tmp,&xx);CHKERRQ(ierr);
2769   ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2770   if (ctype == IS_COLORING_GHOSTED) {
2771     col_start = 0; col_end = N;
2772   } else if (ctype == IS_COLORING_GLOBAL) {
2773     xx           = xx - start;
2774     vscale_array = vscale_array - start;
2775     col_start    = start; col_end = N + start;
2776   }
2777   for (col=col_start; col<col_end; col++) {
2778     /* Loop over each local column, vscale[col] = 1./(epsilon*dx[col]) */
2779     if (coloring->htype[0] == 'w') {
2780       dx = 1.0 + unorm;
2781     } else {
2782       dx = xx[col];
2783     }
2784     if (dx == (PetscScalar)0.0) dx = 1.0;
2785     if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
2786     else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
2787     dx               *= epsilon;
2788     vscale_array[col] = (PetscScalar)1.0/dx;
2789   }
2790   if (ctype == IS_COLORING_GLOBAL) vscale_array = vscale_array + start;
2791   ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2792   if (ctype == IS_COLORING_GLOBAL) {
2793     ierr = VecGhostUpdateBegin(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2794     ierr = VecGhostUpdateEnd(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2795   }
2796 
2797   if (coloring->vscaleforrow) {
2798     vscaleforrow = coloring->vscaleforrow;
2799   } else SETERRQ(PetscObjectComm((PetscObject)J),PETSC_ERR_ARG_NULL,"Null Object: coloring->vscaleforrow");
2800 
2801   /*
2802     Loop over each color
2803   */
2804   ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2805   for (k=0; k<coloring->ncolors; k++) { /* loop over colors */
2806     coloring->currentcolor = k;
2807 
2808     ierr = VecCopy(x1_tmp,w3);CHKERRQ(ierr);
2809     ierr = VecGetArray(w3,&w3_array);CHKERRQ(ierr);
2810     if (ctype == IS_COLORING_GLOBAL) w3_array = w3_array - start;
2811     /*
2812       Loop over each column associated with color
2813       adding the perturbation to the vector w3.
2814     */
2815     for (l=0; l<coloring->ncolumns[k]; l++) { /* loop over columns */
2816       col = coloring->columns[k][l];    /* local column of the matrix we are probing for */
2817       if (coloring->htype[0] == 'w') {
2818         dx = 1.0 + unorm;
2819       } else {
2820         dx = xx[col];
2821       }
2822       if (dx == (PetscScalar)0.0) dx = 1.0;
2823       if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
2824       else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
2825       dx            *= epsilon;
2826       if (!PetscAbsScalar(dx)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Computed 0 differencing parameter");
2827       w3_array[col] += dx;
2828     }
2829     if (ctype == IS_COLORING_GLOBAL) w3_array = w3_array + start;
2830     ierr = VecRestoreArray(w3,&w3_array);CHKERRQ(ierr);
2831 
2832     /*
2833       Evaluate function at w3 = x1 + dx (here dx is a vector of perturbations)
2834                            w2 = F(x1 + dx) - F(x1)
2835     */
2836     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2837     ierr = (*f)(sctx,w3,w2,fctx);CHKERRQ(ierr);
2838     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2839     ierr = VecAXPY(w2,-1.0,w1);CHKERRQ(ierr);
2840 
2841     /*
2842       Loop over rows of vector, putting results into Jacobian matrix
2843     */
2844 #if defined(JACOBIANCOLOROPT)
2845     ierr = PetscTime(&t0);CHKERRQ(ierr);
2846 #endif
2847     ierr = VecGetArray(w2,&y);CHKERRQ(ierr);
2848     for (l=0; l<coloring->nrows[k]; l++) { /* loop over rows */
2849       row     = coloring->rows[k][l];            /* local row index */
2850       y[row] *= vscale_array[vscaleforrow[k][l]];
2851       ca[idx[l]] = y[row];
2852     }
2853     idx = idx + coloring->nrows[k];
2854     ierr = VecRestoreArray(w2,&y);CHKERRQ(ierr);
2855 #if defined(JACOBIANCOLOROPT)
2856     ierr = PetscTime(&t1);CHKERRQ(ierr);
2857     time_setvalues += t1-t0;
2858 #endif
2859   } /* endof for each color */
2860 #if defined(JACOBIANCOLOROPT)
2861   printf("     MatFDColoringApply_SeqAIJ: time_setvalues %g\n",time_setvalues);
2862 #endif
2863   if (ctype == IS_COLORING_GLOBAL) xx = xx + start;
2864   ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2865   ierr = VecRestoreArray(x1_tmp,&xx);CHKERRQ(ierr);
2866 
2867   coloring->currentcolor = -1;
2868   ierr = PetscLogEventEnd(MAT_FDColoringApply,coloring,J,x1,0);CHKERRQ(ierr);
2869   PetscFunctionReturn(0);
2870 }
2871 /* --------------------------------------------------------*/
2872 
2873 #undef __FUNCT__
2874 #define __FUNCT__ "MatFDColoringApply_SeqAIJ_old"
2875 PetscErrorCode MatFDColoringApply_SeqAIJ_old(Mat J,MatFDColoring coloring,Vec x1,MatStructure *flag,void *sctx)
2876 {
2877   PetscErrorCode (*f)(void*,Vec,Vec,void*) = (PetscErrorCode (*)(void*,Vec,Vec,void*))coloring->f;
2878   PetscErrorCode ierr;
2879   PetscInt       k,N,start,end,l,row,col,srow,**vscaleforrow;
2880   PetscScalar    dx,*y,*xx,*w3_array;
2881   PetscScalar    *vscale_array;
2882   PetscReal      epsilon = coloring->error_rel,umin = coloring->umin;
2883   Vec            w1,w2,w3;
2884   void           *fctx = coloring->fctx;
2885   PetscBool      flg   = PETSC_FALSE;
2886 
2887   PetscFunctionBegin;
2888   printf("MatFDColoringApply_SeqAIJ ...\n");
2889   if (!coloring->w1) {
2890     ierr = VecDuplicate(x1,&coloring->w1);CHKERRQ(ierr);
2891     ierr = PetscLogObjectParent((PetscObject)coloring,(PetscObject)coloring->w1);CHKERRQ(ierr);
2892     ierr = VecDuplicate(x1,&coloring->w2);CHKERRQ(ierr);
2893     ierr = PetscLogObjectParent((PetscObject)coloring,(PetscObject)coloring->w2);CHKERRQ(ierr);
2894     ierr = VecDuplicate(x1,&coloring->w3);CHKERRQ(ierr);
2895     ierr = PetscLogObjectParent((PetscObject)coloring,(PetscObject)coloring->w3);CHKERRQ(ierr);
2896   }
2897   w1 = coloring->w1; w2 = coloring->w2; w3 = coloring->w3;
2898 
2899   ierr = MatSetUnfactored(J);CHKERRQ(ierr);
2900   ierr = PetscOptionsGetBool(((PetscObject)coloring)->prefix,"-mat_fd_coloring_dont_rezero",&flg,NULL);CHKERRQ(ierr);
2901   if (flg) {
2902     ierr = PetscInfo(coloring,"Not calling MatZeroEntries()\n");CHKERRQ(ierr);
2903   } else {
2904     PetscBool assembled;
2905     ierr = MatAssembled(J,&assembled);CHKERRQ(ierr);
2906     if (assembled) {
2907       ierr = MatZeroEntries(J);CHKERRQ(ierr);
2908     }
2909   }
2910 
2911   ierr = VecGetOwnershipRange(x1,&start,&end);CHKERRQ(ierr);
2912   ierr = VecGetSize(x1,&N);CHKERRQ(ierr);
2913 
2914   if (!coloring->fset) {
2915     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2916     ierr = (*f)(sctx,x1,w1,fctx);CHKERRQ(ierr);
2917     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2918   } else {
2919     coloring->fset = PETSC_FALSE;
2920   }
2921 
2922   /*
2923       Compute all the scale factors and share with other processors
2924   */
2925   ierr = VecGetArray(x1,&xx);CHKERRQ(ierr);xx = xx - start;
2926   ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);vscale_array = vscale_array - start;
2927   for (k=0; k<coloring->ncolors; k++) {
2928     /*
2929        Loop over each column associated with color adding the
2930        perturbation to the vector w3.
2931     */
2932     for (l=0; l<coloring->ncolumns[k]; l++) {
2933       col = coloring->columns[k][l];    /* column of the matrix we are probing for */
2934       dx  = xx[col];
2935       if (dx == 0.0) dx = 1.0;
2936       if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
2937       else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
2938       dx               *= epsilon;
2939       vscale_array[col] = 1.0/dx;
2940     }
2941   }
2942   vscale_array = vscale_array + start;
2943 
2944   ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2945   ierr = VecGhostUpdateBegin(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2946   ierr = VecGhostUpdateEnd(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2947 
2948   /*  ierr = VecView(coloring->vscale,PETSC_VIEWER_STDOUT_WORLD);
2949       ierr = VecView(x1,PETSC_VIEWER_STDOUT_WORLD);*/
2950 
2951   if (coloring->vscaleforrow) vscaleforrow = coloring->vscaleforrow;
2952   else                        vscaleforrow = coloring->columnsforrow;
2953 
2954   ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2955   /*
2956       Loop over each color
2957   */
2958   for (k=0; k<coloring->ncolors; k++) {
2959     coloring->currentcolor = k;
2960 
2961     ierr = VecCopy(x1,w3);CHKERRQ(ierr);
2962     ierr = VecGetArray(w3,&w3_array);CHKERRQ(ierr);w3_array = w3_array - start;
2963     /*
2964        Loop over each column associated with color adding the
2965        perturbation to the vector w3.
2966     */
2967     for (l=0; l<coloring->ncolumns[k]; l++) {
2968       col = coloring->columns[k][l];    /* column of the matrix we are probing for */
2969       dx  = xx[col];
2970       if (dx == 0.0) dx = 1.0;
2971       if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
2972       else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
2973       dx *= epsilon;
2974       if (!PetscAbsScalar(dx)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Computed 0 differencing parameter");
2975       w3_array[col] += dx;
2976     }
2977     w3_array = w3_array + start; ierr = VecRestoreArray(w3,&w3_array);CHKERRQ(ierr);
2978 
2979     /*
2980        Evaluate function at x1 + dx (here dx is a vector of perturbations)
2981     */
2982 
2983     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2984     ierr = (*f)(sctx,w3,w2,fctx);CHKERRQ(ierr);
2985     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2986     ierr = VecAXPY(w2,-1.0,w1);CHKERRQ(ierr);
2987 
2988     /*
2989        Loop over rows of vector, putting results into Jacobian matrix
2990     */
2991     ierr = VecGetArray(w2,&y);CHKERRQ(ierr);
2992     for (l=0; l<coloring->nrows[k]; l++) {
2993       row     = coloring->rows[k][l];
2994       col     = coloring->columnsforrow[k][l];
2995       y[row] *= vscale_array[vscaleforrow[k][l]];
2996       srow    = row + start;
2997       ierr    = MatSetValues_SeqAIJ(J,1,&srow,1,&col,y+row,INSERT_VALUES);CHKERRQ(ierr);
2998     }
2999     ierr = VecRestoreArray(w2,&y);CHKERRQ(ierr);
3000   }
3001   coloring->currentcolor = k;
3002 
3003   ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
3004   xx   = xx + start;
3005   ierr = VecRestoreArray(x1,&xx);CHKERRQ(ierr);
3006   ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3007   ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3008   PetscFunctionReturn(0);
3009 }
3010 
3011 /*
3012    Computes the number of nonzeros per row needed for preallocation when X and Y
3013    have different nonzero structure.
3014 */
3015 #undef __FUNCT__
3016 #define __FUNCT__ "MatAXPYGetPreallocation_SeqAIJ"
3017 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
3018 {
3019   PetscInt       i,m=Y->rmap->N;
3020   Mat_SeqAIJ     *x  = (Mat_SeqAIJ*)X->data;
3021   Mat_SeqAIJ     *y  = (Mat_SeqAIJ*)Y->data;
3022   const PetscInt *xi = x->i,*yi = y->i;
3023 
3024   PetscFunctionBegin;
3025   /* Set the number of nonzeros in the new matrix */
3026   for (i=0; i<m; i++) {
3027     PetscInt       j,k,nzx = xi[i+1] - xi[i],nzy = yi[i+1] - yi[i];
3028     const PetscInt *xj = x->j+xi[i],*yj = y->j+yi[i];
3029     nnz[i] = 0;
3030     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
3031       for (; k<nzy && yj[k]<xj[j]; k++) nnz[i]++; /* Catch up to X */
3032       if (k<nzy && yj[k]==xj[j]) k++;             /* Skip duplicate */
3033       nnz[i]++;
3034     }
3035     for (; k<nzy; k++) nnz[i]++;
3036   }
3037   PetscFunctionReturn(0);
3038 }
3039 
3040 #undef __FUNCT__
3041 #define __FUNCT__ "MatAXPY_SeqAIJ"
3042 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
3043 {
3044   PetscErrorCode ierr;
3045   PetscInt       i;
3046   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
3047   PetscBLASInt   one=1,bnz;
3048 
3049   PetscFunctionBegin;
3050   ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
3051   if (str == SAME_NONZERO_PATTERN) {
3052     PetscScalar alpha = a;
3053     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
3054     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
3055   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
3056     if (y->xtoy && y->XtoY != X) {
3057       ierr = PetscFree(y->xtoy);CHKERRQ(ierr);
3058       ierr = MatDestroy(&y->XtoY);CHKERRQ(ierr);
3059     }
3060     if (!y->xtoy) { /* get xtoy */
3061       ierr    = MatAXPYGetxtoy_Private(X->rmap->n,x->i,x->j,NULL, y->i,y->j,NULL, &y->xtoy);CHKERRQ(ierr);
3062       y->XtoY = X;
3063       ierr    = PetscObjectReference((PetscObject)X);CHKERRQ(ierr);
3064     }
3065     for (i=0; i<x->nz; i++) y->a[y->xtoy[i]] += a*(x->a[i]);
3066     ierr = PetscInfo3(Y,"ratio of nnz(X)/nnz(Y): %d/%d = %g\n",x->nz,y->nz,(double)(PetscReal)(x->nz)/(y->nz+1));CHKERRQ(ierr);
3067   } else {
3068     Mat      B;
3069     PetscInt *nnz;
3070     ierr = PetscMalloc(Y->rmap->N*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
3071     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
3072     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
3073     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
3074     ierr = MatSetBlockSizes(B,Y->rmap->bs,Y->cmap->bs);CHKERRQ(ierr);
3075     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
3076     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
3077     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
3078     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
3079     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
3080     ierr = PetscFree(nnz);CHKERRQ(ierr);
3081   }
3082   PetscFunctionReturn(0);
3083 }
3084 
3085 #undef __FUNCT__
3086 #define __FUNCT__ "MatConjugate_SeqAIJ"
3087 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
3088 {
3089 #if defined(PETSC_USE_COMPLEX)
3090   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
3091   PetscInt    i,nz;
3092   PetscScalar *a;
3093 
3094   PetscFunctionBegin;
3095   nz = aij->nz;
3096   a  = aij->a;
3097   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
3098 #else
3099   PetscFunctionBegin;
3100 #endif
3101   PetscFunctionReturn(0);
3102 }
3103 
3104 #undef __FUNCT__
3105 #define __FUNCT__ "MatGetRowMaxAbs_SeqAIJ"
3106 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3107 {
3108   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3109   PetscErrorCode ierr;
3110   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3111   PetscReal      atmp;
3112   PetscScalar    *x;
3113   MatScalar      *aa;
3114 
3115   PetscFunctionBegin;
3116   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3117   aa = a->a;
3118   ai = a->i;
3119   aj = a->j;
3120 
3121   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3122   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3123   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3124   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3125   for (i=0; i<m; i++) {
3126     ncols = ai[1] - ai[0]; ai++;
3127     x[i]  = 0.0;
3128     for (j=0; j<ncols; j++) {
3129       atmp = PetscAbsScalar(*aa);
3130       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3131       aa++; aj++;
3132     }
3133   }
3134   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3135   PetscFunctionReturn(0);
3136 }
3137 
3138 #undef __FUNCT__
3139 #define __FUNCT__ "MatGetRowMax_SeqAIJ"
3140 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3141 {
3142   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3143   PetscErrorCode ierr;
3144   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3145   PetscScalar    *x;
3146   MatScalar      *aa;
3147 
3148   PetscFunctionBegin;
3149   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3150   aa = a->a;
3151   ai = a->i;
3152   aj = a->j;
3153 
3154   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3155   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3156   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3157   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3158   for (i=0; i<m; i++) {
3159     ncols = ai[1] - ai[0]; ai++;
3160     if (ncols == A->cmap->n) { /* row is dense */
3161       x[i] = *aa; if (idx) idx[i] = 0;
3162     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
3163       x[i] = 0.0;
3164       if (idx) {
3165         idx[i] = 0; /* in case ncols is zero */
3166         for (j=0;j<ncols;j++) { /* find first implicit 0.0 in the row */
3167           if (aj[j] > j) {
3168             idx[i] = j;
3169             break;
3170           }
3171         }
3172       }
3173     }
3174     for (j=0; j<ncols; j++) {
3175       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3176       aa++; aj++;
3177     }
3178   }
3179   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3180   PetscFunctionReturn(0);
3181 }
3182 
3183 #undef __FUNCT__
3184 #define __FUNCT__ "MatGetRowMinAbs_SeqAIJ"
3185 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3186 {
3187   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3188   PetscErrorCode ierr;
3189   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3190   PetscReal      atmp;
3191   PetscScalar    *x;
3192   MatScalar      *aa;
3193 
3194   PetscFunctionBegin;
3195   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3196   aa = a->a;
3197   ai = a->i;
3198   aj = a->j;
3199 
3200   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3201   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3202   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3203   if (n != A->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector, %d vs. %d rows", A->rmap->n, n);
3204   for (i=0; i<m; i++) {
3205     ncols = ai[1] - ai[0]; ai++;
3206     if (ncols) {
3207       /* Get first nonzero */
3208       for (j = 0; j < ncols; j++) {
3209         atmp = PetscAbsScalar(aa[j]);
3210         if (atmp > 1.0e-12) {
3211           x[i] = atmp;
3212           if (idx) idx[i] = aj[j];
3213           break;
3214         }
3215       }
3216       if (j == ncols) {x[i] = PetscAbsScalar(*aa); if (idx) idx[i] = *aj;}
3217     } else {
3218       x[i] = 0.0; if (idx) idx[i] = 0;
3219     }
3220     for (j = 0; j < ncols; j++) {
3221       atmp = PetscAbsScalar(*aa);
3222       if (atmp > 1.0e-12 && PetscAbsScalar(x[i]) > atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3223       aa++; aj++;
3224     }
3225   }
3226   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3227   PetscFunctionReturn(0);
3228 }
3229 
3230 #undef __FUNCT__
3231 #define __FUNCT__ "MatGetRowMin_SeqAIJ"
3232 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3233 {
3234   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3235   PetscErrorCode ierr;
3236   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3237   PetscScalar    *x;
3238   MatScalar      *aa;
3239 
3240   PetscFunctionBegin;
3241   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3242   aa = a->a;
3243   ai = a->i;
3244   aj = a->j;
3245 
3246   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3247   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3248   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3249   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3250   for (i=0; i<m; i++) {
3251     ncols = ai[1] - ai[0]; ai++;
3252     if (ncols == A->cmap->n) { /* row is dense */
3253       x[i] = *aa; if (idx) idx[i] = 0;
3254     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3255       x[i] = 0.0;
3256       if (idx) {   /* find first implicit 0.0 in the row */
3257         idx[i] = 0; /* in case ncols is zero */
3258         for (j=0; j<ncols; j++) {
3259           if (aj[j] > j) {
3260             idx[i] = j;
3261             break;
3262           }
3263         }
3264       }
3265     }
3266     for (j=0; j<ncols; j++) {
3267       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3268       aa++; aj++;
3269     }
3270   }
3271   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3272   PetscFunctionReturn(0);
3273 }
3274 
3275 #include <petscblaslapack.h>
3276 #include <petsc-private/kernels/blockinvert.h>
3277 
3278 #undef __FUNCT__
3279 #define __FUNCT__ "MatInvertBlockDiagonal_SeqAIJ"
3280 PetscErrorCode  MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3281 {
3282   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
3283   PetscErrorCode ierr;
3284   PetscInt       i,bs = A->rmap->bs,mbs = A->rmap->n/A->rmap->bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3285   MatScalar      *diag,work[25],*v_work;
3286   PetscReal      shift = 0.0;
3287 
3288   PetscFunctionBegin;
3289   if (a->ibdiagvalid) {
3290     if (values) *values = a->ibdiag;
3291     PetscFunctionReturn(0);
3292   }
3293   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3294   if (!a->ibdiag) {
3295     ierr = PetscMalloc(bs2*mbs*sizeof(PetscScalar),&a->ibdiag);CHKERRQ(ierr);
3296     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3297   }
3298   diag = a->ibdiag;
3299   if (values) *values = a->ibdiag;
3300   /* factor and invert each block */
3301   switch (bs) {
3302   case 1:
3303     for (i=0; i<mbs; i++) {
3304       ierr    = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3305       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3306     }
3307     break;
3308   case 2:
3309     for (i=0; i<mbs; i++) {
3310       ij[0] = 2*i; ij[1] = 2*i + 1;
3311       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3312       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift);CHKERRQ(ierr);
3313       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
3314       diag += 4;
3315     }
3316     break;
3317   case 3:
3318     for (i=0; i<mbs; i++) {
3319       ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
3320       ierr  = MatGetValues(A,3,ij,3,ij,diag);CHKERRQ(ierr);
3321       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr);
3322       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3323       diag += 9;
3324     }
3325     break;
3326   case 4:
3327     for (i=0; i<mbs; i++) {
3328       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3329       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3330       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift);CHKERRQ(ierr);
3331       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3332       diag += 16;
3333     }
3334     break;
3335   case 5:
3336     for (i=0; i<mbs; i++) {
3337       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3338       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3339       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift);CHKERRQ(ierr);
3340       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3341       diag += 25;
3342     }
3343     break;
3344   case 6:
3345     for (i=0; i<mbs; i++) {
3346       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;
3347       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3348       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift);CHKERRQ(ierr);
3349       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3350       diag += 36;
3351     }
3352     break;
3353   case 7:
3354     for (i=0; i<mbs; i++) {
3355       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;
3356       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3357       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift);CHKERRQ(ierr);
3358       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3359       diag += 49;
3360     }
3361     break;
3362   default:
3363     ierr = PetscMalloc3(bs,MatScalar,&v_work,bs,PetscInt,&v_pivots,bs,PetscInt,&IJ);CHKERRQ(ierr);
3364     for (i=0; i<mbs; i++) {
3365       for (j=0; j<bs; j++) {
3366         IJ[j] = bs*i + j;
3367       }
3368       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3369       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work);CHKERRQ(ierr);
3370       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3371       diag += bs2;
3372     }
3373     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3374   }
3375   a->ibdiagvalid = PETSC_TRUE;
3376   PetscFunctionReturn(0);
3377 }
3378 
3379 #undef __FUNCT__
3380 #define __FUNCT__ "MatSetRandom_SeqAIJ"
3381 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3382 {
3383   PetscErrorCode ierr;
3384   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3385   PetscScalar    a;
3386   PetscInt       m,n,i,j,col;
3387 
3388   PetscFunctionBegin;
3389   if (!x->assembled) {
3390     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3391     for (i=0; i<m; i++) {
3392       for (j=0; j<aij->imax[i]; j++) {
3393         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3394         col  = (PetscInt)(n*PetscRealPart(a));
3395         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3396       }
3397     }
3398   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet coded");
3399   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3400   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3401   PetscFunctionReturn(0);
3402 }
3403 
3404 extern PetscErrorCode  MatFDColoringApply_AIJ(Mat,MatFDColoring,Vec,MatStructure*,void*);
3405 /* -------------------------------------------------------------------*/
3406 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3407                                         MatGetRow_SeqAIJ,
3408                                         MatRestoreRow_SeqAIJ,
3409                                         MatMult_SeqAIJ,
3410                                 /*  4*/ MatMultAdd_SeqAIJ,
3411                                         MatMultTranspose_SeqAIJ,
3412                                         MatMultTransposeAdd_SeqAIJ,
3413                                         0,
3414                                         0,
3415                                         0,
3416                                 /* 10*/ 0,
3417                                         MatLUFactor_SeqAIJ,
3418                                         0,
3419                                         MatSOR_SeqAIJ,
3420                                         MatTranspose_SeqAIJ,
3421                                 /*1 5*/ MatGetInfo_SeqAIJ,
3422                                         MatEqual_SeqAIJ,
3423                                         MatGetDiagonal_SeqAIJ,
3424                                         MatDiagonalScale_SeqAIJ,
3425                                         MatNorm_SeqAIJ,
3426                                 /* 20*/ 0,
3427                                         MatAssemblyEnd_SeqAIJ,
3428                                         MatSetOption_SeqAIJ,
3429                                         MatZeroEntries_SeqAIJ,
3430                                 /* 24*/ MatZeroRows_SeqAIJ,
3431                                         0,
3432                                         0,
3433                                         0,
3434                                         0,
3435                                 /* 29*/ MatSetUp_SeqAIJ,
3436                                         0,
3437                                         0,
3438                                         0,
3439                                         0,
3440                                 /* 34*/ MatDuplicate_SeqAIJ,
3441                                         0,
3442                                         0,
3443                                         MatILUFactor_SeqAIJ,
3444                                         0,
3445                                 /* 39*/ MatAXPY_SeqAIJ,
3446                                         MatGetSubMatrices_SeqAIJ,
3447                                         MatIncreaseOverlap_SeqAIJ,
3448                                         MatGetValues_SeqAIJ,
3449                                         MatCopy_SeqAIJ,
3450                                 /* 44*/ MatGetRowMax_SeqAIJ,
3451                                         MatScale_SeqAIJ,
3452                                         0,
3453                                         MatDiagonalSet_SeqAIJ,
3454                                         MatZeroRowsColumns_SeqAIJ,
3455                                 /* 49*/ MatSetRandom_SeqAIJ,
3456                                         MatGetRowIJ_SeqAIJ,
3457                                         MatRestoreRowIJ_SeqAIJ,
3458                                         MatGetColumnIJ_SeqAIJ,
3459                                         MatRestoreColumnIJ_SeqAIJ,
3460                                 /* 54*/ MatFDColoringCreate_SeqAIJ,
3461                                         0,
3462                                         0,
3463                                         MatPermute_SeqAIJ,
3464                                         0,
3465                                 /* 59*/ 0,
3466                                         MatDestroy_SeqAIJ,
3467                                         MatView_SeqAIJ,
3468                                         0,
3469                                         MatMatMatMult_SeqAIJ_SeqAIJ_SeqAIJ,
3470                                 /* 64*/ MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ,
3471                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3472                                         0,
3473                                         0,
3474                                         0,
3475                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3476                                         MatGetRowMinAbs_SeqAIJ,
3477                                         0,
3478                                         MatSetColoring_SeqAIJ,
3479                                         0,
3480                                 /* 74*/ MatSetValuesAdifor_SeqAIJ,
3481                                         MatFDColoringApply_AIJ,
3482                                         0,
3483                                         0,
3484                                         0,
3485                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3486                                         0,
3487                                         0,
3488                                         0,
3489                                         MatLoad_SeqAIJ,
3490                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3491                                         MatIsHermitian_SeqAIJ,
3492                                         0,
3493                                         0,
3494                                         0,
3495                                 /* 89*/ MatMatMult_SeqAIJ_SeqAIJ,
3496                                         MatMatMultSymbolic_SeqAIJ_SeqAIJ,
3497                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3498                                         MatPtAP_SeqAIJ_SeqAIJ,
3499                                         MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy,
3500                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ,
3501                                         MatMatTransposeMult_SeqAIJ_SeqAIJ,
3502                                         MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ,
3503                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3504                                         0,
3505                                 /* 99*/ 0,
3506                                         0,
3507                                         0,
3508                                         MatConjugate_SeqAIJ,
3509                                         0,
3510                                 /*104*/ MatSetValuesRow_SeqAIJ,
3511                                         MatRealPart_SeqAIJ,
3512                                         MatImaginaryPart_SeqAIJ,
3513                                         0,
3514                                         0,
3515                                 /*109*/ MatMatSolve_SeqAIJ,
3516                                         0,
3517                                         MatGetRowMin_SeqAIJ,
3518                                         0,
3519                                         MatMissingDiagonal_SeqAIJ,
3520                                 /*114*/ 0,
3521                                         0,
3522                                         0,
3523                                         0,
3524                                         0,
3525                                 /*119*/ 0,
3526                                         0,
3527                                         0,
3528                                         0,
3529                                         MatGetMultiProcBlock_SeqAIJ,
3530                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3531                                         MatGetColumnNorms_SeqAIJ,
3532                                         MatInvertBlockDiagonal_SeqAIJ,
3533                                         0,
3534                                         0,
3535                                 /*129*/ 0,
3536                                         MatTransposeMatMult_SeqAIJ_SeqAIJ,
3537                                         MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ,
3538                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3539                                         MatTransposeColoringCreate_SeqAIJ,
3540                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3541                                         MatTransColoringApplyDenToSp_SeqAIJ,
3542                                         MatRARt_SeqAIJ_SeqAIJ,
3543                                         MatRARtSymbolic_SeqAIJ_SeqAIJ,
3544                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3545                                  /*139*/0,
3546                                         0
3547 };
3548 
3549 #undef __FUNCT__
3550 #define __FUNCT__ "MatSeqAIJSetColumnIndices_SeqAIJ"
3551 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3552 {
3553   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3554   PetscInt   i,nz,n;
3555 
3556   PetscFunctionBegin;
3557   nz = aij->maxnz;
3558   n  = mat->rmap->n;
3559   for (i=0; i<nz; i++) {
3560     aij->j[i] = indices[i];
3561   }
3562   aij->nz = nz;
3563   for (i=0; i<n; i++) {
3564     aij->ilen[i] = aij->imax[i];
3565   }
3566   PetscFunctionReturn(0);
3567 }
3568 
3569 #undef __FUNCT__
3570 #define __FUNCT__ "MatSeqAIJSetColumnIndices"
3571 /*@
3572     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3573        in the matrix.
3574 
3575   Input Parameters:
3576 +  mat - the SeqAIJ matrix
3577 -  indices - the column indices
3578 
3579   Level: advanced
3580 
3581   Notes:
3582     This can be called if you have precomputed the nonzero structure of the
3583   matrix and want to provide it to the matrix object to improve the performance
3584   of the MatSetValues() operation.
3585 
3586     You MUST have set the correct numbers of nonzeros per row in the call to
3587   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3588 
3589     MUST be called before any calls to MatSetValues();
3590 
3591     The indices should start with zero, not one.
3592 
3593 @*/
3594 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3595 {
3596   PetscErrorCode ierr;
3597 
3598   PetscFunctionBegin;
3599   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3600   PetscValidPointer(indices,2);
3601   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3602   PetscFunctionReturn(0);
3603 }
3604 
3605 /* ----------------------------------------------------------------------------------------*/
3606 
3607 #undef __FUNCT__
3608 #define __FUNCT__ "MatStoreValues_SeqAIJ"
3609 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3610 {
3611   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3612   PetscErrorCode ierr;
3613   size_t         nz = aij->i[mat->rmap->n];
3614 
3615   PetscFunctionBegin;
3616   if (aij->nonew != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3617 
3618   /* allocate space for values if not already there */
3619   if (!aij->saved_values) {
3620     ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&aij->saved_values);CHKERRQ(ierr);
3621     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3622   }
3623 
3624   /* copy values over */
3625   ierr = PetscMemcpy(aij->saved_values,aij->a,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3626   PetscFunctionReturn(0);
3627 }
3628 
3629 #undef __FUNCT__
3630 #define __FUNCT__ "MatStoreValues"
3631 /*@
3632     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3633        example, reuse of the linear part of a Jacobian, while recomputing the
3634        nonlinear portion.
3635 
3636    Collect on Mat
3637 
3638   Input Parameters:
3639 .  mat - the matrix (currently only AIJ matrices support this option)
3640 
3641   Level: advanced
3642 
3643   Common Usage, with SNESSolve():
3644 $    Create Jacobian matrix
3645 $    Set linear terms into matrix
3646 $    Apply boundary conditions to matrix, at this time matrix must have
3647 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3648 $      boundary conditions again will not change the nonzero structure
3649 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3650 $    ierr = MatStoreValues(mat);
3651 $    Call SNESSetJacobian() with matrix
3652 $    In your Jacobian routine
3653 $      ierr = MatRetrieveValues(mat);
3654 $      Set nonlinear terms in matrix
3655 
3656   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3657 $    // build linear portion of Jacobian
3658 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3659 $    ierr = MatStoreValues(mat);
3660 $    loop over nonlinear iterations
3661 $       ierr = MatRetrieveValues(mat);
3662 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3663 $       // call MatAssemblyBegin/End() on matrix
3664 $       Solve linear system with Jacobian
3665 $    endloop
3666 
3667   Notes:
3668     Matrix must already be assemblied before calling this routine
3669     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3670     calling this routine.
3671 
3672     When this is called multiple times it overwrites the previous set of stored values
3673     and does not allocated additional space.
3674 
3675 .seealso: MatRetrieveValues()
3676 
3677 @*/
3678 PetscErrorCode  MatStoreValues(Mat mat)
3679 {
3680   PetscErrorCode ierr;
3681 
3682   PetscFunctionBegin;
3683   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3684   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3685   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3686   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3687   PetscFunctionReturn(0);
3688 }
3689 
3690 #undef __FUNCT__
3691 #define __FUNCT__ "MatRetrieveValues_SeqAIJ"
3692 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3693 {
3694   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3695   PetscErrorCode ierr;
3696   PetscInt       nz = aij->i[mat->rmap->n];
3697 
3698   PetscFunctionBegin;
3699   if (aij->nonew != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3700   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3701   /* copy values over */
3702   ierr = PetscMemcpy(aij->a,aij->saved_values,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3703   PetscFunctionReturn(0);
3704 }
3705 
3706 #undef __FUNCT__
3707 #define __FUNCT__ "MatRetrieveValues"
3708 /*@
3709     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3710        example, reuse of the linear part of a Jacobian, while recomputing the
3711        nonlinear portion.
3712 
3713    Collect on Mat
3714 
3715   Input Parameters:
3716 .  mat - the matrix (currently on AIJ matrices support this option)
3717 
3718   Level: advanced
3719 
3720 .seealso: MatStoreValues()
3721 
3722 @*/
3723 PetscErrorCode  MatRetrieveValues(Mat mat)
3724 {
3725   PetscErrorCode ierr;
3726 
3727   PetscFunctionBegin;
3728   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3729   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3730   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3731   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3732   PetscFunctionReturn(0);
3733 }
3734 
3735 
3736 /* --------------------------------------------------------------------------------*/
3737 #undef __FUNCT__
3738 #define __FUNCT__ "MatCreateSeqAIJ"
3739 /*@C
3740    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3741    (the default parallel PETSc format).  For good matrix assembly performance
3742    the user should preallocate the matrix storage by setting the parameter nz
3743    (or the array nnz).  By setting these parameters accurately, performance
3744    during matrix assembly can be increased by more than a factor of 50.
3745 
3746    Collective on MPI_Comm
3747 
3748    Input Parameters:
3749 +  comm - MPI communicator, set to PETSC_COMM_SELF
3750 .  m - number of rows
3751 .  n - number of columns
3752 .  nz - number of nonzeros per row (same for all rows)
3753 -  nnz - array containing the number of nonzeros in the various rows
3754          (possibly different for each row) or NULL
3755 
3756    Output Parameter:
3757 .  A - the matrix
3758 
3759    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3760    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3761    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3762 
3763    Notes:
3764    If nnz is given then nz is ignored
3765 
3766    The AIJ format (also called the Yale sparse matrix format or
3767    compressed row storage), is fully compatible with standard Fortran 77
3768    storage.  That is, the stored row and column indices can begin at
3769    either one (as in Fortran) or zero.  See the users' manual for details.
3770 
3771    Specify the preallocated storage with either nz or nnz (not both).
3772    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3773    allocation.  For large problems you MUST preallocate memory or you
3774    will get TERRIBLE performance, see the users' manual chapter on matrices.
3775 
3776    By default, this format uses inodes (identical nodes) when possible, to
3777    improve numerical efficiency of matrix-vector products and solves. We
3778    search for consecutive rows with the same nonzero structure, thereby
3779    reusing matrix information to achieve increased efficiency.
3780 
3781    Options Database Keys:
3782 +  -mat_no_inode  - Do not use inodes
3783 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3784 
3785    Level: intermediate
3786 
3787 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3788 
3789 @*/
3790 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3791 {
3792   PetscErrorCode ierr;
3793 
3794   PetscFunctionBegin;
3795   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3796   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3797   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3798   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3799   PetscFunctionReturn(0);
3800 }
3801 
3802 #undef __FUNCT__
3803 #define __FUNCT__ "MatSeqAIJSetPreallocation"
3804 /*@C
3805    MatSeqAIJSetPreallocation - For good matrix assembly performance
3806    the user should preallocate the matrix storage by setting the parameter nz
3807    (or the array nnz).  By setting these parameters accurately, performance
3808    during matrix assembly can be increased by more than a factor of 50.
3809 
3810    Collective on MPI_Comm
3811 
3812    Input Parameters:
3813 +  B - The matrix-free
3814 .  nz - number of nonzeros per row (same for all rows)
3815 -  nnz - array containing the number of nonzeros in the various rows
3816          (possibly different for each row) or NULL
3817 
3818    Notes:
3819      If nnz is given then nz is ignored
3820 
3821     The AIJ format (also called the Yale sparse matrix format or
3822    compressed row storage), is fully compatible with standard Fortran 77
3823    storage.  That is, the stored row and column indices can begin at
3824    either one (as in Fortran) or zero.  See the users' manual for details.
3825 
3826    Specify the preallocated storage with either nz or nnz (not both).
3827    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3828    allocation.  For large problems you MUST preallocate memory or you
3829    will get TERRIBLE performance, see the users' manual chapter on matrices.
3830 
3831    You can call MatGetInfo() to get information on how effective the preallocation was;
3832    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3833    You can also run with the option -info and look for messages with the string
3834    malloc in them to see if additional memory allocation was needed.
3835 
3836    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3837    entries or columns indices
3838 
3839    By default, this format uses inodes (identical nodes) when possible, to
3840    improve numerical efficiency of matrix-vector products and solves. We
3841    search for consecutive rows with the same nonzero structure, thereby
3842    reusing matrix information to achieve increased efficiency.
3843 
3844    Options Database Keys:
3845 +  -mat_no_inode  - Do not use inodes
3846 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3847 -  -mat_aij_oneindex - Internally use indexing starting at 1
3848         rather than 0.  Note that when calling MatSetValues(),
3849         the user still MUST index entries starting at 0!
3850 
3851    Level: intermediate
3852 
3853 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatGetInfo()
3854 
3855 @*/
3856 PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
3857 {
3858   PetscErrorCode ierr;
3859 
3860   PetscFunctionBegin;
3861   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3862   PetscValidType(B,1);
3863   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));CHKERRQ(ierr);
3864   PetscFunctionReturn(0);
3865 }
3866 
3867 #undef __FUNCT__
3868 #define __FUNCT__ "MatSeqAIJSetPreallocation_SeqAIJ"
3869 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3870 {
3871   Mat_SeqAIJ     *b;
3872   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3873   PetscErrorCode ierr;
3874   PetscInt       i;
3875 
3876   PetscFunctionBegin;
3877   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3878   if (nz == MAT_SKIP_ALLOCATION) {
3879     skipallocation = PETSC_TRUE;
3880     nz             = 0;
3881   }
3882 
3883   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3884   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3885 
3886   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3887   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %d",nz);
3888   if (nnz) {
3889     for (i=0; i<B->rmap->n; i++) {
3890       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]);
3891       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);
3892     }
3893   }
3894 
3895   B->preallocated = PETSC_TRUE;
3896 
3897   b = (Mat_SeqAIJ*)B->data;
3898 
3899   if (!skipallocation) {
3900     if (!b->imax) {
3901       ierr = PetscMalloc2(B->rmap->n,PetscInt,&b->imax,B->rmap->n,PetscInt,&b->ilen);CHKERRQ(ierr);
3902       ierr = PetscLogObjectMemory((PetscObject)B,2*B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3903     }
3904     if (!nnz) {
3905       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3906       else if (nz < 0) nz = 1;
3907       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
3908       nz = nz*B->rmap->n;
3909     } else {
3910       nz = 0;
3911       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz += nnz[i];}
3912     }
3913     /* b->ilen will count nonzeros in each row so far. */
3914     for (i=0; i<B->rmap->n; i++) b->ilen[i] = 0;
3915 
3916     /* allocate the matrix space */
3917     ierr    = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
3918     ierr    = PetscMalloc3(nz,PetscScalar,&b->a,nz,PetscInt,&b->j,B->rmap->n+1,PetscInt,&b->i);CHKERRQ(ierr);
3919     ierr    = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
3920     b->i[0] = 0;
3921     for (i=1; i<B->rmap->n+1; i++) {
3922       b->i[i] = b->i[i-1] + b->imax[i-1];
3923     }
3924     b->singlemalloc = PETSC_TRUE;
3925     b->free_a       = PETSC_TRUE;
3926     b->free_ij      = PETSC_TRUE;
3927 #if defined(PETSC_THREADCOMM_ACTIVE)
3928     ierr = MatZeroEntries_SeqAIJ(B);CHKERRQ(ierr);
3929 #endif
3930   } else {
3931     b->free_a  = PETSC_FALSE;
3932     b->free_ij = PETSC_FALSE;
3933   }
3934 
3935   b->nz               = 0;
3936   b->maxnz            = nz;
3937   B->info.nz_unneeded = (double)b->maxnz;
3938   if (realalloc) {
3939     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3940   }
3941   PetscFunctionReturn(0);
3942 }
3943 
3944 #undef  __FUNCT__
3945 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR"
3946 /*@
3947    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
3948 
3949    Input Parameters:
3950 +  B - the matrix
3951 .  i - the indices into j for the start of each row (starts with zero)
3952 .  j - the column indices for each row (starts with zero) these must be sorted for each row
3953 -  v - optional values in the matrix
3954 
3955    Level: developer
3956 
3957    The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
3958 
3959 .keywords: matrix, aij, compressed row, sparse, sequential
3960 
3961 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), SeqAIJ
3962 @*/
3963 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
3964 {
3965   PetscErrorCode ierr;
3966 
3967   PetscFunctionBegin;
3968   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3969   PetscValidType(B,1);
3970   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3971   PetscFunctionReturn(0);
3972 }
3973 
3974 #undef  __FUNCT__
3975 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR_SeqAIJ"
3976 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3977 {
3978   PetscInt       i;
3979   PetscInt       m,n;
3980   PetscInt       nz;
3981   PetscInt       *nnz, nz_max = 0;
3982   PetscScalar    *values;
3983   PetscErrorCode ierr;
3984 
3985   PetscFunctionBegin;
3986   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
3987 
3988   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3989   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3990 
3991   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
3992   ierr = PetscMalloc((m+1) * sizeof(PetscInt), &nnz);CHKERRQ(ierr);
3993   for (i = 0; i < m; i++) {
3994     nz     = Ii[i+1]- Ii[i];
3995     nz_max = PetscMax(nz_max, nz);
3996     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
3997     nnz[i] = nz;
3998   }
3999   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
4000   ierr = PetscFree(nnz);CHKERRQ(ierr);
4001 
4002   if (v) {
4003     values = (PetscScalar*) v;
4004   } else {
4005     ierr = PetscMalloc(nz_max*sizeof(PetscScalar), &values);CHKERRQ(ierr);
4006     ierr = PetscMemzero(values, nz_max*sizeof(PetscScalar));CHKERRQ(ierr);
4007   }
4008 
4009   for (i = 0; i < m; i++) {
4010     nz   = Ii[i+1] - Ii[i];
4011     ierr = MatSetValues_SeqAIJ(B, 1, &i, nz, J+Ii[i], values + (v ? Ii[i] : 0), INSERT_VALUES);CHKERRQ(ierr);
4012   }
4013 
4014   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4015   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4016 
4017   if (!v) {
4018     ierr = PetscFree(values);CHKERRQ(ierr);
4019   }
4020   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
4021   PetscFunctionReturn(0);
4022 }
4023 
4024 #include <../src/mat/impls/dense/seq/dense.h>
4025 #include <petsc-private/kernels/petscaxpy.h>
4026 
4027 #undef __FUNCT__
4028 #define __FUNCT__ "MatMatMultNumeric_SeqDense_SeqAIJ"
4029 /*
4030     Computes (B'*A')' since computing B*A directly is untenable
4031 
4032                n                       p                          p
4033         (              )       (              )         (                  )
4034       m (      A       )  *  n (       B      )   =   m (         C        )
4035         (              )       (              )         (                  )
4036 
4037 */
4038 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
4039 {
4040   PetscErrorCode    ierr;
4041   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
4042   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
4043   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
4044   PetscInt          i,n,m,q,p;
4045   const PetscInt    *ii,*idx;
4046   const PetscScalar *b,*a,*a_q;
4047   PetscScalar       *c,*c_q;
4048 
4049   PetscFunctionBegin;
4050   m    = A->rmap->n;
4051   n    = A->cmap->n;
4052   p    = B->cmap->n;
4053   a    = sub_a->v;
4054   b    = sub_b->a;
4055   c    = sub_c->v;
4056   ierr = PetscMemzero(c,m*p*sizeof(PetscScalar));CHKERRQ(ierr);
4057 
4058   ii  = sub_b->i;
4059   idx = sub_b->j;
4060   for (i=0; i<n; i++) {
4061     q = ii[i+1] - ii[i];
4062     while (q-->0) {
4063       c_q = c + m*(*idx);
4064       a_q = a + m*i;
4065       PetscKernelAXPY(c_q,*b,a_q,m);
4066       idx++;
4067       b++;
4068     }
4069   }
4070   PetscFunctionReturn(0);
4071 }
4072 
4073 #undef __FUNCT__
4074 #define __FUNCT__ "MatMatMultSymbolic_SeqDense_SeqAIJ"
4075 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4076 {
4077   PetscErrorCode ierr;
4078   PetscInt       m=A->rmap->n,n=B->cmap->n;
4079   Mat            Cmat;
4080 
4081   PetscFunctionBegin;
4082   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);
4083   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4084   ierr = MatSetSizes(Cmat,m,n,m,n);CHKERRQ(ierr);
4085   ierr = MatSetBlockSizes(Cmat,A->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
4086   ierr = MatSetType(Cmat,MATSEQDENSE);CHKERRQ(ierr);
4087   ierr = MatSeqDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4088 
4089   Cmat->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
4090 
4091   *C = Cmat;
4092   PetscFunctionReturn(0);
4093 }
4094 
4095 /* ----------------------------------------------------------------*/
4096 #undef __FUNCT__
4097 #define __FUNCT__ "MatMatMult_SeqDense_SeqAIJ"
4098 PetscErrorCode MatMatMult_SeqDense_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4099 {
4100   PetscErrorCode ierr;
4101 
4102   PetscFunctionBegin;
4103   if (scall == MAT_INITIAL_MATRIX) {
4104     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4105     ierr = MatMatMultSymbolic_SeqDense_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
4106     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4107   }
4108   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4109   ierr = MatMatMultNumeric_SeqDense_SeqAIJ(A,B,*C);CHKERRQ(ierr);
4110   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4111   PetscFunctionReturn(0);
4112 }
4113 
4114 
4115 /*MC
4116    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
4117    based on compressed sparse row format.
4118 
4119    Options Database Keys:
4120 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
4121 
4122   Level: beginner
4123 
4124 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
4125 M*/
4126 
4127 /*MC
4128    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
4129 
4130    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
4131    and MATMPIAIJ otherwise.  As a result, for single process communicators,
4132   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
4133   for communicators controlling multiple processes.  It is recommended that you call both of
4134   the above preallocation routines for simplicity.
4135 
4136    Options Database Keys:
4137 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
4138 
4139   Developer Notes: Subclasses include MATAIJCUSP, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
4140    enough exist.
4141 
4142   Level: beginner
4143 
4144 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
4145 M*/
4146 
4147 /*MC
4148    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
4149 
4150    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
4151    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
4152    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
4153   for communicators controlling multiple processes.  It is recommended that you call both of
4154   the above preallocation routines for simplicity.
4155 
4156    Options Database Keys:
4157 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
4158 
4159   Level: beginner
4160 
4161 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
4162 M*/
4163 
4164 #if defined(PETSC_HAVE_PASTIX)
4165 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_pastix(Mat,MatFactorType,Mat*);
4166 #endif
4167 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
4168 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_essl(Mat,MatFactorType,Mat*);
4169 #endif
4170 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
4171 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_petsc(Mat,MatFactorType,Mat*);
4172 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_bas(Mat,MatFactorType,Mat*);
4173 extern PetscErrorCode  MatGetFactorAvailable_seqaij_petsc(Mat,MatFactorType,PetscBool*);
4174 #if defined(PETSC_HAVE_MUMPS)
4175 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mumps(Mat,MatFactorType,Mat*);
4176 #endif
4177 #if defined(PETSC_HAVE_SUPERLU)
4178 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu(Mat,MatFactorType,Mat*);
4179 #endif
4180 #if defined(PETSC_HAVE_SUPERLU_DIST)
4181 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu_dist(Mat,MatFactorType,Mat*);
4182 #endif
4183 #if defined(PETSC_HAVE_UMFPACK)
4184 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_umfpack(Mat,MatFactorType,Mat*);
4185 #endif
4186 #if defined(PETSC_HAVE_CHOLMOD)
4187 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_cholmod(Mat,MatFactorType,Mat*);
4188 #endif
4189 #if defined(PETSC_HAVE_LUSOL)
4190 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_lusol(Mat,MatFactorType,Mat*);
4191 #endif
4192 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4193 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_matlab(Mat,MatFactorType,Mat*);
4194 extern PetscErrorCode  MatlabEnginePut_SeqAIJ(PetscObject,void*);
4195 extern PetscErrorCode  MatlabEngineGet_SeqAIJ(PetscObject,void*);
4196 #endif
4197 #if defined(PETSC_HAVE_CLIQUE)
4198 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_clique(Mat,MatFactorType,Mat*);
4199 #endif
4200 
4201 
4202 #undef __FUNCT__
4203 #define __FUNCT__ "MatSeqAIJGetArray"
4204 /*@C
4205    MatSeqAIJGetArray - gives access to the array where the data for a SeqSeqAIJ matrix is stored
4206 
4207    Not Collective
4208 
4209    Input Parameter:
4210 .  mat - a MATSEQDENSE matrix
4211 
4212    Output Parameter:
4213 .   array - pointer to the data
4214 
4215    Level: intermediate
4216 
4217 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4218 @*/
4219 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4220 {
4221   PetscErrorCode ierr;
4222 
4223   PetscFunctionBegin;
4224   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4225   PetscFunctionReturn(0);
4226 }
4227 
4228 #undef __FUNCT__
4229 #define __FUNCT__ "MatSeqAIJRestoreArray"
4230 /*@C
4231    MatSeqAIJRestoreArray - returns access to the array where the data for a SeqSeqAIJ matrix is stored obtained by MatSeqAIJGetArray()
4232 
4233    Not Collective
4234 
4235    Input Parameters:
4236 .  mat - a MATSEQDENSE matrix
4237 .  array - pointer to the data
4238 
4239    Level: intermediate
4240 
4241 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4242 @*/
4243 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4244 {
4245   PetscErrorCode ierr;
4246 
4247   PetscFunctionBegin;
4248   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4249   PetscFunctionReturn(0);
4250 }
4251 
4252 #undef __FUNCT__
4253 #define __FUNCT__ "MatCreate_SeqAIJ"
4254 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4255 {
4256   Mat_SeqAIJ     *b;
4257   PetscErrorCode ierr;
4258   PetscMPIInt    size;
4259 
4260   PetscFunctionBegin;
4261   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4262   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4263 
4264   ierr = PetscNewLog(B,Mat_SeqAIJ,&b);CHKERRQ(ierr);
4265 
4266   B->data = (void*)b;
4267 
4268   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4269 
4270   b->row                = 0;
4271   b->col                = 0;
4272   b->icol               = 0;
4273   b->reallocs           = 0;
4274   b->ignorezeroentries  = PETSC_FALSE;
4275   b->roworiented        = PETSC_TRUE;
4276   b->nonew              = 0;
4277   b->diag               = 0;
4278   b->solve_work         = 0;
4279   B->spptr              = 0;
4280   b->saved_values       = 0;
4281   b->idiag              = 0;
4282   b->mdiag              = 0;
4283   b->ssor_work          = 0;
4284   b->omega              = 1.0;
4285   b->fshift             = 0.0;
4286   b->idiagvalid         = PETSC_FALSE;
4287   b->ibdiagvalid        = PETSC_FALSE;
4288   b->keepnonzeropattern = PETSC_FALSE;
4289   b->xtoy               = 0;
4290   b->XtoY               = 0;
4291   B->same_nonzero       = PETSC_FALSE;
4292 
4293   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4294   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4295   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4296 
4297 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4298   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_matlab_C",MatGetFactor_seqaij_matlab);CHKERRQ(ierr);
4299   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4300   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4301 #endif
4302 #if defined(PETSC_HAVE_PASTIX)
4303   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_pastix_C",MatGetFactor_seqaij_pastix);CHKERRQ(ierr);
4304 #endif
4305 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
4306   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_essl_C",MatGetFactor_seqaij_essl);CHKERRQ(ierr);
4307 #endif
4308 #if defined(PETSC_HAVE_SUPERLU)
4309   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_C",MatGetFactor_seqaij_superlu);CHKERRQ(ierr);
4310 #endif
4311 #if defined(PETSC_HAVE_SUPERLU_DIST)
4312   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_dist_C",MatGetFactor_seqaij_superlu_dist);CHKERRQ(ierr);
4313 #endif
4314 #if defined(PETSC_HAVE_MUMPS)
4315   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mumps_C",MatGetFactor_aij_mumps);CHKERRQ(ierr);
4316 #endif
4317 #if defined(PETSC_HAVE_UMFPACK)
4318   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_umfpack_C",MatGetFactor_seqaij_umfpack);CHKERRQ(ierr);
4319 #endif
4320 #if defined(PETSC_HAVE_CHOLMOD)
4321   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_cholmod_C",MatGetFactor_seqaij_cholmod);CHKERRQ(ierr);
4322 #endif
4323 #if defined(PETSC_HAVE_LUSOL)
4324   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_lusol_C",MatGetFactor_seqaij_lusol);CHKERRQ(ierr);
4325 #endif
4326 #if defined(PETSC_HAVE_CLIQUE)
4327   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_clique_C",MatGetFactor_aij_clique);CHKERRQ(ierr);
4328 #endif
4329 
4330   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_petsc_C",MatGetFactor_seqaij_petsc);CHKERRQ(ierr);
4331   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactorAvailable_petsc_C",MatGetFactorAvailable_seqaij_petsc);CHKERRQ(ierr);
4332   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_bas_C",MatGetFactor_seqaij_bas);CHKERRQ(ierr);
4333   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4334   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4335   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4336   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4337   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4338   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4339   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4340   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4341   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4342   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4343   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4344   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4345   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaij_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
4346   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaij_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
4347   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaij_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
4348   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4349   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4350   PetscFunctionReturn(0);
4351 }
4352 
4353 #undef __FUNCT__
4354 #define __FUNCT__ "MatDuplicateNoCreate_SeqAIJ"
4355 /*
4356     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4357 */
4358 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4359 {
4360   Mat_SeqAIJ     *c,*a = (Mat_SeqAIJ*)A->data;
4361   PetscErrorCode ierr;
4362   PetscInt       i,m = A->rmap->n;
4363 
4364   PetscFunctionBegin;
4365   c = (Mat_SeqAIJ*)C->data;
4366 
4367   C->factortype = A->factortype;
4368   c->row        = 0;
4369   c->col        = 0;
4370   c->icol       = 0;
4371   c->reallocs   = 0;
4372 
4373   C->assembled = PETSC_TRUE;
4374 
4375   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4376   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4377 
4378   ierr = PetscMalloc2(m,PetscInt,&c->imax,m,PetscInt,&c->ilen);CHKERRQ(ierr);
4379   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4380   for (i=0; i<m; i++) {
4381     c->imax[i] = a->imax[i];
4382     c->ilen[i] = a->ilen[i];
4383   }
4384 
4385   /* allocate the matrix space */
4386   if (mallocmatspace) {
4387     ierr = PetscMalloc3(a->i[m],PetscScalar,&c->a,a->i[m],PetscInt,&c->j,m+1,PetscInt,&c->i);CHKERRQ(ierr);
4388     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4389 
4390     c->singlemalloc = PETSC_TRUE;
4391 
4392     ierr = PetscMemcpy(c->i,a->i,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4393     if (m > 0) {
4394       ierr = PetscMemcpy(c->j,a->j,(a->i[m])*sizeof(PetscInt));CHKERRQ(ierr);
4395       if (cpvalues == MAT_COPY_VALUES) {
4396         ierr = PetscMemcpy(c->a,a->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4397       } else {
4398         ierr = PetscMemzero(c->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4399       }
4400     }
4401   }
4402 
4403   c->ignorezeroentries = a->ignorezeroentries;
4404   c->roworiented       = a->roworiented;
4405   c->nonew             = a->nonew;
4406   if (a->diag) {
4407     ierr = PetscMalloc((m+1)*sizeof(PetscInt),&c->diag);CHKERRQ(ierr);
4408     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4409     for (i=0; i<m; i++) {
4410       c->diag[i] = a->diag[i];
4411     }
4412   } else c->diag = 0;
4413 
4414   c->solve_work         = 0;
4415   c->saved_values       = 0;
4416   c->idiag              = 0;
4417   c->ssor_work          = 0;
4418   c->keepnonzeropattern = a->keepnonzeropattern;
4419   c->free_a             = PETSC_TRUE;
4420   c->free_ij            = PETSC_TRUE;
4421   c->xtoy               = 0;
4422   c->XtoY               = 0;
4423 
4424   c->rmax         = a->rmax;
4425   c->nz           = a->nz;
4426   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4427   C->preallocated = PETSC_TRUE;
4428 
4429   c->compressedrow.use   = a->compressedrow.use;
4430   c->compressedrow.nrows = a->compressedrow.nrows;
4431   c->compressedrow.check = a->compressedrow.check;
4432   if (a->compressedrow.use) {
4433     i    = a->compressedrow.nrows;
4434     ierr = PetscMalloc2(i+1,PetscInt,&c->compressedrow.i,i,PetscInt,&c->compressedrow.rindex);CHKERRQ(ierr);
4435     ierr = PetscMemcpy(c->compressedrow.i,a->compressedrow.i,(i+1)*sizeof(PetscInt));CHKERRQ(ierr);
4436     ierr = PetscMemcpy(c->compressedrow.rindex,a->compressedrow.rindex,i*sizeof(PetscInt));CHKERRQ(ierr);
4437   } else {
4438     c->compressedrow.use    = PETSC_FALSE;
4439     c->compressedrow.i      = NULL;
4440     c->compressedrow.rindex = NULL;
4441   }
4442   C->same_nonzero = A->same_nonzero;
4443 
4444   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4445   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4446   PetscFunctionReturn(0);
4447 }
4448 
4449 #undef __FUNCT__
4450 #define __FUNCT__ "MatDuplicate_SeqAIJ"
4451 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4452 {
4453   PetscErrorCode ierr;
4454 
4455   PetscFunctionBegin;
4456   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4457   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4458   ierr = MatSetBlockSizes(*B,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
4459   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4460   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4461   PetscFunctionReturn(0);
4462 }
4463 
4464 #undef __FUNCT__
4465 #define __FUNCT__ "MatLoad_SeqAIJ"
4466 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4467 {
4468   Mat_SeqAIJ     *a;
4469   PetscErrorCode ierr;
4470   PetscInt       i,sum,nz,header[4],*rowlengths = 0,M,N,rows,cols;
4471   int            fd;
4472   PetscMPIInt    size;
4473   MPI_Comm       comm;
4474   PetscInt       bs = 1;
4475 
4476   PetscFunctionBegin;
4477   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
4478   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4479   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"view must have one processor");
4480 
4481   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
4482   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
4483   ierr = PetscOptionsEnd();CHKERRQ(ierr);
4484   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
4485 
4486   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
4487   ierr = PetscBinaryRead(fd,header,4,PETSC_INT);CHKERRQ(ierr);
4488   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
4489   M = header[1]; N = header[2]; nz = header[3];
4490 
4491   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
4492 
4493   /* read in row lengths */
4494   ierr = PetscMalloc(M*sizeof(PetscInt),&rowlengths);CHKERRQ(ierr);
4495   ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
4496 
4497   /* check if sum of rowlengths is same as nz */
4498   for (i=0,sum=0; i< M; i++) sum +=rowlengths[i];
4499   if (sum != nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_READ,"Inconsistant matrix data in file. no-nonzeros = %d, sum-row-lengths = %d\n",nz,sum);
4500 
4501   /* set global size if not set already*/
4502   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) {
4503     ierr = MatSetSizes(newMat,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
4504   } else {
4505     /* if sizes and type are already set, check if the vector global sizes are correct */
4506     ierr = MatGetSize(newMat,&rows,&cols);CHKERRQ(ierr);
4507     if (rows < 0 && cols < 0) { /* user might provide local size instead of global size */
4508       ierr = MatGetLocalSize(newMat,&rows,&cols);CHKERRQ(ierr);
4509     }
4510     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);
4511   }
4512   ierr = MatSeqAIJSetPreallocation_SeqAIJ(newMat,0,rowlengths);CHKERRQ(ierr);
4513   a    = (Mat_SeqAIJ*)newMat->data;
4514 
4515   ierr = PetscBinaryRead(fd,a->j,nz,PETSC_INT);CHKERRQ(ierr);
4516 
4517   /* read in nonzero values */
4518   ierr = PetscBinaryRead(fd,a->a,nz,PETSC_SCALAR);CHKERRQ(ierr);
4519 
4520   /* set matrix "i" values */
4521   a->i[0] = 0;
4522   for (i=1; i<= M; i++) {
4523     a->i[i]      = a->i[i-1] + rowlengths[i-1];
4524     a->ilen[i-1] = rowlengths[i-1];
4525   }
4526   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
4527 
4528   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4529   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4530   PetscFunctionReturn(0);
4531 }
4532 
4533 #undef __FUNCT__
4534 #define __FUNCT__ "MatEqual_SeqAIJ"
4535 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4536 {
4537   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4538   PetscErrorCode ierr;
4539 #if defined(PETSC_USE_COMPLEX)
4540   PetscInt k;
4541 #endif
4542 
4543   PetscFunctionBegin;
4544   /* If the  matrix dimensions are not equal,or no of nonzeros */
4545   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4546     *flg = PETSC_FALSE;
4547     PetscFunctionReturn(0);
4548   }
4549 
4550   /* if the a->i are the same */
4551   ierr = PetscMemcmp(a->i,b->i,(A->rmap->n+1)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4552   if (!*flg) PetscFunctionReturn(0);
4553 
4554   /* if a->j are the same */
4555   ierr = PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4556   if (!*flg) PetscFunctionReturn(0);
4557 
4558   /* if a->a are the same */
4559 #if defined(PETSC_USE_COMPLEX)
4560   for (k=0; k<a->nz; k++) {
4561     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4562       *flg = PETSC_FALSE;
4563       PetscFunctionReturn(0);
4564     }
4565   }
4566 #else
4567   ierr = PetscMemcmp(a->a,b->a,(a->nz)*sizeof(PetscScalar),flg);CHKERRQ(ierr);
4568 #endif
4569   PetscFunctionReturn(0);
4570 }
4571 
4572 #undef __FUNCT__
4573 #define __FUNCT__ "MatCreateSeqAIJWithArrays"
4574 /*@
4575      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4576               provided by the user.
4577 
4578       Collective on MPI_Comm
4579 
4580    Input Parameters:
4581 +   comm - must be an MPI communicator of size 1
4582 .   m - number of rows
4583 .   n - number of columns
4584 .   i - row indices
4585 .   j - column indices
4586 -   a - matrix values
4587 
4588    Output Parameter:
4589 .   mat - the matrix
4590 
4591    Level: intermediate
4592 
4593    Notes:
4594        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4595     once the matrix is destroyed and not before
4596 
4597        You cannot set new nonzero locations into this matrix, that will generate an error.
4598 
4599        The i and j indices are 0 based
4600 
4601        The format which is used for the sparse matrix input, is equivalent to a
4602     row-major ordering.. i.e for the following matrix, the input data expected is
4603     as shown:
4604 
4605         1 0 0
4606         2 0 3
4607         4 5 6
4608 
4609         i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4610         j =  {0,0,2,0,1,2}  [size = nz = 6]; values must be sorted for each row
4611         v =  {1,2,3,4,5,6}  [size = nz = 6]
4612 
4613 
4614 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4615 
4616 @*/
4617 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat)
4618 {
4619   PetscErrorCode ierr;
4620   PetscInt       ii;
4621   Mat_SeqAIJ     *aij;
4622 #if defined(PETSC_USE_DEBUG)
4623   PetscInt jj;
4624 #endif
4625 
4626   PetscFunctionBegin;
4627   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4628   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4629   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4630   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4631   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4632   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,0);CHKERRQ(ierr);
4633   aij  = (Mat_SeqAIJ*)(*mat)->data;
4634   ierr = PetscMalloc2(m,PetscInt,&aij->imax,m,PetscInt,&aij->ilen);CHKERRQ(ierr);
4635 
4636   aij->i            = i;
4637   aij->j            = j;
4638   aij->a            = a;
4639   aij->singlemalloc = PETSC_FALSE;
4640   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4641   aij->free_a       = PETSC_FALSE;
4642   aij->free_ij      = PETSC_FALSE;
4643 
4644   for (ii=0; ii<m; ii++) {
4645     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4646 #if defined(PETSC_USE_DEBUG)
4647     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]);
4648     for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4649       if (j[jj] < j[jj-1]) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column entry number %D (actual colum %D) in row %D is not sorted",jj-i[ii],j[jj],ii);
4650       if (j[jj] == j[jj]-1) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column entry number %D (actual colum %D) in row %D is identical to previous entry",jj-i[ii],j[jj],ii);
4651     }
4652 #endif
4653   }
4654 #if defined(PETSC_USE_DEBUG)
4655   for (ii=0; ii<aij->i[m]; ii++) {
4656     if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %d index = %d",ii,j[ii]);
4657     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]);
4658   }
4659 #endif
4660 
4661   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4662   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4663   PetscFunctionReturn(0);
4664 }
4665 #undef __FUNCT__
4666 #define __FUNCT__ "MatCreateSeqAIJFromTriple"
4667 /*@C
4668      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4669               provided by the user.
4670 
4671       Collective on MPI_Comm
4672 
4673    Input Parameters:
4674 +   comm - must be an MPI communicator of size 1
4675 .   m   - number of rows
4676 .   n   - number of columns
4677 .   i   - row indices
4678 .   j   - column indices
4679 .   a   - matrix values
4680 .   nz  - number of nonzeros
4681 -   idx - 0 or 1 based
4682 
4683    Output Parameter:
4684 .   mat - the matrix
4685 
4686    Level: intermediate
4687 
4688    Notes:
4689        The i and j indices are 0 based
4690 
4691        The format which is used for the sparse matrix input, is equivalent to a
4692     row-major ordering.. i.e for the following matrix, the input data expected is
4693     as shown:
4694 
4695         1 0 0
4696         2 0 3
4697         4 5 6
4698 
4699         i =  {0,1,1,2,2,2}
4700         j =  {0,0,2,0,1,2}
4701         v =  {1,2,3,4,5,6}
4702 
4703 
4704 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4705 
4706 @*/
4707 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat,PetscInt nz,PetscBool idx)
4708 {
4709   PetscErrorCode ierr;
4710   PetscInt       ii, *nnz, one = 1,row,col;
4711 
4712 
4713   PetscFunctionBegin;
4714   ierr = PetscMalloc(m*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
4715   ierr = PetscMemzero(nnz,m*sizeof(PetscInt));CHKERRQ(ierr);
4716   for (ii = 0; ii < nz; ii++) {
4717     nnz[i[ii]] += 1;
4718   }
4719   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4720   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4721   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4722   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4723   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4724   for (ii = 0; ii < nz; ii++) {
4725     if (idx) {
4726       row = i[ii] - 1;
4727       col = j[ii] - 1;
4728     } else {
4729       row = i[ii];
4730       col = j[ii];
4731     }
4732     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4733   }
4734   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4735   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4736   ierr = PetscFree(nnz);CHKERRQ(ierr);
4737   PetscFunctionReturn(0);
4738 }
4739 
4740 #undef __FUNCT__
4741 #define __FUNCT__ "MatSetColoring_SeqAIJ"
4742 PetscErrorCode MatSetColoring_SeqAIJ(Mat A,ISColoring coloring)
4743 {
4744   PetscErrorCode ierr;
4745   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4746 
4747   PetscFunctionBegin;
4748   if (coloring->ctype == IS_COLORING_GLOBAL) {
4749     ierr        = ISColoringReference(coloring);CHKERRQ(ierr);
4750     a->coloring = coloring;
4751   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
4752     PetscInt        i,*larray;
4753     ISColoring      ocoloring;
4754     ISColoringValue *colors;
4755 
4756     /* set coloring for diagonal portion */
4757     ierr = PetscMalloc(A->cmap->n*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4758     for (i=0; i<A->cmap->n; i++) larray[i] = i;
4759     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
4760     ierr = PetscMalloc(A->cmap->n*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4761     for (i=0; i<A->cmap->n; i++) colors[i] = coloring->colors[larray[i]];
4762     ierr        = PetscFree(larray);CHKERRQ(ierr);
4763     ierr        = ISColoringCreate(PETSC_COMM_SELF,coloring->n,A->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4764     a->coloring = ocoloring;
4765   }
4766   PetscFunctionReturn(0);
4767 }
4768 
4769 #undef __FUNCT__
4770 #define __FUNCT__ "MatSetValuesAdifor_SeqAIJ"
4771 PetscErrorCode MatSetValuesAdifor_SeqAIJ(Mat A,PetscInt nl,void *advalues)
4772 {
4773   Mat_SeqAIJ      *a      = (Mat_SeqAIJ*)A->data;
4774   PetscInt        m       = A->rmap->n,*ii = a->i,*jj = a->j,nz,i,j;
4775   MatScalar       *v      = a->a;
4776   PetscScalar     *values = (PetscScalar*)advalues;
4777   ISColoringValue *color;
4778 
4779   PetscFunctionBegin;
4780   if (!a->coloring) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Coloring not set for matrix");
4781   color = a->coloring->colors;
4782   /* loop over rows */
4783   for (i=0; i<m; i++) {
4784     nz = ii[i+1] - ii[i];
4785     /* loop over columns putting computed value into matrix */
4786     for (j=0; j<nz; j++) *v++ = values[color[*jj++]];
4787     values += nl; /* jump to next row of derivatives */
4788   }
4789   PetscFunctionReturn(0);
4790 }
4791 
4792 #undef __FUNCT__
4793 #define __FUNCT__ "MatSeqAIJInvalidateDiagonal"
4794 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4795 {
4796   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4797   PetscErrorCode ierr;
4798 
4799   PetscFunctionBegin;
4800   a->idiagvalid  = PETSC_FALSE;
4801   a->ibdiagvalid = PETSC_FALSE;
4802 
4803   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4804   PetscFunctionReturn(0);
4805 }
4806 
4807 /*
4808     Special version for direct calls from Fortran
4809 */
4810 #include <petsc-private/fortranimpl.h>
4811 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4812 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
4813 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4814 #define matsetvaluesseqaij_ matsetvaluesseqaij
4815 #endif
4816 
4817 /* Change these macros so can be used in void function */
4818 #undef CHKERRQ
4819 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
4820 #undef SETERRQ2
4821 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4822 #undef SETERRQ3
4823 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4824 
4825 #undef __FUNCT__
4826 #define __FUNCT__ "matsetvaluesseqaij_"
4827 PETSC_EXTERN void PETSC_STDCALL matsetvaluesseqaij_(Mat *AA,PetscInt *mm,const PetscInt im[],PetscInt *nn,const PetscInt in[],const PetscScalar v[],InsertMode *isis, PetscErrorCode *_ierr)
4828 {
4829   Mat            A  = *AA;
4830   PetscInt       m  = *mm, n = *nn;
4831   InsertMode     is = *isis;
4832   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4833   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
4834   PetscInt       *imax,*ai,*ailen;
4835   PetscErrorCode ierr;
4836   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
4837   MatScalar      *ap,value,*aa;
4838   PetscBool      ignorezeroentries = a->ignorezeroentries;
4839   PetscBool      roworiented       = a->roworiented;
4840 
4841   PetscFunctionBegin;
4842   MatCheckPreallocated(A,1);
4843   imax  = a->imax;
4844   ai    = a->i;
4845   ailen = a->ilen;
4846   aj    = a->j;
4847   aa    = a->a;
4848 
4849   for (k=0; k<m; k++) { /* loop over added rows */
4850     row = im[k];
4851     if (row < 0) continue;
4852 #if defined(PETSC_USE_DEBUG)
4853     if (row >= A->rmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
4854 #endif
4855     rp   = aj + ai[row]; ap = aa + ai[row];
4856     rmax = imax[row]; nrow = ailen[row];
4857     low  = 0;
4858     high = nrow;
4859     for (l=0; l<n; l++) { /* loop over added columns */
4860       if (in[l] < 0) continue;
4861 #if defined(PETSC_USE_DEBUG)
4862       if (in[l] >= A->cmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
4863 #endif
4864       col = in[l];
4865       if (roworiented) value = v[l + k*n];
4866       else value = v[k + l*m];
4867 
4868       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
4869 
4870       if (col <= lastcol) low = 0;
4871       else high = nrow;
4872       lastcol = col;
4873       while (high-low > 5) {
4874         t = (low+high)/2;
4875         if (rp[t] > col) high = t;
4876         else             low  = t;
4877       }
4878       for (i=low; i<high; i++) {
4879         if (rp[i] > col) break;
4880         if (rp[i] == col) {
4881           if (is == ADD_VALUES) ap[i] += value;
4882           else                  ap[i] = value;
4883           goto noinsert;
4884         }
4885       }
4886       if (value == 0.0 && ignorezeroentries) goto noinsert;
4887       if (nonew == 1) goto noinsert;
4888       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
4889       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
4890       N = nrow++ - 1; a->nz++; high++;
4891       /* shift up all the later entries in this row */
4892       for (ii=N; ii>=i; ii--) {
4893         rp[ii+1] = rp[ii];
4894         ap[ii+1] = ap[ii];
4895       }
4896       rp[i] = col;
4897       ap[i] = value;
4898 noinsert:;
4899       low = i + 1;
4900     }
4901     ailen[row] = nrow;
4902   }
4903   A->same_nonzero = PETSC_FALSE;
4904   PetscFunctionReturnVoid();
4905 }
4906 
4907 
4908