xref: /petsc/src/mat/impls/aij/seq/aij.c (revision 476e0d0aa5a21558d06346d6913ded26b2072ae9)
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 /* Optimize MatFDColoringApply_AIJ() by using array den2sp to skip calling MatSetValues() */
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,l,row,col,N;
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   Mat_SeqAIJ     *csp=(Mat_SeqAIJ*)J->data;
2714   PetscScalar    *ca=csp->a;
2715   const PetscInt ncolors=coloring->ncolors,*ncolumns=coloring->ncolumns,*nrows=coloring->nrows;
2716   PetscInt       *den2sp=coloring->den2sp,*idx;
2717   PetscInt       **rows=coloring->rows,**columns=coloring->columns,ncolumns_k,nrows_k,**columnsforrow=coloring->columnsforrow;
2718 #if defined(JACOBIANCOLOROPT)
2719   PetscLogDouble t0,t1,time_setvalues=0.0;
2720 #endif
2721 
2722   PetscFunctionBegin;
2723   ierr = MatSetUnfactored(J);CHKERRQ(ierr);
2724   ierr = PetscOptionsGetBool(NULL,"-mat_fd_coloring_dont_rezero",&flg,NULL);CHKERRQ(ierr);
2725   if (flg) {
2726     ierr = PetscInfo(coloring,"Not calling MatZeroEntries()\n");CHKERRQ(ierr);
2727   } else {
2728     PetscBool assembled;
2729     ierr = MatAssembled(J,&assembled);CHKERRQ(ierr);
2730     if (assembled) {
2731       ierr = MatZeroEntries(J);CHKERRQ(ierr);
2732     }
2733   }
2734 
2735   if (!coloring->vscale) {
2736     ierr = VecDuplicate(x1,&coloring->vscale);CHKERRQ(ierr);
2737   }
2738 
2739   if (coloring->htype[0] == 'w') { /* tacky test; need to make systematic if we add other approaches to computing h*/
2740     ierr = VecNorm(x1,NORM_2,&unorm);CHKERRQ(ierr);
2741   }
2742 
2743   /* Set w1 = F(x1) */
2744   if (!coloring->fset) {
2745     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2746     ierr = (*f)(sctx,x1,w1,fctx);CHKERRQ(ierr);
2747     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2748   } else {
2749     coloring->fset = PETSC_FALSE;
2750   }
2751 
2752   if (!coloring->w3) {
2753     ierr = VecDuplicate(x1,&coloring->w3);CHKERRQ(ierr);
2754     ierr = PetscLogObjectParent((PetscObject)coloring,(PetscObject)coloring->w3);CHKERRQ(ierr);
2755   }
2756   w3 = coloring->w3;
2757 
2758   /* Compute scale factors: vscale = 1./dx = 1./(epsilon*xx) */
2759   ierr = VecGetArray(x1,&xx);CHKERRQ(ierr);
2760   ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2761   ierr = VecGetSize(x1,&N);CHKERRQ(ierr);
2762   for (col=0; col<N; col++) {
2763     if (coloring->htype[0] == 'w') {
2764       dx = 1.0 + unorm;
2765     } else {
2766       dx = xx[col];
2767     }
2768     if (dx == (PetscScalar)0.0) dx = 1.0;
2769     if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
2770     else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
2771     dx               *= epsilon;
2772     //vscale_array[col] = (PetscScalar)1.0/dx;
2773     vscale_array[col] = (PetscScalar)dx;
2774   }
2775 
2776   idx = den2sp;
2777   for (k=0; k<ncolors; k++) { /* loop over colors */
2778     coloring->currentcolor = k;
2779 
2780     /*
2781       Loop over each column associated with color
2782       adding the perturbation to the vector w3 = x1 + dx.
2783     */
2784     ierr = VecCopy(x1,w3);CHKERRQ(ierr);
2785     ierr = VecGetArray(w3,&w3_array);CHKERRQ(ierr);
2786     ncolumns_k = ncolumns[k];
2787     for (l=0; l<ncolumns_k; l++) { /* loop over columns */
2788       col = columns[k][l];
2789       //w3_array[col] += 1/vscale_array[col];
2790       w3_array[col] += vscale_array[col];
2791     }
2792     ierr = VecRestoreArray(w3,&w3_array);CHKERRQ(ierr);
2793 
2794     /*
2795       Evaluate function at w3 = x1 + dx (here dx is a vector of perturbations)
2796                            w2 = F(x1 + dx) - F(x1)
2797     */
2798     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2799     ierr = (*f)(sctx,w3,w2,fctx);CHKERRQ(ierr);
2800     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2801     ierr = VecAXPY(w2,-1.0,w1);CHKERRQ(ierr);
2802 
2803     /*
2804       Loop over rows of vector, putting w2/dx into Jacobian matrix
2805     */
2806 #if defined(JACOBIANCOLOROPT)
2807     ierr = PetscTime(&t0);CHKERRQ(ierr);
2808 #endif
2809     ierr = VecGetArray(w2,&y);CHKERRQ(ierr);
2810     nrows_k = nrows[k];
2811     for (l=0; l<nrows_k; l++) { /* loop over rows */
2812       row     = rows[k][l];     /* row index */
2813       //y[row] *= vscale_array[columnsforrow[k][l]];
2814       y[row] /= vscale_array[columnsforrow[k][l]];
2815       ca[idx[l]] = y[row];
2816     }
2817     idx += nrows_k;
2818     ierr = VecRestoreArray(w2,&y);CHKERRQ(ierr);
2819 #if defined(JACOBIANCOLOROPT)
2820     ierr = PetscTime(&t1);CHKERRQ(ierr);
2821     time_setvalues += t1-t0;
2822 #endif
2823   } /* endof for each color */
2824 #if defined(JACOBIANCOLOROPT)
2825   printf("     MatFDColoringApply_SeqAIJ: time_setvalues %g\n",time_setvalues);
2826 #endif
2827   ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2828   ierr = VecRestoreArray(x1,&xx);CHKERRQ(ierr);
2829 
2830   coloring->currentcolor = -1;
2831   PetscFunctionReturn(0);
2832 }
2833 /* --------------------------------------------------------*/
2834 
2835 #undef __FUNCT__
2836 #define __FUNCT__ "MatFDColoringApply_SeqAIJ_old"
2837 PetscErrorCode MatFDColoringApply_SeqAIJ_old(Mat J,MatFDColoring coloring,Vec x1,MatStructure *flag,void *sctx)
2838 {
2839   PetscErrorCode (*f)(void*,Vec,Vec,void*) = (PetscErrorCode (*)(void*,Vec,Vec,void*))coloring->f;
2840   PetscErrorCode ierr;
2841   PetscInt       k,N,start,end,l,row,col,srow,**vscaleforrow;
2842   PetscScalar    dx,*y,*xx,*w3_array;
2843   PetscScalar    *vscale_array;
2844   PetscReal      epsilon = coloring->error_rel,umin = coloring->umin;
2845   Vec            w1,w2,w3;
2846   void           *fctx = coloring->fctx;
2847   PetscBool      flg   = PETSC_FALSE;
2848 
2849   PetscFunctionBegin;
2850   printf("MatFDColoringApply_SeqAIJ ...\n");
2851   if (!coloring->w1) {
2852     ierr = VecDuplicate(x1,&coloring->w1);CHKERRQ(ierr);
2853     ierr = PetscLogObjectParent((PetscObject)coloring,(PetscObject)coloring->w1);CHKERRQ(ierr);
2854     ierr = VecDuplicate(x1,&coloring->w2);CHKERRQ(ierr);
2855     ierr = PetscLogObjectParent((PetscObject)coloring,(PetscObject)coloring->w2);CHKERRQ(ierr);
2856     ierr = VecDuplicate(x1,&coloring->w3);CHKERRQ(ierr);
2857     ierr = PetscLogObjectParent((PetscObject)coloring,(PetscObject)coloring->w3);CHKERRQ(ierr);
2858   }
2859   w1 = coloring->w1; w2 = coloring->w2; w3 = coloring->w3;
2860 
2861   ierr = MatSetUnfactored(J);CHKERRQ(ierr);
2862   ierr = PetscOptionsGetBool(((PetscObject)coloring)->prefix,"-mat_fd_coloring_dont_rezero",&flg,NULL);CHKERRQ(ierr);
2863   if (flg) {
2864     ierr = PetscInfo(coloring,"Not calling MatZeroEntries()\n");CHKERRQ(ierr);
2865   } else {
2866     PetscBool assembled;
2867     ierr = MatAssembled(J,&assembled);CHKERRQ(ierr);
2868     if (assembled) {
2869       ierr = MatZeroEntries(J);CHKERRQ(ierr);
2870     }
2871   }
2872 
2873   ierr = VecGetOwnershipRange(x1,&start,&end);CHKERRQ(ierr);
2874   ierr = VecGetSize(x1,&N);CHKERRQ(ierr);
2875 
2876   if (!coloring->fset) {
2877     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2878     ierr = (*f)(sctx,x1,w1,fctx);CHKERRQ(ierr);
2879     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2880   } else {
2881     coloring->fset = PETSC_FALSE;
2882   }
2883 
2884   /*
2885       Compute all the scale factors and share with other processors
2886   */
2887   ierr = VecGetArray(x1,&xx);CHKERRQ(ierr);xx = xx - start;
2888   ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);vscale_array = vscale_array - start;
2889   for (k=0; k<coloring->ncolors; k++) {
2890     /*
2891        Loop over each column associated with color adding the
2892        perturbation to the vector w3.
2893     */
2894     for (l=0; l<coloring->ncolumns[k]; l++) {
2895       col = coloring->columns[k][l];    /* column of the matrix we are probing for */
2896       dx  = xx[col];
2897       if (dx == 0.0) dx = 1.0;
2898       if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
2899       else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
2900       dx               *= epsilon;
2901       vscale_array[col] = 1.0/dx;
2902     }
2903   }
2904   vscale_array = vscale_array + start;
2905 
2906   ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2907   ierr = VecGhostUpdateBegin(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2908   ierr = VecGhostUpdateEnd(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2909 
2910   /*  ierr = VecView(coloring->vscale,PETSC_VIEWER_STDOUT_WORLD);
2911       ierr = VecView(x1,PETSC_VIEWER_STDOUT_WORLD);*/
2912 
2913   if (coloring->vscaleforrow) vscaleforrow = coloring->vscaleforrow;
2914   else                        vscaleforrow = coloring->columnsforrow;
2915 
2916   ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2917   /*
2918       Loop over each color
2919   */
2920   for (k=0; k<coloring->ncolors; k++) {
2921     coloring->currentcolor = k;
2922 
2923     ierr = VecCopy(x1,w3);CHKERRQ(ierr);
2924     ierr = VecGetArray(w3,&w3_array);CHKERRQ(ierr);w3_array = w3_array - start;
2925     /*
2926        Loop over each column associated with color adding the
2927        perturbation to the vector w3.
2928     */
2929     for (l=0; l<coloring->ncolumns[k]; l++) {
2930       col = coloring->columns[k][l];    /* column of the matrix we are probing for */
2931       dx  = xx[col];
2932       if (dx == 0.0) dx = 1.0;
2933       if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
2934       else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
2935       dx *= epsilon;
2936       if (!PetscAbsScalar(dx)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Computed 0 differencing parameter");
2937       w3_array[col] += dx;
2938     }
2939     w3_array = w3_array + start; ierr = VecRestoreArray(w3,&w3_array);CHKERRQ(ierr);
2940 
2941     /*
2942        Evaluate function at x1 + dx (here dx is a vector of perturbations)
2943     */
2944 
2945     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2946     ierr = (*f)(sctx,w3,w2,fctx);CHKERRQ(ierr);
2947     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2948     ierr = VecAXPY(w2,-1.0,w1);CHKERRQ(ierr);
2949 
2950     /*
2951        Loop over rows of vector, putting results into Jacobian matrix
2952     */
2953     ierr = VecGetArray(w2,&y);CHKERRQ(ierr);
2954     for (l=0; l<coloring->nrows[k]; l++) {
2955       row     = coloring->rows[k][l];
2956       col     = coloring->columnsforrow[k][l];
2957       y[row] *= vscale_array[vscaleforrow[k][l]];
2958       srow    = row + start;
2959       ierr    = MatSetValues_SeqAIJ(J,1,&srow,1,&col,y+row,INSERT_VALUES);CHKERRQ(ierr);
2960     }
2961     ierr = VecRestoreArray(w2,&y);CHKERRQ(ierr);
2962   }
2963   coloring->currentcolor = k;
2964 
2965   ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2966   xx   = xx + start;
2967   ierr = VecRestoreArray(x1,&xx);CHKERRQ(ierr);
2968   ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2969   ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2970   PetscFunctionReturn(0);
2971 }
2972 
2973 /*
2974    Computes the number of nonzeros per row needed for preallocation when X and Y
2975    have different nonzero structure.
2976 */
2977 #undef __FUNCT__
2978 #define __FUNCT__ "MatAXPYGetPreallocation_SeqAIJ"
2979 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
2980 {
2981   PetscInt       i,m=Y->rmap->N;
2982   Mat_SeqAIJ     *x  = (Mat_SeqAIJ*)X->data;
2983   Mat_SeqAIJ     *y  = (Mat_SeqAIJ*)Y->data;
2984   const PetscInt *xi = x->i,*yi = y->i;
2985 
2986   PetscFunctionBegin;
2987   /* Set the number of nonzeros in the new matrix */
2988   for (i=0; i<m; i++) {
2989     PetscInt       j,k,nzx = xi[i+1] - xi[i],nzy = yi[i+1] - yi[i];
2990     const PetscInt *xj = x->j+xi[i],*yj = y->j+yi[i];
2991     nnz[i] = 0;
2992     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2993       for (; k<nzy && yj[k]<xj[j]; k++) nnz[i]++; /* Catch up to X */
2994       if (k<nzy && yj[k]==xj[j]) k++;             /* Skip duplicate */
2995       nnz[i]++;
2996     }
2997     for (; k<nzy; k++) nnz[i]++;
2998   }
2999   PetscFunctionReturn(0);
3000 }
3001 
3002 #undef __FUNCT__
3003 #define __FUNCT__ "MatAXPY_SeqAIJ"
3004 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
3005 {
3006   PetscErrorCode ierr;
3007   PetscInt       i;
3008   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
3009   PetscBLASInt   one=1,bnz;
3010 
3011   PetscFunctionBegin;
3012   ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
3013   if (str == SAME_NONZERO_PATTERN) {
3014     PetscScalar alpha = a;
3015     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
3016     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
3017   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
3018     if (y->xtoy && y->XtoY != X) {
3019       ierr = PetscFree(y->xtoy);CHKERRQ(ierr);
3020       ierr = MatDestroy(&y->XtoY);CHKERRQ(ierr);
3021     }
3022     if (!y->xtoy) { /* get xtoy */
3023       ierr    = MatAXPYGetxtoy_Private(X->rmap->n,x->i,x->j,NULL, y->i,y->j,NULL, &y->xtoy);CHKERRQ(ierr);
3024       y->XtoY = X;
3025       ierr    = PetscObjectReference((PetscObject)X);CHKERRQ(ierr);
3026     }
3027     for (i=0; i<x->nz; i++) y->a[y->xtoy[i]] += a*(x->a[i]);
3028     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);
3029   } else {
3030     Mat      B;
3031     PetscInt *nnz;
3032     ierr = PetscMalloc(Y->rmap->N*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
3033     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
3034     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
3035     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
3036     ierr = MatSetBlockSizes(B,Y->rmap->bs,Y->cmap->bs);CHKERRQ(ierr);
3037     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
3038     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
3039     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
3040     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
3041     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
3042     ierr = PetscFree(nnz);CHKERRQ(ierr);
3043   }
3044   PetscFunctionReturn(0);
3045 }
3046 
3047 #undef __FUNCT__
3048 #define __FUNCT__ "MatConjugate_SeqAIJ"
3049 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
3050 {
3051 #if defined(PETSC_USE_COMPLEX)
3052   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
3053   PetscInt    i,nz;
3054   PetscScalar *a;
3055 
3056   PetscFunctionBegin;
3057   nz = aij->nz;
3058   a  = aij->a;
3059   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
3060 #else
3061   PetscFunctionBegin;
3062 #endif
3063   PetscFunctionReturn(0);
3064 }
3065 
3066 #undef __FUNCT__
3067 #define __FUNCT__ "MatGetRowMaxAbs_SeqAIJ"
3068 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3069 {
3070   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3071   PetscErrorCode ierr;
3072   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3073   PetscReal      atmp;
3074   PetscScalar    *x;
3075   MatScalar      *aa;
3076 
3077   PetscFunctionBegin;
3078   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3079   aa = a->a;
3080   ai = a->i;
3081   aj = a->j;
3082 
3083   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3084   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3085   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3086   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3087   for (i=0; i<m; i++) {
3088     ncols = ai[1] - ai[0]; ai++;
3089     x[i]  = 0.0;
3090     for (j=0; j<ncols; j++) {
3091       atmp = PetscAbsScalar(*aa);
3092       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3093       aa++; aj++;
3094     }
3095   }
3096   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3097   PetscFunctionReturn(0);
3098 }
3099 
3100 #undef __FUNCT__
3101 #define __FUNCT__ "MatGetRowMax_SeqAIJ"
3102 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3103 {
3104   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3105   PetscErrorCode ierr;
3106   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3107   PetscScalar    *x;
3108   MatScalar      *aa;
3109 
3110   PetscFunctionBegin;
3111   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3112   aa = a->a;
3113   ai = a->i;
3114   aj = a->j;
3115 
3116   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3117   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3118   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3119   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3120   for (i=0; i<m; i++) {
3121     ncols = ai[1] - ai[0]; ai++;
3122     if (ncols == A->cmap->n) { /* row is dense */
3123       x[i] = *aa; if (idx) idx[i] = 0;
3124     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
3125       x[i] = 0.0;
3126       if (idx) {
3127         idx[i] = 0; /* in case ncols is zero */
3128         for (j=0;j<ncols;j++) { /* find first implicit 0.0 in the row */
3129           if (aj[j] > j) {
3130             idx[i] = j;
3131             break;
3132           }
3133         }
3134       }
3135     }
3136     for (j=0; j<ncols; j++) {
3137       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3138       aa++; aj++;
3139     }
3140   }
3141   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3142   PetscFunctionReturn(0);
3143 }
3144 
3145 #undef __FUNCT__
3146 #define __FUNCT__ "MatGetRowMinAbs_SeqAIJ"
3147 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3148 {
3149   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3150   PetscErrorCode ierr;
3151   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3152   PetscReal      atmp;
3153   PetscScalar    *x;
3154   MatScalar      *aa;
3155 
3156   PetscFunctionBegin;
3157   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3158   aa = a->a;
3159   ai = a->i;
3160   aj = a->j;
3161 
3162   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3163   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3164   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3165   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);
3166   for (i=0; i<m; i++) {
3167     ncols = ai[1] - ai[0]; ai++;
3168     if (ncols) {
3169       /* Get first nonzero */
3170       for (j = 0; j < ncols; j++) {
3171         atmp = PetscAbsScalar(aa[j]);
3172         if (atmp > 1.0e-12) {
3173           x[i] = atmp;
3174           if (idx) idx[i] = aj[j];
3175           break;
3176         }
3177       }
3178       if (j == ncols) {x[i] = PetscAbsScalar(*aa); if (idx) idx[i] = *aj;}
3179     } else {
3180       x[i] = 0.0; if (idx) idx[i] = 0;
3181     }
3182     for (j = 0; j < ncols; j++) {
3183       atmp = PetscAbsScalar(*aa);
3184       if (atmp > 1.0e-12 && PetscAbsScalar(x[i]) > atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3185       aa++; aj++;
3186     }
3187   }
3188   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3189   PetscFunctionReturn(0);
3190 }
3191 
3192 #undef __FUNCT__
3193 #define __FUNCT__ "MatGetRowMin_SeqAIJ"
3194 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3195 {
3196   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3197   PetscErrorCode ierr;
3198   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3199   PetscScalar    *x;
3200   MatScalar      *aa;
3201 
3202   PetscFunctionBegin;
3203   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3204   aa = a->a;
3205   ai = a->i;
3206   aj = a->j;
3207 
3208   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3209   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3210   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3211   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3212   for (i=0; i<m; i++) {
3213     ncols = ai[1] - ai[0]; ai++;
3214     if (ncols == A->cmap->n) { /* row is dense */
3215       x[i] = *aa; if (idx) idx[i] = 0;
3216     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3217       x[i] = 0.0;
3218       if (idx) {   /* find first implicit 0.0 in the row */
3219         idx[i] = 0; /* in case ncols is zero */
3220         for (j=0; j<ncols; j++) {
3221           if (aj[j] > j) {
3222             idx[i] = j;
3223             break;
3224           }
3225         }
3226       }
3227     }
3228     for (j=0; j<ncols; j++) {
3229       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3230       aa++; aj++;
3231     }
3232   }
3233   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3234   PetscFunctionReturn(0);
3235 }
3236 
3237 #include <petscblaslapack.h>
3238 #include <petsc-private/kernels/blockinvert.h>
3239 
3240 #undef __FUNCT__
3241 #define __FUNCT__ "MatInvertBlockDiagonal_SeqAIJ"
3242 PetscErrorCode  MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3243 {
3244   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
3245   PetscErrorCode ierr;
3246   PetscInt       i,bs = A->rmap->bs,mbs = A->rmap->n/A->rmap->bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3247   MatScalar      *diag,work[25],*v_work;
3248   PetscReal      shift = 0.0;
3249 
3250   PetscFunctionBegin;
3251   if (a->ibdiagvalid) {
3252     if (values) *values = a->ibdiag;
3253     PetscFunctionReturn(0);
3254   }
3255   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3256   if (!a->ibdiag) {
3257     ierr = PetscMalloc(bs2*mbs*sizeof(PetscScalar),&a->ibdiag);CHKERRQ(ierr);
3258     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3259   }
3260   diag = a->ibdiag;
3261   if (values) *values = a->ibdiag;
3262   /* factor and invert each block */
3263   switch (bs) {
3264   case 1:
3265     for (i=0; i<mbs; i++) {
3266       ierr    = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3267       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3268     }
3269     break;
3270   case 2:
3271     for (i=0; i<mbs; i++) {
3272       ij[0] = 2*i; ij[1] = 2*i + 1;
3273       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3274       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift);CHKERRQ(ierr);
3275       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
3276       diag += 4;
3277     }
3278     break;
3279   case 3:
3280     for (i=0; i<mbs; i++) {
3281       ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
3282       ierr  = MatGetValues(A,3,ij,3,ij,diag);CHKERRQ(ierr);
3283       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr);
3284       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3285       diag += 9;
3286     }
3287     break;
3288   case 4:
3289     for (i=0; i<mbs; i++) {
3290       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3291       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3292       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift);CHKERRQ(ierr);
3293       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3294       diag += 16;
3295     }
3296     break;
3297   case 5:
3298     for (i=0; i<mbs; i++) {
3299       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3300       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3301       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift);CHKERRQ(ierr);
3302       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3303       diag += 25;
3304     }
3305     break;
3306   case 6:
3307     for (i=0; i<mbs; i++) {
3308       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;
3309       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3310       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift);CHKERRQ(ierr);
3311       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3312       diag += 36;
3313     }
3314     break;
3315   case 7:
3316     for (i=0; i<mbs; i++) {
3317       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;
3318       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3319       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift);CHKERRQ(ierr);
3320       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3321       diag += 49;
3322     }
3323     break;
3324   default:
3325     ierr = PetscMalloc3(bs,MatScalar,&v_work,bs,PetscInt,&v_pivots,bs,PetscInt,&IJ);CHKERRQ(ierr);
3326     for (i=0; i<mbs; i++) {
3327       for (j=0; j<bs; j++) {
3328         IJ[j] = bs*i + j;
3329       }
3330       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3331       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work);CHKERRQ(ierr);
3332       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3333       diag += bs2;
3334     }
3335     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3336   }
3337   a->ibdiagvalid = PETSC_TRUE;
3338   PetscFunctionReturn(0);
3339 }
3340 
3341 #undef __FUNCT__
3342 #define __FUNCT__ "MatSetRandom_SeqAIJ"
3343 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3344 {
3345   PetscErrorCode ierr;
3346   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3347   PetscScalar    a;
3348   PetscInt       m,n,i,j,col;
3349 
3350   PetscFunctionBegin;
3351   if (!x->assembled) {
3352     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3353     for (i=0; i<m; i++) {
3354       for (j=0; j<aij->imax[i]; j++) {
3355         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3356         col  = (PetscInt)(n*PetscRealPart(a));
3357         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3358       }
3359     }
3360   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet coded");
3361   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3362   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3363   PetscFunctionReturn(0);
3364 }
3365 
3366 extern PetscErrorCode  MatFDColoringApply_AIJ(Mat,MatFDColoring,Vec,MatStructure*,void*);
3367 /* -------------------------------------------------------------------*/
3368 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3369                                         MatGetRow_SeqAIJ,
3370                                         MatRestoreRow_SeqAIJ,
3371                                         MatMult_SeqAIJ,
3372                                 /*  4*/ MatMultAdd_SeqAIJ,
3373                                         MatMultTranspose_SeqAIJ,
3374                                         MatMultTransposeAdd_SeqAIJ,
3375                                         0,
3376                                         0,
3377                                         0,
3378                                 /* 10*/ 0,
3379                                         MatLUFactor_SeqAIJ,
3380                                         0,
3381                                         MatSOR_SeqAIJ,
3382                                         MatTranspose_SeqAIJ,
3383                                 /*1 5*/ MatGetInfo_SeqAIJ,
3384                                         MatEqual_SeqAIJ,
3385                                         MatGetDiagonal_SeqAIJ,
3386                                         MatDiagonalScale_SeqAIJ,
3387                                         MatNorm_SeqAIJ,
3388                                 /* 20*/ 0,
3389                                         MatAssemblyEnd_SeqAIJ,
3390                                         MatSetOption_SeqAIJ,
3391                                         MatZeroEntries_SeqAIJ,
3392                                 /* 24*/ MatZeroRows_SeqAIJ,
3393                                         0,
3394                                         0,
3395                                         0,
3396                                         0,
3397                                 /* 29*/ MatSetUp_SeqAIJ,
3398                                         0,
3399                                         0,
3400                                         0,
3401                                         0,
3402                                 /* 34*/ MatDuplicate_SeqAIJ,
3403                                         0,
3404                                         0,
3405                                         MatILUFactor_SeqAIJ,
3406                                         0,
3407                                 /* 39*/ MatAXPY_SeqAIJ,
3408                                         MatGetSubMatrices_SeqAIJ,
3409                                         MatIncreaseOverlap_SeqAIJ,
3410                                         MatGetValues_SeqAIJ,
3411                                         MatCopy_SeqAIJ,
3412                                 /* 44*/ MatGetRowMax_SeqAIJ,
3413                                         MatScale_SeqAIJ,
3414                                         0,
3415                                         MatDiagonalSet_SeqAIJ,
3416                                         MatZeroRowsColumns_SeqAIJ,
3417                                 /* 49*/ MatSetRandom_SeqAIJ,
3418                                         MatGetRowIJ_SeqAIJ,
3419                                         MatRestoreRowIJ_SeqAIJ,
3420                                         MatGetColumnIJ_SeqAIJ,
3421                                         MatRestoreColumnIJ_SeqAIJ,
3422                                 /* 54*/ MatFDColoringCreate_SeqAIJ,
3423                                         0,
3424                                         0,
3425                                         MatPermute_SeqAIJ,
3426                                         0,
3427                                 /* 59*/ 0,
3428                                         MatDestroy_SeqAIJ,
3429                                         MatView_SeqAIJ,
3430                                         0,
3431                                         MatMatMatMult_SeqAIJ_SeqAIJ_SeqAIJ,
3432                                 /* 64*/ MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ,
3433                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3434                                         0,
3435                                         0,
3436                                         0,
3437                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3438                                         MatGetRowMinAbs_SeqAIJ,
3439                                         0,
3440                                         MatSetColoring_SeqAIJ,
3441                                         0,
3442                                 /* 74*/ MatSetValuesAdifor_SeqAIJ,
3443                                         MatFDColoringApply_AIJ,
3444                                         0,
3445                                         0,
3446                                         0,
3447                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3448                                         0,
3449                                         0,
3450                                         0,
3451                                         MatLoad_SeqAIJ,
3452                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3453                                         MatIsHermitian_SeqAIJ,
3454                                         0,
3455                                         0,
3456                                         0,
3457                                 /* 89*/ MatMatMult_SeqAIJ_SeqAIJ,
3458                                         MatMatMultSymbolic_SeqAIJ_SeqAIJ,
3459                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3460                                         MatPtAP_SeqAIJ_SeqAIJ,
3461                                         MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy,
3462                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ,
3463                                         MatMatTransposeMult_SeqAIJ_SeqAIJ,
3464                                         MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ,
3465                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3466                                         0,
3467                                 /* 99*/ 0,
3468                                         0,
3469                                         0,
3470                                         MatConjugate_SeqAIJ,
3471                                         0,
3472                                 /*104*/ MatSetValuesRow_SeqAIJ,
3473                                         MatRealPart_SeqAIJ,
3474                                         MatImaginaryPart_SeqAIJ,
3475                                         0,
3476                                         0,
3477                                 /*109*/ MatMatSolve_SeqAIJ,
3478                                         0,
3479                                         MatGetRowMin_SeqAIJ,
3480                                         0,
3481                                         MatMissingDiagonal_SeqAIJ,
3482                                 /*114*/ 0,
3483                                         0,
3484                                         0,
3485                                         0,
3486                                         0,
3487                                 /*119*/ 0,
3488                                         0,
3489                                         0,
3490                                         0,
3491                                         MatGetMultiProcBlock_SeqAIJ,
3492                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3493                                         MatGetColumnNorms_SeqAIJ,
3494                                         MatInvertBlockDiagonal_SeqAIJ,
3495                                         0,
3496                                         0,
3497                                 /*129*/ 0,
3498                                         MatTransposeMatMult_SeqAIJ_SeqAIJ,
3499                                         MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ,
3500                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3501                                         MatTransposeColoringCreate_SeqAIJ,
3502                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3503                                         MatTransColoringApplyDenToSp_SeqAIJ,
3504                                         MatRARt_SeqAIJ_SeqAIJ,
3505                                         MatRARtSymbolic_SeqAIJ_SeqAIJ,
3506                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3507                                  /*139*/0,
3508                                         0
3509 };
3510 
3511 #undef __FUNCT__
3512 #define __FUNCT__ "MatSeqAIJSetColumnIndices_SeqAIJ"
3513 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3514 {
3515   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3516   PetscInt   i,nz,n;
3517 
3518   PetscFunctionBegin;
3519   nz = aij->maxnz;
3520   n  = mat->rmap->n;
3521   for (i=0; i<nz; i++) {
3522     aij->j[i] = indices[i];
3523   }
3524   aij->nz = nz;
3525   for (i=0; i<n; i++) {
3526     aij->ilen[i] = aij->imax[i];
3527   }
3528   PetscFunctionReturn(0);
3529 }
3530 
3531 #undef __FUNCT__
3532 #define __FUNCT__ "MatSeqAIJSetColumnIndices"
3533 /*@
3534     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3535        in the matrix.
3536 
3537   Input Parameters:
3538 +  mat - the SeqAIJ matrix
3539 -  indices - the column indices
3540 
3541   Level: advanced
3542 
3543   Notes:
3544     This can be called if you have precomputed the nonzero structure of the
3545   matrix and want to provide it to the matrix object to improve the performance
3546   of the MatSetValues() operation.
3547 
3548     You MUST have set the correct numbers of nonzeros per row in the call to
3549   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3550 
3551     MUST be called before any calls to MatSetValues();
3552 
3553     The indices should start with zero, not one.
3554 
3555 @*/
3556 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3557 {
3558   PetscErrorCode ierr;
3559 
3560   PetscFunctionBegin;
3561   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3562   PetscValidPointer(indices,2);
3563   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3564   PetscFunctionReturn(0);
3565 }
3566 
3567 /* ----------------------------------------------------------------------------------------*/
3568 
3569 #undef __FUNCT__
3570 #define __FUNCT__ "MatStoreValues_SeqAIJ"
3571 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3572 {
3573   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3574   PetscErrorCode ierr;
3575   size_t         nz = aij->i[mat->rmap->n];
3576 
3577   PetscFunctionBegin;
3578   if (aij->nonew != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3579 
3580   /* allocate space for values if not already there */
3581   if (!aij->saved_values) {
3582     ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&aij->saved_values);CHKERRQ(ierr);
3583     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3584   }
3585 
3586   /* copy values over */
3587   ierr = PetscMemcpy(aij->saved_values,aij->a,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3588   PetscFunctionReturn(0);
3589 }
3590 
3591 #undef __FUNCT__
3592 #define __FUNCT__ "MatStoreValues"
3593 /*@
3594     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3595        example, reuse of the linear part of a Jacobian, while recomputing the
3596        nonlinear portion.
3597 
3598    Collect on Mat
3599 
3600   Input Parameters:
3601 .  mat - the matrix (currently only AIJ matrices support this option)
3602 
3603   Level: advanced
3604 
3605   Common Usage, with SNESSolve():
3606 $    Create Jacobian matrix
3607 $    Set linear terms into matrix
3608 $    Apply boundary conditions to matrix, at this time matrix must have
3609 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3610 $      boundary conditions again will not change the nonzero structure
3611 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3612 $    ierr = MatStoreValues(mat);
3613 $    Call SNESSetJacobian() with matrix
3614 $    In your Jacobian routine
3615 $      ierr = MatRetrieveValues(mat);
3616 $      Set nonlinear terms in matrix
3617 
3618   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3619 $    // build linear portion of Jacobian
3620 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3621 $    ierr = MatStoreValues(mat);
3622 $    loop over nonlinear iterations
3623 $       ierr = MatRetrieveValues(mat);
3624 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3625 $       // call MatAssemblyBegin/End() on matrix
3626 $       Solve linear system with Jacobian
3627 $    endloop
3628 
3629   Notes:
3630     Matrix must already be assemblied before calling this routine
3631     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3632     calling this routine.
3633 
3634     When this is called multiple times it overwrites the previous set of stored values
3635     and does not allocated additional space.
3636 
3637 .seealso: MatRetrieveValues()
3638 
3639 @*/
3640 PetscErrorCode  MatStoreValues(Mat mat)
3641 {
3642   PetscErrorCode ierr;
3643 
3644   PetscFunctionBegin;
3645   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3646   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3647   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3648   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3649   PetscFunctionReturn(0);
3650 }
3651 
3652 #undef __FUNCT__
3653 #define __FUNCT__ "MatRetrieveValues_SeqAIJ"
3654 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3655 {
3656   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3657   PetscErrorCode ierr;
3658   PetscInt       nz = aij->i[mat->rmap->n];
3659 
3660   PetscFunctionBegin;
3661   if (aij->nonew != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3662   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3663   /* copy values over */
3664   ierr = PetscMemcpy(aij->a,aij->saved_values,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3665   PetscFunctionReturn(0);
3666 }
3667 
3668 #undef __FUNCT__
3669 #define __FUNCT__ "MatRetrieveValues"
3670 /*@
3671     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3672        example, reuse of the linear part of a Jacobian, while recomputing the
3673        nonlinear portion.
3674 
3675    Collect on Mat
3676 
3677   Input Parameters:
3678 .  mat - the matrix (currently on AIJ matrices support this option)
3679 
3680   Level: advanced
3681 
3682 .seealso: MatStoreValues()
3683 
3684 @*/
3685 PetscErrorCode  MatRetrieveValues(Mat mat)
3686 {
3687   PetscErrorCode ierr;
3688 
3689   PetscFunctionBegin;
3690   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3691   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3692   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3693   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3694   PetscFunctionReturn(0);
3695 }
3696 
3697 
3698 /* --------------------------------------------------------------------------------*/
3699 #undef __FUNCT__
3700 #define __FUNCT__ "MatCreateSeqAIJ"
3701 /*@C
3702    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3703    (the default parallel PETSc format).  For good matrix assembly performance
3704    the user should preallocate the matrix storage by setting the parameter nz
3705    (or the array nnz).  By setting these parameters accurately, performance
3706    during matrix assembly can be increased by more than a factor of 50.
3707 
3708    Collective on MPI_Comm
3709 
3710    Input Parameters:
3711 +  comm - MPI communicator, set to PETSC_COMM_SELF
3712 .  m - number of rows
3713 .  n - number of columns
3714 .  nz - number of nonzeros per row (same for all rows)
3715 -  nnz - array containing the number of nonzeros in the various rows
3716          (possibly different for each row) or NULL
3717 
3718    Output Parameter:
3719 .  A - the matrix
3720 
3721    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3722    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3723    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3724 
3725    Notes:
3726    If nnz is given then nz is ignored
3727 
3728    The AIJ format (also called the Yale sparse matrix format or
3729    compressed row storage), is fully compatible with standard Fortran 77
3730    storage.  That is, the stored row and column indices can begin at
3731    either one (as in Fortran) or zero.  See the users' manual for details.
3732 
3733    Specify the preallocated storage with either nz or nnz (not both).
3734    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3735    allocation.  For large problems you MUST preallocate memory or you
3736    will get TERRIBLE performance, see the users' manual chapter on matrices.
3737 
3738    By default, this format uses inodes (identical nodes) when possible, to
3739    improve numerical efficiency of matrix-vector products and solves. We
3740    search for consecutive rows with the same nonzero structure, thereby
3741    reusing matrix information to achieve increased efficiency.
3742 
3743    Options Database Keys:
3744 +  -mat_no_inode  - Do not use inodes
3745 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3746 
3747    Level: intermediate
3748 
3749 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3750 
3751 @*/
3752 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3753 {
3754   PetscErrorCode ierr;
3755 
3756   PetscFunctionBegin;
3757   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3758   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3759   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3760   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3761   PetscFunctionReturn(0);
3762 }
3763 
3764 #undef __FUNCT__
3765 #define __FUNCT__ "MatSeqAIJSetPreallocation"
3766 /*@C
3767    MatSeqAIJSetPreallocation - For good matrix assembly performance
3768    the user should preallocate the matrix storage by setting the parameter nz
3769    (or the array nnz).  By setting these parameters accurately, performance
3770    during matrix assembly can be increased by more than a factor of 50.
3771 
3772    Collective on MPI_Comm
3773 
3774    Input Parameters:
3775 +  B - The matrix-free
3776 .  nz - number of nonzeros per row (same for all rows)
3777 -  nnz - array containing the number of nonzeros in the various rows
3778          (possibly different for each row) or NULL
3779 
3780    Notes:
3781      If nnz is given then nz is ignored
3782 
3783     The AIJ format (also called the Yale sparse matrix format or
3784    compressed row storage), is fully compatible with standard Fortran 77
3785    storage.  That is, the stored row and column indices can begin at
3786    either one (as in Fortran) or zero.  See the users' manual for details.
3787 
3788    Specify the preallocated storage with either nz or nnz (not both).
3789    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3790    allocation.  For large problems you MUST preallocate memory or you
3791    will get TERRIBLE performance, see the users' manual chapter on matrices.
3792 
3793    You can call MatGetInfo() to get information on how effective the preallocation was;
3794    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3795    You can also run with the option -info and look for messages with the string
3796    malloc in them to see if additional memory allocation was needed.
3797 
3798    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3799    entries or columns indices
3800 
3801    By default, this format uses inodes (identical nodes) when possible, to
3802    improve numerical efficiency of matrix-vector products and solves. We
3803    search for consecutive rows with the same nonzero structure, thereby
3804    reusing matrix information to achieve increased efficiency.
3805 
3806    Options Database Keys:
3807 +  -mat_no_inode  - Do not use inodes
3808 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3809 -  -mat_aij_oneindex - Internally use indexing starting at 1
3810         rather than 0.  Note that when calling MatSetValues(),
3811         the user still MUST index entries starting at 0!
3812 
3813    Level: intermediate
3814 
3815 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatGetInfo()
3816 
3817 @*/
3818 PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
3819 {
3820   PetscErrorCode ierr;
3821 
3822   PetscFunctionBegin;
3823   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3824   PetscValidType(B,1);
3825   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));CHKERRQ(ierr);
3826   PetscFunctionReturn(0);
3827 }
3828 
3829 #undef __FUNCT__
3830 #define __FUNCT__ "MatSeqAIJSetPreallocation_SeqAIJ"
3831 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3832 {
3833   Mat_SeqAIJ     *b;
3834   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3835   PetscErrorCode ierr;
3836   PetscInt       i;
3837 
3838   PetscFunctionBegin;
3839   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3840   if (nz == MAT_SKIP_ALLOCATION) {
3841     skipallocation = PETSC_TRUE;
3842     nz             = 0;
3843   }
3844 
3845   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3846   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3847 
3848   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3849   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %d",nz);
3850   if (nnz) {
3851     for (i=0; i<B->rmap->n; i++) {
3852       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]);
3853       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);
3854     }
3855   }
3856 
3857   B->preallocated = PETSC_TRUE;
3858 
3859   b = (Mat_SeqAIJ*)B->data;
3860 
3861   if (!skipallocation) {
3862     if (!b->imax) {
3863       ierr = PetscMalloc2(B->rmap->n,PetscInt,&b->imax,B->rmap->n,PetscInt,&b->ilen);CHKERRQ(ierr);
3864       ierr = PetscLogObjectMemory((PetscObject)B,2*B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3865     }
3866     if (!nnz) {
3867       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3868       else if (nz < 0) nz = 1;
3869       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
3870       nz = nz*B->rmap->n;
3871     } else {
3872       nz = 0;
3873       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz += nnz[i];}
3874     }
3875     /* b->ilen will count nonzeros in each row so far. */
3876     for (i=0; i<B->rmap->n; i++) b->ilen[i] = 0;
3877 
3878     /* allocate the matrix space */
3879     ierr    = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
3880     ierr    = PetscMalloc3(nz,PetscScalar,&b->a,nz,PetscInt,&b->j,B->rmap->n+1,PetscInt,&b->i);CHKERRQ(ierr);
3881     ierr    = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
3882     b->i[0] = 0;
3883     for (i=1; i<B->rmap->n+1; i++) {
3884       b->i[i] = b->i[i-1] + b->imax[i-1];
3885     }
3886     b->singlemalloc = PETSC_TRUE;
3887     b->free_a       = PETSC_TRUE;
3888     b->free_ij      = PETSC_TRUE;
3889 #if defined(PETSC_THREADCOMM_ACTIVE)
3890     ierr = MatZeroEntries_SeqAIJ(B);CHKERRQ(ierr);
3891 #endif
3892   } else {
3893     b->free_a  = PETSC_FALSE;
3894     b->free_ij = PETSC_FALSE;
3895   }
3896 
3897   b->nz               = 0;
3898   b->maxnz            = nz;
3899   B->info.nz_unneeded = (double)b->maxnz;
3900   if (realalloc) {
3901     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3902   }
3903   PetscFunctionReturn(0);
3904 }
3905 
3906 #undef  __FUNCT__
3907 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR"
3908 /*@
3909    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
3910 
3911    Input Parameters:
3912 +  B - the matrix
3913 .  i - the indices into j for the start of each row (starts with zero)
3914 .  j - the column indices for each row (starts with zero) these must be sorted for each row
3915 -  v - optional values in the matrix
3916 
3917    Level: developer
3918 
3919    The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
3920 
3921 .keywords: matrix, aij, compressed row, sparse, sequential
3922 
3923 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), SeqAIJ
3924 @*/
3925 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
3926 {
3927   PetscErrorCode ierr;
3928 
3929   PetscFunctionBegin;
3930   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3931   PetscValidType(B,1);
3932   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3933   PetscFunctionReturn(0);
3934 }
3935 
3936 #undef  __FUNCT__
3937 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR_SeqAIJ"
3938 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3939 {
3940   PetscInt       i;
3941   PetscInt       m,n;
3942   PetscInt       nz;
3943   PetscInt       *nnz, nz_max = 0;
3944   PetscScalar    *values;
3945   PetscErrorCode ierr;
3946 
3947   PetscFunctionBegin;
3948   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
3949 
3950   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3951   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3952 
3953   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
3954   ierr = PetscMalloc((m+1) * sizeof(PetscInt), &nnz);CHKERRQ(ierr);
3955   for (i = 0; i < m; i++) {
3956     nz     = Ii[i+1]- Ii[i];
3957     nz_max = PetscMax(nz_max, nz);
3958     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
3959     nnz[i] = nz;
3960   }
3961   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
3962   ierr = PetscFree(nnz);CHKERRQ(ierr);
3963 
3964   if (v) {
3965     values = (PetscScalar*) v;
3966   } else {
3967     ierr = PetscMalloc(nz_max*sizeof(PetscScalar), &values);CHKERRQ(ierr);
3968     ierr = PetscMemzero(values, nz_max*sizeof(PetscScalar));CHKERRQ(ierr);
3969   }
3970 
3971   for (i = 0; i < m; i++) {
3972     nz   = Ii[i+1] - Ii[i];
3973     ierr = MatSetValues_SeqAIJ(B, 1, &i, nz, J+Ii[i], values + (v ? Ii[i] : 0), INSERT_VALUES);CHKERRQ(ierr);
3974   }
3975 
3976   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3977   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3978 
3979   if (!v) {
3980     ierr = PetscFree(values);CHKERRQ(ierr);
3981   }
3982   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3983   PetscFunctionReturn(0);
3984 }
3985 
3986 #include <../src/mat/impls/dense/seq/dense.h>
3987 #include <petsc-private/kernels/petscaxpy.h>
3988 
3989 #undef __FUNCT__
3990 #define __FUNCT__ "MatMatMultNumeric_SeqDense_SeqAIJ"
3991 /*
3992     Computes (B'*A')' since computing B*A directly is untenable
3993 
3994                n                       p                          p
3995         (              )       (              )         (                  )
3996       m (      A       )  *  n (       B      )   =   m (         C        )
3997         (              )       (              )         (                  )
3998 
3999 */
4000 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
4001 {
4002   PetscErrorCode    ierr;
4003   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
4004   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
4005   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
4006   PetscInt          i,n,m,q,p;
4007   const PetscInt    *ii,*idx;
4008   const PetscScalar *b,*a,*a_q;
4009   PetscScalar       *c,*c_q;
4010 
4011   PetscFunctionBegin;
4012   m    = A->rmap->n;
4013   n    = A->cmap->n;
4014   p    = B->cmap->n;
4015   a    = sub_a->v;
4016   b    = sub_b->a;
4017   c    = sub_c->v;
4018   ierr = PetscMemzero(c,m*p*sizeof(PetscScalar));CHKERRQ(ierr);
4019 
4020   ii  = sub_b->i;
4021   idx = sub_b->j;
4022   for (i=0; i<n; i++) {
4023     q = ii[i+1] - ii[i];
4024     while (q-->0) {
4025       c_q = c + m*(*idx);
4026       a_q = a + m*i;
4027       PetscKernelAXPY(c_q,*b,a_q,m);
4028       idx++;
4029       b++;
4030     }
4031   }
4032   PetscFunctionReturn(0);
4033 }
4034 
4035 #undef __FUNCT__
4036 #define __FUNCT__ "MatMatMultSymbolic_SeqDense_SeqAIJ"
4037 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4038 {
4039   PetscErrorCode ierr;
4040   PetscInt       m=A->rmap->n,n=B->cmap->n;
4041   Mat            Cmat;
4042 
4043   PetscFunctionBegin;
4044   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);
4045   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4046   ierr = MatSetSizes(Cmat,m,n,m,n);CHKERRQ(ierr);
4047   ierr = MatSetBlockSizes(Cmat,A->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
4048   ierr = MatSetType(Cmat,MATSEQDENSE);CHKERRQ(ierr);
4049   ierr = MatSeqDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4050 
4051   Cmat->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
4052 
4053   *C = Cmat;
4054   PetscFunctionReturn(0);
4055 }
4056 
4057 /* ----------------------------------------------------------------*/
4058 #undef __FUNCT__
4059 #define __FUNCT__ "MatMatMult_SeqDense_SeqAIJ"
4060 PetscErrorCode MatMatMult_SeqDense_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4061 {
4062   PetscErrorCode ierr;
4063 
4064   PetscFunctionBegin;
4065   if (scall == MAT_INITIAL_MATRIX) {
4066     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4067     ierr = MatMatMultSymbolic_SeqDense_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
4068     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4069   }
4070   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4071   ierr = MatMatMultNumeric_SeqDense_SeqAIJ(A,B,*C);CHKERRQ(ierr);
4072   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4073   PetscFunctionReturn(0);
4074 }
4075 
4076 
4077 /*MC
4078    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
4079    based on compressed sparse row format.
4080 
4081    Options Database Keys:
4082 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
4083 
4084   Level: beginner
4085 
4086 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
4087 M*/
4088 
4089 /*MC
4090    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
4091 
4092    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
4093    and MATMPIAIJ otherwise.  As a result, for single process communicators,
4094   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
4095   for communicators controlling multiple processes.  It is recommended that you call both of
4096   the above preallocation routines for simplicity.
4097 
4098    Options Database Keys:
4099 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
4100 
4101   Developer Notes: Subclasses include MATAIJCUSP, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
4102    enough exist.
4103 
4104   Level: beginner
4105 
4106 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
4107 M*/
4108 
4109 /*MC
4110    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
4111 
4112    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
4113    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
4114    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
4115   for communicators controlling multiple processes.  It is recommended that you call both of
4116   the above preallocation routines for simplicity.
4117 
4118    Options Database Keys:
4119 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
4120 
4121   Level: beginner
4122 
4123 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
4124 M*/
4125 
4126 #if defined(PETSC_HAVE_PASTIX)
4127 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_pastix(Mat,MatFactorType,Mat*);
4128 #endif
4129 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
4130 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_essl(Mat,MatFactorType,Mat*);
4131 #endif
4132 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
4133 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_petsc(Mat,MatFactorType,Mat*);
4134 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_bas(Mat,MatFactorType,Mat*);
4135 extern PetscErrorCode  MatGetFactorAvailable_seqaij_petsc(Mat,MatFactorType,PetscBool*);
4136 #if defined(PETSC_HAVE_MUMPS)
4137 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mumps(Mat,MatFactorType,Mat*);
4138 #endif
4139 #if defined(PETSC_HAVE_SUPERLU)
4140 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu(Mat,MatFactorType,Mat*);
4141 #endif
4142 #if defined(PETSC_HAVE_SUPERLU_DIST)
4143 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu_dist(Mat,MatFactorType,Mat*);
4144 #endif
4145 #if defined(PETSC_HAVE_UMFPACK)
4146 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_umfpack(Mat,MatFactorType,Mat*);
4147 #endif
4148 #if defined(PETSC_HAVE_CHOLMOD)
4149 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_cholmod(Mat,MatFactorType,Mat*);
4150 #endif
4151 #if defined(PETSC_HAVE_LUSOL)
4152 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_lusol(Mat,MatFactorType,Mat*);
4153 #endif
4154 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4155 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_matlab(Mat,MatFactorType,Mat*);
4156 extern PetscErrorCode  MatlabEnginePut_SeqAIJ(PetscObject,void*);
4157 extern PetscErrorCode  MatlabEngineGet_SeqAIJ(PetscObject,void*);
4158 #endif
4159 #if defined(PETSC_HAVE_CLIQUE)
4160 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_clique(Mat,MatFactorType,Mat*);
4161 #endif
4162 
4163 
4164 #undef __FUNCT__
4165 #define __FUNCT__ "MatSeqAIJGetArray"
4166 /*@C
4167    MatSeqAIJGetArray - gives access to the array where the data for a SeqSeqAIJ matrix is stored
4168 
4169    Not Collective
4170 
4171    Input Parameter:
4172 .  mat - a MATSEQDENSE matrix
4173 
4174    Output Parameter:
4175 .   array - pointer to the data
4176 
4177    Level: intermediate
4178 
4179 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4180 @*/
4181 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4182 {
4183   PetscErrorCode ierr;
4184 
4185   PetscFunctionBegin;
4186   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4187   PetscFunctionReturn(0);
4188 }
4189 
4190 #undef __FUNCT__
4191 #define __FUNCT__ "MatSeqAIJRestoreArray"
4192 /*@C
4193    MatSeqAIJRestoreArray - returns access to the array where the data for a SeqSeqAIJ matrix is stored obtained by MatSeqAIJGetArray()
4194 
4195    Not Collective
4196 
4197    Input Parameters:
4198 .  mat - a MATSEQDENSE matrix
4199 .  array - pointer to the data
4200 
4201    Level: intermediate
4202 
4203 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4204 @*/
4205 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4206 {
4207   PetscErrorCode ierr;
4208 
4209   PetscFunctionBegin;
4210   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4211   PetscFunctionReturn(0);
4212 }
4213 
4214 #undef __FUNCT__
4215 #define __FUNCT__ "MatCreate_SeqAIJ"
4216 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4217 {
4218   Mat_SeqAIJ     *b;
4219   PetscErrorCode ierr;
4220   PetscMPIInt    size;
4221 
4222   PetscFunctionBegin;
4223   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4224   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4225 
4226   ierr = PetscNewLog(B,Mat_SeqAIJ,&b);CHKERRQ(ierr);
4227 
4228   B->data = (void*)b;
4229 
4230   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4231 
4232   b->row                = 0;
4233   b->col                = 0;
4234   b->icol               = 0;
4235   b->reallocs           = 0;
4236   b->ignorezeroentries  = PETSC_FALSE;
4237   b->roworiented        = PETSC_TRUE;
4238   b->nonew              = 0;
4239   b->diag               = 0;
4240   b->solve_work         = 0;
4241   B->spptr              = 0;
4242   b->saved_values       = 0;
4243   b->idiag              = 0;
4244   b->mdiag              = 0;
4245   b->ssor_work          = 0;
4246   b->omega              = 1.0;
4247   b->fshift             = 0.0;
4248   b->idiagvalid         = PETSC_FALSE;
4249   b->ibdiagvalid        = PETSC_FALSE;
4250   b->keepnonzeropattern = PETSC_FALSE;
4251   b->xtoy               = 0;
4252   b->XtoY               = 0;
4253   B->same_nonzero       = PETSC_FALSE;
4254 
4255   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4256   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4257   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4258 
4259 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4260   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_matlab_C",MatGetFactor_seqaij_matlab);CHKERRQ(ierr);
4261   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4262   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4263 #endif
4264 #if defined(PETSC_HAVE_PASTIX)
4265   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_pastix_C",MatGetFactor_seqaij_pastix);CHKERRQ(ierr);
4266 #endif
4267 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
4268   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_essl_C",MatGetFactor_seqaij_essl);CHKERRQ(ierr);
4269 #endif
4270 #if defined(PETSC_HAVE_SUPERLU)
4271   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_C",MatGetFactor_seqaij_superlu);CHKERRQ(ierr);
4272 #endif
4273 #if defined(PETSC_HAVE_SUPERLU_DIST)
4274   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_dist_C",MatGetFactor_seqaij_superlu_dist);CHKERRQ(ierr);
4275 #endif
4276 #if defined(PETSC_HAVE_MUMPS)
4277   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mumps_C",MatGetFactor_aij_mumps);CHKERRQ(ierr);
4278 #endif
4279 #if defined(PETSC_HAVE_UMFPACK)
4280   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_umfpack_C",MatGetFactor_seqaij_umfpack);CHKERRQ(ierr);
4281 #endif
4282 #if defined(PETSC_HAVE_CHOLMOD)
4283   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_cholmod_C",MatGetFactor_seqaij_cholmod);CHKERRQ(ierr);
4284 #endif
4285 #if defined(PETSC_HAVE_LUSOL)
4286   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_lusol_C",MatGetFactor_seqaij_lusol);CHKERRQ(ierr);
4287 #endif
4288 #if defined(PETSC_HAVE_CLIQUE)
4289   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_clique_C",MatGetFactor_aij_clique);CHKERRQ(ierr);
4290 #endif
4291 
4292   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_petsc_C",MatGetFactor_seqaij_petsc);CHKERRQ(ierr);
4293   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactorAvailable_petsc_C",MatGetFactorAvailable_seqaij_petsc);CHKERRQ(ierr);
4294   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_bas_C",MatGetFactor_seqaij_bas);CHKERRQ(ierr);
4295   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4296   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4297   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4298   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4299   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4300   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4301   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4302   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4303   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4304   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4305   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4306   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4307   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaij_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
4308   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaij_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
4309   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaij_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
4310   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4311   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4312   PetscFunctionReturn(0);
4313 }
4314 
4315 #undef __FUNCT__
4316 #define __FUNCT__ "MatDuplicateNoCreate_SeqAIJ"
4317 /*
4318     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4319 */
4320 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4321 {
4322   Mat_SeqAIJ     *c,*a = (Mat_SeqAIJ*)A->data;
4323   PetscErrorCode ierr;
4324   PetscInt       i,m = A->rmap->n;
4325 
4326   PetscFunctionBegin;
4327   c = (Mat_SeqAIJ*)C->data;
4328 
4329   C->factortype = A->factortype;
4330   c->row        = 0;
4331   c->col        = 0;
4332   c->icol       = 0;
4333   c->reallocs   = 0;
4334 
4335   C->assembled = PETSC_TRUE;
4336 
4337   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4338   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4339 
4340   ierr = PetscMalloc2(m,PetscInt,&c->imax,m,PetscInt,&c->ilen);CHKERRQ(ierr);
4341   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4342   for (i=0; i<m; i++) {
4343     c->imax[i] = a->imax[i];
4344     c->ilen[i] = a->ilen[i];
4345   }
4346 
4347   /* allocate the matrix space */
4348   if (mallocmatspace) {
4349     ierr = PetscMalloc3(a->i[m],PetscScalar,&c->a,a->i[m],PetscInt,&c->j,m+1,PetscInt,&c->i);CHKERRQ(ierr);
4350     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4351 
4352     c->singlemalloc = PETSC_TRUE;
4353 
4354     ierr = PetscMemcpy(c->i,a->i,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4355     if (m > 0) {
4356       ierr = PetscMemcpy(c->j,a->j,(a->i[m])*sizeof(PetscInt));CHKERRQ(ierr);
4357       if (cpvalues == MAT_COPY_VALUES) {
4358         ierr = PetscMemcpy(c->a,a->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4359       } else {
4360         ierr = PetscMemzero(c->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4361       }
4362     }
4363   }
4364 
4365   c->ignorezeroentries = a->ignorezeroentries;
4366   c->roworiented       = a->roworiented;
4367   c->nonew             = a->nonew;
4368   if (a->diag) {
4369     ierr = PetscMalloc((m+1)*sizeof(PetscInt),&c->diag);CHKERRQ(ierr);
4370     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4371     for (i=0; i<m; i++) {
4372       c->diag[i] = a->diag[i];
4373     }
4374   } else c->diag = 0;
4375 
4376   c->solve_work         = 0;
4377   c->saved_values       = 0;
4378   c->idiag              = 0;
4379   c->ssor_work          = 0;
4380   c->keepnonzeropattern = a->keepnonzeropattern;
4381   c->free_a             = PETSC_TRUE;
4382   c->free_ij            = PETSC_TRUE;
4383   c->xtoy               = 0;
4384   c->XtoY               = 0;
4385 
4386   c->rmax         = a->rmax;
4387   c->nz           = a->nz;
4388   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4389   C->preallocated = PETSC_TRUE;
4390 
4391   c->compressedrow.use   = a->compressedrow.use;
4392   c->compressedrow.nrows = a->compressedrow.nrows;
4393   c->compressedrow.check = a->compressedrow.check;
4394   if (a->compressedrow.use) {
4395     i    = a->compressedrow.nrows;
4396     ierr = PetscMalloc2(i+1,PetscInt,&c->compressedrow.i,i,PetscInt,&c->compressedrow.rindex);CHKERRQ(ierr);
4397     ierr = PetscMemcpy(c->compressedrow.i,a->compressedrow.i,(i+1)*sizeof(PetscInt));CHKERRQ(ierr);
4398     ierr = PetscMemcpy(c->compressedrow.rindex,a->compressedrow.rindex,i*sizeof(PetscInt));CHKERRQ(ierr);
4399   } else {
4400     c->compressedrow.use    = PETSC_FALSE;
4401     c->compressedrow.i      = NULL;
4402     c->compressedrow.rindex = NULL;
4403   }
4404   C->same_nonzero = A->same_nonzero;
4405 
4406   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4407   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4408   PetscFunctionReturn(0);
4409 }
4410 
4411 #undef __FUNCT__
4412 #define __FUNCT__ "MatDuplicate_SeqAIJ"
4413 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4414 {
4415   PetscErrorCode ierr;
4416 
4417   PetscFunctionBegin;
4418   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4419   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4420   ierr = MatSetBlockSizes(*B,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
4421   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4422   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4423   PetscFunctionReturn(0);
4424 }
4425 
4426 #undef __FUNCT__
4427 #define __FUNCT__ "MatLoad_SeqAIJ"
4428 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4429 {
4430   Mat_SeqAIJ     *a;
4431   PetscErrorCode ierr;
4432   PetscInt       i,sum,nz,header[4],*rowlengths = 0,M,N,rows,cols;
4433   int            fd;
4434   PetscMPIInt    size;
4435   MPI_Comm       comm;
4436   PetscInt       bs = 1;
4437 
4438   PetscFunctionBegin;
4439   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
4440   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4441   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"view must have one processor");
4442 
4443   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
4444   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
4445   ierr = PetscOptionsEnd();CHKERRQ(ierr);
4446   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
4447 
4448   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
4449   ierr = PetscBinaryRead(fd,header,4,PETSC_INT);CHKERRQ(ierr);
4450   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
4451   M = header[1]; N = header[2]; nz = header[3];
4452 
4453   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
4454 
4455   /* read in row lengths */
4456   ierr = PetscMalloc(M*sizeof(PetscInt),&rowlengths);CHKERRQ(ierr);
4457   ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
4458 
4459   /* check if sum of rowlengths is same as nz */
4460   for (i=0,sum=0; i< M; i++) sum +=rowlengths[i];
4461   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);
4462 
4463   /* set global size if not set already*/
4464   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) {
4465     ierr = MatSetSizes(newMat,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
4466   } else {
4467     /* if sizes and type are already set, check if the vector global sizes are correct */
4468     ierr = MatGetSize(newMat,&rows,&cols);CHKERRQ(ierr);
4469     if (rows < 0 && cols < 0) { /* user might provide local size instead of global size */
4470       ierr = MatGetLocalSize(newMat,&rows,&cols);CHKERRQ(ierr);
4471     }
4472     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);
4473   }
4474   ierr = MatSeqAIJSetPreallocation_SeqAIJ(newMat,0,rowlengths);CHKERRQ(ierr);
4475   a    = (Mat_SeqAIJ*)newMat->data;
4476 
4477   ierr = PetscBinaryRead(fd,a->j,nz,PETSC_INT);CHKERRQ(ierr);
4478 
4479   /* read in nonzero values */
4480   ierr = PetscBinaryRead(fd,a->a,nz,PETSC_SCALAR);CHKERRQ(ierr);
4481 
4482   /* set matrix "i" values */
4483   a->i[0] = 0;
4484   for (i=1; i<= M; i++) {
4485     a->i[i]      = a->i[i-1] + rowlengths[i-1];
4486     a->ilen[i-1] = rowlengths[i-1];
4487   }
4488   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
4489 
4490   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4491   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4492   PetscFunctionReturn(0);
4493 }
4494 
4495 #undef __FUNCT__
4496 #define __FUNCT__ "MatEqual_SeqAIJ"
4497 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4498 {
4499   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4500   PetscErrorCode ierr;
4501 #if defined(PETSC_USE_COMPLEX)
4502   PetscInt k;
4503 #endif
4504 
4505   PetscFunctionBegin;
4506   /* If the  matrix dimensions are not equal,or no of nonzeros */
4507   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4508     *flg = PETSC_FALSE;
4509     PetscFunctionReturn(0);
4510   }
4511 
4512   /* if the a->i are the same */
4513   ierr = PetscMemcmp(a->i,b->i,(A->rmap->n+1)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4514   if (!*flg) PetscFunctionReturn(0);
4515 
4516   /* if a->j are the same */
4517   ierr = PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4518   if (!*flg) PetscFunctionReturn(0);
4519 
4520   /* if a->a are the same */
4521 #if defined(PETSC_USE_COMPLEX)
4522   for (k=0; k<a->nz; k++) {
4523     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4524       *flg = PETSC_FALSE;
4525       PetscFunctionReturn(0);
4526     }
4527   }
4528 #else
4529   ierr = PetscMemcmp(a->a,b->a,(a->nz)*sizeof(PetscScalar),flg);CHKERRQ(ierr);
4530 #endif
4531   PetscFunctionReturn(0);
4532 }
4533 
4534 #undef __FUNCT__
4535 #define __FUNCT__ "MatCreateSeqAIJWithArrays"
4536 /*@
4537      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4538               provided by the user.
4539 
4540       Collective on MPI_Comm
4541 
4542    Input Parameters:
4543 +   comm - must be an MPI communicator of size 1
4544 .   m - number of rows
4545 .   n - number of columns
4546 .   i - row indices
4547 .   j - column indices
4548 -   a - matrix values
4549 
4550    Output Parameter:
4551 .   mat - the matrix
4552 
4553    Level: intermediate
4554 
4555    Notes:
4556        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4557     once the matrix is destroyed and not before
4558 
4559        You cannot set new nonzero locations into this matrix, that will generate an error.
4560 
4561        The i and j indices are 0 based
4562 
4563        The format which is used for the sparse matrix input, is equivalent to a
4564     row-major ordering.. i.e for the following matrix, the input data expected is
4565     as shown:
4566 
4567         1 0 0
4568         2 0 3
4569         4 5 6
4570 
4571         i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4572         j =  {0,0,2,0,1,2}  [size = nz = 6]; values must be sorted for each row
4573         v =  {1,2,3,4,5,6}  [size = nz = 6]
4574 
4575 
4576 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4577 
4578 @*/
4579 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat)
4580 {
4581   PetscErrorCode ierr;
4582   PetscInt       ii;
4583   Mat_SeqAIJ     *aij;
4584 #if defined(PETSC_USE_DEBUG)
4585   PetscInt jj;
4586 #endif
4587 
4588   PetscFunctionBegin;
4589   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4590   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4591   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4592   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4593   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4594   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,0);CHKERRQ(ierr);
4595   aij  = (Mat_SeqAIJ*)(*mat)->data;
4596   ierr = PetscMalloc2(m,PetscInt,&aij->imax,m,PetscInt,&aij->ilen);CHKERRQ(ierr);
4597 
4598   aij->i            = i;
4599   aij->j            = j;
4600   aij->a            = a;
4601   aij->singlemalloc = PETSC_FALSE;
4602   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4603   aij->free_a       = PETSC_FALSE;
4604   aij->free_ij      = PETSC_FALSE;
4605 
4606   for (ii=0; ii<m; ii++) {
4607     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4608 #if defined(PETSC_USE_DEBUG)
4609     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]);
4610     for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4611       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);
4612       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);
4613     }
4614 #endif
4615   }
4616 #if defined(PETSC_USE_DEBUG)
4617   for (ii=0; ii<aij->i[m]; ii++) {
4618     if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %d index = %d",ii,j[ii]);
4619     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]);
4620   }
4621 #endif
4622 
4623   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4624   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4625   PetscFunctionReturn(0);
4626 }
4627 #undef __FUNCT__
4628 #define __FUNCT__ "MatCreateSeqAIJFromTriple"
4629 /*@C
4630      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4631               provided by the user.
4632 
4633       Collective on MPI_Comm
4634 
4635    Input Parameters:
4636 +   comm - must be an MPI communicator of size 1
4637 .   m   - number of rows
4638 .   n   - number of columns
4639 .   i   - row indices
4640 .   j   - column indices
4641 .   a   - matrix values
4642 .   nz  - number of nonzeros
4643 -   idx - 0 or 1 based
4644 
4645    Output Parameter:
4646 .   mat - the matrix
4647 
4648    Level: intermediate
4649 
4650    Notes:
4651        The i and j indices are 0 based
4652 
4653        The format which is used for the sparse matrix input, is equivalent to a
4654     row-major ordering.. i.e for the following matrix, the input data expected is
4655     as shown:
4656 
4657         1 0 0
4658         2 0 3
4659         4 5 6
4660 
4661         i =  {0,1,1,2,2,2}
4662         j =  {0,0,2,0,1,2}
4663         v =  {1,2,3,4,5,6}
4664 
4665 
4666 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4667 
4668 @*/
4669 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat,PetscInt nz,PetscBool idx)
4670 {
4671   PetscErrorCode ierr;
4672   PetscInt       ii, *nnz, one = 1,row,col;
4673 
4674 
4675   PetscFunctionBegin;
4676   ierr = PetscMalloc(m*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
4677   ierr = PetscMemzero(nnz,m*sizeof(PetscInt));CHKERRQ(ierr);
4678   for (ii = 0; ii < nz; ii++) {
4679     nnz[i[ii]] += 1;
4680   }
4681   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4682   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4683   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4684   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4685   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4686   for (ii = 0; ii < nz; ii++) {
4687     if (idx) {
4688       row = i[ii] - 1;
4689       col = j[ii] - 1;
4690     } else {
4691       row = i[ii];
4692       col = j[ii];
4693     }
4694     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4695   }
4696   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4697   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4698   ierr = PetscFree(nnz);CHKERRQ(ierr);
4699   PetscFunctionReturn(0);
4700 }
4701 
4702 #undef __FUNCT__
4703 #define __FUNCT__ "MatSetColoring_SeqAIJ"
4704 PetscErrorCode MatSetColoring_SeqAIJ(Mat A,ISColoring coloring)
4705 {
4706   PetscErrorCode ierr;
4707   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4708 
4709   PetscFunctionBegin;
4710   if (coloring->ctype == IS_COLORING_GLOBAL) {
4711     ierr        = ISColoringReference(coloring);CHKERRQ(ierr);
4712     a->coloring = coloring;
4713   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
4714     PetscInt        i,*larray;
4715     ISColoring      ocoloring;
4716     ISColoringValue *colors;
4717 
4718     /* set coloring for diagonal portion */
4719     ierr = PetscMalloc(A->cmap->n*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4720     for (i=0; i<A->cmap->n; i++) larray[i] = i;
4721     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
4722     ierr = PetscMalloc(A->cmap->n*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4723     for (i=0; i<A->cmap->n; i++) colors[i] = coloring->colors[larray[i]];
4724     ierr        = PetscFree(larray);CHKERRQ(ierr);
4725     ierr        = ISColoringCreate(PETSC_COMM_SELF,coloring->n,A->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4726     a->coloring = ocoloring;
4727   }
4728   PetscFunctionReturn(0);
4729 }
4730 
4731 #undef __FUNCT__
4732 #define __FUNCT__ "MatSetValuesAdifor_SeqAIJ"
4733 PetscErrorCode MatSetValuesAdifor_SeqAIJ(Mat A,PetscInt nl,void *advalues)
4734 {
4735   Mat_SeqAIJ      *a      = (Mat_SeqAIJ*)A->data;
4736   PetscInt        m       = A->rmap->n,*ii = a->i,*jj = a->j,nz,i,j;
4737   MatScalar       *v      = a->a;
4738   PetscScalar     *values = (PetscScalar*)advalues;
4739   ISColoringValue *color;
4740 
4741   PetscFunctionBegin;
4742   if (!a->coloring) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Coloring not set for matrix");
4743   color = a->coloring->colors;
4744   /* loop over rows */
4745   for (i=0; i<m; i++) {
4746     nz = ii[i+1] - ii[i];
4747     /* loop over columns putting computed value into matrix */
4748     for (j=0; j<nz; j++) *v++ = values[color[*jj++]];
4749     values += nl; /* jump to next row of derivatives */
4750   }
4751   PetscFunctionReturn(0);
4752 }
4753 
4754 #undef __FUNCT__
4755 #define __FUNCT__ "MatSeqAIJInvalidateDiagonal"
4756 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4757 {
4758   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4759   PetscErrorCode ierr;
4760 
4761   PetscFunctionBegin;
4762   a->idiagvalid  = PETSC_FALSE;
4763   a->ibdiagvalid = PETSC_FALSE;
4764 
4765   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4766   PetscFunctionReturn(0);
4767 }
4768 
4769 /*
4770     Special version for direct calls from Fortran
4771 */
4772 #include <petsc-private/fortranimpl.h>
4773 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4774 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
4775 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4776 #define matsetvaluesseqaij_ matsetvaluesseqaij
4777 #endif
4778 
4779 /* Change these macros so can be used in void function */
4780 #undef CHKERRQ
4781 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
4782 #undef SETERRQ2
4783 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4784 #undef SETERRQ3
4785 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4786 
4787 #undef __FUNCT__
4788 #define __FUNCT__ "matsetvaluesseqaij_"
4789 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)
4790 {
4791   Mat            A  = *AA;
4792   PetscInt       m  = *mm, n = *nn;
4793   InsertMode     is = *isis;
4794   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4795   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
4796   PetscInt       *imax,*ai,*ailen;
4797   PetscErrorCode ierr;
4798   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
4799   MatScalar      *ap,value,*aa;
4800   PetscBool      ignorezeroentries = a->ignorezeroentries;
4801   PetscBool      roworiented       = a->roworiented;
4802 
4803   PetscFunctionBegin;
4804   MatCheckPreallocated(A,1);
4805   imax  = a->imax;
4806   ai    = a->i;
4807   ailen = a->ilen;
4808   aj    = a->j;
4809   aa    = a->a;
4810 
4811   for (k=0; k<m; k++) { /* loop over added rows */
4812     row = im[k];
4813     if (row < 0) continue;
4814 #if defined(PETSC_USE_DEBUG)
4815     if (row >= A->rmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
4816 #endif
4817     rp   = aj + ai[row]; ap = aa + ai[row];
4818     rmax = imax[row]; nrow = ailen[row];
4819     low  = 0;
4820     high = nrow;
4821     for (l=0; l<n; l++) { /* loop over added columns */
4822       if (in[l] < 0) continue;
4823 #if defined(PETSC_USE_DEBUG)
4824       if (in[l] >= A->cmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
4825 #endif
4826       col = in[l];
4827       if (roworiented) value = v[l + k*n];
4828       else value = v[k + l*m];
4829 
4830       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
4831 
4832       if (col <= lastcol) low = 0;
4833       else high = nrow;
4834       lastcol = col;
4835       while (high-low > 5) {
4836         t = (low+high)/2;
4837         if (rp[t] > col) high = t;
4838         else             low  = t;
4839       }
4840       for (i=low; i<high; i++) {
4841         if (rp[i] > col) break;
4842         if (rp[i] == col) {
4843           if (is == ADD_VALUES) ap[i] += value;
4844           else                  ap[i] = value;
4845           goto noinsert;
4846         }
4847       }
4848       if (value == 0.0 && ignorezeroentries) goto noinsert;
4849       if (nonew == 1) goto noinsert;
4850       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
4851       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
4852       N = nrow++ - 1; a->nz++; high++;
4853       /* shift up all the later entries in this row */
4854       for (ii=N; ii>=i; ii--) {
4855         rp[ii+1] = rp[ii];
4856         ap[ii+1] = ap[ii];
4857       }
4858       rp[i] = col;
4859       ap[i] = value;
4860 noinsert:;
4861       low = i + 1;
4862     }
4863     ailen[row] = nrow;
4864   }
4865   A->same_nonzero = PETSC_FALSE;
4866   PetscFunctionReturnVoid();
4867 }
4868 
4869 
4870