xref: /petsc/src/mat/impls/aij/seq/aij.c (revision 4737c552d78cc479762ab66305bcb2fe5e8285f7)
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   }
2774 
2775   idx = den2sp;
2776   for (k=0; k<ncolors; k++) { /* loop over colors */
2777     coloring->currentcolor = k;
2778 
2779     /*
2780       Loop over each column associated with color
2781       adding the perturbation to the vector w3 = x1 + dx.
2782     */
2783     ierr = VecCopy(x1,w3);CHKERRQ(ierr);
2784     ierr = VecGetArray(w3,&w3_array);CHKERRQ(ierr);
2785     ncolumns_k = ncolumns[k];
2786     for (l=0; l<ncolumns_k; l++) { /* loop over columns */
2787       col = columns[k][l];
2788       w3_array[col] += 1/vscale_array[col];
2789     }
2790     ierr = VecRestoreArray(w3,&w3_array);CHKERRQ(ierr);
2791 
2792     /*
2793       Evaluate function at w3 = x1 + dx (here dx is a vector of perturbations)
2794                            w2 = F(x1 + dx) - F(x1)
2795     */
2796     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2797     ierr = (*f)(sctx,w3,w2,fctx);CHKERRQ(ierr);
2798     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2799     ierr = VecAXPY(w2,-1.0,w1);CHKERRQ(ierr);
2800 
2801     /*
2802       Loop over rows of vector, putting w2/dx into Jacobian matrix
2803     */
2804 #if defined(JACOBIANCOLOROPT)
2805     ierr = PetscTime(&t0);CHKERRQ(ierr);
2806 #endif
2807     ierr = VecGetArray(w2,&y);CHKERRQ(ierr);
2808     nrows_k = nrows[k];
2809     for (l=0; l<nrows_k; l++) { /* loop over rows */
2810       row     = rows[k][l];     /* row index */
2811       y[row] *= vscale_array[columnsforrow[k][l]];
2812       ca[idx[l]] = y[row];
2813     }
2814     idx += nrows_k;
2815     ierr = VecRestoreArray(w2,&y);CHKERRQ(ierr);
2816 #if defined(JACOBIANCOLOROPT)
2817     ierr = PetscTime(&t1);CHKERRQ(ierr);
2818     time_setvalues += t1-t0;
2819 #endif
2820   } /* endof for each color */
2821 #if defined(JACOBIANCOLOROPT)
2822   printf("     MatFDColoringApply_SeqAIJ: time_setvalues %g\n",time_setvalues);
2823 #endif
2824   ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2825   ierr = VecRestoreArray(x1,&xx);CHKERRQ(ierr);
2826 
2827   coloring->currentcolor = -1;
2828   PetscFunctionReturn(0);
2829 }
2830 /* --------------------------------------------------------*/
2831 
2832 #undef __FUNCT__
2833 #define __FUNCT__ "MatFDColoringApply_SeqAIJ_old"
2834 PetscErrorCode MatFDColoringApply_SeqAIJ_old(Mat J,MatFDColoring coloring,Vec x1,MatStructure *flag,void *sctx)
2835 {
2836   PetscErrorCode (*f)(void*,Vec,Vec,void*) = (PetscErrorCode (*)(void*,Vec,Vec,void*))coloring->f;
2837   PetscErrorCode ierr;
2838   PetscInt       k,N,start,end,l,row,col,srow,**vscaleforrow;
2839   PetscScalar    dx,*y,*xx,*w3_array;
2840   PetscScalar    *vscale_array;
2841   PetscReal      epsilon = coloring->error_rel,umin = coloring->umin;
2842   Vec            w1,w2,w3;
2843   void           *fctx = coloring->fctx;
2844   PetscBool      flg   = PETSC_FALSE;
2845 
2846   PetscFunctionBegin;
2847   printf("MatFDColoringApply_SeqAIJ ...\n");
2848   if (!coloring->w1) {
2849     ierr = VecDuplicate(x1,&coloring->w1);CHKERRQ(ierr);
2850     ierr = PetscLogObjectParent((PetscObject)coloring,(PetscObject)coloring->w1);CHKERRQ(ierr);
2851     ierr = VecDuplicate(x1,&coloring->w2);CHKERRQ(ierr);
2852     ierr = PetscLogObjectParent((PetscObject)coloring,(PetscObject)coloring->w2);CHKERRQ(ierr);
2853     ierr = VecDuplicate(x1,&coloring->w3);CHKERRQ(ierr);
2854     ierr = PetscLogObjectParent((PetscObject)coloring,(PetscObject)coloring->w3);CHKERRQ(ierr);
2855   }
2856   w1 = coloring->w1; w2 = coloring->w2; w3 = coloring->w3;
2857 
2858   ierr = MatSetUnfactored(J);CHKERRQ(ierr);
2859   ierr = PetscOptionsGetBool(((PetscObject)coloring)->prefix,"-mat_fd_coloring_dont_rezero",&flg,NULL);CHKERRQ(ierr);
2860   if (flg) {
2861     ierr = PetscInfo(coloring,"Not calling MatZeroEntries()\n");CHKERRQ(ierr);
2862   } else {
2863     PetscBool assembled;
2864     ierr = MatAssembled(J,&assembled);CHKERRQ(ierr);
2865     if (assembled) {
2866       ierr = MatZeroEntries(J);CHKERRQ(ierr);
2867     }
2868   }
2869 
2870   ierr = VecGetOwnershipRange(x1,&start,&end);CHKERRQ(ierr);
2871   ierr = VecGetSize(x1,&N);CHKERRQ(ierr);
2872 
2873   if (!coloring->fset) {
2874     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2875     ierr = (*f)(sctx,x1,w1,fctx);CHKERRQ(ierr);
2876     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2877   } else {
2878     coloring->fset = PETSC_FALSE;
2879   }
2880 
2881   /*
2882       Compute all the scale factors and share with other processors
2883   */
2884   ierr = VecGetArray(x1,&xx);CHKERRQ(ierr);xx = xx - start;
2885   ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);vscale_array = vscale_array - start;
2886   for (k=0; k<coloring->ncolors; k++) {
2887     /*
2888        Loop over each column associated with color adding the
2889        perturbation to the vector w3.
2890     */
2891     for (l=0; l<coloring->ncolumns[k]; l++) {
2892       col = coloring->columns[k][l];    /* column of the matrix we are probing for */
2893       dx  = xx[col];
2894       if (dx == 0.0) dx = 1.0;
2895       if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
2896       else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
2897       dx               *= epsilon;
2898       vscale_array[col] = 1.0/dx;
2899     }
2900   }
2901   vscale_array = vscale_array + start;
2902 
2903   ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2904   ierr = VecGhostUpdateBegin(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2905   ierr = VecGhostUpdateEnd(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2906 
2907   /*  ierr = VecView(coloring->vscale,PETSC_VIEWER_STDOUT_WORLD);
2908       ierr = VecView(x1,PETSC_VIEWER_STDOUT_WORLD);*/
2909 
2910   if (coloring->vscaleforrow) vscaleforrow = coloring->vscaleforrow;
2911   else                        vscaleforrow = coloring->columnsforrow;
2912 
2913   ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2914   /*
2915       Loop over each color
2916   */
2917   for (k=0; k<coloring->ncolors; k++) {
2918     coloring->currentcolor = k;
2919 
2920     ierr = VecCopy(x1,w3);CHKERRQ(ierr);
2921     ierr = VecGetArray(w3,&w3_array);CHKERRQ(ierr);w3_array = w3_array - start;
2922     /*
2923        Loop over each column associated with color adding the
2924        perturbation to the vector w3.
2925     */
2926     for (l=0; l<coloring->ncolumns[k]; l++) {
2927       col = coloring->columns[k][l];    /* column of the matrix we are probing for */
2928       dx  = xx[col];
2929       if (dx == 0.0) dx = 1.0;
2930       if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
2931       else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
2932       dx *= epsilon;
2933       if (!PetscAbsScalar(dx)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Computed 0 differencing parameter");
2934       w3_array[col] += dx;
2935     }
2936     w3_array = w3_array + start; ierr = VecRestoreArray(w3,&w3_array);CHKERRQ(ierr);
2937 
2938     /*
2939        Evaluate function at x1 + dx (here dx is a vector of perturbations)
2940     */
2941 
2942     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2943     ierr = (*f)(sctx,w3,w2,fctx);CHKERRQ(ierr);
2944     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2945     ierr = VecAXPY(w2,-1.0,w1);CHKERRQ(ierr);
2946 
2947     /*
2948        Loop over rows of vector, putting results into Jacobian matrix
2949     */
2950     ierr = VecGetArray(w2,&y);CHKERRQ(ierr);
2951     for (l=0; l<coloring->nrows[k]; l++) {
2952       row     = coloring->rows[k][l];
2953       col     = coloring->columnsforrow[k][l];
2954       y[row] *= vscale_array[vscaleforrow[k][l]];
2955       srow    = row + start;
2956       ierr    = MatSetValues_SeqAIJ(J,1,&srow,1,&col,y+row,INSERT_VALUES);CHKERRQ(ierr);
2957     }
2958     ierr = VecRestoreArray(w2,&y);CHKERRQ(ierr);
2959   }
2960   coloring->currentcolor = k;
2961 
2962   ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2963   xx   = xx + start;
2964   ierr = VecRestoreArray(x1,&xx);CHKERRQ(ierr);
2965   ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2966   ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2967   PetscFunctionReturn(0);
2968 }
2969 
2970 /*
2971    Computes the number of nonzeros per row needed for preallocation when X and Y
2972    have different nonzero structure.
2973 */
2974 #undef __FUNCT__
2975 #define __FUNCT__ "MatAXPYGetPreallocation_SeqAIJ"
2976 PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat Y,Mat X,PetscInt *nnz)
2977 {
2978   PetscInt       i,m=Y->rmap->N;
2979   Mat_SeqAIJ     *x  = (Mat_SeqAIJ*)X->data;
2980   Mat_SeqAIJ     *y  = (Mat_SeqAIJ*)Y->data;
2981   const PetscInt *xi = x->i,*yi = y->i;
2982 
2983   PetscFunctionBegin;
2984   /* Set the number of nonzeros in the new matrix */
2985   for (i=0; i<m; i++) {
2986     PetscInt       j,k,nzx = xi[i+1] - xi[i],nzy = yi[i+1] - yi[i];
2987     const PetscInt *xj = x->j+xi[i],*yj = y->j+yi[i];
2988     nnz[i] = 0;
2989     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2990       for (; k<nzy && yj[k]<xj[j]; k++) nnz[i]++; /* Catch up to X */
2991       if (k<nzy && yj[k]==xj[j]) k++;             /* Skip duplicate */
2992       nnz[i]++;
2993     }
2994     for (; k<nzy; k++) nnz[i]++;
2995   }
2996   PetscFunctionReturn(0);
2997 }
2998 
2999 #undef __FUNCT__
3000 #define __FUNCT__ "MatAXPY_SeqAIJ"
3001 PetscErrorCode MatAXPY_SeqAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
3002 {
3003   PetscErrorCode ierr;
3004   PetscInt       i;
3005   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data,*y = (Mat_SeqAIJ*)Y->data;
3006   PetscBLASInt   one=1,bnz;
3007 
3008   PetscFunctionBegin;
3009   ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
3010   if (str == SAME_NONZERO_PATTERN) {
3011     PetscScalar alpha = a;
3012     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
3013     ierr = MatSeqAIJInvalidateDiagonal(Y);CHKERRQ(ierr);
3014   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
3015     if (y->xtoy && y->XtoY != X) {
3016       ierr = PetscFree(y->xtoy);CHKERRQ(ierr);
3017       ierr = MatDestroy(&y->XtoY);CHKERRQ(ierr);
3018     }
3019     if (!y->xtoy) { /* get xtoy */
3020       ierr    = MatAXPYGetxtoy_Private(X->rmap->n,x->i,x->j,NULL, y->i,y->j,NULL, &y->xtoy);CHKERRQ(ierr);
3021       y->XtoY = X;
3022       ierr    = PetscObjectReference((PetscObject)X);CHKERRQ(ierr);
3023     }
3024     for (i=0; i<x->nz; i++) y->a[y->xtoy[i]] += a*(x->a[i]);
3025     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);
3026   } else {
3027     Mat      B;
3028     PetscInt *nnz;
3029     ierr = PetscMalloc(Y->rmap->N*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
3030     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
3031     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
3032     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
3033     ierr = MatSetBlockSizes(B,Y->rmap->bs,Y->cmap->bs);CHKERRQ(ierr);
3034     ierr = MatSetType(B,(MatType) ((PetscObject)Y)->type_name);CHKERRQ(ierr);
3035     ierr = MatAXPYGetPreallocation_SeqAIJ(Y,X,nnz);CHKERRQ(ierr);
3036     ierr = MatSeqAIJSetPreallocation(B,0,nnz);CHKERRQ(ierr);
3037     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
3038     ierr = MatHeaderReplace(Y,B);CHKERRQ(ierr);
3039     ierr = PetscFree(nnz);CHKERRQ(ierr);
3040   }
3041   PetscFunctionReturn(0);
3042 }
3043 
3044 #undef __FUNCT__
3045 #define __FUNCT__ "MatConjugate_SeqAIJ"
3046 PetscErrorCode  MatConjugate_SeqAIJ(Mat mat)
3047 {
3048 #if defined(PETSC_USE_COMPLEX)
3049   Mat_SeqAIJ  *aij = (Mat_SeqAIJ*)mat->data;
3050   PetscInt    i,nz;
3051   PetscScalar *a;
3052 
3053   PetscFunctionBegin;
3054   nz = aij->nz;
3055   a  = aij->a;
3056   for (i=0; i<nz; i++) a[i] = PetscConj(a[i]);
3057 #else
3058   PetscFunctionBegin;
3059 #endif
3060   PetscFunctionReturn(0);
3061 }
3062 
3063 #undef __FUNCT__
3064 #define __FUNCT__ "MatGetRowMaxAbs_SeqAIJ"
3065 PetscErrorCode MatGetRowMaxAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3066 {
3067   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3068   PetscErrorCode ierr;
3069   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3070   PetscReal      atmp;
3071   PetscScalar    *x;
3072   MatScalar      *aa;
3073 
3074   PetscFunctionBegin;
3075   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3076   aa = a->a;
3077   ai = a->i;
3078   aj = a->j;
3079 
3080   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3081   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3082   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3083   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3084   for (i=0; i<m; i++) {
3085     ncols = ai[1] - ai[0]; ai++;
3086     x[i]  = 0.0;
3087     for (j=0; j<ncols; j++) {
3088       atmp = PetscAbsScalar(*aa);
3089       if (PetscAbsScalar(x[i]) < atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3090       aa++; aj++;
3091     }
3092   }
3093   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3094   PetscFunctionReturn(0);
3095 }
3096 
3097 #undef __FUNCT__
3098 #define __FUNCT__ "MatGetRowMax_SeqAIJ"
3099 PetscErrorCode MatGetRowMax_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3100 {
3101   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3102   PetscErrorCode ierr;
3103   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3104   PetscScalar    *x;
3105   MatScalar      *aa;
3106 
3107   PetscFunctionBegin;
3108   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3109   aa = a->a;
3110   ai = a->i;
3111   aj = a->j;
3112 
3113   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3114   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3115   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3116   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3117   for (i=0; i<m; i++) {
3118     ncols = ai[1] - ai[0]; ai++;
3119     if (ncols == A->cmap->n) { /* row is dense */
3120       x[i] = *aa; if (idx) idx[i] = 0;
3121     } else {  /* row is sparse so already KNOW maximum is 0.0 or higher */
3122       x[i] = 0.0;
3123       if (idx) {
3124         idx[i] = 0; /* in case ncols is zero */
3125         for (j=0;j<ncols;j++) { /* find first implicit 0.0 in the row */
3126           if (aj[j] > j) {
3127             idx[i] = j;
3128             break;
3129           }
3130         }
3131       }
3132     }
3133     for (j=0; j<ncols; j++) {
3134       if (PetscRealPart(x[i]) < PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3135       aa++; aj++;
3136     }
3137   }
3138   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3139   PetscFunctionReturn(0);
3140 }
3141 
3142 #undef __FUNCT__
3143 #define __FUNCT__ "MatGetRowMinAbs_SeqAIJ"
3144 PetscErrorCode MatGetRowMinAbs_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3145 {
3146   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3147   PetscErrorCode ierr;
3148   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3149   PetscReal      atmp;
3150   PetscScalar    *x;
3151   MatScalar      *aa;
3152 
3153   PetscFunctionBegin;
3154   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3155   aa = a->a;
3156   ai = a->i;
3157   aj = a->j;
3158 
3159   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3160   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3161   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3162   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);
3163   for (i=0; i<m; i++) {
3164     ncols = ai[1] - ai[0]; ai++;
3165     if (ncols) {
3166       /* Get first nonzero */
3167       for (j = 0; j < ncols; j++) {
3168         atmp = PetscAbsScalar(aa[j]);
3169         if (atmp > 1.0e-12) {
3170           x[i] = atmp;
3171           if (idx) idx[i] = aj[j];
3172           break;
3173         }
3174       }
3175       if (j == ncols) {x[i] = PetscAbsScalar(*aa); if (idx) idx[i] = *aj;}
3176     } else {
3177       x[i] = 0.0; if (idx) idx[i] = 0;
3178     }
3179     for (j = 0; j < ncols; j++) {
3180       atmp = PetscAbsScalar(*aa);
3181       if (atmp > 1.0e-12 && PetscAbsScalar(x[i]) > atmp) {x[i] = atmp; if (idx) idx[i] = *aj;}
3182       aa++; aj++;
3183     }
3184   }
3185   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3186   PetscFunctionReturn(0);
3187 }
3188 
3189 #undef __FUNCT__
3190 #define __FUNCT__ "MatGetRowMin_SeqAIJ"
3191 PetscErrorCode MatGetRowMin_SeqAIJ(Mat A,Vec v,PetscInt idx[])
3192 {
3193   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
3194   PetscErrorCode ierr;
3195   PetscInt       i,j,m = A->rmap->n,*ai,*aj,ncols,n;
3196   PetscScalar    *x;
3197   MatScalar      *aa;
3198 
3199   PetscFunctionBegin;
3200   if (A->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3201   aa = a->a;
3202   ai = a->i;
3203   aj = a->j;
3204 
3205   ierr = VecSet(v,0.0);CHKERRQ(ierr);
3206   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
3207   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
3208   if (n != A->rmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
3209   for (i=0; i<m; i++) {
3210     ncols = ai[1] - ai[0]; ai++;
3211     if (ncols == A->cmap->n) { /* row is dense */
3212       x[i] = *aa; if (idx) idx[i] = 0;
3213     } else {  /* row is sparse so already KNOW minimum is 0.0 or lower */
3214       x[i] = 0.0;
3215       if (idx) {   /* find first implicit 0.0 in the row */
3216         idx[i] = 0; /* in case ncols is zero */
3217         for (j=0; j<ncols; j++) {
3218           if (aj[j] > j) {
3219             idx[i] = j;
3220             break;
3221           }
3222         }
3223       }
3224     }
3225     for (j=0; j<ncols; j++) {
3226       if (PetscRealPart(x[i]) > PetscRealPart(*aa)) {x[i] = *aa; if (idx) idx[i] = *aj;}
3227       aa++; aj++;
3228     }
3229   }
3230   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
3231   PetscFunctionReturn(0);
3232 }
3233 
3234 #include <petscblaslapack.h>
3235 #include <petsc-private/kernels/blockinvert.h>
3236 
3237 #undef __FUNCT__
3238 #define __FUNCT__ "MatInvertBlockDiagonal_SeqAIJ"
3239 PetscErrorCode  MatInvertBlockDiagonal_SeqAIJ(Mat A,const PetscScalar **values)
3240 {
3241   Mat_SeqAIJ     *a = (Mat_SeqAIJ*) A->data;
3242   PetscErrorCode ierr;
3243   PetscInt       i,bs = A->rmap->bs,mbs = A->rmap->n/A->rmap->bs,ipvt[5],bs2 = bs*bs,*v_pivots,ij[7],*IJ,j;
3244   MatScalar      *diag,work[25],*v_work;
3245   PetscReal      shift = 0.0;
3246 
3247   PetscFunctionBegin;
3248   if (a->ibdiagvalid) {
3249     if (values) *values = a->ibdiag;
3250     PetscFunctionReturn(0);
3251   }
3252   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
3253   if (!a->ibdiag) {
3254     ierr = PetscMalloc(bs2*mbs*sizeof(PetscScalar),&a->ibdiag);CHKERRQ(ierr);
3255     ierr = PetscLogObjectMemory((PetscObject)A,bs2*mbs*sizeof(PetscScalar));CHKERRQ(ierr);
3256   }
3257   diag = a->ibdiag;
3258   if (values) *values = a->ibdiag;
3259   /* factor and invert each block */
3260   switch (bs) {
3261   case 1:
3262     for (i=0; i<mbs; i++) {
3263       ierr    = MatGetValues(A,1,&i,1,&i,diag+i);CHKERRQ(ierr);
3264       diag[i] = (PetscScalar)1.0 / (diag[i] + shift);
3265     }
3266     break;
3267   case 2:
3268     for (i=0; i<mbs; i++) {
3269       ij[0] = 2*i; ij[1] = 2*i + 1;
3270       ierr  = MatGetValues(A,2,ij,2,ij,diag);CHKERRQ(ierr);
3271       ierr  = PetscKernel_A_gets_inverse_A_2(diag,shift);CHKERRQ(ierr);
3272       ierr  = PetscKernel_A_gets_transpose_A_2(diag);CHKERRQ(ierr);
3273       diag += 4;
3274     }
3275     break;
3276   case 3:
3277     for (i=0; i<mbs; i++) {
3278       ij[0] = 3*i; ij[1] = 3*i + 1; ij[2] = 3*i + 2;
3279       ierr  = MatGetValues(A,3,ij,3,ij,diag);CHKERRQ(ierr);
3280       ierr  = PetscKernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr);
3281       ierr  = PetscKernel_A_gets_transpose_A_3(diag);CHKERRQ(ierr);
3282       diag += 9;
3283     }
3284     break;
3285   case 4:
3286     for (i=0; i<mbs; i++) {
3287       ij[0] = 4*i; ij[1] = 4*i + 1; ij[2] = 4*i + 2; ij[3] = 4*i + 3;
3288       ierr  = MatGetValues(A,4,ij,4,ij,diag);CHKERRQ(ierr);
3289       ierr  = PetscKernel_A_gets_inverse_A_4(diag,shift);CHKERRQ(ierr);
3290       ierr  = PetscKernel_A_gets_transpose_A_4(diag);CHKERRQ(ierr);
3291       diag += 16;
3292     }
3293     break;
3294   case 5:
3295     for (i=0; i<mbs; i++) {
3296       ij[0] = 5*i; ij[1] = 5*i + 1; ij[2] = 5*i + 2; ij[3] = 5*i + 3; ij[4] = 5*i + 4;
3297       ierr  = MatGetValues(A,5,ij,5,ij,diag);CHKERRQ(ierr);
3298       ierr  = PetscKernel_A_gets_inverse_A_5(diag,ipvt,work,shift);CHKERRQ(ierr);
3299       ierr  = PetscKernel_A_gets_transpose_A_5(diag);CHKERRQ(ierr);
3300       diag += 25;
3301     }
3302     break;
3303   case 6:
3304     for (i=0; i<mbs; i++) {
3305       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;
3306       ierr  = MatGetValues(A,6,ij,6,ij,diag);CHKERRQ(ierr);
3307       ierr  = PetscKernel_A_gets_inverse_A_6(diag,shift);CHKERRQ(ierr);
3308       ierr  = PetscKernel_A_gets_transpose_A_6(diag);CHKERRQ(ierr);
3309       diag += 36;
3310     }
3311     break;
3312   case 7:
3313     for (i=0; i<mbs; i++) {
3314       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;
3315       ierr  = MatGetValues(A,7,ij,7,ij,diag);CHKERRQ(ierr);
3316       ierr  = PetscKernel_A_gets_inverse_A_7(diag,shift);CHKERRQ(ierr);
3317       ierr  = PetscKernel_A_gets_transpose_A_7(diag);CHKERRQ(ierr);
3318       diag += 49;
3319     }
3320     break;
3321   default:
3322     ierr = PetscMalloc3(bs,MatScalar,&v_work,bs,PetscInt,&v_pivots,bs,PetscInt,&IJ);CHKERRQ(ierr);
3323     for (i=0; i<mbs; i++) {
3324       for (j=0; j<bs; j++) {
3325         IJ[j] = bs*i + j;
3326       }
3327       ierr  = MatGetValues(A,bs,IJ,bs,IJ,diag);CHKERRQ(ierr);
3328       ierr  = PetscKernel_A_gets_inverse_A(bs,diag,v_pivots,v_work);CHKERRQ(ierr);
3329       ierr  = PetscKernel_A_gets_transpose_A_N(diag,bs);CHKERRQ(ierr);
3330       diag += bs2;
3331     }
3332     ierr = PetscFree3(v_work,v_pivots,IJ);CHKERRQ(ierr);
3333   }
3334   a->ibdiagvalid = PETSC_TRUE;
3335   PetscFunctionReturn(0);
3336 }
3337 
3338 #undef __FUNCT__
3339 #define __FUNCT__ "MatSetRandom_SeqAIJ"
3340 static PetscErrorCode  MatSetRandom_SeqAIJ(Mat x,PetscRandom rctx)
3341 {
3342   PetscErrorCode ierr;
3343   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)x->data;
3344   PetscScalar    a;
3345   PetscInt       m,n,i,j,col;
3346 
3347   PetscFunctionBegin;
3348   if (!x->assembled) {
3349     ierr = MatGetSize(x,&m,&n);CHKERRQ(ierr);
3350     for (i=0; i<m; i++) {
3351       for (j=0; j<aij->imax[i]; j++) {
3352         ierr = PetscRandomGetValue(rctx,&a);CHKERRQ(ierr);
3353         col  = (PetscInt)(n*PetscRealPart(a));
3354         ierr = MatSetValues(x,1,&i,1,&col,&a,ADD_VALUES);CHKERRQ(ierr);
3355       }
3356     }
3357   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet coded");
3358   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3359   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3360   PetscFunctionReturn(0);
3361 }
3362 
3363 extern PetscErrorCode  MatFDColoringApply_AIJ(Mat,MatFDColoring,Vec,MatStructure*,void*);
3364 /* -------------------------------------------------------------------*/
3365 static struct _MatOps MatOps_Values = { MatSetValues_SeqAIJ,
3366                                         MatGetRow_SeqAIJ,
3367                                         MatRestoreRow_SeqAIJ,
3368                                         MatMult_SeqAIJ,
3369                                 /*  4*/ MatMultAdd_SeqAIJ,
3370                                         MatMultTranspose_SeqAIJ,
3371                                         MatMultTransposeAdd_SeqAIJ,
3372                                         0,
3373                                         0,
3374                                         0,
3375                                 /* 10*/ 0,
3376                                         MatLUFactor_SeqAIJ,
3377                                         0,
3378                                         MatSOR_SeqAIJ,
3379                                         MatTranspose_SeqAIJ,
3380                                 /*1 5*/ MatGetInfo_SeqAIJ,
3381                                         MatEqual_SeqAIJ,
3382                                         MatGetDiagonal_SeqAIJ,
3383                                         MatDiagonalScale_SeqAIJ,
3384                                         MatNorm_SeqAIJ,
3385                                 /* 20*/ 0,
3386                                         MatAssemblyEnd_SeqAIJ,
3387                                         MatSetOption_SeqAIJ,
3388                                         MatZeroEntries_SeqAIJ,
3389                                 /* 24*/ MatZeroRows_SeqAIJ,
3390                                         0,
3391                                         0,
3392                                         0,
3393                                         0,
3394                                 /* 29*/ MatSetUp_SeqAIJ,
3395                                         0,
3396                                         0,
3397                                         0,
3398                                         0,
3399                                 /* 34*/ MatDuplicate_SeqAIJ,
3400                                         0,
3401                                         0,
3402                                         MatILUFactor_SeqAIJ,
3403                                         0,
3404                                 /* 39*/ MatAXPY_SeqAIJ,
3405                                         MatGetSubMatrices_SeqAIJ,
3406                                         MatIncreaseOverlap_SeqAIJ,
3407                                         MatGetValues_SeqAIJ,
3408                                         MatCopy_SeqAIJ,
3409                                 /* 44*/ MatGetRowMax_SeqAIJ,
3410                                         MatScale_SeqAIJ,
3411                                         0,
3412                                         MatDiagonalSet_SeqAIJ,
3413                                         MatZeroRowsColumns_SeqAIJ,
3414                                 /* 49*/ MatSetRandom_SeqAIJ,
3415                                         MatGetRowIJ_SeqAIJ,
3416                                         MatRestoreRowIJ_SeqAIJ,
3417                                         MatGetColumnIJ_SeqAIJ,
3418                                         MatRestoreColumnIJ_SeqAIJ,
3419                                 /* 54*/ MatFDColoringCreate_SeqAIJ,
3420                                         0,
3421                                         0,
3422                                         MatPermute_SeqAIJ,
3423                                         0,
3424                                 /* 59*/ 0,
3425                                         MatDestroy_SeqAIJ,
3426                                         MatView_SeqAIJ,
3427                                         0,
3428                                         MatMatMatMult_SeqAIJ_SeqAIJ_SeqAIJ,
3429                                 /* 64*/ MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ,
3430                                         MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ,
3431                                         0,
3432                                         0,
3433                                         0,
3434                                 /* 69*/ MatGetRowMaxAbs_SeqAIJ,
3435                                         MatGetRowMinAbs_SeqAIJ,
3436                                         0,
3437                                         MatSetColoring_SeqAIJ,
3438                                         0,
3439                                 /* 74*/ MatSetValuesAdifor_SeqAIJ,
3440                                         MatFDColoringApply_AIJ,
3441                                         0,
3442                                         0,
3443                                         0,
3444                                 /* 79*/ MatFindZeroDiagonals_SeqAIJ,
3445                                         0,
3446                                         0,
3447                                         0,
3448                                         MatLoad_SeqAIJ,
3449                                 /* 84*/ MatIsSymmetric_SeqAIJ,
3450                                         MatIsHermitian_SeqAIJ,
3451                                         0,
3452                                         0,
3453                                         0,
3454                                 /* 89*/ MatMatMult_SeqAIJ_SeqAIJ,
3455                                         MatMatMultSymbolic_SeqAIJ_SeqAIJ,
3456                                         MatMatMultNumeric_SeqAIJ_SeqAIJ,
3457                                         MatPtAP_SeqAIJ_SeqAIJ,
3458                                         MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy,
3459                                 /* 94*/ MatPtAPNumeric_SeqAIJ_SeqAIJ,
3460                                         MatMatTransposeMult_SeqAIJ_SeqAIJ,
3461                                         MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ,
3462                                         MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ,
3463                                         0,
3464                                 /* 99*/ 0,
3465                                         0,
3466                                         0,
3467                                         MatConjugate_SeqAIJ,
3468                                         0,
3469                                 /*104*/ MatSetValuesRow_SeqAIJ,
3470                                         MatRealPart_SeqAIJ,
3471                                         MatImaginaryPart_SeqAIJ,
3472                                         0,
3473                                         0,
3474                                 /*109*/ MatMatSolve_SeqAIJ,
3475                                         0,
3476                                         MatGetRowMin_SeqAIJ,
3477                                         0,
3478                                         MatMissingDiagonal_SeqAIJ,
3479                                 /*114*/ 0,
3480                                         0,
3481                                         0,
3482                                         0,
3483                                         0,
3484                                 /*119*/ 0,
3485                                         0,
3486                                         0,
3487                                         0,
3488                                         MatGetMultiProcBlock_SeqAIJ,
3489                                 /*124*/ MatFindNonzeroRows_SeqAIJ,
3490                                         MatGetColumnNorms_SeqAIJ,
3491                                         MatInvertBlockDiagonal_SeqAIJ,
3492                                         0,
3493                                         0,
3494                                 /*129*/ 0,
3495                                         MatTransposeMatMult_SeqAIJ_SeqAIJ,
3496                                         MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ,
3497                                         MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ,
3498                                         MatTransposeColoringCreate_SeqAIJ,
3499                                 /*134*/ MatTransColoringApplySpToDen_SeqAIJ,
3500                                         MatTransColoringApplyDenToSp_SeqAIJ,
3501                                         MatRARt_SeqAIJ_SeqAIJ,
3502                                         MatRARtSymbolic_SeqAIJ_SeqAIJ,
3503                                         MatRARtNumeric_SeqAIJ_SeqAIJ,
3504                                  /*139*/0,
3505                                         0
3506 };
3507 
3508 #undef __FUNCT__
3509 #define __FUNCT__ "MatSeqAIJSetColumnIndices_SeqAIJ"
3510 PetscErrorCode  MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,PetscInt *indices)
3511 {
3512   Mat_SeqAIJ *aij = (Mat_SeqAIJ*)mat->data;
3513   PetscInt   i,nz,n;
3514 
3515   PetscFunctionBegin;
3516   nz = aij->maxnz;
3517   n  = mat->rmap->n;
3518   for (i=0; i<nz; i++) {
3519     aij->j[i] = indices[i];
3520   }
3521   aij->nz = nz;
3522   for (i=0; i<n; i++) {
3523     aij->ilen[i] = aij->imax[i];
3524   }
3525   PetscFunctionReturn(0);
3526 }
3527 
3528 #undef __FUNCT__
3529 #define __FUNCT__ "MatSeqAIJSetColumnIndices"
3530 /*@
3531     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
3532        in the matrix.
3533 
3534   Input Parameters:
3535 +  mat - the SeqAIJ matrix
3536 -  indices - the column indices
3537 
3538   Level: advanced
3539 
3540   Notes:
3541     This can be called if you have precomputed the nonzero structure of the
3542   matrix and want to provide it to the matrix object to improve the performance
3543   of the MatSetValues() operation.
3544 
3545     You MUST have set the correct numbers of nonzeros per row in the call to
3546   MatCreateSeqAIJ(), and the columns indices MUST be sorted.
3547 
3548     MUST be called before any calls to MatSetValues();
3549 
3550     The indices should start with zero, not one.
3551 
3552 @*/
3553 PetscErrorCode  MatSeqAIJSetColumnIndices(Mat mat,PetscInt *indices)
3554 {
3555   PetscErrorCode ierr;
3556 
3557   PetscFunctionBegin;
3558   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3559   PetscValidPointer(indices,2);
3560   ierr = PetscUseMethod(mat,"MatSeqAIJSetColumnIndices_C",(Mat,PetscInt*),(mat,indices));CHKERRQ(ierr);
3561   PetscFunctionReturn(0);
3562 }
3563 
3564 /* ----------------------------------------------------------------------------------------*/
3565 
3566 #undef __FUNCT__
3567 #define __FUNCT__ "MatStoreValues_SeqAIJ"
3568 PetscErrorCode  MatStoreValues_SeqAIJ(Mat mat)
3569 {
3570   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3571   PetscErrorCode ierr;
3572   size_t         nz = aij->i[mat->rmap->n];
3573 
3574   PetscFunctionBegin;
3575   if (aij->nonew != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3576 
3577   /* allocate space for values if not already there */
3578   if (!aij->saved_values) {
3579     ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&aij->saved_values);CHKERRQ(ierr);
3580     ierr = PetscLogObjectMemory((PetscObject)mat,(nz+1)*sizeof(PetscScalar));CHKERRQ(ierr);
3581   }
3582 
3583   /* copy values over */
3584   ierr = PetscMemcpy(aij->saved_values,aij->a,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3585   PetscFunctionReturn(0);
3586 }
3587 
3588 #undef __FUNCT__
3589 #define __FUNCT__ "MatStoreValues"
3590 /*@
3591     MatStoreValues - Stashes a copy of the matrix values; this allows, for
3592        example, reuse of the linear part of a Jacobian, while recomputing the
3593        nonlinear portion.
3594 
3595    Collect on Mat
3596 
3597   Input Parameters:
3598 .  mat - the matrix (currently only AIJ matrices support this option)
3599 
3600   Level: advanced
3601 
3602   Common Usage, with SNESSolve():
3603 $    Create Jacobian matrix
3604 $    Set linear terms into matrix
3605 $    Apply boundary conditions to matrix, at this time matrix must have
3606 $      final nonzero structure (i.e. setting the nonlinear terms and applying
3607 $      boundary conditions again will not change the nonzero structure
3608 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3609 $    ierr = MatStoreValues(mat);
3610 $    Call SNESSetJacobian() with matrix
3611 $    In your Jacobian routine
3612 $      ierr = MatRetrieveValues(mat);
3613 $      Set nonlinear terms in matrix
3614 
3615   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
3616 $    // build linear portion of Jacobian
3617 $    ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);
3618 $    ierr = MatStoreValues(mat);
3619 $    loop over nonlinear iterations
3620 $       ierr = MatRetrieveValues(mat);
3621 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
3622 $       // call MatAssemblyBegin/End() on matrix
3623 $       Solve linear system with Jacobian
3624 $    endloop
3625 
3626   Notes:
3627     Matrix must already be assemblied before calling this routine
3628     Must set the matrix option MatSetOption(mat,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE); before
3629     calling this routine.
3630 
3631     When this is called multiple times it overwrites the previous set of stored values
3632     and does not allocated additional space.
3633 
3634 .seealso: MatRetrieveValues()
3635 
3636 @*/
3637 PetscErrorCode  MatStoreValues(Mat mat)
3638 {
3639   PetscErrorCode ierr;
3640 
3641   PetscFunctionBegin;
3642   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3643   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3644   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3645   ierr = PetscUseMethod(mat,"MatStoreValues_C",(Mat),(mat));CHKERRQ(ierr);
3646   PetscFunctionReturn(0);
3647 }
3648 
3649 #undef __FUNCT__
3650 #define __FUNCT__ "MatRetrieveValues_SeqAIJ"
3651 PetscErrorCode  MatRetrieveValues_SeqAIJ(Mat mat)
3652 {
3653   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)mat->data;
3654   PetscErrorCode ierr;
3655   PetscInt       nz = aij->i[mat->rmap->n];
3656 
3657   PetscFunctionBegin;
3658   if (aij->nonew != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatSetOption(A,MAT_NEW_NONZERO_LOCATIONS,PETSC_FALSE);first");
3659   if (!aij->saved_values) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Must call MatStoreValues(A);first");
3660   /* copy values over */
3661   ierr = PetscMemcpy(aij->a,aij->saved_values,nz*sizeof(PetscScalar));CHKERRQ(ierr);
3662   PetscFunctionReturn(0);
3663 }
3664 
3665 #undef __FUNCT__
3666 #define __FUNCT__ "MatRetrieveValues"
3667 /*@
3668     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
3669        example, reuse of the linear part of a Jacobian, while recomputing the
3670        nonlinear portion.
3671 
3672    Collect on Mat
3673 
3674   Input Parameters:
3675 .  mat - the matrix (currently on AIJ matrices support this option)
3676 
3677   Level: advanced
3678 
3679 .seealso: MatStoreValues()
3680 
3681 @*/
3682 PetscErrorCode  MatRetrieveValues(Mat mat)
3683 {
3684   PetscErrorCode ierr;
3685 
3686   PetscFunctionBegin;
3687   PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
3688   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
3689   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
3690   ierr = PetscUseMethod(mat,"MatRetrieveValues_C",(Mat),(mat));CHKERRQ(ierr);
3691   PetscFunctionReturn(0);
3692 }
3693 
3694 
3695 /* --------------------------------------------------------------------------------*/
3696 #undef __FUNCT__
3697 #define __FUNCT__ "MatCreateSeqAIJ"
3698 /*@C
3699    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
3700    (the default parallel PETSc format).  For good matrix assembly performance
3701    the user should preallocate the matrix storage by setting the parameter nz
3702    (or the array nnz).  By setting these parameters accurately, performance
3703    during matrix assembly can be increased by more than a factor of 50.
3704 
3705    Collective on MPI_Comm
3706 
3707    Input Parameters:
3708 +  comm - MPI communicator, set to PETSC_COMM_SELF
3709 .  m - number of rows
3710 .  n - number of columns
3711 .  nz - number of nonzeros per row (same for all rows)
3712 -  nnz - array containing the number of nonzeros in the various rows
3713          (possibly different for each row) or NULL
3714 
3715    Output Parameter:
3716 .  A - the matrix
3717 
3718    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3719    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3720    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3721 
3722    Notes:
3723    If nnz is given then nz is ignored
3724 
3725    The AIJ format (also called the Yale sparse matrix format or
3726    compressed row storage), is fully compatible with standard Fortran 77
3727    storage.  That is, the stored row and column indices can begin at
3728    either one (as in Fortran) or zero.  See the users' manual for details.
3729 
3730    Specify the preallocated storage with either nz or nnz (not both).
3731    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3732    allocation.  For large problems you MUST preallocate memory or you
3733    will get TERRIBLE performance, see the users' manual chapter on matrices.
3734 
3735    By default, this format uses inodes (identical nodes) when possible, to
3736    improve numerical efficiency of matrix-vector products and solves. We
3737    search for consecutive rows with the same nonzero structure, thereby
3738    reusing matrix information to achieve increased efficiency.
3739 
3740    Options Database Keys:
3741 +  -mat_no_inode  - Do not use inodes
3742 -  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3743 
3744    Level: intermediate
3745 
3746 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
3747 
3748 @*/
3749 PetscErrorCode  MatCreateSeqAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
3750 {
3751   PetscErrorCode ierr;
3752 
3753   PetscFunctionBegin;
3754   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3755   ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
3756   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3757   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
3758   PetscFunctionReturn(0);
3759 }
3760 
3761 #undef __FUNCT__
3762 #define __FUNCT__ "MatSeqAIJSetPreallocation"
3763 /*@C
3764    MatSeqAIJSetPreallocation - For good matrix assembly performance
3765    the user should preallocate the matrix storage by setting the parameter nz
3766    (or the array nnz).  By setting these parameters accurately, performance
3767    during matrix assembly can be increased by more than a factor of 50.
3768 
3769    Collective on MPI_Comm
3770 
3771    Input Parameters:
3772 +  B - The matrix-free
3773 .  nz - number of nonzeros per row (same for all rows)
3774 -  nnz - array containing the number of nonzeros in the various rows
3775          (possibly different for each row) or NULL
3776 
3777    Notes:
3778      If nnz is given then nz is ignored
3779 
3780     The AIJ format (also called the Yale sparse matrix format or
3781    compressed row storage), is fully compatible with standard Fortran 77
3782    storage.  That is, the stored row and column indices can begin at
3783    either one (as in Fortran) or zero.  See the users' manual for details.
3784 
3785    Specify the preallocated storage with either nz or nnz (not both).
3786    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
3787    allocation.  For large problems you MUST preallocate memory or you
3788    will get TERRIBLE performance, see the users' manual chapter on matrices.
3789 
3790    You can call MatGetInfo() to get information on how effective the preallocation was;
3791    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3792    You can also run with the option -info and look for messages with the string
3793    malloc in them to see if additional memory allocation was needed.
3794 
3795    Developers: Use nz of MAT_SKIP_ALLOCATION to not allocate any space for the matrix
3796    entries or columns indices
3797 
3798    By default, this format uses inodes (identical nodes) when possible, to
3799    improve numerical efficiency of matrix-vector products and solves. We
3800    search for consecutive rows with the same nonzero structure, thereby
3801    reusing matrix information to achieve increased efficiency.
3802 
3803    Options Database Keys:
3804 +  -mat_no_inode  - Do not use inodes
3805 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3806 -  -mat_aij_oneindex - Internally use indexing starting at 1
3807         rather than 0.  Note that when calling MatSetValues(),
3808         the user still MUST index entries starting at 0!
3809 
3810    Level: intermediate
3811 
3812 .seealso: MatCreate(), MatCreateAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays(), MatGetInfo()
3813 
3814 @*/
3815 PetscErrorCode  MatSeqAIJSetPreallocation(Mat B,PetscInt nz,const PetscInt nnz[])
3816 {
3817   PetscErrorCode ierr;
3818 
3819   PetscFunctionBegin;
3820   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3821   PetscValidType(B,1);
3822   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[]),(B,nz,nnz));CHKERRQ(ierr);
3823   PetscFunctionReturn(0);
3824 }
3825 
3826 #undef __FUNCT__
3827 #define __FUNCT__ "MatSeqAIJSetPreallocation_SeqAIJ"
3828 PetscErrorCode  MatSeqAIJSetPreallocation_SeqAIJ(Mat B,PetscInt nz,const PetscInt *nnz)
3829 {
3830   Mat_SeqAIJ     *b;
3831   PetscBool      skipallocation = PETSC_FALSE,realalloc = PETSC_FALSE;
3832   PetscErrorCode ierr;
3833   PetscInt       i;
3834 
3835   PetscFunctionBegin;
3836   if (nz >= 0 || nnz) realalloc = PETSC_TRUE;
3837   if (nz == MAT_SKIP_ALLOCATION) {
3838     skipallocation = PETSC_TRUE;
3839     nz             = 0;
3840   }
3841 
3842   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3843   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3844 
3845   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
3846   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %d",nz);
3847   if (nnz) {
3848     for (i=0; i<B->rmap->n; i++) {
3849       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]);
3850       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);
3851     }
3852   }
3853 
3854   B->preallocated = PETSC_TRUE;
3855 
3856   b = (Mat_SeqAIJ*)B->data;
3857 
3858   if (!skipallocation) {
3859     if (!b->imax) {
3860       ierr = PetscMalloc2(B->rmap->n,PetscInt,&b->imax,B->rmap->n,PetscInt,&b->ilen);CHKERRQ(ierr);
3861       ierr = PetscLogObjectMemory((PetscObject)B,2*B->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
3862     }
3863     if (!nnz) {
3864       if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
3865       else if (nz < 0) nz = 1;
3866       for (i=0; i<B->rmap->n; i++) b->imax[i] = nz;
3867       nz = nz*B->rmap->n;
3868     } else {
3869       nz = 0;
3870       for (i=0; i<B->rmap->n; i++) {b->imax[i] = nnz[i]; nz += nnz[i];}
3871     }
3872     /* b->ilen will count nonzeros in each row so far. */
3873     for (i=0; i<B->rmap->n; i++) b->ilen[i] = 0;
3874 
3875     /* allocate the matrix space */
3876     ierr    = MatSeqXAIJFreeAIJ(B,&b->a,&b->j,&b->i);CHKERRQ(ierr);
3877     ierr    = PetscMalloc3(nz,PetscScalar,&b->a,nz,PetscInt,&b->j,B->rmap->n+1,PetscInt,&b->i);CHKERRQ(ierr);
3878     ierr    = PetscLogObjectMemory((PetscObject)B,(B->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
3879     b->i[0] = 0;
3880     for (i=1; i<B->rmap->n+1; i++) {
3881       b->i[i] = b->i[i-1] + b->imax[i-1];
3882     }
3883     b->singlemalloc = PETSC_TRUE;
3884     b->free_a       = PETSC_TRUE;
3885     b->free_ij      = PETSC_TRUE;
3886 #if defined(PETSC_THREADCOMM_ACTIVE)
3887     ierr = MatZeroEntries_SeqAIJ(B);CHKERRQ(ierr);
3888 #endif
3889   } else {
3890     b->free_a  = PETSC_FALSE;
3891     b->free_ij = PETSC_FALSE;
3892   }
3893 
3894   b->nz               = 0;
3895   b->maxnz            = nz;
3896   B->info.nz_unneeded = (double)b->maxnz;
3897   if (realalloc) {
3898     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3899   }
3900   PetscFunctionReturn(0);
3901 }
3902 
3903 #undef  __FUNCT__
3904 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR"
3905 /*@
3906    MatSeqAIJSetPreallocationCSR - Allocates memory for a sparse sequential matrix in AIJ format.
3907 
3908    Input Parameters:
3909 +  B - the matrix
3910 .  i - the indices into j for the start of each row (starts with zero)
3911 .  j - the column indices for each row (starts with zero) these must be sorted for each row
3912 -  v - optional values in the matrix
3913 
3914    Level: developer
3915 
3916    The i,j,v values are COPIED with this routine; to avoid the copy use MatCreateSeqAIJWithArrays()
3917 
3918 .keywords: matrix, aij, compressed row, sparse, sequential
3919 
3920 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatSeqAIJSetPreallocation(), MatCreateSeqAIJ(), SeqAIJ
3921 @*/
3922 PetscErrorCode MatSeqAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[],const PetscScalar v[])
3923 {
3924   PetscErrorCode ierr;
3925 
3926   PetscFunctionBegin;
3927   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3928   PetscValidType(B,1);
3929   ierr = PetscTryMethod(B,"MatSeqAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3930   PetscFunctionReturn(0);
3931 }
3932 
3933 #undef  __FUNCT__
3934 #define __FUNCT__  "MatSeqAIJSetPreallocationCSR_SeqAIJ"
3935 PetscErrorCode  MatSeqAIJSetPreallocationCSR_SeqAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3936 {
3937   PetscInt       i;
3938   PetscInt       m,n;
3939   PetscInt       nz;
3940   PetscInt       *nnz, nz_max = 0;
3941   PetscScalar    *values;
3942   PetscErrorCode ierr;
3943 
3944   PetscFunctionBegin;
3945   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %D", Ii[0]);
3946 
3947   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3948   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3949 
3950   ierr = MatGetSize(B, &m, &n);CHKERRQ(ierr);
3951   ierr = PetscMalloc((m+1) * sizeof(PetscInt), &nnz);CHKERRQ(ierr);
3952   for (i = 0; i < m; i++) {
3953     nz     = Ii[i+1]- Ii[i];
3954     nz_max = PetscMax(nz_max, nz);
3955     if (nz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE, "Local row %D has a negative number of columns %D", i, nnz);
3956     nnz[i] = nz;
3957   }
3958   ierr = MatSeqAIJSetPreallocation(B, 0, nnz);CHKERRQ(ierr);
3959   ierr = PetscFree(nnz);CHKERRQ(ierr);
3960 
3961   if (v) {
3962     values = (PetscScalar*) v;
3963   } else {
3964     ierr = PetscMalloc(nz_max*sizeof(PetscScalar), &values);CHKERRQ(ierr);
3965     ierr = PetscMemzero(values, nz_max*sizeof(PetscScalar));CHKERRQ(ierr);
3966   }
3967 
3968   for (i = 0; i < m; i++) {
3969     nz   = Ii[i+1] - Ii[i];
3970     ierr = MatSetValues_SeqAIJ(B, 1, &i, nz, J+Ii[i], values + (v ? Ii[i] : 0), INSERT_VALUES);CHKERRQ(ierr);
3971   }
3972 
3973   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3974   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3975 
3976   if (!v) {
3977     ierr = PetscFree(values);CHKERRQ(ierr);
3978   }
3979   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3980   PetscFunctionReturn(0);
3981 }
3982 
3983 #include <../src/mat/impls/dense/seq/dense.h>
3984 #include <petsc-private/kernels/petscaxpy.h>
3985 
3986 #undef __FUNCT__
3987 #define __FUNCT__ "MatMatMultNumeric_SeqDense_SeqAIJ"
3988 /*
3989     Computes (B'*A')' since computing B*A directly is untenable
3990 
3991                n                       p                          p
3992         (              )       (              )         (                  )
3993       m (      A       )  *  n (       B      )   =   m (         C        )
3994         (              )       (              )         (                  )
3995 
3996 */
3997 PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat A,Mat B,Mat C)
3998 {
3999   PetscErrorCode    ierr;
4000   Mat_SeqDense      *sub_a = (Mat_SeqDense*)A->data;
4001   Mat_SeqAIJ        *sub_b = (Mat_SeqAIJ*)B->data;
4002   Mat_SeqDense      *sub_c = (Mat_SeqDense*)C->data;
4003   PetscInt          i,n,m,q,p;
4004   const PetscInt    *ii,*idx;
4005   const PetscScalar *b,*a,*a_q;
4006   PetscScalar       *c,*c_q;
4007 
4008   PetscFunctionBegin;
4009   m    = A->rmap->n;
4010   n    = A->cmap->n;
4011   p    = B->cmap->n;
4012   a    = sub_a->v;
4013   b    = sub_b->a;
4014   c    = sub_c->v;
4015   ierr = PetscMemzero(c,m*p*sizeof(PetscScalar));CHKERRQ(ierr);
4016 
4017   ii  = sub_b->i;
4018   idx = sub_b->j;
4019   for (i=0; i<n; i++) {
4020     q = ii[i+1] - ii[i];
4021     while (q-->0) {
4022       c_q = c + m*(*idx);
4023       a_q = a + m*i;
4024       PetscKernelAXPY(c_q,*b,a_q,m);
4025       idx++;
4026       b++;
4027     }
4028   }
4029   PetscFunctionReturn(0);
4030 }
4031 
4032 #undef __FUNCT__
4033 #define __FUNCT__ "MatMatMultSymbolic_SeqDense_SeqAIJ"
4034 PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4035 {
4036   PetscErrorCode ierr;
4037   PetscInt       m=A->rmap->n,n=B->cmap->n;
4038   Mat            Cmat;
4039 
4040   PetscFunctionBegin;
4041   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);
4042   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4043   ierr = MatSetSizes(Cmat,m,n,m,n);CHKERRQ(ierr);
4044   ierr = MatSetBlockSizes(Cmat,A->rmap->bs,B->cmap->bs);CHKERRQ(ierr);
4045   ierr = MatSetType(Cmat,MATSEQDENSE);CHKERRQ(ierr);
4046   ierr = MatSeqDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4047 
4048   Cmat->ops->matmultnumeric = MatMatMultNumeric_SeqDense_SeqAIJ;
4049 
4050   *C = Cmat;
4051   PetscFunctionReturn(0);
4052 }
4053 
4054 /* ----------------------------------------------------------------*/
4055 #undef __FUNCT__
4056 #define __FUNCT__ "MatMatMult_SeqDense_SeqAIJ"
4057 PetscErrorCode MatMatMult_SeqDense_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
4058 {
4059   PetscErrorCode ierr;
4060 
4061   PetscFunctionBegin;
4062   if (scall == MAT_INITIAL_MATRIX) {
4063     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4064     ierr = MatMatMultSymbolic_SeqDense_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
4065     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
4066   }
4067   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4068   ierr = MatMatMultNumeric_SeqDense_SeqAIJ(A,B,*C);CHKERRQ(ierr);
4069   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
4070   PetscFunctionReturn(0);
4071 }
4072 
4073 
4074 /*MC
4075    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
4076    based on compressed sparse row format.
4077 
4078    Options Database Keys:
4079 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
4080 
4081   Level: beginner
4082 
4083 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
4084 M*/
4085 
4086 /*MC
4087    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
4088 
4089    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
4090    and MATMPIAIJ otherwise.  As a result, for single process communicators,
4091   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
4092   for communicators controlling multiple processes.  It is recommended that you call both of
4093   the above preallocation routines for simplicity.
4094 
4095    Options Database Keys:
4096 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
4097 
4098   Developer Notes: Subclasses include MATAIJCUSP, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
4099    enough exist.
4100 
4101   Level: beginner
4102 
4103 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ,MATMPIAIJ
4104 M*/
4105 
4106 /*MC
4107    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
4108 
4109    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
4110    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
4111    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
4112   for communicators controlling multiple processes.  It is recommended that you call both of
4113   the above preallocation routines for simplicity.
4114 
4115    Options Database Keys:
4116 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
4117 
4118   Level: beginner
4119 
4120 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
4121 M*/
4122 
4123 #if defined(PETSC_HAVE_PASTIX)
4124 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_pastix(Mat,MatFactorType,Mat*);
4125 #endif
4126 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
4127 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_essl(Mat,MatFactorType,Mat*);
4128 #endif
4129 PETSC_EXTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat,MatType,MatReuse,Mat*);
4130 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_petsc(Mat,MatFactorType,Mat*);
4131 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_bas(Mat,MatFactorType,Mat*);
4132 extern PetscErrorCode  MatGetFactorAvailable_seqaij_petsc(Mat,MatFactorType,PetscBool*);
4133 #if defined(PETSC_HAVE_MUMPS)
4134 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_mumps(Mat,MatFactorType,Mat*);
4135 #endif
4136 #if defined(PETSC_HAVE_SUPERLU)
4137 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu(Mat,MatFactorType,Mat*);
4138 #endif
4139 #if defined(PETSC_HAVE_SUPERLU_DIST)
4140 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_superlu_dist(Mat,MatFactorType,Mat*);
4141 #endif
4142 #if defined(PETSC_HAVE_UMFPACK)
4143 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_umfpack(Mat,MatFactorType,Mat*);
4144 #endif
4145 #if defined(PETSC_HAVE_CHOLMOD)
4146 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_cholmod(Mat,MatFactorType,Mat*);
4147 #endif
4148 #if defined(PETSC_HAVE_LUSOL)
4149 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_lusol(Mat,MatFactorType,Mat*);
4150 #endif
4151 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4152 PETSC_EXTERN PetscErrorCode MatGetFactor_seqaij_matlab(Mat,MatFactorType,Mat*);
4153 extern PetscErrorCode  MatlabEnginePut_SeqAIJ(PetscObject,void*);
4154 extern PetscErrorCode  MatlabEngineGet_SeqAIJ(PetscObject,void*);
4155 #endif
4156 #if defined(PETSC_HAVE_CLIQUE)
4157 PETSC_EXTERN PetscErrorCode MatGetFactor_aij_clique(Mat,MatFactorType,Mat*);
4158 #endif
4159 
4160 
4161 #undef __FUNCT__
4162 #define __FUNCT__ "MatSeqAIJGetArray"
4163 /*@C
4164    MatSeqAIJGetArray - gives access to the array where the data for a SeqSeqAIJ matrix is stored
4165 
4166    Not Collective
4167 
4168    Input Parameter:
4169 .  mat - a MATSEQDENSE matrix
4170 
4171    Output Parameter:
4172 .   array - pointer to the data
4173 
4174    Level: intermediate
4175 
4176 .seealso: MatSeqAIJRestoreArray(), MatSeqAIJGetArrayF90()
4177 @*/
4178 PetscErrorCode  MatSeqAIJGetArray(Mat A,PetscScalar **array)
4179 {
4180   PetscErrorCode ierr;
4181 
4182   PetscFunctionBegin;
4183   ierr = PetscUseMethod(A,"MatSeqAIJGetArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4184   PetscFunctionReturn(0);
4185 }
4186 
4187 #undef __FUNCT__
4188 #define __FUNCT__ "MatSeqAIJRestoreArray"
4189 /*@C
4190    MatSeqAIJRestoreArray - returns access to the array where the data for a SeqSeqAIJ matrix is stored obtained by MatSeqAIJGetArray()
4191 
4192    Not Collective
4193 
4194    Input Parameters:
4195 .  mat - a MATSEQDENSE matrix
4196 .  array - pointer to the data
4197 
4198    Level: intermediate
4199 
4200 .seealso: MatSeqAIJGetArray(), MatSeqAIJRestoreArrayF90()
4201 @*/
4202 PetscErrorCode  MatSeqAIJRestoreArray(Mat A,PetscScalar **array)
4203 {
4204   PetscErrorCode ierr;
4205 
4206   PetscFunctionBegin;
4207   ierr = PetscUseMethod(A,"MatSeqAIJRestoreArray_C",(Mat,PetscScalar**),(A,array));CHKERRQ(ierr);
4208   PetscFunctionReturn(0);
4209 }
4210 
4211 #undef __FUNCT__
4212 #define __FUNCT__ "MatCreate_SeqAIJ"
4213 PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat B)
4214 {
4215   Mat_SeqAIJ     *b;
4216   PetscErrorCode ierr;
4217   PetscMPIInt    size;
4218 
4219   PetscFunctionBegin;
4220   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
4221   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
4222 
4223   ierr = PetscNewLog(B,Mat_SeqAIJ,&b);CHKERRQ(ierr);
4224 
4225   B->data = (void*)b;
4226 
4227   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
4228 
4229   b->row                = 0;
4230   b->col                = 0;
4231   b->icol               = 0;
4232   b->reallocs           = 0;
4233   b->ignorezeroentries  = PETSC_FALSE;
4234   b->roworiented        = PETSC_TRUE;
4235   b->nonew              = 0;
4236   b->diag               = 0;
4237   b->solve_work         = 0;
4238   B->spptr              = 0;
4239   b->saved_values       = 0;
4240   b->idiag              = 0;
4241   b->mdiag              = 0;
4242   b->ssor_work          = 0;
4243   b->omega              = 1.0;
4244   b->fshift             = 0.0;
4245   b->idiagvalid         = PETSC_FALSE;
4246   b->ibdiagvalid        = PETSC_FALSE;
4247   b->keepnonzeropattern = PETSC_FALSE;
4248   b->xtoy               = 0;
4249   b->XtoY               = 0;
4250   B->same_nonzero       = PETSC_FALSE;
4251 
4252   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4253   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJGetArray_C",MatSeqAIJGetArray_SeqAIJ);CHKERRQ(ierr);
4254   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJRestoreArray_C",MatSeqAIJRestoreArray_SeqAIJ);CHKERRQ(ierr);
4255 
4256 #if defined(PETSC_HAVE_MATLAB_ENGINE)
4257   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_matlab_C",MatGetFactor_seqaij_matlab);CHKERRQ(ierr);
4258   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEnginePut_C",MatlabEnginePut_SeqAIJ);CHKERRQ(ierr);
4259   ierr = PetscObjectComposeFunction((PetscObject)B,"PetscMatlabEngineGet_C",MatlabEngineGet_SeqAIJ);CHKERRQ(ierr);
4260 #endif
4261 #if defined(PETSC_HAVE_PASTIX)
4262   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_pastix_C",MatGetFactor_seqaij_pastix);CHKERRQ(ierr);
4263 #endif
4264 #if defined(PETSC_HAVE_ESSL) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_REAL_SINGLE) && !defined(PETSC_USE_REAL___FLOAT128)
4265   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_essl_C",MatGetFactor_seqaij_essl);CHKERRQ(ierr);
4266 #endif
4267 #if defined(PETSC_HAVE_SUPERLU)
4268   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_C",MatGetFactor_seqaij_superlu);CHKERRQ(ierr);
4269 #endif
4270 #if defined(PETSC_HAVE_SUPERLU_DIST)
4271   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_superlu_dist_C",MatGetFactor_seqaij_superlu_dist);CHKERRQ(ierr);
4272 #endif
4273 #if defined(PETSC_HAVE_MUMPS)
4274   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_mumps_C",MatGetFactor_aij_mumps);CHKERRQ(ierr);
4275 #endif
4276 #if defined(PETSC_HAVE_UMFPACK)
4277   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_umfpack_C",MatGetFactor_seqaij_umfpack);CHKERRQ(ierr);
4278 #endif
4279 #if defined(PETSC_HAVE_CHOLMOD)
4280   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_cholmod_C",MatGetFactor_seqaij_cholmod);CHKERRQ(ierr);
4281 #endif
4282 #if defined(PETSC_HAVE_LUSOL)
4283   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_lusol_C",MatGetFactor_seqaij_lusol);CHKERRQ(ierr);
4284 #endif
4285 #if defined(PETSC_HAVE_CLIQUE)
4286   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_clique_C",MatGetFactor_aij_clique);CHKERRQ(ierr);
4287 #endif
4288 
4289   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_petsc_C",MatGetFactor_seqaij_petsc);CHKERRQ(ierr);
4290   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactorAvailable_petsc_C",MatGetFactorAvailable_seqaij_petsc);CHKERRQ(ierr);
4291   ierr = PetscObjectComposeFunction((PetscObject)B,"MatGetFactor_bas_C",MatGetFactor_seqaij_bas);CHKERRQ(ierr);
4292   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetColumnIndices_C",MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
4293   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_SeqAIJ);CHKERRQ(ierr);
4294   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
4295   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
4296   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqbaij_C",MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
4297   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijperm_C",MatConvert_SeqAIJ_SeqAIJPERM);CHKERRQ(ierr);
4298   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaij_seqaijcrl_C",MatConvert_SeqAIJ_SeqAIJCRL);CHKERRQ(ierr);
4299   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4300   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsHermitianTranspose_C",MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
4301   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
4302   ierr = PetscObjectComposeFunction((PetscObject)B,"MatSeqAIJSetPreallocationCSR_C",MatSeqAIJSetPreallocationCSR_SeqAIJ);CHKERRQ(ierr);
4303   ierr = PetscObjectComposeFunction((PetscObject)B,"MatReorderForNonzeroDiagonal_C",MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
4304   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaij_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
4305   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaij_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
4306   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaij_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
4307   ierr = MatCreate_SeqAIJ_Inode(B);CHKERRQ(ierr);
4308   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
4309   PetscFunctionReturn(0);
4310 }
4311 
4312 #undef __FUNCT__
4313 #define __FUNCT__ "MatDuplicateNoCreate_SeqAIJ"
4314 /*
4315     Given a matrix generated with MatGetFactor() duplicates all the information in A into B
4316 */
4317 PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat C,Mat A,MatDuplicateOption cpvalues,PetscBool mallocmatspace)
4318 {
4319   Mat_SeqAIJ     *c,*a = (Mat_SeqAIJ*)A->data;
4320   PetscErrorCode ierr;
4321   PetscInt       i,m = A->rmap->n;
4322 
4323   PetscFunctionBegin;
4324   c = (Mat_SeqAIJ*)C->data;
4325 
4326   C->factortype = A->factortype;
4327   c->row        = 0;
4328   c->col        = 0;
4329   c->icol       = 0;
4330   c->reallocs   = 0;
4331 
4332   C->assembled = PETSC_TRUE;
4333 
4334   ierr = PetscLayoutReference(A->rmap,&C->rmap);CHKERRQ(ierr);
4335   ierr = PetscLayoutReference(A->cmap,&C->cmap);CHKERRQ(ierr);
4336 
4337   ierr = PetscMalloc2(m,PetscInt,&c->imax,m,PetscInt,&c->ilen);CHKERRQ(ierr);
4338   ierr = PetscLogObjectMemory((PetscObject)C, 2*m*sizeof(PetscInt));CHKERRQ(ierr);
4339   for (i=0; i<m; i++) {
4340     c->imax[i] = a->imax[i];
4341     c->ilen[i] = a->ilen[i];
4342   }
4343 
4344   /* allocate the matrix space */
4345   if (mallocmatspace) {
4346     ierr = PetscMalloc3(a->i[m],PetscScalar,&c->a,a->i[m],PetscInt,&c->j,m+1,PetscInt,&c->i);CHKERRQ(ierr);
4347     ierr = PetscLogObjectMemory((PetscObject)C, a->i[m]*(sizeof(PetscScalar)+sizeof(PetscInt))+(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4348 
4349     c->singlemalloc = PETSC_TRUE;
4350 
4351     ierr = PetscMemcpy(c->i,a->i,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4352     if (m > 0) {
4353       ierr = PetscMemcpy(c->j,a->j,(a->i[m])*sizeof(PetscInt));CHKERRQ(ierr);
4354       if (cpvalues == MAT_COPY_VALUES) {
4355         ierr = PetscMemcpy(c->a,a->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4356       } else {
4357         ierr = PetscMemzero(c->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
4358       }
4359     }
4360   }
4361 
4362   c->ignorezeroentries = a->ignorezeroentries;
4363   c->roworiented       = a->roworiented;
4364   c->nonew             = a->nonew;
4365   if (a->diag) {
4366     ierr = PetscMalloc((m+1)*sizeof(PetscInt),&c->diag);CHKERRQ(ierr);
4367     ierr = PetscLogObjectMemory((PetscObject)C,(m+1)*sizeof(PetscInt));CHKERRQ(ierr);
4368     for (i=0; i<m; i++) {
4369       c->diag[i] = a->diag[i];
4370     }
4371   } else c->diag = 0;
4372 
4373   c->solve_work         = 0;
4374   c->saved_values       = 0;
4375   c->idiag              = 0;
4376   c->ssor_work          = 0;
4377   c->keepnonzeropattern = a->keepnonzeropattern;
4378   c->free_a             = PETSC_TRUE;
4379   c->free_ij            = PETSC_TRUE;
4380   c->xtoy               = 0;
4381   c->XtoY               = 0;
4382 
4383   c->rmax         = a->rmax;
4384   c->nz           = a->nz;
4385   c->maxnz        = a->nz;       /* Since we allocate exactly the right amount */
4386   C->preallocated = PETSC_TRUE;
4387 
4388   c->compressedrow.use   = a->compressedrow.use;
4389   c->compressedrow.nrows = a->compressedrow.nrows;
4390   c->compressedrow.check = a->compressedrow.check;
4391   if (a->compressedrow.use) {
4392     i    = a->compressedrow.nrows;
4393     ierr = PetscMalloc2(i+1,PetscInt,&c->compressedrow.i,i,PetscInt,&c->compressedrow.rindex);CHKERRQ(ierr);
4394     ierr = PetscMemcpy(c->compressedrow.i,a->compressedrow.i,(i+1)*sizeof(PetscInt));CHKERRQ(ierr);
4395     ierr = PetscMemcpy(c->compressedrow.rindex,a->compressedrow.rindex,i*sizeof(PetscInt));CHKERRQ(ierr);
4396   } else {
4397     c->compressedrow.use    = PETSC_FALSE;
4398     c->compressedrow.i      = NULL;
4399     c->compressedrow.rindex = NULL;
4400   }
4401   C->same_nonzero = A->same_nonzero;
4402 
4403   ierr = MatDuplicate_SeqAIJ_Inode(A,cpvalues,&C);CHKERRQ(ierr);
4404   ierr = PetscFunctionListDuplicate(((PetscObject)A)->qlist,&((PetscObject)C)->qlist);CHKERRQ(ierr);
4405   PetscFunctionReturn(0);
4406 }
4407 
4408 #undef __FUNCT__
4409 #define __FUNCT__ "MatDuplicate_SeqAIJ"
4410 PetscErrorCode MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
4411 {
4412   PetscErrorCode ierr;
4413 
4414   PetscFunctionBegin;
4415   ierr = MatCreate(PetscObjectComm((PetscObject)A),B);CHKERRQ(ierr);
4416   ierr = MatSetSizes(*B,A->rmap->n,A->cmap->n,A->rmap->n,A->cmap->n);CHKERRQ(ierr);
4417   ierr = MatSetBlockSizes(*B,A->rmap->bs,A->cmap->bs);CHKERRQ(ierr);
4418   ierr = MatSetType(*B,((PetscObject)A)->type_name);CHKERRQ(ierr);
4419   ierr = MatDuplicateNoCreate_SeqAIJ(*B,A,cpvalues,PETSC_TRUE);CHKERRQ(ierr);
4420   PetscFunctionReturn(0);
4421 }
4422 
4423 #undef __FUNCT__
4424 #define __FUNCT__ "MatLoad_SeqAIJ"
4425 PetscErrorCode MatLoad_SeqAIJ(Mat newMat, PetscViewer viewer)
4426 {
4427   Mat_SeqAIJ     *a;
4428   PetscErrorCode ierr;
4429   PetscInt       i,sum,nz,header[4],*rowlengths = 0,M,N,rows,cols;
4430   int            fd;
4431   PetscMPIInt    size;
4432   MPI_Comm       comm;
4433   PetscInt       bs = 1;
4434 
4435   PetscFunctionBegin;
4436   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
4437   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4438   if (size > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"view must have one processor");
4439 
4440   ierr = PetscOptionsBegin(comm,NULL,"Options for loading SEQAIJ matrix","Mat");CHKERRQ(ierr);
4441   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
4442   ierr = PetscOptionsEnd();CHKERRQ(ierr);
4443   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
4444 
4445   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
4446   ierr = PetscBinaryRead(fd,header,4,PETSC_INT);CHKERRQ(ierr);
4447   if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
4448   M = header[1]; N = header[2]; nz = header[3];
4449 
4450   if (nz < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
4451 
4452   /* read in row lengths */
4453   ierr = PetscMalloc(M*sizeof(PetscInt),&rowlengths);CHKERRQ(ierr);
4454   ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
4455 
4456   /* check if sum of rowlengths is same as nz */
4457   for (i=0,sum=0; i< M; i++) sum +=rowlengths[i];
4458   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);
4459 
4460   /* set global size if not set already*/
4461   if (newMat->rmap->n < 0 && newMat->rmap->N < 0 && newMat->cmap->n < 0 && newMat->cmap->N < 0) {
4462     ierr = MatSetSizes(newMat,PETSC_DECIDE,PETSC_DECIDE,M,N);CHKERRQ(ierr);
4463   } else {
4464     /* if sizes and type are already set, check if the vector global sizes are correct */
4465     ierr = MatGetSize(newMat,&rows,&cols);CHKERRQ(ierr);
4466     if (rows < 0 && cols < 0) { /* user might provide local size instead of global size */
4467       ierr = MatGetLocalSize(newMat,&rows,&cols);CHKERRQ(ierr);
4468     }
4469     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);
4470   }
4471   ierr = MatSeqAIJSetPreallocation_SeqAIJ(newMat,0,rowlengths);CHKERRQ(ierr);
4472   a    = (Mat_SeqAIJ*)newMat->data;
4473 
4474   ierr = PetscBinaryRead(fd,a->j,nz,PETSC_INT);CHKERRQ(ierr);
4475 
4476   /* read in nonzero values */
4477   ierr = PetscBinaryRead(fd,a->a,nz,PETSC_SCALAR);CHKERRQ(ierr);
4478 
4479   /* set matrix "i" values */
4480   a->i[0] = 0;
4481   for (i=1; i<= M; i++) {
4482     a->i[i]      = a->i[i-1] + rowlengths[i-1];
4483     a->ilen[i-1] = rowlengths[i-1];
4484   }
4485   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
4486 
4487   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4488   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4489   PetscFunctionReturn(0);
4490 }
4491 
4492 #undef __FUNCT__
4493 #define __FUNCT__ "MatEqual_SeqAIJ"
4494 PetscErrorCode MatEqual_SeqAIJ(Mat A,Mat B,PetscBool * flg)
4495 {
4496   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data,*b = (Mat_SeqAIJ*)B->data;
4497   PetscErrorCode ierr;
4498 #if defined(PETSC_USE_COMPLEX)
4499   PetscInt k;
4500 #endif
4501 
4502   PetscFunctionBegin;
4503   /* If the  matrix dimensions are not equal,or no of nonzeros */
4504   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n) ||(a->nz != b->nz)) {
4505     *flg = PETSC_FALSE;
4506     PetscFunctionReturn(0);
4507   }
4508 
4509   /* if the a->i are the same */
4510   ierr = PetscMemcmp(a->i,b->i,(A->rmap->n+1)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4511   if (!*flg) PetscFunctionReturn(0);
4512 
4513   /* if a->j are the same */
4514   ierr = PetscMemcmp(a->j,b->j,(a->nz)*sizeof(PetscInt),flg);CHKERRQ(ierr);
4515   if (!*flg) PetscFunctionReturn(0);
4516 
4517   /* if a->a are the same */
4518 #if defined(PETSC_USE_COMPLEX)
4519   for (k=0; k<a->nz; k++) {
4520     if (PetscRealPart(a->a[k]) != PetscRealPart(b->a[k]) || PetscImaginaryPart(a->a[k]) != PetscImaginaryPart(b->a[k])) {
4521       *flg = PETSC_FALSE;
4522       PetscFunctionReturn(0);
4523     }
4524   }
4525 #else
4526   ierr = PetscMemcmp(a->a,b->a,(a->nz)*sizeof(PetscScalar),flg);CHKERRQ(ierr);
4527 #endif
4528   PetscFunctionReturn(0);
4529 }
4530 
4531 #undef __FUNCT__
4532 #define __FUNCT__ "MatCreateSeqAIJWithArrays"
4533 /*@
4534      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
4535               provided by the user.
4536 
4537       Collective on MPI_Comm
4538 
4539    Input Parameters:
4540 +   comm - must be an MPI communicator of size 1
4541 .   m - number of rows
4542 .   n - number of columns
4543 .   i - row indices
4544 .   j - column indices
4545 -   a - matrix values
4546 
4547    Output Parameter:
4548 .   mat - the matrix
4549 
4550    Level: intermediate
4551 
4552    Notes:
4553        The i, j, and a arrays are not copied by this routine, the user must free these arrays
4554     once the matrix is destroyed and not before
4555 
4556        You cannot set new nonzero locations into this matrix, that will generate an error.
4557 
4558        The i and j indices are 0 based
4559 
4560        The format which is used for the sparse matrix input, is equivalent to a
4561     row-major ordering.. i.e for the following matrix, the input data expected is
4562     as shown:
4563 
4564         1 0 0
4565         2 0 3
4566         4 5 6
4567 
4568         i =  {0,1,3,6}  [size = nrow+1  = 3+1]
4569         j =  {0,0,2,0,1,2}  [size = nz = 6]; values must be sorted for each row
4570         v =  {1,2,3,4,5,6}  [size = nz = 6]
4571 
4572 
4573 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateMPIAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4574 
4575 @*/
4576 PetscErrorCode  MatCreateSeqAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat)
4577 {
4578   PetscErrorCode ierr;
4579   PetscInt       ii;
4580   Mat_SeqAIJ     *aij;
4581 #if defined(PETSC_USE_DEBUG)
4582   PetscInt jj;
4583 #endif
4584 
4585   PetscFunctionBegin;
4586   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
4587   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4588   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4589   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4590   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4591   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,MAT_SKIP_ALLOCATION,0);CHKERRQ(ierr);
4592   aij  = (Mat_SeqAIJ*)(*mat)->data;
4593   ierr = PetscMalloc2(m,PetscInt,&aij->imax,m,PetscInt,&aij->ilen);CHKERRQ(ierr);
4594 
4595   aij->i            = i;
4596   aij->j            = j;
4597   aij->a            = a;
4598   aij->singlemalloc = PETSC_FALSE;
4599   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
4600   aij->free_a       = PETSC_FALSE;
4601   aij->free_ij      = PETSC_FALSE;
4602 
4603   for (ii=0; ii<m; ii++) {
4604     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
4605 #if defined(PETSC_USE_DEBUG)
4606     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]);
4607     for (jj=i[ii]+1; jj<i[ii+1]; jj++) {
4608       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);
4609       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);
4610     }
4611 #endif
4612   }
4613 #if defined(PETSC_USE_DEBUG)
4614   for (ii=0; ii<aij->i[m]; ii++) {
4615     if (j[ii] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column index at location = %d index = %d",ii,j[ii]);
4616     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]);
4617   }
4618 #endif
4619 
4620   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4621   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4622   PetscFunctionReturn(0);
4623 }
4624 #undef __FUNCT__
4625 #define __FUNCT__ "MatCreateSeqAIJFromTriple"
4626 /*@C
4627      MatCreateSeqAIJFromTriple - Creates an sequential AIJ matrix using matrix elements (in COO format)
4628               provided by the user.
4629 
4630       Collective on MPI_Comm
4631 
4632    Input Parameters:
4633 +   comm - must be an MPI communicator of size 1
4634 .   m   - number of rows
4635 .   n   - number of columns
4636 .   i   - row indices
4637 .   j   - column indices
4638 .   a   - matrix values
4639 .   nz  - number of nonzeros
4640 -   idx - 0 or 1 based
4641 
4642    Output Parameter:
4643 .   mat - the matrix
4644 
4645    Level: intermediate
4646 
4647    Notes:
4648        The i and j indices are 0 based
4649 
4650        The format which is used for the sparse matrix input, is equivalent to a
4651     row-major ordering.. i.e for the following matrix, the input data expected is
4652     as shown:
4653 
4654         1 0 0
4655         2 0 3
4656         4 5 6
4657 
4658         i =  {0,1,1,2,2,2}
4659         j =  {0,0,2,0,1,2}
4660         v =  {1,2,3,4,5,6}
4661 
4662 
4663 .seealso: MatCreate(), MatCreateAIJ(), MatCreateSeqAIJ(), MatCreateSeqAIJWithArrays(), MatMPIAIJSetPreallocationCSR()
4664 
4665 @*/
4666 PetscErrorCode  MatCreateSeqAIJFromTriple(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt *i,PetscInt *j,PetscScalar *a,Mat *mat,PetscInt nz,PetscBool idx)
4667 {
4668   PetscErrorCode ierr;
4669   PetscInt       ii, *nnz, one = 1,row,col;
4670 
4671 
4672   PetscFunctionBegin;
4673   ierr = PetscMalloc(m*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
4674   ierr = PetscMemzero(nnz,m*sizeof(PetscInt));CHKERRQ(ierr);
4675   for (ii = 0; ii < nz; ii++) {
4676     nnz[i[ii]] += 1;
4677   }
4678   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
4679   ierr = MatSetSizes(*mat,m,n,m,n);CHKERRQ(ierr);
4680   /* ierr = MatSetBlockSizes(*mat,,);CHKERRQ(ierr); */
4681   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
4682   ierr = MatSeqAIJSetPreallocation_SeqAIJ(*mat,0,nnz);CHKERRQ(ierr);
4683   for (ii = 0; ii < nz; ii++) {
4684     if (idx) {
4685       row = i[ii] - 1;
4686       col = j[ii] - 1;
4687     } else {
4688       row = i[ii];
4689       col = j[ii];
4690     }
4691     ierr = MatSetValues(*mat,one,&row,one,&col,&a[ii],ADD_VALUES);CHKERRQ(ierr);
4692   }
4693   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4694   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4695   ierr = PetscFree(nnz);CHKERRQ(ierr);
4696   PetscFunctionReturn(0);
4697 }
4698 
4699 #undef __FUNCT__
4700 #define __FUNCT__ "MatSetColoring_SeqAIJ"
4701 PetscErrorCode MatSetColoring_SeqAIJ(Mat A,ISColoring coloring)
4702 {
4703   PetscErrorCode ierr;
4704   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4705 
4706   PetscFunctionBegin;
4707   if (coloring->ctype == IS_COLORING_GLOBAL) {
4708     ierr        = ISColoringReference(coloring);CHKERRQ(ierr);
4709     a->coloring = coloring;
4710   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
4711     PetscInt        i,*larray;
4712     ISColoring      ocoloring;
4713     ISColoringValue *colors;
4714 
4715     /* set coloring for diagonal portion */
4716     ierr = PetscMalloc(A->cmap->n*sizeof(PetscInt),&larray);CHKERRQ(ierr);
4717     for (i=0; i<A->cmap->n; i++) larray[i] = i;
4718     ierr = ISGlobalToLocalMappingApply(A->cmap->mapping,IS_GTOLM_MASK,A->cmap->n,larray,NULL,larray);CHKERRQ(ierr);
4719     ierr = PetscMalloc(A->cmap->n*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
4720     for (i=0; i<A->cmap->n; i++) colors[i] = coloring->colors[larray[i]];
4721     ierr        = PetscFree(larray);CHKERRQ(ierr);
4722     ierr        = ISColoringCreate(PETSC_COMM_SELF,coloring->n,A->cmap->n,colors,&ocoloring);CHKERRQ(ierr);
4723     a->coloring = ocoloring;
4724   }
4725   PetscFunctionReturn(0);
4726 }
4727 
4728 #undef __FUNCT__
4729 #define __FUNCT__ "MatSetValuesAdifor_SeqAIJ"
4730 PetscErrorCode MatSetValuesAdifor_SeqAIJ(Mat A,PetscInt nl,void *advalues)
4731 {
4732   Mat_SeqAIJ      *a      = (Mat_SeqAIJ*)A->data;
4733   PetscInt        m       = A->rmap->n,*ii = a->i,*jj = a->j,nz,i,j;
4734   MatScalar       *v      = a->a;
4735   PetscScalar     *values = (PetscScalar*)advalues;
4736   ISColoringValue *color;
4737 
4738   PetscFunctionBegin;
4739   if (!a->coloring) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Coloring not set for matrix");
4740   color = a->coloring->colors;
4741   /* loop over rows */
4742   for (i=0; i<m; i++) {
4743     nz = ii[i+1] - ii[i];
4744     /* loop over columns putting computed value into matrix */
4745     for (j=0; j<nz; j++) *v++ = values[color[*jj++]];
4746     values += nl; /* jump to next row of derivatives */
4747   }
4748   PetscFunctionReturn(0);
4749 }
4750 
4751 #undef __FUNCT__
4752 #define __FUNCT__ "MatSeqAIJInvalidateDiagonal"
4753 PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat A)
4754 {
4755   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
4756   PetscErrorCode ierr;
4757 
4758   PetscFunctionBegin;
4759   a->idiagvalid  = PETSC_FALSE;
4760   a->ibdiagvalid = PETSC_FALSE;
4761 
4762   ierr = MatSeqAIJInvalidateDiagonal_Inode(A);CHKERRQ(ierr);
4763   PetscFunctionReturn(0);
4764 }
4765 
4766 /*
4767     Special version for direct calls from Fortran
4768 */
4769 #include <petsc-private/fortranimpl.h>
4770 #if defined(PETSC_HAVE_FORTRAN_CAPS)
4771 #define matsetvaluesseqaij_ MATSETVALUESSEQAIJ
4772 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
4773 #define matsetvaluesseqaij_ matsetvaluesseqaij
4774 #endif
4775 
4776 /* Change these macros so can be used in void function */
4777 #undef CHKERRQ
4778 #define CHKERRQ(ierr) CHKERRABORT(PetscObjectComm((PetscObject)A),ierr)
4779 #undef SETERRQ2
4780 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
4781 #undef SETERRQ3
4782 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
4783 
4784 #undef __FUNCT__
4785 #define __FUNCT__ "matsetvaluesseqaij_"
4786 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)
4787 {
4788   Mat            A  = *AA;
4789   PetscInt       m  = *mm, n = *nn;
4790   InsertMode     is = *isis;
4791   Mat_SeqAIJ     *a = (Mat_SeqAIJ*)A->data;
4792   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N;
4793   PetscInt       *imax,*ai,*ailen;
4794   PetscErrorCode ierr;
4795   PetscInt       *aj,nonew = a->nonew,lastcol = -1;
4796   MatScalar      *ap,value,*aa;
4797   PetscBool      ignorezeroentries = a->ignorezeroentries;
4798   PetscBool      roworiented       = a->roworiented;
4799 
4800   PetscFunctionBegin;
4801   MatCheckPreallocated(A,1);
4802   imax  = a->imax;
4803   ai    = a->i;
4804   ailen = a->ilen;
4805   aj    = a->j;
4806   aa    = a->a;
4807 
4808   for (k=0; k<m; k++) { /* loop over added rows */
4809     row = im[k];
4810     if (row < 0) continue;
4811 #if defined(PETSC_USE_DEBUG)
4812     if (row >= A->rmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Row too large");
4813 #endif
4814     rp   = aj + ai[row]; ap = aa + ai[row];
4815     rmax = imax[row]; nrow = ailen[row];
4816     low  = 0;
4817     high = nrow;
4818     for (l=0; l<n; l++) { /* loop over added columns */
4819       if (in[l] < 0) continue;
4820 #if defined(PETSC_USE_DEBUG)
4821       if (in[l] >= A->cmap->n) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Column too large");
4822 #endif
4823       col = in[l];
4824       if (roworiented) value = v[l + k*n];
4825       else value = v[k + l*m];
4826 
4827       if (value == 0.0 && ignorezeroentries && (is == ADD_VALUES)) continue;
4828 
4829       if (col <= lastcol) low = 0;
4830       else high = nrow;
4831       lastcol = col;
4832       while (high-low > 5) {
4833         t = (low+high)/2;
4834         if (rp[t] > col) high = t;
4835         else             low  = t;
4836       }
4837       for (i=low; i<high; i++) {
4838         if (rp[i] > col) break;
4839         if (rp[i] == col) {
4840           if (is == ADD_VALUES) ap[i] += value;
4841           else                  ap[i] = value;
4842           goto noinsert;
4843         }
4844       }
4845       if (value == 0.0 && ignorezeroentries) goto noinsert;
4846       if (nonew == 1) goto noinsert;
4847       if (nonew == -1) SETERRABORT(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero in the matrix");
4848       MatSeqXAIJReallocateAIJ(A,A->rmap->n,1,nrow,row,col,rmax,aa,ai,aj,rp,ap,imax,nonew,MatScalar);
4849       N = nrow++ - 1; a->nz++; high++;
4850       /* shift up all the later entries in this row */
4851       for (ii=N; ii>=i; ii--) {
4852         rp[ii+1] = rp[ii];
4853         ap[ii+1] = ap[ii];
4854       }
4855       rp[i] = col;
4856       ap[i] = value;
4857 noinsert:;
4858       low = i + 1;
4859     }
4860     ailen[row] = nrow;
4861   }
4862   A->same_nonzero = PETSC_FALSE;
4863   PetscFunctionReturnVoid();
4864 }
4865 
4866 
4867