xref: /petsc/src/mat/impls/aij/seq/aij.c (revision b3cc6726fbddf13cd805f591b2b0fc9b163819ab)
1 
2 /*
3     Defines the basic matrix operations for the AIJ (compressed row)
4   matrix storage format.
5 */
6 
7 #include "src/mat/impls/aij/seq/aij.h"          /*I "petscmat.h" I*/
8 #include "src/inline/spops.h"
9 #include "src/inline/dot.h"
10 #include "petscbt.h"
11 
12 #undef __FUNCT__
13 #define __FUNCT__ "MatGetRowIJ_SeqAIJ"
14 int MatGetRowIJ_SeqAIJ(Mat A,int oshift,PetscTruth symmetric,int *m,int *ia[],int *ja[],PetscTruth *done)
15 {
16   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
17   int        ierr,i,ishift;
18 
19   PetscFunctionBegin;
20   *m     = A->m;
21   if (!ia) PetscFunctionReturn(0);
22   ishift = 0;
23   if (symmetric && !A->structurally_symmetric) {
24     ierr = MatToSymmetricIJ_SeqAIJ(A->m,a->i,a->j,ishift,oshift,ia,ja);CHKERRQ(ierr);
25   } else if (oshift == 1) {
26     int nz = a->i[A->m];
27     /* malloc space and  add 1 to i and j indices */
28     ierr = PetscMalloc((A->m+1)*sizeof(int),ia);CHKERRQ(ierr);
29     ierr = PetscMalloc((nz+1)*sizeof(int),ja);CHKERRQ(ierr);
30     for (i=0; i<nz; i++) (*ja)[i] = a->j[i] + 1;
31     for (i=0; i<A->m+1; i++) (*ia)[i] = a->i[i] + 1;
32   } else {
33     *ia = a->i; *ja = a->j;
34   }
35   PetscFunctionReturn(0);
36 }
37 
38 #undef __FUNCT__
39 #define __FUNCT__ "MatRestoreRowIJ_SeqAIJ"
40 int MatRestoreRowIJ_SeqAIJ(Mat A,int oshift,PetscTruth symmetric,int *n,int *ia[],int *ja[],PetscTruth *done)
41 {
42   int ierr;
43 
44   PetscFunctionBegin;
45   if (!ia) PetscFunctionReturn(0);
46   if ((symmetric && !A->structurally_symmetric) || oshift == 1) {
47     ierr = PetscFree(*ia);CHKERRQ(ierr);
48     ierr = PetscFree(*ja);CHKERRQ(ierr);
49   }
50   PetscFunctionReturn(0);
51 }
52 
53 #undef __FUNCT__
54 #define __FUNCT__ "MatGetColumnIJ_SeqAIJ"
55 int MatGetColumnIJ_SeqAIJ(Mat A,int oshift,PetscTruth symmetric,int *nn,int *ia[],int *ja[],PetscTruth *done)
56 {
57   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
58   int        ierr,i,*collengths,*cia,*cja,n = A->n,m = A->m;
59   int        nz = a->i[m],row,*jj,mr,col;
60 
61   PetscFunctionBegin;
62   *nn     = A->n;
63   if (!ia) PetscFunctionReturn(0);
64   if (symmetric) {
65     ierr = MatToSymmetricIJ_SeqAIJ(A->m,a->i,a->j,0,oshift,ia,ja);CHKERRQ(ierr);
66   } else {
67     ierr = PetscMalloc((n+1)*sizeof(int),&collengths);CHKERRQ(ierr);
68     ierr = PetscMemzero(collengths,n*sizeof(int));CHKERRQ(ierr);
69     ierr = PetscMalloc((n+1)*sizeof(int),&cia);CHKERRQ(ierr);
70     ierr = PetscMalloc((nz+1)*sizeof(int),&cja);CHKERRQ(ierr);
71     jj = a->j;
72     for (i=0; i<nz; i++) {
73       collengths[jj[i]]++;
74     }
75     cia[0] = oshift;
76     for (i=0; i<n; i++) {
77       cia[i+1] = cia[i] + collengths[i];
78     }
79     ierr = PetscMemzero(collengths,n*sizeof(int));CHKERRQ(ierr);
80     jj   = a->j;
81     for (row=0; row<m; row++) {
82       mr = a->i[row+1] - a->i[row];
83       for (i=0; i<mr; i++) {
84         col = *jj++;
85         cja[cia[col] + collengths[col]++ - oshift] = row + oshift;
86       }
87     }
88     ierr = PetscFree(collengths);CHKERRQ(ierr);
89     *ia = cia; *ja = cja;
90   }
91   PetscFunctionReturn(0);
92 }
93 
94 #undef __FUNCT__
95 #define __FUNCT__ "MatRestoreColumnIJ_SeqAIJ"
96 int MatRestoreColumnIJ_SeqAIJ(Mat A,int oshift,PetscTruth symmetric,int *n,int *ia[],int *ja[],PetscTruth *done)
97 {
98   int ierr;
99 
100   PetscFunctionBegin;
101   if (!ia) PetscFunctionReturn(0);
102 
103   ierr = PetscFree(*ia);CHKERRQ(ierr);
104   ierr = PetscFree(*ja);CHKERRQ(ierr);
105 
106   PetscFunctionReturn(0);
107 }
108 
109 #define CHUNKSIZE   15
110 
111 #undef __FUNCT__
112 #define __FUNCT__ "MatSetValues_SeqAIJ"
113 int MatSetValues_SeqAIJ(Mat A,int m,const int im[],int n,const int in[],const PetscScalar v[],InsertMode is)
114 {
115   Mat_SeqAIJ  *a = (Mat_SeqAIJ*)A->data;
116   int         *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N,sorted = a->sorted;
117   int         *imax = a->imax,*ai = a->i,*ailen = a->ilen;
118   int         *aj = a->j,nonew = a->nonew,ierr;
119   PetscScalar *ap,value,*aa = a->a;
120   PetscTruth  ignorezeroentries = ((a->ignorezeroentries && is == ADD_VALUES) ? PETSC_TRUE:PETSC_FALSE);
121   PetscTruth  roworiented = a->roworiented;
122 
123   PetscFunctionBegin;
124   for (k=0; k<m; k++) { /* loop over added rows */
125     row  = im[k];
126     if (row < 0) continue;
127 #if defined(PETSC_USE_BOPT_g)
128     if (row >= A->m) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %d max %d",row,A->m-1);
129 #endif
130     rp   = aj + ai[row]; ap = aa + ai[row];
131     rmax = imax[row]; nrow = ailen[row];
132     low = 0;
133     for (l=0; l<n; l++) { /* loop over added columns */
134       if (in[l] < 0) continue;
135 #if defined(PETSC_USE_BOPT_g)
136       if (in[l] >= A->n) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %d max %d",in[l],A->n-1);
137 #endif
138       col = in[l];
139       if (roworiented) {
140         value = v[l + k*n];
141       } else {
142         value = v[k + l*m];
143       }
144       if (value == 0.0 && ignorezeroentries) continue;
145 
146       if (!sorted) low = 0; high = nrow;
147       while (high-low > 5) {
148         t = (low+high)/2;
149         if (rp[t] > col) high = t;
150         else             low  = t;
151       }
152       for (i=low; i<high; i++) {
153         if (rp[i] > col) break;
154         if (rp[i] == col) {
155           if (is == ADD_VALUES) ap[i] += value;
156           else                  ap[i] = value;
157           goto noinsert;
158         }
159       }
160       if (nonew == 1) goto noinsert;
161       else if (nonew == -1) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at (%d,%d) in the matrix",row,col);
162       if (nrow >= rmax) {
163         /* there is no extra room in row, therefore enlarge */
164         int         new_nz = ai[A->m] + CHUNKSIZE,*new_i,*new_j;
165         size_t      len;
166         PetscScalar *new_a;
167 
168         if (nonew == -2) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at (%d,%d) in the matrix requiring new malloc()",row,col);
169 
170         /* malloc new storage space */
171         len     = ((size_t) new_nz)*(sizeof(int)+sizeof(PetscScalar))+(A->m+1)*sizeof(int);
172 	ierr    = PetscMalloc(len,&new_a);CHKERRQ(ierr);
173         new_j   = (int*)(new_a + new_nz);
174         new_i   = new_j + new_nz;
175 
176         /* copy over old data into new slots */
177         for (ii=0; ii<row+1; ii++) {new_i[ii] = ai[ii];}
178         for (ii=row+1; ii<A->m+1; ii++) {new_i[ii] = ai[ii]+CHUNKSIZE;}
179         ierr = PetscMemcpy(new_j,aj,(ai[row]+nrow)*sizeof(int));CHKERRQ(ierr);
180         len  = (((size_t) new_nz) - CHUNKSIZE - ai[row] - nrow );
181         ierr = PetscMemcpy(new_j+ai[row]+nrow+CHUNKSIZE,aj+ai[row]+nrow,len*sizeof(int));CHKERRQ(ierr);
182         ierr = PetscMemcpy(new_a,aa,(((size_t) ai[row])+nrow)*sizeof(PetscScalar));CHKERRQ(ierr);
183         ierr = PetscMemcpy(new_a+ai[row]+nrow+CHUNKSIZE,aa+ai[row]+nrow,len*sizeof(PetscScalar));CHKERRQ(ierr);
184         /* free up old matrix storage */
185         ierr = PetscFree(a->a);CHKERRQ(ierr);
186         if (!a->singlemalloc) {
187           ierr = PetscFree(a->i);CHKERRQ(ierr);
188           ierr = PetscFree(a->j);CHKERRQ(ierr);
189         }
190         aa = a->a = new_a; ai = a->i = new_i; aj = a->j = new_j;
191         a->singlemalloc = PETSC_TRUE;
192 
193         rp   = aj + ai[row]; ap = aa + ai[row] ;
194         rmax = imax[row] = imax[row] + CHUNKSIZE;
195         PetscLogObjectMemory(A,CHUNKSIZE*(sizeof(int) + sizeof(PetscScalar)));
196         a->maxnz += CHUNKSIZE;
197         a->reallocs++;
198       }
199       N = nrow++ - 1; a->nz++;
200       /* shift up all the later entries in this row */
201       for (ii=N; ii>=i; ii--) {
202         rp[ii+1] = rp[ii];
203         ap[ii+1] = ap[ii];
204       }
205       rp[i] = col;
206       ap[i] = value;
207       noinsert:;
208       low = i + 1;
209     }
210     ailen[row] = nrow;
211   }
212   PetscFunctionReturn(0);
213 }
214 
215 #undef __FUNCT__
216 #define __FUNCT__ "MatGetValues_SeqAIJ"
217 int MatGetValues_SeqAIJ(Mat A,int m,const int im[],int n,const int in[],PetscScalar v[])
218 {
219   Mat_SeqAIJ   *a = (Mat_SeqAIJ*)A->data;
220   int          *rp,k,low,high,t,row,nrow,i,col,l,*aj = a->j;
221   int          *ai = a->i,*ailen = a->ilen;
222   PetscScalar  *ap,*aa = a->a,zero = 0.0;
223 
224   PetscFunctionBegin;
225   for (k=0; k<m; k++) { /* loop over rows */
226     row  = im[k];
227     if (row < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %d",row);
228     if (row >= A->m) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %d max %d",row,A->m-1);
229     rp   = aj + ai[row]; ap = aa + ai[row];
230     nrow = ailen[row];
231     for (l=0; l<n; l++) { /* loop over columns */
232       if (in[l] < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %d",in[l]);
233       if (in[l] >= A->n) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %d max %d",in[l],A->n-1);
234       col = in[l] ;
235       high = nrow; low = 0; /* assume unsorted */
236       while (high-low > 5) {
237         t = (low+high)/2;
238         if (rp[t] > col) high = t;
239         else             low  = t;
240       }
241       for (i=low; i<high; i++) {
242         if (rp[i] > col) break;
243         if (rp[i] == col) {
244           *v++ = ap[i];
245           goto finished;
246         }
247       }
248       *v++ = zero;
249       finished:;
250     }
251   }
252   PetscFunctionReturn(0);
253 }
254 
255 
256 #undef __FUNCT__
257 #define __FUNCT__ "MatView_SeqAIJ_Binary"
258 int MatView_SeqAIJ_Binary(Mat A,PetscViewer viewer)
259 {
260   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
261   int        i,fd,*col_lens,ierr;
262 
263   PetscFunctionBegin;
264   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
265   ierr = PetscMalloc((4+A->m)*sizeof(int),&col_lens);CHKERRQ(ierr);
266   col_lens[0] = MAT_FILE_COOKIE;
267   col_lens[1] = A->m;
268   col_lens[2] = A->n;
269   col_lens[3] = a->nz;
270 
271   /* store lengths of each row and write (including header) to file */
272   for (i=0; i<A->m; i++) {
273     col_lens[4+i] = a->i[i+1] - a->i[i];
274   }
275   ierr = PetscBinaryWrite(fd,col_lens,4+A->m,PETSC_INT,1);CHKERRQ(ierr);
276   ierr = PetscFree(col_lens);CHKERRQ(ierr);
277 
278   /* store column indices (zero start index) */
279   ierr = PetscBinaryWrite(fd,a->j,a->nz,PETSC_INT,0);CHKERRQ(ierr);
280 
281   /* store nonzero values */
282   ierr = PetscBinaryWrite(fd,a->a,a->nz,PETSC_SCALAR,0);CHKERRQ(ierr);
283   PetscFunctionReturn(0);
284 }
285 
286 extern int MatSeqAIJFactorInfo_Matlab(Mat,PetscViewer);
287 
288 #undef __FUNCT__
289 #define __FUNCT__ "MatView_SeqAIJ_ASCII"
290 int MatView_SeqAIJ_ASCII(Mat A,PetscViewer viewer)
291 {
292   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
293   int               ierr,i,j,m = A->m,shift=0;
294   char              *name;
295   PetscViewerFormat format;
296 
297   PetscFunctionBegin;
298   ierr = PetscObjectGetName((PetscObject)A,&name);CHKERRQ(ierr);
299   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
300   if (format == PETSC_VIEWER_ASCII_INFO_DETAIL || format == PETSC_VIEWER_ASCII_INFO) {
301     if (a->inode.size) {
302       ierr = PetscViewerASCIIPrintf(viewer,"using I-node routines: found %d nodes, limit used is %d\n",a->inode.node_count,a->inode.limit);CHKERRQ(ierr);
303     } else {
304       ierr = PetscViewerASCIIPrintf(viewer,"not using I-node routines\n");CHKERRQ(ierr);
305     }
306   } else if (format == PETSC_VIEWER_ASCII_MATLAB) {
307     int nofinalvalue = 0;
308     if ((a->i[m] == a->i[m-1]) || (a->j[a->nz-1] != A->n-!shift)) {
309       nofinalvalue = 1;
310     }
311     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_NO);CHKERRQ(ierr);
312     ierr = PetscViewerASCIIPrintf(viewer,"%% Size = %d %d \n",m,A->n);CHKERRQ(ierr);
313     ierr = PetscViewerASCIIPrintf(viewer,"%% Nonzeros = %d \n",a->nz);CHKERRQ(ierr);
314     ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%d,3);\n",a->nz+nofinalvalue);CHKERRQ(ierr);
315     ierr = PetscViewerASCIIPrintf(viewer,"zzz = [\n");CHKERRQ(ierr);
316 
317     for (i=0; i<m; i++) {
318       for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
319 #if defined(PETSC_USE_COMPLEX)
320         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);
321 #else
322         ierr = PetscViewerASCIIPrintf(viewer,"%d %d  %18.16e\n",i+1,a->j[j]+!shift,a->a[j]);CHKERRQ(ierr);
323 #endif
324       }
325     }
326     if (nofinalvalue) {
327       ierr = PetscViewerASCIIPrintf(viewer,"%d %d  %18.16e\n",m,A->n,0.0);CHKERRQ(ierr);
328     }
329     ierr = PetscViewerASCIIPrintf(viewer,"];\n %s = spconvert(zzz);\n",name);CHKERRQ(ierr);
330     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_YES);CHKERRQ(ierr);
331   } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
332      PetscFunctionReturn(0);
333   } else if (format == PETSC_VIEWER_ASCII_COMMON) {
334     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_NO);CHKERRQ(ierr);
335     for (i=0; i<m; i++) {
336       ierr = PetscViewerASCIIPrintf(viewer,"row %d:",i);CHKERRQ(ierr);
337       for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
338 #if defined(PETSC_USE_COMPLEX)
339         if (PetscImaginaryPart(a->a[j]) > 0.0 && PetscRealPart(a->a[j]) != 0.0) {
340           ierr = PetscViewerASCIIPrintf(viewer," (%d, %g + %g i)",a->j[j]+shift,PetscRealPart(a->a[j]),PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
341         } else if (PetscImaginaryPart(a->a[j]) < 0.0 && PetscRealPart(a->a[j]) != 0.0) {
342           ierr = PetscViewerASCIIPrintf(viewer," (%d, %g - %g i)",a->j[j]+shift,PetscRealPart(a->a[j]),-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
343         } else if (PetscRealPart(a->a[j]) != 0.0) {
344           ierr = PetscViewerASCIIPrintf(viewer," (%d, %g) ",a->j[j]+shift,PetscRealPart(a->a[j]));CHKERRQ(ierr);
345         }
346 #else
347         if (a->a[j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," (%d, %g) ",a->j[j]+shift,a->a[j]);CHKERRQ(ierr);}
348 #endif
349       }
350       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
351     }
352     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_YES);CHKERRQ(ierr);
353   } else if (format == PETSC_VIEWER_ASCII_SYMMODU) {
354     int nzd=0,fshift=1,*sptr;
355     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_NO);CHKERRQ(ierr);
356     ierr = PetscMalloc((m+1)*sizeof(int),&sptr);CHKERRQ(ierr);
357     for (i=0; i<m; i++) {
358       sptr[i] = nzd+1;
359       for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
360         if (a->j[j] >= i) {
361 #if defined(PETSC_USE_COMPLEX)
362           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) nzd++;
363 #else
364           if (a->a[j] != 0.0) nzd++;
365 #endif
366         }
367       }
368     }
369     sptr[m] = nzd+1;
370     ierr = PetscViewerASCIIPrintf(viewer," %d %d\n\n",m,nzd);CHKERRQ(ierr);
371     for (i=0; i<m+1; i+=6) {
372       if (i+4<m) {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);}
373       else if (i+3<m) {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);}
374       else if (i+2<m) {ierr = PetscViewerASCIIPrintf(viewer," %d %d %d %d\n",sptr[i],sptr[i+1],sptr[i+2],sptr[i+3]);CHKERRQ(ierr);}
375       else if (i+1<m) {ierr = PetscViewerASCIIPrintf(viewer," %d %d %d\n",sptr[i],sptr[i+1],sptr[i+2]);CHKERRQ(ierr);}
376       else if (i<m)   {ierr = PetscViewerASCIIPrintf(viewer," %d %d\n",sptr[i],sptr[i+1]);CHKERRQ(ierr);}
377       else            {ierr = PetscViewerASCIIPrintf(viewer," %d\n",sptr[i]);CHKERRQ(ierr);}
378     }
379     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
380     ierr = PetscFree(sptr);CHKERRQ(ierr);
381     for (i=0; i<m; i++) {
382       for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
383         if (a->j[j] >= i) {ierr = PetscViewerASCIIPrintf(viewer," %d ",a->j[j]+fshift);CHKERRQ(ierr);}
384       }
385       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
386     }
387     ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
388     for (i=0; i<m; i++) {
389       for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
390         if (a->j[j] >= i) {
391 #if defined(PETSC_USE_COMPLEX)
392           if (PetscImaginaryPart(a->a[j]) != 0.0 || PetscRealPart(a->a[j]) != 0.0) {
393             ierr = PetscViewerASCIIPrintf(viewer," %18.16e %18.16e ",PetscRealPart(a->a[j]),PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
394           }
395 #else
396           if (a->a[j] != 0.0) {ierr = PetscViewerASCIIPrintf(viewer," %18.16e ",a->a[j]);CHKERRQ(ierr);}
397 #endif
398         }
399       }
400       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
401     }
402     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_YES);CHKERRQ(ierr);
403   } else if (format == PETSC_VIEWER_ASCII_DENSE) {
404     int         cnt = 0,jcnt;
405     PetscScalar value;
406 
407     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_NO);CHKERRQ(ierr);
408     for (i=0; i<m; i++) {
409       jcnt = 0;
410       for (j=0; j<A->n; j++) {
411         if (jcnt < a->i[i+1]-a->i[i] && j == a->j[cnt]) {
412           value = a->a[cnt++];
413           jcnt++;
414         } else {
415           value = 0.0;
416         }
417 #if defined(PETSC_USE_COMPLEX)
418         ierr = PetscViewerASCIIPrintf(viewer," %7.5e+%7.5e i ",PetscRealPart(value),PetscImaginaryPart(value));CHKERRQ(ierr);
419 #else
420         ierr = PetscViewerASCIIPrintf(viewer," %7.5e ",value);CHKERRQ(ierr);
421 #endif
422       }
423       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
424     }
425     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_YES);CHKERRQ(ierr);
426   } else {
427     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_NO);CHKERRQ(ierr);
428     for (i=0; i<m; i++) {
429       ierr = PetscViewerASCIIPrintf(viewer,"row %d:",i);CHKERRQ(ierr);
430       for (j=a->i[i]+shift; j<a->i[i+1]+shift; j++) {
431 #if defined(PETSC_USE_COMPLEX)
432         if (PetscImaginaryPart(a->a[j]) > 0.0) {
433           ierr = PetscViewerASCIIPrintf(viewer," (%d, %g + %g i)",a->j[j]+shift,PetscRealPart(a->a[j]),PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
434         } else if (PetscImaginaryPart(a->a[j]) < 0.0) {
435           ierr = PetscViewerASCIIPrintf(viewer," (%d, %g - %g i)",a->j[j]+shift,PetscRealPart(a->a[j]),-PetscImaginaryPart(a->a[j]));CHKERRQ(ierr);
436         } else {
437           ierr = PetscViewerASCIIPrintf(viewer," (%d, %g) ",a->j[j]+shift,PetscRealPart(a->a[j]));CHKERRQ(ierr);
438         }
439 #else
440         ierr = PetscViewerASCIIPrintf(viewer," (%d, %g) ",a->j[j]+shift,a->a[j]);CHKERRQ(ierr);
441 #endif
442       }
443       ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
444     }
445     ierr = PetscViewerASCIIUseTabs(viewer,PETSC_YES);CHKERRQ(ierr);
446   }
447   ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
448   PetscFunctionReturn(0);
449 }
450 
451 #undef __FUNCT__
452 #define __FUNCT__ "MatView_SeqAIJ_Draw_Zoom"
453 int MatView_SeqAIJ_Draw_Zoom(PetscDraw draw,void *Aa)
454 {
455   Mat               A = (Mat) Aa;
456   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
457   int               ierr,i,j,m = A->m,color;
458   PetscReal         xl,yl,xr,yr,x_l,x_r,y_l,y_r,maxv = 0.0;
459   PetscViewer       viewer;
460   PetscViewerFormat format;
461 
462   PetscFunctionBegin;
463   ierr = PetscObjectQuery((PetscObject)A,"Zoomviewer",(PetscObject*)&viewer);CHKERRQ(ierr);
464   ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
465 
466   ierr = PetscDrawGetCoordinates(draw,&xl,&yl,&xr,&yr);CHKERRQ(ierr);
467   /* loop over matrix elements drawing boxes */
468 
469   if (format != PETSC_VIEWER_DRAW_CONTOUR) {
470     /* Blue for negative, Cyan for zero and  Red for positive */
471     color = PETSC_DRAW_BLUE;
472     for (i=0; i<m; i++) {
473       y_l = m - i - 1.0; y_r = y_l + 1.0;
474       for (j=a->i[i]; j<a->i[i+1]; j++) {
475         x_l = a->j[j] ; x_r = x_l + 1.0;
476 #if defined(PETSC_USE_COMPLEX)
477         if (PetscRealPart(a->a[j]) >=  0.) continue;
478 #else
479         if (a->a[j] >=  0.) continue;
480 #endif
481         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
482       }
483     }
484     color = PETSC_DRAW_CYAN;
485     for (i=0; i<m; i++) {
486       y_l = m - i - 1.0; y_r = y_l + 1.0;
487       for (j=a->i[i]; j<a->i[i+1]; j++) {
488         x_l = a->j[j]; x_r = x_l + 1.0;
489         if (a->a[j] !=  0.) continue;
490         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
491       }
492     }
493     color = PETSC_DRAW_RED;
494     for (i=0; i<m; i++) {
495       y_l = m - i - 1.0; y_r = y_l + 1.0;
496       for (j=a->i[i]; j<a->i[i+1]; j++) {
497         x_l = a->j[j]; x_r = x_l + 1.0;
498 #if defined(PETSC_USE_COMPLEX)
499         if (PetscRealPart(a->a[j]) <=  0.) continue;
500 #else
501         if (a->a[j] <=  0.) continue;
502 #endif
503         ierr = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
504       }
505     }
506   } else {
507     /* use contour shading to indicate magnitude of values */
508     /* first determine max of all nonzero values */
509     int    nz = a->nz,count;
510     PetscDraw   popup;
511     PetscReal scale;
512 
513     for (i=0; i<nz; i++) {
514       if (PetscAbsScalar(a->a[i]) > maxv) maxv = PetscAbsScalar(a->a[i]);
515     }
516     scale = (245.0 - PETSC_DRAW_BASIC_COLORS)/maxv;
517     ierr  = PetscDrawGetPopup(draw,&popup);CHKERRQ(ierr);
518     if (popup) {ierr  = PetscDrawScalePopup(popup,0.0,maxv);CHKERRQ(ierr);}
519     count = 0;
520     for (i=0; i<m; i++) {
521       y_l = m - i - 1.0; y_r = y_l + 1.0;
522       for (j=a->i[i]; j<a->i[i+1]; j++) {
523         x_l = a->j[j]; x_r = x_l + 1.0;
524         color = PETSC_DRAW_BASIC_COLORS + (int)(scale*PetscAbsScalar(a->a[count]));
525         ierr  = PetscDrawRectangle(draw,x_l,y_l,x_r,y_r,color,color,color,color);CHKERRQ(ierr);
526         count++;
527       }
528     }
529   }
530   PetscFunctionReturn(0);
531 }
532 
533 #undef __FUNCT__
534 #define __FUNCT__ "MatView_SeqAIJ_Draw"
535 int MatView_SeqAIJ_Draw(Mat A,PetscViewer viewer)
536 {
537   int        ierr;
538   PetscDraw  draw;
539   PetscReal  xr,yr,xl,yl,h,w;
540   PetscTruth isnull;
541 
542   PetscFunctionBegin;
543   ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
544   ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
545   if (isnull) PetscFunctionReturn(0);
546 
547   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",(PetscObject)viewer);CHKERRQ(ierr);
548   xr  = A->n; yr = A->m; h = yr/10.0; w = xr/10.0;
549   xr += w;    yr += h;  xl = -w;     yl = -h;
550   ierr = PetscDrawSetCoordinates(draw,xl,yl,xr,yr);CHKERRQ(ierr);
551   ierr = PetscDrawZoom(draw,MatView_SeqAIJ_Draw_Zoom,A);CHKERRQ(ierr);
552   ierr = PetscObjectCompose((PetscObject)A,"Zoomviewer",PETSC_NULL);CHKERRQ(ierr);
553   PetscFunctionReturn(0);
554 }
555 
556 #undef __FUNCT__
557 #define __FUNCT__ "MatView_SeqAIJ"
558 int MatView_SeqAIJ(Mat A,PetscViewer viewer)
559 {
560   Mat_SeqAIJ  *a = (Mat_SeqAIJ*)A->data;
561   int         ierr;
562   PetscTruth  issocket,iascii,isbinary,isdraw;
563 
564   PetscFunctionBegin;
565   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_SOCKET,&issocket);CHKERRQ(ierr);
566   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);CHKERRQ(ierr);
567   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_BINARY,&isbinary);CHKERRQ(ierr);
568   ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_DRAW,&isdraw);CHKERRQ(ierr);
569   if (issocket) {
570     ierr = PetscViewerSocketPutSparse_Private(viewer,A->m,A->n,a->nz,a->a,a->i,a->j);CHKERRQ(ierr);
571   } else if (iascii) {
572     ierr = MatView_SeqAIJ_ASCII(A,viewer);CHKERRQ(ierr);
573   } else if (isbinary) {
574     ierr = MatView_SeqAIJ_Binary(A,viewer);CHKERRQ(ierr);
575   } else if (isdraw) {
576     ierr = MatView_SeqAIJ_Draw(A,viewer);CHKERRQ(ierr);
577   } else {
578     SETERRQ1(1,"Viewer type %s not supported by SeqAIJ matrices",((PetscObject)viewer)->type_name);
579   }
580   PetscFunctionReturn(0);
581 }
582 
583 #undef __FUNCT__
584 #define __FUNCT__ "MatAssemblyEnd_SeqAIJ"
585 int MatAssemblyEnd_SeqAIJ(Mat A,MatAssemblyType mode)
586 {
587   Mat_SeqAIJ   *a = (Mat_SeqAIJ*)A->data;
588   int          fshift = 0,i,j,*ai = a->i,*aj = a->j,*imax = a->imax,ierr;
589   int          m = A->m,*ip,N,*ailen = a->ilen,rmax = 0;
590   PetscScalar  *aa = a->a,*ap;
591 
592   PetscFunctionBegin;
593   if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(0);
594 
595   if (m) rmax = ailen[0]; /* determine row with most nonzeros */
596   for (i=1; i<m; i++) {
597     /* move each row back by the amount of empty slots (fshift) before it*/
598     fshift += imax[i-1] - ailen[i-1];
599     rmax   = PetscMax(rmax,ailen[i]);
600     if (fshift) {
601       ip = aj + ai[i] ;
602       ap = aa + ai[i] ;
603       N  = ailen[i];
604       for (j=0; j<N; j++) {
605         ip[j-fshift] = ip[j];
606         ap[j-fshift] = ap[j];
607       }
608     }
609     ai[i] = ai[i-1] + ailen[i-1];
610   }
611   if (m) {
612     fshift += imax[m-1] - ailen[m-1];
613     ai[m]  = ai[m-1] + ailen[m-1];
614   }
615   /* reset ilen and imax for each row */
616   for (i=0; i<m; i++) {
617     ailen[i] = imax[i] = ai[i+1] - ai[i];
618   }
619   a->nz = ai[m];
620 
621   /* diagonals may have moved, so kill the diagonal pointers */
622   if (fshift && a->diag) {
623     ierr = PetscFree(a->diag);CHKERRQ(ierr);
624     PetscLogObjectMemory(A,-(m+1)*sizeof(int));
625     a->diag = 0;
626   }
627   PetscLogInfo(A,"MatAssemblyEnd_SeqAIJ:Matrix size: %d X %d; storage space: %d unneeded,%d used\n",m,A->n,fshift,a->nz);
628   PetscLogInfo(A,"MatAssemblyEnd_SeqAIJ:Number of mallocs during MatSetValues() is %d\n",a->reallocs);
629   PetscLogInfo(A,"MatAssemblyEnd_SeqAIJ:Most nonzeros in any row is %d\n",rmax);
630   a->reallocs          = 0;
631   A->info.nz_unneeded  = (double)fshift;
632   a->rmax              = rmax;
633 
634   /* check out for identical nodes. If found, use inode functions */
635   ierr = Mat_AIJ_CheckInode(A,(PetscTruth)(!fshift));CHKERRQ(ierr);
636 
637   PetscFunctionReturn(0);
638 }
639 
640 #undef __FUNCT__
641 #define __FUNCT__ "MatZeroEntries_SeqAIJ"
642 int MatZeroEntries_SeqAIJ(Mat A)
643 {
644   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
645   int        ierr;
646 
647   PetscFunctionBegin;
648   ierr = PetscMemzero(a->a,(a->i[A->m])*sizeof(PetscScalar));CHKERRQ(ierr);
649   PetscFunctionReturn(0);
650 }
651 
652 #undef __FUNCT__
653 #define __FUNCT__ "MatDestroy_SeqAIJ"
654 int MatDestroy_SeqAIJ(Mat A)
655 {
656   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
657   int        ierr;
658 
659   PetscFunctionBegin;
660 #if defined(PETSC_USE_LOG)
661   PetscLogObjectState((PetscObject)A,"Rows=%d, Cols=%d, NZ=%d",A->m,A->n,a->nz);
662 #endif
663   if (a->freedata) {
664     ierr = PetscFree(a->a);CHKERRQ(ierr);
665     if (!a->singlemalloc) {
666       ierr = PetscFree(a->i);CHKERRQ(ierr);
667       ierr = PetscFree(a->j);CHKERRQ(ierr);
668     }
669   }
670   if (a->row) {
671     ierr = ISDestroy(a->row);CHKERRQ(ierr);
672   }
673   if (a->col) {
674     ierr = ISDestroy(a->col);CHKERRQ(ierr);
675   }
676   if (a->diag) {ierr = PetscFree(a->diag);CHKERRQ(ierr);}
677   if (a->ilen) {ierr = PetscFree(a->ilen);CHKERRQ(ierr);}
678   if (a->imax) {ierr = PetscFree(a->imax);CHKERRQ(ierr);}
679   if (a->idiag) {ierr = PetscFree(a->idiag);CHKERRQ(ierr);}
680   if (a->solve_work) {ierr = PetscFree(a->solve_work);CHKERRQ(ierr);}
681   if (a->inode.size) {ierr = PetscFree(a->inode.size);CHKERRQ(ierr);}
682   if (a->icol) {ierr = ISDestroy(a->icol);CHKERRQ(ierr);}
683   if (a->saved_values) {ierr = PetscFree(a->saved_values);CHKERRQ(ierr);}
684   if (a->coloring) {ierr = ISColoringDestroy(a->coloring);CHKERRQ(ierr);}
685   if (a->xtoy) {ierr = PetscFree(a->xtoy);CHKERRQ(ierr);}
686 
687   ierr = PetscFree(a);CHKERRQ(ierr);
688   PetscFunctionReturn(0);
689 }
690 
691 #undef __FUNCT__
692 #define __FUNCT__ "MatCompress_SeqAIJ"
693 int MatCompress_SeqAIJ(Mat A)
694 {
695   PetscFunctionBegin;
696   PetscFunctionReturn(0);
697 }
698 
699 #undef __FUNCT__
700 #define __FUNCT__ "MatSetOption_SeqAIJ"
701 int MatSetOption_SeqAIJ(Mat A,MatOption op)
702 {
703   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
704 
705   PetscFunctionBegin;
706   switch (op) {
707     case MAT_ROW_ORIENTED:
708       a->roworiented       = PETSC_TRUE;
709       break;
710     case MAT_KEEP_ZEROED_ROWS:
711       a->keepzeroedrows    = PETSC_TRUE;
712       break;
713     case MAT_COLUMN_ORIENTED:
714       a->roworiented       = PETSC_FALSE;
715       break;
716     case MAT_COLUMNS_SORTED:
717       a->sorted            = PETSC_TRUE;
718       break;
719     case MAT_COLUMNS_UNSORTED:
720       a->sorted            = PETSC_FALSE;
721       break;
722     case MAT_NO_NEW_NONZERO_LOCATIONS:
723       a->nonew             = 1;
724       break;
725     case MAT_NEW_NONZERO_LOCATION_ERR:
726       a->nonew             = -1;
727       break;
728     case MAT_NEW_NONZERO_ALLOCATION_ERR:
729       a->nonew             = -2;
730       break;
731     case MAT_YES_NEW_NONZERO_LOCATIONS:
732       a->nonew             = 0;
733       break;
734     case MAT_IGNORE_ZERO_ENTRIES:
735       a->ignorezeroentries = PETSC_TRUE;
736       break;
737     case MAT_USE_INODES:
738       a->inode.use         = PETSC_TRUE;
739       break;
740     case MAT_DO_NOT_USE_INODES:
741       a->inode.use         = PETSC_FALSE;
742       break;
743     case MAT_ROWS_SORTED:
744     case MAT_ROWS_UNSORTED:
745     case MAT_YES_NEW_DIAGONALS:
746     case MAT_IGNORE_OFF_PROC_ENTRIES:
747     case MAT_USE_HASH_TABLE:
748       PetscLogInfo(A,"MatSetOption_SeqAIJ:Option ignored\n");
749       break;
750     case MAT_NO_NEW_DIAGONALS:
751       SETERRQ(PETSC_ERR_SUP,"MAT_NO_NEW_DIAGONALS");
752     case MAT_INODE_LIMIT_1:
753       a->inode.limit  = 1;
754       break;
755     case MAT_INODE_LIMIT_2:
756       a->inode.limit  = 2;
757       break;
758     case MAT_INODE_LIMIT_3:
759       a->inode.limit  = 3;
760       break;
761     case MAT_INODE_LIMIT_4:
762       a->inode.limit  = 4;
763       break;
764     case MAT_INODE_LIMIT_5:
765       a->inode.limit  = 5;
766       break;
767     case MAT_SYMMETRIC:
768     case MAT_STRUCTURALLY_SYMMETRIC:
769     case MAT_NOT_SYMMETRIC:
770     case MAT_NOT_STRUCTURALLY_SYMMETRIC:
771     case MAT_HERMITIAN:
772     case MAT_NOT_HERMITIAN:
773     case MAT_SYMMETRY_ETERNAL:
774     case MAT_NOT_SYMMETRY_ETERNAL:
775       break;
776     default:
777       SETERRQ(PETSC_ERR_SUP,"unknown option");
778   }
779   PetscFunctionReturn(0);
780 }
781 
782 #undef __FUNCT__
783 #define __FUNCT__ "MatGetDiagonal_SeqAIJ"
784 int MatGetDiagonal_SeqAIJ(Mat A,Vec v)
785 {
786   Mat_SeqAIJ   *a = (Mat_SeqAIJ*)A->data;
787   int          i,j,n,ierr;
788   PetscScalar  *x,zero = 0.0;
789 
790   PetscFunctionBegin;
791   ierr = VecSet(&zero,v);CHKERRQ(ierr);
792   ierr = VecGetArray(v,&x);CHKERRQ(ierr);
793   ierr = VecGetLocalSize(v,&n);CHKERRQ(ierr);
794   if (n != A->m) SETERRQ(PETSC_ERR_ARG_SIZ,"Nonconforming matrix and vector");
795   for (i=0; i<A->m; i++) {
796     for (j=a->i[i]; j<a->i[i+1]; j++) {
797       if (a->j[j] == i) {
798         x[i] = a->a[j];
799         break;
800       }
801     }
802   }
803   ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
804   PetscFunctionReturn(0);
805 }
806 
807 
808 #undef __FUNCT__
809 #define __FUNCT__ "MatMultTransposeAdd_SeqAIJ"
810 int MatMultTransposeAdd_SeqAIJ(Mat A,Vec xx,Vec zz,Vec yy)
811 {
812   Mat_SeqAIJ   *a = (Mat_SeqAIJ*)A->data;
813   PetscScalar  *x,*y;
814   int          ierr,m = A->m;
815 #if !defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
816   PetscScalar  *v,alpha;
817   int          n,i,*idx;
818 #endif
819 
820   PetscFunctionBegin;
821   if (zz != yy) {ierr = VecCopy(zz,yy);CHKERRQ(ierr);}
822   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
823   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
824 
825 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTTRANSPOSEAIJ)
826   fortranmulttransposeaddaij_(&m,x,a->i,a->j,a->a,y);
827 #else
828   for (i=0; i<m; i++) {
829     idx   = a->j + a->i[i] ;
830     v     = a->a + a->i[i] ;
831     n     = a->i[i+1] - a->i[i];
832     alpha = x[i];
833     while (n-->0) {y[*idx++] += alpha * *v++;}
834   }
835 #endif
836   PetscLogFlops(2*a->nz);
837   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
838   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
839   PetscFunctionReturn(0);
840 }
841 
842 #undef __FUNCT__
843 #define __FUNCT__ "MatMultTranspose_SeqAIJ"
844 int MatMultTranspose_SeqAIJ(Mat A,Vec xx,Vec yy)
845 {
846   PetscScalar  zero = 0.0;
847   int          ierr;
848 
849   PetscFunctionBegin;
850   ierr = VecSet(&zero,yy);CHKERRQ(ierr);
851   ierr = MatMultTransposeAdd_SeqAIJ(A,xx,yy,yy);CHKERRQ(ierr);
852   PetscFunctionReturn(0);
853 }
854 
855 
856 #undef __FUNCT__
857 #define __FUNCT__ "MatMult_SeqAIJ"
858 int MatMult_SeqAIJ(Mat A,Vec xx,Vec yy)
859 {
860   Mat_SeqAIJ   *a = (Mat_SeqAIJ*)A->data;
861   PetscScalar  *x,*y,*v;
862   int          ierr,m = A->m,*idx,*ii;
863 #if !defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJ)
864   int          n,i,jrow,j;
865   PetscScalar  sum;
866 #endif
867 
868 #if defined(PETSC_HAVE_PRAGMA_DISJOINT)
869 #pragma disjoint(*x,*y,*v)
870 #endif
871 
872   PetscFunctionBegin;
873   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
874   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
875   idx  = a->j;
876   v    = a->a;
877   ii   = a->i;
878 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTAIJ)
879   fortranmultaij_(&m,x,ii,idx,v,y);
880 #else
881   for (i=0; i<m; i++) {
882     jrow = ii[i];
883     n    = ii[i+1] - jrow;
884     sum  = 0.0;
885     for (j=0; j<n; j++) {
886       sum += v[jrow]*x[idx[jrow]]; jrow++;
887      }
888     y[i] = sum;
889   }
890 #endif
891   PetscLogFlops(2*a->nz - m);
892   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
893   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
894   PetscFunctionReturn(0);
895 }
896 
897 #undef __FUNCT__
898 #define __FUNCT__ "MatMultAdd_SeqAIJ"
899 int MatMultAdd_SeqAIJ(Mat A,Vec xx,Vec yy,Vec zz)
900 {
901   Mat_SeqAIJ   *a = (Mat_SeqAIJ*)A->data;
902   PetscScalar  *x,*y,*z,*v;
903   int          ierr,m = A->m,*idx,*ii;
904 #if !defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJ)
905   int          n,i,jrow,j;
906 PetscScalar    sum;
907 #endif
908 
909   PetscFunctionBegin;
910   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
911   ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
912   if (zz != yy) {
913     ierr = VecGetArray(zz,&z);CHKERRQ(ierr);
914   } else {
915     z = y;
916   }
917 
918   idx  = a->j;
919   v    = a->a;
920   ii   = a->i;
921 #if defined(PETSC_USE_FORTRAN_KERNEL_MULTADDAIJ)
922   fortranmultaddaij_(&m,x,ii,idx,v,y,z);
923 #else
924   for (i=0; i<m; i++) {
925     jrow = ii[i];
926     n    = ii[i+1] - jrow;
927     sum  = y[i];
928     for (j=0; j<n; j++) {
929       sum += v[jrow]*x[idx[jrow]]; jrow++;
930      }
931     z[i] = sum;
932   }
933 #endif
934   PetscLogFlops(2*a->nz);
935   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
936   ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
937   if (zz != yy) {
938     ierr = VecRestoreArray(zz,&z);CHKERRQ(ierr);
939   }
940   PetscFunctionReturn(0);
941 }
942 
943 /*
944      Adds diagonal pointers to sparse matrix structure.
945 */
946 #undef __FUNCT__
947 #define __FUNCT__ "MatMarkDiagonal_SeqAIJ"
948 int MatMarkDiagonal_SeqAIJ(Mat A)
949 {
950   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
951   int        i,j,*diag,m = A->m,ierr;
952 
953   PetscFunctionBegin;
954   if (a->diag) PetscFunctionReturn(0);
955 
956   ierr = PetscMalloc((m+1)*sizeof(int),&diag);CHKERRQ(ierr);
957   PetscLogObjectMemory(A,(m+1)*sizeof(int));
958   for (i=0; i<A->m; i++) {
959     diag[i] = a->i[i+1];
960     for (j=a->i[i]; j<a->i[i+1]; j++) {
961       if (a->j[j] == i) {
962         diag[i] = j;
963         break;
964       }
965     }
966   }
967   a->diag = diag;
968   PetscFunctionReturn(0);
969 }
970 
971 /*
972      Checks for missing diagonals
973 */
974 #undef __FUNCT__
975 #define __FUNCT__ "MatMissingDiagonal_SeqAIJ"
976 int MatMissingDiagonal_SeqAIJ(Mat A)
977 {
978   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
979   int        *diag,*jj = a->j,i,ierr;
980 
981   PetscFunctionBegin;
982   ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
983   diag = a->diag;
984   for (i=0; i<A->m; i++) {
985     if (jj[diag[i]] != i) {
986       SETERRQ1(1,"Matrix is missing diagonal number %d",i);
987     }
988   }
989   PetscFunctionReturn(0);
990 }
991 
992 #undef __FUNCT__
993 #define __FUNCT__ "MatRelax_SeqAIJ"
994 int MatRelax_SeqAIJ(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,int its,int lits,Vec xx)
995 {
996   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data;
997   PetscScalar        *x,d,*xs,sum,*t,scale,*idiag=0,*mdiag;
998   const PetscScalar  *v = a->a, *b, *bs,*xb, *ts;
999   int                ierr,n = A->n,m = A->m,i;
1000   const int          *idx,*diag;
1001 
1002   PetscFunctionBegin;
1003   its = its*lits;
1004   if (its <= 0) SETERRQ2(PETSC_ERR_ARG_WRONG,"Relaxation requires global its %d and local its %d both positive",its,lits);
1005 
1006   if (!a->diag) {ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);}
1007   diag = a->diag;
1008   if (!a->idiag) {
1009     ierr     = PetscMalloc(3*m*sizeof(PetscScalar),&a->idiag);CHKERRQ(ierr);
1010     a->ssor  = a->idiag + m;
1011     mdiag    = a->ssor + m;
1012 
1013     v        = a->a;
1014 
1015     /* this is wrong when fshift omega changes each iteration */
1016     if (omega == 1.0 && fshift == 0.0) {
1017       for (i=0; i<m; i++) {
1018         mdiag[i]    = v[diag[i]];
1019         a->idiag[i] = 1.0/v[diag[i]];
1020       }
1021       PetscLogFlops(m);
1022     } else {
1023       for (i=0; i<m; i++) {
1024         mdiag[i]    = v[diag[i]];
1025         a->idiag[i] = omega/(fshift + v[diag[i]]);
1026       }
1027       PetscLogFlops(2*m);
1028     }
1029   }
1030   t     = a->ssor;
1031   idiag = a->idiag;
1032   mdiag = a->idiag + 2*m;
1033 
1034   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1035   if (xx != bb) {
1036     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1037   } else {
1038     b = x;
1039   }
1040 
1041   /* We count flops by assuming the upper triangular and lower triangular parts have the same number of nonzeros */
1042   xs   = x;
1043   if (flag == SOR_APPLY_UPPER) {
1044    /* apply (U + D/omega) to the vector */
1045     bs = b;
1046     for (i=0; i<m; i++) {
1047         d    = fshift + a->a[diag[i]];
1048         n    = a->i[i+1] - diag[i] - 1;
1049         idx  = a->j + diag[i] + 1;
1050         v    = a->a + diag[i] + 1;
1051         sum  = b[i]*d/omega;
1052         SPARSEDENSEDOT(sum,bs,v,idx,n);
1053         x[i] = sum;
1054     }
1055     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1056     if (bb != xx) {ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);}
1057     PetscLogFlops(a->nz);
1058     PetscFunctionReturn(0);
1059   }
1060 
1061 
1062     /* Let  A = L + U + D; where L is lower trianglar,
1063     U is upper triangular, E is diagonal; This routine applies
1064 
1065             (L + E)^{-1} A (U + E)^{-1}
1066 
1067     to a vector efficiently using Eisenstat's trick. This is for
1068     the case of SSOR preconditioner, so E is D/omega where omega
1069     is the relaxation factor.
1070     */
1071 
1072   if (flag == SOR_APPLY_LOWER) {
1073     SETERRQ(PETSC_ERR_SUP,"SOR_APPLY_LOWER is not implemented");
1074   } else if (flag & SOR_EISENSTAT) {
1075     /* Let  A = L + U + D; where L is lower trianglar,
1076     U is upper triangular, E is diagonal; This routine applies
1077 
1078             (L + E)^{-1} A (U + E)^{-1}
1079 
1080     to a vector efficiently using Eisenstat's trick. This is for
1081     the case of SSOR preconditioner, so E is D/omega where omega
1082     is the relaxation factor.
1083     */
1084     scale = (2.0/omega) - 1.0;
1085 
1086     /*  x = (E + U)^{-1} b */
1087     for (i=m-1; i>=0; i--) {
1088       n    = a->i[i+1] - diag[i] - 1;
1089       idx  = a->j + diag[i] + 1;
1090       v    = a->a + diag[i] + 1;
1091       sum  = b[i];
1092       SPARSEDENSEMDOT(sum,xs,v,idx,n);
1093       x[i] = sum*idiag[i];
1094     }
1095 
1096     /*  t = b - (2*E - D)x */
1097     v = a->a;
1098     for (i=0; i<m; i++) { t[i] = b[i] - scale*(v[*diag++])*x[i]; }
1099 
1100     /*  t = (E + L)^{-1}t */
1101     ts = t;
1102     diag = a->diag;
1103     for (i=0; i<m; i++) {
1104       n    = diag[i] - a->i[i];
1105       idx  = a->j + a->i[i];
1106       v    = a->a + a->i[i];
1107       sum  = t[i];
1108       SPARSEDENSEMDOT(sum,ts,v,idx,n);
1109       t[i] = sum*idiag[i];
1110       /*  x = x + t */
1111       x[i] += t[i];
1112     }
1113 
1114     PetscLogFlops(6*m-1 + 2*a->nz);
1115     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1116     if (bb != xx) {ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);}
1117     PetscFunctionReturn(0);
1118   }
1119   if (flag & SOR_ZERO_INITIAL_GUESS) {
1120     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP){
1121 #if defined(PETSC_USE_FORTRAN_KERNEL_RELAXAIJ)
1122       fortranrelaxaijforwardzero_(&m,&omega,x,a->i,a->j,(int *)diag,idiag,a->a,(void*)b);
1123 #else
1124       for (i=0; i<m; i++) {
1125         n    = diag[i] - a->i[i];
1126         idx  = a->j + a->i[i];
1127         v    = a->a + a->i[i];
1128         sum  = b[i];
1129         SPARSEDENSEMDOT(sum,xs,v,idx,n);
1130         x[i] = sum*idiag[i];
1131       }
1132 #endif
1133       xb = x;
1134       PetscLogFlops(a->nz);
1135     } else xb = b;
1136     if ((flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) &&
1137         (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP)) {
1138       for (i=0; i<m; i++) {
1139         x[i] *= mdiag[i];
1140       }
1141       PetscLogFlops(m);
1142     }
1143     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP){
1144 #if defined(PETSC_USE_FORTRAN_KERNEL_RELAXAIJ)
1145       fortranrelaxaijbackwardzero_(&m,&omega,x,a->i,a->j,(int*)diag,idiag,a->a,(void*)xb);
1146 #else
1147       for (i=m-1; i>=0; i--) {
1148         n    = a->i[i+1] - diag[i] - 1;
1149         idx  = a->j + diag[i] + 1;
1150         v    = a->a + diag[i] + 1;
1151         sum  = xb[i];
1152         SPARSEDENSEMDOT(sum,xs,v,idx,n);
1153         x[i] = sum*idiag[i];
1154       }
1155 #endif
1156       PetscLogFlops(a->nz);
1157     }
1158     its--;
1159   }
1160   while (its--) {
1161     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP){
1162 #if defined(PETSC_USE_FORTRAN_KERNEL_RELAXAIJ)
1163       fortranrelaxaijforward_(&m,&omega,x,a->i,a->j,(int*)diag,a->a,(void*)b);
1164 #else
1165       for (i=0; i<m; i++) {
1166         d    = fshift + a->a[diag[i]];
1167         n    = a->i[i+1] - a->i[i];
1168         idx  = a->j + a->i[i];
1169         v    = a->a + a->i[i];
1170         sum  = b[i];
1171         SPARSEDENSEMDOT(sum,xs,v,idx,n);
1172         x[i] = (1. - omega)*x[i] + (sum + mdiag[i]*x[i])*idiag[i];
1173       }
1174 #endif
1175       PetscLogFlops(a->nz);
1176     }
1177     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP){
1178 #if defined(PETSC_USE_FORTRAN_KERNEL_RELAXAIJ)
1179       fortranrelaxaijbackward_(&m,&omega,x,a->i,a->j,(int*)diag,a->a,(void*)b);
1180 #else
1181       for (i=m-1; i>=0; i--) {
1182         d    = fshift + a->a[diag[i]];
1183         n    = a->i[i+1] - a->i[i];
1184         idx  = a->j + a->i[i];
1185         v    = a->a + a->i[i];
1186         sum  = b[i];
1187         SPARSEDENSEMDOT(sum,xs,v,idx,n);
1188         x[i] = (1. - omega)*x[i] + (sum + mdiag[i]*x[i])*idiag[i];
1189       }
1190 #endif
1191       PetscLogFlops(a->nz);
1192     }
1193   }
1194   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1195   if (bb != xx) {ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);}
1196   PetscFunctionReturn(0);
1197 }
1198 
1199 #undef __FUNCT__
1200 #define __FUNCT__ "MatGetInfo_SeqAIJ"
1201 int MatGetInfo_SeqAIJ(Mat A,MatInfoType flag,MatInfo *info)
1202 {
1203   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1204 
1205   PetscFunctionBegin;
1206   info->rows_global    = (double)A->m;
1207   info->columns_global = (double)A->n;
1208   info->rows_local     = (double)A->m;
1209   info->columns_local  = (double)A->n;
1210   info->block_size     = 1.0;
1211   info->nz_allocated   = (double)a->maxnz;
1212   info->nz_used        = (double)a->nz;
1213   info->nz_unneeded    = (double)(a->maxnz - a->nz);
1214   info->assemblies     = (double)A->num_ass;
1215   info->mallocs        = (double)a->reallocs;
1216   info->memory         = A->mem;
1217   if (A->factor) {
1218     info->fill_ratio_given  = A->info.fill_ratio_given;
1219     info->fill_ratio_needed = A->info.fill_ratio_needed;
1220     info->factor_mallocs    = A->info.factor_mallocs;
1221   } else {
1222     info->fill_ratio_given  = 0;
1223     info->fill_ratio_needed = 0;
1224     info->factor_mallocs    = 0;
1225   }
1226   PetscFunctionReturn(0);
1227 }
1228 
1229 #undef __FUNCT__
1230 #define __FUNCT__ "MatZeroRows_SeqAIJ"
1231 int MatZeroRows_SeqAIJ(Mat A,IS is,const PetscScalar *diag)
1232 {
1233   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1234   int         i,ierr,N,*rows,m = A->m - 1;
1235 
1236   PetscFunctionBegin;
1237   ierr = ISGetLocalSize(is,&N);CHKERRQ(ierr);
1238   ierr = ISGetIndices(is,&rows);CHKERRQ(ierr);
1239   if (a->keepzeroedrows) {
1240     for (i=0; i<N; i++) {
1241       if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"row %d out of range", rows[i]);
1242       ierr = PetscMemzero(&a->a[a->i[rows[i]]],a->ilen[rows[i]]*sizeof(PetscScalar));CHKERRQ(ierr);
1243     }
1244     if (diag) {
1245       ierr = MatMissingDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1246       ierr = MatMarkDiagonal_SeqAIJ(A);CHKERRQ(ierr);
1247       for (i=0; i<N; i++) {
1248         a->a[a->diag[rows[i]]] = *diag;
1249       }
1250     }
1251   } else {
1252     if (diag) {
1253       for (i=0; i<N; i++) {
1254         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"row %d out of range", rows[i]);
1255         if (a->ilen[rows[i]] > 0) {
1256           a->ilen[rows[i]]          = 1;
1257           a->a[a->i[rows[i]]] = *diag;
1258           a->j[a->i[rows[i]]] = rows[i];
1259         } else { /* in case row was completely empty */
1260           ierr = MatSetValues_SeqAIJ(A,1,&rows[i],1,&rows[i],diag,INSERT_VALUES);CHKERRQ(ierr);
1261         }
1262       }
1263     } else {
1264       for (i=0; i<N; i++) {
1265         if (rows[i] < 0 || rows[i] > m) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"row %d out of range", rows[i]);
1266         a->ilen[rows[i]] = 0;
1267       }
1268     }
1269   }
1270   ierr = ISRestoreIndices(is,&rows);CHKERRQ(ierr);
1271   ierr = MatAssemblyEnd_SeqAIJ(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1272   PetscFunctionReturn(0);
1273 }
1274 
1275 #undef __FUNCT__
1276 #define __FUNCT__ "MatGetRow_SeqAIJ"
1277 int MatGetRow_SeqAIJ(Mat A,int row,int *nz,int **idx,PetscScalar **v)
1278 {
1279   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1280   int        *itmp;
1281 
1282   PetscFunctionBegin;
1283   if (row < 0 || row >= A->m) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"Row %d out of range",row);
1284 
1285   *nz = a->i[row+1] - a->i[row];
1286   if (v) *v = a->a + a->i[row];
1287   if (idx) {
1288     itmp = a->j + a->i[row];
1289     if (*nz) {
1290       *idx = itmp;
1291     }
1292     else *idx = 0;
1293   }
1294   PetscFunctionReturn(0);
1295 }
1296 
1297 /* remove this function? */
1298 #undef __FUNCT__
1299 #define __FUNCT__ "MatRestoreRow_SeqAIJ"
1300 int MatRestoreRow_SeqAIJ(Mat A,int row,int *nz,int **idx,PetscScalar **v)
1301 {
1302   /* Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1303      int ierr; */
1304 
1305   PetscFunctionBegin;
1306   /* if (idx) {if (*idx && a->indexshift) {ierr = PetscFree(*idx);CHKERRQ(ierr);}} */
1307   PetscFunctionReturn(0);
1308 }
1309 
1310 #undef __FUNCT__
1311 #define __FUNCT__ "MatNorm_SeqAIJ"
1312 int MatNorm_SeqAIJ(Mat A,NormType type,PetscReal *nrm)
1313 {
1314   Mat_SeqAIJ   *a = (Mat_SeqAIJ*)A->data;
1315   PetscScalar  *v = a->a;
1316   PetscReal    sum = 0.0;
1317   int          i,j,ierr;
1318 
1319   PetscFunctionBegin;
1320   if (type == NORM_FROBENIUS) {
1321     for (i=0; i<a->nz; i++) {
1322 #if defined(PETSC_USE_COMPLEX)
1323       sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1324 #else
1325       sum += (*v)*(*v); v++;
1326 #endif
1327     }
1328     *nrm = sqrt(sum);
1329   } else if (type == NORM_1) {
1330     PetscReal *tmp;
1331     int    *jj = a->j;
1332     ierr = PetscMalloc((A->n+1)*sizeof(PetscReal),&tmp);CHKERRQ(ierr);
1333     ierr = PetscMemzero(tmp,A->n*sizeof(PetscReal));CHKERRQ(ierr);
1334     *nrm = 0.0;
1335     for (j=0; j<a->nz; j++) {
1336         tmp[*jj++] += PetscAbsScalar(*v);  v++;
1337     }
1338     for (j=0; j<A->n; j++) {
1339       if (tmp[j] > *nrm) *nrm = tmp[j];
1340     }
1341     ierr = PetscFree(tmp);CHKERRQ(ierr);
1342   } else if (type == NORM_INFINITY) {
1343     *nrm = 0.0;
1344     for (j=0; j<A->m; j++) {
1345       v = a->a + a->i[j];
1346       sum = 0.0;
1347       for (i=0; i<a->i[j+1]-a->i[j]; i++) {
1348         sum += PetscAbsScalar(*v); v++;
1349       }
1350       if (sum > *nrm) *nrm = sum;
1351     }
1352   } else {
1353     SETERRQ(PETSC_ERR_SUP,"No support for two norm");
1354   }
1355   PetscFunctionReturn(0);
1356 }
1357 
1358 #undef __FUNCT__
1359 #define __FUNCT__ "MatTranspose_SeqAIJ"
1360 int MatTranspose_SeqAIJ(Mat A,Mat *B)
1361 {
1362   Mat_SeqAIJ   *a = (Mat_SeqAIJ*)A->data;
1363   Mat          C;
1364   int          i,ierr,*aj = a->j,*ai = a->i,m = A->m,len,*col;
1365   PetscScalar  *array = a->a;
1366 
1367   PetscFunctionBegin;
1368   if (!B && m != A->n) SETERRQ(PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1369   ierr = PetscMalloc((1+A->n)*sizeof(int),&col);CHKERRQ(ierr);
1370   ierr = PetscMemzero(col,(1+A->n)*sizeof(int));CHKERRQ(ierr);
1371 
1372   for (i=0; i<ai[m]; i++) col[aj[i]] += 1;
1373   ierr = MatCreate(A->comm,A->n,m,A->n,m,&C);CHKERRQ(ierr);
1374   ierr = MatSetType(C,A->type_name);CHKERRQ(ierr);
1375   ierr = MatSeqAIJSetPreallocation(C,0,col);CHKERRQ(ierr);
1376   ierr = PetscFree(col);CHKERRQ(ierr);
1377   for (i=0; i<m; i++) {
1378     len    = ai[i+1]-ai[i];
1379     ierr   = MatSetValues(C,len,aj,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
1380     array += len;
1381     aj    += len;
1382   }
1383 
1384   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1385   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1386 
1387   if (B) {
1388     *B = C;
1389   } else {
1390     ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
1391   }
1392   PetscFunctionReturn(0);
1393 }
1394 
1395 EXTERN_C_BEGIN
1396 #undef __FUNCT__
1397 #define __FUNCT__ "MatIsTranspose_SeqAIJ"
1398 int MatIsTranspose_SeqAIJ(Mat A,Mat B,PetscReal tol,PetscTruth *f)
1399 {
1400   Mat_SeqAIJ *aij = (Mat_SeqAIJ *) A->data,*bij = (Mat_SeqAIJ*) A->data;
1401   int        *adx,*bdx,*aii,*bii,*aptr,*bptr; PetscScalar *va,*vb;
1402   int        ma,na,mb,nb, i,ierr;
1403 
1404   PetscFunctionBegin;
1405   bij = (Mat_SeqAIJ *) B->data;
1406 
1407   ierr = MatGetSize(A,&ma,&na);CHKERRQ(ierr);
1408   ierr = MatGetSize(B,&mb,&nb);CHKERRQ(ierr);
1409   if (ma!=nb || na!=mb){
1410     *f = PETSC_FALSE;
1411     PetscFunctionReturn(0);
1412   }
1413   aii = aij->i; bii = bij->i;
1414   adx = aij->j; bdx = bij->j;
1415   va  = aij->a; vb = bij->a;
1416   ierr = PetscMalloc(ma*sizeof(int),&aptr);CHKERRQ(ierr);
1417   ierr = PetscMalloc(mb*sizeof(int),&bptr);CHKERRQ(ierr);
1418   for (i=0; i<ma; i++) aptr[i] = aii[i];
1419   for (i=0; i<mb; i++) bptr[i] = bii[i];
1420 
1421   *f = PETSC_TRUE;
1422   for (i=0; i<ma; i++) {
1423     /*printf("row %d spans %d--%d; we start @ %d\n",
1424       i,idx[ii[i]],idx[ii[i+1]-1],idx[aptr[i]]);*/
1425     while (aptr[i]<aii[i+1]) {
1426       int         idc,idr;
1427       PetscScalar vc,vr;
1428       /* column/row index/value */
1429       idc = adx[aptr[i]];
1430       idr = bdx[bptr[idc]];
1431       vc  = va[aptr[i]];
1432       vr  = vb[bptr[idc]];
1433       /*printf("comparing %d: (%d,%d)=%e to (%d,%d)=%e\n",
1434 	aptr[i],i,idc,vc,idc,idr,vr);*/
1435       if (i!=idr || PetscAbsScalar(vc-vr) > tol) {
1436 	*f = PETSC_FALSE;
1437         goto done;
1438       } else {
1439 	aptr[i]++;
1440         if (B || i!=idc) bptr[idc]++;
1441       }
1442     }
1443   }
1444  done:
1445   ierr = PetscFree(aptr);CHKERRQ(ierr);
1446   if (B) {
1447     ierr = PetscFree(bptr);CHKERRQ(ierr);
1448   }
1449   PetscFunctionReturn(0);
1450 }
1451 EXTERN_C_END
1452 
1453 #undef __FUNCT__
1454 #define __FUNCT__ "MatIsSymmetric_SeqAIJ"
1455 int MatIsSymmetric_SeqAIJ(Mat A,PetscReal tol,PetscTruth *f)
1456 {
1457   int ierr;
1458   PetscFunctionBegin;
1459   ierr = MatIsTranspose_SeqAIJ(A,A,tol,f);CHKERRQ(ierr);
1460   PetscFunctionReturn(0);
1461 }
1462 
1463 #undef __FUNCT__
1464 #define __FUNCT__ "MatDiagonalScale_SeqAIJ"
1465 int MatDiagonalScale_SeqAIJ(Mat A,Vec ll,Vec rr)
1466 {
1467   Mat_SeqAIJ   *a = (Mat_SeqAIJ*)A->data;
1468   PetscScalar  *l,*r,x,*v;
1469   int          ierr,i,j,m = A->m,n = A->n,M,nz = a->nz,*jj;
1470 
1471   PetscFunctionBegin;
1472   if (ll) {
1473     /* The local size is used so that VecMPI can be passed to this routine
1474        by MatDiagonalScale_MPIAIJ */
1475     ierr = VecGetLocalSize(ll,&m);CHKERRQ(ierr);
1476     if (m != A->m) SETERRQ(PETSC_ERR_ARG_SIZ,"Left scaling vector wrong length");
1477     ierr = VecGetArray(ll,&l);CHKERRQ(ierr);
1478     v = a->a;
1479     for (i=0; i<m; i++) {
1480       x = l[i];
1481       M = a->i[i+1] - a->i[i];
1482       for (j=0; j<M; j++) { (*v++) *= x;}
1483     }
1484     ierr = VecRestoreArray(ll,&l);CHKERRQ(ierr);
1485     PetscLogFlops(nz);
1486   }
1487   if (rr) {
1488     ierr = VecGetLocalSize(rr,&n);CHKERRQ(ierr);
1489     if (n != A->n) SETERRQ(PETSC_ERR_ARG_SIZ,"Right scaling vector wrong length");
1490     ierr = VecGetArray(rr,&r);CHKERRQ(ierr);
1491     v = a->a; jj = a->j;
1492     for (i=0; i<nz; i++) {
1493       (*v++) *= r[*jj++];
1494     }
1495     ierr = VecRestoreArray(rr,&r);CHKERRQ(ierr);
1496     PetscLogFlops(nz);
1497   }
1498   PetscFunctionReturn(0);
1499 }
1500 
1501 #undef __FUNCT__
1502 #define __FUNCT__ "MatGetSubMatrix_SeqAIJ"
1503 int MatGetSubMatrix_SeqAIJ(Mat A,IS isrow,IS iscol,int csize,MatReuse scall,Mat *B)
1504 {
1505   Mat_SeqAIJ   *a = (Mat_SeqAIJ*)A->data,*c;
1506   int          *smap,i,k,kstart,kend,ierr,oldcols = A->n,*lens;
1507   int          row,mat_i,*mat_j,tcol,first,step,*mat_ilen,sum,lensi;
1508   int          *irow,*icol,nrows,ncols;
1509   int          *starts,*j_new,*i_new,*aj = a->j,*ai = a->i,ii,*ailen = a->ilen;
1510   PetscScalar  *a_new,*mat_a;
1511   Mat          C;
1512   PetscTruth   stride;
1513 
1514   PetscFunctionBegin;
1515   ierr = ISSorted(isrow,(PetscTruth*)&i);CHKERRQ(ierr);
1516   if (!i) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"ISrow is not sorted");
1517   ierr = ISSorted(iscol,(PetscTruth*)&i);CHKERRQ(ierr);
1518   if (!i) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"IScol is not sorted");
1519 
1520   ierr = ISGetIndices(isrow,&irow);CHKERRQ(ierr);
1521   ierr = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
1522   ierr = ISGetLocalSize(iscol,&ncols);CHKERRQ(ierr);
1523 
1524   ierr = ISStrideGetInfo(iscol,&first,&step);CHKERRQ(ierr);
1525   ierr = ISStride(iscol,&stride);CHKERRQ(ierr);
1526   if (stride && step == 1) {
1527     /* special case of contiguous rows */
1528     ierr   = PetscMalloc((2*nrows+1)*sizeof(int),&lens);CHKERRQ(ierr);
1529     starts = lens + nrows;
1530     /* loop over new rows determining lens and starting points */
1531     for (i=0; i<nrows; i++) {
1532       kstart  = ai[irow[i]];
1533       kend    = kstart + ailen[irow[i]];
1534       for (k=kstart; k<kend; k++) {
1535         if (aj[k] >= first) {
1536           starts[i] = k;
1537           break;
1538 	}
1539       }
1540       sum = 0;
1541       while (k < kend) {
1542         if (aj[k++] >= first+ncols) break;
1543         sum++;
1544       }
1545       lens[i] = sum;
1546     }
1547     /* create submatrix */
1548     if (scall == MAT_REUSE_MATRIX) {
1549       int n_cols,n_rows;
1550       ierr = MatGetSize(*B,&n_rows,&n_cols);CHKERRQ(ierr);
1551       if (n_rows != nrows || n_cols != ncols) SETERRQ(PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
1552       ierr = MatZeroEntries(*B);CHKERRQ(ierr);
1553       C = *B;
1554     } else {
1555       ierr = MatCreate(A->comm,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE,&C);CHKERRQ(ierr);
1556       ierr = MatSetType(C,A->type_name);CHKERRQ(ierr);
1557       ierr = MatSeqAIJSetPreallocation(C,0,lens);CHKERRQ(ierr);
1558     }
1559     c = (Mat_SeqAIJ*)C->data;
1560 
1561     /* loop over rows inserting into submatrix */
1562     a_new    = c->a;
1563     j_new    = c->j;
1564     i_new    = c->i;
1565 
1566     for (i=0; i<nrows; i++) {
1567       ii    = starts[i];
1568       lensi = lens[i];
1569       for (k=0; k<lensi; k++) {
1570         *j_new++ = aj[ii+k] - first;
1571       }
1572       ierr = PetscMemcpy(a_new,a->a + starts[i],lensi*sizeof(PetscScalar));CHKERRQ(ierr);
1573       a_new      += lensi;
1574       i_new[i+1]  = i_new[i] + lensi;
1575       c->ilen[i]  = lensi;
1576     }
1577     ierr = PetscFree(lens);CHKERRQ(ierr);
1578   } else {
1579     ierr  = ISGetIndices(iscol,&icol);CHKERRQ(ierr);
1580     ierr  = PetscMalloc((1+oldcols)*sizeof(int),&smap);CHKERRQ(ierr);
1581 
1582     ierr  = PetscMalloc((1+nrows)*sizeof(int),&lens);CHKERRQ(ierr);
1583     ierr  = PetscMemzero(smap,oldcols*sizeof(int));CHKERRQ(ierr);
1584     for (i=0; i<ncols; i++) smap[icol[i]] = i+1;
1585     /* determine lens of each row */
1586     for (i=0; i<nrows; i++) {
1587       kstart  = ai[irow[i]];
1588       kend    = kstart + a->ilen[irow[i]];
1589       lens[i] = 0;
1590       for (k=kstart; k<kend; k++) {
1591         if (smap[aj[k]]) {
1592           lens[i]++;
1593         }
1594       }
1595     }
1596     /* Create and fill new matrix */
1597     if (scall == MAT_REUSE_MATRIX) {
1598       PetscTruth equal;
1599 
1600       c = (Mat_SeqAIJ *)((*B)->data);
1601       if ((*B)->m  != nrows || (*B)->n != ncols) SETERRQ(PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong size");
1602       ierr = PetscMemcmp(c->ilen,lens,(*B)->m*sizeof(int),&equal);CHKERRQ(ierr);
1603       if (!equal) {
1604         SETERRQ(PETSC_ERR_ARG_SIZ,"Cannot reuse matrix. wrong no of nonzeros");
1605       }
1606       ierr = PetscMemzero(c->ilen,(*B)->m*sizeof(int));CHKERRQ(ierr);
1607       C = *B;
1608     } else {
1609       ierr = MatCreate(A->comm,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE,&C);CHKERRQ(ierr);
1610       ierr = MatSetType(C,A->type_name);CHKERRQ(ierr);
1611       ierr = MatSeqAIJSetPreallocation(C,0,lens);CHKERRQ(ierr);
1612     }
1613     c = (Mat_SeqAIJ *)(C->data);
1614     for (i=0; i<nrows; i++) {
1615       row    = irow[i];
1616       kstart = ai[row];
1617       kend   = kstart + a->ilen[row];
1618       mat_i  = c->i[i];
1619       mat_j  = c->j + mat_i;
1620       mat_a  = c->a + mat_i;
1621       mat_ilen = c->ilen + i;
1622       for (k=kstart; k<kend; k++) {
1623         if ((tcol=smap[a->j[k]])) {
1624           *mat_j++ = tcol - 1;
1625           *mat_a++ = a->a[k];
1626           (*mat_ilen)++;
1627 
1628         }
1629       }
1630     }
1631     /* Free work space */
1632     ierr = ISRestoreIndices(iscol,&icol);CHKERRQ(ierr);
1633     ierr = PetscFree(smap);CHKERRQ(ierr);
1634     ierr = PetscFree(lens);CHKERRQ(ierr);
1635   }
1636   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1637   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1638 
1639   ierr = ISRestoreIndices(isrow,&irow);CHKERRQ(ierr);
1640   *B = C;
1641   PetscFunctionReturn(0);
1642 }
1643 
1644 /*
1645 */
1646 #undef __FUNCT__
1647 #define __FUNCT__ "MatILUFactor_SeqAIJ"
1648 int MatILUFactor_SeqAIJ(Mat inA,IS row,IS col,MatFactorInfo *info)
1649 {
1650   Mat_SeqAIJ *a = (Mat_SeqAIJ*)inA->data;
1651   int        ierr;
1652   Mat        outA;
1653   PetscTruth row_identity,col_identity;
1654 
1655   PetscFunctionBegin;
1656   if (info->levels != 0) SETERRQ(PETSC_ERR_SUP,"Only levels=0 supported for in-place ilu");
1657   ierr = ISIdentity(row,&row_identity);CHKERRQ(ierr);
1658   ierr = ISIdentity(col,&col_identity);CHKERRQ(ierr);
1659   if (!row_identity || !col_identity) {
1660     SETERRQ(1,"Row and column permutations must be identity for in-place ILU");
1661   }
1662 
1663   outA          = inA;
1664   inA->factor   = FACTOR_LU;
1665   a->row        = row;
1666   a->col        = col;
1667   ierr = PetscObjectReference((PetscObject)row);CHKERRQ(ierr);
1668   ierr = PetscObjectReference((PetscObject)col);CHKERRQ(ierr);
1669 
1670   /* Create the inverse permutation so that it can be used in MatLUFactorNumeric() */
1671   if (a->icol) {ierr = ISDestroy(a->icol);CHKERRQ(ierr);} /* need to remove old one */
1672   ierr = ISInvertPermutation(col,PETSC_DECIDE,&a->icol);CHKERRQ(ierr);
1673   PetscLogObjectParent(inA,a->icol);
1674 
1675   if (!a->solve_work) { /* this matrix may have been factored before */
1676      ierr = PetscMalloc((inA->m+1)*sizeof(PetscScalar),&a->solve_work);CHKERRQ(ierr);
1677   }
1678 
1679   if (!a->diag) {
1680     ierr = MatMarkDiagonal_SeqAIJ(inA);CHKERRQ(ierr);
1681   }
1682   ierr = MatLUFactorNumeric_SeqAIJ(inA,&outA);CHKERRQ(ierr);
1683   PetscFunctionReturn(0);
1684 }
1685 
1686 #include "petscblaslapack.h"
1687 #undef __FUNCT__
1688 #define __FUNCT__ "MatScale_SeqAIJ"
1689 int MatScale_SeqAIJ(const PetscScalar *alpha,Mat inA)
1690 {
1691   Mat_SeqAIJ *a = (Mat_SeqAIJ*)inA->data;
1692   int        one = 1;
1693 
1694   PetscFunctionBegin;
1695   BLscal_(&a->nz,(PetscScalar*)alpha,a->a,&one);
1696   PetscLogFlops(a->nz);
1697   PetscFunctionReturn(0);
1698 }
1699 
1700 #undef __FUNCT__
1701 #define __FUNCT__ "MatGetSubMatrices_SeqAIJ"
1702 int MatGetSubMatrices_SeqAIJ(Mat A,int n,const IS irow[],const IS icol[],MatReuse scall,Mat *B[])
1703 {
1704   int        ierr,i;
1705 
1706   PetscFunctionBegin;
1707   if (scall == MAT_INITIAL_MATRIX) {
1708     ierr = PetscMalloc((n+1)*sizeof(Mat),B);CHKERRQ(ierr);
1709   }
1710 
1711   for (i=0; i<n; i++) {
1712     ierr = MatGetSubMatrix_SeqAIJ(A,irow[i],icol[i],PETSC_DECIDE,scall,&(*B)[i]);CHKERRQ(ierr);
1713   }
1714   PetscFunctionReturn(0);
1715 }
1716 
1717 #undef __FUNCT__
1718 #define __FUNCT__ "MatGetBlockSize_SeqAIJ"
1719 int MatGetBlockSize_SeqAIJ(Mat A,int *bs)
1720 {
1721   PetscFunctionBegin;
1722   *bs = 1;
1723   PetscFunctionReturn(0);
1724 }
1725 
1726 #undef __FUNCT__
1727 #define __FUNCT__ "MatIncreaseOverlap_SeqAIJ"
1728 int MatIncreaseOverlap_SeqAIJ(Mat A,int is_max,IS is[],int ov)
1729 {
1730   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1731   int        row,i,j,k,l,m,n,*idx,ierr,*nidx,isz,val;
1732   int        start,end,*ai,*aj;
1733   PetscBT    table;
1734 
1735   PetscFunctionBegin;
1736   m     = A->m;
1737   ai    = a->i;
1738   aj    = a->j;
1739 
1740   if (ov < 0)  SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"illegal negative overlap value used");
1741 
1742   ierr = PetscMalloc((m+1)*sizeof(int),&nidx);CHKERRQ(ierr);
1743   ierr = PetscBTCreate(m,table);CHKERRQ(ierr);
1744 
1745   for (i=0; i<is_max; i++) {
1746     /* Initialize the two local arrays */
1747     isz  = 0;
1748     ierr = PetscBTMemzero(m,table);CHKERRQ(ierr);
1749 
1750     /* Extract the indices, assume there can be duplicate entries */
1751     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
1752     ierr = ISGetLocalSize(is[i],&n);CHKERRQ(ierr);
1753 
1754     /* Enter these into the temp arrays. I.e., mark table[row], enter row into new index */
1755     for (j=0; j<n ; ++j){
1756       if(!PetscBTLookupSet(table,idx[j])) { nidx[isz++] = idx[j];}
1757     }
1758     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
1759     ierr = ISDestroy(is[i]);CHKERRQ(ierr);
1760 
1761     k = 0;
1762     for (j=0; j<ov; j++){ /* for each overlap */
1763       n = isz;
1764       for (; k<n ; k++){ /* do only those rows in nidx[k], which are not done yet */
1765         row   = nidx[k];
1766         start = ai[row];
1767         end   = ai[row+1];
1768         for (l = start; l<end ; l++){
1769           val = aj[l] ;
1770           if (!PetscBTLookupSet(table,val)) {nidx[isz++] = val;}
1771         }
1772       }
1773     }
1774     ierr = ISCreateGeneral(PETSC_COMM_SELF,isz,nidx,(is+i));CHKERRQ(ierr);
1775   }
1776   ierr = PetscBTDestroy(table);CHKERRQ(ierr);
1777   ierr = PetscFree(nidx);CHKERRQ(ierr);
1778   PetscFunctionReturn(0);
1779 }
1780 
1781 /* -------------------------------------------------------------- */
1782 #undef __FUNCT__
1783 #define __FUNCT__ "MatPermute_SeqAIJ"
1784 int MatPermute_SeqAIJ(Mat A,IS rowp,IS colp,Mat *B)
1785 {
1786   Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
1787   int               i,ierr,nz,m = A->m,n = A->n,*col;
1788   int               *row,*cnew,j,*lens;
1789   IS                icolp,irowp;
1790   const int         *cwork;
1791   const PetscScalar *vwork;
1792 
1793   PetscFunctionBegin;
1794   ierr = ISInvertPermutation(rowp,PETSC_DECIDE,&irowp);CHKERRQ(ierr);
1795   ierr = ISGetIndices(irowp,&row);CHKERRQ(ierr);
1796   ierr = ISInvertPermutation(colp,PETSC_DECIDE,&icolp);CHKERRQ(ierr);
1797   ierr = ISGetIndices(icolp,&col);CHKERRQ(ierr);
1798 
1799   /* determine lengths of permuted rows */
1800   ierr = PetscMalloc((m+1)*sizeof(int),&lens);CHKERRQ(ierr);
1801   for (i=0; i<m; i++) {
1802     lens[row[i]] = a->i[i+1] - a->i[i];
1803   }
1804   ierr = MatCreate(A->comm,m,n,m,n,B);CHKERRQ(ierr);
1805   ierr = MatSetType(*B,A->type_name);CHKERRQ(ierr);
1806   ierr = MatSeqAIJSetPreallocation(*B,0,lens);CHKERRQ(ierr);
1807   ierr = PetscFree(lens);CHKERRQ(ierr);
1808 
1809   ierr = PetscMalloc(n*sizeof(int),&cnew);CHKERRQ(ierr);
1810   for (i=0; i<m; i++) {
1811     ierr = MatGetRow(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
1812     for (j=0; j<nz; j++) { cnew[j] = col[cwork[j]];}
1813     ierr = MatSetValues(*B,1,&row[i],nz,cnew,vwork,INSERT_VALUES);CHKERRQ(ierr);
1814     ierr = MatRestoreRow(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
1815   }
1816   ierr = PetscFree(cnew);CHKERRQ(ierr);
1817   ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1818   ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1819   ierr = ISRestoreIndices(irowp,&row);CHKERRQ(ierr);
1820   ierr = ISRestoreIndices(icolp,&col);CHKERRQ(ierr);
1821   ierr = ISDestroy(irowp);CHKERRQ(ierr);
1822   ierr = ISDestroy(icolp);CHKERRQ(ierr);
1823   PetscFunctionReturn(0);
1824 }
1825 
1826 #undef __FUNCT__
1827 #define __FUNCT__ "MatPrintHelp_SeqAIJ"
1828 int MatPrintHelp_SeqAIJ(Mat A)
1829 {
1830   static PetscTruth called = PETSC_FALSE;
1831   MPI_Comm          comm = A->comm;
1832   int               ierr;
1833 
1834   PetscFunctionBegin;
1835   if (called) {PetscFunctionReturn(0);} else called = PETSC_TRUE;
1836   ierr = (*PetscHelpPrintf)(comm," Options for MATSEQAIJ and MATMPIAIJ matrix formats (the defaults):\n");CHKERRQ(ierr);
1837   ierr = (*PetscHelpPrintf)(comm,"  -mat_lu_pivotthreshold <threshold>: Set pivoting threshold\n");CHKERRQ(ierr);
1838   ierr = (*PetscHelpPrintf)(comm,"  -mat_aij_oneindex: internal indices begin at 1 instead of the default 0.\n");CHKERRQ(ierr);
1839   ierr = (*PetscHelpPrintf)(comm,"  -mat_aij_no_inode: Do not use inodes\n");CHKERRQ(ierr);
1840   ierr = (*PetscHelpPrintf)(comm,"  -mat_aij_inode_limit <limit>: Set inode limit (max limit=5)\n");CHKERRQ(ierr);
1841   PetscFunctionReturn(0);
1842 }
1843 
1844 #undef __FUNCT__
1845 #define __FUNCT__ "MatCopy_SeqAIJ"
1846 int MatCopy_SeqAIJ(Mat A,Mat B,MatStructure str)
1847 {
1848   int        ierr;
1849 
1850   PetscFunctionBegin;
1851   /* If the two matrices have the same copy implementation, use fast copy. */
1852   if (str == SAME_NONZERO_PATTERN && (A->ops->copy == B->ops->copy)) {
1853     Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1854     Mat_SeqAIJ *b = (Mat_SeqAIJ*)B->data;
1855 
1856     if (a->i[A->m] != b->i[B->m]) {
1857       SETERRQ(1,"Number of nonzeros in two matrices are different");
1858     }
1859     ierr = PetscMemcpy(b->a,a->a,(a->i[A->m])*sizeof(PetscScalar));CHKERRQ(ierr);
1860   } else {
1861     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
1862   }
1863   PetscFunctionReturn(0);
1864 }
1865 
1866 #undef __FUNCT__
1867 #define __FUNCT__ "MatSetUpPreallocation_SeqAIJ"
1868 int MatSetUpPreallocation_SeqAIJ(Mat A)
1869 {
1870   int        ierr;
1871 
1872   PetscFunctionBegin;
1873   ierr =  MatSeqAIJSetPreallocation(A,PETSC_DEFAULT,0);CHKERRQ(ierr);
1874   PetscFunctionReturn(0);
1875 }
1876 
1877 #undef __FUNCT__
1878 #define __FUNCT__ "MatGetArray_SeqAIJ"
1879 int MatGetArray_SeqAIJ(Mat A,PetscScalar *array[])
1880 {
1881   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1882   PetscFunctionBegin;
1883   *array = a->a;
1884   PetscFunctionReturn(0);
1885 }
1886 
1887 #undef __FUNCT__
1888 #define __FUNCT__ "MatRestoreArray_SeqAIJ"
1889 int MatRestoreArray_SeqAIJ(Mat A,PetscScalar *array[])
1890 {
1891   PetscFunctionBegin;
1892   PetscFunctionReturn(0);
1893 }
1894 
1895 #undef __FUNCT__
1896 #define __FUNCT__ "MatFDColoringApply_SeqAIJ"
1897 int MatFDColoringApply_SeqAIJ(Mat J,MatFDColoring coloring,Vec x1,MatStructure *flag,void *sctx)
1898 {
1899   int           (*f)(void *,Vec,Vec,void*) = (int (*)(void *,Vec,Vec,void *))coloring->f;
1900   int           k,ierr,N,start,end,l,row,col,srow,**vscaleforrow,m1,m2;
1901   PetscScalar   dx,mone = -1.0,*y,*xx,*w3_array;
1902   PetscScalar   *vscale_array;
1903   PetscReal     epsilon = coloring->error_rel,umin = coloring->umin;
1904   Vec           w1,w2,w3;
1905   void          *fctx = coloring->fctx;
1906   PetscTruth    flg;
1907 
1908   PetscFunctionBegin;
1909   if (!coloring->w1) {
1910     ierr = VecDuplicate(x1,&coloring->w1);CHKERRQ(ierr);
1911     PetscLogObjectParent(coloring,coloring->w1);
1912     ierr = VecDuplicate(x1,&coloring->w2);CHKERRQ(ierr);
1913     PetscLogObjectParent(coloring,coloring->w2);
1914     ierr = VecDuplicate(x1,&coloring->w3);CHKERRQ(ierr);
1915     PetscLogObjectParent(coloring,coloring->w3);
1916   }
1917   w1 = coloring->w1; w2 = coloring->w2; w3 = coloring->w3;
1918 
1919   ierr = MatSetUnfactored(J);CHKERRQ(ierr);
1920   ierr = PetscOptionsHasName(coloring->prefix,"-mat_fd_coloring_dont_rezero",&flg);CHKERRQ(ierr);
1921   if (flg) {
1922     PetscLogInfo(coloring,"MatFDColoringApply_SeqAIJ: Not calling MatZeroEntries()\n");
1923   } else {
1924     ierr = MatZeroEntries(J);CHKERRQ(ierr);
1925   }
1926 
1927   ierr = VecGetOwnershipRange(x1,&start,&end);CHKERRQ(ierr);
1928   ierr = VecGetSize(x1,&N);CHKERRQ(ierr);
1929 
1930   /*
1931        This is a horrible, horrible, hack. See DMMGComputeJacobian_Multigrid() it inproperly sets
1932      coloring->F for the coarser grids from the finest
1933   */
1934   if (coloring->F) {
1935     ierr = VecGetLocalSize(coloring->F,&m1);CHKERRQ(ierr);
1936     ierr = VecGetLocalSize(w1,&m2);CHKERRQ(ierr);
1937     if (m1 != m2) {
1938       coloring->F = 0;
1939     }
1940   }
1941 
1942   if (coloring->F) {
1943     w1          = coloring->F;
1944     coloring->F = 0;
1945   } else {
1946     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
1947     ierr = (*f)(sctx,x1,w1,fctx);CHKERRQ(ierr);
1948     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
1949   }
1950 
1951   /*
1952       Compute all the scale factors and share with other processors
1953   */
1954   ierr = VecGetArray(x1,&xx);CHKERRQ(ierr);xx = xx - start;
1955   ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);vscale_array = vscale_array - start;
1956   for (k=0; k<coloring->ncolors; k++) {
1957     /*
1958        Loop over each column associated with color adding the
1959        perturbation to the vector w3.
1960     */
1961     for (l=0; l<coloring->ncolumns[k]; l++) {
1962       col = coloring->columns[k][l];    /* column of the matrix we are probing for */
1963       dx  = xx[col];
1964       if (dx == 0.0) dx = 1.0;
1965 #if !defined(PETSC_USE_COMPLEX)
1966       if (dx < umin && dx >= 0.0)      dx = umin;
1967       else if (dx < 0.0 && dx > -umin) dx = -umin;
1968 #else
1969       if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
1970       else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
1971 #endif
1972       dx                *= epsilon;
1973       vscale_array[col] = 1.0/dx;
1974     }
1975   }
1976   vscale_array = vscale_array + start;ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
1977   ierr = VecGhostUpdateBegin(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1978   ierr = VecGhostUpdateEnd(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1979 
1980   /*  ierr = VecView(coloring->vscale,PETSC_VIEWER_STDOUT_WORLD);
1981       ierr = VecView(x1,PETSC_VIEWER_STDOUT_WORLD);*/
1982 
1983   if (coloring->vscaleforrow) vscaleforrow = coloring->vscaleforrow;
1984   else                        vscaleforrow = coloring->columnsforrow;
1985 
1986   ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
1987   /*
1988       Loop over each color
1989   */
1990   for (k=0; k<coloring->ncolors; k++) {
1991     coloring->currentcolor = k;
1992     ierr = VecCopy(x1,w3);CHKERRQ(ierr);
1993     ierr = VecGetArray(w3,&w3_array);CHKERRQ(ierr);w3_array = w3_array - start;
1994     /*
1995        Loop over each column associated with color adding the
1996        perturbation to the vector w3.
1997     */
1998     for (l=0; l<coloring->ncolumns[k]; l++) {
1999       col = coloring->columns[k][l];    /* column of the matrix we are probing for */
2000       dx  = xx[col];
2001       if (dx == 0.0) dx = 1.0;
2002 #if !defined(PETSC_USE_COMPLEX)
2003       if (dx < umin && dx >= 0.0)      dx = umin;
2004       else if (dx < 0.0 && dx > -umin) dx = -umin;
2005 #else
2006       if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
2007       else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
2008 #endif
2009       dx            *= epsilon;
2010       if (!PetscAbsScalar(dx)) SETERRQ(1,"Computed 0 differencing parameter");
2011       w3_array[col] += dx;
2012     }
2013     w3_array = w3_array + start; ierr = VecRestoreArray(w3,&w3_array);CHKERRQ(ierr);
2014 
2015     /*
2016        Evaluate function at x1 + dx (here dx is a vector of perturbations)
2017     */
2018 
2019     ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2020     ierr = (*f)(sctx,w3,w2,fctx);CHKERRQ(ierr);
2021     ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
2022     ierr = VecAXPY(&mone,w1,w2);CHKERRQ(ierr);
2023 
2024     /*
2025        Loop over rows of vector, putting results into Jacobian matrix
2026     */
2027     ierr = VecGetArray(w2,&y);CHKERRQ(ierr);
2028     for (l=0; l<coloring->nrows[k]; l++) {
2029       row    = coloring->rows[k][l];
2030       col    = coloring->columnsforrow[k][l];
2031       y[row] *= vscale_array[vscaleforrow[k][l]];
2032       srow   = row + start;
2033       ierr   = MatSetValues_SeqAIJ(J,1,&srow,1,&col,y+row,INSERT_VALUES);CHKERRQ(ierr);
2034     }
2035     ierr = VecRestoreArray(w2,&y);CHKERRQ(ierr);
2036   }
2037   coloring->currentcolor = k;
2038   ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
2039   xx = xx + start; ierr  = VecRestoreArray(x1,&xx);CHKERRQ(ierr);
2040   ierr  = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2041   ierr  = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2042   PetscFunctionReturn(0);
2043 }
2044 
2045 #include "petscblaslapack.h"
2046 #undef __FUNCT__
2047 #define __FUNCT__ "MatAXPY_SeqAIJ"
2048 int MatAXPY_SeqAIJ(const PetscScalar a[],Mat X,Mat Y,MatStructure str)
2049 {
2050   int        ierr,one=1,i;
2051   Mat_SeqAIJ *x  = (Mat_SeqAIJ *)X->data,*y = (Mat_SeqAIJ *)Y->data;
2052 
2053   PetscFunctionBegin;
2054   if (str == SAME_NONZERO_PATTERN) {
2055     BLaxpy_(&x->nz,(PetscScalar*)a,x->a,&one,y->a,&one);
2056   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2057     if (y->xtoy && y->XtoY != X) {
2058       ierr = PetscFree(y->xtoy);CHKERRQ(ierr);
2059       ierr = MatDestroy(y->XtoY);CHKERRQ(ierr);
2060     }
2061     if (!y->xtoy) { /* get xtoy */
2062       ierr = MatAXPYGetxtoy_Private(X->m,x->i,x->j,PETSC_NULL, y->i,y->j,PETSC_NULL, &y->xtoy);CHKERRQ(ierr);
2063       y->XtoY = X;
2064     }
2065     for (i=0; i<x->nz; i++) y->a[y->xtoy[i]] += (*a)*(x->a[i]);
2066     PetscLogInfo(0,"MatAXPY_SeqAIJ: ratio of nnz(X)/nnz(Y): %d/%d = %g\n",x->nz,y->nz,(PetscReal)(x->nz)/y->nz);
2067   } else {
2068     ierr = MatAXPY_Basic(a,X,Y,str);CHKERRQ(ierr);
2069   }
2070   PetscFunctionReturn(0);
2071 }
2072 
2073 /* -------------------------------------------------------------------*/
2074 static struct _MatOps MatOps_Values = {MatSetValues_SeqAIJ,
2075        MatGetRow_SeqAIJ,
2076        MatRestoreRow_SeqAIJ,
2077        MatMult_SeqAIJ,
2078 /* 4*/ MatMultAdd_SeqAIJ,
2079        MatMultTranspose_SeqAIJ,
2080        MatMultTransposeAdd_SeqAIJ,
2081        MatSolve_SeqAIJ,
2082        MatSolveAdd_SeqAIJ,
2083        MatSolveTranspose_SeqAIJ,
2084 /*10*/ MatSolveTransposeAdd_SeqAIJ,
2085        MatLUFactor_SeqAIJ,
2086        0,
2087        MatRelax_SeqAIJ,
2088        MatTranspose_SeqAIJ,
2089 /*15*/ MatGetInfo_SeqAIJ,
2090        MatEqual_SeqAIJ,
2091        MatGetDiagonal_SeqAIJ,
2092        MatDiagonalScale_SeqAIJ,
2093        MatNorm_SeqAIJ,
2094 /*20*/ 0,
2095        MatAssemblyEnd_SeqAIJ,
2096        MatCompress_SeqAIJ,
2097        MatSetOption_SeqAIJ,
2098        MatZeroEntries_SeqAIJ,
2099 /*25*/ MatZeroRows_SeqAIJ,
2100        MatLUFactorSymbolic_SeqAIJ,
2101        MatLUFactorNumeric_SeqAIJ,
2102        MatCholeskyFactorSymbolic_SeqAIJ,
2103        MatCholeskyFactorNumeric_SeqAIJ,
2104 /*30*/ MatSetUpPreallocation_SeqAIJ,
2105        MatILUFactorSymbolic_SeqAIJ,
2106        MatICCFactorSymbolic_SeqAIJ,
2107        MatGetArray_SeqAIJ,
2108        MatRestoreArray_SeqAIJ,
2109 /*35*/ MatDuplicate_SeqAIJ,
2110        0,
2111        0,
2112        MatILUFactor_SeqAIJ,
2113        0,
2114 /*40*/ MatAXPY_SeqAIJ,
2115        MatGetSubMatrices_SeqAIJ,
2116        MatIncreaseOverlap_SeqAIJ,
2117        MatGetValues_SeqAIJ,
2118        MatCopy_SeqAIJ,
2119 /*45*/ MatPrintHelp_SeqAIJ,
2120        MatScale_SeqAIJ,
2121        0,
2122        0,
2123        MatILUDTFactor_SeqAIJ,
2124 /*50*/ MatGetBlockSize_SeqAIJ,
2125        MatGetRowIJ_SeqAIJ,
2126        MatRestoreRowIJ_SeqAIJ,
2127        MatGetColumnIJ_SeqAIJ,
2128        MatRestoreColumnIJ_SeqAIJ,
2129 /*55*/ MatFDColoringCreate_SeqAIJ,
2130        0,
2131        0,
2132        MatPermute_SeqAIJ,
2133        0,
2134 /*60*/ 0,
2135        MatDestroy_SeqAIJ,
2136        MatView_SeqAIJ,
2137        MatGetPetscMaps_Petsc,
2138        0,
2139 /*65*/ 0,
2140        0,
2141        0,
2142        0,
2143        0,
2144 /*70*/ 0,
2145        0,
2146        MatSetColoring_SeqAIJ,
2147        MatSetValuesAdic_SeqAIJ,
2148        MatSetValuesAdifor_SeqAIJ,
2149 /*75*/ MatFDColoringApply_SeqAIJ,
2150        0,
2151        0,
2152        0,
2153        0,
2154 /*80*/ 0,
2155        0,
2156        0,
2157        0,
2158 /*85*/ MatLoad_SeqAIJ,
2159        MatIsSymmetric_SeqAIJ,
2160 };
2161 
2162 EXTERN_C_BEGIN
2163 #undef __FUNCT__
2164 #define __FUNCT__ "MatSeqAIJSetColumnIndices_SeqAIJ"
2165 int MatSeqAIJSetColumnIndices_SeqAIJ(Mat mat,int *indices)
2166 {
2167   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)mat->data;
2168   int        i,nz,n;
2169 
2170   PetscFunctionBegin;
2171 
2172   nz = aij->maxnz;
2173   n  = mat->n;
2174   for (i=0; i<nz; i++) {
2175     aij->j[i] = indices[i];
2176   }
2177   aij->nz = nz;
2178   for (i=0; i<n; i++) {
2179     aij->ilen[i] = aij->imax[i];
2180   }
2181 
2182   PetscFunctionReturn(0);
2183 }
2184 EXTERN_C_END
2185 
2186 #undef __FUNCT__
2187 #define __FUNCT__ "MatSeqAIJSetColumnIndices"
2188 /*@
2189     MatSeqAIJSetColumnIndices - Set the column indices for all the rows
2190        in the matrix.
2191 
2192   Input Parameters:
2193 +  mat - the SeqAIJ matrix
2194 -  indices - the column indices
2195 
2196   Level: advanced
2197 
2198   Notes:
2199     This can be called if you have precomputed the nonzero structure of the
2200   matrix and want to provide it to the matrix object to improve the performance
2201   of the MatSetValues() operation.
2202 
2203     You MUST have set the correct numbers of nonzeros per row in the call to
2204   MatCreateSeqAIJ().
2205 
2206     MUST be called before any calls to MatSetValues();
2207 
2208     The indices should start with zero, not one.
2209 
2210 @*/
2211 int MatSeqAIJSetColumnIndices(Mat mat,int *indices)
2212 {
2213   int ierr,(*f)(Mat,int *);
2214 
2215   PetscFunctionBegin;
2216   PetscValidHeaderSpecific(mat,MAT_COOKIE,1);
2217   PetscValidPointer(indices,2);
2218   ierr = PetscObjectQueryFunction((PetscObject)mat,"MatSeqAIJSetColumnIndices_C",(void (**)(void))&f);CHKERRQ(ierr);
2219   if (f) {
2220     ierr = (*f)(mat,indices);CHKERRQ(ierr);
2221   } else {
2222     SETERRQ(1,"Wrong type of matrix to set column indices");
2223   }
2224   PetscFunctionReturn(0);
2225 }
2226 
2227 /* ----------------------------------------------------------------------------------------*/
2228 
2229 EXTERN_C_BEGIN
2230 #undef __FUNCT__
2231 #define __FUNCT__ "MatStoreValues_SeqAIJ"
2232 int MatStoreValues_SeqAIJ(Mat mat)
2233 {
2234   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)mat->data;
2235   size_t       nz = aij->i[mat->m],ierr;
2236 
2237   PetscFunctionBegin;
2238   if (aij->nonew != 1) {
2239     SETERRQ(1,"Must call MatSetOption(A,MAT_NO_NEW_NONZERO_LOCATIONS);first");
2240   }
2241 
2242   /* allocate space for values if not already there */
2243   if (!aij->saved_values) {
2244     ierr = PetscMalloc((nz+1)*sizeof(PetscScalar),&aij->saved_values);CHKERRQ(ierr);
2245   }
2246 
2247   /* copy values over */
2248   ierr = PetscMemcpy(aij->saved_values,aij->a,nz*sizeof(PetscScalar));CHKERRQ(ierr);
2249   PetscFunctionReturn(0);
2250 }
2251 EXTERN_C_END
2252 
2253 #undef __FUNCT__
2254 #define __FUNCT__ "MatStoreValues"
2255 /*@
2256     MatStoreValues - Stashes a copy of the matrix values; this allows, for
2257        example, reuse of the linear part of a Jacobian, while recomputing the
2258        nonlinear portion.
2259 
2260    Collect on Mat
2261 
2262   Input Parameters:
2263 .  mat - the matrix (currently on AIJ matrices support this option)
2264 
2265   Level: advanced
2266 
2267   Common Usage, with SNESSolve():
2268 $    Create Jacobian matrix
2269 $    Set linear terms into matrix
2270 $    Apply boundary conditions to matrix, at this time matrix must have
2271 $      final nonzero structure (i.e. setting the nonlinear terms and applying
2272 $      boundary conditions again will not change the nonzero structure
2273 $    ierr = MatSetOption(mat,MAT_NO_NEW_NONZERO_LOCATIONS);
2274 $    ierr = MatStoreValues(mat);
2275 $    Call SNESSetJacobian() with matrix
2276 $    In your Jacobian routine
2277 $      ierr = MatRetrieveValues(mat);
2278 $      Set nonlinear terms in matrix
2279 
2280   Common Usage without SNESSolve(), i.e. when you handle nonlinear solve yourself:
2281 $    // build linear portion of Jacobian
2282 $    ierr = MatSetOption(mat,MAT_NO_NEW_NONZERO_LOCATIONS);
2283 $    ierr = MatStoreValues(mat);
2284 $    loop over nonlinear iterations
2285 $       ierr = MatRetrieveValues(mat);
2286 $       // call MatSetValues(mat,...) to set nonliner portion of Jacobian
2287 $       // call MatAssemblyBegin/End() on matrix
2288 $       Solve linear system with Jacobian
2289 $    endloop
2290 
2291   Notes:
2292     Matrix must already be assemblied before calling this routine
2293     Must set the matrix option MatSetOption(mat,MAT_NO_NEW_NONZERO_LOCATIONS); before
2294     calling this routine.
2295 
2296 .seealso: MatRetrieveValues()
2297 
2298 @*/
2299 int MatStoreValues(Mat mat)
2300 {
2301   int ierr,(*f)(Mat);
2302 
2303   PetscFunctionBegin;
2304   PetscValidHeaderSpecific(mat,MAT_COOKIE,1);
2305   if (!mat->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
2306   if (mat->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2307 
2308   ierr = PetscObjectQueryFunction((PetscObject)mat,"MatStoreValues_C",(void (**)(void))&f);CHKERRQ(ierr);
2309   if (f) {
2310     ierr = (*f)(mat);CHKERRQ(ierr);
2311   } else {
2312     SETERRQ(1,"Wrong type of matrix to store values");
2313   }
2314   PetscFunctionReturn(0);
2315 }
2316 
2317 EXTERN_C_BEGIN
2318 #undef __FUNCT__
2319 #define __FUNCT__ "MatRetrieveValues_SeqAIJ"
2320 int MatRetrieveValues_SeqAIJ(Mat mat)
2321 {
2322   Mat_SeqAIJ *aij = (Mat_SeqAIJ *)mat->data;
2323   int        nz = aij->i[mat->m],ierr;
2324 
2325   PetscFunctionBegin;
2326   if (aij->nonew != 1) {
2327     SETERRQ(1,"Must call MatSetOption(A,MAT_NO_NEW_NONZERO_LOCATIONS);first");
2328   }
2329   if (!aij->saved_values) {
2330     SETERRQ(1,"Must call MatStoreValues(A);first");
2331   }
2332 
2333   /* copy values over */
2334   ierr = PetscMemcpy(aij->a,aij->saved_values,nz*sizeof(PetscScalar));CHKERRQ(ierr);
2335   PetscFunctionReturn(0);
2336 }
2337 EXTERN_C_END
2338 
2339 #undef __FUNCT__
2340 #define __FUNCT__ "MatRetrieveValues"
2341 /*@
2342     MatRetrieveValues - Retrieves the copy of the matrix values; this allows, for
2343        example, reuse of the linear part of a Jacobian, while recomputing the
2344        nonlinear portion.
2345 
2346    Collect on Mat
2347 
2348   Input Parameters:
2349 .  mat - the matrix (currently on AIJ matrices support this option)
2350 
2351   Level: advanced
2352 
2353 .seealso: MatStoreValues()
2354 
2355 @*/
2356 int MatRetrieveValues(Mat mat)
2357 {
2358   int ierr,(*f)(Mat);
2359 
2360   PetscFunctionBegin;
2361   PetscValidHeaderSpecific(mat,MAT_COOKIE,1);
2362   if (!mat->assembled) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
2363   if (mat->factor) SETERRQ(PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
2364 
2365   ierr = PetscObjectQueryFunction((PetscObject)mat,"MatRetrieveValues_C",(void (**)(void))&f);CHKERRQ(ierr);
2366   if (f) {
2367     ierr = (*f)(mat);CHKERRQ(ierr);
2368   } else {
2369     SETERRQ(1,"Wrong type of matrix to retrieve values");
2370   }
2371   PetscFunctionReturn(0);
2372 }
2373 
2374 
2375 /* --------------------------------------------------------------------------------*/
2376 #undef __FUNCT__
2377 #define __FUNCT__ "MatCreateSeqAIJ"
2378 /*@C
2379    MatCreateSeqAIJ - Creates a sparse matrix in AIJ (compressed row) format
2380    (the default parallel PETSc format).  For good matrix assembly performance
2381    the user should preallocate the matrix storage by setting the parameter nz
2382    (or the array nnz).  By setting these parameters accurately, performance
2383    during matrix assembly can be increased by more than a factor of 50.
2384 
2385    Collective on MPI_Comm
2386 
2387    Input Parameters:
2388 +  comm - MPI communicator, set to PETSC_COMM_SELF
2389 .  m - number of rows
2390 .  n - number of columns
2391 .  nz - number of nonzeros per row (same for all rows)
2392 -  nnz - array containing the number of nonzeros in the various rows
2393          (possibly different for each row) or PETSC_NULL
2394 
2395    Output Parameter:
2396 .  A - the matrix
2397 
2398    Notes:
2399    The AIJ format (also called the Yale sparse matrix format or
2400    compressed row storage), is fully compatible with standard Fortran 77
2401    storage.  That is, the stored row and column indices can begin at
2402    either one (as in Fortran) or zero.  See the users' manual for details.
2403 
2404    Specify the preallocated storage with either nz or nnz (not both).
2405    Set nz=PETSC_DEFAULT and nnz=PETSC_NULL for PETSc to control dynamic memory
2406    allocation.  For large problems you MUST preallocate memory or you
2407    will get TERRIBLE performance, see the users' manual chapter on matrices.
2408 
2409    By default, this format uses inodes (identical nodes) when possible, to
2410    improve numerical efficiency of matrix-vector products and solves. We
2411    search for consecutive rows with the same nonzero structure, thereby
2412    reusing matrix information to achieve increased efficiency.
2413 
2414    Options Database Keys:
2415 +  -mat_aij_no_inode  - Do not use inodes
2416 .  -mat_aij_inode_limit <limit> - Sets inode limit (max limit=5)
2417 -  -mat_aij_oneindex - Internally use indexing starting at 1
2418         rather than 0.  Note that when calling MatSetValues(),
2419         the user still MUST index entries starting at 0!
2420 
2421    Level: intermediate
2422 
2423 .seealso: MatCreate(), MatCreateMPIAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
2424 
2425 @*/
2426 int MatCreateSeqAIJ(MPI_Comm comm,int m,int n,int nz,const int nnz[],Mat *A)
2427 {
2428   int ierr;
2429 
2430   PetscFunctionBegin;
2431   ierr = MatCreate(comm,m,n,m,n,A);CHKERRQ(ierr);
2432   ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
2433   ierr = MatSeqAIJSetPreallocation(*A,nz,nnz);CHKERRQ(ierr);
2434   PetscFunctionReturn(0);
2435 }
2436 
2437 #define SKIP_ALLOCATION -4
2438 
2439 #undef __FUNCT__
2440 #define __FUNCT__ "MatSeqAIJSetPreallocation"
2441 /*@C
2442    MatSeqAIJSetPreallocation - For good matrix assembly performance
2443    the user should preallocate the matrix storage by setting the parameter nz
2444    (or the array nnz).  By setting these parameters accurately, performance
2445    during matrix assembly can be increased by more than a factor of 50.
2446 
2447    Collective on MPI_Comm
2448 
2449    Input Parameters:
2450 +  comm - MPI communicator, set to PETSC_COMM_SELF
2451 .  m - number of rows
2452 .  n - number of columns
2453 .  nz - number of nonzeros per row (same for all rows)
2454 -  nnz - array containing the number of nonzeros in the various rows
2455          (possibly different for each row) or PETSC_NULL
2456 
2457    Output Parameter:
2458 .  A - the matrix
2459 
2460    Notes:
2461    The AIJ format (also called the Yale sparse matrix format or
2462    compressed row storage), is fully compatible with standard Fortran 77
2463    storage.  That is, the stored row and column indices can begin at
2464    either one (as in Fortran) or zero.  See the users' manual for details.
2465 
2466    Specify the preallocated storage with either nz or nnz (not both).
2467    Set nz=PETSC_DEFAULT and nnz=PETSC_NULL for PETSc to control dynamic memory
2468    allocation.  For large problems you MUST preallocate memory or you
2469    will get TERRIBLE performance, see the users' manual chapter on matrices.
2470 
2471    By default, this format uses inodes (identical nodes) when possible, to
2472    improve numerical efficiency of matrix-vector products and solves. We
2473    search for consecutive rows with the same nonzero structure, thereby
2474    reusing matrix information to achieve increased efficiency.
2475 
2476    Options Database Keys:
2477 +  -mat_aij_no_inode  - Do not use inodes
2478 .  -mat_aij_inode_limit <limit> - Sets inode limit (max limit=5)
2479 -  -mat_aij_oneindex - Internally use indexing starting at 1
2480         rather than 0.  Note that when calling MatSetValues(),
2481         the user still MUST index entries starting at 0!
2482 
2483    Level: intermediate
2484 
2485 .seealso: MatCreate(), MatCreateMPIAIJ(), MatSetValues(), MatSeqAIJSetColumnIndices(), MatCreateSeqAIJWithArrays()
2486 
2487 @*/
2488 int MatSeqAIJSetPreallocation(Mat B,int nz,const int nnz[])
2489 {
2490   int ierr,(*f)(Mat,int,const int[]);
2491 
2492   PetscFunctionBegin;
2493   ierr = PetscObjectQueryFunction((PetscObject)B,"MatSeqAIJSetPreallocation_C",(void (**)(void))&f);CHKERRQ(ierr);
2494   if (f) {
2495     ierr = (*f)(B,nz,nnz);CHKERRQ(ierr);
2496   }
2497   PetscFunctionReturn(0);
2498 }
2499 
2500 EXTERN_C_BEGIN
2501 #undef __FUNCT__
2502 #define __FUNCT__ "MatSeqAIJSetPreallocation_SeqAIJ"
2503 int MatSeqAIJSetPreallocation_SeqAIJ(Mat B,int nz,int *nnz)
2504 {
2505   Mat_SeqAIJ *b;
2506   size_t     len = 0;
2507   PetscTruth skipallocation = PETSC_FALSE;
2508   int        i,ierr;
2509 
2510   PetscFunctionBegin;
2511 
2512   if (nz == SKIP_ALLOCATION) {
2513     skipallocation = PETSC_TRUE;
2514     nz             = 0;
2515   }
2516 
2517   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
2518   if (nz < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %d",nz);
2519   if (nnz) {
2520     for (i=0; i<B->m; i++) {
2521       if (nnz[i] < 0) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"nnz cannot be less than 0: local row %d value %d",i,nnz[i]);
2522       if (nnz[i] > B->n) SETERRQ3(PETSC_ERR_ARG_OUTOFRANGE,"nnz cannot be greater than row length: local row %d value %d rowlength %d",i,nnz[i],B->n);
2523     }
2524   }
2525 
2526   B->preallocated = PETSC_TRUE;
2527   b = (Mat_SeqAIJ*)B->data;
2528 
2529   ierr = PetscMalloc((B->m+1)*sizeof(int),&b->imax);CHKERRQ(ierr);
2530   if (!nnz) {
2531     if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 10;
2532     else if (nz <= 0)        nz = 1;
2533     for (i=0; i<B->m; i++) b->imax[i] = nz;
2534     nz = nz*B->m;
2535   } else {
2536     nz = 0;
2537     for (i=0; i<B->m; i++) {b->imax[i] = nnz[i]; nz += nnz[i];}
2538   }
2539 
2540   if (!skipallocation) {
2541     /* allocate the matrix space */
2542     len             = ((size_t) nz)*(sizeof(int) + sizeof(PetscScalar)) + (B->m+1)*sizeof(int);
2543     ierr            = PetscMalloc(len,&b->a);CHKERRQ(ierr);
2544     b->j            = (int*)(b->a + nz);
2545     ierr            = PetscMemzero(b->j,nz*sizeof(int));CHKERRQ(ierr);
2546     b->i            = b->j + nz;
2547     b->i[0] = 0;
2548     for (i=1; i<B->m+1; i++) {
2549       b->i[i] = b->i[i-1] + b->imax[i-1];
2550     }
2551     b->singlemalloc = PETSC_TRUE;
2552     b->freedata     = PETSC_TRUE;
2553   } else {
2554     b->freedata     = PETSC_FALSE;
2555   }
2556 
2557   /* b->ilen will count nonzeros in each row so far. */
2558   ierr = PetscMalloc((B->m+1)*sizeof(int),&b->ilen);CHKERRQ(ierr);
2559   PetscLogObjectMemory(B,len+2*(B->m+1)*sizeof(int)+sizeof(struct _p_Mat)+sizeof(Mat_SeqAIJ));
2560   for (i=0; i<B->m; i++) { b->ilen[i] = 0;}
2561 
2562   b->nz                = 0;
2563   b->maxnz             = nz;
2564   B->info.nz_unneeded  = (double)b->maxnz;
2565   PetscFunctionReturn(0);
2566 }
2567 EXTERN_C_END
2568 
2569 /*MC
2570    MATSEQAIJ - MATSEQAIJ = "seqaij" - A matrix type to be used for sequential sparse matrices,
2571    based on compressed sparse row format.
2572 
2573    Options Database Keys:
2574 . -mat_type seqaij - sets the matrix type to "seqaij" during a call to MatSetFromOptions()
2575 
2576   Level: beginner
2577 
2578 .seealso: MatCreateSeqAIJ(), MatSetFromOptions(), MatSetType(), MatCreate(), MatType
2579 M*/
2580 
2581 EXTERN_C_BEGIN
2582 #undef __FUNCT__
2583 #define __FUNCT__ "MatCreate_SeqAIJ"
2584 int MatCreate_SeqAIJ(Mat B)
2585 {
2586   Mat_SeqAIJ *b;
2587   int        ierr,size;
2588 
2589   PetscFunctionBegin;
2590   ierr = MPI_Comm_size(B->comm,&size);CHKERRQ(ierr);
2591   if (size > 1) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Comm must be of size 1");
2592 
2593   B->m = B->M = PetscMax(B->m,B->M);
2594   B->n = B->N = PetscMax(B->n,B->N);
2595 
2596   ierr = PetscNew(Mat_SeqAIJ,&b);CHKERRQ(ierr);
2597   B->data             = (void*)b;
2598   ierr = PetscMemzero(b,sizeof(Mat_SeqAIJ));CHKERRQ(ierr);
2599   ierr = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
2600   B->factor           = 0;
2601   B->lupivotthreshold = 1.0;
2602   B->mapping          = 0;
2603   ierr = PetscOptionsGetReal(B->prefix,"-mat_lu_pivotthreshold",&B->lupivotthreshold,PETSC_NULL);CHKERRQ(ierr);
2604   ierr = PetscOptionsHasName(B->prefix,"-pc_ilu_preserve_row_sums",&b->ilu_preserve_row_sums);CHKERRQ(ierr);
2605   b->row              = 0;
2606   b->col              = 0;
2607   b->icol             = 0;
2608   b->reallocs         = 0;
2609 
2610   ierr = PetscMapCreateMPI(B->comm,B->m,B->m,&B->rmap);CHKERRQ(ierr);
2611   ierr = PetscMapCreateMPI(B->comm,B->n,B->n,&B->cmap);CHKERRQ(ierr);
2612 
2613   b->sorted            = PETSC_FALSE;
2614   b->ignorezeroentries = PETSC_FALSE;
2615   b->roworiented       = PETSC_TRUE;
2616   b->nonew             = 0;
2617   b->diag              = 0;
2618   b->solve_work        = 0;
2619   B->spptr             = 0;
2620   b->inode.use         = PETSC_TRUE;
2621   b->inode.node_count  = 0;
2622   b->inode.size        = 0;
2623   b->inode.limit       = 5;
2624   b->inode.max_limit   = 5;
2625   b->saved_values      = 0;
2626   b->idiag             = 0;
2627   b->ssor              = 0;
2628   b->keepzeroedrows    = PETSC_FALSE;
2629   b->xtoy              = 0;
2630   b->XtoY              = 0;
2631 
2632   ierr = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJ);CHKERRQ(ierr);
2633 
2634   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatSeqAIJSetColumnIndices_C",
2635                                      "MatSeqAIJSetColumnIndices_SeqAIJ",
2636                                      MatSeqAIJSetColumnIndices_SeqAIJ);CHKERRQ(ierr);
2637   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatStoreValues_C",
2638                                      "MatStoreValues_SeqAIJ",
2639                                      MatStoreValues_SeqAIJ);CHKERRQ(ierr);
2640   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatRetrieveValues_C",
2641                                      "MatRetrieveValues_SeqAIJ",
2642                                      MatRetrieveValues_SeqAIJ);CHKERRQ(ierr);
2643   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_seqaij_seqsbaij_C",
2644                                      "MatConvert_SeqAIJ_SeqSBAIJ",
2645                                       MatConvert_SeqAIJ_SeqSBAIJ);CHKERRQ(ierr);
2646   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_seqaij_seqbaij_C",
2647                                      "MatConvert_SeqAIJ_SeqBAIJ",
2648                                       MatConvert_SeqAIJ_SeqBAIJ);CHKERRQ(ierr);
2649   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatIsTranspose_C",
2650                                      "MatIsTranspose_SeqAIJ",
2651                                       MatIsTranspose_SeqAIJ);CHKERRQ(ierr);
2652   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatSeqAIJSetPreallocation_C",
2653                                      "MatSeqAIJSetPreallocation_SeqAIJ",
2654                                       MatSeqAIJSetPreallocation_SeqAIJ);CHKERRQ(ierr);
2655   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatReorderForNonzeroDiagonal_C",
2656                                      "MatReorderForNonzeroDiagonal_SeqAIJ",
2657                                       MatReorderForNonzeroDiagonal_SeqAIJ);CHKERRQ(ierr);
2658   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatAdjustForInodes_C",
2659                                      "MatAdjustForInodes_SeqAIJ",
2660                                       MatAdjustForInodes_SeqAIJ);CHKERRQ(ierr);
2661   ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatSeqAIJGetInodeSizes_C",
2662                                      "MatSeqAIJGetInodeSizes_SeqAIJ",
2663                                       MatSeqAIJGetInodeSizes_SeqAIJ);CHKERRQ(ierr);
2664   ierr = RegisterApplyPtAPRoutines_Private(B);CHKERRQ(ierr);
2665   PetscFunctionReturn(0);
2666 }
2667 EXTERN_C_END
2668 
2669 #undef __FUNCT__
2670 #define __FUNCT__ "MatDuplicate_SeqAIJ"
2671 int MatDuplicate_SeqAIJ(Mat A,MatDuplicateOption cpvalues,Mat *B)
2672 {
2673   Mat        C;
2674   Mat_SeqAIJ *c,*a = (Mat_SeqAIJ*)A->data;
2675   int        i,m = A->m,ierr;
2676   size_t     len;
2677 
2678   PetscFunctionBegin;
2679   *B = 0;
2680   ierr = MatCreate(A->comm,A->m,A->n,A->m,A->n,&C);CHKERRQ(ierr);
2681   ierr = MatSetType(C,A->type_name);CHKERRQ(ierr);
2682   ierr = PetscMemcpy(C->ops,A->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2683 
2684   c    = (Mat_SeqAIJ*)C->data;
2685 
2686   C->factor         = A->factor;
2687   c->row            = 0;
2688   c->col            = 0;
2689   c->icol           = 0;
2690   c->keepzeroedrows = a->keepzeroedrows;
2691   C->assembled      = PETSC_TRUE;
2692 
2693   C->M          = A->m;
2694   C->N          = A->n;
2695 
2696   ierr = PetscMalloc((m+1)*sizeof(int),&c->imax);CHKERRQ(ierr);
2697   ierr = PetscMalloc((m+1)*sizeof(int),&c->ilen);CHKERRQ(ierr);
2698   for (i=0; i<m; i++) {
2699     c->imax[i] = a->imax[i];
2700     c->ilen[i] = a->ilen[i];
2701   }
2702 
2703   /* allocate the matrix space */
2704   c->singlemalloc = PETSC_TRUE;
2705   len   = ((size_t) (m+1))*sizeof(int)+(a->i[m])*(sizeof(PetscScalar)+sizeof(int));
2706   ierr  = PetscMalloc(len,&c->a);CHKERRQ(ierr);
2707   c->j  = (int*)(c->a + a->i[m] );
2708   c->i  = c->j + a->i[m];
2709   ierr = PetscMemcpy(c->i,a->i,(m+1)*sizeof(int));CHKERRQ(ierr);
2710   if (m > 0) {
2711     ierr = PetscMemcpy(c->j,a->j,(a->i[m])*sizeof(int));CHKERRQ(ierr);
2712     if (cpvalues == MAT_COPY_VALUES) {
2713       ierr = PetscMemcpy(c->a,a->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
2714     } else {
2715       ierr = PetscMemzero(c->a,(a->i[m])*sizeof(PetscScalar));CHKERRQ(ierr);
2716     }
2717   }
2718 
2719   PetscLogObjectMemory(C,len+2*(m+1)*sizeof(int)+sizeof(struct _p_Mat)+sizeof(Mat_SeqAIJ));
2720   c->sorted      = a->sorted;
2721   c->roworiented = a->roworiented;
2722   c->nonew       = a->nonew;
2723   c->ilu_preserve_row_sums = a->ilu_preserve_row_sums;
2724   c->saved_values = 0;
2725   c->idiag        = 0;
2726   c->ssor         = 0;
2727   c->ignorezeroentries = a->ignorezeroentries;
2728   c->freedata     = PETSC_TRUE;
2729 
2730   if (a->diag) {
2731     ierr = PetscMalloc((m+1)*sizeof(int),&c->diag);CHKERRQ(ierr);
2732     PetscLogObjectMemory(C,(m+1)*sizeof(int));
2733     for (i=0; i<m; i++) {
2734       c->diag[i] = a->diag[i];
2735     }
2736   } else c->diag        = 0;
2737   c->inode.use          = a->inode.use;
2738   c->inode.limit        = a->inode.limit;
2739   c->inode.max_limit    = a->inode.max_limit;
2740   if (a->inode.size){
2741     ierr                = PetscMalloc((m+1)*sizeof(int),&c->inode.size);CHKERRQ(ierr);
2742     c->inode.node_count = a->inode.node_count;
2743     ierr                = PetscMemcpy(c->inode.size,a->inode.size,(m+1)*sizeof(int));CHKERRQ(ierr);
2744   } else {
2745     c->inode.size       = 0;
2746     c->inode.node_count = 0;
2747   }
2748   c->nz                 = a->nz;
2749   c->maxnz              = a->maxnz;
2750   c->solve_work         = 0;
2751   C->preallocated       = PETSC_TRUE;
2752 
2753   *B = C;
2754   ierr = PetscFListDuplicate(A->qlist,&C->qlist);CHKERRQ(ierr);
2755   PetscFunctionReturn(0);
2756 }
2757 
2758 #undef __FUNCT__
2759 #define __FUNCT__ "MatLoad_SeqAIJ"
2760 int MatLoad_SeqAIJ(PetscViewer viewer,const MatType type,Mat *A)
2761 {
2762   Mat_SeqAIJ   *a;
2763   Mat          B;
2764   int          i,nz,ierr,fd,header[4],size,*rowlengths = 0,M,N;
2765   MPI_Comm     comm;
2766 
2767   PetscFunctionBegin;
2768   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2769   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2770   if (size > 1) SETERRQ(PETSC_ERR_ARG_SIZ,"view must have one processor");
2771   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2772   ierr = PetscBinaryRead(fd,header,4,PETSC_INT);CHKERRQ(ierr);
2773   if (header[0] != MAT_FILE_COOKIE) SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"not matrix object in file");
2774   M = header[1]; N = header[2]; nz = header[3];
2775 
2776   if (nz < 0) {
2777     SETERRQ(PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as SeqAIJ");
2778   }
2779 
2780   /* read in row lengths */
2781   ierr = PetscMalloc(M*sizeof(int),&rowlengths);CHKERRQ(ierr);
2782   ierr = PetscBinaryRead(fd,rowlengths,M,PETSC_INT);CHKERRQ(ierr);
2783 
2784   /* create our matrix */
2785   ierr = MatCreate(comm,PETSC_DECIDE,PETSC_DECIDE,M,N,&B);CHKERRQ(ierr);
2786   ierr = MatSetType(B,type);CHKERRQ(ierr);
2787   ierr = MatSeqAIJSetPreallocation(B,0,rowlengths);CHKERRQ(ierr);
2788   a = (Mat_SeqAIJ*)B->data;
2789 
2790   /* read in column indices and adjust for Fortran indexing*/
2791   ierr = PetscBinaryRead(fd,a->j,nz,PETSC_INT);CHKERRQ(ierr);
2792 
2793   /* read in nonzero values */
2794   ierr = PetscBinaryRead(fd,a->a,nz,PETSC_SCALAR);CHKERRQ(ierr);
2795 
2796   /* set matrix "i" values */
2797   a->i[0] = 0;
2798   for (i=1; i<= M; i++) {
2799     a->i[i]      = a->i[i-1] + rowlengths[i-1];
2800     a->ilen[i-1] = rowlengths[i-1];
2801   }
2802   ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2803 
2804   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2805   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2806   *A = B;
2807   PetscFunctionReturn(0);
2808 }
2809 
2810 #undef __FUNCT__
2811 #define __FUNCT__ "MatEqual_SeqAIJ"
2812 int MatEqual_SeqAIJ(Mat A,Mat B,PetscTruth* flg)
2813 {
2814   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data,*b = (Mat_SeqAIJ *)B->data;
2815   int        ierr;
2816 
2817   PetscFunctionBegin;
2818   /* If the  matrix dimensions are not equal,or no of nonzeros */
2819   if ((A->m != B->m) || (A->n != B->n) ||(a->nz != b->nz)) {
2820     *flg = PETSC_FALSE;
2821     PetscFunctionReturn(0);
2822   }
2823 
2824   /* if the a->i are the same */
2825   ierr = PetscMemcmp(a->i,b->i,(A->m+1)*sizeof(int),flg);CHKERRQ(ierr);
2826   if (*flg == PETSC_FALSE) PetscFunctionReturn(0);
2827 
2828   /* if a->j are the same */
2829   ierr = PetscMemcmp(a->j,b->j,(a->nz)*sizeof(int),flg);CHKERRQ(ierr);
2830   if (*flg == PETSC_FALSE) PetscFunctionReturn(0);
2831 
2832   /* if a->a are the same */
2833   ierr = PetscMemcmp(a->a,b->a,(a->nz)*sizeof(PetscScalar),flg);CHKERRQ(ierr);
2834 
2835   PetscFunctionReturn(0);
2836 
2837 }
2838 
2839 #undef __FUNCT__
2840 #define __FUNCT__ "MatCreateSeqAIJWithArrays"
2841 /*@C
2842      MatCreateSeqAIJWithArrays - Creates an sequential AIJ matrix using matrix elements (in CSR format)
2843               provided by the user.
2844 
2845       Coolective on MPI_Comm
2846 
2847    Input Parameters:
2848 +   comm - must be an MPI communicator of size 1
2849 .   m - number of rows
2850 .   n - number of columns
2851 .   i - row indices
2852 .   j - column indices
2853 -   a - matrix values
2854 
2855    Output Parameter:
2856 .   mat - the matrix
2857 
2858    Level: intermediate
2859 
2860    Notes:
2861        The i, j, and a arrays are not copied by this routine, the user must free these arrays
2862     once the matrix is destroyed
2863 
2864        You cannot set new nonzero locations into this matrix, that will generate an error.
2865 
2866        The i and j indices are 0 based
2867 
2868 .seealso: MatCreate(), MatCreateMPIAIJ(), MatCreateSeqAIJ()
2869 
2870 @*/
2871 int MatCreateSeqAIJWithArrays(MPI_Comm comm,int m,int n,int* i,int*j,PetscScalar *a,Mat *mat)
2872 {
2873   int        ierr,ii;
2874   Mat_SeqAIJ *aij;
2875 
2876   PetscFunctionBegin;
2877   ierr = MatCreate(comm,m,n,m,n,mat);CHKERRQ(ierr);
2878   ierr = MatSetType(*mat,MATSEQAIJ);CHKERRQ(ierr);
2879   ierr = MatSeqAIJSetPreallocation(*mat,SKIP_ALLOCATION,0);CHKERRQ(ierr);
2880   aij  = (Mat_SeqAIJ*)(*mat)->data;
2881 
2882   if (i[0] != 0) {
2883     SETERRQ(1,"i (row indices) must start with 0");
2884   }
2885   aij->i = i;
2886   aij->j = j;
2887   aij->a = a;
2888   aij->singlemalloc = PETSC_FALSE;
2889   aij->nonew        = -1;             /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
2890   aij->freedata     = PETSC_FALSE;
2891 
2892   for (ii=0; ii<m; ii++) {
2893     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
2894 #if defined(PETSC_USE_BOPT_g)
2895     if (i[ii+1] - i[ii] < 0) SETERRQ2(1,"Negative row length in i (row indices) row = %d length = %d",ii,i[ii+1] - i[ii]);
2896 #endif
2897   }
2898 #if defined(PETSC_USE_BOPT_g)
2899   for (ii=0; ii<aij->i[m]; ii++) {
2900     if (j[ii] < 0) SETERRQ2(1,"Negative column index at location = %d index = %d",ii,j[ii]);
2901     if (j[ii] > n - 1) SETERRQ2(1,"Column index to large at location = %d index = %d",ii,j[ii]);
2902   }
2903 #endif
2904 
2905   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2906   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2907   PetscFunctionReturn(0);
2908 }
2909 
2910 #undef __FUNCT__
2911 #define __FUNCT__ "MatSetColoring_SeqAIJ"
2912 int MatSetColoring_SeqAIJ(Mat A,ISColoring coloring)
2913 {
2914   int        ierr;
2915   Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2916 
2917   PetscFunctionBegin;
2918   if (coloring->ctype == IS_COLORING_LOCAL) {
2919     ierr        = ISColoringReference(coloring);CHKERRQ(ierr);
2920     a->coloring = coloring;
2921   } else if (coloring->ctype == IS_COLORING_GHOSTED) {
2922     int             i,*larray;
2923     ISColoring      ocoloring;
2924     ISColoringValue *colors;
2925 
2926     /* set coloring for diagonal portion */
2927     ierr = PetscMalloc((A->n+1)*sizeof(int),&larray);CHKERRQ(ierr);
2928     for (i=0; i<A->n; i++) {
2929       larray[i] = i;
2930     }
2931     ierr = ISGlobalToLocalMappingApply(A->mapping,IS_GTOLM_MASK,A->n,larray,PETSC_NULL,larray);CHKERRQ(ierr);
2932     ierr = PetscMalloc((A->n+1)*sizeof(ISColoringValue),&colors);CHKERRQ(ierr);
2933     for (i=0; i<A->n; i++) {
2934       colors[i] = coloring->colors[larray[i]];
2935     }
2936     ierr = PetscFree(larray);CHKERRQ(ierr);
2937     ierr = ISColoringCreate(PETSC_COMM_SELF,A->n,colors,&ocoloring);CHKERRQ(ierr);
2938     a->coloring = ocoloring;
2939   }
2940   PetscFunctionReturn(0);
2941 }
2942 
2943 #if defined(PETSC_HAVE_ADIC) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_SINGLE)
2944 EXTERN_C_BEGIN
2945 #include "adic/ad_utils.h"
2946 EXTERN_C_END
2947 
2948 #undef __FUNCT__
2949 #define __FUNCT__ "MatSetValuesAdic_SeqAIJ"
2950 int MatSetValuesAdic_SeqAIJ(Mat A,void *advalues)
2951 {
2952   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
2953   int             m = A->m,*ii = a->i,*jj = a->j,nz,i,j,nlen;
2954   PetscScalar     *v = a->a,*values = ((PetscScalar*)advalues)+1;
2955   ISColoringValue *color;
2956 
2957   PetscFunctionBegin;
2958   if (!a->coloring) SETERRQ(1,"Coloring not set for matrix");
2959   nlen  = PetscADGetDerivTypeSize()/sizeof(PetscScalar);
2960   color = a->coloring->colors;
2961   /* loop over rows */
2962   for (i=0; i<m; i++) {
2963     nz = ii[i+1] - ii[i];
2964     /* loop over columns putting computed value into matrix */
2965     for (j=0; j<nz; j++) {
2966       *v++ = values[color[*jj++]];
2967     }
2968     values += nlen; /* jump to next row of derivatives */
2969   }
2970   PetscFunctionReturn(0);
2971 }
2972 
2973 #else
2974 
2975 #undef __FUNCT__
2976 #define __FUNCT__ "MatSetValuesAdic_SeqAIJ"
2977 int MatSetValuesAdic_SeqAIJ(Mat A,void *advalues)
2978 {
2979   PetscFunctionBegin;
2980   SETERRQ(1,"PETSc installed without ADIC");
2981 }
2982 
2983 #endif
2984 
2985 #undef __FUNCT__
2986 #define __FUNCT__ "MatSetValuesAdifor_SeqAIJ"
2987 int MatSetValuesAdifor_SeqAIJ(Mat A,int nl,void *advalues)
2988 {
2989   Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
2990   int             m = A->m,*ii = a->i,*jj = a->j,nz,i,j;
2991   PetscScalar     *v = a->a,*values = (PetscScalar *)advalues;
2992   ISColoringValue *color;
2993 
2994   PetscFunctionBegin;
2995   if (!a->coloring) SETERRQ(1,"Coloring not set for matrix");
2996   color = a->coloring->colors;
2997   /* loop over rows */
2998   for (i=0; i<m; i++) {
2999     nz = ii[i+1] - ii[i];
3000     /* loop over columns putting computed value into matrix */
3001     for (j=0; j<nz; j++) {
3002       *v++ = values[color[*jj++]];
3003     }
3004     values += nl; /* jump to next row of derivatives */
3005   }
3006   PetscFunctionReturn(0);
3007 }
3008 
3009