xref: /petsc/src/mat/impls/aij/seq/aijfact.c (revision cf23486d5c98bd4e00855d1002c8d80fadf08e91)
1 #ifdef PETSC_RCS_HEADER
2 static char vcid[] = "$Id: aijfact.c,v 1.120 1999/06/30 23:51:02 balay Exp bsmith $";
3 #endif
4 
5 #include "src/mat/impls/aij/seq/aij.h"
6 #include "src/vec/vecimpl.h"
7 #include "src/inline/dot.h"
8 
9 #undef __FUNC__
10 #define __FUNC__ "MatOrdering_Flow_SeqAIJ"
11 int MatOrdering_Flow_SeqAIJ(Mat mat,MatOrderingType type,IS *irow,IS *icol)
12 {
13   PetscFunctionBegin;
14 
15   SETERRQ(PETSC_ERR_SUP,0,"Code not written");
16 #if !defined(PETSC_USE_DEBUG)
17   PetscFunctionReturn(0);
18 #endif
19 }
20 
21 /*
22     Factorization code for AIJ format.
23 */
24 #undef __FUNC__
25 #define __FUNC__ "MatLUFactorSymbolic_SeqAIJ"
26 int MatLUFactorSymbolic_SeqAIJ(Mat A,IS isrow,IS iscol,double f,Mat *B)
27 {
28   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data, *b;
29   IS         isicol;
30   int        *r,*ic, ierr, i, n = a->m, *ai = a->i, *aj = a->j;
31   int        *ainew,*ajnew, jmax,*fill, *ajtmp, nz,shift = a->indexshift;
32   int        *idnew, idx, row,m,fm, nnz, nzi, realloc = 0,nzbd,*im;
33 
34   PetscFunctionBegin;
35   PetscValidHeaderSpecific(isrow,IS_COOKIE);
36   PetscValidHeaderSpecific(iscol,IS_COOKIE);
37 
38   ierr = ISInvertPermutation(iscol,&isicol);CHKERRQ(ierr);
39   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
40   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
41 
42   /* get new row pointers */
43   ainew    = (int *) PetscMalloc( (n+1)*sizeof(int) );CHKPTRQ(ainew);
44   ainew[0] = -shift;
45   /* don't know how many column pointers are needed so estimate */
46   jmax  = (int) (f*ai[n]+(!shift));
47   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) );CHKPTRQ(ajnew);
48   /* fill is a linked list of nonzeros in active row */
49   fill = (int *) PetscMalloc( (2*n+1)*sizeof(int));CHKPTRQ(fill);
50   im   = fill + n + 1;
51   /* idnew is location of diagonal in factor */
52   idnew    = (int *) PetscMalloc( (n+1)*sizeof(int));CHKPTRQ(idnew);
53   idnew[0] = -shift;
54 
55   for ( i=0; i<n; i++ ) {
56     /* first copy previous fill into linked list */
57     nnz     = nz    = ai[r[i]+1] - ai[r[i]];
58     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
59     ajtmp   = aj + ai[r[i]] + shift;
60     fill[n] = n;
61     while (nz--) {
62       fm  = n;
63       idx = ic[*ajtmp++ + shift];
64       do {
65         m  = fm;
66         fm = fill[m];
67       } while (fm < idx);
68       fill[m]   = idx;
69       fill[idx] = fm;
70     }
71     row = fill[n];
72     while ( row < i ) {
73       ajtmp = ajnew + idnew[row] + (!shift);
74       nzbd  = 1 + idnew[row] - ainew[row];
75       nz    = im[row] - nzbd;
76       fm    = row;
77       while (nz-- > 0) {
78         idx = *ajtmp++ + shift;
79         nzbd++;
80         if (idx == i) im[row] = nzbd;
81         do {
82           m  = fm;
83           fm = fill[m];
84         } while (fm < idx);
85         if (fm != idx) {
86           fill[m]   = idx;
87           fill[idx] = fm;
88           fm        = idx;
89           nnz++;
90         }
91       }
92       row = fill[row];
93     }
94     /* copy new filled row into permanent storage */
95     ainew[i+1] = ainew[i] + nnz;
96     if (ainew[i+1] > jmax) {
97 
98       /* estimate how much additional space we will need */
99       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
100       /* just double the memory each time */
101       int maxadd = jmax;
102       /* maxadd = (int) ((f*(ai[n]+(!shift))*(n-i+5))/n); */
103       if (maxadd < nnz) maxadd = (n-i)*(nnz+1);
104       jmax += maxadd;
105 
106       /* allocate a longer ajnew */
107       ajtmp = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(ajtmp);
108       ierr  = PetscMemcpy(ajtmp,ajnew,(ainew[i]+shift)*sizeof(int));CHKERRQ(ierr);
109       ierr = PetscFree(ajnew);CHKERRQ(ierr);
110       ajnew = ajtmp;
111       realloc++; /* count how many times we realloc */
112     }
113     ajtmp = ajnew + ainew[i] + shift;
114     fm    = fill[n];
115     nzi   = 0;
116     im[i] = nnz;
117     while (nnz--) {
118       if (fm < i) nzi++;
119       *ajtmp++ = fm - shift;
120       fm       = fill[fm];
121     }
122     idnew[i] = ainew[i] + nzi;
123   }
124   if (ai[n] != 0) {
125     double af = ((double)ainew[n])/((double)ai[n]);
126     PLogInfo(A,"MatLUFactorSymbolic_SeqAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
127              realloc,f,af);
128     PLogInfo(A,"MatLUFactorSymbolic_SeqAIJ:Run with -pc_lu_fill %g or use \n",af);
129     PLogInfo(A,"MatLUFactorSymbolic_SeqAIJ:PCLUSetFill(pc,%g);\n",af);
130     PLogInfo(A,"MatLUFactorSymbolic_SeqAIJ:for best performance.\n");
131   } else {
132     PLogInfo(A,"MatLUFactorSymbolic_SeqAIJ: Empty matrix\n");
133   }
134 
135   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
136   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
137 
138   ierr = PetscFree(fill);CHKERRQ(ierr);
139 
140   /* put together the new matrix */
141   ierr = MatCreateSeqAIJ(A->comm,n,n,0,PETSC_NULL,B);CHKERRQ(ierr);
142   PLogObjectParent(*B,isicol);
143   b = (Mat_SeqAIJ *) (*B)->data;
144   ierr = PetscFree(b->imax);CHKERRQ(ierr);
145   b->singlemalloc = 0;
146   /* the next line frees the default space generated by the Create() */
147   ierr = PetscFree(b->a);CHKERRQ(ierr);
148   ierr = PetscFree(b->ilen);CHKERRQ(ierr);
149   b->a          = (Scalar *) PetscMalloc((ainew[n]+shift+1)*sizeof(Scalar));CHKPTRQ(b->a);
150   b->j          = ajnew;
151   b->i          = ainew;
152   b->diag       = idnew;
153   b->ilen       = 0;
154   b->imax       = 0;
155   b->row        = isrow;
156   b->col        = iscol;
157   b->icol       = isicol;
158   b->solve_work = (Scalar *) PetscMalloc( (n+1)*sizeof(Scalar));CHKPTRQ(b->solve_work);
159   /* In b structure:  Free imax, ilen, old a, old j.
160      Allocate idnew, solve_work, new a, new j */
161   PLogObjectMemory(*B,(ainew[n]+shift-n)*(sizeof(int)+sizeof(Scalar)));
162   b->maxnz = b->nz = ainew[n] + shift;
163 
164   (*B)->factor                 =  FACTOR_LU;;
165   (*B)->info.factor_mallocs    = realloc;
166   (*B)->info.fill_ratio_given  = f;
167   (*B)->ops->lufactornumeric   =  A->ops->lufactornumeric; /* Use Inode variant if A has inodes */
168 
169   if (ai[n] != 0) {
170     (*B)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[n]);
171   } else {
172     (*B)->info.fill_ratio_needed = 0.0;
173   }
174   PetscFunctionReturn(0);
175 }
176 /* ----------------------------------------------------------- */
177 int Mat_AIJ_CheckInode(Mat);
178 
179 #undef __FUNC__
180 #define __FUNC__ "MatLUFactorNumeric_SeqAIJ"
181 int MatLUFactorNumeric_SeqAIJ(Mat A,Mat *B)
182 {
183   Mat        C = *B;
184   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data, *b = (Mat_SeqAIJ *)C->data;
185   IS         isrow = b->row, isicol = b->icol;
186   int        *r,*ic, ierr, i, j, n = a->m, *ai = b->i, *aj = b->j;
187   int        *ajtmpold, *ajtmp, nz, row, *ics, shift = a->indexshift;
188   int        *diag_offset = b->diag,diag,k;
189   int        preserve_row_sums = (int) a->ilu_preserve_row_sums;
190   register   int    *pj;
191   Scalar     *rtmp,*v, *pc, multiplier,sum,inner_sum,*rowsums = 0;
192   double     ssum;
193   register   Scalar *pv, *rtmps,*u_values;
194 
195   PetscFunctionBegin;
196 
197   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
198   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
199   rtmp  = (Scalar *) PetscMalloc( (n+1)*sizeof(Scalar) );CHKPTRQ(rtmp);
200   ierr  = PetscMemzero(rtmp,(n+1)*sizeof(Scalar));CHKERRQ(ierr);
201   rtmps = rtmp + shift; ics = ic + shift;
202 
203   /* precalculate row sums */
204   if (preserve_row_sums) {
205     rowsums = (Scalar *) PetscMalloc( n*sizeof(Scalar) );CHKPTRQ(rowsums);
206     for ( i=0; i<n; i++ ) {
207       nz  = a->i[r[i]+1] - a->i[r[i]];
208       v   = a->a + a->i[r[i]] + shift;
209       sum = 0.0;
210       for ( j=0; j<nz; j++ ) sum += v[j];
211       rowsums[i] = sum;
212     }
213   }
214 
215   for ( i=0; i<n; i++ ) {
216     nz    = ai[i+1] - ai[i];
217     ajtmp = aj + ai[i] + shift;
218     for  ( j=0; j<nz; j++ ) rtmps[ajtmp[j]] = 0.0;
219 
220     /* load in initial (unfactored row) */
221     nz       = a->i[r[i]+1] - a->i[r[i]];
222     ajtmpold = a->j + a->i[r[i]] + shift;
223     v        = a->a + a->i[r[i]] + shift;
224     for ( j=0; j<nz; j++ ) rtmp[ics[ajtmpold[j]]] =  v[j];
225 
226     row = *ajtmp++ + shift;
227     while  (row < i ) {
228       pc = rtmp + row;
229       if (*pc != 0.0) {
230         pv         = b->a + diag_offset[row] + shift;
231         pj         = b->j + diag_offset[row] + (!shift);
232         multiplier = *pc / *pv++;
233         *pc        = multiplier;
234         nz         = ai[row+1] - diag_offset[row] - 1;
235         for (j=0; j<nz; j++) rtmps[pj[j]] -= multiplier * pv[j];
236         PLogFlops(2*nz);
237       }
238       row = *ajtmp++ + shift;
239     }
240     /* finished row so stick it into b->a */
241     pv = b->a + ai[i] + shift;
242     pj = b->j + ai[i] + shift;
243     nz = ai[i+1] - ai[i];
244     for ( j=0; j<nz; j++ ) {pv[j] = rtmps[pj[j]];}
245     diag = diag_offset[i] - ai[i];
246     /*
247           Possibly adjust diagonal entry on current row to force
248         LU matrix to have same row sum as initial matrix.
249     */
250     if (pv[diag] == 0.0) {
251       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot row %d",i);
252     }
253     if (preserve_row_sums) {
254       pj  = b->j + ai[i] + shift;
255       sum = rowsums[i];
256       for ( j=0; j<diag; j++ ) {
257         u_values  = b->a + diag_offset[pj[j]] + shift;
258         nz        = ai[pj[j]+1] - diag_offset[pj[j]];
259         inner_sum = 0.0;
260         for ( k=0; k<nz; k++ ) {
261           inner_sum += u_values[k];
262         }
263         sum -= pv[j]*inner_sum;
264 
265       }
266       nz       = ai[i+1] - diag_offset[i] - 1;
267       u_values = b->a + diag_offset[i] + 1 + shift;
268       for ( k=0; k<nz; k++ ) {
269         sum -= u_values[k];
270       }
271       ssum = PetscAbsScalar(sum/pv[diag]);
272       if (ssum < 1000. && ssum > .001) pv[diag] = sum;
273     }
274     /* check pivot entry for current row */
275   }
276 
277   /* invert diagonal entries for simplier triangular solves */
278   for ( i=0; i<n; i++ ) {
279     b->a[diag_offset[i]+shift] = 1.0/b->a[diag_offset[i]+shift];
280   }
281 
282   if (preserve_row_sums) {ierr = PetscFree(rowsums);CHKERRQ(ierr);}
283   ierr = PetscFree(rtmp);CHKERRQ(ierr);
284   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
285   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
286   C->factor = FACTOR_LU;
287   ierr = Mat_AIJ_CheckInode(C);CHKERRQ(ierr);
288   C->assembled = PETSC_TRUE;
289   PLogFlops(b->n);
290   PetscFunctionReturn(0);
291 }
292 /* ----------------------------------------------------------- */
293 #undef __FUNC__
294 #define __FUNC__ "MatLUFactor_SeqAIJ"
295 int MatLUFactor_SeqAIJ(Mat A,IS row,IS col,double f)
296 {
297   Mat_SeqAIJ     *mat = (Mat_SeqAIJ *) A->data;
298   int            ierr;
299   Mat            C;
300   PetscOps       *Abops;
301   MatOps         Aops;
302 
303   PetscFunctionBegin;
304   ierr = MatLUFactorSymbolic(A,row,col,f,&C);CHKERRQ(ierr);
305   ierr = MatLUFactorNumeric(A,&C);CHKERRQ(ierr);
306 
307   /* free all the data structures from mat */
308   ierr = PetscFree(mat->a);CHKERRQ(ierr);
309   if (!mat->singlemalloc) {
310     ierr = PetscFree(mat->i);CHKERRQ(ierr);
311     ierr = PetscFree(mat->j);CHKERRQ(ierr);
312   }
313   if (mat->diag) {ierr = PetscFree(mat->diag);CHKERRQ(ierr);}
314   if (mat->ilen) {ierr = PetscFree(mat->ilen);CHKERRQ(ierr);}
315   if (mat->imax) {ierr = PetscFree(mat->imax);CHKERRQ(ierr);}
316   if (mat->solve_work) {ierr = PetscFree(mat->solve_work);CHKERRQ(ierr);}
317   if (mat->inode.size) {ierr = PetscFree(mat->inode.size);CHKERRQ(ierr);}
318   if (mat->icol) {ierr = ISDestroy(mat->icol);CHKERRQ(ierr);}
319   ierr = PetscFree(mat);CHKERRQ(ierr);
320 
321   ierr = MapDestroy(A->rmap);CHKERRQ(ierr);
322   ierr = MapDestroy(A->cmap);CHKERRQ(ierr);
323 
324   /*
325        This is horrible, horrible code. We need to keep the
326     A pointers for the bops and ops but copy everything
327     else from C.
328   */
329   Abops = A->bops;
330   Aops  = A->ops;
331   ierr = PetscMemcpy(A,C,sizeof(struct _p_Mat));CHKERRQ(ierr);
332   mat = (Mat_SeqAIJ *) A->data;
333   PLogObjectParent(A,mat->icol);
334 
335   A->bops  = Abops;
336   A->ops   = Aops;
337   A->qlist = 0;
338 
339   PetscHeaderDestroy(C);
340   PetscFunctionReturn(0);
341 }
342 /* ----------------------------------------------------------- */
343 #undef __FUNC__
344 #define __FUNC__ "MatSolve_SeqAIJ"
345 int MatSolve_SeqAIJ(Mat A,Vec bb, Vec xx)
346 {
347   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data;
348   IS         iscol = a->col, isrow = a->row;
349   int        *r,*c, ierr, i,  n = a->m, *vi, *ai = a->i, *aj = a->j;
350   int        nz,shift = a->indexshift,*rout,*cout;
351   Scalar     *x,*b,*tmp, *tmps, *aa = a->a, sum, *v;
352 
353   PetscFunctionBegin;
354   if (!n) PetscFunctionReturn(0);
355 
356   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
357   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
358   tmp  = a->solve_work;
359 
360   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
361   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
362 
363   /* forward solve the lower triangular */
364   tmp[0] = b[*r++];
365   tmps   = tmp + shift;
366   for ( i=1; i<n; i++ ) {
367     v   = aa + ai[i] + shift;
368     vi  = aj + ai[i] + shift;
369     nz  = a->diag[i] - ai[i];
370     sum = b[*r++];
371     while (nz--) sum -= *v++ * tmps[*vi++];
372     tmp[i] = sum;
373   }
374 
375   /* backward solve the upper triangular */
376   for ( i=n-1; i>=0; i-- ){
377     v   = aa + a->diag[i] + (!shift);
378     vi  = aj + a->diag[i] + (!shift);
379     nz  = ai[i+1] - a->diag[i] - 1;
380     sum = tmp[i];
381     while (nz--) sum -= *v++ * tmps[*vi++];
382     x[*c--] = tmp[i] = sum*aa[a->diag[i]+shift];
383   }
384 
385   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
386   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
387   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
388   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
389   PLogFlops(2*a->nz - a->n);
390   PetscFunctionReturn(0);
391 }
392 
393 /* ----------------------------------------------------------- */
394 #undef __FUNC__
395 #define __FUNC__ "MatSolve_SeqAIJ_NaturalOrdering"
396 int MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb, Vec xx)
397 {
398   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data;
399   int        n = a->m, *ai = a->i, *aj = a->j, *adiag = a->diag,ierr;
400   Scalar     *x,*b, *aa = a->a, sum;
401 #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
402   int        adiag_i,i,*vi,nz,ai_i;
403   Scalar     *v;
404 #endif
405 
406   PetscFunctionBegin;
407   if (!n) PetscFunctionReturn(0);
408   if (a->indexshift) {
409      ierr = MatSolve_SeqAIJ(A,bb,xx);CHKERRQ(ierr);
410      PetscFunctionReturn(0);
411   }
412 
413   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
414   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
415 
416 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
417   fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
418 #else
419   /* forward solve the lower triangular */
420   x[0] = b[0];
421   for ( i=1; i<n; i++ ) {
422     ai_i = ai[i];
423     v    = aa + ai_i;
424     vi   = aj + ai_i;
425     nz   = adiag[i] - ai_i;
426     sum  = b[i];
427     while (nz--) sum -= *v++ * x[*vi++];
428     x[i] = sum;
429   }
430 
431   /* backward solve the upper triangular */
432   for ( i=n-1; i>=0; i-- ){
433     adiag_i = adiag[i];
434     v       = aa + adiag_i + 1;
435     vi      = aj + adiag_i + 1;
436     nz      = ai[i+1] - adiag_i - 1;
437     sum     = x[i];
438     while (nz--) sum -= *v++ * x[*vi++];
439     x[i]    = sum*aa[adiag_i];
440   }
441 #endif
442   PLogFlops(2*a->nz - a->n);
443   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
444   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
445   PetscFunctionReturn(0);
446 }
447 
448 #undef __FUNC__
449 #define __FUNC__ "MatSolveAdd_SeqAIJ"
450 int MatSolveAdd_SeqAIJ(Mat A,Vec bb, Vec yy, Vec xx)
451 {
452   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data;
453   IS         iscol = a->col, isrow = a->row;
454   int        *r,*c, ierr, i,  n = a->m, *vi, *ai = a->i, *aj = a->j;
455   int        nz, shift = a->indexshift,*rout,*cout;
456   Scalar     *x,*b,*tmp, *aa = a->a, sum, *v;
457 
458   PetscFunctionBegin;
459   if (yy != xx) {ierr = VecCopy(yy,xx);CHKERRQ(ierr);}
460 
461   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
462   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
463   tmp  = a->solve_work;
464 
465   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
466   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
467 
468   /* forward solve the lower triangular */
469   tmp[0] = b[*r++];
470   for ( i=1; i<n; i++ ) {
471     v   = aa + ai[i] + shift;
472     vi  = aj + ai[i] + shift;
473     nz  = a->diag[i] - ai[i];
474     sum = b[*r++];
475     while (nz--) sum -= *v++ * tmp[*vi++ + shift];
476     tmp[i] = sum;
477   }
478 
479   /* backward solve the upper triangular */
480   for ( i=n-1; i>=0; i-- ){
481     v   = aa + a->diag[i] + (!shift);
482     vi  = aj + a->diag[i] + (!shift);
483     nz  = ai[i+1] - a->diag[i] - 1;
484     sum = tmp[i];
485     while (nz--) sum -= *v++ * tmp[*vi++ + shift];
486     tmp[i] = sum*aa[a->diag[i]+shift];
487     x[*c--] += tmp[i];
488   }
489 
490   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
491   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
492   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
493   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
494   PLogFlops(2*a->nz);
495 
496   PetscFunctionReturn(0);
497 }
498 /* -------------------------------------------------------------------*/
499 #undef __FUNC__
500 #define __FUNC__ "MatSolveTrans_SeqAIJ"
501 int MatSolveTrans_SeqAIJ(Mat A,Vec bb, Vec xx)
502 {
503   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data;
504   IS         iscol = a->col, isrow = a->row;
505   int        *r,*c, ierr, i, n = a->m, *vi, *ai = a->i, *aj = a->j;
506   int        nz,shift = a->indexshift,*rout,*cout;
507   Scalar     *x,*b,*tmp, *aa = a->a, *v;
508 
509   PetscFunctionBegin;
510   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
511   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
512   tmp  = a->solve_work;
513 
514   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
515   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
516 
517   /* copy the b into temp work space according to permutation */
518   for ( i=0; i<n; i++ ) tmp[i] = b[c[i]];
519 
520   /* forward solve the U^T */
521   for ( i=0; i<n; i++ ) {
522     v   = aa + a->diag[i] + shift;
523     vi  = aj + a->diag[i] + (!shift);
524     nz  = ai[i+1] - a->diag[i] - 1;
525     tmp[i] *= *v++;
526     while (nz--) {
527       tmp[*vi++ + shift] -= (*v++)*tmp[i];
528     }
529   }
530 
531   /* backward solve the L^T */
532   for ( i=n-1; i>=0; i-- ){
533     v   = aa + a->diag[i] - 1 + shift;
534     vi  = aj + a->diag[i] - 1 + shift;
535     nz  = a->diag[i] - ai[i];
536     while (nz--) {
537       tmp[*vi-- + shift] -= (*v--)*tmp[i];
538     }
539   }
540 
541   /* copy tmp into x according to permutation */
542   for ( i=0; i<n; i++ ) x[r[i]] = tmp[i];
543 
544   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
545   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
546   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
547   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
548 
549   PLogFlops(2*a->nz-a->n);
550   PetscFunctionReturn(0);
551 }
552 
553 #undef __FUNC__
554 #define __FUNC__ "MatSolveTransAdd_SeqAIJ"
555 int MatSolveTransAdd_SeqAIJ(Mat A,Vec bb, Vec zz,Vec xx)
556 {
557   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data;
558   IS         iscol = a->col, isrow = a->row;
559   int        *r,*c, ierr, i, n = a->m, *vi, *ai = a->i, *aj = a->j;
560   int        nz,shift = a->indexshift, *rout, *cout;
561   Scalar     *x,*b,*tmp, *aa = a->a, *v;
562 
563   PetscFunctionBegin;
564   if (zz != xx) VecCopy(zz,xx);
565 
566   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
567   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
568   tmp = a->solve_work;
569 
570   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
571   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
572 
573   /* copy the b into temp work space according to permutation */
574   for ( i=0; i<n; i++ ) tmp[i] = b[c[i]];
575 
576   /* forward solve the U^T */
577   for ( i=0; i<n; i++ ) {
578     v   = aa + a->diag[i] + shift;
579     vi  = aj + a->diag[i] + (!shift);
580     nz  = ai[i+1] - a->diag[i] - 1;
581     tmp[i] *= *v++;
582     while (nz--) {
583       tmp[*vi++ + shift] -= (*v++)*tmp[i];
584     }
585   }
586 
587   /* backward solve the L^T */
588   for ( i=n-1; i>=0; i-- ){
589     v   = aa + a->diag[i] - 1 + shift;
590     vi  = aj + a->diag[i] - 1 + shift;
591     nz  = a->diag[i] - ai[i];
592     while (nz--) {
593       tmp[*vi-- + shift] -= (*v--)*tmp[i];
594     }
595   }
596 
597   /* copy tmp into x according to permutation */
598   for ( i=0; i<n; i++ ) x[r[i]] += tmp[i];
599 
600   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
601   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
602   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
603   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
604 
605   PLogFlops(2*a->nz);
606   PetscFunctionReturn(0);
607 }
608 /* ----------------------------------------------------------------*/
609 extern int MatMissingDiag_SeqAIJ(Mat);
610 
611 #undef __FUNC__
612 #define __FUNC__ "MatILUFactorSymbolic_SeqAIJ"
613 int MatILUFactorSymbolic_SeqAIJ(Mat A,IS isrow,IS iscol,MatILUInfo *info,Mat *fact)
614 {
615   Mat_SeqAIJ *a = (Mat_SeqAIJ *) A->data, *b;
616   IS         isicol;
617   int        *r,*ic, ierr, prow, n = a->m, *ai = a->i, *aj = a->j;
618   int        *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
619   int        *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0, dcount = 0;
620   int        incrlev,nnz,i,shift = a->indexshift,levels,diagonal_fill;
621   PetscTruth col_identity, row_identity;
622   double     f;
623 
624   PetscFunctionBegin;
625   if (info) {
626     f             = info->fill;
627     levels        = (int) info->levels;
628     diagonal_fill = (int) info->diagonal_fill;
629   } else {
630     f             = 1.0;
631     levels        = 0;
632     diagonal_fill = 0;
633   }
634   ierr = ISInvertPermutation(iscol,&isicol);CHKERRQ(ierr);
635 
636   /* special case that simply copies fill pattern */
637   ierr = ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
638   if (levels == 0 && row_identity && col_identity) {
639     ierr = MatDuplicate_SeqAIJ(A,MAT_DO_NOT_COPY_VALUES,fact);CHKERRQ(ierr);
640     (*fact)->factor = FACTOR_LU;
641     b               = (Mat_SeqAIJ *) (*fact)->data;
642     if (!b->diag) {
643       ierr = MatMarkDiag_SeqAIJ(*fact);CHKERRQ(ierr);
644     }
645     ierr = MatMissingDiag_SeqAIJ(*fact);CHKERRQ(ierr);
646     b->row              = isrow;
647     b->col              = iscol;
648     b->icol             = isicol;
649     b->solve_work       = (Scalar *) PetscMalloc((b->m+1)*sizeof(Scalar));CHKPTRQ(b->solve_work);
650     (*fact)->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
651     PetscFunctionReturn(0);
652   }
653 
654   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
655   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
656 
657   /* get new row pointers */
658   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) );CHKPTRQ(ainew);
659   ainew[0] = -shift;
660   /* don't know how many column pointers are needed so estimate */
661   jmax = (int) (f*(ai[n]+!shift));
662   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) );CHKPTRQ(ajnew);
663   /* ajfill is level of fill for each fill entry */
664   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) );CHKPTRQ(ajfill);
665   /* fill is a linked list of nonzeros in active row */
666   fill = (int *) PetscMalloc( (n+1)*sizeof(int));CHKPTRQ(fill);
667   /* im is level for each filled value */
668   im = (int *) PetscMalloc( (n+1)*sizeof(int));CHKPTRQ(im);
669   /* dloc is location of diagonal in factor */
670   dloc = (int *) PetscMalloc( (n+1)*sizeof(int));CHKPTRQ(dloc);
671   dloc[0]  = 0;
672   for ( prow=0; prow<n; prow++ ) {
673 
674     /* copy current row into linked list */
675     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
676     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
677     xi      = aj + ai[r[prow]] + shift;
678     fill[n]    = n;
679     fill[prow] = -1; /* marker to indicate if diagonal exists */
680     while (nz--) {
681       fm  = n;
682       idx = ic[*xi++ + shift];
683       do {
684         m  = fm;
685         fm = fill[m];
686       } while (fm < idx);
687       fill[m]   = idx;
688       fill[idx] = fm;
689       im[idx]   = 0;
690     }
691 
692     /* make sure diagonal entry is included */
693     if (diagonal_fill && fill[prow] == -1) {
694       fm = n;
695       while (fill[fm] < prow) fm = fill[fm];
696       fill[prow] = fill[fm]; /* insert diagonal into linked list */
697       fill[fm]   = prow;
698       im[prow]   = 0;
699       nzf++;
700       dcount++;
701     }
702 
703     nzi = 0;
704     row = fill[n];
705     while ( row < prow ) {
706       incrlev = im[row] + 1;
707       nz      = dloc[row];
708       xi      = ajnew  + ainew[row] + shift + nz + 1;
709       flev    = ajfill + ainew[row] + shift + nz + 1;
710       nnz     = ainew[row+1] - ainew[row] - nz - 1;
711       fm      = row;
712       while (nnz-- > 0) {
713         idx = *xi++ + shift;
714         if (*flev + incrlev > levels) {
715           flev++;
716           continue;
717         }
718         do {
719           m  = fm;
720           fm = fill[m];
721         } while (fm < idx);
722         if (fm != idx) {
723           im[idx]   = *flev + incrlev;
724           fill[m]   = idx;
725           fill[idx] = fm;
726           fm        = idx;
727           nzf++;
728         } else {
729           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
730         }
731         flev++;
732       }
733       row = fill[row];
734       nzi++;
735     }
736     /* copy new filled row into permanent storage */
737     ainew[prow+1] = ainew[prow] + nzf;
738     if (ainew[prow+1] > jmax-shift) {
739 
740       /* estimate how much additional space we will need */
741       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
742       /* just double the memory each time */
743       /*  maxadd = (int) ((f*(ai[n]+!shift)*(n-prow+5))/n); */
744       int maxadd = jmax;
745       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
746       jmax += maxadd;
747 
748       /* allocate a longer ajnew and ajfill */
749       xi     = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
750       ierr   = PetscMemcpy(xi,ajnew,(ainew[prow]+shift)*sizeof(int));CHKERRQ(ierr);
751       ierr = PetscFree(ajnew);CHKERRQ(ierr);
752       ajnew  = xi;
753       xi     = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
754       ierr   = PetscMemcpy(xi,ajfill,(ainew[prow]+shift)*sizeof(int));CHKERRQ(ierr);
755       ierr = PetscFree(ajfill);CHKERRQ(ierr);
756       ajfill = xi;
757       realloc++; /* count how many times we realloc */
758     }
759     xi          = ajnew + ainew[prow] + shift;
760     flev        = ajfill + ainew[prow] + shift;
761     dloc[prow]  = nzi;
762     fm          = fill[n];
763     while (nzf--) {
764       *xi++   = fm - shift;
765       *flev++ = im[fm];
766       fm      = fill[fm];
767     }
768     /* make sure row has diagonal entry */
769     if (ajnew[ainew[prow]+shift+dloc[prow]]+shift != prow) {
770       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,1,"Row %d has missing diagonal in factored matrix\n\
771     try running with -pc_ilu_nonzeros_along_diagonal or -pc_ilu_diagonal_fill",prow);
772     }
773   }
774   ierr = PetscFree(ajfill); CHKERRQ(ierr);
775   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
776   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
777   ierr = PetscFree(fill);CHKERRQ(ierr);
778   ierr = PetscFree(im);CHKERRQ(ierr);
779 
780   {
781     double af = ((double)ainew[n])/((double)ai[n]);
782     PLogInfo(A,"MatILUFactorSymbolic_SeqAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
783              realloc,f,af);
784     PLogInfo(A,"MatILUFactorSymbolic_SeqAIJ:Run with -pc_ilu_fill %g or use \n",af);
785     PLogInfo(A,"MatILUFactorSymbolic_SeqAIJ:PCILUSetFill(pc,%g);\n",af);
786     PLogInfo(A,"MatILUFactorSymbolic_SeqAIJ:for best performance.\n");
787     if (diagonal_fill) {
788       PLogInfo(A,"MatILUFactorSymbolic_SeqAIJ:Detected and replace %d missing diagonals",dcount);
789     }
790   }
791 
792   /* put together the new matrix */
793   ierr = MatCreateSeqAIJ(A->comm,n,n,0,PETSC_NULL,fact);CHKERRQ(ierr);
794   PLogObjectParent(*fact,isicol);
795   b = (Mat_SeqAIJ *) (*fact)->data;
796   ierr = PetscFree(b->imax);CHKERRQ(ierr);
797   b->singlemalloc = 0;
798   len = (ainew[n] + shift)*sizeof(Scalar);
799   /* the next line frees the default space generated by the Create() */
800   ierr = PetscFree(b->a);CHKERRQ(ierr);
801   ierr = PetscFree(b->ilen);CHKERRQ(ierr);
802   b->a          = (Scalar *) PetscMalloc( len+1 );CHKPTRQ(b->a);
803   b->j          = ajnew;
804   b->i          = ainew;
805   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
806   b->diag       = dloc;
807   b->ilen       = 0;
808   b->imax       = 0;
809   b->row        = isrow;
810   b->col        = iscol;
811   b->icol       = isicol;
812   b->solve_work = (Scalar *) PetscMalloc( (n+1)*sizeof(Scalar));CHKPTRQ(b->solve_work);
813   /* In b structure:  Free imax, ilen, old a, old j.
814      Allocate dloc, solve_work, new a, new j */
815   PLogObjectMemory(*fact,(ainew[n]+shift-n) * (sizeof(int)+sizeof(Scalar)));
816   b->maxnz          = b->nz = ainew[n] + shift;
817   (*fact)->factor   = FACTOR_LU;
818 
819   (*fact)->info.factor_mallocs    = realloc;
820   (*fact)->info.fill_ratio_given  = f;
821   (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);
822   (*fact)->factor                 =  FACTOR_LU;;
823 
824   PetscFunctionReturn(0);
825 }
826 
827 
828 
829 
830