xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision 00a98328c1f4fb9da36b452d9383e7a2e935b046)
1 #ifndef lint
2 static char vcid[] = "$Id: baijfact.c,v 1.30 1996/09/14 03:08:32 bsmith Exp bsmith $";
3 #endif
4 /*
5     Factorization code for BAIJ format.
6 */
7 
8 #include "src/mat/impls/baij/seq/baij.h"
9 #include "src/vec/vecimpl.h"
10 #include "src/inline/ilu.h"
11 
12 
13 /*
14     The symbolic factorization code is identical to that for AIJ format,
15   except for very small changes since this is now a SeqBAIJ datastructure.
16   NOT good code reuse.
17 */
18 int MatLUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,Mat *B)
19 {
20   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
21   IS          isicol;
22   int         *r,*ic, ierr, i, n = a->mbs, *ai = a->i, *aj = a->j;
23   int         *ainew,*ajnew, jmax,*fill, *ajtmp, nz, bs = a->bs, bs2=a->bs2;
24   int         *idnew, idx, row,m,fm, nnz, nzi,realloc = 0,nzbd,*im;
25 
26   PetscValidHeaderSpecific(isrow,IS_COOKIE);
27   PetscValidHeaderSpecific(iscol,IS_COOKIE);
28   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
29   ISGetIndices(isrow,&r); ISGetIndices(isicol,&ic);
30 
31   /* get new row pointers */
32   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
33   ainew[0] = 0;
34   /* don't know how many column pointers are needed so estimate */
35   jmax = (int) (f*ai[n] + 1);
36   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
37   /* fill is a linked list of nonzeros in active row */
38   fill = (int *) PetscMalloc( (2*n+1)*sizeof(int)); CHKPTRQ(fill);
39   im = fill + n + 1;
40   /* idnew is location of diagonal in factor */
41   idnew = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(idnew);
42   idnew[0] = 0;
43 
44   for ( i=0; i<n; i++ ) {
45     /* first copy previous fill into linked list */
46     nnz     = nz    = ai[r[i]+1] - ai[r[i]];
47     ajtmp   = aj + ai[r[i]];
48     fill[n] = n;
49     while (nz--) {
50       fm  = n;
51       idx = ic[*ajtmp++];
52       do {
53         m  = fm;
54         fm = fill[m];
55       } while (fm < idx);
56       fill[m]   = idx;
57       fill[idx] = fm;
58     }
59     row = fill[n];
60     while ( row < i ) {
61       ajtmp = ajnew + idnew[row] + 1;
62       nzbd  = 1 + idnew[row] - ainew[row];
63       nz    = im[row] - nzbd;
64       fm    = row;
65       while (nz-- > 0) {
66         idx = *ajtmp++;
67         nzbd++;
68         if (idx == i) im[row] = nzbd;
69         do {
70           m  = fm;
71           fm = fill[m];
72         } while (fm < idx);
73         if (fm != idx) {
74           fill[m]   = idx;
75           fill[idx] = fm;
76           fm        = idx;
77           nnz++;
78         }
79       }
80       row = fill[row];
81     }
82     /* copy new filled row into permanent storage */
83     ainew[i+1] = ainew[i] + nnz;
84     if (ainew[i+1] > jmax) {
85       /* allocate a longer ajnew */
86       int maxadd;
87       maxadd = (int) ((f*(ai[n]+1)*(n-i+5))/n);
88       if (maxadd < nnz) maxadd = (n-i)*(nnz+1);
89       jmax += maxadd;
90       ajtmp = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(ajtmp);
91       PetscMemcpy(ajtmp,ajnew,ainew[i]*sizeof(int));
92       PetscFree(ajnew);
93       ajnew = ajtmp;
94       realloc++; /* count how many times we realloc */
95     }
96     ajtmp = ajnew + ainew[i];
97     fm    = fill[n];
98     nzi   = 0;
99     im[i] = nnz;
100     while (nnz--) {
101       if (fm < i) nzi++;
102       *ajtmp++ = fm;
103       fm       = fill[fm];
104     }
105     idnew[i] = ainew[i] + nzi;
106   }
107 
108   PLogInfo(A,
109     "Info:MatLUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
110                              realloc,f,((double)ainew[n])/((double)ai[i]));
111 
112   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
113   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
114 
115   PetscFree(fill);
116 
117   /* put together the new matrix */
118   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,B); CHKERRQ(ierr);
119   PLogObjectParent(*B,isicol);
120   ierr = ISDestroy(isicol); CHKERRQ(ierr);
121   b = (Mat_SeqBAIJ *) (*B)->data;
122   PetscFree(b->imax);
123   b->singlemalloc = 0;
124   /* the next line frees the default space generated by the Create() */
125   PetscFree(b->a); PetscFree(b->ilen);
126   b->a          = (Scalar *) PetscMalloc((ainew[n]+1)*sizeof(Scalar)*bs2);CHKPTRQ(b->a);
127   b->j          = ajnew;
128   b->i          = ainew;
129   b->diag       = idnew;
130   b->ilen       = 0;
131   b->imax       = 0;
132   b->row        = isrow;
133   b->col        = iscol;
134   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
135   CHKPTRQ(b->solve_work);
136   /* In b structure:  Free imax, ilen, old a, old j.
137      Allocate idnew, solve_work, new a, new j */
138   PLogObjectMemory(*B,(ainew[n]-n)*(sizeof(int)+sizeof(Scalar)));
139   b->maxnz = b->nz = ainew[n];
140 
141   (*B)->info.factor_mallocs    = realloc;
142   (*B)->info.fill_ratio_given  = f;
143   (*B)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[i]);
144 
145   return 0;
146 }
147 
148 /* ----------------------------------------------------------- */
149 int MatLUFactorNumeric_SeqBAIJ_N(Mat A,Mat *B)
150 {
151   Mat             C = *B;
152   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
153   IS              iscol = b->col, isrow = b->row, isicol;
154   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
155   int             *ajtmpold, *ajtmp, nz, row, bslog,*ai=a->i,*aj=a->j;
156   int             *diag_offset=b->diag,diag,bs=a->bs,bs2 = bs*bs,*v_pivots;
157   Scalar          *ba = b->a,*aa = a->a;
158   register Scalar *pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
159   register int    *pj;
160 
161   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
162   PLogObjectParent(*B,isicol);
163   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
164   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
165   rtmp  = (Scalar *) PetscMalloc(bs2*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
166   PetscMemzero(rtmp,bs2*(n+1)*sizeof(Scalar));
167   /* generate work space needed by dense LU factorization */
168   v_work     = (Scalar *) PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(Scalar));
169                CHKPTRQ(v_work);
170   multiplier = v_work + bs;
171   v_pivots   = (int *) (multiplier + bs2);
172 
173   /* flops in while loop */
174   bslog = 2*bs*bs2;
175 
176   for ( i=0; i<n; i++ ) {
177     nz    = bi[i+1] - bi[i];
178     ajtmp = bj + bi[i];
179     for  ( j=0; j<nz; j++ ) {
180       PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(Scalar));
181     }
182     /* load in initial (unfactored row) */
183     nz       = ai[r[i]+1] - ai[r[i]];
184     ajtmpold = aj + ai[r[i]];
185     v        = aa + bs2*ai[r[i]];
186     for ( j=0; j<nz; j++ ) {
187       PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(Scalar));
188     }
189     row = *ajtmp++;
190     while (row < i) {
191       pc = rtmp + bs2*row;
192 /*      if (*pc) { */
193         pv = ba + bs2*diag_offset[row];
194         pj = bj + diag_offset[row] + 1;
195         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
196         nz = bi[row+1] - diag_offset[row] - 1;
197         pv += bs2;
198         for (j=0; j<nz; j++) {
199           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
200         }
201         PLogFlops(bslog*(nz+1)-bs);
202 /*      } */
203         row = *ajtmp++;
204     }
205     /* finished row so stick it into b->a */
206     pv = ba + bs2*bi[i];
207     pj = bj + bi[i];
208     nz = bi[i+1] - bi[i];
209     for ( j=0; j<nz; j++ ) {
210       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(Scalar));
211     }
212     diag = diag_offset[i] - bi[i];
213     /* invert diagonal block */
214     w = pv + bs2*diag;
215     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
216   }
217 
218   PetscFree(rtmp); PetscFree(v_work);
219   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
220   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
221   ierr = ISDestroy(isicol); CHKERRQ(ierr);
222   C->factor = FACTOR_LU;
223   C->assembled = PETSC_TRUE;
224   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
225   return 0;
226 }
227 /* ------------------------------------------------------------*/
228 /*
229       Version for when blocks are 5 by 5
230 */
231 int MatLUFactorNumeric_SeqBAIJ_5(Mat A,Mat *B)
232 {
233   Mat             C = *B;
234   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
235   IS              iscol = b->col, isrow = b->row, isicol;
236   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
237   int             *ajtmpold, *ajtmp, nz, row, v_pivots[5];
238   int             *diag_offset = b->diag,bs = 5,idx,*ai=a->i,*aj=a->j;
239   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
240   Scalar          p1,p2,p3,p4,v_work[5],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
241   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
242   Scalar          x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
243   Scalar          p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
244   Scalar          m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
245   Scalar          *ba = b->a,*aa = a->a;
246   register int    *pj;
247 
248   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
249   PLogObjectParent(*B,isicol);
250   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
251   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
252   rtmp  = (Scalar *) PetscMalloc(25*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
253 
254   for ( i=0; i<n; i++ ) {
255     nz    = bi[i+1] - bi[i];
256     ajtmp = bj + bi[i];
257     for  ( j=0; j<nz; j++ ) {
258       x = rtmp+25*ajtmp[j];
259       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
260       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
261       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
262     }
263     /* load in initial (unfactored row) */
264     idx      = r[i];
265     nz       = ai[idx+1] - ai[idx];
266     ajtmpold = aj + ai[idx];
267     v        = aa + 25*ai[idx];
268     for ( j=0; j<nz; j++ ) {
269       x    = rtmp+25*ic[ajtmpold[j]];
270       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
271       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
272       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
273       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
274       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
275       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
276       v    += 25;
277     }
278     row = *ajtmp++;
279     while (row < i) {
280       pc = rtmp + 25*row;
281       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
282       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
283       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
284       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
285       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
286       p25 = pc[24];
287       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
288           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
289           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
290           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
291           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
292           p24 != 0.0 || p25 != 0.0) {
293         pv = ba + 25*diag_offset[row];
294         pj = bj + diag_offset[row] + 1;
295         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
296         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
297         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
298         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
299         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
300         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
301         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
302         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
303         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
304         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
305         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
306 
307         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
308         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
309         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
310         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
311         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
312 
313         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
314         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
315         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
316         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
317         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
318 
319         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
320         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
321         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
322         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
323         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
324 
325         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
326         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
327         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
328         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
329         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
330 
331         nz = bi[row+1] - diag_offset[row] - 1;
332         pv += 25;
333         for (j=0; j<nz; j++) {
334           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
335           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
336           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
337           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
338           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
339           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
340           x    = rtmp + 25*pj[j];
341           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
342           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
343           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
344           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
345           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
346 
347           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
348           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
349           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
350           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
351           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
352 
353           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
354           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
355           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
356           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
357           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
358 
359           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
360           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
361           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
362           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
363           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
364 
365           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
366           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
367           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
368           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
369           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
370 
371           pv   += 25;
372         }
373         PLogFlops(250*nz+225);
374       }
375       row = *ajtmp++;
376     }
377     /* finished row so stick it into b->a */
378     pv = ba + 25*bi[i];
379     pj = bj + bi[i];
380     nz = bi[i+1] - bi[i];
381     for ( j=0; j<nz; j++ ) {
382       x     = rtmp+25*pj[j];
383       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
384       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
385       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
386       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
387       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
388       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
389       pv   += 25;
390     }
391     /* invert diagonal block */
392     w = ba + 25*diag_offset[i];
393     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
394   }
395 
396   PetscFree(rtmp);
397   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
398   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
399   ierr = ISDestroy(isicol); CHKERRQ(ierr);
400   C->factor = FACTOR_LU;
401   C->assembled = PETSC_TRUE;
402   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
403   return 0;
404 }
405 
406 /* ------------------------------------------------------------*/
407 /*
408       Version for when blocks are 4 by 4
409 */
410 int MatLUFactorNumeric_SeqBAIJ_4(Mat A,Mat *B)
411 {
412   Mat             C = *B;
413   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
414   IS              iscol = b->col, isrow = b->row, isicol;
415   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
416   int             *ajtmpold, *ajtmp, nz, row, v_pivots[4];
417   int             *diag_offset = b->diag,bs = 4,idx,*ai=a->i,*aj=a->j;
418   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
419   Scalar          p1,p2,p3,p4,v_work[4],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
420   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
421   Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
422   Scalar          m13,m14,m15,m16;
423   Scalar          *ba = b->a,*aa = a->a;
424   register int    *pj;
425 
426   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
427   PLogObjectParent(*B,isicol);
428   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
429   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
430   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
431 
432   for ( i=0; i<n; i++ ) {
433     nz    = bi[i+1] - bi[i];
434     ajtmp = bj + bi[i];
435     for  ( j=0; j<nz; j++ ) {
436       x = rtmp+16*ajtmp[j];
437       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
438       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
439     }
440     /* load in initial (unfactored row) */
441     idx      = r[i];
442     nz       = ai[idx+1] - ai[idx];
443     ajtmpold = aj + ai[idx];
444     v        = aa + 16*ai[idx];
445     for ( j=0; j<nz; j++ ) {
446       x    = rtmp+16*ic[ajtmpold[j]];
447       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
448       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
449       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
450       x[14] = v[14]; x[15] = v[15];
451       v    += 16;
452     }
453     row = *ajtmp++;
454     while (row < i) {
455       pc = rtmp + 16*row;
456       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
457       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
458       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
459       p15 = pc[14]; p16 = pc[15];
460       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
461           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
462           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
463           || p16 != 0.0) {
464         pv = ba + 16*diag_offset[row];
465         pj = bj + diag_offset[row] + 1;
466         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
467         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
468         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
469         x15 = pv[14]; x16 = pv[15];
470         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
471         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
472         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
473         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
474 
475         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
476         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
477         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
478         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
479 
480         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
481         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
482         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
483         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
484 
485         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
486         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
487         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
488         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
489 
490         nz = bi[row+1] - diag_offset[row] - 1;
491         pv += 16;
492         for (j=0; j<nz; j++) {
493           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
494           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
495           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
496           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
497           x    = rtmp + 16*pj[j];
498           x[0] -= m1*x1 + m5*x2  + m9*x3 + m13*x4;
499           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
500           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
501           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
502 
503           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
504           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
505           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
506           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
507 
508           x[8] -= m1*x9  + m5*x10  + m9*x11 + m13*x12;
509           x[9] -= m2*x9  + m6*x10  + m10*x11 + m14*x12;
510           x[10] -= m3*x9 + m7*x10  + m11*x11 + m15*x12;
511           x[11] -= m4*x9 + m8*x10  + m12*x11 + m16*x12;
512 
513           x[12] -= m1*x13 + m5*x14  + m9*x15 + m13*x16;
514           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
515           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
516           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
517 
518           pv   += 16;
519         }
520         PLogFlops(128*nz+112);
521       }
522       row = *ajtmp++;
523     }
524     /* finished row so stick it into b->a */
525     pv = ba + 16*bi[i];
526     pj = bj + bi[i];
527     nz = bi[i+1] - bi[i];
528     for ( j=0; j<nz; j++ ) {
529       x     = rtmp+16*pj[j];
530       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
531       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
532       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
533       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
534       pv   += 16;
535     }
536     /* invert diagonal block */
537     w = ba + 16*diag_offset[i];
538     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
539   }
540 
541   PetscFree(rtmp);
542   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
543   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
544   ierr = ISDestroy(isicol); CHKERRQ(ierr);
545   C->factor = FACTOR_LU;
546   C->assembled = PETSC_TRUE;
547   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
548   return 0;
549 }
550 /* ------------------------------------------------------------*/
551 /*
552       Version for when blocks are 3 by 3
553 */
554 int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
555 {
556   Mat             C = *B;
557   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
558   IS              iscol = b->col, isrow = b->row, isicol;
559   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
560   int             *ajtmpold, *ajtmp, nz, row, *ai=a->i,*aj=a->j;
561   int             *diag_offset = b->diag,idx;
562   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
563   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
564   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
565   Scalar          *ba = b->a,*aa = a->a;
566   register int    *pj;
567 
568   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
569   PLogObjectParent(*B,isicol);
570   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
571   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
572   rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
573 
574   for ( i=0; i<n; i++ ) {
575     nz    = bi[i+1] - bi[i];
576     ajtmp = bj + bi[i];
577     for  ( j=0; j<nz; j++ ) {
578       x = rtmp + 9*ajtmp[j];
579       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
580     }
581     /* load in initial (unfactored row) */
582     idx      = r[i];
583     nz       = ai[idx+1] - ai[idx];
584     ajtmpold = aj + ai[idx];
585     v        = aa + 9*ai[idx];
586     for ( j=0; j<nz; j++ ) {
587       x    = rtmp + 9*ic[ajtmpold[j]];
588       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
589       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
590       v    += 9;
591     }
592     row = *ajtmp++;
593     while (row < i) {
594       pc = rtmp + 9*row;
595       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
596       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
597       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
598           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
599         pv = ba + 9*diag_offset[row];
600         pj = bj + diag_offset[row] + 1;
601         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
602         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
603         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
604         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
605         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
606 
607         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
608         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
609         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
610 
611         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
612         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
613         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
614         nz = bi[row+1] - diag_offset[row] - 1;
615         pv += 9;
616         for (j=0; j<nz; j++) {
617           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
618           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
619           x    = rtmp + 9*pj[j];
620           x[0] -= m1*x1 + m4*x2 + m7*x3;
621           x[1] -= m2*x1 + m5*x2 + m8*x3;
622           x[2] -= m3*x1 + m6*x2 + m9*x3;
623 
624           x[3] -= m1*x4 + m4*x5 + m7*x6;
625           x[4] -= m2*x4 + m5*x5 + m8*x6;
626           x[5] -= m3*x4 + m6*x5 + m9*x6;
627 
628           x[6] -= m1*x7 + m4*x8 + m7*x9;
629           x[7] -= m2*x7 + m5*x8 + m8*x9;
630           x[8] -= m3*x7 + m6*x8 + m9*x9;
631           pv   += 9;
632         }
633         PLogFlops(54*nz+36);
634       }
635       row = *ajtmp++;
636     }
637     /* finished row so stick it into b->a */
638     pv = ba + 9*bi[i];
639     pj = bj + bi[i];
640     nz = bi[i+1] - bi[i];
641     for ( j=0; j<nz; j++ ) {
642       x     = rtmp + 9*pj[j];
643       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
644       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
645       pv   += 9;
646     }
647     /* invert diagonal block */
648     w = ba + 9*diag_offset[i];
649     ierr = Kernel_A_gets_inverse_A_3(w); CHKERRQ(ierr);
650   }
651 
652   PetscFree(rtmp);
653   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
654   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
655   ierr = ISDestroy(isicol); CHKERRQ(ierr);
656   C->factor = FACTOR_LU;
657   C->assembled = PETSC_TRUE;
658   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
659   return 0;
660 }
661 
662 /* ------------------------------------------------------------*/
663 /*
664       Version for when blocks are 2 by 2
665 */
666 int MatLUFactorNumeric_SeqBAIJ_2(Mat A,Mat *B)
667 {
668   Mat             C = *B;
669   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
670   IS              iscol = b->col, isrow = b->row, isicol;
671   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
672   int             *ajtmpold, *ajtmp, nz, row, v_pivots[2];
673   int             *diag_offset=b->diag,bs = 2,idx,*ai=a->i,*aj=a->j;
674   register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
675   Scalar          p1,p2,p3,p4,v_work[2];
676   Scalar          *ba = b->a,*aa = a->a;
677   register int    *pj;
678 
679   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
680   PLogObjectParent(*B,isicol);
681   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
682   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
683   rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
684 
685   for ( i=0; i<n; i++ ) {
686     nz    = bi[i+1] - bi[i];
687     ajtmp = bj + bi[i];
688     for  ( j=0; j<nz; j++ ) {
689       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
690     }
691     /* load in initial (unfactored row) */
692     idx      = r[i];
693     nz       = ai[idx+1] - ai[idx];
694     ajtmpold = aj + ai[idx];
695     v        = aa + 4*ai[idx];
696     for ( j=0; j<nz; j++ ) {
697       x    = rtmp+4*ic[ajtmpold[j]];
698       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
699       v    += 4;
700     }
701     row = *ajtmp++;
702     while (row < i) {
703       pc = rtmp + 4*row;
704       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
705       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
706         pv = ba + 4*diag_offset[row];
707         pj = bj + diag_offset[row] + 1;
708         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
709         pc[0] = m1 = p1*x1 + p3*x2;
710         pc[1] = m2 = p2*x1 + p4*x2;
711         pc[2] = m3 = p1*x3 + p3*x4;
712         pc[3] = m4 = p2*x3 + p4*x4;
713         nz = bi[row+1] - diag_offset[row] - 1;
714         pv += 4;
715         for (j=0; j<nz; j++) {
716           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
717           x    = rtmp + 4*pj[j];
718           x[0] -= m1*x1 + m3*x2;
719           x[1] -= m2*x1 + m4*x2;
720           x[2] -= m1*x3 + m3*x4;
721           x[3] -= m2*x3 + m4*x4;
722           pv   += 4;
723         }
724         PLogFlops(16*nz+12);
725       }
726       row = *ajtmp++;
727     }
728     /* finished row so stick it into b->a */
729     pv = ba + 4*bi[i];
730     pj = bj + bi[i];
731     nz = bi[i+1] - bi[i];
732     for ( j=0; j<nz; j++ ) {
733       x     = rtmp+4*pj[j];
734       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
735       pv   += 4;
736     }
737     /* invert diagonal block */
738     w = ba + 4*diag_offset[i];
739     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
740   }
741 
742   PetscFree(rtmp);
743   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
744   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
745   ierr = ISDestroy(isicol); CHKERRQ(ierr);
746   C->factor = FACTOR_LU;
747   C->assembled = PETSC_TRUE;
748   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
749   return 0;
750 }
751 
752 /* ----------------------------------------------------------- */
753 /*
754      Version for when blocks are 1 by 1.
755 */
756 int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
757 {
758   Mat             C = *B;
759   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
760   IS              iscol = b->col, isrow = b->row, isicol;
761   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
762   int             *ajtmpold, *ajtmp, nz, row,*ai = a->i,*aj = a->j;
763   int             *diag_offset = b->diag,diag;
764   register Scalar *pv,*v,*rtmp,multiplier,*pc;
765   Scalar          *ba = b->a,*aa = a->a;
766   register int    *pj;
767 
768   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
769   PLogObjectParent(*B,isicol);
770   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
771   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
772   rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
773 
774   for ( i=0; i<n; i++ ) {
775     nz    = bi[i+1] - bi[i];
776     ajtmp = bj + bi[i];
777     for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;
778 
779     /* load in initial (unfactored row) */
780     nz       = ai[r[i]+1] - ai[r[i]];
781     ajtmpold = aj + ai[r[i]];
782     v        = aa + ai[r[i]];
783     for ( j=0; j<nz; j++ ) rtmp[ic[ajtmpold[j]]] =  v[j];
784 
785     row = *ajtmp++;
786     while (row < i) {
787       pc = rtmp + row;
788       if (*pc != 0.0) {
789         pv         = ba + diag_offset[row];
790         pj         = bj + diag_offset[row] + 1;
791         multiplier = *pc * *pv++;
792         *pc        = multiplier;
793         nz         = bi[row+1] - diag_offset[row] - 1;
794         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
795         PLogFlops(1+2*nz);
796       }
797       row = *ajtmp++;
798     }
799     /* finished row so stick it into b->a */
800     pv = ba + bi[i];
801     pj = bj + bi[i];
802     nz = bi[i+1] - bi[i];
803     for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
804     diag = diag_offset[i] - bi[i];
805     /* check pivot entry for current row */
806     if (pv[diag] == 0.0) {
807       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"MatLUFactorNumeric_SeqBAIJ_1:Zero pivot");
808     }
809     pv[diag] = 1.0/pv[diag];
810   }
811 
812   PetscFree(rtmp);
813   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
814   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
815   ierr = ISDestroy(isicol); CHKERRQ(ierr);
816   C->factor    = FACTOR_LU;
817   C->assembled = PETSC_TRUE;
818   PLogFlops(b->n);
819   return 0;
820 }
821 
822 /* ----------------------------------------------------------- */
823 int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
824 {
825   Mat_SeqBAIJ *mat = (Mat_SeqBAIJ *) A->data;
826   int         ierr;
827   Mat         C;
828 
829   ierr = MatLUFactorSymbolic_SeqBAIJ(A,row,col,f,&C); CHKERRQ(ierr);
830   ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);
831 
832   /* free all the data structures from mat */
833   PetscFree(mat->a);
834   if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
835   if (mat->diag) PetscFree(mat->diag);
836   if (mat->ilen) PetscFree(mat->ilen);
837   if (mat->imax) PetscFree(mat->imax);
838   if (mat->solve_work) PetscFree(mat->solve_work);
839   if (mat->mult_work) PetscFree(mat->mult_work);
840   PetscFree(mat);
841 
842   PetscMemcpy(A,C,sizeof(struct _Mat));
843   PetscHeaderDestroy(C);
844   return 0;
845 }
846 /* ----------------------------------------------------------- */
847 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
848 {
849   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
850   IS              iscol=a->col,isrow=a->row;
851   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
852   int             nz,bs=a->bs,bs2=a->bs2,*rout,*cout;
853   Scalar          *aa=a->a,*sum;
854   register Scalar *x,*b,*lsum,*tmp,*v;
855 
856   VecGetArray_Fast(bb,b);
857   VecGetArray_Fast(xx,x);
858   tmp  = a->solve_work;
859 
860   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
861   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
862 
863   /* forward solve the lower triangular */
864   PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
865   for ( i=1; i<n; i++ ) {
866     v   = aa + bs2*ai[i];
867     vi  = aj + ai[i];
868     nz  = a->diag[i] - ai[i];
869     sum = tmp + bs*i;
870     PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
871     while (nz--) {
872       Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++));
873       v += bs2;
874     }
875   }
876   /* backward solve the upper triangular */
877   lsum = a->solve_work + a->n;
878   for ( i=n-1; i>=0; i-- ){
879     v   = aa + bs2*(a->diag[i] + 1);
880     vi  = aj + a->diag[i] + 1;
881     nz  = ai[i+1] - a->diag[i] - 1;
882     PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
883     while (nz--) {
884       Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++));
885       v += bs2;
886     }
887     Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs);
888     PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
889   }
890 
891   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
892   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
893   VecRestoreArray_Fast(bb,b);
894   VecRestoreArray_Fast(xx,x);
895   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
896   return 0;
897 }
898 
899 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
900 {
901   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
902   IS              iscol=a->col,isrow=a->row;
903   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
904   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
905   register Scalar *x,*b,*tmp,*v;
906 
907   VecGetArray_Fast(bb,b);
908   VecGetArray_Fast(xx,x);
909   tmp  = a->solve_work;
910 
911   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
912   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
913 
914   /* forward solve the lower triangular */
915   idx    = 5*(*r++);
916   tmp[0] = b[idx];   tmp[1] = b[1+idx];
917   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
918   for ( i=1; i<n; i++ ) {
919     v     = aa + 25*ai[i];
920     vi    = aj + ai[i];
921     nz    = a->diag[i] - ai[i];
922     idx   = 5*(*r++);
923     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
924     sum5  = b[4+idx];
925     while (nz--) {
926       idx   = 5*(*vi++);
927       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
928       x4    = tmp[3+idx];x5 = tmp[4+idx];
929       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
930       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
931       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
932       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
933       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
934       v += 25;
935     }
936     idx = 5*i;
937     tmp[idx]   = sum1;tmp[1+idx] = sum2;
938     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
939   }
940   /* backward solve the upper triangular */
941   for ( i=n-1; i>=0; i-- ){
942     v    = aa + 25*a->diag[i] + 25;
943     vi   = aj + a->diag[i] + 1;
944     nz   = ai[i+1] - a->diag[i] - 1;
945     idt  = 5*i;
946     sum1 = tmp[idt];  sum2 = tmp[1+idt];
947     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
948     while (nz--) {
949       idx   = 5*(*vi++);
950       x1    = tmp[idx];   x2 = tmp[1+idx];
951       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
952       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
953       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
954       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
955       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
956       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
957       v += 25;
958     }
959     idc = 5*(*c--);
960     v   = aa + 25*a->diag[i];
961     x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
962                                  v[15]*sum4+v[20]*sum5;
963     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
964                                  v[16]*sum4+v[21]*sum5;
965     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
966                                  v[17]*sum4+v[22]*sum5;
967     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
968                                  v[18]*sum4+v[23]*sum5;
969     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
970                                  v[19]*sum4+v[24]*sum5;
971   }
972 
973   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
974   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
975   VecRestoreArray_Fast(bb,b);
976   VecRestoreArray_Fast(xx,x);
977   PLogFlops(2*25*(a->nz) - a->n);
978   return 0;
979 }
980 
981 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
982 {
983   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
984   IS              iscol=a->col,isrow=a->row;
985   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
986   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
987   register Scalar *x,*b,*tmp,*v;
988 
989   VecGetArray_Fast(bb,b);
990   VecGetArray_Fast(xx,x);
991   tmp  = a->solve_work;
992 
993   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
994   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
995 
996   /* forward solve the lower triangular */
997   idx    = 4*(*r++);
998   tmp[0] = b[idx];   tmp[1] = b[1+idx];
999   tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
1000   for ( i=1; i<n; i++ ) {
1001     v     = aa + 16*ai[i];
1002     vi    = aj + ai[i];
1003     nz    = a->diag[i] - ai[i];
1004     idx   = 4*(*r++);
1005     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1006     while (nz--) {
1007       idx   = 4*(*vi++);
1008       x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
1009       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1010       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1011       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1012       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1013       v += 16;
1014     }
1015     idx = 4*i;
1016     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1017     tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1018   }
1019   /* backward solve the upper triangular */
1020   for ( i=n-1; i>=0; i-- ){
1021     v    = aa + 16*a->diag[i] + 16;
1022     vi   = aj + a->diag[i] + 1;
1023     nz   = ai[i+1] - a->diag[i] - 1;
1024     idt  = 4*i;
1025     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1026     sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1027     while (nz--) {
1028       idx   = 4*(*vi++);
1029       x1    = tmp[idx];   x2 = tmp[1+idx];
1030       x3    = tmp[2+idx]; x4 = tmp[3+idx];
1031       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1032       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1033       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1034       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1035       v += 16;
1036     }
1037     idc = 4*(*c--);
1038     v   = aa + 16*a->diag[i];
1039     x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1040     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1041     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1042     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1043   }
1044 
1045   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1046   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1047   VecRestoreArray_Fast(bb,b);
1048   VecRestoreArray_Fast(xx,x);
1049   PLogFlops(2*16*(a->nz) - a->n);
1050   return 0;
1051 }
1052 
1053 
1054 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
1055 {
1056   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1057   IS              iscol=a->col,isrow=a->row;
1058   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1059   Scalar          *aa=a->a,sum1,sum2,sum3,x1,x2,x3;
1060   register Scalar *x,*b,*tmp,*v;
1061 
1062   VecGetArray_Fast(bb,b);
1063   VecGetArray_Fast(xx,x);
1064   tmp  = a->solve_work;
1065 
1066   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1067   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1068 
1069   /* forward solve the lower triangular */
1070   idx    = 3*(*r++);
1071   tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
1072   for ( i=1; i<n; i++ ) {
1073     v     = aa + 9*ai[i];
1074     vi    = aj + ai[i];
1075     nz    = a->diag[i] - ai[i];
1076     idx   = 3*(*r++);
1077     sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
1078     while (nz--) {
1079       idx   = 3*(*vi++);
1080       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1081       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1082       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1083       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1084       v += 9;
1085     }
1086     idx = 3*i;
1087     tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
1088   }
1089   /* backward solve the upper triangular */
1090   for ( i=n-1; i>=0; i-- ){
1091     v    = aa + 9*a->diag[i] + 9;
1092     vi   = aj + a->diag[i] + 1;
1093     nz   = ai[i+1] - a->diag[i] - 1;
1094     idt  = 3*i;
1095     sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
1096     while (nz--) {
1097       idx   = 3*(*vi++);
1098       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1099       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1100       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1101       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1102       v += 9;
1103     }
1104     idc = 3*(*c--);
1105     v   = aa + 9*a->diag[i];
1106     x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
1107     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
1108     x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
1109   }
1110   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1111   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1112   VecRestoreArray_Fast(bb,b);
1113   VecRestoreArray_Fast(xx,x);
1114   PLogFlops(2*9*(a->nz) - a->n);
1115   return 0;
1116 }
1117 
1118 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
1119 {
1120   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1121   IS              iscol=a->col,isrow=a->row;
1122   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1123   Scalar          *aa=a->a,sum1,sum2,x1,x2;
1124   register Scalar *x,*b,*tmp,*v;
1125 
1126   VecGetArray_Fast(bb,b);
1127   VecGetArray_Fast(xx,x);
1128   tmp  = a->solve_work;
1129 
1130   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1131   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1132 
1133   /* forward solve the lower triangular */
1134   idx    = 2*(*r++);
1135   tmp[0] = b[idx]; tmp[1] = b[1+idx];
1136   for ( i=1; i<n; i++ ) {
1137     v     = aa + 4*ai[i];
1138     vi    = aj + ai[i];
1139     nz    = a->diag[i] - ai[i];
1140     idx   = 2*(*r++);
1141     sum1  = b[idx]; sum2 = b[1+idx];
1142     while (nz--) {
1143       idx   = 2*(*vi++);
1144       x1    = tmp[idx]; x2 = tmp[1+idx];
1145       sum1 -= v[0]*x1 + v[2]*x2;
1146       sum2 -= v[1]*x1 + v[3]*x2;
1147       v += 4;
1148     }
1149     idx = 2*i;
1150     tmp[idx] = sum1; tmp[1+idx] = sum2;
1151   }
1152   /* backward solve the upper triangular */
1153   for ( i=n-1; i>=0; i-- ){
1154     v    = aa + 4*a->diag[i] + 4;
1155     vi   = aj + a->diag[i] + 1;
1156     nz   = ai[i+1] - a->diag[i] - 1;
1157     idt  = 2*i;
1158     sum1 = tmp[idt]; sum2 = tmp[1+idt];
1159     while (nz--) {
1160       idx   = 2*(*vi++);
1161       x1    = tmp[idx]; x2 = tmp[1+idx];
1162       sum1 -= v[0]*x1 + v[2]*x2;
1163       sum2 -= v[1]*x1 + v[3]*x2;
1164       v += 4;
1165     }
1166     idc = 2*(*c--);
1167     v   = aa + 4*a->diag[i];
1168     x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
1169     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
1170   }
1171   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1172   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1173   VecRestoreArray_Fast(bb,b);
1174   VecRestoreArray_Fast(xx,x);
1175   PLogFlops(2*4*(a->nz) - a->n);
1176   return 0;
1177 }
1178 
1179 
1180 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
1181 {
1182   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1183   IS              iscol=a->col,isrow=a->row;
1184   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout;
1185   Scalar          *aa=a->a,sum1;
1186   register Scalar *x,*b,*tmp,*v;
1187 
1188   if (!n) return 0;
1189 
1190   VecGetArray_Fast(bb,b);
1191   VecGetArray_Fast(xx,x);
1192   tmp  = a->solve_work;
1193 
1194   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1195   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1196 
1197   /* forward solve the lower triangular */
1198   tmp[0] = b[*r++];
1199   for ( i=1; i<n; i++ ) {
1200     v     = aa + ai[i];
1201     vi    = aj + ai[i];
1202     nz    = a->diag[i] - ai[i];
1203     sum1  = b[*r++];
1204     while (nz--) {
1205       sum1 -= (*v++)*tmp[*vi++];
1206     }
1207     tmp[i] = sum1;
1208   }
1209   /* backward solve the upper triangular */
1210   for ( i=n-1; i>=0; i-- ){
1211     v    = aa + a->diag[i] + 1;
1212     vi   = aj + a->diag[i] + 1;
1213     nz   = ai[i+1] - a->diag[i] - 1;
1214     sum1 = tmp[i];
1215     while (nz--) {
1216       sum1 -= (*v++)*tmp[*vi++];
1217     }
1218     x[*c--] = tmp[i] = aa[a->diag[i]]*sum1;
1219   }
1220 
1221   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1222   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1223   VecRestoreArray_Fast(bb,b);
1224   VecRestoreArray_Fast(xx,x);
1225   PLogFlops(2*1*(a->nz) - a->n);
1226   return 0;
1227 }
1228 
1229 /* ----------------------------------------------------------------*/
1230 /*
1231      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
1232    except that the data structure of Mat_SeqAIJ is slightly different.
1233    Not a good example of code reuse.
1234 */
1235 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
1236                                  Mat *fact)
1237 {
1238   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
1239   IS          isicol;
1240   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
1241   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
1242   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
1243   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
1244   PetscTruth  col_identity, row_identity;
1245 
1246   /* special case that simply copies fill pattern */
1247   PetscValidHeaderSpecific(isrow,IS_COOKIE);
1248   PetscValidHeaderSpecific(iscol,IS_COOKIE);
1249   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
1250   if (levels == 0 && row_identity && col_identity) {
1251     ierr = MatConvertSameType_SeqBAIJ(A,fact,DO_NOT_COPY_VALUES); CHKERRQ(ierr);
1252     (*fact)->factor = FACTOR_LU;
1253     b               = (Mat_SeqBAIJ *) (*fact)->data;
1254     if (!b->diag) {
1255       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
1256     }
1257     b->row        = isrow;
1258     b->col        = iscol;
1259     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
1260     return 0;
1261   }
1262 
1263   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
1264   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
1265   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
1266 
1267   /* get new row pointers */
1268   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
1269   ainew[0] = 0;
1270   /* don't know how many column pointers are needed so estimate */
1271   jmax = (int) (f*ai[n] + 1);
1272   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
1273   /* ajfill is level of fill for each fill entry */
1274   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
1275   /* fill is a linked list of nonzeros in active row */
1276   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
1277   /* im is level for each filled value */
1278   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
1279   /* dloc is location of diagonal in factor */
1280   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
1281   dloc[0]  = 0;
1282   for ( prow=0; prow<n; prow++ ) {
1283     /* first copy previous fill into linked list */
1284     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
1285     xi      = aj + ai[r[prow]];
1286     fill[n] = n;
1287     while (nz--) {
1288       fm  = n;
1289       idx = ic[*xi++];
1290       do {
1291         m  = fm;
1292         fm = fill[m];
1293       } while (fm < idx);
1294       fill[m]   = idx;
1295       fill[idx] = fm;
1296       im[idx]   = 0;
1297     }
1298     nzi = 0;
1299     row = fill[n];
1300     while ( row < prow ) {
1301       incrlev = im[row] + 1;
1302       nz      = dloc[row];
1303       xi      = ajnew  + ainew[row] + nz;
1304       flev    = ajfill + ainew[row] + nz + 1;
1305       nnz     = ainew[row+1] - ainew[row] - nz - 1;
1306       if (*xi++ != row) {
1307         SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"MatILUFactorSymbolic_SeqBAIJ:zero pivot");
1308       }
1309       fm      = row;
1310       while (nnz-- > 0) {
1311         idx = *xi++;
1312         if (*flev + incrlev > levels) {
1313           flev++;
1314           continue;
1315         }
1316         do {
1317           m  = fm;
1318           fm = fill[m];
1319         } while (fm < idx);
1320         if (fm != idx) {
1321           im[idx]   = *flev + incrlev;
1322           fill[m]   = idx;
1323           fill[idx] = fm;
1324           fm        = idx;
1325           nzf++;
1326         }
1327         else {
1328           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
1329         }
1330         flev++;
1331       }
1332       row = fill[row];
1333       nzi++;
1334     }
1335     /* copy new filled row into permanent storage */
1336     ainew[prow+1] = ainew[prow] + nzf;
1337     if (ainew[prow+1] > jmax) {
1338       /* allocate a longer ajnew */
1339       int maxadd;
1340       maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n);
1341       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
1342       jmax += maxadd;
1343       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1344       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
1345       PetscFree(ajnew);
1346       ajnew = xi;
1347       /* allocate a longer ajfill */
1348       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1349       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
1350       PetscFree(ajfill);
1351       ajfill = xi;
1352       realloc++;
1353     }
1354     xi          = ajnew + ainew[prow];
1355     flev        = ajfill + ainew[prow];
1356     dloc[prow]  = nzi;
1357     fm          = fill[n];
1358     while (nzf--) {
1359       *xi++   = fm;
1360       *flev++ = im[fm];
1361       fm      = fill[fm];
1362     }
1363   }
1364   PetscFree(ajfill);
1365   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1366   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
1367   ierr = ISDestroy(isicol); CHKERRQ(ierr);
1368   PetscFree(fill); PetscFree(im);
1369 
1370   PLogInfo(A,
1371     "Info:MatILUFactorSymbolic_SeqBAIJ:Realloc %d Fill ratio:given %g needed %g\n",
1372                              realloc,f,((double)ainew[n])/((double)ai[prow]));
1373 
1374   /* put together the new matrix */
1375   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
1376   b = (Mat_SeqBAIJ *) (*fact)->data;
1377   PetscFree(b->imax);
1378   b->singlemalloc = 0;
1379   len = bs2*ainew[n]*sizeof(Scalar);
1380   /* the next line frees the default space generated by the Create() */
1381   PetscFree(b->a); PetscFree(b->ilen);
1382   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
1383   b->j          = ajnew;
1384   b->i          = ainew;
1385   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
1386   b->diag       = dloc;
1387   b->ilen       = 0;
1388   b->imax       = 0;
1389   b->row        = isrow;
1390   b->col        = iscol;
1391   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
1392   CHKPTRQ(b->solve_work);
1393   /* In b structure:  Free imax, ilen, old a, old j.
1394      Allocate dloc, solve_work, new a, new j */
1395   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
1396   b->maxnz          = b->nz = ainew[n];
1397   (*fact)->factor   = FACTOR_LU;
1398 
1399   (*fact)->info.factor_mallocs    = realloc;
1400   (*fact)->info.fill_ratio_given  = f;
1401   (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);
1402 
1403   return 0;
1404 }
1405 
1406 
1407 
1408 
1409