xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision 83e2fdc756c13f964f3ed5aaff42e3626c5b72bc)
1 #ifdef PETSC_RCS_HEADER
2 static char vcid[] = "$Id: baijfact.c,v 1.51 1997/07/25 22:14:05 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 #undef __FUNC__
19 #define __FUNC__ "MatLUFactorSymbolic_SeqBAIJ"
20 int MatLUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,Mat *B)
21 {
22   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
23   IS          isicol;
24   int         *r,*ic, ierr, i, n = a->mbs, *ai = a->i, *aj = a->j;
25   int         *ainew,*ajnew, jmax,*fill, *ajtmp, nz, bs = a->bs, bs2=a->bs2;
26   int         *idnew, idx, row,m,fm, nnz, nzi,realloc = 0,nzbd,*im;
27 
28   PetscValidHeaderSpecific(isrow,IS_COOKIE);
29   PetscValidHeaderSpecific(iscol,IS_COOKIE);
30   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
31   ISGetIndices(isrow,&r); ISGetIndices(isicol,&ic);
32 
33   /* get new row pointers */
34   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
35   ainew[0] = 0;
36   /* don't know how many column pointers are needed so estimate */
37   jmax = (int) (f*ai[n] + 1);
38   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
39   /* fill is a linked list of nonzeros in active row */
40   fill = (int *) PetscMalloc( (2*n+1)*sizeof(int)); CHKPTRQ(fill);
41   im = fill + n + 1;
42   /* idnew is location of diagonal in factor */
43   idnew = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(idnew);
44   idnew[0] = 0;
45 
46   for ( i=0; i<n; i++ ) {
47     /* first copy previous fill into linked list */
48     nnz     = nz    = ai[r[i]+1] - ai[r[i]];
49     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
50     ajtmp   = aj + ai[r[i]];
51     fill[n] = n;
52     while (nz--) {
53       fm  = n;
54       idx = ic[*ajtmp++];
55       do {
56         m  = fm;
57         fm = fill[m];
58       } while (fm < idx);
59       fill[m]   = idx;
60       fill[idx] = fm;
61     }
62     row = fill[n];
63     while ( row < i ) {
64       ajtmp = ajnew + idnew[row] + 1;
65       nzbd  = 1 + idnew[row] - ainew[row];
66       nz    = im[row] - nzbd;
67       fm    = row;
68       while (nz-- > 0) {
69         idx = *ajtmp++;
70         nzbd++;
71         if (idx == i) im[row] = nzbd;
72         do {
73           m  = fm;
74           fm = fill[m];
75         } while (fm < idx);
76         if (fm != idx) {
77           fill[m]   = idx;
78           fill[idx] = fm;
79           fm        = idx;
80           nnz++;
81         }
82       }
83       row = fill[row];
84     }
85     /* copy new filled row into permanent storage */
86     ainew[i+1] = ainew[i] + nnz;
87     if (ainew[i+1] > jmax) {
88       /* allocate a longer ajnew */
89       int maxadd;
90       maxadd = (int) ((f*(ai[n]+1)*(n-i+5))/n);
91       if (maxadd < nnz) maxadd = (n-i)*(nnz+1);
92       jmax += maxadd;
93       ajtmp = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(ajtmp);
94       PetscMemcpy(ajtmp,ajnew,ainew[i]*sizeof(int));
95       PetscFree(ajnew);
96       ajnew = ajtmp;
97       realloc++; /* count how many times we realloc */
98     }
99     ajtmp = ajnew + ainew[i];
100     fm    = fill[n];
101     nzi   = 0;
102     im[i] = nnz;
103     while (nnz--) {
104       if (fm < i) nzi++;
105       *ajtmp++ = fm;
106       fm       = fill[fm];
107     }
108     idnew[i] = ainew[i] + nzi;
109   }
110 
111   if (ai[n] != 0) {
112     double af = ((double)ainew[n])/((double)ai[n]);
113     PLogInfo(A,"Info:MatLUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
114              realloc,f,af);
115     PLogInfo(A,"Info:MatLUFactorSymbolic_SeqBAIJ:Run with -pc_lu_fill %g or use \n",af);
116     PLogInfo(A,"Info:MatLUFactorSymbolic_SeqBAIJ:PCLUSetFill(pc,%g);\n",af);
117     PLogInfo(A,"Info:MatLUFactorSymbolic_SeqBAIJ:for best performance.\n");
118   } else {
119      PLogInfo(A,"Info:MatLUFactorSymbolic_SeqBAIJ:Empty matrix.\n");
120   }
121 
122   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
123   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
124 
125   PetscFree(fill);
126 
127   /* put together the new matrix */
128   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,B); CHKERRQ(ierr);
129   PLogObjectParent(*B,isicol);
130   ierr = ISDestroy(isicol); CHKERRQ(ierr);
131   b = (Mat_SeqBAIJ *) (*B)->data;
132   PetscFree(b->imax);
133   b->singlemalloc = 0;
134   /* the next line frees the default space generated by the Create() */
135   PetscFree(b->a); PetscFree(b->ilen);
136   b->a          = (Scalar *) PetscMalloc((ainew[n]+1)*sizeof(Scalar)*bs2);CHKPTRQ(b->a);
137   b->j          = ajnew;
138   b->i          = ainew;
139   b->diag       = idnew;
140   b->ilen       = 0;
141   b->imax       = 0;
142   b->row        = isrow;
143   b->col        = iscol;
144   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
145   CHKPTRQ(b->solve_work);
146   /* In b structure:  Free imax, ilen, old a, old j.
147      Allocate idnew, solve_work, new a, new j */
148   PLogObjectMemory(*B,(ainew[n]-n)*(sizeof(int)+sizeof(Scalar)));
149   b->maxnz = b->nz = ainew[n];
150 
151   (*B)->info.factor_mallocs    = realloc;
152   (*B)->info.fill_ratio_given  = f;
153   if (ai[i] != 0) {
154     (*B)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[i]);
155   } else {
156     (*B)->info.fill_ratio_needed = 0.0;
157   }
158 
159 
160   return 0;
161 }
162 
163 /* ----------------------------------------------------------- */
164 #undef __FUNC__
165 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_N"
166 int MatLUFactorNumeric_SeqBAIJ_N(Mat A,Mat *B)
167 {
168   Mat             C = *B;
169   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
170   IS              iscol = b->col, isrow = b->row, isicol;
171   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
172   int             *ajtmpold, *ajtmp, nz, row, bslog,*ai=a->i,*aj=a->j,k,flg;
173   int             *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots;
174   Scalar          *ba = b->a,*aa = a->a;
175   register Scalar *pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
176   register int    *pj;
177 
178   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
179   PLogObjectParent(*B,isicol);
180   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
181   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
182   rtmp  = (Scalar *) PetscMalloc(bs2*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
183   PetscMemzero(rtmp,bs2*(n+1)*sizeof(Scalar));
184   /* generate work space needed by dense LU factorization */
185   v_work     = (Scalar *) PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(Scalar));
186                CHKPTRQ(v_work);
187   multiplier = v_work + bs;
188   v_pivots   = (int *) (multiplier + bs2);
189 
190   /* flops in while loop */
191   bslog = 2*bs*bs2;
192 
193   for ( i=0; i<n; i++ ) {
194     nz    = bi[i+1] - bi[i];
195     ajtmp = bj + bi[i];
196     for  ( j=0; j<nz; j++ ) {
197       PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(Scalar));
198     }
199     /* load in initial (unfactored row) */
200     nz       = ai[r[i]+1] - ai[r[i]];
201     ajtmpold = aj + ai[r[i]];
202     v        = aa + bs2*ai[r[i]];
203     for ( j=0; j<nz; j++ ) {
204       PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(Scalar));
205     }
206     row = *ajtmp++;
207     while (row < i) {
208       pc = rtmp + bs2*row;
209 /*      if (*pc) { */
210       for ( flg=0,k=0; k<bs2; k++ ) { if (pc[k]!=0.0) { flg =1; break; }}
211       if (flg) {
212         pv = ba + bs2*diag_offset[row];
213         pj = bj + diag_offset[row] + 1;
214         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
215         nz = bi[row+1] - diag_offset[row] - 1;
216         pv += bs2;
217         for (j=0; j<nz; j++) {
218           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
219         }
220         PLogFlops(bslog*(nz+1)-bs);
221       }
222         row = *ajtmp++;
223     }
224     /* finished row so stick it into b->a */
225     pv = ba + bs2*bi[i];
226     pj = bj + bi[i];
227     nz = bi[i+1] - bi[i];
228     for ( j=0; j<nz; j++ ) {
229       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(Scalar));
230     }
231     diag = diag_offset[i] - bi[i];
232     /* invert diagonal block */
233     w = pv + bs2*diag;
234     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
235   }
236 
237   PetscFree(rtmp); PetscFree(v_work);
238   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
239   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
240   ierr = ISDestroy(isicol); CHKERRQ(ierr);
241   C->factor = FACTOR_LU;
242   C->assembled = PETSC_TRUE;
243   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
244   return 0;
245 }
246 /* ------------------------------------------------------------*/
247 /*
248       Version for when blocks are 5 by 5
249 */
250 #undef __FUNC__
251 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_5"
252 int MatLUFactorNumeric_SeqBAIJ_5(Mat A,Mat *B)
253 {
254   Mat             C = *B;
255   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
256   IS              iscol = b->col, isrow = b->row, isicol;
257   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
258   int             *ajtmpold, *ajtmp, nz, row;
259   int             *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j;
260   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
261   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
262   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
263   Scalar          x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
264   Scalar          p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
265   Scalar          m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
266   Scalar          *ba = b->a,*aa = a->a;
267   register int    *pj;
268 
269   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
270   PLogObjectParent(*B,isicol);
271   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
272   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
273   rtmp  = (Scalar *) PetscMalloc(25*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
274 
275   for ( i=0; i<n; i++ ) {
276     nz    = bi[i+1] - bi[i];
277     ajtmp = bj + bi[i];
278     for  ( j=0; j<nz; j++ ) {
279       x = rtmp+25*ajtmp[j];
280       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
281       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
282       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
283     }
284     /* load in initial (unfactored row) */
285     idx      = r[i];
286     nz       = ai[idx+1] - ai[idx];
287     ajtmpold = aj + ai[idx];
288     v        = aa + 25*ai[idx];
289     for ( j=0; j<nz; j++ ) {
290       x    = rtmp+25*ic[ajtmpold[j]];
291       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
292       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
293       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
294       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
295       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
296       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
297       v    += 25;
298     }
299     row = *ajtmp++;
300     while (row < i) {
301       pc = rtmp + 25*row;
302       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
303       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
304       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
305       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
306       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
307       p25 = pc[24];
308       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
309           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
310           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
311           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
312           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
313           p24 != 0.0 || p25 != 0.0) {
314         pv = ba + 25*diag_offset[row];
315         pj = bj + diag_offset[row] + 1;
316         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
317         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
318         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
319         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
320         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
321         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
322         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
323         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
324         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
325         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
326         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
327 
328         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
329         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
330         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
331         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
332         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
333 
334         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
335         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
336         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
337         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
338         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
339 
340         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
341         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
342         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
343         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
344         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
345 
346         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
347         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
348         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
349         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
350         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
351 
352         nz = bi[row+1] - diag_offset[row] - 1;
353         pv += 25;
354         for (j=0; j<nz; j++) {
355           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
356           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
357           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
358           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
359           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
360           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
361           x    = rtmp + 25*pj[j];
362           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
363           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
364           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
365           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
366           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
367 
368           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
369           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
370           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
371           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
372           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
373 
374           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
375           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
376           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
377           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
378           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
379 
380           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
381           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
382           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
383           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
384           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
385 
386           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
387           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
388           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
389           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
390           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
391 
392           pv   += 25;
393         }
394         PLogFlops(250*nz+225);
395       }
396       row = *ajtmp++;
397     }
398     /* finished row so stick it into b->a */
399     pv = ba + 25*bi[i];
400     pj = bj + bi[i];
401     nz = bi[i+1] - bi[i];
402     for ( j=0; j<nz; j++ ) {
403       x     = rtmp+25*pj[j];
404       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
405       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
406       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
407       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
408       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
409       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
410       pv   += 25;
411     }
412     /* invert diagonal block */
413     w = ba + 25*diag_offset[i];
414     ierr = Kernel_A_gets_inverse_A_5(w); CHKERRQ(ierr);
415   }
416 
417   PetscFree(rtmp);
418   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
419   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
420   ierr = ISDestroy(isicol); CHKERRQ(ierr);
421   C->factor = FACTOR_LU;
422   C->assembled = PETSC_TRUE;
423   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
424   return 0;
425 }
426 
427 /* ------------------------------------------------------------*/
428 /*
429       Version for when blocks are 4 by 4
430 */
431 #undef __FUNC__
432 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_4"
433 int MatLUFactorNumeric_SeqBAIJ_4(Mat A,Mat *B)
434 {
435   Mat             C = *B;
436   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
437   IS              iscol = b->col, isrow = b->row, isicol;
438   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
439   int             *ajtmpold, *ajtmp, nz, row;
440   int             *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j;
441   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
442   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
443   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
444   Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
445   Scalar          m13,m14,m15,m16;
446   Scalar          *ba = b->a,*aa = a->a;
447   register int    *pj;
448 
449   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
450   PLogObjectParent(*B,isicol);
451   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
452   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
453   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
454 
455   for ( i=0; i<n; i++ ) {
456     nz    = bi[i+1] - bi[i];
457     ajtmp = bj + bi[i];
458     for  ( j=0; j<nz; j++ ) {
459       x = rtmp+16*ajtmp[j];
460       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
461       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
462     }
463     /* load in initial (unfactored row) */
464     idx      = r[i];
465     nz       = ai[idx+1] - ai[idx];
466     ajtmpold = aj + ai[idx];
467     v        = aa + 16*ai[idx];
468     for ( j=0; j<nz; j++ ) {
469       x    = rtmp+16*ic[ajtmpold[j]];
470       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
471       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
472       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
473       x[14] = v[14]; x[15] = v[15];
474       v    += 16;
475     }
476     row = *ajtmp++;
477     while (row < i) {
478       pc  = rtmp + 16*row;
479       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
480       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
481       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
482       p15 = pc[14]; p16 = pc[15];
483       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
484           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
485           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
486           || p16 != 0.0) {
487         pv = ba + 16*diag_offset[row];
488         pj = bj + diag_offset[row] + 1;
489         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
490         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
491         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
492         x15 = pv[14]; x16 = pv[15];
493         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
494         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
495         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
496         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
497 
498         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
499         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
500         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
501         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
502 
503         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
504         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
505         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
506         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
507 
508         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
509         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
510         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
511         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
512 
513         nz = bi[row+1] - diag_offset[row] - 1;
514         pv += 16;
515         for (j=0; j<nz; j++) {
516           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
517           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
518           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
519           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
520           x    = rtmp + 16*pj[j];
521           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
522           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
523           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
524           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
525 
526           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
527           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
528           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
529           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
530 
531           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
532           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
533           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
534           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
535 
536           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
537           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
538           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
539           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
540 
541           pv   += 16;
542         }
543         PLogFlops(128*nz+112);
544       }
545       row = *ajtmp++;
546     }
547     /* finished row so stick it into b->a */
548     pv = ba + 16*bi[i];
549     pj = bj + bi[i];
550     nz = bi[i+1] - bi[i];
551     for ( j=0; j<nz; j++ ) {
552       x      = rtmp+16*pj[j];
553       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
554       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
555       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
556       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
557       pv   += 16;
558     }
559     /* invert diagonal block */
560     w = ba + 16*diag_offset[i];
561     ierr = Kernel_A_gets_inverse_A_4(w); CHKERRQ(ierr);
562   }
563 
564   PetscFree(rtmp);
565   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
566   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
567   ierr = ISDestroy(isicol); CHKERRQ(ierr);
568   C->factor = FACTOR_LU;
569   C->assembled = PETSC_TRUE;
570   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
571   return 0;
572 }
573 /*
574       Version for when blocks are 4 by 4 Using natural ordering
575 */
576 #undef __FUNC__
577 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering"
578 int MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering(Mat A,Mat *B)
579 {
580   Mat             C = *B;
581   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
582   int             ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
583   int             *ajtmpold, *ajtmp, nz, row;
584   int             *diag_offset = b->diag,*ai=a->i,*aj=a->j;
585   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
586   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
587   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
588   Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
589   Scalar          m13,m14,m15,m16;
590   Scalar          *ba = b->a,*aa = a->a;
591   register int    *pj;
592 
593   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
594 
595   for ( i=0; i<n; i++ ) {
596     nz    = bi[i+1] - bi[i];
597     ajtmp = bj + bi[i];
598     for  ( j=0; j<nz; j++ ) {
599       x = rtmp+16*ajtmp[j];
600       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
601       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
602     }
603     /* load in initial (unfactored row) */
604     nz       = ai[i+1] - ai[i];
605     ajtmpold = aj + ai[i];
606     v        = aa + 16*ai[i];
607     for ( j=0; j<nz; j++ ) {
608       x    = rtmp+16*ajtmpold[j];
609       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
610       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
611       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
612       x[14] = v[14]; x[15] = v[15];
613       v    += 16;
614     }
615     row = *ajtmp++;
616     while (row < i) {
617       pc  = rtmp + 16*row;
618       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
619       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
620       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
621       p15 = pc[14]; p16 = pc[15];
622       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
623           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
624           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
625           || p16 != 0.0) {
626         pv = ba + 16*diag_offset[row];
627         pj = bj + diag_offset[row] + 1;
628         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
629         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
630         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
631         x15 = pv[14]; x16 = pv[15];
632         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
633         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
634         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
635         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
636 
637         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
638         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
639         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
640         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
641 
642         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
643         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
644         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
645         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
646 
647         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
648         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
649         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
650         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
651 
652         nz = bi[row+1] - diag_offset[row] - 1;
653         pv += 16;
654         for (j=0; j<nz; j++) {
655           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
656           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
657           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
658           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
659           x    = rtmp + 16*pj[j];
660           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
661           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
662           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
663           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
664 
665           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
666           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
667           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
668           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
669 
670           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
671           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
672           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
673           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
674 
675           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
676           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
677           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
678           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
679 
680           pv   += 16;
681         }
682         PLogFlops(128*nz+112);
683       }
684       row = *ajtmp++;
685     }
686     /* finished row so stick it into b->a */
687     pv = ba + 16*bi[i];
688     pj = bj + bi[i];
689     nz = bi[i+1] - bi[i];
690     for ( j=0; j<nz; j++ ) {
691       x      = rtmp+16*pj[j];
692       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
693       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
694       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
695       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
696       pv   += 16;
697     }
698     /* invert diagonal block */
699     w = ba + 16*diag_offset[i];
700     ierr = Kernel_A_gets_inverse_A_4(w); CHKERRQ(ierr);
701   }
702 
703   PetscFree(rtmp);
704   C->factor    = FACTOR_LU;
705   C->assembled = PETSC_TRUE;
706   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
707   return 0;
708 }
709 
710 /* ------------------------------------------------------------*/
711 /*
712       Version for when blocks are 3 by 3
713 */
714 #undef __FUNC__
715 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_3"
716 int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
717 {
718   Mat             C = *B;
719   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
720   IS              iscol = b->col, isrow = b->row, isicol;
721   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
722   int             *ajtmpold, *ajtmp, nz, row, *ai=a->i,*aj=a->j;
723   int             *diag_offset = b->diag,idx;
724   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
725   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
726   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
727   Scalar          *ba = b->a,*aa = a->a;
728   register int    *pj;
729 
730   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
731   PLogObjectParent(*B,isicol);
732   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
733   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
734   rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
735 
736   for ( i=0; i<n; i++ ) {
737     nz    = bi[i+1] - bi[i];
738     ajtmp = bj + bi[i];
739     for  ( j=0; j<nz; j++ ) {
740       x = rtmp + 9*ajtmp[j];
741       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
742     }
743     /* load in initial (unfactored row) */
744     idx      = r[i];
745     nz       = ai[idx+1] - ai[idx];
746     ajtmpold = aj + ai[idx];
747     v        = aa + 9*ai[idx];
748     for ( j=0; j<nz; j++ ) {
749       x    = rtmp + 9*ic[ajtmpold[j]];
750       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
751       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
752       v    += 9;
753     }
754     row = *ajtmp++;
755     while (row < i) {
756       pc = rtmp + 9*row;
757       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
758       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
759       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
760           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
761         pv = ba + 9*diag_offset[row];
762         pj = bj + diag_offset[row] + 1;
763         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
764         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
765         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
766         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
767         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
768 
769         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
770         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
771         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
772 
773         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
774         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
775         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
776         nz = bi[row+1] - diag_offset[row] - 1;
777         pv += 9;
778         for (j=0; j<nz; j++) {
779           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
780           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
781           x    = rtmp + 9*pj[j];
782           x[0] -= m1*x1 + m4*x2 + m7*x3;
783           x[1] -= m2*x1 + m5*x2 + m8*x3;
784           x[2] -= m3*x1 + m6*x2 + m9*x3;
785 
786           x[3] -= m1*x4 + m4*x5 + m7*x6;
787           x[4] -= m2*x4 + m5*x5 + m8*x6;
788           x[5] -= m3*x4 + m6*x5 + m9*x6;
789 
790           x[6] -= m1*x7 + m4*x8 + m7*x9;
791           x[7] -= m2*x7 + m5*x8 + m8*x9;
792           x[8] -= m3*x7 + m6*x8 + m9*x9;
793           pv   += 9;
794         }
795         PLogFlops(54*nz+36);
796       }
797       row = *ajtmp++;
798     }
799     /* finished row so stick it into b->a */
800     pv = ba + 9*bi[i];
801     pj = bj + bi[i];
802     nz = bi[i+1] - bi[i];
803     for ( j=0; j<nz; j++ ) {
804       x     = rtmp + 9*pj[j];
805       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
806       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
807       pv   += 9;
808     }
809     /* invert diagonal block */
810     w = ba + 9*diag_offset[i];
811     ierr = Kernel_A_gets_inverse_A_3(w); CHKERRQ(ierr);
812   }
813 
814   PetscFree(rtmp);
815   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
816   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
817   ierr = ISDestroy(isicol); CHKERRQ(ierr);
818   C->factor = FACTOR_LU;
819   C->assembled = PETSC_TRUE;
820   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
821   return 0;
822 }
823 
824 /* ------------------------------------------------------------*/
825 /*
826       Version for when blocks are 2 by 2
827 */
828 #undef __FUNC__
829 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_2"
830 int MatLUFactorNumeric_SeqBAIJ_2(Mat A,Mat *B)
831 {
832   Mat             C = *B;
833   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
834   IS              iscol = b->col, isrow = b->row, isicol;
835   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
836   int             *ajtmpold, *ajtmp, nz, row, v_pivots[2];
837   int             *diag_offset=b->diag,bs = 2,idx,*ai=a->i,*aj=a->j;
838   register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
839   Scalar          p1,p2,p3,p4,v_work[2];
840   Scalar          *ba = b->a,*aa = a->a;
841   register int    *pj;
842 
843   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
844   PLogObjectParent(*B,isicol);
845   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
846   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
847   rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
848 
849   for ( i=0; i<n; i++ ) {
850     nz    = bi[i+1] - bi[i];
851     ajtmp = bj + bi[i];
852     for  ( j=0; j<nz; j++ ) {
853       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
854     }
855     /* load in initial (unfactored row) */
856     idx      = r[i];
857     nz       = ai[idx+1] - ai[idx];
858     ajtmpold = aj + ai[idx];
859     v        = aa + 4*ai[idx];
860     for ( j=0; j<nz; j++ ) {
861       x    = rtmp+4*ic[ajtmpold[j]];
862       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
863       v    += 4;
864     }
865     row = *ajtmp++;
866     while (row < i) {
867       pc = rtmp + 4*row;
868       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
869       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
870         pv = ba + 4*diag_offset[row];
871         pj = bj + diag_offset[row] + 1;
872         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
873         pc[0] = m1 = p1*x1 + p3*x2;
874         pc[1] = m2 = p2*x1 + p4*x2;
875         pc[2] = m3 = p1*x3 + p3*x4;
876         pc[3] = m4 = p2*x3 + p4*x4;
877         nz = bi[row+1] - diag_offset[row] - 1;
878         pv += 4;
879         for (j=0; j<nz; j++) {
880           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
881           x    = rtmp + 4*pj[j];
882           x[0] -= m1*x1 + m3*x2;
883           x[1] -= m2*x1 + m4*x2;
884           x[2] -= m1*x3 + m3*x4;
885           x[3] -= m2*x3 + m4*x4;
886           pv   += 4;
887         }
888         PLogFlops(16*nz+12);
889       }
890       row = *ajtmp++;
891     }
892     /* finished row so stick it into b->a */
893     pv = ba + 4*bi[i];
894     pj = bj + bi[i];
895     nz = bi[i+1] - bi[i];
896     for ( j=0; j<nz; j++ ) {
897       x     = rtmp+4*pj[j];
898       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
899       pv   += 4;
900     }
901     /* invert diagonal block */
902     w = ba + 4*diag_offset[i];
903     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
904   }
905 
906   PetscFree(rtmp);
907   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
908   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
909   ierr = ISDestroy(isicol); CHKERRQ(ierr);
910   C->factor = FACTOR_LU;
911   C->assembled = PETSC_TRUE;
912   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
913   return 0;
914 }
915 
916 /* ----------------------------------------------------------- */
917 /*
918      Version for when blocks are 1 by 1.
919 */
920 #undef __FUNC__
921 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_1"
922 int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
923 {
924   Mat             C = *B;
925   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
926   IS              iscol = b->col, isrow = b->row, isicol;
927   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
928   int             *ajtmpold, *ajtmp, nz, row,*ai = a->i,*aj = a->j;
929   int             *diag_offset = b->diag,diag;
930   register Scalar *pv,*v,*rtmp,multiplier,*pc;
931   Scalar          *ba = b->a,*aa = a->a;
932   register int    *pj;
933 
934   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
935   PLogObjectParent(*B,isicol);
936   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
937   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
938   rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
939 
940   for ( i=0; i<n; i++ ) {
941     nz    = bi[i+1] - bi[i];
942     ajtmp = bj + bi[i];
943     for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;
944 
945     /* load in initial (unfactored row) */
946     nz       = ai[r[i]+1] - ai[r[i]];
947     ajtmpold = aj + ai[r[i]];
948     v        = aa + ai[r[i]];
949     for ( j=0; j<nz; j++ ) rtmp[ic[ajtmpold[j]]] =  v[j];
950 
951     row = *ajtmp++;
952     while (row < i) {
953       pc = rtmp + row;
954       if (*pc != 0.0) {
955         pv         = ba + diag_offset[row];
956         pj         = bj + diag_offset[row] + 1;
957         multiplier = *pc * *pv++;
958         *pc        = multiplier;
959         nz         = bi[row+1] - diag_offset[row] - 1;
960         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
961         PLogFlops(1+2*nz);
962       }
963       row = *ajtmp++;
964     }
965     /* finished row so stick it into b->a */
966     pv = ba + bi[i];
967     pj = bj + bi[i];
968     nz = bi[i+1] - bi[i];
969     for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
970     diag = diag_offset[i] - bi[i];
971     /* check pivot entry for current row */
972     if (pv[diag] == 0.0) {
973       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
974     }
975     pv[diag] = 1.0/pv[diag];
976   }
977 
978   PetscFree(rtmp);
979   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
980   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
981   ierr = ISDestroy(isicol); CHKERRQ(ierr);
982   C->factor    = FACTOR_LU;
983   C->assembled = PETSC_TRUE;
984   PLogFlops(b->n);
985   return 0;
986 }
987 
988 /* ----------------------------------------------------------- */
989 #undef __FUNC__
990 #define __FUNC__ "MatLUFactor_SeqBAIJ"
991 int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
992 {
993   Mat_SeqBAIJ *mat = (Mat_SeqBAIJ *) A->data;
994   int         ierr;
995   Mat         C;
996 
997   ierr = MatLUFactorSymbolic(A,row,col,f,&C); CHKERRQ(ierr);
998   ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);
999 
1000   /* free all the data structures from mat */
1001   PetscFree(mat->a);
1002   if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
1003   if (mat->diag) PetscFree(mat->diag);
1004   if (mat->ilen) PetscFree(mat->ilen);
1005   if (mat->imax) PetscFree(mat->imax);
1006   if (mat->solve_work) PetscFree(mat->solve_work);
1007   if (mat->mult_work) PetscFree(mat->mult_work);
1008   PetscFree(mat);
1009 
1010   PetscMemcpy(A,C,sizeof(struct _p_Mat));
1011   PetscHeaderDestroy(C);
1012   return 0;
1013 }
1014 /* ----------------------------------------------------------- */
1015 #undef __FUNC__
1016 #define __FUNC__ "MatSolve_SeqBAIJ_N"
1017 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
1018 {
1019   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1020   IS              iscol=a->col,isrow=a->row;
1021   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
1022   int             nz,bs=a->bs,bs2=a->bs2,*rout,*cout;
1023   Scalar          *aa=a->a,*sum;
1024   register Scalar *x,*b,*lsum,*tmp,*v;
1025 
1026   VecGetArray_Fast(bb,b);
1027   VecGetArray_Fast(xx,x);
1028   tmp  = a->solve_work;
1029 
1030   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1031   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1032 
1033   /* forward solve the lower triangular */
1034   PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
1035   for ( i=1; i<n; i++ ) {
1036     v   = aa + bs2*ai[i];
1037     vi  = aj + ai[i];
1038     nz  = a->diag[i] - ai[i];
1039     sum = tmp + bs*i;
1040     PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
1041     while (nz--) {
1042       Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++));
1043       v += bs2;
1044     }
1045   }
1046   /* backward solve the upper triangular */
1047   lsum = a->solve_work + a->n;
1048   for ( i=n-1; i>=0; i-- ){
1049     v   = aa + bs2*(a->diag[i] + 1);
1050     vi  = aj + a->diag[i] + 1;
1051     nz  = ai[i+1] - a->diag[i] - 1;
1052     PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
1053     while (nz--) {
1054       Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++));
1055       v += bs2;
1056     }
1057     Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs);
1058     PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
1059   }
1060 
1061   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1062   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1063   VecRestoreArray_Fast(bb,b);
1064   VecRestoreArray_Fast(xx,x);
1065   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
1066   return 0;
1067 }
1068 
1069 #undef __FUNC__
1070 #define __FUNC__ "MatSolve_SeqBAIJ_7"
1071 int MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
1072 {
1073   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1074   IS              iscol=a->col,isrow=a->row;
1075   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1076   int             *diag = a->diag;
1077   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,sum6,sum7,x1,x2,x3,x4,x5,x6,x7;
1078   register Scalar *x,*b,*tmp,*v;
1079 
1080   VecGetArray_Fast(bb,b);
1081   VecGetArray_Fast(xx,x);
1082   tmp  = a->solve_work;
1083 
1084   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1085   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1086 
1087   /* forward solve the lower triangular */
1088   idx    = 7*(*r++);
1089   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1090   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
1091   tmp[5] = b[5+idx]; tmp[6] = b[6+idx];
1092 
1093   for ( i=1; i<n; i++ ) {
1094     v     = aa + 49*ai[i];
1095     vi    = aj + ai[i];
1096     nz    = diag[i] - ai[i];
1097     idx   = 7*(*r++);
1098     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1099     sum5  = b[4+idx];sum6 = b[5+idx];sum7 = b[6+idx];
1100     while (nz--) {
1101       idx   = 7*(*vi++);
1102       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
1103       x4    = tmp[3+idx];x5 = tmp[4+idx];
1104       x6    = tmp[5+idx];x7 = tmp[6+idx];
1105       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
1106       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
1107       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
1108       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
1109       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
1110       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
1111       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
1112       v += 49;
1113     }
1114     idx = 7*i;
1115     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1116     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
1117     tmp[5+idx] = sum6;tmp[6+idx] = sum7;
1118   }
1119   /* backward solve the upper triangular */
1120   for ( i=n-1; i>=0; i-- ){
1121     v    = aa + 49*diag[i] + 49;
1122     vi   = aj + diag[i] + 1;
1123     nz   = ai[i+1] - diag[i] - 1;
1124     idt  = 7*i;
1125     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1126     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
1127     sum6 = tmp[5+idt];sum7 = tmp[6+idt];
1128     while (nz--) {
1129       idx   = 7*(*vi++);
1130       x1    = tmp[idx];   x2 = tmp[1+idx];
1131       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
1132       x6    = tmp[5+idx]; x7 = tmp[6+idx];
1133       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
1134       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
1135       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
1136       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
1137       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
1138       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
1139       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
1140       v += 49;
1141     }
1142     idc = 7*(*c--);
1143     v   = aa + 49*diag[i];
1144     x[idc]   = tmp[idt]   = v[0]*sum1+v[7]*sum2+v[14]*sum3+
1145                                  v[21]*sum4+v[28]*sum5+v[35]*sum6+v[42]*sum7;
1146     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[8]*sum2+v[15]*sum3+
1147                                  v[22]*sum4+v[29]*sum5+v[36]*sum6+v[43]*sum7;
1148     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[9]*sum2+v[16]*sum3+
1149                                  v[23]*sum4+v[30]*sum5+v[37]*sum6+v[44]*sum7;
1150     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[10]*sum2+v[17]*sum3+
1151                                  v[24]*sum4+v[31]*sum5+v[38]*sum6+v[45]*sum7;
1152     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[11]*sum2+v[18]*sum3+
1153                                  v[25]*sum4+v[32]*sum5+v[39]*sum6+v[46]*sum7;
1154     x[5+idc] = tmp[5+idt] = v[5]*sum1+v[12]*sum2+v[19]*sum3+
1155                                  v[26]*sum4+v[33]*sum5+v[40]*sum6+v[47]*sum7;
1156     x[6+idc] = tmp[6+idt] = v[6]*sum1+v[13]*sum2+v[20]*sum3+
1157                                  v[27]*sum4+v[34]*sum5+v[41]*sum6+v[48]*sum7;
1158   }
1159 
1160   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1161   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1162   VecRestoreArray_Fast(bb,b);
1163   VecRestoreArray_Fast(xx,x);
1164   PLogFlops(2*49*(a->nz) - a->n);
1165   return 0;
1166 }
1167 
1168 #undef __FUNC__
1169 #define __FUNC__ "MatSolve_SeqBAIJ_5"
1170 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
1171 {
1172   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1173   IS              iscol=a->col,isrow=a->row;
1174   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1175   int             *diag = a->diag;
1176   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
1177   register Scalar *x,*b,*tmp,*v;
1178 
1179   VecGetArray_Fast(bb,b);
1180   VecGetArray_Fast(xx,x);
1181   tmp  = a->solve_work;
1182 
1183   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1184   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1185 
1186   /* forward solve the lower triangular */
1187   idx    = 5*(*r++);
1188   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1189   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
1190   for ( i=1; i<n; i++ ) {
1191     v     = aa + 25*ai[i];
1192     vi    = aj + ai[i];
1193     nz    = diag[i] - ai[i];
1194     idx   = 5*(*r++);
1195     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1196     sum5  = b[4+idx];
1197     while (nz--) {
1198       idx   = 5*(*vi++);
1199       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
1200       x4    = tmp[3+idx];x5 = tmp[4+idx];
1201       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1202       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1203       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1204       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1205       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1206       v += 25;
1207     }
1208     idx = 5*i;
1209     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1210     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
1211   }
1212   /* backward solve the upper triangular */
1213   for ( i=n-1; i>=0; i-- ){
1214     v    = aa + 25*diag[i] + 25;
1215     vi   = aj + diag[i] + 1;
1216     nz   = ai[i+1] - diag[i] - 1;
1217     idt  = 5*i;
1218     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1219     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
1220     while (nz--) {
1221       idx   = 5*(*vi++);
1222       x1    = tmp[idx];   x2 = tmp[1+idx];
1223       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
1224       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1225       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1226       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1227       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1228       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1229       v += 25;
1230     }
1231     idc = 5*(*c--);
1232     v   = aa + 25*diag[i];
1233     x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
1234                                  v[15]*sum4+v[20]*sum5;
1235     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
1236                                  v[16]*sum4+v[21]*sum5;
1237     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
1238                                  v[17]*sum4+v[22]*sum5;
1239     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
1240                                  v[18]*sum4+v[23]*sum5;
1241     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
1242                                  v[19]*sum4+v[24]*sum5;
1243   }
1244 
1245   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1246   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1247   VecRestoreArray_Fast(bb,b);
1248   VecRestoreArray_Fast(xx,x);
1249   PLogFlops(2*25*(a->nz) - a->n);
1250   return 0;
1251 }
1252 
1253 #undef __FUNC__
1254 #define __FUNC__ "MatSolve_SeqBAIJ_4"
1255 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
1256 {
1257   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
1258   IS              iscol=a->col,isrow=a->row;
1259   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1260   int             *diag = a->diag;
1261   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
1262   register Scalar *x,*b,*tmp,*v;
1263 
1264   VecGetArray_Fast(bb,b);
1265   VecGetArray_Fast(xx,x);
1266   tmp  = a->solve_work;
1267 
1268   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1269   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1270 
1271   /* forward solve the lower triangular */
1272   idx    = 4*(*r++);
1273   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1274   tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
1275   for ( i=1; i<n; i++ ) {
1276     v     = aa + 16*ai[i];
1277     vi    = aj + ai[i];
1278     nz    = diag[i] - ai[i];
1279     idx   = 4*(*r++);
1280     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1281     while (nz--) {
1282       idx   = 4*(*vi++);
1283       x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
1284       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1285       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1286       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1287       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1288       v    += 16;
1289     }
1290     idx        = 4*i;
1291     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1292     tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1293   }
1294   /* backward solve the upper triangular */
1295   for ( i=n-1; i>=0; i-- ){
1296     v    = aa + 16*diag[i] + 16;
1297     vi   = aj + diag[i] + 1;
1298     nz   = ai[i+1] - diag[i] - 1;
1299     idt  = 4*i;
1300     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1301     sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1302     while (nz--) {
1303       idx   = 4*(*vi++);
1304       x1    = tmp[idx];   x2 = tmp[1+idx];
1305       x3    = tmp[2+idx]; x4 = tmp[3+idx];
1306       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1307       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1308       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1309       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1310       v += 16;
1311     }
1312     idc      = 4*(*c--);
1313     v        = aa + 16*diag[i];
1314     x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1315     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1316     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1317     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1318   }
1319 
1320   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1321   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1322   VecRestoreArray_Fast(bb,b);
1323   VecRestoreArray_Fast(xx,x);
1324   PLogFlops(2*16*(a->nz) - a->n);
1325   return 0;
1326 }
1327 
1328 /*
1329       Special case where the matrix was ILU(0) factored in the natural
1330    ordering. This eliminates the need for the column and row permutation.
1331 */
1332 #undef __FUNC__
1333 #define __FUNC__ "MatSolve_SeqBAIJ_4_NaturalOrdering"
1334 int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
1335 {
1336   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
1337   int             i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
1338   int             *diag = a->diag,jdx;
1339   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
1340   register Scalar *x,*b,*v;
1341 
1342   VecGetArray_Fast(bb,b);
1343   VecGetArray_Fast(xx,x);
1344 
1345   /* forward solve the lower triangular */
1346   idx    = 0;
1347   x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; x[3] = b[3+idx];
1348   for ( i=1; i<n; i++ ) {
1349     v     =  aa + 16*ai[i];
1350     vi    =  aj + ai[i];
1351     nz    =  diag[i] - ai[i];
1352     idx   =  4*i;
1353     sum1  =  b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1354     while (nz--) {
1355       jdx   = 4*(*vi++);
1356       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];
1357       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1358       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1359       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1360       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1361       v    += 16;
1362     }
1363     x[idx]   = sum1;
1364     x[1+idx] = sum2;
1365     x[2+idx] = sum3;
1366     x[3+idx] = sum4;
1367   }
1368   /* backward solve the upper triangular */
1369   for ( i=n-1; i>=0; i-- ){
1370     v    = aa + 16*diag[i] + 16;
1371     vi   = aj + diag[i] + 1;
1372     nz   = ai[i+1] - diag[i] - 1;
1373     idt  = 4*i;
1374     sum1 = x[idt];  sum2 = x[1+idt];
1375     sum3 = x[2+idt];sum4 = x[3+idt];
1376     while (nz--) {
1377       idx   = 4*(*vi++);
1378       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx];
1379       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1380       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1381       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1382       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1383       v += 16;
1384     }
1385     v        = aa + 16*diag[i];
1386     x[idt]   = v[0]*sum1 + v[4]*sum2 + v[8]*sum3  + v[12]*sum4;
1387     x[1+idt] = v[1]*sum1 + v[5]*sum2 + v[9]*sum3  + v[13]*sum4;
1388     x[2+idt] = v[2]*sum1 + v[6]*sum2 + v[10]*sum3 + v[14]*sum4;
1389     x[3+idt] = v[3]*sum1 + v[7]*sum2 + v[11]*sum3 + v[15]*sum4;
1390   }
1391 
1392   VecRestoreArray_Fast(bb,b);
1393   VecRestoreArray_Fast(xx,x);
1394   PLogFlops(2*16*(a->nz) - a->n);
1395   return 0;
1396 }
1397 
1398 
1399 #undef __FUNC__
1400 #define __FUNC__ "MatSolve_SeqBAIJ_3"
1401 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
1402 {
1403   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1404   IS              iscol=a->col,isrow=a->row;
1405   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1406   int             *diag = a->diag;
1407   Scalar          *aa=a->a,sum1,sum2,sum3,x1,x2,x3;
1408   register Scalar *x,*b,*tmp,*v;
1409 
1410   VecGetArray_Fast(bb,b);
1411   VecGetArray_Fast(xx,x);
1412   tmp  = a->solve_work;
1413 
1414   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1415   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1416 
1417   /* forward solve the lower triangular */
1418   idx    = 3*(*r++);
1419   tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
1420   for ( i=1; i<n; i++ ) {
1421     v     = aa + 9*ai[i];
1422     vi    = aj + ai[i];
1423     nz    = diag[i] - ai[i];
1424     idx   = 3*(*r++);
1425     sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
1426     while (nz--) {
1427       idx   = 3*(*vi++);
1428       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1429       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1430       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1431       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1432       v += 9;
1433     }
1434     idx = 3*i;
1435     tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
1436   }
1437   /* backward solve the upper triangular */
1438   for ( i=n-1; i>=0; i-- ){
1439     v    = aa + 9*diag[i] + 9;
1440     vi   = aj + diag[i] + 1;
1441     nz   = ai[i+1] - diag[i] - 1;
1442     idt  = 3*i;
1443     sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
1444     while (nz--) {
1445       idx   = 3*(*vi++);
1446       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1447       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1448       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1449       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1450       v += 9;
1451     }
1452     idc = 3*(*c--);
1453     v   = aa + 9*diag[i];
1454     x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
1455     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
1456     x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
1457   }
1458   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1459   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1460   VecRestoreArray_Fast(bb,b);
1461   VecRestoreArray_Fast(xx,x);
1462   PLogFlops(2*9*(a->nz) - a->n);
1463   return 0;
1464 }
1465 
1466 #undef __FUNC__
1467 #define __FUNC__ "MatSolve_SeqBAIJ_2"
1468 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
1469 {
1470   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1471   IS              iscol=a->col,isrow=a->row;
1472   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1473   int             *diag = a->diag;
1474   Scalar          *aa=a->a,sum1,sum2,x1,x2;
1475   register Scalar *x,*b,*tmp,*v;
1476 
1477   VecGetArray_Fast(bb,b);
1478   VecGetArray_Fast(xx,x);
1479   tmp  = a->solve_work;
1480 
1481   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1482   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1483 
1484   /* forward solve the lower triangular */
1485   idx    = 2*(*r++);
1486   tmp[0] = b[idx]; tmp[1] = b[1+idx];
1487   for ( i=1; i<n; i++ ) {
1488     v     = aa + 4*ai[i];
1489     vi    = aj + ai[i];
1490     nz    = diag[i] - ai[i];
1491     idx   = 2*(*r++);
1492     sum1  = b[idx]; sum2 = b[1+idx];
1493     while (nz--) {
1494       idx   = 2*(*vi++);
1495       x1    = tmp[idx]; x2 = tmp[1+idx];
1496       sum1 -= v[0]*x1 + v[2]*x2;
1497       sum2 -= v[1]*x1 + v[3]*x2;
1498       v += 4;
1499     }
1500     idx = 2*i;
1501     tmp[idx] = sum1; tmp[1+idx] = sum2;
1502   }
1503   /* backward solve the upper triangular */
1504   for ( i=n-1; i>=0; i-- ){
1505     v    = aa + 4*diag[i] + 4;
1506     vi   = aj + diag[i] + 1;
1507     nz   = ai[i+1] - diag[i] - 1;
1508     idt  = 2*i;
1509     sum1 = tmp[idt]; sum2 = tmp[1+idt];
1510     while (nz--) {
1511       idx   = 2*(*vi++);
1512       x1    = tmp[idx]; x2 = tmp[1+idx];
1513       sum1 -= v[0]*x1 + v[2]*x2;
1514       sum2 -= v[1]*x1 + v[3]*x2;
1515       v += 4;
1516     }
1517     idc = 2*(*c--);
1518     v   = aa + 4*diag[i];
1519     x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
1520     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
1521   }
1522   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1523   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1524   VecRestoreArray_Fast(bb,b);
1525   VecRestoreArray_Fast(xx,x);
1526   PLogFlops(2*4*(a->nz) - a->n);
1527   return 0;
1528 }
1529 
1530 
1531 #undef __FUNC__
1532 #define __FUNC__ "MatSolve_SeqBAIJ_1"
1533 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
1534 {
1535   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1536   IS              iscol=a->col,isrow=a->row;
1537   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout;
1538   int             *diag = a->diag;
1539   Scalar          *aa=a->a,sum1;
1540   register Scalar *x,*b,*tmp,*v;
1541 
1542   if (!n) return 0;
1543 
1544   VecGetArray_Fast(bb,b);
1545   VecGetArray_Fast(xx,x);
1546   tmp  = a->solve_work;
1547 
1548   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1549   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1550 
1551   /* forward solve the lower triangular */
1552   tmp[0] = b[*r++];
1553   for ( i=1; i<n; i++ ) {
1554     v     = aa + ai[i];
1555     vi    = aj + ai[i];
1556     nz    = diag[i] - ai[i];
1557     sum1  = b[*r++];
1558     while (nz--) {
1559       sum1 -= (*v++)*tmp[*vi++];
1560     }
1561     tmp[i] = sum1;
1562   }
1563   /* backward solve the upper triangular */
1564   for ( i=n-1; i>=0; i-- ){
1565     v    = aa + diag[i] + 1;
1566     vi   = aj + diag[i] + 1;
1567     nz   = ai[i+1] - diag[i] - 1;
1568     sum1 = tmp[i];
1569     while (nz--) {
1570       sum1 -= (*v++)*tmp[*vi++];
1571     }
1572     x[*c--] = tmp[i] = aa[diag[i]]*sum1;
1573   }
1574 
1575   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1576   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1577   VecRestoreArray_Fast(bb,b);
1578   VecRestoreArray_Fast(xx,x);
1579   PLogFlops(2*1*(a->nz) - a->n);
1580   return 0;
1581 }
1582 
1583 extern int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat,Vec,Vec);
1584 /* ----------------------------------------------------------------*/
1585 /*
1586      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
1587    except that the data structure of Mat_SeqAIJ is slightly different.
1588    Not a good example of code reuse.
1589 */
1590 #undef __FUNC__
1591 #define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ"
1592 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
1593                                  Mat *fact)
1594 {
1595   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
1596   IS          isicol;
1597   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
1598   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
1599   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
1600   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
1601   PetscTruth  col_identity, row_identity;
1602 
1603   /* special case that simply copies fill pattern */
1604   PetscValidHeaderSpecific(isrow,IS_COOKIE);
1605   PetscValidHeaderSpecific(iscol,IS_COOKIE);
1606   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
1607   if (levels == 0 && row_identity && col_identity) {
1608     ierr = MatConvertSameType_SeqBAIJ(A,fact,DO_NOT_COPY_VALUES); CHKERRQ(ierr);
1609     (*fact)->factor = FACTOR_LU;
1610     b               = (Mat_SeqBAIJ *) (*fact)->data;
1611     if (!b->diag) {
1612       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
1613     }
1614     b->row        = isrow;
1615     b->col        = iscol;
1616     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
1617     /*
1618         Blocksize 4 has a special faster solver for ILU(0) factorization
1619         with natural ordering
1620     */
1621     if (b->bs == 4) {
1622       (*fact)->ops.lufactornumeric = MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering;
1623       (*fact)->ops.solve           = MatSolve_SeqBAIJ_4_NaturalOrdering;
1624     }
1625     return 0;
1626   }
1627 
1628   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
1629   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
1630   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
1631 
1632   /* get new row pointers */
1633   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
1634   ainew[0] = 0;
1635   /* don't know how many column pointers are needed so estimate */
1636   jmax = (int) (f*ai[n] + 1);
1637   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
1638   /* ajfill is level of fill for each fill entry */
1639   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
1640   /* fill is a linked list of nonzeros in active row */
1641   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
1642   /* im is level for each filled value */
1643   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
1644   /* dloc is location of diagonal in factor */
1645   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
1646   dloc[0]  = 0;
1647   for ( prow=0; prow<n; prow++ ) {
1648     /* first copy previous fill into linked list */
1649     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
1650     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
1651     xi      = aj + ai[r[prow]];
1652     fill[n] = n;
1653     while (nz--) {
1654       fm  = n;
1655       idx = ic[*xi++];
1656       do {
1657         m  = fm;
1658         fm = fill[m];
1659       } while (fm < idx);
1660       fill[m]   = idx;
1661       fill[idx] = fm;
1662       im[idx]   = 0;
1663     }
1664     nzi = 0;
1665     row = fill[n];
1666     while ( row < prow ) {
1667       incrlev = im[row] + 1;
1668       nz      = dloc[row];
1669       xi      = ajnew  + ainew[row] + nz;
1670       flev    = ajfill + ainew[row] + nz + 1;
1671       nnz     = ainew[row+1] - ainew[row] - nz - 1;
1672       if (*xi++ != row) {
1673         SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot: try running with -pc_ilu_nonzeros_along_diagonal");
1674       }
1675       fm      = row;
1676       while (nnz-- > 0) {
1677         idx = *xi++;
1678         if (*flev + incrlev > levels) {
1679           flev++;
1680           continue;
1681         }
1682         do {
1683           m  = fm;
1684           fm = fill[m];
1685         } while (fm < idx);
1686         if (fm != idx) {
1687           im[idx]   = *flev + incrlev;
1688           fill[m]   = idx;
1689           fill[idx] = fm;
1690           fm        = idx;
1691           nzf++;
1692         }
1693         else {
1694           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
1695         }
1696         flev++;
1697       }
1698       row = fill[row];
1699       nzi++;
1700     }
1701     /* copy new filled row into permanent storage */
1702     ainew[prow+1] = ainew[prow] + nzf;
1703     if (ainew[prow+1] > jmax) {
1704       /* allocate a longer ajnew */
1705       int maxadd;
1706       maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n);
1707       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
1708       jmax += maxadd;
1709       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1710       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
1711       PetscFree(ajnew);
1712       ajnew = xi;
1713       /* allocate a longer ajfill */
1714       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1715       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
1716       PetscFree(ajfill);
1717       ajfill = xi;
1718       realloc++;
1719     }
1720     xi          = ajnew + ainew[prow];
1721     flev        = ajfill + ainew[prow];
1722     dloc[prow]  = nzi;
1723     fm          = fill[n];
1724     while (nzf--) {
1725       *xi++   = fm;
1726       *flev++ = im[fm];
1727       fm      = fill[fm];
1728     }
1729   }
1730   PetscFree(ajfill);
1731   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1732   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
1733   ierr = ISDestroy(isicol); CHKERRQ(ierr);
1734   PetscFree(fill); PetscFree(im);
1735 
1736   {
1737     double af = ((double)ainew[n])/((double)ai[n]);
1738     PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
1739              realloc,f,af);
1740     PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:Run with -pc_ilu_fill %g or use \n",af);
1741     PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:PCILUSetFill(pc,%g);\n",af);
1742     PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:for best performance.\n");
1743   }
1744 
1745   /* put together the new matrix */
1746   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
1747   b = (Mat_SeqBAIJ *) (*fact)->data;
1748   PetscFree(b->imax);
1749   b->singlemalloc = 0;
1750   len = bs2*ainew[n]*sizeof(Scalar);
1751   /* the next line frees the default space generated by the Create() */
1752   PetscFree(b->a); PetscFree(b->ilen);
1753   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
1754   b->j          = ajnew;
1755   b->i          = ainew;
1756   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
1757   b->diag       = dloc;
1758   b->ilen       = 0;
1759   b->imax       = 0;
1760   b->row        = isrow;
1761   b->col        = iscol;
1762   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
1763   CHKPTRQ(b->solve_work);
1764   /* In b structure:  Free imax, ilen, old a, old j.
1765      Allocate dloc, solve_work, new a, new j */
1766   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
1767   b->maxnz          = b->nz = ainew[n];
1768   (*fact)->factor   = FACTOR_LU;
1769 
1770   (*fact)->info.factor_mallocs    = realloc;
1771   (*fact)->info.fill_ratio_given  = f;
1772   (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);
1773 
1774   return 0;
1775 }
1776 
1777 
1778 
1779 
1780