xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision 95b207ea01a3fbf8432ea0e0186aba3bf9cd0565)
1 #ifdef PETSC_RCS_HEADER
2 static char vcid[] = "$Id: baijfact.c,v 1.50 1997/07/09 20:55:07 balay 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 printf("greetings\n");
594 
595   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
596 
597   for ( i=0; i<n; i++ ) {
598     nz    = bi[i+1] - bi[i];
599     ajtmp = bj + bi[i];
600     for  ( j=0; j<nz; j++ ) {
601       x = rtmp+16*ajtmp[j];
602       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
603       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
604     }
605     /* load in initial (unfactored row) */
606     nz       = ai[i+1] - ai[i];
607     ajtmpold = aj + ai[i];
608     v        = aa + 16*ai[i];
609     for ( j=0; j<nz; j++ ) {
610       x    = rtmp+16*ajtmpold[j];
611       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
612       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
613       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
614       x[14] = v[14]; x[15] = v[15];
615       v    += 16;
616     }
617     row = *ajtmp++;
618     while (row < i) {
619       pc  = rtmp + 16*row;
620       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
621       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
622       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
623       p15 = pc[14]; p16 = pc[15];
624       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
625           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
626           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
627           || p16 != 0.0) {
628         pv = ba + 16*diag_offset[row];
629         pj = bj + diag_offset[row] + 1;
630         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
631         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
632         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
633         x15 = pv[14]; x16 = pv[15];
634         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
635         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
636         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
637         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
638 
639         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
640         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
641         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
642         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
643 
644         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
645         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
646         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
647         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
648 
649         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
650         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
651         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
652         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
653 
654         nz = bi[row+1] - diag_offset[row] - 1;
655         pv += 16;
656         for (j=0; j<nz; j++) {
657           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
658           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
659           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
660           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
661           x    = rtmp + 16*pj[j];
662           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
663           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
664           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
665           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
666 
667           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
668           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
669           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
670           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
671 
672           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
673           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
674           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
675           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
676 
677           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
678           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
679           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
680           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
681 
682           pv   += 16;
683         }
684         PLogFlops(128*nz+112);
685       }
686       row = *ajtmp++;
687     }
688     /* finished row so stick it into b->a */
689     pv = ba + 16*bi[i];
690     pj = bj + bi[i];
691     nz = bi[i+1] - bi[i];
692     for ( j=0; j<nz; j++ ) {
693       x      = rtmp+16*pj[j];
694       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
695       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
696       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
697       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
698       pv   += 16;
699     }
700     /* invert diagonal block */
701     w = ba + 16*diag_offset[i];
702     ierr = Kernel_A_gets_inverse_A_4(w); CHKERRQ(ierr);
703   }
704 
705   PetscFree(rtmp);
706   C->factor    = FACTOR_LU;
707   C->assembled = PETSC_TRUE;
708   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
709   return 0;
710 }
711 
712 /* ------------------------------------------------------------*/
713 /*
714       Version for when blocks are 3 by 3
715 */
716 #undef __FUNC__
717 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_3"
718 int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
719 {
720   Mat             C = *B;
721   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
722   IS              iscol = b->col, isrow = b->row, isicol;
723   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
724   int             *ajtmpold, *ajtmp, nz, row, *ai=a->i,*aj=a->j;
725   int             *diag_offset = b->diag,idx;
726   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
727   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
728   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
729   Scalar          *ba = b->a,*aa = a->a;
730   register int    *pj;
731 
732   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
733   PLogObjectParent(*B,isicol);
734   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
735   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
736   rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
737 
738   for ( i=0; i<n; i++ ) {
739     nz    = bi[i+1] - bi[i];
740     ajtmp = bj + bi[i];
741     for  ( j=0; j<nz; j++ ) {
742       x = rtmp + 9*ajtmp[j];
743       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
744     }
745     /* load in initial (unfactored row) */
746     idx      = r[i];
747     nz       = ai[idx+1] - ai[idx];
748     ajtmpold = aj + ai[idx];
749     v        = aa + 9*ai[idx];
750     for ( j=0; j<nz; j++ ) {
751       x    = rtmp + 9*ic[ajtmpold[j]];
752       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
753       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
754       v    += 9;
755     }
756     row = *ajtmp++;
757     while (row < i) {
758       pc = rtmp + 9*row;
759       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
760       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
761       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
762           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
763         pv = ba + 9*diag_offset[row];
764         pj = bj + diag_offset[row] + 1;
765         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
766         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
767         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
768         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
769         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
770 
771         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
772         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
773         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
774 
775         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
776         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
777         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
778         nz = bi[row+1] - diag_offset[row] - 1;
779         pv += 9;
780         for (j=0; j<nz; j++) {
781           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
782           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
783           x    = rtmp + 9*pj[j];
784           x[0] -= m1*x1 + m4*x2 + m7*x3;
785           x[1] -= m2*x1 + m5*x2 + m8*x3;
786           x[2] -= m3*x1 + m6*x2 + m9*x3;
787 
788           x[3] -= m1*x4 + m4*x5 + m7*x6;
789           x[4] -= m2*x4 + m5*x5 + m8*x6;
790           x[5] -= m3*x4 + m6*x5 + m9*x6;
791 
792           x[6] -= m1*x7 + m4*x8 + m7*x9;
793           x[7] -= m2*x7 + m5*x8 + m8*x9;
794           x[8] -= m3*x7 + m6*x8 + m9*x9;
795           pv   += 9;
796         }
797         PLogFlops(54*nz+36);
798       }
799       row = *ajtmp++;
800     }
801     /* finished row so stick it into b->a */
802     pv = ba + 9*bi[i];
803     pj = bj + bi[i];
804     nz = bi[i+1] - bi[i];
805     for ( j=0; j<nz; j++ ) {
806       x     = rtmp + 9*pj[j];
807       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
808       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
809       pv   += 9;
810     }
811     /* invert diagonal block */
812     w = ba + 9*diag_offset[i];
813     ierr = Kernel_A_gets_inverse_A_3(w); CHKERRQ(ierr);
814   }
815 
816   PetscFree(rtmp);
817   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
818   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
819   ierr = ISDestroy(isicol); CHKERRQ(ierr);
820   C->factor = FACTOR_LU;
821   C->assembled = PETSC_TRUE;
822   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
823   return 0;
824 }
825 
826 /* ------------------------------------------------------------*/
827 /*
828       Version for when blocks are 2 by 2
829 */
830 #undef __FUNC__
831 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_2"
832 int MatLUFactorNumeric_SeqBAIJ_2(Mat A,Mat *B)
833 {
834   Mat             C = *B;
835   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
836   IS              iscol = b->col, isrow = b->row, isicol;
837   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
838   int             *ajtmpold, *ajtmp, nz, row, v_pivots[2];
839   int             *diag_offset=b->diag,bs = 2,idx,*ai=a->i,*aj=a->j;
840   register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
841   Scalar          p1,p2,p3,p4,v_work[2];
842   Scalar          *ba = b->a,*aa = a->a;
843   register int    *pj;
844 
845   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
846   PLogObjectParent(*B,isicol);
847   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
848   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
849   rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
850 
851   for ( i=0; i<n; i++ ) {
852     nz    = bi[i+1] - bi[i];
853     ajtmp = bj + bi[i];
854     for  ( j=0; j<nz; j++ ) {
855       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
856     }
857     /* load in initial (unfactored row) */
858     idx      = r[i];
859     nz       = ai[idx+1] - ai[idx];
860     ajtmpold = aj + ai[idx];
861     v        = aa + 4*ai[idx];
862     for ( j=0; j<nz; j++ ) {
863       x    = rtmp+4*ic[ajtmpold[j]];
864       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
865       v    += 4;
866     }
867     row = *ajtmp++;
868     while (row < i) {
869       pc = rtmp + 4*row;
870       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
871       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
872         pv = ba + 4*diag_offset[row];
873         pj = bj + diag_offset[row] + 1;
874         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
875         pc[0] = m1 = p1*x1 + p3*x2;
876         pc[1] = m2 = p2*x1 + p4*x2;
877         pc[2] = m3 = p1*x3 + p3*x4;
878         pc[3] = m4 = p2*x3 + p4*x4;
879         nz = bi[row+1] - diag_offset[row] - 1;
880         pv += 4;
881         for (j=0; j<nz; j++) {
882           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
883           x    = rtmp + 4*pj[j];
884           x[0] -= m1*x1 + m3*x2;
885           x[1] -= m2*x1 + m4*x2;
886           x[2] -= m1*x3 + m3*x4;
887           x[3] -= m2*x3 + m4*x4;
888           pv   += 4;
889         }
890         PLogFlops(16*nz+12);
891       }
892       row = *ajtmp++;
893     }
894     /* finished row so stick it into b->a */
895     pv = ba + 4*bi[i];
896     pj = bj + bi[i];
897     nz = bi[i+1] - bi[i];
898     for ( j=0; j<nz; j++ ) {
899       x     = rtmp+4*pj[j];
900       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
901       pv   += 4;
902     }
903     /* invert diagonal block */
904     w = ba + 4*diag_offset[i];
905     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
906   }
907 
908   PetscFree(rtmp);
909   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
910   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
911   ierr = ISDestroy(isicol); CHKERRQ(ierr);
912   C->factor = FACTOR_LU;
913   C->assembled = PETSC_TRUE;
914   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
915   return 0;
916 }
917 
918 /* ----------------------------------------------------------- */
919 /*
920      Version for when blocks are 1 by 1.
921 */
922 #undef __FUNC__
923 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_1"
924 int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
925 {
926   Mat             C = *B;
927   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
928   IS              iscol = b->col, isrow = b->row, isicol;
929   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
930   int             *ajtmpold, *ajtmp, nz, row,*ai = a->i,*aj = a->j;
931   int             *diag_offset = b->diag,diag;
932   register Scalar *pv,*v,*rtmp,multiplier,*pc;
933   Scalar          *ba = b->a,*aa = a->a;
934   register int    *pj;
935 
936   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
937   PLogObjectParent(*B,isicol);
938   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
939   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
940   rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
941 
942   for ( i=0; i<n; i++ ) {
943     nz    = bi[i+1] - bi[i];
944     ajtmp = bj + bi[i];
945     for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;
946 
947     /* load in initial (unfactored row) */
948     nz       = ai[r[i]+1] - ai[r[i]];
949     ajtmpold = aj + ai[r[i]];
950     v        = aa + ai[r[i]];
951     for ( j=0; j<nz; j++ ) rtmp[ic[ajtmpold[j]]] =  v[j];
952 
953     row = *ajtmp++;
954     while (row < i) {
955       pc = rtmp + row;
956       if (*pc != 0.0) {
957         pv         = ba + diag_offset[row];
958         pj         = bj + diag_offset[row] + 1;
959         multiplier = *pc * *pv++;
960         *pc        = multiplier;
961         nz         = bi[row+1] - diag_offset[row] - 1;
962         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
963         PLogFlops(1+2*nz);
964       }
965       row = *ajtmp++;
966     }
967     /* finished row so stick it into b->a */
968     pv = ba + bi[i];
969     pj = bj + bi[i];
970     nz = bi[i+1] - bi[i];
971     for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
972     diag = diag_offset[i] - bi[i];
973     /* check pivot entry for current row */
974     if (pv[diag] == 0.0) {
975       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
976     }
977     pv[diag] = 1.0/pv[diag];
978   }
979 
980   PetscFree(rtmp);
981   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
982   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
983   ierr = ISDestroy(isicol); CHKERRQ(ierr);
984   C->factor    = FACTOR_LU;
985   C->assembled = PETSC_TRUE;
986   PLogFlops(b->n);
987   return 0;
988 }
989 
990 /* ----------------------------------------------------------- */
991 #undef __FUNC__
992 #define __FUNC__ "MatLUFactor_SeqBAIJ"
993 int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
994 {
995   Mat_SeqBAIJ *mat = (Mat_SeqBAIJ *) A->data;
996   int         ierr;
997   Mat         C;
998 
999   ierr = MatLUFactorSymbolic(A,row,col,f,&C); CHKERRQ(ierr);
1000   ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);
1001 
1002   /* free all the data structures from mat */
1003   PetscFree(mat->a);
1004   if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
1005   if (mat->diag) PetscFree(mat->diag);
1006   if (mat->ilen) PetscFree(mat->ilen);
1007   if (mat->imax) PetscFree(mat->imax);
1008   if (mat->solve_work) PetscFree(mat->solve_work);
1009   if (mat->mult_work) PetscFree(mat->mult_work);
1010   PetscFree(mat);
1011 
1012   PetscMemcpy(A,C,sizeof(struct _p_Mat));
1013   PetscHeaderDestroy(C);
1014   return 0;
1015 }
1016 /* ----------------------------------------------------------- */
1017 #undef __FUNC__
1018 #define __FUNC__ "MatSolve_SeqBAIJ_N"
1019 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
1020 {
1021   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1022   IS              iscol=a->col,isrow=a->row;
1023   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
1024   int             nz,bs=a->bs,bs2=a->bs2,*rout,*cout;
1025   Scalar          *aa=a->a,*sum;
1026   register Scalar *x,*b,*lsum,*tmp,*v;
1027 
1028   VecGetArray_Fast(bb,b);
1029   VecGetArray_Fast(xx,x);
1030   tmp  = a->solve_work;
1031 
1032   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1033   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1034 
1035   /* forward solve the lower triangular */
1036   PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
1037   for ( i=1; i<n; i++ ) {
1038     v   = aa + bs2*ai[i];
1039     vi  = aj + ai[i];
1040     nz  = a->diag[i] - ai[i];
1041     sum = tmp + bs*i;
1042     PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
1043     while (nz--) {
1044       Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++));
1045       v += bs2;
1046     }
1047   }
1048   /* backward solve the upper triangular */
1049   lsum = a->solve_work + a->n;
1050   for ( i=n-1; i>=0; i-- ){
1051     v   = aa + bs2*(a->diag[i] + 1);
1052     vi  = aj + a->diag[i] + 1;
1053     nz  = ai[i+1] - a->diag[i] - 1;
1054     PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
1055     while (nz--) {
1056       Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++));
1057       v += bs2;
1058     }
1059     Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs);
1060     PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
1061   }
1062 
1063   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1064   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1065   VecRestoreArray_Fast(bb,b);
1066   VecRestoreArray_Fast(xx,x);
1067   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
1068   return 0;
1069 }
1070 
1071 #undef __FUNC__
1072 #define __FUNC__ "MatSolve_SeqBAIJ_7"
1073 int MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
1074 {
1075   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1076   IS              iscol=a->col,isrow=a->row;
1077   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1078   int             *diag = a->diag;
1079   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,sum6,sum7,x1,x2,x3,x4,x5,x6,x7;
1080   register Scalar *x,*b,*tmp,*v;
1081 
1082   VecGetArray_Fast(bb,b);
1083   VecGetArray_Fast(xx,x);
1084   tmp  = a->solve_work;
1085 
1086   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1087   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1088 
1089   /* forward solve the lower triangular */
1090   idx    = 7*(*r++);
1091   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1092   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
1093   tmp[5] = b[5+idx]; tmp[6] = b[6+idx];
1094 
1095   for ( i=1; i<n; i++ ) {
1096     v     = aa + 49*ai[i];
1097     vi    = aj + ai[i];
1098     nz    = diag[i] - ai[i];
1099     idx   = 7*(*r++);
1100     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1101     sum5  = b[4+idx];sum6 = b[5+idx];sum7 = b[6+idx];
1102     while (nz--) {
1103       idx   = 7*(*vi++);
1104       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
1105       x4    = tmp[3+idx];x5 = tmp[4+idx];
1106       x6    = tmp[5+idx];x7 = tmp[6+idx];
1107       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
1108       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
1109       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
1110       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
1111       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
1112       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
1113       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
1114       v += 49;
1115     }
1116     idx = 7*i;
1117     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1118     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
1119     tmp[5+idx] = sum6;tmp[6+idx] = sum7;
1120   }
1121   /* backward solve the upper triangular */
1122   for ( i=n-1; i>=0; i-- ){
1123     v    = aa + 49*diag[i] + 49;
1124     vi   = aj + diag[i] + 1;
1125     nz   = ai[i+1] - diag[i] - 1;
1126     idt  = 7*i;
1127     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1128     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
1129     sum6 = tmp[5+idt];sum7 = tmp[6+idt];
1130     while (nz--) {
1131       idx   = 7*(*vi++);
1132       x1    = tmp[idx];   x2 = tmp[1+idx];
1133       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
1134       x6    = tmp[5+idx]; x7 = tmp[6+idx];
1135       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
1136       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
1137       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
1138       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
1139       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
1140       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
1141       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
1142       v += 49;
1143     }
1144     idc = 7*(*c--);
1145     v   = aa + 49*diag[i];
1146     x[idc]   = tmp[idt]   = v[0]*sum1+v[7]*sum2+v[14]*sum3+
1147                                  v[21]*sum4+v[28]*sum5+v[35]*sum6+v[42]*sum7;
1148     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[8]*sum2+v[15]*sum3+
1149                                  v[22]*sum4+v[29]*sum5+v[36]*sum6+v[43]*sum7;
1150     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[9]*sum2+v[16]*sum3+
1151                                  v[23]*sum4+v[30]*sum5+v[37]*sum6+v[44]*sum7;
1152     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[10]*sum2+v[17]*sum3+
1153                                  v[24]*sum4+v[31]*sum5+v[38]*sum6+v[45]*sum7;
1154     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[11]*sum2+v[18]*sum3+
1155                                  v[25]*sum4+v[32]*sum5+v[39]*sum6+v[46]*sum7;
1156     x[5+idc] = tmp[5+idt] = v[5]*sum1+v[12]*sum2+v[19]*sum3+
1157                                  v[26]*sum4+v[33]*sum5+v[40]*sum6+v[47]*sum7;
1158     x[6+idc] = tmp[6+idt] = v[6]*sum1+v[13]*sum2+v[20]*sum3+
1159                                  v[27]*sum4+v[34]*sum5+v[41]*sum6+v[48]*sum7;
1160   }
1161 
1162   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1163   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1164   VecRestoreArray_Fast(bb,b);
1165   VecRestoreArray_Fast(xx,x);
1166   PLogFlops(2*49*(a->nz) - a->n);
1167   return 0;
1168 }
1169 
1170 #undef __FUNC__
1171 #define __FUNC__ "MatSolve_SeqBAIJ_5"
1172 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
1173 {
1174   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1175   IS              iscol=a->col,isrow=a->row;
1176   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1177   int             *diag = a->diag;
1178   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
1179   register Scalar *x,*b,*tmp,*v;
1180 
1181   VecGetArray_Fast(bb,b);
1182   VecGetArray_Fast(xx,x);
1183   tmp  = a->solve_work;
1184 
1185   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1186   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1187 
1188   /* forward solve the lower triangular */
1189   idx    = 5*(*r++);
1190   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1191   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
1192   for ( i=1; i<n; i++ ) {
1193     v     = aa + 25*ai[i];
1194     vi    = aj + ai[i];
1195     nz    = diag[i] - ai[i];
1196     idx   = 5*(*r++);
1197     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1198     sum5  = b[4+idx];
1199     while (nz--) {
1200       idx   = 5*(*vi++);
1201       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
1202       x4    = tmp[3+idx];x5 = tmp[4+idx];
1203       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1204       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1205       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1206       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1207       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1208       v += 25;
1209     }
1210     idx = 5*i;
1211     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1212     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
1213   }
1214   /* backward solve the upper triangular */
1215   for ( i=n-1; i>=0; i-- ){
1216     v    = aa + 25*diag[i] + 25;
1217     vi   = aj + diag[i] + 1;
1218     nz   = ai[i+1] - diag[i] - 1;
1219     idt  = 5*i;
1220     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1221     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
1222     while (nz--) {
1223       idx   = 5*(*vi++);
1224       x1    = tmp[idx];   x2 = tmp[1+idx];
1225       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
1226       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1227       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1228       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1229       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1230       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1231       v += 25;
1232     }
1233     idc = 5*(*c--);
1234     v   = aa + 25*diag[i];
1235     x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
1236                                  v[15]*sum4+v[20]*sum5;
1237     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
1238                                  v[16]*sum4+v[21]*sum5;
1239     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
1240                                  v[17]*sum4+v[22]*sum5;
1241     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
1242                                  v[18]*sum4+v[23]*sum5;
1243     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
1244                                  v[19]*sum4+v[24]*sum5;
1245   }
1246 
1247   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1248   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1249   VecRestoreArray_Fast(bb,b);
1250   VecRestoreArray_Fast(xx,x);
1251   PLogFlops(2*25*(a->nz) - a->n);
1252   return 0;
1253 }
1254 
1255 #undef __FUNC__
1256 #define __FUNC__ "MatSolve_SeqBAIJ_4"
1257 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
1258 {
1259   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
1260   IS              iscol=a->col,isrow=a->row;
1261   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1262   int             *diag = a->diag;
1263   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
1264   register Scalar *x,*b,*tmp,*v;
1265 
1266   VecGetArray_Fast(bb,b);
1267   VecGetArray_Fast(xx,x);
1268   tmp  = a->solve_work;
1269 
1270   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1271   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1272 
1273   /* forward solve the lower triangular */
1274   idx    = 4*(*r++);
1275   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1276   tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
1277   for ( i=1; i<n; i++ ) {
1278     v     = aa + 16*ai[i];
1279     vi    = aj + ai[i];
1280     nz    = diag[i] - ai[i];
1281     idx   = 4*(*r++);
1282     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1283     while (nz--) {
1284       idx   = 4*(*vi++);
1285       x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
1286       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1287       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1288       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1289       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1290       v    += 16;
1291     }
1292     idx        = 4*i;
1293     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1294     tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1295   }
1296   /* backward solve the upper triangular */
1297   for ( i=n-1; i>=0; i-- ){
1298     v    = aa + 16*diag[i] + 16;
1299     vi   = aj + diag[i] + 1;
1300     nz   = ai[i+1] - diag[i] - 1;
1301     idt  = 4*i;
1302     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1303     sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1304     while (nz--) {
1305       idx   = 4*(*vi++);
1306       x1    = tmp[idx];   x2 = tmp[1+idx];
1307       x3    = tmp[2+idx]; x4 = tmp[3+idx];
1308       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1309       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1310       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1311       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1312       v += 16;
1313     }
1314     idc      = 4*(*c--);
1315     v        = aa + 16*diag[i];
1316     x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1317     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1318     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1319     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1320   }
1321 
1322   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1323   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1324   VecRestoreArray_Fast(bb,b);
1325   VecRestoreArray_Fast(xx,x);
1326   PLogFlops(2*16*(a->nz) - a->n);
1327   return 0;
1328 }
1329 
1330 /*
1331       Special case where the matrix was ILU(0) factored in the natural
1332    ordering. This eliminates the need for the column and row permutation.
1333 */
1334 #undef __FUNC__
1335 #define __FUNC__ "MatSolve_SeqBAIJ_4_NaturalOrdering"
1336 int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
1337 {
1338   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
1339   int             i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
1340   int             *diag = a->diag,jdx;
1341   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
1342   register Scalar *x,*b,*v;
1343 
1344   VecGetArray_Fast(bb,b);
1345   VecGetArray_Fast(xx,x);
1346 
1347   /* forward solve the lower triangular */
1348   idx    = 0;
1349   x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; x[3] = b[3+idx];
1350   for ( i=1; i<n; i++ ) {
1351     v     =  aa + 16*ai[i];
1352     vi    =  aj + ai[i];
1353     nz    =  diag[i] - ai[i];
1354     idx   =  4*i;
1355     sum1  =  b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1356     while (nz--) {
1357       jdx   = 4*(*vi++);
1358       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];
1359       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1360       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1361       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1362       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1363       v    += 16;
1364     }
1365     x[idx]   = sum1;
1366     x[1+idx] = sum2;
1367     x[2+idx] = sum3;
1368     x[3+idx] = sum4;
1369   }
1370   /* backward solve the upper triangular */
1371   for ( i=n-1; i>=0; i-- ){
1372     v    = aa + 16*diag[i] + 16;
1373     vi   = aj + diag[i] + 1;
1374     nz   = ai[i+1] - diag[i] - 1;
1375     idt  = 4*i;
1376     sum1 = x[idt];  sum2 = x[1+idt];
1377     sum3 = x[2+idt];sum4 = x[3+idt];
1378     while (nz--) {
1379       idx   = 4*(*vi++);
1380       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx];
1381       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1382       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1383       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1384       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1385       v += 16;
1386     }
1387     v        = aa + 16*diag[i];
1388     x[idt]   = v[0]*sum1 + v[4]*sum2 + v[8]*sum3  + v[12]*sum4;
1389     x[1+idt] = v[1]*sum1 + v[5]*sum2 + v[9]*sum3  + v[13]*sum4;
1390     x[2+idt] = v[2]*sum1 + v[6]*sum2 + v[10]*sum3 + v[14]*sum4;
1391     x[3+idt] = v[3]*sum1 + v[7]*sum2 + v[11]*sum3 + v[15]*sum4;
1392   }
1393 
1394   VecRestoreArray_Fast(bb,b);
1395   VecRestoreArray_Fast(xx,x);
1396   PLogFlops(2*16*(a->nz) - a->n);
1397   return 0;
1398 }
1399 
1400 
1401 #undef __FUNC__
1402 #define __FUNC__ "MatSolve_SeqBAIJ_3"
1403 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
1404 {
1405   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1406   IS              iscol=a->col,isrow=a->row;
1407   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1408   int             *diag = a->diag;
1409   Scalar          *aa=a->a,sum1,sum2,sum3,x1,x2,x3;
1410   register Scalar *x,*b,*tmp,*v;
1411 
1412   VecGetArray_Fast(bb,b);
1413   VecGetArray_Fast(xx,x);
1414   tmp  = a->solve_work;
1415 
1416   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1417   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1418 
1419   /* forward solve the lower triangular */
1420   idx    = 3*(*r++);
1421   tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
1422   for ( i=1; i<n; i++ ) {
1423     v     = aa + 9*ai[i];
1424     vi    = aj + ai[i];
1425     nz    = diag[i] - ai[i];
1426     idx   = 3*(*r++);
1427     sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
1428     while (nz--) {
1429       idx   = 3*(*vi++);
1430       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1431       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1432       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1433       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1434       v += 9;
1435     }
1436     idx = 3*i;
1437     tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
1438   }
1439   /* backward solve the upper triangular */
1440   for ( i=n-1; i>=0; i-- ){
1441     v    = aa + 9*diag[i] + 9;
1442     vi   = aj + diag[i] + 1;
1443     nz   = ai[i+1] - diag[i] - 1;
1444     idt  = 3*i;
1445     sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
1446     while (nz--) {
1447       idx   = 3*(*vi++);
1448       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1449       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1450       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1451       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1452       v += 9;
1453     }
1454     idc = 3*(*c--);
1455     v   = aa + 9*diag[i];
1456     x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
1457     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
1458     x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
1459   }
1460   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1461   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1462   VecRestoreArray_Fast(bb,b);
1463   VecRestoreArray_Fast(xx,x);
1464   PLogFlops(2*9*(a->nz) - a->n);
1465   return 0;
1466 }
1467 
1468 #undef __FUNC__
1469 #define __FUNC__ "MatSolve_SeqBAIJ_2"
1470 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
1471 {
1472   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1473   IS              iscol=a->col,isrow=a->row;
1474   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1475   int             *diag = a->diag;
1476   Scalar          *aa=a->a,sum1,sum2,x1,x2;
1477   register Scalar *x,*b,*tmp,*v;
1478 
1479   VecGetArray_Fast(bb,b);
1480   VecGetArray_Fast(xx,x);
1481   tmp  = a->solve_work;
1482 
1483   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1484   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1485 
1486   /* forward solve the lower triangular */
1487   idx    = 2*(*r++);
1488   tmp[0] = b[idx]; tmp[1] = b[1+idx];
1489   for ( i=1; i<n; i++ ) {
1490     v     = aa + 4*ai[i];
1491     vi    = aj + ai[i];
1492     nz    = diag[i] - ai[i];
1493     idx   = 2*(*r++);
1494     sum1  = b[idx]; sum2 = b[1+idx];
1495     while (nz--) {
1496       idx   = 2*(*vi++);
1497       x1    = tmp[idx]; x2 = tmp[1+idx];
1498       sum1 -= v[0]*x1 + v[2]*x2;
1499       sum2 -= v[1]*x1 + v[3]*x2;
1500       v += 4;
1501     }
1502     idx = 2*i;
1503     tmp[idx] = sum1; tmp[1+idx] = sum2;
1504   }
1505   /* backward solve the upper triangular */
1506   for ( i=n-1; i>=0; i-- ){
1507     v    = aa + 4*diag[i] + 4;
1508     vi   = aj + diag[i] + 1;
1509     nz   = ai[i+1] - diag[i] - 1;
1510     idt  = 2*i;
1511     sum1 = tmp[idt]; sum2 = tmp[1+idt];
1512     while (nz--) {
1513       idx   = 2*(*vi++);
1514       x1    = tmp[idx]; x2 = tmp[1+idx];
1515       sum1 -= v[0]*x1 + v[2]*x2;
1516       sum2 -= v[1]*x1 + v[3]*x2;
1517       v += 4;
1518     }
1519     idc = 2*(*c--);
1520     v   = aa + 4*diag[i];
1521     x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
1522     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
1523   }
1524   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1525   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1526   VecRestoreArray_Fast(bb,b);
1527   VecRestoreArray_Fast(xx,x);
1528   PLogFlops(2*4*(a->nz) - a->n);
1529   return 0;
1530 }
1531 
1532 
1533 #undef __FUNC__
1534 #define __FUNC__ "MatSolve_SeqBAIJ_1"
1535 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
1536 {
1537   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1538   IS              iscol=a->col,isrow=a->row;
1539   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout;
1540   int             *diag = a->diag;
1541   Scalar          *aa=a->a,sum1;
1542   register Scalar *x,*b,*tmp,*v;
1543 
1544   if (!n) return 0;
1545 
1546   VecGetArray_Fast(bb,b);
1547   VecGetArray_Fast(xx,x);
1548   tmp  = a->solve_work;
1549 
1550   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1551   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1552 
1553   /* forward solve the lower triangular */
1554   tmp[0] = b[*r++];
1555   for ( i=1; i<n; i++ ) {
1556     v     = aa + ai[i];
1557     vi    = aj + ai[i];
1558     nz    = diag[i] - ai[i];
1559     sum1  = b[*r++];
1560     while (nz--) {
1561       sum1 -= (*v++)*tmp[*vi++];
1562     }
1563     tmp[i] = sum1;
1564   }
1565   /* backward solve the upper triangular */
1566   for ( i=n-1; i>=0; i-- ){
1567     v    = aa + diag[i] + 1;
1568     vi   = aj + diag[i] + 1;
1569     nz   = ai[i+1] - diag[i] - 1;
1570     sum1 = tmp[i];
1571     while (nz--) {
1572       sum1 -= (*v++)*tmp[*vi++];
1573     }
1574     x[*c--] = tmp[i] = aa[diag[i]]*sum1;
1575   }
1576 
1577   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1578   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1579   VecRestoreArray_Fast(bb,b);
1580   VecRestoreArray_Fast(xx,x);
1581   PLogFlops(2*1*(a->nz) - a->n);
1582   return 0;
1583 }
1584 
1585 extern int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat,Vec,Vec);
1586 /* ----------------------------------------------------------------*/
1587 /*
1588      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
1589    except that the data structure of Mat_SeqAIJ is slightly different.
1590    Not a good example of code reuse.
1591 */
1592 #undef __FUNC__
1593 #define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ"
1594 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
1595                                  Mat *fact)
1596 {
1597   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
1598   IS          isicol;
1599   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
1600   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
1601   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
1602   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
1603   PetscTruth  col_identity, row_identity;
1604 
1605   /* special case that simply copies fill pattern */
1606   PetscValidHeaderSpecific(isrow,IS_COOKIE);
1607   PetscValidHeaderSpecific(iscol,IS_COOKIE);
1608   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
1609   if (levels == 0 && row_identity && col_identity) {
1610     ierr = MatConvertSameType_SeqBAIJ(A,fact,DO_NOT_COPY_VALUES); CHKERRQ(ierr);
1611     (*fact)->factor = FACTOR_LU;
1612     b               = (Mat_SeqBAIJ *) (*fact)->data;
1613     if (!b->diag) {
1614       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
1615     }
1616     b->row        = isrow;
1617     b->col        = iscol;
1618     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
1619     /*
1620         Blocksize 4 has a special faster solver for ILU(0) factorization
1621         with natural ordering
1622     */
1623     if (b->bs == 4) {
1624       (*fact)->ops.lufactornumeric = MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering;
1625       (*fact)->ops.solve           = MatSolve_SeqBAIJ_4_NaturalOrdering;
1626     }
1627     return 0;
1628   }
1629 
1630   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
1631   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
1632   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
1633 
1634   /* get new row pointers */
1635   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
1636   ainew[0] = 0;
1637   /* don't know how many column pointers are needed so estimate */
1638   jmax = (int) (f*ai[n] + 1);
1639   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
1640   /* ajfill is level of fill for each fill entry */
1641   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
1642   /* fill is a linked list of nonzeros in active row */
1643   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
1644   /* im is level for each filled value */
1645   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
1646   /* dloc is location of diagonal in factor */
1647   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
1648   dloc[0]  = 0;
1649   for ( prow=0; prow<n; prow++ ) {
1650     /* first copy previous fill into linked list */
1651     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
1652     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
1653     xi      = aj + ai[r[prow]];
1654     fill[n] = n;
1655     while (nz--) {
1656       fm  = n;
1657       idx = ic[*xi++];
1658       do {
1659         m  = fm;
1660         fm = fill[m];
1661       } while (fm < idx);
1662       fill[m]   = idx;
1663       fill[idx] = fm;
1664       im[idx]   = 0;
1665     }
1666     nzi = 0;
1667     row = fill[n];
1668     while ( row < prow ) {
1669       incrlev = im[row] + 1;
1670       nz      = dloc[row];
1671       xi      = ajnew  + ainew[row] + nz;
1672       flev    = ajfill + ainew[row] + nz + 1;
1673       nnz     = ainew[row+1] - ainew[row] - nz - 1;
1674       if (*xi++ != row) {
1675         SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot: try running with -pc_ilu_nonzeros_along_diagonal");
1676       }
1677       fm      = row;
1678       while (nnz-- > 0) {
1679         idx = *xi++;
1680         if (*flev + incrlev > levels) {
1681           flev++;
1682           continue;
1683         }
1684         do {
1685           m  = fm;
1686           fm = fill[m];
1687         } while (fm < idx);
1688         if (fm != idx) {
1689           im[idx]   = *flev + incrlev;
1690           fill[m]   = idx;
1691           fill[idx] = fm;
1692           fm        = idx;
1693           nzf++;
1694         }
1695         else {
1696           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
1697         }
1698         flev++;
1699       }
1700       row = fill[row];
1701       nzi++;
1702     }
1703     /* copy new filled row into permanent storage */
1704     ainew[prow+1] = ainew[prow] + nzf;
1705     if (ainew[prow+1] > jmax) {
1706       /* allocate a longer ajnew */
1707       int maxadd;
1708       maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n);
1709       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
1710       jmax += maxadd;
1711       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1712       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
1713       PetscFree(ajnew);
1714       ajnew = xi;
1715       /* allocate a longer ajfill */
1716       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1717       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
1718       PetscFree(ajfill);
1719       ajfill = xi;
1720       realloc++;
1721     }
1722     xi          = ajnew + ainew[prow];
1723     flev        = ajfill + ainew[prow];
1724     dloc[prow]  = nzi;
1725     fm          = fill[n];
1726     while (nzf--) {
1727       *xi++   = fm;
1728       *flev++ = im[fm];
1729       fm      = fill[fm];
1730     }
1731   }
1732   PetscFree(ajfill);
1733   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1734   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
1735   ierr = ISDestroy(isicol); CHKERRQ(ierr);
1736   PetscFree(fill); PetscFree(im);
1737 
1738   {
1739     double af = ((double)ainew[n])/((double)ai[n]);
1740     PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
1741              realloc,f,af);
1742     PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:Run with -pc_ilu_fill %g or use \n",af);
1743     PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:PCILUSetFill(pc,%g);\n",af);
1744     PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:for best performance.\n");
1745   }
1746 
1747   /* put together the new matrix */
1748   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
1749   b = (Mat_SeqBAIJ *) (*fact)->data;
1750   PetscFree(b->imax);
1751   b->singlemalloc = 0;
1752   len = bs2*ainew[n]*sizeof(Scalar);
1753   /* the next line frees the default space generated by the Create() */
1754   PetscFree(b->a); PetscFree(b->ilen);
1755   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
1756   b->j          = ajnew;
1757   b->i          = ainew;
1758   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
1759   b->diag       = dloc;
1760   b->ilen       = 0;
1761   b->imax       = 0;
1762   b->row        = isrow;
1763   b->col        = iscol;
1764   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
1765   CHKPTRQ(b->solve_work);
1766   /* In b structure:  Free imax, ilen, old a, old j.
1767      Allocate dloc, solve_work, new a, new j */
1768   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
1769   b->maxnz          = b->nz = ainew[n];
1770   (*fact)->factor   = FACTOR_LU;
1771 
1772   (*fact)->info.factor_mallocs    = realloc;
1773   (*fact)->info.fill_ratio_given  = f;
1774   (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);
1775 
1776   return 0;
1777 }
1778 
1779 
1780 
1781 
1782