xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision bcff55d9c22a11117c657f321125d3821e9fb4a8)
1 #ifdef PETSC_RCS_HEADER
2 static char vcid[] = "$Id: baijfact.c,v 1.49 1997/07/09 13:09:54 bsmith Exp balay $";
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 /*
575       Version for when blocks are 3 by 3
576 */
577 #undef __FUNC__
578 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_3"
579 int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
580 {
581   Mat             C = *B;
582   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
583   IS              iscol = b->col, isrow = b->row, isicol;
584   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
585   int             *ajtmpold, *ajtmp, nz, row, *ai=a->i,*aj=a->j;
586   int             *diag_offset = b->diag,idx;
587   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
588   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
589   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
590   Scalar          *ba = b->a,*aa = a->a;
591   register int    *pj;
592 
593   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
594   PLogObjectParent(*B,isicol);
595   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
596   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
597   rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
598 
599   for ( i=0; i<n; i++ ) {
600     nz    = bi[i+1] - bi[i];
601     ajtmp = bj + bi[i];
602     for  ( j=0; j<nz; j++ ) {
603       x = rtmp + 9*ajtmp[j];
604       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
605     }
606     /* load in initial (unfactored row) */
607     idx      = r[i];
608     nz       = ai[idx+1] - ai[idx];
609     ajtmpold = aj + ai[idx];
610     v        = aa + 9*ai[idx];
611     for ( j=0; j<nz; j++ ) {
612       x    = rtmp + 9*ic[ajtmpold[j]];
613       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
614       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
615       v    += 9;
616     }
617     row = *ajtmp++;
618     while (row < i) {
619       pc = rtmp + 9*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       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) {
624         pv = ba + 9*diag_offset[row];
625         pj = bj + diag_offset[row] + 1;
626         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
627         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
628         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
629         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
630         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
631 
632         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
633         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
634         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
635 
636         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
637         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
638         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
639         nz = bi[row+1] - diag_offset[row] - 1;
640         pv += 9;
641         for (j=0; j<nz; j++) {
642           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
643           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
644           x    = rtmp + 9*pj[j];
645           x[0] -= m1*x1 + m4*x2 + m7*x3;
646           x[1] -= m2*x1 + m5*x2 + m8*x3;
647           x[2] -= m3*x1 + m6*x2 + m9*x3;
648 
649           x[3] -= m1*x4 + m4*x5 + m7*x6;
650           x[4] -= m2*x4 + m5*x5 + m8*x6;
651           x[5] -= m3*x4 + m6*x5 + m9*x6;
652 
653           x[6] -= m1*x7 + m4*x8 + m7*x9;
654           x[7] -= m2*x7 + m5*x8 + m8*x9;
655           x[8] -= m3*x7 + m6*x8 + m9*x9;
656           pv   += 9;
657         }
658         PLogFlops(54*nz+36);
659       }
660       row = *ajtmp++;
661     }
662     /* finished row so stick it into b->a */
663     pv = ba + 9*bi[i];
664     pj = bj + bi[i];
665     nz = bi[i+1] - bi[i];
666     for ( j=0; j<nz; j++ ) {
667       x     = rtmp + 9*pj[j];
668       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
669       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
670       pv   += 9;
671     }
672     /* invert diagonal block */
673     w = ba + 9*diag_offset[i];
674     ierr = Kernel_A_gets_inverse_A_3(w); CHKERRQ(ierr);
675   }
676 
677   PetscFree(rtmp);
678   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
679   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
680   ierr = ISDestroy(isicol); CHKERRQ(ierr);
681   C->factor = FACTOR_LU;
682   C->assembled = PETSC_TRUE;
683   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
684   return 0;
685 }
686 
687 /* ------------------------------------------------------------*/
688 /*
689       Version for when blocks are 2 by 2
690 */
691 #undef __FUNC__
692 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_2"
693 int MatLUFactorNumeric_SeqBAIJ_2(Mat A,Mat *B)
694 {
695   Mat             C = *B;
696   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
697   IS              iscol = b->col, isrow = b->row, isicol;
698   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
699   int             *ajtmpold, *ajtmp, nz, row, v_pivots[2];
700   int             *diag_offset=b->diag,bs = 2,idx,*ai=a->i,*aj=a->j;
701   register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
702   Scalar          p1,p2,p3,p4,v_work[2];
703   Scalar          *ba = b->a,*aa = a->a;
704   register int    *pj;
705 
706   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
707   PLogObjectParent(*B,isicol);
708   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
709   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
710   rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
711 
712   for ( i=0; i<n; i++ ) {
713     nz    = bi[i+1] - bi[i];
714     ajtmp = bj + bi[i];
715     for  ( j=0; j<nz; j++ ) {
716       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
717     }
718     /* load in initial (unfactored row) */
719     idx      = r[i];
720     nz       = ai[idx+1] - ai[idx];
721     ajtmpold = aj + ai[idx];
722     v        = aa + 4*ai[idx];
723     for ( j=0; j<nz; j++ ) {
724       x    = rtmp+4*ic[ajtmpold[j]];
725       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
726       v    += 4;
727     }
728     row = *ajtmp++;
729     while (row < i) {
730       pc = rtmp + 4*row;
731       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
732       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
733         pv = ba + 4*diag_offset[row];
734         pj = bj + diag_offset[row] + 1;
735         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
736         pc[0] = m1 = p1*x1 + p3*x2;
737         pc[1] = m2 = p2*x1 + p4*x2;
738         pc[2] = m3 = p1*x3 + p3*x4;
739         pc[3] = m4 = p2*x3 + p4*x4;
740         nz = bi[row+1] - diag_offset[row] - 1;
741         pv += 4;
742         for (j=0; j<nz; j++) {
743           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
744           x    = rtmp + 4*pj[j];
745           x[0] -= m1*x1 + m3*x2;
746           x[1] -= m2*x1 + m4*x2;
747           x[2] -= m1*x3 + m3*x4;
748           x[3] -= m2*x3 + m4*x4;
749           pv   += 4;
750         }
751         PLogFlops(16*nz+12);
752       }
753       row = *ajtmp++;
754     }
755     /* finished row so stick it into b->a */
756     pv = ba + 4*bi[i];
757     pj = bj + bi[i];
758     nz = bi[i+1] - bi[i];
759     for ( j=0; j<nz; j++ ) {
760       x     = rtmp+4*pj[j];
761       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
762       pv   += 4;
763     }
764     /* invert diagonal block */
765     w = ba + 4*diag_offset[i];
766     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
767   }
768 
769   PetscFree(rtmp);
770   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
771   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
772   ierr = ISDestroy(isicol); CHKERRQ(ierr);
773   C->factor = FACTOR_LU;
774   C->assembled = PETSC_TRUE;
775   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
776   return 0;
777 }
778 
779 /* ----------------------------------------------------------- */
780 /*
781      Version for when blocks are 1 by 1.
782 */
783 #undef __FUNC__
784 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_1"
785 int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
786 {
787   Mat             C = *B;
788   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
789   IS              iscol = b->col, isrow = b->row, isicol;
790   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
791   int             *ajtmpold, *ajtmp, nz, row,*ai = a->i,*aj = a->j;
792   int             *diag_offset = b->diag,diag;
793   register Scalar *pv,*v,*rtmp,multiplier,*pc;
794   Scalar          *ba = b->a,*aa = a->a;
795   register int    *pj;
796 
797   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
798   PLogObjectParent(*B,isicol);
799   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
800   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
801   rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
802 
803   for ( i=0; i<n; i++ ) {
804     nz    = bi[i+1] - bi[i];
805     ajtmp = bj + bi[i];
806     for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;
807 
808     /* load in initial (unfactored row) */
809     nz       = ai[r[i]+1] - ai[r[i]];
810     ajtmpold = aj + ai[r[i]];
811     v        = aa + ai[r[i]];
812     for ( j=0; j<nz; j++ ) rtmp[ic[ajtmpold[j]]] =  v[j];
813 
814     row = *ajtmp++;
815     while (row < i) {
816       pc = rtmp + row;
817       if (*pc != 0.0) {
818         pv         = ba + diag_offset[row];
819         pj         = bj + diag_offset[row] + 1;
820         multiplier = *pc * *pv++;
821         *pc        = multiplier;
822         nz         = bi[row+1] - diag_offset[row] - 1;
823         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
824         PLogFlops(1+2*nz);
825       }
826       row = *ajtmp++;
827     }
828     /* finished row so stick it into b->a */
829     pv = ba + bi[i];
830     pj = bj + bi[i];
831     nz = bi[i+1] - bi[i];
832     for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
833     diag = diag_offset[i] - bi[i];
834     /* check pivot entry for current row */
835     if (pv[diag] == 0.0) {
836       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
837     }
838     pv[diag] = 1.0/pv[diag];
839   }
840 
841   PetscFree(rtmp);
842   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
843   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
844   ierr = ISDestroy(isicol); CHKERRQ(ierr);
845   C->factor    = FACTOR_LU;
846   C->assembled = PETSC_TRUE;
847   PLogFlops(b->n);
848   return 0;
849 }
850 
851 /* ----------------------------------------------------------- */
852 #undef __FUNC__
853 #define __FUNC__ "MatLUFactor_SeqBAIJ"
854 int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
855 {
856   Mat_SeqBAIJ *mat = (Mat_SeqBAIJ *) A->data;
857   int         ierr;
858   Mat         C;
859 
860   ierr = MatLUFactorSymbolic(A,row,col,f,&C); CHKERRQ(ierr);
861   ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);
862 
863   /* free all the data structures from mat */
864   PetscFree(mat->a);
865   if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
866   if (mat->diag) PetscFree(mat->diag);
867   if (mat->ilen) PetscFree(mat->ilen);
868   if (mat->imax) PetscFree(mat->imax);
869   if (mat->solve_work) PetscFree(mat->solve_work);
870   if (mat->mult_work) PetscFree(mat->mult_work);
871   PetscFree(mat);
872 
873   PetscMemcpy(A,C,sizeof(struct _p_Mat));
874   PetscHeaderDestroy(C);
875   return 0;
876 }
877 /* ----------------------------------------------------------- */
878 #undef __FUNC__
879 #define __FUNC__ "MatSolve_SeqBAIJ_N"
880 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
881 {
882   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
883   IS              iscol=a->col,isrow=a->row;
884   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
885   int             nz,bs=a->bs,bs2=a->bs2,*rout,*cout;
886   Scalar          *aa=a->a,*sum;
887   register Scalar *x,*b,*lsum,*tmp,*v;
888 
889   VecGetArray_Fast(bb,b);
890   VecGetArray_Fast(xx,x);
891   tmp  = a->solve_work;
892 
893   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
894   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
895 
896   /* forward solve the lower triangular */
897   PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
898   for ( i=1; i<n; i++ ) {
899     v   = aa + bs2*ai[i];
900     vi  = aj + ai[i];
901     nz  = a->diag[i] - ai[i];
902     sum = tmp + bs*i;
903     PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
904     while (nz--) {
905       Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++));
906       v += bs2;
907     }
908   }
909   /* backward solve the upper triangular */
910   lsum = a->solve_work + a->n;
911   for ( i=n-1; i>=0; i-- ){
912     v   = aa + bs2*(a->diag[i] + 1);
913     vi  = aj + a->diag[i] + 1;
914     nz  = ai[i+1] - a->diag[i] - 1;
915     PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
916     while (nz--) {
917       Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++));
918       v += bs2;
919     }
920     Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs);
921     PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
922   }
923 
924   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
925   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
926   VecRestoreArray_Fast(bb,b);
927   VecRestoreArray_Fast(xx,x);
928   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
929   return 0;
930 }
931 
932 #undef __FUNC__
933 #define __FUNC__ "MatSolve_SeqBAIJ_7"
934 int MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
935 {
936   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
937   IS              iscol=a->col,isrow=a->row;
938   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
939   int             *diag = a->diag;
940   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,sum6,sum7,x1,x2,x3,x4,x5,x6,x7;
941   register Scalar *x,*b,*tmp,*v;
942 
943   VecGetArray_Fast(bb,b);
944   VecGetArray_Fast(xx,x);
945   tmp  = a->solve_work;
946 
947   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
948   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
949 
950   /* forward solve the lower triangular */
951   idx    = 7*(*r++);
952   tmp[0] = b[idx];   tmp[1] = b[1+idx];
953   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
954   tmp[5] = b[5+idx]; tmp[6] = b[6+idx];
955 
956   for ( i=1; i<n; i++ ) {
957     v     = aa + 49*ai[i];
958     vi    = aj + ai[i];
959     nz    = diag[i] - ai[i];
960     idx   = 7*(*r++);
961     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
962     sum5  = b[4+idx];sum6 = b[5+idx];sum7 = b[6+idx];
963     while (nz--) {
964       idx   = 7*(*vi++);
965       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
966       x4    = tmp[3+idx];x5 = tmp[4+idx];
967       x6    = tmp[5+idx];x7 = tmp[6+idx];
968       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
969       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
970       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
971       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
972       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
973       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
974       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
975       v += 49;
976     }
977     idx = 7*i;
978     tmp[idx]   = sum1;tmp[1+idx] = sum2;
979     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
980     tmp[5+idx] = sum6;tmp[6+idx] = sum7;
981   }
982   /* backward solve the upper triangular */
983   for ( i=n-1; i>=0; i-- ){
984     v    = aa + 49*diag[i] + 49;
985     vi   = aj + diag[i] + 1;
986     nz   = ai[i+1] - diag[i] - 1;
987     idt  = 7*i;
988     sum1 = tmp[idt];  sum2 = tmp[1+idt];
989     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
990     sum6 = tmp[5+idt];sum7 = tmp[6+idt];
991     while (nz--) {
992       idx   = 7*(*vi++);
993       x1    = tmp[idx];   x2 = tmp[1+idx];
994       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
995       x6    = tmp[5+idx]; x7 = tmp[6+idx];
996       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
997       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
998       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
999       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
1000       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
1001       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
1002       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
1003       v += 49;
1004     }
1005     idc = 7*(*c--);
1006     v   = aa + 49*diag[i];
1007     x[idc]   = tmp[idt]   = v[0]*sum1+v[7]*sum2+v[14]*sum3+
1008                                  v[21]*sum4+v[28]*sum5+v[35]*sum6+v[42]*sum7;
1009     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[8]*sum2+v[15]*sum3+
1010                                  v[22]*sum4+v[29]*sum5+v[36]*sum6+v[43]*sum7;
1011     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[9]*sum2+v[16]*sum3+
1012                                  v[23]*sum4+v[30]*sum5+v[37]*sum6+v[44]*sum7;
1013     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[10]*sum2+v[17]*sum3+
1014                                  v[24]*sum4+v[31]*sum5+v[38]*sum6+v[45]*sum7;
1015     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[11]*sum2+v[18]*sum3+
1016                                  v[25]*sum4+v[32]*sum5+v[39]*sum6+v[46]*sum7;
1017     x[5+idc] = tmp[5+idt] = v[5]*sum1+v[12]*sum2+v[19]*sum3+
1018                                  v[26]*sum4+v[33]*sum5+v[40]*sum6+v[47]*sum7;
1019     x[6+idc] = tmp[6+idt] = v[6]*sum1+v[13]*sum2+v[20]*sum3+
1020                                  v[27]*sum4+v[34]*sum5+v[41]*sum6+v[48]*sum7;
1021   }
1022 
1023   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1024   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1025   VecRestoreArray_Fast(bb,b);
1026   VecRestoreArray_Fast(xx,x);
1027   PLogFlops(2*49*(a->nz) - a->n);
1028   return 0;
1029 }
1030 
1031 #undef __FUNC__
1032 #define __FUNC__ "MatSolve_SeqBAIJ_5"
1033 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
1034 {
1035   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1036   IS              iscol=a->col,isrow=a->row;
1037   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1038   int             *diag = a->diag;
1039   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
1040   register Scalar *x,*b,*tmp,*v;
1041 
1042   VecGetArray_Fast(bb,b);
1043   VecGetArray_Fast(xx,x);
1044   tmp  = a->solve_work;
1045 
1046   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1047   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1048 
1049   /* forward solve the lower triangular */
1050   idx    = 5*(*r++);
1051   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1052   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
1053   for ( i=1; i<n; i++ ) {
1054     v     = aa + 25*ai[i];
1055     vi    = aj + ai[i];
1056     nz    = diag[i] - ai[i];
1057     idx   = 5*(*r++);
1058     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1059     sum5  = b[4+idx];
1060     while (nz--) {
1061       idx   = 5*(*vi++);
1062       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
1063       x4    = tmp[3+idx];x5 = tmp[4+idx];
1064       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1065       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1066       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1067       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1068       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1069       v += 25;
1070     }
1071     idx = 5*i;
1072     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1073     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
1074   }
1075   /* backward solve the upper triangular */
1076   for ( i=n-1; i>=0; i-- ){
1077     v    = aa + 25*diag[i] + 25;
1078     vi   = aj + diag[i] + 1;
1079     nz   = ai[i+1] - diag[i] - 1;
1080     idt  = 5*i;
1081     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1082     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
1083     while (nz--) {
1084       idx   = 5*(*vi++);
1085       x1    = tmp[idx];   x2 = tmp[1+idx];
1086       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
1087       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1088       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1089       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1090       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1091       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1092       v += 25;
1093     }
1094     idc = 5*(*c--);
1095     v   = aa + 25*diag[i];
1096     x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
1097                                  v[15]*sum4+v[20]*sum5;
1098     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
1099                                  v[16]*sum4+v[21]*sum5;
1100     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
1101                                  v[17]*sum4+v[22]*sum5;
1102     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
1103                                  v[18]*sum4+v[23]*sum5;
1104     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
1105                                  v[19]*sum4+v[24]*sum5;
1106   }
1107 
1108   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1109   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1110   VecRestoreArray_Fast(bb,b);
1111   VecRestoreArray_Fast(xx,x);
1112   PLogFlops(2*25*(a->nz) - a->n);
1113   return 0;
1114 }
1115 
1116 #undef __FUNC__
1117 #define __FUNC__ "MatSolve_SeqBAIJ_4"
1118 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
1119 {
1120   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
1121   IS              iscol=a->col,isrow=a->row;
1122   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1123   int             *diag = a->diag;
1124   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
1125   register Scalar *x,*b,*tmp,*v;
1126 
1127   VecGetArray_Fast(bb,b);
1128   VecGetArray_Fast(xx,x);
1129   tmp  = a->solve_work;
1130 
1131   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1132   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1133 
1134   /* forward solve the lower triangular */
1135   idx    = 4*(*r++);
1136   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1137   tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
1138   for ( i=1; i<n; i++ ) {
1139     v     = aa + 16*ai[i];
1140     vi    = aj + ai[i];
1141     nz    = diag[i] - ai[i];
1142     idx   = 4*(*r++);
1143     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1144     while (nz--) {
1145       idx   = 4*(*vi++);
1146       x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
1147       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1148       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1149       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1150       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1151       v    += 16;
1152     }
1153     idx        = 4*i;
1154     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1155     tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1156   }
1157   /* backward solve the upper triangular */
1158   for ( i=n-1; i>=0; i-- ){
1159     v    = aa + 16*diag[i] + 16;
1160     vi   = aj + diag[i] + 1;
1161     nz   = ai[i+1] - diag[i] - 1;
1162     idt  = 4*i;
1163     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1164     sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1165     while (nz--) {
1166       idx   = 4*(*vi++);
1167       x1    = tmp[idx];   x2 = tmp[1+idx];
1168       x3    = tmp[2+idx]; x4 = tmp[3+idx];
1169       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1170       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1171       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1172       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1173       v += 16;
1174     }
1175     idc      = 4*(*c--);
1176     v        = aa + 16*diag[i];
1177     x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1178     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1179     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1180     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1181   }
1182 
1183   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1184   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1185   VecRestoreArray_Fast(bb,b);
1186   VecRestoreArray_Fast(xx,x);
1187   PLogFlops(2*16*(a->nz) - a->n);
1188   return 0;
1189 }
1190 
1191 /*
1192       Special case where the matrix was ILU(0) factored in the natural
1193    ordering. This eliminates the need for the column and row permutation.
1194 */
1195 #undef __FUNC__
1196 #define __FUNC__ "MatSolve_SeqBAIJ_4_NaturalOrdering"
1197 int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
1198 {
1199   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
1200   int             i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
1201   int             *diag = a->diag,jdx;
1202   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
1203   register Scalar *x,*b,*v;
1204 
1205   VecGetArray_Fast(bb,b);
1206   VecGetArray_Fast(xx,x);
1207 
1208   /* forward solve the lower triangular */
1209   idx    = 0;
1210   x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; x[3] = b[3+idx];
1211   for ( i=1; i<n; i++ ) {
1212     v     =  aa + 16*ai[i];
1213     vi    =  aj + ai[i];
1214     nz    =  diag[i] - ai[i];
1215     idx   =  4*i;
1216     sum1  =  b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1217     while (nz--) {
1218       jdx   = 4*(*vi++);
1219       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];
1220       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1221       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1222       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1223       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1224       v    += 16;
1225     }
1226     x[idx]   = sum1;
1227     x[1+idx] = sum2;
1228     x[2+idx] = sum3;
1229     x[3+idx] = sum4;
1230   }
1231   /* backward solve the upper triangular */
1232   for ( i=n-1; i>=0; i-- ){
1233     v    = aa + 16*diag[i] + 16;
1234     vi   = aj + diag[i] + 1;
1235     nz   = ai[i+1] - diag[i] - 1;
1236     idt  = 4*i;
1237     sum1 = x[idt];  sum2 = x[1+idt];
1238     sum3 = x[2+idt];sum4 = x[3+idt];
1239     while (nz--) {
1240       idx   = 4*(*vi++);
1241       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx];
1242       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1243       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1244       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1245       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1246       v += 16;
1247     }
1248     v        = aa + 16*diag[i];
1249     x[idt]   = v[0]*sum1 + v[4]*sum2 + v[8]*sum3  + v[12]*sum4;
1250     x[1+idt] = v[1]*sum1 + v[5]*sum2 + v[9]*sum3  + v[13]*sum4;
1251     x[2+idt] = v[2]*sum1 + v[6]*sum2 + v[10]*sum3 + v[14]*sum4;
1252     x[3+idt] = v[3]*sum1 + v[7]*sum2 + v[11]*sum3 + v[15]*sum4;
1253   }
1254 
1255   VecRestoreArray_Fast(bb,b);
1256   VecRestoreArray_Fast(xx,x);
1257   PLogFlops(2*16*(a->nz) - a->n);
1258   return 0;
1259 }
1260 
1261 
1262 #undef __FUNC__
1263 #define __FUNC__ "MatSolve_SeqBAIJ_3"
1264 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
1265 {
1266   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1267   IS              iscol=a->col,isrow=a->row;
1268   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1269   int             *diag = a->diag;
1270   Scalar          *aa=a->a,sum1,sum2,sum3,x1,x2,x3;
1271   register Scalar *x,*b,*tmp,*v;
1272 
1273   VecGetArray_Fast(bb,b);
1274   VecGetArray_Fast(xx,x);
1275   tmp  = a->solve_work;
1276 
1277   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1278   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1279 
1280   /* forward solve the lower triangular */
1281   idx    = 3*(*r++);
1282   tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
1283   for ( i=1; i<n; i++ ) {
1284     v     = aa + 9*ai[i];
1285     vi    = aj + ai[i];
1286     nz    = diag[i] - ai[i];
1287     idx   = 3*(*r++);
1288     sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
1289     while (nz--) {
1290       idx   = 3*(*vi++);
1291       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1292       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1293       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1294       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1295       v += 9;
1296     }
1297     idx = 3*i;
1298     tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
1299   }
1300   /* backward solve the upper triangular */
1301   for ( i=n-1; i>=0; i-- ){
1302     v    = aa + 9*diag[i] + 9;
1303     vi   = aj + diag[i] + 1;
1304     nz   = ai[i+1] - diag[i] - 1;
1305     idt  = 3*i;
1306     sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
1307     while (nz--) {
1308       idx   = 3*(*vi++);
1309       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1310       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1311       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1312       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1313       v += 9;
1314     }
1315     idc = 3*(*c--);
1316     v   = aa + 9*diag[i];
1317     x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
1318     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
1319     x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
1320   }
1321   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1322   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1323   VecRestoreArray_Fast(bb,b);
1324   VecRestoreArray_Fast(xx,x);
1325   PLogFlops(2*9*(a->nz) - a->n);
1326   return 0;
1327 }
1328 
1329 #undef __FUNC__
1330 #define __FUNC__ "MatSolve_SeqBAIJ_2"
1331 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
1332 {
1333   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1334   IS              iscol=a->col,isrow=a->row;
1335   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1336   int             *diag = a->diag;
1337   Scalar          *aa=a->a,sum1,sum2,x1,x2;
1338   register Scalar *x,*b,*tmp,*v;
1339 
1340   VecGetArray_Fast(bb,b);
1341   VecGetArray_Fast(xx,x);
1342   tmp  = a->solve_work;
1343 
1344   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1345   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1346 
1347   /* forward solve the lower triangular */
1348   idx    = 2*(*r++);
1349   tmp[0] = b[idx]; tmp[1] = b[1+idx];
1350   for ( i=1; i<n; i++ ) {
1351     v     = aa + 4*ai[i];
1352     vi    = aj + ai[i];
1353     nz    = diag[i] - ai[i];
1354     idx   = 2*(*r++);
1355     sum1  = b[idx]; sum2 = b[1+idx];
1356     while (nz--) {
1357       idx   = 2*(*vi++);
1358       x1    = tmp[idx]; x2 = tmp[1+idx];
1359       sum1 -= v[0]*x1 + v[2]*x2;
1360       sum2 -= v[1]*x1 + v[3]*x2;
1361       v += 4;
1362     }
1363     idx = 2*i;
1364     tmp[idx] = sum1; tmp[1+idx] = sum2;
1365   }
1366   /* backward solve the upper triangular */
1367   for ( i=n-1; i>=0; i-- ){
1368     v    = aa + 4*diag[i] + 4;
1369     vi   = aj + diag[i] + 1;
1370     nz   = ai[i+1] - diag[i] - 1;
1371     idt  = 2*i;
1372     sum1 = tmp[idt]; sum2 = tmp[1+idt];
1373     while (nz--) {
1374       idx   = 2*(*vi++);
1375       x1    = tmp[idx]; x2 = tmp[1+idx];
1376       sum1 -= v[0]*x1 + v[2]*x2;
1377       sum2 -= v[1]*x1 + v[3]*x2;
1378       v += 4;
1379     }
1380     idc = 2*(*c--);
1381     v   = aa + 4*diag[i];
1382     x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
1383     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
1384   }
1385   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1386   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1387   VecRestoreArray_Fast(bb,b);
1388   VecRestoreArray_Fast(xx,x);
1389   PLogFlops(2*4*(a->nz) - a->n);
1390   return 0;
1391 }
1392 
1393 
1394 #undef __FUNC__
1395 #define __FUNC__ "MatSolve_SeqBAIJ_1"
1396 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
1397 {
1398   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1399   IS              iscol=a->col,isrow=a->row;
1400   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout;
1401   int             *diag = a->diag;
1402   Scalar          *aa=a->a,sum1;
1403   register Scalar *x,*b,*tmp,*v;
1404 
1405   if (!n) return 0;
1406 
1407   VecGetArray_Fast(bb,b);
1408   VecGetArray_Fast(xx,x);
1409   tmp  = a->solve_work;
1410 
1411   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1412   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1413 
1414   /* forward solve the lower triangular */
1415   tmp[0] = b[*r++];
1416   for ( i=1; i<n; i++ ) {
1417     v     = aa + ai[i];
1418     vi    = aj + ai[i];
1419     nz    = diag[i] - ai[i];
1420     sum1  = b[*r++];
1421     while (nz--) {
1422       sum1 -= (*v++)*tmp[*vi++];
1423     }
1424     tmp[i] = sum1;
1425   }
1426   /* backward solve the upper triangular */
1427   for ( i=n-1; i>=0; i-- ){
1428     v    = aa + diag[i] + 1;
1429     vi   = aj + diag[i] + 1;
1430     nz   = ai[i+1] - diag[i] - 1;
1431     sum1 = tmp[i];
1432     while (nz--) {
1433       sum1 -= (*v++)*tmp[*vi++];
1434     }
1435     x[*c--] = tmp[i] = aa[diag[i]]*sum1;
1436   }
1437 
1438   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1439   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1440   VecRestoreArray_Fast(bb,b);
1441   VecRestoreArray_Fast(xx,x);
1442   PLogFlops(2*1*(a->nz) - a->n);
1443   return 0;
1444 }
1445 
1446 extern int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat,Vec,Vec);
1447 /* ----------------------------------------------------------------*/
1448 /*
1449      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
1450    except that the data structure of Mat_SeqAIJ is slightly different.
1451    Not a good example of code reuse.
1452 */
1453 #undef __FUNC__
1454 #define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ"
1455 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
1456                                  Mat *fact)
1457 {
1458   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
1459   IS          isicol;
1460   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
1461   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
1462   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
1463   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
1464   PetscTruth  col_identity, row_identity;
1465 
1466   /* special case that simply copies fill pattern */
1467   PetscValidHeaderSpecific(isrow,IS_COOKIE);
1468   PetscValidHeaderSpecific(iscol,IS_COOKIE);
1469   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
1470   if (levels == 0 && row_identity && col_identity) {
1471     ierr = MatConvertSameType_SeqBAIJ(A,fact,DO_NOT_COPY_VALUES); CHKERRQ(ierr);
1472     (*fact)->factor = FACTOR_LU;
1473     b               = (Mat_SeqBAIJ *) (*fact)->data;
1474     if (!b->diag) {
1475       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
1476     }
1477     b->row        = isrow;
1478     b->col        = iscol;
1479     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
1480     /*
1481         Blocksize 4 has a special faster solver for ILU(0) factorization
1482         with natural ordering
1483     */
1484     if (b->bs == 4) {
1485       (*fact)->ops.solve = MatSolve_SeqBAIJ_4_NaturalOrdering;
1486     }
1487     return 0;
1488   }
1489 
1490   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
1491   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
1492   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
1493 
1494   /* get new row pointers */
1495   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
1496   ainew[0] = 0;
1497   /* don't know how many column pointers are needed so estimate */
1498   jmax = (int) (f*ai[n] + 1);
1499   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
1500   /* ajfill is level of fill for each fill entry */
1501   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
1502   /* fill is a linked list of nonzeros in active row */
1503   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
1504   /* im is level for each filled value */
1505   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
1506   /* dloc is location of diagonal in factor */
1507   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
1508   dloc[0]  = 0;
1509   for ( prow=0; prow<n; prow++ ) {
1510     /* first copy previous fill into linked list */
1511     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
1512     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
1513     xi      = aj + ai[r[prow]];
1514     fill[n] = n;
1515     while (nz--) {
1516       fm  = n;
1517       idx = ic[*xi++];
1518       do {
1519         m  = fm;
1520         fm = fill[m];
1521       } while (fm < idx);
1522       fill[m]   = idx;
1523       fill[idx] = fm;
1524       im[idx]   = 0;
1525     }
1526     nzi = 0;
1527     row = fill[n];
1528     while ( row < prow ) {
1529       incrlev = im[row] + 1;
1530       nz      = dloc[row];
1531       xi      = ajnew  + ainew[row] + nz;
1532       flev    = ajfill + ainew[row] + nz + 1;
1533       nnz     = ainew[row+1] - ainew[row] - nz - 1;
1534       if (*xi++ != row) {
1535         SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot: try running with -pc_ilu_nonzeros_along_diagonal");
1536       }
1537       fm      = row;
1538       while (nnz-- > 0) {
1539         idx = *xi++;
1540         if (*flev + incrlev > levels) {
1541           flev++;
1542           continue;
1543         }
1544         do {
1545           m  = fm;
1546           fm = fill[m];
1547         } while (fm < idx);
1548         if (fm != idx) {
1549           im[idx]   = *flev + incrlev;
1550           fill[m]   = idx;
1551           fill[idx] = fm;
1552           fm        = idx;
1553           nzf++;
1554         }
1555         else {
1556           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
1557         }
1558         flev++;
1559       }
1560       row = fill[row];
1561       nzi++;
1562     }
1563     /* copy new filled row into permanent storage */
1564     ainew[prow+1] = ainew[prow] + nzf;
1565     if (ainew[prow+1] > jmax) {
1566       /* allocate a longer ajnew */
1567       int maxadd;
1568       maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n);
1569       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
1570       jmax += maxadd;
1571       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1572       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
1573       PetscFree(ajnew);
1574       ajnew = xi;
1575       /* allocate a longer ajfill */
1576       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1577       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
1578       PetscFree(ajfill);
1579       ajfill = xi;
1580       realloc++;
1581     }
1582     xi          = ajnew + ainew[prow];
1583     flev        = ajfill + ainew[prow];
1584     dloc[prow]  = nzi;
1585     fm          = fill[n];
1586     while (nzf--) {
1587       *xi++   = fm;
1588       *flev++ = im[fm];
1589       fm      = fill[fm];
1590     }
1591   }
1592   PetscFree(ajfill);
1593   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1594   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
1595   ierr = ISDestroy(isicol); CHKERRQ(ierr);
1596   PetscFree(fill); PetscFree(im);
1597 
1598   {
1599     double af = ((double)ainew[n])/((double)ai[n]);
1600     PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
1601              realloc,f,af);
1602     PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:Run with -pc_ilu_fill %g or use \n",af);
1603     PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:PCILUSetFill(pc,%g);\n",af);
1604     PLogInfo(A,"Info:MatILUFactorSymbolic_SeqBAIJ:for best performance.\n");
1605   }
1606 
1607   /* put together the new matrix */
1608   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
1609   b = (Mat_SeqBAIJ *) (*fact)->data;
1610   PetscFree(b->imax);
1611   b->singlemalloc = 0;
1612   len = bs2*ainew[n]*sizeof(Scalar);
1613   /* the next line frees the default space generated by the Create() */
1614   PetscFree(b->a); PetscFree(b->ilen);
1615   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
1616   b->j          = ajnew;
1617   b->i          = ainew;
1618   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
1619   b->diag       = dloc;
1620   b->ilen       = 0;
1621   b->imax       = 0;
1622   b->row        = isrow;
1623   b->col        = iscol;
1624   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
1625   CHKPTRQ(b->solve_work);
1626   /* In b structure:  Free imax, ilen, old a, old j.
1627      Allocate dloc, solve_work, new a, new j */
1628   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
1629   b->maxnz          = b->nz = ainew[n];
1630   (*fact)->factor   = FACTOR_LU;
1631 
1632   (*fact)->info.factor_mallocs    = realloc;
1633   (*fact)->info.fill_ratio_given  = f;
1634   (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);
1635 
1636   return 0;
1637 }
1638 
1639 
1640 
1641 
1642